Artin representation data - 12.38149546589908416.18t315.a

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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, 3, 13, 31], 'Baselabel': '12.38149546589908416.18t315.a', 'CharacterField': 1, 'Conductor': 38149546589908416, 'Container': '18t315', 'Dets': ['1.31.2t1.a.a'], 'Dim': 12, 'GalConjSigns': [1], 'Galn': 9, 'GaloisConjugates': [{'Sign': 1, 'Character': [[12], [4], [2], [0], [0], [2], [0], [3], [-3], [0], [0], [0], [2], [-1], [-2], [1], [0], [-1], [-1], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [23, 23, 24, 25, 8, 7], 'LocalFactors': [[[1], [-12], [66], [-220], [495], [-792], [924], [-792], [495], [-220], [66], [-12], [1]], [[1], [-4], [2], [12], [-17], [-8], [28], [-8], [-17], [12], [2], [-4], [1]], [[1], [-2], [-4], [10], [5], [-20], [0], [20], [-5], [-10], [4], [2], [-1]], [[1], [0], [-6], [0], [15], [0], [-20], [0], [15], [0], [-6], [0], [1]], [[1], [0], [-6], [0], [15], [0], [-20], [0], [15], [0], [-6], [0], [1]], [[1], [-2], [-4], [10], [5], [-20], [0], [20], [-5], [-10], [4], [2], [-1]], [[1], [0], [0], [-4], [0], [0], [6], [0], [0], [-4], [0], [0], [1]], [[1], [-3], [3], [-4], [9], [-9], [6], [-9], [9], [-4], [3], [-3], [1]], [[1], [3], [6], [5], [0], [-9], [-12], [-9], [0], [5], [6], [3], [1]], [[1], [0], [0], [-4], [0], [0], [6], [0], [0], [-4], [0], [0], [1]], [[1], [0], [0], [0], [-3], [0], [0], [0], [3], [0], [0], [0], [-1]], [[1], [0], [0], [0], [-3], [0], [0], [0], [3], [0], [0], [0], [-1]], [[1], [-2], [2], [-2], [2], [-2], [0], [2], [-2], [2], [-2], [2], [-1]], [[1], [1], [2], [1], [2], [1], [0], [-1], [-2], [-1], [-2], [-1], [-1]], [[1], [2], [2], [0], [-2], [-2], [-2], [-2], [-2], [0], [2], [2], [1]], [[1], [-1], [2], [-3], [4], [-5], [4], [-5], [4], [-3], [2], [-1], [1]], [[1], [0], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [0], [1]], [[1], [1], [-1], [-2], [-1], [1], [0], [-1], [1], [2], [1], [-1], [-1]], [[1], [1], [2], [1], [2], [1], [0], [-1], [-2], [-1], [-2], [-1], [-1]], [[1], [0], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [0], [1]], [[1], [0], [0], [-1], [0], [0], [0], [0], [0], [-1], [0], [0], [1]], [[1], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [-1]], [[1], [0], [0], [0], [0], [0], [-1]], [[1], [1], [1], [0], [0], [0], [-1], [-1], [-1]], [[1], [-1], [-3], [3], [3], [-3], [-1], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T31', 'Galt': 31, 'HardPrimes': [2, 3, 13, 31, 173, 9130463], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [-1, 0, 13, 15, -3, 8, 2, 3, -1, 1], 'NumBadPrimes': 4, 'Proj_GAP': [1296, 3490], 'Proj_Polynomial': [-1, 0, 13, 15, -3, 8, 2, 3, -1, 1], 'Proj_nTj': [9, 31]}
• 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], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.31.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [-1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [1], [1], [1], [-1], [-1], [1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.403.2t1.a', 'Character': [[1], [-1], [1], [-1], [1], [-1], [1], [1], [1], [1], [-1], [1], [1], [1], [-1], [-1], [1], [1], [-1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.13.2t1.a', 'Character': [[1], [-1], [-1], [-1], [1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [1], [-1], [1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.5239.6t3.b', 'Character': [[2], [-2], [0], [-2], [2], [0], [2], [2], [2], [-1], [0], [0], [0], [0], [-2], [-2], [2], [0], [0], [1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.31.3t2.b', 'Character': [[2], [2], [0], [2], [2], [0], [2], [2], [2], [-1], [0], [0], [0], [0], [2], [2], [2], [0], [0], [-1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.47151.4t5.a', 'Character': [[3], [-1], [1], [3], [-1], [1], [3], [3], [3], [0], [-1], [-1], [1], [1], [-1], [-1], [-1], [1], [1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.112437.6t11.b', 'Character': [[3], [1], [-1], [-3], [-1], [1], [3], [3], [3], [0], [-1], [1], [-1], [-1], [1], [1], [-1], [-1], [1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.1461681.6t8.a', 'Character': [[3], [-1], [-1], [3], [-1], [-1], [3], [3], [3], [0], [1], [1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.3627.6t11.b', 'Character': [[3], [1], [1], [-3], [-1], [-1], [3], [3], [3], [0], [1], [-1], [1], [1], [1], [1], [-1], [1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.223075008.9t31.a', 'Character': [[6], [4], [2], [0], [2], [0], [3], [-3], [0], [0], [2], [0], [-1], [2], [1], [-2], [-1], [-1], [0], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.6371245303488.18t300.a', 'Character': [[6], [-4], [-2], [0], [2], [0], [3], [-3], [0], [0], [2], [0], [1], [-2], [-1], [2], [-1], [1], [0], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.223075008.18t319.a', 'Character': [[6], [4], [-2], [0], [2], [0], [3], [-3], [0], [0], [-2], [0], [1], [-2], [1], [-2], [-1], [1], [0], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.6371245303488.18t311.a', 'Character': [[6], [-4], [2], [0], [2], [0], [3], [-3], [0], [0], [-2], [0], [-1], [2], [-1], [2], [-1], [-1], [0], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.136736726128704.24t2893.a', 'Character': [[8], [0], [-4], [0], [0], [0], [-4], [-1], [2], [2], [0], [0], [2], [2], [0], [0], [0], [-1], [0], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.136736726128704.12t213.a', 'Character': [[8], [0], [4], [0], [0], [0], [-4], [-1], [2], [2], [0], [0], [-2], [-2], [0], [0], [0], [1], [0], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.1089589200154374269376.36t2217.a', 'Character': [[12], [-4], [-2], [0], [0], [2], [0], [3], [-3], [0], [0], [0], [-2], [1], [2], [-1], [0], [1], [-1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.1047095221348353672870336.36t2214.a', 'Character': [[12], [-4], [2], [0], [0], [-2], [0], [3], [-3], [0], [0], [0], [2], [-1], [2], [-1], [0], [-1], [1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.115122513360689390260224.36t2210.a', 'Character': [[12], [0], [0], [0], [-4], [0], [6], [-6], [0], [0], [0], [0], [0], [0], [0], [0], [2], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.36661714272901987776.36t2216.a', 'Character': [[12], [4], [-2], [0], [0], [-2], [0], [3], [-3], [0], [0], [0], [-2], [1], [-2], [1], [0], [1], [1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.38149546589908416.18t315.a', 'Character': [[12], [4], [2], [0], [0], [2], [0], [3], [-3], [0], [0], [0], [2], [-1], [-2], [1], [0], [-1], [-1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '16.18696932272396203182772719616.24t2912.a', 'Character': [[16], [0], [0], [0], [0], [0], [-8], [-2], [4], [-2], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [1], [0]], 'CharacterField': 1}], 'ComplexConjugation': 6, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '9', 'Order': 2, 'Representative': [2, 1, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '18', 'Order': 2, 'Representative': [3, 4, 1, 2, 5, 6, 8, 7, 9]}, {'Size': '27', 'Order': 2, 'Representative': [2, 1, 4, 3, 6, 5, 7, 8, 9]}, {'Size': '27', 'Order': 2, 'Representative': [2, 1, 3, 4, 6, 5, 7, 8, 9]}, {'Size': '54', 'Order': 2, 'Representative': [5, 6, 4, 3, 1, 2, 7, 9, 8]}, {'Size': '6', 'Order': 3, 'Representative': [1, 2, 3, 4, 6, 9, 7, 8, 5]}, {'Size': '8', 'Order': 3, 'Representative': [8, 1, 7, 3, 9, 5, 4, 2, 6]}, {'Size': '12', 'Order': 3, 'Representative': [8, 1, 3, 4, 9, 5, 7, 2, 6]}, {'Size': '72', 'Order': 3, 'Representative': [3, 4, 5, 6, 1, 2, 9, 7, 8]}, {'Size': '54', 'Order': 4, 'Representative': [5, 6, 3, 4, 2, 1, 7, 9, 8]}, {'Size': '162', 'Order': 4, 'Representative': [5, 6, 4, 3, 2, 1, 7, 9, 8]}, {'Size': '36', 'Order': 6, 'Representative': [3, 4, 1, 2, 6, 9, 8, 7, 5]}, {'Size': '36', 'Order': 6, 'Representative': [5, 6, 3, 4, 8, 1, 7, 9, 2]}, {'Size': '36', 'Order': 6, 'Representative': [2, 1, 3, 4, 6, 9, 7, 8, 5]}, {'Size': '36', 'Order': 6, 'Representative': [2, 1, 4, 7, 6, 9, 3, 8, 5]}, {'Size': '54', 'Order': 6, 'Representative': [2, 1, 4, 3, 9, 5, 7, 8, 6]}, {'Size': '72', 'Order': 6, 'Representative': [3, 4, 8, 1, 6, 9, 2, 7, 5]}, {'Size': '108', 'Order': 6, 'Representative': [5, 6, 4, 3, 8, 1, 7, 9, 2]}, {'Size': '216', 'Order': 6, 'Representative': [3, 4, 5, 6, 2, 1, 9, 7, 8]}, {'Size': '144', 'Order': 9, 'Representative': [3, 4, 5, 6, 8, 1, 9, 7, 2]}, {'Size': '108', 'Order': 12, 'Representative': [3, 4, 2, 1, 6, 9, 8, 7, 5]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 2]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 3]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 15, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 2, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['3077494145534709', '1632418063287264', '295925982327246', '25304896115970', '7433729896987', '6247993946922', '2144682714227', '361685738404', '45000100591', '9970715480', '3022381856', '696720558', '114610644', '13716622', '1196837', '74534', '3155', '82', '1'], 'ConjugacyClass': 3}, {'RootOf': ['220236132867884711936', '27317235712144703488', '22481538124949225472', '21537905183104696320', '-4508585975802232832', '-3749448593807769600', '-645011798444998656', '-97235176578351104', '74165788510519296', '40743006022402048', '2595495969685504', '-1538679110172672', '-393395389464576', '-36043589484544', '17013607661568', '7686895517696', '754760796160', '-150031119360', '-37101843968', '-962336000', '421837056', '37536384', '-1399872', '-322464', '-8936', '756', '54', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 2, 2, 2]}, {'Data': 0, 'Classes': 11, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 4]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 3, 3]}, {'Data': 0, 'Classes': 14, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 6]}, {'Data': 0, 'Classes': 17, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2, 3]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 2, 2]}, {'Data': 0, 'Classes': 12, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 4]}, {'Data': 0, 'Classes': 16, 'Algorithm': 'CYC', 'CycleType': [1, 2, 3, 3]}, {'Data': 0, 'Classes': 19, 'Algorithm': 'CYC', 'CycleType': [1, 2, 6]}, {'Data': 0, 'Classes': 13, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 3]}, {'Data': 0, 'Classes': 22, 'Algorithm': 'CYC', 'CycleType': [2, 3, 4]}, {'Data': {'Powers': [1, 2], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['4096', '-2048', '384', '-32', '1'], 'ConjugacyClass': 8}, {'RootOf': ['5023954195394003653365743391447097', '-3716504858024117711995473874190220', '1156067129744512169255168747921358', '-82049915355111499806072494087052', '6986343627050120198798939264409', '-14333505627698409486565976753184', '5722242706614912908897472944656', '-1019836045162258014776055410592', '96970477764955788832023858900', '-16364347918138357497743489104', '5038959967653815364753547848', '-934005635404546214385071568', '113962592016579260293995012', '-15692180333224060105776864', '2868923590490986521750000', '-387009209467494446235744', '32565956902727496849918', '-2945727115448866292808', '462664100905711541140', '-55407418618338658248', '1925566883213777646', '299800475504362272', '-7047485412418704', '-5003703204118368', '170272527901924', '48748906879920', '-1732654324536', '-405805726928', '19267848564', '2093553120', '-134864496', '-5143200', '411153', '10868', '-882', '-12', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': {'Powers': [1, 5], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['488044916207891768670994037676703744', '-632140482939779402875715868617080832', '401977422099250185169046359448223744', '-174414370432194180496653805017890816', '59943592795926199292815293997383680', '-17511048347116186917169654610788352', '4474320690112784740521565661167616', '-1015712051989411699709805443678208', '207713216273396050754194812960768', '-38679772556999731496580200529920', '6602164578765146645859795992576', '-1037880082852059328099769122816', '151005836780430186074515439616', '-20430657747560756098094858240', '2580681645246849492537311232', '-305388271226267927545118720', '33965959670537865500033024', '-3560254801584633936871424', '352366253228758383198208', '-32976468975168053837824', '2921539858567147683840', '-245174549620935229440', '19487420927632982016', '-1466426043974795264', '104390081715556352', '-7017825123684352', '444305750793216', '-26408774610944', '1468076319488', '-75817469952', '3600146624', '-155393856', '6013152', '-202192', '5488', '-104', '1'], 'ConjugacyClass': 18}, {'RootOf': ['1523940045731498250538078605843706719141331231294133937572238111845022470367607717596239960628773641', '5627184443342087380035343640757312071169957756023478964123753178389367387901217560539863541537121276', '5275197648003651732348948262243588418139763036340415558092928213672944062532704376629674924718144698', '-747746188277727250717188201223092438019735756588653302904891275655541211218267114447558345237488788', '-1848661723563621237933177889510630485414230264640541052514523024610033662991594405050883102648420793', '-394524351618366756581282395922077034797701892834527629109640407481785927754134317776732266042846504', '128702651351301454184683428694812162964056306858938043146198857521338910400300958230354634843199068', '78365198465736024909854981379959293782486564873219020520189502074005388039539644735150398000460824', '14358899971886878652220931252776183792502375574362653527805510390110442183443249648914798046276547', '-7648997526722669282414037396213498673262451195883132378958266242130862975306955412952071865761412', '-3877026304774098424981088502404495866851747873677733135039998953909411280123498607750763400927550', '1064131447624672982953369911507857152474997766349905048946451707142634620576107395886355396844300', 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