Artin representation data - 12.332355654611454976.18t315.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, 19, 107], 'Baselabel': '12.332355654611454976.18t315.a', 'CharacterField': 1, 'Conductor': 332355654611454976, 'Container': '18t315', 'Dets': ['1.19.2t1.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, 18, 24, 25, 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], [1], [1]], [[1], [-1], [0], [0], [0], [0], [-1], [1]], [[1], [0], [0], [0], [-2], [0], [0], [0], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T31', 'Galt': 31, 'HardPrimes': [2, 3, 19, 107, 3931], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [1, 1, 0, 2, 0, 2, 0, -2, -1, 1], 'NumBadPrimes': 3, 'Proj_GAP': [1296, 3490], 'Proj_Polynomial': [1, 1, 0, 2, 0, 2, 0, -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': '1.19.2t1.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': '1.107.2t1.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': '1.2033.2t1.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': '2.870124.6t3.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': '2.76.3t2.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': '3.870124.4t5.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': '3.154508.6t11.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': '3.16532356.6t8.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': '3.8132.6t11.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': '6.2472128.9t31.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': '6.116980444221795008.18t300.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': '6.892438208.18t319.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': '6.324045551860928.18t311.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': '8.1578689359404411136.24t2893.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': '8.12113852406016.12t213.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': '12.15726981821359361510359591936.36t2217.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': '12.43565046596563328283544576.36t2214.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': '12.289190631613137649537024.36t2210.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': '12.119980391314735246336.36t2216.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': '12.332355654611454976.18t315.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': '16.4781002473693245899149315948544.24t2912.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': [5, 2, 3, 4, 1, 6, 7, 8, 9]}, {'Size': '18', 'Order': 2, 'Representative': [2, 1, 3, 4, 7, 6, 5, 9, 8]}, {'Size': '27', 'Order': 2, 'Representative': [5, 7, 4, 3, 1, 6, 2, 8, 9]}, {'Size': '27', 'Order': 2, 'Representative': [5, 7, 3, 4, 1, 6, 2, 8, 9]}, {'Size': '54', 'Order': 2, 'Representative': [5, 3, 2, 7, 1, 8, 4, 6, 9]}, {'Size': '6', 'Order': 3, 'Representative': [1, 2, 4, 6, 5, 3, 7, 8, 9]}, {'Size': '8', 'Order': 3, 'Representative': [5, 7, 4, 6, 9, 3, 8, 2, 1]}, {'Size': '12', 'Order': 3, 'Representative': [1, 7, 4, 6, 5, 3, 8, 2, 9]}, {'Size': '72', 'Order': 3, 'Representative': [2, 3, 1, 5, 7, 9, 4, 6, 8]}, {'Size': '54', 'Order': 4, 'Representative': [7, 1, 3, 4, 2, 6, 5, 9, 8]}, {'Size': '162', 'Order': 4, 'Representative': [4, 2, 1, 5, 3, 9, 8, 7, 6]}, {'Size': '36', 'Order': 6, 'Representative': [2, 1, 4, 6, 7, 3, 5, 9, 8]}, {'Size': '36', 'Order': 6, 'Representative': [3, 2, 5, 9, 4, 1, 7, 8, 6]}, {'Size': '36', 'Order': 6, 'Representative': [5, 2, 4, 6, 1, 3, 7, 8, 9]}, {'Size': '36', 'Order': 6, 'Representative': [5, 7, 4, 6, 1, 3, 8, 2, 9]}, {'Size': '54', 'Order': 6, 'Representative': [5, 7, 6, 3, 1, 4, 2, 8, 9]}, {'Size': '72', 'Order': 6, 'Representative': [2, 5, 4, 6, 7, 3, 9, 1, 8]}, {'Size': '108', 'Order': 6, 'Representative': [5, 3, 7, 8, 1, 2, 4, 6, 9]}, {'Size': '216', 'Order': 6, 'Representative': [7, 3, 1, 5, 2, 9, 4, 6, 8]}, {'Size': '144', 'Order': 9, 'Representative': [2, 3, 5, 9, 7, 1, 4, 6, 8]}, {'Size': '108', 'Order': 12, 'Representative': [7, 1, 4, 6, 2, 3, 5, 9, 8]}], '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': ['8095113313949', '-11266239378422', '5841583360829', '-887070723804', '-426230980472', '240570373868', '-39026025736', '-5294590636', '3524908970', '-586932960', '-8559782', '21114284', '-3891936', '240148', '28528', '-7716', '785', '-42', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-3872464530701565863', '-317031565782964853', '2110240528648810039', '-111573956171382035', '-469208586531176994', '73549634313294586', '49820782787132634', '-12122317204331554', '-2443275628400909', '804924365862073', '75415126561605', '-24165969461689', '-5919650105708', '1092870482044', '288843549212', '-61876050508', '-3032354897', '588734541', '233890641', '-17662037', '-9374290', '1758954', '-138134', '25998', '-6427', '783', '-45', '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': ['16', '32', '24', '8', '1'], 'ConjugacyClass': 8}, {'RootOf': ['-288151493755665383424000', '-685158738779653432934400', '-987925139829202039603200', '-982109693204055956914176', '-626350568908743610728448', '-208870476945199896461312', '41267103974554620395520', '89960561399762014699520', '42643432866280477032448', '3377576795267152216064', '-5174756073933007486976', '-2213375379022320500736', '-140452762520137498624', '150214081892754259968', '46724158540443680768', '1733691144944156672', '-1810539917781336064', '-371799807174049792', '-2313947935637504', '6958451457425408', '180696320344064', '-176799834908672', '-10770978185216', '3902679826432', '417618341120', '-57334216192', '-8433848832', '947319680', '192758656', '-4580864', '-2205920', '42688', '26464', '376', '-160', '0', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': {'Powers': [1, 5], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['77769258041344', '-46524293709824', '-390159962996736', '-199263480971264', '1100312874057728', '1229644170788864', '-1096615712522240', '-2713842635243520', '-372243847708672', '2430833424596992', '1676734055317504', '-707449456164864', '-1065726184783872', '-82566313803776', '309992315879424', '86156439683072', '-38800196124672', '-20619283513344', '-206380896256', '2104349081600', '622244003840', '-16968007680', '-58199552000', '-14703849472', '-233521664', '834936320', '258900480', '29532800', '-3598912', '-2082240', '-414192', '-34624', '3392', '1480', '248', '24', '1'], 'ConjugacyClass': 18}, {'RootOf': ['95432958742058031232061575094850379599867719383594893140298647494910279680', '693881659307788127686447768354790142220784217858655002181885335963210612736', '2572700123507486850893280044732849930160027303386115783170119420818495635456', '6220627740445580823446707673560773610005714492370713556306961031705999179776', '10557062987348653286776473994699219345565633625235655650866952843942086836224', '12808022164177929428557785844525700712387844464184379523384184481519780233216', '10814735287856811222459991075715560996328743929281315102220742889349616500736', '5480915306087885219743885451769122383135797881271114132908156106736578592768', '107171031419779430122062988835701229655584116804207690655726394770072797184', '-2653964004198856131452466224814236092366299067246760368939607258894782431232', '-2641563467808983680344576985151529365982866573543214892964563716519317471232', '-1372067263041544207689264836213695648910314758022167902799893737050340327424', '-267328472336083970959929354091357484687987106066825583974390384760144789504', '190437985817091946272135792981838648183915762674054893151813609894474416128', '198924487123034643425864455451343322233505533791631180912346136092480634880', '81491635471198056813283944127517254878701562252947955591860715954194350080', '4521889958009797296470769743457662969889585593852188645063617211407532032', '-14612749246023399522010239216007726856937589318680281058288008479312445440', '-8936431608859704493841960918552252548189957446828233930528685039795830784', '-2032927406772145459473808128125606417355559023490246815753130467097837568', '470741225630761697722497612917108681524060434693785711220291369256878080', '523298810111086677085709381566052058134741822828447382520514712642256896', '162310187301205672032811687297010530117205465867512075617065647103541248', 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