Artin representation data - 18.417941444393576367118610333696.36t1758.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, 97], 'Baselabel': '18.417941444393576367118610333696.36t1758.a', 'CharacterField': 1, 'Conductor': 417941444393576367118610333696, 'Container': '36t1758', 'Dets': ['1.776.2t1.a.a'], 'Dim': 18, 'GalConjSigns': [1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[18], [-6], [2], [0], [0], [-2], [0], [0], [0], [0], [-2], [0], [0], [2], [0], [0], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [21, 17, 22, 15], 'LocalFactors': [[[1], [-18], [153], [-816], [3060], [-8568], [18564], [-31824], [43758], [-48620], [43758], [-31824], [18564], [-8568], [3060], [-816], [153], [-18], [1]], [[1], [6], [9], [-16], [-60], [-24], [116], [144], [-66], [-220], [-66], [144], [116], [-24], [-60], [-16], [9], [6], [1]], [[1], [-2], [-7], [16], [20], [-56], [-28], [112], [14], [-140], [14], [112], [-28], [-56], [20], [16], [-7], [-2], [1]], [[1], [0], [-9], [0], [36], [0], [-84], [0], [126], [0], [-126], [0], [84], [0], [-36], [0], [9], [0], [-1]], [[1], [0], [-9], [0], [36], [0], [-84], [0], [126], [0], [-126], [0], [84], [0], [-36], [0], [9], [0], [-1]], [[1], [2], [-7], [-16], [20], [56], [-28], [-112], [14], [140], [14], [-112], [-28], [56], [20], [-16], [-7], [2], [1]], [[1], [0], [-9], [0], [36], [0], [-84], [0], [126], [0], [-126], [0], [84], [0], [-36], [0], [9], [0], [-1]], [[1], [0], [0], [-6], [0], [0], [15], [0], [0], [-20], [0], [0], [15], [0], [0], [-6], [0], [0], [1]], [[1], [0], [0], [-6], [0], [0], [15], [0], [0], [-20], [0], [0], [15], [0], [0], [-6], [0], [0], [1]], [[1], [0], [3], [0], [0], [0], [-8], [0], [-6], [0], [6], [0], [8], [0], [0], [0], [-3], [0], [-1]], [[1], [2], [1], [0], [-4], [-8], [-4], [0], [6], [12], [6], [0], [-4], [-8], [-4], [0], [1], [2], [1]], [[1], [0], [3], [0], [0], [0], [-8], [0], [-6], [0], [6], [0], [8], [0], [0], [0], [-3], [0], [-1]], [[1], [0], [-1], [0], [-4], [0], [4], [0], [6], [0], [-6], [0], [-4], [0], [4], [0], [1], [0], [-1]], [[1], [-2], [5], [-8], [8], [-8], [0], [8], [-14], [20], [-14], [8], [0], [-8], [8], [-8], [5], [-2], [1]], [[1], [0], [1], [0], [-4], [0], [-4], [0], [6], [0], [6], [0], [-4], [0], [-4], [0], [1], [0], [1]], [[1], [0], [0], [2], [0], [0], [-1], [0], [0], [-4], [0], [0], [-1], [0], [0], [2], [0], [0], [1]], [[1], [0], [0], [0], [0], [0], [-3], [0], [0], [0], [0], [0], [3], [0], [0], [0], [0], [0], [-1]], [[1], [0], [0], [0], [0], [0], [-3], [0], [0], [0], [0], [0], [3], [0], [0], [0], [0], [0], [-1]], [[1], [0], [1], [0], [0], [0], [0], [0], [-2], [0], [-2], [0], [0], [0], [0], [0], [1], [0], [1]], [[1], [0], [0], [0], [0], [0], [1], [0], [0], [0], [0], [0], [-1], [0], [0], [0], [0], [0], [-1]], [[1], [0], [0], [-1]], [[1], [1], [-4], [-4], [6], [6], [-4], [-4], [1], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T47', 'Galt': 47, 'HardPrimes': [2, 7, 97, 107], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [7, 16, -10, -12, 10, -4, -6, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [7, 16, -10, -12, 10, -4, -6, 0, 1], 'Proj_nTj': [8, 47]}
• 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], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.97.2t1.a', 'Character': [[1], [1], [1], [-1], [1], [1], [-1], [1], [1], [-1], [1], [-1], [1], [1], [-1], [1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.776.2t1.a', 'Character': [[1], [1], [1], [-1], [-1], [1], [-1], [1], [1], [-1], [1], [-1], [-1], [1], [1], [1], [-1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.8.2t1.a', 'Character': [[1], [1], [1], [1], [-1], [1], [1], [1], [1], [1], [1], [1], [-1], [1], [-1], [1], [1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.776.4t3.b', 'Character': [[2], [2], [2], [0], [0], [-2], [0], [2], [2], [0], [-2], [0], [0], [-2], [0], [2], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.75272.6t13.a', 'Character': [[4], [4], [4], [0], [2], [0], [0], [-2], [1], [0], [0], [0], [2], [0], [0], [-2], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.58411072.12t34.a', 'Character': [[4], [4], [4], [-2], [0], [0], [-2], [1], [-2], [-2], [0], [-2], [0], [0], [0], [1], [1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.4817408.12t34.a', 'Character': [[4], [4], [4], [0], [-2], [0], [0], [-2], [1], [0], [0], [0], [-2], [0], [0], [-2], [0], [1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.6208.6t13.a', 'Character': [[4], [4], [4], [2], [0], [0], [2], [1], [-2], [2], [0], [2], [0], [0], [0], [1], [-1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.308314112.12t201.a', 'Character': [[6], [2], [-2], [-2], [0], [-2], [2], [3], [0], [-4], [2], [0], [0], [0], [0], [-1], [1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.29906468864.12t202.b', 'Character': [[6], [2], [-2], [-4], [0], [2], [0], [3], [0], [-2], [-2], [2], [0], [0], [0], [-1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.29906468864.8t47.a', 'Character': [[6], [2], [-2], [4], [0], [2], [0], [3], [0], [2], [-2], [-2], [0], [0], [0], [-1], [1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.2900927479808.12t200.a', 'Character': [[6], [2], [-2], [2], [0], [-2], [-2], [3], [0], [4], [2], [0], [0], [0], [0], [-1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '9.281389965541376.16t1294.a', 'Character': [[9], [-3], [1], [3], [3], [1], [-1], [0], [0], [-3], [1], [1], [-1], [-1], [1], [0], [0], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '9.2900927479808.18t272.a', 'Character': [[9], [-3], [1], [-3], [3], [1], [1], [0], [0], [3], [1], [-1], [-1], [-1], [-1], [0], [0], [0], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '9.1485274869661696.18t273.a', 'Character': [[9], [-3], [1], [-3], [-3], [1], [1], [0], [0], [3], [1], [-1], [1], [-1], [1], [0], [0], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '9.144071662357184512.18t274.a', 'Character': [[9], [-3], [1], [3], [-3], [1], [-1], [0], [0], [-3], [1], [1], [1], [-1], [-1], [0], [0], [0], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.86756497351599940698112.36t1763.a', 'Character': [[12], [4], [-4], [-2], [0], [0], [-2], [-3], [0], [2], [0], [2], [0], [0], [0], [1], [1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.9220586390859808768.24t2821.a', 'Character': [[12], [4], [-4], [2], [0], [0], [2], [-3], [0], [-2], [0], [-2], [0], [0], [0], [1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '18.417941444393576367118610333696.36t1758.a', 'Character': [[18], [-6], [2], [0], [0], [-2], [0], [0], [0], [0], [-2], [0], [0], [2], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 6, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '6', 'Order': 2, 'Representative': [4, 2, 8, 1, 5, 6, 7, 3]}, {'Size': '9', 'Order': 2, 'Representative': [4, 6, 8, 1, 7, 2, 5, 3]}, {'Size': '12', 'Order': 2, 'Representative': [3, 2, 1, 4, 5, 6, 7, 8]}, {'Size': '24', 'Order': 2, 'Representative': [2, 1, 5, 6, 3, 4, 8, 7]}, {'Size': '36', 'Order': 2, 'Representative': [3, 5, 1, 4, 2, 6, 7, 8]}, {'Size': '36', 'Order': 2, 'Representative': [3, 6, 1, 4, 7, 2, 5, 8]}, {'Size': '16', 'Order': 3, 'Representative': [1, 2, 4, 8, 5, 6, 7, 3]}, {'Size': '64', 'Order': 3, 'Representative': [1, 2, 4, 8, 6, 7, 5, 3]}, {'Size': '12', 'Order': 4, 'Representative': [3, 2, 4, 8, 5, 6, 7, 1]}, {'Size': '36', 'Order': 4, 'Representative': [3, 5, 4, 8, 6, 7, 2, 1]}, {'Size': '36', 'Order': 4, 'Representative': [4, 5, 8, 1, 6, 7, 2, 3]}, {'Size': '72', 'Order': 4, 'Representative': [6, 1, 7, 2, 3, 4, 8, 5]}, {'Size': '72', 'Order': 4, 'Representative': [3, 5, 1, 4, 6, 7, 2, 8]}, {'Size': '144', 'Order': 4, 'Representative': [5, 1, 2, 6, 3, 4, 8, 7]}, {'Size': '48', 'Order': 6, 'Representative': [1, 6, 8, 3, 7, 2, 5, 4]}, {'Size': '96', 'Order': 6, 'Representative': [1, 5, 4, 8, 2, 6, 7, 3]}, {'Size': '192', 'Order': 6, 'Representative': [2, 1, 6, 7, 3, 4, 8, 5]}, {'Size': '144', 'Order': 8, 'Representative': [5, 1, 6, 7, 3, 4, 8, 2]}, {'Size': '96', 'Order': 12, 'Representative': [1, 5, 4, 8, 6, 7, 2, 3]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 2]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-16787392', '-563136', '176048', '5136', '-752', '-8', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-89532300163405703841702417979670528', '-99743952682875081477343295337136128', '-16021655576958099318988775073251328', '15366373676736455058001696785432576', '7524496207582726206962975757041664', '1343408000347898864455669495365632', '-515578088352751263133706202644480', '-333141001891692266945077565194240', '-25487739260391403419414353149952', '13202260886857605838541909131264', '2184550094877601576300971032576', '-85184085942098044086487351296', '-38635829281156688725783347200', '-1259626740709026163393560576', '360653632668553002526441472', '33620807826082431486918656', '-1760393706970940673425408', '-350443377205662507991040', '-1779749964426627219456', '2314669457937457020928', '109579300599867166720', '-11283252352729423872', '-810711684130893824', '17463766266146816', '5641557324680192', '-39044811005952', '-14938038000640', '-805603640832', '76726603648', '1169378304', '-34185216', '-12534336', '411008', '5280', '376', '-48', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 10, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 4]}, {'Data': 0, 'Classes': 17, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 3]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2, 2]}, {'Data': 0, 'Classes': 14, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 4]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [1, 1, 3, 3]}, {'Data': 0, 'Classes': 16, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 3]}, {'Data': 0, 'Classes': 20, 'Algorithm': 'CYC', 'CycleType': [1, 3, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['716460032', '621199360', '245423360', '57901760', '8969088', '943856', '67280', '3112', '84', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-5275851842701416726528', '2264257006912755728384', '897811935149131038720', '-337491591026148638720', '-12913350670511243264', '1990926358175285248', '-6380434517246345216', '2430175483557969920', '-342269690914996224', '-7231781322293248', '24043264586477568', '-9210526751633408', '2240186516313088', '-399430206393344', '55265178454528', '-6126424263680', '554391987264', '-41451418240', '2575441600', '-132918400', '5644816', '-193184', '5104', '-96', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1, 3], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['96015613621728903430144', '87559200620382001561600', '38006927875343140847616', '10429464549235818430464', '2026498318472407203840', '295934169794042642432', '33642687352833187840', '3042646526499598336', '221795199100760064', '13120718035922944', '630974061159168', '24591343324672', '770408791360', '19123990848', '367596560', '5275536', '53192', '336', '1'], 'ConjugacyClass': 12}, {'RootOf': ['2592715319140486949540236134805632142103570796074201291385628549251682784883245056', '186698188166427471647673413894726208316746994618285663210904362338343380211204096', '4078430945199083833539791035310389166733997172689662696062612556204043764376797184', '-4033169894583037098501326072811972226149310394683737610487680225995604086103212032', '3187402574210699641007959188448426147468308236188304662902207494981078053900255232', '-3621963798483347387997879974793721427530504667581759355840806301936519704161026048', '2992533617633084297989934056170021981588074618548137452352474087854264359441137664', '-1630694299758554742628629451746078485223930891758826270477299544111439906246492160', '638270060168626780856266555866292455771822749242630784271741764000384045732069376', '-193408604429211497759666396416624553269364736124574080111412216178230644459962368', '47860062267230948064481292964189242329113879407673988019455912714762214302547968', '-10021850819664720308375303134597440141636930732566743011940216434914300635643904', '1808937504989524749958545178922002164061956045047921191492275456245982633656320', '-280595622326196750739445125304113294956329242700090340427153769885773722550272', '35845386208413585065574450888732905398116172967540934714383756436611459448832', '-3160167978569526871822375957270279940535367453283181798470653994731007115264', '-30628234101607693770553823799719953583716052855994537858286093191889289216', '96245860118282409351241405944986426842421177276185067996434631258884014080', '-28158997569893117666310829956264206573074573113809565792964360364382748672', '5824596440718692138556462953811132891324607237024784068881564088393531392', '-975940420109942807047010737079737892785032009868750503310273676614565888', '133035251561153153583200655467934260187158602000747048533488079531409408', '-13221248414282003617985793160786076904129760224147981285542176923582464', '361706554121079650745417124830066594647828798126166864265651351977984', '241555282977953482733019181242521530316778862928669321784328686927872', '-80302116897684458590015924293928322048030110304845532758780369960960', '17381070715644863232355968689924663326542590110914067790659829366784', 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