From 48b96c317b353e6f49951c6c0cfd98caa0704f05 Mon Sep 17 00:00:00 2001 From: Jean Michel Date: Mon, 21 Oct 2024 18:51:40 +0200 Subject: [PATCH] modify data for twisted doubles --- src/Families.jl | 102 ++++++++++++++++++++++++++++++++---------- src/Format.jl | 1 + src/tbl/cmp4_22.jl | 2 +- src/tbl/cmplxg24.jl | 2 +- src/tbl/cmplxg26.jl | 2 +- src/tbl/cmplxg27.jl | 2 +- src/tbl/cmplxg32.jl | 2 +- src/tbl/cmplxg33.jl | 2 +- src/tbl/cmplxg34.jl | 2 +- src/tbl/coxh3.jl | 2 +- src/tbl/coxh4.jl | 4 +- src/tbl/weyle7.jl | 2 +- src/tbl/weyle8.jl | 2 +- tools/tbl/cmp4_22.jl | 2 +- tools/tbl/cmplxg24.jl | 2 +- tools/tbl/cmplxg26.jl | 2 +- tools/tbl/cmplxg27.jl | 2 +- tools/tbl/cmplxg32.jl | 2 +- tools/tbl/cmplxg33.jl | 2 +- tools/tbl/cmplxg34.jl | 2 +- tools/tbl/coxh3.jl | 2 +- tools/tbl/coxh4.jl | 2 +- tools/tbl/weyle7.jl | 2 +- tools/tbl/weyle8.jl | 2 +- 24 files changed, 102 insertions(+), 47 deletions(-) diff --git a/src/Families.jl b/src/Families.jl index 35f9accf..4a1a8550 100644 --- a/src/Families.jl +++ b/src/Families.jl @@ -359,26 +359,19 @@ chevieset(:families,:C2, :mellin=>[[1,1,0,0],[1,-1,0,0],[0,0,1,1],[0,0,1,-1]], :mellinLabels=>["(1,1)","(1,g2)","(g2,1)","(g2,g2)"]))) -chevieset(:families,Symbol("C'2"), - Family(Dict(:group=>"C2",:name=>"C'_2", - :explanation=>"TwistedDrinfeldDouble(Z/2)", - :charLabels=>["(1,1)", "(1,\\varepsilon)", "(g_2,1)","(g_2,\\varepsilon)"], - :fourierMat=>1//2*[1 1 -1 -1;1 1 1 1;-1 1 1 -1;-1 1 -1 1], +chevieset(:families,:LTQZ2, + Family(Dict(:group=>Group(Perm(1,2)),:cocycle=>-1,:pivotal=>(1,-1), + :explanation=>"Lusztig's TwistedDrinfeldDouble(Z/2)", + :charparams=>[[1,1],[1,-1],[-1,E(4)],[-1,-E(4)]], + :charLabels=>[ "(1,1)","(1,-1)","(-1,\\zeta_4)","(-1,-\\zeta_4)"], + :bar=>[1,1],:defect=>1, + :fourierMat=>[[1,1,-1,-1],[1,1,1,1],[-1,1,1,-1],[-1,1,-1,1]]//2, :eigenvalues=>[1,1,E(4),-E(4)], - :qEigen=>[0,0,1,1]//2, + :name=>"LusztigTwistedDrinfeldDoubleCyclic(2,-1,[1,-1])", + :explanation=>"LusztigTwistedDrinfeldDoubleCyclic(2,-1,[1,-1])", + :qEigen=>[ 0, 0, 1/2, 1/2 ], :perm=>Perm(3,4), - :lusztig=>true, # does not satisfy (ST)^3=1 but (SPT)^3=1 - :cospecial=>2))) - -chevieset(:families,Symbol("C'\"2"), - Family(Dict(:group=>"C2", :name=>"C'''_2", - :explanation=>"TwistedDrinfeldDouble(Z/2)'", - :charLabels=>["(1,1)", "(1,\\varepsilon)", "(g_2,1)", "(g_2,\\varepsilon)"], - :fourierMat=>1//2*[1 1 -1 -1;1 1 1 1;-1 1 -1 1;-1 1 1 -1], - :eigenvalues=>[1,1,E(4),-E(4)], - :qEigen=>[0,0,1,1]//2, - :perm=>Perm(3,4), - :cospecial=>2))) + :lusztig=>true)))# does not satisfy (ST)^3=1 but (SPT)^3=1 chevieset(:families,:S3, Family(Dict(:group=>"S3", :name=>"D(\\mathfrak S_3)", @@ -459,12 +452,6 @@ f.eigenvalues.//=f.eigenvalues[2] f.special=2 f.qEigen=[1,0,1,0].//2 chevieset(:families,:Z4,f) - -f=chevieget(:families,:ExtPowCyclic)(9,1) -f.perm=perm"(2,9)(3,8)(4,7)(5,6)" -f.qEigen=[0,2,1,0,2,1,0,2,1].//3 -#if f.eigenvalues!=map(i->E(9)^(5*i^2),0:8) error() end -chevieset(:families,:Z9,f) end chevieset(:families,:QZ,function(n,pivotal=nothing) @@ -797,6 +784,73 @@ chevieset(:families,:G4,function() drinfeld_double(g4;pivotal=(g4(1,2)^3,[E(3),E(3)])) end) +""" +`TwistedDrinfeldDoubleCyclic(n,ζ,piv=[1,1])` + +compute the modular data of the category of modules over the twisted +Drinfeld double of a cyclic group G of order n + +arguments are `(n,ζ,piv=[1,1])`, where `n` is the order of the group, +`ζ` is the value of the 3-cocycle on `(ζₙ,ζₙⁿ⁻¹,ζₙⁿ⁻¹)` and `piv` is +a pivotal structure different form the usual one (on vector spaces) + +The result is a `GapObj` with fields: + .group: the group + .cocycle: `ζ`, the value of the 3-cocycle on the element `(ζₙ,ζₙ,ζₙⁿ⁻¹)` + .pivotal: a pair `[k,alpha]` where the 2-cocycle associated with `k` is a + coboundary (an integer in `0:n-1`), and alpha the corresponding + 1-cocycle (a n^2-th root of unity) (for the cyclic group, the Schur + multiplier is trivial, therefore these pairs correspond exactly to + simple objects of the category) + .charparams: labels of lines of the fourier matrix by + pairs [x,chi]: elt of G, projective character of G for the + corresponding cocycle + .special is the position of the special line (here 1 where (x,chi)=(1,1) is) + .eigenvalues are the eigenvalues chi(x)/chi(1) + (inverse of the T-matrix of the category) + .fourierMat is the Fourier matrix (renormalized S-matrix) + .bar is the object \\overline{1} needed to renormalise the S-matrix + (related to the non sphericity of the pivotal structure) + + In general, we have the relation `(ST)³=τ id`, where the explicit value + of `τ` can be computed using Gauss sums. +""" +function TwistedDrinfeldDoubleCyclic(n,ζ,pivotal=[1,1]) + ζ=Root1(ζ) + piv1e,piv2=Root1.(pivotal) + piv1=Int(Root1(piv1e).r*n) + piv=(piv1,piv2) + G=crg(n,1,1) + res=Family(Dict(:group=>G)) + res.cocycle=ζ + # 3-cocycle associated to ζ: (a,b,c)->ζ^(a*(b+c)^quo), where 0<=a,b,cmap(j->(i,root(prod(k->θ(i,1,k),1:n-1),n)*E(n,j)),0:n-1),0:n-1) + # if a is a representation with cocycle θᵢ then + # 1=a(n)=θₐ(1,n-1)⁻¹a(1)a(n-1)=…=θₐ(1,n-1)⁻¹*θₐ(1,n-2)⁻¹…θₐ(1,1)⁻¹a(1)^n + simple=vcat(simple...) + if !(piv in simple) return end + #if the given pivotal structure is not of the expected form, we bail out + res.pivotal=(piv1e,piv2) + res.charparams=[(E(n,i1),i2) for (i1,i2) in simple] + res.charLabels=map(x->xrepr(x;TeX=true),res.charparams) + res.bar=(E(n,-2piv1), inv(piv2^2*γ(1,piv1,-piv1)*γ(1,piv1,-2piv1))) + res.fourierMat=[piv2^i1*piv2^j1*i2^piv1*j2^piv1*i2^j1*j2^i1 + for (i1,i2) in simple, (j1,j2) in simple]//(n*piv2^(-2piv1)) + res.eigenvalues=[piv2^i1*i2^piv1*i2^i1 for (i1,i2) in simple] + res.defect=sum(res.eigenvalues)//n*piv2^(-2piv1) + res.name="TwistedDrinfeldDouble(ℤ/$n,"*xrepr(ζ;TeX=true) + res.qEigen=map(x->conj(x[1]).r,res.charparams) + if piv!=(0,1) res.name*=","*xrepr(res.pivotal;TeX=true) end + res.name*=")" + res.perm=Perm(Int.(res.fourierMat^2*(1:n^2))) + res +end + +chevieset(:families,:TQZ,TwistedDrinfeldDoubleCyclic) + """ `family_imprimitive(S)` diff --git a/src/Format.jl b/src/Format.jl index fab26233..ebc743b0 100644 --- a/src/Format.jl +++ b/src/Format.jl @@ -262,6 +262,7 @@ function Base.show(io::IO,t::Table) col0=(-1 in row_seps) && !isnothing(col_labels) ranges=map((x,y)->cols[y:y+x-1],column_repartition, pushfirst!(cumsum(column_repartition)[1:end-1].+1,1)) + append!(col_seps,cumsum(column_repartition)[1:end-1]) for ci in ranges if TeX alignt=-1 in col_seps ? '|' : "" diff --git a/src/tbl/cmp4_22.jl b/src/tbl/cmp4_22.jl index 1e416f80..4612b4cb 100644 --- a/src/tbl/cmp4_22.jl +++ b/src/tbl/cmp4_22.jl @@ -808,7 +808,7 @@ chevieset(:G4_22, :UnipotentCharacters, function (ST,) end return res end - return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:2, :rank => 2, :ST => 14), :levi => [], :parameterExponents => [1, 1], :charNumbers => [1, 2, 3, 4, 5, 6, 8, 7, 9, 12, 11, 10, 15, 14, 13, 16, 20, 18, 21, 17, 19, 22, 23, 24], :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1], :rank => 1, :p => 6, :q => 1), :levi => [2], :parameterExponents => [[3, 4, 4, 0, 4, 4]], :charNumbers => [66, 26, 27, 79, 28, 25], :eigenvalue => J ^ 2, :cuspidalName => ImprimitiveCuspidalName([[], [0, 1], [0, 1]])), cuspidal(34, 1), cuspidal(35, 1, 2), cuspidal(29, -1), cuspidal(30, -1, 2), cuspidal(31, -1, 3), cuspidal(32, -1, 4), cuspidal(33, -1, 5), cuspidal(73, -1, 6), cuspidal(74, -1, 7), cuspidal(40, J), cuspidal(41, J, 2), cuspidal(42, J, 3), cuspidal(43, J, 4), cuspidal(50, J, 5), cuspidal(51, J, 6), cuspidal(36, J ^ 2), cuspidal(37, J ^ 2, 2), cuspidal(52, -J), cuspidal(53, -J, 2), cuspidal(38, -(J ^ 2)), cuspidal(39, -(J ^ 2), 2), cuspidal(54, -I), cuspidal(55, -I, 2), cuspidal(56, I, 3), cuspidal(57, I, 4), cuspidal(58, I), cuspidal(59, I, 2), cuspidal(60, -I, 3), cuspidal(61, -I, 4), cuspidal(46, E(8)), cuspidal(47, E(8, 3), 2), cuspidal(48, E(8, 3)), cuspidal(49, E(8), 2), cuspidal(69, E(9, 5), 1 // 3), cuspidal(70, E(9, 5), 2, 2 // 3), cuspidal(71, E(9, 8), 1 // 3), cuspidal(72, E(9, 8), 2, 2 // 3), cuspidal(67, E(9, 2), 1 // 3), cuspidal(68, E(9, 2), 2, 2 // 3), cuspidal(62, E(12)), cuspidal(63, E(12, 7), 2), cuspidal(64, E(12, 7)), cuspidal(65, E(12), 2), cuspidal(75, E(16, 5), 1 // 2), cuspidal(77, E(16, 13), 1 // 2), cuspidal(78, E(16, 15), 1 // 2), cuspidal(76, E(16, 7), 1 // 2), cuspidal(44, E(24, 11)), cuspidal(45, E(24, 17))], :families => [Family("C1", [1]), Family(conj(((CHEVIE[:families])[:X])(3)) * Family("G14"), [26, 37, 28, 39, 14, 3, 34, 18, 46, 48, 15, 13, 30, 29, 59, 60, 55, 56, 25, 36, 27, 38, 2, 11, 16, 35, 49, 47, 12, 10, 32, 31, 58, 61, 54, 57, 4, 17, 22, 33, 41, 40, 43, 42, 44, 45, 51, 50, 53, 52, 64, 65, 62, 63], Dict{Symbol, Any}(:signs => [-1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1], :ennola => 32)), Family(((CHEVIE[:families])[:X])(3), [23, 24, 66], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 2)), Family("Z9", [19, 70, 67, 20, 72, 71, 21, 68, 69], Dict{Symbol, Any}(:cospecial => 4, :ennola => 6)), Family(Dict{Symbol, Any}(:fourierMat => OnMatrices([[1, 1, 2, 1, 1, -(root(-2)), -(root(-2)), -(root(-2)), -(root(-2))], [1, 1, 2, 1, 1, root(-2), root(-2), root(-2), root(-2)], [2, 2, 0, -2, -2, 0, 0, 0, 0], [1, 1, -2, 1, 1, -(root(-2)), root(-2), -(root(-2)), root(-2)], [1, 1, -2, 1, 1, root(-2), -(root(-2)), root(-2), -(root(-2))], [-(root(-2)), root(-2), 0, -(root(-2)), root(-2), 0, -2 * E(4), 0, 2 * E(4)], [-(root(-2)), root(-2), 0, root(-2), -(root(-2)), -2 * E(4), 0, 2 * E(4), 0], [-(root(-2)), root(-2), 0, -(root(-2)), root(-2), 0, 2 * E(4), 0, -2 * E(4)], [-(root(-2)), root(-2), 0, root(-2), -(root(-2)), 2 * E(4), 0, -2 * E(4), 0]] // 4, perm"(4,5)"), :explanation => "everything to explain", :eigenvalues => [1, 1, 1, -1, -1, E(16, 5), E(16, 7), -(E(16, 5)), -(E(16, 7))], :qEigen => [0, 0, 0, 0, 0, 1 // 2, 1 // 2, 1 // 2, 1 // 2], :special => 2, :ennola => -4), [8, 9, 7, 73, 74, 75, 76, 77, 78]), Family(((CHEVIE[:families])[:X])(3), [5, 6, 79], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -2))], :a => [0, 1, 1, 1, 20, 20, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 1, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 20], :A => [0, 23, 23, 23, 28, 28, 27, 27, 27, 23, 23, 23, 23, 23, 23, 23, 23, 23, 26, 26, 26, 23, 25, 25, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 25, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 27, 28]) + return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:2, :rank => 2, :ST => 14), :levi => [], :parameterExponents => [1, 1], :charNumbers => [1, 2, 3, 4, 5, 6, 8, 7, 9, 12, 11, 10, 15, 14, 13, 16, 20, 18, 21, 17, 19, 22, 23, 24], :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1], :rank => 1, :p => 6, :q => 1), :levi => [2], :parameterExponents => [[3, 4, 4, 0, 4, 4]], :charNumbers => [66, 26, 27, 79, 28, 25], :eigenvalue => J ^ 2, :cuspidalName => ImprimitiveCuspidalName([[], [0, 1], [0, 1]])), cuspidal(34, 1), cuspidal(35, 1, 2), cuspidal(29, -1), cuspidal(30, -1, 2), cuspidal(31, -1, 3), cuspidal(32, -1, 4), cuspidal(33, -1, 5), cuspidal(73, -1, 6), cuspidal(74, -1, 7), cuspidal(40, J), cuspidal(41, J, 2), cuspidal(42, J, 3), cuspidal(43, J, 4), cuspidal(50, J, 5), cuspidal(51, J, 6), cuspidal(36, J ^ 2), cuspidal(37, J ^ 2, 2), cuspidal(52, -J), cuspidal(53, -J, 2), cuspidal(38, -(J ^ 2)), cuspidal(39, -(J ^ 2), 2), cuspidal(54, -I), cuspidal(55, -I, 2), cuspidal(56, I, 3), cuspidal(57, I, 4), cuspidal(58, I), cuspidal(59, I, 2), cuspidal(60, -I, 3), cuspidal(61, -I, 4), cuspidal(46, E(8)), cuspidal(47, E(8, 3), 2), cuspidal(48, E(8, 3)), cuspidal(49, E(8), 2), cuspidal(69, E(9, 5), 1 // 3), cuspidal(70, E(9, 5), 2, 2 // 3), cuspidal(71, E(9, 8), 1 // 3), cuspidal(72, E(9, 8), 2, 2 // 3), cuspidal(67, E(9, 2), 1 // 3), cuspidal(68, E(9, 2), 2, 2 // 3), cuspidal(62, E(12)), cuspidal(63, E(12, 7), 2), cuspidal(64, E(12, 7)), cuspidal(65, E(12), 2), cuspidal(75, E(16, 5), 1 // 2), cuspidal(77, E(16, 13), 1 // 2), cuspidal(78, E(16, 15), 1 // 2), cuspidal(76, E(16, 7), 1 // 2), cuspidal(44, E(24, 11)), cuspidal(45, E(24, 17))], :families => [Family("C1", [1]), Family(conj(((CHEVIE[:families])[:X])(3)) * Family("G14"), [26, 37, 28, 39, 14, 3, 34, 18, 46, 48, 15, 13, 30, 29, 59, 60, 55, 56, 25, 36, 27, 38, 2, 11, 16, 35, 49, 47, 12, 10, 32, 31, 58, 61, 54, 57, 4, 17, 22, 33, 41, 40, 43, 42, 44, 45, 51, 50, 53, 52, 64, 65, 62, 63], Dict{Symbol, Any}(:signs => [-1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1], :ennola => 32)), Family(((CHEVIE[:families])[:X])(3), [23, 24, 66], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 2)), Family(((CHEVIE[:families])[:TQZ])(3, E(3, 2)), [19, 20, 21, 68, 70, 72, 67, 71, 69], Dict{Symbol, Any}(:cospecial => 2, :ennola => 8)), Family(Dict{Symbol, Any}(:fourierMat => OnMatrices([[1, 1, 2, 1, 1, -(root(-2)), -(root(-2)), -(root(-2)), -(root(-2))], [1, 1, 2, 1, 1, root(-2), root(-2), root(-2), root(-2)], [2, 2, 0, -2, -2, 0, 0, 0, 0], [1, 1, -2, 1, 1, -(root(-2)), root(-2), -(root(-2)), root(-2)], [1, 1, -2, 1, 1, root(-2), -(root(-2)), root(-2), -(root(-2))], [-(root(-2)), root(-2), 0, -(root(-2)), root(-2), 0, -2 * E(4), 0, 2 * E(4)], [-(root(-2)), root(-2), 0, root(-2), -(root(-2)), -2 * E(4), 0, 2 * E(4), 0], [-(root(-2)), root(-2), 0, -(root(-2)), root(-2), 0, 2 * E(4), 0, -2 * E(4)], [-(root(-2)), root(-2), 0, root(-2), -(root(-2)), 2 * E(4), 0, -2 * E(4), 0]] // 4, perm"(4,5)"), :explanation => "everything to explain", :eigenvalues => [1, 1, 1, -1, -1, E(16, 5), E(16, 7), -(E(16, 5)), -(E(16, 7))], :qEigen => [0, 0, 0, 0, 0, 1 // 2, 1 // 2, 1 // 2, 1 // 2], :special => 2, :ennola => -4), [8, 9, 7, 73, 74, 75, 76, 77, 78]), Family(((CHEVIE[:families])[:X])(3), [5, 6, 79], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -2))], :a => [0, 1, 1, 1, 20, 20, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 1, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 20], :A => [0, 23, 23, 23, 28, 28, 27, 27, 27, 23, 23, 23, 23, 23, 23, 23, 23, 23, 26, 26, 26, 23, 25, 25, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 25, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 27, 28]) else return false end diff --git a/src/tbl/cmplxg24.jl b/src/tbl/cmplxg24.jl index ab434319..2b577c2e 100644 --- a/src/tbl/cmplxg24.jl +++ b/src/tbl/cmplxg24.jl @@ -89,7 +89,7 @@ chevieset(:G24, :HeckeRepresentation, function (para, roots, i) end) (CHEVIE[:families])[:X7] = Dict{Symbol, Any}(:name => "X7", :fourierMat => [[-1 // 2, 1 // 2, root(-7) // 2, root(-7) // 2, -1, -1, -1], [1 // 2, -1 // 2, root(-7) // 2, root(-7) // 2, 1, 1, 1], [root(-7) // 2, root(-7) // 2, root(-7) // 2, -(root(-7)) // 2, 0, 0, 0], [root(-7) // 2, root(-7) // 2, -(root(-7)) // 2, root(-7) // 2, 0, 0, 0], [-1, 1, 0, 0, -(E(7, 6)) - E(7), -(E(7, 5)) - E(7, 2), -(E(7, 4)) - E(7, 3)], [-1, 1, 0, 0, -(E(7, 5)) - E(7, 2), -(E(7, 4)) - E(7, 3), -(E(7, 6)) - E(7)], [-1, 1, 0, 0, -(E(7, 4)) - E(7, 3), -(E(7, 6)) - E(7), -(E(7, 5)) - E(7, 2)]] // root(-7), :eigenvalues => [1, 1, 1, -1, E(7, 4), E(7, 2), E(7)], :explanation => "mystery G24", :special => 1, :cospecial => 2) chevieset(:G24, :UnipotentCharacters, function () - return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:3, :rank => 3, :ST => 24), :levi => [], :parameterExponents => [1, 1, 1], :charNumbers => 1:12, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [1], :rank => 1), :levi => [2, 3], :parameterExponents => [7], :charNumbers => [19, 13], :eigenvalue => -1, :cuspidalName => "B_2"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [17], :eigenvalue => E(4), :qEigen => 1 // 2, :cuspidalName => "G_{24}[i]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [18], :eigenvalue => -(E(4)), :qEigen => 1 // 2, :cuspidalName => "G_{24}[-i]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [20], :eigenvalue => E(7, 3), :cuspidalName => "G_{24}[\\zeta_7^3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [21], :eigenvalue => E(7, 5), :cuspidalName => "G_{24}[\\zeta_7^5]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [22], :eigenvalue => E(7, 6), :cuspidalName => "G_{24}[\\zeta_7^6]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [14], :eigenvalue => E(7, 4), :cuspidalName => "G_{24}[\\zeta_7^4]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [15], :eigenvalue => E(7, 2), :cuspidalName => "G_{24}[\\zeta_7^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [16], :eigenvalue => E(7), :cuspidalName => "G_{24}[\\zeta_7]")], :families => [Family("C1", [1]), Family("X7", [4, 6, 7, 13, 14, 15, 16], Dict{Symbol, Any}(:ennola => 2)), Family("C1", [10], Dict{Symbol, Any}(:ennola => -1)), Family("C'\"2", [11, 12, 17, 18], Dict{Symbol, Any}(:ennola => -3)), Family("C1", [9]), conj(Family("X7", [3, 5, 8, 19, 20, 21, 22], Dict{Symbol, Any}(:ennola => -2))), Family("C1", [2], Dict{Symbol, Any}(:ennola => -1))], :a => [0, 21, 8, 1, 8, 1, 1, 8, 6, 3, 4, 4, 1, 1, 1, 1, 4, 4, 8, 8, 8, 8], :A => [0, 21, 20, 13, 20, 13, 13, 20, 18, 15, 17, 17, 13, 13, 13, 13, 17, 17, 20, 20, 20, 20], :curtis => [2, 1, 6, 5, 4, 3, 8, 7, 10, 9, 12, 11, 19, -20, -21, -22, -18, -17, 13, -14, -15, -16]) + return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:3, :rank => 3, :ST => 24), :levi => [], :parameterExponents => [1, 1, 1], :charNumbers => 1:12, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [1], :rank => 1), :levi => [2, 3], :parameterExponents => [7], :charNumbers => [19, 13], :eigenvalue => -1, :cuspidalName => "B_2"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [17], :eigenvalue => E(4), :qEigen => 1 // 2, :cuspidalName => "G_{24}[i]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [18], :eigenvalue => -(E(4)), :qEigen => 1 // 2, :cuspidalName => "G_{24}[-i]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [20], :eigenvalue => E(7, 3), :cuspidalName => "G_{24}[\\zeta_7^3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [21], :eigenvalue => E(7, 5), :cuspidalName => "G_{24}[\\zeta_7^5]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [22], :eigenvalue => E(7, 6), :cuspidalName => "G_{24}[\\zeta_7^6]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [14], :eigenvalue => E(7, 4), :cuspidalName => "G_{24}[\\zeta_7^4]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [15], :eigenvalue => E(7, 2), :cuspidalName => "G_{24}[\\zeta_7^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [16], :eigenvalue => E(7), :cuspidalName => "G_{24}[\\zeta_7]")], :families => [Family("C1", [1]), Family("X7", [4, 6, 7, 13, 14, 15, 16], Dict{Symbol, Any}(:ennola => 2)), Family("C1", [10], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [11, 12, 18, 17], Dict{Symbol, Any}(:cospecial => 2, :ennola => -4)), Family("C1", [9]), conj(Family("X7", [3, 5, 8, 19, 20, 21, 22], Dict{Symbol, Any}(:ennola => -2))), Family("C1", [2], Dict{Symbol, Any}(:ennola => -1))], :a => [0, 21, 8, 1, 8, 1, 1, 8, 6, 3, 4, 4, 1, 1, 1, 1, 4, 4, 8, 8, 8, 8], :A => [0, 21, 20, 13, 20, 13, 13, 20, 18, 15, 17, 17, 13, 13, 13, 13, 17, 17, 20, 20, 20, 20], :curtis => [2, 1, 6, 5, 4, 3, 8, 7, 10, 9, 12, 11, 19, -20, -21, -22, -18, -17, 13, -14, -15, -16]) end) chevieset(:G24, :Invariants, [function (x, y, z) return (((((-42 * x ^ 2 * y * z - 12 * x ^ 2 * y ^ 2) + 21 // 2 * x ^ 2 * z ^ 2) - 9 // 2 * y ^ 2 * z ^ 2) - 6 * y ^ 3 * z) + 14 * x ^ 4 + 18 // 7 * y ^ 4) - 21 // 8 * z ^ 4 diff --git a/src/tbl/cmplxg26.jl b/src/tbl/cmplxg26.jl index e8f4b8f6..a32b34e9 100644 --- a/src/tbl/cmplxg26.jl +++ b/src/tbl/cmplxg26.jl @@ -127,7 +127,7 @@ chevieset(:G26, :UnipotentCharacters, function () local i3, J J = E(3) i3 = root(-3) - return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:3, :rank => 3, :ST => 26), :levi => [], :parameterExponents => [1, 1, 1], :charNumbers => 1:48, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1, 3, 13], :rank => 2, :p => 6, :q => 2), :levi => [2], :parameterExponents => [[0, 2, 2], 3, 1], :charNumbers => [102, 68, 71, 66, 53, 70, 60, 67, 54, 103, 69, 72, 99, 59, 98, 65, 50, 49], :eigenvalue => J ^ 2, :cuspidalName => ImprimitiveCuspidalName([[], [0, 1], [0, 1]])), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1], :rank => 1, :p => 6, :q => 1), :levi => 2:3, :parameterExponents => [[3, 4, 3, 0, 3, 4]], :charNumbers => [73, 61, 74, 104, 75, 62], :eigenvalue => -1, :cuspidalName => "G_4"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [3], :rank => 1, :p => 6, :q => 1), :levi => 1:2, :parameterExponents => [[4, 3, 1, 1, 0, 1]], :charNumbers => [51, 55, 76, 81, 100, 78], :eigenvalue => J, :cuspidalName => ImprimitiveCuspidalName([[0], [], [0, 1, 2]])), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [3], :rank => 1, :p => 6, :q => 1), :levi => 1:2, :parameterExponents => [[4, 1, 0, 1, 1, 3]], :charNumbers => [52, 79, 101, 80, 77, 56], :eigenvalue => J, :cuspidalName => ImprimitiveCuspidalName([[0], [0, 1, 2], []])), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [92], :eigenvalue => 1, :cuspidalName => "G_{26}[1]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [93], :eigenvalue => 1, :cuspidalName => "G_{26}^2[1]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [94], :eigenvalue => 1, :cuspidalName => "G_{26}^3[1]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [82], :eigenvalue => -1, :cuspidalName => "G_{26}[-1]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [83], :eigenvalue => -1, :cuspidalName => "G_{26}^2[-1]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [88], :eigenvalue => E(3), :cuspidalName => "G_{26}[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [89], :eigenvalue => E(3), :cuspidalName => "G_{26}^2[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [64], :eigenvalue => E(3, 2), :cuspidalName => "G_{26}[\\zeta_{3}^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [84], :eigenvalue => E(3, 2), :cuspidalName => "G_{26}^2[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [85], :eigenvalue => E(3, 2), :cuspidalName => "G_{26}^3[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [90], :eigenvalue => -(E(3)), :cuspidalName => "G_{26}[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [91], :eigenvalue => -(E(3)), :cuspidalName => "G_{26}^2[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [63], :eigenvalue => -(E(3, 2)), :cuspidalName => "G_{26}[-\\zeta_{3}^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [86], :eigenvalue => -(E(3, 2)), :cuspidalName => "G_{26}^2[-\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [87], :eigenvalue => -(E(3, 2)), :cuspidalName => "G_{26}^3[-\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [57], :eigenvalue => E(4), :cuspidalName => "G_{26}[i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [58], :eigenvalue => -(E(4)), :cuspidalName => "G_{26}[-i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [95], :eigenvalue => E(9, 8), :cuspidalName => "G_{26}[\\zeta_9^8]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [96], :eigenvalue => E(9, 5), :cuspidalName => "G_{26}[\\zeta_9^5]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [97], :eigenvalue => E(9, 2), :cuspidalName => "G_{26}[\\zeta_9^2]")], :families => [Family("C1", [1]), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [24, 18, 2, 52, 50, 10, 49, 12, 51], Dict{Symbol, Any}(:signs => [-1, -1, -1, 1, 1, 1, -1, 1, 1], :ennola => 4)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [31, 37, 13, 55, 53, 23, 54, 17, 56], Dict{Symbol, Any}(:signs => [-1, -1, -1, 1, 1, 1, -1, 1, 1], :ennola => -9)), Family("C'\"2", [40, 39, 57, 58], Dict{Symbol, Any}(:ennola => 3)), Family(Family("C2") * ((CHEVIE[:families])[:X])(3), [33, 27, 59, 22, 16, 60, 48, 46, 64, 61, 62, 63], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1], :ennola => 12, :special => 1, :cospecial => 2)), Family(((CHEVIE[:families])[:X])(3), [32, 38, 65], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 2)), Family(Dict{Symbol, Any}(:fourierMat => [[-(root(-3)), root(-3), -9 * E(3, 2), -9 * E(3), 9, 9, 9, (3 - root(-3)) * 3, (3 + root(-3)) * 3, ((3 - root(-3)) * 3) // 2, ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, ((3 + root(-3)) * 3) // 2, root(-3), -(root(-3)), root(-3) * 2, -(root(-3)) * 2, (-3 + root(-3)) * 3, (3 + root(-3)) * 3, root(-3) * 6, ((3 + root(-3)) * 3) // 2, ((-3 + root(-3)) * 3) // 2, 9 * E(3), -9 * E(3, 2), 9, 9 * E(3, 2), 9 * E(3), -9 * E(3), -9 * E(3, 2), ((-3 - root(-3)) * 3) // 2, ((-3 + root(-3)) * 3) // 2, (3 + root(-3)) * 3, (3 - root(-3)) * 3, -9, -9, ((3 + root(-3)) * 3) // 2, ((-3 + root(-3)) * 3) // 2, 9 * E(3), -9 * E(3, 2), ((3 + root(-3)) * 3) // 2, ((-3 + root(-3)) * 3) // 2, 9 * E(3), 9 * E(3, 2), root(-3) * 2, root(-3), root(-3), root(-3) * 6, root(-3) * 6, root(-3) * 6], [root(-3), -(root(-3)), -9 * E(3), -9 * E(3, 2), 9, 9, 9, (3 + root(-3)) * 3, (3 - root(-3)) * 3, ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, -(root(-3)), root(-3), -(root(-3)) * 2, root(-3) * 2, (-3 - root(-3)) * 3, (3 - root(-3)) * 3, -(root(-3)) * 6, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 9 * E(3, 2), -9 * E(3), 9, 9 * E(3), 9 * E(3, 2), -9 * E(3, 2), -9 * E(3), ((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, (3 - root(-3)) * 3, (3 + root(-3)) * 3, -9, -9, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 9 * E(3, 2), -9 * E(3), ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 9 * E(3, 2), 9 * E(3), -(root(-3)) * 2, -(root(-3)), -(root(-3)), -(root(-3)) * 6, -(root(-3)) * 6, -(root(-3)) * 6], [-9 * E(3, 2), -9 * E(3), 9, 9, -9, -9 * E(3), -9 * E(3, 2), 0, 0, -9, -9, 9, 9, -9, -9, 0, 0, 0, 0, 0, -9 * E(3), 9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9, 9, 9, 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), 0, 0, -9 * E(3), -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), 9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), 0, 9 * E(3), -9 * E(3, 2), 0, 0, 0], [-9 * E(3), -9 * E(3, 2), 9, 9, -9, -9 * E(3, 2), -9 * E(3), 0, 0, -9, -9, 9, 9, -9, -9, 0, 0, 0, 0, 0, -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), 9 * E(3), 9, 9, 9, 9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, 0, -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), -9 * E(3), 9 * E(3, 2), -9 * E(3), 9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, 9 * E(3, 2), -9 * E(3), 0, 0, 0], [9, 9, -9, -9, 9, 9, 9, 0, 0, 9, 9, -9, -9, 9, 9, 0, 0, 0, 0, 0, 9, -9, 9, -9, -9, -9, -9, -9, -9, -9, -9, 0, 0, 9, 9, -9, 9, -9, 9, -9, 9, -9, -9, 0, -9, 9, 0, 0, 0], [9, 9, -9 * E(3), -9 * E(3, 2), 9, 9, 9, 0, 0, 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9, 9, 0, 0, 0, 0, 0, 9 * E(3, 2), -9 * E(3), 9 * E(3, 2), -9 * E(3), -9, -9 * E(3), -9 * E(3, 2), -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), -9 * E(3), 0, 0, 9, 9, -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), 0, -9, 9, 0, 0, 0], [9, 9, -9 * E(3, 2), -9 * E(3), 9, 9, 9, 0, 0, 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), 9, 9, 0, 0, 0, 0, 0, 9 * E(3), -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9, -9 * E(3, 2), -9 * E(3), -9 * 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0, 0], [((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 9 * E(3), 9 * E(3, 2), -9, -9 * E(3), -9 * E(3, 2), 0, 0, -9 * E(3), -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), root(-3) * 3, -(root(-3)) * 3, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, 0, 0, 0, -9, 9, -9, 9, -9, -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, 0, 9 * E(3), 9 * E(3, 2), -9, 9, -9, 9, -9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), root(-3) * 6, ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 0, 0, 0], [(3 + root(-3)) * 3, (3 - root(-3)) * 3, 0, 0, 0, 0, 0, 18 * E(3, 2), 18 * E(3), 0, 0, 0, 0, root(-3) * 6, -(root(-3)) * 6, (-3 + root(-3)) * 3, (-3 - root(-3)) * 3, -18, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18 * E(3, 2), 18 * E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -(root(-3)) * 6, (3 - root(-3)) * 3, (-3 - root(-3)) * 3, 0, 0, 0], [(3 - root(-3)) * 3, (3 + root(-3)) * 3, 0, 0, 0, 0, 0, 18 * E(3), 18 * E(3, 2), 0, 0, 0, 0, -(root(-3)) * 6, root(-3) * 6, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, -18, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18 * E(3), 18 * E(3, 2), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, root(-3) * 6, (3 + root(-3)) * 3, (-3 + root(-3)) * 3, 0, 0, 0], [-9, -9, -9 * E(3), -9 * E(3, 2), 9, 9, 9, 0, 0, -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9, -9, 0, 0, 0, 0, 0, -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), -9, -9 * E(3), -9 * E(3, 2), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), 0, 0, 9, 9, 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), -9 * E(3), 0, 9, -9, 0, 0, 0], [-9, -9, -9 * E(3, 2), -9 * E(3), 9, 9, 9, 0, 0, -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9, -9, 0, 0, 0, 0, 0, -9 * E(3), 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9, -9 * E(3, 2), -9 * E(3), -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, 0, 9, 9, 9 * E(3), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 0, 9, -9, 0, 0, 0], [((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 9 * E(3), 9 * E(3, 2), -9, -9 * E(3, 2), -9 * E(3), 0, 0, 9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), root(-3) * 3, -(root(-3)) * 3, (3 - root(-3)) * 3, (3 + root(-3)) * 3, 0, 0, 0, 9 * E(3), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), -9, -9 * E(3), -9 * E(3, 2), 9, 9, -9, -9, 0, 0, 9 * E(3, 2), 9 * E(3), 9 * E(3), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9, -9, -9, -9, root(-3) * 6, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 0, 0, 0], [((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -9 * E(3, 2), -9 * E(3), 9, 9 * E(3), 9 * E(3, 2), 0, 0, -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), -9 * E(3), root(-3) * 3, -(root(-3)) * 3, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, 0, 0, 0, -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), 9, 9 * E(3, 2), 9 * E(3), -9, -9, 9, 9, 0, 0, -9 * E(3), -9 * E(3, 2), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), -9, 9, 9, 9, root(-3) * 6, ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 0, 0, 0], [9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9, -9 * E(3, 2), -9 * E(3), 0, 0, 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9, 9, 0, 0, 0, 0, 0, 9 * E(3), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9, 9 * E(3), 9 * E(3, 2), 9, 9, -9, -9, 0, 0, -9 * E(3, 2), -9 * E(3), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9, 9, 9, 9, 0, -9 * E(3, 2), 9 * E(3), 0, 0, 0], [-9 * E(3, 2), -9 * E(3), -9 * E(3, 2), -9 * E(3), 9, 9 * E(3), 9 * E(3, 2), 0, 0, -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9, -9, 0, 0, 0, 0, 0, -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), -9, -9 * E(3, 2), -9 * E(3), -9, -9, 9, 9, 0, 0, 9 * E(3), 9 * E(3, 2), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9 * E(3), 9, -9, -9, -9, 0, 9 * E(3), -9 * E(3, 2), 0, 0, 0], [((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 9 * E(3, 2), 9 * E(3), -9, -9 * E(3, 2), -9 * E(3), 0, 0, 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), root(-3) * 3, -(root(-3)) * 3, (3 - root(-3)) * 3, (3 + root(-3)) * 3, 0, 0, 0, 9, -9, -9, 9, -9, -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), 0, 0, 9 * E(3, 2), 9 * E(3), 9, -9, -9, 9, 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), -9 * E(3), root(-3) * 6, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 0, 0, 0], [((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -9 * E(3), -9 * E(3, 2), 9, 9 * E(3), 9 * E(3, 2), 0, 0, -9 * E(3), -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), root(-3) * 3, -(root(-3)) * 3, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, 0, 0, 0, -9, 9, 9, -9, 9, 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, 0, -9 * E(3), -9 * E(3, 2), -9, 9, 9, -9, -9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), root(-3) * 6, ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 0, 0, 0], [9 * E(3), 9 * E(3, 2), 9 * E(3, 2), 9 * E(3), -9, -9 * E(3, 2), -9 * E(3), 0, 0, 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), 9, 9, 0, 0, 0, 0, 0, 9, -9, -9, 9, 9, 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), 0, 0, -9 * E(3, 2), -9 * E(3), -9, 9, 9, -9, -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), 0, -9 * E(3, 2), 9 * E(3), 0, 0, 0], [9 * E(3, 2), 9 * E(3), 9 * E(3), 9 * E(3, 2), -9, -9 * E(3), -9 * E(3, 2), 0, 0, 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9, 9, 0, 0, 0, 0, 0, 9, -9, -9, 9, 9, 9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 0, 0, -9 * E(3), -9 * E(3, 2), -9, 9, 9, -9, -9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, -9 * E(3), 9 * E(3, 2), 0, 0, 0], [root(-3) * 2, -(root(-3)) * 2, 0, 0, 0, 0, 0, root(-3) * 6, -(root(-3)) * 6, -(root(-3)) * 6, root(-3) * 6, -(root(-3)) * 6, root(-3) * 6, -(root(-3)) * 2, root(-3) * 2, -(root(-3)) * 4, root(-3) * 4, -(root(-3)) * 6, -(root(-3)) * 6, -(root(-3)) * 12, root(-3) * 6, root(-3) * 6, 0, 0, 0, 0, 0, 0, 0, -(root(-3)) * 6, root(-3) * 6, -(root(-3)) * 6, root(-3) * 6, 0, 0, root(-3) * 6, root(-3) * 6, 0, 0, root(-3) * 6, root(-3) * 6, 0, 0, -(root(-3)) * 4, -(root(-3)) * 2, -(root(-3)) * 2, root(-3) * 6, root(-3) * 6, root(-3) * 6], [root(-3), -(root(-3)), 9 * E(3), 9 * E(3, 2), -9, -9, -9, (3 + root(-3)) * 3, (3 - root(-3)) * 3, ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, -(root(-3)), root(-3), -(root(-3)) * 2, root(-3) * 2, (-3 - root(-3)) * 3, (3 - root(-3)) * 3, -(root(-3)) * 6, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -9 * E(3, 2), 9 * E(3), -9, -9 * E(3), -9 * E(3, 2), 9 * E(3, 2), 9 * E(3), ((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, (3 - root(-3)) * 3, (3 + root(-3)) * 3, 9, 9, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -9 * E(3, 2), 9 * E(3), ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -9 * E(3, 2), -9 * E(3), -(root(-3)) * 2, -(root(-3)), -(root(-3)), -(root(-3)) * 6, -(root(-3)) * 6, -(root(-3)) * 6], [root(-3), -(root(-3)), -9 * E(3, 2), -9 * E(3), 9, 9, 9, (-3 + root(-3)) * 3, (-3 - root(-3)) * 3, ((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, ((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -(root(-3)), root(-3), -(root(-3)) * 2, root(-3) * 2, (3 - root(-3)) * 3, (-3 - root(-3)) * 3, -(root(-3)) * 6, ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 9 * E(3), -9 * E(3, 2), 9, 9 * E(3, 2), 9 * E(3), -9 * E(3), -9 * E(3, 2), ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, -9, -9, ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 9 * E(3), -9 * E(3, 2), ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 9 * E(3), 9 * E(3, 2), -(root(-3)) * 2, -(root(-3)), -(root(-3)), -(root(-3)) * 6, -(root(-3)) * 6, -(root(-3)) * 6], [root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -(root(-3)) * 6, root(-3) * 6, root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, root(-3) * 6, -(root(-3)) * 6, -(root(-3)) * 6, 18 * E(9, 7) - 18 * E(9, 2), -18 * E(9, 5) + 18 * E(9, 4), ((-18 * E(9, 7) + 18 * E(9, 5)) - 18 * E(9, 4)) + 18 * E(9, 2)], [root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -(root(-3)) * 6, root(-3) * 6, root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, root(-3) * 6, -(root(-3)) * 6, -(root(-3)) * 6, -18 * E(9, 5) + 18 * E(9, 4), ((-18 * E(9, 7) + 18 * E(9, 5)) - 18 * E(9, 4)) + 18 * E(9, 2), 18 * E(9, 7) - 18 * E(9, 2)], [root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -(root(-3)) * 6, root(-3) * 6, root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, root(-3) * 6, -(root(-3)) * 6, -(root(-3)) * 6, ((-18 * E(9, 7) + 18 * E(9, 5)) - 18 * E(9, 4)) + 18 * E(9, 2), 18 * E(9, 7) - 18 * E(9, 2), -18 * E(9, 5) + 18 * E(9, 4)]] // 54, :eigenvalues => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, E(3, 2), E(3, 2), E(3, 2), E(3, 2), E(3, 2), E(3, 2), E(3, 2), -1, -1, -1, E(3), E(3), E(3), E(3), E(3), E(3), -1, -1, E(3, 2), E(3, 2), -(E(3, 2)), -(E(3, 2)), E(3), E(3), -(E(3)), -(E(3)), 1, 1, 1, E(9, 8), E(9, 5), E(9, 2)], :explanation => "mystery G26", :special => 1, :cospecial => 2), [43, 42, 28, 34, 8, 41, 44, 29, 35, 15, 21, 45, 47, 6, 5, 11, 9, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1], :ennola => -2)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [30, 36, 14, 101, 99, 26, 98, 20, 100], Dict{Symbol, Any}(:signs => [-1, -1, -1, 1, 1, 1, -1, 1, 1], :ennola => 9)), Family(((CHEVIE[:families])[:X])(3), [25, 19, 102], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -3)), Family("X5", [4, 7, 104, 103, 3], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, 1], :ennola => 5))], :a => [0, 1, 21, 21, 6, 6, 21, 6, 6, 1, 6, 1, 2, 11, 6, 4, 2, 1, 16, 11, 6, 4, 2, 1, 16, 11, 4, 6, 6, 11, 2, 5, 4, 6, 6, 11, 2, 5, 3, 3, 6, 6, 6, 6, 6, 4, 6, 4, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 11, 11, 11, 11, 16, 21, 21], :A => [0, 17, 33, 33, 30, 30, 33, 30, 30, 17, 30, 17, 22, 31, 30, 26, 22, 17, 32, 31, 30, 26, 22, 17, 32, 31, 26, 30, 30, 31, 22, 25, 26, 30, 30, 31, 22, 25, 24, 24, 30, 30, 30, 30, 30, 26, 30, 26, 17, 17, 17, 17, 22, 22, 22, 22, 24, 24, 26, 26, 26, 26, 26, 26, 25, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 31, 31, 31, 32, 33, 33]) + return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:3, :rank => 3, :ST => 26), :levi => [], :parameterExponents => [1, 1, 1], :charNumbers => 1:48, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1, 3, 13], :rank => 2, :p => 6, :q => 2), :levi => [2], :parameterExponents => [[0, 2, 2], 3, 1], :charNumbers => [102, 68, 71, 66, 53, 70, 60, 67, 54, 103, 69, 72, 99, 59, 98, 65, 50, 49], :eigenvalue => J ^ 2, :cuspidalName => ImprimitiveCuspidalName([[], [0, 1], [0, 1]])), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1], :rank => 1, :p => 6, :q => 1), :levi => 2:3, :parameterExponents => [[3, 4, 3, 0, 3, 4]], :charNumbers => [73, 61, 74, 104, 75, 62], :eigenvalue => -1, :cuspidalName => "G_4"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [3], :rank => 1, :p => 6, :q => 1), :levi => 1:2, :parameterExponents => [[4, 3, 1, 1, 0, 1]], :charNumbers => [51, 55, 76, 81, 100, 78], :eigenvalue => J, :cuspidalName => ImprimitiveCuspidalName([[0], [], [0, 1, 2]])), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [3], :rank => 1, :p => 6, :q => 1), :levi => 1:2, :parameterExponents => [[4, 1, 0, 1, 1, 3]], :charNumbers => [52, 79, 101, 80, 77, 56], :eigenvalue => J, :cuspidalName => ImprimitiveCuspidalName([[0], [0, 1, 2], []])), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [92], :eigenvalue => 1, :cuspidalName => "G_{26}[1]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [93], :eigenvalue => 1, :cuspidalName => "G_{26}^2[1]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [94], :eigenvalue => 1, :cuspidalName => "G_{26}^3[1]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [82], :eigenvalue => -1, :cuspidalName => "G_{26}[-1]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [83], :eigenvalue => -1, :cuspidalName => "G_{26}^2[-1]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [88], :eigenvalue => E(3), :cuspidalName => "G_{26}[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [89], :eigenvalue => E(3), :cuspidalName => "G_{26}^2[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [64], :eigenvalue => E(3, 2), :cuspidalName => "G_{26}[\\zeta_{3}^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [84], :eigenvalue => E(3, 2), :cuspidalName => "G_{26}^2[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [85], :eigenvalue => E(3, 2), :cuspidalName => "G_{26}^3[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [90], :eigenvalue => -(E(3)), :cuspidalName => "G_{26}[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [91], :eigenvalue => -(E(3)), :cuspidalName => "G_{26}^2[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [63], :eigenvalue => -(E(3, 2)), :cuspidalName => "G_{26}[-\\zeta_{3}^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [86], :eigenvalue => -(E(3, 2)), :cuspidalName => "G_{26}^2[-\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [87], :eigenvalue => -(E(3, 2)), :cuspidalName => "G_{26}^3[-\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [57], :eigenvalue => E(4), :cuspidalName => "G_{26}[i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [58], :eigenvalue => -(E(4)), :cuspidalName => "G_{26}[-i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [95], :eigenvalue => E(9, 8), :cuspidalName => "G_{26}[\\zeta_9^8]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [96], :eigenvalue => E(9, 5), :cuspidalName => "G_{26}[\\zeta_9^5]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [97], :eigenvalue => E(9, 2), :cuspidalName => "G_{26}[\\zeta_9^2]")], :families => [Family("C1", [1]), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [24, 18, 2, 52, 50, 10, 49, 12, 51], Dict{Symbol, Any}(:signs => [-1, -1, -1, 1, 1, 1, -1, 1, 1], :ennola => 4)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [31, 37, 13, 55, 53, 23, 54, 17, 56], Dict{Symbol, Any}(:signs => [-1, -1, -1, 1, 1, 1, -1, 1, 1], :ennola => -9)), Family(((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [40, 39, 58, 57], Dict{Symbol, Any}(:cospecial => 2, :ennola => 4)), Family(Family("C2") * ((CHEVIE[:families])[:X])(3), [33, 27, 59, 22, 16, 60, 48, 46, 64, 61, 62, 63], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1], :ennola => 12, :special => 1, :cospecial => 2)), Family(((CHEVIE[:families])[:X])(3), [32, 38, 65], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 2)), Family(Dict{Symbol, Any}(:fourierMat => [[-(root(-3)), root(-3), -9 * E(3, 2), -9 * E(3), 9, 9, 9, (3 - root(-3)) * 3, (3 + root(-3)) * 3, ((3 - root(-3)) * 3) // 2, ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, ((3 + root(-3)) * 3) // 2, root(-3), -(root(-3)), root(-3) * 2, -(root(-3)) * 2, (-3 + root(-3)) * 3, (3 + root(-3)) * 3, root(-3) * 6, ((3 + root(-3)) * 3) // 2, ((-3 + root(-3)) * 3) // 2, 9 * E(3), -9 * E(3, 2), 9, 9 * E(3, 2), 9 * E(3), -9 * E(3), -9 * E(3, 2), ((-3 - root(-3)) * 3) // 2, ((-3 + root(-3)) * 3) // 2, (3 + root(-3)) * 3, (3 - root(-3)) * 3, -9, -9, ((3 + root(-3)) * 3) // 2, ((-3 + root(-3)) * 3) // 2, 9 * E(3), -9 * E(3, 2), ((3 + root(-3)) * 3) // 2, ((-3 + root(-3)) * 3) // 2, 9 * E(3), 9 * E(3, 2), root(-3) * 2, root(-3), root(-3), root(-3) * 6, root(-3) * 6, root(-3) * 6], [root(-3), -(root(-3)), -9 * E(3), -9 * E(3, 2), 9, 9, 9, (3 + root(-3)) * 3, (3 - root(-3)) * 3, ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, -(root(-3)), root(-3), -(root(-3)) * 2, root(-3) * 2, (-3 - root(-3)) * 3, (3 - root(-3)) * 3, -(root(-3)) * 6, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 9 * E(3, 2), -9 * E(3), 9, 9 * E(3), 9 * E(3, 2), -9 * E(3, 2), -9 * E(3), ((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, (3 - root(-3)) * 3, (3 + root(-3)) * 3, -9, -9, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 9 * E(3, 2), -9 * E(3), ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 9 * E(3, 2), 9 * E(3), -(root(-3)) * 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E(3, 2), -9 * E(3), 9 * E(3), -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), 9, -9, 9, 9, root(-3) * 6, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 0, 0, 0], [((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 9 * E(3, 2), 9 * E(3), -9, -9 * E(3), -9 * E(3, 2), 0, 0, -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), -9 * E(3), root(-3) * 3, -(root(-3)) * 3, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, 0, 0, 0, -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), 9 * E(3), -9, -9 * E(3, 2), -9 * E(3), 9, 9, 9, 9, 0, 0, 9 * E(3), 9 * E(3, 2), -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), 9 * E(3), -9, 9, -9, -9, root(-3) * 6, ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 0, 0, 0], [9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9, 9 * E(3, 2), 9 * E(3), 0, 0, 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9, 9, 0, 0, 0, 0, 0, 9 * E(3), -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9, -9 * E(3), -9 * E(3, 2), -9, -9, -9, -9, 0, 0, 9 * E(3, 2), 9 * E(3), -9 * E(3), 9 * E(3, 2), -9 * E(3), 9 * E(3, 2), -9, 9, -9, -9, 0, -9 * E(3, 2), 9 * E(3), 0, 0, 0], [-9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9, -9 * E(3), -9 * E(3, 2), 0, 0, -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9, -9, 0, 0, 0, 0, 0, -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), 9 * E(3), 9, 9 * E(3, 2), 9 * E(3), 9, 9, 9, 9, 0, 0, -9 * E(3), -9 * E(3, 2), 9 * E(3, 2), -9 * E(3), 9 * E(3, 2), -9 * E(3), 9, -9, 9, 9, 0, 9 * E(3), -9 * E(3, 2), 0, 0, 0], [9, 9, 9, 9, -9, -9, -9, 0, 0, 9, 9, -9, -9, 9, 9, 0, 0, 0, 0, 0, 9, -9, -9, 9, 9, 9, 9, 9, 9, -9, -9, 0, 0, -9, -9, -9, 9, 9, -9, -9, 9, 9, 9, 0, -9, 9, 0, 0, 0], [9 * E(3, 2), 9 * E(3), 9, 9, -9, -9 * E(3), -9 * E(3, 2), 0, 0, 9, 9, -9, -9, 9, 9, 0, 0, 0, 0, 0, 9 * E(3), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9, 9, 9, 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), 0, 0, -9 * E(3), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), 0, -9 * E(3), 9 * E(3, 2), 0, 0, 0], [9 * E(3), 9 * E(3, 2), 9, 9, -9, -9 * E(3, 2), -9 * E(3), 0, 0, 9, 9, -9, -9, 9, 9, 0, 0, 0, 0, 0, 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9 * E(3), 9, 9, 9, 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 0, 0, -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, -9 * E(3, 2), 9 * E(3), 0, 0, 0], [-9 * E(3), -9 * E(3, 2), 9 * E(3, 2), 9 * E(3), -9, -9 * E(3, 2), -9 * E(3), 0, 0, -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9, -9, 0, 0, 0, 0, 0, -9, 9, -9, 9, 9, 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), 0, 0, -9 * E(3, 2), -9 * E(3), 9, -9, 9, -9, 9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), 0, 9 * E(3, 2), -9 * E(3), 0, 0, 0], [-9 * E(3, 2), -9 * E(3), 9 * E(3), 9 * E(3, 2), -9, -9 * E(3), -9 * E(3, 2), 0, 0, -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9, -9, 0, 0, 0, 0, 0, -9, 9, -9, 9, 9, 9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, 0, -9 * E(3), -9 * E(3, 2), 9, -9, 9, -9, 9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, 9 * E(3), -9 * E(3, 2), 0, 0, 0], [((-3 - root(-3)) * 3) // 2, ((-3 + root(-3)) * 3) // 2, 9 * E(3, 2), 9 * E(3), -9, -9 * E(3, 2), -9 * E(3), 0, 0, -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), -9 * E(3), -(root(-3)) * 3, root(-3) * 3, (-3 + root(-3)) * 3, (-3 - root(-3)) * 3, 0, 0, 0, -9, 9, -9, 9, -9, -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), 0, 0, 9 * E(3, 2), 9 * E(3), -9, 9, -9, 9, -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), -(root(-3)) * 6, ((-3 + root(-3)) * 3) // 2, ((3 + root(-3)) * 3) // 2, 0, 0, 0], [((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 9 * E(3), 9 * E(3, 2), -9, -9 * E(3), -9 * E(3, 2), 0, 0, -9 * E(3), -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), root(-3) * 3, -(root(-3)) * 3, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, 0, 0, 0, -9, 9, -9, 9, -9, -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, 0, 9 * E(3), 9 * E(3, 2), -9, 9, -9, 9, -9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), root(-3) * 6, ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 0, 0, 0], [(3 + root(-3)) * 3, (3 - root(-3)) * 3, 0, 0, 0, 0, 0, 18 * E(3, 2), 18 * E(3), 0, 0, 0, 0, root(-3) * 6, -(root(-3)) * 6, (-3 + root(-3)) * 3, (-3 - root(-3)) * 3, -18, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18 * E(3, 2), 18 * E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -(root(-3)) * 6, (3 - root(-3)) * 3, (-3 - root(-3)) * 3, 0, 0, 0], [(3 - root(-3)) * 3, (3 + root(-3)) * 3, 0, 0, 0, 0, 0, 18 * E(3), 18 * E(3, 2), 0, 0, 0, 0, -(root(-3)) * 6, root(-3) * 6, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, -18, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18 * E(3), 18 * E(3, 2), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, root(-3) * 6, (3 + root(-3)) * 3, (-3 + root(-3)) * 3, 0, 0, 0], [-9, -9, -9 * E(3), -9 * E(3, 2), 9, 9, 9, 0, 0, -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9, -9, 0, 0, 0, 0, 0, -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), -9, -9 * E(3), -9 * E(3, 2), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), 0, 0, 9, 9, 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), -9 * E(3), 0, 9, -9, 0, 0, 0], [-9, -9, -9 * E(3, 2), -9 * E(3), 9, 9, 9, 0, 0, -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9, -9, 0, 0, 0, 0, 0, -9 * E(3), 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9, -9 * E(3, 2), -9 * E(3), -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, 0, 9, 9, 9 * E(3), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 0, 9, -9, 0, 0, 0], [((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 9 * E(3), 9 * E(3, 2), -9, -9 * E(3, 2), -9 * E(3), 0, 0, 9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), root(-3) * 3, -(root(-3)) * 3, (3 - root(-3)) * 3, (3 + root(-3)) * 3, 0, 0, 0, 9 * E(3), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), -9, -9 * E(3), -9 * E(3, 2), 9, 9, -9, -9, 0, 0, 9 * E(3, 2), 9 * E(3), 9 * E(3), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9, -9, -9, -9, root(-3) * 6, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 0, 0, 0], [((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -9 * E(3, 2), -9 * E(3), 9, 9 * E(3), 9 * E(3, 2), 0, 0, -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), -9 * E(3), root(-3) * 3, -(root(-3)) * 3, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, 0, 0, 0, -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), 9, 9 * E(3, 2), 9 * E(3), -9, -9, 9, 9, 0, 0, -9 * E(3), -9 * E(3, 2), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), -9, 9, 9, 9, root(-3) * 6, ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 0, 0, 0], [9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9, -9 * E(3, 2), -9 * E(3), 0, 0, 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9, 9, 0, 0, 0, 0, 0, 9 * E(3), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9, 9 * E(3), 9 * E(3, 2), 9, 9, -9, -9, 0, 0, -9 * E(3, 2), -9 * E(3), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9, 9, 9, 9, 0, -9 * E(3, 2), 9 * E(3), 0, 0, 0], [-9 * E(3, 2), -9 * E(3), -9 * E(3, 2), -9 * E(3), 9, 9 * E(3), 9 * E(3, 2), 0, 0, -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9, -9, 0, 0, 0, 0, 0, -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), -9, -9 * E(3, 2), -9 * E(3), -9, -9, 9, 9, 0, 0, 9 * E(3), 9 * E(3, 2), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9 * E(3), 9, -9, -9, -9, 0, 9 * E(3), -9 * E(3, 2), 0, 0, 0], [((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 9 * E(3, 2), 9 * E(3), -9, -9 * E(3, 2), -9 * E(3), 0, 0, 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), root(-3) * 3, -(root(-3)) * 3, (3 - root(-3)) * 3, (3 + root(-3)) * 3, 0, 0, 0, 9, -9, -9, 9, -9, -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), 0, 0, 9 * E(3, 2), 9 * E(3), 9, -9, -9, 9, 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), -9 * E(3), root(-3) * 6, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 0, 0, 0], [((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -9 * E(3), -9 * E(3, 2), 9, 9 * E(3), 9 * E(3, 2), 0, 0, -9 * E(3), -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), root(-3) * 3, -(root(-3)) * 3, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, 0, 0, 0, -9, 9, 9, -9, 9, 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, 0, -9 * E(3), -9 * E(3, 2), -9, 9, 9, -9, -9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), root(-3) * 6, ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 0, 0, 0], [9 * E(3), 9 * E(3, 2), 9 * E(3, 2), 9 * E(3), -9, -9 * E(3, 2), -9 * E(3), 0, 0, 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), 9, 9, 0, 0, 0, 0, 0, 9, -9, -9, 9, 9, 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), 0, 0, -9 * E(3, 2), -9 * E(3), -9, 9, 9, -9, -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), 0, -9 * E(3, 2), 9 * E(3), 0, 0, 0], [9 * E(3, 2), 9 * E(3), 9 * E(3), 9 * E(3, 2), -9, -9 * E(3), -9 * E(3, 2), 0, 0, 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9, 9, 0, 0, 0, 0, 0, 9, -9, -9, 9, 9, 9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 0, 0, -9 * E(3), -9 * E(3, 2), -9, 9, 9, -9, -9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, -9 * E(3), 9 * E(3, 2), 0, 0, 0], [root(-3) * 2, -(root(-3)) * 2, 0, 0, 0, 0, 0, root(-3) * 6, -(root(-3)) * 6, -(root(-3)) * 6, root(-3) * 6, -(root(-3)) * 6, root(-3) * 6, -(root(-3)) * 2, root(-3) * 2, -(root(-3)) * 4, root(-3) * 4, -(root(-3)) * 6, -(root(-3)) * 6, -(root(-3)) * 12, root(-3) * 6, root(-3) * 6, 0, 0, 0, 0, 0, 0, 0, -(root(-3)) * 6, root(-3) * 6, -(root(-3)) * 6, root(-3) * 6, 0, 0, root(-3) * 6, root(-3) * 6, 0, 0, root(-3) * 6, root(-3) * 6, 0, 0, -(root(-3)) * 4, -(root(-3)) * 2, -(root(-3)) * 2, root(-3) * 6, root(-3) * 6, root(-3) * 6], [root(-3), -(root(-3)), 9 * E(3), 9 * E(3, 2), -9, -9, -9, (3 + root(-3)) * 3, (3 - root(-3)) * 3, ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, -(root(-3)), root(-3), -(root(-3)) * 2, root(-3) * 2, (-3 - root(-3)) * 3, (3 - root(-3)) * 3, -(root(-3)) * 6, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -9 * E(3, 2), 9 * E(3), -9, -9 * E(3), -9 * E(3, 2), 9 * E(3, 2), 9 * E(3), ((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, (3 - root(-3)) * 3, (3 + root(-3)) * 3, 9, 9, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -9 * E(3, 2), 9 * E(3), ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -9 * E(3, 2), -9 * E(3), -(root(-3)) * 2, -(root(-3)), -(root(-3)), -(root(-3)) * 6, -(root(-3)) * 6, -(root(-3)) * 6], [root(-3), -(root(-3)), -9 * E(3, 2), -9 * E(3), 9, 9, 9, (-3 + root(-3)) * 3, (-3 - root(-3)) * 3, ((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, ((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -(root(-3)), root(-3), -(root(-3)) * 2, root(-3) * 2, (3 - root(-3)) * 3, (-3 - root(-3)) * 3, -(root(-3)) * 6, ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 9 * E(3), -9 * E(3, 2), 9, 9 * E(3, 2), 9 * E(3), -9 * E(3), -9 * E(3, 2), ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, -9, -9, ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 9 * E(3), -9 * E(3, 2), ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 9 * E(3), 9 * E(3, 2), -(root(-3)) * 2, -(root(-3)), -(root(-3)), -(root(-3)) * 6, -(root(-3)) * 6, -(root(-3)) * 6], [root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -(root(-3)) * 6, root(-3) * 6, root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, root(-3) * 6, -(root(-3)) * 6, -(root(-3)) * 6, 18 * E(9, 7) - 18 * E(9, 2), -18 * E(9, 5) + 18 * E(9, 4), ((-18 * E(9, 7) + 18 * E(9, 5)) - 18 * E(9, 4)) + 18 * E(9, 2)], [root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -(root(-3)) * 6, root(-3) * 6, root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, root(-3) * 6, -(root(-3)) * 6, -(root(-3)) * 6, -18 * E(9, 5) + 18 * E(9, 4), ((-18 * E(9, 7) + 18 * E(9, 5)) - 18 * E(9, 4)) + 18 * E(9, 2), 18 * E(9, 7) - 18 * E(9, 2)], [root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -(root(-3)) * 6, root(-3) * 6, root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, root(-3) * 6, -(root(-3)) * 6, -(root(-3)) * 6, ((-18 * E(9, 7) + 18 * E(9, 5)) - 18 * E(9, 4)) + 18 * E(9, 2), 18 * E(9, 7) - 18 * E(9, 2), -18 * E(9, 5) + 18 * E(9, 4)]] // 54, :eigenvalues => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, E(3, 2), E(3, 2), E(3, 2), E(3, 2), E(3, 2), E(3, 2), E(3, 2), -1, -1, -1, E(3), E(3), E(3), E(3), E(3), E(3), -1, -1, E(3, 2), E(3, 2), -(E(3, 2)), -(E(3, 2)), E(3), E(3), -(E(3)), -(E(3)), 1, 1, 1, E(9, 8), E(9, 5), E(9, 2)], :explanation => "mystery G26", :special => 1, :cospecial => 2), [43, 42, 28, 34, 8, 41, 44, 29, 35, 15, 21, 45, 47, 6, 5, 11, 9, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1], :ennola => -2)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [30, 36, 14, 101, 99, 26, 98, 20, 100], Dict{Symbol, Any}(:signs => [-1, -1, -1, 1, 1, 1, -1, 1, 1], :ennola => 9)), Family(((CHEVIE[:families])[:X])(3), [25, 19, 102], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -3)), Family("X5", [4, 7, 104, 103, 3], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, 1], :ennola => 5))], :a => [0, 1, 21, 21, 6, 6, 21, 6, 6, 1, 6, 1, 2, 11, 6, 4, 2, 1, 16, 11, 6, 4, 2, 1, 16, 11, 4, 6, 6, 11, 2, 5, 4, 6, 6, 11, 2, 5, 3, 3, 6, 6, 6, 6, 6, 4, 6, 4, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 11, 11, 11, 11, 16, 21, 21], :A => [0, 17, 33, 33, 30, 30, 33, 30, 30, 17, 30, 17, 22, 31, 30, 26, 22, 17, 32, 31, 30, 26, 22, 17, 32, 31, 26, 30, 30, 31, 22, 25, 26, 30, 30, 31, 22, 25, 24, 24, 30, 30, 30, 30, 30, 26, 30, 26, 17, 17, 17, 17, 22, 22, 22, 22, 24, 24, 26, 26, 26, 26, 26, 26, 25, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 31, 31, 31, 32, 33, 33]) end) chevieset(:G26, :Invariants, [function (x1, x2, x3) return ((-10 * x1 ^ 3 * x2 ^ 3 - 10 * x1 ^ 3 * x3 ^ 3) - 10 * x2 ^ 3 * x3 ^ 3) + x1 ^ 6 + x2 ^ 6 + x3 ^ 6 diff --git a/src/tbl/cmplxg27.jl b/src/tbl/cmplxg27.jl index 8d109f21..133545e4 100644 --- a/src/tbl/cmplxg27.jl +++ b/src/tbl/cmplxg27.jl @@ -138,7 +138,7 @@ chevieset(:G27, :HeckeRepresentation, function (para, rootpara, i) end) (CHEVIE[:families])[:Y6] = Dict{Symbol, Any}(:name => "Y_6", :explanation => "subcategory of DQ(B2).20", :fourierMat => [[-(root(5)), -(root(5)), -2 * root(5), -2 * root(5), -5, -5], [-(root(5)), -(root(5)), -2 * root(5), -2 * root(5), 5, 5], [-2 * root(5), -2 * root(5), -5 + root(5), 5 + root(5), 0, 0], [-2 * root(5), -2 * root(5), 5 + root(5), -5 + root(5), 0, 0], [-5, 5, 0, 0, 5, -5], [-5, 5, 0, 0, -5, 5]] // 10, :eigenvalues => [1, 1, E(5, 3), E(5, 2), -1, 1], :special => 1, :cospecial => 1) chevieset(:G27, :UnipotentCharacters, function () - return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:3, :rank => 3, :ST => 27), :levi => [], :parameterExponents => [1, 1, 1], :charNumbers => 1:34, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [2], :rank => 1, :p => 6, :q => 1), :levi => [1, 8], :parameterExponents => [[5 // 2, 5, 0, 5 // 2, 0, 5]], :charNumbers => [56, 37, 79, 55, 77, 39], :eigenvalue => E(5, 2), :cuspidalName => "I_2(5)[1,3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [2], :rank => 1, :p => 6, :q => 1), :levi => [1, 8], :parameterExponents => [[5 // 2, 5, 0, 5 // 2, 0, 5]], :charNumbers => [58, 38, 80, 57, 78, 40], :eigenvalue => E(5, 3), :cuspidalName => "I_2(5)[1,2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1], :rank => 1, :p => 6, :q => 1), :levi => [2, 3], :parameterExponents => [[4, 5, 0, 1, 0, 5]], :charNumbers => [47, 35, 76, 74, 75, 36], :eigenvalue => -1, :cuspidalName => "B_2"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [65], :eigenvalue => E(4), :cuspidalName => "G_{27}[i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [63], :eigenvalue => E(4), :cuspidalName => "G_{27}^2[i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [64], :eigenvalue => -(E(4)), :cuspidalName => "G_{27}[-i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [66], :eigenvalue => -(E(4)), :cuspidalName => "G_{27}^2[-i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [83], :eigenvalue => E(3), :cuspidalName => "G_{27}[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [84], :eigenvalue => E(3), :cuspidalName => "G_{27}^2[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [85], :eigenvalue => E(3), :cuspidalName => "G_{27}^3[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [54], :eigenvalue => E(3), :cuspidalName => "G_{27}^4[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [67], :eigenvalue => E(3, 2), :cuspidalName => "G_{27}[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [43], :eigenvalue => E(3, 2), :cuspidalName => "G_{27}^2[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [44], :eigenvalue => E(3, 2), :cuspidalName => "G_{27}^3[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [45], :eigenvalue => E(3, 2), :cuspidalName => "G_{27}^4[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [86], :eigenvalue => -(E(3)), :cuspidalName => "G_{27}[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [46], :eigenvalue => -(E(3, 2)), :cuspidalName => "G_{27}^2[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [51], :eigenvalue => E(9), :cuspidalName => "G_{27}[\\zeta_9]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [53], :eigenvalue => E(9), :cuspidalName => "G_{27}^2[\\zeta_9]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [72], :eigenvalue => E(9, 2), :cuspidalName => "G_{27}[\\zeta_9^2]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [68], :eigenvalue => E(9, 2), :cuspidalName => "G_{27}^2[E9^2]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [50], :eigenvalue => E(9, 4), :cuspidalName => "G_{27}[\\zeta_9^4]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [49], :eigenvalue => E(9, 4), :cuspidalName => "G_{27}^2[\\zeta_9^4]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [70], :eigenvalue => E(9, 5), :cuspidalName => "G_{27}[\\zeta_9^5]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [69], :eigenvalue => E(9, 5), :cuspidalName => "G_{27}^2[\\zeta_9^5]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [52], :eigenvalue => E(9, 7), :cuspidalName => "G_{27}[\\zeta_9^7]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [48], :eigenvalue => E(9, 7), :cuspidalName => "G_{27}^2[\\zeta_9^7]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [73], :eigenvalue => E(9, 8), :cuspidalName => "G_{27}[\\zeta_9^8]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [71], :eigenvalue => E(9, 8), :cuspidalName => "G_{27}^2[\\zeta_9^8]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [41], :eigenvalue => E(15), :cuspidalName => "G_{27}[\\zeta_{15}]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [42], :eigenvalue => E(15, 4), :cuspidalName => "G_{27}[\\zeta_{15}^4]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [81], :eigenvalue => E(15, 11), :cuspidalName => "G_{27}[\\zeta_{15}^{11}]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [82], :eigenvalue => E(15, 14), :cuspidalName => "G_{27}[\\zeta_{15}^{14}]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [59], :eigenvalue => E(20, 17), :cuspidalName => "G_{27}[\\zeta_{20}^{17}]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [61], :eigenvalue => E(20, 13), :cuspidalName => "G_{27}[\\zeta_{20}^{13}]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0, :qEigen => 1 // 2), :levi => 1:3, :parameterExponents => [], :charNumbers => [60], :eigenvalue => E(20, 7), :cuspidalName => "G_{27}[\\zeta_{20}^7]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [62], :eigenvalue => E(20, 3), :cuspidalName => "G_{27}[\\zeta_{20}^3]", :qEigen => 1 // 2)], :families => [Family("C1", [1]), Family(((CHEVIE[:families])[:X])(3) * Family("Y6"), [5, 3, 38, 37, 35, 16, 9, 7, 40, 39, 36, 18, 44, 43, 42, 41, 46, 45], Dict{Symbol, Any}(:signs => [-1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1], :ennola => -14)), Family("C2", [30, 11, 12, 47], Dict{Symbol, Any}(:ennola => -4)), conj(Family("Z9", [23, 49, 48, 28, 53, 51, 26, 52, 50], Dict{Symbol, Any}(:special => 7, :cospecial => 1, :ennola => 2))), conj(Family(((CHEVIE[:families])[:X])(3), [33, 31, 54], Dict{Symbol, Any}(:ennola => -3))), Family(Family("C'\"2") * ((CHEVIE[:families])[:Dihedral])(5), [19, 21, 58, 56, 20, 22, 57, 55, 65, 63, 59, 61, 66, 64, 60, 62], Dict{Symbol, Any}(:ennola => -9, :special => 1, :cospecial => 5)), Family(((CHEVIE[:families])[:X])(3), [34, 32, 67], Dict{Symbol, Any}(:ennola => -2)), Family("Z9", [24, 69, 68, 27, 73, 71, 25, 72, 70], Dict{Symbol, Any}(:cospecial => 4, :signs => [1, 1, -1, 1, 1, -1, 1, 1, -1], :ennola => 6)), Family("C2", [29, 13, 14, 74], Dict{Symbol, Any}(:ennola => 4)), conj(Family(((CHEVIE[:families])[:X])(3) * Family("Y6"), [6, 4, 77, 78, 75, 15, 10, 8, 79, 80, 76, 17, 84, 83, 81, 82, 86, 85], Dict{Symbol, Any}(:signs => [-1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1], :ennola => 8))), Family("C1", [2], Dict{Symbol, Any}(:ennola => -1))], :a => [0, 45, 1, 16, 1, 16, 1, 16, 1, 16, 3, 3, 12, 12, 16, 1, 16, 1, 6, 6, 6, 6, 4, 9, 9, 4, 9, 4, 12, 3, 5, 8, 5, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 9, 9, 9, 9, 9, 9, 12, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16], :A => [0, 45, 29, 44, 29, 44, 29, 44, 29, 44, 33, 33, 42, 42, 44, 29, 44, 29, 39, 39, 39, 39, 36, 41, 41, 36, 41, 36, 42, 33, 37, 40, 37, 40, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 33, 36, 36, 36, 36, 36, 36, 37, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 40, 41, 41, 41, 41, 41, 41, 42, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44]) + return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:3, :rank => 3, :ST => 27), :levi => [], :parameterExponents => [1, 1, 1], :charNumbers => 1:34, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [2], :rank => 1, :p => 6, :q => 1), :levi => [1, 8], :parameterExponents => [[5 // 2, 5, 0, 5 // 2, 0, 5]], :charNumbers => [56, 37, 79, 55, 77, 39], :eigenvalue => E(5, 2), :cuspidalName => "I_2(5)[1,3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [2], :rank => 1, :p => 6, :q => 1), :levi => [1, 8], :parameterExponents => [[5 // 2, 5, 0, 5 // 2, 0, 5]], :charNumbers => [58, 38, 80, 57, 78, 40], :eigenvalue => E(5, 3), :cuspidalName => "I_2(5)[1,2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1], :rank => 1, :p => 6, :q => 1), :levi => [2, 3], :parameterExponents => [[4, 5, 0, 1, 0, 5]], :charNumbers => [47, 35, 76, 74, 75, 36], :eigenvalue => -1, :cuspidalName => "B_2"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [65], :eigenvalue => E(4), :cuspidalName => "G_{27}[i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [63], :eigenvalue => E(4), :cuspidalName => "G_{27}^2[i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [64], :eigenvalue => -(E(4)), :cuspidalName => "G_{27}[-i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [66], :eigenvalue => -(E(4)), :cuspidalName => "G_{27}^2[-i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [83], :eigenvalue => E(3), :cuspidalName => "G_{27}[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [84], :eigenvalue => E(3), :cuspidalName => "G_{27}^2[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [85], :eigenvalue => E(3), :cuspidalName => "G_{27}^3[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [54], :eigenvalue => E(3), :cuspidalName => "G_{27}^4[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [67], :eigenvalue => E(3, 2), :cuspidalName => "G_{27}[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [43], :eigenvalue => E(3, 2), :cuspidalName => "G_{27}^2[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [44], :eigenvalue => E(3, 2), :cuspidalName => "G_{27}^3[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [45], :eigenvalue => E(3, 2), :cuspidalName => "G_{27}^4[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [86], :eigenvalue => -(E(3)), :cuspidalName => "G_{27}[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [46], :eigenvalue => -(E(3, 2)), :cuspidalName => "G_{27}^2[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [51], :eigenvalue => E(9), :cuspidalName => "G_{27}[\\zeta_9]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [53], :eigenvalue => E(9), :cuspidalName => "G_{27}^2[\\zeta_9]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [72], :eigenvalue => E(9, 2), :cuspidalName => "G_{27}[\\zeta_9^2]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [68], :eigenvalue => E(9, 2), :cuspidalName => "G_{27}^2[\\zeta_9^2]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [50], :eigenvalue => E(9, 4), :cuspidalName => "G_{27}[\\zeta_9^4]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [49], :eigenvalue => E(9, 4), :cuspidalName => "G_{27}^2[\\zeta_9^4]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [70], :eigenvalue => E(9, 5), :cuspidalName => "G_{27}[\\zeta_9^5]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [69], :eigenvalue => E(9, 5), :cuspidalName => "G_{27}^2[\\zeta_9^5]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [52], :eigenvalue => E(9, 7), :cuspidalName => "G_{27}[\\zeta_9^7]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [48], :eigenvalue => E(9, 7), :cuspidalName => "G_{27}^2[\\zeta_9^7]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [73], :eigenvalue => E(9, 8), :cuspidalName => "G_{27}[\\zeta_9^8]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [71], :eigenvalue => E(9, 8), :cuspidalName => "G_{27}^2[\\zeta_9^8]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [41], :eigenvalue => E(15), :cuspidalName => "G_{27}[\\zeta_{15}]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [42], :eigenvalue => E(15, 4), :cuspidalName => "G_{27}[\\zeta_{15}^4]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [81], :eigenvalue => E(15, 11), :cuspidalName => "G_{27}[\\zeta_{15}^{11}]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [82], :eigenvalue => E(15, 14), :cuspidalName => "G_{27}[\\zeta_{15}^{14}]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [59], :eigenvalue => E(20, 17), :cuspidalName => "G_{27}[\\zeta_{20}^{17}]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [61], :eigenvalue => E(20, 13), :cuspidalName => "G_{27}[\\zeta_{20}^{13}]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0, :qEigen => 1 // 2), :levi => 1:3, :parameterExponents => [], :charNumbers => [60], :eigenvalue => E(20, 7), :cuspidalName => "G_{27}[\\zeta_{20}^7]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [62], :eigenvalue => E(20, 3), :cuspidalName => "G_{27}[\\zeta_{20}^3]", :qEigen => 1 // 2)], :families => [Family("C1", [1]), Family(((CHEVIE[:families])[:X])(3) * Family("Y6"), [5, 3, 38, 37, 35, 16, 9, 7, 40, 39, 36, 18, 44, 43, 42, 41, 46, 45], Dict{Symbol, Any}(:signs => [-1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1], :ennola => -14)), Family("C2", [30, 11, 12, 47], Dict{Symbol, Any}(:ennola => -4)), Family(((CHEVIE[:families])[:TQZ])(3, E(3), [1, E(3)]), [26, 28, 23, 49, 52, 53, 51, 48, 50], Dict{Symbol, Any}(:cospecial => 3, :ennola => 4)), conj(Family(((CHEVIE[:families])[:X])(3), [33, 31, 54], Dict{Symbol, Any}(:ennola => -3))), Family(((CHEVIE[:families])[:Dihedral])(5) * ((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [19, 20, 66, 65, 21, 22, 64, 63, 58, 57, 60, 59, 56, 55, 62, 61], Dict{Symbol, Any}(:cospecial => 2, :ennola => -4)), Family(((CHEVIE[:families])[:X])(3), [34, 32, 67], Dict{Symbol, Any}(:ennola => -2)), Family(((CHEVIE[:families])[:TQZ])(3, E(3, 2)), [24, 27, 25, 72, 69, 73, 68, 71, 70], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, -1, -1, -1], :cospecial => 2, :ennola => 8)), Family("C2", [29, 13, 14, 74], Dict{Symbol, Any}(:ennola => 4)), conj(Family(((CHEVIE[:families])[:X])(3) * Family("Y6"), [6, 4, 77, 78, 75, 15, 10, 8, 79, 80, 76, 17, 84, 83, 81, 82, 86, 85], Dict{Symbol, Any}(:signs => [-1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1], :ennola => 8))), Family("C1", [2], Dict{Symbol, Any}(:ennola => -1))], :a => [0, 45, 1, 16, 1, 16, 1, 16, 1, 16, 3, 3, 12, 12, 16, 1, 16, 1, 6, 6, 6, 6, 4, 9, 9, 4, 9, 4, 12, 3, 5, 8, 5, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 9, 9, 9, 9, 9, 9, 12, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16], :A => [0, 45, 29, 44, 29, 44, 29, 44, 29, 44, 33, 33, 42, 42, 44, 29, 44, 29, 39, 39, 39, 39, 36, 41, 41, 36, 41, 36, 42, 33, 37, 40, 37, 40, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 33, 36, 36, 36, 36, 36, 36, 37, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 40, 41, 41, 41, 41, 41, 41, 42, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44]) end) chevieset(:G27, :Invariants, [function (x, y, z) return ((((((-90 * x ^ 2 * y ^ 2 * z ^ 2 + 180 * x ^ 2 * y ^ 3 * z + 30 * x ^ 2 * y ^ 4) - 135 * x ^ 2 * z ^ 4) + 135 * y ^ 2 * z ^ 4 + 90 * x ^ 4 * y * z) - 30 * x ^ 4 * y ^ 2) + 45 * x ^ 4 * z ^ 2 + 45 * y ^ 4 * z ^ 2 + 18 * y ^ 5 * z + 10 * x ^ 6) - 10 * y ^ 6) - 27 * z ^ 6 diff --git a/src/tbl/cmplxg32.jl b/src/tbl/cmplxg32.jl index f2067a2c..d076f5c5 100644 --- a/src/tbl/cmplxg32.jl +++ b/src/tbl/cmplxg32.jl @@ -380,5 +380,5 @@ chevieset(:G32, :UnipotentCharacters, function () end return res end - return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:4, :rank => 4, :ST => 32), :levi => [], :parameterExponents => [1, 1, 1, 1], :charNumbers => 1:102, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 2:4, :rank => 3, :ST => 26), :levi => [1], :parameterExponents => [3, 1, 1], :charNumbers => [103, 171, 240, 241, 121, 120, 242, 117, 234, 105, 233, 104, 108, 238, 199, 126, 162, 109, 235, 173, 200, 127, 163, 110, 236, 172, 130, 203, 161, 226, 119, 175, 131, 204, 160, 225, 118, 174, 152, 153, 177, 179, 178, 176, 201, 128, 202, 129], :eigenvalue => J ^ 2, :cuspidalName => ImprimitiveCuspidalName([[], [0, 1], [0, 1]])), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [4, 3], :rank => 2, :ST => 5), :levi => 1:2, :parameterExponents => [1, [0, 4, 4]], :charNumbers => [239, 113, 114, 246, 135, 132, 245, 133, 134, 136, 230, 229, 124, 208, 206, 123, 205, 207, 182, 181, 180], :eigenvalue => -1, :cuspidalName => "G_4"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [2, 4], :rank => 2, :p => 6, :q => 1), :levi => [1, 3], :parameterExponents => [[3, 3, 2, 0, 0, 2], 3], :charNumbers => [188, 122, 137, 184, 190, 140, 187, 139, 189, 183, 138, 227, 212, 209, 164, 244, 237, 210, 243, 211, 228, 107, 106, 111, 185, 186, 112], :eigenvalue => J, :cuspidalName => Concatenation(ImprimitiveCuspidalName([[], [0, 1], [0, 1]]), "\\otimes ", ImprimitiveCuspidalName([[], [0, 1], [0, 1]]))), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [4], :rank => 1, :p => 6, :q => 1), :levi => 1:3, :parameterExponents => [[6, 4, 1, 0, 1, 4]], :charNumbers => [116, 143, 217, 232, 218, 144], :eigenvalue => J, :cuspidalName => "G_{25}[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [4], :rank => 1, :p => 6, :q => 1), :levi => 1:3, :parameterExponents => [[6, 1, 4, 0, 4, 1]], :charNumbers => [115, 216, 145, 231, 146, 215], :eigenvalue => -J, :cuspidalName => "G_{25}[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [3], :rank => 1, :p => 6, :q => 1), :levi => [1, 2, 4], :parameterExponents => [[9, 8, 5, 0, 5, 8]], :charNumbers => [125, 142, 213, 247, 214, 141], :eigenvalue => -(J ^ 2), :cuspidalName => Concatenation("G_4\\otimes ", ImprimitiveCuspidalName([[], [0, 1], [0, 1]]))), cuspidal(147, 1), cuspidal(148, 1, 2), cuspidal(219, 1, 3), cuspidal(149, -1), cuspidal(191, -1, 2), cuspidal(192, -1, 3), cuspidal(220, -1, 4), cuspidal(151, E(4)), cuspidal(154, E(4), 2, 1 // 2), cuspidal(155, E(4), 3, 1 // 2), cuspidal(150, -(E(4))), cuspidal(156, -(E(4)), 2, 1 // 2), cuspidal(157, -(E(4)), 3, 1 // 2), cuspidal(193, J ^ 2), cuspidal(194, J ^ 2, 2), cuspidal(197, -J), cuspidal(198, -J, 2), cuspidal(195, -(J ^ 2)), cuspidal(196, -(J ^ 2), 2), cuspidal(221, E(5)), cuspidal(222, E(5, 2)), cuspidal(223, E(5, 3)), cuspidal(224, E(5, 4)), cuspidal(165, E(9, 5), 2 // 3), cuspidal(170, E(9, 5), 2, 1 // 3), cuspidal(166, E(9, 2), 1 // 3), cuspidal(168, E(9, 2), 2, 2 // 3), cuspidal(167, E(9, 8), 2 // 3), cuspidal(169, E(9, 8), 2, 1 // 3), cuspidal(158, E(12, 11), 1 // 2), cuspidal(159, E(12, 5), 1 // 2)], :families => [Family("C1", [1]), Family(((CHEVIE[:families])[:X])(3), [9, 6, 103], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 3)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [20, 23, 26, 106, 104, 15, 105, 12, 107], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, 1, 1, 1, 1], :ennola => 8)), Family(((CHEVIE[:families])[:X])(3), [37, 34, 108], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -1)), Family(((CHEVIE[:families])[:X])(6), [57, 64, 49, 61, 54, 111, 113, 109, 115, 17, 116, 110, 18, 114, 112], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1], :ennola => 5)), Family(((CHEVIE[:families])[:X])(3) * Family("X5"), [46, 72, 123, 119, 41, 44, 69, 124, 118, 45, 120, 117, 125, 122, 121], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1], :ennola => -10)), Family(((CHEVIE[:families])[:G4])(), [73, 76, 147, 133, 132, 149, 80, 13, 10, 32, 43, 40, 97, 148, 52, 150, 136, 151, 126, 139, 27, 130, 138, 84, 128, 135, 144, 141, 74, 145, 143, 142, 77, 146, 129, 134, 137, 81, 127, 140, 28, 131], Dict{Symbol, Any}(:signs => [1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1], :ennola => 9)), Family(((CHEVIE[:families])[:X])(3) * Family("C'\"2"), [93, 96, 154, 156, 94, 95, 155, 157, 153, 152, 158, 159], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1], :cospecial => 6, :ennola => 8)), Family(((CHEVIE[:families])[:X])(3) * ((CHEVIE[:families])[:X])(3), [85, 87, 161, 88, 82, 160, 163, 162, 164], Dict{Symbol, Any}(:signs => [1, 1, -1, 1, 1, -1, -1, -1, 1], :cospecial => 5, :ennola => -6)), Family("Z9", [100, 165, 166, 101, 167, 169, 102, 168, 170], Dict{Symbol, Any}(:special => 7, :ennola => 9)), Family(Family("X5") * ((CHEVIE[:families])[:QZ])(3), [53, 21, 59, 90, 185, 177, 47, 187, 193, 79, 33, 36, 98, 184, 179, 99, 183, 178, 180, 182, 181, 192, 198, 196, 191, 197, 195, 171, 172, 173, 174, 68, 189, 175, 71, 190, 56, 60, 24, 48, 188, 194, 89, 186, 176], Dict{Symbol, Any}(:signs => [-1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1], :ennola => 41)), Family(Dict{Symbol, Any}(:fourierMat => [[-1, -1, 1, 1, 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5, 5, 5, -1, -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5, 5, -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 1, 5, -6, -6, -6, -6], [-1, -1, 1, 1, 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, 5, 5, -1, -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5, 5, -5 * E(3), -5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), 1, 5, -6, -6, -6, -6], [1, 1, -1, -1, -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5, 5, 5, 1, 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5, 5, -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -1, 5, 6, 6, 6, 6], [1, 1, -1, -1, -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, 5, 5, 1, 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), 5, 5, -5 * E(3), -5 * E(3, 2), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), -1, 5, 6, 6, 6, 6], [5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5, 5, 5, 5, 5, 5, 5 * E(3), 5 * E(3, 2), 5, 5, -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5, -5, 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3), 5 * E(3, 2), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), -5, 5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5, 5, 5, 5, 5, 5, 5 * E(3, 2), 5 * E(3), 5, 5, -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5, -5, 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3, 2), 5 * E(3), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5, 5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5, 5, 5, 5, -5, -5, -5 * E(3), -5 * E(3, 2), -5, 5, -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5, 5, -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3), -5 * E(3, 2), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5, -5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5, 5, 5, 5, -5, -5, -5 * E(3, 2), -5 * E(3), -5, 5, -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5, 5, -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), -5 * E(3), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5, -5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5, 5, -5, -5, 5, 5, 5 * E(3), 5 * E(3, 2), 5, 5, -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5, 5, 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3), -5 * E(3, 2), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5, -5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, 5, -5, -5, 5, 5, 5 * E(3, 2), 5 * E(3), 5, 5, -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), 5, 5, 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), -5 * E(3), -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, -5, 0, 0, 0, 0], [5, 5, 5, 5, 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, 5, 5, 5, -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), -5, -5, 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5, -5, 0, 0, 0, 0], [5, 5, 5, 5, 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5, 5, 5, 5, -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5, -5, 5 * E(3, 2), 5 * E(3), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, -5, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, -5, -5, 5, 5, 5, 5, 5, 5, -5, 5, 5, -5, 5, -5, -5, -5, 5, 5, 5, 5, 5, 5, 5, -5, -5, 5, -5, 5, 5, -5, 0, 0, 0, 0], [-1, -1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, -1, -5, 5, -5, 5, 5, -5, 5, 5, -5, -5, 5, 5, 5, 5, -5, 5, 5, -5, 5, -5, 1, 5, -6, -6, -6, -6], [-5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3, 2), -5 * E(3), -5, -5, 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), -5, -5, -5, -5, 5 * E(3), -5 * E(3, 2), -5, 5, -5, 5, 5, -5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3), 5 * E(3, 2), 5, 5, -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), -5 * E(3, 2), -5 * E(3), 5, 5, 5, 5, -5 * E(3, 2), 5 * E(3), 5, -5, 5, -5, -5, 5, 0, 0, 0, 0], [-5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5, -5, 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3, 2), 5 * E(3), -5 * E(3), -5 * E(3, 2), 5, 5, -5, -5, -5 * E(3), 5 * E(3, 2), 5, -5, -5, 5, 5, 5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3), -5 * E(3, 2), -5, 5, -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3), -5 * E(3, 2), 5 * E(3, 2), 5 * E(3), -5, -5, 5, 5, 5 * E(3, 2), -5 * E(3), -5, 5, 5, -5, -5, -5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5, 5, -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), 5, 5, 5, 5, 5 * E(3), -5 * E(3, 2), -5, 5, -5, 5, 5, -5, 0, 0, 0, 0], [-5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3), -5 * E(3, 2), -5, -5, 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3), 5 * E(3, 2), -5 * E(3, 2), -5 * E(3), -5, -5, -5, -5, -5 * E(3, 2), 5 * E(3), 5, -5, 5, -5, -5, 5, 0, 0, 0, 0], [5, 5, 5, 5, 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5, -5, -5, 5, -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5, 5, -5 * E(3), -5 * E(3, 2), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5, 5, 0, 0, 0, 0], [5, 5, 5, 5, 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5, -5, -5, 5, -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, 5, -5 * E(3, 2), -5 * E(3), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, 5, 0, 0, 0, 0], [-5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5, -5, 5, 5, 5, 5, 5 * E(3), 5 * E(3, 2), 5, -5, 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5, 5, 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3), -5 * E(3, 2), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5, -5, 0, 0, 0, 0], [-5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5, -5, 5, 5, 5, 5, 5 * E(3, 2), 5 * E(3), 5, -5, 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), 5, 5, 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3, 2), -5 * E(3), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5, -5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5, 5, -5, 5, 5, -5, 5, -5, -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5, -5, -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5, -5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, 5, -5, 5, 5, -5, 5, -5, -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, -5, -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, -5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5, 5, -5, 5, -5, 5, 5, -5, 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5, 5, 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), -5, 5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, 5, -5, 5, -5, 5, 5, -5, 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5, 5, 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5, 5, 0, 0, 0, 0], [-5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5, -5, 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), 5, 5, -5, -5, 5 * E(3), -5 * E(3, 2), -5, 5, 5, -5, -5, -5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3), -5 * E(3, 2), -5, 5, -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3), 5 * E(3, 2), -5 * E(3, 2), -5 * E(3), -5, -5, 5, 5, -5 * E(3, 2), 5 * E(3), 5, -5, -5, 5, 5, 5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5, 5, -5, 5, 5, -5, -5, 5, 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5, 5, 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5, 5, 0, 0, 0, 0], [-5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, -5, 5, -5, -5, 5, 5, -5, -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5, -5, -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5, -5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5, 5, -5, 5, -5, 5, -5, 5, -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5, -5, -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5, -5, 0, 0, 0, 0], [-5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, -5, 5, -5, 5, -5, 5, -5, 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5, 5, 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, 5, 0, 0, 0, 0], [1, 1, -1, -1, -5, -5, -5, -5, 5, 5, 5, 5, 5, 1, 5, -5, 5, -5, 5, -5, 5, 5, -5, -5, 5, 5, -5, -5, -5, 5, 5, -5, -5, 5, -1, 5, 6, 6, 6, 6], [5, 5, 5, 5, 5, 5, -5, -5, -5, -5, -5, -5, -5, 5, -5, 5, 5, -5, -5, 5, 5, 5, -5, -5, -5, -5, 5, 5, -5, 5, 5, -5, -5, 5, 5, 5, 0, 0, 0, 0], [-6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 9 - 3 * root(5), -6 - 6 * root(5), -6 + 6 * root(5), 9 + 3 * root(5)], [-6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -6 - 6 * root(5), 9 + 3 * root(5), 9 - 3 * root(5), -6 + 6 * root(5)], [-6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -6 + 6 * root(5), 9 - 3 * root(5), 9 + 3 * root(5), -6 - 6 * root(5)], [-6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 9 + 3 * root(5), -6 + 6 * root(5), -6 - 6 * root(5), 9 - 3 * root(5)]] // 30, :eigenvalues => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, J ^ 2, J ^ 2, J ^ 2, J ^ 2, J ^ 2, J ^ 2, -1, -1, -1, -1, J, J, J, J, -(J ^ 2), -(J ^ 2), -J, -J, J, J, 1, -1, E(5), E(5, 2), E(5, 3), E(5, 4)], :explanation => "mystery G32", :name => "?40", :special => 3, :cospecial => 4, :ennola => 14), [8, 5, 65, 62, 86, 83, 66, 63, 51, 50, 67, 70, 91, 92, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), Family(((CHEVIE[:families])[:X])(6), [58, 75, 25, 78, 55, 227, 229, 225, 231, 30, 232, 226, 29, 230, 228], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1], :ennola => -15)), Family(((CHEVIE[:families])[:X])(3) * ((CHEVIE[:families])[:X])(3), [38, 42, 234, 39, 35, 233, 236, 235, 237], Dict{Symbol, Any}(:signs => [1, 1, -1, 1, 1, -1, -1, -1, 1], :cospecial => 5, :ennola => 3)), Family("X5", [19, 31, 239, 238, 22], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, 1], :ennola => -5)), Family(conj(((CHEVIE[:families])[:X])(6)), [14, 7, 16, 4, 11, 240, 246, 244, 247, 2, 242, 243, 3, 245, 241], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1], :special => 13, :cospecial => 10, :ennola => 15))], :a => [0, 40, 40, 40, 15, 1, 40, 15, 1, 6, 40, 2, 6, 40, 2, 40, 4, 4, 30, 2, 12, 30, 2, 12, 20, 2, 6, 6, 20, 20, 30, 6, 12, 3, 25, 12, 3, 25, 25, 6, 5, 25, 6, 5, 5, 5, 12, 12, 4, 15, 15, 6, 12, 4, 20, 12, 4, 20, 12, 12, 4, 15, 15, 4, 15, 15, 15, 12, 5, 15, 12, 5, 6, 6, 20, 6, 6, 20, 12, 6, 6, 9, 15, 6, 9, 15, 9, 9, 12, 12, 15, 15, 8, 8, 8, 8, 6, 12, 12, 10, 10, 10, 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 20, 20, 20, 20, 20, 20, 20, 20, 25, 25, 25, 25, 25, 30, 30, 40, 40, 40, 40, 40, 40, 40, 40], :A => [0, 80, 80, 80, 75, 29, 80, 75, 29, 66, 80, 46, 66, 80, 46, 80, 56, 56, 78, 46, 72, 78, 46, 72, 76, 46, 66, 66, 76, 76, 78, 66, 72, 51, 77, 72, 51, 77, 77, 66, 61, 77, 66, 61, 61, 61, 72, 72, 56, 75, 75, 66, 72, 56, 76, 72, 56, 76, 72, 72, 56, 75, 75, 56, 75, 75, 75, 72, 61, 75, 72, 61, 66, 66, 76, 66, 66, 76, 72, 66, 66, 69, 75, 66, 69, 75, 69, 69, 72, 72, 75, 75, 67, 67, 67, 67, 66, 72, 72, 70, 70, 70, 29, 46, 46, 46, 46, 51, 56, 56, 56, 56, 56, 56, 56, 56, 61, 61, 61, 61, 61, 61, 61, 61, 61, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 67, 67, 67, 67, 67, 67, 67, 67, 69, 69, 69, 69, 69, 70, 70, 70, 70, 70, 70, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 76, 76, 76, 76, 76, 76, 76, 76, 77, 77, 77, 77, 77, 78, 78, 80, 80, 80, 80, 80, 80, 80, 80]) + return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:4, :rank => 4, :ST => 32), :levi => [], :parameterExponents => [1, 1, 1, 1], :charNumbers => 1:102, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 2:4, :rank => 3, :ST => 26), :levi => [1], :parameterExponents => [3, 1, 1], :charNumbers => [103, 171, 240, 241, 121, 120, 242, 117, 234, 105, 233, 104, 108, 238, 199, 126, 162, 109, 235, 173, 200, 127, 163, 110, 236, 172, 130, 203, 161, 226, 119, 175, 131, 204, 160, 225, 118, 174, 152, 153, 177, 179, 178, 176, 201, 128, 202, 129], :eigenvalue => J ^ 2, :cuspidalName => ImprimitiveCuspidalName([[], [0, 1], [0, 1]])), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [4, 3], :rank => 2, :ST => 5), :levi => 1:2, :parameterExponents => [1, [0, 4, 4]], :charNumbers => [239, 113, 114, 246, 135, 132, 245, 133, 134, 136, 230, 229, 124, 208, 206, 123, 205, 207, 182, 181, 180], :eigenvalue => -1, :cuspidalName => "G_4"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [2, 4], :rank => 2, :p => 6, :q => 1), :levi => [1, 3], :parameterExponents => [[3, 3, 2, 0, 0, 2], 3], :charNumbers => [188, 122, 137, 184, 190, 140, 187, 139, 189, 183, 138, 227, 212, 209, 164, 244, 237, 210, 243, 211, 228, 107, 106, 111, 185, 186, 112], :eigenvalue => J, :cuspidalName => Concatenation(ImprimitiveCuspidalName([[], [0, 1], [0, 1]]), "\\otimes ", ImprimitiveCuspidalName([[], [0, 1], [0, 1]]))), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [4], :rank => 1, :p => 6, :q => 1), :levi => 1:3, :parameterExponents => [[6, 4, 1, 0, 1, 4]], :charNumbers => [116, 143, 217, 232, 218, 144], :eigenvalue => J, :cuspidalName => "G_{25}[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [4], :rank => 1, :p => 6, :q => 1), :levi => 1:3, :parameterExponents => [[6, 1, 4, 0, 4, 1]], :charNumbers => [115, 216, 145, 231, 146, 215], :eigenvalue => -J, :cuspidalName => "G_{25}[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [3], :rank => 1, :p => 6, :q => 1), :levi => [1, 2, 4], :parameterExponents => [[9, 8, 5, 0, 5, 8]], :charNumbers => [125, 142, 213, 247, 214, 141], :eigenvalue => -(J ^ 2), :cuspidalName => Concatenation("G_4\\otimes ", ImprimitiveCuspidalName([[], [0, 1], [0, 1]]))), cuspidal(147, 1), cuspidal(148, 1, 2), cuspidal(219, 1, 3), cuspidal(149, -1), cuspidal(191, -1, 2), cuspidal(192, -1, 3), cuspidal(220, -1, 4), cuspidal(151, E(4)), cuspidal(154, E(4), 2, 1 // 2), cuspidal(155, E(4), 3, 1 // 2), cuspidal(150, -(E(4))), cuspidal(156, -(E(4)), 2, 1 // 2), cuspidal(157, -(E(4)), 3, 1 // 2), cuspidal(193, J ^ 2), cuspidal(194, J ^ 2, 2), cuspidal(197, -J), cuspidal(198, -J, 2), cuspidal(195, -(J ^ 2)), cuspidal(196, -(J ^ 2), 2), cuspidal(221, E(5)), cuspidal(222, E(5, 2)), cuspidal(223, E(5, 3)), cuspidal(224, E(5, 4)), cuspidal(165, E(9, 5), 2 // 3), cuspidal(170, E(9, 5), 2, 1 // 3), cuspidal(166, E(9, 2), 1 // 3), cuspidal(168, E(9, 2), 2, 2 // 3), cuspidal(167, E(9, 8), 2 // 3), cuspidal(169, E(9, 8), 2, 1 // 3), cuspidal(158, E(12, 11), 1 // 2), cuspidal(159, E(12, 5), 1 // 2)], :families => [Family("C1", [1]), Family(((CHEVIE[:families])[:X])(3), [9, 6, 103], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 3)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [20, 23, 26, 106, 104, 15, 105, 12, 107], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, 1, 1, 1, 1], :ennola => 8)), Family(((CHEVIE[:families])[:X])(3), [37, 34, 108], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -1)), Family(((CHEVIE[:families])[:X])(6), [57, 64, 49, 61, 54, 111, 113, 109, 115, 17, 116, 110, 18, 114, 112], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1], :ennola => 5)), Family(((CHEVIE[:families])[:X])(3) * Family("X5"), [46, 72, 123, 119, 41, 44, 69, 124, 118, 45, 120, 117, 125, 122, 121], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1], :ennola => -10)), Family(((CHEVIE[:families])[:G4])(), [73, 76, 147, 133, 132, 149, 80, 13, 10, 32, 43, 40, 97, 148, 52, 150, 136, 151, 126, 139, 27, 130, 138, 84, 128, 135, 144, 141, 74, 145, 143, 142, 77, 146, 129, 134, 137, 81, 127, 140, 28, 131], Dict{Symbol, Any}(:signs => [1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1], :ennola => 9)), Family(((CHEVIE[:families])[:X])(3) * ((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [93, 96, 156, 154, 94, 95, 157, 155, 153, 152, 159, 158], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1], :cospecial => 6, :ennola => 7)), Family(((CHEVIE[:families])[:X])(3) * ((CHEVIE[:families])[:X])(3), [85, 87, 161, 88, 82, 160, 163, 162, 164], Dict{Symbol, Any}(:signs => [1, 1, -1, 1, 1, -1, -1, -1, 1], :cospecial => 5, :ennola => -6)), Family(((CHEVIE[:families])[:TQZ])(3, E(3, 2), [1, E(3, 2)]), [102, 100, 101, 167, 168, 165, 170, 166, 169], Dict{Symbol, Any}(:ennola => 7)), Family(Family("X5") * ((CHEVIE[:families])[:QZ])(3), [53, 21, 59, 90, 185, 177, 47, 187, 193, 79, 33, 36, 98, 184, 179, 99, 183, 178, 180, 182, 181, 192, 198, 196, 191, 197, 195, 171, 172, 173, 174, 68, 189, 175, 71, 190, 56, 60, 24, 48, 188, 194, 89, 186, 176], Dict{Symbol, Any}(:signs => [-1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1], :ennola => 41)), Family(Dict{Symbol, Any}(:fourierMat => [[-1, -1, 1, 1, 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5, 5, 5, -1, -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5, 5, -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 1, 5, -6, -6, -6, -6], [-1, -1, 1, 1, 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, 5, 5, -1, -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5, 5, -5 * E(3), -5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), 1, 5, -6, -6, -6, -6], [1, 1, -1, -1, -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5, 5, 5, 1, 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5, 5, -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -1, 5, 6, 6, 6, 6], [1, 1, -1, -1, -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, 5, 5, 1, 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), 5, 5, -5 * E(3), -5 * E(3, 2), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), -1, 5, 6, 6, 6, 6], [5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5, 5, 5, 5, 5, 5, 5 * E(3), 5 * E(3, 2), 5, 5, -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5, -5, 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3), 5 * E(3, 2), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), -5, 5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5, 5, 5, 5, 5, 5, 5 * E(3, 2), 5 * E(3), 5, 5, -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5, -5, 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3, 2), 5 * E(3), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5, 5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5, 5, 5, 5, -5, -5, -5 * E(3), -5 * E(3, 2), -5, 5, -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5, 5, -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3), -5 * E(3, 2), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5, -5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5, 5, 5, 5, -5, -5, -5 * E(3, 2), -5 * E(3), -5, 5, -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5, 5, -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), -5 * E(3), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5, -5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5, 5, -5, -5, 5, 5, 5 * E(3), 5 * E(3, 2), 5, 5, -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5, 5, 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3), -5 * E(3, 2), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5, -5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, 5, -5, -5, 5, 5, 5 * E(3, 2), 5 * E(3), 5, 5, -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), 5, 5, 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), -5 * E(3), -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, -5, 0, 0, 0, 0], [5, 5, 5, 5, 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, 5, 5, 5, -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), -5, -5, 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5, -5, 0, 0, 0, 0], [5, 5, 5, 5, 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5, 5, 5, 5, -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5, -5, 5 * E(3, 2), 5 * E(3), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, -5, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, -5, -5, 5, 5, 5, 5, 5, 5, -5, 5, 5, -5, 5, -5, -5, -5, 5, 5, 5, 5, 5, 5, 5, -5, -5, 5, -5, 5, 5, -5, 0, 0, 0, 0], [-1, -1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, -1, -5, 5, -5, 5, 5, -5, 5, 5, -5, -5, 5, 5, 5, 5, -5, 5, 5, -5, 5, -5, 1, 5, -6, -6, -6, -6], [-5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3, 2), -5 * E(3), -5, -5, 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), -5, -5, -5, -5, 5 * E(3), -5 * E(3, 2), -5, 5, -5, 5, 5, -5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3), 5 * E(3, 2), 5, 5, -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), -5 * E(3, 2), -5 * E(3), 5, 5, 5, 5, -5 * E(3, 2), 5 * E(3), 5, -5, 5, -5, -5, 5, 0, 0, 0, 0], [-5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5, -5, 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3, 2), 5 * E(3), -5 * E(3), -5 * E(3, 2), 5, 5, -5, -5, -5 * E(3), 5 * E(3, 2), 5, -5, -5, 5, 5, 5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3), -5 * E(3, 2), -5, 5, -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3), -5 * E(3, 2), 5 * E(3, 2), 5 * E(3), -5, -5, 5, 5, 5 * E(3, 2), -5 * E(3), -5, 5, 5, -5, -5, -5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5, 5, -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), 5, 5, 5, 5, 5 * E(3), -5 * E(3, 2), -5, 5, -5, 5, 5, -5, 0, 0, 0, 0], [-5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3), -5 * E(3, 2), -5, -5, 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3), 5 * E(3, 2), -5 * E(3, 2), -5 * E(3), -5, -5, -5, -5, -5 * E(3, 2), 5 * E(3), 5, -5, 5, -5, -5, 5, 0, 0, 0, 0], [5, 5, 5, 5, 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5, -5, -5, 5, -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5, 5, -5 * E(3), -5 * E(3, 2), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5, 5, 0, 0, 0, 0], [5, 5, 5, 5, 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5, -5, -5, 5, -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, 5, -5 * E(3, 2), -5 * E(3), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, 5, 0, 0, 0, 0], [-5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5, -5, 5, 5, 5, 5, 5 * E(3), 5 * E(3, 2), 5, -5, 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5, 5, 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3), -5 * E(3, 2), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5, -5, 0, 0, 0, 0], [-5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5, -5, 5, 5, 5, 5, 5 * E(3, 2), 5 * E(3), 5, -5, 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), 5, 5, 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3, 2), -5 * E(3), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5, -5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5, 5, -5, 5, 5, -5, 5, -5, -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5, -5, -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5, -5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, 5, -5, 5, 5, -5, 5, -5, -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, -5, -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, -5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5, 5, -5, 5, -5, 5, 5, -5, 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5, 5, 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), -5, 5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, 5, -5, 5, -5, 5, 5, -5, 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5, 5, 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5, 5, 0, 0, 0, 0], [-5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5, -5, 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), 5, 5, -5, -5, 5 * E(3), -5 * E(3, 2), -5, 5, 5, -5, -5, -5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3), -5 * E(3, 2), -5, 5, -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3), 5 * E(3, 2), -5 * E(3, 2), -5 * E(3), -5, -5, 5, 5, -5 * E(3, 2), 5 * E(3), 5, -5, -5, 5, 5, 5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5, 5, -5, 5, 5, -5, -5, 5, 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5, 5, 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5, 5, 0, 0, 0, 0], [-5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, -5, 5, -5, -5, 5, 5, -5, -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5, -5, -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5, -5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5, 5, -5, 5, -5, 5, -5, 5, -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5, -5, -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5, -5, 0, 0, 0, 0], [-5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, -5, 5, -5, 5, -5, 5, -5, 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5, 5, 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, 5, 0, 0, 0, 0], [1, 1, -1, -1, -5, -5, -5, -5, 5, 5, 5, 5, 5, 1, 5, -5, 5, -5, 5, -5, 5, 5, -5, -5, 5, 5, -5, -5, -5, 5, 5, -5, -5, 5, -1, 5, 6, 6, 6, 6], [5, 5, 5, 5, 5, 5, -5, -5, -5, -5, -5, -5, -5, 5, -5, 5, 5, -5, -5, 5, 5, 5, -5, -5, -5, -5, 5, 5, -5, 5, 5, -5, -5, 5, 5, 5, 0, 0, 0, 0], [-6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 9 - 3 * root(5), -6 - 6 * root(5), -6 + 6 * root(5), 9 + 3 * root(5)], [-6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -6 - 6 * root(5), 9 + 3 * root(5), 9 - 3 * root(5), -6 + 6 * root(5)], [-6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -6 + 6 * root(5), 9 - 3 * root(5), 9 + 3 * root(5), -6 - 6 * root(5)], [-6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 9 + 3 * root(5), -6 + 6 * root(5), -6 - 6 * root(5), 9 - 3 * root(5)]] // 30, :eigenvalues => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, J ^ 2, J ^ 2, J ^ 2, J ^ 2, J ^ 2, J ^ 2, -1, -1, -1, -1, J, J, J, J, -(J ^ 2), -(J ^ 2), -J, -J, J, J, 1, -1, E(5), E(5, 2), E(5, 3), E(5, 4)], :explanation => "mystery G32", :name => "?40", :special => 3, :cospecial => 4, :ennola => 14), [8, 5, 65, 62, 86, 83, 66, 63, 51, 50, 67, 70, 91, 92, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), Family(((CHEVIE[:families])[:X])(6), [58, 75, 25, 78, 55, 227, 229, 225, 231, 30, 232, 226, 29, 230, 228], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1], :ennola => -15)), Family(((CHEVIE[:families])[:X])(3) * ((CHEVIE[:families])[:X])(3), [38, 42, 234, 39, 35, 233, 236, 235, 237], Dict{Symbol, Any}(:signs => [1, 1, -1, 1, 1, -1, -1, -1, 1], :cospecial => 5, :ennola => 3)), Family("X5", [19, 31, 239, 238, 22], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, 1], :ennola => -5)), Family(conj(((CHEVIE[:families])[:X])(6)), [14, 7, 16, 4, 11, 240, 246, 244, 247, 2, 242, 243, 3, 245, 241], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1], :special => 13, :cospecial => 10, :ennola => 15))], :a => [0, 40, 40, 40, 15, 1, 40, 15, 1, 6, 40, 2, 6, 40, 2, 40, 4, 4, 30, 2, 12, 30, 2, 12, 20, 2, 6, 6, 20, 20, 30, 6, 12, 3, 25, 12, 3, 25, 25, 6, 5, 25, 6, 5, 5, 5, 12, 12, 4, 15, 15, 6, 12, 4, 20, 12, 4, 20, 12, 12, 4, 15, 15, 4, 15, 15, 15, 12, 5, 15, 12, 5, 6, 6, 20, 6, 6, 20, 12, 6, 6, 9, 15, 6, 9, 15, 9, 9, 12, 12, 15, 15, 8, 8, 8, 8, 6, 12, 12, 10, 10, 10, 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 20, 20, 20, 20, 20, 20, 20, 20, 25, 25, 25, 25, 25, 30, 30, 40, 40, 40, 40, 40, 40, 40, 40], :A => [0, 80, 80, 80, 75, 29, 80, 75, 29, 66, 80, 46, 66, 80, 46, 80, 56, 56, 78, 46, 72, 78, 46, 72, 76, 46, 66, 66, 76, 76, 78, 66, 72, 51, 77, 72, 51, 77, 77, 66, 61, 77, 66, 61, 61, 61, 72, 72, 56, 75, 75, 66, 72, 56, 76, 72, 56, 76, 72, 72, 56, 75, 75, 56, 75, 75, 75, 72, 61, 75, 72, 61, 66, 66, 76, 66, 66, 76, 72, 66, 66, 69, 75, 66, 69, 75, 69, 69, 72, 72, 75, 75, 67, 67, 67, 67, 66, 72, 72, 70, 70, 70, 29, 46, 46, 46, 46, 51, 56, 56, 56, 56, 56, 56, 56, 56, 61, 61, 61, 61, 61, 61, 61, 61, 61, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 67, 67, 67, 67, 67, 67, 67, 67, 69, 69, 69, 69, 69, 70, 70, 70, 70, 70, 70, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 76, 76, 76, 76, 76, 76, 76, 76, 77, 77, 77, 77, 77, 78, 78, 80, 80, 80, 80, 80, 80, 80, 80]) end) diff --git a/src/tbl/cmplxg33.jl b/src/tbl/cmplxg33.jl index 08b6293d..b9f4d395 100644 --- a/src/tbl/cmplxg33.jl +++ b/src/tbl/cmplxg33.jl @@ -173,7 +173,7 @@ chevieset(:G33, :Representation, (i->begin chevieset(:G33, :UnipotentCharacters, function () local J J = E(3) - return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:5, :rank => 5, :ST => 33), :levi => [], :parameterExponents => [1, 1, 1, 1, 1], :charNumbers => 1:40, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1, 5], :rank => 2, :ST => 4), :levi => 2:4, :parameterExponents => [3, 3], :charNumbers => [41, 58, 57, 59, 43, 44, 51], :eigenvalue => J, :cuspidalName => "G_{3,3,3}[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1, 5], :rank => 2, :ST => 4), :levi => 2:4, :parameterExponents => [[3, 3, 0], [3, 3, 0]], :charNumbers => [46, 45, 64, 55, 56, 47, 54], :eigenvalue => J ^ 2, :cuspidalName => "G_{3,3,3}[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [4], :rank => 1, :p => 6, :q => 1), :levi => [1, 2, 3, 209], :parameterExponents => [[5, 4, 1, 0, 1, 4]], :charNumbers => [42, 49, 60, 63, 61, 48], :eigenvalue => -1, :cuspidalName => "D_4"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:5, :parameterExponents => [], :charNumbers => [52], :eigenvalue => E(4), :cuspidalName => "G_{33}[i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:5, :parameterExponents => [], :charNumbers => [53], :eigenvalue => -(E(4)), :cuspidalName => "G_{33}[-i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:5, :parameterExponents => [], :charNumbers => [62], :eigenvalue => -J, :cuspidalName => "G_{33}[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:5, :parameterExponents => [], :charNumbers => [50], :eigenvalue => -(J ^ 2), :cuspidalName => "G_{33}[-\\zeta_3^2]")], :families => [Family("C1", [1]), Family(conj(((CHEVIE[:families])[:X])(3)), [4, 6, 41], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -1)), Family("C1", [15]), Family("C2", [22, 8, 19, 42], Dict{Symbol, Any}(:ennola => -2)), Family(conj(((CHEVIE[:families])[:X])(6)), [25, 30, 17, 28, 23, 45, 48, 43, 50, 9, 47, 44, 11, 49, 46], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1], :ennola => -13)), Family("C1", [39]), Family("C1", [36], Dict{Symbol, Any}(:ennola => -1)), Family(conj(((CHEVIE[:families])[:X])(3)), [34, 32, 51], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -1)), Family("C'\"2", [37, 38, 52, 53], Dict{Symbol, Any}(:ennola => -3)), Family("C1", [14], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:X])(3), [33, 31, 54], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 1)), Family("C1", [40], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [35]), Family("C1", [13]), Family(((CHEVIE[:families])[:X])(6), [26, 29, 18, 27, 24, 57, 60, 55, 62, 10, 59, 56, 12, 61, 58], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1], :ennola => 13)), Family("C2", [21, 7, 20, 63], Dict{Symbol, Any}(:ennola => 2)), Family("C1", [16], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:X])(3), [3, 5, 64], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 1)), Family("C1", [2], Dict{Symbol, Any}(:ennola => -1))], :a => [0, 45, 28, 1, 28, 1, 18, 3, 4, 13, 4, 13, 12, 9, 2, 23, 4, 13, 3, 18, 18, 3, 4, 13, 4, 13, 13, 4, 13, 4, 10, 7, 10, 7, 10, 7, 8, 8, 6, 11, 1, 3, 4, 4, 4, 4, 4, 4, 4, 4, 7, 8, 8, 10, 13, 13, 13, 13, 13, 13, 13, 13, 18, 28], :A => [0, 45, 44, 17, 44, 17, 42, 27, 32, 41, 32, 41, 36, 33, 22, 43, 32, 41, 27, 42, 42, 27, 32, 41, 32, 41, 41, 32, 41, 32, 38, 35, 38, 35, 38, 35, 37, 37, 34, 39, 17, 27, 32, 32, 32, 32, 32, 32, 32, 32, 35, 37, 37, 38, 41, 41, 41, 41, 41, 41, 41, 41, 42, 44], :curtis => [2, 1, 6, 5, 4, 3, 8, 7, 12, 11, 10, 9, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 26, 25, 24, 23, 30, 29, 28, 27, 34, 33, 32, 31, 36, 35, 38, 37, 40, 39, -64, 63, -56, -55, -58, -57, -59, 61, 60, -62, -54, -53, -52, -51, -44, -43, -46, -45, -47, 49, 48, -50, 42, -41]) + return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:5, :rank => 5, :ST => 33), :levi => [], :parameterExponents => [1, 1, 1, 1, 1], :charNumbers => 1:40, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1, 5], :rank => 2, :ST => 4), :levi => 2:4, :parameterExponents => [3, 3], :charNumbers => [41, 58, 57, 59, 43, 44, 51], :eigenvalue => J, :cuspidalName => "G_{3,3,3}[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1, 5], :rank => 2, :ST => 4), :levi => 2:4, :parameterExponents => [[3, 3, 0], [3, 3, 0]], :charNumbers => [46, 45, 64, 55, 56, 47, 54], :eigenvalue => J ^ 2, :cuspidalName => "G_{3,3,3}[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [4], :rank => 1, :p => 6, :q => 1), :levi => [1, 2, 3, 209], :parameterExponents => [[5, 4, 1, 0, 1, 4]], :charNumbers => [42, 49, 60, 63, 61, 48], :eigenvalue => -1, :cuspidalName => "D_4"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:5, :parameterExponents => [], :charNumbers => [52], :eigenvalue => E(4), :cuspidalName => "G_{33}[i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:5, :parameterExponents => [], :charNumbers => [53], :eigenvalue => -(E(4)), :cuspidalName => "G_{33}[-i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:5, :parameterExponents => [], :charNumbers => [62], :eigenvalue => -J, :cuspidalName => "G_{33}[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:5, :parameterExponents => [], :charNumbers => [50], :eigenvalue => -(J ^ 2), :cuspidalName => "G_{33}[-\\zeta_3^2]")], :families => [Family("C1", [1]), Family(conj(((CHEVIE[:families])[:X])(3)), [4, 6, 41], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -1)), Family("C1", [15]), Family("C2", [22, 8, 19, 42], Dict{Symbol, Any}(:ennola => -2)), Family(conj(((CHEVIE[:families])[:X])(6)), [25, 30, 17, 28, 23, 45, 48, 43, 50, 9, 47, 44, 11, 49, 46], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1], :ennola => -13)), Family("C1", [39]), Family("C1", [36], Dict{Symbol, Any}(:ennola => -1)), Family(conj(((CHEVIE[:families])[:X])(3)), [34, 32, 51], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -1)), Family(((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [37, 38, 53, 52], Dict{Symbol, Any}(:cospecial => 2, :ennola => -4)), Family("C1", [14], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:X])(3), [33, 31, 54], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 1)), Family("C1", [40], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [35]), Family("C1", [13]), Family(((CHEVIE[:families])[:X])(6), [26, 29, 18, 27, 24, 57, 60, 55, 62, 10, 59, 56, 12, 61, 58], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1], :ennola => 13)), Family("C2", [21, 7, 20, 63], Dict{Symbol, Any}(:ennola => 2)), Family("C1", [16], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:X])(3), [3, 5, 64], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 1)), Family("C1", [2], Dict{Symbol, Any}(:ennola => -1))], :a => [0, 45, 28, 1, 28, 1, 18, 3, 4, 13, 4, 13, 12, 9, 2, 23, 4, 13, 3, 18, 18, 3, 4, 13, 4, 13, 13, 4, 13, 4, 10, 7, 10, 7, 10, 7, 8, 8, 6, 11, 1, 3, 4, 4, 4, 4, 4, 4, 4, 4, 7, 8, 8, 10, 13, 13, 13, 13, 13, 13, 13, 13, 18, 28], :A => [0, 45, 44, 17, 44, 17, 42, 27, 32, 41, 32, 41, 36, 33, 22, 43, 32, 41, 27, 42, 42, 27, 32, 41, 32, 41, 41, 32, 41, 32, 38, 35, 38, 35, 38, 35, 37, 37, 34, 39, 17, 27, 32, 32, 32, 32, 32, 32, 32, 32, 35, 37, 37, 38, 41, 41, 41, 41, 41, 41, 41, 41, 42, 44], :curtis => [2, 1, 6, 5, 4, 3, 8, 7, 12, 11, 10, 9, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 26, 25, 24, 23, 30, 29, 28, 27, 34, 33, 32, 31, 36, 35, 38, 37, 40, 39, -64, 63, -56, -55, -58, -57, -59, 61, 60, -62, -54, -53, -52, -51, -44, -43, -46, -45, -47, 49, 48, -50, 42, -41]) end) chevieset(:G33, :Invariants, [function (x, y, z, t, u) local a1, a4 diff --git a/src/tbl/cmplxg34.jl b/src/tbl/cmplxg34.jl index f28c07f0..2f63bf7c 100644 --- a/src/tbl/cmplxg34.jl +++ b/src/tbl/cmplxg34.jl @@ -445,7 +445,7 @@ chevieset(:G34, :UnipotentCharacters, function () end return res end - return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:6, :rank => 6, :ST => 34), :levi => [], :parameterExponents => [1, 1, 1, 1, 1, 1], :charNumbers => 1:169, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6, 5, 1], :rank => 3, :ST => 26), :levi => 2:4, :parameterExponents => [1, 3, 3], :charNumbers => [170, 171, 340, 341, 325, 324, 342, 326, 220, 185, 219, 186, 216, 274, 249, 226, 184, 173, 334, 332, 251, 225, 183, 174, 335, 333, 232, 253, 299, 310, 189, 208, 231, 255, 298, 309, 190, 209, 197, 198, 280, 281, 282, 279, 245, 224, 247, 223], :eigenvalue => J, :cuspidalName => "G_{3,3,3}[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6, 5, 1], :rank => 3, :ST => 26), :levi => 2:4, :parameterExponents => [1, [3, 3, 0], [3, 3, 0]], :charNumbers => [176, 191, 348, 192, 347, 175, 331, 300, 193, 177, 330, 301, 244, 302, 187, 181, 278, 252, 338, 337, 339, 336, 188, 182, 277, 250, 311, 322, 256, 284, 207, 218, 206, 217, 312, 323, 254, 283, 227, 230, 314, 315, 228, 229, 276, 248, 275, 246], :eigenvalue => J ^ 2, :cuspidalName => "G_{3,3,3}[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [4, 6], :rank => 2, :p => 6, :q => 1), :levi => [1, 2, 3, 348], :parameterExponents => [[5, 4, 1, 0, 1, 4], 4], :charNumbers => [235, 194, 236, 273, 237, 195, 286, 259, 289, 257, 205, 343, 328, 313, 258, 346, 327, 288, 344, 260, 285, 172, 179, 233, 287, 234, 178], :eigenvalue => -1, :cuspidalName => "D_4"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6], :rank => 1, :p => 6, :q => 1), :levi => 1:5, :parameterExponents => [[5, 0, 7, 2, 7, 0]], :charNumbers => [221, 317, 199, 296, 200, 316], :eigenvalue => E(4), :cuspidalName => "G_{33}[i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6], :rank => 1, :p => 6, :q => 1), :levi => 1:5, :parameterExponents => [[5, 0, 7, 2, 7, 0]], :charNumbers => [222, 319, 201, 297, 202, 318], :eigenvalue => -(E(4)), :qEigen => 1 // 2, :cuspidalName => "G_{33}[-i]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6], :rank => 1, :p => 6, :q => 1), :levi => 1:5, :parameterExponents => [[3, 8, 7, 0, 7, 8]], :charNumbers => [329, 238, 261, 345, 263, 239], :eigenvalue => -J, :cuspidalName => "G_{33}[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6], :rank => 1, :p => 6, :q => 1), :levi => 1:5, :parameterExponents => [[8, 1, 0, 5, 0, 1]], :charNumbers => [180, 262, 291, 196, 290, 264], :eigenvalue => -(J ^ 2), :cuspidalName => "G_{33}[-\\zeta_3^2]"), cuspidal(265, 1), cuspidal(266, -1), cuspidal(294, J), cuspidal(295, J, 2), cuspidal(242, J ^ 2), cuspidal(243, J ^ 2, 2), cuspidal(292, -J), cuspidal(293, -J, 2), cuspidal(240, -(J ^ 2)), cuspidal(241, -(J ^ 2), 2), cuspidal(267, E(7)), cuspidal(268, E(7, 2)), cuspidal(269, E(7, 3)), cuspidal(270, E(7, 4)), cuspidal(271, E(7, 5)), cuspidal(272, E(7, 6)), cuspidal(212, E(9), 1 // 3), cuspidal(214, E(9), 2, 2 // 3), cuspidal(307, E(9, 2), 2 // 3), cuspidal(303, E(9, 2), 2, 1 // 3), cuspidal(210, E(9, 4), 1 // 3), cuspidal(215, E(9, 4), 2, 2 // 3), cuspidal(304, E(9, 5), 2 // 3), cuspidal(305, E(9, 5), 2, 1 // 3), cuspidal(211, E(9, 7), 2 // 3), cuspidal(213, E(9, 7), 2, 1 // 3), cuspidal(306, E(9, 8), 1 // 3), cuspidal(308, E(9, 8), 2, 2 // 3), cuspidal(203, E(12, 7), 1 // 2), cuspidal(320, E(12, 11), 1 // 2), cuspidal(204, E(12), 1 // 2), cuspidal(321, E(12, 5), 1 // 2)], :families => [Family("C1", [1]), Family(conj(((CHEVIE[:families])[:X])(3)), [5, 3, 170], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 2)), Family(conj(((CHEVIE[:families])[:X])(3)), [17, 15, 171], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -3)), Family("C2", [24, 14, 20, 172], Dict{Symbol, Any}(:ennola => -4)), Family(((CHEVIE[:families])[:X])(3) * conj(Family("X5")), [42, 55, 178, 174, 8, 10, 53, 179, 173, 46, 176, 177, 180, 37, 175], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1], :ennola => 15)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [57, 59, 26, 184, 182, 32, 181, 31, 183], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, -1, 1, -1, -1], :ennola => -7)), Family(((CHEVIE[:families])[:QZ])(3), [81, 68, 71, 45, 185, 188, 39, 186, 187], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, -1, -1], :ennola => 6)), Family(((CHEVIE[:families])[:X])(3) * conj(Family("X5")), [109, 89, 194, 190, 35, 33, 91, 195, 189, 107, 192, 193, 196, 116, 191], Dict{Symbol, Any}(:signs => [1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1], :ennola => -15)), Family(conj(((CHEVIE[:families])[:X])(3)) * Family("C'\"2"), [103, 96, 199, 201, 101, 98, 200, 202, 198, 197, 203, 204], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], :cospecial => 6, :ennola => 11)), Family("C1", [28], Dict{Symbol, Any}(:ennola => -1)), Family("C2", [124, 63, 105, 205], Dict{Symbol, Any}(:ennola => -4)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [84, 86, 22, 209, 207, 78, 206, 79, 208], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, -1, 1, -1, -1], :ennola => 4)), Family(conj(Family("Z9")), [141, 215, 213, 145, 214, 212, 143, 211, 210], Dict{Symbol, Any}(:special => 7, :cospecial => 1, :ennola => 2)), Family(conj(((CHEVIE[:families])[:X])(3)), [134, 136, 216], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 3)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [154, 156, 129, 220, 218, 74, 217, 72, 219], Dict{Symbol, Any}(:signs => [1, 1, 1, -1, -1, -1, 1, -1, 1], :ennola => -9)), Family("C1", [67]), Family("C'\"2", [159, 161, 221, 222], Dict{Symbol, Any}(:ennola => -3)), Family(((CHEVIE[:families])[:QZ])(6, [Perm(), [E(6)]]), [152, 164, 118, 162, 150, 65, 240, 225, 236, 228, 238, 113, 232, 242, 94, 224, 230, 146, 233, 49, 235, 47, 234, 83, 229, 148, 231, 243, 92, 223, 239, 111, 241, 226, 237, 227], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1], :ennola => 33)), Family(((CHEVIE[:families])[:X])(3), [132, 130, 244], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -2)), Family(((CHEVIE[:families])[:F42])(), [169, 265, 122, 121, 12, 11, 52, 166, 245, 252, 119, 249, 248, 138, 262, 255, 258, 254, 263, 167, 247, 250, 120, 251, 246, 139, 264, 253, 257, 256, 261, 168, 259, 126, 266, 127, 260, 51, 267, 268, 269, 270, 271, 272], Dict{Symbol, Any}(:signs => [1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1], :ennola => 3)), Family("C2", [125, 61, 106, 273], Dict{Symbol, Any}(:ennola => 4)), Family(conj(((CHEVIE[:families])[:X])(3)), [133, 131, 274], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -3)), Family(((CHEVIE[:families])[:QZ])(6, [Perm(), [E(3)]]), [151, 64, 153, 163, 117, 165, 280, 288, 277, 292, 114, 290, 284, 147, 282, 276, 93, 294, 48, 287, 50, 285, 82, 286, 281, 275, 95, 295, 283, 149, 278, 293, 112, 291, 279, 289], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1], :ennola => -8)), Family("C'\"2", [160, 158, 296, 297], Dict{Symbol, Any}(:ennola => 3)), Family("C1", [66]), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [157, 155, 128, 298, 300, 73, 301, 75, 299], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, -1, -1, -1, -1], :ennola => 8)), Family(((CHEVIE[:families])[:X])(3), [137, 135, 302], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 2)), Family("Z9", [140, 304, 303, 144, 308, 306, 142, 307, 305], Dict{Symbol, Any}(:special => 1, :cospecial => 4, :ennola => 6)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [85, 87, 21, 309, 311, 77, 312, 76, 310], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, -1, 1, -1, -1], :ennola => 4)), Family("C2", [123, 62, 104, 313], Dict{Symbol, Any}(:ennola => -4)), Family("C1", [27], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:X])(3) * Family("C'\"2"), [97, 102, 316, 318, 99, 100, 317, 319, 315, 314, 320, 321], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], :cospecial => 6, :ennola => -7)), Family(conj(((CHEVIE[:families])[:X])(3)) * Family("X5"), [108, 88, 327, 323, 34, 36, 90, 328, 322, 110, 325, 326, 329, 115, 324], Dict{Symbol, Any}(:signs => [1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1], :ennola => -10)), Family(((CHEVIE[:families])[:QZ])(3), [80, 69, 70, 41, 332, 331, 44, 333, 330], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, -1, 1, 1, 1], :ennola => -5)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [58, 60, 25, 334, 336, 30, 337, 29, 335], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, -1, 1, -1, -1], :ennola => -7)), Family(conj(((CHEVIE[:families])[:X])(3)) * Family("X5"), [40, 56, 343, 339, 7, 9, 54, 344, 338, 43, 341, 342, 345, 38, 340], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1], :ennola => 10)), Family("C2", [23, 13, 19, 346], Dict{Symbol, Any}(:ennola => -4)), Family(((CHEVIE[:families])[:X])(3), [18, 16, 347], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -2)), Family(((CHEVIE[:families])[:X])(3), [6, 4, 348], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 3)), Family("C1", [2])], :a => [0, 126, 1, 85, 1, 85, 46, 4, 46, 4, 15, 15, 57, 3, 2, 68, 2, 68, 57, 3, 28, 10, 57, 3, 41, 5, 45, 9, 41, 41, 5, 5, 7, 31, 7, 31, 4, 46, 6, 46, 36, 4, 46, 36, 6, 4, 13, 19, 13, 19, 15, 15, 4, 46, 4, 46, 5, 41, 5, 41, 18, 27, 9, 19, 13, 30, 12, 6, 36, 36, 6, 11, 23, 11, 23, 28, 28, 10, 10, 36, 6, 19, 13, 10, 28, 10, 28, 31, 7, 31, 7, 13, 19, 13, 19, 8, 29, 8, 29, 29, 8, 29, 8, 27, 9, 18, 7, 31, 7, 31, 13, 19, 13, 19, 31, 7, 19, 13, 15, 15, 15, 15, 27, 9, 18, 15, 15, 23, 11, 14, 20, 14, 20, 11, 23, 11, 23, 15, 15, 24, 10, 24, 10, 24, 10, 13, 19, 13, 19, 13, 19, 13, 19, 11, 23, 11, 23, 21, 12, 21, 12, 13, 19, 13, 19, 15, 15, 15, 15, 1, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 18, 20, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 21, 21, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 28, 28, 28, 28, 27, 29, 29, 29, 29, 29, 29, 29, 29, 31, 31, 31, 31, 31, 31, 31, 31, 36, 36, 36, 36, 41, 41, 41, 41, 46, 46, 46, 46, 46, 46, 46, 46, 57, 68, 85], :A => [0, 126, 41, 125, 41, 125, 122, 80, 122, 80, 111, 111, 123, 69, 58, 124, 58, 124, 123, 69, 116, 98, 123, 69, 121, 85, 117, 81, 121, 121, 85, 85, 95, 119, 95, 119, 80, 122, 90, 122, 120, 80, 122, 120, 90, 80, 107, 113, 107, 113, 111, 111, 80, 122, 80, 122, 85, 121, 85, 121, 108, 117, 99, 113, 107, 114, 96, 90, 120, 120, 90, 103, 115, 103, 115, 116, 116, 98, 98, 120, 90, 113, 107, 98, 116, 98, 116, 119, 95, 119, 95, 107, 113, 107, 113, 97, 118, 97, 118, 118, 97, 118, 97, 117, 99, 108, 95, 119, 95, 119, 107, 113, 107, 113, 119, 95, 113, 107, 111, 111, 111, 111, 117, 99, 108, 111, 111, 115, 103, 106, 112, 106, 112, 103, 115, 103, 115, 111, 111, 116, 102, 116, 102, 116, 102, 107, 113, 107, 113, 107, 113, 107, 113, 103, 115, 103, 115, 114, 105, 114, 105, 107, 113, 107, 113, 111, 111, 111, 111, 41, 58, 69, 80, 80, 80, 80, 80, 80, 80, 80, 85, 85, 85, 85, 90, 90, 90, 90, 95, 95, 95, 95, 95, 95, 95, 95, 97, 97, 97, 97, 97, 97, 97, 97, 99, 98, 98, 98, 98, 102, 102, 102, 102, 102, 102, 103, 103, 103, 103, 103, 105, 105, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 106, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 108, 112, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 114, 114, 115, 115, 115, 115, 115, 116, 116, 116, 116, 116, 116, 116, 116, 116, 116, 117, 118, 118, 118, 118, 118, 118, 118, 118, 119, 119, 119, 119, 119, 119, 119, 119, 120, 120, 120, 120, 121, 121, 121, 121, 122, 122, 122, 122, 122, 122, 122, 122, 123, 124, 125]) + return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:6, :rank => 6, :ST => 34), :levi => [], :parameterExponents => [1, 1, 1, 1, 1, 1], :charNumbers => 1:169, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6, 5, 1], :rank => 3, :ST => 26), :levi => 2:4, :parameterExponents => [1, 3, 3], :charNumbers => [170, 171, 340, 341, 325, 324, 342, 326, 220, 185, 219, 186, 216, 274, 249, 226, 184, 173, 334, 332, 251, 225, 183, 174, 335, 333, 232, 253, 299, 310, 189, 208, 231, 255, 298, 309, 190, 209, 197, 198, 280, 281, 282, 279, 245, 224, 247, 223], :eigenvalue => J, :cuspidalName => "G_{3,3,3}[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6, 5, 1], :rank => 3, :ST => 26), :levi => 2:4, :parameterExponents => [1, [3, 3, 0], [3, 3, 0]], :charNumbers => [176, 191, 348, 192, 347, 175, 331, 300, 193, 177, 330, 301, 244, 302, 187, 181, 278, 252, 338, 337, 339, 336, 188, 182, 277, 250, 311, 322, 256, 284, 207, 218, 206, 217, 312, 323, 254, 283, 227, 230, 314, 315, 228, 229, 276, 248, 275, 246], :eigenvalue => J ^ 2, :cuspidalName => "G_{3,3,3}[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [4, 6], :rank => 2, :p => 6, :q => 1), :levi => [1, 2, 3, 348], :parameterExponents => [[5, 4, 1, 0, 1, 4], 4], :charNumbers => [235, 194, 236, 273, 237, 195, 286, 259, 289, 257, 205, 343, 328, 313, 258, 346, 327, 288, 344, 260, 285, 172, 179, 233, 287, 234, 178], :eigenvalue => -1, :cuspidalName => "D_4"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6], :rank => 1, :p => 6, :q => 1), :levi => 1:5, :parameterExponents => [[5, 0, 7, 2, 7, 0]], :charNumbers => [221, 317, 199, 296, 200, 316], :eigenvalue => E(4), :cuspidalName => "G_{33}[i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6], :rank => 1, :p => 6, :q => 1), :levi => 1:5, :parameterExponents => [[5, 0, 7, 2, 7, 0]], :charNumbers => [222, 319, 201, 297, 202, 318], :eigenvalue => -(E(4)), :qEigen => 1 // 2, :cuspidalName => "G_{33}[-i]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6], :rank => 1, :p => 6, :q => 1), :levi => 1:5, :parameterExponents => [[3, 8, 7, 0, 7, 8]], :charNumbers => [329, 238, 261, 345, 263, 239], :eigenvalue => -J, :cuspidalName => "G_{33}[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6], :rank => 1, :p => 6, :q => 1), :levi => 1:5, :parameterExponents => [[8, 1, 0, 5, 0, 1]], :charNumbers => [180, 262, 291, 196, 290, 264], :eigenvalue => -(J ^ 2), :cuspidalName => "G_{33}[-\\zeta_3^2]"), cuspidal(265, 1), cuspidal(266, -1), cuspidal(294, J), cuspidal(295, J, 2), cuspidal(242, J ^ 2), cuspidal(243, J ^ 2, 2), cuspidal(292, -J), cuspidal(293, -J, 2), cuspidal(240, -(J ^ 2)), cuspidal(241, -(J ^ 2), 2), cuspidal(267, E(7)), cuspidal(268, E(7, 2)), cuspidal(269, E(7, 3)), cuspidal(270, E(7, 4)), cuspidal(271, E(7, 5)), cuspidal(272, E(7, 6)), cuspidal(212, E(9), 1 // 3), cuspidal(214, E(9), 2, 2 // 3), cuspidal(307, E(9, 2), 2 // 3), cuspidal(303, E(9, 2), 2, 1 // 3), cuspidal(210, E(9, 4), 1 // 3), cuspidal(215, E(9, 4), 2, 2 // 3), cuspidal(304, E(9, 5), 2 // 3), cuspidal(305, E(9, 5), 2, 1 // 3), cuspidal(211, E(9, 7), 2 // 3), cuspidal(213, E(9, 7), 2, 1 // 3), cuspidal(306, E(9, 8), 1 // 3), cuspidal(308, E(9, 8), 2, 2 // 3), cuspidal(203, E(12, 7), 1 // 2), cuspidal(320, E(12, 11), 1 // 2), cuspidal(204, E(12), 1 // 2), cuspidal(321, E(12, 5), 1 // 2)], :families => [Family("C1", [1]), Family(conj(((CHEVIE[:families])[:X])(3)), [5, 3, 170], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 2)), Family(conj(((CHEVIE[:families])[:X])(3)), [17, 15, 171], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -3)), Family("C2", [24, 14, 20, 172], Dict{Symbol, Any}(:ennola => -4)), Family(((CHEVIE[:families])[:X])(3) * conj(Family("X5")), [42, 55, 178, 174, 8, 10, 53, 179, 173, 46, 176, 177, 180, 37, 175], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1], :ennola => 15)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [57, 59, 26, 184, 182, 32, 181, 31, 183], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, -1, 1, -1, -1], :ennola => -7)), Family(((CHEVIE[:families])[:QZ])(3), [81, 68, 71, 45, 185, 188, 39, 186, 187], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, -1, -1], :ennola => 6)), Family(((CHEVIE[:families])[:X])(3) * conj(Family("X5")), [109, 89, 194, 190, 35, 33, 91, 195, 189, 107, 192, 193, 196, 116, 191], Dict{Symbol, Any}(:signs => [1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1], :ennola => -15)), Family(conj(((CHEVIE[:families])[:X])(3)) * ((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [103, 96, 201, 199, 101, 98, 202, 200, 198, 197, 204, 203], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], :cospecial => 6, :ennola => 12)), Family("C1", [28], Dict{Symbol, Any}(:ennola => -1)), Family("C2", [124, 63, 105, 205], Dict{Symbol, Any}(:ennola => -4)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [84, 86, 22, 209, 207, 78, 206, 79, 208], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, -1, 1, -1, -1], :ennola => 4)), Family(((CHEVIE[:families])[:TQZ])(3, E(3), [1, E(3)]), [143, 145, 141, 215, 211, 214, 212, 213, 210], Dict{Symbol, Any}(:cospecial => 3, :ennola => 4)), Family(conj(((CHEVIE[:families])[:X])(3)), [134, 136, 216], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 3)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [154, 156, 129, 220, 218, 74, 217, 72, 219], Dict{Symbol, Any}(:signs => [1, 1, 1, -1, -1, -1, 1, -1, 1], :ennola => -9)), Family("C1", [67]), Family(((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [159, 161, 222, 221], Dict{Symbol, Any}(:cospecial => 2, :ennola => -4)), Family(((CHEVIE[:families])[:QZ])(6, [Perm(), [E(6)]]), [152, 164, 118, 162, 150, 65, 240, 225, 236, 228, 238, 113, 232, 242, 94, 224, 230, 146, 233, 49, 235, 47, 234, 83, 229, 148, 231, 243, 92, 223, 239, 111, 241, 226, 237, 227], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1], :ennola => 33)), Family(((CHEVIE[:families])[:X])(3), [132, 130, 244], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -2)), Family(((CHEVIE[:families])[:F42])(), [169, 265, 122, 121, 12, 11, 52, 166, 245, 252, 119, 249, 248, 138, 262, 255, 258, 254, 263, 167, 247, 250, 120, 251, 246, 139, 264, 253, 257, 256, 261, 168, 259, 126, 266, 127, 260, 51, 267, 268, 269, 270, 271, 272], Dict{Symbol, Any}(:signs => [1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1], :ennola => 3)), Family("C2", [125, 61, 106, 273], Dict{Symbol, Any}(:ennola => 4)), Family(conj(((CHEVIE[:families])[:X])(3)), [133, 131, 274], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -3)), Family(((CHEVIE[:families])[:QZ])(6, [Perm(), [E(3)]]), [151, 64, 153, 163, 117, 165, 280, 288, 277, 292, 114, 290, 284, 147, 282, 276, 93, 294, 48, 287, 50, 285, 82, 286, 281, 275, 95, 295, 283, 149, 278, 293, 112, 291, 279, 289], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1], :ennola => -8)), Family(((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [160, 158, 297, 296], Dict{Symbol, Any}(:cospecial => 2, :ennola => 4)), Family("C1", [66]), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [157, 155, 128, 298, 300, 73, 301, 75, 299], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, -1, -1, -1, -1], :ennola => 8)), Family(((CHEVIE[:families])[:X])(3), [137, 135, 302], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 2)), Family(((CHEVIE[:families])[:TQZ])(3, E(3, 2)), [140, 144, 142, 307, 304, 308, 303, 306, 305], Dict{Symbol, Any}(:cospecial => 2, :ennola => 8)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [85, 87, 21, 309, 311, 77, 312, 76, 310], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, -1, 1, -1, -1], :ennola => 4)), Family("C2", [123, 62, 104, 313], Dict{Symbol, Any}(:ennola => -4)), Family("C1", [27], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:X])(3) * ((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [97, 102, 318, 316, 99, 100, 319, 317, 315, 314, 321, 320], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], :cospecial => 6, :ennola => -8)), Family(conj(((CHEVIE[:families])[:X])(3)) * Family("X5"), [108, 88, 327, 323, 34, 36, 90, 328, 322, 110, 325, 326, 329, 115, 324], Dict{Symbol, Any}(:signs => [1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1], :ennola => -10)), Family(((CHEVIE[:families])[:QZ])(3), [80, 69, 70, 41, 332, 331, 44, 333, 330], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, -1, 1, 1, 1], :ennola => -5)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [58, 60, 25, 334, 336, 30, 337, 29, 335], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, -1, 1, -1, -1], :ennola => -7)), Family(conj(((CHEVIE[:families])[:X])(3)) * Family("X5"), [40, 56, 343, 339, 7, 9, 54, 344, 338, 43, 341, 342, 345, 38, 340], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1], :ennola => 10)), Family("C2", [23, 13, 19, 346], Dict{Symbol, Any}(:ennola => -4)), Family(((CHEVIE[:families])[:X])(3), [18, 16, 347], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -2)), Family(((CHEVIE[:families])[:X])(3), [6, 4, 348], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 3)), Family("C1", [2])], :a => [0, 126, 1, 85, 1, 85, 46, 4, 46, 4, 15, 15, 57, 3, 2, 68, 2, 68, 57, 3, 28, 10, 57, 3, 41, 5, 45, 9, 41, 41, 5, 5, 7, 31, 7, 31, 4, 46, 6, 46, 36, 4, 46, 36, 6, 4, 13, 19, 13, 19, 15, 15, 4, 46, 4, 46, 5, 41, 5, 41, 18, 27, 9, 19, 13, 30, 12, 6, 36, 36, 6, 11, 23, 11, 23, 28, 28, 10, 10, 36, 6, 19, 13, 10, 28, 10, 28, 31, 7, 31, 7, 13, 19, 13, 19, 8, 29, 8, 29, 29, 8, 29, 8, 27, 9, 18, 7, 31, 7, 31, 13, 19, 13, 19, 31, 7, 19, 13, 15, 15, 15, 15, 27, 9, 18, 15, 15, 23, 11, 14, 20, 14, 20, 11, 23, 11, 23, 15, 15, 24, 10, 24, 10, 24, 10, 13, 19, 13, 19, 13, 19, 13, 19, 11, 23, 11, 23, 21, 12, 21, 12, 13, 19, 13, 19, 15, 15, 15, 15, 1, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 18, 20, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 21, 21, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 28, 28, 28, 28, 27, 29, 29, 29, 29, 29, 29, 29, 29, 31, 31, 31, 31, 31, 31, 31, 31, 36, 36, 36, 36, 41, 41, 41, 41, 46, 46, 46, 46, 46, 46, 46, 46, 57, 68, 85], :A => [0, 126, 41, 125, 41, 125, 122, 80, 122, 80, 111, 111, 123, 69, 58, 124, 58, 124, 123, 69, 116, 98, 123, 69, 121, 85, 117, 81, 121, 121, 85, 85, 95, 119, 95, 119, 80, 122, 90, 122, 120, 80, 122, 120, 90, 80, 107, 113, 107, 113, 111, 111, 80, 122, 80, 122, 85, 121, 85, 121, 108, 117, 99, 113, 107, 114, 96, 90, 120, 120, 90, 103, 115, 103, 115, 116, 116, 98, 98, 120, 90, 113, 107, 98, 116, 98, 116, 119, 95, 119, 95, 107, 113, 107, 113, 97, 118, 97, 118, 118, 97, 118, 97, 117, 99, 108, 95, 119, 95, 119, 107, 113, 107, 113, 119, 95, 113, 107, 111, 111, 111, 111, 117, 99, 108, 111, 111, 115, 103, 106, 112, 106, 112, 103, 115, 103, 115, 111, 111, 116, 102, 116, 102, 116, 102, 107, 113, 107, 113, 107, 113, 107, 113, 103, 115, 103, 115, 114, 105, 114, 105, 107, 113, 107, 113, 111, 111, 111, 111, 41, 58, 69, 80, 80, 80, 80, 80, 80, 80, 80, 85, 85, 85, 85, 90, 90, 90, 90, 95, 95, 95, 95, 95, 95, 95, 95, 97, 97, 97, 97, 97, 97, 97, 97, 99, 98, 98, 98, 98, 102, 102, 102, 102, 102, 102, 103, 103, 103, 103, 103, 105, 105, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 106, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 108, 112, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 114, 114, 115, 115, 115, 115, 115, 116, 116, 116, 116, 116, 116, 116, 116, 116, 116, 117, 118, 118, 118, 118, 118, 118, 118, 118, 119, 119, 119, 119, 119, 119, 119, 119, 120, 120, 120, 120, 121, 121, 121, 121, 122, 122, 122, 122, 122, 122, 122, 122, 123, 124, 125]) end) chevieset(:G34, :Invariants, function () local r diff --git a/src/tbl/coxh3.jl b/src/tbl/coxh3.jl index 76990674..5feb3f4c 100644 --- a/src/tbl/coxh3.jl +++ b/src/tbl/coxh3.jl @@ -91,7 +91,7 @@ chevieset(:H3, :HeckeRepresentation, function (param, sqrtparam, i) end) chevieset(:H3, :UnipotentCharacters, function () local res - res = Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "H", :indices => 1:3, :rank => 3), :levi => [], :eigenvalue => 1, :parameterExponents => [1, 1, 1], :cuspidalName => "", :charNumbers => 1:10), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [3], :rank => 1), :levi => 1:2, :eigenvalue => E(5, 2), :parameterExponents => [5], :cuspidalName => "I_2(5)[1,3]", :charNumbers => [11, 13]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [3], :rank => 1), :levi => 1:2, :eigenvalue => E(5, 3), :parameterExponents => [5], :cuspidalName => "I_2(5)[1,2]", :charNumbers => [12, 14]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :eigenvalue => E(4), :qEigen => 1 // 2, :parameterExponents => [], :cuspidalName => "H_3[i]", :charNumbers => [15]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :eigenvalue => -(E(4)), :qEigen => 1 // 2, :parameterExponents => [], :cuspidalName => "H_3[-i]", :charNumbers => [16])], :families => [Family("C1", [2]), Family(((CHEVIE[:families])[:Dihedral])(5), [7, 8, 14, 13], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [4]), Family("C'\"2", [9, 10, 15, 16], Dict{Symbol, Any}(:ennola => 3)), Family("C1", [3], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:Dihedral])(5), [5, 6, 12, 11], Dict{Symbol, Any}(:ennola => 1)), Family("C1", [1], Dict{Symbol, Any}(:ennola => -1))], :a => [15, 0, 5, 2, 6, 6, 1, 1, 3, 3, 6, 6, 1, 1, 3, 3], :A => [15, 0, 13, 10, 14, 14, 9, 9, 12, 12, 14, 14, 9, 9, 12, 12]) + res = Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "H", :indices => 1:3, :rank => 3), :levi => [], :eigenvalue => 1, :parameterExponents => [1, 1, 1], :cuspidalName => "", :charNumbers => 1:10), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [3], :rank => 1), :levi => 1:2, :eigenvalue => E(5, 2), :parameterExponents => [5], :cuspidalName => "I_2(5)[1,3]", :charNumbers => [11, 13]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [3], :rank => 1), :levi => 1:2, :eigenvalue => E(5, 3), :parameterExponents => [5], :cuspidalName => "I_2(5)[1,2]", :charNumbers => [12, 14]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :eigenvalue => E(4), :qEigen => 1 // 2, :parameterExponents => [], :cuspidalName => "H_3[i]", :charNumbers => [15]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :eigenvalue => -(E(4)), :qEigen => 1 // 2, :parameterExponents => [], :cuspidalName => "H_3[-i]", :charNumbers => [16])], :families => [Family("C1", [2]), Family(((CHEVIE[:families])[:Dihedral])(5), [7, 8, 14, 13], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [4]), Family(((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [9, 10, 16, 15], Dict{Symbol, Any}(:cospecial => 2, :ennola => 4)), Family("C1", [3], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:Dihedral])(5), [5, 6, 12, 11], Dict{Symbol, Any}(:ennola => 1)), Family("C1", [1], Dict{Symbol, Any}(:ennola => -1))], :a => [15, 0, 5, 2, 6, 6, 1, 1, 3, 3, 6, 6, 1, 1, 3, 3], :A => [15, 0, 13, 10, 14, 14, 9, 9, 12, 12, 14, 14, 9, 9, 12, 12]) return res end) chevieset(:H3, :Discriminant, function () diff --git a/src/tbl/coxh4.jl b/src/tbl/coxh4.jl index 6a974a3c..c895aa56 100644 --- a/src/tbl/coxh4.jl +++ b/src/tbl/coxh4.jl @@ -85,7 +85,7 @@ chevieset(:H4, :HeckeRepresentation, function (param, sqrtparam, i) chevieset(:H4, :Representation, function (i,) return (chevieget(:H4, :HeckeRepresentation))([[1, -1], [1, -1], [1, -1], [1, -1]], [1, 1, 1, 1], i) end) -(CHEVIE[:families])[:HS4] = Dict{Symbol, Any}(:group => "SL2(5)", :name => "H4", :explanation => "DrinfeldDouble(SL_2(5))?√5", :charLabels => map((i->begin +(CHEVIE[:families])[:HS4] = Dict{Symbol, Any}(:group => "SL2(5)", :name => "H4", :explanation => "DrinfeldDouble(SL_2(5))?ER(5)", :charLabels => map((i->begin "?" end), 1:74), :fourierMat => 1 // 60 * [[18, 0, -18, -6, -6, 18, 6, 6, 6, 6, -6, -6, -6, -6, 12, 0, 6, 6, -6, -6, -6, -6, 6, 6, 0, -18, 6, 6, 6, 6, -6, -6, 12, 0, 6, 6, -6, -6, -6, -6, 6, 6, 0, 0, 0, 0, 0, 0, -6, -6, 6, 6, -6, -6, 6, 6, 0, 0, 0, 0, -6, -6, -6, -6, 0, 0, 0, 0, -6, -6, -6, -6, 12, 12], [0, 45 // 2, 0, 0, 0, 0, -15, -15, 15 // 2, 15 // 2, 0, 0, 0, 0, -15 // 2, 15, 0, 0, 0, 0, 0, 0, 0, 0, 45 // 2, 0, -15, -15, 15 // 2, 15 // 2, 0, 0, -15 // 2, 15, 0, 0, 0, 0, 0, 0, 0, 0, -15, -15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 15], [-18, 0, 18, -6, -6, 18, -6, -6, 6, 6, 6, 6, 6, 6, -12, 0, 6, 6, -6, -6, 6, 6, -6, -6, 0, -18, 6, 6, -6, -6, -6, -6, 12, 0, -6, -6, 6, 6, -6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, -6, -6, -6, -6, 6, 6, 0, 0, 0, 0, -6, -6, -6, -6, 0, 0, 0, 0, 6, 6, 6, 6, 12, -12], [-6, 0, -6, 12 - 2 * root(5), 12 + 2 * root(5), -6, -3 - 3 * root(5), -3 + 3 * root(5), 3 - root(5), 3 + root(5), -2, -2, 12 + 2 * root(5), 12 - 2 * root(5), 6, -10, 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 0, -6, -3 - 3 * root(5), -3 + 3 * root(5), 3 - root(5), 3 + root(5), -2, -2, 6, -10, 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 0, 0, 10, 10, 10, 10, 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), -2 * root(5), -2 * root(5), -2 * root(5), -2 * root(5), -3 + root(5), -3 + root(5), -3 - root(5), -3 - root(5), -4 * root(5), -4 * root(5), -4 * root(5), -4 * root(5), -3 - root(5), -3 - root(5), -3 + root(5), -3 + root(5), 4, 4], [-6, 0, -6, 12 + 2 * root(5), 12 - 2 * root(5), -6, -3 + 3 * root(5), -3 - 3 * root(5), 3 + root(5), 3 - root(5), -2, -2, 12 - 2 * root(5), 12 + 2 * root(5), 6, -10, 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 0, -6, -3 + 3 * root(5), -3 - 3 * root(5), 3 + root(5), 3 - root(5), -2, -2, 6, -10, 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 0, 0, 10, 10, 10, 10, 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 2 * root(5), 2 * root(5), 2 * root(5), 2 * root(5), -3 - root(5), -3 - root(5), -3 + root(5), -3 + root(5), 4 * root(5), 4 * root(5), 4 * root(5), 4 * root(5), -3 + root(5), -3 + root(5), -3 - root(5), -3 - root(5), 4, 4], [18, 0, 18, -6, -6, 18, -6, -6, 6, 6, 6, 6, -6, -6, 12, 0, 6, 6, -6, -6, 6, 6, -6, -6, 0, 18, -6, -6, 6, 6, 6, 6, 12, 0, 6, 6, -6, -6, 6, 6, -6, -6, 0, 0, 0, 0, 0, 0, 6, 6, -6, -6, 6, 6, -6, -6, 0, 0, 0, 0, -6, -6, -6, -6, 0, 0, 0, 0, -6, -6, -6, -6, -12, -12], [6, -15, -6, -3 - 3 * root(5), -3 + 3 * root(5), -6, 12, 12, 3, 3, 3 - 3 * root(5), 3 + 3 * root(5), 3 - 3 * root(5), 3 + 3 * root(5), 9, 0, 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 15, 6, -12, -12, -3, -3, -3 + 3 * root(5), -3 - 3 * root(5), -9, 0, -3 - 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), 0, 0, 0, 0, 0, 0, 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), 0, 0, 0, 0, -3 + 3 * root(5), -3 + 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 0, 0, 0, 0, 3 + 3 * root(5), 3 + 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), 6, -6], [6, -15, -6, -3 + 3 * root(5), -3 - 3 * root(5), -6, 12, 12, 3, 3, 3 + 3 * root(5), 3 - 3 * root(5), 3 + 3 * root(5), 3 - 3 * root(5), 9, 0, 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 15, 6, -12, -12, -3, -3, -3 - 3 * root(5), -3 + 3 * root(5), -9, 0, -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), 0, 0, 0, 0, 0, 0, 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), 0, 0, 0, 0, -3 - 3 * root(5), -3 - 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 0, 0, 0, 0, 3 - 3 * root(5), 3 - 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), 6, -6], [6, 15 // 2, 6, 3 - root(5), 3 + root(5), 6, 3, 3, (9 - 4 * root(5)) // 2, (9 + 4 * root(5)) // 2, 7 - 3 * root(5), 7 + 3 * root(5), 3 + root(5), 3 - root(5), 3 // 2, 5, -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), 15 // 2, 6, 3, 3, (9 - 4 * root(5)) // 2, (9 + 4 * root(5)) // 2, 7 - 3 * root(5), 7 + 3 * root(5), 3 // 2, 5, -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), 15, 15, 10, 10, 10, 10, -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), 2 * root(5), 2 * root(5), 2 * root(5), 2 * root(5), 3 - root(5), 3 - root(5), 3 + root(5), 3 + root(5), 4 * root(5), 4 * root(5), 4 * root(5), 4 * root(5), 3 + root(5), 3 + root(5), 3 - root(5), 3 - root(5), 1, 1], [6, 15 // 2, 6, 3 + root(5), 3 - root(5), 6, 3, 3, (9 + 4 * root(5)) // 2, (9 - 4 * root(5)) // 2, 7 + 3 * root(5), 7 - 3 * root(5), 3 - root(5), 3 + root(5), 3 // 2, 5, -3 - 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), 15 // 2, 6, 3, 3, (9 + 4 * root(5)) // 2, (9 - 4 * root(5)) // 2, 7 + 3 * root(5), 7 - 3 * root(5), 3 // 2, 5, -3 - 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), 15, 15, 10, 10, 10, 10, -3 - 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), -2 * root(5), -2 * root(5), -2 * root(5), -2 * root(5), 3 + root(5), 3 + root(5), 3 - root(5), 3 - root(5), -4 * root(5), -4 * root(5), -4 * root(5), -4 * root(5), 3 - root(5), 3 - root(5), 3 + root(5), 3 + root(5), 1, 1], [-6, 0, 6, -2, -2, 6, 3 - 3 * root(5), 3 + 3 * root(5), 7 - 3 * root(5), 7 + 3 * root(5), 2, 2, 2, 2, 6, 10, -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), 0, -6, -3 + 3 * root(5), -3 - 3 * root(5), -7 + 3 * root(5), -7 - 3 * root(5), -2, -2, -6, -10, 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 0, 0, -10, -10, 10, 10, -3 - 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), -10, -10, 10, 10, 3 - 3 * root(5), 3 - 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), 0, 0, 0, 0, -3 - 3 * root(5), -3 - 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 4, -4], [-6, 0, 6, -2, -2, 6, 3 + 3 * root(5), 3 - 3 * root(5), 7 + 3 * root(5), 7 - 3 * root(5), 2, 2, 2, 2, 6, 10, -3 - 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), 0, -6, -3 - 3 * root(5), -3 + 3 * root(5), -7 - 3 * root(5), -7 + 3 * root(5), -2, -2, -6, -10, 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 0, 0, -10, -10, 10, 10, -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), -10, -10, 10, 10, 3 + 3 * root(5), 3 + 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), 0, 0, 0, 0, -3 + 3 * root(5), -3 + 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 4, -4], [-6, 0, 6, 12 + 2 * root(5), 12 - 2 * root(5), -6, 3 - 3 * root(5), 3 + 3 * root(5), 3 + root(5), 3 - root(5), 2, 2, 12 - 2 * root(5), 12 + 2 * root(5), 6, 10, 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), 0, 6, 3 - 3 * root(5), 3 + 3 * root(5), 3 + root(5), 3 - root(5), 2, 2, 6, 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3 + 3 * root(5), -12, 12, -3 + 3 * root(5), 0, 6, 3 - 3 * root(5), 3 + 3 * root(5), -3 - 3 * root(5), -3 + 3 * root(5), -3 - 3 * root(5), -3 + 3 * root(5), 6, 0, -3 - 3 * root(5), 12, -12, 3 - 3 * root(5), -3 - 3 * root(5), 12, -12, 3 - 3 * root(5), 0, 0, 0, 0, 0, 0, 3 - 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 - 3 * root(5), -3 + 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 + 3 * root(5), 0, 0, 0, 0, -3 + 3 * root(5), -3 - 3 * root(5), -3 + 3 * root(5), -3 - 3 * root(5), 0, 0, 0, 0, 3 - 3 * root(5), 3 + 3 * root(5), 3 - 3 * root(5), 3 + 3 * root(5), 6, -6], [0, 45 // 2, 0, 0, 0, 0, 15, 15, 15 // 2, 15 // 2, 0, 0, 0, 0, -15 // 2, -15, 0, 0, 0, 0, 0, 0, 0, 0, 45 // 2, 0, 15, 15, 15 // 2, 15 // 2, 0, 0, -15 // 2, -15, 0, 0, 0, 0, 0, 0, 0, 0, -15, -15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15, -15], [-18, 0, -18, -6, -6, 18, 6, 6, 6, 6, -6, -6, 6, 6, -12, 0, 6, 6, -6, -6, -6, -6, 6, 6, 0, 18, -6, -6, -6, -6, 6, 6, 12, 0, -6, 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-6, -12, -12, 3, 3, -3 - 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 - 3 * root(5), 9, 0, 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), 15, -6, 12, 12, -3, -3, 3 + 3 * root(5), 3 - 3 * root(5), -9, 0, -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 0, 0, 0, 0, 0, 0, -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 0, 0, 0, 0, -3 - 3 * root(5), -3 - 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 0, 0, 0, 0, 3 - 3 * root(5), 3 - 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), -6, 6], [6, 15 // 2, -6, 3 - root(5), 3 + root(5), 6, -3, -3, (9 - 4 * root(5)) // 2, (9 + 4 * root(5)) // 2, -7 + 3 * root(5), -7 - 3 * root(5), 3 + root(5), 3 - root(5), 3 // 2, -5, -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 15 // 2, -6, -3, -3, (9 - 4 * root(5)) // 2, (9 + 4 * root(5)) // 2, -7 + 3 * root(5), -7 - 3 * root(5), 3 // 2, -5, -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 15, 15, -10, -10, -10, -10, 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 2 * root(5), 2 * root(5), 2 * root(5), 2 * root(5), 3 - root(5), 3 - root(5), 3 + root(5), 3 + root(5), 4 * root(5), 4 * root(5), 4 * root(5), 4 * root(5), 3 + root(5), 3 + root(5), 3 - root(5), 3 - root(5), -1, -1], [6, 15 // 2, -6, 3 + root(5), 3 - root(5), 6, -3, -3, (9 + 4 * root(5)) // 2, (9 - 4 * root(5)) // 2, -7 - 3 * root(5), -7 + 3 * root(5), 3 - root(5), 3 + root(5), 3 // 2, -5, -3 - 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 15 // 2, -6, -3, -3, (9 + 4 * root(5)) // 2, (9 - 4 * root(5)) // 2, -7 - 3 * root(5), -7 + 3 * root(5), 3 // 2, -5, -3 - 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 15, 15, -10, -10, -10, -10, 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), -2 * root(5), -2 * root(5), -2 * root(5), -2 * root(5), 3 + root(5), 3 + root(5), 3 - root(5), 3 - root(5), -4 * root(5), -4 * root(5), -4 * root(5), -4 * root(5), 3 - root(5), 3 - root(5), 3 + root(5), 3 + root(5), -1, -1], [-6, 0, -6, -2, -2, 6, -3 + 3 * root(5), -3 - 3 * root(5), 7 - 3 * root(5), 7 + 3 * root(5), -2, -2, 2, 2, 6, -10, -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), 0, 6, 3 - 3 * root(5), 3 + 3 * root(5), -7 + 3 * 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root(5), 0, 0, 10, 10, -10, -10, 3 - 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), -3 + 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 + 3 * root(5), -10, -10, 10, 10, 3 + 3 * root(5), 3 + 3 * root(5), 3 - 3 * root(5), 3 - 3 * root(5), 0, 0, 0, 0, -3 + 3 * root(5), -3 + 3 * root(5), -3 - 3 * root(5), -3 - 3 * root(5), -4, 4], [12, -15 // 2, 12, 6, 6, 12, -9, -9, 3 // 2, 3 // 2, -6, -6, 6, 6, 21 // 2, -15, -6, -6, 6, 6, -6, -6, 6, 6, -15 // 2, 12, -9, -9, 3 // 2, 3 // 2, -6, -6, 21 // 2, -15, -6, -6, 6, 6, -6, -6, 6, 6, -15, -15, 0, 0, 0, 0, -6, -6, 6, 6, -6, -6, 6, 6, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 6, 6, -3, -3], [0, 15, 0, -10, -10, 0, 0, 0, 5, 5, -10, -10, 10, 10, 15, -20, 0, 0, 0, 0, 0, 0, 0, 0, -15, 0, 0, 0, -5, -5, 10, 10, -15, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, -10, 10, 10, 0, 0, 0, 0, 0, 0, 0, 0, 10, 10, -10, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, -10], [6, 0, -6, 3 + 3 * root(5), 3 - 3 * root(5), 6, -3 - 3 * root(5), -3 + 3 * root(5), 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* root(5), -3 - 3 * root(5), 12, -12, 3 - 3 * root(5), -4 * root(5), -4 * root(5), -4 * root(5), -4 * root(5), 2 - 2 * root(5), 7 + root(5), 7 - root(5), 2 + 2 * root(5), 10 + 2 * root(5), -10 + 2 * root(5), -10 + 2 * root(5), 10 + 2 * root(5), 7 - root(5), 2 + 2 * root(5), 2 - 2 * root(5), 7 + root(5), 6, 6], [-6, 0, 6, -3 - root(5), -3 + root(5), -6, 3 + 3 * root(5), 3 - 3 * root(5), 3 + root(5), 3 - root(5), -3 - 3 * root(5), -3 + 3 * root(5), -3 + root(5), -3 - root(5), 6, 0, 3 - 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 - 3 * root(5), -3 + 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 + 3 * root(5), 0, 6, 3 + 3 * root(5), 3 - 3 * root(5), 3 + root(5), 3 - root(5), -3 - 3 * root(5), -3 + 3 * root(5), 6, 0, 3 - 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 - 3 * root(5), -3 + 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 + 3 * root(5), 0, 0, 0, 0, 0, 0, 12, -3 - 3 * root(5), 3 - 3 * root(5), -12, 12, -3 - 3 * root(5), 3 - 3 * root(5), -12, -4 * root(5), -4 * root(5), -4 * root(5), -4 * root(5), 7 + root(5), 2 - 2 * root(5), 2 + 2 * root(5), 7 - root(5), -10 + 2 * root(5), 10 + 2 * root(5), 10 + 2 * root(5), -10 + 2 * root(5), 2 + 2 * root(5), 7 - root(5), 7 + root(5), 2 - 2 * root(5), 6, 6], [-6, 0, 6, -3 + root(5), -3 - root(5), -6, 3 - 3 * root(5), 3 + 3 * root(5), 3 - root(5), 3 + root(5), -3 + 3 * root(5), -3 - 3 * root(5), -3 - root(5), -3 + root(5), 6, 0, 3 + 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 + 3 * root(5), -3 - 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 - 3 * root(5), 0, 6, 3 - 3 * root(5), 3 + 3 * root(5), 3 - root(5), 3 + root(5), -3 + 3 * root(5), -3 - 3 * root(5), 6, 0, 3 + 3 * root(5), 3 - 3 * root(5), -3 - 3 * root(5), -3 + 3 * root(5), -3 - 3 * root(5), -3 + 3 * root(5), 3 + 3 * root(5), 3 - 3 * root(5), 0, 0, 0, 0, 0, 0, 12, -3 + 3 * root(5), 3 + 3 * root(5), -12, 12, -3 + 3 * root(5), 3 + 3 * root(5), -12, 4 * root(5), 4 * root(5), 4 * root(5), 4 * root(5), 7 - root(5), 2 + 2 * root(5), 2 - 2 * root(5), 7 + root(5), -10 - 2 * root(5), 10 - 2 * root(5), 10 - 2 * root(5), -10 - 2 * root(5), 2 - 2 * root(5), 7 + root(5), 7 - root(5), 2 + 2 * root(5), 6, 6], [-6, 0, 6, -3 + root(5), -3 - root(5), -6, 3 - 3 * root(5), 3 + 3 * root(5), 3 - root(5), 3 + root(5), -3 + 3 * root(5), -3 - 3 * root(5), -3 - root(5), -3 + root(5), 6, 0, 3 - 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 - 3 * root(5), -3 + 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 + 3 * root(5), 0, 6, 3 - 3 * root(5), 3 + 3 * root(5), 3 - root(5), 3 + root(5), -3 + 3 * root(5), -3 - 3 * root(5), 6, 0, 3 - 3 * root(5), 3 + 3 * root(5), -3 + 3 * root(5), -3 - 3 * root(5), -3 + 3 * root(5), -3 - 3 * root(5), 3 - 3 * root(5), 3 + 3 * root(5), 0, 0, 0, 0, 0, 0, -3 + 3 * root(5), 12, -12, 3 + 3 * root(5), -3 + 3 * root(5), 12, -12, 3 + 3 * root(5), 4 * root(5), 4 * root(5), 4 * root(5), 4 * root(5), 2 + 2 * root(5), 7 - root(5), 7 + root(5), 2 - 2 * root(5), 10 - 2 * root(5), -10 - 2 * root(5), -10 - 2 * root(5), 10 - 2 * root(5), 7 + root(5), 2 - 2 * root(5), 2 + 2 * root(5), 7 - root(5), 6, 6], [12, 15, 12, 4, 4, -12, 6, 6, 1, 1, 4, 4, -4, -4, 3, -10, 6, 6, -6, -6, -6, -6, 6, 6, -15, -12, -6, -6, -1, -1, -4, -4, -3, 10, -6, -6, 6, 6, 6, 6, -6, -6, 0, 0, 10, 10, -10, -10, -6, -6, 6, 6, 6, 6, -6, -6, -10, -10, 10, 10, -6, -6, -6, -6, 0, 0, 0, 0, 6, 6, 6, 6, 8, -8], [12, 15, -12, 4, 4, -12, -6, -6, 1, 1, -4, -4, -4, -4, 3, 10, 6, 6, -6, -6, 6, 6, -6, -6, -15, 12, 6, 6, -1, -1, 4, 4, -3, -10, -6, -6, 6, 6, -6, -6, 6, 6, 0, 0, -10, -10, 10, 10, 6, 6, -6, -6, -6, -6, 6, 6, -10, -10, 10, 10, -6, -6, -6, -6, 0, 0, 0, 0, 6, 6, 6, 6, -8, 8]], :eigenvalues => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, E(5, 3), E(5, 2), E(5, 3), E(5, 2), E(5, 3), E(5, 2), E(5, 3), E(5, 2), 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, E(5, 3), E(5, 2), E(5, 3), E(5, 2), -(E(5, 3)), -(E(5, 2)), -(E(5, 3)), -(E(5, 2)), E(4), -(E(4)), E(3), E(3, 2), -(E(3, 2)), -(E(3)), E(5, 4), E(5), E(5, 4), E(5), -(E(5, 4)), -(E(5)), -(E(5, 4)), -(E(5)), E(3), E(3, 2), E(3), E(3, 2), E(5, 4), E(5), E(5, 4), E(5), E(15, 2), E(15, 13), E(15, 8), E(15, 7), E(5, 4), E(5), E(5, 4), E(5), -1, 1], :perm => perm"(17,18)(19,20)(21,22)(23,24)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)", :special => 9) chevieset(:H4, :UnipotentCharacters, function () @@ -100,6 +100,6 @@ chevieset(:H4, :UnipotentCharacters, function () res = Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:4, :parameterExponents => [], :charNumbers => [arg[1]], :eigenvalue => arg[2], :cuspidalName => n) return res end - return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "H", :indices => 1:4, :rank => 4), :levi => [], :eigenvalue => 1, :parameterExponents => [1, 1, 1, 1], :cuspidalName => "", :charNumbers => 1:34), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "I", :indices => [4, 3], :rank => 2, :bond => 10), :levi => 1:2, :eigenvalue => E(5, 3), :parameterExponents => [1, 5], :cuspidalName => "I_2(5)[1,2]", :charNumbers => [35, 44, 37, 45, 47, 53, 49, 51]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "I", :indices => [4, 3], :rank => 2, :bond => 10), :levi => 1:2, :eigenvalue => E(5, 2), :parameterExponents => [1, 5], :cuspidalName => "I_2(5)[1,3]", :charNumbers => [36, 43, 38, 46, 48, 54, 50, 52]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [4], :rank => 1), :levi => 1:3, :eigenvalue => E(4), :parameterExponents => [15], :cuspidalName => "H_3[i]", :charNumbers => [41, 39], :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [4], :rank => 1), :levi => 1:3, :eigenvalue => -(E(4)), :parameterExponents => [15], :cuspidalName => "H_3[-i]", :charNumbers => [42, 40], :qEigen => 1 // 2), cuspidal(55, 1), cuspidal(56, -1), cuspidal(57, -1, 2), cuspidal(58, -1, 3), cuspidal(59, 1, 2), cuspidal(60, 1, 3), cuspidal(61, -1, 4), cuspidal(62, -1, 5), cuspidal(63, 1, 4), cuspidal(64, -1, 6), cuspidal(65, E(5, 3)), cuspidal(66, E(5, 2)), cuspidal(67, E(5, 3), 2), cuspidal(68, E(5, 2), 2), cuspidal(69, -(E(5, 3))), cuspidal(70, -(E(5, 2))), cuspidal(71, -(E(5, 3)), 2), cuspidal(72, -(E(5, 2)), 2), cuspidal(73, E(4)), cuspidal(74, -(E(4))), cuspidal(75, E(3)), cuspidal(76, E(3, 2)), cuspidal(77, -(E(3, 2))), cuspidal(78, -(E(3))), cuspidal(79, E(5, 4)), cuspidal(80, E(5)), cuspidal(81, E(5, 4), 2), cuspidal(82, E(5), 2), cuspidal(83, -(E(5, 4))), cuspidal(84, -(E(5))), cuspidal(85, -(E(5, 4)), 2), cuspidal(86, -(E(5)), 2), cuspidal(87, E(3), 2), cuspidal(88, E(3, 2), 2), cuspidal(89, E(3), 3), cuspidal(90, E(3, 2), 3), cuspidal(91, E(5, 4), 3), cuspidal(92, E(5), 3), cuspidal(93, E(5, 4), 4), cuspidal(94, E(5), 4), cuspidal(95, E(15, 2)), cuspidal(96, E(15, 13)), cuspidal(97, E(15, 8)), cuspidal(98, E(15, 7)), cuspidal(99, E(5, 4), 5), cuspidal(100, E(5), 5), cuspidal(101, E(5, 4), 6), cuspidal(102, E(5), 6), cuspidal(103, -1, 7), cuspidal(104, 1, 5)], :families => [Family("C1", [1]), Family("C1", [2]), Family("C1", [27]), Family("C1", [28]), Family("C1", [31], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [32], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:Dihedral])(5), [3, 5, 35, 36], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:Dihedral])(5), [11, 13, 37, 38], Dict{Symbol, Any}(:ennola => 1)), Family(((CHEVIE[:families])[:Dihedral])(5), [12, 14, 44, 43], Dict{Symbol, Any}(:ennola => 1)), Family(((CHEVIE[:families])[:Dihedral])(5), [4, 6, 45, 46], Dict{Symbol, Any}(:ennola => -1)), Family("C'\"2", [18, 20, 39, 40], Dict{Symbol, Any}(:ennola => 4)), Family("C'\"2", [21, 19, 41, 42], Dict{Symbol, Any}(:ennola => -4)), Family("HS4", [15, 9, 10, 7, 8, 22, 16, 17, 26, 25, 24, 23, 29, 30, 33, 34, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104], Dict{Symbol, Any}(:ennola => 29))], :a => [0, 60, 1, 31, 1, 31, 6, 6, 6, 6, 2, 22, 2, 22, 6, 6, 6, 3, 18, 3, 18, 6, 6, 6, 6, 6, 4, 16, 6, 6, 5, 15, 6, 6, 1, 1, 2, 2, 3, 3, 18, 18, 22, 22, 31, 31, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], :A => [0, 60, 29, 59, 29, 59, 54, 54, 54, 54, 38, 58, 38, 58, 54, 54, 54, 42, 57, 42, 57, 54, 54, 54, 54, 54, 44, 56, 54, 54, 45, 55, 54, 54, 29, 29, 38, 38, 42, 42, 57, 57, 58, 58, 59, 59, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54]) + return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "H", :indices => 1:4, :rank => 4), :levi => [], :eigenvalue => 1, :parameterExponents => [1, 1, 1, 1], :cuspidalName => "", :charNumbers => 1:34), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "I", :indices => [4, 3], :rank => 2, :bond => 10), :levi => 1:2, :eigenvalue => E(5, 3), :parameterExponents => [1, 5], :cuspidalName => "I_2(5)[1,2]", :charNumbers => [35, 44, 37, 45, 47, 53, 49, 51]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "I", :indices => [4, 3], :rank => 2, :bond => 10), :levi => 1:2, :eigenvalue => E(5, 2), :parameterExponents => [1, 5], :cuspidalName => "I_2(5)[1,3]", :charNumbers => [36, 43, 38, 46, 48, 54, 50, 52]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [4], :rank => 1), :levi => 1:3, :eigenvalue => E(4), :parameterExponents => [15], :cuspidalName => "H_3[i]", :charNumbers => [41, 39], :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [4], :rank => 1), :levi => 1:3, :eigenvalue => -(E(4)), :parameterExponents => [15], :cuspidalName => "H_3[-i]", :charNumbers => [42, 40], :qEigen => 1 // 2), cuspidal(55, 1), cuspidal(56, -1), cuspidal(57, -1, 2), cuspidal(58, -1, 3), cuspidal(59, 1, 2), cuspidal(60, 1, 3), cuspidal(61, -1, 4), cuspidal(62, -1, 5), cuspidal(63, 1, 4), cuspidal(64, -1, 6), cuspidal(65, E(5, 3)), cuspidal(66, E(5, 2)), cuspidal(67, E(5, 3), 2), cuspidal(68, E(5, 2), 2), cuspidal(69, -(E(5, 3))), cuspidal(70, -(E(5, 2))), cuspidal(71, -(E(5, 3)), 2), cuspidal(72, -(E(5, 2)), 2), cuspidal(73, E(4)), cuspidal(74, -(E(4))), cuspidal(75, E(3)), cuspidal(76, E(3, 2)), cuspidal(77, -(E(3, 2))), cuspidal(78, -(E(3))), cuspidal(79, E(5, 4)), cuspidal(80, E(5)), cuspidal(81, E(5, 4), 2), cuspidal(82, E(5), 2), cuspidal(83, -(E(5, 4))), cuspidal(84, -(E(5))), cuspidal(85, -(E(5, 4)), 2), cuspidal(86, -(E(5)), 2), cuspidal(87, E(3), 2), cuspidal(88, E(3, 2), 2), cuspidal(89, E(3), 3), cuspidal(90, E(3, 2), 3), cuspidal(91, E(5, 4), 3), cuspidal(92, E(5), 3), cuspidal(93, E(5, 4), 4), cuspidal(94, E(5), 4), cuspidal(95, E(15, 2)), cuspidal(96, E(15, 13)), cuspidal(97, E(15, 8)), cuspidal(98, E(15, 7)), cuspidal(99, E(5, 4), 5), cuspidal(100, E(5), 5), cuspidal(101, E(5, 4), 6), cuspidal(102, E(5), 6), cuspidal(103, -1, 7), cuspidal(104, 1, 5)], :families => [Family("C1", [1]), Family("C1", [2]), Family("C1", [27]), Family("C1", [28]), Family("C1", [31], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [32], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:Dihedral])(5), [3, 5, 35, 36], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:Dihedral])(5), [11, 13, 37, 38], Dict{Symbol, Any}(:ennola => 1)), Family(((CHEVIE[:families])[:Dihedral])(5), [12, 14, 44, 43], Dict{Symbol, Any}(:ennola => 1)), Family(((CHEVIE[:families])[:Dihedral])(5), [4, 6, 45, 46], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [18, 20, 40, 39], Dict{Symbol, Any}(:cospecial => 2, :ennola => 3)), Family(((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [21, 19, 42, 41], Dict{Symbol, Any}(:cospecial => 2, :ennola => -3)), Family("HS4", [15, 9, 10, 7, 8, 22, 16, 17, 26, 25, 24, 23, 29, 30, 33, 34, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104], Dict{Symbol, Any}(:ennola => 29))], :a => [0, 60, 1, 31, 1, 31, 6, 6, 6, 6, 2, 22, 2, 22, 6, 6, 6, 3, 18, 3, 18, 6, 6, 6, 6, 6, 4, 16, 6, 6, 5, 15, 6, 6, 1, 1, 2, 2, 3, 3, 18, 18, 22, 22, 31, 31, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], :A => [0, 60, 29, 59, 29, 59, 54, 54, 54, 54, 38, 58, 38, 58, 54, 54, 54, 42, 57, 42, 57, 54, 54, 54, 54, 54, 44, 56, 54, 54, 45, 55, 54, 54, 29, 29, 38, 38, 42, 42, 57, 57, 58, 58, 59, 59, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54]) end) chevieset(:H4, :KLeftCellRepresentatives, [Dict{Symbol, Any}(:character => [1], :duflo => [1, 2, 3, 4], :reps => ""), Dict{Symbol, Any}(:character => [2], :duflo => [61, 62, 63, 64], :reps => ""), Dict{Symbol, Any}(:character => [5, 3], :duflo => [1, 2, 8, 64], :reps => [[16, 2, 3, 87]]), Dict{Symbol, Any}(:character => [6, 4], :duflo => [1, 66, 63, 64], :reps => [[9, 65, 71, 64]]), Dict{Symbol, Any}(:character => [13, 11], :duflo => [2, 1, 27, 103], :reps => [[3, 20, 1, 110]]), Dict{Symbol, Any}(:character => [14, 12], :duflo => [1, 66, 68, 4], :reps => [[9, 65, 76, 4]]), Dict{Symbol, Any}(:character => [20, 18], :duflo => [1, 2, 32, 120], :reps => [[23, 3, 2, 116], [24, 23, 112, 2], [33, 1, 110, 32]]), Dict{Symbol, Any}(:character => [20, 18], :duflo => [19, 85, 10, 20], :reps => [[12, 6, 10, 109], [13, 20, 97, 6], [19, 12, 80, 70]]), Dict{Symbol, Any}(:character => [21, 19], :duflo => [10, 63, 62, 94], :reps => [[15, 62, 73, 83], [15, 77, 13, 94], [21, 85, 5, 83]]), Dict{Symbol, Any}(:character => [21, 19], :duflo => [19, 85, 10, 88], :reps => [[13, 81, 6, 76], [17, 67, 69, 88], [19, 69, 70, 76]]), Dict{Symbol, Any}(:character => [27], :duflo => [2, 1, 24, 119], :reps => [[1, 35, 120, 39], [38, 2, 116, 24]]), Dict{Symbol, Any}(:character => [27], :duflo => [12, 21, 102, 30], :reps => [[1, 12, 25, 119], [35, 1, 107, 25]]), Dict{Symbol, Any}(:character => [27], :duflo => [33, 11, 115, 18], :reps => [[2, 30, 74, 100], [2, 30, 114, 40]]), Dict{Symbol, Any}(:character => [28], :duflo => [1, 76, 4, 3], :reps => [[27, 72, 73, 86], [28, 92, 14, 86]]), Dict{Symbol, Any}(:character => [28], :duflo => [36, 117, 54, 74], :reps => [[24, 102, 21, 18], [46, 110, 34, 100]]), Dict{Symbol, Any}(:character => [28], :duflo => [40, 102, 30, 96], :reps => [[19, 94, 16, 10], [32, 68, 77, 96]]), Dict{Symbol, Any}(:character => [31], :duflo => [1, 2, 3, 100], :reps => [[2, 28, 119, 44], [3, 39, 117, 1], [31, 1, 107, 3]]), Dict{Symbol, Any}(:character => [31], :duflo => [1, 31, 119, 46], :reps => [[1, 31, 85, 106], [15, 30, 114, 12], [34, 12, 116, 15]]), Dict{Symbol, Any}(:character => [31], :duflo => [1, 35, 106, 4], :reps => [[4, 17, 1, 117], [17, 16, 115, 48], [40, 4, 110, 1]]), Dict{Symbol, Any}(:character => [31], :duflo => [34, 107, 3, 52], :reps => [[3, 39, 116, 12], [6, 24, 73, 112], [6, 24, 119, 52]]), Dict{Symbol, Any}(:character => [32], :duflo => [2, 1, 79, 64], :reps => [[25, 97, 20, 1], [26, 64, 71, 101], [34, 96, 29, 101]]), Dict{Symbol, Any}(:character => [32], :duflo => [27, 106, 26, 13], :reps => [[4, 13, 92, 66], [34, 66, 70, 103], [42, 107, 36, 103]]), Dict{Symbol, Any}(:character => [32], :duflo => [31, 62, 63, 113], :reps => [[23, 10, 107, 62], [38, 117, 39, 10], [42, 105, 41, 113]]), Dict{Symbol, Any}(:character => [32], :duflo => [45, 109, 44, 110], :reps => [[16, 17, 102, 69], [32, 115, 36, 17], [37, 69, 67, 110]]), Dict{Symbol, Any}(:character => [34, 34, 33, 30, 29, 26, 25, 24, 23, 22, 10, 9], :duflo => [14, 64, 63, 62], :reps => [[5, 28, 100, 86], [5, 28, 117, 26], [5, 32, 105, 64], [10, 26, 90, 101], [10, 26, 120, 41], [13, 29, 110, 75], [13, 29, 118, 15], [15, 30, 102, 89], [15, 30, 120, 29], [16, 15, 111, 13], [16, 31, 112, 63], [17, 16, 88, 99], [17, 16, 117, 39], [17, 18, 92, 80], [17, 18, 108, 20], [18, 15, 80, 102], [18, 15, 116, 42], [20, 13, 77, 110], [20, 13, 119, 50], [24, 63, 62, 78], [24, 63, 82, 18], [26, 17, 101, 88], [26, 17, 119, 28], [28, 20, 103, 77], [28, 20, 116, 17], [29, 10, 91, 90], [29, 10, 114, 30], [30, 5, 89, 100], [30, 5, 118, 40], [33, 62, 78, 70], [33, 62, 92, 10], [36, 104, 5, 13], [37, 75, 98, 13], [37, 111, 13, 26], [41, 75, 64, 102], [41, 75, 106, 42], [42, 63, 113, 16], [42, 115, 16, 41], [43, 64, 109, 5], [43, 112, 5, 42], [45, 70, 80, 90], [45, 70, 103, 30], [46, 78, 70, 80], [46, 78, 91, 20], [47, 88, 99, 26], [47, 117, 26, 15], [49, 77, 110, 28], [49, 119, 28, 29], [50, 86, 63, 101], [50, 86, 105, 41], [52, 80, 102, 17], [53, 89, 100, 15], [53, 118, 15, 28], [55, 90, 101, 29]]), Dict{Symbol, Any}(:character => [34, 34, 33, 30, 29, 26, 25, 24, 23, 22, 10, 9], :duflo => [31, 62, 92, 14], :reps => [[4, 21, 104, 5], [4, 40, 115, 62], [5, 30, 103, 81], [5, 30, 117, 21], [11, 20, 97, 78], [11, 20, 113, 18], [11, 33, 109, 68], [14, 21, 88, 101], [14, 21, 119, 41], [15, 18, 82, 107], [15, 18, 120, 47], [18, 25, 107, 80], [18, 25, 118, 20], [20, 28, 106, 85], [20, 28, 119, 25], [21, 22, 101, 90], [21, 22, 120, 30], [22, 11, 90, 97], [22, 11, 117, 37], [25, 4, 80, 98], [25, 4, 113, 38], [25, 14, 93, 88], [25, 14, 114, 28], [26, 96, 11, 5], [27, 68, 62, 73], [28, 5, 85, 103], [28, 5, 118, 43], [30, 15, 100, 82], [30, 15, 116, 22], [31, 62, 73, 74], [34, 81, 89, 5], [34, 104, 5, 18], [39, 80, 98, 18], [39, 113, 18, 21], [41, 62, 110, 4], [41, 112, 4, 47], [42, 73, 74, 75], [42, 73, 93, 15], [43, 78, 62, 107], [43, 78, 109, 47], [46, 68, 111, 11], [46, 115, 11, 41], [47, 81, 68, 101], [47, 81, 108, 41], [48, 74, 75, 88], [48, 74, 100, 28], [49, 75, 88, 82], [49, 75, 106, 22], [50, 90, 97, 21], [50, 117, 21, 20], [51, 85, 103, 20], [51, 118, 20, 30], [52, 82, 107, 30], [55, 88, 101, 25]]), Dict{Symbol, Any}(:character => [34, 34, 33, 33, 30, 29, 26, 25, 24, 23, 22, 17, 16, 15], :duflo => [19, 97, 52, 86], :reps => [[1, 12, 64, 102], [1, 12, 106, 42], [1, 35, 106, 85], [1, 35, 119, 25], [7, 1, 88, 8], [7, 36, 111, 74], [7, 36, 120, 14], [8, 25, 107, 1], [12, 21, 77, 110], [12, 21, 119, 50], [14, 25, 91, 96], [14, 25, 118, 36], [16, 7, 87, 81], [16, 7, 102, 21], [16, 31, 108, 79], [16, 31, 118, 19], [17, 16, 94, 87], [17, 16, 115, 27], [17, 26, 104, 72], [18, 17, 95, 94], [18, 17, 119, 34], [19, 8, 76, 105], [19, 8, 115, 45], [19, 14, 86, 91], [21, 14, 114, 7], [25, 18, 96, 95], [25, 18, 120, 35], [26, 7, 72, 111], [26, 7, 116, 51], [27, 19, 109, 76], [27, 19, 117, 16], [31, 1, 79, 106], [31, 1, 117, 46], [32, 102, 17, 1], [34, 12, 103, 77], [35, 1, 107, 64], [38, 76, 105, 27], [38, 115, 27, 25], [40, 85, 90, 1], [40, 107, 1, 27], [41, 75, 74, 66], [43, 74, 66, 91], [43, 74, 97, 31], [44, 66, 91, 78], [44, 66, 108, 18], [45, 77, 74, 94], [45, 77, 110, 34], [45, 119, 34, 14], [46, 74, 100, 7], [46, 114, 7, 34], [48, 72, 111, 17], [48, 116, 17, 36], [49, 85, 72, 96], [49, 85, 103, 36], [50, 78, 79, 95], [50, 78, 109, 35], [51, 79, 106, 16], [51, 117, 16, 35], [54, 95, 94, 25], [56, 91, 96, 19], [57, 96, 95, 14]]), Dict{Symbol, Any}(:character => [34, 34, 33, 33, 30, 30, 29, 29, 26, 25, 24, 23, 17, 16, 8, 7], :duflo => [1, 35, 102, 64], :reps => [[1, 7, 63, 97], [1, 7, 100, 37], [1, 31, 100, 89], [1, 31, 118, 29], [2, 16, 64, 111], [2, 16, 113, 51], [2, 38, 113, 70], [2, 38, 119, 10], [7, 23, 80, 107], [7, 23, 118, 47], [10, 29, 93, 98], [10, 29, 120, 38], [11, 2, 77, 83], [11, 2, 97, 23], [11, 33, 105, 86], [11, 33, 120, 26], [13, 20, 91, 96], [13, 20, 118, 36], [13, 22, 95, 76], [16, 17, 73, 112], [16, 17, 119, 52], [17, 26, 112, 71], [17, 26, 117, 11], [20, 11, 96, 77], [20, 11, 111, 17], [20, 28, 110, 67], [22, 11, 76, 105], [22, 11, 115, 45], [23, 10, 109, 2], [26, 10, 88, 93], [26, 10, 114, 33], [28, 2, 67, 113], [28, 2, 116, 53], [29, 13, 98, 91], [29, 13, 119, 31], [31, 1, 104, 63], [31, 16, 103, 73], [33, 1, 86, 100], [33, 1, 117, 40], [34, 71, 101, 17], [34, 111, 17, 29], [36, 7, 102, 80], [38, 2, 109, 64], [38, 71, 64, 105], [38, 71, 108, 45], [39, 104, 1, 17], [40, 70, 99, 2], [40, 109, 2, 36], [41, 80, 70, 96], [41, 80, 107, 36], [41, 118, 36, 10], [42, 70, 76, 93], [42, 70, 103, 33], [43, 64, 107, 1], [43, 110, 1, 45], [45, 67, 113, 20], [45, 116, 20, 38], [47, 73, 86, 91], [47, 73, 112, 31], [47, 119, 31, 26], [48, 82, 70, 76], [49, 91, 96, 29], [50, 76, 105, 13], [52, 89, 67, 98], [52, 89, 102, 38], [53, 86, 100, 11], [53, 117, 11, 31], [56, 93, 98, 26], [57, 98, 91, 10]])]) diff --git a/src/tbl/weyle7.jl b/src/tbl/weyle7.jl index 84555e17..24d8c3fc 100644 --- a/src/tbl/weyle7.jl +++ b/src/tbl/weyle7.jl @@ -131,7 +131,7 @@ chevieset(:E7, :DecompositionMatrix, function (p,) end end) chevieset(:E7, :UnipotentCharacters, function () - return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "E", :indices => 1:7, :rank => 7), :levi => [], :eigenvalue => 1, :parameterExponents => [1, 1, 1, 1, 1, 1, 1], :cuspidalName => "", :charNumbers => 1:60), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "B", :indices => [7, 6, 1], :cartanType => 1, :rank => 3), :levi => 2:5, :eigenvalue => -1, :parameterExponents => [1, 4, 4], :cuspidalName => "D_4", :charNumbers => [67, 66, 64, 61, 69, 65, 68, 62, 70, 63]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [7], :rank => 1), :levi => 1:6, :eigenvalue => E(3), :parameterExponents => [9], :cuspidalName => "E_6[\\zeta_3]", :charNumbers => [71, 72]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [7], :rank => 1), :levi => 1:6, :eigenvalue => E(3, 2), :parameterExponents => [9], :cuspidalName => "E_6[\\zeta_3^2]", :charNumbers => [73, 74]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:7, :eigenvalue => -(E(4)), :parameterExponents => [], :cuspidalName => "E_7[-i]", :charNumbers => [75], :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:7, :eigenvalue => E(4), :parameterExponents => [], :cuspidalName => "E_7[i]", :charNumbers => [76], :qEigen => 1 // 2)], :families => [Family("C1", [1]), Family("C1", [2], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [3]), Family("C1", [4], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [9]), Family("C1", [10], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [11]), Family("C1", [12], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [25]), Family("C1", [26], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [27]), Family("C1", [28], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [31]), Family("C1", [32], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [35]), Family("C1", [36], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [37]), Family("C1", [38], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [39]), Family("C1", [40], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [41]), Family("C1", [42], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [53]), Family("C1", [54], Dict{Symbol, Any}(:ennola => -1)), Family("C2", [18, 15, 7, 70], Dict{Symbol, Any}(:ennola => -4)), Family("C2", [29, 6, 24, 63], Dict{Symbol, Any}(:ennola => 4)), Family("C2", [55, 44, 33, 65], Dict{Symbol, Any}(:ennola => 3)), Family("C2", [57, 21, 52, 69], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [58, 22, 51, 62], Dict{Symbol, Any}(:ennola => -2)), Family("C2", [56, 43, 34, 66], Dict{Symbol, Any}(:ennola => -3)), Family("C2", [30, 5, 23, 67], Dict{Symbol, Any}(:ennola => -4)), Family("C2", [17, 16, 8, 61], Dict{Symbol, Any}(:ennola => 4)), Family("C'2", [60, 59, 76, 75], Dict{Symbol, Any}(:ennola => 3)), Family("S3", [50, 47, 20, 46, 14, 68, 72, 74], Dict{Symbol, Any}(:ennola => -5)), Family("S3", [49, 48, 19, 45, 13, 64, 71, 73], Dict{Symbol, Any}(:ennola => 5))], :a => [0, 63, 46, 1, 25, 4, 3, 30, 36, 3, 2, 37, 16, 7, 3, 30, 30, 3, 16, 7, 10, 13, 25, 4, 6, 21, 12, 15, 4, 25, 6, 21, 8, 15, 22, 5, 20, 7, 6, 21, 10, 13, 15, 8, 16, 7, 7, 16, 16, 7, 13, 10, 14, 9, 8, 15, 10, 13, 11, 11, 30, 13, 4, 16, 8, 15, 25, 7, 10, 3, 16, 7, 16, 7, 11, 11], :A => [0, 63, 62, 17, 59, 38, 33, 60, 60, 27, 26, 61, 56, 47, 33, 60, 60, 33, 56, 47, 50, 53, 59, 38, 42, 57, 48, 51, 38, 59, 42, 57, 48, 55, 58, 41, 56, 43, 42, 57, 50, 53, 55, 48, 56, 47, 47, 56, 56, 47, 53, 50, 54, 49, 48, 55, 50, 53, 52, 52, 60, 53, 38, 56, 48, 55, 59, 47, 50, 33, 56, 47, 56, 47, 52, 52]) + return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "E", :indices => 1:7, :rank => 7), :levi => [], :eigenvalue => 1, :parameterExponents => [1, 1, 1, 1, 1, 1, 1], :cuspidalName => "", :charNumbers => 1:60), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "B", :indices => [7, 6, 1], :cartanType => 1, :rank => 3), :levi => 2:5, :eigenvalue => -1, :parameterExponents => [1, 4, 4], :cuspidalName => "D_4", :charNumbers => [67, 66, 64, 61, 69, 65, 68, 62, 70, 63]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [7], :rank => 1), :levi => 1:6, :eigenvalue => E(3), :parameterExponents => [9], :cuspidalName => "E_6[\\zeta_3]", :charNumbers => [71, 72]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [7], :rank => 1), :levi => 1:6, :eigenvalue => E(3, 2), :parameterExponents => [9], :cuspidalName => "E_6[\\zeta_3^2]", :charNumbers => [73, 74]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:7, :eigenvalue => -(E(4)), :parameterExponents => [], :cuspidalName => "E_7[-i]", :charNumbers => [75], :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:7, :eigenvalue => E(4), :parameterExponents => [], :cuspidalName => "E_7[i]", :charNumbers => [76], :qEigen => 1 // 2)], :families => [Family("C1", [1]), Family("C1", [2], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [3]), Family("C1", [4], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [9]), Family("C1", [10], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [11]), Family("C1", [12], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [25]), Family("C1", [26], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [27]), Family("C1", [28], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [31]), Family("C1", [32], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [35]), Family("C1", [36], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [37]), Family("C1", [38], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [39]), Family("C1", [40], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [41]), Family("C1", [42], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [53]), Family("C1", [54], Dict{Symbol, Any}(:ennola => -1)), Family("C2", [18, 15, 7, 70], Dict{Symbol, Any}(:ennola => -4)), Family("C2", [29, 6, 24, 63], Dict{Symbol, Any}(:ennola => 4)), Family("C2", [55, 44, 33, 65], Dict{Symbol, Any}(:ennola => 3)), Family("C2", [57, 21, 52, 69], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [58, 22, 51, 62], Dict{Symbol, Any}(:ennola => -2)), Family("C2", [56, 43, 34, 66], Dict{Symbol, Any}(:ennola => -3)), Family("C2", [30, 5, 23, 67], Dict{Symbol, Any}(:ennola => -4)), Family("C2", [17, 16, 8, 61], Dict{Symbol, Any}(:ennola => 4)), Family("LTQZ2", [60, 59, 76, 75], Dict{Symbol, Any}(:cospecial => 2, :ennola => 3)), Family("S3", [50, 47, 20, 46, 14, 68, 72, 74], Dict{Symbol, Any}(:ennola => -5)), Family("S3", [49, 48, 19, 45, 13, 64, 71, 73], Dict{Symbol, Any}(:ennola => 5))], :a => [0, 63, 46, 1, 25, 4, 3, 30, 36, 3, 2, 37, 16, 7, 3, 30, 30, 3, 16, 7, 10, 13, 25, 4, 6, 21, 12, 15, 4, 25, 6, 21, 8, 15, 22, 5, 20, 7, 6, 21, 10, 13, 15, 8, 16, 7, 7, 16, 16, 7, 13, 10, 14, 9, 8, 15, 10, 13, 11, 11, 30, 13, 4, 16, 8, 15, 25, 7, 10, 3, 16, 7, 16, 7, 11, 11], :A => [0, 63, 62, 17, 59, 38, 33, 60, 60, 27, 26, 61, 56, 47, 33, 60, 60, 33, 56, 47, 50, 53, 59, 38, 42, 57, 48, 51, 38, 59, 42, 57, 48, 55, 58, 41, 56, 43, 42, 57, 50, 53, 55, 48, 56, 47, 47, 56, 56, 47, 53, 50, 54, 49, 48, 55, 50, 53, 52, 52, 60, 53, 38, 56, 48, 55, 59, 47, 50, 33, 56, 47, 56, 47, 52, 52]) end) chevieset(:E7, :UnipotentClasses, function (p,) local uc, Z, c, class diff --git a/src/tbl/weyle8.jl b/src/tbl/weyle8.jl index 829de76d..5317ad1f 100644 --- a/src/tbl/weyle8.jl +++ b/src/tbl/weyle8.jl @@ -116,7 +116,7 @@ chevieset(:E8, :DecompositionMatrix, function (p,) end end) chevieset(:E8, :UnipotentCharacters, function () - return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "E", :indices => 1:8, :rank => 8), :levi => [], :eigenvalue => 1, :parameterExponents => [1, 1, 1, 1, 1, 1, 1, 1], :cuspidalName => "", :charNumbers => 1:112), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [8], :rank => 1), :levi => 1:7, :eigenvalue => -(E(4)), :parameterExponents => [15], :cuspidalName => "E_7[-i]", :qEigen => 1 // 2, :charNumbers => [114, 113]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [8], :rank => 1), :levi => 1:7, :eigenvalue => E(4), :parameterExponents => [15], :cuspidalName => "E_7[i]", :qEigen => 1 // 2, :charNumbers => [116, 115]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "F", :indices => [8, 7, 6, 1], :rank => 4), :levi => 2:5, :eigenvalue => -1, :parameterExponents => [1, 1, 4, 4], :cuspidalName => "D_4", :charNumbers => [117, 119, 118, 120, 126, 123, 125, 124, 131, 139, 141, 140, 138, 132, 133, 121, 128, 130, 129, 127, 135, 136, 134, 137, 122]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "G", :indices => [8, 7], :rank => 2), :levi => 1:6, :eigenvalue => E(3), :parameterExponents => [1, 9], :cuspidalName => "E_6[\\zeta_3]", :charNumbers => [142, 145, 143, 144, 152, 153]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "G", :indices => [8, 7], :rank => 2), :levi => 1:6, :eigenvalue => E(3, 2), :parameterExponents => [1, 9], :cuspidalName => "E_6[\\zeta_3^2]", :charNumbers => [148, 151, 149, 150, 146, 147]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => -1, :parameterExponents => [], :cuspidalName => "E_8[-1]", :charNumbers => [154]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => -(E(3, 2)), :parameterExponents => [], :cuspidalName => "E_8[-\\zeta_3^2]", :charNumbers => [155]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => -(E(3)), :parameterExponents => [], :cuspidalName => "E_8[-\\zeta_3]", :charNumbers => [156]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => -(E(4)), :parameterExponents => [], :cuspidalName => "E_8[-i]", :charNumbers => [157]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(3, 2), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_3^2]", :charNumbers => [158]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(3), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_3]", :charNumbers => [159]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(5, 4), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_5^4]", :charNumbers => [160]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(5, 3), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_5^3]", :charNumbers => [161]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(5, 2), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_5^2]", :charNumbers => [162]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(5), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_5]", :charNumbers => [163]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(4), :parameterExponents => [], :cuspidalName => "E_8[i]", :charNumbers => [164]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => 1, :parameterExponents => [], :cuspidalName => "E_8^2[1]", :charNumbers => [165]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => 1, :parameterExponents => [], :cuspidalName => "E_8[1]", :charNumbers => [166])], :families => [Family("C1", [1]), Family("C1", [2]), Family("C1", [5]), Family("C1", [6]), Family("C1", [22]), Family("C1", [23]), Family("C1", [24]), Family("C1", [25]), Family("C1", [39]), Family("C1", [57]), Family("C1", [58]), Family("C1", [66]), Family("C1", [67]), Family("C1", [68], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [69], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [81], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [82], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [100], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [101], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [107], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [108], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [109], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [110], Dict{Symbol, Any}(:ennola => -1)), Family("C2", [72, 10, 3, 117], Dict{Symbol, Any}(:ennola => -4)), Family("C2", [15, 8, 74, 125], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [29, 77, 18, 118], Dict{Symbol, Any}(:ennola => 3)), Family("C2", [54, 35, 89, 139], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [51, 91, 84, 129], Dict{Symbol, Any}(:ennola => 4)), Family("C2", [64, 32, 102, 126], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [97, 27, 48, 140], Dict{Symbol, Any}(:ennola => -4)), Family("C2", [111, 60, 95, 135], Dict{Symbol, Any}(:ennola => -3)), Family("C2", [112, 61, 96, 136], Dict{Symbol, Any}(:ennola => -3)), Family("C2", [65, 33, 103, 123], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [98, 28, 49, 141], Dict{Symbol, Any}(:ennola => -4)), Family("C2", [52, 92, 85, 130], Dict{Symbol, Any}(:ennola => 4)), Family("C2", [55, 36, 90, 138], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [30, 78, 19, 119], Dict{Symbol, Any}(:ennola => 3)), Family("C2", [16, 9, 75, 124], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [73, 11, 4, 120], Dict{Symbol, Any}(:ennola => -4)), Family("C'2", [105, 62, 115, 113], Dict{Symbol, Any}(:ennola => 4)), Family("C'2", [63, 106, 116, 114], Dict{Symbol, Any}(:ennola => -4)), Family("S3", [93, 40, 79, 86, 70, 128, 142, 148], Dict{Symbol, Any}(:ennola => -5)), Family("S3", [43, 37, 13, 45, 20, 134, 143, 149], Dict{Symbol, Any}(:ennola => 1)), Family("S3", [44, 38, 14, 46, 21, 137, 144, 150], Dict{Symbol, Any}(:ennola => 1)), Family("S3", [94, 41, 80, 87, 71, 127, 145, 151], Dict{Symbol, Any}(:ennola => -5)), Family("S5", [53, 165, 7, 59, 56, 31, 34, 104, 154, 121, 76, 133, 99, 50, 166, 12, 42, 122, 47, 26, 152, 159, 146, 158, 88, 132, 153, 156, 147, 155, 83, 131, 164, 157, 17, 163, 162, 161, 160], Dict{Symbol, Any}(:ennola => 2))], :a => [0, 120, 3, 63, 2, 74, 16, 4, 52, 3, 63, 16, 8, 32, 4, 52, 16, 6, 42, 8, 32, 12, 36, 6, 46, 16, 13, 25, 6, 42, 16, 12, 24, 16, 10, 30, 8, 32, 20, 7, 37, 16, 8, 32, 8, 32, 16, 13, 25, 16, 10, 28, 16, 10, 30, 16, 14, 22, 16, 15, 21, 11, 26, 12, 24, 14, 22, 1, 91, 7, 37, 3, 63, 4, 52, 16, 6, 42, 7, 37, 5, 47, 16, 10, 28, 7, 37, 16, 10, 30, 10, 28, 7, 37, 15, 21, 13, 25, 16, 9, 31, 12, 24, 16, 11, 26, 15, 21, 13, 23, 15, 21, 11, 26, 11, 26, 3, 6, 42, 63, 16, 16, 24, 52, 4, 12, 37, 7, 10, 28, 16, 16, 16, 8, 15, 21, 32, 30, 10, 13, 25, 7, 8, 32, 37, 16, 16, 7, 8, 32, 37, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16], :A => [0, 120, 57, 117, 46, 118, 104, 68, 116, 57, 117, 104, 88, 112, 68, 116, 104, 78, 114, 88, 112, 84, 108, 74, 114, 104, 95, 107, 78, 114, 104, 96, 108, 104, 90, 110, 88, 112, 100, 83, 113, 104, 88, 112, 88, 112, 104, 95, 107, 104, 92, 110, 104, 90, 110, 104, 98, 106, 104, 99, 105, 94, 109, 96, 108, 98, 106, 29, 119, 83, 113, 57, 117, 68, 116, 104, 78, 114, 83, 113, 73, 115, 104, 92, 110, 83, 113, 104, 90, 110, 92, 110, 83, 113, 99, 105, 95, 107, 104, 89, 111, 96, 108, 104, 94, 109, 99, 105, 97, 107, 99, 105, 94, 109, 94, 109, 57, 78, 114, 117, 104, 104, 108, 116, 68, 96, 113, 83, 92, 110, 104, 104, 104, 88, 99, 105, 112, 110, 90, 95, 107, 83, 88, 112, 113, 104, 104, 83, 88, 112, 113, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104]) + return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "E", :indices => 1:8, :rank => 8), :levi => [], :eigenvalue => 1, :parameterExponents => [1, 1, 1, 1, 1, 1, 1, 1], :cuspidalName => "", :charNumbers => 1:112), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [8], :rank => 1), :levi => 1:7, :eigenvalue => -(E(4)), :parameterExponents => [15], :cuspidalName => "E_7[-i]", :qEigen => 1 // 2, :charNumbers => [114, 113]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [8], :rank => 1), :levi => 1:7, :eigenvalue => E(4), :parameterExponents => [15], :cuspidalName => "E_7[i]", :qEigen => 1 // 2, :charNumbers => [116, 115]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "F", :indices => [8, 7, 6, 1], :rank => 4), :levi => 2:5, :eigenvalue => -1, :parameterExponents => [1, 1, 4, 4], :cuspidalName => "D_4", :charNumbers => [117, 119, 118, 120, 126, 123, 125, 124, 131, 139, 141, 140, 138, 132, 133, 121, 128, 130, 129, 127, 135, 136, 134, 137, 122]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "G", :indices => [8, 7], :rank => 2), :levi => 1:6, :eigenvalue => E(3), :parameterExponents => [1, 9], :cuspidalName => "E_6[\\zeta_3]", :charNumbers => [142, 145, 143, 144, 152, 153]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "G", :indices => [8, 7], :rank => 2), :levi => 1:6, :eigenvalue => E(3, 2), :parameterExponents => [1, 9], :cuspidalName => "E_6[\\zeta_3^2]", :charNumbers => [148, 151, 149, 150, 146, 147]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => -1, :parameterExponents => [], :cuspidalName => "E_8[-1]", :charNumbers => [154]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => -(E(3, 2)), :parameterExponents => [], :cuspidalName => "E_8[-\\zeta_3^2]", :charNumbers => [155]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => -(E(3)), :parameterExponents => [], :cuspidalName => "E_8[-\\zeta_3]", :charNumbers => [156]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => -(E(4)), :parameterExponents => [], :cuspidalName => "E_8[-i]", :charNumbers => [157]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(3, 2), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_3^2]", :charNumbers => [158]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(3), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_3]", :charNumbers => [159]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(5, 4), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_5^4]", :charNumbers => [160]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(5, 3), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_5^3]", :charNumbers => [161]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(5, 2), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_5^2]", :charNumbers => [162]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(5), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_5]", :charNumbers => [163]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(4), :parameterExponents => [], :cuspidalName => "E_8[i]", :charNumbers => [164]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => 1, :parameterExponents => [], :cuspidalName => "E_8^2[1]", :charNumbers => [165]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => 1, :parameterExponents => [], :cuspidalName => "E_8[1]", :charNumbers => [166])], :families => [Family("C1", [1]), Family("C1", [2]), Family("C1", [5]), Family("C1", [6]), Family("C1", [22]), Family("C1", [23]), Family("C1", [24]), Family("C1", [25]), Family("C1", [39]), Family("C1", [57]), Family("C1", [58]), Family("C1", [66]), Family("C1", [67]), Family("C1", [68], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [69], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [81], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [82], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [100], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [101], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [107], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [108], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [109], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [110], Dict{Symbol, Any}(:ennola => -1)), Family("C2", [72, 10, 3, 117], Dict{Symbol, Any}(:ennola => -4)), Family("C2", [15, 8, 74, 125], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [29, 77, 18, 118], Dict{Symbol, Any}(:ennola => 3)), Family("C2", [54, 35, 89, 139], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [51, 91, 84, 129], Dict{Symbol, Any}(:ennola => 4)), Family("C2", [64, 32, 102, 126], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [97, 27, 48, 140], Dict{Symbol, Any}(:ennola => -4)), Family("C2", [111, 60, 95, 135], Dict{Symbol, Any}(:ennola => -3)), Family("C2", [112, 61, 96, 136], Dict{Symbol, Any}(:ennola => -3)), Family("C2", [65, 33, 103, 123], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [98, 28, 49, 141], Dict{Symbol, Any}(:ennola => -4)), Family("C2", [52, 92, 85, 130], Dict{Symbol, Any}(:ennola => 4)), Family("C2", [55, 36, 90, 138], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [30, 78, 19, 119], Dict{Symbol, Any}(:ennola => 3)), Family("C2", [16, 9, 75, 124], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [73, 11, 4, 120], Dict{Symbol, Any}(:ennola => -4)), Family("LTQZ2", [105, 62, 115, 113], Dict{Symbol, Any}(:cospecial => 2, :ennola => 4)), Family("LTQZ2", [63, 106, 116, 114], Dict{Symbol, Any}(:cospecial => 2, :ennola => -4)), Family("S3", [93, 40, 79, 86, 70, 128, 142, 148], Dict{Symbol, Any}(:ennola => -5)), Family("S3", [43, 37, 13, 45, 20, 134, 143, 149], Dict{Symbol, Any}(:ennola => 1)), Family("S3", [44, 38, 14, 46, 21, 137, 144, 150], Dict{Symbol, Any}(:ennola => 1)), Family("S3", [94, 41, 80, 87, 71, 127, 145, 151], Dict{Symbol, Any}(:ennola => -5)), Family("S5", [53, 165, 7, 59, 56, 31, 34, 104, 154, 121, 76, 133, 99, 50, 166, 12, 42, 122, 47, 26, 152, 159, 146, 158, 88, 132, 153, 156, 147, 155, 83, 131, 164, 157, 17, 163, 162, 161, 160], Dict{Symbol, Any}(:ennola => 2))], :a => [0, 120, 3, 63, 2, 74, 16, 4, 52, 3, 63, 16, 8, 32, 4, 52, 16, 6, 42, 8, 32, 12, 36, 6, 46, 16, 13, 25, 6, 42, 16, 12, 24, 16, 10, 30, 8, 32, 20, 7, 37, 16, 8, 32, 8, 32, 16, 13, 25, 16, 10, 28, 16, 10, 30, 16, 14, 22, 16, 15, 21, 11, 26, 12, 24, 14, 22, 1, 91, 7, 37, 3, 63, 4, 52, 16, 6, 42, 7, 37, 5, 47, 16, 10, 28, 7, 37, 16, 10, 30, 10, 28, 7, 37, 15, 21, 13, 25, 16, 9, 31, 12, 24, 16, 11, 26, 15, 21, 13, 23, 15, 21, 11, 26, 11, 26, 3, 6, 42, 63, 16, 16, 24, 52, 4, 12, 37, 7, 10, 28, 16, 16, 16, 8, 15, 21, 32, 30, 10, 13, 25, 7, 8, 32, 37, 16, 16, 7, 8, 32, 37, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16], :A => [0, 120, 57, 117, 46, 118, 104, 68, 116, 57, 117, 104, 88, 112, 68, 116, 104, 78, 114, 88, 112, 84, 108, 74, 114, 104, 95, 107, 78, 114, 104, 96, 108, 104, 90, 110, 88, 112, 100, 83, 113, 104, 88, 112, 88, 112, 104, 95, 107, 104, 92, 110, 104, 90, 110, 104, 98, 106, 104, 99, 105, 94, 109, 96, 108, 98, 106, 29, 119, 83, 113, 57, 117, 68, 116, 104, 78, 114, 83, 113, 73, 115, 104, 92, 110, 83, 113, 104, 90, 110, 92, 110, 83, 113, 99, 105, 95, 107, 104, 89, 111, 96, 108, 104, 94, 109, 99, 105, 97, 107, 99, 105, 94, 109, 94, 109, 57, 78, 114, 117, 104, 104, 108, 116, 68, 96, 113, 83, 92, 110, 104, 104, 104, 88, 99, 105, 112, 110, 90, 95, 107, 83, 88, 112, 113, 104, 104, 83, 88, 112, 113, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104]) end) chevieset(:E8, :UnipotentClasses, function (p,) local uc, Z, l, l1, i, s, c, class diff --git a/tools/tbl/cmp4_22.jl b/tools/tbl/cmp4_22.jl index 1e416f80..4612b4cb 100644 --- a/tools/tbl/cmp4_22.jl +++ b/tools/tbl/cmp4_22.jl @@ -808,7 +808,7 @@ chevieset(:G4_22, :UnipotentCharacters, function (ST,) end return res end - return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:2, :rank => 2, :ST => 14), :levi => [], :parameterExponents => [1, 1], :charNumbers => [1, 2, 3, 4, 5, 6, 8, 7, 9, 12, 11, 10, 15, 14, 13, 16, 20, 18, 21, 17, 19, 22, 23, 24], :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1], :rank => 1, :p => 6, :q => 1), :levi => [2], :parameterExponents => [[3, 4, 4, 0, 4, 4]], :charNumbers => [66, 26, 27, 79, 28, 25], :eigenvalue => J ^ 2, :cuspidalName => ImprimitiveCuspidalName([[], [0, 1], [0, 1]])), cuspidal(34, 1), cuspidal(35, 1, 2), cuspidal(29, -1), cuspidal(30, -1, 2), cuspidal(31, -1, 3), cuspidal(32, -1, 4), cuspidal(33, -1, 5), cuspidal(73, -1, 6), cuspidal(74, -1, 7), cuspidal(40, J), cuspidal(41, J, 2), cuspidal(42, J, 3), cuspidal(43, J, 4), cuspidal(50, J, 5), cuspidal(51, J, 6), cuspidal(36, J ^ 2), cuspidal(37, J ^ 2, 2), cuspidal(52, -J), cuspidal(53, -J, 2), cuspidal(38, -(J ^ 2)), cuspidal(39, -(J ^ 2), 2), cuspidal(54, -I), cuspidal(55, -I, 2), cuspidal(56, I, 3), cuspidal(57, I, 4), cuspidal(58, I), cuspidal(59, I, 2), cuspidal(60, -I, 3), cuspidal(61, -I, 4), cuspidal(46, E(8)), cuspidal(47, E(8, 3), 2), cuspidal(48, E(8, 3)), cuspidal(49, E(8), 2), cuspidal(69, E(9, 5), 1 // 3), cuspidal(70, E(9, 5), 2, 2 // 3), cuspidal(71, E(9, 8), 1 // 3), cuspidal(72, E(9, 8), 2, 2 // 3), cuspidal(67, E(9, 2), 1 // 3), cuspidal(68, E(9, 2), 2, 2 // 3), cuspidal(62, E(12)), cuspidal(63, E(12, 7), 2), cuspidal(64, E(12, 7)), cuspidal(65, E(12), 2), cuspidal(75, E(16, 5), 1 // 2), cuspidal(77, E(16, 13), 1 // 2), cuspidal(78, E(16, 15), 1 // 2), cuspidal(76, E(16, 7), 1 // 2), cuspidal(44, E(24, 11)), cuspidal(45, E(24, 17))], :families => [Family("C1", [1]), Family(conj(((CHEVIE[:families])[:X])(3)) * Family("G14"), [26, 37, 28, 39, 14, 3, 34, 18, 46, 48, 15, 13, 30, 29, 59, 60, 55, 56, 25, 36, 27, 38, 2, 11, 16, 35, 49, 47, 12, 10, 32, 31, 58, 61, 54, 57, 4, 17, 22, 33, 41, 40, 43, 42, 44, 45, 51, 50, 53, 52, 64, 65, 62, 63], Dict{Symbol, Any}(:signs => [-1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1], :ennola => 32)), Family(((CHEVIE[:families])[:X])(3), [23, 24, 66], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 2)), Family("Z9", [19, 70, 67, 20, 72, 71, 21, 68, 69], Dict{Symbol, Any}(:cospecial => 4, :ennola => 6)), Family(Dict{Symbol, Any}(:fourierMat => OnMatrices([[1, 1, 2, 1, 1, -(root(-2)), -(root(-2)), -(root(-2)), -(root(-2))], [1, 1, 2, 1, 1, root(-2), root(-2), root(-2), root(-2)], [2, 2, 0, -2, -2, 0, 0, 0, 0], [1, 1, -2, 1, 1, -(root(-2)), root(-2), -(root(-2)), root(-2)], [1, 1, -2, 1, 1, root(-2), -(root(-2)), root(-2), -(root(-2))], [-(root(-2)), root(-2), 0, -(root(-2)), root(-2), 0, -2 * E(4), 0, 2 * E(4)], [-(root(-2)), root(-2), 0, root(-2), -(root(-2)), -2 * E(4), 0, 2 * E(4), 0], [-(root(-2)), root(-2), 0, -(root(-2)), root(-2), 0, 2 * E(4), 0, -2 * E(4)], [-(root(-2)), root(-2), 0, root(-2), -(root(-2)), 2 * E(4), 0, -2 * E(4), 0]] // 4, perm"(4,5)"), :explanation => "everything to explain", :eigenvalues => [1, 1, 1, -1, -1, E(16, 5), E(16, 7), -(E(16, 5)), -(E(16, 7))], :qEigen => [0, 0, 0, 0, 0, 1 // 2, 1 // 2, 1 // 2, 1 // 2], :special => 2, :ennola => -4), [8, 9, 7, 73, 74, 75, 76, 77, 78]), Family(((CHEVIE[:families])[:X])(3), [5, 6, 79], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -2))], :a => [0, 1, 1, 1, 20, 20, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 1, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 20], :A => [0, 23, 23, 23, 28, 28, 27, 27, 27, 23, 23, 23, 23, 23, 23, 23, 23, 23, 26, 26, 26, 23, 25, 25, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 25, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 27, 28]) + return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:2, :rank => 2, :ST => 14), :levi => [], :parameterExponents => [1, 1], :charNumbers => [1, 2, 3, 4, 5, 6, 8, 7, 9, 12, 11, 10, 15, 14, 13, 16, 20, 18, 21, 17, 19, 22, 23, 24], :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1], :rank => 1, :p => 6, :q => 1), :levi => [2], :parameterExponents => [[3, 4, 4, 0, 4, 4]], :charNumbers => [66, 26, 27, 79, 28, 25], :eigenvalue => J ^ 2, :cuspidalName => ImprimitiveCuspidalName([[], [0, 1], [0, 1]])), cuspidal(34, 1), cuspidal(35, 1, 2), cuspidal(29, -1), cuspidal(30, -1, 2), cuspidal(31, -1, 3), cuspidal(32, -1, 4), cuspidal(33, -1, 5), cuspidal(73, -1, 6), cuspidal(74, -1, 7), cuspidal(40, J), cuspidal(41, J, 2), cuspidal(42, J, 3), cuspidal(43, J, 4), cuspidal(50, J, 5), cuspidal(51, J, 6), cuspidal(36, J ^ 2), cuspidal(37, J ^ 2, 2), cuspidal(52, -J), cuspidal(53, -J, 2), cuspidal(38, -(J ^ 2)), cuspidal(39, -(J ^ 2), 2), cuspidal(54, -I), cuspidal(55, -I, 2), cuspidal(56, I, 3), cuspidal(57, I, 4), cuspidal(58, I), cuspidal(59, I, 2), cuspidal(60, -I, 3), cuspidal(61, -I, 4), cuspidal(46, E(8)), cuspidal(47, E(8, 3), 2), cuspidal(48, E(8, 3)), cuspidal(49, E(8), 2), cuspidal(69, E(9, 5), 1 // 3), cuspidal(70, E(9, 5), 2, 2 // 3), cuspidal(71, E(9, 8), 1 // 3), cuspidal(72, E(9, 8), 2, 2 // 3), cuspidal(67, E(9, 2), 1 // 3), cuspidal(68, E(9, 2), 2, 2 // 3), cuspidal(62, E(12)), cuspidal(63, E(12, 7), 2), cuspidal(64, E(12, 7)), cuspidal(65, E(12), 2), cuspidal(75, E(16, 5), 1 // 2), cuspidal(77, E(16, 13), 1 // 2), cuspidal(78, E(16, 15), 1 // 2), cuspidal(76, E(16, 7), 1 // 2), cuspidal(44, E(24, 11)), cuspidal(45, E(24, 17))], :families => [Family("C1", [1]), Family(conj(((CHEVIE[:families])[:X])(3)) * Family("G14"), [26, 37, 28, 39, 14, 3, 34, 18, 46, 48, 15, 13, 30, 29, 59, 60, 55, 56, 25, 36, 27, 38, 2, 11, 16, 35, 49, 47, 12, 10, 32, 31, 58, 61, 54, 57, 4, 17, 22, 33, 41, 40, 43, 42, 44, 45, 51, 50, 53, 52, 64, 65, 62, 63], Dict{Symbol, Any}(:signs => [-1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1], :ennola => 32)), Family(((CHEVIE[:families])[:X])(3), [23, 24, 66], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 2)), Family(((CHEVIE[:families])[:TQZ])(3, E(3, 2)), [19, 20, 21, 68, 70, 72, 67, 71, 69], Dict{Symbol, Any}(:cospecial => 2, :ennola => 8)), Family(Dict{Symbol, Any}(:fourierMat => OnMatrices([[1, 1, 2, 1, 1, -(root(-2)), -(root(-2)), -(root(-2)), -(root(-2))], [1, 1, 2, 1, 1, root(-2), root(-2), root(-2), root(-2)], [2, 2, 0, -2, -2, 0, 0, 0, 0], [1, 1, -2, 1, 1, -(root(-2)), root(-2), -(root(-2)), root(-2)], [1, 1, -2, 1, 1, root(-2), -(root(-2)), root(-2), -(root(-2))], [-(root(-2)), root(-2), 0, -(root(-2)), root(-2), 0, -2 * E(4), 0, 2 * E(4)], [-(root(-2)), root(-2), 0, root(-2), -(root(-2)), -2 * E(4), 0, 2 * E(4), 0], [-(root(-2)), root(-2), 0, -(root(-2)), root(-2), 0, 2 * E(4), 0, -2 * E(4)], [-(root(-2)), root(-2), 0, root(-2), -(root(-2)), 2 * E(4), 0, -2 * E(4), 0]] // 4, perm"(4,5)"), :explanation => "everything to explain", :eigenvalues => [1, 1, 1, -1, -1, E(16, 5), E(16, 7), -(E(16, 5)), -(E(16, 7))], :qEigen => [0, 0, 0, 0, 0, 1 // 2, 1 // 2, 1 // 2, 1 // 2], :special => 2, :ennola => -4), [8, 9, 7, 73, 74, 75, 76, 77, 78]), Family(((CHEVIE[:families])[:X])(3), [5, 6, 79], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -2))], :a => [0, 1, 1, 1, 20, 20, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 1, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 20], :A => [0, 23, 23, 23, 28, 28, 27, 27, 27, 23, 23, 23, 23, 23, 23, 23, 23, 23, 26, 26, 26, 23, 25, 25, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 25, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 27, 28]) else return false end diff --git a/tools/tbl/cmplxg24.jl b/tools/tbl/cmplxg24.jl index ab434319..2b577c2e 100644 --- a/tools/tbl/cmplxg24.jl +++ b/tools/tbl/cmplxg24.jl @@ -89,7 +89,7 @@ chevieset(:G24, :HeckeRepresentation, function (para, roots, i) end) (CHEVIE[:families])[:X7] = Dict{Symbol, Any}(:name => "X7", :fourierMat => [[-1 // 2, 1 // 2, root(-7) // 2, root(-7) // 2, -1, -1, -1], [1 // 2, -1 // 2, root(-7) // 2, root(-7) // 2, 1, 1, 1], [root(-7) // 2, root(-7) // 2, root(-7) // 2, -(root(-7)) // 2, 0, 0, 0], [root(-7) // 2, root(-7) // 2, -(root(-7)) // 2, root(-7) // 2, 0, 0, 0], [-1, 1, 0, 0, -(E(7, 6)) - E(7), -(E(7, 5)) - E(7, 2), -(E(7, 4)) - E(7, 3)], [-1, 1, 0, 0, -(E(7, 5)) - E(7, 2), -(E(7, 4)) - E(7, 3), -(E(7, 6)) - E(7)], [-1, 1, 0, 0, -(E(7, 4)) - E(7, 3), -(E(7, 6)) - E(7), -(E(7, 5)) - E(7, 2)]] // root(-7), :eigenvalues => [1, 1, 1, -1, E(7, 4), E(7, 2), E(7)], :explanation => "mystery G24", :special => 1, :cospecial => 2) chevieset(:G24, :UnipotentCharacters, function () - return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:3, :rank => 3, :ST => 24), :levi => [], :parameterExponents => [1, 1, 1], :charNumbers => 1:12, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [1], :rank => 1), :levi => [2, 3], :parameterExponents => [7], :charNumbers => [19, 13], :eigenvalue => -1, :cuspidalName => "B_2"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [17], :eigenvalue => E(4), :qEigen => 1 // 2, :cuspidalName => "G_{24}[i]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [18], :eigenvalue => -(E(4)), :qEigen => 1 // 2, :cuspidalName => "G_{24}[-i]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [20], :eigenvalue => E(7, 3), :cuspidalName => "G_{24}[\\zeta_7^3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [21], :eigenvalue => E(7, 5), :cuspidalName => "G_{24}[\\zeta_7^5]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [22], :eigenvalue => E(7, 6), :cuspidalName => "G_{24}[\\zeta_7^6]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [14], :eigenvalue => E(7, 4), :cuspidalName => "G_{24}[\\zeta_7^4]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [15], :eigenvalue => E(7, 2), :cuspidalName => "G_{24}[\\zeta_7^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [16], :eigenvalue => E(7), :cuspidalName => "G_{24}[\\zeta_7]")], :families => [Family("C1", [1]), Family("X7", [4, 6, 7, 13, 14, 15, 16], Dict{Symbol, Any}(:ennola => 2)), Family("C1", [10], Dict{Symbol, Any}(:ennola => -1)), Family("C'\"2", [11, 12, 17, 18], Dict{Symbol, Any}(:ennola => -3)), Family("C1", [9]), conj(Family("X7", [3, 5, 8, 19, 20, 21, 22], Dict{Symbol, Any}(:ennola => -2))), Family("C1", [2], Dict{Symbol, Any}(:ennola => -1))], :a => [0, 21, 8, 1, 8, 1, 1, 8, 6, 3, 4, 4, 1, 1, 1, 1, 4, 4, 8, 8, 8, 8], :A => [0, 21, 20, 13, 20, 13, 13, 20, 18, 15, 17, 17, 13, 13, 13, 13, 17, 17, 20, 20, 20, 20], :curtis => [2, 1, 6, 5, 4, 3, 8, 7, 10, 9, 12, 11, 19, -20, -21, -22, -18, -17, 13, -14, -15, -16]) + return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:3, :rank => 3, :ST => 24), :levi => [], :parameterExponents => [1, 1, 1], :charNumbers => 1:12, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [1], :rank => 1), :levi => [2, 3], :parameterExponents => [7], :charNumbers => [19, 13], :eigenvalue => -1, :cuspidalName => "B_2"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [17], :eigenvalue => E(4), :qEigen => 1 // 2, :cuspidalName => "G_{24}[i]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [18], :eigenvalue => -(E(4)), :qEigen => 1 // 2, :cuspidalName => "G_{24}[-i]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [20], :eigenvalue => E(7, 3), :cuspidalName => "G_{24}[\\zeta_7^3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [21], :eigenvalue => E(7, 5), :cuspidalName => "G_{24}[\\zeta_7^5]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [22], :eigenvalue => E(7, 6), :cuspidalName => "G_{24}[\\zeta_7^6]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [14], :eigenvalue => E(7, 4), :cuspidalName => "G_{24}[\\zeta_7^4]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [15], :eigenvalue => E(7, 2), :cuspidalName => "G_{24}[\\zeta_7^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [16], :eigenvalue => E(7), :cuspidalName => "G_{24}[\\zeta_7]")], :families => [Family("C1", [1]), Family("X7", [4, 6, 7, 13, 14, 15, 16], Dict{Symbol, Any}(:ennola => 2)), Family("C1", [10], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [11, 12, 18, 17], Dict{Symbol, Any}(:cospecial => 2, :ennola => -4)), Family("C1", [9]), conj(Family("X7", [3, 5, 8, 19, 20, 21, 22], Dict{Symbol, Any}(:ennola => -2))), Family("C1", [2], Dict{Symbol, Any}(:ennola => -1))], :a => [0, 21, 8, 1, 8, 1, 1, 8, 6, 3, 4, 4, 1, 1, 1, 1, 4, 4, 8, 8, 8, 8], :A => [0, 21, 20, 13, 20, 13, 13, 20, 18, 15, 17, 17, 13, 13, 13, 13, 17, 17, 20, 20, 20, 20], :curtis => [2, 1, 6, 5, 4, 3, 8, 7, 10, 9, 12, 11, 19, -20, -21, -22, -18, -17, 13, -14, -15, -16]) end) chevieset(:G24, :Invariants, [function (x, y, z) return (((((-42 * x ^ 2 * y * z - 12 * x ^ 2 * y ^ 2) + 21 // 2 * x ^ 2 * z ^ 2) - 9 // 2 * y ^ 2 * z ^ 2) - 6 * y ^ 3 * z) + 14 * x ^ 4 + 18 // 7 * y ^ 4) - 21 // 8 * z ^ 4 diff --git a/tools/tbl/cmplxg26.jl b/tools/tbl/cmplxg26.jl index e8f4b8f6..a32b34e9 100644 --- a/tools/tbl/cmplxg26.jl +++ b/tools/tbl/cmplxg26.jl @@ -127,7 +127,7 @@ chevieset(:G26, :UnipotentCharacters, function () local i3, J J = E(3) i3 = root(-3) - return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:3, :rank => 3, :ST => 26), :levi => [], :parameterExponents => [1, 1, 1], :charNumbers => 1:48, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1, 3, 13], :rank => 2, :p => 6, :q => 2), :levi => [2], :parameterExponents => [[0, 2, 2], 3, 1], :charNumbers => [102, 68, 71, 66, 53, 70, 60, 67, 54, 103, 69, 72, 99, 59, 98, 65, 50, 49], :eigenvalue => J ^ 2, :cuspidalName => ImprimitiveCuspidalName([[], [0, 1], [0, 1]])), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1], :rank => 1, :p => 6, :q => 1), :levi => 2:3, :parameterExponents => [[3, 4, 3, 0, 3, 4]], :charNumbers => [73, 61, 74, 104, 75, 62], :eigenvalue => -1, :cuspidalName => "G_4"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [3], :rank => 1, :p => 6, :q => 1), :levi => 1:2, :parameterExponents => [[4, 3, 1, 1, 0, 1]], :charNumbers => [51, 55, 76, 81, 100, 78], :eigenvalue => J, :cuspidalName => ImprimitiveCuspidalName([[0], [], [0, 1, 2]])), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [3], :rank => 1, :p => 6, :q => 1), :levi => 1:2, :parameterExponents => [[4, 1, 0, 1, 1, 3]], :charNumbers => [52, 79, 101, 80, 77, 56], :eigenvalue => J, :cuspidalName => ImprimitiveCuspidalName([[0], [0, 1, 2], []])), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [92], :eigenvalue => 1, :cuspidalName => "G_{26}[1]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [93], :eigenvalue => 1, :cuspidalName => "G_{26}^2[1]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [94], :eigenvalue => 1, :cuspidalName => "G_{26}^3[1]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [82], :eigenvalue => -1, :cuspidalName => "G_{26}[-1]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [83], :eigenvalue => -1, :cuspidalName => "G_{26}^2[-1]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [88], :eigenvalue => E(3), :cuspidalName => "G_{26}[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [89], :eigenvalue => E(3), :cuspidalName => "G_{26}^2[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [64], :eigenvalue => E(3, 2), :cuspidalName => "G_{26}[\\zeta_{3}^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [84], :eigenvalue => E(3, 2), :cuspidalName => "G_{26}^2[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [85], :eigenvalue => E(3, 2), :cuspidalName => "G_{26}^3[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [90], :eigenvalue => -(E(3)), :cuspidalName => "G_{26}[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [91], :eigenvalue => -(E(3)), :cuspidalName => "G_{26}^2[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [63], :eigenvalue => -(E(3, 2)), :cuspidalName => "G_{26}[-\\zeta_{3}^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [86], :eigenvalue => -(E(3, 2)), :cuspidalName => "G_{26}^2[-\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [87], :eigenvalue => -(E(3, 2)), :cuspidalName => "G_{26}^3[-\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [57], :eigenvalue => E(4), :cuspidalName => "G_{26}[i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [58], :eigenvalue => -(E(4)), :cuspidalName => "G_{26}[-i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [95], :eigenvalue => E(9, 8), :cuspidalName => "G_{26}[\\zeta_9^8]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [96], :eigenvalue => E(9, 5), :cuspidalName => "G_{26}[\\zeta_9^5]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [97], :eigenvalue => E(9, 2), :cuspidalName => "G_{26}[\\zeta_9^2]")], :families => [Family("C1", [1]), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [24, 18, 2, 52, 50, 10, 49, 12, 51], Dict{Symbol, Any}(:signs => [-1, -1, -1, 1, 1, 1, -1, 1, 1], :ennola => 4)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [31, 37, 13, 55, 53, 23, 54, 17, 56], Dict{Symbol, Any}(:signs => [-1, -1, -1, 1, 1, 1, -1, 1, 1], :ennola => -9)), Family("C'\"2", [40, 39, 57, 58], Dict{Symbol, Any}(:ennola => 3)), Family(Family("C2") * ((CHEVIE[:families])[:X])(3), [33, 27, 59, 22, 16, 60, 48, 46, 64, 61, 62, 63], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1], :ennola => 12, :special => 1, :cospecial => 2)), 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root(-3) * 3, -(root(-3)) * 3, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, 0, 0, 0, -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), 9 * E(3), -9, -9 * E(3, 2), -9 * E(3), 9, 9, 9, 9, 0, 0, 9 * E(3), 9 * E(3, 2), -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), 9 * E(3), -9, 9, -9, -9, root(-3) * 6, ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 0, 0, 0], [9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9, 9 * E(3, 2), 9 * E(3), 0, 0, 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9, 9, 0, 0, 0, 0, 0, 9 * E(3), -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9, -9 * E(3), -9 * E(3, 2), -9, -9, -9, -9, 0, 0, 9 * E(3, 2), 9 * E(3), -9 * E(3), 9 * E(3, 2), -9 * E(3), 9 * E(3, 2), -9, 9, -9, -9, 0, -9 * E(3, 2), 9 * E(3), 0, 0, 0], [-9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9, -9 * E(3), -9 * E(3, 2), 0, 0, -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9, -9, 0, 0, 0, 0, 0, -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), 9 * E(3), 9, 9 * E(3, 2), 9 * E(3), 9, 9, 9, 9, 0, 0, -9 * E(3), -9 * E(3, 2), 9 * E(3, 2), -9 * E(3), 9 * E(3, 2), -9 * E(3), 9, -9, 9, 9, 0, 9 * E(3), -9 * E(3, 2), 0, 0, 0], [9, 9, 9, 9, -9, -9, -9, 0, 0, 9, 9, -9, -9, 9, 9, 0, 0, 0, 0, 0, 9, -9, -9, 9, 9, 9, 9, 9, 9, -9, -9, 0, 0, -9, -9, -9, 9, 9, -9, -9, 9, 9, 9, 0, -9, 9, 0, 0, 0], [9 * E(3, 2), 9 * E(3), 9, 9, -9, -9 * E(3), -9 * E(3, 2), 0, 0, 9, 9, -9, -9, 9, 9, 0, 0, 0, 0, 0, 9 * E(3), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9, 9, 9, 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), 0, 0, -9 * E(3), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), 0, -9 * E(3), 9 * E(3, 2), 0, 0, 0], [9 * E(3), 9 * E(3, 2), 9, 9, -9, -9 * E(3, 2), -9 * E(3), 0, 0, 9, 9, -9, -9, 9, 9, 0, 0, 0, 0, 0, 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9 * E(3), 9, 9, 9, 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 0, 0, -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, -9 * E(3, 2), 9 * E(3), 0, 0, 0], [-9 * E(3), -9 * E(3, 2), 9 * E(3, 2), 9 * E(3), -9, -9 * E(3, 2), -9 * E(3), 0, 0, -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9, -9, 0, 0, 0, 0, 0, -9, 9, -9, 9, 9, 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), 0, 0, -9 * E(3, 2), -9 * E(3), 9, -9, 9, -9, 9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), 0, 9 * E(3, 2), -9 * E(3), 0, 0, 0], [-9 * E(3, 2), -9 * E(3), 9 * E(3), 9 * E(3, 2), -9, -9 * E(3), -9 * E(3, 2), 0, 0, -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9, -9, 0, 0, 0, 0, 0, -9, 9, -9, 9, 9, 9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, 0, -9 * E(3), -9 * E(3, 2), 9, -9, 9, -9, 9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, 9 * E(3), -9 * E(3, 2), 0, 0, 0], [((-3 - root(-3)) * 3) // 2, ((-3 + root(-3)) * 3) // 2, 9 * E(3, 2), 9 * E(3), -9, -9 * E(3, 2), -9 * E(3), 0, 0, -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), -9 * E(3), -(root(-3)) * 3, root(-3) * 3, (-3 + root(-3)) * 3, (-3 - root(-3)) * 3, 0, 0, 0, -9, 9, -9, 9, -9, -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), 0, 0, 9 * E(3, 2), 9 * E(3), -9, 9, -9, 9, -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), -(root(-3)) * 6, ((-3 + root(-3)) * 3) // 2, ((3 + root(-3)) * 3) // 2, 0, 0, 0], [((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 9 * E(3), 9 * E(3, 2), -9, -9 * E(3), -9 * E(3, 2), 0, 0, -9 * E(3), -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), root(-3) * 3, -(root(-3)) * 3, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, 0, 0, 0, -9, 9, -9, 9, -9, -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, 0, 9 * E(3), 9 * E(3, 2), -9, 9, -9, 9, -9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), root(-3) * 6, ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 0, 0, 0], [(3 + root(-3)) * 3, (3 - root(-3)) * 3, 0, 0, 0, 0, 0, 18 * E(3, 2), 18 * E(3), 0, 0, 0, 0, root(-3) * 6, -(root(-3)) * 6, (-3 + root(-3)) * 3, (-3 - root(-3)) * 3, -18, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18 * E(3, 2), 18 * E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -(root(-3)) * 6, (3 - root(-3)) * 3, (-3 - root(-3)) * 3, 0, 0, 0], [(3 - root(-3)) * 3, (3 + root(-3)) * 3, 0, 0, 0, 0, 0, 18 * E(3), 18 * E(3, 2), 0, 0, 0, 0, -(root(-3)) * 6, root(-3) * 6, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, -18, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18 * E(3), 18 * E(3, 2), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, root(-3) * 6, (3 + root(-3)) * 3, (-3 + root(-3)) * 3, 0, 0, 0], [-9, -9, -9 * E(3), -9 * E(3, 2), 9, 9, 9, 0, 0, -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9, -9, 0, 0, 0, 0, 0, -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), -9, -9 * E(3), -9 * E(3, 2), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), 0, 0, 9, 9, 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), -9 * E(3), 0, 9, -9, 0, 0, 0], [-9, -9, -9 * E(3, 2), -9 * E(3), 9, 9, 9, 0, 0, -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9, -9, 0, 0, 0, 0, 0, -9 * E(3), 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9, -9 * E(3, 2), -9 * E(3), -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, 0, 9, 9, 9 * E(3), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 0, 9, -9, 0, 0, 0], [((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 9 * E(3), 9 * E(3, 2), -9, -9 * E(3, 2), -9 * E(3), 0, 0, 9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), root(-3) * 3, -(root(-3)) * 3, (3 - root(-3)) * 3, (3 + root(-3)) * 3, 0, 0, 0, 9 * E(3), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), -9, -9 * E(3), -9 * E(3, 2), 9, 9, -9, -9, 0, 0, 9 * E(3, 2), 9 * E(3), 9 * E(3), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9, -9, -9, -9, root(-3) * 6, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 0, 0, 0], [((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -9 * E(3, 2), -9 * E(3), 9, 9 * E(3), 9 * E(3, 2), 0, 0, -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), -9 * E(3), root(-3) * 3, -(root(-3)) * 3, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, 0, 0, 0, -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), 9, 9 * E(3, 2), 9 * E(3), -9, -9, 9, 9, 0, 0, -9 * E(3), -9 * E(3, 2), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), -9, 9, 9, 9, root(-3) * 6, ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 0, 0, 0], [9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9, -9 * E(3, 2), -9 * E(3), 0, 0, 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9, 9, 0, 0, 0, 0, 0, 9 * E(3), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9, 9 * E(3), 9 * E(3, 2), 9, 9, -9, -9, 0, 0, -9 * E(3, 2), -9 * E(3), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9, 9, 9, 9, 0, -9 * E(3, 2), 9 * E(3), 0, 0, 0], [-9 * E(3, 2), -9 * E(3), -9 * E(3, 2), -9 * E(3), 9, 9 * E(3), 9 * E(3, 2), 0, 0, -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9, -9, 0, 0, 0, 0, 0, -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), -9, -9 * E(3, 2), -9 * E(3), -9, -9, 9, 9, 0, 0, 9 * E(3), 9 * E(3, 2), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9 * E(3), 9, -9, -9, -9, 0, 9 * E(3), -9 * E(3, 2), 0, 0, 0], [((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 9 * E(3, 2), 9 * E(3), -9, -9 * E(3, 2), -9 * E(3), 0, 0, 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), root(-3) * 3, -(root(-3)) * 3, (3 - root(-3)) * 3, (3 + root(-3)) * 3, 0, 0, 0, 9, -9, -9, 9, -9, -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), 0, 0, 9 * E(3, 2), 9 * E(3), 9, -9, -9, 9, 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), -9 * E(3), root(-3) * 6, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 0, 0, 0], [((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -9 * E(3), -9 * E(3, 2), 9, 9 * E(3), 9 * E(3, 2), 0, 0, -9 * E(3), -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), root(-3) * 3, -(root(-3)) * 3, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, 0, 0, 0, -9, 9, 9, -9, 9, 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, 0, -9 * E(3), -9 * E(3, 2), -9, 9, 9, -9, -9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), root(-3) * 6, ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 0, 0, 0], [9 * E(3), 9 * E(3, 2), 9 * E(3, 2), 9 * E(3), -9, -9 * E(3, 2), -9 * E(3), 0, 0, 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), 9, 9, 0, 0, 0, 0, 0, 9, -9, -9, 9, 9, 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), 0, 0, -9 * E(3, 2), -9 * E(3), -9, 9, 9, -9, -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), 0, -9 * E(3, 2), 9 * E(3), 0, 0, 0], [9 * E(3, 2), 9 * E(3), 9 * E(3), 9 * E(3, 2), -9, -9 * E(3), -9 * E(3, 2), 0, 0, 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9, 9, 0, 0, 0, 0, 0, 9, -9, -9, 9, 9, 9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 0, 0, -9 * E(3), -9 * E(3, 2), -9, 9, 9, -9, -9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, -9 * E(3), 9 * E(3, 2), 0, 0, 0], [root(-3) * 2, -(root(-3)) * 2, 0, 0, 0, 0, 0, root(-3) * 6, -(root(-3)) * 6, -(root(-3)) * 6, root(-3) * 6, -(root(-3)) * 6, root(-3) * 6, -(root(-3)) * 2, root(-3) * 2, -(root(-3)) * 4, root(-3) * 4, -(root(-3)) * 6, -(root(-3)) * 6, -(root(-3)) * 12, root(-3) * 6, root(-3) * 6, 0, 0, 0, 0, 0, 0, 0, -(root(-3)) * 6, root(-3) * 6, -(root(-3)) * 6, root(-3) * 6, 0, 0, root(-3) * 6, root(-3) * 6, 0, 0, root(-3) * 6, root(-3) * 6, 0, 0, -(root(-3)) * 4, -(root(-3)) * 2, -(root(-3)) * 2, root(-3) * 6, root(-3) * 6, root(-3) * 6], [root(-3), -(root(-3)), 9 * E(3), 9 * E(3, 2), -9, -9, -9, (3 + root(-3)) * 3, (3 - root(-3)) * 3, ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, -(root(-3)), root(-3), -(root(-3)) * 2, root(-3) * 2, (-3 - root(-3)) * 3, (3 - root(-3)) * 3, -(root(-3)) * 6, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -9 * E(3, 2), 9 * E(3), -9, -9 * E(3), -9 * E(3, 2), 9 * E(3, 2), 9 * E(3), ((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, (3 - root(-3)) * 3, (3 + root(-3)) * 3, 9, 9, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -9 * E(3, 2), 9 * E(3), ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -9 * E(3, 2), -9 * E(3), -(root(-3)) * 2, -(root(-3)), -(root(-3)), -(root(-3)) * 6, -(root(-3)) * 6, -(root(-3)) * 6], [root(-3), -(root(-3)), -9 * E(3, 2), -9 * E(3), 9, 9, 9, (-3 + root(-3)) * 3, (-3 - root(-3)) * 3, ((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, ((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -(root(-3)), root(-3), -(root(-3)) * 2, root(-3) * 2, (3 - root(-3)) * 3, (-3 - root(-3)) * 3, -(root(-3)) * 6, ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 9 * E(3), -9 * E(3, 2), 9, 9 * E(3, 2), 9 * E(3), -9 * E(3), -9 * E(3, 2), ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, -9, -9, ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 9 * E(3), -9 * E(3, 2), ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 9 * E(3), 9 * E(3, 2), -(root(-3)) * 2, -(root(-3)), -(root(-3)), -(root(-3)) * 6, -(root(-3)) * 6, -(root(-3)) * 6], [root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -(root(-3)) * 6, root(-3) * 6, root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, root(-3) * 6, -(root(-3)) * 6, -(root(-3)) * 6, 18 * E(9, 7) - 18 * E(9, 2), -18 * E(9, 5) + 18 * E(9, 4), ((-18 * E(9, 7) + 18 * E(9, 5)) - 18 * E(9, 4)) + 18 * E(9, 2)], [root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -(root(-3)) * 6, root(-3) * 6, root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, root(-3) * 6, -(root(-3)) * 6, -(root(-3)) * 6, -18 * E(9, 5) + 18 * E(9, 4), ((-18 * E(9, 7) + 18 * E(9, 5)) - 18 * E(9, 4)) + 18 * E(9, 2), 18 * E(9, 7) - 18 * E(9, 2)], [root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -(root(-3)) * 6, root(-3) * 6, root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, root(-3) * 6, -(root(-3)) * 6, -(root(-3)) * 6, ((-18 * E(9, 7) + 18 * E(9, 5)) - 18 * E(9, 4)) + 18 * E(9, 2), 18 * E(9, 7) - 18 * E(9, 2), -18 * E(9, 5) + 18 * E(9, 4)]] // 54, :eigenvalues => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, E(3, 2), E(3, 2), E(3, 2), E(3, 2), E(3, 2), E(3, 2), E(3, 2), -1, -1, -1, E(3), E(3), E(3), E(3), E(3), E(3), -1, -1, E(3, 2), E(3, 2), -(E(3, 2)), -(E(3, 2)), E(3), E(3), -(E(3)), -(E(3)), 1, 1, 1, E(9, 8), E(9, 5), E(9, 2)], :explanation => "mystery G26", :special => 1, :cospecial => 2), [43, 42, 28, 34, 8, 41, 44, 29, 35, 15, 21, 45, 47, 6, 5, 11, 9, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1], :ennola => -2)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [30, 36, 14, 101, 99, 26, 98, 20, 100], Dict{Symbol, Any}(:signs => [-1, -1, -1, 1, 1, 1, -1, 1, 1], :ennola => 9)), Family(((CHEVIE[:families])[:X])(3), [25, 19, 102], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -3)), Family("X5", [4, 7, 104, 103, 3], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, 1], :ennola => 5))], :a => [0, 1, 21, 21, 6, 6, 21, 6, 6, 1, 6, 1, 2, 11, 6, 4, 2, 1, 16, 11, 6, 4, 2, 1, 16, 11, 4, 6, 6, 11, 2, 5, 4, 6, 6, 11, 2, 5, 3, 3, 6, 6, 6, 6, 6, 4, 6, 4, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 11, 11, 11, 11, 16, 21, 21], :A => [0, 17, 33, 33, 30, 30, 33, 30, 30, 17, 30, 17, 22, 31, 30, 26, 22, 17, 32, 31, 30, 26, 22, 17, 32, 31, 26, 30, 30, 31, 22, 25, 26, 30, 30, 31, 22, 25, 24, 24, 30, 30, 30, 30, 30, 26, 30, 26, 17, 17, 17, 17, 22, 22, 22, 22, 24, 24, 26, 26, 26, 26, 26, 26, 25, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 31, 31, 31, 32, 33, 33]) + return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:3, :rank => 3, :ST => 26), :levi => [], :parameterExponents => [1, 1, 1], :charNumbers => 1:48, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1, 3, 13], :rank => 2, :p => 6, :q => 2), :levi => [2], :parameterExponents => [[0, 2, 2], 3, 1], :charNumbers => [102, 68, 71, 66, 53, 70, 60, 67, 54, 103, 69, 72, 99, 59, 98, 65, 50, 49], :eigenvalue => J ^ 2, :cuspidalName => ImprimitiveCuspidalName([[], [0, 1], [0, 1]])), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1], :rank => 1, :p => 6, :q => 1), :levi => 2:3, :parameterExponents => [[3, 4, 3, 0, 3, 4]], :charNumbers => [73, 61, 74, 104, 75, 62], :eigenvalue => -1, :cuspidalName => "G_4"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [3], :rank => 1, :p => 6, :q => 1), :levi => 1:2, :parameterExponents => [[4, 3, 1, 1, 0, 1]], :charNumbers => [51, 55, 76, 81, 100, 78], :eigenvalue => J, :cuspidalName => ImprimitiveCuspidalName([[0], [], [0, 1, 2]])), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [3], :rank => 1, :p => 6, :q => 1), :levi => 1:2, :parameterExponents => [[4, 1, 0, 1, 1, 3]], :charNumbers => [52, 79, 101, 80, 77, 56], :eigenvalue => J, :cuspidalName => ImprimitiveCuspidalName([[0], [0, 1, 2], []])), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [92], :eigenvalue => 1, :cuspidalName => "G_{26}[1]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [93], :eigenvalue => 1, :cuspidalName => "G_{26}^2[1]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [94], :eigenvalue => 1, :cuspidalName => "G_{26}^3[1]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [82], :eigenvalue => -1, :cuspidalName => "G_{26}[-1]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [83], :eigenvalue => -1, :cuspidalName => "G_{26}^2[-1]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [88], :eigenvalue => E(3), :cuspidalName => "G_{26}[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [89], :eigenvalue => E(3), :cuspidalName => "G_{26}^2[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [64], :eigenvalue => E(3, 2), :cuspidalName => "G_{26}[\\zeta_{3}^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [84], :eigenvalue => E(3, 2), :cuspidalName => "G_{26}^2[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [85], :eigenvalue => E(3, 2), :cuspidalName => "G_{26}^3[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [90], :eigenvalue => -(E(3)), :cuspidalName => "G_{26}[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [91], :eigenvalue => -(E(3)), :cuspidalName => "G_{26}^2[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [63], :eigenvalue => -(E(3, 2)), :cuspidalName => "G_{26}[-\\zeta_{3}^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [86], :eigenvalue => -(E(3, 2)), :cuspidalName => "G_{26}^2[-\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [87], :eigenvalue => -(E(3, 2)), :cuspidalName => "G_{26}^3[-\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [57], :eigenvalue => E(4), :cuspidalName => "G_{26}[i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [58], :eigenvalue => -(E(4)), :cuspidalName => "G_{26}[-i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [95], :eigenvalue => E(9, 8), :cuspidalName => "G_{26}[\\zeta_9^8]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [96], :eigenvalue => E(9, 5), :cuspidalName => "G_{26}[\\zeta_9^5]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [97], :eigenvalue => E(9, 2), :cuspidalName => "G_{26}[\\zeta_9^2]")], :families => [Family("C1", [1]), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [24, 18, 2, 52, 50, 10, 49, 12, 51], Dict{Symbol, Any}(:signs => [-1, -1, -1, 1, 1, 1, -1, 1, 1], :ennola => 4)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [31, 37, 13, 55, 53, 23, 54, 17, 56], Dict{Symbol, Any}(:signs => [-1, -1, -1, 1, 1, 1, -1, 1, 1], :ennola => -9)), Family(((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [40, 39, 58, 57], Dict{Symbol, Any}(:cospecial => 2, :ennola => 4)), Family(Family("C2") * ((CHEVIE[:families])[:X])(3), [33, 27, 59, 22, 16, 60, 48, 46, 64, 61, 62, 63], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1], :ennola => 12, :special => 1, :cospecial => 2)), Family(((CHEVIE[:families])[:X])(3), [32, 38, 65], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 2)), Family(Dict{Symbol, Any}(:fourierMat => [[-(root(-3)), root(-3), -9 * E(3, 2), -9 * E(3), 9, 9, 9, (3 - root(-3)) * 3, (3 + root(-3)) * 3, ((3 - root(-3)) * 3) // 2, ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, ((3 + root(-3)) * 3) // 2, root(-3), -(root(-3)), root(-3) * 2, -(root(-3)) * 2, (-3 + root(-3)) * 3, (3 + root(-3)) * 3, root(-3) * 6, ((3 + root(-3)) * 3) // 2, ((-3 + root(-3)) * 3) // 2, 9 * E(3), -9 * E(3, 2), 9, 9 * E(3, 2), 9 * E(3), -9 * E(3), -9 * E(3, 2), ((-3 - root(-3)) * 3) // 2, ((-3 + root(-3)) * 3) // 2, (3 + root(-3)) * 3, (3 - root(-3)) * 3, -9, -9, ((3 + root(-3)) * 3) // 2, ((-3 + root(-3)) * 3) // 2, 9 * E(3), -9 * E(3, 2), ((3 + root(-3)) * 3) // 2, ((-3 + root(-3)) * 3) // 2, 9 * E(3), 9 * E(3, 2), root(-3) * 2, root(-3), root(-3), root(-3) * 6, root(-3) * 6, root(-3) * 6], [root(-3), -(root(-3)), -9 * E(3), -9 * E(3, 2), 9, 9, 9, (3 + root(-3)) * 3, (3 - root(-3)) * 3, ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, -(root(-3)), root(-3), -(root(-3)) * 2, root(-3) * 2, (-3 - root(-3)) * 3, (3 - root(-3)) * 3, -(root(-3)) * 6, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 9 * E(3, 2), -9 * E(3), 9, 9 * E(3), 9 * E(3, 2), -9 * E(3, 2), -9 * E(3), ((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, (3 - root(-3)) * 3, (3 + root(-3)) * 3, -9, -9, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 9 * E(3, 2), -9 * E(3), ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 9 * E(3, 2), 9 * E(3), -(root(-3)) * 2, -(root(-3)), -(root(-3)), -(root(-3)) * 6, -(root(-3)) * 6, -(root(-3)) * 6], [-9 * E(3, 2), -9 * E(3), 9, 9, -9, -9 * E(3), -9 * E(3, 2), 0, 0, -9, -9, 9, 9, -9, -9, 0, 0, 0, 0, 0, -9 * E(3), 9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9, 9, 9, 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), 0, 0, -9 * E(3), -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), 9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), 0, 9 * E(3), -9 * E(3, 2), 0, 0, 0], [-9 * E(3), -9 * E(3, 2), 9, 9, -9, -9 * E(3, 2), -9 * E(3), 0, 0, -9, -9, 9, 9, -9, -9, 0, 0, 0, 0, 0, -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), 9 * E(3), 9, 9, 9, 9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, 0, -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), -9 * E(3), 9 * E(3, 2), -9 * E(3), 9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, 9 * E(3, 2), -9 * E(3), 0, 0, 0], [9, 9, -9, -9, 9, 9, 9, 0, 0, 9, 9, -9, -9, 9, 9, 0, 0, 0, 0, 0, 9, -9, 9, -9, -9, -9, -9, -9, -9, -9, -9, 0, 0, 9, 9, -9, 9, -9, 9, -9, 9, -9, -9, 0, -9, 9, 0, 0, 0], [9, 9, -9 * E(3), -9 * E(3, 2), 9, 9, 9, 0, 0, 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9, 9, 0, 0, 0, 0, 0, 9 * E(3, 2), -9 * E(3), 9 * E(3, 2), -9 * E(3), -9, -9 * E(3), -9 * E(3, 2), -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), -9 * E(3), 0, 0, 9, 9, -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), 0, -9, 9, 0, 0, 0], [9, 9, -9 * E(3, 2), -9 * E(3), 9, 9, 9, 0, 0, 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), 9, 9, 0, 0, 0, 0, 0, 9 * E(3), -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9, -9 * E(3, 2), -9 * E(3), -9 * E(3), -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 0, 0, 9, 9, -9 * E(3), 9 * E(3, 2), -9 * E(3), 9 * E(3, 2), -9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 0, -9, 9, 0, 0, 0], [(3 - root(-3)) * 3, (3 + root(-3)) * 3, 0, 0, 0, 0, 0, 18, 18, 0, 0, 0, 0, -(root(-3)) * 6, root(-3) * 6, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, -18 * E(3, 2), 18 * E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18 * E(3, 2), 18 * E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, root(-3) * 6, (3 + root(-3)) * 3, (-3 + root(-3)) * 3, 0, 0, 0], [(3 + root(-3)) * 3, (3 - root(-3)) * 3, 0, 0, 0, 0, 0, 18, 18, 0, 0, 0, 0, root(-3) * 6, -(root(-3)) * 6, (-3 + root(-3)) * 3, (-3 - root(-3)) * 3, -18 * E(3), 18 * E(3, 2), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18 * E(3), 18 * E(3, 2), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -(root(-3)) * 6, (3 - root(-3)) * 3, (-3 - root(-3)) * 3, 0, 0, 0], [((3 - root(-3)) * 3) // 2, ((3 + root(-3)) * 3) // 2, -9, -9, 9, 9 * E(3), 9 * E(3, 2), 0, 0, 9, 9, 9, 9, -(root(-3)) * 3, root(-3) * 3, (3 + root(-3)) * 3, (3 - root(-3)) * 3, 0, 0, 0, 9 * E(3), -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), 9, 9, 9, -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), -9 * E(3), 0, 0, -9 * E(3), -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), 9 * E(3), -9 * E(3, 2), 9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3), -(root(-3)) * 6, ((3 + root(-3)) * 3) // 2, ((-3 + root(-3)) * 3) // 2, 0, 0, 0], [((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, -9, -9, 9, 9 * E(3, 2), 9 * E(3), 0, 0, 9, 9, 9, 9, root(-3) * 3, -(root(-3)) * 3, (3 - root(-3)) * 3, (3 + root(-3)) * 3, 0, 0, 0, 9 * E(3, 2), -9 * E(3), 9 * E(3, 2), -9 * E(3), 9, 9, 9, -9 * E(3), -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 0, 0, -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), -9 * E(3), 9 * E(3, 2), -9 * E(3), 9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), root(-3) * 6, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 0, 0, 0], [((3 - root(-3)) * 3) // 2, ((3 + root(-3)) * 3) // 2, 9, 9, -9, -9 * E(3), -9 * E(3, 2), 0, 0, 9, 9, 9, 9, -(root(-3)) * 3, root(-3) * 3, (3 + root(-3)) * 3, (3 - root(-3)) * 3, 0, 0, 0, 9 * E(3), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), -9, -9, -9, 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), 0, 0, 9 * E(3), 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), 9 * E(3, 2), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), -9 * E(3), -(root(-3)) * 6, ((3 + root(-3)) * 3) // 2, ((-3 + root(-3)) * 3) // 2, 0, 0, 0], [((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 9, 9, -9, -9 * E(3, 2), -9 * E(3), 0, 0, 9, 9, 9, 9, root(-3) * 3, -(root(-3)) * 3, (3 - root(-3)) * 3, (3 + root(-3)) * 3, 0, 0, 0, 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9 * E(3), -9, -9, -9, 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 0, 0, 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3), -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), root(-3) * 6, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, 0, 0, 0], [root(-3), -(root(-3)), -9, -9, 9, 9, 9, -(root(-3)) * 6, root(-3) * 6, -(root(-3)) * 3, root(-3) * 3, -(root(-3)) * 3, root(-3) * 3, -(root(-3)), root(-3), -(root(-3)) * 2, root(-3) * 2, root(-3) * 6, root(-3) * 6, -(root(-3)) * 6, root(-3) * 3, root(-3) * 3, 9, -9, 9, 9, 9, -9, -9, -(root(-3)) * 3, root(-3) * 3, root(-3) * 6, -(root(-3)) * 6, -9, -9, root(-3) * 3, root(-3) * 3, 9, -9, root(-3) * 3, root(-3) * 3, 9, 9, -(root(-3)) * 2, -(root(-3)), -(root(-3)), -(root(-3)) * 6, -(root(-3)) * 6, -(root(-3)) * 6], [-(root(-3)), root(-3), -9, -9, 9, 9, 9, root(-3) * 6, -(root(-3)) * 6, root(-3) * 3, -(root(-3)) * 3, root(-3) * 3, -(root(-3)) * 3, root(-3), -(root(-3)), root(-3) * 2, -(root(-3)) * 2, -(root(-3)) * 6, -(root(-3)) * 6, root(-3) * 6, -(root(-3)) * 3, -(root(-3)) * 3, 9, -9, 9, 9, 9, -9, -9, root(-3) * 3, -(root(-3)) * 3, -(root(-3)) * 6, root(-3) * 6, -9, -9, -(root(-3)) * 3, -(root(-3)) * 3, 9, -9, -(root(-3)) * 3, -(root(-3)) * 3, 9, 9, root(-3) * 2, root(-3), root(-3), root(-3) * 6, root(-3) * 6, root(-3) * 6], [root(-3) * 2, -(root(-3)) * 2, 0, 0, 0, 0, 0, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, (3 + root(-3)) * 3, (3 - root(-3)) * 3, (3 + root(-3)) * 3, (3 - root(-3)) * 3, -(root(-3)) * 2, root(-3) * 2, -(root(-3)) * 4, root(-3) * 4, (3 + root(-3)) * 3, (-3 + root(-3)) * 3, -(root(-3)) * 12, (3 - root(-3)) * 3, (-3 - root(-3)) * 3, 0, 0, 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2, -9 * E(3), -9 * E(3, 2), 9, 9 * E(3), 9 * E(3, 2), 0, 0, -9 * E(3), -9 * E(3, 2), -9 * E(3), -9 * E(3, 2), root(-3) * 3, -(root(-3)) * 3, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, 0, 0, 0, -9, 9, 9, -9, 9, 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, 0, -9 * E(3), -9 * E(3, 2), -9, 9, 9, -9, -9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), root(-3) * 6, ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 0, 0, 0], [9 * E(3), 9 * E(3, 2), 9 * E(3, 2), 9 * E(3), -9, -9 * E(3, 2), -9 * E(3), 0, 0, 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), 9, 9, 0, 0, 0, 0, 0, 9, -9, -9, 9, 9, 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), -9 * E(3, 2), -9 * E(3), 0, 0, -9 * E(3, 2), -9 * E(3), -9, 9, 9, -9, -9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 9 * E(3), 0, -9 * E(3, 2), 9 * E(3), 0, 0, 0], [9 * E(3, 2), 9 * E(3), 9 * E(3), 9 * E(3, 2), -9, -9 * E(3), -9 * E(3, 2), 0, 0, 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 9, 9, 0, 0, 0, 0, 0, 9, -9, -9, 9, 9, 9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), -9 * E(3), -9 * E(3, 2), 0, 0, -9 * E(3), -9 * E(3, 2), -9, 9, 9, -9, -9 * E(3), 9 * E(3, 2), 9 * E(3), 9 * E(3, 2), 0, -9 * E(3), 9 * E(3, 2), 0, 0, 0], [root(-3) * 2, -(root(-3)) * 2, 0, 0, 0, 0, 0, root(-3) * 6, -(root(-3)) * 6, -(root(-3)) * 6, root(-3) * 6, -(root(-3)) * 6, root(-3) * 6, -(root(-3)) * 2, root(-3) * 2, -(root(-3)) * 4, root(-3) * 4, -(root(-3)) * 6, -(root(-3)) * 6, -(root(-3)) * 12, root(-3) * 6, root(-3) * 6, 0, 0, 0, 0, 0, 0, 0, -(root(-3)) * 6, root(-3) * 6, -(root(-3)) * 6, root(-3) * 6, 0, 0, root(-3) * 6, root(-3) * 6, 0, 0, root(-3) * 6, root(-3) * 6, 0, 0, -(root(-3)) * 4, -(root(-3)) * 2, -(root(-3)) * 2, root(-3) * 6, root(-3) * 6, root(-3) * 6], [root(-3), -(root(-3)), 9 * E(3), 9 * E(3, 2), -9, -9, -9, (3 + root(-3)) * 3, (3 - root(-3)) * 3, ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, -(root(-3)), root(-3), -(root(-3)) * 2, root(-3) * 2, (-3 - root(-3)) * 3, (3 - root(-3)) * 3, -(root(-3)) * 6, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -9 * E(3, 2), 9 * E(3), -9, -9 * E(3), -9 * E(3, 2), 9 * E(3, 2), 9 * E(3), ((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, (3 - root(-3)) * 3, (3 + root(-3)) * 3, 9, 9, ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -9 * E(3, 2), 9 * E(3), ((3 - root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -9 * E(3, 2), -9 * E(3), -(root(-3)) * 2, -(root(-3)), -(root(-3)), -(root(-3)) * 6, -(root(-3)) * 6, -(root(-3)) * 6], [root(-3), -(root(-3)), -9 * E(3, 2), -9 * E(3), 9, 9, 9, (-3 + root(-3)) * 3, (-3 - root(-3)) * 3, ((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, ((-3 + root(-3)) * 3) // 2, ((-3 - root(-3)) * 3) // 2, -(root(-3)), root(-3), -(root(-3)) * 2, root(-3) * 2, (3 - root(-3)) * 3, (-3 - root(-3)) * 3, -(root(-3)) * 6, ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 9 * E(3), -9 * E(3, 2), 9, 9 * E(3, 2), 9 * E(3), -9 * E(3), -9 * E(3, 2), ((3 + root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, (-3 - root(-3)) * 3, (-3 + root(-3)) * 3, -9, -9, ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 9 * E(3), -9 * E(3, 2), ((-3 - root(-3)) * 3) // 2, ((3 - root(-3)) * 3) // 2, 9 * E(3), 9 * E(3, 2), -(root(-3)) * 2, -(root(-3)), -(root(-3)), -(root(-3)) * 6, -(root(-3)) * 6, -(root(-3)) * 6], [root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -(root(-3)) * 6, root(-3) * 6, root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, root(-3) * 6, -(root(-3)) * 6, -(root(-3)) * 6, 18 * E(9, 7) - 18 * E(9, 2), -18 * E(9, 5) + 18 * E(9, 4), ((-18 * E(9, 7) + 18 * E(9, 5)) - 18 * E(9, 4)) + 18 * E(9, 2)], [root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -(root(-3)) * 6, root(-3) * 6, root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, root(-3) * 6, -(root(-3)) * 6, -(root(-3)) * 6, -18 * E(9, 5) + 18 * E(9, 4), ((-18 * E(9, 7) + 18 * E(9, 5)) - 18 * E(9, 4)) + 18 * E(9, 2), 18 * E(9, 7) - 18 * E(9, 2)], [root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -(root(-3)) * 6, root(-3) * 6, root(-3) * 6, -(root(-3)) * 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, root(-3) * 6, -(root(-3)) * 6, -(root(-3)) * 6, ((-18 * E(9, 7) + 18 * E(9, 5)) - 18 * E(9, 4)) + 18 * E(9, 2), 18 * E(9, 7) - 18 * E(9, 2), -18 * E(9, 5) + 18 * E(9, 4)]] // 54, :eigenvalues => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, E(3, 2), E(3, 2), E(3, 2), E(3, 2), E(3, 2), E(3, 2), E(3, 2), -1, -1, -1, E(3), E(3), E(3), E(3), E(3), E(3), -1, -1, E(3, 2), E(3, 2), -(E(3, 2)), -(E(3, 2)), E(3), E(3), -(E(3)), -(E(3)), 1, 1, 1, E(9, 8), E(9, 5), E(9, 2)], :explanation => "mystery G26", :special => 1, :cospecial => 2), [43, 42, 28, 34, 8, 41, 44, 29, 35, 15, 21, 45, 47, 6, 5, 11, 9, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1], :ennola => -2)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [30, 36, 14, 101, 99, 26, 98, 20, 100], Dict{Symbol, Any}(:signs => [-1, -1, -1, 1, 1, 1, -1, 1, 1], :ennola => 9)), Family(((CHEVIE[:families])[:X])(3), [25, 19, 102], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -3)), Family("X5", [4, 7, 104, 103, 3], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, 1], :ennola => 5))], :a => [0, 1, 21, 21, 6, 6, 21, 6, 6, 1, 6, 1, 2, 11, 6, 4, 2, 1, 16, 11, 6, 4, 2, 1, 16, 11, 4, 6, 6, 11, 2, 5, 4, 6, 6, 11, 2, 5, 3, 3, 6, 6, 6, 6, 6, 4, 6, 4, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 11, 11, 11, 11, 16, 21, 21], :A => [0, 17, 33, 33, 30, 30, 33, 30, 30, 17, 30, 17, 22, 31, 30, 26, 22, 17, 32, 31, 30, 26, 22, 17, 32, 31, 26, 30, 30, 31, 22, 25, 26, 30, 30, 31, 22, 25, 24, 24, 30, 30, 30, 30, 30, 26, 30, 26, 17, 17, 17, 17, 22, 22, 22, 22, 24, 24, 26, 26, 26, 26, 26, 26, 25, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 31, 31, 31, 32, 33, 33]) end) chevieset(:G26, :Invariants, [function (x1, x2, x3) return ((-10 * x1 ^ 3 * x2 ^ 3 - 10 * x1 ^ 3 * x3 ^ 3) - 10 * x2 ^ 3 * x3 ^ 3) + x1 ^ 6 + x2 ^ 6 + x3 ^ 6 diff --git a/tools/tbl/cmplxg27.jl b/tools/tbl/cmplxg27.jl index 8d109f21..133545e4 100644 --- a/tools/tbl/cmplxg27.jl +++ b/tools/tbl/cmplxg27.jl @@ -138,7 +138,7 @@ chevieset(:G27, :HeckeRepresentation, function (para, rootpara, i) end) (CHEVIE[:families])[:Y6] = Dict{Symbol, Any}(:name => "Y_6", :explanation => "subcategory of DQ(B2).20", :fourierMat => [[-(root(5)), -(root(5)), -2 * root(5), -2 * root(5), -5, -5], [-(root(5)), -(root(5)), -2 * root(5), -2 * root(5), 5, 5], [-2 * root(5), -2 * root(5), -5 + root(5), 5 + root(5), 0, 0], [-2 * root(5), -2 * root(5), 5 + root(5), -5 + root(5), 0, 0], [-5, 5, 0, 0, 5, -5], [-5, 5, 0, 0, -5, 5]] // 10, :eigenvalues => [1, 1, E(5, 3), E(5, 2), -1, 1], :special => 1, :cospecial => 1) chevieset(:G27, :UnipotentCharacters, function () - return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:3, :rank => 3, :ST => 27), :levi => [], :parameterExponents => [1, 1, 1], :charNumbers => 1:34, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [2], :rank => 1, :p => 6, :q => 1), :levi => [1, 8], :parameterExponents => [[5 // 2, 5, 0, 5 // 2, 0, 5]], :charNumbers => [56, 37, 79, 55, 77, 39], :eigenvalue => E(5, 2), :cuspidalName => "I_2(5)[1,3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [2], :rank => 1, :p => 6, :q => 1), :levi => [1, 8], :parameterExponents => [[5 // 2, 5, 0, 5 // 2, 0, 5]], :charNumbers => [58, 38, 80, 57, 78, 40], :eigenvalue => E(5, 3), :cuspidalName => "I_2(5)[1,2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1], :rank => 1, :p => 6, :q => 1), :levi => [2, 3], :parameterExponents => [[4, 5, 0, 1, 0, 5]], :charNumbers => [47, 35, 76, 74, 75, 36], :eigenvalue => -1, :cuspidalName => "B_2"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [65], :eigenvalue => E(4), :cuspidalName => "G_{27}[i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [63], :eigenvalue => E(4), :cuspidalName => "G_{27}^2[i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [64], :eigenvalue => -(E(4)), :cuspidalName => "G_{27}[-i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [66], :eigenvalue => -(E(4)), :cuspidalName => "G_{27}^2[-i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [83], :eigenvalue => E(3), :cuspidalName => "G_{27}[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [84], :eigenvalue => E(3), :cuspidalName => "G_{27}^2[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [85], :eigenvalue => E(3), :cuspidalName => "G_{27}^3[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [54], :eigenvalue => E(3), :cuspidalName => "G_{27}^4[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [67], :eigenvalue => E(3, 2), :cuspidalName => "G_{27}[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [43], :eigenvalue => E(3, 2), :cuspidalName => "G_{27}^2[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [44], :eigenvalue => E(3, 2), :cuspidalName => "G_{27}^3[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [45], :eigenvalue => E(3, 2), :cuspidalName => "G_{27}^4[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [86], :eigenvalue => -(E(3)), :cuspidalName => "G_{27}[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [46], :eigenvalue => -(E(3, 2)), :cuspidalName => "G_{27}^2[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [51], :eigenvalue => E(9), :cuspidalName => "G_{27}[\\zeta_9]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [53], :eigenvalue => E(9), :cuspidalName => "G_{27}^2[\\zeta_9]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [72], :eigenvalue => E(9, 2), :cuspidalName => "G_{27}[\\zeta_9^2]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [68], :eigenvalue => E(9, 2), :cuspidalName => "G_{27}^2[E9^2]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [50], :eigenvalue => E(9, 4), :cuspidalName => "G_{27}[\\zeta_9^4]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [49], :eigenvalue => E(9, 4), :cuspidalName => "G_{27}^2[\\zeta_9^4]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [70], :eigenvalue => E(9, 5), :cuspidalName => "G_{27}[\\zeta_9^5]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [69], :eigenvalue => E(9, 5), :cuspidalName => "G_{27}^2[\\zeta_9^5]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [52], :eigenvalue => E(9, 7), :cuspidalName => "G_{27}[\\zeta_9^7]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [48], :eigenvalue => E(9, 7), :cuspidalName => "G_{27}^2[\\zeta_9^7]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [73], :eigenvalue => E(9, 8), :cuspidalName => "G_{27}[\\zeta_9^8]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [71], :eigenvalue => E(9, 8), :cuspidalName => "G_{27}^2[\\zeta_9^8]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [41], :eigenvalue => E(15), :cuspidalName => "G_{27}[\\zeta_{15}]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [42], :eigenvalue => E(15, 4), :cuspidalName => "G_{27}[\\zeta_{15}^4]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [81], :eigenvalue => E(15, 11), :cuspidalName => "G_{27}[\\zeta_{15}^{11}]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [82], :eigenvalue => E(15, 14), :cuspidalName => "G_{27}[\\zeta_{15}^{14}]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [59], :eigenvalue => E(20, 17), :cuspidalName => "G_{27}[\\zeta_{20}^{17}]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [61], :eigenvalue => E(20, 13), :cuspidalName => "G_{27}[\\zeta_{20}^{13}]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0, :qEigen => 1 // 2), :levi => 1:3, :parameterExponents => [], :charNumbers => [60], :eigenvalue => E(20, 7), :cuspidalName => "G_{27}[\\zeta_{20}^7]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [62], :eigenvalue => E(20, 3), :cuspidalName => "G_{27}[\\zeta_{20}^3]", :qEigen => 1 // 2)], :families => [Family("C1", [1]), Family(((CHEVIE[:families])[:X])(3) * Family("Y6"), [5, 3, 38, 37, 35, 16, 9, 7, 40, 39, 36, 18, 44, 43, 42, 41, 46, 45], Dict{Symbol, Any}(:signs => [-1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1], :ennola => -14)), Family("C2", [30, 11, 12, 47], Dict{Symbol, Any}(:ennola => -4)), conj(Family("Z9", [23, 49, 48, 28, 53, 51, 26, 52, 50], Dict{Symbol, Any}(:special => 7, :cospecial => 1, :ennola => 2))), conj(Family(((CHEVIE[:families])[:X])(3), [33, 31, 54], Dict{Symbol, Any}(:ennola => -3))), Family(Family("C'\"2") * ((CHEVIE[:families])[:Dihedral])(5), [19, 21, 58, 56, 20, 22, 57, 55, 65, 63, 59, 61, 66, 64, 60, 62], Dict{Symbol, Any}(:ennola => -9, :special => 1, :cospecial => 5)), Family(((CHEVIE[:families])[:X])(3), [34, 32, 67], Dict{Symbol, Any}(:ennola => -2)), Family("Z9", [24, 69, 68, 27, 73, 71, 25, 72, 70], Dict{Symbol, Any}(:cospecial => 4, :signs => [1, 1, -1, 1, 1, -1, 1, 1, -1], :ennola => 6)), Family("C2", [29, 13, 14, 74], Dict{Symbol, Any}(:ennola => 4)), conj(Family(((CHEVIE[:families])[:X])(3) * Family("Y6"), [6, 4, 77, 78, 75, 15, 10, 8, 79, 80, 76, 17, 84, 83, 81, 82, 86, 85], Dict{Symbol, Any}(:signs => [-1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1], :ennola => 8))), Family("C1", [2], Dict{Symbol, Any}(:ennola => -1))], :a => [0, 45, 1, 16, 1, 16, 1, 16, 1, 16, 3, 3, 12, 12, 16, 1, 16, 1, 6, 6, 6, 6, 4, 9, 9, 4, 9, 4, 12, 3, 5, 8, 5, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 9, 9, 9, 9, 9, 9, 12, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16], :A => [0, 45, 29, 44, 29, 44, 29, 44, 29, 44, 33, 33, 42, 42, 44, 29, 44, 29, 39, 39, 39, 39, 36, 41, 41, 36, 41, 36, 42, 33, 37, 40, 37, 40, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 33, 36, 36, 36, 36, 36, 36, 37, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 40, 41, 41, 41, 41, 41, 41, 42, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44]) + return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:3, :rank => 3, :ST => 27), :levi => [], :parameterExponents => [1, 1, 1], :charNumbers => 1:34, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [2], :rank => 1, :p => 6, :q => 1), :levi => [1, 8], :parameterExponents => [[5 // 2, 5, 0, 5 // 2, 0, 5]], :charNumbers => [56, 37, 79, 55, 77, 39], :eigenvalue => E(5, 2), :cuspidalName => "I_2(5)[1,3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [2], :rank => 1, :p => 6, :q => 1), :levi => [1, 8], :parameterExponents => [[5 // 2, 5, 0, 5 // 2, 0, 5]], :charNumbers => [58, 38, 80, 57, 78, 40], :eigenvalue => E(5, 3), :cuspidalName => "I_2(5)[1,2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1], :rank => 1, :p => 6, :q => 1), :levi => [2, 3], :parameterExponents => [[4, 5, 0, 1, 0, 5]], :charNumbers => [47, 35, 76, 74, 75, 36], :eigenvalue => -1, :cuspidalName => "B_2"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [65], :eigenvalue => E(4), :cuspidalName => "G_{27}[i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [63], :eigenvalue => E(4), :cuspidalName => "G_{27}^2[i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [64], :eigenvalue => -(E(4)), :cuspidalName => "G_{27}[-i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [66], :eigenvalue => -(E(4)), :cuspidalName => "G_{27}^2[-i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [83], :eigenvalue => E(3), :cuspidalName => "G_{27}[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [84], :eigenvalue => E(3), :cuspidalName => "G_{27}^2[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [85], :eigenvalue => E(3), :cuspidalName => "G_{27}^3[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [54], :eigenvalue => E(3), :cuspidalName => "G_{27}^4[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [67], :eigenvalue => E(3, 2), :cuspidalName => "G_{27}[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [43], :eigenvalue => E(3, 2), :cuspidalName => "G_{27}^2[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [44], :eigenvalue => E(3, 2), :cuspidalName => "G_{27}^3[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [45], :eigenvalue => E(3, 2), :cuspidalName => "G_{27}^4[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [86], :eigenvalue => -(E(3)), :cuspidalName => "G_{27}[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [46], :eigenvalue => -(E(3, 2)), :cuspidalName => "G_{27}^2[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [51], :eigenvalue => E(9), :cuspidalName => "G_{27}[\\zeta_9]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [53], :eigenvalue => E(9), :cuspidalName => "G_{27}^2[\\zeta_9]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [72], :eigenvalue => E(9, 2), :cuspidalName => "G_{27}[\\zeta_9^2]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [68], :eigenvalue => E(9, 2), :cuspidalName => "G_{27}^2[\\zeta_9^2]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [50], :eigenvalue => E(9, 4), :cuspidalName => "G_{27}[\\zeta_9^4]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [49], :eigenvalue => E(9, 4), :cuspidalName => "G_{27}^2[\\zeta_9^4]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [70], :eigenvalue => E(9, 5), :cuspidalName => "G_{27}[\\zeta_9^5]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [69], :eigenvalue => E(9, 5), :cuspidalName => "G_{27}^2[\\zeta_9^5]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [52], :eigenvalue => E(9, 7), :cuspidalName => "G_{27}[\\zeta_9^7]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [48], :eigenvalue => E(9, 7), :cuspidalName => "G_{27}^2[\\zeta_9^7]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [73], :eigenvalue => E(9, 8), :cuspidalName => "G_{27}[\\zeta_9^8]", :qEigen => 2 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [71], :eigenvalue => E(9, 8), :cuspidalName => "G_{27}^2[\\zeta_9^8]", :qEigen => 1 // 3), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [41], :eigenvalue => E(15), :cuspidalName => "G_{27}[\\zeta_{15}]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [42], :eigenvalue => E(15, 4), :cuspidalName => "G_{27}[\\zeta_{15}^4]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [81], :eigenvalue => E(15, 11), :cuspidalName => "G_{27}[\\zeta_{15}^{11}]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [82], :eigenvalue => E(15, 14), :cuspidalName => "G_{27}[\\zeta_{15}^{14}]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [59], :eigenvalue => E(20, 17), :cuspidalName => "G_{27}[\\zeta_{20}^{17}]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [61], :eigenvalue => E(20, 13), :cuspidalName => "G_{27}[\\zeta_{20}^{13}]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0, :qEigen => 1 // 2), :levi => 1:3, :parameterExponents => [], :charNumbers => [60], :eigenvalue => E(20, 7), :cuspidalName => "G_{27}[\\zeta_{20}^7]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :parameterExponents => [], :charNumbers => [62], :eigenvalue => E(20, 3), :cuspidalName => "G_{27}[\\zeta_{20}^3]", :qEigen => 1 // 2)], :families => [Family("C1", [1]), Family(((CHEVIE[:families])[:X])(3) * Family("Y6"), [5, 3, 38, 37, 35, 16, 9, 7, 40, 39, 36, 18, 44, 43, 42, 41, 46, 45], Dict{Symbol, Any}(:signs => [-1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1], :ennola => -14)), Family("C2", [30, 11, 12, 47], Dict{Symbol, Any}(:ennola => -4)), Family(((CHEVIE[:families])[:TQZ])(3, E(3), [1, E(3)]), [26, 28, 23, 49, 52, 53, 51, 48, 50], Dict{Symbol, Any}(:cospecial => 3, :ennola => 4)), conj(Family(((CHEVIE[:families])[:X])(3), [33, 31, 54], Dict{Symbol, Any}(:ennola => -3))), Family(((CHEVIE[:families])[:Dihedral])(5) * ((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [19, 20, 66, 65, 21, 22, 64, 63, 58, 57, 60, 59, 56, 55, 62, 61], Dict{Symbol, Any}(:cospecial => 2, :ennola => -4)), Family(((CHEVIE[:families])[:X])(3), [34, 32, 67], Dict{Symbol, Any}(:ennola => -2)), Family(((CHEVIE[:families])[:TQZ])(3, E(3, 2)), [24, 27, 25, 72, 69, 73, 68, 71, 70], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, -1, -1, -1], :cospecial => 2, :ennola => 8)), Family("C2", [29, 13, 14, 74], Dict{Symbol, Any}(:ennola => 4)), conj(Family(((CHEVIE[:families])[:X])(3) * Family("Y6"), [6, 4, 77, 78, 75, 15, 10, 8, 79, 80, 76, 17, 84, 83, 81, 82, 86, 85], Dict{Symbol, Any}(:signs => [-1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1], :ennola => 8))), Family("C1", [2], Dict{Symbol, Any}(:ennola => -1))], :a => [0, 45, 1, 16, 1, 16, 1, 16, 1, 16, 3, 3, 12, 12, 16, 1, 16, 1, 6, 6, 6, 6, 4, 9, 9, 4, 9, 4, 12, 3, 5, 8, 5, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 9, 9, 9, 9, 9, 9, 12, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16], :A => [0, 45, 29, 44, 29, 44, 29, 44, 29, 44, 33, 33, 42, 42, 44, 29, 44, 29, 39, 39, 39, 39, 36, 41, 41, 36, 41, 36, 42, 33, 37, 40, 37, 40, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 33, 36, 36, 36, 36, 36, 36, 37, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 40, 41, 41, 41, 41, 41, 41, 42, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44]) end) chevieset(:G27, :Invariants, [function (x, y, z) return ((((((-90 * x ^ 2 * y ^ 2 * z ^ 2 + 180 * x ^ 2 * y ^ 3 * z + 30 * x ^ 2 * y ^ 4) - 135 * x ^ 2 * z ^ 4) + 135 * y ^ 2 * z ^ 4 + 90 * x ^ 4 * y * z) - 30 * x ^ 4 * y ^ 2) + 45 * x ^ 4 * z ^ 2 + 45 * y ^ 4 * z ^ 2 + 18 * y ^ 5 * z + 10 * x ^ 6) - 10 * y ^ 6) - 27 * z ^ 6 diff --git a/tools/tbl/cmplxg32.jl b/tools/tbl/cmplxg32.jl index f2067a2c..d076f5c5 100644 --- a/tools/tbl/cmplxg32.jl +++ b/tools/tbl/cmplxg32.jl @@ -380,5 +380,5 @@ chevieset(:G32, :UnipotentCharacters, function () end return res end - return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:4, :rank => 4, :ST => 32), :levi => [], :parameterExponents => [1, 1, 1, 1], :charNumbers => 1:102, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 2:4, :rank => 3, :ST => 26), :levi => [1], :parameterExponents => [3, 1, 1], :charNumbers => [103, 171, 240, 241, 121, 120, 242, 117, 234, 105, 233, 104, 108, 238, 199, 126, 162, 109, 235, 173, 200, 127, 163, 110, 236, 172, 130, 203, 161, 226, 119, 175, 131, 204, 160, 225, 118, 174, 152, 153, 177, 179, 178, 176, 201, 128, 202, 129], :eigenvalue => J ^ 2, :cuspidalName => ImprimitiveCuspidalName([[], [0, 1], [0, 1]])), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [4, 3], :rank => 2, :ST => 5), :levi => 1:2, :parameterExponents => [1, [0, 4, 4]], :charNumbers => [239, 113, 114, 246, 135, 132, 245, 133, 134, 136, 230, 229, 124, 208, 206, 123, 205, 207, 182, 181, 180], :eigenvalue => -1, :cuspidalName => "G_4"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [2, 4], :rank => 2, :p => 6, :q => 1), :levi => [1, 3], :parameterExponents => [[3, 3, 2, 0, 0, 2], 3], :charNumbers => [188, 122, 137, 184, 190, 140, 187, 139, 189, 183, 138, 227, 212, 209, 164, 244, 237, 210, 243, 211, 228, 107, 106, 111, 185, 186, 112], :eigenvalue => J, :cuspidalName => Concatenation(ImprimitiveCuspidalName([[], [0, 1], [0, 1]]), "\\otimes ", ImprimitiveCuspidalName([[], [0, 1], [0, 1]]))), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [4], :rank => 1, :p => 6, :q => 1), :levi => 1:3, :parameterExponents => [[6, 4, 1, 0, 1, 4]], :charNumbers => [116, 143, 217, 232, 218, 144], :eigenvalue => J, :cuspidalName => "G_{25}[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [4], :rank => 1, :p => 6, :q => 1), :levi => 1:3, :parameterExponents => [[6, 1, 4, 0, 4, 1]], :charNumbers => [115, 216, 145, 231, 146, 215], :eigenvalue => -J, :cuspidalName => "G_{25}[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [3], :rank => 1, :p => 6, :q => 1), :levi => [1, 2, 4], :parameterExponents => [[9, 8, 5, 0, 5, 8]], :charNumbers => [125, 142, 213, 247, 214, 141], :eigenvalue => -(J ^ 2), :cuspidalName => Concatenation("G_4\\otimes ", ImprimitiveCuspidalName([[], [0, 1], [0, 1]]))), cuspidal(147, 1), cuspidal(148, 1, 2), cuspidal(219, 1, 3), cuspidal(149, -1), cuspidal(191, -1, 2), cuspidal(192, -1, 3), cuspidal(220, -1, 4), cuspidal(151, E(4)), cuspidal(154, E(4), 2, 1 // 2), cuspidal(155, E(4), 3, 1 // 2), cuspidal(150, -(E(4))), cuspidal(156, -(E(4)), 2, 1 // 2), cuspidal(157, -(E(4)), 3, 1 // 2), cuspidal(193, J ^ 2), cuspidal(194, J ^ 2, 2), cuspidal(197, -J), cuspidal(198, -J, 2), cuspidal(195, -(J ^ 2)), cuspidal(196, -(J ^ 2), 2), cuspidal(221, E(5)), cuspidal(222, E(5, 2)), cuspidal(223, E(5, 3)), cuspidal(224, E(5, 4)), cuspidal(165, E(9, 5), 2 // 3), cuspidal(170, E(9, 5), 2, 1 // 3), cuspidal(166, E(9, 2), 1 // 3), cuspidal(168, E(9, 2), 2, 2 // 3), cuspidal(167, E(9, 8), 2 // 3), cuspidal(169, E(9, 8), 2, 1 // 3), cuspidal(158, E(12, 11), 1 // 2), cuspidal(159, E(12, 5), 1 // 2)], :families => [Family("C1", [1]), Family(((CHEVIE[:families])[:X])(3), [9, 6, 103], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 3)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [20, 23, 26, 106, 104, 15, 105, 12, 107], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, 1, 1, 1, 1], :ennola => 8)), Family(((CHEVIE[:families])[:X])(3), [37, 34, 108], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -1)), Family(((CHEVIE[:families])[:X])(6), [57, 64, 49, 61, 54, 111, 113, 109, 115, 17, 116, 110, 18, 114, 112], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1], :ennola => 5)), Family(((CHEVIE[:families])[:X])(3) * Family("X5"), [46, 72, 123, 119, 41, 44, 69, 124, 118, 45, 120, 117, 125, 122, 121], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1], :ennola => -10)), Family(((CHEVIE[:families])[:G4])(), [73, 76, 147, 133, 132, 149, 80, 13, 10, 32, 43, 40, 97, 148, 52, 150, 136, 151, 126, 139, 27, 130, 138, 84, 128, 135, 144, 141, 74, 145, 143, 142, 77, 146, 129, 134, 137, 81, 127, 140, 28, 131], Dict{Symbol, Any}(:signs => [1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1], :ennola => 9)), Family(((CHEVIE[:families])[:X])(3) * Family("C'\"2"), [93, 96, 154, 156, 94, 95, 155, 157, 153, 152, 158, 159], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1], :cospecial => 6, :ennola => 8)), Family(((CHEVIE[:families])[:X])(3) * ((CHEVIE[:families])[:X])(3), [85, 87, 161, 88, 82, 160, 163, 162, 164], Dict{Symbol, Any}(:signs => [1, 1, -1, 1, 1, -1, -1, -1, 1], :cospecial => 5, :ennola => -6)), Family("Z9", [100, 165, 166, 101, 167, 169, 102, 168, 170], Dict{Symbol, Any}(:special => 7, :ennola => 9)), Family(Family("X5") * ((CHEVIE[:families])[:QZ])(3), [53, 21, 59, 90, 185, 177, 47, 187, 193, 79, 33, 36, 98, 184, 179, 99, 183, 178, 180, 182, 181, 192, 198, 196, 191, 197, 195, 171, 172, 173, 174, 68, 189, 175, 71, 190, 56, 60, 24, 48, 188, 194, 89, 186, 176], Dict{Symbol, Any}(:signs => [-1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1], :ennola => 41)), 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E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, -5, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, -5, -5, 5, 5, 5, 5, 5, 5, -5, 5, 5, -5, 5, -5, -5, -5, 5, 5, 5, 5, 5, 5, 5, -5, -5, 5, -5, 5, 5, -5, 0, 0, 0, 0], [-1, -1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, -1, -5, 5, -5, 5, 5, -5, 5, 5, -5, -5, 5, 5, 5, 5, -5, 5, 5, -5, 5, -5, 1, 5, -6, -6, -6, -6], [-5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3, 2), -5 * E(3), -5, -5, 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), -5, -5, -5, -5, 5 * E(3), -5 * E(3, 2), -5, 5, -5, 5, 5, -5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3), 5 * E(3, 2), 5, 5, -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), -5 * E(3, 2), 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-5, -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5, -5, -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5, -5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, 5, -5, 5, 5, -5, 5, -5, -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, -5, -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, -5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5, 5, -5, 5, -5, 5, 5, -5, 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5, 5, 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), -5, 5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, 5, -5, 5, -5, 5, 5, -5, 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5, 5, 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5, 5, 0, 0, 0, 0], [-5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5, -5, 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), 5, 5, -5, -5, 5 * E(3), -5 * E(3, 2), -5, 5, 5, -5, -5, -5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3), -5 * E(3, 2), -5, 5, -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3), 5 * E(3, 2), -5 * E(3, 2), -5 * E(3), -5, -5, 5, 5, -5 * E(3, 2), 5 * E(3), 5, -5, -5, 5, 5, 5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5, 5, -5, 5, 5, -5, -5, 5, 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5, 5, 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5, 5, 0, 0, 0, 0], [-5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, -5, 5, -5, -5, 5, 5, -5, -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5, -5, -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5, -5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5, 5, -5, 5, -5, 5, -5, 5, -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5, -5, -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5, -5, 0, 0, 0, 0], [-5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, -5, 5, -5, 5, -5, 5, -5, 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5, 5, 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, 5, 0, 0, 0, 0], [1, 1, -1, -1, -5, -5, -5, -5, 5, 5, 5, 5, 5, 1, 5, -5, 5, -5, 5, -5, 5, 5, -5, -5, 5, 5, -5, -5, -5, 5, 5, -5, -5, 5, -1, 5, 6, 6, 6, 6], [5, 5, 5, 5, 5, 5, -5, -5, -5, -5, -5, -5, -5, 5, -5, 5, 5, -5, -5, 5, 5, 5, -5, -5, -5, -5, 5, 5, -5, 5, 5, -5, -5, 5, 5, 5, 0, 0, 0, 0], [-6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 9 - 3 * root(5), -6 - 6 * root(5), -6 + 6 * root(5), 9 + 3 * root(5)], [-6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -6 - 6 * root(5), 9 + 3 * root(5), 9 - 3 * root(5), -6 + 6 * root(5)], [-6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -6 + 6 * root(5), 9 - 3 * root(5), 9 + 3 * root(5), -6 - 6 * root(5)], [-6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 9 + 3 * root(5), -6 + 6 * root(5), -6 - 6 * root(5), 9 - 3 * root(5)]] // 30, :eigenvalues => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, J ^ 2, J ^ 2, J ^ 2, J ^ 2, J ^ 2, J ^ 2, -1, -1, -1, -1, J, J, J, J, -(J ^ 2), -(J ^ 2), -J, -J, J, J, 1, -1, E(5), E(5, 2), E(5, 3), E(5, 4)], :explanation => "mystery G32", :name => "?40", :special => 3, :cospecial => 4, :ennola => 14), [8, 5, 65, 62, 86, 83, 66, 63, 51, 50, 67, 70, 91, 92, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), Family(((CHEVIE[:families])[:X])(6), [58, 75, 25, 78, 55, 227, 229, 225, 231, 30, 232, 226, 29, 230, 228], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1], :ennola => -15)), Family(((CHEVIE[:families])[:X])(3) * ((CHEVIE[:families])[:X])(3), [38, 42, 234, 39, 35, 233, 236, 235, 237], Dict{Symbol, Any}(:signs => [1, 1, -1, 1, 1, -1, -1, -1, 1], :cospecial => 5, :ennola => 3)), Family("X5", [19, 31, 239, 238, 22], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, 1], :ennola => -5)), Family(conj(((CHEVIE[:families])[:X])(6)), [14, 7, 16, 4, 11, 240, 246, 244, 247, 2, 242, 243, 3, 245, 241], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1], :special => 13, :cospecial => 10, :ennola => 15))], :a => [0, 40, 40, 40, 15, 1, 40, 15, 1, 6, 40, 2, 6, 40, 2, 40, 4, 4, 30, 2, 12, 30, 2, 12, 20, 2, 6, 6, 20, 20, 30, 6, 12, 3, 25, 12, 3, 25, 25, 6, 5, 25, 6, 5, 5, 5, 12, 12, 4, 15, 15, 6, 12, 4, 20, 12, 4, 20, 12, 12, 4, 15, 15, 4, 15, 15, 15, 12, 5, 15, 12, 5, 6, 6, 20, 6, 6, 20, 12, 6, 6, 9, 15, 6, 9, 15, 9, 9, 12, 12, 15, 15, 8, 8, 8, 8, 6, 12, 12, 10, 10, 10, 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 20, 20, 20, 20, 20, 20, 20, 20, 25, 25, 25, 25, 25, 30, 30, 40, 40, 40, 40, 40, 40, 40, 40], :A => [0, 80, 80, 80, 75, 29, 80, 75, 29, 66, 80, 46, 66, 80, 46, 80, 56, 56, 78, 46, 72, 78, 46, 72, 76, 46, 66, 66, 76, 76, 78, 66, 72, 51, 77, 72, 51, 77, 77, 66, 61, 77, 66, 61, 61, 61, 72, 72, 56, 75, 75, 66, 72, 56, 76, 72, 56, 76, 72, 72, 56, 75, 75, 56, 75, 75, 75, 72, 61, 75, 72, 61, 66, 66, 76, 66, 66, 76, 72, 66, 66, 69, 75, 66, 69, 75, 69, 69, 72, 72, 75, 75, 67, 67, 67, 67, 66, 72, 72, 70, 70, 70, 29, 46, 46, 46, 46, 51, 56, 56, 56, 56, 56, 56, 56, 56, 61, 61, 61, 61, 61, 61, 61, 61, 61, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 67, 67, 67, 67, 67, 67, 67, 67, 69, 69, 69, 69, 69, 70, 70, 70, 70, 70, 70, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 76, 76, 76, 76, 76, 76, 76, 76, 77, 77, 77, 77, 77, 78, 78, 80, 80, 80, 80, 80, 80, 80, 80]) + return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:4, :rank => 4, :ST => 32), :levi => [], :parameterExponents => [1, 1, 1, 1], :charNumbers => 1:102, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 2:4, :rank => 3, :ST => 26), :levi => [1], :parameterExponents => [3, 1, 1], :charNumbers => [103, 171, 240, 241, 121, 120, 242, 117, 234, 105, 233, 104, 108, 238, 199, 126, 162, 109, 235, 173, 200, 127, 163, 110, 236, 172, 130, 203, 161, 226, 119, 175, 131, 204, 160, 225, 118, 174, 152, 153, 177, 179, 178, 176, 201, 128, 202, 129], :eigenvalue => J ^ 2, :cuspidalName => ImprimitiveCuspidalName([[], [0, 1], [0, 1]])), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [4, 3], :rank => 2, :ST => 5), :levi => 1:2, :parameterExponents => [1, [0, 4, 4]], :charNumbers => [239, 113, 114, 246, 135, 132, 245, 133, 134, 136, 230, 229, 124, 208, 206, 123, 205, 207, 182, 181, 180], :eigenvalue => -1, :cuspidalName => "G_4"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [2, 4], :rank => 2, :p => 6, :q => 1), :levi => [1, 3], :parameterExponents => [[3, 3, 2, 0, 0, 2], 3], :charNumbers => [188, 122, 137, 184, 190, 140, 187, 139, 189, 183, 138, 227, 212, 209, 164, 244, 237, 210, 243, 211, 228, 107, 106, 111, 185, 186, 112], :eigenvalue => J, :cuspidalName => Concatenation(ImprimitiveCuspidalName([[], [0, 1], [0, 1]]), "\\otimes ", ImprimitiveCuspidalName([[], [0, 1], [0, 1]]))), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [4], :rank => 1, :p => 6, :q => 1), :levi => 1:3, :parameterExponents => [[6, 4, 1, 0, 1, 4]], :charNumbers => [116, 143, 217, 232, 218, 144], :eigenvalue => J, :cuspidalName => "G_{25}[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [4], :rank => 1, :p => 6, :q => 1), :levi => 1:3, :parameterExponents => [[6, 1, 4, 0, 4, 1]], :charNumbers => [115, 216, 145, 231, 146, 215], :eigenvalue => -J, :cuspidalName => "G_{25}[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [3], :rank => 1, :p => 6, :q => 1), :levi => [1, 2, 4], :parameterExponents => [[9, 8, 5, 0, 5, 8]], :charNumbers => [125, 142, 213, 247, 214, 141], :eigenvalue => -(J ^ 2), :cuspidalName => Concatenation("G_4\\otimes ", ImprimitiveCuspidalName([[], [0, 1], [0, 1]]))), cuspidal(147, 1), cuspidal(148, 1, 2), cuspidal(219, 1, 3), cuspidal(149, -1), cuspidal(191, -1, 2), cuspidal(192, -1, 3), cuspidal(220, -1, 4), cuspidal(151, E(4)), cuspidal(154, E(4), 2, 1 // 2), cuspidal(155, E(4), 3, 1 // 2), cuspidal(150, -(E(4))), cuspidal(156, -(E(4)), 2, 1 // 2), cuspidal(157, -(E(4)), 3, 1 // 2), cuspidal(193, J ^ 2), cuspidal(194, J ^ 2, 2), cuspidal(197, -J), cuspidal(198, -J, 2), cuspidal(195, -(J ^ 2)), cuspidal(196, -(J ^ 2), 2), cuspidal(221, E(5)), cuspidal(222, E(5, 2)), cuspidal(223, E(5, 3)), cuspidal(224, E(5, 4)), cuspidal(165, E(9, 5), 2 // 3), cuspidal(170, E(9, 5), 2, 1 // 3), cuspidal(166, E(9, 2), 1 // 3), cuspidal(168, E(9, 2), 2, 2 // 3), cuspidal(167, E(9, 8), 2 // 3), cuspidal(169, E(9, 8), 2, 1 // 3), cuspidal(158, E(12, 11), 1 // 2), cuspidal(159, E(12, 5), 1 // 2)], :families => [Family("C1", [1]), Family(((CHEVIE[:families])[:X])(3), [9, 6, 103], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 3)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [20, 23, 26, 106, 104, 15, 105, 12, 107], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, 1, 1, 1, 1], :ennola => 8)), Family(((CHEVIE[:families])[:X])(3), [37, 34, 108], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -1)), Family(((CHEVIE[:families])[:X])(6), [57, 64, 49, 61, 54, 111, 113, 109, 115, 17, 116, 110, 18, 114, 112], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1], :ennola => 5)), Family(((CHEVIE[:families])[:X])(3) * Family("X5"), [46, 72, 123, 119, 41, 44, 69, 124, 118, 45, 120, 117, 125, 122, 121], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1], :ennola => -10)), Family(((CHEVIE[:families])[:G4])(), [73, 76, 147, 133, 132, 149, 80, 13, 10, 32, 43, 40, 97, 148, 52, 150, 136, 151, 126, 139, 27, 130, 138, 84, 128, 135, 144, 141, 74, 145, 143, 142, 77, 146, 129, 134, 137, 81, 127, 140, 28, 131], Dict{Symbol, Any}(:signs => [1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1], :ennola => 9)), Family(((CHEVIE[:families])[:X])(3) * ((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [93, 96, 156, 154, 94, 95, 157, 155, 153, 152, 159, 158], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1], :cospecial => 6, :ennola => 7)), Family(((CHEVIE[:families])[:X])(3) * ((CHEVIE[:families])[:X])(3), [85, 87, 161, 88, 82, 160, 163, 162, 164], Dict{Symbol, Any}(:signs => [1, 1, -1, 1, 1, -1, -1, -1, 1], :cospecial => 5, :ennola => -6)), Family(((CHEVIE[:families])[:TQZ])(3, E(3, 2), [1, E(3, 2)]), [102, 100, 101, 167, 168, 165, 170, 166, 169], Dict{Symbol, Any}(:ennola => 7)), Family(Family("X5") * ((CHEVIE[:families])[:QZ])(3), [53, 21, 59, 90, 185, 177, 47, 187, 193, 79, 33, 36, 98, 184, 179, 99, 183, 178, 180, 182, 181, 192, 198, 196, 191, 197, 195, 171, 172, 173, 174, 68, 189, 175, 71, 190, 56, 60, 24, 48, 188, 194, 89, 186, 176], Dict{Symbol, Any}(:signs => [-1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1], :ennola => 41)), Family(Dict{Symbol, Any}(:fourierMat => [[-1, -1, 1, 1, 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5, 5, 5, -1, -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5, 5, -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 1, 5, -6, -6, -6, -6], [-1, -1, 1, 1, 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, 5, 5, -1, -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5, 5, -5 * E(3), -5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), 1, 5, -6, -6, -6, -6], [1, 1, -1, -1, -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5, 5, 5, 1, 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5, 5, -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -1, 5, 6, 6, 6, 6], [1, 1, -1, -1, -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, 5, 5, 1, 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), 5, 5, -5 * E(3), -5 * E(3, 2), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), -1, 5, 6, 6, 6, 6], [5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5, 5, 5, 5, 5, 5, 5 * E(3), 5 * E(3, 2), 5, 5, -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5, -5, 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3), 5 * E(3, 2), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), -5, 5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5, 5, 5, 5, 5, 5, 5 * E(3, 2), 5 * E(3), 5, 5, -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5, -5, 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3, 2), 5 * E(3), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5, 5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5, 5, 5, 5, -5, -5, -5 * E(3), -5 * E(3, 2), -5, 5, -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5, 5, -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3), -5 * E(3, 2), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5, -5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5, 5, 5, 5, -5, -5, -5 * E(3, 2), -5 * E(3), -5, 5, -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5, 5, -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), -5 * E(3), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5, -5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5, 5, -5, -5, 5, 5, 5 * E(3), 5 * E(3, 2), 5, 5, -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5, 5, 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3), -5 * E(3, 2), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5, -5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, 5, -5, -5, 5, 5, 5 * E(3, 2), 5 * E(3), 5, 5, -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), 5, 5, 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), -5 * E(3), -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, -5, 0, 0, 0, 0], [5, 5, 5, 5, 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, 5, 5, 5, -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), -5, -5, 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5, -5, 0, 0, 0, 0], [5, 5, 5, 5, 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5, 5, 5, 5, -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5, -5, 5 * E(3, 2), 5 * E(3), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, -5, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, -5, -5, 5, 5, 5, 5, 5, 5, -5, 5, 5, -5, 5, -5, -5, -5, 5, 5, 5, 5, 5, 5, 5, -5, -5, 5, -5, 5, 5, -5, 0, 0, 0, 0], [-1, -1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, -1, -5, 5, -5, 5, 5, -5, 5, 5, -5, -5, 5, 5, 5, 5, -5, 5, 5, -5, 5, -5, 1, 5, -6, -6, -6, -6], [-5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3, 2), -5 * E(3), -5, -5, 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), -5, -5, -5, -5, 5 * E(3), -5 * E(3, 2), -5, 5, -5, 5, 5, -5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3), 5 * E(3, 2), 5, 5, -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), -5 * E(3, 2), -5 * E(3), 5, 5, 5, 5, -5 * E(3, 2), 5 * E(3), 5, -5, 5, -5, -5, 5, 0, 0, 0, 0], [-5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5, -5, 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3, 2), 5 * E(3), -5 * E(3), -5 * E(3, 2), 5, 5, -5, -5, -5 * E(3), 5 * E(3, 2), 5, -5, -5, 5, 5, 5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3), -5 * E(3, 2), -5, 5, -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3), -5 * E(3, 2), 5 * E(3, 2), 5 * E(3), -5, -5, 5, 5, 5 * E(3, 2), -5 * E(3), -5, 5, 5, -5, -5, -5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5, 5, -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), 5, 5, 5, 5, 5 * E(3), -5 * E(3, 2), -5, 5, -5, 5, 5, -5, 0, 0, 0, 0], [-5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3), -5 * E(3, 2), -5, -5, 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3), 5 * E(3, 2), -5 * E(3, 2), -5 * E(3), -5, -5, -5, -5, -5 * E(3, 2), 5 * E(3), 5, -5, 5, -5, -5, 5, 0, 0, 0, 0], [5, 5, 5, 5, 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5, -5, -5, 5, -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5, 5, -5 * E(3), -5 * E(3, 2), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5, 5, 0, 0, 0, 0], [5, 5, 5, 5, 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5, -5, -5, 5, -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, 5, -5 * E(3, 2), -5 * E(3), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, 5, 0, 0, 0, 0], [-5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5, -5, 5, 5, 5, 5, 5 * E(3), 5 * E(3, 2), 5, -5, 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5, 5, 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3), -5 * E(3, 2), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5, -5, 0, 0, 0, 0], [-5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5, -5, 5, 5, 5, 5, 5 * E(3, 2), 5 * E(3), 5, -5, 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), 5, 5, 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3, 2), -5 * E(3), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5, -5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5, 5, -5, 5, 5, -5, 5, -5, -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5, -5, -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), 5 * E(3), 5, -5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, 5, -5, 5, 5, -5, 5, -5, -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, -5, -5 * E(3), 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, -5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5, 5, -5, 5, -5, 5, 5, -5, 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5, 5, 5 * E(3, 2), -5 * E(3), 5 * E(3, 2), -5 * E(3), -5, 5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, 5, -5, 5, -5, 5, 5, -5, 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5, 5, 5 * E(3), -5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5, 5, 0, 0, 0, 0], [-5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5, -5, 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3, 2), -5 * E(3), 5 * E(3), 5 * E(3, 2), 5, 5, -5, -5, 5 * E(3), -5 * E(3, 2), -5, 5, 5, -5, -5, -5, 0, 0, 0, 0], [5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3), -5 * E(3, 2), -5, 5, -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3), 5 * E(3, 2), -5 * E(3, 2), -5 * E(3), -5, -5, 5, 5, -5 * E(3, 2), 5 * E(3), 5, -5, -5, 5, 5, 5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5, 5, -5, 5, 5, -5, -5, 5, 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5, 5, 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5, 5, 0, 0, 0, 0], [-5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, -5, 5, -5, -5, 5, 5, -5, -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5, -5, -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5, -5, 0, 0, 0, 0], [5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5, 5, -5, 5, -5, 5, -5, 5, -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), 5, -5, -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5, -5, 0, 0, 0, 0], [-5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5 * E(3), -5 * E(3), -5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5 * E(3), 5 * E(3, 2), 5, -5, 5, -5, 5, -5, 5, -5, 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), 5 * E(3), 5 * E(3, 2), -5 * E(3), -5 * E(3, 2), -5, 5, 5 * E(3), -5 * E(3, 2), -5 * E(3), 5 * E(3, 2), 5, 5, 0, 0, 0, 0], [1, 1, -1, -1, -5, -5, -5, -5, 5, 5, 5, 5, 5, 1, 5, -5, 5, -5, 5, -5, 5, 5, -5, -5, 5, 5, -5, -5, -5, 5, 5, -5, -5, 5, -1, 5, 6, 6, 6, 6], [5, 5, 5, 5, 5, 5, -5, -5, -5, -5, -5, -5, -5, 5, -5, 5, 5, -5, -5, 5, 5, 5, -5, -5, -5, -5, 5, 5, -5, 5, 5, -5, -5, 5, 5, 5, 0, 0, 0, 0], [-6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 9 - 3 * root(5), -6 - 6 * root(5), -6 + 6 * root(5), 9 + 3 * root(5)], [-6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -6 - 6 * root(5), 9 + 3 * root(5), 9 - 3 * root(5), -6 + 6 * root(5)], [-6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -6 + 6 * root(5), 9 - 3 * root(5), 9 + 3 * root(5), -6 - 6 * root(5)], [-6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 9 + 3 * root(5), -6 + 6 * root(5), -6 - 6 * root(5), 9 - 3 * root(5)]] // 30, :eigenvalues => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, J ^ 2, J ^ 2, J ^ 2, J ^ 2, J ^ 2, J ^ 2, -1, -1, -1, -1, J, J, J, J, -(J ^ 2), -(J ^ 2), -J, -J, J, J, 1, -1, E(5), E(5, 2), E(5, 3), E(5, 4)], :explanation => "mystery G32", :name => "?40", :special => 3, :cospecial => 4, :ennola => 14), [8, 5, 65, 62, 86, 83, 66, 63, 51, 50, 67, 70, 91, 92, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), Family(((CHEVIE[:families])[:X])(6), [58, 75, 25, 78, 55, 227, 229, 225, 231, 30, 232, 226, 29, 230, 228], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1], :ennola => -15)), Family(((CHEVIE[:families])[:X])(3) * ((CHEVIE[:families])[:X])(3), [38, 42, 234, 39, 35, 233, 236, 235, 237], Dict{Symbol, Any}(:signs => [1, 1, -1, 1, 1, -1, -1, -1, 1], :cospecial => 5, :ennola => 3)), Family("X5", [19, 31, 239, 238, 22], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, 1], :ennola => -5)), Family(conj(((CHEVIE[:families])[:X])(6)), [14, 7, 16, 4, 11, 240, 246, 244, 247, 2, 242, 243, 3, 245, 241], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1], :special => 13, :cospecial => 10, :ennola => 15))], :a => [0, 40, 40, 40, 15, 1, 40, 15, 1, 6, 40, 2, 6, 40, 2, 40, 4, 4, 30, 2, 12, 30, 2, 12, 20, 2, 6, 6, 20, 20, 30, 6, 12, 3, 25, 12, 3, 25, 25, 6, 5, 25, 6, 5, 5, 5, 12, 12, 4, 15, 15, 6, 12, 4, 20, 12, 4, 20, 12, 12, 4, 15, 15, 4, 15, 15, 15, 12, 5, 15, 12, 5, 6, 6, 20, 6, 6, 20, 12, 6, 6, 9, 15, 6, 9, 15, 9, 9, 12, 12, 15, 15, 8, 8, 8, 8, 6, 12, 12, 10, 10, 10, 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 20, 20, 20, 20, 20, 20, 20, 20, 25, 25, 25, 25, 25, 30, 30, 40, 40, 40, 40, 40, 40, 40, 40], :A => [0, 80, 80, 80, 75, 29, 80, 75, 29, 66, 80, 46, 66, 80, 46, 80, 56, 56, 78, 46, 72, 78, 46, 72, 76, 46, 66, 66, 76, 76, 78, 66, 72, 51, 77, 72, 51, 77, 77, 66, 61, 77, 66, 61, 61, 61, 72, 72, 56, 75, 75, 66, 72, 56, 76, 72, 56, 76, 72, 72, 56, 75, 75, 56, 75, 75, 75, 72, 61, 75, 72, 61, 66, 66, 76, 66, 66, 76, 72, 66, 66, 69, 75, 66, 69, 75, 69, 69, 72, 72, 75, 75, 67, 67, 67, 67, 66, 72, 72, 70, 70, 70, 29, 46, 46, 46, 46, 51, 56, 56, 56, 56, 56, 56, 56, 56, 61, 61, 61, 61, 61, 61, 61, 61, 61, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 67, 67, 67, 67, 67, 67, 67, 67, 69, 69, 69, 69, 69, 70, 70, 70, 70, 70, 70, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 76, 76, 76, 76, 76, 76, 76, 76, 77, 77, 77, 77, 77, 78, 78, 80, 80, 80, 80, 80, 80, 80, 80]) end) diff --git a/tools/tbl/cmplxg33.jl b/tools/tbl/cmplxg33.jl index 08b6293d..b9f4d395 100644 --- a/tools/tbl/cmplxg33.jl +++ b/tools/tbl/cmplxg33.jl @@ -173,7 +173,7 @@ chevieset(:G33, :Representation, (i->begin chevieset(:G33, :UnipotentCharacters, function () local J J = E(3) - return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:5, :rank => 5, :ST => 33), :levi => [], :parameterExponents => [1, 1, 1, 1, 1], :charNumbers => 1:40, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1, 5], :rank => 2, :ST => 4), :levi => 2:4, :parameterExponents => [3, 3], :charNumbers => [41, 58, 57, 59, 43, 44, 51], :eigenvalue => J, :cuspidalName => "G_{3,3,3}[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1, 5], :rank => 2, :ST => 4), :levi => 2:4, :parameterExponents => [[3, 3, 0], [3, 3, 0]], :charNumbers => [46, 45, 64, 55, 56, 47, 54], :eigenvalue => J ^ 2, :cuspidalName => "G_{3,3,3}[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [4], :rank => 1, :p => 6, :q => 1), :levi => [1, 2, 3, 209], :parameterExponents => [[5, 4, 1, 0, 1, 4]], :charNumbers => [42, 49, 60, 63, 61, 48], :eigenvalue => -1, :cuspidalName => "D_4"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:5, :parameterExponents => [], :charNumbers => [52], :eigenvalue => E(4), :cuspidalName => "G_{33}[i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:5, :parameterExponents => [], :charNumbers => [53], :eigenvalue => -(E(4)), :cuspidalName => "G_{33}[-i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:5, :parameterExponents => [], :charNumbers => [62], :eigenvalue => -J, :cuspidalName => "G_{33}[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:5, :parameterExponents => [], :charNumbers => [50], :eigenvalue => -(J ^ 2), :cuspidalName => "G_{33}[-\\zeta_3^2]")], :families => [Family("C1", [1]), Family(conj(((CHEVIE[:families])[:X])(3)), [4, 6, 41], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -1)), Family("C1", [15]), Family("C2", [22, 8, 19, 42], Dict{Symbol, Any}(:ennola => -2)), Family(conj(((CHEVIE[:families])[:X])(6)), [25, 30, 17, 28, 23, 45, 48, 43, 50, 9, 47, 44, 11, 49, 46], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1], :ennola => -13)), Family("C1", [39]), Family("C1", [36], Dict{Symbol, Any}(:ennola => -1)), Family(conj(((CHEVIE[:families])[:X])(3)), [34, 32, 51], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -1)), Family("C'\"2", [37, 38, 52, 53], Dict{Symbol, Any}(:ennola => -3)), Family("C1", [14], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:X])(3), [33, 31, 54], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 1)), Family("C1", [40], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [35]), Family("C1", [13]), Family(((CHEVIE[:families])[:X])(6), [26, 29, 18, 27, 24, 57, 60, 55, 62, 10, 59, 56, 12, 61, 58], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1], :ennola => 13)), Family("C2", [21, 7, 20, 63], Dict{Symbol, Any}(:ennola => 2)), Family("C1", [16], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:X])(3), [3, 5, 64], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 1)), Family("C1", [2], Dict{Symbol, Any}(:ennola => -1))], :a => [0, 45, 28, 1, 28, 1, 18, 3, 4, 13, 4, 13, 12, 9, 2, 23, 4, 13, 3, 18, 18, 3, 4, 13, 4, 13, 13, 4, 13, 4, 10, 7, 10, 7, 10, 7, 8, 8, 6, 11, 1, 3, 4, 4, 4, 4, 4, 4, 4, 4, 7, 8, 8, 10, 13, 13, 13, 13, 13, 13, 13, 13, 18, 28], :A => [0, 45, 44, 17, 44, 17, 42, 27, 32, 41, 32, 41, 36, 33, 22, 43, 32, 41, 27, 42, 42, 27, 32, 41, 32, 41, 41, 32, 41, 32, 38, 35, 38, 35, 38, 35, 37, 37, 34, 39, 17, 27, 32, 32, 32, 32, 32, 32, 32, 32, 35, 37, 37, 38, 41, 41, 41, 41, 41, 41, 41, 41, 42, 44], :curtis => [2, 1, 6, 5, 4, 3, 8, 7, 12, 11, 10, 9, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 26, 25, 24, 23, 30, 29, 28, 27, 34, 33, 32, 31, 36, 35, 38, 37, 40, 39, -64, 63, -56, -55, -58, -57, -59, 61, 60, -62, -54, -53, -52, -51, -44, -43, -46, -45, -47, 49, 48, -50, 42, -41]) + return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:5, :rank => 5, :ST => 33), :levi => [], :parameterExponents => [1, 1, 1, 1, 1], :charNumbers => 1:40, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1, 5], :rank => 2, :ST => 4), :levi => 2:4, :parameterExponents => [3, 3], :charNumbers => [41, 58, 57, 59, 43, 44, 51], :eigenvalue => J, :cuspidalName => "G_{3,3,3}[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [1, 5], :rank => 2, :ST => 4), :levi => 2:4, :parameterExponents => [[3, 3, 0], [3, 3, 0]], :charNumbers => [46, 45, 64, 55, 56, 47, 54], :eigenvalue => J ^ 2, :cuspidalName => "G_{3,3,3}[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [4], :rank => 1, :p => 6, :q => 1), :levi => [1, 2, 3, 209], :parameterExponents => [[5, 4, 1, 0, 1, 4]], :charNumbers => [42, 49, 60, 63, 61, 48], :eigenvalue => -1, :cuspidalName => "D_4"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:5, :parameterExponents => [], :charNumbers => [52], :eigenvalue => E(4), :cuspidalName => "G_{33}[i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:5, :parameterExponents => [], :charNumbers => [53], :eigenvalue => -(E(4)), :cuspidalName => "G_{33}[-i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:5, :parameterExponents => [], :charNumbers => [62], :eigenvalue => -J, :cuspidalName => "G_{33}[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:5, :parameterExponents => [], :charNumbers => [50], :eigenvalue => -(J ^ 2), :cuspidalName => "G_{33}[-\\zeta_3^2]")], :families => [Family("C1", [1]), Family(conj(((CHEVIE[:families])[:X])(3)), [4, 6, 41], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -1)), Family("C1", [15]), Family("C2", [22, 8, 19, 42], Dict{Symbol, Any}(:ennola => -2)), Family(conj(((CHEVIE[:families])[:X])(6)), [25, 30, 17, 28, 23, 45, 48, 43, 50, 9, 47, 44, 11, 49, 46], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1], :ennola => -13)), Family("C1", [39]), Family("C1", [36], Dict{Symbol, Any}(:ennola => -1)), Family(conj(((CHEVIE[:families])[:X])(3)), [34, 32, 51], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -1)), Family(((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [37, 38, 53, 52], Dict{Symbol, Any}(:cospecial => 2, :ennola => -4)), Family("C1", [14], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:X])(3), [33, 31, 54], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 1)), Family("C1", [40], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [35]), Family("C1", [13]), Family(((CHEVIE[:families])[:X])(6), [26, 29, 18, 27, 24, 57, 60, 55, 62, 10, 59, 56, 12, 61, 58], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1], :ennola => 13)), Family("C2", [21, 7, 20, 63], Dict{Symbol, Any}(:ennola => 2)), Family("C1", [16], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:X])(3), [3, 5, 64], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 1)), Family("C1", [2], Dict{Symbol, Any}(:ennola => -1))], :a => [0, 45, 28, 1, 28, 1, 18, 3, 4, 13, 4, 13, 12, 9, 2, 23, 4, 13, 3, 18, 18, 3, 4, 13, 4, 13, 13, 4, 13, 4, 10, 7, 10, 7, 10, 7, 8, 8, 6, 11, 1, 3, 4, 4, 4, 4, 4, 4, 4, 4, 7, 8, 8, 10, 13, 13, 13, 13, 13, 13, 13, 13, 18, 28], :A => [0, 45, 44, 17, 44, 17, 42, 27, 32, 41, 32, 41, 36, 33, 22, 43, 32, 41, 27, 42, 42, 27, 32, 41, 32, 41, 41, 32, 41, 32, 38, 35, 38, 35, 38, 35, 37, 37, 34, 39, 17, 27, 32, 32, 32, 32, 32, 32, 32, 32, 35, 37, 37, 38, 41, 41, 41, 41, 41, 41, 41, 41, 42, 44], :curtis => [2, 1, 6, 5, 4, 3, 8, 7, 12, 11, 10, 9, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 26, 25, 24, 23, 30, 29, 28, 27, 34, 33, 32, 31, 36, 35, 38, 37, 40, 39, -64, 63, -56, -55, -58, -57, -59, 61, 60, -62, -54, -53, -52, -51, -44, -43, -46, -45, -47, 49, 48, -50, 42, -41]) end) chevieset(:G33, :Invariants, [function (x, y, z, t, u) local a1, a4 diff --git a/tools/tbl/cmplxg34.jl b/tools/tbl/cmplxg34.jl index f28c07f0..2f63bf7c 100644 --- a/tools/tbl/cmplxg34.jl +++ b/tools/tbl/cmplxg34.jl @@ -445,7 +445,7 @@ chevieset(:G34, :UnipotentCharacters, function () end return res end - return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:6, :rank => 6, :ST => 34), :levi => [], :parameterExponents => [1, 1, 1, 1, 1, 1], :charNumbers => 1:169, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6, 5, 1], :rank => 3, :ST => 26), :levi => 2:4, :parameterExponents => [1, 3, 3], :charNumbers => [170, 171, 340, 341, 325, 324, 342, 326, 220, 185, 219, 186, 216, 274, 249, 226, 184, 173, 334, 332, 251, 225, 183, 174, 335, 333, 232, 253, 299, 310, 189, 208, 231, 255, 298, 309, 190, 209, 197, 198, 280, 281, 282, 279, 245, 224, 247, 223], :eigenvalue => J, :cuspidalName => "G_{3,3,3}[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6, 5, 1], :rank => 3, :ST => 26), :levi => 2:4, :parameterExponents => [1, [3, 3, 0], [3, 3, 0]], :charNumbers => [176, 191, 348, 192, 347, 175, 331, 300, 193, 177, 330, 301, 244, 302, 187, 181, 278, 252, 338, 337, 339, 336, 188, 182, 277, 250, 311, 322, 256, 284, 207, 218, 206, 217, 312, 323, 254, 283, 227, 230, 314, 315, 228, 229, 276, 248, 275, 246], :eigenvalue => J ^ 2, :cuspidalName => "G_{3,3,3}[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [4, 6], :rank => 2, :p => 6, :q => 1), :levi => [1, 2, 3, 348], :parameterExponents => [[5, 4, 1, 0, 1, 4], 4], :charNumbers => [235, 194, 236, 273, 237, 195, 286, 259, 289, 257, 205, 343, 328, 313, 258, 346, 327, 288, 344, 260, 285, 172, 179, 233, 287, 234, 178], :eigenvalue => -1, :cuspidalName => "D_4"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6], :rank => 1, :p => 6, :q => 1), :levi => 1:5, :parameterExponents => [[5, 0, 7, 2, 7, 0]], :charNumbers => [221, 317, 199, 296, 200, 316], :eigenvalue => E(4), :cuspidalName => "G_{33}[i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6], :rank => 1, :p => 6, :q => 1), :levi => 1:5, :parameterExponents => [[5, 0, 7, 2, 7, 0]], :charNumbers => [222, 319, 201, 297, 202, 318], :eigenvalue => -(E(4)), :qEigen => 1 // 2, :cuspidalName => "G_{33}[-i]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6], :rank => 1, :p => 6, :q => 1), :levi => 1:5, :parameterExponents => [[3, 8, 7, 0, 7, 8]], :charNumbers => [329, 238, 261, 345, 263, 239], :eigenvalue => -J, :cuspidalName => "G_{33}[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6], :rank => 1, :p => 6, :q => 1), :levi => 1:5, :parameterExponents => [[8, 1, 0, 5, 0, 1]], :charNumbers => [180, 262, 291, 196, 290, 264], :eigenvalue => -(J ^ 2), :cuspidalName => "G_{33}[-\\zeta_3^2]"), cuspidal(265, 1), cuspidal(266, -1), cuspidal(294, J), cuspidal(295, J, 2), cuspidal(242, J ^ 2), cuspidal(243, J ^ 2, 2), cuspidal(292, -J), cuspidal(293, -J, 2), cuspidal(240, -(J ^ 2)), cuspidal(241, -(J ^ 2), 2), cuspidal(267, E(7)), cuspidal(268, E(7, 2)), cuspidal(269, E(7, 3)), cuspidal(270, E(7, 4)), cuspidal(271, E(7, 5)), cuspidal(272, E(7, 6)), cuspidal(212, E(9), 1 // 3), cuspidal(214, E(9), 2, 2 // 3), cuspidal(307, E(9, 2), 2 // 3), cuspidal(303, E(9, 2), 2, 1 // 3), cuspidal(210, E(9, 4), 1 // 3), cuspidal(215, E(9, 4), 2, 2 // 3), cuspidal(304, E(9, 5), 2 // 3), cuspidal(305, E(9, 5), 2, 1 // 3), cuspidal(211, E(9, 7), 2 // 3), cuspidal(213, E(9, 7), 2, 1 // 3), cuspidal(306, E(9, 8), 1 // 3), cuspidal(308, E(9, 8), 2, 2 // 3), cuspidal(203, E(12, 7), 1 // 2), cuspidal(320, E(12, 11), 1 // 2), cuspidal(204, E(12), 1 // 2), cuspidal(321, E(12, 5), 1 // 2)], :families => [Family("C1", [1]), Family(conj(((CHEVIE[:families])[:X])(3)), [5, 3, 170], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 2)), Family(conj(((CHEVIE[:families])[:X])(3)), [17, 15, 171], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -3)), Family("C2", [24, 14, 20, 172], Dict{Symbol, Any}(:ennola => -4)), Family(((CHEVIE[:families])[:X])(3) * conj(Family("X5")), [42, 55, 178, 174, 8, 10, 53, 179, 173, 46, 176, 177, 180, 37, 175], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1], :ennola => 15)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [57, 59, 26, 184, 182, 32, 181, 31, 183], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, -1, 1, -1, -1], :ennola => -7)), Family(((CHEVIE[:families])[:QZ])(3), [81, 68, 71, 45, 185, 188, 39, 186, 187], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, -1, -1], :ennola => 6)), Family(((CHEVIE[:families])[:X])(3) * conj(Family("X5")), [109, 89, 194, 190, 35, 33, 91, 195, 189, 107, 192, 193, 196, 116, 191], Dict{Symbol, Any}(:signs => [1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1], :ennola => -15)), Family(conj(((CHEVIE[:families])[:X])(3)) * Family("C'\"2"), [103, 96, 199, 201, 101, 98, 200, 202, 198, 197, 203, 204], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], :cospecial => 6, :ennola => 11)), Family("C1", [28], Dict{Symbol, Any}(:ennola => -1)), Family("C2", [124, 63, 105, 205], Dict{Symbol, Any}(:ennola => -4)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [84, 86, 22, 209, 207, 78, 206, 79, 208], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, -1, 1, -1, -1], :ennola => 4)), Family(conj(Family("Z9")), [141, 215, 213, 145, 214, 212, 143, 211, 210], Dict{Symbol, Any}(:special => 7, :cospecial => 1, :ennola => 2)), Family(conj(((CHEVIE[:families])[:X])(3)), [134, 136, 216], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 3)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [154, 156, 129, 220, 218, 74, 217, 72, 219], Dict{Symbol, Any}(:signs => [1, 1, 1, -1, -1, -1, 1, -1, 1], :ennola => -9)), Family("C1", [67]), Family("C'\"2", [159, 161, 221, 222], Dict{Symbol, Any}(:ennola => -3)), Family(((CHEVIE[:families])[:QZ])(6, [Perm(), [E(6)]]), [152, 164, 118, 162, 150, 65, 240, 225, 236, 228, 238, 113, 232, 242, 94, 224, 230, 146, 233, 49, 235, 47, 234, 83, 229, 148, 231, 243, 92, 223, 239, 111, 241, 226, 237, 227], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1], :ennola => 33)), Family(((CHEVIE[:families])[:X])(3), [132, 130, 244], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -2)), Family(((CHEVIE[:families])[:F42])(), [169, 265, 122, 121, 12, 11, 52, 166, 245, 252, 119, 249, 248, 138, 262, 255, 258, 254, 263, 167, 247, 250, 120, 251, 246, 139, 264, 253, 257, 256, 261, 168, 259, 126, 266, 127, 260, 51, 267, 268, 269, 270, 271, 272], Dict{Symbol, Any}(:signs => [1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1], :ennola => 3)), Family("C2", [125, 61, 106, 273], Dict{Symbol, Any}(:ennola => 4)), Family(conj(((CHEVIE[:families])[:X])(3)), [133, 131, 274], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -3)), Family(((CHEVIE[:families])[:QZ])(6, [Perm(), [E(3)]]), [151, 64, 153, 163, 117, 165, 280, 288, 277, 292, 114, 290, 284, 147, 282, 276, 93, 294, 48, 287, 50, 285, 82, 286, 281, 275, 95, 295, 283, 149, 278, 293, 112, 291, 279, 289], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1], :ennola => -8)), Family("C'\"2", [160, 158, 296, 297], Dict{Symbol, Any}(:ennola => 3)), Family("C1", [66]), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [157, 155, 128, 298, 300, 73, 301, 75, 299], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, -1, -1, -1, -1], :ennola => 8)), Family(((CHEVIE[:families])[:X])(3), [137, 135, 302], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 2)), Family("Z9", [140, 304, 303, 144, 308, 306, 142, 307, 305], Dict{Symbol, Any}(:special => 1, :cospecial => 4, :ennola => 6)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [85, 87, 21, 309, 311, 77, 312, 76, 310], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, -1, 1, -1, -1], :ennola => 4)), Family("C2", [123, 62, 104, 313], Dict{Symbol, Any}(:ennola => -4)), Family("C1", [27], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:X])(3) * Family("C'\"2"), [97, 102, 316, 318, 99, 100, 317, 319, 315, 314, 320, 321], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], :cospecial => 6, :ennola => -7)), Family(conj(((CHEVIE[:families])[:X])(3)) * Family("X5"), [108, 88, 327, 323, 34, 36, 90, 328, 322, 110, 325, 326, 329, 115, 324], Dict{Symbol, Any}(:signs => [1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1], :ennola => -10)), Family(((CHEVIE[:families])[:QZ])(3), [80, 69, 70, 41, 332, 331, 44, 333, 330], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, -1, 1, 1, 1], :ennola => -5)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [58, 60, 25, 334, 336, 30, 337, 29, 335], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, -1, 1, -1, -1], :ennola => -7)), Family(conj(((CHEVIE[:families])[:X])(3)) * Family("X5"), [40, 56, 343, 339, 7, 9, 54, 344, 338, 43, 341, 342, 345, 38, 340], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1], :ennola => 10)), Family("C2", [23, 13, 19, 346], Dict{Symbol, Any}(:ennola => -4)), Family(((CHEVIE[:families])[:X])(3), [18, 16, 347], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -2)), Family(((CHEVIE[:families])[:X])(3), [6, 4, 348], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 3)), Family("C1", [2])], :a => [0, 126, 1, 85, 1, 85, 46, 4, 46, 4, 15, 15, 57, 3, 2, 68, 2, 68, 57, 3, 28, 10, 57, 3, 41, 5, 45, 9, 41, 41, 5, 5, 7, 31, 7, 31, 4, 46, 6, 46, 36, 4, 46, 36, 6, 4, 13, 19, 13, 19, 15, 15, 4, 46, 4, 46, 5, 41, 5, 41, 18, 27, 9, 19, 13, 30, 12, 6, 36, 36, 6, 11, 23, 11, 23, 28, 28, 10, 10, 36, 6, 19, 13, 10, 28, 10, 28, 31, 7, 31, 7, 13, 19, 13, 19, 8, 29, 8, 29, 29, 8, 29, 8, 27, 9, 18, 7, 31, 7, 31, 13, 19, 13, 19, 31, 7, 19, 13, 15, 15, 15, 15, 27, 9, 18, 15, 15, 23, 11, 14, 20, 14, 20, 11, 23, 11, 23, 15, 15, 24, 10, 24, 10, 24, 10, 13, 19, 13, 19, 13, 19, 13, 19, 11, 23, 11, 23, 21, 12, 21, 12, 13, 19, 13, 19, 15, 15, 15, 15, 1, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 18, 20, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 21, 21, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 28, 28, 28, 28, 27, 29, 29, 29, 29, 29, 29, 29, 29, 31, 31, 31, 31, 31, 31, 31, 31, 36, 36, 36, 36, 41, 41, 41, 41, 46, 46, 46, 46, 46, 46, 46, 46, 57, 68, 85], :A => [0, 126, 41, 125, 41, 125, 122, 80, 122, 80, 111, 111, 123, 69, 58, 124, 58, 124, 123, 69, 116, 98, 123, 69, 121, 85, 117, 81, 121, 121, 85, 85, 95, 119, 95, 119, 80, 122, 90, 122, 120, 80, 122, 120, 90, 80, 107, 113, 107, 113, 111, 111, 80, 122, 80, 122, 85, 121, 85, 121, 108, 117, 99, 113, 107, 114, 96, 90, 120, 120, 90, 103, 115, 103, 115, 116, 116, 98, 98, 120, 90, 113, 107, 98, 116, 98, 116, 119, 95, 119, 95, 107, 113, 107, 113, 97, 118, 97, 118, 118, 97, 118, 97, 117, 99, 108, 95, 119, 95, 119, 107, 113, 107, 113, 119, 95, 113, 107, 111, 111, 111, 111, 117, 99, 108, 111, 111, 115, 103, 106, 112, 106, 112, 103, 115, 103, 115, 111, 111, 116, 102, 116, 102, 116, 102, 107, 113, 107, 113, 107, 113, 107, 113, 103, 115, 103, 115, 114, 105, 114, 105, 107, 113, 107, 113, 111, 111, 111, 111, 41, 58, 69, 80, 80, 80, 80, 80, 80, 80, 80, 85, 85, 85, 85, 90, 90, 90, 90, 95, 95, 95, 95, 95, 95, 95, 95, 97, 97, 97, 97, 97, 97, 97, 97, 99, 98, 98, 98, 98, 102, 102, 102, 102, 102, 102, 103, 103, 103, 103, 103, 105, 105, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 106, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 108, 112, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 114, 114, 115, 115, 115, 115, 115, 116, 116, 116, 116, 116, 116, 116, 116, 116, 116, 117, 118, 118, 118, 118, 118, 118, 118, 118, 119, 119, 119, 119, 119, 119, 119, 119, 120, 120, 120, 120, 121, 121, 121, 121, 122, 122, 122, 122, 122, 122, 122, 122, 123, 124, 125]) + return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => 1:6, :rank => 6, :ST => 34), :levi => [], :parameterExponents => [1, 1, 1, 1, 1, 1], :charNumbers => 1:169, :eigenvalue => 1, :cuspidalName => ""), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6, 5, 1], :rank => 3, :ST => 26), :levi => 2:4, :parameterExponents => [1, 3, 3], :charNumbers => [170, 171, 340, 341, 325, 324, 342, 326, 220, 185, 219, 186, 216, 274, 249, 226, 184, 173, 334, 332, 251, 225, 183, 174, 335, 333, 232, 253, 299, 310, 189, 208, 231, 255, 298, 309, 190, 209, 197, 198, 280, 281, 282, 279, 245, 224, 247, 223], :eigenvalue => J, :cuspidalName => "G_{3,3,3}[\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6, 5, 1], :rank => 3, :ST => 26), :levi => 2:4, :parameterExponents => [1, [3, 3, 0], [3, 3, 0]], :charNumbers => [176, 191, 348, 192, 347, 175, 331, 300, 193, 177, 330, 301, 244, 302, 187, 181, 278, 252, 338, 337, 339, 336, 188, 182, 277, 250, 311, 322, 256, 284, 207, 218, 206, 217, 312, 323, 254, 283, 227, 230, 314, 315, 228, 229, 276, 248, 275, 246], :eigenvalue => J ^ 2, :cuspidalName => "G_{3,3,3}[\\zeta_3^2]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [4, 6], :rank => 2, :p => 6, :q => 1), :levi => [1, 2, 3, 348], :parameterExponents => [[5, 4, 1, 0, 1, 4], 4], :charNumbers => [235, 194, 236, 273, 237, 195, 286, 259, 289, 257, 205, 343, 328, 313, 258, 346, 327, 288, 344, 260, 285, 172, 179, 233, 287, 234, 178], :eigenvalue => -1, :cuspidalName => "D_4"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6], :rank => 1, :p => 6, :q => 1), :levi => 1:5, :parameterExponents => [[5, 0, 7, 2, 7, 0]], :charNumbers => [221, 317, 199, 296, 200, 316], :eigenvalue => E(4), :cuspidalName => "G_{33}[i]", :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6], :rank => 1, :p => 6, :q => 1), :levi => 1:5, :parameterExponents => [[5, 0, 7, 2, 7, 0]], :charNumbers => [222, 319, 201, 297, 202, 318], :eigenvalue => -(E(4)), :qEigen => 1 // 2, :cuspidalName => "G_{33}[-i]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6], :rank => 1, :p => 6, :q => 1), :levi => 1:5, :parameterExponents => [[3, 8, 7, 0, 7, 8]], :charNumbers => [329, 238, 261, 345, 263, 239], :eigenvalue => -J, :cuspidalName => "G_{33}[-\\zeta_3]"), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "ST", :indices => [6], :rank => 1, :p => 6, :q => 1), :levi => 1:5, :parameterExponents => [[8, 1, 0, 5, 0, 1]], :charNumbers => [180, 262, 291, 196, 290, 264], :eigenvalue => -(J ^ 2), :cuspidalName => "G_{33}[-\\zeta_3^2]"), cuspidal(265, 1), cuspidal(266, -1), cuspidal(294, J), cuspidal(295, J, 2), cuspidal(242, J ^ 2), cuspidal(243, J ^ 2, 2), cuspidal(292, -J), cuspidal(293, -J, 2), cuspidal(240, -(J ^ 2)), cuspidal(241, -(J ^ 2), 2), cuspidal(267, E(7)), cuspidal(268, E(7, 2)), cuspidal(269, E(7, 3)), cuspidal(270, E(7, 4)), cuspidal(271, E(7, 5)), cuspidal(272, E(7, 6)), cuspidal(212, E(9), 1 // 3), cuspidal(214, E(9), 2, 2 // 3), cuspidal(307, E(9, 2), 2 // 3), cuspidal(303, E(9, 2), 2, 1 // 3), cuspidal(210, E(9, 4), 1 // 3), cuspidal(215, E(9, 4), 2, 2 // 3), cuspidal(304, E(9, 5), 2 // 3), cuspidal(305, E(9, 5), 2, 1 // 3), cuspidal(211, E(9, 7), 2 // 3), cuspidal(213, E(9, 7), 2, 1 // 3), cuspidal(306, E(9, 8), 1 // 3), cuspidal(308, E(9, 8), 2, 2 // 3), cuspidal(203, E(12, 7), 1 // 2), cuspidal(320, E(12, 11), 1 // 2), cuspidal(204, E(12), 1 // 2), cuspidal(321, E(12, 5), 1 // 2)], :families => [Family("C1", [1]), Family(conj(((CHEVIE[:families])[:X])(3)), [5, 3, 170], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 2)), Family(conj(((CHEVIE[:families])[:X])(3)), [17, 15, 171], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -3)), Family("C2", [24, 14, 20, 172], Dict{Symbol, Any}(:ennola => -4)), Family(((CHEVIE[:families])[:X])(3) * conj(Family("X5")), [42, 55, 178, 174, 8, 10, 53, 179, 173, 46, 176, 177, 180, 37, 175], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1], :ennola => 15)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [57, 59, 26, 184, 182, 32, 181, 31, 183], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, -1, 1, -1, -1], :ennola => -7)), Family(((CHEVIE[:families])[:QZ])(3), [81, 68, 71, 45, 185, 188, 39, 186, 187], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, -1, -1], :ennola => 6)), Family(((CHEVIE[:families])[:X])(3) * conj(Family("X5")), [109, 89, 194, 190, 35, 33, 91, 195, 189, 107, 192, 193, 196, 116, 191], Dict{Symbol, Any}(:signs => [1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1], :ennola => -15)), Family(conj(((CHEVIE[:families])[:X])(3)) * ((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [103, 96, 201, 199, 101, 98, 202, 200, 198, 197, 204, 203], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], :cospecial => 6, :ennola => 12)), Family("C1", [28], Dict{Symbol, Any}(:ennola => -1)), Family("C2", [124, 63, 105, 205], Dict{Symbol, Any}(:ennola => -4)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [84, 86, 22, 209, 207, 78, 206, 79, 208], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, -1, 1, -1, -1], :ennola => 4)), Family(((CHEVIE[:families])[:TQZ])(3, E(3), [1, E(3)]), [143, 145, 141, 215, 211, 214, 212, 213, 210], Dict{Symbol, Any}(:cospecial => 3, :ennola => 4)), Family(conj(((CHEVIE[:families])[:X])(3)), [134, 136, 216], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 3)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [154, 156, 129, 220, 218, 74, 217, 72, 219], Dict{Symbol, Any}(:signs => [1, 1, 1, -1, -1, -1, 1, -1, 1], :ennola => -9)), Family("C1", [67]), Family(((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [159, 161, 222, 221], Dict{Symbol, Any}(:cospecial => 2, :ennola => -4)), Family(((CHEVIE[:families])[:QZ])(6, [Perm(), [E(6)]]), [152, 164, 118, 162, 150, 65, 240, 225, 236, 228, 238, 113, 232, 242, 94, 224, 230, 146, 233, 49, 235, 47, 234, 83, 229, 148, 231, 243, 92, 223, 239, 111, 241, 226, 237, 227], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1], :ennola => 33)), Family(((CHEVIE[:families])[:X])(3), [132, 130, 244], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -2)), Family(((CHEVIE[:families])[:F42])(), [169, 265, 122, 121, 12, 11, 52, 166, 245, 252, 119, 249, 248, 138, 262, 255, 258, 254, 263, 167, 247, 250, 120, 251, 246, 139, 264, 253, 257, 256, 261, 168, 259, 126, 266, 127, 260, 51, 267, 268, 269, 270, 271, 272], Dict{Symbol, Any}(:signs => [1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1], :ennola => 3)), Family("C2", [125, 61, 106, 273], Dict{Symbol, Any}(:ennola => 4)), Family(conj(((CHEVIE[:families])[:X])(3)), [133, 131, 274], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -3)), Family(((CHEVIE[:families])[:QZ])(6, [Perm(), [E(3)]]), [151, 64, 153, 163, 117, 165, 280, 288, 277, 292, 114, 290, 284, 147, 282, 276, 93, 294, 48, 287, 50, 285, 82, 286, 281, 275, 95, 295, 283, 149, 278, 293, 112, 291, 279, 289], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1], :ennola => -8)), Family(((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [160, 158, 297, 296], Dict{Symbol, Any}(:cospecial => 2, :ennola => 4)), Family("C1", [66]), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [157, 155, 128, 298, 300, 73, 301, 75, 299], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, -1, -1, -1, -1], :ennola => 8)), Family(((CHEVIE[:families])[:X])(3), [137, 135, 302], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 2)), Family(((CHEVIE[:families])[:TQZ])(3, E(3, 2)), [140, 144, 142, 307, 304, 308, 303, 306, 305], Dict{Symbol, Any}(:cospecial => 2, :ennola => 8)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [85, 87, 21, 309, 311, 77, 312, 76, 310], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, -1, 1, -1, -1], :ennola => 4)), Family("C2", [123, 62, 104, 313], Dict{Symbol, Any}(:ennola => -4)), Family("C1", [27], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:X])(3) * ((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [97, 102, 318, 316, 99, 100, 319, 317, 315, 314, 321, 320], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], :cospecial => 6, :ennola => -8)), Family(conj(((CHEVIE[:families])[:X])(3)) * Family("X5"), [108, 88, 327, 323, 34, 36, 90, 328, 322, 110, 325, 326, 329, 115, 324], Dict{Symbol, Any}(:signs => [1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1], :ennola => -10)), Family(((CHEVIE[:families])[:QZ])(3), [80, 69, 70, 41, 332, 331, 44, 333, 330], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, -1, 1, 1, 1], :ennola => -5)), Family(((CHEVIE[:families])[:QZ])(3, [Perm(), [E(3)]]), [58, 60, 25, 334, 336, 30, 337, 29, 335], Dict{Symbol, Any}(:signs => [1, 1, 1, 1, -1, -1, 1, -1, -1], :ennola => -7)), Family(conj(((CHEVIE[:families])[:X])(3)) * Family("X5"), [40, 56, 343, 339, 7, 9, 54, 344, 338, 43, 341, 342, 345, 38, 340], Dict{Symbol, Any}(:signs => [1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1], :ennola => 10)), Family("C2", [23, 13, 19, 346], Dict{Symbol, Any}(:ennola => -4)), Family(((CHEVIE[:families])[:X])(3), [18, 16, 347], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => -2)), Family(((CHEVIE[:families])[:X])(3), [6, 4, 348], Dict{Symbol, Any}(:signs => [1, 1, -1], :ennola => 3)), Family("C1", [2])], :a => [0, 126, 1, 85, 1, 85, 46, 4, 46, 4, 15, 15, 57, 3, 2, 68, 2, 68, 57, 3, 28, 10, 57, 3, 41, 5, 45, 9, 41, 41, 5, 5, 7, 31, 7, 31, 4, 46, 6, 46, 36, 4, 46, 36, 6, 4, 13, 19, 13, 19, 15, 15, 4, 46, 4, 46, 5, 41, 5, 41, 18, 27, 9, 19, 13, 30, 12, 6, 36, 36, 6, 11, 23, 11, 23, 28, 28, 10, 10, 36, 6, 19, 13, 10, 28, 10, 28, 31, 7, 31, 7, 13, 19, 13, 19, 8, 29, 8, 29, 29, 8, 29, 8, 27, 9, 18, 7, 31, 7, 31, 13, 19, 13, 19, 31, 7, 19, 13, 15, 15, 15, 15, 27, 9, 18, 15, 15, 23, 11, 14, 20, 14, 20, 11, 23, 11, 23, 15, 15, 24, 10, 24, 10, 24, 10, 13, 19, 13, 19, 13, 19, 13, 19, 11, 23, 11, 23, 21, 12, 21, 12, 13, 19, 13, 19, 15, 15, 15, 15, 1, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 18, 20, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 21, 21, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 28, 28, 28, 28, 27, 29, 29, 29, 29, 29, 29, 29, 29, 31, 31, 31, 31, 31, 31, 31, 31, 36, 36, 36, 36, 41, 41, 41, 41, 46, 46, 46, 46, 46, 46, 46, 46, 57, 68, 85], :A => [0, 126, 41, 125, 41, 125, 122, 80, 122, 80, 111, 111, 123, 69, 58, 124, 58, 124, 123, 69, 116, 98, 123, 69, 121, 85, 117, 81, 121, 121, 85, 85, 95, 119, 95, 119, 80, 122, 90, 122, 120, 80, 122, 120, 90, 80, 107, 113, 107, 113, 111, 111, 80, 122, 80, 122, 85, 121, 85, 121, 108, 117, 99, 113, 107, 114, 96, 90, 120, 120, 90, 103, 115, 103, 115, 116, 116, 98, 98, 120, 90, 113, 107, 98, 116, 98, 116, 119, 95, 119, 95, 107, 113, 107, 113, 97, 118, 97, 118, 118, 97, 118, 97, 117, 99, 108, 95, 119, 95, 119, 107, 113, 107, 113, 119, 95, 113, 107, 111, 111, 111, 111, 117, 99, 108, 111, 111, 115, 103, 106, 112, 106, 112, 103, 115, 103, 115, 111, 111, 116, 102, 116, 102, 116, 102, 107, 113, 107, 113, 107, 113, 107, 113, 103, 115, 103, 115, 114, 105, 114, 105, 107, 113, 107, 113, 111, 111, 111, 111, 41, 58, 69, 80, 80, 80, 80, 80, 80, 80, 80, 85, 85, 85, 85, 90, 90, 90, 90, 95, 95, 95, 95, 95, 95, 95, 95, 97, 97, 97, 97, 97, 97, 97, 97, 99, 98, 98, 98, 98, 102, 102, 102, 102, 102, 102, 103, 103, 103, 103, 103, 105, 105, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 106, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 111, 108, 112, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 113, 114, 114, 115, 115, 115, 115, 115, 116, 116, 116, 116, 116, 116, 116, 116, 116, 116, 117, 118, 118, 118, 118, 118, 118, 118, 118, 119, 119, 119, 119, 119, 119, 119, 119, 120, 120, 120, 120, 121, 121, 121, 121, 122, 122, 122, 122, 122, 122, 122, 122, 123, 124, 125]) end) chevieset(:G34, :Invariants, function () local r diff --git a/tools/tbl/coxh3.jl b/tools/tbl/coxh3.jl index 76990674..5feb3f4c 100644 --- a/tools/tbl/coxh3.jl +++ b/tools/tbl/coxh3.jl @@ -91,7 +91,7 @@ chevieset(:H3, :HeckeRepresentation, function (param, sqrtparam, i) end) chevieset(:H3, :UnipotentCharacters, function () local res - res = Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "H", :indices => 1:3, :rank => 3), :levi => [], :eigenvalue => 1, :parameterExponents => [1, 1, 1], :cuspidalName => "", :charNumbers => 1:10), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [3], :rank => 1), :levi => 1:2, :eigenvalue => E(5, 2), :parameterExponents => [5], :cuspidalName => "I_2(5)[1,3]", :charNumbers => [11, 13]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [3], :rank => 1), :levi => 1:2, :eigenvalue => E(5, 3), :parameterExponents => [5], :cuspidalName => "I_2(5)[1,2]", :charNumbers => [12, 14]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :eigenvalue => E(4), :qEigen => 1 // 2, :parameterExponents => [], :cuspidalName => "H_3[i]", :charNumbers => [15]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :eigenvalue => -(E(4)), :qEigen => 1 // 2, :parameterExponents => [], :cuspidalName => "H_3[-i]", :charNumbers => [16])], :families => [Family("C1", [2]), Family(((CHEVIE[:families])[:Dihedral])(5), [7, 8, 14, 13], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [4]), Family("C'\"2", [9, 10, 15, 16], Dict{Symbol, Any}(:ennola => 3)), Family("C1", [3], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:Dihedral])(5), [5, 6, 12, 11], Dict{Symbol, Any}(:ennola => 1)), Family("C1", [1], Dict{Symbol, Any}(:ennola => -1))], :a => [15, 0, 5, 2, 6, 6, 1, 1, 3, 3, 6, 6, 1, 1, 3, 3], :A => [15, 0, 13, 10, 14, 14, 9, 9, 12, 12, 14, 14, 9, 9, 12, 12]) + res = Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "H", :indices => 1:3, :rank => 3), :levi => [], :eigenvalue => 1, :parameterExponents => [1, 1, 1], :cuspidalName => "", :charNumbers => 1:10), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [3], :rank => 1), :levi => 1:2, :eigenvalue => E(5, 2), :parameterExponents => [5], :cuspidalName => "I_2(5)[1,3]", :charNumbers => [11, 13]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [3], :rank => 1), :levi => 1:2, :eigenvalue => E(5, 3), :parameterExponents => [5], :cuspidalName => "I_2(5)[1,2]", :charNumbers => [12, 14]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :eigenvalue => E(4), :qEigen => 1 // 2, :parameterExponents => [], :cuspidalName => "H_3[i]", :charNumbers => [15]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:3, :eigenvalue => -(E(4)), :qEigen => 1 // 2, :parameterExponents => [], :cuspidalName => "H_3[-i]", :charNumbers => [16])], :families => [Family("C1", [2]), Family(((CHEVIE[:families])[:Dihedral])(5), [7, 8, 14, 13], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [4]), Family(((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [9, 10, 16, 15], Dict{Symbol, Any}(:cospecial => 2, :ennola => 4)), Family("C1", [3], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:Dihedral])(5), [5, 6, 12, 11], Dict{Symbol, Any}(:ennola => 1)), Family("C1", [1], Dict{Symbol, Any}(:ennola => -1))], :a => [15, 0, 5, 2, 6, 6, 1, 1, 3, 3, 6, 6, 1, 1, 3, 3], :A => [15, 0, 13, 10, 14, 14, 9, 9, 12, 12, 14, 14, 9, 9, 12, 12]) return res end) chevieset(:H3, :Discriminant, function () diff --git a/tools/tbl/coxh4.jl b/tools/tbl/coxh4.jl index 5b42f532..c895aa56 100644 --- a/tools/tbl/coxh4.jl +++ b/tools/tbl/coxh4.jl @@ -100,6 +100,6 @@ chevieset(:H4, :UnipotentCharacters, function () res = Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:4, :parameterExponents => [], :charNumbers => [arg[1]], :eigenvalue => arg[2], :cuspidalName => n) return res end - return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "H", :indices => 1:4, :rank => 4), :levi => [], :eigenvalue => 1, :parameterExponents => [1, 1, 1, 1], :cuspidalName => "", :charNumbers => 1:34), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "I", :indices => [4, 3], :rank => 2, :bond => 10), :levi => 1:2, :eigenvalue => E(5, 3), :parameterExponents => [1, 5], :cuspidalName => "I_2(5)[1,2]", :charNumbers => [35, 44, 37, 45, 47, 53, 49, 51]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "I", :indices => [4, 3], :rank => 2, :bond => 10), :levi => 1:2, :eigenvalue => E(5, 2), :parameterExponents => [1, 5], :cuspidalName => "I_2(5)[1,3]", :charNumbers => [36, 43, 38, 46, 48, 54, 50, 52]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [4], :rank => 1), :levi => 1:3, :eigenvalue => E(4), :parameterExponents => [15], :cuspidalName => "H_3[i]", :charNumbers => [41, 39], :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [4], :rank => 1), :levi => 1:3, :eigenvalue => -(E(4)), :parameterExponents => [15], :cuspidalName => "H_3[-i]", :charNumbers => [42, 40], :qEigen => 1 // 2), cuspidal(55, 1), cuspidal(56, -1), cuspidal(57, -1, 2), cuspidal(58, -1, 3), cuspidal(59, 1, 2), cuspidal(60, 1, 3), cuspidal(61, -1, 4), cuspidal(62, -1, 5), cuspidal(63, 1, 4), cuspidal(64, -1, 6), cuspidal(65, E(5, 3)), cuspidal(66, E(5, 2)), cuspidal(67, E(5, 3), 2), cuspidal(68, E(5, 2), 2), cuspidal(69, -(E(5, 3))), cuspidal(70, -(E(5, 2))), cuspidal(71, -(E(5, 3)), 2), cuspidal(72, -(E(5, 2)), 2), cuspidal(73, E(4)), cuspidal(74, -(E(4))), cuspidal(75, E(3)), cuspidal(76, E(3, 2)), cuspidal(77, -(E(3, 2))), cuspidal(78, -(E(3))), cuspidal(79, E(5, 4)), cuspidal(80, E(5)), cuspidal(81, E(5, 4), 2), cuspidal(82, E(5), 2), cuspidal(83, -(E(5, 4))), cuspidal(84, -(E(5))), cuspidal(85, -(E(5, 4)), 2), cuspidal(86, -(E(5)), 2), cuspidal(87, E(3), 2), cuspidal(88, E(3, 2), 2), cuspidal(89, E(3), 3), cuspidal(90, E(3, 2), 3), cuspidal(91, E(5, 4), 3), cuspidal(92, E(5), 3), cuspidal(93, E(5, 4), 4), cuspidal(94, E(5), 4), cuspidal(95, E(15, 2)), cuspidal(96, E(15, 13)), cuspidal(97, E(15, 8)), cuspidal(98, E(15, 7)), cuspidal(99, E(5, 4), 5), cuspidal(100, E(5), 5), cuspidal(101, E(5, 4), 6), cuspidal(102, E(5), 6), cuspidal(103, -1, 7), cuspidal(104, 1, 5)], :families => [Family("C1", [1]), Family("C1", [2]), Family("C1", [27]), Family("C1", [28]), Family("C1", [31], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [32], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:Dihedral])(5), [3, 5, 35, 36], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:Dihedral])(5), [11, 13, 37, 38], Dict{Symbol, Any}(:ennola => 1)), Family(((CHEVIE[:families])[:Dihedral])(5), [12, 14, 44, 43], Dict{Symbol, Any}(:ennola => 1)), Family(((CHEVIE[:families])[:Dihedral])(5), [4, 6, 45, 46], Dict{Symbol, Any}(:ennola => -1)), Family("C'\"2", [18, 20, 39, 40], Dict{Symbol, Any}(:ennola => 4)), Family("C'\"2", [21, 19, 41, 42], Dict{Symbol, Any}(:ennola => -4)), Family("HS4", [15, 9, 10, 7, 8, 22, 16, 17, 26, 25, 24, 23, 29, 30, 33, 34, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104], Dict{Symbol, Any}(:ennola => 29))], :a => [0, 60, 1, 31, 1, 31, 6, 6, 6, 6, 2, 22, 2, 22, 6, 6, 6, 3, 18, 3, 18, 6, 6, 6, 6, 6, 4, 16, 6, 6, 5, 15, 6, 6, 1, 1, 2, 2, 3, 3, 18, 18, 22, 22, 31, 31, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], :A => [0, 60, 29, 59, 29, 59, 54, 54, 54, 54, 38, 58, 38, 58, 54, 54, 54, 42, 57, 42, 57, 54, 54, 54, 54, 54, 44, 56, 54, 54, 45, 55, 54, 54, 29, 29, 38, 38, 42, 42, 57, 57, 58, 58, 59, 59, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54]) + return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "H", :indices => 1:4, :rank => 4), :levi => [], :eigenvalue => 1, :parameterExponents => [1, 1, 1, 1], :cuspidalName => "", :charNumbers => 1:34), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "I", :indices => [4, 3], :rank => 2, :bond => 10), :levi => 1:2, :eigenvalue => E(5, 3), :parameterExponents => [1, 5], :cuspidalName => "I_2(5)[1,2]", :charNumbers => [35, 44, 37, 45, 47, 53, 49, 51]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "I", :indices => [4, 3], :rank => 2, :bond => 10), :levi => 1:2, :eigenvalue => E(5, 2), :parameterExponents => [1, 5], :cuspidalName => "I_2(5)[1,3]", :charNumbers => [36, 43, 38, 46, 48, 54, 50, 52]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [4], :rank => 1), :levi => 1:3, :eigenvalue => E(4), :parameterExponents => [15], :cuspidalName => "H_3[i]", :charNumbers => [41, 39], :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [4], :rank => 1), :levi => 1:3, :eigenvalue => -(E(4)), :parameterExponents => [15], :cuspidalName => "H_3[-i]", :charNumbers => [42, 40], :qEigen => 1 // 2), cuspidal(55, 1), cuspidal(56, -1), cuspidal(57, -1, 2), cuspidal(58, -1, 3), cuspidal(59, 1, 2), cuspidal(60, 1, 3), cuspidal(61, -1, 4), cuspidal(62, -1, 5), cuspidal(63, 1, 4), cuspidal(64, -1, 6), cuspidal(65, E(5, 3)), cuspidal(66, E(5, 2)), cuspidal(67, E(5, 3), 2), cuspidal(68, E(5, 2), 2), cuspidal(69, -(E(5, 3))), cuspidal(70, -(E(5, 2))), cuspidal(71, -(E(5, 3)), 2), cuspidal(72, -(E(5, 2)), 2), cuspidal(73, E(4)), cuspidal(74, -(E(4))), cuspidal(75, E(3)), cuspidal(76, E(3, 2)), cuspidal(77, -(E(3, 2))), cuspidal(78, -(E(3))), cuspidal(79, E(5, 4)), cuspidal(80, E(5)), cuspidal(81, E(5, 4), 2), cuspidal(82, E(5), 2), cuspidal(83, -(E(5, 4))), cuspidal(84, -(E(5))), cuspidal(85, -(E(5, 4)), 2), cuspidal(86, -(E(5)), 2), cuspidal(87, E(3), 2), cuspidal(88, E(3, 2), 2), cuspidal(89, E(3), 3), cuspidal(90, E(3, 2), 3), cuspidal(91, E(5, 4), 3), cuspidal(92, E(5), 3), cuspidal(93, E(5, 4), 4), cuspidal(94, E(5), 4), cuspidal(95, E(15, 2)), cuspidal(96, E(15, 13)), cuspidal(97, E(15, 8)), cuspidal(98, E(15, 7)), cuspidal(99, E(5, 4), 5), cuspidal(100, E(5), 5), cuspidal(101, E(5, 4), 6), cuspidal(102, E(5), 6), cuspidal(103, -1, 7), cuspidal(104, 1, 5)], :families => [Family("C1", [1]), Family("C1", [2]), Family("C1", [27]), Family("C1", [28]), Family("C1", [31], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [32], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:Dihedral])(5), [3, 5, 35, 36], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:Dihedral])(5), [11, 13, 37, 38], Dict{Symbol, Any}(:ennola => 1)), Family(((CHEVIE[:families])[:Dihedral])(5), [12, 14, 44, 43], Dict{Symbol, Any}(:ennola => 1)), Family(((CHEVIE[:families])[:Dihedral])(5), [4, 6, 45, 46], Dict{Symbol, Any}(:ennola => -1)), Family(((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [18, 20, 40, 39], Dict{Symbol, Any}(:cospecial => 2, :ennola => 3)), Family(((CHEVIE[:families])[:TQZ])(2, -1, [1, -1]), [21, 19, 42, 41], Dict{Symbol, Any}(:cospecial => 2, :ennola => -3)), Family("HS4", [15, 9, 10, 7, 8, 22, 16, 17, 26, 25, 24, 23, 29, 30, 33, 34, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104], Dict{Symbol, Any}(:ennola => 29))], :a => [0, 60, 1, 31, 1, 31, 6, 6, 6, 6, 2, 22, 2, 22, 6, 6, 6, 3, 18, 3, 18, 6, 6, 6, 6, 6, 4, 16, 6, 6, 5, 15, 6, 6, 1, 1, 2, 2, 3, 3, 18, 18, 22, 22, 31, 31, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], :A => [0, 60, 29, 59, 29, 59, 54, 54, 54, 54, 38, 58, 38, 58, 54, 54, 54, 42, 57, 42, 57, 54, 54, 54, 54, 54, 44, 56, 54, 54, 45, 55, 54, 54, 29, 29, 38, 38, 42, 42, 57, 57, 58, 58, 59, 59, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54]) end) chevieset(:H4, :KLeftCellRepresentatives, [Dict{Symbol, Any}(:character => [1], :duflo => [1, 2, 3, 4], :reps => ""), Dict{Symbol, Any}(:character => [2], :duflo => [61, 62, 63, 64], :reps => ""), Dict{Symbol, Any}(:character => [5, 3], :duflo => [1, 2, 8, 64], :reps => [[16, 2, 3, 87]]), Dict{Symbol, Any}(:character => [6, 4], :duflo => [1, 66, 63, 64], :reps => [[9, 65, 71, 64]]), Dict{Symbol, Any}(:character => [13, 11], :duflo => [2, 1, 27, 103], :reps => [[3, 20, 1, 110]]), Dict{Symbol, Any}(:character => [14, 12], :duflo => [1, 66, 68, 4], :reps => [[9, 65, 76, 4]]), Dict{Symbol, Any}(:character => [20, 18], :duflo => [1, 2, 32, 120], :reps => [[23, 3, 2, 116], [24, 23, 112, 2], [33, 1, 110, 32]]), Dict{Symbol, Any}(:character => [20, 18], :duflo => [19, 85, 10, 20], :reps => [[12, 6, 10, 109], [13, 20, 97, 6], [19, 12, 80, 70]]), Dict{Symbol, Any}(:character => [21, 19], :duflo => [10, 63, 62, 94], :reps => [[15, 62, 73, 83], [15, 77, 13, 94], [21, 85, 5, 83]]), Dict{Symbol, Any}(:character => [21, 19], :duflo => [19, 85, 10, 88], :reps => [[13, 81, 6, 76], [17, 67, 69, 88], [19, 69, 70, 76]]), Dict{Symbol, Any}(:character => [27], :duflo => [2, 1, 24, 119], :reps => [[1, 35, 120, 39], [38, 2, 116, 24]]), Dict{Symbol, Any}(:character => [27], :duflo => [12, 21, 102, 30], :reps => [[1, 12, 25, 119], [35, 1, 107, 25]]), Dict{Symbol, Any}(:character => [27], :duflo => [33, 11, 115, 18], :reps => [[2, 30, 74, 100], [2, 30, 114, 40]]), Dict{Symbol, Any}(:character => [28], :duflo => [1, 76, 4, 3], :reps => [[27, 72, 73, 86], [28, 92, 14, 86]]), Dict{Symbol, Any}(:character => [28], :duflo => [36, 117, 54, 74], :reps => [[24, 102, 21, 18], [46, 110, 34, 100]]), Dict{Symbol, Any}(:character => [28], :duflo => [40, 102, 30, 96], :reps => [[19, 94, 16, 10], [32, 68, 77, 96]]), Dict{Symbol, Any}(:character => [31], :duflo => [1, 2, 3, 100], :reps => [[2, 28, 119, 44], [3, 39, 117, 1], [31, 1, 107, 3]]), Dict{Symbol, Any}(:character => [31], :duflo => [1, 31, 119, 46], :reps => [[1, 31, 85, 106], [15, 30, 114, 12], [34, 12, 116, 15]]), Dict{Symbol, Any}(:character => [31], :duflo => [1, 35, 106, 4], :reps => [[4, 17, 1, 117], [17, 16, 115, 48], [40, 4, 110, 1]]), Dict{Symbol, Any}(:character => [31], :duflo => [34, 107, 3, 52], :reps => [[3, 39, 116, 12], [6, 24, 73, 112], [6, 24, 119, 52]]), Dict{Symbol, Any}(:character => [32], :duflo => [2, 1, 79, 64], :reps => [[25, 97, 20, 1], [26, 64, 71, 101], [34, 96, 29, 101]]), Dict{Symbol, Any}(:character => [32], :duflo => [27, 106, 26, 13], :reps => [[4, 13, 92, 66], [34, 66, 70, 103], [42, 107, 36, 103]]), Dict{Symbol, Any}(:character => [32], :duflo => [31, 62, 63, 113], :reps => [[23, 10, 107, 62], [38, 117, 39, 10], [42, 105, 41, 113]]), Dict{Symbol, Any}(:character => [32], :duflo => [45, 109, 44, 110], :reps => [[16, 17, 102, 69], [32, 115, 36, 17], [37, 69, 67, 110]]), Dict{Symbol, Any}(:character => [34, 34, 33, 30, 29, 26, 25, 24, 23, 22, 10, 9], :duflo => [14, 64, 63, 62], :reps => [[5, 28, 100, 86], [5, 28, 117, 26], [5, 32, 105, 64], [10, 26, 90, 101], [10, 26, 120, 41], [13, 29, 110, 75], [13, 29, 118, 15], [15, 30, 102, 89], [15, 30, 120, 29], [16, 15, 111, 13], [16, 31, 112, 63], [17, 16, 88, 99], [17, 16, 117, 39], [17, 18, 92, 80], [17, 18, 108, 20], [18, 15, 80, 102], [18, 15, 116, 42], [20, 13, 77, 110], [20, 13, 119, 50], [24, 63, 62, 78], [24, 63, 82, 18], [26, 17, 101, 88], [26, 17, 119, 28], [28, 20, 103, 77], [28, 20, 116, 17], [29, 10, 91, 90], [29, 10, 114, 30], [30, 5, 89, 100], [30, 5, 118, 40], [33, 62, 78, 70], [33, 62, 92, 10], [36, 104, 5, 13], [37, 75, 98, 13], [37, 111, 13, 26], [41, 75, 64, 102], [41, 75, 106, 42], [42, 63, 113, 16], [42, 115, 16, 41], [43, 64, 109, 5], [43, 112, 5, 42], [45, 70, 80, 90], [45, 70, 103, 30], [46, 78, 70, 80], [46, 78, 91, 20], [47, 88, 99, 26], [47, 117, 26, 15], [49, 77, 110, 28], [49, 119, 28, 29], [50, 86, 63, 101], [50, 86, 105, 41], [52, 80, 102, 17], [53, 89, 100, 15], [53, 118, 15, 28], [55, 90, 101, 29]]), Dict{Symbol, Any}(:character => [34, 34, 33, 30, 29, 26, 25, 24, 23, 22, 10, 9], :duflo => [31, 62, 92, 14], :reps => [[4, 21, 104, 5], [4, 40, 115, 62], [5, 30, 103, 81], [5, 30, 117, 21], [11, 20, 97, 78], [11, 20, 113, 18], [11, 33, 109, 68], [14, 21, 88, 101], [14, 21, 119, 41], [15, 18, 82, 107], [15, 18, 120, 47], [18, 25, 107, 80], [18, 25, 118, 20], [20, 28, 106, 85], [20, 28, 119, 25], [21, 22, 101, 90], [21, 22, 120, 30], [22, 11, 90, 97], [22, 11, 117, 37], [25, 4, 80, 98], [25, 4, 113, 38], [25, 14, 93, 88], [25, 14, 114, 28], [26, 96, 11, 5], [27, 68, 62, 73], [28, 5, 85, 103], [28, 5, 118, 43], [30, 15, 100, 82], [30, 15, 116, 22], [31, 62, 73, 74], [34, 81, 89, 5], [34, 104, 5, 18], [39, 80, 98, 18], [39, 113, 18, 21], [41, 62, 110, 4], [41, 112, 4, 47], [42, 73, 74, 75], [42, 73, 93, 15], [43, 78, 62, 107], [43, 78, 109, 47], [46, 68, 111, 11], [46, 115, 11, 41], [47, 81, 68, 101], [47, 81, 108, 41], [48, 74, 75, 88], [48, 74, 100, 28], [49, 75, 88, 82], [49, 75, 106, 22], [50, 90, 97, 21], [50, 117, 21, 20], [51, 85, 103, 20], [51, 118, 20, 30], [52, 82, 107, 30], [55, 88, 101, 25]]), Dict{Symbol, Any}(:character => [34, 34, 33, 33, 30, 29, 26, 25, 24, 23, 22, 17, 16, 15], :duflo => [19, 97, 52, 86], :reps => [[1, 12, 64, 102], [1, 12, 106, 42], [1, 35, 106, 85], [1, 35, 119, 25], [7, 1, 88, 8], [7, 36, 111, 74], [7, 36, 120, 14], [8, 25, 107, 1], [12, 21, 77, 110], [12, 21, 119, 50], [14, 25, 91, 96], [14, 25, 118, 36], [16, 7, 87, 81], [16, 7, 102, 21], [16, 31, 108, 79], [16, 31, 118, 19], [17, 16, 94, 87], [17, 16, 115, 27], [17, 26, 104, 72], [18, 17, 95, 94], [18, 17, 119, 34], [19, 8, 76, 105], [19, 8, 115, 45], [19, 14, 86, 91], [21, 14, 114, 7], [25, 18, 96, 95], [25, 18, 120, 35], [26, 7, 72, 111], [26, 7, 116, 51], [27, 19, 109, 76], [27, 19, 117, 16], [31, 1, 79, 106], [31, 1, 117, 46], [32, 102, 17, 1], [34, 12, 103, 77], [35, 1, 107, 64], [38, 76, 105, 27], [38, 115, 27, 25], [40, 85, 90, 1], [40, 107, 1, 27], [41, 75, 74, 66], [43, 74, 66, 91], [43, 74, 97, 31], [44, 66, 91, 78], [44, 66, 108, 18], [45, 77, 74, 94], [45, 77, 110, 34], [45, 119, 34, 14], [46, 74, 100, 7], [46, 114, 7, 34], [48, 72, 111, 17], [48, 116, 17, 36], [49, 85, 72, 96], [49, 85, 103, 36], [50, 78, 79, 95], [50, 78, 109, 35], [51, 79, 106, 16], [51, 117, 16, 35], [54, 95, 94, 25], [56, 91, 96, 19], [57, 96, 95, 14]]), Dict{Symbol, Any}(:character => [34, 34, 33, 33, 30, 30, 29, 29, 26, 25, 24, 23, 17, 16, 8, 7], :duflo => [1, 35, 102, 64], :reps => [[1, 7, 63, 97], [1, 7, 100, 37], [1, 31, 100, 89], [1, 31, 118, 29], [2, 16, 64, 111], [2, 16, 113, 51], [2, 38, 113, 70], [2, 38, 119, 10], [7, 23, 80, 107], [7, 23, 118, 47], [10, 29, 93, 98], [10, 29, 120, 38], [11, 2, 77, 83], [11, 2, 97, 23], [11, 33, 105, 86], [11, 33, 120, 26], [13, 20, 91, 96], [13, 20, 118, 36], [13, 22, 95, 76], [16, 17, 73, 112], [16, 17, 119, 52], [17, 26, 112, 71], [17, 26, 117, 11], [20, 11, 96, 77], [20, 11, 111, 17], [20, 28, 110, 67], [22, 11, 76, 105], [22, 11, 115, 45], [23, 10, 109, 2], [26, 10, 88, 93], [26, 10, 114, 33], [28, 2, 67, 113], [28, 2, 116, 53], [29, 13, 98, 91], [29, 13, 119, 31], [31, 1, 104, 63], [31, 16, 103, 73], [33, 1, 86, 100], [33, 1, 117, 40], [34, 71, 101, 17], [34, 111, 17, 29], [36, 7, 102, 80], [38, 2, 109, 64], [38, 71, 64, 105], [38, 71, 108, 45], [39, 104, 1, 17], [40, 70, 99, 2], [40, 109, 2, 36], [41, 80, 70, 96], [41, 80, 107, 36], [41, 118, 36, 10], [42, 70, 76, 93], [42, 70, 103, 33], [43, 64, 107, 1], [43, 110, 1, 45], [45, 67, 113, 20], [45, 116, 20, 38], [47, 73, 86, 91], [47, 73, 112, 31], [47, 119, 31, 26], [48, 82, 70, 76], [49, 91, 96, 29], [50, 76, 105, 13], [52, 89, 67, 98], [52, 89, 102, 38], [53, 86, 100, 11], [53, 117, 11, 31], [56, 93, 98, 26], [57, 98, 91, 10]])]) diff --git a/tools/tbl/weyle7.jl b/tools/tbl/weyle7.jl index 84555e17..24d8c3fc 100644 --- a/tools/tbl/weyle7.jl +++ b/tools/tbl/weyle7.jl @@ -131,7 +131,7 @@ chevieset(:E7, :DecompositionMatrix, function (p,) end end) chevieset(:E7, :UnipotentCharacters, function () - return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "E", :indices => 1:7, :rank => 7), :levi => [], :eigenvalue => 1, :parameterExponents => [1, 1, 1, 1, 1, 1, 1], :cuspidalName => "", :charNumbers => 1:60), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "B", :indices => [7, 6, 1], :cartanType => 1, :rank => 3), :levi => 2:5, :eigenvalue => -1, :parameterExponents => [1, 4, 4], :cuspidalName => "D_4", :charNumbers => [67, 66, 64, 61, 69, 65, 68, 62, 70, 63]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [7], :rank => 1), :levi => 1:6, :eigenvalue => E(3), :parameterExponents => [9], :cuspidalName => "E_6[\\zeta_3]", :charNumbers => [71, 72]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [7], :rank => 1), :levi => 1:6, :eigenvalue => E(3, 2), :parameterExponents => [9], :cuspidalName => "E_6[\\zeta_3^2]", :charNumbers => [73, 74]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:7, :eigenvalue => -(E(4)), :parameterExponents => [], :cuspidalName => "E_7[-i]", :charNumbers => [75], :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:7, :eigenvalue => E(4), :parameterExponents => [], :cuspidalName => "E_7[i]", :charNumbers => [76], :qEigen => 1 // 2)], :families => [Family("C1", [1]), Family("C1", [2], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [3]), Family("C1", [4], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [9]), Family("C1", [10], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [11]), Family("C1", [12], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [25]), Family("C1", [26], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [27]), Family("C1", [28], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [31]), Family("C1", [32], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [35]), Family("C1", [36], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [37]), Family("C1", [38], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [39]), Family("C1", [40], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [41]), Family("C1", [42], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [53]), Family("C1", [54], Dict{Symbol, Any}(:ennola => -1)), Family("C2", [18, 15, 7, 70], Dict{Symbol, Any}(:ennola => -4)), Family("C2", [29, 6, 24, 63], Dict{Symbol, Any}(:ennola => 4)), Family("C2", [55, 44, 33, 65], Dict{Symbol, Any}(:ennola => 3)), Family("C2", [57, 21, 52, 69], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [58, 22, 51, 62], Dict{Symbol, Any}(:ennola => -2)), Family("C2", [56, 43, 34, 66], Dict{Symbol, Any}(:ennola => -3)), Family("C2", [30, 5, 23, 67], Dict{Symbol, Any}(:ennola => -4)), Family("C2", [17, 16, 8, 61], Dict{Symbol, Any}(:ennola => 4)), Family("C'2", [60, 59, 76, 75], Dict{Symbol, Any}(:ennola => 3)), Family("S3", [50, 47, 20, 46, 14, 68, 72, 74], Dict{Symbol, Any}(:ennola => -5)), Family("S3", [49, 48, 19, 45, 13, 64, 71, 73], Dict{Symbol, Any}(:ennola => 5))], :a => [0, 63, 46, 1, 25, 4, 3, 30, 36, 3, 2, 37, 16, 7, 3, 30, 30, 3, 16, 7, 10, 13, 25, 4, 6, 21, 12, 15, 4, 25, 6, 21, 8, 15, 22, 5, 20, 7, 6, 21, 10, 13, 15, 8, 16, 7, 7, 16, 16, 7, 13, 10, 14, 9, 8, 15, 10, 13, 11, 11, 30, 13, 4, 16, 8, 15, 25, 7, 10, 3, 16, 7, 16, 7, 11, 11], :A => [0, 63, 62, 17, 59, 38, 33, 60, 60, 27, 26, 61, 56, 47, 33, 60, 60, 33, 56, 47, 50, 53, 59, 38, 42, 57, 48, 51, 38, 59, 42, 57, 48, 55, 58, 41, 56, 43, 42, 57, 50, 53, 55, 48, 56, 47, 47, 56, 56, 47, 53, 50, 54, 49, 48, 55, 50, 53, 52, 52, 60, 53, 38, 56, 48, 55, 59, 47, 50, 33, 56, 47, 56, 47, 52, 52]) + return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "E", :indices => 1:7, :rank => 7), :levi => [], :eigenvalue => 1, :parameterExponents => [1, 1, 1, 1, 1, 1, 1], :cuspidalName => "", :charNumbers => 1:60), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "B", :indices => [7, 6, 1], :cartanType => 1, :rank => 3), :levi => 2:5, :eigenvalue => -1, :parameterExponents => [1, 4, 4], :cuspidalName => "D_4", :charNumbers => [67, 66, 64, 61, 69, 65, 68, 62, 70, 63]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [7], :rank => 1), :levi => 1:6, :eigenvalue => E(3), :parameterExponents => [9], :cuspidalName => "E_6[\\zeta_3]", :charNumbers => [71, 72]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [7], :rank => 1), :levi => 1:6, :eigenvalue => E(3, 2), :parameterExponents => [9], :cuspidalName => "E_6[\\zeta_3^2]", :charNumbers => [73, 74]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:7, :eigenvalue => -(E(4)), :parameterExponents => [], :cuspidalName => "E_7[-i]", :charNumbers => [75], :qEigen => 1 // 2), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:7, :eigenvalue => E(4), :parameterExponents => [], :cuspidalName => "E_7[i]", :charNumbers => [76], :qEigen => 1 // 2)], :families => [Family("C1", [1]), Family("C1", [2], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [3]), Family("C1", [4], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [9]), Family("C1", [10], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [11]), Family("C1", [12], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [25]), Family("C1", [26], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [27]), Family("C1", [28], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [31]), Family("C1", [32], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [35]), Family("C1", [36], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [37]), Family("C1", [38], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [39]), Family("C1", [40], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [41]), Family("C1", [42], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [53]), Family("C1", [54], Dict{Symbol, Any}(:ennola => -1)), Family("C2", [18, 15, 7, 70], Dict{Symbol, Any}(:ennola => -4)), Family("C2", [29, 6, 24, 63], Dict{Symbol, Any}(:ennola => 4)), Family("C2", [55, 44, 33, 65], Dict{Symbol, Any}(:ennola => 3)), Family("C2", [57, 21, 52, 69], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [58, 22, 51, 62], Dict{Symbol, Any}(:ennola => -2)), Family("C2", [56, 43, 34, 66], Dict{Symbol, Any}(:ennola => -3)), Family("C2", [30, 5, 23, 67], Dict{Symbol, Any}(:ennola => -4)), Family("C2", [17, 16, 8, 61], Dict{Symbol, Any}(:ennola => 4)), Family("LTQZ2", [60, 59, 76, 75], Dict{Symbol, Any}(:cospecial => 2, :ennola => 3)), Family("S3", [50, 47, 20, 46, 14, 68, 72, 74], Dict{Symbol, Any}(:ennola => -5)), Family("S3", [49, 48, 19, 45, 13, 64, 71, 73], Dict{Symbol, Any}(:ennola => 5))], :a => [0, 63, 46, 1, 25, 4, 3, 30, 36, 3, 2, 37, 16, 7, 3, 30, 30, 3, 16, 7, 10, 13, 25, 4, 6, 21, 12, 15, 4, 25, 6, 21, 8, 15, 22, 5, 20, 7, 6, 21, 10, 13, 15, 8, 16, 7, 7, 16, 16, 7, 13, 10, 14, 9, 8, 15, 10, 13, 11, 11, 30, 13, 4, 16, 8, 15, 25, 7, 10, 3, 16, 7, 16, 7, 11, 11], :A => [0, 63, 62, 17, 59, 38, 33, 60, 60, 27, 26, 61, 56, 47, 33, 60, 60, 33, 56, 47, 50, 53, 59, 38, 42, 57, 48, 51, 38, 59, 42, 57, 48, 55, 58, 41, 56, 43, 42, 57, 50, 53, 55, 48, 56, 47, 47, 56, 56, 47, 53, 50, 54, 49, 48, 55, 50, 53, 52, 52, 60, 53, 38, 56, 48, 55, 59, 47, 50, 33, 56, 47, 56, 47, 52, 52]) end) chevieset(:E7, :UnipotentClasses, function (p,) local uc, Z, c, class diff --git a/tools/tbl/weyle8.jl b/tools/tbl/weyle8.jl index 829de76d..5317ad1f 100644 --- a/tools/tbl/weyle8.jl +++ b/tools/tbl/weyle8.jl @@ -116,7 +116,7 @@ chevieset(:E8, :DecompositionMatrix, function (p,) end end) chevieset(:E8, :UnipotentCharacters, function () - return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "E", :indices => 1:8, :rank => 8), :levi => [], :eigenvalue => 1, :parameterExponents => [1, 1, 1, 1, 1, 1, 1, 1], :cuspidalName => "", :charNumbers => 1:112), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [8], :rank => 1), :levi => 1:7, :eigenvalue => -(E(4)), :parameterExponents => [15], :cuspidalName => "E_7[-i]", :qEigen => 1 // 2, :charNumbers => [114, 113]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [8], :rank => 1), :levi => 1:7, :eigenvalue => E(4), :parameterExponents => [15], :cuspidalName => "E_7[i]", :qEigen => 1 // 2, :charNumbers => [116, 115]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "F", :indices => [8, 7, 6, 1], :rank => 4), :levi => 2:5, :eigenvalue => -1, :parameterExponents => [1, 1, 4, 4], :cuspidalName => "D_4", :charNumbers => [117, 119, 118, 120, 126, 123, 125, 124, 131, 139, 141, 140, 138, 132, 133, 121, 128, 130, 129, 127, 135, 136, 134, 137, 122]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "G", :indices => [8, 7], :rank => 2), :levi => 1:6, :eigenvalue => E(3), :parameterExponents => [1, 9], :cuspidalName => "E_6[\\zeta_3]", :charNumbers => [142, 145, 143, 144, 152, 153]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "G", :indices => [8, 7], :rank => 2), :levi => 1:6, :eigenvalue => E(3, 2), :parameterExponents => [1, 9], :cuspidalName => "E_6[\\zeta_3^2]", :charNumbers => [148, 151, 149, 150, 146, 147]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => -1, :parameterExponents => [], :cuspidalName => "E_8[-1]", :charNumbers => [154]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => -(E(3, 2)), :parameterExponents => [], :cuspidalName => "E_8[-\\zeta_3^2]", :charNumbers => [155]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => -(E(3)), :parameterExponents => [], :cuspidalName => "E_8[-\\zeta_3]", :charNumbers => [156]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => -(E(4)), :parameterExponents => [], :cuspidalName => "E_8[-i]", :charNumbers => [157]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(3, 2), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_3^2]", :charNumbers => [158]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(3), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_3]", :charNumbers => [159]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(5, 4), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_5^4]", :charNumbers => [160]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(5, 3), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_5^3]", :charNumbers => [161]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(5, 2), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_5^2]", :charNumbers => [162]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(5), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_5]", :charNumbers => [163]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(4), :parameterExponents => [], :cuspidalName => "E_8[i]", :charNumbers => [164]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => 1, :parameterExponents => [], :cuspidalName => "E_8^2[1]", :charNumbers => [165]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => 1, :parameterExponents => [], :cuspidalName => "E_8[1]", :charNumbers => [166])], :families => [Family("C1", [1]), Family("C1", [2]), Family("C1", [5]), Family("C1", [6]), Family("C1", [22]), Family("C1", [23]), Family("C1", [24]), Family("C1", [25]), Family("C1", [39]), Family("C1", [57]), Family("C1", [58]), Family("C1", [66]), Family("C1", [67]), Family("C1", [68], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [69], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [81], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [82], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [100], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [101], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [107], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [108], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [109], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [110], Dict{Symbol, Any}(:ennola => -1)), Family("C2", [72, 10, 3, 117], Dict{Symbol, Any}(:ennola => -4)), Family("C2", [15, 8, 74, 125], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [29, 77, 18, 118], Dict{Symbol, Any}(:ennola => 3)), Family("C2", [54, 35, 89, 139], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [51, 91, 84, 129], Dict{Symbol, Any}(:ennola => 4)), Family("C2", [64, 32, 102, 126], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [97, 27, 48, 140], Dict{Symbol, Any}(:ennola => -4)), Family("C2", [111, 60, 95, 135], Dict{Symbol, Any}(:ennola => -3)), Family("C2", [112, 61, 96, 136], Dict{Symbol, Any}(:ennola => -3)), Family("C2", [65, 33, 103, 123], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [98, 28, 49, 141], Dict{Symbol, Any}(:ennola => -4)), Family("C2", [52, 92, 85, 130], Dict{Symbol, Any}(:ennola => 4)), Family("C2", [55, 36, 90, 138], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [30, 78, 19, 119], Dict{Symbol, Any}(:ennola => 3)), Family("C2", [16, 9, 75, 124], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [73, 11, 4, 120], Dict{Symbol, Any}(:ennola => -4)), Family("C'2", [105, 62, 115, 113], Dict{Symbol, Any}(:ennola => 4)), Family("C'2", [63, 106, 116, 114], Dict{Symbol, Any}(:ennola => -4)), Family("S3", [93, 40, 79, 86, 70, 128, 142, 148], Dict{Symbol, Any}(:ennola => -5)), Family("S3", [43, 37, 13, 45, 20, 134, 143, 149], Dict{Symbol, Any}(:ennola => 1)), Family("S3", [44, 38, 14, 46, 21, 137, 144, 150], Dict{Symbol, Any}(:ennola => 1)), Family("S3", [94, 41, 80, 87, 71, 127, 145, 151], Dict{Symbol, Any}(:ennola => -5)), Family("S5", [53, 165, 7, 59, 56, 31, 34, 104, 154, 121, 76, 133, 99, 50, 166, 12, 42, 122, 47, 26, 152, 159, 146, 158, 88, 132, 153, 156, 147, 155, 83, 131, 164, 157, 17, 163, 162, 161, 160], Dict{Symbol, Any}(:ennola => 2))], :a => [0, 120, 3, 63, 2, 74, 16, 4, 52, 3, 63, 16, 8, 32, 4, 52, 16, 6, 42, 8, 32, 12, 36, 6, 46, 16, 13, 25, 6, 42, 16, 12, 24, 16, 10, 30, 8, 32, 20, 7, 37, 16, 8, 32, 8, 32, 16, 13, 25, 16, 10, 28, 16, 10, 30, 16, 14, 22, 16, 15, 21, 11, 26, 12, 24, 14, 22, 1, 91, 7, 37, 3, 63, 4, 52, 16, 6, 42, 7, 37, 5, 47, 16, 10, 28, 7, 37, 16, 10, 30, 10, 28, 7, 37, 15, 21, 13, 25, 16, 9, 31, 12, 24, 16, 11, 26, 15, 21, 13, 23, 15, 21, 11, 26, 11, 26, 3, 6, 42, 63, 16, 16, 24, 52, 4, 12, 37, 7, 10, 28, 16, 16, 16, 8, 15, 21, 32, 30, 10, 13, 25, 7, 8, 32, 37, 16, 16, 7, 8, 32, 37, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16], :A => [0, 120, 57, 117, 46, 118, 104, 68, 116, 57, 117, 104, 88, 112, 68, 116, 104, 78, 114, 88, 112, 84, 108, 74, 114, 104, 95, 107, 78, 114, 104, 96, 108, 104, 90, 110, 88, 112, 100, 83, 113, 104, 88, 112, 88, 112, 104, 95, 107, 104, 92, 110, 104, 90, 110, 104, 98, 106, 104, 99, 105, 94, 109, 96, 108, 98, 106, 29, 119, 83, 113, 57, 117, 68, 116, 104, 78, 114, 83, 113, 73, 115, 104, 92, 110, 83, 113, 104, 90, 110, 92, 110, 83, 113, 99, 105, 95, 107, 104, 89, 111, 96, 108, 104, 94, 109, 99, 105, 97, 107, 99, 105, 94, 109, 94, 109, 57, 78, 114, 117, 104, 104, 108, 116, 68, 96, 113, 83, 92, 110, 104, 104, 104, 88, 99, 105, 112, 110, 90, 95, 107, 83, 88, 112, 113, 104, 104, 83, 88, 112, 113, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104]) + return Dict{Symbol, Any}(:harishChandra => [Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "E", :indices => 1:8, :rank => 8), :levi => [], :eigenvalue => 1, :parameterExponents => [1, 1, 1, 1, 1, 1, 1, 1], :cuspidalName => "", :charNumbers => 1:112), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [8], :rank => 1), :levi => 1:7, :eigenvalue => -(E(4)), :parameterExponents => [15], :cuspidalName => "E_7[-i]", :qEigen => 1 // 2, :charNumbers => [114, 113]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [8], :rank => 1), :levi => 1:7, :eigenvalue => E(4), :parameterExponents => [15], :cuspidalName => "E_7[i]", :qEigen => 1 // 2, :charNumbers => [116, 115]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "F", :indices => [8, 7, 6, 1], :rank => 4), :levi => 2:5, :eigenvalue => -1, :parameterExponents => [1, 1, 4, 4], :cuspidalName => "D_4", :charNumbers => [117, 119, 118, 120, 126, 123, 125, 124, 131, 139, 141, 140, 138, 132, 133, 121, 128, 130, 129, 127, 135, 136, 134, 137, 122]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "G", :indices => [8, 7], :rank => 2), :levi => 1:6, :eigenvalue => E(3), :parameterExponents => [1, 9], :cuspidalName => "E_6[\\zeta_3]", :charNumbers => [142, 145, 143, 144, 152, 153]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "G", :indices => [8, 7], :rank => 2), :levi => 1:6, :eigenvalue => E(3, 2), :parameterExponents => [1, 9], :cuspidalName => "E_6[\\zeta_3^2]", :charNumbers => [148, 151, 149, 150, 146, 147]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => -1, :parameterExponents => [], :cuspidalName => "E_8[-1]", :charNumbers => [154]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => -(E(3, 2)), :parameterExponents => [], :cuspidalName => "E_8[-\\zeta_3^2]", :charNumbers => [155]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => -(E(3)), :parameterExponents => [], :cuspidalName => "E_8[-\\zeta_3]", :charNumbers => [156]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => -(E(4)), :parameterExponents => [], :cuspidalName => "E_8[-i]", :charNumbers => [157]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(3, 2), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_3^2]", :charNumbers => [158]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(3), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_3]", :charNumbers => [159]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(5, 4), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_5^4]", :charNumbers => [160]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(5, 3), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_5^3]", :charNumbers => [161]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(5, 2), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_5^2]", :charNumbers => [162]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(5), :parameterExponents => [], :cuspidalName => "E_8[\\zeta_5]", :charNumbers => [163]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => E(4), :parameterExponents => [], :cuspidalName => "E_8[i]", :charNumbers => [164]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => 1, :parameterExponents => [], :cuspidalName => "E_8^2[1]", :charNumbers => [165]), Dict{Symbol, Any}(:relativeType => Dict{Symbol, Any}(:series => "A", :indices => [], :rank => 0), :levi => 1:8, :eigenvalue => 1, :parameterExponents => [], :cuspidalName => "E_8[1]", :charNumbers => [166])], :families => [Family("C1", [1]), Family("C1", [2]), Family("C1", [5]), Family("C1", [6]), Family("C1", [22]), Family("C1", [23]), Family("C1", [24]), Family("C1", [25]), Family("C1", [39]), Family("C1", [57]), Family("C1", [58]), Family("C1", [66]), Family("C1", [67]), Family("C1", [68], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [69], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [81], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [82], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [100], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [101], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [107], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [108], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [109], Dict{Symbol, Any}(:ennola => -1)), Family("C1", [110], Dict{Symbol, Any}(:ennola => -1)), Family("C2", [72, 10, 3, 117], Dict{Symbol, Any}(:ennola => -4)), Family("C2", [15, 8, 74, 125], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [29, 77, 18, 118], Dict{Symbol, Any}(:ennola => 3)), Family("C2", [54, 35, 89, 139], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [51, 91, 84, 129], Dict{Symbol, Any}(:ennola => 4)), Family("C2", [64, 32, 102, 126], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [97, 27, 48, 140], Dict{Symbol, Any}(:ennola => -4)), Family("C2", [111, 60, 95, 135], Dict{Symbol, Any}(:ennola => -3)), Family("C2", [112, 61, 96, 136], Dict{Symbol, Any}(:ennola => -3)), Family("C2", [65, 33, 103, 123], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [98, 28, 49, 141], Dict{Symbol, Any}(:ennola => -4)), Family("C2", [52, 92, 85, 130], Dict{Symbol, Any}(:ennola => 4)), Family("C2", [55, 36, 90, 138], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [30, 78, 19, 119], Dict{Symbol, Any}(:ennola => 3)), Family("C2", [16, 9, 75, 124], Dict{Symbol, Any}(:ennola => 2)), Family("C2", [73, 11, 4, 120], Dict{Symbol, Any}(:ennola => -4)), Family("LTQZ2", [105, 62, 115, 113], Dict{Symbol, Any}(:cospecial => 2, :ennola => 4)), Family("LTQZ2", [63, 106, 116, 114], Dict{Symbol, Any}(:cospecial => 2, :ennola => -4)), Family("S3", [93, 40, 79, 86, 70, 128, 142, 148], Dict{Symbol, Any}(:ennola => -5)), Family("S3", [43, 37, 13, 45, 20, 134, 143, 149], Dict{Symbol, Any}(:ennola => 1)), Family("S3", [44, 38, 14, 46, 21, 137, 144, 150], Dict{Symbol, Any}(:ennola => 1)), Family("S3", [94, 41, 80, 87, 71, 127, 145, 151], Dict{Symbol, Any}(:ennola => -5)), Family("S5", [53, 165, 7, 59, 56, 31, 34, 104, 154, 121, 76, 133, 99, 50, 166, 12, 42, 122, 47, 26, 152, 159, 146, 158, 88, 132, 153, 156, 147, 155, 83, 131, 164, 157, 17, 163, 162, 161, 160], Dict{Symbol, Any}(:ennola => 2))], :a => [0, 120, 3, 63, 2, 74, 16, 4, 52, 3, 63, 16, 8, 32, 4, 52, 16, 6, 42, 8, 32, 12, 36, 6, 46, 16, 13, 25, 6, 42, 16, 12, 24, 16, 10, 30, 8, 32, 20, 7, 37, 16, 8, 32, 8, 32, 16, 13, 25, 16, 10, 28, 16, 10, 30, 16, 14, 22, 16, 15, 21, 11, 26, 12, 24, 14, 22, 1, 91, 7, 37, 3, 63, 4, 52, 16, 6, 42, 7, 37, 5, 47, 16, 10, 28, 7, 37, 16, 10, 30, 10, 28, 7, 37, 15, 21, 13, 25, 16, 9, 31, 12, 24, 16, 11, 26, 15, 21, 13, 23, 15, 21, 11, 26, 11, 26, 3, 6, 42, 63, 16, 16, 24, 52, 4, 12, 37, 7, 10, 28, 16, 16, 16, 8, 15, 21, 32, 30, 10, 13, 25, 7, 8, 32, 37, 16, 16, 7, 8, 32, 37, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16], :A => [0, 120, 57, 117, 46, 118, 104, 68, 116, 57, 117, 104, 88, 112, 68, 116, 104, 78, 114, 88, 112, 84, 108, 74, 114, 104, 95, 107, 78, 114, 104, 96, 108, 104, 90, 110, 88, 112, 100, 83, 113, 104, 88, 112, 88, 112, 104, 95, 107, 104, 92, 110, 104, 90, 110, 104, 98, 106, 104, 99, 105, 94, 109, 96, 108, 98, 106, 29, 119, 83, 113, 57, 117, 68, 116, 104, 78, 114, 83, 113, 73, 115, 104, 92, 110, 83, 113, 104, 90, 110, 92, 110, 83, 113, 99, 105, 95, 107, 104, 89, 111, 96, 108, 104, 94, 109, 99, 105, 97, 107, 99, 105, 94, 109, 94, 109, 57, 78, 114, 117, 104, 104, 108, 116, 68, 96, 113, 83, 92, 110, 104, 104, 104, 88, 99, 105, 112, 110, 90, 95, 107, 83, 88, 112, 113, 104, 104, 83, 88, 112, 113, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104, 104]) end) chevieset(:E8, :UnipotentClasses, function (p,) local uc, Z, l, l1, i, s, c, class