Artin representation data - 2.3800.12t18.e

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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': [2, 5, 19], 'Baselabel': '2.3800.12t18.e', 'CharacterField': 3, 'Conductor': 3800, 'Container': '12t18', 'Dets': ['1.152.6t1.c.b', '1.152.6t1.c.a'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 12, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, 2], [-2, -2], [1, 1], [0, -1], [-1], [0, -2], [2, 2], [-1, -1], [0, 1], [1], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [19, 13, 20, 1, 15, 21, 3, 8, 10, 13, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, -2], [-1, -1]], [[1], [2, 2], [0, 1]], [[1], [-1, -1], [0, 1]], [[1], [0, 1], [-1, -1]], [[1], [1], [1]], [[1], [0, 2], [-1, -1]], [[1], [-2, -2], [0, 1]], [[1], [1, 1], [0, 1]], [[1], [0, -1], [-1, -1]], [[1], [-1], [1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0, 1]], [[1]], [[1], [0, -1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [-2, -2], [0, 2], [0, -1], [1, 1], [-1], [2, 2], [0, -2], [0, 1], [-1, -1], [1], [0], [0], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [19, 13, 20, 1, 15, 21, 3, 8, 10, 13, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [2, 2], [0, 1]], [[1], [0, -2], [-1, -1]], [[1], [0, 1], [-1, -1]], [[1], [-1, -1], [0, 1]], [[1], [1], [1]], [[1], [-2, -2], [0, 1]], [[1], [0, 2], [-1, -1]], [[1], [0, -1], [-1, -1]], [[1], [1, 1], [0, 1]], [[1], [-1], [1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [-1, -1]], [[1]], [[1], [1, 1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '12T18', 'Galt': 18, 'HardPrimes': [2, 3, 5, 11, 13, 19, 37, 131, 283, 307, 19961], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [2339, -672, 2012, -1480, -120, 238, -164, 224, -70, -20, 17, -6, 1], 'NumBadPrimes': 3, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-88, 32, -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], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.40.2t1.b', 'Character': [[1], [-1], [-1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.8.2t1.b', 'Character': [[1], [1], [-1], [-1], [1], [1], [1], [1], [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], [-1], [-1], [-1], [-1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.152.6t1.c', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.95.6t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [1, 1], [0, -1], [0, -1], [1, 1], [-1, 0], [0, 1], [-1, -1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.19.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.19.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.760.6t1.b', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [1, 1], [0, -1], [0, -1], [1, 1], [-1, 0], [0, -1], [1, 1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.152.6t1.c', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.760.6t1.b', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [0, -1], [1, 1], [1, 1], [0, -1], [-1, 0], [1, 1], [0, -1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.95.6t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [0, -1], [1, 1], [1, 1], [0, -1], [-1, 0], [-1, -1], [0, 1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.72200.3t2.a', 'Character': [[2], [2], [0], [0], [2], [2], [-1], [-1], [-1], [2], [2], [-1], [-1], [-1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.72200.6t3.e', 'Character': [[2], [-2], [0], [0], [2], [2], [-1], [-1], [-1], [-2], [-2], [1], [1], [1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.3800.6t5.c', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [1, 1], [0, -1], [-1, 0], [0, 2], [-2, -2], [1, 1], [0, -1], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.3800.12t18.e', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [1, 1], [0, -1], [-1, 0], [0, -2], [2, 2], [-1, -1], [0, 1], [1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.3800.6t5.c', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [0, -1], [1, 1], [-1, 0], [-2, -2], [0, 2], [0, -1], [1, 1], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.3800.12t18.e', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [0, -1], [1, 1], [-1, 0], [2, 2], [0, -2], [0, 1], [-1, -1], [1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}], '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': [4, 6, 5, 1, 3, 2, 10, 12, 11, 7, 9, 8]}, {'Size': '3', 'Order': 2, 'Representative': [9, 3, 2, 11, 6, 5, 12, 10, 1, 8, 4, 7]}, {'Size': '3', 'Order': 2, 'Representative': [11, 5, 6, 9, 2, 3, 8, 7, 4, 12, 1, 10]}, {'Size': '1', 'Order': 3, 'Representative': [8, 11, 4, 12, 1, 9, 2, 5, 10, 6, 7, 3]}, {'Size': '1', 'Order': 3, 'Representative': [5, 7, 12, 3, 8, 10, 11, 1, 6, 9, 2, 4]}, {'Size': '2', 'Order': 3, 'Representative': [1, 11, 3, 4, 5, 9, 2, 8, 10, 6, 7, 12]}, {'Size': '2', 'Order': 3, 'Representative': [1, 7, 3, 4, 5, 10, 11, 8, 6, 9, 2, 12]}, {'Size': '2', 'Order': 3, 'Representative': [8, 7, 4, 12, 1, 10, 11, 5, 6, 9, 2, 3]}, {'Size': '1', 'Order': 6, 'Representative': [12, 9, 1, 8, 4, 11, 6, 3, 7, 2, 10, 5]}, {'Size': '1', 'Order': 6, 'Representative': [3, 10, 8, 5, 12, 7, 9, 4, 2, 11, 6, 1]}, {'Size': '2', 'Order': 6, 'Representative': [4, 9, 5, 1, 3, 11, 6, 12, 7, 2, 10, 8]}, {'Size': '2', 'Order': 6, 'Representative': [4, 10, 5, 1, 3, 7, 9, 12, 2, 11, 6, 8]}, {'Size': '2', 'Order': 6, 'Representative': [12, 10, 1, 8, 4, 7, 9, 3, 2, 11, 6, 5]}, {'Size': '3', 'Order': 6, 'Representative': [6, 12, 7, 2, 10, 8, 4, 9, 5, 1, 3, 11]}, {'Size': '3', 'Order': 6, 'Representative': [10, 4, 11, 7, 9, 1, 3, 6, 8, 5, 12, 2]}, {'Size': '3', 'Order': 6, 'Representative': [2, 8, 10, 6, 7, 12, 1, 11, 3, 4, 5, 9]}, {'Size': '3', 'Order': 6, 'Representative': [7, 1, 9, 10, 11, 4, 5, 2, 12, 3, 8, 6]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['3425', '-30', '1'], 'ConjugacyClass': 7}, {'RootOf': ['4950', '100', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-30', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-144838', '-1993', '24', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-63068', '3682', '-46', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['50', '0', '1'], 'ConjugacyClass': 12}, {'RootOf': ['900', '-60', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-60', '1'], 'ConjugacyClass': 5}, {'RootOf': ['70', '1'], 'ConjugacyClass': 6}, {'RootOf': ['75', '10', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['30', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-30', '1'], 'ConjugacyClass': 11}, {'RootOf': ['50', '0', '1'], 'ConjugacyClass': 14}, {'RootOf': ['343462', '477', '24', '1'], 'ConjugacyClass': 15}, {'RootOf': ['4312', '1142', '24', '1'], 'ConjugacyClass': 16}, {'RootOf': ['-260668', '2162', '-46', '1'], 'ConjugacyClass': 17}, {'RootOf': ['87032', '-1828', '-46', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [6, 6]}], 'Frobs': [10, 13, 16, 4, 1, 17, 13, 7, 17, 15, 3, 4, 5, 10, 17, 17, 8, 15, 11, 16, 13, 16, 14, 7, 13, 15, 4, 14, 16, 14, 17, 8, 12, 6, 16, 3, 18, 2, 17, 18, 9, 15, 3, 13, 4, 15, 8, 18, 14, 3, 13, 3, 6, 6, 12, 18, 16, 16, 4, 7, 10, 4, 13, 3, 12, 17, 9, 10, 10, 3, 14, 16, 17, 4, 9, 18, 15, 18, 5, 6, 9, 16, 15, 12, 16, 11, 9, 14, 16, 4, 14, 15, 4, 5, 8, 17, 15, 1, 12, 15, 12, 17, 14, 9, 9, 2, 13, 11, 15, 9, 4, 18, 12, 1, 15, 8, 13, 4, 4, 7, 15, 2, 4, 14, 9, 16, 15, 16, 18, 4, 8, 18, 15, 18, 1, 7, 17, 14, 4, 9, 6, 15, 17, 11, 3, 16, 18, 10, 7, 4, 18, 9, 12, 17, 13, 3, 3, 8, 12, 15, 10, 10, 18, 8, 2, 18, 16, 17], 'G-Gens': [[4, 6, 5, 1, 3, 2, 10, 12, 11, 7, 9, 8], [6, 12, 7, 2, 10, 8, 4, 9, 5, 1, 3, 11], [1, 11, 3, 4, 5, 9, 2, 8, 10, 6, 7, 12], [8, 11, 4, 12, 1, 9, 2, 5, 10, 6, 7, 3]], 'G-Name': 'C6*S3', 'Polynomial': [2339, -672, 2012, -1480, -120, 238, -164, 224, -70, -20, 17, -6, 1], 'QpRts': [['9325105753', '5893304382', '-20019581662', '15878234998', '23176385749', '2566921348'], ['-20746622423', '-16833709999', '22325094704', '-27800626142', '32771726734', '30938764865'], ['-30048981080', '16270579371', '-11449327296', '15926560883', '-3167231602', '-34993428637'], ['-25941403367', '-23975652122', '26512707741', '21555477641', '17183690075', '-12613661305'], ['14883710382', '21361455903', '-36792557397', '-5913033573', '-25576317315', '17183239362'], ['16448608443', '3999407163', '18304969872', '-17529768502', '14829207904', '16840161895'], ['-32688202540', '10804666713', '28712787522', '32026493790', '5219366290', '38266538308'], ['1454080995', '4337133855', '27076523269', '7739536891', '-21360432086', '19527928255'], ['-10670518030', '-18108608980', '-19532967748', '38473628471', '12370284894', '37108370695'], ['12059068311', '4686951596', '-19561256779', '-36227362944', '32649879115', '-1445770457'], ['27771927836', '-25562850854', '-21302266436', '-21930605964', '-14230729372', '-30172406857'], ['38153225726', '17127322972', '5725874210', '-22198535549', '4445154895', '-4895672191']], 'QpRts-minpoly': [5, 1, 9, 9, 1, 0, 1], 'QpRts-p': 23, 'QpRts-prec': 8, 'Size': 36, 'TransitiveDegree': 12}