Artin representation data - 12.56773591412619443.18t218.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': [2243], 'Baselabel': '12.56773591412619443.18t218.a', 'CharacterField': 1, 'Conductor': 56773591412619443, 'Container': '18t218', 'Dets': ['1.2243.2t1.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': [13, 2, 13, 2, 15], '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], [2], [3], [1], [-1], [-3], [-2], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T30', 'Galt': 30, 'HardPrimes': [2, 11, 23, 383, 2243], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [16, 72, -116, 106, -51, 41, -18, 6, -2, 1], 'NumBadPrimes': 1, 'Proj_GAP': [648, 703], 'Proj_Polynomial': [16, 72, -116, 106, -51, 41, -18, 6, -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': '1.2243.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [1], [1], [-1], [1], [-1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.2243.3t2.a', 'Character': [[2], [2], [0], [2], [2], [2], [-1], [0], [2], [0], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.5031049.6t8.a', 'Character': [[3], [-1], [-1], [3], [3], [3], [0], [1], [-1], [-1], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.2243.4t5.a', 'Character': [[3], [-1], [1], [3], [3], [3], [0], [-1], [-1], [1], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.11284642907.18t217.a', 'Character': [[6], [2], [0], [3], [-3], [0], [0], [-2], [-1], [0], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.11284642907.9t30.a', 'Character': [[6], [2], [0], [3], [-3], [0], [0], [2], [-1], [0], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.11284642907.36t1121.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': '6.11284642907.36t1121.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': '8.25311454040401.12t177.a', 'Character': [[8], [0], [0], [-4], [-1], [2], [-1], [0], [0], [0], [-1], [2], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.25311454040401.12t177.b', 'Character': [[8], [0], [0], [-4], [-1], [2], [-1], [0], [0], [0], [2], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.25311454040401.12t178.a', 'Character': [[8], [0], [0], [-4], [-1], [2], [2], [0], [0], [0], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.285630720302867636085707.36t1123.a', 'Character': [[12], [0], [-2], [0], [3], [-3], [0], [0], [0], [1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.56773591412619443.18t218.a', 'Character': [[12], [0], [2], [0], [3], [-3], [0], [0], [0], [-1], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '27', 'Order': 2, 'Representative': [1, 2, 5, 6, 3, 4, 7, 8, 9]}, {'Size': '54', 'Order': 2, 'Representative': [3, 5, 1, 6, 2, 4, 8, 7, 9]}, {'Size': '6', 'Order': 3, 'Representative': [1, 2, 3, 9, 5, 4, 7, 8, 6]}, {'Size': '8', 'Order': 3, 'Representative': [2, 8, 5, 6, 7, 9, 3, 1, 4]}, {'Size': '12', 'Order': 3, 'Representative': [1, 2, 7, 9, 3, 4, 5, 8, 6]}, {'Size': '72', 'Order': 3, 'Representative': [3, 5, 4, 1, 6, 2, 9, 7, 8]}, {'Size': '54', 'Order': 4, 'Representative': [1, 2, 4, 5, 6, 3, 9, 8, 7]}, {'Size': '54', 'Order': 6, 'Representative': [2, 1, 5, 6, 3, 9, 7, 8, 4]}, {'Size': '108', 'Order': 6, 'Representative': [2, 1, 4, 7, 6, 3, 9, 8, 5]}, {'Size': '72', 'Order': 9, 'Representative': [3, 5, 4, 2, 6, 8, 9, 7, 1]}, {'Size': '72', 'Order': 9, 'Representative': [3, 5, 4, 8, 6, 1, 9, 7, 2]}, {'Size': '54', 'Order': 12, 'Representative': [5, 3, 1, 9, 2, 4, 8, 7, 6]}, {'Size': '54', 'Order': 12, 'Representative': [5, 3, 1, 6, 2, 9, 8, 7, 4]}], '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': ['486851497355421898505804895821249760890860734275649664', '-1363349316139650296596541570357545503655912586377948016', '1725393198519963651218881726317444921505485229940458712', '-1182073991999021377906931357739269679498432929493031056', '501192184089556908407425176169625030121619980460237812', '-132063563392903629674386283707537617144791399036717147', '13981761288490816123417718190342526957148222563149033', '3229582980411760881213331881559474573161210598902252', '-1166600987528520927627092735569851146985657883095336', '-50198081579275931941787787088002766062300231079767', '116503346189728442128321784889471784230181788919277', '-37763513230882400630643002410462272645757039248500', '7201107470881281778896098041294966297420959720528', '-914212474190592946715003083534037660019669582071', '77017306889001977169124925677203244517810019877', '-4085700168295989161533744063416129716963244146', '324797229654286222042060598853193799718976020', '-95405137202340983405992815606923842229185608', '21905730932897243227119330100461439902562724', '-3250056196072916627660258001606245635777136', '333321044365227072261948492918815624791800', '-22638292581997618335541895281110482392343', '766763459220217789304881841385531876091', '32120647960879015860149969268304433452', '-5648476549858497469156765737833120818', '329482448450640379162744680098807988', '956950102235453244235521724717916', '-780036844799535534656546122681880', '69857302880586222565520996040522', '3397150583152279058426960869518', '70984662241302486036989594796', '28507989666534562740323396622', '2871399330608005685398854630', '253885071840619216800401273', '17534403947578481028612065', '2243363268581794136793886', '212034739862233473368372', '15243552086412257671454', '1437857154866938408900', '126776386698695796314', '10296815760639185492', '827730996129605238', '66398041910448948', '5361556309638530', '399333618509096', '27559272009083', '1887101136661', '123514624042', '7452187072', '412609233', '19180093', '652586', '14452', '183', '1'], 'ConjugacyClass': 13}, {'RootOf': ['13466625826605986666647256431889341642382622115361024', '-31916220532554659794265260749489088161098834429026192', '58696635871012647948816122143298837132801361960999864', '-63692109624720447433891753633079880626106894451525472', '47102574597665051936835092930494364726199075690620892', '-26467494753331702837342281589267881871055217935145131', '12062894377285873289681979615775407788360982191178369', '-4604924355411323266346622839496574021770480638805292', '1493591094849010272562005749769926816969033300208888', '-414932860762771087514081364634038658793284428729659', '100036699291575681518841504044112499042944285042361', '-21479333912362336719195943166181167570120817614484', '4258978752625017931238720383797985200481769910496', '-799240243310374673598553700252759723498601134547', '140695713200587163877854632584464803599685804409', '-22514790238584367198516392697243980044089798786', '3192449743793652749841900404997398751439580324', '-396882803978941018410026054696885877642774712', '42924935619548021210736610131231887034922004', '-3942955525412207752489968419227321014330792', '290847541899013017914727835430841427102480', '-15211386478058362380879082825855796519323', '311687707381566979108397323723301799311', '40880162049662862665640749082122307052', '-6129850997080223603238623099051029458', '460591645989179745420052524739496376', '-17650945365369447759017999324975792', '81258447997237986683434495888596', '40020357642305176088247090378750', '-4251520106891453335504184082978', '742379761009900977340785439980', '19409448095826573342336033826', '-4999822953514199747632289246', '-128687297787312648374798823', '28339193862834569943530289', '3545430987878756104724954', '82241828596202342541488', '-15795782084544451490354', '-1479357857762287130676', '-95037851328624091122', '-8006969764179653632', '-463936514179726330', '-5994927556677108', '1162623791795158', '150683872967012', '16583397072723', '1578386728861', '118270552846', '7401970788', '412393905', '19180093', '652586', '14452', '183', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [2, 3, 4]}, {'Data': {'Powers': [1, 2], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['279841', '-48668', '3174', '-92', '1'], 'ConjugacyClass': 5}, {'RootOf': ['3735627991493711529682356135047407725524951932361', '4694227265357166287085367624328753834156631436840', '2853425785434299637610171982034154155801047833138', '1129124388899879919856768764173494239149078296948', '329697368018455820233440976285053718475671498037', '76178174748918561193542549513138440405601314132', '14552576253858802887752327856179845669999439148', '2366819443253207143935897888428221938917288136', '334466083995057504088057472115352511945372590', '41672463145331491142083836778521083292681008', '4627163987538588490568369804124259999866988', '461532199991157191681248194233317393957384', '41596919550385414063460093275406391777858', '3402046295421955718895527521869857605092', '253230392963990498194870387417497174822', '17186142544016666686254681318384411392', '1064353217128538190987089502118308769', '60144522188201280381979907641475796', '3098027936986683365468570626738262', '145195657885077223306079622660292', '6174853467448058185567914373215', '237443705194200636305884634988', '8219695343120325187178109802', '254843852707933934336981648', '7034820053955258449031196', '171749241357207758068780', '3680622294884316427972', '68639343718361384292', '1102654841574960739', '15072567987951612', '172637794769038', '1623949868684', '12205948119', '70430880', '292762', '780', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': [2, 3, 4, 5, 6, 7, 8, 9, 1], 'Classes': [{'RootOf': ['1356531803968', '1'], 'ConjugacyClass': 12}, {'RootOf': ['-1356531803968', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'ALT', 'CycleType': [9]}], 'Frobs': [14, 11, 10, 12, 2, 8, 11, 8, 14, 13, 12, 8, 10, 9, 14, 9, 10, 9, 12, 12, 10, 14, 12, 7, 6, 9, 12, 11, 11, 13, 10, 8, 13, 6, 10, 7, 10, 12, 8, 11, 10, 3, 7, 8, 11, 7, 11, 9, 7, 13, 10, 7, 13, 7, 7, 7, 10, 7, 7, 12, 3, 3, 14, 11, 11, 7, 9, 13, 3, 13, 14, 7, 13, 14, 8, 2, 12, 10, 10, 14, 14, 7, 10, 9, 7, 11, 12, 7, 7, 11, 6, 14, 13, 3, 14, 13, 2, 13, 10, 12, 7, 7, 9, 7, 13, 2, 13, 11, 11, 10, 11, 8, 9, 13, 7, 12, 10, 6, 10, 13, 3, 7, 10, 2, 8, 12, 9, 2, 12, 14, 3, 6, 7, 4, 11, 12, 10, 12, 10, 2, 13, 10, 9, 14, 11, 11, 3, 9, 7, 3, 11, 7, 11, 7, 10, 9, 8, 14, 8, 2, 13, 14, 7, 12, 2, 7, 14, 12], 'G-Gens': [[5, 3, 1, 4, 2, 6, 8, 7, 9], [3, 5, 4, 1, 6, 2, 9, 7, 8], [1, 2, 5, 4, 7, 6, 3, 8, 9], [2, 8, 3, 4, 5, 6, 7, 1, 9]], 'G-Name': 'H648', 'Polynomial': [16, 72, -116, 106, -51, 41, -18, 6, -2, 1], 'QpRts': [['-683728771864945221042397910208331637480072187072488780381664376986726738950142867763787965888967741236251609036', '876624013884617890092686953512083511411822093397696221098020033926534899357605402438811952537041009474379981035', '-205675967235418088887323119164236918142141691271651745316499522827827745347155851690658339711552962571510484611'], ['681921682124507272293183229543747166785602027236650079481325671371327998845089793919483854515961602543462500981', '144482929550357549589067051766640987185929121776088578145122205600081394966542950738476006882897738917251574798', '-280804813085051067277597631345795846443001108396316030696367789211416063297269493630083124837062005734008344995'], ['250254733265348290573995297969937181611571757657062814539664145012512603675685530666507160341038723141468617738', '0', '0'], ['-317719756921095870464292728926382751660404434659075366308199229568240964479288254478882069390467430226177371317', '-820382030143184075043064720231095410810469461366273428845255823466599016308306626072497049647000850743646231868', '-100241578222812914831393329357842998787843647937327801911564375826489259637425151117757638449385270389499223188'], ['-655853579840241213137706214276848361076824003647396121630596440094306730665380190062915588683022203549269545429', '0', '0'], ['301841042365178374078998200152352625469761258119634111542360552270659394048068067080540330347611232569065231663', '37754140875957258868534238094582065169862607082165393637759837552119234989504463281505975486741859552911032241', '-602455954704183995299920912125197893956426271493251079650537627739867415048170601964460748879033360841859213465'], ['-280147856227891506175885026844951783782223277519481530802427414371424206948555511107248541558615595748385599309', '0', '0'], ['-163635344704122478083391117845578289258026675549020796689862661103466705992484712335030202643927361483478268376', '795316585652274923995474207562707875473079501883339772899057407132968351171766160142532571738044854363069716488', '486480780320469156164920750510032764585142799667967776012867312039243808644425345320741464548614968305518829606'], ['867067851803262351957496270436055849390615535434115590249399753469665350467008144081333022960388773989566043087', '782627889267226816174530482136513345640606854284108035207495985914479781318802162790991074160258991190735199627', '702697532926996910131314241483040892744269919430578881562102003566356674685595753082218387328418631231358436653']], 'QpRts-minpoly': [92, 9, 0, 1], 'QpRts-p': 97, 'QpRts-prec': 56, 'Size': 648, 'TransitiveDegree': 9}