Artin representation data - 16.65929453268141847321729.24t1334.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, 11], 'Baselabel': '16.65929453268141847321729.24t1334.a', 'CharacterField': 1, 'Conductor': 65929453268141847321729, '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': [10, 12, 10, 13, 2], '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]], [[1], [0], [0], [0], [0], [0], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T26', 'Galt': 26, 'HardPrimes': [2, 3, 5, 11, 193], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [6, -27, -9, 15, 18, 3, -9, -3, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [432, 734], 'Proj_Polynomial': [6, -27, -9, 15, 18, 3, -9, -3, 0, 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': '2.3267.3t2.b', 'Character': [[2], [2], [0], [2], [-1], [-1], [2], [-1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.3267.24t22.b', '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], [1, 0, 0, 0], [0, 0, 0, 0], [0, -1, 0, -1], [0, 1, 0, 1]], 'CharacterField': 8}, {'GalConj': 2, 'Baselabel': '2.3267.24t22.b', '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], [1, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 1], [0, -1, 0, -1]], 'CharacterField': 8}, {'GalConj': 1, 'Baselabel': '3.3267.4t5.c', 'Character': [[3], [3], [1], [3], [0], [0], [-1], [0], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.9801.6t8.e', 'Character': [[3], [3], [-1], [3], [0], [0], [-1], [0], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.9801.8t23.b', 'Character': [[4], [-4], [0], [4], [1], [1], [0], [-1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.2824440448203.9t26.a', 'Character': [[8], [0], [2], [-1], [2], [-1], [0], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.2824440448203.18t157.a', 'Character': [[8], [0], [-2], [-1], [2], [-1], [0], [0], [1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '16.65929453268141847321729.24t1334.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, 7, 9, 5, 1, 3, 2, 4]}, {'Size': '36', 'Order': 2, 'Representative': [1, 2, 4, 3, 6, 5, 8, 7, 9]}, {'Size': '8', 'Order': 3, 'Representative': [5, 3, 4, 2, 6, 1, 8, 9, 7]}, {'Size': '24', 'Order': 3, 'Representative': [2, 9, 3, 6, 5, 8, 7, 4, 1]}, {'Size': '48', 'Order': 3, 'Representative': [8, 1, 5, 6, 9, 7, 4, 2, 3]}, {'Size': '54', 'Order': 4, 'Representative': [4, 7, 2, 6, 5, 9, 8, 3, 1]}, {'Size': '72', 'Order': 6, 'Representative': [7, 3, 9, 6, 1, 4, 2, 8, 5]}, {'Size': '72', 'Order': 6, 'Representative': [2, 9, 8, 7, 4, 3, 6, 5, 1]}, {'Size': '54', 'Order': 8, 'Representative': [2, 4, 1, 7, 5, 8, 6, 9, 3]}, {'Size': '54', 'Order': 8, 'Representative': [8, 9, 6, 3, 5, 2, 1, 4, 7]}], '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': 8, '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': ['118309775032239425918509712175', '-116770386626466876139408958925', '51615475878805133582656127619', '-14499182304708364642137969798', '2910087017693771042197081521', '-424760943382617962985355620', '43211739645386001730131516', '-2697784514136640943262990', '52375567009487792703201', '5859008296539219785907', '-205782024229965759951', '-88871610833564372793', '15829679976053579082', '-1447205717131168788', '91513063213181883', '-4287417674535027', '121117532747670', '-3164524102962', '348465305286', '-24912974304', '1333217799', '-68880294', '-379890', '-7128', '-4779', '-27', '0', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-2412937372657799383718678948925', '479698704318570840055370278926', '58429220419578386757748617270', '-11486073043756589006845252584', '-1189263464640757815836932233', '228158114448491287516130679', '-11165550155818008073332507', '675529524382338778053852', '92861710495616916024768', '-31052044685330557266951', '3298374294000164677107', '-304505422947270340074', '26383103957126213973', '-1673968194195129486', '111050697414442149', '-7059649361148450', '331085612886057', '-20232315270081', '908915830209', '-10457381799', '1141974855', '29319651', '-6441687', '146043', '-12528', '837', '0', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'RES', 'CycleType': [1, 8]}, {'Data': {'Powers': [1, 2], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['8019', '-2376', '0', '27', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-301639614770582978440617', '-412164791539693915264245', '-248837669413295290582419', '-65290704577930526338485', '-8132272825480381830015', '-2103383971307474712855', '-992737744547768225010', '-206065608286735356687', '-6954514832983472694', '4314130231780727973', '743816564189100126', '25384201090452603', '-6453358844198679', '-1046754068730210', '-80851040739909', '-4319704524204', '-160073849403', '6539053941', '2151638316', '218712474', '12988512', '490635', '11700', '162', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [3, 6]}], 'Frobs': [11, 3, 11, 8, 9, 8, 11, 7, 10, 9, 8, 7, 11, 7, 10, 9, 10, 7, 5, 9, 8, 6, 9, 3, 6, 10, 5, 3, 8, 9, 6, 9, 10, 8, 10, 5, 6, 8, 9, 9, 9, 8, 10, 2, 11, 7, 7, 8, 3, 7, 3, 9, 8, 11, 11, 10, 11, 6, 8, 3, 8, 9, 6, 3, 5, 11, 8, 4, 11, 7, 9, 11, 8, 8, 8, 10, 9, 8, 10, 7, 10, 8, 9, 8, 8, 11, 10, 7, 9, 8, 9, 10, 5, 11, 6, 11, 3, 9, 4, 8, 6, 11, 11, 9, 6, 7, 11, 10, 11, 6, 5, 6, 3, 6, 8, 9, 5, 10, 11, 11, 8, 6, 3, 10, 6, 10, 5, 3, 7, 7, 6, 11, 8, 6, 9, 5, 9, 8, 10, 3, 8, 11, 7, 10, 2, 11, 6, 10, 7, 3, 7, 10, 8, 10, 7, 9, 8, 9, 5, 9, 3, 11, 2, 10, 9, 3, 8, 6], 'G-Gens': [[5, 2, 3, 4, 6, 1, 9, 7, 8], [5, 3, 4, 2, 6, 1, 8, 9, 7], [7, 5, 6, 1, 8, 9, 4, 2, 3], [2, 4, 1, 7, 5, 8, 6, 9, 3], [8, 5, 9, 4, 3, 1, 6, 7, 2], [1, 5, 9, 4, 8, 3, 7, 2, 6]], 'G-Name': 'H432', 'Polynomial': [6, -27, -9, 15, 18, 3, -9, -3, 0, 1], 'QpRts': [['-494525458643449292717583992694068727710038271310073946919991', '240764811332538970891389566413834552166990732281511660776301', '80145263250834801023529971824359548195181577317691555720936', '-503823689153200088659549960868467929854954814445897876181418'], ['-267066881539499867882546008057237247899217401697483169217154', '-527636061339010294573276202801243558125502220833100347436078', '521804076481535050534602726717474821030518534055247741252526', '541888229761533432527924932380192488952452343482185796302342'], ['144301955152835310624948062680506780355999746487367358518223', '366471116715544350123007918135915836989159316719902630441083', '-271353765980133628084703632448892823238643509903503276122275', '-307235864308569397501251935979919682571978982322152753863152'], ['-91338544029472324740832882878015235440887196491450479111653', '0', '0', '0'], ['-421656377280721037645476205701703905506684761619700961234107', '100347540843394629544377380496924535015232340914754716465815', '131358170930280309122007417215306664201325380056645713444032', '-94922805120539855501051746071060993536751470334773824201927'], ['315709104551419930957280906566989493972137874848373982537215', '210273116006856740910644823112496632381684763269786278780303', '48696543669000450756045069274438401029232219905962782449652', '502038084177593105638642103280100243608870906832917711162128'], ['-211765447074223669748758307728156077186614831330509263220460', '-79599866709073026441121281748506831030647828168313943781306', '-330595573752236223473429066092941545987056601469436020851187', '269171323700236053632876964468195123474481453285864833742228'], ['630461728664309337926255430276093503664773183842593237389312', '315375992214547907243725860246537184493022605766087264854961', '-531386235805039353328512388786010059997132551097726693990820', '-575994986306988520764625802939563091947935920444311216994673'], ['395879920198801613226712997535591415750531657270883241258615', '-625996649064799277698748063855958351889939709950628260101079', '351331521205758593450459902296264994766574951135118198097136', '168879707249935270627035445730523841875816483946167330034472']], 'QpRts-minpoly': [2, 11, 2, 0, 1], 'QpRts-p': 19, 'QpRts-prec': 47, 'Size': 432, 'TransitiveDegree': 9}