Artin representation data - 1.27.9t1.a

Formats: - HTML - YAML - JSON - 2023-11-30T20:33:58.640522

• 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': '1.27.9t1.a', 'CharacterField': 9, 'Conductor': 27, 'Container': '9t1', 'Dets': ['27.16', '27.13', '27.7', '27.4', '27.25', '27.22'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0, 0, 0], 'Galn': 9, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [-1, 0, 0, -1], [0, 1], [0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1], [0, 0, -1, 0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [5, 10, 4, 7, 6], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 1, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, 0, 0, -1], [0, 0, 0, 1], [0, 0, 1], [0, 0, 0, 0, 1], [0, 0, -1, 0, 0, -1], [0, 1], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1]], 'GalOrbIndex': 2, 'HardFactors': [5, 10, 4, 7, 6], 'LocalFactors': [[[1], [-1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [-1, 0, 0, -1], [0, 0, 0, 0, 1], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1], [0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [5, 10, 4, 7, 6], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, 0, 0, -1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 1], [0, -1, 0, 0, -1], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1]], 'GalOrbIndex': 4, 'HardFactors': [5, 10, 4, 7, 6], 'LocalFactors': [[[1], [-1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [-1, 0, 0, -1], [0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 1], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1], [0, 0, 1]], 'GalOrbIndex': 5, 'HardFactors': [5, 10, 4, 7, 6], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, 0, 0, -1], [0, 0, 0, 1], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 1], [0, 1]], 'GalOrbIndex': 6, 'HardFactors': [5, 10, 4, 7, 6], 'LocalFactors': [[[1], [-1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0], 'GaloisLabel': '9T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 7, 23], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-1, 9, 0, -30, 0, 27, 0, -9, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
• 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': '1.27.9t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1, 0], [0, 0, -1, 0, 0, -1]], 'CharacterField': 9}, {'GalConj': 2, 'Baselabel': '1.27.9t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, -1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1, 0]], 'CharacterField': 9}, {'GalConj': 1, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 3, 'Baselabel': '1.27.9t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1]], 'CharacterField': 9}, {'GalConj': 4, 'Baselabel': '1.27.9t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, -1, 0, 0, -1, 0], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1, 0]], 'CharacterField': 9}, {'GalConj': 2, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 5, 'Baselabel': '1.27.9t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [-1, 0, 0, -1, 0, 0], [0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]], 'CharacterField': 9}, {'GalConj': 6, 'Baselabel': '1.27.9t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]], 'CharacterField': 9}], 'ComplexConjugation': 1, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '1', 'Order': 3, 'Representative': [8, 5, 4, 9, 7, 1, 2, 6, 3]}, {'Size': '1', 'Order': 3, 'Representative': [6, 7, 9, 3, 2, 8, 5, 1, 4]}, {'Size': '1', 'Order': 9, 'Representative': [7, 3, 6, 1, 4, 5, 9, 2, 8]}, {'Size': '1', 'Order': 9, 'Representative': [9, 6, 5, 7, 1, 4, 8, 3, 2]}, {'Size': '1', 'Order': 9, 'Representative': [2, 4, 1, 8, 9, 7, 3, 5, 6]}, {'Size': '1', 'Order': 9, 'Representative': [3, 1, 7, 2, 8, 9, 6, 4, 5]}, {'Size': '1', 'Order': 9, 'Representative': [5, 9, 8, 6, 3, 2, 4, 7, 1]}, {'Size': '1', 'Order': 9, 'Representative': [4, 8, 2, 5, 6, 3, 1, 9, 7]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['1215', '1'], 'ConjugacyClass': 2}, {'RootOf': ['1242', '1'], 'ConjugacyClass': 3}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['-783', '1'], 'ConjugacyClass': 4}, {'RootOf': ['2322', '1'], 'ConjugacyClass': 5}, {'RootOf': ['1080', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-1188', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-297', '1'], 'ConjugacyClass': 8}, {'RootOf': ['-1134', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [9]}], 'Frobs': [5, 1, 4, 7, 9, 8, 2, 3, 6, 5, 6, 2, 8, 9, 7, 1, 4, 7, 8, 2, 3, 5, 5, 3, 9, 7, 4, 1, 1, 4, 3, 6, 5, 6, 8, 9, 4, 1, 4, 9, 2, 3, 5, 6, 3, 2, 4, 7, 9, 8, 2, 6, 5, 3, 8, 7, 1, 1, 7, 9, 8, 6, 2, 8, 9, 7, 7, 8, 6, 5, 5, 3, 9, 4, 1, 4, 9, 3, 6, 6, 8, 9, 1, 1, 7, 9, 2, 5, 5, 6, 3, 7, 1, 4, 8, 2, 6, 3, 2, 1, 7, 2, 6, 5, 6, 2, 7, 1, 4, 7, 8, 3, 6, 5, 2, 7, 4, 1, 4, 9, 8, 5, 5, 3, 9, 1, 7, 2, 5, 6, 2, 8, 4, 1, 4, 8, 2, 6, 8, 1, 1, 9, 8, 2, 3, 5, 9, 7, 4, 1, 8, 2, 3, 6, 9, 7, 1, 9, 3, 6, 5, 3, 4, 1, 4, 9, 3, 5], 'G-Gens': [[7, 3, 6, 1, 4, 5, 9, 2, 8], [8, 5, 4, 9, 7, 1, 2, 6, 3]], 'G-Name': 'C9', 'Polynomial': [-1, 9, 0, -30, 0, 27, 0, -9, 0, 1], 'QpRts': [['9900227', '-3563406', '2781556'], ['-11822817', '10792826', '-5665441'], ['8059992', '8019304', '-12047581'], ['-272410', '2856816', '-408615'], ['1776652', '-1506447', '2664978'], ['-680418', '6195608', '-1020627'], ['10046165', '-9286379', '3000463'], ['-9219809', '-2632202', '-1760929'], ['-7787582', '-10876120', '-11681373']], 'QpRts-minpoly': [14, 1, 0, 1], 'QpRts-p': 17, 'QpRts-prec': 6, 'Size': 9, 'TransitiveDegree': 9}