data:
- - BadPrimes:
    - 2
    - 23
    Baselabel: 3.33856.6t8.a
    CharacterField: 1
    Conductor: 33856
    Container: 6t8
    Dets:
    - 1.1.1t1.a.a
    Dim: 3
    GalConjSigns:
    - 1
    Galn: 6
    GaloisConjugates:
    - Character:
      - - 3
      - - -1
      - - -1
      - - 0
      - - 1
      GalOrbIndex: 1
      HardFactors:
      - 6
      - 7
      LocalFactors:
      - - - 1
        - - -3
        - - 3
        - - -1
      - - - 1
        - - 1
        - - -1
        - - -1
      - - - 1
        - - 1
        - - -1
        - - -1
      - - - 1
        - - 0
        - - 0
        - - -1
      - - - 1
        - - -1
        - - 1
        - - -1
      - - - 1
      - - - 1
        - - 1
      Sign: 1
    GaloisConjugatesSigns:
    - 1
    GaloisLabel: 6T7
    Galt: 7
    HardPrimes:
    - 2
    - 23
    Hide: 1
    Indicator: 1
    Is_Even: true
    NFGal:
    - -1
    - 0
    - 0
    - 0
    - 1
    - 0
    - 1
    NumBadPrimes: 2
    Proj_GAP:
    - 24
    - 12
    Proj_Polynomial:
    - -1
    - 0
    - 0
    - 0
    - 1
    - 0
    - 1
    Proj_nTj:
    - 6
    - 7
    id: 519638
- - ArtinReps:
    - Baselabel: 1.1.1t1.a
      Character:
      - - 1
      - - 1
      - - 1
      - - 1
      - - 1
      CharacterField: 1
      GalConj: 1
    - Baselabel: 1.23.2t1.a
      Character:
      - - 1
      - - 1
      - - -1
      - - 1
      - - -1
      CharacterField: 1
      GalConj: 1
    - Baselabel: 2.23.3t2.b
      Character:
      - - 2
      - - 2
      - - 0
      - - -1
      - - 0
      CharacterField: 1
      GalConj: 1
    - Baselabel: 3.33856.6t8.a
      Character:
      - - 3
      - - -1
      - - -1
      - - 0
      - - 1
      CharacterField: 1
      GalConj: 1
    - Baselabel: 3.1472.4t5.a
      Character:
      - - 3
      - - -1
      - - 1
      - - 0
      - - -1
      CharacterField: 1
      GalConj: 1
    ComplexConjugation: 3
    ConjClasses:
    - Order: 1
      Representative:
      - 1
      - 2
      - 3
      - 4
      - 5
      - 6
      Size: '1'
    - Order: 2
      Representative:
      - 1
      - 5
      - 6
      - 4
      - 2
      - 3
      Size: '3'
    - Order: 2
      Representative:
      - 2
      - 1
      - 3
      - 5
      - 4
      - 6
      Size: '6'
    - Order: 3
      Representative:
      - 5
      - 3
      - 4
      - 2
      - 6
      - 1
      Size: '8'
    - Order: 4
      Representative:
      - 4
      - 3
      - 5
      - 1
      - 6
      - 2
      Size: '6'
    FrobResolvents:
    - Algorithm: CYC
      Classes: 1
      CycleType:
      - 1
      - 1
      - 1
      - 1
      - 1
      - 1
      Data: 0
    - Algorithm: RES
      Classes:
      - ConjugacyClass: 2
        RootOf:
        - '1512'
        - '-36'
        - '6'
        - '1'
      - ConjugacyClass: 3
        RootOf:
        - '-2006208'
        - '373248'
        - '-69984'
        - '5616'
        - '36'
        - '-12'
        - '1'
      CycleType:
      - 1
      - 1
      - 2
      - 2
      Data:
        Powers:
        - 1
        Resolvent:
        - 1
        - -3
        - 1
    - Algorithm: CYC
      Classes: 5
      CycleType:
      - 2
      - 4
      Data: 0
    - Algorithm: CYC
      Classes: 4
      CycleType:
      - 3
      - 3
      Data: 0
    Frobs:
    - 4
    - 4
    - 5
    - 5
    - 5
    - 4
    - 5
    - 3
    - 3
    - 4
    - 4
    - 5
    - 4
    - 3
    - 4
    - 3
    - 2
    - 3
    - 5
    - 4
    - 4
    - 3
    - 5
    - 3
    - 5
    - 2
    - 5
    - 3
    - 3
    - 5
    - 4
    - 4
    - 3
    - 4
    - 3
    - 4
    - 3
    - 4
    - 2
    - 2
    - 4
    - 5
    - 5
    - 4
    - 4
    - 5
    - 2
    - 1
    - 5
    - 3
    - 4
    - 4
    - 5
    - 5
    - 4
    - 3
    - 4
    - 2
    - 4
    - 5
    - 5
    - 3
    - 2
    - 4
    - 3
    - 2
    - 4
    - 3
    - 1
    - 4
    - 4
    - 3
    - 5
    - 5
    - 3
    - 3
    - 3
    - 4
    - 5
    - 4
    - 3
    - 5
    - 3
    - 5
    - 4
    - 4
    - 1
    - 5
    - 4
    - 1
    - 3
    - 5
    - 4
    - 4
    - 4
    - 3
    - 4
    - 3
    - 5
    - 4
    - 4
    - 3
    - 3
    - 5
    - 5
    - 4
    - 4
    - 2
    - 2
    - 4
    - 2
    - 5
    - 3
    - 3
    - 3
    - 3
    - 5
    - 4
    - 4
    - 5
    - 3
    - 4
    - 3
    - 4
    - 2
    - 5
    - 5
    - 2
    - 5
    - 5
    - 4
    - 5
    - 3
    - 5
    - 4
    - 5
    - 3
    - 3
    - 3
    - 2
    - 4
    - 2
    - 4
    - 3
    - 2
    - 5
    - 2
    - 4
    - 4
    - 4
    - 2
    - 5
    - 2
    - 4
    - 3
    - 3
    - 5
    - 4
    - 5
    - 5
    - 4
    - 3
    - 4
    - 3
    - 5
    - 3
    - 2
    - 2
    G-Gens:
    - - 5
      - 3
      - 4
      - 2
      - 6
      - 1
    - - 2
      - 1
      - 3
      - 5
      - 4
      - 6
    - - 5
      - 4
      - 3
      - 2
      - 1
      - 6
    - - 2
      - 3
      - 1
      - 5
      - 6
      - 4
    G-Name: S4
    Polynomial:
    - -1
    - 0
    - 0
    - 0
    - 1
    - 0
    - 1
    QpRts:
    - - '-2572774549'
      - '0'
    - - '2088193370'
      - '-3031558358'
    - - '-5705554691'
      - '-3031558358'
    - - '2572774549'
      - '0'
    - - '-2088193370'
      - '3031558358'
    - - '5705554691'
      - '3031558358'
    QpRts-minpoly:
    - 2
    - 18
    - 1
    QpRts-p: 19
    QpRts-prec: 8
    Size: 24
    TransitiveDegree: 6
    id: 513934
label_cols:
- Baselabel
- Polynomial
labels:
- 3.33856.6t8.a
- - -1
  - 0
  - 0
  - 0
  - 1
  - 0
  - 1
tables:
- artin_reps
- artin_field_data
timestamp: '2024-05-19T11:37:14.501867'