Artin representation data - 1.99.30t1.a

Formats: - HTML - YAML - JSON - 2024-04-27T21:49:26.980759

• 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': '1.99.30t1.a', 'CharacterField': 15, 'Conductor': 99, 'Container': '30t1', 'Dets': ['99.85', '99.52', '99.13', '99.79', '99.94', '99.61', '99.40', '99.7'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0, 0, 0, 0, 0], 'Galn': 30, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-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, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, -1], [1, 0, -1, 1, 0, 0, 1, -1], [0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, -1], [0, 0, 0, 0, 0, 0, -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], [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], [0, -1], [0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [28, 31, 21, 31, 30, 26, 23, 28, 5, 17, 17, 18, 27, 30, 1], 'LocalFactors': [[[1], [-1]], [[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, 0, 0, 0, 0, -1]], [[1], [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], [0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 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], [-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], [0, 1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-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], [0, 0, 0, 0, 0, -1], [1, 0, 0, 0, 0, 1], [1, 0, -1, 1, 0, 0, 1, -1], [0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, -1], [0, 0, 0, 0, 0, 0, -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], [-1, 1, 0, 0, 1, -1, 0, 1], [0, -1], [1, -1, 0, 1, -1, 1, 0, -1], [0, 0, 0, 0, -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]], 'GalOrbIndex': 2, 'HardFactors': [28, 31, 21, 31, 30, 26, 23, 28, 5, 17, 17, 18, 27, 30, 1], 'LocalFactors': [[[1], [-1]], [[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], [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, -1, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 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], [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], [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]]]}, {'Sign': 0, 'Character': [[1], [-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], [1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, -1], [0, 0, 0, -1], [1, 0, -1, 1, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, -1], [0, 0, 1, 0, 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], [0, 1, 0, 0, 0, 0, 1], [0, 0, -1], [0, -1], [1, -1, 0, 1, -1, 1, 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]], 'GalOrbIndex': 3, 'HardFactors': [28, 31, 21, 31, 30, 26, 23, 28, 5, 17, 17, 18, 27, 30, 1], 'LocalFactors': [[[1], [-1]], [[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], [-1, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [-1, 0, 1, -1, 0, 0, -1, 1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [0, 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], [-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], [0, -1, 0, 0, 0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [-1, 1, 0, -1, 1, -1, 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]]]}, {'Sign': 0, 'Character': [[1], [-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, 0, 0, 0, 0, -1], [1, 0, 0, 0, 0, 1], [0, 0, 0, -1], [1, 0, -1, 1, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, -1], [0, 0, 1, 0, 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], [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], [0, 0, -1], [0, 0, 0, 0, -1], [1, -1, 0, 1, -1, 1, 0, -1], [-1, 0, 1, -1, 1, 0, -1, 1]], 'GalOrbIndex': 4, 'HardFactors': [28, 31, 21, 31, 30, 26, 23, 28, 5, 17, 17, 18, 27, 30, 1], 'LocalFactors': [[[1], [-1]], [[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, 0, 0, 0, 0, 1]], [[1], [-1, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [-1, 0, 1, -1, 0, 0, -1, 1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, -1, 0, 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], [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], [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]]]}, {'Sign': 0, 'Character': [[1], [-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, 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, 1, 0, 0, 1, -1], [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], [-1, 0, 1, -1, 1, 0, -1, 1], [1, -1, 0, 1, -1, 1, 0, -1], [0, 0, 0, 0, -1], [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]], 'GalOrbIndex': 5, 'HardFactors': [28, 31, 21, 31, 30, 26, 23, 28, 5, 17, 17, 18, 27, 30, 1], 'LocalFactors': [[[1], [-1]], [[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, 0, 0, 0, -1]], [[1], [0, 0, 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, 0, 0, -1, 1]], [[1], [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], [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], [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]]]}, {'Sign': 0, 'Character': [[1], [-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, 0, -1], [1, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, -1], [1, 0, -1, 1, 0, 0, 1, -1], [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], [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], [1, -1, 0, 1, -1, 1, 0, -1], [0, -1], [0, 0, -1], [0, 1, 0, 0, 0, 0, 1]], 'GalOrbIndex': 6, 'HardFactors': [28, 31, 21, 31, 30, 26, 23, 28, 5, 17, 17, 18, 27, 30, 1], 'LocalFactors': [[[1], [-1]], [[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, 0, 1]], [[1], [-1, 0, 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, 0, 0, -1, 1]], [[1], [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], [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], [-1, 1, 0, -1, 1, -1, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 1]], [[1], [0, -1, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-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], [1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, -1], [0, 0, 0, -1], [0, 0, 1, 0, 0, 0, 0, 1], [1, 0, -1, 1, 0, 0, 1, -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], [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], [0, 0, 0, 0, -1], [1, -1, 0, 1, -1, 1, 0, -1], [0, -1], [-1, 1, 0, 0, 1, -1, 0, 1]], 'GalOrbIndex': 7, 'HardFactors': [28, 31, 21, 31, 30, 26, 23, 28, 5, 17, 17, 18, 27, 30, 1], 'LocalFactors': [[[1], [-1]], [[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], [-1, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [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, -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], [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], [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]]]}, {'Sign': 0, 'Character': [[1], [-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, -1], [1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, -1], [0, 0, 0, -1], [0, 0, 1, 0, 0, 0, 0, 1], [1, 0, -1, 1, 0, 0, 1, -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], [0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -1], [0, 0, -1], [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]], 'GalOrbIndex': 8, 'HardFactors': [28, 31, 21, 31, 30, 26, 23, 28, 5, 17, 17, 18, 27, 30, 1], 'LocalFactors': [[[1], [-1]], [[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, 1]], [[1], [-1, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, -1, 0, 0, 0, 0, -1]], [[1], [-1, 0, 1, -1, 0, 0, -1, 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], [0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [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]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0, 0, 0], 'GaloisLabel': '30T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 11, 13, 29, 61, 79, 181, 257, 499, 31513, 227191, 2828641, 14317073], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 3, 9, 26, 75, 216, 622, 1791, 5157, 14849, 42756, 10314, 16093, 5523, 6255, 2672, 2493, 1224, 1000, 507, 297, -109, 90, -27, 28, -6, 9, -1, 3, 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], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.11.2t1.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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [1, 0], [1, 0], [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], [0, 1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.99.6t1.a', 'Character': [[1, 0], [-1, 0], [0, 1], [-1, -1], [1, 0], [1, 0], [1, 0], [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], [0, -1], [0, -1], [1, 1], [0, -1], [1, 1], [0, -1], [1, 1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [1, 0], [1, 0], [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], [-1, -1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.99.6t1.a', 'Character': [[1, 0], [-1, 0], [-1, -1], [0, 1], [1, 0], [1, 0], [1, 0], [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], [1, 1], [1, 1], [0, -1], [1, 1], [0, -1], [1, 1], [0, -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, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1], [1, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 1, 0], [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], [0, 1, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [-1, -1, -1, -1]], 'CharacterField': 5}, {'GalConj': 1, 'Baselabel': '1.11.10t1.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], [-1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, -1], [1, 1, 1, 1], [0, -1, 0, 0], [0, 0, -1, 0], [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], [0, -1, 0, 0], [0, 0, -1, 0], [0, -1, 0, 0], [0, 0, 0, -1], [0, 0, -1, 0], [1, 1, 1, 1], [0, 0, 0, -1], [1, 1, 1, 1]], 'CharacterField': 5}, {'GalConj': 1, 'Baselabel': '1.99.15t1.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], [-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, 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, -1, 0, 0, 0, 0, -1], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [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], [-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], [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]], 'CharacterField': 15}, {'GalConj': 1, 'Baselabel': '1.99.30t1.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], [-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, 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, 1, 0, 0, 0, 0, 1], [0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0], [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], [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], [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]], 'CharacterField': 15}, {'GalConj': 2, 'Baselabel': '1.99.15t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0], [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], [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, -1, 0, 0, 0, 0, -1], [0, 0, 0, 1, 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], [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], [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], [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]], 'CharacterField': 15}, {'GalConj': 2, 'Baselabel': '1.99.30t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0], [-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], [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, 1, 0, 0, 0, 0, 1], [0, 0, 0, -1, 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], [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], [-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], [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]], 'CharacterField': 15}, {'GalConj': 2, 'Baselabel': '1.11.5t1.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], [1, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [-1, -1, -1, -1], [-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], [0, 0, 1, 0], [-1, -1, -1, -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]], 'CharacterField': 5}, {'GalConj': 2, 'Baselabel': '1.11.10t1.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, -1], [0, 1, 0, 0], [0, 0, 0, 1], [-1, 0, 0, 0], [-1, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, -1], [0, 0, -1, 0], [1, 1, 1, 1], [-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], [0, 0, -1, 0], [1, 1, 1, 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]], 'CharacterField': 5}, {'GalConj': 3, 'Baselabel': '1.99.15t1.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], [-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], [-1, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [-1, 0, 1, -1, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 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, 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], [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], [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]], 'CharacterField': 15}, {'GalConj': 3, 'Baselabel': '1.99.30t1.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], [-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], [1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0], [1, 0, -1, 1, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 1, 0, 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, 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], [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], [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]], 'CharacterField': 15}, {'GalConj': 4, 'Baselabel': '1.99.15t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0], [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, 0, 0, 0, 0, 1, 0, 0], [-1, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [-1, 0, 1, -1, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, 0, 0, -1], [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], [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], [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]], 'CharacterField': 15}, {'GalConj': 4, 'Baselabel': '1.99.30t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0], [-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, 0, 0, 0, 0, -1, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0], [1, 0, -1, 1, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 1, 0, 0, 0, 0, 1], [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], [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], [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]], 'CharacterField': 15}, {'GalConj': 3, 'Baselabel': '1.11.5t1.a', 'Character': [[1, 0, 0, 0], [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], [1, 0, 0, 0], [1, 0, 0, 0], [-1, -1, -1, -1], [0, 0, 1, 0], [0, 0, 0, 1], [0, 1, 0, 0], [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], [0, 0, 0, 1], [0, 1, 0, 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]], 'CharacterField': 5}, {'GalConj': 3, 'Baselabel': '1.11.10t1.a', 'Character': [[1, 0, 0, 0], [-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], [-1, 0, 0, 0], [-1, 0, 0, 0], [1, 1, 1, 1], [0, 0, -1, 0], [0, 0, 0, -1], [0, -1, 0, 0], [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], [0, 0, 0, -1], [0, -1, 0, 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]], 'CharacterField': 5}, {'GalConj': 5, 'Baselabel': '1.99.15t1.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], [-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, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, -1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 1, 0], [-1, 0, 1, -1, 0, 0, -1, 1], [0, 0, 0, 1, 0, 0, 0, 0], [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], [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], [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]], 'CharacterField': 15}, {'GalConj': 5, 'Baselabel': '1.99.30t1.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], [-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, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, -1, 0], [1, 0, -1, 1, 0, 0, 1, -1], [0, 0, 0, -1, 0, 0, 0, 0], [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], [-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], [-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]], 'CharacterField': 15}, {'GalConj': 6, 'Baselabel': '1.99.15t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0], [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, 0, 1, 0, 0], [-1, 0, 0, 0, 0, -1, 0, 0], [0, 0, -1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 1, 0], [-1, 0, 1, -1, 0, 0, -1, 1], [0, 0, 0, 1, 0, 0, 0, 0], [-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], [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], [-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]], 'CharacterField': 15}, {'GalConj': 6, 'Baselabel': '1.99.30t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0], [-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, 0, -1, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, -1, 0], [1, 0, -1, 1, 0, 0, 1, -1], [0, 0, 0, -1, 0, 0, 0, 0], [-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], [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], [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]], 'CharacterField': 15}, {'GalConj': 4, 'Baselabel': '1.11.5t1.a', 'Character': [[1, 0, 0, 0], [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, 0, 0, 0], [1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [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], [-1, -1, -1, -1], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 0, 1, 0], [0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0]], 'CharacterField': 5}, {'GalConj': 4, 'Baselabel': '1.11.10t1.a', 'Character': [[1, 0, 0, 0], [-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, 0, 0, 0], [-1, 0, 0, 0], [0, 0, -1, 0], [0, -1, 0, 0], [1, 1, 1, 1], [0, 0, 0, -1], [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], [1, 1, 1, 1], [0, 0, 0, -1], [1, 1, 1, 1], [0, 0, -1, 0], [0, 0, 0, -1], [0, -1, 0, 0], [0, 0, -1, 0], [0, -1, 0, 0]], 'CharacterField': 5}, {'GalConj': 7, 'Baselabel': '1.99.15t1.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], [-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], [-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, 0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, -1], [-1, 0, 1, -1, 0, 0, -1, 1], [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], [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], [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]], 'CharacterField': 15}, {'GalConj': 7, 'Baselabel': '1.99.30t1.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], [-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], [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, 0, -1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1], [1, 0, -1, 1, 0, 0, 1, -1], [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], [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], [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]], 'CharacterField': 15}, {'GalConj': 8, 'Baselabel': '1.99.15t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0], [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, 1, 0, 0], [-1, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, -1], [-1, 0, 1, -1, 0, 0, -1, 1], [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], [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], [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]], 'CharacterField': 15}, {'GalConj': 8, 'Baselabel': '1.99.30t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0], [-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, -1, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1], [1, 0, -1, 1, 0, 0, 1, -1], [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], [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], [-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]], 'CharacterField': 15}], '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, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]}, {'Size': '1', 'Order': 2, 'Representative': [30, 26, 5, 23, 3, 24, 9, 11, 7, 12, 8, 10, 14, 13, 28, 17, 16, 27, 20, 19, 22, 21, 4, 6, 29, 2, 18, 15, 25, 1]}, {'Size': '1', 'Order': 3, 'Representative': [17, 29, 30, 18, 1, 4, 19, 7, 20, 21, 9, 22, 10, 12, 2, 3, 5, 6, 8, 11, 13, 14, 27, 23, 28, 25, 24, 26, 15, 16]}, {'Size': '1', 'Order': 3, 'Representative': [5, 15, 16, 6, 17, 18, 8, 19, 11, 13, 20, 14, 21, 22, 29, 30, 1, 4, 7, 9, 10, 12, 24, 27, 26, 28, 23, 25, 2, 3]}, {'Size': '1', 'Order': 5, 'Representative': [12, 6, 13, 7, 14, 8, 30, 3, 1, 29, 5, 25, 2, 26, 18, 21, 22, 19, 16, 17, 15, 28, 9, 11, 23, 24, 20, 27, 4, 10]}, {'Size': '1', 'Order': 5, 'Representative': [25, 8, 2, 30, 26, 3, 10, 13, 12, 4, 14, 23, 6, 24, 19, 15, 28, 16, 21, 22, 18, 27, 1, 5, 9, 11, 17, 20, 7, 29]}, {'Size': '1', 'Order': 5, 'Representative': [23, 3, 6, 10, 24, 13, 29, 2, 25, 7, 26, 9, 8, 11, 16, 18, 27, 21, 15, 28, 19, 20, 12, 14, 1, 5, 22, 17, 30, 4]}, {'Size': '1', 'Order': 5, 'Representative': [9, 13, 8, 29, 11, 2, 4, 6, 23, 30, 24, 1, 3, 5, 21, 19, 20, 15, 18, 27, 16, 17, 25, 26, 12, 14, 28, 22, 10, 7]}, {'Size': '1', 'Order': 6, 'Representative': [3, 28, 17, 24, 16, 27, 11, 20, 8, 14, 19, 13, 22, 21, 25, 1, 30, 23, 9, 7, 12, 10, 6, 18, 2, 15, 4, 29, 26, 5]}, {'Size': '1', 'Order': 6, 'Representative': [16, 25, 1, 27, 30, 23, 20, 9, 19, 22, 7, 21, 12, 10, 26, 5, 3, 24, 11, 8, 14, 13, 18, 4, 15, 29, 6, 2, 28, 17]}, {'Size': '1', 'Order': 10, 'Representative': [4, 5, 24, 12, 6, 14, 25, 26, 29, 9, 2, 7, 11, 8, 17, 27, 18, 22, 28, 15, 20, 19, 10, 13, 30, 3, 21, 16, 1, 23]}, {'Size': '1', 'Order': 10, 'Representative': [7, 14, 11, 25, 8, 26, 23, 24, 4, 1, 6, 30, 5, 3, 22, 20, 19, 28, 27, 18, 17, 16, 29, 2, 10, 13, 15, 21, 12, 9]}, {'Size': '1', 'Order': 10, 'Representative': [10, 24, 14, 9, 13, 11, 1, 5, 30, 25, 3, 29, 26, 2, 27, 22, 21, 20, 17, 16, 28, 15, 7, 8, 4, 6, 19, 18, 23, 12]}, {'Size': '1', 'Order': 10, 'Representative': [29, 11, 26, 1, 2, 5, 12, 14, 10, 23, 13, 4, 24, 6, 20, 28, 15, 17, 22, 21, 27, 18, 30, 3, 7, 8, 16, 19, 9, 25]}, {'Size': '1', 'Order': 15, 'Representative': [26, 19, 15, 3, 28, 16, 13, 21, 14, 6, 22, 24, 18, 27, 7, 29, 25, 30, 10, 12, 4, 23, 5, 17, 11, 20, 1, 9, 8, 2]}, {'Size': '1', 'Order': 15, 'Representative': [20, 10, 7, 15, 9, 29, 18, 4, 27, 16, 23, 17, 30, 1, 13, 8, 11, 2, 6, 24, 3, 5, 28, 25, 22, 12, 26, 14, 21, 19]}, {'Size': '1', 'Order': 15, 'Representative': [24, 16, 18, 13, 27, 21, 2, 15, 26, 8, 28, 11, 19, 20, 30, 4, 23, 10, 29, 25, 7, 9, 14, 22, 5, 17, 12, 1, 3, 6]}, {'Size': '1', 'Order': 15, 'Representative': [11, 21, 19, 2, 20, 15, 6, 18, 24, 3, 27, 5, 16, 17, 10, 7, 9, 29, 4, 23, 30, 1, 26, 28, 14, 22, 25, 12, 13, 8]}, {'Size': '1', 'Order': 15, 'Representative': [22, 4, 10, 19, 12, 7, 16, 30, 17, 15, 1, 28, 29, 25, 6, 13, 14, 8, 3, 5, 2, 26, 20, 9, 27, 23, 11, 24, 18, 21]}, {'Size': '1', 'Order': 15, 'Representative': [28, 7, 29, 16, 25, 30, 21, 10, 22, 18, 12, 27, 4, 23, 8, 2, 26, 3, 13, 14, 6, 24, 17, 1, 20, 9, 5, 11, 19, 15]}, {'Size': '1', 'Order': 15, 'Representative': [14, 18, 21, 8, 22, 19, 3, 16, 5, 2, 17, 26, 15, 28, 4, 10, 12, 7, 30, 1, 29, 25, 11, 20, 24, 27, 9, 23, 6, 13]}, {'Size': '1', 'Order': 15, 'Representative': [27, 30, 4, 21, 23, 10, 15, 29, 28, 19, 25, 20, 7, 9, 3, 6, 24, 13, 2, 26, 8, 11, 22, 12, 17, 1, 14, 5, 16, 18]}, {'Size': '1', 'Order': 30, 'Representative': [21, 23, 12, 20, 10, 9, 17, 1, 16, 28, 30, 15, 25, 29, 24, 14, 13, 11, 5, 3, 26, 2, 19, 7, 18, 4, 8, 6, 27, 22]}, {'Size': '1', 'Order': 30, 'Representative': [15, 9, 25, 17, 29, 1, 22, 12, 21, 27, 10, 18, 23, 4, 11, 26, 2, 5, 14, 13, 24, 6, 16, 30, 19, 7, 3, 8, 20, 28]}, {'Size': '1', 'Order': 30, 'Representative': [13, 27, 22, 11, 21, 20, 5, 17, 3, 26, 16, 2, 28, 15, 23, 12, 10, 9, 1, 30, 25, 29, 8, 19, 6, 18, 7, 4, 24, 14]}, {'Size': '1', 'Order': 30, 'Representative': [18, 1, 23, 22, 4, 12, 28, 25, 15, 20, 29, 19, 9, 7, 5, 24, 6, 14, 26, 2, 11, 8, 21, 10, 16, 30, 13, 3, 17, 27]}, {'Size': '1', 'Order': 30, 'Representative': [2, 20, 28, 5, 15, 17, 14, 22, 13, 24, 21, 6, 27, 18, 9, 25, 29, 1, 12, 10, 23, 4, 3, 16, 8, 19, 30, 7, 11, 26]}, {'Size': '1', 'Order': 30, 'Representative': [19, 12, 9, 28, 7, 25, 27, 23, 18, 17, 4, 16, 1, 30, 14, 11, 8, 26, 24, 6, 5, 3, 15, 29, 21, 10, 2, 13, 22, 20]}, {'Size': '1', 'Order': 30, 'Representative': [6, 17, 27, 14, 18, 22, 26, 28, 2, 11, 15, 8, 20, 19, 1, 23, 4, 12, 25, 29, 9, 7, 13, 21, 3, 16, 10, 30, 5, 24]}, {'Size': '1', 'Order': 30, 'Representative': [8, 22, 20, 26, 19, 28, 24, 27, 6, 5, 18, 3, 17, 16, 12, 9, 7, 25, 23, 4, 1, 30, 2, 15, 13, 21, 29, 10, 14, 11]}], '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, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['6', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-3', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [30, 29, 28, 27, 26, 25, 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': ['2000883312', '1'], 'ConjugacyClass': 5}, {'RootOf': ['36656289', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-1736999958', '1'], 'ConjugacyClass': 7}, {'RootOf': ['537264837', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [5, 5, 5, 5, 5, 5]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-3', '1'], 'ConjugacyClass': 9}, {'RootOf': ['6', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [6, 6, 6, 6, 6]}, {'Data': {'Powers': [1], 'Resolvent': [30, 29, 28, 27, 26, 25, 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': ['1166441286', '1'], 'ConjugacyClass': 11}, {'RootOf': ['135257649', '1'], 'ConjugacyClass': 12}, {'RootOf': ['-1476761958', '1'], 'ConjugacyClass': 13}, {'RootOf': ['-660118383', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [10, 10, 10]}, {'Data': {'Powers': [1], 'Resolvent': [30, 29, 28, 27, 26, 25, 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': ['-9247401', '1'], 'ConjugacyClass': 15}, {'RootOf': ['-437881995', '1'], 'ConjugacyClass': 16}, {'RootOf': ['322469952', '1'], 'ConjugacyClass': 17}, {'RootOf': ['-99382842', '1'], 'ConjugacyClass': 18}, {'RootOf': ['-1633750812', '1'], 'ConjugacyClass': 19}, {'RootOf': ['-27408888', '1'], 'ConjugacyClass': 20}, {'RootOf': ['-367132500', '1'], 'ConjugacyClass': 21}, {'RootOf': ['1414530006', '1'], 'ConjugacyClass': 22}], 'Algorithm': 'RES', 'CycleType': [15, 15]}, {'Data': {'Powers': [1], 'Resolvent': [30, 29, 28, 27, 26, 25, 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': ['1201462470', '1'], 'ConjugacyClass': 23}, {'RootOf': ['537383637', '1'], 'ConjugacyClass': 24}, {'RootOf': ['275299488', '1'], 'ConjugacyClass': 25}, {'RootOf': ['-952539666', '1'], 'ConjugacyClass': 26}, {'RootOf': ['122734746', '1'], 'ConjugacyClass': 27}, {'RootOf': ['-108046335', '1'], 'ConjugacyClass': 28}, {'RootOf': ['-213901620', '1'], 'ConjugacyClass': 29}, {'RootOf': ['-27211314', '1'], 'ConjugacyClass': 30}], 'Algorithm': 'RES', 'CycleType': [30]}], 'Frobs': [28, 6, 21, 26, 3, 30, 13, 14, 4, 26, 18, 7, 27, 10, 20, 8, 17, 23, 4, 5, 11, 28, 23, 1, 16, 28, 17, 14, 2, 15, 13, 9, 19, 29, 25, 24, 15, 8, 30, 24, 6, 5, 22, 25, 2, 1, 30, 20, 26, 18, 12, 27, 10, 8, 17, 10, 5, 11, 28, 23, 27, 29, 2, 15, 19, 16, 3, 29, 25, 24, 3, 11, 22, 9, 5, 18, 22, 1, 21, 30, 4, 20, 12, 7, 10, 20, 8, 23, 10, 4, 5, 23, 6, 29, 17, 14, 15, 7, 13, 12, 24, 11, 30, 24, 9, 5, 22, 2, 21, 26, 30, 14, 4, 20, 7, 20, 21, 8, 17, 10, 4, 28, 23, 1, 16, 14, 19, 7, 3, 29, 12, 25, 15, 8, 30, 9, 6, 25, 21, 13, 14, 26, 18, 12, 7, 20, 23, 10, 4, 5, 27, 1, 6, 29, 19, 16, 13, 19, 12, 25, 3, 11, 9, 6, 18, 22, 1, 26], 'G-Gens': [[21, 23, 12, 20, 10, 9, 17, 1, 16, 28, 30, 15, 25, 29, 24, 14, 13, 11, 5, 3, 26, 2, 19, 7, 18, 4, 8, 6, 27, 22], [30, 26, 5, 23, 3, 24, 9, 11, 7, 12, 8, 10, 14, 13, 28, 17, 16, 27, 20, 19, 22, 21, 4, 6, 29, 2, 18, 15, 25, 1], [3, 28, 17, 24, 16, 27, 11, 20, 8, 14, 19, 13, 22, 21, 25, 1, 30, 23, 9, 7, 12, 10, 6, 18, 2, 15, 4, 29, 26, 5]], 'G-Name': 'C30', 'Polynomial': [1, 3, 9, 26, 75, 216, 622, 1791, 5157, 14849, 42756, 10314, 16093, 5523, 6255, 2672, 2493, 1224, 1000, 507, 297, -109, 90, -27, 28, -6, 9, -1, 3, 0, 1], 'QpRts': [['2150583646561', '12046866721021', '-1534793344851', '10421279743646', '-7893227044772', '12937784153580', '2695952238280', '-11065749491064', '2790761362272', '10161876193983', '-11708923350791', '-61015025201', '11612777228614', '6919803126847', '-4577266044491'], ['1671730387875', '-3439187101835', '5076019187591', '-12723967025605', '4570113971698', '5607667142996', '1030654779229', '-9834907308985', '6796014601068', '-12479105626247', '-4699936123539', '2741190770366', '5691440866308', '8709826167433', '3487861245041'], ['1754851573893', '4406013251337', '6042160323956', '13135036650087', '-6080716383407', '-435411322698', '2376363815064', '4280611831642', '-12136538981920', '8756122939141', '9065705704043', '9496526211121', '-3864992126364', '12574869049858', '1535670577305'], ['-8189633317286', '12206584862071', '-5759212746962', '-8112274908206', '2604730536710', '-11629595605832', '6679877055147', '-11483873687790', '4528505735656', '2226665151639', '3712961033232', '7006258435245', '-5856668327994', '-11041585528054', '-8586543825858'], ['13157992338713', '1002926278365', '6101546531616', '10790444862129', '-12853116776061', '1757199257473', '1855574099236', '-1169235093840', '1667823326064', '10618348889826', '5370600735843', '9186333392822', '-517099122359', '4041301633945', '3898715389487'], ['8062110349606', '12882843687986', '-5506492255389', '-8167973412031', '1597504863046', '10538204726360', '-11616743400218', '-5430576296198', '-385371511635', '-3302736615511', '12338481554311', '8039270425165', '-320018915824', '1363409500890', '400490747792'], ['10489326365747', '-10592841211019', '3460786650150', '1200316855737', '-6964201953545', '5191891445854', '-343486065229', '-8417268383079', '-6184349199597', '-306572493617', '-209764533374', '-10312097430494', '9167081914930', '2076733377097', '7953970414474'], ['-12416122033598', '7946020313545', '6970197027711', '10003458135591', '-1417133812398', '12812483073554', '382547311564', '10014657737236', '946805125251', '-6326580966792', '-6813667784599', '2937826813001', '12097872689741', '-11568460815291', '-4828976422291'], ['-5905210151547', '1149183293485', '-6926133148600', '11496446870005', '11033148481287', '-10020522469901', '-1097707105054', '3750962878711', '12619457240916', '11484952814738', '-1790129103888', '-12317031308020', '4966630145809', '-4004933563737', '-7366802990128'], ['-12911315224022', '-9905661377402', '-1551694250531', '-8074026779591', '-9231530684093', '-11399057650033', '8982456995749', '11673606546618', '-4196785427119', '10681925474537', '8590870399290', '-9252321295310', '-5535761135706', '-8387011643605', '-7398163841404'], ['5727074681779', '-7673846437424', '-10199102258008', '8885654630886', '8826587860348', '8324342572531', '4525945021952', '4421989684835', '769676893105', '9315360017476', '-10808527414512', '-8634588720219', '7882110818404', '-5062997100541', '-11140026944162'], ['606056643901', '-1022281524633', '-5403329460708', '9104212491078', '3587912316794', '-7137270530502', '-1395166792876', '-7332751879619', '5077688673836', '-6858455698491', '-1728687395389', '4257283106478', '-8363834675871', '-4300057416384', '-11704032782234'], ['-3113766891817', '8700514063884', '4654383876149', '10037748184378', '6994756729914', '-8328309503039', '796273901976', '2309395761780', '-4023728624736', '-4476363221242', '1829087022836', '-4251031514865', '12147714181095', '9357551570135', '2085716296240'], ['-9082134224048', '243174472943', '-3039246783886', '-681408719848', '5176243485710', '-9219542328615', '-9398262288483', '-7125278036998', '8475456191065', '1055046723129', '7954860111595', '-2504647944465', '13071249459517', '10144125100615', '6382121371140'], ['-11567470364095', '2429181209584', '6225098255702', '-7996921461942', '-5024025763427', '8274146151902', '7856421528297', '-1075958534972', '7162002312001', '-10266222320484', '-12302745809307', '12860035978025', '4575398698984', '5848677060193', '6185030290268'], ['-10976897888448', '-2007913953014', '3059396503268', '299210154350', '-3471214674258', '8016878025291', '-1162667075323', '178155900995', '4959654197259', '-3083714061291', '-7172675367278', '-7129904925146', '5436332831433', '-4161001377987', '-12274617427904'], ['11131046175397', '-13049792999386', '-4566753186765', '5227897554896', '-5693278339838', '11744638749618', '-4551526337516', '12234984584904', '-4458584688336', '5659397076862', '6338322614948', '-9125318367621', '-11095678106255', '-10961104760792', '678550655004'], ['127522967680', '1350193610614', '11265705002351', '-10159373840434', '-4202235399756', '1091390879472', '4936866345071', '-9525172176683', '-4143134224021', '1076071463872', '10388179573128', '11394093300261', '6176687243818', '9678176027164', '8186053078066'], ['1926795667851', '2646820897474', '-10430983677861', '-11203774991328', '8381335765943', '8435247641263', '-39061246335', '-1597389354157', '5237544074346', '6633153460409', '7023432317973', '7374270617493', '5174667556000', '9491727438194', '-3124993992183'], ['178135469768', '6524663143939', '-9314386754063', '6057520659780', '6579885819036', '1696179897370', '-3428237916898', '-8172952563546', '13050488026650', '5639309328457', '12598656518400', '-5488002132432', '-12848740964213', '9067930664278', '-7932792226381'], ['-10414540044832', '1205147313518', '-3102689625618', '-1963721404787', '2236773954179', '-6712255007599', '-9778730897725', '12456619852273', '8220514051855', '-6205562253295', '-10419957422126', '-12936269350496', '-6611953045389', '-970539926530', '5312447545164'], ['8476077580147', '779107051690', '8442576244594', '-8422803771230', '-8764155802504', '-10082809301554', '10793429081359', '-11981592244054', '12886477295770', '5803408975362', '-6226172716206', '-1752635162013', '-4707414783646', '-5844067684231', '5321911411094'], ['-7991837109622', '-11628488255126', '-9774022659960', '-11564540397140', '-1132191004062', '-11615808646125', '-12818559522052', '-230928146488', '12877923160774', '-9444043955041', '7204694232556', '-7251166943942', '-4121831278919', '3925250862905', '-5588909687630'], ['-10685721562286', '-10454834836947', '-2153953025284', '1991567557761', '-5851083850339', '-7168727627442', '4725952278916', '-10898699722669', '-6173352783440', '1584075399470', '-3948508125732', '4106081039164', '9680737590238', '12453470635772', '2766192226930'], ['-7646996085648', '6123981876112', '10596729199484', '4899724749856', '-12590914933939', '-1964663364142', '10277255243971', '-300367634206', '6768289878258', '6470590382259', '-4403183834550', '-12724087151760', '7688320267316', '2292654847387', '5976501502858'], ['-11446216428185', '306923706145', '-6771660500979', '10790309337094', '11508716345488', '9130493373497', '-12066210630686', '-5273943295809', '-2734467085421', '8110458464272', '4747371378773', '-4455211981211', '-4980079935179', '-985931834593', '-5032014844975'], ['-7762063488763', '-4356299068598', '11927975685244', '9572972839379', '6983274854401', '-7655085887104', '8092607243136', '11129627869157', '-6704570377334', '7859968555571', '-3256186106824', '3145085904778', '-5558906311319', '10060900661994', '2822717460700'], ['-7346409646838', '-6430905582257', '-3825068698505', '10749588073721', '1082198588451', '-7165830009355', '1788955386715', '5574310930015', '-4033822792837', '11858573314140', '-344187544223', '-9260323027700', '-2708240332137', '-1306723012794', '-944486657883'], ['9895739976220', '1010005892251', '-11301117443293', '-5718733673124', '453911791729', '12557808865773', '-8887076307526', '10910865843957', '12481605247602', '-3694294213940', '-9436940227825', '10838395412280', '-10266839565292', '11881118933045', '-9672891535309'], ['9222046314555', '-2398099298323', '-9101556827224', '13005375356234', '9551931057665', '-7581466702593', '-1213696739741', '-4458767732637', '7176884784661', '-5672408877850', '-1893030336765', '-2366621285975', '-1571340705069', '-8413867671871', '10738946850599']], 'QpRts-minpoly': [28, 25, 23, 13, 12, 29, 30, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'QpRts-p': 31, 'QpRts-prec': 9, 'Size': 30, 'TransitiveDegree': 30}