Artin representation data - 2.1539.24t21.a

Formats: - HTML - YAML - JSON - 2023-06-08T05:09:47.264457

• 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': [3, 19], 'Baselabel': '2.1539.24t21.a', 'CharacterField': 4, 'Conductor': 1539, 'Container': '24t21', 'Dets': ['1.19.2t1.a.a', '1.19.2t1.a.a'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 16, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [-1], [-1], [0, -2], [0, 2], [0], [1], [1], [0, 1], [0, 1], [0, -1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [13, 15, 16, 4, 13, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [1], [1]], [[1], [0, 2], [-1]], [[1], [0, -2], [-1]], [[1], [0], [1]], [[1], [-1], [1]], [[1], [-1], [1]], [[1], [0, -1], [-1]], [[1], [0, -1], [-1]], [[1], [0, 1], [-1]], [[1], [0, 1], [-1]], [[1]], [[1], [0, -1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [-1], [-1], [0, 2], [0, -2], [0], [1], [1], [0, -1], [0, -1], [0, 1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [13, 15, 16, 4, 13, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [1], [1]], [[1], [0, -2], [-1]], [[1], [0, 2], [-1]], [[1], [0], [1]], [[1], [-1], [1]], [[1], [-1], [1]], [[1], [0, 1], [-1]], [[1], [0, 1], [-1]], [[1], [0, -1], [-1]], [[1], [0, -1], [-1]], [[1]], [[1], [0, 1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '16T60', 'Galt': 60, 'HardPrimes': [2, 3, 19, 1031, 1181, 27253], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, -1, 9, -23, 43, -57, 55, -23, -12, 32, -27, 15, -1, -4, 6, -3, 1], 'NumBadPrimes': 2, 'Proj_GAP': [12, 3], 'Proj_Polynomial': [20, 1, 3, -1, 1], 'Proj_nTj': [4, 4]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.19.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [-1], [-1], [1], [1], [1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.171.6t1.f', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, -1], [0, 1], [-1, 0], [-1, 0], [1, 0], [0, 1], [-1, -1], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.171.6t1.f', 'Character': [[1, 0], [1, 0], [-1, 0], [0, 1], [-1, -1], [-1, 0], [-1, 0], [1, 0], [-1, -1], [0, 1], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.1539.24t21.a', 'Character': [[2, 0], [-2, 0], [0, 0], [-1, 0], [-1, 0], [0, -2], [0, 2], [0, 0], [1, 0], [1, 0], [0, 1], [0, 1], [0, -1], [0, -1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '2.1539.24t21.a', 'Character': [[2, 0], [-2, 0], [0, 0], [-1, 0], [-1, 0], [0, 2], [0, -2], [0, 0], [1, 0], [1, 0], [0, -1], [0, -1], [0, 1], [0, 1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '2.171.16t60.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [1, 0, -1, 0], [0, 0, 0, 2], [0, 0, 0, -2], [0, 0, 0, 0], [-1, 0, 1, 0], [0, 0, -1, 0], [0, -1, 0, 1], [0, 1, 0, 0], [0, 1, 0, -1], [0, -1, 0, 0]], 'CharacterField': 12}, {'GalConj': 2, 'Baselabel': '2.171.16t60.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [1, 0, -1, 0], [0, 0, 1, 0], [0, 0, 0, -2], [0, 0, 0, 2], [0, 0, 0, 0], [0, 0, -1, 0], [-1, 0, 1, 0], [0, -1, 0, 0], [0, 1, 0, -1], [0, 1, 0, 0], [0, -1, 0, 1]], 'CharacterField': 12}, {'GalConj': 3, 'Baselabel': '2.171.16t60.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [1, 0, -1, 0], [0, 0, 1, 0], [0, 0, 0, 2], [0, 0, 0, -2], [0, 0, 0, 0], [0, 0, -1, 0], [-1, 0, 1, 0], [0, 1, 0, 0], [0, -1, 0, 1], [0, -1, 0, 0], [0, 1, 0, -1]], 'CharacterField': 12}, {'GalConj': 4, 'Baselabel': '2.171.16t60.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [1, 0, -1, 0], [0, 0, 0, -2], [0, 0, 0, 2], [0, 0, 0, 0], [-1, 0, 1, 0], [0, 0, -1, 0], [0, 1, 0, -1], [0, -1, 0, 0], [0, -1, 0, 1], [0, 1, 0, 0]], 'CharacterField': 12}, {'GalConj': 1, 'Baselabel': '3.1539.6t6.a', 'Character': [[3], [3], [1], [0], [0], [-3], [-3], [-1], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.29241.4t4.b', 'Character': [[3], [3], [-1], [0], [0], [3], [3], [-1], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]}, {'Size': '1', 'Order': 2, 'Representative': [9, 10, 11, 12, 13, 14, 15, 16, 1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '6', 'Order': 2, 'Representative': [14, 7, 12, 11, 8, 9, 2, 5, 6, 15, 4, 3, 16, 1, 10, 13]}, {'Size': '4', 'Order': 3, 'Representative': [7, 8, 10, 9, 5, 6, 12, 11, 15, 16, 2, 1, 13, 14, 4, 3]}, {'Size': '4', 'Order': 3, 'Representative': [12, 11, 16, 15, 5, 6, 1, 2, 4, 3, 8, 7, 13, 14, 9, 10]}, {'Size': '1', 'Order': 4, 'Representative': [8, 4, 7, 10, 6, 13, 11, 9, 16, 12, 15, 2, 14, 5, 3, 1]}, {'Size': '1', 'Order': 4, 'Representative': [16, 12, 15, 2, 14, 5, 3, 1, 8, 4, 7, 10, 6, 13, 11, 9]}, {'Size': '6', 'Order': 4, 'Representative': [13, 3, 10, 7, 1, 8, 12, 14, 5, 11, 2, 15, 9, 16, 4, 6]}, {'Size': '4', 'Order': 6, 'Representative': [4, 3, 8, 7, 13, 14, 9, 10, 12, 11, 16, 15, 5, 6, 1, 2]}, {'Size': '4', 'Order': 6, 'Representative': [15, 16, 2, 1, 13, 14, 4, 3, 7, 8, 10, 9, 5, 6, 12, 11]}, {'Size': '4', 'Order': 12, 'Representative': [11, 9, 12, 16, 6, 13, 2, 15, 3, 1, 4, 8, 14, 5, 10, 7]}, {'Size': '4', 'Order': 12, 'Representative': [2, 15, 1, 3, 6, 13, 8, 4, 10, 7, 9, 11, 14, 5, 16, 12]}, {'Size': '4', 'Order': 12, 'Representative': [3, 1, 4, 8, 14, 5, 10, 7, 11, 9, 12, 16, 6, 13, 2, 15]}, {'Size': '4', 'Order': 12, 'Representative': [10, 7, 9, 11, 14, 5, 16, 12, 2, 15, 1, 3, 6, 13, 8, 4]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['4680', '672', '54', '9', '1'], 'ConjugacyClass': 4}, {'RootOf': ['4299', '730', '63', '3', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['17', '1'], 'ConjugacyClass': 2}, {'RootOf': ['10392', '2988', '-870', '-403', '-18', '9', '1'], 'ConjugacyClass': 3}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['6051', '1050', '105', '11', '1'], 'ConjugacyClass': 9}, {'RootOf': ['19520', '3232', '84', '5', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [2, 2, 6, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-5', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-9', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-1623', '468', '-411', '-56', '108', '-18', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [4, 4, 4, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['18966', '111', '69', '-8', '1'], 'ConjugacyClass': 11}, {'RootOf': ['1688', '332', '120', '7', '1'], 'ConjugacyClass': 12}, {'RootOf': ['495', '206', '81', '3', '1'], 'ConjugacyClass': 13}, {'RootOf': ['3861', '651', '-63', '-12', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [4, 12]}], 'Frobs': [13, 14, 9, 10, 4, 14, 8, 7, 5, 11, 12, 3, 14, 10, 10, 3, 12, 4, 12, 3, 8, 11, 4, 3, 13, 10, 14, 3, 6, 12, 3, 9, 4, 5, 9, 13, 9, 8, 14, 11, 7, 3, 10, 12, 8, 8, 14, 13, 11, 5, 8, 5, 11, 8, 14, 10, 3, 8, 10, 13, 9, 12, 3, 5, 4, 13, 11, 14, 5, 4, 10, 8, 4, 12, 3, 12, 4, 8, 14, 12, 9, 13, 3, 3, 13, 10, 6, 10, 10, 9, 2, 4, 3, 9, 5, 8, 12, 6, 3, 8, 11, 1, 14, 13, 5, 8, 4, 8, 12, 11, 12, 8, 9, 4, 8, 13, 5, 8, 5, 13, 14, 13, 13, 3, 4, 8, 10, 8, 4, 9, 1, 14, 14, 8, 5, 9, 7, 14, 14, 1, 3, 4, 9, 3, 3, 13, 10, 11, 9, 3, 14, 8, 8, 12, 13, 11, 8, 10, 8, 12, 10, 3, 9, 3, 14, 13, 3, 10], 'G-Gens': [[7, 8, 10, 9, 5, 6, 12, 11, 15, 16, 2, 1, 13, 14, 4, 3], [12, 16, 14, 1, 15, 3, 5, 2, 4, 8, 6, 9, 7, 11, 13, 10], [9, 10, 11, 12, 13, 14, 15, 16, 1, 2, 3, 4, 5, 6, 7, 8], [13, 3, 10, 7, 1, 8, 12, 14, 5, 11, 2, 15, 9, 16, 4, 6], [8, 4, 7, 10, 6, 13, 11, 9, 16, 12, 15, 2, 14, 5, 3, 1]], 'G-Name': 'SL2(F3):C2', 'Polynomial': [1, -1, 9, -23, 43, -57, 55, -23, -12, 32, -27, 15, -1, -4, 6, -3, 1], 'QpRts': [['152451188502203', '137472685283749', '154342777782583', '-55020595850744', '-228448295156525', '26036241376137'], ['-225269417067431', '-207529121109203', '230646516391495', '43402735467305', '102929267385015', '-188215108299921'], ['142582015760015', '-75968382766930', '50546572833613', '30044602081068', '221072513511354', '-237901318702629'], ['32366218071345', '-130431949632101', '158930532157861', '-211923300727797', '-226513620316950', '97499747675543'], ['113836942107865', '-248290613164160', '229955558434548', '228196895533786', '165218278502225', '172948104856128'], ['45811883027021', '-11077082067592', '-136919566443540', '157155174365223', '56633177046289', '-237746135252136'], ['83244780867968', '-89578135038654', '-241125898887939', '-218383258630658', '-196398149123986', '-4006403587935'], ['-86934594610968', '151988819168851', '212262564988591', '-50391004294468', '-64973214079697', '-146548127958997'], ['37507088048590', '-15641077355032', '-213391321861404', '-215829949641592', '-246191699279671', '173556774181065'], ['89647071696450', '243871739245924', '-115791942636174', '28211052330570', '-187634616867145', '-100941164615128'], ['147499504991365', '75968382766930', '-50546572833613', '-30044602081068', '-221072513511354', '237901318702629'], ['54934420256280', '173097860462462', '-193545764590591', '207676203062940', '-203458866960697', '-129651983935681'], ['-125219482096921', '83793094405082', '-136291781922997', '46900747623407', '236801591274775', '162203727783651'], ['112197444724694', '180557915949842', '-109319543318562', '-46680369711589', '-160614790267800', '60566108579996'], ['-22212557469331', '89578135038654', '241125898887939', '218383258630658', '196398149123986', '4006403587935'], ['-49849894872299', '144780340749021', '-80878028981810', '-131697588157041', '-248932435153505', '110291815609343']], 'QpRts-minpoly': [3, 21, 28, 19, 0, 0, 1], 'QpRts-p': 43, 'QpRts-prec': 9, 'Size': 48, 'TransitiveDegree': 16}