data: - - BadPrimes: - 2 - 11 Baselabel: 3.340736.42t37.a CharacterField: 7 Conductor: 340736 Container: 42t37 Dets: - 1.1.1t1.a.a - 1.1.1t1.a.a Dim: 3 GalConjSigns: - 0 - 0 Galn: 7 GaloisConjugates: - Character: - - 3 - - -1 - - 0 - - 1 - - 0 - 1 - 1 - 0 - 1 - - -1 - -1 - -1 - 0 - -1 GalOrbIndex: 1 HardFactors: - 7 - 7 - 4 LocalFactors: - - - 1 - - -3 - - 3 - - -1 - - - 1 - - 1 - - -1 - - -1 - - - 1 - - 0 - - 0 - - -1 - - - 1 - - -1 - - 1 - - -1 - - - 1 - - 0 - -1 - -1 - 0 - -1 - - -1 - -1 - -1 - 0 - -1 - - -1 - - - 1 - - 1 - 1 - 1 - 0 - 1 - - 0 - 1 - 1 - 0 - 1 - - -1 - - - 1 Sign: 0 - Character: - - 3 - - -1 - - 0 - - 1 - - -1 - -1 - -1 - 0 - -1 - - 0 - 1 - 1 - 0 - 1 GalOrbIndex: 2 HardFactors: - 7 - 7 - 4 LocalFactors: - - - 1 - - -3 - - 3 - - -1 - - - 1 - - 1 - - -1 - - -1 - - - 1 - - 0 - - 0 - - -1 - - - 1 - - -1 - - 1 - - -1 - - - 1 - - 1 - 1 - 1 - 0 - 1 - - 0 - 1 - 1 - 0 - 1 - - -1 - - - 1 - - 0 - -1 - -1 - 0 - -1 - - -1 - -1 - -1 - 0 - -1 - - -1 - - - 1 Sign: 0 GaloisConjugatesSigns: - 0 - 0 GaloisLabel: 7T5 Galt: 5 HardPrimes: - 2 - 11 - 193 Hide: 0 Indicator: 0 Is_Even: true NFGal: - -2 - 10 - 10 - -14 - -12 - 2 - -1 - 1 NumBadPrimes: 2 Proj_GAP: - 168 - 42 Proj_Polynomial: - -2 - 10 - 10 - -14 - -12 - 2 - -1 - 1 Proj_nTj: - 7 - 5 id: 710720 - - ArtinReps: - Baselabel: 1.1.1t1.a Character: - - 1 - - 1 - - 1 - - 1 - - 1 - - 1 CharacterField: 1 GalConj: 1 - Baselabel: 3.340736.42t37.a Character: - - 3 - 0 - 0 - 0 - 0 - 0 - - -1 - 0 - 0 - 0 - 0 - 0 - - 0 - 0 - 0 - 0 - 0 - 0 - - 1 - 0 - 0 - 0 - 0 - 0 - - 0 - 1 - 1 - 0 - 1 - 0 - - -1 - -1 - -1 - 0 - -1 - 0 CharacterField: 7 GalConj: 1 - Baselabel: 3.340736.42t37.a Character: - - 3 - 0 - 0 - 0 - 0 - 0 - - -1 - 0 - 0 - 0 - 0 - 0 - - 0 - 0 - 0 - 0 - 0 - 0 - - 1 - 0 - 0 - 0 - 0 - 0 - - -1 - -1 - -1 - 0 - -1 - 0 - - 0 - 1 - 1 - 0 - 1 - 0 CharacterField: 7 GalConj: 2 - Baselabel: 6.1814078464.7t5.a Character: - - 6 - - 2 - - 0 - - 0 - - -1 - - -1 CharacterField: 1 GalConj: 1 - Baselabel: 7.116101021696.8t37.a Character: - - 7 - - -1 - - 1 - - -1 - - 0 - - 0 CharacterField: 1 GalConj: 1 - Baselabel: 8.464404086784.21t14.a Character: - - 8 - - 0 - - -1 - - 0 - - 1 - - 1 CharacterField: 1 GalConj: 1 ComplexConjugation: 2 ConjClasses: - Order: 1 Representative: - 1 - 2 - 3 - 4 - 5 - 6 - 7 Size: '1' - Order: 2 Representative: - 1 - 6 - 4 - 3 - 5 - 2 - 7 Size: '21' - Order: 3 Representative: - 4 - 7 - 2 - 5 - 1 - 6 - 3 Size: '56' - Order: 4 Representative: - 7 - 1 - 3 - 2 - 6 - 5 - 4 Size: '42' - Order: 7 Representative: - 7 - 1 - 4 - 6 - 2 - 5 - 3 Size: '24' - Order: 7 Representative: - 4 - 3 - 5 - 2 - 7 - 1 - 6 Size: '24' FrobResolvents: - Algorithm: CYC Classes: 1 CycleType: - 1 - 1 - 1 - 1 - 1 - 1 - 1 Data: 0 - Algorithm: CYC Classes: 2 CycleType: - 1 - 1 - 1 - 2 - 2 Data: 0 - Algorithm: CYC Classes: 4 CycleType: - 1 - 2 - 4 Data: 0 - Algorithm: CYC Classes: 3 CycleType: - 1 - 3 - 3 Data: 0 - Algorithm: ALT Classes: - ConjugacyClass: 5 RootOf: - '8220256' - '1' - ConjugacyClass: 6 RootOf: - '-8220256' - '1' CycleType: - 7 Data: - 2 - 3 - 4 - 5 - 6 - 7 - 1 Frobs: - 4 - 4 - 6 - 6 - 3 - 6 - 2 - 3 - 3 - 3 - 6 - 3 - 3 - 6 - 3 - 3 - 2 - 4 - 4 - 6 - 3 - 5 - 6 - 4 - 3 - 4 - 4 - 3 - 3 - 5 - 3 - 3 - 4 - 5 - 6 - 4 - 4 - 3 - 2 - 6 - 4 - 4 - 5 - 4 - 3 - 5 - 4 - 3 - 5 - 3 - 6 - 3 - 3 - 3 - 6 - 5 - 2 - 4 - 4 - 3 - 4 - 6 - 4 - 3 - 3 - 5 - 6 - 6 - 3 - 4 - 2 - 3 - 6 - 4 - 5 - 3 - 2 - 5 - 4 - 3 - 3 - 3 - 3 - 3 - 3 - 4 - 4 - 3 - 4 - 6 - 3 - 4 - 6 - 3 - 5 - 3 - 3 - 3 - 3 - 5 - 3 - 3 - 5 - 6 - 5 - 4 - 2 - 4 - 4 - 3 - 2 - 3 - 6 - 3 - 2 - 3 - 4 - 2 - 5 - 5 - 3 - 4 - 4 - 4 - 3 - 4 - 6 - 4 - 6 - 2 - 4 - 4 - 5 - 3 - 4 - 4 - 4 - 2 - 3 - 3 - 2 - 4 - 6 - 6 - 4 - 2 - 5 - 3 - 2 - 5 - 3 - 6 - 6 - 3 - 6 - 4 - 4 - 5 - 2 - 3 - 6 - 3 - 4 - 2 - 4 - 3 - 4 - 4 G-Gens: - - 7 - 1 - 3 - 2 - 6 - 5 - 4 - - 1 - 6 - 4 - 3 - 5 - 2 - 7 G-Name: PSL(2,7) Polynomial: - -2 - 10 - 10 - -14 - -12 - 2 - -1 - 1 QpRts: - - '442892015' - '-52149453' - '258062547' - - '248457184' - '-195327249' - '-333862364' - - '-147025242' - '-90096700' - '-258700339' - - '1169085' - '0' - '0' - - '209128544' - '-175713873' - '58667278' - - '399898588' - '227863326' - '-316729825' - - '-260648434' - '285423949' - '-301309036' QpRts-minpoly: - 17 - 4 - 0 - 1 QpRts-p: 19 QpRts-prec: 7 Size: 168 TransitiveDegree: 7 id: 594197 label_cols: - Baselabel - Polynomial labels: - 3.340736.42t37.a - - -2 - 10 - 10 - -14 - -12 - 2 - -1 - 1 tables: - artin_reps - artin_field_data timestamp: '2024-05-17T15:18:52.279505'