Artin representation data - 4.63423.12t175.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, 29], 'Baselabel': '4.63423.12t175.a', 'CharacterField': 3, 'Conductor': 63423, 'Container': '12t175', 'Dets': ['1.29.2t1.a.a', '1.29.2t1.a.a'], 'Dim': 4, 'GalConjSigns': [0, 0], 'Galn': 9, 'GaloisConjugates': [{'Sign': 0, 'Character': [[4], [2], [0], [1, 3], [-2, -3], [-2], [1], [1], [0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1], [0], [-1, -1], [0, 1]], 'GalOrbIndex': 1, 'HardFactors': [9, 18, 17, 19, 14, 9, 13, 17], 'LocalFactors': [[[1], [-4], [6], [-4], [1]], [[1], [-2], [0], [2], [-1]], [[1], [0], [-2], [0], [1]], [[1], [-1, -3], [-3], [2, 3], [1]], [[1], [2, 3], [-3], [-1, -3], [1]], [[1], [2], [3], [2], [1]], [[1], [-1], [0], [-1], [1]], [[1], [-1], [0], [-1], [1]], [[1], [0], [0], [0], [-1]], [[1], [2, 2], [1, 2], [0, 2], [-1]], [[1], [0, -2], [-1, -2], [-2, -2], [-1]], [[1], [-1, -1], [1, 2], [0, -1], [-1]], [[1], [0, 1], [-1, -2], [1, 1], [-1]], [[1], [1], [0], [-1], [-1]], [[1], [0], [1], [0], [1]], [[1], [1, 1], [0], [0, -1], [1]], [[1], [0, -1], [0], [1, 1], [1]], [[1], [1, 1]], [[1], [-1], [-1], [1]]]}, {'Sign': 0, 'Character': [[4], [2], [0], [-2, -3], [1, 3], [-2], [1], [1], [0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1], [0], [0, 1], [-1, -1]], 'GalOrbIndex': 2, 'HardFactors': [9, 18, 17, 19, 14, 9, 13, 17], 'LocalFactors': [[[1], [-4], [6], [-4], [1]], [[1], [-2], [0], [2], [-1]], [[1], [0], [-2], [0], [1]], [[1], [2, 3], [-3], [-1, -3], [1]], [[1], [-1, -3], [-3], [2, 3], [1]], [[1], [2], [3], [2], [1]], [[1], [-1], [0], [-1], [1]], [[1], [-1], [0], [-1], [1]], [[1], [0], [0], [0], [-1]], [[1], [0, -2], [-1, -2], [-2, -2], [-1]], [[1], [2, 2], [1, 2], [0, 2], [-1]], [[1], [0, 1], [-1, -2], [1, 1], [-1]], [[1], [-1, -1], [1, 2], [0, -1], [-1]], [[1], [1], [0], [-1], [-1]], [[1], [0], [1], [0], [1]], [[1], [0, -1], [0], [1, 1], [1]], [[1], [1, 1], [0], [0, -1], [1]], [[1], [0, -1]], [[1], [-1], [-1], [1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '9T29', 'Galt': 29, 'HardPrimes': [2, 3, 5, 29, 37, 43, 3593, 126271], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [3, -36, 81, -36, -27, 9, -6, 9, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [648, 704], 'Proj_Polynomial': [3, -36, 81, -36, -27, 9, -6, 9, 0, 1], 'Proj_nTj': [9, 29]}
• 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], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.29.2t1.a', 'Character': [[1], [-1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [-1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.2349.3t2.a', 'Character': [[2], [0], [2], [2], [2], [2], [2], [-1], [0], [0], [0], [0], [0], [0], [2], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.2349.4t5.a', 'Character': [[3], [1], [-1], [3], [3], [3], [3], [0], [-1], [1], [1], [1], [1], [1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.68121.6t8.a', 'Character': [[3], [-1], [-1], [3], [3], [3], [3], [0], [1], [-1], [-1], [-1], [-1], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.53338743.24t1527.a', 'Character': [[4, 0], [-2, 0], [0, 0], [1, 3], [-2, -3], [-2, 0], [1, 0], [1, 0], [0, 0], [2, 2], [0, -2], [-1, -1], [0, 1], [1, 0], [0, 0], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '4.63423.12t175.a', 'Character': [[4, 0], [2, 0], [0, 0], [1, 3], [-2, -3], [-2, 0], [1, 0], [1, 0], [0, 0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1, 0], [0, 0], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '4.53338743.24t1527.a', 'Character': [[4, 0], [-2, 0], [0, 0], [-2, -3], [1, 3], [-2, 0], [1, 0], [1, 0], [0, 0], [0, -2], [2, 2], [0, 1], [-1, -1], [1, 0], [0, 0], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '4.63423.12t175.a', 'Character': [[4, 0], [2, 0], [0, 0], [-2, -3], [1, 3], [-2, 0], [1, 0], [1, 0], [0, 0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1, 0], [0, 0], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '6.3382903097289.18t220.a', 'Character': [[6], [-2], [2], [-3], [-3], [3], [0], [0], [0], [1], [1], [1], [1], [-2], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.4022476929.9t29.a', 'Character': [[6], [2], [2], [-3], [-3], [3], [0], [0], [0], [-1], [-1], [-1], [-1], [2], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.116651830941.36t1131.a', 'Character': [[6, 0], [0, 0], [-2, 0], [-3, 0], [-3, 0], [3, 0], [0, 0], [0, 0], [0, 0], [-1, -2], [1, 2], [-1, -2], [1, 2], [0, 0], [1, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '6.116651830941.36t1131.a', 'Character': [[6, 0], [0, 0], [-2, 0], [-3, 0], [-3, 0], [3, 0], [0, 0], [0, 0], [0, 0], [1, 2], [-1, -2], [1, 2], [-1, -2], [0, 0], [1, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '8.274015150880409.24t1540.a', 'Character': [[8, 0], [0, 0], [0, 0], [2, 6], [-4, -6], [-4, 0], [2, 0], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '8.274015150880409.24t1540.a', 'Character': [[8, 0], [0, 0], [0, 0], [-4, -6], [2, 6], [-4, 0], [2, 0], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '12.52136588742864540021.18t219.a', 'Character': [[12], [2], [0], [3], [3], [0], [-3], [0], [0], [2], [2], [-1], [-1], [-1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.43846871132749078157661.36t1126.a', 'Character': [[12], [-2], [0], [3], [3], [0], [-3], [0], [0], [-2], [-2], [1], [1], [1], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '18', 'Order': 2, 'Representative': [6, 2, 5, 8, 3, 1, 7, 4, 9]}, {'Size': '27', 'Order': 2, 'Representative': [3, 2, 1, 4, 8, 6, 7, 5, 9]}, {'Size': '4', 'Order': 3, 'Representative': [4, 9, 1, 3, 6, 8, 2, 5, 7]}, {'Size': '4', 'Order': 3, 'Representative': [3, 7, 4, 1, 8, 5, 9, 6, 2]}, {'Size': '6', 'Order': 3, 'Representative': [3, 2, 4, 1, 5, 6, 7, 8, 9]}, {'Size': '12', 'Order': 3, 'Representative': [1, 7, 3, 4, 8, 5, 9, 6, 2]}, {'Size': '72', 'Order': 3, 'Representative': [8, 3, 6, 5, 7, 2, 4, 9, 1]}, {'Size': '162', 'Order': 4, 'Representative': [5, 9, 8, 6, 3, 4, 7, 1, 2]}, {'Size': '18', 'Order': 6, 'Representative': [6, 9, 5, 8, 3, 1, 2, 4, 7]}, {'Size': '18', 'Order': 6, 'Representative': [6, 7, 5, 8, 3, 1, 9, 4, 2]}, {'Size': '36', 'Order': 6, 'Representative': [8, 9, 6, 5, 3, 1, 2, 4, 7]}, {'Size': '36', 'Order': 6, 'Representative': [6, 7, 5, 8, 4, 3, 9, 1, 2]}, {'Size': '36', 'Order': 6, 'Representative': [7, 1, 2, 9, 5, 6, 4, 8, 3]}, {'Size': '54', 'Order': 6, 'Representative': [4, 2, 1, 3, 5, 8, 9, 6, 7]}, {'Size': '72', 'Order': 9, 'Representative': [2, 5, 7, 9, 4, 3, 8, 1, 6]}, {'Size': '72', 'Order': 9, 'Representative': [5, 4, 8, 6, 9, 7, 1, 2, 3]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 3]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 2, 2]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 3, 3]}, {'Data': 0, 'Classes': 14, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 6]}, {'Data': 0, 'Classes': 15, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2, 3]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-16943755272860035605375', '-7475348545090813966725', '-1501722803822607651510', '-228310200716489379459', '-28323378930216222144', '-2814005465254637010', '-236231092245090348', '-15978666558333123', '-861695013399084', '-36946644433236', '-1023190580961', '-12130083963', '1158852663', '80033022', '3995406', '121068', '3456', '54', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-17551553734450443285828', '-8596410075333431597520', '-1840841488035396986031', '-289492312510328810040', '-35905984963911509931', '-3490898549550048648', '-277656788041823655', '-17510609518799220', '-871660439259822', '-33173175247668', '-728022344661', '3979998828', '1715979978', '97511526', '4301100', '127062', '3456', '54', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['120285', '26271', '1728', '36', '1'], 'ConjugacyClass': 4}, {'RootOf': ['102303', '24273', '1728', '36', '1'], 'ConjugacyClass': 5}, {'RootOf': ['1901270741244135156735529786255660156378107416139379105219739388051828994206812928', '-1417629762004707093281310783524425421165900052684798837243590526635606942931704448', '690155830806259126002744069954717650055962408498441925315926603583516755002866048', '-1012058552916156615283769805278037461523100877100428504737014408681423996452846496', '689565973906173181046200409853351593185446744212691650116708755635393844542986032', '-231675178034120843405887837501027898593242334181495669531528831019293456534674296', '62836543187758273625615043784248504360939425051732327478326085130419960463935744', '-12767309819440850788803372161038089232871997644834991080273805139694024004373794', '1683572904914982436475857265063070319530033521960648411185070343575736230837313', '-151141862502649735666286004604893056324871351294542405087561703354991679463921', '1521813124320827388223625815832775055021785871489187411750726545390387840995', '2051493134397153276177431481255953089179910206935421510139274010759618302538', '-229561015523588726513181387666710303500535113955735281040188929568241282436', '7279105652840947589590317776075433828251215672783617180776686600665379023', '1920176301184148371985573640026335806602956252228786947015825147797108049', '-542539786958187650823910105905774500598578839619901393110542952992701432', '67687775767507323499030690332675149856925465388959910097138857911827693', '-5666984046308948773359183465742536955376082970880382700807418561613525', '325634263579743826416102689549370561279179862978894630347449833650667', '-1510770578561433673990019824461397144714035565210657015109449892874', '-2026394736892935674942970783264896095075873012471387952527966495377', '267942182914801203425854367324016428299578363186140599159652399919', '-20355172285639462656374310002138233783029380217836533249479577047', '665851466413024570701225269882837907888427406265491197446378978', '85887958365147282880291203485428318810802667367011228740586369', '-20640036554129253275125320626258618582302272724962629309821617', '2713478506391772246662719567817399095894533161170571169737253', '-290304316045039299312935065275281124662602029755202149457204', '27071218557007006275609841092464235657479443128368604784533', '-2297589921075789229578366581161791237003200763832024457637', '181318721136149484335090818210547188996904190880879732557', '-13415916888753489004020380658526201605688239870766891668', '937225533831106081570360413721742174601868987928112531', '-61996795501232675145696114600821848828695444974124117', '3908019753399272857503630107774474952350307547942113', '-232883703536276866789330338492395150314141532542068', '13256257210157894253826980292844470700857247942469', '-711779002221979088683364843268472809261778875021', '36142467289964637805054688984539630203824282853', '-1703486276110689074414474664615126347460589398', '73984536548992415769183388961980783379690445', '-2777334184431293857109152203349943596221219', '80319298970019280899635180221827710243151', '-645831048713564613856716478377198587448', '-148321855970637844421342453114983774725', '15933921489422834872574616689127604815', '-1164151259320826727326729780362133217', '72569654331973837171592034520870236', '-4055252629463729391711714489443871', '209746602185183176926404506080465', '-10029488599424331921327996003651', '457156030125354850277106619320', '-18416470167813488584125854061', '718703264911948143142144725', '-21951869408453774778333381', '558590146001921707382232', '2321105051870202050343', '-1042165613448415548117', '95322436963249492359', '-5937574633912706580', '304691700751522623', '-15802712027969445', '688135949977113', '-29653220022804', '1254032765595', '-42517884717', '1892798199', '-41881050', '2430486', '-19602', '2268', '0', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['1717167592930303560911658778211671024067474928', '-670002491506154612089927753799094085471999368', '41593302124583850666002635311065522732716392', '-9124022409648493228114459410507777248848752', '1944607463268956317577291155073601364212975', '133721235883361022524366396839026920591166', '50705799468997205245081913894453573015136', '4980251223111563715351239075427714280224', '751203396867782496546988743699189025551', '68741002836922083921160155407192324832', '7325601845034447505871890049548125747', '597105241773330621390309447209452440', '51426297209894357557173196992859497', '3731781196443066866409379293370782', '274570095390658472282499228162879', '17859606770040437870322851386458', '1155018338235112545835687525815', '67784452965064066288791084138', '3914300473656072120458445987', '208107972485985438948396078', '10816298023247775407636379', '521410055254041748292028', '24445671450084933473565', '1065316703683277789082', '44912072729310995961', '1754977403251433826', '65881473946040025', '2271890790597096', '74516384492991', '2206187998794', '61243717923', '1486523826', '33140583', '605178', '9828', '108', '1'], 'ConjugacyClass': 12}, {'RootOf': ['1988815776847467687705238178427310758039007749', '-589045737445271417742213809471197701250407726', '44932519821358523483711060455351825673175603', '-12757470237764526297450821863999015076450310', 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{'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['7093047316566396701535303902448513353113591570155787450448188199228737307086152960', '-2639771117472456299408692828930922380844165631112670854945756737368952142935735168', '1569462590413924475294278634037210376661572422818065024136586203632469394990475008', '-364491121182932468576835022350994631563081667155893810745645916295595025761095936', '128287619964175315768585398975246559531273417637533184722049138219924300081332656', '-18307606687945203229771459458256364334093375314245359075091794447666779513420640', '4096423107376590601819832307066037772845552348059546102479127690729283648226784', '-89809491794498185733429227156001398170460663164458009463429349122492002556438', '35193412580664684208983837610122223090822126540614524986132894388491235687637', '17709179829398936110082414767928814605634171547959478515522703609245432617388', '-1109379756678602362107383291341896453111699361143876742972325963453183721540', 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