Artin representation data - 16.52515441317197610947265625.24t1334.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': [3, 5, 31], 'Baselabel': '16.52515441317197610947265625.24t1334.a', 'CharacterField': 1, 'Conductor': 52515441317197610947265625, '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': [12, 13, 10, 14, 2, 4, 4], '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], [-4], [0], [6], [0], [-4], [0], [1]], [[1], [0], [0], [0], [0], [0], [-1]], [[1], [0], [0], [-2], [0], [0], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T26', 'Galt': 26, 'HardPrimes': [3, 5, 11, 31, 1217, 8893, 694873], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [46, 113, -55, -192, -14, 90, -4, -9, -3, 1], 'NumBadPrimes': 3, 'Proj_GAP': [432, 734], 'Proj_Polynomial': [46, 113, -55, -192, -14, 90, -4, -9, -3, 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': '2.72075.3t2.a', 'Character': [[2], [2], [0], [2], [-1], [-1], [2], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.72075.24t22.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': '2.72075.24t22.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': '3.72075.4t5.a', 'Character': [[3], [3], [1], [3], [0], [0], [-1], [1], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.216225.6t8.a', 'Character': [[3], [3], [-1], [3], [0], [0], [-1], [-1], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.216225.8t23.a', 'Character': [[4], [-4], [0], [4], [1], [1], [0], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.374415615421875.9t26.a', 'Character': [[8], [0], [2], [-1], [2], [-1], [0], [-1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.3369740538796875.18t157.a', 'Character': [[8], [0], [-2], [-1], [2], [-1], [0], [1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '16.52515441317197610947265625.24t1334.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': [6, 8, 9, 5, 4, 1, 7, 2, 3]}, {'Size': '36', 'Order': 2, 'Representative': [1, 2, 3, 6, 8, 4, 9, 5, 7]}, {'Size': '8', 'Order': 3, 'Representative': [3, 1, 2, 5, 7, 8, 4, 9, 6]}, {'Size': '24', 'Order': 3, 'Representative': [8, 2, 7, 4, 1, 6, 9, 5, 3]}, {'Size': '48', 'Order': 3, 'Representative': [9, 1, 4, 5, 3, 8, 6, 7, 2]}, {'Size': '54', 'Order': 4, 'Representative': [2, 6, 4, 9, 3, 8, 7, 1, 5]}, {'Size': '72', 'Order': 6, 'Representative': [8, 1, 5, 2, 6, 3, 4, 9, 7]}, {'Size': '72', 'Order': 6, 'Representative': [1, 8, 5, 2, 4, 7, 6, 9, 3]}, {'Size': '54', 'Order': 8, 'Representative': [5, 3, 6, 8, 2, 4, 7, 9, 1]}, {'Size': '54', 'Order': 8, 'Representative': [4, 9, 1, 2, 8, 5, 7, 3, 6]}], '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': ['-9874597943352001699394159694090581209545922329', '-638980643539797231450033600191364926631390984', '165144303659566923566379294776703450879145203', '785831781098159983208425859743587422379111', '-989398867987202684052908121886684779683022', '54692144034735804189100827607398508353396', '-1252087900121108622150354592286936999856', '-6593151892706626468714677718586187744', '1308965291872769533150684642137179526', '-31061852741268869251747579166586956', '118942163975195292565315690907280', '8256562908930401905432734218697', '-212070118621991449692451938838', '1947452358259300530086986041', '11083497672219129659891793', '-693815832600822766720190', '7576048132933093721118', '-56269642680007685307', '-786326670047540605', '26437832399644626', '-411314256677202', '6011098098362', '-83965066767', '961700904', '-10296504', '92946', '-486', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-6198071044812288013130828211973848099142505931246', '480189936707384902966051765439148382243958057763', '-17695169832501993612095066425332401249794984521', '211705953250916072650300835645008863506611224', '7371429872102793451362994663559412333106389', '-173003975672116822149693815291873634724599', '-5535093827056813649915637463488473634028', '126707330796548296332915707567344904772', '1568572830433963068154469816128737303', '-14120524859967910850991804124615862', '-996120592656060150860232881877258', '-907376681837624785214501626200', '349704751531359640069827051955', '3359083839329918293854764235', '-130570693613987335127959830', '-871001361399758825626749', '25572866277991072823646', '277868530558057324350', '-4717794869693848993', '-41128196173202358', '388437056413740', '8006584922208', '-65608860354', '-272074287', '-772527', '71040', '-486', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'RES', 'CycleType': [1, 8]}, {'Data': {'Powers': [1, 2], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['700569', '-269766', '-5910', '39', '1'], 'ConjugacyClass': 4}, {'RootOf': ['1599703516534186295879864723806856355', '390635063061979098573327019590609003', '51244801245888446930406040490258664', '4444221964931393034563411921199558', '261824016564422880456491058396795', '9194351871607845467497155549315', '55688388207467667292804253578', '-17300773498885366976197872212', '-1279980738390305034917898498', '-49796459864331324588707287', '-954688298941319155582235', '11107480788328500897777', '1594543178605931054171', '65077527168645653182', '1622031646519646115', '30591752507830110', '573064226766098', '12959038031445', '328663941974', '6437374377', '81438450', '1080691', '20236', '234', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [3, 6]}], 'Frobs': [11, 3, 8, 9, 10, 7, 10, 9, 11, 8, 6, 6, 3, 7, 11, 8, 11, 9, 6, 8, 5, 7, 11, 11, 7, 10, 6, 11, 9, 8, 6, 11, 8, 7, 8, 7, 6, 4, 11, 8, 10, 7, 11, 7, 10, 9, 6, 9, 11, 7, 8, 11, 5, 10, 3, 8, 3, 6, 5, 8, 9, 10, 9, 8, 9, 8, 6, 9, 8, 9, 11, 10, 9, 5, 9, 8, 11, 5, 11, 7, 10, 7, 10, 7, 7, 11, 11, 9, 3, 5, 11, 10, 5, 3, 9, 8, 10, 8, 9, 2, 6, 11, 3, 8, 9, 9, 3, 8, 11, 6, 6, 9, 11, 5, 5, 11, 9, 10, 11, 8, 9, 2, 11, 10, 7, 8, 7, 11, 7, 9, 9, 8, 9, 9, 8, 9, 8, 9, 3, 8, 5, 3, 9, 3, 6, 8, 9, 8, 9, 10, 7, 10, 9, 8, 7, 11, 4, 11, 7, 3, 3, 8, 7, 8, 8, 11, 2, 7], 'G-Gens': [[3, 1, 2, 7, 4, 6, 5, 8, 9], [9, 5, 2, 3, 4, 6, 8, 1, 7], [5, 2, 9, 4, 8, 6, 3, 1, 7], [3, 1, 2, 5, 7, 8, 4, 9, 6], [5, 4, 7, 6, 8, 2, 9, 1, 3], [5, 3, 6, 8, 2, 4, 7, 9, 1]], 'G-Name': 'H432', 'Polynomial': [46, 113, -55, -192, -14, 90, -4, -9, -3, 1], 'QpRts': [['6579277849772695188258324933683067381177848144731305357651893973228163702676291752', '0', '0', '0'], ['-13074813617972964313752039616591973679795891213252266413642125650686331818079226880', '-5162500296392750187146968131743905138664654520508357757214698529375529857845498530', '-9675348262665738494334747085235781930878951960756136059077762248947787540920195736', '13045183758035071940609216531878611994735007007429840121892355618311695195305237351'], ['-9552211179548841538626249843222763388255582703291715782599160373181157461735317445', '10538805587132052384287072351000172043891882648312710188774496919776321993139704353', '1267804131944203475804746185637955887933066909808197822462860510934224792392483996', '-12411840554573406115507833362132181675916746616234164112579055362915382697850636124'], ['-3036298444158196206586313008600035243071302650694398440018993198784437578693652748', '-900941800619723111931844481057952208388130587444427699249424912446865834375393856', '11320022664405289584099258806478037204612323128954370174223643074941845262302977063', '-8169752857110226164667297285135231023307356553291462617420724928472880506585430260'], ['10698883115171064801430030300787063060625027757429422814671310197499232145116253126', '893601894060865451497864943287218525395170525619456187264603723995912498802215592', '-1841254673866789231243015812117835364065986083117092050072454476334975653422965168', '2368740426918721835949158037559083504802500201394071150261034418856519382478654973'], ['1931605636143039922168110939984167871093989390776870406725428681883045899767813930', '-8516971890581664087608441313452963503502264282288161518472340848075740316464916380', '79056392204513312582056809611734904342633411607571370101019842488191948410884748', '10772619886483378308604602847829017015749490091624193215604106580732340611687826300'], ['5230370730423547679269902734290904296030639912835020697839190968266944168756189719', '3402875213912059872000078792053831898652722468765120183562531394371358076519239740', '-3176592580187873855144646500010729698546015191594519119133141671217398264289791583', '10180222137774488751758071939681039145396197813934543830051782573387553670811801949'], ['7524183399659938590578035746900400586330974289484502521164545641631073978316734572', '-6269907184800167648637969162543485430622398653423808618824402114396704634096421415', '10248798804588324249773016711715661407011871134065030286687356214348538401950676908', '-3002083630380387661050541207305513823620760592589747159574334674252831879933256200'], ['-6300997489490284122739802187230830884135702928018741161792090239856533036125086023', '6015038477289327327540207002457083813237672400967469034159234366151248074321070496', '-8222486476421929041536669116079042410408941348967422425191521246212638946424070228', '-12783089167147640895695377502374825137838331352267274428235164225647013775914197989']], 'QpRts-minpoly': [2, 12, 3, 0, 1], 'QpRts-p': 13, 'QpRts-prec': 74, 'Size': 432, 'TransitiveDegree': 9}