Artin representation data - 2.243.6t5.b

Formats: - HTML - YAML - JSON - 2025-07-17T18:33:09.010786

• 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], 'Baselabel': '2.243.6t5.b', 'CharacterField': 3, 'Conductor': 243, 'Container': '6t5', 'Dets': ['1.9.6t1.a.a', '1.9.6t1.a.b'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [0], [0, 2], [-2, -2], [-1], [1, 1], [0, -1], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [10], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [0, -2], [-1, -1]], [[1], [2, 2], [0, 1]], [[1], [1], [1]], [[1], [-1, -1], [0, 1]], [[1], [0, 1], [-1, -1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[2], [0], [-2, -2], [0, 2], [-1], [0, -1], [1, 1], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [10], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [2, 2], [0, 1]], [[1], [0, -2], [-1, -1]], [[1], [1], [1]], [[1], [0, 1], [-1, -1]], [[1], [-1, -1], [0, 1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T5', 'Galt': 5, 'HardPrimes': [3], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [3, 0, 0, -3, 0, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-3, 0, 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': '1.3.2t1.a', 'Character': [[1], [-1], [1], [1], [1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.9.6t1.a', 'Character': [[1, 0], [-1, 0], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.9.6t1.a', 'Character': [[1, 0], [-1, 0], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.243.3t2.b', 'Character': [[2], [0], [2], [2], [-1], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.243.6t5.b', 'Character': [[2, 0], [0, 0], [0, 2], [-2, -2], [-1, 0], [1, 1], [0, -1], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.243.6t5.b', 'Character': [[2, 0], [0, 0], [-2, -2], [0, 2], [-1, 0], [0, -1], [1, 1], [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': [6, 5, 4, 3, 2, 1]}, {'Size': '1', 'Order': 3, 'Representative': [3, 6, 5, 2, 1, 4]}, {'Size': '1', 'Order': 3, 'Representative': [5, 4, 1, 6, 3, 2]}, {'Size': '2', 'Order': 3, 'Representative': [3, 4, 5, 6, 1, 2]}, {'Size': '2', 'Order': 3, 'Representative': [1, 6, 3, 2, 5, 4]}, {'Size': '2', 'Order': 3, 'Representative': [1, 4, 3, 6, 5, 2]}, {'Size': '3', 'Order': 6, 'Representative': [4, 5, 2, 3, 6, 1]}, {'Size': '3', 'Order': 6, 'Representative': [6, 3, 4, 1, 2, 5]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['0', '0', '1'], 'ConjugacyClass': 6}, {'RootOf': ['81', '-9', '1'], 'ConjugacyClass': 7}], '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': ['9', '1'], 'ConjugacyClass': 3}, {'RootOf': ['0', '1'], 'ConjugacyClass': 4}, {'RootOf': ['81', '9', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [2, 5, -2, -7, 1]}, 'Classes': [{'RootOf': ['41472', '0', '0', '1'], 'ConjugacyClass': 8}, {'RootOf': ['10125', '0', '0', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [6]}], 'Frobs': [8, 1, 9, 6, 8, 7, 2, 5, 9, 8, 7, 5, 9, 6, 8, 2, 9, 4, 3, 2, 1, 6, 8, 2, 6, 8, 3, 2, 5, 9, 5, 9, 8, 7, 9, 4, 7, 5, 9, 8, 2, 5, 8, 3, 2, 5, 7, 6, 8, 7, 2, 9, 6, 2, 9, 8, 2, 1, 6, 8, 7, 9, 1, 9, 6, 8, 6, 7, 9, 6, 8, 2, 4, 7, 5, 9, 8, 5, 9, 7, 9, 6, 2, 5, 4, 8, 2, 6, 8, 7, 2, 8, 5, 9, 3, 2, 9, 2, 1, 5, 4, 2, 9, 8, 7, 1, 8, 2, 9, 6, 7, 1, 9, 4, 5, 8, 3, 2, 9, 8, 3, 6, 8, 2, 6, 2, 6, 2, 4, 7, 5, 9, 7, 1, 9, 7, 2, 3, 9, 2, 5, 8, 7, 2, 5, 8, 4, 8, 7, 2, 7, 2, 5, 9, 6, 8, 1, 8, 5, 9, 8, 2, 3, 2, 9, 8, 1, 4], 'G-Gens': [[6, 5, 4, 3, 2, 1], [3, 4, 5, 6, 1, 2], [1, 6, 3, 2, 5, 4]], 'G-Name': 'C3*S3', 'Polynomial': [3, 0, 0, -3, 0, 0, 1], 'QpRts': [['-118686069', '119683109'], ['8080610', '26717018'], ['-9053005', '-26717018'], ['18077552', '-119683109'], ['127739074', '-92966091'], ['-26158162', '92966091']], 'QpRts-minpoly': [3, 16, 1], 'QpRts-p': 17, 'QpRts-prec': 7, 'Size': 18, 'TransitiveDegree': 6}