Artin representation data - 2.1024.8t8.a

Formats: - HTML - YAML - JSON - 2025-10-05T22:11:31.616999

• 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], 'Baselabel': '2.1024.8t8.a', 'CharacterField': 8, 'Conductor': 1024, 'Container': '8t8', 'Dets': ['1.8.2t1.b.a', '1.8.2t1.b.a'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 8, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [0], [0, -1, 0, -1], [0, 1, 0, 1]], 'GalOrbIndex': 1, 'HardFactors': [8], '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]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [0], [0, 1, 0, 1], [0, -1, 0, -1]], 'GalOrbIndex': 2, 'HardFactors': [8], '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]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '8T8', 'Galt': 8, 'HardPrimes': [2], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [-2, 0, 0, 0, 0, 0, 0, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [8, 3], 'Proj_Polynomial': [-2, 0, 0, 0, 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': '1.8.2t1.a', 'Character': [[1], [1], [1], [1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.8.2t1.b', 'Character': [[1], [1], [-1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.4.2t1.a', 'Character': [[1], [1], [-1], [1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.256.4t3.c', 'Character': [[2], [2], [0], [-2], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.1024.8t8.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': '2.1024.8t8.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': 3, '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': [7, 8, 3, 5, 4, 6, 1, 2]}, {'Size': '2', 'Order': 4, 'Representative': [2, 8, 4, 6, 3, 5, 1, 7]}, {'Size': '4', 'Order': 4, 'Representative': [6, 4, 1, 7, 2, 8, 5, 3]}, {'Size': '2', 'Order': 8, 'Representative': [6, 5, 7, 1, 8, 2, 4, 3]}, {'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': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['256', '0', '1'], 'ConjugacyClass': 4}, {'RootOf': ['2654208', '0', '0', '0', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [4, 4]}, {'Data': {'Powers': [1, 3], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['16', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-16', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [8]}], 'Frobs': [1, 5, 6, 3, 5, 6, 4, 5, 3, 6, 3, 7, 4, 5, 3, 6, 5, 7, 5, 3, 1, 3, 5, 1, 4, 7, 3, 5, 7, 2, 3, 5, 4, 5, 7, 3, 7, 5, 3, 6, 5, 7, 3, 4, 6, 3, 5, 3, 5, 6, 1, 3, 4, 5, 1, 3, 7, 3, 6, 2, 5, 6, 5, 3, 4, 6, 5, 1, 5, 6, 2, 3, 3, 6, 5, 3, 7, 7, 4, 4, 5, 6, 3, 4, 3, 5, 4, 4, 7, 3, 5, 3, 3, 5, 5, 3, 7, 4, 5, 7, 5, 6, 5, 4, 5, 2, 5, 2, 3, 1, 3, 6, 2, 5, 3, 4, 5, 3, 7, 5, 7, 4, 7, 5, 5, 7, 7, 3, 3, 6, 5, 3, 3, 7, 4, 4, 7, 5, 7, 4, 5, 6, 3, 5, 7, 3, 6, 4, 5, 3, 7, 1, 5, 3, 5, 3, 3, 4, 1, 7, 5, 4, 3, 5, 4, 3, 3, 7], 'G-Gens': [[8, 7, 6, 5, 4, 3, 2, 1], [6, 4, 1, 7, 2, 8, 5, 3], [7, 8, 3, 5, 4, 6, 1, 2], [2, 8, 4, 6, 3, 5, 1, 7]], 'G-Name': 'SD16', 'Polynomial': [-2, 0, 0, 0, 0, 0, 0, 0, 1], 'QpRts': [['-1795192381283'], ['4615444505392'], ['-2251544581922'], ['-1962462648212'], ['1962462648212'], ['2251544581922'], ['-4615444505392'], ['1795192381283']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 73, 'QpRts-prec': 7, 'Size': 16, 'TransitiveDegree': 8}