Artin representation data - 2.2023.12t11.a

Formats: - HTML - YAML - JSON - 2025-10-09T13:56:52.846662

• 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': [7, 17], 'Baselabel': '2.2023.12t11.a', 'CharacterField': 4, 'Conductor': 2023, 'Container': '12t11', 'Dets': ['1.119.2t1.a.a', '1.119.2t1.a.a'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 12, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [-1], [0, -2], [0, 2], [0], [0], [1], [0, -1], [0, 1]], 'GalOrbIndex': 1, 'HardFactors': [10, 8, 8, 13, 7, 14, 3, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [0, 2], [-1]], [[1], [0, -2], [-1]], [[1], [0], [1]], [[1], [0], [1]], [[1], [-1], [1]], [[1], [0, 1], [-1]], [[1], [0, -1], [-1]], [[1], [0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [-1], [0, 2], [0, -2], [0], [0], [1], [0, 1], [0, -1]], 'GalOrbIndex': 2, 'HardFactors': [10, 8, 8, 13, 7, 14, 3, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [0, -2], [-1]], [[1], [0, 2], [-1]], [[1], [0], [1]], [[1], [0], [1]], [[1], [-1], [1]], [[1], [0, -1], [-1]], [[1], [0, 1], [-1]], [[1], [0, 1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '12T11', 'Galt': 11, 'HardPrimes': [2, 3, 5, 7, 11, 17, 19, 701], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [-1, -61, 399, -909, 1107, -989, 704, -386, 185, -70, 25, -6, 1], 'NumBadPrimes': 2, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [5, 6, -1, 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], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.7.2t1.a', 'Character': [[1], [1], [-1], [-1], [1], [1], [1], [-1], [-1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.17.2t1.a', 'Character': [[1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.119.2t1.a', 'Character': [[1], [1], [-1], [-1], [1], [-1], [-1], [1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.17.4t1.a', 'Character': [[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': '1.119.4t1.a', 'Character': [[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': '1.17.4t1.a', 'Character': [[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': '1.119.4t1.a', 'Character': [[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': '2.2023.3t2.b', 'Character': [[2], [2], [0], [0], [-1], [2], [2], [0], [0], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.2023.6t3.b', 'Character': [[2], [2], [0], [0], [-1], [-2], [-2], [0], [0], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.2023.12t11.a', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [-1, 0], [0, -2], [0, 2], [0, 0], [0, 0], [1, 0], [0, -1], [0, 1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '2.2023.12t11.a', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [-1, 0], [0, 2], [0, -2], [0, 0], [0, 0], [1, 0], [0, 1], [0, -1]], 'CharacterField': 4}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]}, {'Size': '1', 'Order': 2, 'Representative': [5, 7, 10, 11, 1, 8, 2, 6, 12, 3, 4, 9]}, {'Size': '3', 'Order': 2, 'Representative': [1, 11, 8, 7, 5, 10, 4, 3, 9, 6, 2, 12]}, {'Size': '3', 'Order': 2, 'Representative': [5, 4, 6, 2, 1, 3, 11, 10, 12, 8, 7, 9]}, {'Size': '2', 'Order': 3, 'Representative': [7, 11, 9, 1, 2, 10, 4, 3, 8, 12, 5, 6]}, {'Size': '1', 'Order': 4, 'Representative': [9, 6, 11, 3, 12, 7, 8, 2, 5, 4, 10, 1]}, {'Size': '1', 'Order': 4, 'Representative': [12, 8, 4, 10, 9, 2, 6, 7, 1, 11, 3, 5]}, {'Size': '3', 'Order': 4, 'Representative': [6, 9, 4, 10, 8, 5, 12, 1, 7, 11, 3, 2]}, {'Size': '3', 'Order': 4, 'Representative': [8, 12, 11, 3, 6, 1, 9, 5, 2, 4, 10, 7]}, {'Size': '2', 'Order': 6, 'Representative': [11, 1, 6, 2, 4, 9, 5, 12, 10, 8, 7, 3]}, {'Size': '2', 'Order': 12, 'Representative': [6, 3, 1, 12, 8, 11, 10, 4, 7, 5, 9, 2]}, {'Size': '2', 'Order': 12, 'Representative': [8, 10, 5, 9, 6, 4, 3, 11, 2, 1, 12, 7]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-10', '1'], 'ConjugacyClass': 2}, {'RootOf': ['10424', '96', '38', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['11', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-91', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-9345', '3151', '-103', '1'], 'ConjugacyClass': 8}, {'RootOf': ['-95535', '5871', '-137', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [4, 4, 4]}, {'Data': 0, 'Classes': 10, 'Algorithm': 'CYC', 'CycleType': [6, 6]}, {'Data': {'Powers': [1, 5], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['-12', '1'], 'ConjugacyClass': 11}, {'RootOf': ['-148', '1'], 'ConjugacyClass': 12}], 'Algorithm': 'RES', 'CycleType': [12]}], 'Frobs': [10, 9, 9, 8, 7, 3, 3, 4, 11, 12, 9, 12, 8, 10, 3, 10, 4, 8, 1, 12, 9, 11, 4, 3, 9, 3, 3, 12, 11, 11, 10, 9, 5, 9, 5, 2, 3, 11, 9, 9, 10, 8, 5, 7, 7, 9, 11, 4, 8, 4, 12, 1, 9, 3, 4, 10, 9, 3, 6, 10, 8, 3, 3, 9, 8, 7, 10, 12, 11, 4, 3, 10, 8, 5, 12, 4, 10, 8, 7, 3, 8, 1, 11, 4, 9, 5, 7, 10, 4, 5, 4, 9, 11, 2, 11, 8, 3, 8, 3, 6, 12, 5, 4, 2, 11, 3, 4, 4, 1, 8, 9, 5, 12, 8, 10, 12, 9, 3, 11, 5, 4, 11, 9, 12, 8, 1, 6, 9, 3, 4, 10, 6, 6, 2, 3, 3, 4, 9, 4, 11, 9, 12, 7, 11, 3, 8, 9, 8, 4, 1, 11, 9, 5, 9, 11, 11, 5, 8, 4, 8, 12, 5, 10, 4, 2, 9, 6, 8], 'G-Gens': [[5, 7, 10, 11, 1, 8, 2, 6, 12, 3, 4, 9], [6, 3, 1, 12, 8, 11, 10, 4, 7, 5, 9, 2], [1, 11, 8, 7, 5, 10, 4, 3, 9, 6, 2, 12], [7, 11, 9, 1, 2, 10, 4, 3, 8, 12, 5, 6]], 'G-Name': 'C4*S3', 'Polynomial': [-1, -61, 399, -909, 1107, -989, 704, -386, 185, -70, 25, -6, 1], 'QpRts': [['-75828214325502', '166538812843636', '-286909838143909', '-38757645340870'], ['-240771630749941', '66367558537054', '115081994199704', '68003984035142'], ['-101684886182475', '-226036555613068', '-243242732859111', '363443387334183'], ['95970525449713', '-249290671804097', '-354842215540716', '-391612501384535'], ['75828214325503', '-166538812843636', '286909838143909', '38757645340870'], ['-177560761130359', '-66749670090225', '263624431670875', '-47749784053056'], ['240771630749942', '-66367558537054', '-115081994199704', '-68003984035142'], ['177560761130360', '66749670090225', '-263624431670875', '47749784053056'], ['333216711720095', '-394189868109261', '-149186623160779', '-158490684540095'], ['101684886182476', '226036555613068', '243242732859111', '-363443387334183'], ['-95970525449712', '249290671804097', '354842215540716', '391612501384535'], ['-333216711720094', '394189868109261', '149186623160779', '158490684540095']], 'QpRts-minpoly': [3, 16, 3, 0, 1], 'QpRts-p': 31, 'QpRts-prec': 10, 'Size': 24, 'TransitiveDegree': 12}