Artin representation data - 1.55.10t1.a

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• 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': [5, 11], 'Baselabel': '1.55.10t1.a', 'CharacterField': 5, 'Conductor': 55, 'Container': '10t1', 'Dets': ['55.49', '55.14', '55.4', '55.9'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 10, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 0, 0, -1], [1, 1, 1, 1], [0, -1], [0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [10, 9, 11, 11, 3, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, 0, 1]], [[1], [-1, -1, -1, -1]], [[1], [0, 1]], [[1], [0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [-1, -1, -1, -1], [0, 1], [0, 0, 0, 1], [0, -1], [0, 0, 0, -1], [0, 0, -1], [1, 1, 1, 1]], 'GalOrbIndex': 2, 'HardFactors': [10, 9, 11, 11, 3, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [-1, -1, -1, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1], [0, 0, 1], [1, 1, 1, 1], [0, 0, -1], [0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 3, 'HardFactors': [10, 9, 11, 11, 3, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, -1]], [[1], [-1, -1, -1, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1], [0, 1], [0, 0, -1], [0, -1], [1, 1, 1, 1], [0, 0, 0, -1]], 'GalOrbIndex': 4, 'HardFactors': [10, 9, 11, 11, 3, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [-1, -1, -1, -1]], [[1], [0, 0, 0, 1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '10T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 11, 19, 331], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-1, -3, 18, 7, -52, -11, 46, 8, -13, -1, 1], 'NumBadPrimes': 2, '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], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.5.2t1.a', 'Character': [[1], [-1], [1], [1], [1], [1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.11.5t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 1, 0]], 'CharacterField': 5}, {'GalConj': 1, 'Baselabel': '1.55.10t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 0, 0, -1], [1, 1, 1, 1], [0, -1, 0, 0], [0, 0, -1, 0]], 'CharacterField': 5}, {'GalConj': 2, 'Baselabel': '1.11.5t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [-1, -1, -1, -1]], 'CharacterField': 5}, {'GalConj': 2, 'Baselabel': '1.55.10t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 0, 1], [0, -1, 0, 0], [0, 0, 0, -1], [0, 0, -1, 0], [1, 1, 1, 1]], 'CharacterField': 5}, {'GalConj': 3, 'Baselabel': '1.11.5t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 0, 1, 0], [0, 0, 0, 1], [0, 1, 0, 0]], 'CharacterField': 5}, {'GalConj': 3, 'Baselabel': '1.55.10t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 1, 0], [1, 1, 1, 1], [0, 0, -1, 0], [0, 0, 0, -1], [0, -1, 0, 0]], 'CharacterField': 5}, {'GalConj': 4, 'Baselabel': '1.11.5t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1]], 'CharacterField': 5}, {'GalConj': 4, 'Baselabel': '1.55.10t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, -1, 0], [0, -1, 0, 0], [1, 1, 1, 1], [0, 0, 0, -1]], 'CharacterField': 5}], 'ComplexConjugation': 1, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]}, {'Size': '1', 'Order': 2, 'Representative': [5, 6, 8, 7, 1, 2, 4, 3, 10, 9]}, {'Size': '1', 'Order': 5, 'Representative': [6, 4, 10, 8, 2, 7, 3, 9, 5, 1]}, {'Size': '1', 'Order': 5, 'Representative': [7, 8, 1, 9, 4, 3, 10, 5, 2, 6]}, {'Size': '1', 'Order': 5, 'Representative': [3, 9, 6, 5, 8, 10, 1, 2, 4, 7]}, {'Size': '1', 'Order': 5, 'Representative': [10, 5, 7, 2, 9, 1, 6, 4, 8, 3]}, {'Size': '1', 'Order': 10, 'Representative': [8, 10, 2, 1, 3, 9, 5, 6, 7, 4]}, {'Size': '1', 'Order': 10, 'Representative': [9, 1, 4, 6, 10, 5, 2, 7, 3, 8]}, {'Size': '1', 'Order': 10, 'Representative': [2, 7, 9, 3, 6, 4, 8, 10, 1, 5]}, {'Size': '1', 'Order': 10, 'Representative': [4, 3, 5, 10, 7, 8, 9, 1, 6, 2]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [2, 5, -2, -7, 1]}, 'Classes': [{'RootOf': ['31', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-112', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-508', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-387', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [5, 5]}, {'Data': {'Powers': [1], 'Resolvent': [2, 5, -2, -7, 1]}, 'Classes': [{'RootOf': ['202', '1'], 'ConjugacyClass': 7}, {'RootOf': ['158', '1'], 'ConjugacyClass': 8}, {'RootOf': ['-29', '1'], 'ConjugacyClass': 9}, {'RootOf': ['48', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [10]}], 'Frobs': [10, 9, 5, 8, 1, 10, 7, 3, 2, 6, 4, 8, 3, 2, 9, 10, 6, 5, 2, 5, 8, 4, 7, 1, 10, 4, 8, 9, 1, 9, 7, 1, 7, 6, 5, 3, 9, 10, 10, 9, 3, 5, 6, 7, 2, 1, 4, 9, 8, 4, 10, 3, 1, 4, 8, 2, 5, 6, 10, 5, 9, 8, 2, 3, 7, 10, 1, 8, 7, 3, 2, 6, 8, 2, 5, 10, 6, 2, 5, 4, 1, 3, 4, 8, 1, 9, 4, 7, 1, 2, 7, 5, 9, 6, 6, 9, 3, 6, 7, 4, 9, 8, 10, 3, 1, 7, 8, 2, 5, 6, 10, 9, 2, 3, 6, 3, 7, 10, 8, 1, 1, 10, 7, 2, 4, 3, 5, 6, 2, 8, 4, 7, 3, 10, 4, 1, 9, 7, 7, 5, 3, 6, 10, 10, 6, 3, 7, 2, 1, 7, 9, 1, 9, 8, 7, 4, 5, 5, 10, 5, 2, 8, 2, 3, 10, 8, 1, 8], 'G-Gens': [[8, 10, 2, 1, 3, 9, 5, 6, 7, 4], [5, 6, 8, 7, 1, 2, 4, 3, 10, 9]], 'G-Name': 'C10', 'Polynomial': [-1, -3, 18, 7, -52, -11, 46, 8, -13, -1, 1], 'QpRts': [['-1199005', '-396874', '432125', '1202768', '763897'], ['-872735', '-283425', '1074908', '1084154', '1070462'], ['-507302', '420246', '-888119', '-118184', '317798'], ['-1137944', '-191862', '-353474', '-1199222', '385135'], ['-1045125', '-400469', '1051199', '674875', '-210685'], ['-1167787', '-1137195', '-421907', '479172', '-466348'], ['-1010159', '-584516', '51155', '-1094710', '-426941'], ['1203929', '-609451', '1105490', '-120415', '-886471'], ['839950', '-990892', '-402024', '-439392', '-358441'], ['-56019', '-777760', '826746', '-469046', '-188406']], 'QpRts-minpoly': [17, 5, 0, 0, 0, 1], 'QpRts-p': 19, 'QpRts-prec': 5, 'Size': 10, 'TransitiveDegree': 10}