Artin representation data - 1.99.15t1.a

Formats: - HTML - YAML - JSON - 2025-04-19T19:02:58.718185

• 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, 11], 'Baselabel': '1.99.15t1.a', 'CharacterField': 15, 'Conductor': 99, 'Container': '15t1', 'Dets': ['99.70', '99.4', '99.16', '99.49', '99.97', '99.31', '99.25', '99.58'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0, 0, 0, 0, 0], 'Galn': 15, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 0, 1], [-1, 0, 0, 0, 0, -1], [0, 0, -1, 0, 0, 0, 0, -1], [-1, 0, 1, -1, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 1], [0, 0, 0, 0, 1], [-1, 1, 0, -1, 1, -1, 0, 1], [1, 0, -1, 1, -1, 0, 1, -1], [0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, -1, 0, 0, 0, 0, -1], [1, -1, 0, 0, -1, 1, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [15, 16, 8, 12, 16, 6, 1, 1, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [1, 0, 0, 0, 0, 1]], [[1], [0, 0, 1, 0, 0, 0, 0, 1]], [[1], [1, 0, -1, 1, 0, 0, 1, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [1, -1, 0, 1, -1, 1, 0, -1]], [[1], [-1, 0, 1, -1, 1, 0, -1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 1, 0, 0, 0, 0, 1]], [[1], [-1, 1, 0, 0, 1, -1, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 0, -1, 0, 0, 0, 0, -1], [-1, 0, 1, -1, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [1, 0, -1, 1, -1, 0, 1, -1], [1, -1, 0, 0, -1, 1, 0, -1], [0, 0, 0, 0, 1], [0, -1, 0, 0, 0, 0, -1], [0, 0, 1], [0, 1], [-1, 1, 0, -1, 1, -1, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [15, 16, 8, 12, 16, 6, 1, 1, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 0, 0, 1]], [[1], [1, 0, -1, 1, 0, 0, 1, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [-1, 0, 1, -1, 1, 0, -1, 1]], [[1], [-1, 1, 0, 0, 1, -1, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 1, 0, 0, 0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [1, -1, 0, 1, -1, 1, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 0, 1], [-1, 0, 0, 0, 0, -1], [-1, 0, 1, -1, 0, 0, -1, 1], [0, 0, 0, 1], [0, 0, -1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 1], [1, 0, -1, 1, -1, 0, 1, -1], [1, -1, 0, 0, -1, 1, 0, -1], [0, -1, 0, 0, 0, 0, -1], [-1, 1, 0, -1, 1, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 1], [0, 1]], 'GalOrbIndex': 3, 'HardFactors': [15, 16, 8, 12, 16, 6, 1, 1, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [1, 0, 0, 0, 0, 1]], [[1], [1, 0, -1, 1, 0, 0, 1, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [-1, 0, 1, -1, 1, 0, -1, 1]], [[1], [-1, 1, 0, 0, 1, -1, 0, 1]], [[1], [0, 1, 0, 0, 0, 0, 1]], [[1], [1, -1, 0, 1, -1, 1, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 1], [-1, 0, 1, -1, 0, 0, -1, 1], [0, 0, 0, 1], [0, 0, -1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [-1, 1, 0, -1, 1, -1, 0, 1], [0, 1], [1, -1, 0, 0, -1, 1, 0, -1], [0, 0, 1], [1, 0, -1, 1, -1, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 1], [0, -1, 0, 0, 0, 0, -1]], 'GalOrbIndex': 4, 'HardFactors': [15, 16, 8, 12, 16, 6, 1, 1, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [1, 0, -1, 1, 0, 0, 1, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [1, -1, 0, 1, -1, 1, 0, -1]], [[1], [0, -1]], [[1], [-1, 1, 0, 0, 1, -1, 0, 1]], [[1], [0, 0, -1]], [[1], [-1, 0, 1, -1, 1, 0, -1, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 1, 0, 0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 0, 1], [-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], [-1, 0, 1, -1, 0, 0, -1, 1], [0, -1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 1], [1, 0, -1, 1, -1, 0, 1, -1], [0, 0, 1], [1, -1, 0, 0, -1, 1, 0, -1], [0, 1], [-1, 1, 0, -1, 1, -1, 0, 1], [0, 0, 0, 0, 1]], 'GalOrbIndex': 5, 'HardFactors': [15, 16, 8, 12, 16, 6, 1, 1, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [1, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, -1, 1, 0, 0, 1, -1]], [[1], [0, 1, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [-1, 0, 1, -1, 1, 0, -1, 1]], [[1], [0, 0, -1]], [[1], [-1, 1, 0, 0, 1, -1, 0, 1]], [[1], [0, -1]], [[1], [1, -1, 0, 1, -1, 1, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, -1, 0, 0, 0, 0, -1], [0, 0, 0, 1], [-1, 0, 1, -1, 0, 0, -1, 1], [0, 1], [0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [-1, 1, 0, -1, 1, -1, 0, 1], [0, -1, 0, 0, 0, 0, -1], [1, -1, 0, 0, -1, 1, 0, -1], [1, 0, -1, 1, -1, 0, 1, -1]], 'GalOrbIndex': 6, 'HardFactors': [15, 16, 8, 12, 16, 6, 1, 1, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, -1, 1, 0, 0, 1, -1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [1, -1, 0, 1, -1, 1, 0, -1]], [[1], [0, 1, 0, 0, 0, 0, 1]], [[1], [-1, 1, 0, 0, 1, -1, 0, 1]], [[1], [-1, 0, 1, -1, 1, 0, -1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 0, 1], [-1, 0, 0, 0, 0, -1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [-1, 0, 1, -1, 0, 0, -1, 1], [0, 0, -1, 0, 0, 0, 0, -1], [-1, 1, 0, -1, 1, -1, 0, 1], [0, 1], [0, 0, 1], [0, -1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 1], [1, -1, 0, 0, -1, 1, 0, -1], [1, 0, -1, 1, -1, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 7, 'HardFactors': [15, 16, 8, 12, 16, 6, 1, 1, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [1, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [1, 0, -1, 1, 0, 0, 1, -1]], [[1], [0, 0, 1, 0, 0, 0, 0, 1]], [[1], [1, -1, 0, 1, -1, 1, 0, -1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 1, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [-1, 1, 0, 0, 1, -1, 0, 1]], [[1], [-1, 0, 1, -1, 1, 0, -1, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [-1, 0, 1, -1, 0, 0, -1, 1], [0, 0, -1, 0, 0, 0, 0, -1], [1, -1, 0, 0, -1, 1, 0, -1], [0, -1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 1], [1, 0, -1, 1, -1, 0, 1, -1], [-1, 1, 0, -1, 1, -1, 0, 1], [0, 0, 0, 0, 1], [0, 0, 1]], 'GalOrbIndex': 8, 'HardFactors': [15, 16, 8, 12, 16, 6, 1, 1, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [1, 0, -1, 1, 0, 0, 1, -1]], [[1], [0, 0, 1, 0, 0, 0, 0, 1]], [[1], [-1, 1, 0, 0, 1, -1, 0, 1]], [[1], [0, 1, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [-1, 0, 1, -1, 1, 0, -1, 1]], [[1], [1, -1, 0, 1, -1, 1, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0, 0, 0], 'GaloisLabel': '15T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 7, 11, 37, 89, 109, 3167, 5347], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-1, -9, 27, 150, -168, -765, 384, 1473, -288, -976, 60, 252, -4, -27, 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [0, 1], [-1, -1], [1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [0, 1], [-1, -1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [-1, -1], [0, 1], [1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [-1, -1], [0, 1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.11.5t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [1, 0, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 0, 1, 0], [0, 1, 0, 0]], 'CharacterField': 5}, {'GalConj': 1, 'Baselabel': '1.99.15t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [-1, 0, 0, 0, 0, -1, 0, 0], [0, 0, -1, 0, 0, 0, 0, -1], [-1, 0, 1, -1, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [-1, 1, 0, -1, 1, -1, 0, 1], [1, 0, -1, 1, -1, 0, 1, -1], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1], [0, -1, 0, 0, 0, 0, -1, 0], [1, -1, 0, 0, -1, 1, 0, -1]], 'CharacterField': 15}, {'GalConj': 2, 'Baselabel': '1.99.15t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, -1, 0, 0, 0, 0, -1], [-1, 0, 1, -1, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1], [1, 0, -1, 1, -1, 0, 1, -1], [1, -1, 0, 0, -1, 1, 0, -1], [0, 0, 0, 0, 1, 0, 0, 0], [0, -1, 0, 0, 0, 0, -1, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [-1, 1, 0, -1, 1, -1, 0, 1]], 'CharacterField': 15}, {'GalConj': 2, 'Baselabel': '1.11.5t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [1, 0, 0, 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], [0, 0, 1, 0], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 0, 1, 0]], 'CharacterField': 5}, {'GalConj': 3, 'Baselabel': '1.99.15t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [-1, 0, 0, 0, 0, -1, 0, 0], [-1, 0, 1, -1, 0, 0, -1, 1], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 1, 0], [1, 0, -1, 1, -1, 0, 1, -1], [1, -1, 0, 0, -1, 1, 0, -1], [0, -1, 0, 0, 0, 0, -1, 0], [-1, 1, 0, -1, 1, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0]], 'CharacterField': 15}, {'GalConj': 4, 'Baselabel': '1.99.15t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [-1, 0, 1, -1, 0, 0, -1, 1], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0, 0, 0], [-1, 1, 0, -1, 1, -1, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0], [1, -1, 0, 0, -1, 1, 0, -1], [0, 0, 1, 0, 0, 0, 0, 0], [1, 0, -1, 1, -1, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 1], [0, -1, 0, 0, 0, 0, -1, 0]], 'CharacterField': 15}, {'GalConj': 3, 'Baselabel': '1.11.5t1.a', 'Character': [[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, 0, 1, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]], 'CharacterField': 5}, {'GalConj': 5, 'Baselabel': '1.99.15t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [-1, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, 0, 0, -1], [0, 0, 0, 1, 0, 0, 0, 0], [-1, 0, 1, -1, 0, 0, -1, 1], [0, -1, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 1], [1, 0, -1, 1, -1, 0, 1, -1], [0, 0, 1, 0, 0, 0, 0, 0], [1, -1, 0, 0, -1, 1, 0, -1], [0, 1, 0, 0, 0, 0, 0, 0], [-1, 1, 0, -1, 1, -1, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0]], 'CharacterField': 15}, {'GalConj': 6, 'Baselabel': '1.99.15t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, 0, 0, -1], [0, 0, 0, 1, 0, 0, 0, 0], [-1, 0, 1, -1, 0, 0, -1, 1], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1], [-1, 1, 0, -1, 1, -1, 0, 1], [0, -1, 0, 0, 0, 0, -1, 0], [1, -1, 0, 0, -1, 1, 0, -1], [1, 0, -1, 1, -1, 0, 1, -1]], 'CharacterField': 15}, {'GalConj': 4, 'Baselabel': '1.11.5t1.a', 'Character': [[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, 1, 0, 0], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 0, 1, 0], [0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 0, 1], [-1, -1, -1, -1]], 'CharacterField': 5}, {'GalConj': 7, 'Baselabel': '1.99.15t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [-1, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [-1, 0, 1, -1, 0, 0, -1, 1], [0, 0, -1, 0, 0, 0, 0, -1], [-1, 1, 0, -1, 1, -1, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 1, 0, 0, 0], [1, -1, 0, 0, -1, 1, 0, -1], [1, 0, -1, 1, -1, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 1]], 'CharacterField': 15}, {'GalConj': 8, 'Baselabel': '1.99.15t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [-1, 0, 1, -1, 0, 0, -1, 1], [0, 0, -1, 0, 0, 0, 0, -1], [1, -1, 0, 0, -1, 1, 0, -1], [0, -1, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0], [1, 0, -1, 1, -1, 0, 1, -1], [-1, 1, 0, -1, 1, -1, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0]], 'CharacterField': 15}], 'ComplexConjugation': 1, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]}, {'Size': '1', 'Order': 3, 'Representative': [2, 14, 6, 9, 4, 8, 15, 3, 5, 13, 10, 7, 11, 1, 12]}, {'Size': '1', 'Order': 3, 'Representative': [14, 1, 8, 5, 9, 3, 12, 6, 4, 11, 13, 15, 10, 2, 7]}, {'Size': '1', 'Order': 5, 'Representative': [3, 6, 4, 12, 15, 9, 11, 5, 7, 14, 2, 13, 1, 8, 10]}, {'Size': '1', 'Order': 5, 'Representative': [4, 9, 12, 13, 10, 7, 2, 15, 11, 8, 6, 1, 3, 5, 14]}, {'Size': '1', 'Order': 5, 'Representative': [12, 7, 13, 1, 14, 11, 6, 10, 2, 5, 9, 3, 4, 15, 8]}, {'Size': '1', 'Order': 5, 'Representative': [13, 11, 1, 3, 8, 2, 9, 14, 6, 15, 7, 4, 12, 10, 5]}, {'Size': '1', 'Order': 15, 'Representative': [6, 8, 9, 7, 12, 5, 10, 4, 15, 1, 14, 11, 2, 3, 13]}, {'Size': '1', 'Order': 15, 'Representative': [5, 4, 15, 10, 11, 12, 1, 7, 13, 6, 3, 14, 8, 9, 2]}, {'Size': '1', 'Order': 15, 'Representative': [11, 10, 2, 6, 3, 14, 5, 1, 8, 12, 15, 9, 7, 13, 4]}, {'Size': '1', 'Order': 15, 'Representative': [9, 5, 7, 11, 13, 15, 14, 12, 10, 3, 8, 2, 6, 4, 1]}, {'Size': '1', 'Order': 15, 'Representative': [15, 12, 10, 14, 2, 13, 3, 11, 1, 9, 4, 8, 5, 7, 6]}, {'Size': '1', 'Order': 15, 'Representative': [8, 3, 5, 15, 7, 4, 13, 9, 12, 2, 1, 10, 14, 6, 11]}, {'Size': '1', 'Order': 15, 'Representative': [7, 15, 11, 2, 1, 10, 8, 13, 14, 4, 5, 6, 9, 12, 3]}, {'Size': '1', 'Order': 15, 'Representative': [10, 13, 14, 8, 6, 1, 4, 2, 3, 7, 12, 5, 15, 11, 9]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-12', '1'], 'ConjugacyClass': 2}, {'RootOf': ['24', '1'], 'ConjugacyClass': 3}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [2, 5, -2, -7, 1]}, 'Classes': [{'RootOf': ['-1164', '1'], 'ConjugacyClass': 4}, {'RootOf': ['222', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-999', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-570', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [5, 5, 5]}, {'Data': {'Powers': [1], 'Resolvent': [2, 5, -2, -7, 1]}, 'Classes': [{'RootOf': ['402', '1'], 'ConjugacyClass': 8}, {'RootOf': ['69', '1'], 'ConjugacyClass': 9}, {'RootOf': ['600', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-291', '1'], 'ConjugacyClass': 11}, {'RootOf': ['531', '1'], 'ConjugacyClass': 12}, {'RootOf': ['762', '1'], 'ConjugacyClass': 13}, {'RootOf': ['468', '1'], 'ConjugacyClass': 14}, {'RootOf': ['-30', '1'], 'ConjugacyClass': 15}], 'Algorithm': 'RES', 'CycleType': [15]}], 'Frobs': [15, 5, 8, 12, 3, 10, 4, 5, 2, 12, 10, 6, 11, 3, 9, 7, 14, 13, 2, 4, 6, 15, 13, 1, 15, 15, 14, 5, 1, 11, 4, 2, 13, 14, 8, 9, 11, 7, 10, 9, 5, 4, 12, 8, 1, 1, 10, 9, 12, 10, 7, 11, 3, 7, 14, 3, 4, 6, 15, 13, 11, 14, 1, 11, 13, 15, 3, 14, 8, 9, 3, 6, 12, 2, 4, 10, 12, 1, 8, 10, 2, 9, 7, 6, 3, 9, 7, 13, 3, 2, 4, 13, 5, 14, 14, 5, 11, 6, 4, 7, 9, 6, 10, 9, 2, 4, 12, 1, 8, 12, 10, 5, 2, 9, 6, 9, 8, 7, 14, 3, 2, 15, 13, 1, 15, 5, 13, 6, 3, 14, 7, 8, 11, 7, 10, 2, 5, 8, 8, 4, 5, 12, 10, 7, 6, 9, 13, 3, 2, 4, 11, 1, 5, 14, 13, 15, 4, 13, 7, 8, 3, 6, 2, 5, 10, 12, 1, 12], 'G-Gens': [[3, 6, 4, 12, 15, 9, 11, 5, 7, 14, 2, 13, 1, 8, 10], [2, 14, 6, 9, 4, 8, 15, 3, 5, 13, 10, 7, 11, 1, 12]], 'G-Name': 'C15', 'Polynomial': [-1, -9, 27, 150, -168, -765, 384, 1473, -288, -976, 60, 252, -4, -27, 0, 1], 'QpRts': [['-2520305', '-968833', '-462147', '3215615', '2602327'], ['-4983762', '-1214146', '10250282', '3965346', '-4556661'], ['-5210873', '10035721', '-11288519', '-4010881', '-760883'], ['-11163922', '-9478334', '1785600', '9841818', '-2167802'], ['-10576654', '5638342', '8178192', '10921660', '9525394'], ['5560481', '10060890', '-5807065', '-310222', '-9479534'], ['4451633', '7273059', '6127234', '-4574151', '-10865594'], ['-349608', '4040958', '-7041985', '4321103', '10240417'], ['-2396993', '3839992', '-9963792', '3374091', '-7357592'], ['-7236348', '137851', '9996616', '7802767', '1631992'], ['-9323525', '4177774', '-606659', '-2455064', '8121812'], ['3461963', '4727071', '-4782546', '-3698849', '10080162'], ['-7577696', '-4315625', '-9389957', '-5347703', '-9753804'], ['7504067', '2182979', '-9788135', '-7180961', '1954334'], ['-7913596', '-12000130', '-1344688', '8273000', '785432']], 'QpRts-minpoly': [14, 1, 0, 0, 0, 1], 'QpRts-p': 17, 'QpRts-prec': 6, 'Size': 15, 'TransitiveDegree': 15}