Artin representation data - 2.2025.24t65.a

Formats: - HTML - YAML - JSON - 2023-12-05T17:50:17.705069

• artin_reps •

  Column	Type
  BadPrimes	jsonb
  Baselabel	text
  CharacterField	smallint
  Conductor	numeric
  Container	text
  Dets	text[]
  Dim	smallint
  GalConjSigns	jsonb
  Galn	smallint
  GaloisConjugates	jsonb
  GaloisConjugatesSigns	integer[]
  GaloisLabel	text
  Galt	integer
  HardPrimes	jsonb
  Hide	smallint
  Indicator	smallint
  Is_Even	boolean
  NFGal	jsonb
  NumBadPrimes	smallint
  Proj_GAP	integer[]
  Proj_Polynomial	numeric[]
  Proj_nTj	integer[]

  
  {'BadPrimes': [3, 5], 'Baselabel': '2.2025.24t65.a', 'CharacterField': 12, 'Conductor': 2025, 'Container': '24t65', 'Dets': ['1.9.6t1.a.b', '1.9.6t1.a.a', '1.9.6t1.a.a', '1.9.6t1.a.b'], 'Dim': 2, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 24, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, 0, -2], [-2, 0, 2], [1, 0, -1], [0, 0, 1], [-1], [0, 0, 0, 2], [0, 0, 0, -2], [0], [0], [2, 0, -2], [0, 0, 2], [-1, 0, 1], [0, 0, -1], [1], [0], [0], [0], [0], [0, -2, 0, 2], [0, 2], [0, 2, 0, -2], [0, -2], [0, 0, 0, 1], [0, 0, 0, -1], [0, -1], [0, 1, 0, -1], [0, 1], [0, -1, 0, 1], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [32, 37, 37, 34, 19, 20, 8, 33, 24, 26], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, 0, 2], [-1, 0, 1]], [[1], [2, 0, -2], [0, 0, -1]], [[1], [-1, 0, 1], [0, 0, -1]], [[1], [0, 0, -1], [-1, 0, 1]], [[1], [1], [1]], [[1], [0, 0, 0, -2], [-1]], [[1], [0, 0, 0, 2], [-1]], [[1], [0], [1]], [[1], [0], [1]], [[1], [-2, 0, 2], [0, 0, -1]], [[1], [0, 0, -2], [-1, 0, 1]], [[1], [1, 0, -1], [0, 0, -1]], [[1], [0, 0, 1], [-1, 0, 1]], [[1], [-1], [1]], [[1], [0], [1, 0, -1]], [[1], [0], [0, 0, 1]], [[1], [0], [1, 0, -1]], [[1], [0], [0, 0, 1]], [[1], [0, 2, 0, -2], [1, 0, -1]], [[1], [0, -2], [0, 0, 1]], [[1], [0, -2, 0, 2], [1, 0, -1]], [[1], [0, 2], [0, 0, 1]], [[1], [0, 0, 0, -1], [-1]], [[1], [0, 0, 0, 1], [-1]], [[1], [0, 1], [0, 0, 1]], [[1], [0, -1, 0, 1], [1, 0, -1]], [[1], [0, -1], [0, 0, 1]], [[1], [0, 1, 0, -1], [1, 0, -1]], [[1], [0], [0, 0, -1]], [[1], [0], [-1, 0, 1]], [[1], [0], [0, 0, -1]], [[1], [0], [-1, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [-2, 0, 2], [0, 0, -2], [0, 0, 1], [1, 0, -1], [-1], [0, 0, 0, 2], [0, 0, 0, -2], [0], [0], [0, 0, 2], [2, 0, -2], [0, 0, -1], [-1, 0, 1], [1], [0], [0], [0], [0], [0, 2], [0, -2, 0, 2], [0, -2], [0, 2, 0, -2], [0, 0, 0, 1], [0, 0, 0, -1], [0, 1, 0, -1], [0, -1], [0, -1, 0, 1], [0, 1], [0], [0], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [32, 37, 37, 34, 19, 20, 8, 33, 24, 26], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [2, 0, -2], [0, 0, -1]], [[1], [0, 0, 2], [-1, 0, 1]], [[1], [0, 0, -1], [-1, 0, 1]], [[1], [-1, 0, 1], [0, 0, -1]], [[1], [1], [1]], [[1], [0, 0, 0, -2], [-1]], [[1], [0, 0, 0, 2], [-1]], [[1], [0], [1]], [[1], [0], [1]], [[1], [0, 0, -2], [-1, 0, 1]], [[1], [-2, 0, 2], [0, 0, -1]], [[1], [0, 0, 1], [-1, 0, 1]], [[1], [1, 0, -1], [0, 0, -1]], [[1], [-1], [1]], [[1], [0], [0, 0, 1]], [[1], [0], [1, 0, -1]], [[1], [0], [0, 0, 1]], [[1], [0], [1, 0, -1]], [[1], [0, -2], [0, 0, 1]], [[1], [0, 2, 0, -2], [1, 0, -1]], [[1], [0, 2], [0, 0, 1]], [[1], [0, -2, 0, 2], [1, 0, -1]], [[1], [0, 0, 0, -1], [-1]], [[1], [0, 0, 0, 1], [-1]], [[1], [0, -1, 0, 1], [1, 0, -1]], [[1], [0, 1], [0, 0, 1]], [[1], [0, 1, 0, -1], [1, 0, -1]], [[1], [0, -1], [0, 0, 1]], [[1], [0], [-1, 0, 1]], [[1], [0], [0, 0, -1]], [[1], [0], [-1, 0, 1]], [[1], [0], [0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [-2, 0, 2], [0, 0, -2], [0, 0, 1], [1, 0, -1], [-1], [0, 0, 0, -2], [0, 0, 0, 2], [0], [0], [0, 0, 2], [2, 0, -2], [0, 0, -1], [-1, 0, 1], [1], [0], [0], [0], [0], [0, -2], [0, 2, 0, -2], [0, 2], [0, -2, 0, 2], [0, 0, 0, -1], [0, 0, 0, 1], [0, -1, 0, 1], [0, 1], [0, 1, 0, -1], [0, -1], [0], [0], [0], [0]], 'GalOrbIndex': 3, 'HardFactors': [32, 37, 37, 34, 19, 20, 8, 33, 24, 26], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [2, 0, -2], [0, 0, -1]], [[1], [0, 0, 2], [-1, 0, 1]], [[1], [0, 0, -1], [-1, 0, 1]], [[1], [-1, 0, 1], [0, 0, -1]], [[1], [1], [1]], [[1], [0, 0, 0, 2], [-1]], [[1], [0, 0, 0, -2], [-1]], [[1], [0], [1]], [[1], [0], [1]], [[1], [0, 0, -2], [-1, 0, 1]], [[1], [-2, 0, 2], [0, 0, -1]], [[1], [0, 0, 1], [-1, 0, 1]], [[1], [1, 0, -1], [0, 0, -1]], [[1], [-1], [1]], [[1], [0], [0, 0, 1]], [[1], [0], [1, 0, -1]], [[1], [0], [0, 0, 1]], [[1], [0], [1, 0, -1]], [[1], [0, 2], [0, 0, 1]], [[1], [0, -2, 0, 2], [1, 0, -1]], [[1], [0, -2], [0, 0, 1]], [[1], [0, 2, 0, -2], [1, 0, -1]], [[1], [0, 0, 0, 1], [-1]], [[1], [0, 0, 0, -1], [-1]], [[1], [0, 1, 0, -1], [1, 0, -1]], [[1], [0, -1], [0, 0, 1]], [[1], [0, -1, 0, 1], [1, 0, -1]], [[1], [0, 1], [0, 0, 1]], [[1], [0], [-1, 0, 1]], [[1], [0], [0, 0, -1]], [[1], [0], [-1, 0, 1]], [[1], [0], [0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, 0, -2], [-2, 0, 2], [1, 0, -1], [0, 0, 1], [-1], [0, 0, 0, -2], [0, 0, 0, 2], [0], [0], [2, 0, -2], [0, 0, 2], [-1, 0, 1], [0, 0, -1], [1], [0], [0], [0], [0], [0, 2, 0, -2], [0, -2], [0, -2, 0, 2], [0, 2], [0, 0, 0, -1], [0, 0, 0, 1], [0, 1], [0, -1, 0, 1], [0, -1], [0, 1, 0, -1], [0], [0], [0], [0]], 'GalOrbIndex': 4, 'HardFactors': [32, 37, 37, 34, 19, 20, 8, 33, 24, 26], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, 0, 2], [-1, 0, 1]], [[1], [2, 0, -2], [0, 0, -1]], [[1], [-1, 0, 1], [0, 0, -1]], [[1], [0, 0, -1], [-1, 0, 1]], [[1], [1], [1]], [[1], [0, 0, 0, 2], [-1]], [[1], [0, 0, 0, -2], [-1]], [[1], [0], [1]], [[1], [0], [1]], [[1], [-2, 0, 2], [0, 0, -1]], [[1], [0, 0, -2], [-1, 0, 1]], [[1], [1, 0, -1], [0, 0, -1]], [[1], [0, 0, 1], [-1, 0, 1]], [[1], [-1], [1]], [[1], [0], [1, 0, -1]], [[1], [0], [0, 0, 1]], [[1], [0], [1, 0, -1]], [[1], [0], [0, 0, 1]], [[1], [0, -2, 0, 2], [1, 0, -1]], [[1], [0, 2], [0, 0, 1]], [[1], [0, 2, 0, -2], [1, 0, -1]], [[1], [0, -2], [0, 0, 1]], [[1], [0, 0, 0, 1], [-1]], [[1], [0, 0, 0, -1], [-1]], [[1], [0, -1], [0, 0, 1]], [[1], [0, 1, 0, -1], [1, 0, -1]], [[1], [0, 1], [0, 0, 1]], [[1], [0, -1, 0, 1], [1, 0, -1]], [[1], [0], [0, 0, -1]], [[1], [0], [-1, 0, 1]], [[1], [0], [0, 0, -1]], [[1], [0], [-1, 0, 1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '24T65', 'Galt': 65, 'HardPrimes': [2, 3, 5, 7, 11, 59, 61, 67, 113, 977], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 0, 0, -3, 0, 0, 5, 0, 0, -8, 0, 0, 9, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-1, 3, 0, 1], 'Proj_nTj': [3, 2]}
• artin_field_data •

  Column	Type
  ArtinReps	jsonb
  ComplexConjugation	smallint
  ConjClasses	jsonb
  FrobResolvents	jsonb
  Frobs	jsonb
  G-Gens	jsonb
  G-Name	text
  Polynomial	jsonb
  QpRts	jsonb
  QpRts-minpoly	jsonb
  QpRts-p	integer
  QpRts-prec	integer
  Size	numeric
  TransitiveDegree	smallint

  
  {'ArtinReps': [{'GalConj': 1, 'Baselabel': '1.1.1t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.3.2t1.a', 'Character': [[1], [1], [-1], [-1], [1], [1], [1], [1], [1], [-1], [-1], [1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.15.2t1.a', 'Character': [[1], [1], [-1], [-1], [1], [1], [1], [1], [1], [1], [1], [-1], [-1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.5.2t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.45.6t1.b', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [0, -1], [1, 1], [0, -1], [1, 1], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.45.6t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, -1], [1, 1], [0, -1], [1, 1], [-1, 0], [-1, 0], [1, 1], [0, -1], [1, 1], [0, -1], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.9.6t1.a', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [-1, 0], [-1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [1, 1], [0, -1], [1, 1], [0, -1], [1, 1], [0, -1], [1, 1], [0, -1], [-1, 0], [-1, 0], [0, -1], [1, 1], [0, -1], [1, 1], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.9.6t1.a', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [-1, 0], [-1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [0, -1], [1, 1], [0, -1], [1, 1], [0, -1], [1, 1], [0, -1], [1, 1], [-1, 0], [-1, 0], [1, 1], [0, -1], [1, 1], [0, -1], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.45.6t1.b', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [1, 1], [0, -1], [1, 1], [0, -1], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.45.6t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 1], [0, -1], [1, 1], [0, -1], [-1, 0], [-1, 0], [0, -1], [1, 1], [0, -1], [1, 1], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.5.4t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [0, -1], [0, 1], [0, -1], [0, 1], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [0, 1], [0, -1], [0, -1], [0, 1], [0, -1], [0, 1], [0, 1], [0, -1], [0, -1], [0, -1], [0, -1], [0, 1], [0, 1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '1.15.4t1.a', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [0, -1], [0, 1], [0, 1], [0, -1], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [1, 0], [1, 0], [0, 1], [0, 1], [0, -1], [0, -1], [0, 1], [0, -1], [0, 1], [0, 1], [0, -1], [0, -1], [0, 1], [0, 1], [0, -1], [0, -1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '1.15.4t1.a', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [0, -1], [0, -1], [0, 1], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [1, 0], [1, 0], [0, -1], [0, -1], [0, 1], [0, 1], [0, -1], [0, 1], [0, -1], [0, -1], [0, 1], [0, 1], [0, -1], [0, -1], [0, 1], [0, 1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '1.5.4t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [0, -1], [0, 1], [0, -1], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [1, 0], [1, 0], [-1, 0], [-1, 0], [0, -1], [0, -1], [0, 1], [0, 1], [0, -1], [0, 1], [0, -1], [0, -1], [0, 1], [0, 1], [0, 1], [0, 1], [0, -1], [0, -1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '1.45.12t1.b', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [-1, 0, 0, 0], [1, 0, 0, 0], [0, 0, -1, 0], [-1, 0, 1, 0], [-1, 0, 1, 0], [0, 0, -1, 0], [1, 0, 0, 0], [0, 0, 0, -1], [0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 0, -1], [1, 0, -1, 0], [0, 0, 1, 0], [1, 0, -1, 0], [0, 0, 1, 0], [-1, 0, 0, 0], [0, 0, 1, 0], [1, 0, -1, 0], [0, 0, -1, 0], [-1, 0, 1, 0], [0, 1, 0, -1], [0, -1, 0, 0], [0, -1, 0, 1], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 0, -1], [0, -1, 0, 0], [0, 1, 0, -1], [0, 1, 0, 0], [0, -1, 0, 1], [0, -1, 0, 0], [0, 1, 0, -1], [0, 1, 0, 0], [0, -1, 0, 1]], 'CharacterField': 12}, {'GalConj': 2, 'Baselabel': '1.45.12t1.b', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [-1, 0, 0, 0], [1, 0, 0, 0], [-1, 0, 1, 0], [0, 0, -1, 0], [0, 0, -1, 0], [-1, 0, 1, 0], [1, 0, 0, 0], [0, 0, 0, -1], [0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 0, -1], [0, 0, 1, 0], [1, 0, -1, 0], [0, 0, 1, 0], [1, 0, -1, 0], [-1, 0, 0, 0], [1, 0, -1, 0], [0, 0, 1, 0], [-1, 0, 1, 0], [0, 0, -1, 0], [0, -1, 0, 0], [0, 1, 0, -1], [0, 1, 0, 0], [0, -1, 0, 1], [0, 0, 0, 1], [0, 0, 0, -1], [0, 1, 0, -1], [0, -1, 0, 0], [0, -1, 0, 1], [0, 1, 0, 0], [0, 1, 0, -1], [0, -1, 0, 0], [0, -1, 0, 1], [0, 1, 0, 0]], 'CharacterField': 12}, {'GalConj': 1, 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[0, -2], [0, -2], [0, -1], [0, 1], [0, -1], [0, -1], [0, 1], [0, 1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '2.675.12t11.a', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [2, 0], [2, 0], [-1, 0], [-1, 0], [-1, 0], [0, 2], [0, -2], [0, 0], [0, 0], [-2, 0], [-2, 0], [1, 0], [1, 0], [1, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -2], [0, -2], [0, 2], [0, 2], [0, 1], [0, -1], [0, 1], [0, 1], [0, -1], [0, -1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '2.2025.24t65.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -2, 0], [-2, 0, 2, 0], [1, 0, -1, 0], [0, 0, 1, 0], [-1, 0, 0, 0], [0, 0, 0, 2], [0, 0, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [2, 0, -2, 0], [0, 0, 2, 0], [-1, 0, 1, 0], [0, 0, -1, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, 0, 2], [0, 2, 0, 0], [0, 2, 0, -2], [0, -2, 0, 0], [0, 0, 0, 1], [0, 0, 0, -1], [0, -1, 0, 0], [0, 1, 0, -1], [0, 1, 0, 0], [0, -1, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]], 'CharacterField': 12}, {'GalConj': 2, 'Baselabel': '2.2025.24t65.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-2, 0, 2, 0], [0, 0, -2, 0], [0, 0, 1, 0], [1, 0, -1, 0], [-1, 0, 0, 0], [0, 0, 0, 2], [0, 0, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 2, 0], [2, 0, -2, 0], [0, 0, -1, 0], [-1, 0, 1, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 2, 0, 0], [0, -2, 0, 2], [0, -2, 0, 0], [0, 2, 0, -2], [0, 0, 0, 1], [0, 0, 0, -1], [0, 1, 0, -1], [0, -1, 0, 0], [0, -1, 0, 1], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]], 'CharacterField': 12}, {'GalConj': 3, 'Baselabel': '2.2025.24t65.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-2, 0, 2, 0], [0, 0, -2, 0], [0, 0, 1, 0], [1, 0, -1, 0], [-1, 0, 0, 0], [0, 0, 0, -2], [0, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 2, 0], [2, 0, -2, 0], [0, 0, -1, 0], [-1, 0, 1, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, 0, 0], [0, 2, 0, -2], [0, 2, 0, 0], [0, -2, 0, 2], [0, 0, 0, -1], [0, 0, 0, 1], [0, -1, 0, 1], [0, 1, 0, 0], [0, 1, 0, -1], [0, -1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]], 'CharacterField': 12}, {'GalConj': 4, 'Baselabel': '2.2025.24t65.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -2, 0], [-2, 0, 2, 0], [1, 0, -1, 0], [0, 0, 1, 0], [-1, 0, 0, 0], [0, 0, 0, -2], [0, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, 0], [2, 0, -2, 0], [0, 0, 2, 0], [-1, 0, 1, 0], [0, 0, -1, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 2, 0, -2], [0, -2, 0, 0], [0, -2, 0, 2], [0, 2, 0, 0], [0, 0, 0, -1], [0, 0, 0, 1], [0, 1, 0, 0], [0, -1, 0, 1], [0, -1, 0, 0], [0, 1, 0, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]], 'CharacterField': 12}], 'ComplexConjugation': 4, 'ConjClasses': [{'Size': '1', 'Order': 1, 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5, 14, 7, 24, 17, 18, 3, 20, 13, 22, 15, 8]}, {'Size': '2', 'Order': 3, 'Representative': [9, 18, 11, 20, 21, 14, 23, 16, 17, 2, 19, 4, 5, 22, 7, 24, 1, 10, 3, 12, 13, 6, 15, 8]}, {'Size': '1', 'Order': 4, 'Representative': [10, 6, 23, 1, 3, 20, 24, 5, 2, 22, 15, 17, 19, 12, 16, 21, 18, 14, 7, 9, 11, 4, 8, 13]}, {'Size': '1', 'Order': 4, 'Representative': [4, 9, 5, 22, 8, 2, 19, 23, 20, 1, 21, 14, 24, 18, 11, 15, 12, 17, 13, 6, 16, 10, 3, 7]}, {'Size': '3', 'Order': 4, 'Representative': [21, 3, 20, 16, 6, 23, 17, 2, 5, 11, 4, 24, 14, 7, 1, 10, 13, 19, 12, 8, 22, 15, 9, 18]}, {'Size': '3', 'Order': 4, 'Representative': [15, 8, 2, 11, 9, 5, 14, 20, 23, 16, 10, 19, 17, 13, 22, 4, 7, 24, 18, 3, 1, 21, 6, 12]}, {'Size': '1', 'Order': 6, 'Representative': [14, 4, 16, 18, 15, 1, 5, 11, 22, 12, 24, 2, 23, 9, 13, 19, 6, 20, 8, 10, 7, 17, 21, 3]}, {'Size': '1', 'Order': 6, 'Representative': [6, 12, 24, 2, 7, 17, 21, 19, 14, 20, 8, 10, 15, 1, 5, 3, 22, 4, 16, 18, 23, 9, 13, 11]}, {'Size': '2', 'Order': 6, 'Representative': [22, 20, 24, 10, 7, 9, 21, 19, 6, 4, 8, 18, 15, 17, 5, 3, 14, 12, 16, 2, 23, 1, 13, 11]}, {'Size': '2', 'Order': 6, 'Representative': [22, 20, 16, 10, 15, 9, 5, 11, 6, 4, 24, 18, 23, 17, 13, 19, 14, 12, 8, 2, 7, 1, 21, 3]}, {'Size': '2', 'Order': 6, 'Representative': [14, 4, 24, 18, 7, 1, 21, 19, 22, 12, 8, 2, 15, 9, 5, 3, 6, 20, 16, 10, 23, 17, 13, 11]}, {'Size': '3', 'Order': 6, 'Representative': [8, 13, 14, 23, 18, 19, 4, 17, 24, 5, 6, 15, 10, 11, 20, 9, 16, 21, 22, 7, 2, 3, 12, 1]}, {'Size': '3', 'Order': 6, 'Representative': [24, 21, 22, 7, 10, 11, 20, 1, 16, 13, 14, 23, 2, 3, 12, 17, 8, 5, 6, 15, 18, 19, 4, 9]}, {'Size': '3', 'Order': 6, 'Representative': [3, 7, 17, 5, 12, 24, 10, 14, 19, 23, 9, 21, 4, 16, 2, 6, 11, 15, 1, 13, 20, 8, 18, 22]}, {'Size': '3', 'Order': 6, 'Representative': [19, 15, 1, 13, 4, 16, 2, 22, 11, 7, 17, 5, 20, 8, 18, 14, 3, 23, 9, 21, 12, 24, 10, 6]}, {'Size': '1', 'Order': 12, 'Representative': [20, 17, 13, 6, 24, 18, 11, 7, 12, 9, 5, 22, 16, 10, 3, 23, 4, 1, 21, 14, 8, 2, 19, 15]}, {'Size': '1', 'Order': 12, 'Representative': [12, 1, 21, 14, 16, 10, 3, 15, 4, 17, 13, 6, 8, 2, 19, 7, 20, 9, 5, 22, 24, 18, 11, 23]}, {'Size': '1', 'Order': 12, 'Representative': [2, 14, 7, 9, 19, 12, 16, 13, 18, 6, 23, 1, 11, 4, 8, 5, 10, 22, 15, 17, 3, 20, 24, 21]}, {'Size': '1', 'Order': 12, 'Representative': [18, 22, 15, 17, 11, 4, 8, 21, 10, 14, 7, 9, 3, 20, 24, 13, 2, 6, 23, 1, 19, 12, 16, 5]}, {'Size': '2', 'Order': 12, 'Representative': [20, 17, 21, 6, 16, 18, 3, 15, 12, 9, 13, 22, 8, 10, 19, 7, 4, 1, 5, 14, 24, 2, 11, 23]}, {'Size': '2', 'Order': 12, 'Representative': [2, 14, 15, 9, 11, 12, 8, 21, 18, 6, 7, 1, 3, 4, 24, 13, 10, 22, 23, 17, 19, 20, 16, 5]}, {'Size': '2', 'Order': 12, 'Representative': [4, 9, 13, 22, 24, 2, 11, 7, 20, 1, 5, 14, 16, 18, 3, 23, 12, 17, 21, 6, 8, 10, 19, 15]}, {'Size': '2', 'Order': 12, 'Representative': [4, 9, 21, 22, 16, 2, 3, 15, 20, 1, 13, 14, 8, 18, 19, 7, 12, 17, 5, 6, 24, 10, 11, 23]}, {'Size': '2', 'Order': 12, 'Representative': [10, 6, 7, 1, 19, 20, 16, 13, 2, 22, 23, 17, 11, 12, 8, 5, 18, 14, 15, 9, 3, 4, 24, 21]}, {'Size': '2', 'Order': 12, 'Representative': [10, 6, 15, 1, 11, 20, 8, 21, 2, 22, 7, 17, 3, 12, 24, 13, 18, 14, 23, 9, 19, 4, 16, 5]}, {'Size': '3', 'Order': 12, 'Representative': [5, 19, 20, 8, 6, 7, 17, 2, 13, 3, 4, 16, 14, 15, 1, 10, 21, 11, 12, 24, 22, 23, 9, 18]}, {'Size': '3', 'Order': 12, 'Representative': [21, 3, 4, 16, 22, 23, 9, 10, 5, 11, 12, 24, 6, 7, 17, 18, 13, 19, 20, 8, 14, 15, 1, 2]}, {'Size': '3', 'Order': 12, 'Representative': [23, 24, 2, 3, 9, 13, 14, 20, 7, 8, 10, 11, 17, 21, 22, 4, 15, 16, 18, 19, 1, 5, 6, 12]}, {'Size': '3', 'Order': 12, 'Representative': [15, 8, 10, 11, 1, 5, 6, 4, 23, 16, 18, 19, 9, 13, 14, 12, 7, 24, 2, 3, 17, 21, 22, 20]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['9', '6', '1'], 'ConjugacyClass': 7}, {'RootOf': ['36', '-12', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['9', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-5832', '972', '0', '1'], 'ConjugacyClass': 3}, {'RootOf': ['139968', '-3888', '0', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['54', '-9', '1'], 'ConjugacyClass': 16}, {'RootOf': ['216', '18', '1'], 'ConjugacyClass': 17}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2, 6, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['12', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-6', '1'], 'ConjugacyClass': 6}, {'RootOf': ['9', '6', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3, 3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [2, 5, -2, -7, 1]}, 'Classes': [{'RootOf': ['-39', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-24', '1'], 'ConjugacyClass': 11}, {'RootOf': ['1512', '-108', '0', '1'], 'ConjugacyClass': 12}, {'RootOf': ['-1728', '432', '0', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'RES', 'CycleType': [4, 4, 4, 4, 4, 4]}, {'Data': {'Powers': [1], 'Resolvent': [2, 5, -2, -7, 1]}, 'Classes': [{'RootOf': ['846', '-3', '1'], 'ConjugacyClass': 29}, {'RootOf': ['954', '-21', '1'], 'ConjugacyClass': 30}, {'RootOf': ['576', '-33', '1'], 'ConjugacyClass': 31}, {'RootOf': ['1224', '-6', '1'], 'ConjugacyClass': 32}], 'Algorithm': 'RES', 'CycleType': [4, 4, 4, 12]}, {'Data': {'Powers': [1], 'Resolvent': [2, 5, -2, -7, 1]}, 'Classes': [{'RootOf': ['-18', '1'], 'ConjugacyClass': 14}, {'RootOf': ['36', '1'], 'ConjugacyClass': 15}, {'RootOf': ['216', '18', '1'], 'ConjugacyClass': 18}, {'RootOf': ['-3321', '-27', '0', '1'], 'ConjugacyClass': 19}, {'RootOf': ['49653', '2727', '0', '1'], 'ConjugacyClass': 20}, {'RootOf': ['59049', '-2187', '0', '1'], 'ConjugacyClass': 21}, {'RootOf': ['139968', '-3888', '0', '1'], 'ConjugacyClass': 22}], 'Algorithm': 'RES', 'CycleType': [6, 6, 6, 6]}, {'Data': {'Powers': [1], 'Resolvent': [2, 5, -2, -7, 1]}, 'Classes': [{'RootOf': ['21', '1'], 'ConjugacyClass': 23}, {'RootOf': ['3', '1'], 'ConjugacyClass': 24}, {'RootOf': ['6', '1'], 'ConjugacyClass': 25}, {'RootOf': ['33', '1'], 'ConjugacyClass': 26}, {'RootOf': ['3519', '24', '1'], 'ConjugacyClass': 27}, {'RootOf': ['3114', '39', '1'], 'ConjugacyClass': 28}, {'RootOf': ['1512', '-108', '0', '1'], 'ConjugacyClass': 33}, {'RootOf': ['-12096', '-432', '0', '1'], 'ConjugacyClass': 34}, {'RootOf': ['-1728', '432', '0', '1'], 'ConjugacyClass': 35}, {'RootOf': ['13824', '1728', '0', '1'], 'ConjugacyClass': 36}], 'Algorithm': 'RES', 'CycleType': [12, 12]}], 'Frobs': [32, 29, 20, 34, 19, 35, 28, 18, 29, 21, 7, 12, 20, 36, 25, 27, 22, 8, 33, 3, 13, 17, 30, 4, 34, 19, 35, 10, 18, 24, 12, 20, 32, 14, 22, 5, 33, 13, 31, 30, 4, 9, 19, 35, 28, 2, 7, 36, 32, 16, 11, 22, 8, 3, 31, 23, 4, 9, 34, 19, 35, 29, 12, 20, 36, 32, 5, 33, 26, 17, 23, 4, 34, 35, 18, 29, 21, 12, 20, 16, 22, 8, 3, 13, 17, 30, 4, 34, 19, 35, 28, 21, 12, 20, 16, 27, 22, 3, 13, 1, 34, 10, 24, 21, 7, 12, 32, 27, 22, 8, 33, 13, 31, 15, 9, 19, 35, 28, 29, 21, 6, 36, 25, 27, 8, 3, 15, 4, 34, 35, 18, 24, 7, 12, 20, 16, 27, 33, 31, 4, 1, 19, 35, 28, 2, 21, 36, 32, 16, 27, 33, 3, 13, 31, 34, 19, 2, 21, 12, 20, 32, 11, 33, 3, 26, 30, 9, 34], 'G-Gens': [[22, 20, 8, 10, 23, 9, 13, 3, 6, 4, 16, 18, 7, 17, 21, 11, 14, 12, 24, 2, 15, 1, 5, 19], [20, 17, 13, 6, 24, 18, 11, 7, 12, 9, 5, 22, 16, 10, 3, 23, 4, 1, 21, 14, 8, 2, 19, 15], [1, 2, 19, 4, 13, 6, 15, 24, 9, 10, 3, 12, 21, 14, 23, 8, 17, 18, 11, 20, 5, 22, 7, 16], [4, 9, 5, 22, 8, 2, 19, 23, 20, 1, 21, 14, 24, 18, 11, 15, 12, 17, 13, 6, 16, 10, 3, 7], [21, 3, 20, 16, 6, 23, 17, 2, 5, 11, 4, 24, 14, 7, 1, 10, 13, 19, 12, 8, 22, 15, 9, 18]], 'G-Name': 'C12*S3', 'Polynomial': [1, 0, 0, -3, 0, 0, 5, 0, 0, -8, 0, 0, 9, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 1], 'QpRts': [['25631066990', '-88953768002', '122725802152', '-17991015850', '-96579851483', '43734370171', '41265839673', '-106647756717', '40582417063', '110160412704', '-98047063645', '32376420337'], ['101234224494', '59257263942', '60551559974', '22364721123', '134080307202', '104683830716', '-8289385166', '85648929558', '-80063192955', '86633407276', '-15077864387', '133841601250'], ['46872258866', '26364504489', '-90134405218', '-119611028133', '106044457763', '-89257530581', '8434729750', '-43020796729', '49203348395', '-31810418511', '111996179940', '-108588005576'], ['29274729056', '-17571951977', '-98044981004', '49561826799', '-97111549926', '-61928215437', '-110833790830', '-58159927544', '66643881777', '-71134546932', '87969149959', '78092054712'], ['-18372536697', '-90575740854', '1798168205', '-6459140217', '93870456535', '77337707364', '75541806995', '113758353244', '36888232876', '-27740499136', '-80681798320', '-103914939662'], ['-56662041730', '-7613786068', '63035097588', '-70956468322', '-62787243328', '-93550994954', '-132468958523', '-26936175916', '32644354670', '58579386132', '21130609115', '8718129796'], ['-71723141213', '-115555534209', '70777867931', '-79713381546', '-99124444015', '117394501770', '-73447829522', '-114364544150', '42491928811', '-14207128143', '39510087743', '-13775981120'], ['109764506249', '-6315446700', '-94751373907', '-121882382994', '-69533868991', '-29678138473', '-105331237235', '-82930399636', '-115750394741', '-46880181302', '-96123129922', '-132902898378'], ['117433589210', '124249736629', '-64360058692', '64403523613', '-107345190961', '29723975342', '-98961356076', '125867883327', '71070278826', '-109650825522', '-44982872644', '47695334395'], ['31457932651', '8471349100', '113004743881', '-124713011624', '-99875303288', '25331908644', '-59403739310', '36051197170', '48321575991', '94814257030', '-39604884733', '-54375754548'], ['37018572962', '47230976159', '60774482963', '-134315319598', '-46412461069', '60618103275', '43555394764', '-62132618272', '-75238227767', '52122972825', '-66454396883', '8205468111'], ['-97684045796', '-33392636169', '-52341601258', '-91638661149', '-126891159828', '44517230607', '131142725179', '-111009097578', '-26043737081', '-91763857651', '67365758278', '-81550163765'], ['-69838656488', '107567570372', '-92066547226', '87255637767', '82040035428', '-8707900645', '-2533523463', '-135859102038', '64094072739', '27389945089', '-94488843661', '-83821967123'], ['2049765490', '-115681184947', '-43762881375', '37125396487', '-121689356143', '-134070983004', '4041419679', '-11653025798', '-47475152711', '68678217044', '72578019211', '110795755257'], ['89321102612', '133532241496', '74111307179', '6456843186', '95324514602', '-20204552428', '119895589040', '-124381896604', '77040142044', '103506070360', '76041385723', '-20102232726'], ['116693413022', '80579068364', '-15202386284', '-91033914505', '54131038224', '-78089230931', '13458411304', '-123767403437', '-22101161372', '116498204005', '-122059704469', '25085325505'], ['128753954907', '-35295968627', '-58365743460', '-46412507763', '-67893568663', '-73458345513', '57695516403', '-19220126610', '-111652695889', '-509587182', '-128788674818', '-80071754732'], ['-132692157145', '-67728613042', '98262307252', '102348290501', '-34205003914', '-130015739360', '67693124476', '-121700126728', '31741616964', '90370946801', '54682749120', '-79465846702'], ['-83890831828', '-73595480648', '29359922255', '-17892263376', '-59631996694', '28639427306', '-51990124514', '105153415001', '26034879372', '-20312554314', '-45541783057', '100382537465'], ['68409316740', '50964588146', '-121432028845', '42076834350', '-47815901353', '17410984830', '-20308934349', '-102649585985', '-40600144696', '-108920206524', '116483702870', '3458109053'], ['88211193185', '-16991829518', '90268379021', '-80796497550', '95908119144', '-68629806719', '-73008283532', '22100748794', '-100982305615', '350554047', '-96647969126', '-84081704322'], ['54612276240', '123294971015', '-19272216213', '33831071835', '-87342011636', '-44196633149', '128427538844', '38589201714', '14830798041', '-127257603176', '-93708628326', '-119513885053'], ['-17597961399', '-17976707287', '126929435997', '73256538360', '3799929413', '-97189949342', '-46447759518', '-33072170353', '-119532070855', '-89298942217', '-115551473466', '33878213846'], ['45360691836', '-74263621664', '109953760191', '-58902313608', '15402830767', '107767369404', '91872825931', '-65120808034', '-133967054994', '-69618022703', '-53635776716', '107817572873']], 'QpRts-minpoly': [3, 38, 23, 6, 17, 16, 27, 34, 0, 0, 0, 0, 1], 'QpRts-p': 43, 'QpRts-prec': 7, 'Size': 72, 'TransitiveDegree': 24}