Artin representation data - 2.3700.12t18.b

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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, 37], 'Baselabel': '2.3700.12t18.b', 'CharacterField': 3, 'Conductor': 3700, 'Container': '12t18', 'Dets': ['1.148.6t1.b.b', '1.148.6t1.b.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, 15, 20, 15, 3, 11, 3, 21, 3, 15, 13, 1, 16], '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], [0, -1]], [[1], [0], [1, 1]], [[1], [-1, -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, 15, 20, 15, 3, 11, 3, 21, 3, 15, 13, 1, 16], '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], [1, 1]], [[1], [0], [0, -1]], [[1], [0, 1]], [[1]], [[1], [-1, -1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '12T18', 'Galt': 18, 'HardPrimes': [2, 3, 5, 7, 11, 13, 23, 37, 47, 107, 157, 269, 271], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 4, -7, -28, 43, 42, -72, -28, 49, 12, -10, -2, 1], 'NumBadPrimes': 3, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [26, -12, -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': '1.4.2t1.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': '1.20.2t1.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': '1.148.6t1.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], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.37.3t1.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], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.37.3t1.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], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.740.6t1.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], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.185.6t1.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], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.148.6t1.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], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.185.6t1.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], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.740.6t1.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], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.5476.3t2.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': '2.136900.6t3.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': '2.3700.12t18.b', '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': '2.148.6t5.b', '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': '2.3700.12t18.b', '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': '2.148.6t5.b', '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, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6]}, {'Size': '3', 'Order': 2, 'Representative': [9, 4, 7, 2, 6, 5, 3, 10, 1, 8, 12, 11]}, {'Size': '3', 'Order': 2, 'Representative': [2, 1, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3]}, {'Size': '1', 'Order': 3, 'Representative': [12, 3, 5, 7, 2, 4, 6, 9, 11, 1, 8, 10]}, {'Size': '1', 'Order': 3, 'Representative': [10, 5, 2, 6, 3, 7, 4, 11, 8, 12, 9, 1]}, {'Size': '2', 'Order': 3, 'Representative': [1, 5, 2, 4, 3, 6, 7, 11, 8, 10, 9, 12]}, {'Size': '2', 'Order': 3, 'Representative': [1, 3, 5, 4, 2, 6, 7, 9, 11, 10, 8, 12]}, {'Size': '2', 'Order': 3, 'Representative': [10, 3, 5, 6, 2, 7, 4, 9, 11, 12, 8, 1]}, {'Size': '1', 'Order': 6, 'Representative': [6, 9, 11, 1, 8, 10, 12, 3, 5, 7, 2, 4]}, {'Size': '1', 'Order': 6, 'Representative': [4, 11, 8, 12, 9, 1, 10, 5, 2, 6, 3, 7]}, {'Size': '2', 'Order': 6, 'Representative': [7, 9, 11, 10, 8, 12, 1, 3, 5, 4, 2, 6]}, {'Size': '2', 'Order': 6, 'Representative': [7, 11, 8, 10, 9, 12, 1, 5, 2, 4, 3, 6]}, {'Size': '2', 'Order': 6, 'Representative': [6, 11, 8, 1, 9, 10, 12, 5, 2, 7, 3, 4]}, {'Size': '3', 'Order': 6, 'Representative': [8, 6, 4, 5, 7, 3, 2, 12, 10, 11, 1, 9]}, {'Size': '3', 'Order': 6, 'Representative': [11, 7, 6, 3, 4, 2, 5, 1, 12, 9, 10, 8]}, {'Size': '3', 'Order': 6, 'Representative': [3, 12, 10, 8, 1, 11, 9, 6, 4, 2, 7, 5]}, {'Size': '3', 'Order': 6, 'Representative': [5, 10, 1, 9, 12, 8, 11, 4, 7, 3, 6, 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': ['416', '-8', '1'], 'ConjugacyClass': 7}, {'RootOf': ['1360', '-56', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['8', '1'], 'ConjugacyClass': 2}, {'RootOf': ['8', '9', '8', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-512', '144', '-32', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['85', '14', '1'], 'ConjugacyClass': 12}, {'RootOf': ['26', '2', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-24', '1'], 'ConjugacyClass': 5}, {'RootOf': ['24', '1'], 'ConjugacyClass': 6}, {'RootOf': ['16', '0', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['6', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-6', '1'], 'ConjugacyClass': 11}, {'RootOf': ['1', '0', '1'], 'ConjugacyClass': 14}, {'RootOf': ['-214', '9', '8', '1'], 'ConjugacyClass': 15}, {'RootOf': ['156', '46', '8', '1'], 'ConjugacyClass': 16}, {'RootOf': ['-9984', '736', '-32', '1'], 'ConjugacyClass': 17}, {'RootOf': ['13696', '144', '-32', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [6, 6]}], 'Frobs': [10, 15, 8, 15, 4, 11, 13, 18, 3, 9, 4, 14, 8, 3, 3, 10, 17, 8, 15, 18, 2, 18, 16, 7, 14, 9, 3, 15, 7, 10, 16, 17, 14, 17, 9, 18, 13, 16, 15, 13, 4, 8, 4, 14, 13, 4, 4, 3, 15, 8, 14, 17, 6, 4, 13, 15, 1, 17, 12, 7, 15, 12, 3, 17, 13, 13, 17, 12, 3, 7, 13, 4, 15, 12, 17, 15, 8, 14, 1, 7, 17, 9, 18, 14, 18, 3, 6, 12, 5, 15, 3, 17, 3, 4, 18, 16, 7, 6, 15, 9, 3, 13, 3, 9, 17, 10, 15, 14, 18, 7, 16, 13, 10, 4, 17, 7, 3, 15, 12, 18, 8, 11, 14, 16, 17, 5, 1, 17, 15, 11, 4, 15, 4, 13, 7, 1, 12, 3, 10, 6, 18, 6, 16, 15, 5, 17, 13, 14, 4, 16, 14, 8, 15, 3, 15, 4, 4, 8, 13, 7, 16, 10, 15, 17, 10, 16, 4, 10], 'G-Gens': [[12, 3, 5, 7, 2, 4, 6, 9, 11, 1, 8, 10], [8, 6, 4, 5, 7, 3, 2, 12, 10, 11, 1, 9], [7, 9, 11, 10, 8, 12, 1, 3, 5, 4, 2, 6], [7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6]], 'G-Name': 'C6*S3', 'Polynomial': [1, 4, -7, -28, 43, 42, -72, -28, 49, 12, -10, -2, 1], 'QpRts': [['-2525999371', '-2937681124', '-141020936', '956343096', '3513763624', '1004246170'], ['-4628245536', '77325767', '-2009549036', '-4180504443', '2338584486', '1654745347'], ['-2804424238', '389742368', '-1577642362', '4615731578', '564008735', '-5187951160'], ['1165689951', '-2192629178', '5195760187', '-4104016311', '5014270302', '2966766612'], ['1349629863', '4667921878', '-3481772088', '3510801206', '-2740370679', '2560401873'], ['906947385', '-3133604139', '2436644776', '5025573029', '-4230838567', '-1393466541'], ['4288283938', '-349678884', '-4610463313', '-2329744942', '1193902086', '-4630148716'], ['1641865507', '2798640123', '2215746578', '-1825323586', '2573889833', '3758005272'], ['1948390558', '1881152045', '-640233179', '-2865628179', '-3666231838', '-5109700389'], ['1700799715', '-3551891567', '-4815155345', '-1725762280', '778837706', '-4717004227'], ['1670226808', '789717192', '-5111049286', '744923424', '930119463', '2324499057'], ['-4713164578', '1560985519', '1934234631', '2177607408', '4334564222', '-3834892671']], 'QpRts-minpoly': [2, 11, 11, 10, 0, 0, 1], 'QpRts-p': 13, 'QpRts-prec': 9, 'Size': 36, 'TransitiveDegree': 12}