Artin representation data - 12.9121115669451776.18t218.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': [2, 389], 'Baselabel': '12.9121115669451776.18t218.a', 'CharacterField': 1, 'Conductor': 9121115669451776, 'Container': '18t218', 'Dets': ['1.389.2t1.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': [15, 9, 16, 4], '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], [1]], [[1], [-1], [-3], [3], [3], [-3], [-1], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T30', 'Galt': 30, 'HardPrimes': [2, 11, 389, 24461483], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [1, -5, -4, 16, -6, -12, 12, -2, -3, 1], 'NumBadPrimes': 2, 'Proj_GAP': [648, 703], 'Proj_Polynomial': [1, -5, -4, 16, -6, -12, 12, -2, -3, 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': '1.389.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [1], [1], [-1], [1], [-1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.1556.3t2.a', 'Character': [[2], [2], [0], [2], [2], [2], [-1], [0], [2], [0], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.605284.6t8.a', 'Character': [[3], [-1], [-1], [3], [3], [3], [0], [1], [-1], [-1], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.1556.4t5.a', 'Character': [[3], [-1], [1], [3], [3], [3], [0], [-1], [-1], [1], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.3767287616.18t217.a', 'Character': [[6], [2], [0], [3], [-3], [0], [0], [-2], [-1], [0], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.3767287616.9t30.a', 'Character': [[6], [2], [0], [3], [-3], [0], [0], [2], [-1], [0], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.3767287616.36t1121.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': '6.3767287616.36t1121.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': '8.5861899530496.12t177.a', 'Character': [[8], [0], [0], [-4], [-1], [2], [-1], [0], [0], [0], [-1], [2], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.1465474882624.12t177.a', 'Character': [[8], [0], [0], [-4], [-1], [2], [-1], [0], [0], [0], [2], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.5861899530496.12t178.a', 'Character': [[8], [0], [0], [-4], [-1], [2], [2], [0], [0], [0], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.1380216344217112196096.36t1123.a', 'Character': [[12], [0], [-2], [0], [3], [-3], [0], [0], [0], [1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.9121115669451776.18t218.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': [7, 2, 5, 4, 3, 6, 1, 8, 9]}, {'Size': '54', 'Order': 2, 'Representative': [7, 3, 2, 5, 4, 9, 1, 8, 6]}, {'Size': '6', 'Order': 3, 'Representative': [8, 2, 3, 4, 5, 6, 1, 7, 9]}, {'Size': '8', 'Order': 3, 'Representative': [7, 4, 5, 9, 6, 3, 8, 1, 2]}, {'Size': '12', 'Order': 3, 'Representative': [8, 2, 6, 4, 3, 5, 1, 7, 9]}, {'Size': '72', 'Order': 3, 'Representative': [2, 3, 1, 5, 7, 8, 4, 9, 6]}, {'Size': '54', 'Order': 4, 'Representative': [5, 2, 1, 4, 7, 8, 3, 6, 9]}, {'Size': '54', 'Order': 6, 'Representative': [7, 4, 5, 2, 3, 6, 8, 1, 9]}, {'Size': '108', 'Order': 6, 'Representative': [6, 4, 1, 2, 7, 8, 3, 5, 9]}, {'Size': '72', 'Order': 9, 'Representative': [4, 3, 1, 5, 7, 8, 9, 2, 6]}, {'Size': '72', 'Order': 9, 'Representative': [9, 3, 1, 5, 7, 8, 2, 4, 6]}, {'Size': '54', 'Order': 12, 'Representative': [8, 5, 2, 3, 4, 9, 1, 7, 6]}, {'Size': '54', 'Order': 12, 'Representative': [7, 5, 2, 3, 4, 9, 8, 1, 6]}], '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': ['-13331900172231189994927308870266929814875503833072273', '16277269278225370473033522467715532066002430884663466', '-14339083405394065800829510641202173377012382944380335', '13492918639491166584156154005427335320068513527492794', '-11234569663063406419811347142606242580895044088571921', '7331704952244988900968600463179908361403065858817464', '-3770503023768133959542978667216453876881753171472227', '1577449769143164581855729332384294776265917371189072', '-552037263499591132958018636933833485438514880174086', '164832965798291911205893924274512646311170902971668', '-42529021952506598754904164756798196973321741487298', '9543871995226149055847227337326213687496357905356', '-1863521901949827980076854225783633681746920062366', '314264028926007651127125903223959124653340718776', '-44832368672272542259724876058122930362851331874', '5135632090912271847791469224082858902659924704', '-399340846953930562668208044978683662614044691', '980873429936176013292012475495754318554358', '6459043615170452694897742030139245396303611', '-1368855044504566673065268678763252069328242', '177351031225899806933144266057728148670629', '-14480972769710090434263056001785210911952', '246079384978408711933330611413374119911', '145904466020798389594943387793280271328', '-27994419471939044030266391699039368996', '2848895901310267447966448793884410648', '-129067694139612762933450173633350188', '-11588947365384737201016659134002488', '3027138546955390583066261755999212', '-305210041237986061975738477288016', '11907587590377460535163426075636', '1220743246056348938872241161728', '-246742813954467693963321966183', '18490232324736592796326083126', '-180656935119583457338155913', '-108172679934271163535877770', '11666192860656133184764553', '-443175401137316703696168', '-24099264231828546142757', '4221308760098167849040', '-228102234554926666230', '-120280508762744556', '875914424336670606', '-61267761157645524', '1400619928464658', '81957061626008', '-8665818555186', '336692034464', '-2355363285', '-443945238', '27099549', '-859774', '16771', '-192', '1'], 'ConjugacyClass': 13}, {'RootOf': ['-20628291220592947349050286209021265054634024631209', '-83506226397581408335324576169018041093678850496118', '-95301294018211217905424988014447082102010563620695', '38188753215970803045750979496575642963430177742554', '67092695791821832666741733980286155816000965356599', '-51779679160330343438459709966320755127601613008040', '1644688848567069002035919768911701071812636529941', '21393307485323639814483859875034552334592764472400', '-21554434808572209236915802295201166051738075299726', '13928617139846940988882093803703865852895051694132', '-6819790975728765459352627209945211664442418339162', '2641681632807514528254436614225627323565158599916', '-827252268597981397644539706585141782159775953318', '212244890968195565187710099892194019872103676952', '-44772404529789551869576046677190403675968877210', '7673660661044743752046316622175655833038072096', '-1024989480365234323366172545308522143187314659', '93504371432993773701343672790126243810792886', '-2201196986304797756322950547359534051064725', '-1073202954718317361055692574744171792305970', '232779890905521374117836286955946068412277', '-25537957884525597339065506251531676952720', '1123097063351021877949571443376091094935', '147105028229263558663854222402428920544', '-36332170008213068515720903236266984244', '3728638953793253901114070891676433752', '-143949293494329068625897327965060700', '-17950148030708366949905964859146232', '3772251588583992968487875033694428', '-320555777495775295865660297693072', '6955780413334093608823519233284', '1817983585721358851248998559104', '-263887617128975675282311250847', '15705488392888739169383738006', '179800632659939949870350127', '-121566836869848489805987562', '10727498275372296575448817', '-300770850426423121410312', '-30562119990343989822413', '4107493592751500608080', '-196704342821110964190', '-1874282595843982924', '903942497860740566', '-58983745059884852', '1213115445617834', '89014796438136', '-8823341245258', '338713913312', '-2367002165', '-443945238', '27099549', '-859774', '16771', '-192', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [2, 3, 4]}, {'Data': {'Powers': [1, 2], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['256', '-256', '96', '-16', '1'], 'ConjugacyClass': 5}, {'RootOf': ['27565669445955965529056104589629960192', '-83805931915176672039930780076107341824', '168961720553397575775647503987752046592', '-153594192891345113638970405246381641728', '79268124812033317739382379141851643904', '-26061936807819003279392381565592070144', '5488313737737576020668770337480081408', '-561789268974164055296153293013633024', '-77350748997755321084999185046569984', '50059183551127813423260269927086080', '-12761775300966133285810271461662720', '2128058172288034948556409652269056', '-224876202378049874732014688495616', '4156130535146052742021990914048', '4446924126898445017237727930880', '-1246417601622932548619527366144', '222961891117628421711272478464', '-31402631654181224446801700736', '3709440167589378613051194880', '-377864222723580388826542336', '33676013333397008489027072', '-2646912631480838839759296', '184276728535637639343040', '-11384982538309488093440', '624219889152752215632', '-30324711005716529568', '1301165296624262400', '-49070899349115792', '1615388042132224', '-45982934749944', '1117410322808', '-22774117696', '379628168', '-4984484', '48496', '-312', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': [2, 3, 4, 5, 6, 7, 8, 9, 1], 'Classes': [{'RootOf': ['26632496', '1'], 'ConjugacyClass': 12}, {'RootOf': ['-26632496', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'ALT', 'CycleType': [9]}], 'Frobs': [10, 14, 12, 11, 9, 12, 9, 11, 10, 14, 8, 13, 11, 10, 10, 14, 12, 10, 12, 10, 7, 7, 13, 3, 12, 3, 14, 10, 13, 11, 12, 10, 2, 3, 8, 10, 9, 8, 13, 11, 12, 12, 14, 9, 8, 8, 7, 7, 13, 13, 13, 12, 3, 10, 10, 10, 7, 14, 7, 13, 7, 2, 8, 7, 12, 14, 9, 2, 7, 14, 4, 2, 13, 9, 10, 12, 2, 8, 10, 11, 11, 10, 7, 7, 10, 7, 8, 12, 13, 11, 4, 10, 8, 11, 10, 7, 6, 14, 8, 13, 10, 6, 8, 7, 8, 10, 13, 10, 2, 13, 11, 10, 14, 2, 8, 7, 10, 13, 9, 11, 12, 3, 10, 7, 11, 9, 11, 12, 10, 7, 8, 11, 8, 8, 11, 11, 11, 9, 6, 13, 14, 10, 9, 9, 3, 3, 10, 12, 7, 11, 11, 8, 10, 14, 9, 5, 7, 8, 11, 3, 5, 12, 8, 12, 3, 11, 7, 3], 'G-Gens': [[1, 5, 2, 3, 4, 9, 7, 8, 6], [1, 2, 5, 4, 6, 3, 7, 8, 9], [2, 3, 1, 5, 7, 8, 4, 9, 6], [1, 4, 3, 9, 5, 6, 7, 8, 2]], 'G-Name': 'H648', 'Polynomial': [1, -5, -4, 16, -6, -12, 12, -2, -3, 1], 'QpRts': [['530423621687014762057399577146838071290078384942882899934386960276649477847682050655928113701745844609137912084412595', '-1105670984094772396300218143927155062451857780403016586792913886304132507684564442358997185292752190019440502460403351', '473416246236954075321152211176511102765336835926552273462897095665507533196798311952716736457243951933243485548574857'], ['-821357005960136735285119036268224302204434538129045799452032193384632758795826234568324730009786881327557822902604204', '774887480384399838191911579251301822874999389868674101112651551635343514810747940829056707797221230906761116146640148', '-649972680652251882995300084216071829141458111123397288306308936910591584878189906931788494734082120148301951470844791'], ['158640590690236086672269326926660085793122883041428232618433823122252227185607533811489786995547323421523862199383356', '762268061340830796118405926442484520814375934041012575555880760190185910234668806647163275766803754177831788687586018', '807324565800428127829574726405468278468602982119201994761115558987599335602765028146281019975550596732992791957151982'], ['-991458332264022863842079017339028354274313456861871526601248285230983404277436680310500505421031441936221980224857594', '343402922753941600181812217484670541637481846362004011237033126113946597449895635711833909525948435841608713772817333', '1170241559206850033038353873994383278069991272429208618916720610098452092810527075208574357759027594095603097783669378'], ['-349910800977890165328337404747673505439732251773622020425132927615478440662006169602447300728246268650058510530181390', '-307614856116876222681699002720314443283326643543237316820693459331728918458504840364105847534532361320192314091023926', '929103158706549162566826545212522598084034148880651989534232144792053634527220349446405634322984410740742220453170428'], ['191270210287654078656068077821013419646609368732193787806699104493226213476398635790957513732698945228534648330798035', '-454653205223954573436706923722170077531049290497775258735187300858456991776163966283057428232271392857639474596562092', '714554646737254945792679539958371782751293959475108902845385560971905991480105037714885459893287135288104362879073807'], ['613471237890593247392381565354012370417157085522960412460042015986330221179295036458692180845075311564550792596631477', '-878038762881936224378650091118220217260400563746509516055861286143811857573282872483624068636381083155830070773376644', '-194285768182656795749625750180060333822760798169297572234973887784045483547767869438099596868341661340803216566249220'], ['-1143894859577608009449781142500850441707235470465843312394428976262979699026977087114620294546821156173688704681044071', '-467272624267523615510212576530987379591672746325436784291958092303614596352243100464950860262688869586568802055616222', '-279130478054297279571526460996450768942576037757254701227923207881462049649030442514617139588902290592440268982325637'], ['-638167033020072637061882757969110002825183095484045561087452786135942798536827500428746878761003819498059572161934418', '-1118290403138341438373723796735972364512481236230678112349684677749290112260643576540890617323169666748369829919457481', '-520268878554598150043053789778311448928533161305811330610411673187860507932337168276785863024945473947301146312824587']], 'QpRts-minpoly': [68, 2, 0, 1], 'QpRts-p': 73, 'QpRts-prec': 63, 'Size': 648, 'TransitiveDegree': 9}