Artin representation data - 2.952.12t18.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, 7, 17], 'Baselabel': '2.952.12t18.b', 'CharacterField': 3, 'Conductor': 952, 'Container': '12t18', 'Dets': ['1.952.6t1.a.b', '1.952.6t1.a.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], [2, 2], [0, -2], [1], [0, 1], [-1, -1], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [19, 15, 20, 15, 21, 7, 2, 10, 15, 8, 1, 15, 10, 3], '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], [-2, -2], [0, 1]], [[1], [0, 2], [-1, -1]], [[1], [-1], [1]], [[1], [0, -1], [-1, -1]], [[1], [1, 1], [0, 1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0, -1]], [[1], [-1, -1]], [[1], [1, 1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1], [0, -2], [2, 2], [1], [-1, -1], [0, 1], [0], [0], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [19, 15, 20, 15, 21, 7, 2, 10, 15, 8, 1, 15, 10, 3], '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], [0, 2], [-1, -1]], [[1], [-2, -2], [0, 1]], [[1], [-1], [1]], [[1], [1, 1], [0, 1]], [[1], [0, -1], [-1, -1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [1, 1]], [[1], [0, 1]], [[1], [0, -1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '12T18', 'Galt': 18, 'HardPrimes': [2, 3, 7, 11, 17, 19, 29, 31, 53, 59, 83, 647, 1151, 1163], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [59, -122, 221, -100, -141, 266, -147, 14, 65, -52, 25, -6, 1], 'NumBadPrimes': 3, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-14, 7, 0, 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': '1.17.2t1.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': '1.136.2t1.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': '1.56.6t1.c', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [1, 1], [0, -1], [-1, 0], [0, -1], [1, 1], [-1, -1], [0, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.119.6t1.b', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [1, 1], [0, -1], [-1, 0], [0, -1], [1, 1], [1, 1], [0, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.119.6t1.b', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [0, -1], [1, 1], [-1, 0], [1, 1], [0, -1], [0, -1], [1, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.56.6t1.c', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [0, -1], [1, 1], [-1, 0], [1, 1], [0, -1], [0, 1], [-1, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.952.6t1.a', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [1, 1], [0, -1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.952.6t1.a', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [0, -1], [1, 1], [1, 1], [0, -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], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 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], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.6664.3t2.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': '2.6664.6t3.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': '2.952.6t5.b', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1, 0], [0, 2], [-2, -2], [-1, 0], [1, 1], [0, -1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.952.12t18.b', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1, 0], [2, 2], [0, -2], [1, 0], [0, 1], [-1, -1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.952.12t18.b', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1, 0], [0, -2], [2, 2], [1, 0], [-1, -1], [0, 1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.952.6t5.b', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1, 0], [-2, -2], [0, 2], [-1, 0], [0, -1], [1, 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': [12, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 1]}, {'Size': '3', 'Order': 2, 'Representative': [6, 9, 8, 11, 10, 1, 12, 3, 2, 5, 4, 7]}, {'Size': '1', 'Order': 3, 'Representative': [10, 7, 6, 2, 3, 5, 4, 1, 12, 8, 9, 11]}, {'Size': '1', 'Order': 3, 'Representative': [8, 4, 5, 7, 6, 3, 2, 10, 11, 1, 12, 9]}, {'Size': '2', 'Order': 3, 'Representative': [1, 2, 5, 4, 6, 3, 7, 8, 11, 10, 12, 9]}, {'Size': '2', 'Order': 3, 'Representative': [1, 2, 6, 4, 3, 5, 7, 8, 12, 10, 9, 11]}, {'Size': '2', 'Order': 3, 'Representative': [10, 7, 5, 2, 6, 3, 4, 1, 11, 8, 12, 9]}, {'Size': '1', 'Order': 6, 'Representative': [2, 10, 11, 1, 12, 9, 8, 4, 5, 7, 6, 3]}, {'Size': '1', 'Order': 6, 'Representative': [4, 1, 12, 8, 9, 11, 10, 7, 6, 2, 3, 5]}, {'Size': '2', 'Order': 6, 'Representative': [2, 10, 12, 1, 9, 11, 8, 4, 6, 7, 3, 5]}, {'Size': '2', 'Order': 6, 'Representative': [7, 8, 11, 10, 12, 9, 1, 2, 5, 4, 6, 3]}, {'Size': '2', 'Order': 6, 'Representative': [7, 8, 12, 10, 9, 11, 1, 2, 6, 4, 3, 5]}, {'Size': '3', 'Order': 6, 'Representative': [9, 5, 4, 6, 7, 2, 3, 11, 10, 12, 1, 8]}, {'Size': '3', 'Order': 6, 'Representative': [11, 6, 7, 3, 2, 4, 5, 12, 1, 9, 8, 10]}, {'Size': '3', 'Order': 6, 'Representative': [5, 12, 1, 9, 8, 10, 11, 6, 7, 3, 2, 4]}, {'Size': '3', 'Order': 6, 'Representative': [3, 11, 10, 12, 1, 8, 9, 5, 4, 6, 7, 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': ['2422', '92', '1'], 'ConjugacyClass': 7}, {'RootOf': ['2840', '104', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['6', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-5146', '885', '-52', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-4228', '322', '-42', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['178', '24', '1'], 'ConjugacyClass': 13}, {'RootOf': ['475', '42', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['26', '1'], 'ConjugacyClass': 5}, {'RootOf': ['14', '1'], 'ConjugacyClass': 6}, {'RootOf': ['434', '40', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['18', '1'], 'ConjugacyClass': 10}, {'RootOf': ['36', '1'], 'ConjugacyClass': 11}, {'RootOf': ['865', '54', '1'], 'ConjugacyClass': 12}, {'RootOf': ['-6378', '1151', '-52', '1'], 'ConjugacyClass': 15}, {'RootOf': ['-8632', '1074', '-52', '1'], 'ConjugacyClass': 16}, {'RootOf': ['-868', '1246', '-42', '1'], 'ConjugacyClass': 17}, {'RootOf': ['-3248', '840', '-42', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [6, 6]}], 'Frobs': [5, 15, 13, 10, 15, 4, 15, 7, 13, 2, 10, 13, 3, 9, 17, 18, 8, 11, 8, 12, 15, 11, 1, 7, 3, 18, 17, 16, 14, 3, 4, 16, 8, 3, 17, 18, 18, 16, 12, 13, 8, 12, 17, 15, 12, 14, 3, 4, 15, 17, 16, 4, 15, 1, 7, 18, 14, 17, 10, 9, 15, 4, 9, 14, 16, 13, 7, 3, 15, 4, 8, 17, 14, 17, 3, 17, 18, 13, 16, 6, 3, 4, 14, 9, 13, 7, 3, 7, 4, 4, 7, 14, 14, 9, 16, 12, 17, 15, 5, 11, 3, 18, 8, 7, 15, 6, 9, 5, 18, 3, 13, 18, 3, 15, 4, 15, 3, 18, 13, 9, 18, 3, 11, 15, 16, 4, 13, 11, 4, 17, 8, 2, 13, 4, 7, 9, 18, 15, 4, 15, 3, 13, 10, 3, 18, 12, 2, 15, 7, 17, 11, 3, 1, 11, 15, 12, 17, 16, 9, 14, 16, 9, 4, 7, 8, 14, 14, 10], 'G-Gens': [[1, 2, 5, 4, 6, 3, 7, 8, 11, 10, 12, 9], [2, 10, 11, 1, 12, 9, 8, 4, 5, 7, 6, 3], [9, 5, 4, 6, 7, 2, 3, 11, 10, 12, 1, 8], [7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6]], 'G-Name': 'C6*S3', 'Polynomial': [59, -122, 221, -100, -141, 266, -147, 14, 65, -52, 25, -6, 1], 'QpRts': [['4703720762', '-7506326084', '-12325257910', '10837306595', '4166869805', '5976304961'], ['-5014578489', '7033276915', '-4229967939', '6703746588', '-11051677402', '-320024377'], ['1139363069', '11486811174', '1240039764', '11058333527', '1819758881', '-5986444997'], ['8497446318', '9932848785', '10841182293', '-4154509142', '-1541806344', '-11792306989'], ['-2538983823', '5016592075', '1275858513', '-6241556024', '13719622426', '9391594199'], ['-5745902936', '12484287150', '4320603691', '-9994588438', '11480197504', '12339184575'], ['-2869246383', '13638219937', '7806749518', '-1073517882', '9967893602', '11843831341'], ['-5850335003', '3002083056', '-12211396899', '-3430292503', '-5388447044', '4246633925'], ['8670363788', '4659954907', '2608232436', '-6627817792', '-8822147135', '-11461869681'], ['5801539932', '1412511502', '10118690937', '-8882733656', '3847167383', '-9954438861'], ['-9372740892', '-3875621077', '-5019477620', '2482425029', '-264817000', '5241469017'], ['2579353663', '-2259410118', '-4425256784', '9323203698', '9579999435', '-9523933113']], 'QpRts-minpoly': [3, 8, 16, 19, 0, 0, 1], 'QpRts-p': 31, 'QpRts-prec': 7, 'Size': 36, 'TransitiveDegree': 12}