Artin representation data - 2.3040.12t18.c

Formats: - HTML - YAML - JSON - 2024-09-10T07:12:16.420026

• 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': '2.3040.12t18.c', 'CharacterField': 3, 'Conductor': 3040, 'Container': '12t18', 'Dets': ['1.760.6t1.b.b', '1.760.6t1.b.a'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 12, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1], [0, -2], [2, 2], [0, 1], [-1, -1], [1], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [19, 15, 20, 10, 15, 20, 7, 7, 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], [0, 1], [-1, -1]], [[1], [-1, -1], [0, 1]], [[1], [1], [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], [0, -1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1]], [[1], [-1, -1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1], [2, 2], [0, -2], [-1, -1], [0, 1], [1], [0], [0], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [19, 15, 20, 10, 15, 20, 7, 7, 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], [-1, -1], [0, 1]], [[1], [0, 1], [-1, -1]], [[1], [1], [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], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1]], [[1], [0, 1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '12T18', 'Galt': 18, 'HardPrimes': [2, 3, 5, 13, 17, 19, 23, 127, 1367], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [41, -52, 92, -60, 79, -52, 58, -36, 28, -16, 10, -4, 1], 'NumBadPrimes': 3, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [26, -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], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.20.2t1.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': '1.40.2t1.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.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': '1.760.6t1.b', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.19.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.19.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.152.6t1.b', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [0, -1], [1, 1], [0, -1], [1, 1], [-1, 0], [-1, -1], [0, 1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.380.6t1.b', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [0, -1], [1, 1], [0, -1], [1, 1], [-1, 0], [1, 1], [0, -1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.760.6t1.b', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.380.6t1.b', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [1, 1], [0, -1], [1, 1], [0, -1], [-1, 0], [0, -1], [1, 1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.152.6t1.b', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [1, 1], [0, -1], [1, 1], [0, -1], [-1, 0], [0, 1], [-1, -1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.14440.3t2.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': '2.57760.6t3.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': '2.760.6t5.a', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1, 0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.3040.12t18.c', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1, 0], [0, -2], [2, 2], [0, 1], [-1, -1], [1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.760.6t5.a', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1, 0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.3040.12t18.c', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1, 0], [2, 2], [0, -2], [-1, -1], [0, 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': [7, 11, 12, 8, 9, 10, 1, 4, 5, 6, 2, 3]}, {'Size': '3', 'Order': 2, 'Representative': [4, 3, 2, 1, 6, 5, 8, 7, 10, 9, 12, 11]}, {'Size': '3', 'Order': 2, 'Representative': [8, 12, 11, 7, 10, 9, 4, 1, 6, 5, 3, 2]}, {'Size': '1', 'Order': 3, 'Representative': [3, 6, 5, 2, 1, 4, 12, 11, 7, 8, 10, 9]}, {'Size': '1', 'Order': 3, 'Representative': [5, 4, 1, 6, 3, 2, 9, 10, 12, 11, 8, 7]}, {'Size': '2', 'Order': 3, 'Representative': [1, 4, 3, 6, 5, 2, 7, 10, 9, 11, 8, 12]}, {'Size': '2', 'Order': 3, 'Representative': [1, 6, 3, 2, 5, 4, 7, 11, 9, 8, 10, 12]}, {'Size': '2', 'Order': 3, 'Representative': [5, 6, 1, 2, 3, 4, 9, 11, 12, 8, 10, 7]}, {'Size': '1', 'Order': 6, 'Representative': [12, 10, 9, 11, 7, 8, 3, 2, 1, 4, 6, 5]}, {'Size': '1', 'Order': 6, 'Representative': [9, 8, 7, 10, 12, 11, 5, 6, 3, 2, 4, 1]}, {'Size': '2', 'Order': 6, 'Representative': [7, 8, 12, 10, 9, 11, 1, 6, 5, 2, 4, 3]}, {'Size': '2', 'Order': 6, 'Representative': [7, 10, 12, 11, 9, 8, 1, 2, 5, 4, 6, 3]}, {'Size': '2', 'Order': 6, 'Representative': [9, 10, 7, 11, 12, 8, 5, 2, 3, 4, 6, 1]}, {'Size': '3', 'Order': 6, 'Representative': [6, 1, 4, 5, 2, 3, 10, 9, 11, 12, 7, 8]}, {'Size': '3', 'Order': 6, 'Representative': [2, 5, 6, 3, 4, 1, 11, 12, 8, 7, 9, 10]}, {'Size': '3', 'Order': 6, 'Representative': [10, 7, 8, 9, 11, 12, 6, 5, 2, 3, 1, 4]}, {'Size': '3', 'Order': 6, 'Representative': [11, 9, 10, 12, 8, 7, 2, 3, 4, 1, 5, 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': ['44', '4', '1'], 'ConjugacyClass': 7}, {'RootOf': ['64', '16', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['16', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-768', '236', '-28', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-160', '-20', '-4', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['140', '20', '1'], 'ConjugacyClass': 12}, {'RootOf': ['256', '32', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['8', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-4', '1'], 'ConjugacyClass': 6}, {'RootOf': ['44', '4', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['16', '1'], 'ConjugacyClass': 10}, {'RootOf': ['4', '1'], 'ConjugacyClass': 11}, {'RootOf': ['140', '20', '1'], 'ConjugacyClass': 14}, {'RootOf': ['1664', '160', '-28', '1'], 'ConjugacyClass': 15}, {'RootOf': ['-768', '236', '-28', '1'], 'ConjugacyClass': 16}, {'RootOf': ['1664', '-96', '-4', '1'], 'ConjugacyClass': 17}, {'RootOf': ['-160', '-20', '-4', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [6, 6]}], 'Frobs': [6, 17, 17, 9, 14, 10, 15, 12, 7, 18, 3, 14, 8, 17, 5, 12, 11, 18, 18, 15, 15, 15, 4, 7, 15, 18, 9, 4, 17, 3, 7, 13, 16, 10, 17, 3, 13, 4, 7, 13, 14, 18, 3, 15, 14, 16, 13, 8, 4, 4, 15, 3, 5, 10, 16, 8, 17, 15, 2, 7, 17, 14, 17, 3, 16, 12, 14, 15, 17, 4, 3, 15, 5, 14, 2, 6, 18, 13, 6, 7, 14, 17, 16, 16, 15, 18, 9, 3, 17, 9, 4, 16, 9, 13, 13, 7, 18, 1, 18, 18, 18, 12, 4, 9, 2, 3, 17, 16, 16, 9, 9, 13, 16, 14, 16, 6, 17, 9, 14, 12, 18, 3, 14, 4, 14, 17, 18, 15, 6, 14, 13, 8, 16, 13, 9, 5, 12, 4, 14, 1, 12, 18, 7, 18, 4, 15, 11, 15, 12, 9, 13, 9, 18, 5, 17, 3, 3, 8, 16, 18, 17, 15, 6, 11, 3, 8, 15, 12], 'G-Gens': [[7, 11, 12, 8, 9, 10, 1, 4, 5, 6, 2, 3], [6, 1, 4, 5, 2, 3, 10, 9, 11, 12, 7, 8], [1, 4, 3, 6, 5, 2, 7, 10, 9, 11, 8, 12], [3, 6, 5, 2, 1, 4, 12, 11, 7, 8, 10, 9]], 'G-Name': 'C6*S3', 'Polynomial': [41, -52, 92, -60, 79, -52, 58, -36, 28, -16, 10, -4, 1], 'QpRts': [['-12458536', '386070224', '-148838308', '-65268002', '88443206', '-187088770'], ['286168368', '175840286', '-46179036', '-212989762', '277934083', '45960220'], ['320364347', '100153897', '270722224', '99814112', '-190120617', '-240446565'], ['-310712702', '-182040835', '10561543', '333885634', '234887247', '176763217'], ['344361177', '-405457327', '-251934980', '-375548514', '152547714', '103280535'], ['-263282317', '86967343', '-94433571', '353832445', '353779694', '268752484'], ['-405848888', '-211594786', '-334047839', '162066934', '326439911', '300991337'], ['111627667', '36024876', '-174647988', '-254510151', '-342846769', '-150887397'], ['-49029175', '-187391616', '378586210', '-148213578', '390544419', '-224370079'], ['159058052', '305033054', '-279643102', '-234563340', '-223954322', '-58898130'], ['-107221984', '393905997', '-231388567', '14345174', '-299799933', '-281690394'], ['-73026005', '318219608', '85512693', '327149048', '47876088', '247633542']], 'QpRts-minpoly': [2, 11, 11, 10, 0, 0, 1], 'QpRts-p': 13, 'QpRts-prec': 8, 'Size': 36, 'TransitiveDegree': 12}