Artin representation data - 2.2016.12t18.d

Formats: - HTML - YAML - JSON - 2026-04-21T02:39:59.236215

• 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': '2.2016.12t18.d', 'CharacterField': 3, 'Conductor': 2016, 'Container': '12t18', 'Dets': ['1.504.6t1.f.b', '1.504.6t1.f.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, 20, 7, 21, 16, 16, 3, 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], [-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, 20, 7, 21, 16, 16, 3, 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], [1]], [[1], [0, 1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '12T18', 'Galt': 18, 'HardPrimes': [2, 3, 5, 7, 67, 149, 271, 12277], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [625, -500, 200, -80, -34, 120, -80, 36, -7, -4, 8, -4, 1], 'NumBadPrimes': 3, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-26, -3, 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': '1.56.2t1.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': '1.56.2t1.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': '1.504.6t1.f', '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': '1.9.3t1.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': '1.9.3t1.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': '1.36.6t1.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': '1.504.6t1.m', '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': '1.504.6t1.f', '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': '1.504.6t1.m', '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': '1.36.6t1.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': '2.4536.3t2.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': '2.18144.6t3.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': '2.504.6t5.b', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1, 0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.2016.12t18.d', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1, 0], [0, -2], [2, 2], [0, 1], [-1, -1], [1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.504.6t5.b', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1, 0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.2016.12t18.d', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1, 0], [2, 2], [0, -2], [-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': [11, 3, 2, 6, 7, 4, 5, 9, 8, 12, 1, 10]}, {'Size': '3', 'Order': 2, 'Representative': [5, 9, 8, 12, 1, 10, 11, 3, 2, 6, 7, 4]}, {'Size': '1', 'Order': 3, 'Representative': [12, 7, 5, 3, 4, 2, 6, 1, 11, 9, 10, 8]}, {'Size': '1', 'Order': 3, 'Representative': [8, 6, 4, 5, 3, 7, 2, 12, 10, 11, 9, 1]}, {'Size': '2', 'Order': 3, 'Representative': [1, 2, 4, 5, 3, 6, 7, 8, 10, 11, 9, 12]}, {'Size': '2', 'Order': 3, 'Representative': [1, 2, 5, 3, 4, 6, 7, 8, 11, 9, 10, 12]}, {'Size': '2', 'Order': 3, 'Representative': [8, 6, 5, 3, 4, 7, 2, 12, 11, 9, 10, 1]}, {'Size': '1', 'Order': 6, 'Representative': [6, 1, 11, 9, 10, 8, 12, 7, 5, 3, 4, 2]}, {'Size': '1', 'Order': 6, 'Representative': [2, 12, 10, 11, 9, 1, 8, 6, 4, 5, 3, 7]}, {'Size': '2', 'Order': 6, 'Representative': [7, 8, 10, 11, 9, 12, 1, 2, 4, 5, 3, 6]}, {'Size': '2', 'Order': 6, 'Representative': [7, 8, 11, 9, 10, 12, 1, 2, 5, 3, 4, 6]}, {'Size': '2', 'Order': 6, 'Representative': [2, 12, 11, 9, 10, 1, 8, 6, 5, 3, 4, 7]}, {'Size': '3', 'Order': 6, 'Representative': [9, 4, 6, 7, 2, 5, 3, 10, 12, 1, 8, 11]}, {'Size': '3', 'Order': 6, 'Representative': [10, 5, 7, 2, 6, 3, 4, 11, 1, 8, 12, 9]}, {'Size': '3', 'Order': 6, 'Representative': [3, 10, 12, 1, 8, 11, 9, 4, 6, 7, 2, 5]}, {'Size': '3', 'Order': 6, 'Representative': [4, 11, 1, 8, 12, 9, 10, 5, 7, 2, 6, 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': [0, 0, 1]}, 'Classes': [{'RootOf': ['322', '28', '1'], 'ConjugacyClass': 7}, {'RootOf': ['4', '4', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-20', '1'], 'ConjugacyClass': 2}, {'RootOf': ['2168', '-18', '12', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-2168', '-18', '-12', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['322', '-28', '1'], 'ConjugacyClass': 12}, {'RootOf': ['4', '-4', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-16', '1'], 'ConjugacyClass': 5}, {'RootOf': ['8', '1'], 'ConjugacyClass': 6}, {'RootOf': ['142', '-8', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['16', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-8', '1'], 'ConjugacyClass': 11}, {'RootOf': ['142', '8', '1'], 'ConjugacyClass': 14}, {'RootOf': ['5408', '36', '12', '1'], 'ConjugacyClass': 15}, {'RootOf': ['-30016', '-126', '12', '1'], 'ConjugacyClass': 16}, {'RootOf': ['-5408', '36', '-12', '1'], 'ConjugacyClass': 17}, {'RootOf': ['30016', '-126', '-12', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [6, 6]}], 'Frobs': [6, 2, 7, 11, 17, 5, 3, 14, 12, 15, 18, 3, 16, 17, 17, 3, 10, 8, 18, 14, 3, 13, 11, 3, 15, 8, 18, 4, 3, 7, 14, 12, 6, 12, 16, 13, 7, 4, 18, 6, 4, 9, 13, 7, 3, 4, 18, 17, 13, 7, 9, 12, 15, 14, 16, 13, 9, 4, 15, 8, 12, 7, 14, 18, 15, 15, 17, 5, 18, 6, 15, 14, 17, 16, 4, 18, 15, 1, 7, 16, 12, 15, 2, 3, 17, 17, 9, 8, 8, 12, 2, 17, 14, 18, 18, 4, 5, 3, 14, 3, 17, 3, 12, 6, 18, 3, 13, 3, 10, 15, 18, 3, 5, 13, 14, 8, 10, 4, 16, 17, 7, 8, 6, 4, 13, 3, 15, 4, 17, 7, 4, 10, 12, 3, 16, 16, 9, 10, 7, 1, 2, 15, 10, 4, 1, 17, 8, 15, 10, 14, 16, 3, 4, 18, 17, 13, 14, 15, 3, 7, 17, 1, 12, 14, 5, 17, 2, 8], 'G-Gens': [[1, 2, 4, 5, 3, 6, 7, 8, 10, 11, 9, 12], [9, 4, 6, 7, 2, 5, 3, 10, 12, 1, 8, 11], [12, 7, 5, 3, 4, 2, 6, 1, 11, 9, 10, 8], [7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6]], 'G-Name': 'C6*S3', 'Polynomial': [625, -500, 200, -80, -34, 120, -80, 36, -7, -4, 8, -4, 1], 'QpRts': [['298401620', '309057712', '-278068698', '-209408578', '-317221707', '107019125'], ['-90600663', '-269545748', '237392542', '-3066360', '-282285827', '16389048'], ['-159760550', '10113099', '316663917', '90777703', '243195835', '200786379'], ['-443976546', '-280643846', '-72874867', '-391348815', '365844358', '328006246'], ['-243713319', '398168338', '326296320', '178264367', '163132845', '-21621190'], ['-234527834', '-325499816', '128028732', '-83219659', '-162353530', '358545001'], ['-255020772', '-223886064', '-217148601', '340345502', '-428136007', '147438747'], ['225543159', '-342833992', '-66322667', '-329112474', '-47932289', '-433628190'], ['-401351252', '-183577867', '-138542146', '429729314', '190381438', '-214649693'], ['-333817352', '-42185828', '408896749', '210217541', '-262484559', '-23101349'], ['249636886', '98126104', '53431766', '376231629', '193801822', '-269420393'], ['-398556851', '-41163831', '196118692', '284461569', '344057621', '-195763731']], 'QpRts-minpoly': [2, 6, 17, 17, 0, 0, 1], 'QpRts-p': 19, 'QpRts-prec': 7, 'Size': 36, 'TransitiveDegree': 12}