data:
- - BadPrimes:
    - 71
    Baselabel: 2.71.7t2.a
    CharacterField: 7
    Conductor: 71
    Container: 7t2
    Dets:
    - 1.71.2t1.a.a
    - 1.71.2t1.a.a
    - 1.71.2t1.a.a
    Dim: 2
    GalConjSigns:
    - 1
    - 1
    - 1
    Galn: 7
    GaloisConjugates:
    - Character:
      - - 2
      - - 0
      - - -1
        - 0
        - -1
        - -1
        - -1
        - -1
      - - 0
        - 0
        - 1
        - 0
        - 0
        - 1
      - - 0
        - 0
        - 0
        - 1
        - 1
      GalOrbIndex: 1
      HardFactors:
      - 4
      - 3
      - 5
      - 6
      LocalFactors:
      - - - 1
        - - -2
        - - 1
      - - - 1
        - - 0
        - - -1
      - - - 1
        - - 1
          - 0
          - 1
          - 1
          - 1
          - 1
        - - 1
      - - - 1
        - - 0
          - 0
          - -1
          - 0
          - 0
          - -1
        - - 1
      - - - 1
        - - 0
          - 0
          - 0
          - -1
          - -1
        - - 1
      - - - 1
        - - -1
      Sign: 1
    - Character:
      - - 2
      - - 0
      - - 0
        - 0
        - 0
        - 1
        - 1
      - - -1
        - 0
        - -1
        - -1
        - -1
        - -1
      - - 0
        - 0
        - 1
        - 0
        - 0
        - 1
      GalOrbIndex: 2
      HardFactors:
      - 4
      - 3
      - 5
      - 6
      LocalFactors:
      - - - 1
        - - -2
        - - 1
      - - - 1
        - - 0
        - - -1
      - - - 1
        - - 0
          - 0
          - 0
          - -1
          - -1
        - - 1
      - - - 1
        - - 1
          - 0
          - 1
          - 1
          - 1
          - 1
        - - 1
      - - - 1
        - - 0
          - 0
          - -1
          - 0
          - 0
          - -1
        - - 1
      - - - 1
        - - -1
      Sign: 1
    - Character:
      - - 2
      - - 0
      - - 0
        - 0
        - 1
        - 0
        - 0
        - 1
      - - 0
        - 0
        - 0
        - 1
        - 1
      - - -1
        - 0
        - -1
        - -1
        - -1
        - -1
      GalOrbIndex: 3
      HardFactors:
      - 4
      - 3
      - 5
      - 6
      LocalFactors:
      - - - 1
        - - -2
        - - 1
      - - - 1
        - - 0
        - - -1
      - - - 1
        - - 0
          - 0
          - -1
          - 0
          - 0
          - -1
        - - 1
      - - - 1
        - - 0
          - 0
          - 0
          - -1
          - -1
        - - 1
      - - - 1
        - - 1
          - 0
          - 1
          - 1
          - 1
          - 1
        - - 1
      - - - 1
        - - -1
      Sign: 1
    GaloisConjugatesSigns:
    - 1
    - 1
    - 1
    GaloisLabel: 7T2
    Galt: 2
    HardPrimes:
    - 2
    - 3
    - 5
    - 71
    Hide: 0
    Indicator: 1
    Is_Even: false
    NFGal:
    - 1
    - 2
    - -1
    - -1
    - 1
    - -1
    - -1
    - 1
    NumBadPrimes: 1
    Proj_GAP:
    - 14
    - 1
    Proj_Polynomial:
    - 1
    - 2
    - -1
    - -1
    - 1
    - -1
    - -1
    - 1
    Proj_nTj:
    - 7
    - 2
    id: 492390
- - ArtinReps:
    - Baselabel: 1.1.1t1.a
      Character:
      - - 1
      - - 1
      - - 1
      - - 1
      - - 1
      CharacterField: 1
      GalConj: 1
    - Baselabel: 1.71.2t1.a
      Character:
      - - 1
      - - -1
      - - 1
      - - 1
      - - 1
      CharacterField: 1
      GalConj: 1
    - Baselabel: 2.71.7t2.a
      Character:
      - - 2
        - 0
        - 0
        - 0
        - 0
        - 0
      - - 0
        - 0
        - 0
        - 0
        - 0
        - 0
      - - -1
        - 0
        - -1
        - -1
        - -1
        - -1
      - - 0
        - 0
        - 1
        - 0
        - 0
        - 1
      - - 0
        - 0
        - 0
        - 1
        - 1
        - 0
      CharacterField: 7
      GalConj: 1
    - Baselabel: 2.71.7t2.a
      Character:
      - - 2
        - 0
        - 0
        - 0
        - 0
        - 0
      - - 0
        - 0
        - 0
        - 0
        - 0
        - 0
      - - 0
        - 0
        - 0
        - 1
        - 1
        - 0
      - - -1
        - 0
        - -1
        - -1
        - -1
        - -1
      - - 0
        - 0
        - 1
        - 0
        - 0
        - 1
      CharacterField: 7
      GalConj: 2
    - Baselabel: 2.71.7t2.a
      Character:
      - - 2
        - 0
        - 0
        - 0
        - 0
        - 0
      - - 0
        - 0
        - 0
        - 0
        - 0
        - 0
      - - 0
        - 0
        - 1
        - 0
        - 0
        - 1
      - - 0
        - 0
        - 0
        - 1
        - 1
        - 0
      - - -1
        - 0
        - -1
        - -1
        - -1
        - -1
      CharacterField: 7
      GalConj: 3
    ComplexConjugation: 2
    ConjClasses:
    - Order: 1
      Representative:
      - 1
      - 2
      - 3
      - 4
      - 5
      - 6
      - 7
      Size: '1'
    - Order: 2
      Representative:
      - 2
      - 1
      - 6
      - 7
      - 5
      - 3
      - 4
      Size: '7'
    - Order: 7
      Representative:
      - 3
      - 7
      - 5
      - 1
      - 6
      - 2
      - 4
      Size: '2'
    - Order: 7
      Representative:
      - 5
      - 4
      - 6
      - 3
      - 2
      - 7
      - 1
      Size: '2'
    - Order: 7
      Representative:
      - 6
      - 1
      - 2
      - 5
      - 7
      - 4
      - 3
      Size: '2'
    FrobResolvents:
    - Algorithm: CYC
      Classes: 1
      CycleType:
      - 1
      - 1
      - 1
      - 1
      - 1
      - 1
      - 1
      Data: 0
    - Algorithm: CYC
      Classes: 2
      CycleType:
      - 1
      - 2
      - 2
      - 2
      Data: 0
    - Algorithm: RES
      Classes:
      - ConjugacyClass: 3
        RootOf:
        - '6'
        - '1'
      - ConjugacyClass: 4
        RootOf:
        - '-6'
        - '1'
      - ConjugacyClass: 5
        RootOf:
        - '-14'
        - '1'
      CycleType:
      - 7
      Data:
        Powers:
        - 1
        - 6
        Resolvent:
        - 1
        - -3
        - 1
    Frobs:
    - 4
    - 3
    - 5
    - 2
    - 2
    - 2
    - 2
    - 4
    - 2
    - 3
    - 2
    - 4
    - 2
    - 5
    - 2
    - 2
    - 2
    - 2
    - 2
    - 1
    - 5
    - 5
    - 4
    - 3
    - 2
    - 4
    - 3
    - 1
    - 3
    - 2
    - 2
    - 5
    - 2
    - 2
    - 2
    - 3
    - 3
    - 2
    - 5
    - 2
    - 5
    - 2
    - 3
    - 2
    - 2
    - 4
    - 2
    - 4
    - 2
    - 5
    - 4
    - 2
    - 2
    - 4
    - 2
    - 5
    - 2
    - 3
    - 4
    - 2
    - 2
    - 1
    - 2
    - 4
    - 4
    - 2
    - 2
    - 2
    - 2
    - 2
    - 2
    - 5
    - 5
    - 5
    - 3
    - 2
    - 2
    - 2
    - 2
    - 3
    - 3
    - 2
    - 4
    - 2
    - 2
    - 2
    - 2
    - 2
    - 2
    - 4
    - 2
    - 2
    - 2
    - 2
    - 3
    - 3
    - 1
    - 5
    - 2
    - 2
    - 4
    - 3
    - 2
    - 5
    - 4
    - 5
    - 3
    - 3
    - 2
    - 2
    - 2
    - 3
    - 5
    - 2
    - 2
    - 4
    - 1
    - 1
    - 2
    - 3
    - 2
    - 2
    - 3
    - 2
    - 2
    - 2
    - 2
    - 4
    - 2
    - 2
    - 1
    - 2
    - 2
    - 2
    - 2
    - 2
    - 2
    - 3
    - 4
    - 2
    - 5
    - 4
    - 2
    - 2
    - 4
    - 4
    - 3
    - 3
    - 2
    - 2
    - 5
    - 5
    - 2
    - 2
    - 2
    - 2
    - 2
    - 4
    - 2
    - 4
    - 5
    - 5
    - 2
    - 1
    - 3
    - 4
    - 2
    - 5
    G-Gens:
    - - 2
      - 1
      - 6
      - 7
      - 5
      - 3
      - 4
    - - 7
      - 3
      - 2
      - 4
      - 6
      - 5
      - 1
    G-Name: D14
    Polynomial:
    - 1
    - 2
    - -1
    - -1
    - 1
    - -1
    - -1
    - 1
    QpRts:
    - - '22012'
      - '33430'
    - - '68266'
      - '-58174'
    - - '46567'
      - '-60846'
    - - '-50947'
      - '-33430'
    - - '-7669'
      - '58174'
    - - '-67564'
      - '0'
    - - '-10664'
      - '60846'
    QpRts-minpoly:
    - 2
    - 7
    - 1
    QpRts-p: 11
    QpRts-prec: 5
    Size: 14
    TransitiveDegree: 7
    id: 492623
label_cols:
- Baselabel
- Polynomial
labels:
- 2.71.7t2.a
- - 1
  - 2
  - -1
  - -1
  - 1
  - -1
  - -1
  - 1
tables:
- artin_reps
- artin_field_data
timestamp: '2024-04-25T13:48:52.477812'