Artin representation data - 8.17703899136.12t213.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, 7, 11], 'Baselabel': '8.17703899136.12t213.a', 'CharacterField': 1, 'Conductor': 17703899136, 'Container': '12t213', 'Dets': ['1.1.1t1.a.a'], 'Dim': 8, 'GalConjSigns': [1], 'Galn': 9, 'GaloisConjugates': [{'Sign': 1, 'Character': [[8], [0], [4], [0], [0], [0], [-4], [-1], [2], [2], [0], [0], [-2], [-2], [0], [0], [0], [1], [0], [0], [-1], [0]], 'GalOrbIndex': 1, 'HardFactors': [23, 24, 25, 26], 'LocalFactors': [[[1], [-8], [28], [-56], [70], [-56], [28], [-8], [1]], [[1], [0], [-4], [0], [6], [0], [-4], [0], [1]], [[1], [-4], [4], [4], [-10], [4], [4], [-4], [1]], [[1], [0], [-4], [0], [6], [0], [-4], [0], [1]], [[1], [0], [-4], [0], [6], [0], [-4], [0], [1]], [[1], [0], [-4], [0], [6], [0], [-4], [0], [1]], [[1], [4], [10], [16], [19], [16], [10], [4], [1]], [[1], [1], [1], [-2], [-2], [-2], [1], [1], [1]], [[1], [-2], [1], [-2], [4], [-2], [1], [-2], [1]], [[1], [-2], [1], [-2], [4], [-2], [1], [-2], [1]], [[1], [0], [0], [0], [-2], [0], [0], [0], [1]], [[1], [0], [0], [0], [-2], [0], [0], [0], [1]], [[1], [2], [4], [4], [5], [4], [4], [2], [1]], [[1], [2], [1], [-2], [-4], [-2], [1], [2], [1]], [[1], [0], [2], [0], [3], [0], [2], [0], [1]], [[1], [0], [-1], [0], [0], [0], [-1], [0], [1]], [[1], [0], [2], [0], [3], [0], [2], [0], [1]], [[1], [-1], [1], [-2], [2], [-2], [1], [-1], [1]], [[1], [0], [-1], [0], [0], [0], [-1], [0], [1]], [[1], [0], [-1], [0], [0], [0], [-1], [0], [1]], [[1], [1], [1], [1], [1], [1], [1], [1], [1]], [[1], [0], [0], [0], [1], [0], [0], [0], [1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [0], [0], [-2], [0], [0], [1]], [[1], [0], [0], [0], [0], [0], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T31', 'Galt': 31, 'HardPrimes': [2, 3, 7, 11], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [1, 0, -4, 3, 3, 1, -3, 0, -1, 1], 'NumBadPrimes': 4, 'Proj_GAP': [1296, 3490], 'Proj_Polynomial': [1, 0, -4, 3, 3, 1, -3, 0, -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': '1.231.2t1.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': '1.77.2t1.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': '2.231.6t3.f', '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': '2.231.3t2.a', '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': '3.133056.4t5.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': '3.10245312.6t11.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': '3.3415104.6t8.d', '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': '3.44352.6t11.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': '6.10245312.9t31.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': '6.60744454848.18t300.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': '6.546700093632.18t319.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': '6.92207808.18t311.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': '8.622345892187672576.24t2893.b', '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': '8.17703899136.12t213.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': '12.82806855030922962272256.36t2217.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': '12.13966411710393483264.36t2214.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': '12.206479430726457256574976.36t2210.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': '12.82806855030922962272256.36t2216.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': '12.13966411710393483264.18t315.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': '16.11017948902994485668097294336.24t2912.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': [1, 4, 3, 2, 5, 6, 7, 8, 9]}, {'Size': '18', 'Order': 2, 'Representative': [2, 1, 3, 6, 5, 4, 7, 9, 8]}, {'Size': '27', 'Order': 2, 'Representative': [6, 4, 5, 2, 3, 1, 7, 8, 9]}, {'Size': '27', 'Order': 2, 'Representative': [1, 4, 5, 2, 3, 6, 7, 8, 9]}, {'Size': '54', 'Order': 2, 'Representative': [3, 4, 1, 2, 6, 5, 8, 7, 9]}, {'Size': '6', 'Order': 3, 'Representative': [1, 2, 5, 4, 7, 6, 3, 8, 9]}, {'Size': '8', 'Order': 3, 'Representative': [8, 9, 7, 2, 3, 1, 5, 6, 4]}, {'Size': '12', 'Order': 3, 'Representative': [6, 2, 5, 4, 7, 8, 3, 1, 9]}, {'Size': '72', 'Order': 3, 'Representative': [3, 1, 2, 6, 4, 5, 9, 7, 8]}, {'Size': '54', 'Order': 4, 'Representative': [1, 3, 4, 5, 2, 6, 9, 8, 7]}, {'Size': '162', 'Order': 4, 'Representative': [1, 3, 4, 5, 2, 8, 9, 6, 7]}, {'Size': '36', 'Order': 6, 'Representative': [2, 1, 5, 6, 7, 4, 3, 9, 8]}, {'Size': '36', 'Order': 6, 'Representative': [1, 3, 9, 5, 2, 6, 4, 8, 7]}, {'Size': '36', 'Order': 6, 'Representative': [1, 4, 5, 2, 7, 6, 3, 8, 9]}, {'Size': '36', 'Order': 6, 'Representative': [6, 4, 5, 2, 7, 8, 3, 1, 9]}, {'Size': '54', 'Order': 6, 'Representative': [8, 4, 5, 2, 3, 1, 7, 6, 9]}, {'Size': '72', 'Order': 6, 'Representative': [4, 1, 5, 6, 7, 9, 3, 2, 8]}, {'Size': '108', 'Order': 6, 'Representative': [3, 4, 6, 2, 8, 5, 1, 7, 9]}, {'Size': '216', 'Order': 6, 'Representative': [3, 1, 4, 6, 2, 5, 9, 7, 8]}, {'Size': '144', 'Order': 9, 'Representative': [3, 1, 9, 6, 2, 5, 4, 7, 8]}, {'Size': '108', 'Order': 12, 'Representative': [6, 3, 4, 5, 2, 8, 9, 1, 7]}], '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': ['5632521219297', '-4996900926360', '1740247642800', '-448142972382', '173125319706', '-71121880242', '24572369619', '-7924026978', '2367263541', '-614517282', '138495663', '-27682212', '4867825', '-736968', '94884', '-10094', '813', '-42', '1'], 'ConjugacyClass': 3}, {'RootOf': ['157017321439571168', '-328151740938387120', '371688117567624000', '-452298345412736784', '579103950917374992', '-588127103023647816', '448008539261996352', '-264121209938639304', '125037060715786014', '-48801462165476851', '15898217471248428', '-4291529500497141', '915988478125626', '-128497159458063', '-2292249961566', '8697502819356', '-3397889885364', '882866498220', '-176453881666', '28253721159', '-3668217102', '385789383', '-32531436', '2155491', '-108444', '3906', '-90', '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': ['0', '0', '0', '0', '1'], 'ConjugacyClass': 8}, {'RootOf': ['295867724809654638144', '521050690280203130880', '1108273910229330757632', '4431332939976711515520', '7058655175039626476448', '3743148910776030929376', '-3900408323862601237608', '-9899873332094284235568', '-11047626697681246087575', '-8574456561531398517492', '-5172019404702395775066', '-2526210272693324972700', '-1005794945069331748779', '-317458822104543563352', '-71587437337795787604', '-6722502879622814856', '2683357355530441170', '1488883218338666808', '351763804367102772', '36554276988904104', '-2209156578239760', '-1088407178176176', '-179287819696476', '-89289356893992', '-45678716397945', '-13856719607964', '-2667374989182', '-328792190148', '-21389969925', '602401320', '322513344', '40749984', '3117375', '159084', '5346', '108', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': {'Powers': [1, 5], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['313428044617661546496', '4028679010333507977216', '12662719977270710108160', '-4584010557857609023488', '-19161445465526663577600', '-8163406359382536880128', '6571588157115222417408', '7750960776065190739968', '2294209668246163490304', '-734779601878077902592', '-769139825367397772160', '-188176389042825151632', '36878264960863311225', '34985091858705056376', '7360023345574102344', '-975726119134687248', '-872784708912709308', '-166210844085508320', '13284103829952060', '12897958292816616', '2357940930269094', '-71219876201280', '-115133678794548', '-21210661240920', '-289318800942', '591827832936', '115213288140', '5715197784', '-1479404187', '-333122184', '-25974072', '707904', '366702', '39384', '2268', '72', '1'], 'ConjugacyClass': 18}, {'RootOf': ['1761193062344882338329107430122986272984870587760601495548491842191360', '13161978613524273225574301456151466884672373951442985358963687034978304', '45960754987828143518307674278148347939420956323510708899151892166213632', '98164093671948707889032221749678154747537980353729194205648064539000832', '139915371464672421548576903332582011180403052800028645044746709716959232', '133645197791126622869842058181186034888858738238542651463765528980488192', '75626922746145181361530534776600346936304692323434841840979937555644416', '6024470764861503056976187897209061036255192267061175346860042743709696', '-30020335718910761989638623849351282690318397514574470386083817682108416', '-23589164948698282732905556625343360201581069159627814023200530656919552', '27446124917159936323147134142357480926632145448924843399362964881408', '14286560588357043600586482110257552031371982519792736887970809946046464', '13174853796368514618317704463697576786422814699268718702047711970721792', '5769152814587053835319084509053842192074427776096833282985282926804992', '794757225339994742490720743099517630733588415668911781133485052264448', '-125363429355199094183167186317796744485926510674198225607116274270208', '586740340039457491319029011005899340952124151198216735587182123933696', '973991329445430916157206445071532861461182139103844873189219877158912', '770550274866696373679628796881414277149058504231588071707733869051904', '422223892246059271849496539221114621781949616237856817846503957561344', '204482939255165910824923788983124044302424972156610550388765009473536', '113697116125429880516366769080347682093858511881975708862880873390080', '71914429785640123391988497554772432662094261360815244192549895352320', 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