Artin representation data - 2.1776.8t6.a

Formats: - HTML - YAML - JSON - 2025-10-19T21:24:42.332065

• 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, 37], 'Baselabel': '2.1776.8t6.a', 'CharacterField': 8, 'Conductor': 1776, 'Container': '8t6', 'Dets': ['1.111.2t1.a.a', '1.111.2t1.a.a'], 'Dim': 2, 'GalConjSigns': [1, 1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[2], [-2], [0], [0], [0], [0, 1, 0, -1], [0, -1, 0, 1]], 'GalOrbIndex': 1, 'HardFactors': [8, 9, 10], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0], [1]], [[1], [0, -1, 0, 1], [1]], [[1], [0, 1, 0, -1], [1]], [[1]], [[1], [-1]], [[1], [1]]]}, {'Sign': 1, 'Character': [[2], [-2], [0], [0], [0], [0, -1, 0, 1], [0, 1, 0, -1]], 'GalOrbIndex': 2, 'HardFactors': [8, 9, 10], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0], [1]], [[1], [0, 1, 0, -1], [1]], [[1], [0, -1, 0, 1], [1]], [[1]], [[1], [-1]], [[1], [1]]]}], 'GaloisConjugatesSigns': [1, 1], 'GaloisLabel': '8T6', 'Galt': 6, 'HardPrimes': [2, 3, 37], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [37, 0, 17, 0, 18, 0, 8, 0, 1], 'NumBadPrimes': 3, 'Proj_GAP': [8, 3], 'Proj_Polynomial': [3, 0, -2, -1, 1], 'Proj_nTj': [4, 3]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.37.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.3.2t1.a', 'Character': [[1], [1], [1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.111.2t1.a', 'Character': [[1], [1], [-1], [-1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.111.4t3.b', 'Character': [[2], [2], [0], [0], [-2], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.1776.8t6.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, -1], [0, -1, 0, 1]], 'CharacterField': 8}, {'GalConj': 2, 'Baselabel': '2.1776.8t6.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1, 0, 1], [0, 1, 0, -1]], 'CharacterField': 8}], 'ComplexConjugation': 4, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [8, 7, 6, 5, 4, 3, 2, 1]}, {'Size': '4', 'Order': 2, 'Representative': [8, 2, 4, 3, 6, 5, 7, 1]}, {'Size': '4', 'Order': 2, 'Representative': [5, 6, 7, 8, 1, 2, 3, 4]}, {'Size': '2', 'Order': 4, 'Representative': [7, 1, 5, 3, 6, 4, 8, 2]}, {'Size': '2', 'Order': 8, 'Representative': [4, 6, 8, 7, 2, 1, 3, 5]}, {'Size': '2', 'Order': 8, 'Representative': [3, 4, 2, 8, 1, 7, 5, 6]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['48', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-7527168', '0', '-2736', '0', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [4, 4]}, {'Data': {'Powers': [1, 7], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['12', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-12', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [8]}], 'Frobs': [7, 1, 7, 5, 4, 3, 6, 3, 6, 6, 3, 3, 4, 3, 4, 4, 7, 3, 5, 4, 5, 3, 4, 7, 3, 4, 3, 4, 3, 7, 2, 7, 4, 5, 4, 1, 5, 3, 7, 4, 6, 5, 7, 3, 4, 3, 2, 1, 6, 2, 4, 6, 3, 6, 7, 4, 4, 5, 3, 7, 3, 4, 2, 6, 3, 4, 3, 2, 7, 5, 6, 4, 2, 5, 5, 7, 7, 5, 6, 3, 4, 3, 6, 5, 3, 4, 6, 3, 7, 3, 7, 7, 3, 4, 3, 7, 4, 4, 3, 3, 3, 6, 6, 7, 5, 3, 6, 4, 4, 5, 3, 1, 4, 1, 3, 4, 3, 7, 6, 4, 3, 5, 4, 7, 5, 6, 3, 4, 3, 1, 1, 4, 5, 3, 4, 3, 4, 2, 7, 7, 5, 4, 1, 6, 3, 4, 3, 7, 3, 4, 5, 4, 3, 4, 3, 7, 3, 4, 2, 4, 6, 4, 3, 4, 6, 4, 3, 3], 'G-Gens': [[8, 7, 6, 5, 4, 3, 2, 1], [4, 6, 8, 7, 2, 1, 3, 5], [7, 1, 5, 3, 6, 4, 8, 2], [8, 2, 4, 3, 6, 5, 7, 1]], 'G-Name': 'D16', 'Polynomial': [37, 0, 17, 0, 18, 0, 8, 0, 1], 'QpRts': [['2937399714270'], ['70413736119'], ['3325151015490'], ['356068785386'], ['-356068785386'], ['-3325151015490'], ['-70413736119'], ['-2937399714270']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 151, 'QpRts-prec': 6, 'Size': 16, 'TransitiveDegree': 8}