Artin representation data - 2.1664.8t17.b

Formats: - HTML - YAML - JSON - 2026-05-12T12:02:12.020297

• 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, 13], 'Baselabel': '2.1664.8t17.b', 'CharacterField': 4, 'Conductor': 1664, 'Container': '8t17', 'Dets': ['1.104.4t1.b.b', '1.104.4t1.b.a'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 8, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, 2], [0, -2], [0], [1, -1], [1, 1], [-1, 1], [-1, -1], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [15, 3, 16], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, -2], [-1]], [[1], [0, 2], [-1]], [[1], [0], [1]], [[1], [-1, 1], [0, -1]], [[1], [-1, -1], [0, 1]], [[1], [1, -1], [0, -1]], [[1], [1, 1], [0, 1]], [[1], [0], [1]], [[1], [0], [0, -1]], [[1], [0], [0, 1]], [[1]], [[1], [0, -1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, -2], [0, 2], [0], [1, 1], [1, -1], [-1, -1], [-1, 1], [0], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [15, 3, 16], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, 2], [-1]], [[1], [0, -2], [-1]], [[1], [0], [1]], [[1], [-1, -1], [0, 1]], [[1], [-1, 1], [0, -1]], [[1], [1, 1], [0, 1]], [[1], [1, -1], [0, -1]], [[1], [0], [1]], [[1], [0], [0, 1]], [[1], [0], [0, -1]], [[1]], [[1], [0, 1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '8T17', 'Galt': 17, 'HardPrimes': [2, 3, 13], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [52, 0, 0, 0, 8, 0, 0, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [8, 3], 'Proj_Polynomial': [-52, 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], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.52.2t1.a', 'Character': [[1], [1], [1], [-1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.13.2t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.4.2t1.a', 'Character': [[1], [1], [1], [-1], [1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.104.4t1.b', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [1, 0], [0, 1], [0, -1], [0, 1], [0, -1], [1, 0], [0, 1], [0, -1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '1.104.4t1.a', 'Character': [[1, 0], [1, 0], [-1, 0], [1, 0], [-1, 0], [-1, 0], [1, 0], [0, -1], [0, 1], [0, -1], [0, 1], [-1, 0], [0, 1], [0, -1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '1.104.4t1.b', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [1, 0], [0, -1], [0, 1], [0, -1], [0, 1], [1, 0], [0, -1], [0, 1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '1.104.4t1.a', 'Character': [[1, 0], [1, 0], [-1, 0], [1, 0], [-1, 0], [-1, 0], [1, 0], [0, 1], [0, -1], [0, 1], [0, -1], [-1, 0], [0, -1], [0, 1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '2.10816.4t3.c', 'Character': [[2], [2], [-2], [0], [2], [2], [-2], [0], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.208.4t3.b', 'Character': [[2], [2], [2], [0], [-2], [-2], [-2], [0], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.1664.8t17.b', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 2], [0, -2], [0, 0], [1, -1], [1, 1], [-1, 1], [-1, -1], [0, 0], [0, 0], [0, 0]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '2.1664.8t17.b', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, -2], [0, 2], [0, 0], [1, 1], [1, -1], [-1, -1], [-1, 1], [0, 0], [0, 0], [0, 0]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '2.21632.8t17.b', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, -2], [0, 2], [0, 0], [-1, -1], [-1, 1], [1, 1], [1, -1], [0, 0], [0, 0], [0, 0]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '2.21632.8t17.b', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 2], [0, -2], [0, 0], [-1, 1], [-1, -1], [1, -1], [1, 1], [0, 0], [0, 0], [0, 0]], 'CharacterField': 4}], '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': '2', 'Order': 2, 'Representative': [1, 7, 3, 5, 4, 6, 2, 8]}, {'Size': '4', 'Order': 2, 'Representative': [4, 3, 2, 1, 8, 7, 6, 5]}, {'Size': '1', 'Order': 4, 'Representative': [6, 4, 1, 7, 2, 8, 5, 3]}, {'Size': '1', 'Order': 4, 'Representative': [3, 5, 8, 2, 7, 1, 4, 6]}, {'Size': '2', 'Order': 4, 'Representative': [6, 5, 1, 2, 7, 8, 4, 3]}, {'Size': '2', 'Order': 4, 'Representative': [1, 5, 3, 2, 7, 6, 4, 8]}, {'Size': '2', 'Order': 4, 'Representative': [1, 4, 3, 7, 2, 6, 5, 8]}, {'Size': '2', 'Order': 4, 'Representative': [6, 7, 1, 5, 4, 8, 2, 3]}, {'Size': '2', 'Order': 4, 'Representative': [3, 7, 8, 5, 4, 1, 2, 6]}, {'Size': '4', 'Order': 4, 'Representative': [7, 1, 4, 6, 3, 5, 8, 2]}, {'Size': '4', 'Order': 8, 'Representative': [4, 1, 2, 6, 3, 7, 8, 5]}, {'Size': '4', 'Order': 8, 'Representative': [7, 6, 4, 8, 1, 5, 3, 2]}], '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, 1, 1, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['128', '-16', '1'], 'ConjugacyClass': 8}, {'RootOf': ['3200', '80', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 4]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['0', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-17252352', '0', '0', '0', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['128', '16', '1'], 'ConjugacyClass': 10}, {'RootOf': ['3200', '-80', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'RES', 'CycleType': [2, 2, 4]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['48', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-48', '1'], 'ConjugacyClass': 6}, {'RootOf': ['1024', '0', '1'], 'ConjugacyClass': 7}, {'RootOf': ['0', '0', '0', '0', '1'], 'ConjugacyClass': 12}], 'Algorithm': 'RES', 'CycleType': [4, 4]}, {'Data': {'Powers': [1], 'Resolvent': [8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['1520816128', '0', '0', '0', '1'], 'ConjugacyClass': 13}, {'RootOf': ['14900973568', '0', '0', '0', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [8]}], 'Frobs': [8, 4, 11, 14, 13, 9, 6, 14, 4, 6, 13, 8, 10, 12, 14, 3, 13, 3, 14, 13, 11, 12, 14, 9, 10, 1, 4, 4, 9, 7, 4, 4, 9, 4, 9, 14, 5, 13, 14, 2, 12, 7, 12, 11, 11, 4, 4, 13, 14, 8, 3, 13, 9, 12, 3, 12, 5, 14, 1, 11, 12, 10, 13, 4, 7, 11, 14, 5, 4, 10, 8, 14, 12, 5, 14, 13, 7, 8, 9, 8, 4, 9, 13, 3, 4, 4, 9, 8, 11, 14, 12, 14, 13, 12, 14, 12, 11, 7, 4, 8, 4, 8, 12, 3, 12, 10, 14, 11, 12, 7, 12, 11, 10, 13, 14, 5, 14, 4, 5, 4, 8, 6, 3, 13, 14, 7, 10, 4, 4, 9, 13, 13, 4, 3, 9, 8, 11, 13, 7, 7, 14, 11, 4, 13, 2, 14, 10, 3, 4, 13, 11, 3, 12, 12, 12, 12, 12, 8, 1, 9, 13, 3, 13, 4, 10, 14, 12, 3], 'G-Gens': [[1, 5, 3, 2, 7, 6, 4, 8], [8, 7, 6, 5, 4, 3, 2, 1], [4, 1, 2, 6, 3, 7, 8, 5], [1, 7, 3, 5, 4, 6, 2, 8], [6, 5, 1, 2, 7, 8, 4, 3]], 'G-Name': 'C4wrC2', 'Polynomial': [52, 0, 0, 0, 8, 0, 0, 0, 1], 'QpRts': [['37572689302707490'], ['35456114526821034'], ['530332988247700437'], ['-390292321786141148'], ['390292321786141148'], ['-530332988247700437'], ['-35456114526821034'], ['-37572689302707490']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 101, 'QpRts-prec': 9, 'Size': 32, 'TransitiveDegree': 8}