Artin representation data - 12.7319366412146449.18t218.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': [1489], 'Baselabel': '12.7319366412146449.18t218.a', 'CharacterField': 1, 'Conductor': 7319366412146449, 'Container': '18t218', 'Dets': ['1.1489.2t1.a.a'], 'Dim': 12, 'GalConjSigns': [1], 'Galn': 9, 'GaloisConjugates': [{'Sign': 1, 'Character': [[12], [0], [2], [0], [3], [-3], [0], [0], [0], [-1], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [11, 8, 13, 15, 13], 'LocalFactors': [[[1], [-12], [66], [-220], [495], [-792], [924], [-792], [495], [-220], [66], [-12], [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], [0], [0], [-2], [0], [0], [0], [0], [0], [1]], [[1], [1], [2], [1], [2], [1], [0], [-1], [-2], [-1], [-2], [-1], [-1]], [[1], [0], [0], [-1], [0], [0], [0], [0], [0], [-1], [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], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [-1]], [[1], [-1], [-3], [3], [3], [-3], [-1], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T30', 'Galt': 30, 'HardPrimes': [2, 7, 809, 1489, 31771], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [29, 14, 18, 35, -33, -25, 11, -1, -2, 1], 'NumBadPrimes': 1, 'Proj_GAP': [648, 703], 'Proj_Polynomial': [29, 14, 18, 35, -33, -25, 11, -1, -2, 1], 'Proj_nTj': [9, 30]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.1489.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [1], [1], [-1], [1], [-1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.1489.3t2.a', 'Character': [[2], [2], [0], [2], [2], [2], [-1], [0], [2], [0], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.2217121.6t8.a', 'Character': [[3], [-1], [-1], [3], [3], [3], [0], [1], [-1], [-1], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.1489.4t5.a', 'Character': [[3], [-1], [1], [3], [3], [3], [0], [-1], [-1], [1], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.3301293169.18t217.a', 'Character': [[6], [2], [0], [3], [-3], [0], [0], [-2], [-1], [0], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.3301293169.9t30.a', 'Character': [[6], [2], [0], [3], [-3], [0], [0], [2], [-1], [0], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.3301293169.36t1121.a', 'Character': [[6, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [3, 0, 0, 0], [-3, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 2, 0, -1], [0, -2, 0, 1]], 'CharacterField': 12}, {'GalConj': 2, 'Baselabel': '6.3301293169.36t1121.a', 'Character': [[6, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [3, 0, 0, 0], [-3, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, 0, 1], [0, 2, 0, -1]], 'CharacterField': 12}, {'GalConj': 1, 'Baselabel': '8.4915625528641.12t177.a', 'Character': [[8], [0], [0], [-4], [-1], [2], [-1], [0], [0], [0], [-1], [2], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.4915625528641.12t177.b', 'Character': [[8], [0], [0], [-4], [-1], [2], [-1], [0], [0], [0], [2], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.4915625528641.12t178.a', 'Character': [[8], [0], [0], [-4], [-1], [2], [2], [0], [0], [0], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.16227920979064547153329.36t1123.a', 'Character': [[12], [0], [-2], [0], [3], [-3], [0], [0], [0], [1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.7319366412146449.18t218.a', 'Character': [[12], [0], [2], [0], [3], [-3], [0], [0], [0], [-1], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '27', 'Order': 2, 'Representative': [3, 2, 1, 4, 5, 7, 6, 8, 9]}, {'Size': '54', 'Order': 2, 'Representative': [6, 4, 7, 2, 5, 1, 3, 9, 8]}, {'Size': '6', 'Order': 3, 'Representative': [1, 2, 3, 4, 5, 7, 9, 8, 6]}, {'Size': '8', 'Order': 3, 'Representative': [3, 4, 8, 5, 2, 7, 9, 1, 6]}, {'Size': '12', 'Order': 3, 'Representative': [3, 2, 8, 4, 5, 7, 9, 1, 6]}, {'Size': '72', 'Order': 3, 'Representative': [6, 1, 7, 3, 8, 2, 4, 9, 5]}, {'Size': '54', 'Order': 4, 'Representative': [6, 2, 7, 4, 5, 3, 1, 9, 8]}, {'Size': '54', 'Order': 6, 'Representative': [3, 4, 1, 2, 5, 9, 6, 8, 7]}, {'Size': '108', 'Order': 6, 'Representative': [6, 4, 7, 2, 5, 8, 1, 9, 3]}, {'Size': '72', 'Order': 9, 'Representative': [6, 1, 7, 3, 8, 4, 5, 9, 2]}, {'Size': '72', 'Order': 9, 'Representative': [6, 1, 7, 3, 8, 5, 2, 9, 4]}, {'Size': '54', 'Order': 12, 'Representative': [2, 3, 4, 1, 8, 7, 9, 5, 6]}, {'Size': '54', 'Order': 12, 'Representative': [2, 3, 4, 1, 8, 9, 6, 5, 7]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 3]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 4]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 3, 3]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2, 3]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 2, 2]}, {'Data': 0, 'Classes': 10, 'Algorithm': 'CYC', 'CycleType': [1, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['37715175995240174300591811913907344479557889156219514904675633', '35083309738404533392542512632803852112534412896651120815739372', '15930881152140351093530186676054099296719281848145220888546922', '4985324443250915571237413951645453602707030731512694313605775', '1256566477753839242928544870276452097225441083625748753520053', '271214902754959128505985201511349110050774998933732190030765', '51177766112339867391596763524496889126432447625717082873101', '8675758778758520800225612225199361521535417479909577458457', '1345302956292314795086134660462490150466573965504212834080', '191412407853269013077050810095400760656541798901615669047', '25319052715294683648125403475614124105208754382385327688', '3131532246364766757689569856244971390832384932665389686', '362636535555583762823483053323095046416285551921323255', '39588293223618553221932683041645976229770543883764966', '4085926203205940848111178043161766198045157806209186', '398360555745501183702666412790719545696093502434287', '36861956096532517083649690040415758519504971487489', '3248507535583689703465877916549054141914269647893', '269048406669144149959093139289076848213671719217', '21814084851251949329055279979695728573351572424', '1554294752140299264347125061098038193614119999', '127908419639682399369452670900741953118658541', '6147431800267019661658293087533640388161710', '733987024060071150420674250101615575477533', '6543705105533261091044590705698012668487', '4047974093584059092097586622240395795426', '-80716176751350894830016830455756796107', '15463534978733423462003441511012047074', '-198722642570368629339699067549366479', '969190048375956054304245311698162', '3603073776159713663975102596184679', '-380684480384799502081716195575461', '31513379397669956940940044440580', '-2031802336678156493975944309231', '96675032763523984824622480794', '-3072324441185696615003395635', '-33755230071381202105989624', '12560276709062830287093252', '-1091596611263220094440421', '61900645285762783860050', '-2351188380921282918447', '29895478611769503743', '4325314340298788100', '-486993492037734669', '33158629992340358', '-1765404565821365', '78508796394178', '-2988626222350', '97719708906', '-2733461480', '64387113', '-1238027', '18515', '-192', '1'], 'ConjugacyClass': 13}, {'RootOf': ['152827565646658791637694550985994194938411421567621670364887', '309665683350994954558467167042254351114609103776437138679011', '255147417178770339190612905338387255109656892854416712924445', '133518512433426030270495303938921854699708568698020004188783', '52889549804099280329094986628735430370965052930606608794823', '15637151622816441148666888545358134089004829714140121384364', '3830709765970483272431122446457992337296420601049231004616', '841273673071925200141026891559932287814648764517270097950', '147107406519541332749763602237417733134310137010154749321', '29284127036378811815294758753327145917382107712724734995', '3153143019865629351204867606434998759527802292187062571', '831385356372619243668968754932870943036887067238136069', '17116945892338040032448655553935921642921836107773755', '22089094380948482429117677718608500962040385841125614', '-1296274063381949719850527170359095942409682102590745', '526576654950521949597341713867544398501770782473588', '-50959906713101661298635805017746119031542597054766', '10073540968615751415277077363927547578778632540917', '-1039785052795556889288982395596799834719777429065', '144983765465858115319420449847955213462046204747', '-13970555705068202345644348022383652543830958013', '1530679883309464873048466134197543490028164609', '-130443951580666949232257234616634537487649851', '11620126883536113627278744874833206171609024', '-843415658102663002906855486134413305583156', '60558650956291715322166097721736057511555', '-3508718909886915789205463955369612551660', '185051617167908005351092590326251747103', '-6382311405116316817298298047149714817', '42727017072369426201785274512485901', '22164183921557185604887675063444700', '-2529161820757870547994021519861063', '197014225230324411466738976702319', '-12078104686895346453989928951167', '601515949279035473214786166563', '-23266718776731244517273569771', '519546452657551296882463202', '12393454499150142300387483', '-2344130034023377598381011', '166929431235198229170795', '-8391928217236193507743', '310098535302070116269', '-6683838815076141882', '-115621956231422187', '22427686062593520', '-1502409108150230', '73201522907614', '-2904340195084', '96759552569', '-2727707984', '64387113', '-1238027', '18515', '-192', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [2, 3, 4]}, {'Data': {'Powers': [1, 2], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['16', '-32', '24', '-8', '1'], 'ConjugacyClass': 5}, {'RootOf': ['404748908723674333032666464555070920145614771', '-162401020191058280957544298954229853002449686', '44887506316774139543111020910888534594138805', '-12245676800997471051187349421155679436422772', '2845304304401025705797493542957388400404680', '-558102130844795712889642083141277058699843', '98328776312687005563417816759240885351052', '-15724515196166416341842474745424705740943', '2258811378830174331587941754932353778278', '-289664772486353084144876355433051048098', '33032798828603737518893289616449620105', '-3352408694628402961322582084929249763', '304494859449555804296123802512783936', '-24957294442780257428713628039368550', '1867610438950689486953462144770491', '-129660172846133367999159288906920', '8502829464922405292925732427388', '-534530719029270481487301056726', '32386749351347306959898723954', '-1879576616836467134016416648', '103217668575351390185507665', '-5313041815104355998677446', '256263558492362770565818', '-11708825797240283803352', '515709270328700281282', '-22149989769843146400', '921238328296503498', '-36139357162046940', '1291265213779754', '-40625689744948', '1091847074922', '-24321438476', '433433804', '-5895470', '57068', '-348', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': [2, 3, 4, 5, 6, 7, 8, 9, 1], 'Classes': [{'RootOf': ['-493081059037', '1'], 'ConjugacyClass': 11}, {'RootOf': ['493081059037', '1'], 'ConjugacyClass': 12}], 'Algorithm': 'ALT', 'CycleType': [9]}], 'Frobs': [11, 12, 12, 8, 7, 10, 14, 9, 14, 8, 2, 7, 14, 10, 9, 8, 10, 6, 7, 10, 14, 7, 7, 10, 13, 14, 8, 10, 8, 10, 10, 11, 11, 7, 12, 10, 2, 11, 14, 10, 6, 13, 10, 9, 14, 10, 14, 13, 14, 10, 7, 12, 10, 14, 3, 13, 11, 11, 13, 13, 9, 9, 3, 7, 2, 7, 2, 11, 3, 12, 10, 13, 14, 2, 12, 10, 9, 12, 8, 11, 14, 10, 11, 12, 13, 11, 10, 13, 10, 7, 12, 14, 10, 12, 7, 6, 12, 12, 9, 11, 7, 11, 9, 10, 14, 12, 3, 3, 10, 7, 7, 10, 14, 3, 8, 14, 11, 3, 7, 11, 10, 8, 12, 3, 3, 8, 14, 8, 3, 14, 12, 9, 3, 11, 11, 11, 11, 10, 13, 13, 3, 13, 7, 11, 9, 8, 13, 4, 8, 9, 3, 12, 8, 12, 10, 12, 12, 13, 8, 4, 11, 12, 13, 14, 12, 10, 12, 10], 'G-Gens': [[3, 2, 8, 4, 5, 6, 7, 1, 9], [6, 1, 7, 3, 8, 2, 4, 9, 5], [1, 4, 3, 5, 2, 6, 7, 8, 9], [2, 3, 4, 1, 8, 6, 7, 5, 9]], 'G-Name': 'H648', 'Polynomial': [29, 14, 18, 35, -33, -25, 11, -1, -2, 1], 'QpRts': [['79495818921319034354128870723250952348402165962641790346934498164229660742234052121005568832977678155508094773441019704', '89159745618827308601831456261016297443928954885825693127318261907303657466166059006073487423027266575284793684430082758', '180275297717597961376236323575041553504637691987059474281074117818529670320117143034622266746058746824683440765875092695'], ['85776059772845870062698964102102717881442222429552577551583498788725946618331976620266471797310383957065616789071154594', '190510249957074577303061201063095582120120067275596565773626278571642487486679559075298228082963430414894640971087402267', '-188641752544268470740410027371283694375591750883575238692505252317980968230704355357866858881874843850365453764703088249'], ['154178540321169128145151662271935587354985398432922914657766752580676880703559076345001998970572955244912214844216010592', '-155046986513795671994733776521223712862273106580910473242630610470717334541836373360501048905993848588234409161129639154', '196278738017565838617169778906902546720334098944976858061966743764911217454686791082621501775543449058127180781041162171'], ['61740739995493899866295682311950908921585798440895294263643296386583717711943645171761514315597441947416883241996742423', '-158607119249437262092450758181676293867448074899458020559894234054924276240774337742645077034074228052957949146168278357', '-164214034817870471603794123042678551609394796944301365759939871427685690251843029841317917777921334774218485010042102027'], ['-147862137341438858887984912706265731144703231022379293903554344051322318207983577961492881678144531793195639403350503096', '-31903130707637315210610442881419288252671992376138545213732044516718211245905221332653151048889202361936691824919123910', '-61238220139488956157628355556965179621340079287929466467290815924893919940676166378015271240691774470419824431731853345'], ['140329427444777820484069923802075006995377628256032454969841627596382324754712325210911410301123992384695490701618793503', '0', '0'], ['-61876374954215374725817594636471651303558135598945236926216182482109534436324478870091116914658128617920579542748184013', '0', '0'], ['-34477025515135127693207415050450878085148991631635548380519767688269473161389665124502308346512335909441616780723007188', '65887240894968363392902320260207415418344151695084780115312348563413677075670314354427561482966582012949615476699556396', '37539971766464098508426403488983325381354836183769738576695078087119690648419617459956279378885757212193141659560788755'], ['136788958856811506896497325152800512637943771846721118340256560375663373698140198064339390622220497725963298582955017104', '0', '0']], 'QpRts-minpoly': [59, 7, 0, 1], 'QpRts-p': 61, 'QpRts-prec': 67, 'Size': 648, 'TransitiveDegree': 9}