Artin representation data - 9.116095057920000.18t274.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, 5], 'Baselabel': '9.116095057920000.18t274.a', 'CharacterField': 1, 'Conductor': 116095057920000, 'Container': '18t274', 'Dets': ['1.3.2t1.a.a'], 'Dim': 9, 'GalConjSigns': [1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[9], [-3], [1], [3], [-3], [1], [-1], [0], [0], [-3], [1], [1], [1], [-1], [-1], [0], [0], [0], [1], [0]], 'GalOrbIndex': 1, 'HardFactors': [21, 22, 23, 8, 3], 'LocalFactors': [[[1], [-9], [36], [-84], [126], [-126], [84], [-36], [9], [-1]], [[1], [3], [0], [-8], [-6], [6], [8], [0], [-3], [-1]], [[1], [-1], [-4], [4], [6], [-6], [-4], [4], [1], [-1]], [[1], [-3], [0], [8], [-6], [-6], [8], [0], [-3], [1]], [[1], [3], [0], [-8], [-6], [6], [8], [0], [-3], [-1]], [[1], [-1], [-4], [4], [6], [-6], [-4], [4], [1], [-1]], [[1], [1], [-4], [-4], [6], [6], [-4], [-4], [1], [1]], [[1], [0], [0], [-3], [0], [0], [3], [0], [0], [-1]], [[1], [0], [0], [-3], [0], [0], [3], [0], [0], [-1]], [[1], [3], [6], [10], [12], [12], [10], [6], [3], [1]], [[1], [-1], [0], [0], [-2], [2], [0], [0], [1], [-1]], [[1], [-1], [2], [-2], [0], [0], [-2], [2], [-1], [1]], [[1], [-1], [0], [0], [-2], [2], [0], [0], [1], [-1]], [[1], [1], [2], [2], [0], [0], [-2], [-2], [-1], [-1]], [[1], [1], [0], [0], [-2], [-2], [0], [0], [1], [1]], [[1], [0], [0], [1], [0], [0], [-1], [0], [0], [-1]], [[1], [0], [0], [-1], [0], [0], [-1], [0], [0], [1]], [[1], [0], [0], [1], [0], [0], [-1], [0], [0], [-1]], [[1], [-1], [0], [0], [0], [0], [0], [0], [-1], [1]], [[1], [0], [0], [1], [0], [0], [1], [0], [0], [1]], [[1], [0], [1]], [[1]], [[1], [1], [0], [0], [-1], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T47', 'Galt': 47, 'HardPrimes': [2, 3, 5, 37, 1153], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [-3, 0, -2, 0, 6, -8, -6, 0, 1], 'NumBadPrimes': 3, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [-3, 0, -2, 0, 6, -8, -6, 0, 1], 'Proj_nTj': [8, 47]}
• 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]], '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]], '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]], '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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.14400.4t3.a', 'Character': [[2], [2], [2], [0], [0], [-2], [0], [2], [2], [0], [-2], [0], [0], [-2], [0], [2], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.388800.6t13.a', 'Character': [[4], [4], [4], [0], [2], [0], [0], [-2], [1], [0], [0], [0], [2], [0], [0], [-2], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.1555200.12t34.a', 'Character': [[4], [4], [4], [-2], [0], [0], [-2], [1], [-2], [-2], [0], [-2], [0], [0], [0], [1], [1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.6220800.12t34.a', 'Character': [[4], [4], [4], [0], [-2], [0], [0], [-2], [1], [0], [0], [0], [-2], [0], [0], [-2], [0], [1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.1555200.6t13.a', 'Character': [[4], [4], [4], [2], [0], [0], [2], [1], [-2], [2], [0], [2], [0], [0], [0], [1], [-1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.358318080000.12t201.k', 'Character': [[6], [2], [-2], [-2], [0], [-2], [2], [3], [0], [-4], [2], [0], [0], [0], [0], [-1], [1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.298598400.12t202.b', 'Character': [[6], [2], [-2], [-4], [0], [2], [0], [3], [0], [-2], [-2], [2], [0], [0], [0], [-1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.298598400.8t47.a', 'Character': [[6], [2], [-2], [4], [0], [2], [0], [3], [0], [2], [-2], [-2], [0], [0], [0], [-1], [1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.358318080000.12t200.k', 'Character': [[6], [2], [-2], [2], [0], [-2], [-2], [3], [0], [4], [2], [0], [0], [0], [0], [-1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '9.154793410560000.16t1294.b', 'Character': [[9], [-3], [1], [3], [3], [1], [-1], [0], [0], [-3], [1], [1], [-1], [-1], [1], [0], [0], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '9.464380231680000.18t272.b', 'Character': [[9], [-3], [1], [-3], [3], [1], [1], [0], [0], [3], [1], [-1], [-1], [-1], [-1], [0], [0], [0], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '9.38698352640000.18t273.a', 'Character': [[9], [-3], [1], [-3], [-3], [1], [1], [0], [0], [3], [1], [-1], [1], [-1], [1], [0], [0], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '9.116095057920000.18t274.a', 'Character': [[9], [-3], [1], [3], [-3], [1], [-1], [0], [0], [-3], [1], [1], [1], [-1], [-1], [0], [0], [0], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.962938848411648000000.36t1763.a', 'Character': [[12], [4], [-4], [-2], [0], [0], [-2], [-3], [0], [2], [0], [2], [0], [0], [0], [1], [1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.962938848411648000000.24t2821.a', 'Character': [[12], [4], [-4], [2], [0], [0], [2], [-3], [0], [-2], [0], [-2], [0], [0], [0], [1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '18.21564899957517047562240000000000.36t1758.a', 'Character': [[18], [-6], [2], [0], [0], [-2], [0], [0], [0], [0], [-2], [0], [0], [2], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 7, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '6', 'Order': 2, 'Representative': [1, 5, 6, 4, 2, 3, 7, 8]}, {'Size': '9', 'Order': 2, 'Representative': [7, 5, 6, 8, 2, 3, 1, 4]}, {'Size': '12', 'Order': 2, 'Representative': [1, 3, 2, 4, 5, 6, 7, 8]}, {'Size': '24', 'Order': 2, 'Representative': [2, 1, 4, 3, 7, 8, 5, 6]}, {'Size': '36', 'Order': 2, 'Representative': [4, 3, 2, 1, 5, 6, 7, 8]}, {'Size': '36', 'Order': 2, 'Representative': [7, 3, 2, 8, 5, 6, 1, 4]}, {'Size': '16', 'Order': 3, 'Representative': [1, 2, 5, 4, 6, 3, 7, 8]}, {'Size': '64', 'Order': 3, 'Representative': [1, 5, 3, 7, 6, 2, 8, 4]}, {'Size': '12', 'Order': 4, 'Representative': [1, 3, 5, 4, 6, 2, 7, 8]}, {'Size': '36', 'Order': 4, 'Representative': [4, 3, 5, 7, 6, 2, 8, 1]}, {'Size': '36', 'Order': 4, 'Representative': [4, 5, 6, 7, 2, 3, 8, 1]}, {'Size': '72', 'Order': 4, 'Representative': [2, 7, 8, 3, 1, 4, 5, 6]}, {'Size': '72', 'Order': 4, 'Representative': [4, 3, 2, 7, 5, 6, 8, 1]}, {'Size': '144', 'Order': 4, 'Representative': [2, 4, 1, 3, 7, 8, 5, 6]}, {'Size': '48', 'Order': 6, 'Representative': [7, 2, 6, 8, 3, 5, 1, 4]}, {'Size': '96', 'Order': 6, 'Representative': [1, 3, 2, 8, 5, 6, 4, 7]}, {'Size': '192', 'Order': 6, 'Representative': [3, 4, 1, 5, 7, 8, 6, 2]}, {'Size': '144', 'Order': 8, 'Representative': [2, 4, 7, 3, 8, 1, 5, 6]}, {'Size': '96', 'Order': 12, 'Representative': [4, 2, 5, 7, 6, 3, 8, 1]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 2]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-1163264', '-135168', '134208', '-23872', '1920', '-72', '1'], 'ConjugacyClass': 2}, {'RootOf': ['677310737705557537261020669523945599270912', '-601643066649421448068163808821548563824640', '229642840384883891928408157198614653829120', '-42066197507412409481074307340059931574272', '-567841684698286833748467867888019046400', '2839374266604371425455715207013065555968', '-1036400167026601376080925498832190439424', '249696187568893372835672439165208756224', '-47212286940145156803132775136445333504', '7476688406975627675460262730091462656', '-1047123839665157583064115953388224512', '138243102323407798761475861553086464', '-18052206123037011609007050624860160', '2323174154077242173296983989551104', '-282995221945346116945937845714944', '31546184658492397238998183968768', '-3181046705670296874933681389568', '290346217075016223012657561600', '-23908192475353112813517144064', '1742206555924748953483345920', '-107580562835192093001904128', '5134572235700540320874496', '-137088127384970647707648', '-4610377722477989191680', '916767092860295245824', '-72452435177488121856', '4048042380618728448', '-176460648457757696', '6188241377024640', '-176037333004800', '4049104314240', '-74398324608', '1068311808', '-11565312', '88848', '-432', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 10, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 4]}, {'Data': 0, 'Classes': 17, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 3]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2, 2]}, {'Data': 0, 'Classes': 14, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 4]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [1, 1, 3, 3]}, {'Data': 0, 'Classes': 16, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 3]}, {'Data': 0, 'Classes': 20, 'Algorithm': 'CYC', 'CycleType': [1, 3, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-168951808', '58540032', '6635520', '-411648', '78336', '25920', '960', '-288', '0', '1'], 'ConjugacyClass': 3}, {'RootOf': ['1335490366664337260544', '3183672644799993741312', '3646130897808437280768', '2689783877496773541888', '1446948807564431720448', '609164239434644717568', '210136981127538147328', '61279423799950835712', '15421793861876908032', '3390089945866567680', '654295139286515712', '110879114223550464', '16448938984587264', '2126707570114560', '238430926651392', '23049427959808', '1908467486208', '134169919488', '7913766912', '385030656', '15072192', '456960', '10080', '144', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1, 3], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['245191943809889468416', '54497415945227599872', '-247133072120610816', '-942091006289903616', '-141656054160162816', '2385412746117120', '403971711959040', '-33300856700928', '1111295655936', '-236212781056', '9767890944', '2689376256', '-208312320', '-8133120', '803520', '6720', '-1440', '0', '1'], 'ConjugacyClass': 12}, {'RootOf': ['-11576109355440948233809003865570780699622002392417708470138448327721774072463360000', '-46583814745494559469506594881586712686580133755003387596422797735100201501280174080', '-92311036524095109557908693924926987741077752781957094523316620458188189563311095808', '-119898767377581856808814988379615065439434868007452749027696906252380304518829572096', '-114573979358489609260436034735279060376014490813555093398244653760129104830571479040', '-85661322240558774756457450410528351003110468457226000883343546962077581562903265280', '-51981118847766630782139841279922730299220915892211769431066284667992068938683908096', '-26177662857136217226725611510950632620837753299023101894439505936700800250033471488', '-11067587137282336363215678666282185998794886826939675652608427894620671157546778624', '-3930270336458565313293036252638348191253942375315440517518246455505167719377928192', '-1152638707813211673133812645512590375411844080633967142107912361968669826194866176', '-262912079780653393265386762663303390062633928765728753675560132618415130068123648', '-36119220723078966323507265816534523679948792261529143049669547633084264932704256', '4015607604497210671836915136948841164590392851314785829929082400530169759531008', '5116355471031927600814152903881251885669919323304205930505756142139773049372672', '2294511637285763597742617418977397452474135793561671407169760592463971315875840', '767462580053267591802826816187255451971078872072033855922378542626882937946112', '216045518486806101419758502359501554480763558938279125378561820850234759053312', '53534772713108236569702848919537755385296644276291961101866364445467688828928', '11942503018798020570195548290062348953779427543483897554035314339335209222144', '2430635085707540412565047030588835780406748303891545012659389378336412139520', '455349442737750345852484837225523733857699974042599950938307318813892280320', '79014233667121862248515853165806578308979024932139247975460848911259795456', '12760188126517841267130167355556774772925656513456694251852560730639302656', '1924886861500146534075659167360434918894825801532976522067599843993321472', '272043283219302998497957862047174008988176607599035862300388170651402240', '36108550634002174853277936920329064193474494407767804213876834894348288', '4510208735038416914643951569201108553134709091271248864886707990822912', '531044415275913991156490690251342080626795798426889327078503142653952', '59024146269991107285613440553537627619623366200326568230595908861952', '6200307612359215544066757151968259644781654298778218475606371205120', '616195371079629005496822191765070821492659454369627588130339028992', '57984240504724021692809305081394584806086476980447055297822851072', '5169973299799481095189990303310504557294488619980375987515817984', '437014496570619196289481134365835315080060095255815193561661440', '35036587288560617644309347032932322587536072094338586515603456', '2665052338351866117643288524713664409074294855385373942480896', '192371322990219016593885556761312639340012521242765574537216', '13178718890422603587719237585224547895222436495839492833280', '856856634371576572533716629945162353911476364150638116864', '52869585689811281765810905629121853702023799710056185856', '3095166414552595455230621123143528640915266845303373824', '171876500321074223862571052548080949147097520559620096', '9049674404857884244512396372709715045204380845342720', '451561525875025509676270340377409428390684045344768', '21340470127263619426047159870368108335184377544704', '954506704035140624541458027199608330041342033920', '40371308034368729206854477186455401024022642688', '1613088926539323168883207926827258726357925888', '60819831775347284401296822602147760030351360', '2161096806617129877449246980879350302244864', '72261945526595635489603818415911119880192', '2270024935739392867787778208123796324352', '66868315281446316681752617974195290112', '1843118134626962085661110107518271488', '47421824842915424028785909465874432', '1135795323857896092193779443171328', '25243724152915313322476414435328', '518766842871221933111362191360', 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