data:
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    Baselabel: 1.17.8t1.a
    CharacterField: 8
    Conductor: 17
    Container: 8t1
    Dets:
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    - '17.2'
    - '17.9'
    - '17.15'
    Dim: 1
    GalConjSigns:
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    - 0
    - 0
    - 0
    Galn: 8
    GaloisConjugates:
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      - - -1
      - - 0
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      - - 0
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      GalOrbIndex: 1
      HardFactors:
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      LocalFactors:
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        - - -1
      - - - 1
        - - 1
      - - - 1
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    - Character:
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        - 0
        - 1
      - - 0
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      - - 0
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        - 0
        - -1
      - - 0
        - -1
      GalOrbIndex: 2
      HardFactors:
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      - 7
      LocalFactors:
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        - - -1
      - - - 1
        - - 1
      - - - 1
        - - 0
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    - Character:
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      GalOrbIndex: 3
      HardFactors:
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      LocalFactors:
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      - - - 1
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      - - - 1
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    - Character:
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      GalOrbIndex: 4
      HardFactors:
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      - 7
      LocalFactors:
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      - - - 1
        - - 1
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      Sign: 0
    GaloisConjugatesSigns:
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    - 0
    - 0
    - 0
    GaloisLabel: 8T1
    Galt: 1
    HardPrimes:
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    - 31
    Hide: 0
    Indicator: 0
    Is_Even: true
    NFGal:
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    - 4
    - -10
    - -10
    - 15
    - 6
    - -7
    - -1
    - 1
    NumBadPrimes: 1
    Proj_GAP:
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    - 1
    Proj_Polynomial:
    - 0
    - 1
    Proj_nTj:
    - 1
    - 1
    id: 446563
- - ArtinReps:
    - Baselabel: 1.1.1t1.a
      Character:
      - - 1
      - - 1
      - - 1
      - - 1
      - - 1
      - - 1
      - - 1
      - - 1
      CharacterField: 1
      GalConj: 1
    - Baselabel: 1.17.8t1.a
      Character:
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        - 0
        - 0
        - 0
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        - 0
        - 0
        - 0
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        - 0
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        - -1
      CharacterField: 8
      GalConj: 1
    - Baselabel: 1.17.4t1.a
      Character:
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      - - 1
        - 0
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        - 0
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      CharacterField: 4
      GalConj: 1
    - Baselabel: 1.17.8t1.a
      Character:
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        - 0
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        - 0
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        - -1
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        - 0
        - -1
      - - 0
        - -1
        - 0
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      CharacterField: 8
      GalConj: 2
    - Baselabel: 1.17.2t1.a
      Character:
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      - - 1
      - - 1
      - - 1
      - - -1
      - - -1
      - - -1
      - - -1
      CharacterField: 1
      GalConj: 1
    - Baselabel: 1.17.8t1.a
      Character:
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        - 0
      - - 0
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        - 0
        - 0
        - -1
      - - 0
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        - 0
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      - - 0
        - 0
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      CharacterField: 8
      GalConj: 3
    - Baselabel: 1.17.4t1.a
      Character:
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        - 0
      - - 1
        - 0
      - - -1
        - 0
      - - -1
        - 0
      - - 0
        - -1
      - - 0
        - 1
      - - 0
        - -1
      - - 0
        - 1
      CharacterField: 4
      GalConj: 2
    - Baselabel: 1.17.8t1.a
      Character:
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        - 0
        - 0
        - 0
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        - 0
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        - 0
      - - 0
        - 0
        - -1
        - 0
      - - 0
        - 0
        - 1
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      - - 0
        - 0
        - 0
        - -1
      - - 0
        - -1
        - 0
        - 0
      - - 0
        - 0
        - 0
        - 1
      - - 0
        - 1
        - 0
        - 0
      CharacterField: 8
      GalConj: 4
    ComplexConjugation: 1
    ConjClasses:
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      Representative:
      - 1
      - 2
      - 3
      - 4
      - 5
      - 6
      - 7
      - 8
      Size: '1'
    - Order: 2
      Representative:
      - 2
      - 1
      - 7
      - 5
      - 4
      - 8
      - 3
      - 6
      Size: '1'
    - Order: 4
      Representative:
      - 3
      - 7
      - 2
      - 8
      - 6
      - 4
      - 1
      - 5
      Size: '1'
    - Order: 4
      Representative:
      - 7
      - 3
      - 1
      - 6
      - 8
      - 5
      - 2
      - 4
      Size: '1'
    - Order: 8
      Representative:
      - 8
      - 6
      - 5
      - 1
      - 2
      - 7
      - 4
      - 3
      Size: '1'
    - Order: 8
      Representative:
      - 5
      - 4
      - 6
      - 3
      - 7
      - 1
      - 8
      - 2
      Size: '1'
    - Order: 8
      Representative:
      - 6
      - 8
      - 4
      - 2
      - 1
      - 3
      - 5
      - 7
      Size: '1'
    - Order: 8
      Representative:
      - 4
      - 5
      - 8
      - 7
      - 3
      - 2
      - 6
      - 1
      Size: '1'
    FrobResolvents:
    - Algorithm: CYC
      Classes: 1
      CycleType:
      - 1
      - 1
      - 1
      - 1
      - 1
      - 1
      - 1
      - 1
      Data: 0
    - Algorithm: CYC
      Classes: 2
      CycleType:
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      - 2
      - 2
      - 2
      Data: 0
    - Algorithm: RES
      Classes:
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        RootOf:
        - '-4'
        - '1'
      - ConjugacyClass: 4
        RootOf:
        - '13'
        - '1'
      CycleType:
      - 4
      - 4
      Data:
        Powers:
        - 1
        Resolvent:
        - 0
        - 0
        - 1
    - Algorithm: RES
      Classes:
      - ConjugacyClass: 5
        RootOf:
        - '-116'
        - '1'
      - ConjugacyClass: 6
        RootOf:
        - '88'
        - '1'
      - ConjugacyClass: 7
        RootOf:
        - '-643'
        - '1'
      - ConjugacyClass: 8
        RootOf:
        - '37'
        - '1'
      CycleType:
      - 8
      Data:
        Powers:
        - 1
        Resolvent:
        - 8
        - 7
        - 6
        - 5
        - 4
        - 3
        - 2
        - 1
    Frobs:
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    - 7
    - 5
    - 8
    - 6
    - 2
    - 1
    - 4
    - 6
    - 5
    - 7
    - 7
    - 8
    - 3
    - 2
    - 4
    - 3
    - 8
    - 1
    - 7
    - 5
    - 6
    - 4
    - 2
    - 5
    - 1
    - 1
    - 5
    - 8
    - 6
    - 3
    - 5
    - 1
    - 7
    - 2
    - 4
    - 2
    - 8
    - 7
    - 7
    - 3
    - 6
    - 2
    - 6
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    - 8
    - 4
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    - 3
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    - 1
    - 7
    - 2
    - 4
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    - 1
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    - 2
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    - 6
    - 3
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    - 8
    - 3
    - 2
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    - 1
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    - 3
    - 4
    - 6
    - 8
    - 1
    - 6
    - 2
    - 6
    - 3
    - 7
    - 1
    - 8
    - 4
    - 4
    - 2
    - 3
    - 7
    - 6
    - 4
    - 6
    - 8
    - 1
    - 6
    - 2
    - 7
    - 7
    - 2
    - 4
    - 3
    - 8
    - 1
    - 3
    - 4
    - 2
    - 6
    - 5
    - 1
    - 5
    - 8
    - 4
    - 5
    - 7
    - 1
    - 8
    - 2
    - 4
    - 8
    - 7
    - 7
    - 6
    - 2
    - 5
    - 5
    - 2
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    - 3
    - 5
    - 7
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    - 2
    - 2
    - 3
    - 5
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    - 8
    - 5
    - 5
    - 8
    - 6
    - 2
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    - 7
    - 8
    - 3
    - 2
    - 8
    - 7
    - 1
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    - 6
    - 8
    - 1
    - 6
    - 4
    - 6
    - 5
    - 1
    - 4
    - 4
    - 3
    - 7
    - 5
    - 6
    G-Gens:
    - - 8
      - 6
      - 5
      - 1
      - 2
      - 7
      - 4
      - 3
    - - 3
      - 7
      - 2
      - 8
      - 6
      - 4
      - 1
      - 5
    - - 2
      - 1
      - 7
      - 5
      - 4
      - 8
      - 3
      - 6
    G-Name: C8
    Polynomial:
    - 1
    - 4
    - -10
    - -10
    - 15
    - 6
    - -7
    - -1
    - 1
    QpRts:
    - - '339272929'
    - - '443617057'
    - - '107125985'
    - - '-168679434'
    - - '-339091377'
    - - '-279750341'
    - - '-43358595'
    - - '-59136223'
    QpRts-minpoly:
    - -1
    - 1
    QpRts-p: 67
    QpRts-prec: 5
    Size: 8
    TransitiveDegree: 8
    id: 446793
label_cols:
- Baselabel
- Polynomial
labels:
- 1.17.8t1.a
- - 1
  - 4
  - -10
  - -10
  - 15
  - 6
  - -7
  - -1
  - 1
tables:
- artin_reps
- artin_field_data
timestamp: '2024-04-19T21:42:15.418267'