Artin representation data - 12.373677297806380032.36t2216.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, 41], 'Baselabel': '12.373677297806380032.36t2216.a', 'CharacterField': 1, 'Conductor': 373677297806380032, 'Container': '36t2216', 'Dets': ['1.3.2t1.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], '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], [1]], [[1]], [[1], [0], [0], [0], [-2], [0], [0], [0], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T31', 'Galt': 31, 'HardPrimes': [2, 3, 41, 89], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [2, 0, -6, 0, 0, 6, 0, 0, 0, 1], 'NumBadPrimes': 3, 'Proj_GAP': [1296, 3490], 'Proj_Polynomial': [2, 0, -6, 0, 0, 6, 0, 0, 0, 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': '1.3.2t1.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': '1.123.2t1.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': '1.41.2t1.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': '2.181548.6t3.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': '2.108.3t2.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': '3.181548.4t5.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': '3.13284.6t11.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': '3.544644.6t8.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': '3.4428.6t11.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': '6.51648192.9t31.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': '6.145945446674112.18t300.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': '6.51648192.18t319.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': '6.145945446674112.18t311.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': '8.42715740489984.24t2893.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': '8.42715740489984.12t213.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': '12.117324748302961582844928.36t2217.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': '12.1055922734726654245604352.36t2214.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': '12.7537818451350298005504.36t2210.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': '12.373677297806380032.36t2216.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': '12.41519699756264448.18t315.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': '16.36948848333555085362187485184.24t2912.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, 2, 6, 4, 5, 3, 7, 8, 9]}, {'Size': '18', 'Order': 2, 'Representative': [1, 3, 2, 4, 6, 5, 7, 9, 8]}, {'Size': '27', 'Order': 2, 'Representative': [4, 5, 6, 1, 2, 3, 7, 8, 9]}, {'Size': '27', 'Order': 2, 'Representative': [4, 2, 6, 1, 5, 3, 7, 8, 9]}, {'Size': '54', 'Order': 2, 'Representative': [2, 1, 6, 5, 4, 3, 8, 7, 9]}, {'Size': '6', 'Order': 3, 'Representative': [4, 2, 3, 7, 5, 6, 1, 8, 9]}, {'Size': '8', 'Order': 3, 'Representative': [7, 8, 9, 1, 2, 3, 4, 5, 6]}, {'Size': '12', 'Order': 3, 'Representative': [4, 5, 3, 7, 8, 6, 1, 2, 9]}, {'Size': '72', 'Order': 3, 'Representative': [3, 1, 2, 6, 4, 5, 9, 7, 8]}, {'Size': '54', 'Order': 4, 'Representative': [6, 2, 1, 3, 5, 4, 9, 8, 7]}, {'Size': '162', 'Order': 4, 'Representative': [6, 2, 1, 3, 8, 4, 9, 5, 7]}, {'Size': '36', 'Order': 6, 'Representative': [4, 3, 2, 7, 6, 5, 1, 9, 8]}, {'Size': '36', 'Order': 6, 'Representative': [9, 2, 1, 3, 5, 4, 6, 8, 7]}, {'Size': '36', 'Order': 6, 'Representative': [4, 2, 6, 7, 5, 3, 1, 8, 9]}, {'Size': '36', 'Order': 6, 'Representative': [4, 5, 6, 7, 8, 3, 1, 2, 9]}, {'Size': '54', 'Order': 6, 'Representative': [4, 8, 6, 1, 2, 3, 7, 5, 9]}, {'Size': '72', 'Order': 6, 'Representative': [4, 6, 2, 7, 9, 5, 1, 3, 8]}, {'Size': '108', 'Order': 6, 'Representative': [5, 1, 6, 8, 4, 3, 2, 7, 9]}, {'Size': '216', 'Order': 6, 'Representative': [6, 1, 2, 3, 4, 5, 9, 7, 8]}, {'Size': '144', 'Order': 9, 'Representative': [9, 1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '108', 'Order': 12, 'Representative': [6, 5, 1, 3, 8, 4, 9, 2, 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': ['-49875438353472', '-144156729957120', '7579016937216', '-8781940000512', '2002679360064', '-251130235680', '129588758496', '-9228385728', '4099784544', '-482267736', '79430544', '-14401368', '1363176', '-258984', '23616', '-2610', '252', '-12', '1'], 'ConjugacyClass': 3}, {'RootOf': ['849312064299073536', '1880619570947948544', '1922507410853855232', '1080176653205766144', '298751777719713792', '-13320654069694464', '-38343689977724928', '-9258255802957824', '1482023071383552', '1210592825966592', '166782160207872', '-39507148210176', '-14674415321088', '-254119182336', '637232873472', '113407672320', '-3372668928', '-3209186304', '-168334848', '76702464', '13872384', '767232', '176256', '75168', '13320', '1188', '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': ['1296', '864', '216', '24', '1'], 'ConjugacyClass': 8}, {'RootOf': ['193028131223363026961068032', '-28903987449562847485206528', '-655429598254550488298655744', '1223917919082968545477472256', '-1244314870283559667230498816', '806860700599396418728648704', '-331351722023223200017453056', '76002986466207825504325632', '-1410473908663488908485632', '-5257536033142088208857088', '1709678620769676288491520', '-168936051273725008968192', '-46609843041859790039040', '19977949818994085116416', '-3014350422246885646080', '23939563434039392256', '75808468891037352960', '-14766989846312067840', '1251385237340766720', '-17586310353674112', '-5801955823916928', '1118590430633280', '-399227317899264', '99035655973344', '-13004886196656', '650873921472', '49620090672', '-6845214096', '-446560128', '103994280', '7417656', '-3911328', '561600', '-46260', '2376', '-72', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': {'Powers': [1, 5], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['32726512980441315542541677727744', '65358933630204232436042275504128', '57719505172787559854322498551808', '33239512662442450686584314601472', '14865692165184561187175234445312', '5406480364989206200097596059648', '1690513502767382922074646626304', '463330609710573493062995300352', '113853312556295186109548519424', '25385200107194246713307476992', '5183971920415364622358053888', '978223695458012506049080320', '171255160624647733201926144', '27995861803589271549757440', '4282971980008389204091392', '615559471034966076522240', '83320683449065643344896', '10632020797497675018240', '1283435975226009410496', '146379372231781170432', '15826313831717410560', '1620290172078086400', '157067724478776768', '14458085359092288', '1255189390601184', '103504493850048', '8042026221216', '586771851600', '40707510336', '2590502256', '156244356', '8748864', '423504', '20772', '792', '24', '1'], 'ConjugacyClass': 18}, {'RootOf': ['19738766205876131371872026364439276558707065326560261304527088378374839599104', '-165160954862406557660004063379733107939664138256080192315801526496208332259328', '3495270692257224912356215626943323379207577235633867192847001957186633830760448', '-7096202996801647858514833543855070522690640349831123856287486647569734409650176', '8763660629798967639493314109118036241487283131352693901524844535454546773671936', '-22738727412653313911833617725746047615290944275874794303125959802695975415316480', '56583006263737799384481879966132556819851793685855660586573988588800142945026048', '-92904620695617160136493876190743121057505241697811537861847261058887982503690240', '111395805051538402700864216087447995014558329454373610749011982985978665085435904', '-110437356828619340817843296168078566493421819279749540374711798894198554806452224', '100675852555879594990312256534042895011588634777119975098631537668910581165326336', '-89181246178320722198907158946012307213375564391615785067150103547314953540075520', '75700781041035109229392762873716287417721149439069525858698305046144329489317888', '-58877594840841316007811121728807722253348168869951838053267959531174519331880960', '40534891872666948521285380957283311357410407883484682859025273935808276954349568', '-24303932832170462515474855305214022085241462291112897925814855111323973563973632', '12624561351834380599192022081546874148066415250288239270896684552066408227274752', 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