Artin representation data - 12.137686639750742016.18t315.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, 11], 'Baselabel': '12.137686639750742016.18t315.a', 'CharacterField': 1, 'Conductor': 137686639750742016, 'Container': '18t315', 'Dets': ['1.4.2t1.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, 24, 25, 11, 4], '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], [1], [0], [-1], [-1]], [[1], [0], [0], [0], [-2], [0], [0], [0], [1]], [[1], [1], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T31', 'Galt': 31, 'HardPrimes': [2, 3, 11, 31, 101], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [24, -8, -20, 24, 6, -10, 5, -2, -1, 1], 'NumBadPrimes': 3, 'Proj_GAP': [1296, 3490], 'Proj_Polynomial': [24, -8, -20, 24, 6, -10, 5, -2, -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': '1.4.2t1.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': '1.3.2t1.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': '1.12.2t1.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': '2.4356.6t3.d', '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': '2.484.3t2.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': '3.17424.4t5.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': '3.23232.6t11.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': '3.69696.6t8.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': '3.5808.6t11.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': '6.340139712.9t31.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': '6.440821066752.18t300.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': '6.5442235392.18t319.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': '6.27551316672.18t311.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': '8.1137906113642496.24t2893.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': '8.4444945756416.12t213.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': '12.178441885116961652736.36t2217.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': '12.11152617819810103296.36t2214.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': '12.2399052011016928886784.36t2210.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': '12.2202986236011872256.36t2216.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': '12.137686639750742016.18t315.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': '16.41801082239958968923324416.24t2912.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, 9, 6, 7, 8, 5]}, {'Size': '27', 'Order': 2, 'Representative': [2, 1, 4, 3, 5, 7, 6, 8, 9]}, {'Size': '27', 'Order': 2, 'Representative': [2, 1, 4, 3, 5, 6, 7, 8, 9]}, {'Size': '54', 'Order': 2, 'Representative': [2, 1, 6, 7, 8, 3, 4, 5, 9]}, {'Size': '6', 'Order': 3, 'Representative': [1, 2, 3, 4, 5, 7, 8, 6, 9]}, {'Size': '8', 'Order': 3, 'Representative': [2, 9, 4, 5, 3, 7, 8, 6, 1]}, {'Size': '12', 'Order': 3, 'Representative': [1, 2, 4, 5, 3, 7, 8, 6, 9]}, {'Size': '72', 'Order': 3, 'Representative': [3, 4, 6, 7, 8, 1, 2, 9, 5]}, {'Size': '54', 'Order': 4, 'Representative': [4, 3, 1, 2, 9, 6, 7, 8, 5]}, {'Size': '162', 'Order': 4, 'Representative': [7, 6, 3, 5, 4, 1, 2, 9, 8]}, {'Size': '36', 'Order': 6, 'Representative': [3, 4, 1, 2, 9, 7, 8, 6, 5]}, {'Size': '36', 'Order': 6, 'Representative': [6, 7, 3, 4, 5, 2, 9, 1, 8]}, {'Size': '36', 'Order': 6, 'Representative': [2, 1, 3, 4, 5, 7, 8, 6, 9]}, {'Size': '36', 'Order': 6, 'Representative': [2, 1, 4, 5, 3, 7, 8, 6, 9]}, {'Size': '54', 'Order': 6, 'Representative': [2, 1, 4, 3, 5, 8, 6, 7, 9]}, {'Size': '72', 'Order': 6, 'Representative': [3, 4, 2, 9, 1, 7, 8, 6, 5]}, {'Size': '108', 'Order': 6, 'Representative': [2, 1, 6, 7, 8, 4, 5, 3, 9]}, {'Size': '216', 'Order': 6, 'Representative': [4, 3, 6, 7, 8, 1, 2, 9, 5]}, {'Size': '144', 'Order': 9, 'Representative': [3, 4, 6, 7, 8, 2, 9, 1, 5]}, {'Size': '108', 'Order': 12, 'Representative': [4, 3, 1, 2, 9, 7, 8, 6, 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': ['-603696794697728', '-1440233073672192', '-1167672006344704', '-329718701899776', '-2209176074240', '-1017490383872', '-4349986092224', '-1020721233920', '-41642258944', '12902670528', '1648416176', '-1971264', '-9470176', '-31712', '56284', '496', '-152', '12', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-241379645873391541403935155', '-445208422412685663329846288', '-338111116068420376913098603', '-144560293804810834341026519', '-39548444800330245515053068', '-5741448746391220536093048', '192136265305044693911256', '338557454633913467104284', '95648556630804645787506', '16186407265354037291404', '1866917309638613581162', '148245381571614858702', '6856068030260740710', '-128828235414408252', '-68887468448498514', '-8997684117789750', '-797778772801995', '-51366896587908', '-2092199030119', '2546011413', '9566346174', '1058312112', '79373106', '4609350', '202713', '6228', '117', '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': ['625', '500', '150', '20', '1'], 'ConjugacyClass': 8}, {'RootOf': ['329358679317574052926582468724452753408', '8086173110879859560093530742920839168', '-105827722255709898124350376303189295104', '31429511285394490781493012055191453696', '5196399642770137235470794322478104576', '-5197695715745102301536933733994594304', '1520839544108415386298930061155237888', '-272664330749119641928287236183293952', '37959972405614923625953570091696128', '-5166538217151496423802463538118656', '738086951062566273296947663077376', '-96104905005580726758468235558912', '10427898937424635056443432894464', '-1004355495237468314188687343616', '97999764758527363525502042112', '-9680597308697963679858556928', '855001484090307301320556544', '-64365832349122365424664576', '4533819289573685835694080', '-332603925072024617549824', '22925244828873747779584', '-1194155930252549603328', '39689824251229999104', '-630036658386034688', '-69588546777204736', '19151371624370176', '-2493068500888064', '190660315828224', '-8248041593088', '80663183744', '14883917312', '-1161264192', '47516656', '-1248848', '21272', '-216', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': {'Powers': [1, 5], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['14517620971533852890092889557958656', '-20290840896989427549726502324535296', '8032375861387713520120116302577664', '-555593860888381805092408542101504', '-117027300123657491619957135966208', '34992545761538315135412421787648', '-3341503580880723727743850053632', '5378927155212026660558369161216', '105097522677714817252116697088', '-144477041389151680067847847936', '33365941257034970425844428800', '4419225703238509463120818176', '940456504815775571993728000', '65944339151980448749402112', '-40692552716034330321263616', '1957932181967791933009920', '583259296427449126646656', '-130178880040410263117440', '-17719888418302193728', '1733489032501076565440', '-87452409342759222080', '-11096182482047375152', '1382923614021951424', '39534347135345648', '-13000268453432783', '-27457118959156', '81118544671186', '-644578439780', '-344570189425', '4767359080', '1013312124', '-21449208', '-1889569', '63100', '1362', '-84', '1'], 'ConjugacyClass': 18}, {'RootOf': ['1238387879834798197332025924472931394584345551277848288008230440290571815405243076113213658161654059072035096432214016', '-701730559516338467010934629779516617907708470931691432539609714791414067639806375321170319829829399854173527614685184', '209019240358910282887860693802903902456315443602487767363981528333180389956863331209052432071171432439073525997764608', '-82716573021916651796872478518508029896999420964149868179728309648020750582905022000709707480205829596541553314103296', '28510573547599667839256095258757305711676607195196550439127259923259630177097813680490118844875998283035807676628992', '-6379384051089464691541466337632757390131408141492467003713056429182955906944873719144772954882986976864080693821440', '1530925966520467249478927375511445851926932199423603967967010682248258179247120688698413693247695050566819574185984', '-476567553672478441685784674830876374711247531941588536548087792743871902638854476799672902074069086441566243913728', '107400525097978060696972512849846588361808053120531122206441174774612984879122498576598041908071087119126207922176', 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