Artin representation data - 2.2175.9t3.a

Formats: - HTML - YAML - JSON - 2025-11-09T12:56:11.249617

• 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, 5, 29], 'Baselabel': '2.2175.9t3.a', 'CharacterField': 9, 'Conductor': 2175, 'Container': '9t3', 'Dets': ['1.87.2t1.a.a', '1.87.2t1.a.a', '1.87.2t1.a.a'], 'Dim': 2, 'GalConjSigns': [1, 1, 1], 'Galn': 9, 'GaloisConjugates': [{'Sign': 1, 'Character': [[2], [0], [-1], [0, -1, 1, 0, -1], [0, 0, 0, 0, 1, 1], [0, 1, -1, 0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [7, 8, 7], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [0, 1, -1, 0, 1], [1]], [[1], [0, 0, 0, 0, -1, -1], [1]], [[1], [0, -1, 1, 0, 0, 1], [1]], [[1], [-1]], [[1]]]}, {'Sign': 1, 'Character': [[2], [0], [-1], [0, 0, 0, 0, 1, 1], [0, 1, -1, 0, 0, -1], [0, -1, 1, 0, -1]], 'GalOrbIndex': 2, 'HardFactors': [7, 8, 7], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [0, 0, 0, 0, -1, -1], [1]], [[1], [0, -1, 1, 0, 0, 1], [1]], [[1], [0, 1, -1, 0, 1], [1]], [[1], [-1]], [[1]]]}, {'Sign': 1, 'Character': [[2], [0], [-1], [0, 1, -1, 0, 0, -1], [0, -1, 1, 0, -1], [0, 0, 0, 0, 1, 1]], 'GalOrbIndex': 3, 'HardFactors': [7, 8, 7], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [0, -1, 1, 0, 0, 1], [1]], [[1], [0, 1, -1, 0, 1], [1]], [[1], [0, 0, 0, 0, -1, -1], [1]], [[1], [-1]], [[1]]]}], 'GaloisConjugatesSigns': [1, 1, 1], 'GaloisLabel': '9T3', 'Galt': 3, 'HardPrimes': [3, 5, 29], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [-45, 45, -60, 24, -41, 11, -11, 4, -1, 1], 'NumBadPrimes': 3, 'Proj_GAP': [18, 1], 'Proj_Polynomial': [-45, 45, -60, 24, -41, 11, -11, 4, -1, 1], 'Proj_nTj': [9, 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.87.2t1.a', 'Character': [[1], [-1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.87.3t2.a', 'Character': [[2], [0], [2], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.2175.9t3.a', 'Character': [[2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, -1, 1, 0, -1, 0], [0, 0, 0, 0, 1, 1], [0, 1, -1, 0, 0, -1]], 'CharacterField': 9}, {'GalConj': 2, 'Baselabel': '2.2175.9t3.a', 'Character': [[2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1], [0, 1, -1, 0, 0, -1], [0, -1, 1, 0, -1, 0]], 'CharacterField': 9}, {'GalConj': 3, 'Baselabel': '2.2175.9t3.a', 'Character': [[2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 1, -1, 0, 0, -1], [0, -1, 1, 0, -1, 0], [0, 0, 0, 0, 1, 1]], 'CharacterField': 9}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '9', 'Order': 2, 'Representative': [3, 4, 1, 2, 8, 9, 7, 5, 6]}, {'Size': '2', 'Order': 3, 'Representative': [7, 5, 1, 9, 6, 2, 3, 4, 8]}, {'Size': '2', 'Order': 9, 'Representative': [8, 7, 9, 5, 3, 1, 4, 2, 6]}, {'Size': '2', 'Order': 9, 'Representative': [2, 4, 6, 3, 9, 8, 5, 7, 1]}, {'Size': '2', 'Order': 9, 'Representative': [4, 3, 8, 6, 1, 7, 9, 5, 2]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 2, 2]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [3, 3, 3]}, {'Data': {'Powers': [1, 8], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-19', '1'], 'ConjugacyClass': 4}, {'RootOf': ['26', '1'], 'ConjugacyClass': 5}, {'RootOf': ['6', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [9]}], 'Frobs': [4, 1, 2, 5, 6, 4, 6, 2, 2, 1, 2, 2, 3, 2, 5, 2, 2, 2, 6, 2, 2, 2, 2, 4, 2, 4, 3, 2, 4, 5, 2, 5, 3, 5, 2, 3, 2, 2, 2, 2, 2, 6, 1, 2, 2, 4, 2, 6, 2, 2, 2, 2, 5, 4, 2, 3, 6, 2, 6, 2, 3, 4, 2, 5, 5, 4, 2, 2, 2, 3, 2, 3, 2, 1, 2, 2, 4, 3, 2, 2, 2, 2, 2, 2, 6, 4, 5, 5, 3, 4, 3, 3, 1, 3, 4, 4, 2, 2, 4, 2, 6, 2, 6, 5, 3, 2, 2, 2, 5, 2, 2, 5, 3, 2, 5, 5, 6, 2, 6, 5, 4, 4, 6, 2, 6, 2, 3, 2, 2, 2, 2, 5, 2, 2, 2, 2, 1, 3, 3, 6, 6, 2, 2, 3, 2, 6, 2, 2, 2, 2, 3, 5, 1, 5, 2, 4, 4, 2, 4, 2, 6, 2, 2, 3, 2, 3, 4, 2], 'G-Gens': [[3, 4, 1, 2, 8, 9, 7, 5, 6], [7, 5, 1, 9, 6, 2, 3, 4, 8], [8, 7, 9, 5, 3, 1, 4, 2, 6]], 'G-Name': 'D18', 'Polynomial': [-45, 45, -60, 24, -41, 11, -11, 4, -1, 1], 'QpRts': [['37996814', '-11282799', '-30594079'], ['-6070423', '46046473', '-38037896'], ['-36276175', '49493878', '31780739'], ['-55831523', '50950804', '-25153824'], ['-45819780', '-22532660', '-39733831'], ['-6101475', '-23513813', '-38084474'], ['57601760', '-38211079', '-1186660'], ['41819358', '30008074', '-52461804'], ['12681445', '34897323', '-38240573']], 'QpRts-minpoly': [35, 1, 0, 1], 'QpRts-p': 41, 'QpRts-prec': 5, 'Size': 18, 'TransitiveDegree': 9}