Artin representation data - 16.55586726597831627718001881.24t1334.a

Formats: - HTML - YAML - JSON - 2023-12-03T18:04:48.212552

• 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': [3, 7, 17], 'Baselabel': '16.55586726597831627718001881.24t1334.a', 'CharacterField': 1, 'Conductor': 55586726597831627718001881, 'Container': '24t1334', 'Dets': ['1.1.1t1.a.a'], 'Dim': 16, 'GalConjSigns': [1], 'Galn': 9, 'GaloisConjugates': [{'Sign': 1, 'Character': [[16], [0], [0], [-2], [-2], [1], [0], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [10, 12, 13, 14, 2, 10], 'LocalFactors': [[[1], [-16], [120], [-560], [1820], [-4368], [8008], [-11440], [12870], [-11440], [8008], [-4368], [1820], [-560], [120], [-16], [1]], [[1], [0], [-8], [0], [28], [0], [-56], [0], [70], [0], [-56], [0], [28], [0], [-8], [0], [1]], [[1], [0], [-8], [0], [28], [0], [-56], [0], [70], [0], [-56], [0], [28], [0], [-8], [0], [1]], [[1], [2], [3], [-2], [-7], [-12], [-2], [8], [18], [8], [-2], [-12], [-7], [-2], [3], [2], [1]], [[1], [2], [3], [-2], [-7], [-12], [-2], [8], [18], [8], [-2], [-12], [-7], [-2], [3], [2], [1]], [[1], [-1], [0], [-5], [5], [0], [10], [-10], [0], [-10], [10], [0], [5], [-5], [0], [-1], [1]], [[1], [0], [0], [0], [-4], [0], [0], [0], [6], [0], [0], [0], [-4], [0], [0], [0], [1]], [[1], [0], [1], [0], [1], [0], [-2], [0], [-2], [0], [-2], [0], [1], [0], [1], [0], [1]], [[1], [0], [1], [0], [1], [0], [-2], [0], [-2], [0], [-2], [0], [1], [0], [1], [0], [1]], [[1], [0], [0], [0], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [0], [0], [0], [1]], [[1], [0], [0], [0], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [0], [0], [0], [1]], [[1], [0], [-1]], [[1], [1], [1], [-2], [-2], [-2], [1], [1], [1]], [[1], [0], [-3], [0], [3], [0], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T26', 'Galt': 26, 'HardPrimes': [2, 3, 7, 17, 29927, 441359], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [63, -161, 181, -101, 49, -62, 52, -14, -2, 1], 'NumBadPrimes': 3, 'Proj_GAP': [432, 734], 'Proj_Polynomial': [63, -161, 181, -101, 49, -62, 52, -14, -2, 1], 'Proj_nTj': [9, 26]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.3.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [1], [1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.867.3t2.b', 'Character': [[2], [2], [0], [2], [-1], [-1], [2], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.127449.24t22.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [2, 0, 0, 0], [-1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, -1, 0, -1], [0, 1, 0, 1]], 'CharacterField': 8}, {'GalConj': 2, 'Baselabel': '2.127449.24t22.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [2, 0, 0, 0], [-1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 1], [0, -1, 0, -1]], 'CharacterField': 8}, {'GalConj': 1, 'Baselabel': '3.7803.4t5.a', 'Character': [[3], [3], [1], [3], [0], [0], [-1], [1], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.2601.6t8.a', 'Character': [[3], [3], [-1], [3], [0], [0], [-1], [-1], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.56205009.8t23.a', 'Character': [[4], [-4], [0], [4], [1], [1], [0], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.126746061030603.9t26.a', 'Character': [[8], [0], [2], [-1], [2], [-1], [0], [-1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.126746061030603.18t157.a', 'Character': [[8], [0], [-2], [-1], [2], [-1], [0], [1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '16.55586726597831627718001881.24t1334.a', 'Character': [[16], [0], [0], [-2], [-2], [1], [0], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '9', 'Order': 2, 'Representative': [9, 4, 6, 2, 5, 3, 8, 7, 1]}, {'Size': '36', 'Order': 2, 'Representative': [9, 3, 2, 6, 5, 4, 7, 8, 1]}, {'Size': '8', 'Order': 3, 'Representative': [5, 8, 2, 6, 9, 7, 4, 3, 1]}, {'Size': '24', 'Order': 3, 'Representative': [3, 2, 7, 4, 5, 8, 1, 9, 6]}, {'Size': '48', 'Order': 3, 'Representative': [2, 8, 4, 6, 9, 3, 5, 1, 7]}, {'Size': '54', 'Order': 4, 'Representative': [7, 6, 2, 3, 5, 4, 9, 1, 8]}, {'Size': '72', 'Order': 6, 'Representative': [4, 9, 1, 2, 7, 3, 8, 5, 6]}, {'Size': '72', 'Order': 6, 'Representative': [2, 1, 7, 8, 4, 6, 9, 3, 5]}, {'Size': '54', 'Order': 8, 'Representative': [1, 9, 8, 2, 7, 5, 4, 6, 3]}, {'Size': '54', 'Order': 8, 'Representative': [1, 5, 4, 6, 3, 9, 8, 2, 7]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 2, 2]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 3, 3]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 2, 2]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [1, 2, 6]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [1, 4, 4]}, {'Data': {'Powers': [1, 3], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-186922160661924416401075082227182791797110531016', '17653428190976851197619930162647239528607430659', '-433307543487667233351335466466524728886925560', '-11508231761119705697768723057137147866467014', '1119876826735090022196870133740199749023244', '-39528497913142826246653367313510413141559', '-477255085674886333531564639200456788624', '124173181641779439978814681590897474441', '-3623813964554052165583108579409675574', '-133708222845154066107316734691151218', '12018819823128734272154899129531971', '-309480953572893203796997014609129', '323143006854130973825093513023', '180404656413646310615127605853', '-4601631190042256946003283233', '32610808049363415609955049', '762483177886283691655098', '-22218320946342843578841', '235116049457611601905', '-545669166293990061', '-13706748845817666', '147324024308813', '-308811143562', '-4035395091', '27603322', '-13059', '-384', '1'], 'ConjugacyClass': 10}, {'RootOf': ['2116227626295942343423507905705176582271359512025', '-256123874509802753657352873402070532436191182245', '17288320095935652068390788778309370463729638921', '-933068415083423418180161404487122937638079377', '44580748102304679630042187254816518627618286', '-1883168907566114793068783806588035063451446', '70880203112088249438651630268397891579365', '-2421151367247581985714883087945116445695', '75680319876842559659229171314610942006', '-2166823890595275945323832265260922681', '56812790920406735568905815484384442', '-1360271387376366548891989678114338', '29621752676121878817607195116457', '-582523395276502247455193450028', '10165546331992108925703989667', '-153334905580838514251367550', '1930790807088481884530568', '-18748560774242773780656', '105386692994159258422', '348001176576420984', '-13576066785966576', '112560636155432', '-149334852030', '-3916140090', '24927724', '-7452', '-384', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'RES', 'CycleType': [1, 8]}, {'Data': {'Powers': [1, 2], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['2733589', '-195944', '6549', '-128', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-135615209473449722250316291282380276119', '30786136912830845465025038436775431054', '-1649262933273519790025926855318985439', '-357755232998963247721842429021920971', '90536289458728390910966690515622508', '-11265057239854502974976027734569384', '983756268973198121184163957494277', '-66722149698660667446118900679070', '3684212626398928560040104296523', '-170059054437731740637937880402', '6668205842493296970383865156', '-224306854514993114556551721', '6509185059335194963012177', '-163336467650651930853996', '3542798022050192047410', '-66226494398872843879', '1060910805653186310', '-14436386545735962', '164741089807936', '-1547941359192', '11663517168', '-67735210', '284442', '-768', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [3, 6]}], 'Frobs': [11, 3, 11, 5, 8, 6, 3, 9, 10, 3, 6, 9, 8, 9, 8, 8, 8, 9, 9, 11, 7, 7, 10, 11, 9, 10, 9, 11, 7, 10, 6, 11, 3, 6, 11, 6, 6, 7, 10, 11, 8, 6, 11, 5, 3, 4, 5, 7, 3, 7, 8, 11, 7, 8, 8, 11, 11, 9, 6, 8, 9, 8, 7, 11, 9, 11, 9, 2, 11, 7, 8, 3, 5, 7, 9, 8, 8, 7, 10, 9, 10, 9, 3, 9, 5, 10, 10, 7, 11, 5, 8, 3, 6, 11, 5, 3, 11, 10, 7, 7, 9, 8, 10, 10, 9, 6, 11, 8, 8, 5, 9, 9, 3, 7, 9, 3, 9, 10, 8, 10, 9, 6, 8, 11, 6, 3, 5, 11, 6, 6, 9, 3, 6, 9, 10, 4, 11, 6, 11, 11, 6, 8, 6, 8, 9, 10, 9, 11, 6, 10, 7, 10, 7, 8, 6, 11, 7, 8, 6, 8, 11, 11, 7, 8, 8, 3, 7, 6], 'G-Gens': [[7, 2, 1, 4, 5, 9, 3, 6, 8], [3, 4, 7, 5, 2, 9, 1, 6, 8], [8, 2, 1, 9, 7, 3, 4, 6, 5], [9, 2, 3, 6, 1, 7, 4, 8, 5], [4, 9, 1, 2, 7, 3, 8, 5, 6], [5, 8, 2, 6, 9, 7, 4, 3, 1]], 'G-Name': 'H432', 'Polynomial': [63, -161, 181, -101, 49, -62, 52, -14, -2, 1], 'QpRts': [['-278488097140750046433569551534095543384994638792384386250089395071907133439138045863', '0', '0', '0'], ['176411712494771794637696103548217413579177427441984746775000356146230615399300532830', '333545721734642364045855933584019405915471721231309602307653334319298628984950840157', '-328597153906406917696443104504359544028743301678030926022693199687386788901415994040', '71350738810770668102379905684706643591475127671111131657595548496163756931048710185'], ['-147517527029886071908597958519369120075804132237229551686183800075360543445759548004', '-29617959931308904352843055484880592070596095165995184123547175796090372309170384064', '19932828406048503021560620999727213669252912214674016262297148756008512143008263381', '260083268580414089564431222055385848424130566711334485053936927616910605793103568244'], ['165546170875961206632055688834557710140828079560690234023923621176675933514193080698', '110496539277269198862667100452777271801213931951966858132390057581997555323910965621', '146202924545173753464110518900756318835218378527994093706961629317261264577915043910', '277160859325290462173554648461496515893272758135045824981457317194014111137525697912'], ['-159698899094741481141721285039974831630824876523231593376946111362651964864004747029', '-73020241902607984511559406560030199400303273638402105454330192661989954028892504133', '87353683523013611082489014352739237710332363702966008908908242196398144859545300504', '135657504529555267616958671462190231747312708296281016872096346878647933147278332588'], ['-66747292126695838694631448694679988894066683021689886735035256551708011374906099689', '22996422059482881108134057957790785001899432562889616366550106505603260306285400176', '84027210302295179266322881196229814914115587913742928965487213034344530411126178791', '239529672153595272872320748517671954593781352946968580648250476510466294338505589869'], ['-86430405531034868731170726099570072105451705365464048889873369144292332843920231051', '-223533325731756702569190193179938987545039062858276194008525126300187222921459692900', '-254109004801454128659418178712746512674115767797775411101209618097854862829109376990', '263223458185674296582308923549508652983528341216443657803931389225183845314561516995'], ['-301297678440888897778786500894135959258315076388387859350973509587237232796736946884', '142654746385796408059366148212042307814421226072304519999682244514280039906719111343', '87973251850231872173747038812262980169644477055107301131950840024585086108186069699', '-93289644845397661028830071610913994893399886810565412437793241297942178752675252358'], ['-8955925252716983872739044056426630778080173926546209911354928267915713641543525799', '-283521901891517260642430584981779991517067880155797113219873248162911935262343736200', '157216260081098127347631208955390491404295350061321988148297744456644113630744514745', '260640025752059978699805396790908192474962590337897826223590020852888399075682898151']], 'QpRts-minpoly': [5, 56, 16, 0, 1], 'QpRts-p': 73, 'QpRts-prec': 45, 'Size': 432, 'TransitiveDegree': 9}