Artin representation data - 2.180.6t5.b

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• 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, 5], 'Baselabel': '2.180.6t5.b', 'CharacterField': 3, 'Conductor': 180, 'Container': '6t5', 'Dets': ['1.180.6t1.b.a', '1.180.6t1.b.b'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [0], [0, 2], [-2, -2], [1, 1], [0, -1], [-1], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [10, 11, 11], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [0, -2], [-1, -1]], [[1], [2, 2], [0, 1]], [[1], [-1, -1], [0, 1]], [[1], [0, 1], [-1, -1]], [[1], [1], [1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [1, 1]], [[1], [0, -1]]]}, {'Sign': 0, 'Character': [[2], [0], [-2, -2], [0, 2], [0, -1], [1, 1], [-1], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [10, 11, 11], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [2, 2], [0, 1]], [[1], [0, -2], [-1, -1]], [[1], [0, 1], [-1, -1]], [[1], [-1, -1], [0, 1]], [[1], [1], [1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0, -1]], [[1], [1, 1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T5', 'Galt': 5, 'HardPrimes': [2, 3, 5], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, -4, 7, -4, 2, -2, 1], 'NumBadPrimes': 3, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-8, -3, 0, 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.20.2t1.a', 'Character': [[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, -1], [0, 1], [1, 0], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.180.6t1.b', 'Character': [[1, 0], [-1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.180.6t1.b', 'Character': [[1, 0], [-1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.1620.3t2.b', 'Character': [[2], [0], [2], [2], [-1], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.180.6t5.b', 'Character': [[2, 0], [0, 0], [0, 2], [-2, -2], [1, 1], [0, -1], [-1, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.180.6t5.b', 'Character': [[2, 0], [0, 0], [-2, -2], [0, 2], [0, -1], [1, 1], [-1, 0], [0, 0], [0, 0]], 'CharacterField': 3}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6]}, {'Size': '3', 'Order': 2, 'Representative': [5, 4, 6, 2, 1, 3]}, {'Size': '1', 'Order': 3, 'Representative': [6, 1, 4, 5, 3, 2]}, {'Size': '1', 'Order': 3, 'Representative': [2, 6, 5, 3, 4, 1]}, {'Size': '2', 'Order': 3, 'Representative': [6, 1, 3, 4, 5, 2]}, {'Size': '2', 'Order': 3, 'Representative': [2, 6, 3, 4, 5, 1]}, {'Size': '2', 'Order': 3, 'Representative': [6, 1, 5, 3, 4, 2]}, {'Size': '3', 'Order': 6, 'Representative': [3, 5, 6, 2, 1, 4]}, {'Size': '3', 'Order': 6, 'Representative': [5, 4, 1, 6, 2, 3]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['6', '-2', '1'], 'ConjugacyClass': 5}, {'RootOf': ['29', '-6', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 3]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['6', '1'], 'ConjugacyClass': 3}, {'RootOf': ['2', '1'], 'ConjugacyClass': 4}, {'RootOf': ['21', '8', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['172', '42', '0', '1'], 'ConjugacyClass': 8}, {'RootOf': ['-26', '33', '0', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [6]}], 'Frobs': [4, 5, 9, 5, 8, 9, 2, 2, 6, 5, 9, 2, 6, 4, 5, 2, 9, 5, 6, 2, 2, 8, 5, 7, 8, 4, 3, 7, 7, 9, 7, 9, 8, 9, 6, 8, 9, 1, 6, 8, 2, 7, 8, 9, 2, 2, 9, 5, 4, 6, 2, 9, 5, 2, 9, 4, 7, 2, 8, 5, 6, 9, 7, 9, 8, 8, 8, 9, 3, 5, 8, 2, 4, 9, 2, 3, 5, 2, 3, 3, 9, 4, 2, 2, 8, 5, 1, 8, 5, 3, 1, 8, 1, 9, 9, 7, 6, 7, 7, 7, 5, 2, 6, 4, 9, 2, 5, 2, 9, 4, 6, 2, 9, 8, 2, 5, 6, 7, 9, 8, 3, 8, 8, 1, 8, 7, 5, 2, 5, 9, 2, 6, 9, 2, 6, 6, 2, 3, 9, 1, 2, 5, 6, 7, 7, 8, 8, 8, 9, 7, 9, 7, 7, 3, 5, 8, 2, 4, 2, 6, 5, 2, 6, 2, 9, 5, 2, 8], 'G-Gens': [[6, 1, 3, 4, 5, 2], [1, 2, 5, 3, 4, 6], [5, 4, 6, 2, 1, 3]], 'G-Name': 'C3*S3', 'Polynomial': [1, -4, 7, -4, 2, -2, 1], 'QpRts': [['-22787', '522498'], ['483805', '130905'], ['-190818', '-130905'], ['136387', '-522498'], ['127458', '307567'], ['-534043', '-307567']], 'QpRts-minpoly': [3, 16, 1], 'QpRts-p': 17, 'QpRts-prec': 5, 'Size': 18, 'TransitiveDegree': 6}