Artin representation data - 2.36703.12t19.a

Formats: - HTML - YAML - JSON - 2025-04-04T15:34:47.488762

• 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': [17, 127], 'Baselabel': '2.36703.12t19.a', 'CharacterField': 3, 'Conductor': 36703, 'Container': '12t19', 'Dets': ['1.127.3t1.a.a', '1.127.3t1.a.b'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 12, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [-2, -2], [0, 2], [-1], [1, 1], [0, -1], [0], [0], [0, -2], [2, 2], [1], [-1, -1], [0, 1], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [12, 16, 16, 19, 1, 7, 20, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [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], [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], [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, 2], [-2, -2], [-1], [0, -1], [1, 1], [0], [0], [2, 2], [0, -2], [1], [0, 1], [-1, -1], [0], [0], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [12, 16, 16, 19, 1, 7, 20, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [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], [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], [-1, -1]], [[1], [0], [0, 1]], [[1], [0], [-1, -1]], [[1], [0], [0, 1]], [[1]], [[1], [0, 1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '12T19', 'Galt': 19, 'HardPrimes': [2, 3, 7, 17, 47, 103, 127, 3229], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-13, 120, -279, -241, 1081, 249, -1027, -117, 283, 20, -29, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [47, -42, -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': '1.17.2t1.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': '1.2159.6t1.a', 'Character': [[1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [-1, 0], [-1, 0], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.127.3t1.a', 'Character': [[1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.127.3t1.a', 'Character': [[1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.2159.6t1.a', 'Character': [[1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [-1, 0], [-1, 0], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.17.4t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [0, -1], [0, 1], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [0, 1], [0, 1], [0, -1], [0, -1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '1.17.4t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [0, -1], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [0, -1], [0, -1], [0, 1], [0, 1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '1.2159.12t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, -1, 0], [-1, 0, 1, 0], [1, 0, 0, 0], [0, 0, -1, 0], [-1, 0, 1, 0], [0, 0, 0, -1], [0, 0, 0, 1], [1, 0, -1, 0], [0, 0, 1, 0], [-1, 0, 0, 0], [0, 0, 1, 0], [1, 0, -1, 0], [0, 1, 0, -1], [0, -1, 0, 0], [0, -1, 0, 1], [0, 1, 0, 0]], 'CharacterField': 12}, {'GalConj': 2, 'Baselabel': '1.2159.12t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, -1, 0], [-1, 0, 1, 0], [1, 0, 0, 0], [0, 0, -1, 0], [-1, 0, 1, 0], [0, 0, 0, 1], [0, 0, 0, -1], [1, 0, -1, 0], [0, 0, 1, 0], [-1, 0, 0, 0], [0, 0, 1, 0], [1, 0, -1, 0], [0, -1, 0, 1], [0, 1, 0, 0], [0, 1, 0, -1], [0, -1, 0, 0]], 'CharacterField': 12}, {'GalConj': 3, 'Baselabel': '1.2159.12t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [-1, 0, 1, 0], [0, 0, -1, 0], [1, 0, 0, 0], [-1, 0, 1, 0], [0, 0, -1, 0], [0, 0, 0, -1], [0, 0, 0, 1], [0, 0, 1, 0], [1, 0, -1, 0], [-1, 0, 0, 0], [1, 0, -1, 0], [0, 0, 1, 0], [0, -1, 0, 0], [0, 1, 0, -1], [0, 1, 0, 0], [0, -1, 0, 1]], 'CharacterField': 12}, {'GalConj': 4, 'Baselabel': '1.2159.12t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [-1, 0, 1, 0], [0, 0, -1, 0], [1, 0, 0, 0], [-1, 0, 1, 0], [0, 0, -1, 0], [0, 0, 0, 1], [0, 0, 0, -1], [0, 0, 1, 0], [1, 0, -1, 0], [-1, 0, 0, 0], [1, 0, -1, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, -1, 0, 1], [0, -1, 0, 0], [0, 1, 0, -1]], 'CharacterField': 12}, {'GalConj': 1, 'Baselabel': '2.274193.3t2.a', 'Character': [[2], [2], [2], [2], [-1], [-1], [-1], [0], [0], [2], [2], [-1], [-1], [-1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.4661281.12t5.a', 'Character': [[2], [-2], [2], [2], [-1], [-1], [-1], [0], [0], [-2], [-2], [1], [1], [1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.2159.6t5.a', 'Character': [[2, 0], [2, 0], [0, 2], [-2, -2], [-1, 0], [0, -1], [1, 1], [0, 0], [0, 0], [-2, -2], [0, 2], [-1, 0], [0, -1], [1, 1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.36703.12t19.a', 'Character': [[2, 0], [-2, 0], [-2, -2], [0, 2], [-1, 0], [1, 1], [0, -1], [0, 0], [0, 0], [0, -2], [2, 2], [1, 0], [-1, -1], [0, 1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.2159.6t5.a', 'Character': [[2, 0], [2, 0], [-2, -2], [0, 2], [-1, 0], [1, 1], [0, -1], [0, 0], [0, 0], [0, 2], [-2, -2], [-1, 0], [1, 1], [0, -1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.36703.12t19.a', 'Character': [[2, 0], [-2, 0], [0, 2], [-2, -2], [-1, 0], [0, -1], [1, 1], [0, 0], [0, 0], [2, 2], [0, -2], [1, 0], [0, 1], [-1, -1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}], 'ComplexConjugation': 1, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]}, {'Size': '1', 'Order': 2, 'Representative': [9, 8, 7, 12, 10, 11, 3, 2, 1, 5, 6, 4]}, {'Size': '1', 'Order': 3, 'Representative': [3, 1, 2, 6, 4, 5, 8, 9, 7, 12, 10, 11]}, {'Size': '1', 'Order': 3, 'Representative': [2, 3, 1, 5, 6, 4, 9, 7, 8, 11, 12, 10]}, {'Size': '2', 'Order': 3, 'Representative': [2, 3, 1, 6, 4, 5, 9, 7, 8, 12, 10, 11]}, {'Size': '2', 'Order': 3, 'Representative': [1, 2, 3, 5, 6, 4, 7, 8, 9, 11, 12, 10]}, {'Size': '2', 'Order': 3, 'Representative': [1, 2, 3, 6, 4, 5, 7, 8, 9, 12, 10, 11]}, {'Size': '3', 'Order': 4, 'Representative': [4, 5, 6, 9, 8, 7, 11, 10, 12, 2, 3, 1]}, {'Size': '3', 'Order': 4, 'Representative': [12, 10, 11, 1, 2, 3, 6, 5, 4, 8, 7, 9]}, {'Size': '1', 'Order': 6, 'Representative': [8, 7, 9, 10, 11, 12, 1, 3, 2, 6, 4, 5]}, {'Size': '1', 'Order': 6, 'Representative': [7, 9, 8, 11, 12, 10, 2, 1, 3, 4, 5, 6]}, {'Size': '2', 'Order': 6, 'Representative': [7, 9, 8, 10, 11, 12, 2, 1, 3, 6, 4, 5]}, {'Size': '2', 'Order': 6, 'Representative': [9, 8, 7, 10, 11, 12, 3, 2, 1, 6, 4, 5]}, {'Size': '2', 'Order': 6, 'Representative': [9, 8, 7, 11, 12, 10, 3, 2, 1, 4, 5, 6]}, {'Size': '3', 'Order': 12, 'Representative': [11, 12, 10, 3, 1, 2, 5, 4, 6, 9, 8, 7]}, {'Size': '3', 'Order': 12, 'Representative': [10, 11, 12, 2, 3, 1, 4, 6, 5, 7, 9, 8]}, {'Size': '3', 'Order': 12, 'Representative': [6, 4, 5, 7, 9, 8, 10, 12, 11, 1, 2, 3]}, {'Size': '3', 'Order': 12, 'Representative': [5, 6, 4, 8, 7, 9, 12, 11, 10, 3, 1, 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': ['-52', '-8', '1'], 'ConjugacyClass': 6}, {'RootOf': ['784', '-56', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 3, 3]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['101', '26', '1'], 'ConjugacyClass': 13}, {'RootOf': ['121', '-22', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-28', '1'], 'ConjugacyClass': 3}, {'RootOf': ['20', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-52', '-8', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-856', '172', '32', '1'], 'ConjugacyClass': 8}, {'RootOf': ['-9016', '1464', '-70', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [4, 4, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['37', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-11', '1'], 'ConjugacyClass': 11}, {'RootOf': ['101', '26', '1'], 'ConjugacyClass': 12}], 'Algorithm': 'RES', 'CycleType': [6, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-9016', '1464', '-70', '1'], 'ConjugacyClass': 15}, {'RootOf': ['5208', '956', '-70', '1'], 'ConjugacyClass': 16}, {'RootOf': ['-856', '172', '32', '1'], 'ConjugacyClass': 17}, {'RootOf': ['-3904', '-336', '32', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [12]}], 'Frobs': [12, 18, 8, 16, 15, 7, 3, 12, 16, 17, 18, 17, 15, 13, 1, 11, 13, 9, 7, 18, 8, 16, 13, 5, 18, 4, 7, 8, 15, 16, 14, 8, 1, 18, 6, 10, 4, 15, 8, 18, 14, 9, 5, 9, 16, 17, 15, 10, 9, 12, 17, 7, 18, 4, 14, 13, 18, 6, 18, 12, 15, 6, 3, 18, 15, 9, 12, 17, 15, 12, 7, 13, 16, 5, 8, 2, 2, 9, 9, 7, 9, 5, 9, 14, 17, 4, 15, 12, 2, 3, 13, 17, 15, 13, 15, 9, 1, 16, 7, 8, 17, 6, 11, 2, 9, 6, 14, 13, 3, 15, 18, 6, 17, 9, 2, 18, 8, 7, 15, 7, 14, 9, 17, 18, 16, 5, 17, 17, 7, 13, 14, 8, 17, 12, 5, 7, 13, 8, 10, 9, 17, 17, 9, 16, 4, 9, 17, 9, 10, 7, 16, 8, 4, 8, 15, 15, 4, 9, 14, 16, 17, 5, 13, 13, 13, 8, 8, 9], 'G-Gens': [[11, 12, 10, 3, 1, 2, 5, 4, 6, 9, 8, 7], [9, 8, 7, 12, 10, 11, 3, 2, 1, 5, 6, 4], [1, 2, 3, 5, 6, 4, 7, 8, 9, 11, 12, 10], [7, 9, 8, 10, 11, 12, 2, 1, 3, 6, 4, 5]], 'G-Name': 'C3^2:C4', 'Polynomial': [-13, 120, -279, -241, 1081, 249, -1027, -117, 283, 20, -29, -1, 1], 'QpRts': [['-1431336377880', '1408977576189', '-142849851233', '-732963161945'], ['1050781325804', '-1298443668278', '780597021855', '1451720602570'], ['1207244049617', '-124835194819', '163295043766', '-1124096105929'], ['-599940178312', '286465807209', '523689102312', '683290418492'], ['-646119871684', '-1247346963799', '829833997311', '292157474508'], ['-20169545282', '1460074280668', '-93612875777', '1250216546014'], ['-42114359317', '2594728098', '392779433526', '1336978663102'], ['-198577083130', '-1171013745361', '1010081411615', '770052535580'], ['462048049207', '1536407499106', '86634538527', '-1414631228935'], ['-151315342932', '1444704724525', '-773618684605', '-1287305919649'], ['474634983470', '1009383132971', '1445677278328', '-329246848143'], ['-105135649560', '-164225340488', '-1079763579604', '-896172975665']], 'QpRts-minpoly': [2, 40, 3, 0, 1], 'QpRts-p': 61, 'QpRts-prec': 7, 'Size': 36, 'TransitiveDegree': 12}