Artin representation data - 2.3800.12t18.d

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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.d', '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], [-2, -2], [0, 2], [-1], [0, -1], [1, 1], [0, -2], [2, 2], [1], [0, 1], [-1, -1], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [19, 13, 20, 3, 10, 21, 16, 8, 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]], [[1], [0, 1], [-1, -1]], [[1], [-1, -1], [0, 1]], [[1], [0, 2], [-1, -1]], [[1], [-2, -2], [0, 1]], [[1], [-1], [1]], [[1], [0, -1], [-1, -1]], [[1], [1, 1], [0, 1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0, 1]], [[1]], [[1], [1, 1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, 2], [-2, -2], [-1], [1, 1], [0, -1], [2, 2], [0, -2], [1], [-1, -1], [0, 1], [0], [0], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [19, 13, 20, 3, 10, 21, 16, 8, 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]], [[1], [-1, -1], [0, 1]], [[1], [0, 1], [-1, -1]], [[1], [-2, -2], [0, 1]], [[1], [0, 2], [-1, -1]], [[1], [-1], [1]], [[1], [1, 1], [0, 1]], [[1], [0, -1], [-1, -1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [-1, -1]], [[1]], [[1], [0, -1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '12T18', 'Galt': 18, 'HardPrimes': [2, 3, 5, 7, 17, 19, 47, 499, 691], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [9, 12, -16, -24, 45, 50, -6, -42, 13, 10, -1, -2, 1], 'NumBadPrimes': 3, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [7, 13, -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': '1.5.2t1.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': '1.8.2t1.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': '1.40.2t1.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': '1.760.6t1.b', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [0, -1], [1, 1], [-1, 0], [0, -1], [1, 1], [0, 1], [-1, -1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.95.6t1.a', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [0, -1], [1, 1], [-1, 0], [0, -1], [1, 1], [0, -1], [1, 1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.95.6t1.a', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [1, 1], [0, -1], [-1, 0], [1, 1], [0, -1], [1, 1], [0, -1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.152.6t1.c', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [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, 0], [-1, -1], [0, 1], [1, 1], [0, -1], [-1, 0], [1, 1], [0, -1], [-1, -1], [0, 1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.152.6t1.c', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [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], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [-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, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.2888.3t2.b', '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.c', 'Character': [[2], [-2], [0], [0], [2], [2], [-1], [-1], [-1], [-2], [-2], [1], [1], [1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.152.6t5.a', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [-1, 0], [0, -1], [1, 1], [0, 2], [-2, -2], [-1, 0], [0, -1], [1, 1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.152.6t5.a', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [-1, 0], [1, 1], [0, -1], [-2, -2], [0, 2], [-1, 0], [1, 1], [0, -1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.3800.12t18.d', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [-1, 0], [0, -1], [1, 1], [0, -2], [2, 2], [1, 0], [0, 1], [-1, -1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.3800.12t18.d', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [-1, 0], [1, 1], [0, -1], [2, 2], [0, -2], [1, 0], [-1, -1], [0, 1], [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, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6]}, {'Size': '3', 'Order': 2, 'Representative': [6, 11, 10, 9, 8, 1, 12, 5, 4, 3, 2, 7]}, {'Size': '3', 'Order': 2, 'Representative': [9, 12, 7, 11, 10, 8, 3, 6, 1, 5, 4, 2]}, {'Size': '1', 'Order': 3, 'Representative': [10, 1, 11, 8, 12, 3, 4, 7, 5, 2, 6, 9]}, {'Size': '1', 'Order': 3, 'Representative': [2, 10, 6, 7, 9, 11, 8, 4, 12, 1, 3, 5]}, {'Size': '2', 'Order': 3, 'Representative': [10, 1, 6, 8, 9, 11, 4, 7, 12, 2, 3, 5]}, {'Size': '2', 'Order': 3, 'Representative': [1, 2, 11, 4, 12, 3, 7, 8, 5, 10, 6, 9]}, {'Size': '2', 'Order': 3, 'Representative': [1, 2, 6, 4, 9, 11, 7, 8, 12, 10, 3, 5]}, {'Size': '1', 'Order': 6, 'Representative': [8, 4, 12, 1, 3, 5, 2, 10, 6, 7, 9, 11]}, {'Size': '1', 'Order': 6, 'Representative': [4, 7, 5, 2, 6, 9, 10, 1, 11, 8, 12, 3]}, {'Size': '2', 'Order': 6, 'Representative': [8, 4, 5, 1, 6, 9, 2, 10, 11, 7, 12, 3]}, {'Size': '2', 'Order': 6, 'Representative': [7, 8, 5, 10, 6, 9, 1, 2, 11, 4, 12, 3]}, {'Size': '2', 'Order': 6, 'Representative': [7, 8, 12, 10, 3, 5, 1, 2, 6, 4, 9, 11]}, {'Size': '3', 'Order': 6, 'Representative': [3, 6, 10, 5, 8, 1, 9, 12, 4, 11, 2, 7]}, {'Size': '3', 'Order': 6, 'Representative': [6, 11, 1, 9, 4, 2, 12, 5, 7, 3, 10, 8]}, {'Size': '3', 'Order': 6, 'Representative': [9, 12, 4, 11, 2, 7, 3, 6, 10, 5, 8, 1]}, {'Size': '3', 'Order': 6, 'Representative': [12, 5, 7, 3, 10, 8, 6, 11, 1, 9, 4, 2]}], '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': ['96', '-16', '1'], 'ConjugacyClass': 8}, {'RootOf': ['432', '24', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-4', '1'], 'ConjugacyClass': 2}, {'RootOf': ['172', '33', '2', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-11008', '528', '-8', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['6', '4', '1'], 'ConjugacyClass': 13}, {'RootOf': ['27', '-6', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-32', '1'], 'ConjugacyClass': 5}, {'RootOf': ['8', '1'], 'ConjugacyClass': 6}, {'RootOf': ['656', '-24', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-2', '1'], 'ConjugacyClass': 10}, {'RootOf': ['8', '1'], 'ConjugacyClass': 11}, {'RootOf': ['41', '6', '1'], 'ConjugacyClass': 12}, {'RootOf': ['20', '14', '2', '1'], 'ConjugacyClass': 15}, {'RootOf': ['-56', '-5', '2', '1'], 'ConjugacyClass': 16}, {'RootOf': ['-1280', '224', '-8', '1'], 'ConjugacyClass': 17}, {'RootOf': ['3584', '-80', '-8', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [6, 6]}], 'Frobs': [15, 13, 15, 3, 7, 16, 10, 8, 16, 18, 4, 3, 8, 10, 16, 16, 8, 18, 14, 17, 13, 17, 12, 5, 13, 18, 3, 2, 17, 12, 16, 8, 14, 9, 17, 4, 15, 12, 16, 15, 7, 18, 4, 10, 3, 18, 6, 15, 12, 4, 13, 4, 9, 9, 14, 15, 17, 17, 3, 9, 13, 3, 13, 4, 14, 16, 7, 13, 13, 4, 12, 17, 16, 3, 1, 15, 18, 15, 8, 9, 1, 17, 18, 11, 17, 14, 7, 12, 17, 3, 12, 18, 3, 6, 8, 16, 18, 7, 11, 18, 11, 16, 12, 1, 7, 12, 10, 14, 18, 7, 3, 15, 14, 1, 18, 8, 13, 3, 3, 5, 18, 2, 3, 2, 1, 17, 18, 17, 15, 3, 8, 15, 18, 15, 7, 5, 16, 12, 3, 7, 5, 18, 16, 14, 4, 17, 15, 13, 9, 3, 15, 7, 14, 16, 13, 4, 4, 8, 14, 18, 10, 13, 15, 8, 12, 15, 17, 16], 'G-Gens': [[6, 11, 10, 9, 8, 1, 12, 5, 4, 3, 2, 7], [1, 2, 11, 4, 12, 3, 7, 8, 5, 10, 6, 9], [8, 4, 5, 1, 6, 9, 2, 10, 11, 7, 12, 3], [7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6]], 'G-Name': 'C6*S3', 'Polynomial': [9, 12, -16, -24, 45, 50, -6, -42, 13, 10, -1, -2, 1], 'QpRts': [['-595924578', '-1106519744', '-2124490726', '962587910', '-2371146698', '-2054200619'], ['3040199995', '2809805371', '-987768934', '-369140165', '-2424073695', '-324915178'], ['-3481856889', '-3262034006', '827132459', '115268206', '302023456', '1462775851'], ['2051743942', '-1330138067', '540350059', '1032952934', '3368102144', '1862228583'], ['-175502760', '492901100', '-3315721598', '2697873805', '812679136', '-454673672'], ['-1170635562', '-3377637634', '-3095868459', '-71275337', '-1884040992', '3446497155'], ['2445910766', '3257892577', '1546428294', '-2182010113', '-2394312204', '-2232008970'], ['1643832638', '1162870582', '-2749474765', '2622583743', '1341005370', '-74933642'], ['2759885721', '2953105551', '-204731657', '-2537813576', '2550228996', '2228767817'], ['-1610005321', '2181846722', '-3200801369', '-2066974309', '2480425083', '2823829826'], ['-3157535085', '2754539291', '1606039588', '1429533695', '-3078944595', '1621770406'], ['-1750112865', '439125698', '-2792607774', '-1633586793', '1298053999', '-1329380116']], 'QpRts-minpoly': [3, 3, 10, 0, 2, 0, 1], 'QpRts-p': 17, 'QpRts-prec': 8, 'Size': 36, 'TransitiveDegree': 12}