Artin representation data - 2.3328.24t65.a

Formats: - HTML - YAML - JSON - 2026-03-07T12:37:55.769157

• 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': [2, 13], 'Baselabel': '2.3328.24t65.a', 'CharacterField': 12, 'Conductor': 3328, 'Container': '24t65', 'Dets': ['1.104.6t1.d.b', '1.104.6t1.d.b', '1.104.6t1.d.a', '1.104.6t1.d.a'], 'Dim': 2, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 24, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [-2, 0, 2], [0, 0, -2], [-1], [1, 0, -1], [0, 0, 1], [0, 0, 0, -2], [0, 0, 0, 2], [0], [0], [2, 0, -2], [0, 0, 2], [1], [-1, 0, 1], [0, 0, -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': [37, 33, 27, 20, 33, 38, 34, 19, 32, 3, 15, 33, 24, 23, 14], '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], [1], [1]], [[1], [-1, 0, 1], [0, 0, -1]], [[1], [0, 0, -1], [-1, 0, 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], [1]], [[1], [1, 0, -1], [0, 0, -1]], [[1], [0, 0, 1], [-1, 0, 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, 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, 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], [-1, 0, 1]], [[1], [0], [0, 0, -1]], [[1], [0], [-1, 0, 1]], [[1], [0], [0, 0, -1]], [[1]], [[1], [0, -1, 0, 1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [-2, 0, 2], [0, 0, -2], [-1], [1, 0, -1], [0, 0, 1], [0, 0, 0, 2], [0, 0, 0, -2], [0], [0], [2, 0, -2], [0, 0, 2], [1], [-1, 0, 1], [0, 0, -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': [37, 33, 27, 20, 33, 38, 34, 19, 32, 3, 15, 33, 24, 23, 14], '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], [1], [1]], [[1], [-1, 0, 1], [0, 0, -1]], [[1], [0, 0, -1], [-1, 0, 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], [1]], [[1], [1, 0, -1], [0, 0, -1]], [[1], [0, 0, 1], [-1, 0, 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, 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, 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], [-1, 0, 1]], [[1], [0], [0, 0, -1]], [[1], [0], [-1, 0, 1]], [[1], [0], [0, 0, -1]], [[1]], [[1], [0, 1, 0, -1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, 0, -2], [-2, 0, 2], [-1], [0, 0, 1], [1, 0, -1], [0, 0, 0, 2], [0, 0, 0, -2], [0], [0], [0, 0, 2], [2, 0, -2], [1], [0, 0, -1], [-1, 0, 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': [37, 33, 27, 20, 33, 38, 34, 19, 32, 3, 15, 33, 24, 23, 14], '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], [1]], [[1], [0, 0, -1], [-1, 0, 1]], [[1], [-1, 0, 1], [0, 0, -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], [-1], [1]], [[1], [0, 0, 1], [-1, 0, 1]], [[1], [1, 0, -1], [0, 0, -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, 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, -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], [0, 0, -1]], [[1], [0], [-1, 0, 1]], [[1], [0], [0, 0, -1]], [[1], [0], [-1, 0, 1]], [[1]], [[1], [0, -1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, 0, -2], [-2, 0, 2], [-1], [0, 0, 1], [1, 0, -1], [0, 0, 0, -2], [0, 0, 0, 2], [0], [0], [0, 0, 2], [2, 0, -2], [1], [0, 0, -1], [-1, 0, 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': [37, 33, 27, 20, 33, 38, 34, 19, 32, 3, 15, 33, 24, 23, 14], '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], [1]], [[1], [0, 0, -1], [-1, 0, 1]], [[1], [-1, 0, 1], [0, 0, -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], [-1], [1]], [[1], [0, 0, 1], [-1, 0, 1]], [[1], [1, 0, -1], [0, 0, -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, -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, 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], [0, 0, -1]], [[1], [0], [-1, 0, 1]], [[1], [0], [0, 0, -1]], [[1], [0], [-1, 0, 1]], [[1]], [[1], [0, 1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '24T65', 'Galt': 65, 'HardPrimes': [2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 89, 379, 24533, 51109, 3443017], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 0, 0, 0, 8, 0, 0, 0, 18, 0, 0, 0, -8, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [12, -4, -1, 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': '1.8.2t1.b', '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': '1.4.2t1.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': '1.8.2t1.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': '1.52.6t1.b', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [1, 1], [0, -1], [1, 1], [0, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.52.6t1.b', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [0, -1], [1, 1], [0, -1], [1, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.104.6t1.d', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [-1, 0], [-1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [1, 1], [0, -1], [1, 1], [0, -1], [0, -1], [1, 1], [0, -1], [1, 1], [-1, 0], [-1, 0], [0, -1], [1, 1], [0, -1], [1, 1], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.13.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [0, 1], [-1, -1], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.13.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [-1, -1], [0, 1], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.104.6t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [-1, -1], [0, 1], [0, -1], [1, 1], [0, -1], [1, 1], [-1, 0], [-1, 0], [0, -1], [1, 1], [0, -1], [1, 1], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.104.6t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 1], [0, -1], [1, 1], [0, -1], [-1, 0], [-1, 0], [1, 1], [0, -1], [1, 1], [0, -1], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.104.6t1.d', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [-1, 0], [-1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [0, -1], [1, 1], [0, -1], [1, 1], [1, 1], [0, -1], [1, 1], [0, -1], [-1, 0], [-1, 0], [1, 1], [0, -1], [1, 1], [0, -1], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.16.4t1.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': '1.16.4t1.b', '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': '1.16.4t1.b', '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': '1.16.4t1.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': '1.208.12t1.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], [1, 0, 0, 0], [-1, 0, 1, 0], [0, 0, -1, 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, 0, 0], [1, 0, -1, 0], [0, 0, 1, 0], [0, 0, -1, 0], [-1, 0, 1, 0], [0, 0, 1, 0], [1, 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, 0], [0, -1, 0, 1], [0, -1, 0, 0], [0, 1, 0, -1], [0, -1, 0, 1], [0, 1, 0, 0], [0, 1, 0, -1], [0, -1, 0, 0]], 'CharacterField': 12}, {'GalConj': 1, 'Baselabel': '1.208.12t1.a', '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, 0, 0], [0, 0, -1, 0], [-1, 0, 1, 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], [-1, 0, 0, 0], [0, 0, 1, 0], [1, 0, -1, 0], [1, 0, -1, 0], [0, 0, 1, 0], [-1, 0, 1, 0], [0, 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, 1], [0, 1, 0, 0], [0, 1, 0, -1], [0, -1, 0, 0], [0, -1, 0, 0], [0, 1, 0, -1], [0, 1, 0, 0], [0, -1, 0, 1]], 'CharacterField': 12}, 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'Order': 6, 'Representative': [11, 1, 9, 6, 20, 24, 17, 19, 10, 15, 14, 4, 23, 13, 21, 18, 8, 12, 5, 7, 22, 3, 2, 16]}, {'Size': '2', 'Order': 6, 'Representative': [13, 14, 22, 16, 19, 18, 20, 17, 3, 9, 23, 24, 1, 2, 10, 4, 7, 6, 8, 5, 15, 21, 11, 12]}, {'Size': '2', 'Order': 6, 'Representative': [13, 14, 9, 16, 20, 18, 17, 19, 10, 15, 23, 24, 1, 2, 21, 4, 8, 6, 5, 7, 22, 3, 11, 12]}, {'Size': '3', 'Order': 6, 'Representative': [15, 21, 2, 8, 4, 17, 18, 24, 23, 13, 10, 19, 3, 9, 14, 20, 16, 5, 6, 12, 11, 1, 22, 7]}, {'Size': '3', 'Order': 6, 'Representative': [22, 3, 13, 5, 18, 19, 24, 4, 14, 11, 21, 20, 10, 15, 1, 17, 6, 7, 12, 16, 2, 23, 9, 8]}, {'Size': '3', 'Order': 6, 'Representative': [3, 9, 14, 20, 16, 5, 6, 12, 11, 1, 22, 7, 15, 21, 2, 8, 4, 17, 18, 24, 23, 13, 10, 19]}, {'Size': '3', 'Order': 6, 'Representative': [10, 15, 1, 17, 6, 7, 12, 16, 2, 23, 9, 8, 22, 3, 13, 5, 18, 19, 24, 4, 14, 11, 21, 20]}, {'Size': '1', 'Order': 12, 'Representative': [12, 18, 7, 14, 15, 13, 22, 9, 17, 8, 4, 11, 24, 6, 19, 2, 3, 1, 10, 21, 5, 20, 16, 23]}, {'Size': '1', 'Order': 12, 'Representative': [6, 4, 5, 23, 9, 2, 15, 22, 20, 7, 24, 13, 18, 16, 17, 11, 21, 14, 3, 10, 8, 19, 12, 1]}, {'Size': '1', 'Order': 12, 'Representative': [24, 6, 19, 2, 3, 1, 10, 21, 5, 20, 16, 23, 12, 18, 7, 14, 15, 13, 22, 9, 17, 8, 4, 11]}, {'Size': '1', 'Order': 12, 'Representative': [18, 16, 17, 11, 21, 14, 3, 10, 8, 19, 12, 1, 6, 4, 5, 23, 9, 2, 15, 22, 20, 7, 24, 13]}, {'Size': '2', 'Order': 12, 'Representative': [6, 4, 7, 23, 15, 2, 22, 9, 17, 8, 24, 13, 18, 16, 19, 11, 3, 14, 10, 21, 5, 20, 12, 1]}, {'Size': '2', 'Order': 12, 'Representative': [18, 16, 19, 11, 3, 14, 10, 21, 5, 20, 12, 1, 6, 4, 7, 23, 15, 2, 22, 9, 17, 8, 24, 13]}, {'Size': '2', 'Order': 12, 'Representative': [16, 24, 5, 1, 9, 11, 15, 22, 20, 7, 18, 2, 4, 12, 17, 13, 21, 23, 3, 10, 8, 19, 6, 14]}, {'Size': '2', 'Order': 12, 'Representative': [16, 24, 7, 1, 15, 11, 22, 9, 17, 8, 18, 2, 4, 12, 19, 13, 3, 23, 10, 21, 5, 20, 6, 14]}, {'Size': '2', 'Order': 12, 'Representative': [4, 12, 17, 13, 21, 23, 3, 10, 8, 19, 6, 14, 16, 24, 5, 1, 9, 11, 15, 22, 20, 7, 18, 2]}, {'Size': '2', 'Order': 12, 'Representative': [4, 12, 19, 13, 3, 23, 10, 21, 5, 20, 6, 14, 16, 24, 7, 1, 15, 11, 22, 9, 17, 8, 18, 2]}, {'Size': '3', 'Order': 12, 'Representative': [20, 7, 24, 15, 1, 10, 23, 14, 6, 4, 5, 21, 8, 19, 12, 3, 13, 22, 11, 2, 18, 16, 17, 9]}, {'Size': '3', 'Order': 12, 'Representative': [17, 8, 4, 22, 23, 21, 14, 1, 12, 18, 7, 3, 5, 20, 16, 10, 11, 9, 2, 13, 24, 6, 19, 15]}, {'Size': '3', 'Order': 12, 'Representative': [8, 19, 12, 3, 13, 22, 11, 2, 18, 16, 17, 9, 20, 7, 24, 15, 1, 10, 23, 14, 6, 4, 5, 21]}, {'Size': '3', 'Order': 12, 'Representative': [5, 20, 16, 10, 11, 9, 2, 13, 24, 6, 19, 15, 17, 8, 4, 22, 23, 21, 14, 1, 12, 18, 7, 3]}], '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': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['208', '-24', '1'], 'ConjugacyClass': 8}, {'RootOf': ['0', '0', '1'], 'ConjugacyClass': 9}], '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': ['0', '1'], 'ConjugacyClass': 2}, {'RootOf': ['193536', '-2304', '24', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-193536', '-2304', '-24', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['208', '24', '1'], 'ConjugacyClass': 17}, {'RootOf': ['0', '0', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2, 6, 6]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['0', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-24', '1'], 'ConjugacyClass': 6}, {'RootOf': ['208', '-24', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3, 3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['-3992', '1'], 'ConjugacyClass': 10}, {'RootOf': ['3992', '1'], 'ConjugacyClass': 11}, {'RootOf': ['-53420141312', '2465488', '-2880', '1'], 'ConjugacyClass': 12}, {'RootOf': ['53420141312', '2465488', '2880', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'RES', 'CycleType': [4, 4, 4, 4, 4, 4]}, {'Data': {'Powers': [1], 'Resolvent': [24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['10867744', '-6024', '1'], 'ConjugacyClass': 29}, {'RootOf': ['762320', '-976', '1'], 'ConjugacyClass': 30}, {'RootOf': ['10867744', '6024', '1'], 'ConjugacyClass': 31}, {'RootOf': ['762320', '976', '1'], 'ConjugacyClass': 32}], 'Algorithm': 'RES', 'CycleType': [4, 4, 4, 12]}, {'Data': {'Powers': [1], 'Resolvent': [24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['2424', '1'], 'ConjugacyClass': 14}, {'RootOf': ['-1704', '1'], 'ConjugacyClass': 15}, {'RootOf': ['6500176', '720', '1'], 'ConjugacyClass': 16}, {'RootOf': ['-29663947136', '6520656', '-488', '1'], 'ConjugacyClass': 19}, {'RootOf': ['41654844928', '-6638048', '-488', '1'], 'ConjugacyClass': 20}, {'RootOf': ['29663947136', '6520656', '488', '1'], 'ConjugacyClass': 21}, {'RootOf': ['-41654844928', '-6638048', '488', '1'], 'ConjugacyClass': 22}], 'Algorithm': 'RES', 'CycleType': [6, 6, 6, 6]}, {'Data': {'Powers': [1], 'Resolvent': [24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['3016', '1'], 'ConjugacyClass': 23}, {'RootOf': ['-2032', '1'], 'ConjugacyClass': 24}, {'RootOf': ['-3016', '1'], 'ConjugacyClass': 25}, {'RootOf': ['2032', '1'], 'ConjugacyClass': 26}, {'RootOf': ['4502160', '984', '1'], 'ConjugacyClass': 27}, {'RootOf': ['4502160', '-984', '1'], 'ConjugacyClass': 28}, {'RootOf': ['-714689152', '10357008', '2880', '1'], 'ConjugacyClass': 33}, {'RootOf': ['-9964946688', '-2801696', '2880', '1'], 'ConjugacyClass': 34}, {'RootOf': ['714689152', '10357008', '-2880', '1'], 'ConjugacyClass': 35}, {'RootOf': ['9964946688', '-2801696', '-2880', '1'], 'ConjugacyClass': 36}], 'Algorithm': 'RES', 'CycleType': [12, 12]}], 'Frobs': [15, 35, 27, 22, 33, 28, 8, 36, 21, 32, 3, 30, 18, 34, 3, 27, 34, 31, 35, 22, 16, 3, 12, 15, 5, 30, 4, 33, 11, 8, 19, 12, 17, 34, 29, 4, 28, 36, 21, 25, 35, 27, 20, 9, 24, 22, 35, 19, 36, 10, 2, 3, 8, 34, 9, 21, 25, 19, 29, 16, 33, 29, 12, 4, 2, 28, 34, 7, 34, 26, 9, 4, 19, 29, 33, 20, 27, 25, 9, 17, 35, 27, 19, 8, 21, 13, 5, 18, 31, 3, 12, 19, 22, 33, 12, 22, 32, 16, 33, 28, 12, 32, 36, 15, 13, 7, 33, 7, 4, 18, 20, 30, 17, 13, 22, 8, 36, 21, 26, 36, 30, 9, 10, 34, 35, 11, 29, 20, 4, 28, 35, 21, 19, 24, 14, 6, 23, 36, 25, 18, 13, 24, 22, 13, 32, 22, 27, 16, 13, 3, 31, 9, 12, 21, 33, 3, 22, 8, 16, 11, 35, 14, 4, 34, 9, 4, 19, 29], 'G-Gens': [[1, 2, 10, 4, 7, 6, 8, 5, 15, 21, 11, 12, 13, 14, 22, 16, 19, 18, 20, 17, 3, 9, 23, 24], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [23, 13, 21, 18, 8, 12, 5, 7, 22, 3, 2, 16, 11, 1, 9, 6, 20, 24, 17, 19, 10, 15, 14, 4], [15, 21, 2, 8, 4, 17, 18, 24, 23, 13, 10, 19, 3, 9, 14, 20, 16, 5, 6, 12, 11, 1, 22, 7], [16, 24, 8, 1, 22, 11, 9, 15, 19, 5, 18, 2, 4, 12, 20, 13, 10, 23, 21, 3, 7, 17, 6, 14]], 'G-Name': 'C12*S3', 'Polynomial': [1, 0, 0, 0, 8, 0, 0, 0, 18, 0, 0, 0, -8, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 1], 'QpRts': [['-320174967275968633', '-138794001450385216', '-284643224749106787', '-182042857938439432', '24242890931366709', '201119029671204150', '-454987797855353437', '-133013914002962948', '249184193247930815', '316658089133540679', '-60226894247990623', '-357687976888183989'], ['259356592902006890', '-281765254103692052', '-393878854387163441', '52487908985739485', 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