Artin representation data - 12.332552906075897856.18t315.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, 29], 'Baselabel': '12.332552906075897856.18t315.a', 'CharacterField': 1, 'Conductor': 332552906075897856, 'Container': '18t315', 'Dets': ['1.24.2t1.b.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, 7, 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], [1], [-1], [1], [-1], [0], [-1]], [[1], [0], [-1]], [[1], [1], [1], [0], [0], [0], [-1], [-1], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T31', 'Galt': 31, 'HardPrimes': [2, 3, 29, 5532563, 7496648429], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [-8, -9, -18, -15, -18, -9, -6, 0, 0, 1], 'NumBadPrimes': 3, 'Proj_GAP': [1296, 3490], 'Proj_Polynomial': [-8, -9, -18, -15, -18, -9, -6, 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': '1.24.2t1.b', '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': '1.696.2t1.b', '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': '1.29.2t1.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': '2.181656.6t3.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': '2.216.3t2.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': '3.181656.4t5.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': '3.150336.6t11.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': '3.4359744.6t8.e', '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': '3.6264.6t11.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': '6.292253184.9t31.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': '6.206705124232704.18t300.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': '6.292253184.18t319.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': '6.206705124232704.18t311.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': '8.171066309709824.24t2893.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': '8.171066309709824.12t213.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': '12.235208351962267111489536.36t2217.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': '12.135480010730265856217972736.36t2214.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': '12.60410230706123300929536.36t2210.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': '12.191550473899717165056.36t2216.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': '12.332552906075897856.18t315.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': '16.2370358267736731420389650989056.24t2912.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, 3, 5, 4, 6, 7, 8, 9]}, {'Size': '18', 'Order': 2, 'Representative': [4, 5, 7, 1, 2, 6, 3, 8, 9]}, {'Size': '27', 'Order': 2, 'Representative': [2, 1, 3, 5, 4, 8, 7, 6, 9]}, {'Size': '27', 'Order': 2, 'Representative': [2, 1, 3, 5, 4, 6, 7, 8, 9]}, {'Size': '54', 'Order': 2, 'Representative': [6, 8, 9, 5, 4, 1, 7, 2, 3]}, {'Size': '6', 'Order': 3, 'Representative': [1, 2, 3, 4, 5, 8, 7, 9, 6]}, {'Size': '8', 'Order': 3, 'Representative': [2, 3, 1, 5, 7, 8, 4, 9, 6]}, {'Size': '12', 'Order': 3, 'Representative': [2, 3, 1, 4, 5, 8, 7, 9, 6]}, {'Size': '72', 'Order': 3, 'Representative': [6, 8, 9, 1, 2, 4, 3, 5, 7]}, {'Size': '54', 'Order': 4, 'Representative': [4, 5, 7, 2, 1, 6, 3, 8, 9]}, {'Size': '162', 'Order': 4, 'Representative': [1, 3, 2, 8, 6, 4, 9, 5, 7]}, {'Size': '36', 'Order': 6, 'Representative': [4, 5, 7, 1, 2, 8, 3, 9, 6]}, {'Size': '36', 'Order': 6, 'Representative': [1, 2, 3, 6, 8, 5, 9, 7, 4]}, {'Size': '36', 'Order': 6, 'Representative': [1, 2, 3, 5, 4, 8, 7, 9, 6]}, {'Size': '36', 'Order': 6, 'Representative': [2, 3, 1, 5, 4, 8, 7, 9, 6]}, {'Size': '54', 'Order': 6, 'Representative': [2, 1, 3, 5, 4, 9, 7, 6, 8]}, {'Size': '72', 'Order': 6, 'Representative': [5, 7, 4, 1, 2, 8, 3, 9, 6]}, {'Size': '108', 'Order': 6, 'Representative': [6, 8, 9, 5, 4, 2, 7, 3, 1]}, {'Size': '216', 'Order': 6, 'Representative': [6, 8, 9, 2, 1, 4, 3, 5, 7]}, {'Size': '144', 'Order': 9, 'Representative': [6, 8, 9, 1, 2, 5, 3, 7, 4]}, {'Size': '108', 'Order': 12, 'Representative': [4, 5, 7, 2, 1, 8, 3, 9, 6]}], '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': ['21744836745439536', '8081368770693456', '6375777811453116', '363452074235442', '252759318449031', '-42595979460192', '-1465418847105', '-150192063162', '114885528093', '-17814983184', '3098711943', '-611595036', '97541172', '-12384576', '1234170', '-87066', '3879', '-96', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-107162256855871809170077609944', '-701456562758779679565951300', '-4126754298662971365448509912', '646913701873530256308389919', '-50752683562376370054287700', '20039114664036201785906124', '-2016299669416669337223582', '236290973468700132775746', '-44502385501208623961178', '3876440931436091788647', '-439037025218382393072', '56196925814723606163', '-4388292248544435546', '431098233092324739', '-42743192956952328', '2943357073817670', '-244851591599874', '19874848427343', '-1181345256702', '82283981058', '-5563154520', '274977666', '-15530778', '862731', '-31986', '1269', '-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': ['20736', '6912', '864', '48', '1'], 'ConjugacyClass': 8}, {'RootOf': ['804423751003969321077810844397568', '993920271895375582926977463103488', '509391137066209183007612026795008', '175232667148638311200256095610880', '66854330042722180648628161036032', '26409485442263844418029055980288', '7097995523098417753633516790976', '1253023167698587396639867770432', '73158071070572389822311207216', '-43362741151569695181026119488', '-20906639182414769110198752708', '-5944551804458471303193428244', '-1298718751703819153536615023', '-234394746972120430945043436', '-36192755764952441885357586', '-4910293398752374601872872', '-601633938233465505304425', '-68471182290272841800640', '-7417607529108096966564', '-774052121834501187744', '-77524579210043456055', '-7352155697566989852', '-651393545994994230', '-53644713570194364', '-4129539596401221', '-301151831663376', '-20973270526722', '-1369676867760', '-78962109579', '-3494232108', '-65529000', '6542532', '864243', '57636', '2538', '72', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': {'Powers': [1, 5], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['2239183455676768266350478336', '21364378981458592481448371712', '92296572106574369097908725824', '241477153811215640295189760512', '432367948292937220944160972128', '567971409396036218836541575824', '572996689001396795733150844980', '458656285096787724455563423764', '298528188982278909808082207769', '161061436426925496068535077028', '73156230573766290183018883446', '28336629328843088281399535232', '9462033057762444708346258917', '2748939890717786738747433480', '700360545037784790242989764', '157541045516843401922518728', '31469143587445408359386034', '5609146703203164980091312', '895670919706492322533836', '128524311902958533307360', '16610354258406178397832', '1936064897869676500080', '203611619380156407432', '19310752671252714900', '1649001421712816343', '126432677083264740', '8667610447746330', '528195854241072', '28384732761363', '1330817388624', '53658012276', '1824227244', '50865975', '1116756', '18090', '192', '1'], 'ConjugacyClass': 18}, {'RootOf': ['-47475338933227852770105697262927607016585195937798176679800711666968377225306919838313502832852992', '-124622218480857522960431736716271752831185030425149297399264288479907195547223507087594819166404608', '-185032902369259375894952728575537804656729553262522930498653702271080663619977145742040966302269440', '-201053442427680070075973066728200525124978194150342522875950932089409582139102552385323409231314944', '-175687858032022340003389517951765968867150398702850885019779155743658827340454534604797835602821120', '-129878014487137014085768593096858560503189229464760245552838478711272496818875300643106852172726272', '-83902103276064764991524953052295387991112139091169545539972768770715072709863693538365071544287232', '-48424151371420529959318937499953910947926607285448463392616587252501627344416616490262033013932032', '-25373467513287921220189369633578540638249089018564353595607268062114030089934377144499835179433984', '-12216170434454858478990882112744260025081123588102278115383032040534682663979578964699593975726080', '-5452517667631868783416220583240817930542035028250229313663056191044175108597739972928875017125888', 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