data:
- - BadPrimes:
    - 2
    - 5
    - 19
    Baselabel: 3.36100.12t33.a
    CharacterField: 5
    Conductor: 36100
    Container: 12t33
    Dets:
    - 1.1.1t1.a.a
    - 1.1.1t1.a.a
    Dim: 3
    GalConjSigns:
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    - 1
    Galn: 5
    GaloisConjugates:
    - Character:
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      - - -1
      - - 0
      - - 0
        - 0
        - -1
        - -1
      - - 1
        - 0
        - 1
        - 1
      GalOrbIndex: 1
      HardFactors:
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      - 3
      - 6
      LocalFactors:
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        - - -1
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          - 0
          - -1
          - -1
        - - 1
          - 0
          - 1
          - 1
        - - -1
      - - - 1
        - - 1
      Sign: 1
    - Character:
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      - - -1
      - - 0
      - - 1
        - 0
        - 1
        - 1
      - - 0
        - 0
        - -1
        - -1
      GalOrbIndex: 2
      HardFactors:
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      - 6
      - 3
      - 6
      LocalFactors:
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        - - -3
        - - 3
        - - -1
      - - - 1
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        - - 0
          - 0
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          - 1
        - - 0
          - 0
          - -1
          - -1
        - - -1
      - - - 1
        - - 1
      Sign: 1
    GaloisConjugatesSigns:
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    - 1
    GaloisLabel: 5T4
    Galt: 4
    HardPrimes:
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    - 5
    - 13
    - 19
    Hide: 0
    Indicator: 1
    Is_Even: true
    NFGal:
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    - 64
    - 6
    - -11
    - -1
    - 1
    NumBadPrimes: 3
    Proj_GAP:
    - 60
    - 5
    Proj_Polynomial:
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    - 64
    - 6
    - -11
    - -1
    - 1
    Proj_nTj:
    - 5
    - 4
    id: 575002
- - ArtinReps:
    - Baselabel: 1.1.1t1.a
      Character:
      - - 1
      - - 1
      - - 1
      - - 1
      - - 1
      CharacterField: 1
      GalConj: 1
    - Baselabel: 3.36100.12t33.a
      Character:
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        - 0
        - 0
        - 0
      - - -1
        - 0
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        - 0
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        - 0
        - 0
        - 0
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        - -1
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        - 0
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        - 1
      CharacterField: 5
      GalConj: 1
    - Baselabel: 3.36100.12t33.a
      Character:
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        - 0
        - 0
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        - 0
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      - - 0
        - 0
        - -1
        - -1
      CharacterField: 5
      GalConj: 2
    - Baselabel: 4.13032100.5t4.a
      Character:
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      - - 0
      - - 1
      - - -1
      - - -1
      CharacterField: 1
      GalConj: 1
    - Baselabel: 5.52128400.6t12.a
      Character:
      - - 5
      - - 1
      - - -1
      - - 0
      - - 0
      CharacterField: 1
      GalConj: 1
    ComplexConjugation: 2
    ConjClasses:
    - Order: 1
      Representative:
      - 1
      - 2
      - 3
      - 4
      - 5
      Size: '1'
    - Order: 2
      Representative:
      - 2
      - 1
      - 4
      - 3
      - 5
      Size: '15'
    - Order: 3
      Representative:
      - 2
      - 3
      - 1
      - 4
      - 5
      Size: '20'
    - Order: 5
      Representative:
      - 2
      - 3
      - 4
      - 5
      - 1
      Size: '12'
    - Order: 5
      Representative:
      - 3
      - 1
      - 4
      - 5
      - 2
      Size: '12'
    FrobResolvents:
    - Algorithm: CYC
      Classes: 1
      CycleType:
      - 1
      - 1
      - 1
      - 1
      - 1
      Data: 0
    - Algorithm: CYC
      Classes: 3
      CycleType:
      - 1
      - 1
      - 3
      Data: 0
    - Algorithm: CYC
      Classes: 2
      CycleType:
      - 1
      - 2
      - 2
      Data: 0
    - Algorithm: ALT
      Classes:
      - ConjugacyClass: 4
        RootOf:
        - '-46930'
        - '1'
      - ConjugacyClass: 5
        RootOf:
        - '46930'
        - '1'
      CycleType:
      - 5
      Data:
      - 2
      - 3
      - 4
      - 5
      - 1
    Frobs:
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    - 3
    - 2
    - 4
    - 4
    - 3
    - 5
    - 2
    - 3
    - 2
    - 3
    - 3
    - 3
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    - 3
    - 3
    - 3
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    - 2
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    - 2
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    - 5
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    - 5
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    - 3
    - 3
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    - 5
    - 2
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    - 5
    - 5
    - 2
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    - 2
    - 3
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    - 5
    - 4
    - 5
    - 4
    - 3
    - 3
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    - 3
    - 3
    - 3
    - 3
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    - 5
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    - 2
    - 2
    - 1
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    - 2
    - 3
    - 2
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    - 2
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    - 5
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    - 2
    - 3
    - 3
    - 2
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    - 5
    - 5
    - 5
    - 2
    - 3
    - 5
    - 2
    - 4
    - 2
    - 2
    - 5
    - 5
    - 2
    - 4
    - 2
    G-Gens:
    - - 2
      - 3
      - 1
      - 4
      - 5
    - - 1
      - 2
      - 4
      - 5
      - 3
    G-Name: A5
    Polynomial:
    - -74
    - 64
    - 6
    - -11
    - -1
    - 1
    QpRts:
    - - '21048361107626'
    - - '23060360102725'
    - - '8868405430094'
    - - '-24267791115441'
    - - '24904388669554'
    QpRts-minpoly:
    - -1
    - 1
    QpRts-p: 557
    QpRts-prec: 5
    Size: 60
    TransitiveDegree: 5
    id: 554060
label_cols:
- Baselabel
- Polynomial
labels:
- 3.36100.12t33.a
- - -74
  - 64
  - 6
  - -11
  - -1
  - 1
tables:
- artin_reps
- artin_field_data
timestamp: '2024-05-09T22:05:12.781141'