Artin representation data - 1.108.18t1.a

Formats: - HTML - YAML - JSON - 2026-03-09T09:58:14.822633

• 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, 3], 'Baselabel': '1.108.18t1.a', 'CharacterField': 9, 'Conductor': 108, 'Container': '18t1', 'Dets': ['108.103', '108.79', '108.31', '108.7', '108.67', '108.43'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0, 0, 0], 'Galn': 18, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 1], [-1, 0, 0, -1], [0, 0, 0, -1], [1, 0, 0, 1], [0, 1], [0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1], [0, 0, -1, 0, 0, -1], [0, -1], [0, 0, 0, 0, 0, -1], [0, 1, 0, 0, 1], [0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 1, 0, 0, 1]], 'GalOrbIndex': 1, 'HardFactors': [19, 19, 12, 16], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [-1, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, -1, 0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, -1, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, 0, 0, -1], [0, 0, 0, 1], [1, 0, 0, 1], [0, 0, 0, -1], [0, 0, 1], [0, 0, 0, 0, 1], [0, 0, -1, 0, 0, -1], [0, 1], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1], [0, 0, -1], [0, -1], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 1, 0, 0, 1], [0, 1, 0, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [19, 19, 12, 16], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [-1, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, -1, 0, 0, -1]], [[1], [0, -1, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 1], [-1, 0, 0, -1], [0, 0, 0, -1], [1, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1], [0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, -1], [0, 0, -1], [0, -1], [0, 0, 1, 0, 0, 1], [0, 1, 0, 0, 1], [0, 0, 0, 0, 0, -1]], 'GalOrbIndex': 3, 'HardFactors': [19, 19, 12, 16], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [-1, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, -1, 0, 0, -1]], [[1], [0, -1, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, 0, 0, -1], [0, 0, 0, 1], [1, 0, 0, 1], [0, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 1], [0, -1, 0, 0, -1], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, -1], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0, 1], [0, -1], [0, 0, -1], [0, 0, 0, 0, -1]], 'GalOrbIndex': 4, 'HardFactors': [19, 19, 12, 16], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [-1, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, -1, 0, 0, -1]], [[1], [0, 0, -1, 0, 0, -1]], [[1], [0, 1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 1], [-1, 0, 0, -1], [0, 0, 0, -1], [1, 0, 0, 1], [0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 1], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1], [0, 0, 1], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0, 1], [0, 0, 0, 0, -1], [0, 0, 0, 0, 0, -1], [0, -1], [0, 0, -1]], 'GalOrbIndex': 5, 'HardFactors': [19, 19, 12, 16], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [-1, 0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1, 0, 0, -1]], [[1], [0, 0, -1, 0, 0, -1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, 0, 0, -1], [0, 0, 0, 1], [1, 0, 0, 1], [0, 0, 0, -1], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 1], [0, 1], [0, 0, 1, 0, 0, 1], [0, 0, 0, 0, -1], [0, 0, -1], [0, 1, 0, 0, 1], [0, 0, 0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 6, 'HardFactors': [19, 19, 12, 16], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [-1, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, -1, 0, 0, -1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [0, -1, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0], 'GaloisLabel': '18T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 499], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 0, 81, 0, 540, 0, 1386, 0, 1782, 0, 1287, 0, 546, 0, 135, 0, 18, 0, 1], 'NumBadPrimes': 2, '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]], '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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.27.9t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1, 0], [0, 0, -1, 0, 0, -1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, -1]], 'CharacterField': 9}, {'GalConj': 1, 'Baselabel': '1.108.18t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, -1, 0, 0], [1, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1, 0], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1], [0, 1, 0, 0, 1, 0], [0, 0, -1, 0, 0, 0], [0, 0, 0, 0, -1, 0], [0, 0, 1, 0, 0, 1]], 'CharacterField': 9}, {'GalConj': 2, 'Baselabel': '1.27.9t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, -1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1, 0]], 'CharacterField': 9}, {'GalConj': 2, 'Baselabel': '1.108.18t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 1, 0, 0], [0, 0, 0, -1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, -1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1, 0], [0, 0, -1, 0, 0, 0], [0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -1, 0], [0, 0, 1, 0, 0, 1], [0, 1, 0, 0, 1, 0]], 'CharacterField': 9}, {'GalConj': 1, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.36.6t1.b', 'Character': [[1, 0], [-1, 0], [1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, -1], [1, 1], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 3, 'Baselabel': '1.27.9t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 1]], 'CharacterField': 9}, {'GalConj': 3, 'Baselabel': '1.108.18t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, -1, 0, 0], [1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, -1, 0], [0, 0, -1, 0, 0, 0], [0, -1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1], [0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, -1]], 'CharacterField': 9}, {'GalConj': 4, 'Baselabel': '1.27.9t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, -1, 0, 0, -1, 0], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1, 0], [0, 0, -1, 0, 0, -1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0]], 'CharacterField': 9}, {'GalConj': 4, 'Baselabel': '1.108.18t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 1, 0, 0], [0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, -1, 0, 0, -1, 0], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, -1], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 0, 1], [0, -1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0], [0, 0, 0, 0, -1, 0]], 'CharacterField': 9}, {'GalConj': 2, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.36.6t1.b', 'Character': [[1, 0], [-1, 0], [1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 1], [0, -1], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 5, 'Baselabel': '1.27.9t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0], [-1, 0, 0, -1, 0, 0], [0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, -1, 0, 0, -1, 0], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]], 'CharacterField': 9}, {'GalConj': 5, 'Baselabel': '1.108.18t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, -1, 0, 0], [1, 0, 0, 1, 0, 0], [0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 0, 1], [0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, -1], [0, -1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0]], 'CharacterField': 9}, {'GalConj': 6, 'Baselabel': '1.27.9t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]], 'CharacterField': 9}, {'GalConj': 6, 'Baselabel': '1.108.18t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0], [1, 0, 0, 1, 0, 0], [0, 0, 0, -1, 0, 0], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1], [0, 0, 0, 0, -1, 0], [0, 0, -1, 0, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, -1], [0, -1, 0, 0, 0, 0]], 'CharacterField': 9}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]}, {'Size': '1', 'Order': 2, 'Representative': [10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '1', 'Order': 3, 'Representative': [9, 16, 10, 17, 11, 4, 5, 15, 12, 18, 7, 1, 8, 2, 13, 14, 6, 3]}, {'Size': '1', 'Order': 3, 'Representative': [12, 14, 18, 6, 7, 17, 11, 13, 1, 3, 5, 9, 15, 16, 8, 2, 4, 10]}, {'Size': '1', 'Order': 6, 'Representative': [18, 7, 1, 8, 2, 13, 14, 6, 3, 9, 16, 10, 17, 11, 4, 5, 15, 12]}, {'Size': '1', 'Order': 6, 'Representative': [3, 5, 9, 15, 16, 8, 2, 4, 10, 12, 14, 18, 6, 7, 17, 11, 13, 1]}, {'Size': '1', 'Order': 9, 'Representative': [16, 17, 11, 12, 13, 9, 15, 10, 14, 7, 8, 2, 3, 4, 18, 6, 1, 5]}, {'Size': '1', 'Order': 9, 'Representative': [6, 1, 8, 2, 3, 14, 18, 7, 4, 15, 10, 17, 11, 12, 5, 9, 16, 13]}, {'Size': '1', 'Order': 9, 'Representative': [14, 6, 7, 1, 8, 12, 13, 18, 2, 5, 15, 16, 10, 17, 3, 4, 9, 11]}, {'Size': '1', 'Order': 9, 'Representative': [4, 9, 15, 16, 10, 2, 3, 5, 17, 13, 18, 6, 7, 1, 11, 12, 14, 8]}, {'Size': '1', 'Order': 9, 'Representative': [2, 4, 5, 9, 15, 1, 8, 3, 16, 11, 13, 14, 18, 6, 10, 17, 12, 7]}, {'Size': '1', 'Order': 9, 'Representative': [17, 12, 13, 14, 18, 16, 10, 11, 6, 8, 3, 4, 5, 9, 7, 1, 2, 15]}, {'Size': '1', 'Order': 18, 'Representative': [7, 8, 2, 3, 4, 18, 6, 1, 5, 16, 17, 11, 12, 13, 9, 15, 10, 14]}, {'Size': '1', 'Order': 18, 'Representative': [13, 18, 6, 7, 1, 11, 12, 14, 8, 4, 9, 15, 16, 10, 2, 3, 5, 17]}, {'Size': '1', 'Order': 18, 'Representative': [11, 13, 14, 18, 6, 10, 17, 12, 7, 2, 4, 5, 9, 15, 1, 8, 3, 16]}, {'Size': '1', 'Order': 18, 'Representative': [15, 10, 17, 11, 12, 5, 9, 16, 13, 6, 1, 8, 2, 3, 14, 18, 7, 4]}, {'Size': '1', 'Order': 18, 'Representative': [5, 15, 16, 10, 17, 3, 4, 9, 11, 14, 6, 7, 1, 8, 12, 13, 18, 2]}, {'Size': '1', 'Order': 18, 'Representative': [8, 3, 4, 5, 9, 7, 1, 2, 15, 17, 12, 13, 14, 18, 16, 10, 11, 6]}], '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]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['-201654', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-201600', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['201654', '1'], 'ConjugacyClass': 5}, {'RootOf': ['201600', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [6, 6, 6]}, {'Data': {'Powers': [1], 'Resolvent': [18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['-42516', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-105390', '1'], 'ConjugacyClass': 8}, {'RootOf': ['107874', '1'], 'ConjugacyClass': 9}, {'RootOf': ['-110574', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-65358', '1'], 'ConjugacyClass': 11}, {'RootOf': ['215964', '1'], 'ConjugacyClass': 12}], 'Algorithm': 'RES', 'CycleType': [9, 9]}, {'Data': {'Powers': [1], 'Resolvent': [18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['42516', '1'], 'ConjugacyClass': 13}, {'RootOf': ['110574', '1'], 'ConjugacyClass': 14}, {'RootOf': ['65358', '1'], 'ConjugacyClass': 15}, {'RootOf': ['105390', '1'], 'ConjugacyClass': 16}, {'RootOf': ['-107874', '1'], 'ConjugacyClass': 17}, {'RootOf': ['-215964', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [18]}], 'Frobs': [11, 2, 12, 17, 13, 8, 4, 5, 14, 11, 14, 4, 8, 13, 17, 1, 18, 9, 16, 6, 3, 15, 15, 3, 7, 9, 18, 2, 1, 12, 5, 14, 11, 14, 8, 13, 12, 2, 18, 7, 6, 3, 15, 10, 3, 6, 18, 17, 13, 8, 4, 14, 11, 5, 8, 17, 1, 2, 9, 7, 16, 10, 6, 16, 7, 9, 17, 8, 14, 11, 11, 5, 13, 12, 2, 18, 7, 3, 10, 10, 16, 7, 2, 1, 17, 13, 4, 11, 11, 14, 5, 17, 2, 18, 16, 6, 10, 3, 6, 1, 17, 4, 14, 11, 14, 4, 17, 1, 18, 9, 16, 3, 10, 15, 6, 9, 18, 2, 12, 13, 8, 11, 11, 5, 13, 1, 9, 6, 15, 10, 6, 16, 18, 1, 12, 8, 4, 14, 8, 1, 2, 7, 16, 6, 3, 15, 7, 9, 18, 2, 8, 4, 5, 14, 13, 17, 2, 7, 3, 10, 15, 3, 18, 2, 12, 13, 5, 11], 'G-Gens': [[9, 16, 10, 17, 11, 4, 5, 15, 12, 18, 7, 1, 8, 2, 13, 14, 6, 3], [16, 17, 11, 12, 13, 9, 15, 10, 14, 7, 8, 2, 3, 4, 18, 6, 1, 5], [10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9]], 'G-Name': 'C18', 'Polynomial': [1, 0, 81, 0, 540, 0, 1386, 0, 1782, 0, 1287, 0, 546, 0, 135, 0, 18, 0, 1], 'QpRts': [['-8086010261', '832053007', '-3629175038', '3347196137', '-1820347684', '2272835425', '5260564804', '4980958075', '-4019017310'], ['-6662903692', '6838721773', '-4160462872', '-6244350133', '7604757434', '-6852622849', '-3365194076', '4244362967', '-4183708126'], ['-3443059971', '590094775', '630426367', '-5104906293', '5897176226', '-7397570376', '3262190409', '-3482047758', '-2768682950'], ['5263123384', '474330860', '7979979431', '4052009432', '2991313565', '2967661634', '5673019454', '-3591381296', '285746203'], ['-2112796360', '1281275654', '-64266253', '4459921050', '-7364363143', '542343190', '3361473635', '-4285116785', '-7990161641'], ['-6936069810', '-1283161451', '-2207005216', '5568194553', '2382785891', '4628411975', '-8304323972', '3334387210', '800453443'], ['-4550107332', '5557446119', '-4096196619', '6545605126', '-2280755732', '-7394966039', '-6726667711', '8529479752', '3806453515'], ['-1672946426', '-808830591', '5772974215', '-7629672324', '5374099456', '7596073609', '-2631304518', '-256994086', '1086199646'], ['4642950290', '-241958232', '4259601405', '-8452102430', '7717523910', '7579470508', '-1998374395', '-8463005833', '1250334360'], ['8086010261', '-832053007', '3629175038', '-3347196137', '1820347684', '-2272835425', '-5260564804', '-4980958075', '4019017310'], ['6662903692', '-6838721773', '4160462872', '6244350133', '-7604757434', '6852622849', '3365194076', '-4244362967', '4183708126'], ['3443059971', '-590094775', '-630426367', '5104906293', '-5897176226', '7397570376', '-3262190409', '3482047758', '2768682950'], ['-5263123384', '-474330860', '-7979979431', '-4052009432', '-2991313565', '-2967661634', '-5673019454', '3591381296', '-285746203'], ['2112796360', '-1281275654', '64266253', '-4459921050', '7364363143', '-542343190', '-3361473635', '4285116785', '7990161641'], ['6936069810', '1283161451', '2207005216', '-5568194553', '-2382785891', '-4628411975', '8304323972', '-3334387210', '-800453443'], ['4550107332', '-5557446119', '4096196619', '-6545605126', '2280755732', '7394966039', '6726667711', '-8529479752', '-3806453515'], ['1672946426', '808830591', '-5772974215', '7629672324', '-5374099456', '-7596073609', '2631304518', '256994086', '-1086199646'], ['-4642950290', '241958232', '-4259601405', '8452102430', '-7717523910', '-7579470508', '1998374395', '8463005833', '-1250334360']], 'QpRts-minpoly': [27, 22, 22, 4, 0, 0, 0, 0, 0, 1], 'QpRts-p': 29, 'QpRts-prec': 7, 'Size': 18, 'TransitiveDegree': 18}