data: - - BadPrimes: - 13 - 331 Baselabel: 3.727207.6t11.b CharacterField: 1 Conductor: 727207 Container: 6t11 Dets: - 1.4303.2t1.a.a Dim: 3 GalConjSigns: - 1 Galn: 6 GaloisConjugates: - Character: - - 3 - - -3 - - 1 - - -1 - - 1 - - -1 - - 0 - - 1 - - -1 - - 0 GalOrbIndex: 1 HardFactors: - 9 - 11 - 3 - 3 - 12 LocalFactors: - - - 1 - - -3 - - 3 - - -1 - - - 1 - - 3 - - 3 - - 1 - - - 1 - - -1 - - -1 - - 1 - - - 1 - - 1 - - -1 - - -1 - - - 1 - - -1 - - -1 - - 1 - - - 1 - - 1 - - -1 - - -1 - - - 1 - - 0 - - 0 - - -1 - - - 1 - - -1 - - 1 - - -1 - - - 1 - - 1 - - 1 - - 1 - - - 1 - - 0 - - 0 - - 1 - - - 1 - - - 1 - - 2 - - 1 Sign: 1 GaloisConjugatesSigns: - 1 GaloisLabel: 6T11 Galt: 11 HardPrimes: - 3 - 13 - 89 - 107 - 331 Hide: 0 Indicator: 1 Is_Even: false NFGal: - -182 - 13 - 51 - 42 - -15 - -2 - 1 NumBadPrimes: 2 Proj_GAP: - 24 - 12 Proj_Polynomial: - -1 - 1 - 1 - -1 - 1 Proj_nTj: - 4 - 5 id: 556203 - - ArtinReps: - Baselabel: 1.1.1t1.a Character: - - 1 - - 1 - - 1 - - 1 - - 1 - - 1 - - 1 - - 1 - - 1 - - 1 CharacterField: 1 GalConj: 1 - Baselabel: 1.4303.2t1.a Character: - - 1 - - -1 - - -1 - - 1 - - -1 - - 1 - - 1 - - 1 - - -1 - - -1 CharacterField: 1 GalConj: 1 - Baselabel: 1.331.2t1.a Character: - - 1 - - 1 - - 1 - - 1 - - -1 - - -1 - - 1 - - -1 - - -1 - - 1 CharacterField: 1 GalConj: 1 - Baselabel: 1.13.2t1.a Character: - - 1 - - -1 - - -1 - - 1 - - 1 - - -1 - - 1 - - -1 - - 1 - - -1 CharacterField: 1 GalConj: 1 - Baselabel: 2.55939.6t3.a Character: - - 2 - - -2 - - -2 - - 2 - - 0 - - 0 - - -1 - - 0 - - 0 - - 1 CharacterField: 1 GalConj: 1 - Baselabel: 2.331.3t2.a Character: - - 2 - - 2 - - 2 - - 2 - - 0 - - 0 - - -1 - - 0 - - 0 - - -1 CharacterField: 1 GalConj: 1 - Baselabel: 3.331.4t5.a Character: - - 3 - - 3 - - -1 - - -1 - - 1 - - 1 - - 0 - - -1 - - -1 - - 0 CharacterField: 1 GalConj: 1 - Baselabel: 3.727207.6t11.b Character: - - 3 - - -3 - - 1 - - -1 - - 1 - - -1 - - 0 - - 1 - - -1 - - 0 CharacterField: 1 GalConj: 1 - Baselabel: 3.240705517.6t11.b Character: - - 3 - - -3 - - 1 - - -1 - - -1 - - 1 - - 0 - - -1 - - 1 - - 0 CharacterField: 1 GalConj: 1 - Baselabel: 3.109561.6t8.c Character: - - 3 - - 3 - - -1 - - -1 - - -1 - - -1 - - 0 - - 1 - - 1 - - 0 CharacterField: 1 GalConj: 1 ComplexConjugation: 5 ConjClasses: - Order: 1 Representative: - 1 - 2 - 3 - 4 - 5 - 6 Size: '1' - Order: 2 Representative: - 6 - 4 - 5 - 2 - 3 - 1 Size: '1' - Order: 2 Representative: - 1 - 2 - 5 - 4 - 3 - 6 Size: '3' - Order: 2 Representative: - 1 - 4 - 5 - 2 - 3 - 6 Size: '3' - Order: 2 Representative: - 2 - 1 - 3 - 6 - 5 - 4 Size: '6' - Order: 2 Representative: - 2 - 1 - 5 - 6 - 3 - 4 Size: '6' - Order: 3 Representative: - 3 - 1 - 2 - 6 - 4 - 5 Size: '8' - Order: 4 Representative: - 1 - 3 - 4 - 5 - 2 - 6 Size: '6' - Order: 4 Representative: - 4 - 1 - 5 - 6 - 3 - 2 Size: '6' - Order: 6 Representative: - 3 - 1 - 4 - 6 - 2 - 5 Size: '8' FrobResolvents: - Algorithm: CYC Classes: 1 CycleType: - 1 - 1 - 1 - 1 - 1 - 1 Data: 0 - Algorithm: CYC Classes: 3 CycleType: - 1 - 1 - 1 - 1 - 2 Data: 0 - Algorithm: RES Classes: - ConjugacyClass: 4 RootOf: - '247424' - '688' - '6' - '1' - ConjugacyClass: 5 RootOf: - '-33090579367' - '1827261556' - '-33142864' - '545207' - '985' - '-29' - '1' CycleType: - 1 - 1 - 2 - 2 Data: Powers: - 1 Resolvent: - 0 - 0 - 1 - Algorithm: CYC Classes: 8 CycleType: - 1 - 1 - 4 Data: 0 - Algorithm: RES Classes: - ConjugacyClass: 2 RootOf: - '-11' - '1' - ConjugacyClass: 6 RootOf: - '-6546229' - '2339860' - '-562888' - '38597' - '673' - '-107' - '1' CycleType: - 2 - 2 - 2 Data: Powers: - 1 Resolvent: - 0 - 0 - 1 - Algorithm: CYC Classes: 9 CycleType: - 2 - 4 Data: 0 - Algorithm: CYC Classes: 7 CycleType: - 3 - 3 Data: 0 - Algorithm: CYC Classes: 10 CycleType: - 6 Data: 0 Frobs: - 8 - 9 - 10 - 8 - 8 - 5 - 7 - 10 - 5 - 9 - 10 - 8 - 8 - 7 - 6 - 7 - 6 - 9 - 10 - 10 - 6 - 7 - 3 - 3 - 8 - 5 - 4 - 5 - 10 - 1 - 7 - 7 - 8 - 4 - 10 - 6 - 7 - 10 - 10 - 4 - 7 - 9 - 7 - 3 - 10 - 9 - 5 - 10 - 6 - 8 - 7 - 3 - 10 - 9 - 5 - 9 - 7 - 10 - 5 - 10 - 7 - 3 - 6 - 5 - 7 - 8 - 6 - 7 - 4 - 6 - 10 - 6 - 4 - 9 - 6 - 8 - 4 - 6 - 10 - 8 - 7 - 8 - 3 - 7 - 9 - 5 - 10 - 10 - 10 - 3 - 5 - 6 - 10 - 9 - 6 - 4 - 8 - 9 - 9 - 6 - 7 - 6 - 7 - 7 - 9 - 8 - 3 - 8 - 7 - 7 - 7 - 6 - 6 - 6 - 8 - 5 - 6 - 7 - 5 - 7 - 8 - 9 - 5 - 2 - 6 - 7 - 6 - 5 - 9 - 3 - 10 - 10 - 4 - 1 - 6 - 6 - 10 - 3 - 5 - 5 - 10 - 6 - 7 - 10 - 7 - 3 - 10 - 7 - 7 - 8 - 3 - 7 - 9 - 7 - 1 - 9 - 5 - 6 - 9 - 10 - 8 - 4 - 6 - 5 - 8 - 10 - 7 - 7 G-Gens: - - 1 - 3 - 2 - 5 - 4 - 6 - - 3 - 1 - 2 - 6 - 4 - 5 - - 1 - 2 - 5 - 4 - 3 - 6 G-Name: C2*S4 Polynomial: - -182 - 13 - 51 - 42 - -15 - -2 - 1 QpRts: - - '229021954608349720' - '0' - - '99882287984873621' - '56537621814321614' - - '-236772679969489731' - '-215263850899556859' - - '251477293429465244' - '215263850899556859' - - '-79335046242945507' - '-56537621814321614' - - '239762552126214038' - '0' QpRts-minpoly: - 5 - 21 - 1 QpRts-p: 23 QpRts-prec: 13 Size: 48 TransitiveDegree: 6 id: 543749 label_cols: - Baselabel - Polynomial labels: - 3.727207.6t11.b - - -182 - 13 - 51 - 42 - -15 - -2 - 1 tables: - artin_reps - artin_field_data timestamp: '2024-05-17T15:53:07.598082'