Artin representation data - 2.672.12t18.d

Formats: - HTML - YAML - JSON - 2024-04-29T13:18:09.543289

• 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, 3, 7], 'Baselabel': '2.672.12t18.d', 'CharacterField': 3, 'Conductor': 672, 'Container': '12t18', 'Dets': ['1.168.6t1.c.b', '1.168.6t1.c.a'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 12, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1], [2, 2], [0, -2], [0, 1], [-1, -1], [1], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [19, 20, 7, 20, 12, 16, 15], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [2, 2], [0, 1]], [[1], [0, -2], [-1, -1]], [[1], [-1, -1], [0, 1]], [[1], [0, 1], [-1, -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], [0, 1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1], [0, -2], [2, 2], [-1, -1], [0, 1], [1], [0], [0], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [19, 20, 7, 20, 12, 16, 15], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, -2], [-1, -1]], [[1], [2, 2], [0, 1]], [[1], [0, 1], [-1, -1]], [[1], [-1, -1], [0, 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]], [[1], [-1, -1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '12T18', 'Galt': 18, 'HardPrimes': [2, 3, 5, 7, 11, 23, 431], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 0, 0, 0, 22, 0, 2, 0, 1, 0, -2, 0, 1], 'NumBadPrimes': 3, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-6, -2, -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': '1.24.2t1.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': '1.24.2t1.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': '1.4.2t1.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': '1.28.6t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [0, 1], [-1, -1], [0, 1], [-1, -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': '1.168.6t1.b', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -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': '1.168.6t1.b', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 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': '1.168.6t1.c', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [-1, -1], [0, 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': '1.7.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -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': '1.28.6t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [-1, -1], [0, 1], [-1, -1], [0, 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': '1.7.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 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': '1.168.6t1.c', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [0, 1], [-1, -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': '2.1176.3t2.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': '2.4704.6t3.g', 'Character': [[2], [-2], [0], [0], [2], [2], [-1], [-1], [-1], [-2], [-2], [1], [1], [1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.672.12t18.d', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1, 0], [2, 2], [0, -2], [0, 1], [-1, -1], [1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.168.6t5.c', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [1, 1], [0, -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': '2.672.12t18.d', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [0, -1], [1, 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': '2.168.6t5.c', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1, 0], [0, 2], [-2, -2], [1, 1], [0, -1], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}], 'ComplexConjugation': 4, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]}, {'Size': '1', 'Order': 2, 'Representative': [7, 8, 10, 9, 12, 11, 1, 2, 4, 3, 6, 5]}, {'Size': '3', 'Order': 2, 'Representative': [5, 10, 8, 6, 1, 4, 12, 3, 11, 2, 9, 7]}, {'Size': '3', 'Order': 2, 'Representative': [12, 3, 2, 11, 7, 9, 5, 10, 6, 8, 4, 1]}, {'Size': '1', 'Order': 3, 'Representative': [3, 4, 11, 12, 8, 7, 10, 9, 5, 6, 1, 2]}, {'Size': '1', 'Order': 3, 'Representative': [11, 12, 1, 2, 9, 10, 6, 5, 8, 7, 3, 4]}, {'Size': '2', 'Order': 3, 'Representative': [11, 2, 1, 4, 5, 10, 6, 8, 9, 7, 3, 12]}, {'Size': '2', 'Order': 3, 'Representative': [3, 2, 11, 4, 5, 7, 10, 8, 9, 6, 1, 12]}, {'Size': '2', 'Order': 3, 'Representative': [3, 12, 11, 2, 9, 7, 10, 5, 8, 6, 1, 4]}, {'Size': '1', 'Order': 6, 'Representative': [10, 9, 6, 5, 2, 1, 3, 4, 12, 11, 7, 8]}, {'Size': '1', 'Order': 6, 'Representative': [6, 5, 7, 8, 4, 3, 11, 12, 2, 1, 10, 9]}, {'Size': '2', 'Order': 6, 'Representative': [10, 8, 6, 9, 12, 1, 3, 2, 4, 11, 7, 5]}, {'Size': '2', 'Order': 6, 'Representative': [6, 8, 7, 9, 12, 3, 11, 2, 4, 1, 10, 5]}, {'Size': '2', 'Order': 6, 'Representative': [6, 9, 7, 5, 2, 3, 11, 4, 12, 1, 10, 8]}, {'Size': '3', 'Order': 6, 'Representative': [9, 7, 5, 10, 11, 2, 4, 1, 3, 12, 8, 6]}, {'Size': '3', 'Order': 6, 'Representative': [8, 6, 9, 7, 3, 12, 2, 11, 1, 4, 5, 10]}, {'Size': '3', 'Order': 6, 'Representative': [4, 1, 12, 3, 6, 8, 9, 7, 10, 5, 2, 11]}, {'Size': '3', 'Order': 6, 'Representative': [2, 11, 4, 1, 10, 5, 8, 6, 7, 9, 12, 3]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['11484', '-156', '1'], 'ConjugacyClass': 7}, {'RootOf': ['9496', '-128', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['-12', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-24192', '2016', '-84', '1'], 'ConjugacyClass': 3}, {'RootOf': ['24192', '2016', '84', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['9496', '128', '1'], 'ConjugacyClass': 12}, {'RootOf': ['11484', '156', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['-80', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-108', '1'], 'ConjugacyClass': 6}, {'RootOf': ['8836', '-188', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['80', '1'], 'ConjugacyClass': 10}, {'RootOf': ['108', '1'], 'ConjugacyClass': 11}, {'RootOf': ['8836', '188', '1'], 'ConjugacyClass': 14}, {'RootOf': ['614496', '26200', '292', '1'], 'ConjugacyClass': 15}, {'RootOf': ['650112', '26844', '292', '1'], 'ConjugacyClass': 16}, {'RootOf': ['-614496', '26200', '-292', '1'], 'ConjugacyClass': 17}, {'RootOf': ['-650112', '26844', '-292', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [6, 6]}], 'Frobs': [5, 11, 7, 11, 12, 3, 15, 18, 18, 9, 12, 16, 3, 4, 18, 8, 12, 16, 17, 4, 6, 13, 14, 16, 9, 6, 10, 13, 15, 3, 14, 13, 15, 4, 5, 12, 15, 18, 4, 5, 11, 3, 18, 8, 1, 11, 4, 14, 12, 16, 16, 4, 8, 14, 16, 17, 8, 13, 15, 3, 17, 9, 4, 17, 7, 7, 18, 9, 11, 3, 15, 18, 12, 16, 4, 18, 6, 16, 16, 8, 2, 3, 17, 1, 13, 13, 3, 7, 1, 2, 10, 17, 12, 14, 18, 4, 7, 15, 18, 16, 4, 8, 12, 16, 17, 8, 14, 16, 17, 9, 13, 15, 3, 17, 14, 15, 4, 17, 7, 2, 15, 9, 7, 12, 18, 9, 16, 18, 14, 16, 17, 4, 13, 3, 16, 9, 6, 17, 9, 15, 4, 7, 11, 14, 15, 4, 3, 15, 18, 18, 16, 3, 4, 18, 17, 4, 10, 16, 9, 8, 10, 3, 14, 13, 15, 17, 12, 15], 'G-Gens': [[1, 4, 3, 12, 8, 6, 7, 9, 5, 10, 11, 2], [7, 8, 10, 9, 12, 11, 1, 2, 4, 3, 6, 5], [9, 7, 5, 10, 11, 2, 4, 1, 3, 12, 8, 6], [10, 8, 6, 9, 12, 1, 3, 2, 4, 11, 7, 5]], 'G-Name': 'C6*S3', 'Polynomial': [1, 0, 0, 0, 22, 0, 2, 0, 1, 0, -2, 0, 1], 'QpRts': [['34051472499', '-37632524077', '1305120772', '-46650935087', '23903822485', '-58198916861'], ['59137603315', '-28808662060', '-11069491164', '-9565893083', '33866705887', '-17259556136'], ['-32274819289', '12502682359', '-54888748747', '-52789169832', '-26569507386', '-1597256812'], ['-47658826266', '47917675854', '-46177179738', '-32384491259', '12329738991', '-12576406737'], ['-43414261401', '-12331042379', '-12785903434', '-50996777020', '-24233541939', '48888873871'], ['-4502541050', '-56569897891', '-9122860507', '10101378900', '45492204779', '18928663071'], ['-34051472499', '37632524077', '-1305120772', '46650935087', '-23903822485', '58198916861'], ['-59137603315', '28808662060', '11069491164', '9565893083', '-33866705887', '17259556136'], ['47658826266', '-47917675854', '46177179738', '32384491259', '-12329738991', '12576406737'], ['32274819289', '-12502682359', '54888748747', '52789169832', '26569507386', '1597256812'], ['4502541050', '56569897891', '9122860507', '-10101378900', '-45492204779', '-18928663071'], ['43414261401', '12331042379', '12785903434', '50996777020', '24233541939', '-48888873871']], 'QpRts-minpoly': [3, 3, 10, 0, 2, 0, 1], 'QpRts-p': 17, 'QpRts-prec': 9, 'Size': 36, 'TransitiveDegree': 12}