Artin representation data - 1.25.20t1.a

Formats: - HTML - YAML - JSON - 2025-03-21T06:56:29.831330

• 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': [5], 'Baselabel': '1.25.20t1.a', 'CharacterField': 20, 'Conductor': 25, 'Container': '20t1', 'Dets': ['25.2', '25.3', '25.8', '25.12', '25.13', '25.17', '25.22', '25.23'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0, 0, 0, 0, 0], 'Galn': 20, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, -1], [-1, 0, 1, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 1], [0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 1], [1, 0, -1, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 1], [0, -1, 0, 1, 0, -1, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, -1], [0, -1], [0, 1, 0, -1, 0, 1, 0, -1], [0, 0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [14, 13, 21, 19, 20, 18], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [1, 0, -1, 0, 1, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, -1]], [[1], [-1, 0, 1, 0, -1, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 1, 0, -1, 0, 1, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 1]], [[1], [0, -1, 0, 1, 0, -1, 0, 1]], [[1], [0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, -1], [0, 0, -1], [-1, 0, 1, 0, -1, 0, 1], [0, 0, 0, 0, 1], [1, 0, -1, 0, 1, 0, -1], [0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 1], [0, -1, 0, 1, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 1], [0, 1, 0, -1, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 2, 'HardFactors': [14, 13, 21, 19, 20, 18], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [1, 0, -1, 0, 1, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [-1, 0, 1, 0, -1, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 1, 0, -1, 0, 1, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, -1, 0, 1, 0, -1, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [-1, 0, 1, 0, -1, 0, 1], [0, 0, -1], [0, 0, 0, 0, 0, 0, -1], [0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, -1], [1, 0, -1, 0, 1, 0, -1], [0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, -1, 0, 1, 0, -1, 0, 1], [0, -1], [0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, -1], [0, 1, 0, -1, 0, 1, 0, -1]], 'GalOrbIndex': 3, 'HardFactors': [14, 13, 21, 19, 20, 18], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [1, 0, -1, 0, 1, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 1]], [[1], [-1, 0, 1, 0, -1, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 1, 0, -1, 0, 1, 0, -1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, -1, 0, 1, 0, -1, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, -1], [0, 0, -1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, -1], [-1, 0, 1, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0, 1], [1, 0, -1, 0, 1, 0, -1], [0, 0, 1], [0, 0, 0, 0, -1], [0, 0, 0, 1], [0, -1, 0, 1, 0, -1, 0, 1], [0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, -1], [0, 1, 0, -1, 0, 1, 0, -1], [0, -1], [0, 0, 0, 0, 0, 0, 0, -1]], 'GalOrbIndex': 4, 'HardFactors': [14, 13, 21, 19, 20, 18], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [1, 0, -1, 0, 1, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [-1, 0, 1, 0, -1, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 1, 0, -1, 0, 1, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, -1, 0, 1, 0, -1, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 0, -1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, -1], [-1, 0, 1, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0, 1], [1, 0, -1, 0, 1, 0, -1], [0, 0, 1], [0, 0, 0, 0, -1], [0, 0, 0, -1], [0, 1, 0, -1, 0, 1, 0, -1], [0, -1], [0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 1], [0, -1, 0, 1, 0, -1, 0, 1], [0, 1], [0, 0, 0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 5, 'HardFactors': [14, 13, 21, 19, 20, 18], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [1, 0, -1, 0, 1, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [-1, 0, 1, 0, -1, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, -1, 0, 1, 0, -1, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 1, 0, -1, 0, 1, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 1], [-1, 0, 1, 0, -1, 0, 1], [0, 0, -1], [0, 0, 0, 0, 0, 0, -1], [0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, -1], [1, 0, -1, 0, 1, 0, -1], [0, -1], [0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, -1], [0, 1, 0, -1, 0, 1, 0, -1], [0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, -1, 0, 1, 0, -1, 0, 1]], 'GalOrbIndex': 6, 'HardFactors': [14, 13, 21, 19, 20, 18], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [1, 0, -1, 0, 1, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 1]], [[1], [-1, 0, 1, 0, -1, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, -1, 0, 1, 0, -1, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 1, 0, -1, 0, 1, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, -1], [0, 0, -1], [-1, 0, 1, 0, -1, 0, 1], [0, 0, 0, 0, 1], [1, 0, -1, 0, 1, 0, -1], [0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 1], [0, 1, 0, -1, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, -1], [0, -1], [0, -1, 0, 1, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 1]], 'GalOrbIndex': 7, 'HardFactors': [14, 13, 21, 19, 20, 18], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [1, 0, -1, 0, 1, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [-1, 0, 1, 0, -1, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1, 0, 1, 0, -1, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1], [0, 1, 0, -1, 0, 1, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 1], [-1, 0, 1, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 1], [0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 1], [1, 0, -1, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, -1], [0, -1], [0, 1, 0, -1, 0, 1, 0, -1], [0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 1], [0, -1, 0, 1, 0, -1, 0, 1], [0, 0, 0, 1]], 'GalOrbIndex': 8, 'HardFactors': [14, 13, 21, 19, 20, 18], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [1, 0, -1, 0, 1, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, -1]], [[1], [-1, 0, 1, 0, -1, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 1]], [[1], [0, -1, 0, 1, 0, -1, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 1, 0, -1, 0, 1, 0, -1]], [[1], [0, 0, 0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0, 0, 0], 'GaloisLabel': '20T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 13, 17, 23], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
• 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]], 'CharacterField': 1}, {'GalConj': 2, 'Baselabel': '1.5.4t1.a', 'Character': [[1, 0], [-1, 0], [0, -1], [0, 1], [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]], 'CharacterField': 4}, {'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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.5.4t1.a', 'Character': [[1, 0], [-1, 0], [0, 1], [0, -1], [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]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '1.25.5t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [1, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 0, 1, 0], [0, 0, 0, 1], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 1, 0], [0, 0, 0, 1], [0, 1, 0, 0]], 'CharacterField': 5}, {'GalConj': 3, 'Baselabel': '1.25.20t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [-1, 0, 1, 0, -1, 0, 1, 0], [0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, -1, 0, 0, 0], [1, 0, -1, 0, 1, 0, -1, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1], [0, -1, 0, 1, 0, -1, 0, 1], [0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1], [0, 1, 0, -1, 0, 1, 0, -1]], 'CharacterField': 20}, {'GalConj': 4, 'Baselabel': '1.25.10t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [-1, 0, 0, 0], [-1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 1, 0], [1, 1, 1, 1], [0, 0, -1, 0], [0, 0, 0, -1], [0, -1, 0, 0], [1, 1, 1, 1], [0, 0, -1, 0], [0, 0, 0, -1], [0, -1, 0, 0]], 'CharacterField': 5}, {'GalConj': 6, 'Baselabel': '1.25.20t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [-1, 0, 1, 0, -1, 0, 1, 0], [0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, -1, 0, 0, 0], [1, 0, -1, 0, 1, 0, -1, 0], [0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1], [0, 1, 0, -1, 0, 1, 0, -1], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1], [0, -1, 0, 1, 0, -1, 0, 1]], 'CharacterField': 20}, {'GalConj': 2, 'Baselabel': '1.25.5t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [1, 0, 0, 0], [1, 0, 0, 0], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 1, 0]], 'CharacterField': 5}, {'GalConj': 8, 'Baselabel': '1.25.20t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [-1, 0, 1, 0, -1, 0, 1, 0], [0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [1, 0, -1, 0, 1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, -1], [0, -1, 0, 0, 0, 0, 0, 0], [0, 1, 0, -1, 0, 1, 0, -1], [0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0], [0, -1, 0, 1, 0, -1, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0]], 'CharacterField': 20}, {'GalConj': 3, 'Baselabel': '1.25.10t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [-1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 1, 0], [-1, -1, -1, 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1]}, {'Size': '1', 'Order': 20, 'Representative': [19, 12, 14, 9, 11, 4, 6, 1, 3, 16, 18, 13, 15, 8, 10, 5, 7, 20, 2, 17]}, {'Size': '1', 'Order': 20, 'Representative': [16, 11, 13, 2, 4, 19, 1, 10, 12, 7, 9, 18, 20, 15, 17, 6, 8, 3, 5, 14]}], '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]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['0', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-5', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [4, 4, 4, 4, 4]}, {'Data': {'Powers': [1], 'Resolvent': [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['-75', '1'], 'ConjugacyClass': 5}, {'RootOf': ['100', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-325', '1'], 'ConjugacyClass': 7}, {'RootOf': ['350', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [5, 5, 5, 5]}, {'Data': {'Powers': [1], 'Resolvent': [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['150', '1'], 'ConjugacyClass': 9}, {'RootOf': ['50', '1'], 'ConjugacyClass': 10}, {'RootOf': ['400', '1'], 'ConjugacyClass': 11}, {'RootOf': ['-175', '1'], 'ConjugacyClass': 12}], 'Algorithm': 'RES', 'CycleType': [10, 10]}, {'Data': {'Powers': [1], 'Resolvent': [-8, 13, -9, 1, -7, 20, -9, 8, 13, 5, -18, -11, -12, 18, 12, 6, -15, -14, -20, -13]}, 'Classes': [{'RootOf': ['75', '1'], 'ConjugacyClass': 13}, {'RootOf': ['130', '1'], 'ConjugacyClass': 14}, {'RootOf': ['-320', '1'], 'ConjugacyClass': 15}, {'RootOf': ['425', '1'], 'ConjugacyClass': 16}, {'RootOf': ['105', '1'], 'ConjugacyClass': 17}, {'RootOf': ['-150', '1'], 'ConjugacyClass': 18}, {'RootOf': ['-225', '1'], 'ConjugacyClass': 19}, {'RootOf': ['455', '1'], 'ConjugacyClass': 20}], 'Algorithm': 'RES', 'CycleType': [20]}], 'Frobs': [14, 13, 1, 3, 6, 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