Artin representation data - 9.123112996892103868416.18t274.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, 3, 13], 'Baselabel': '9.123112996892103868416.18t274.a', 'CharacterField': 1, 'Conductor': 123112996892103868416, 'Container': '18t274', 'Dets': ['1.39.2t1.a.a'], 'Dim': 9, 'GalConjSigns': [1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[9], [-3], [1], [3], [-3], [1], [-1], [0], [0], [-3], [1], [1], [1], [-1], [-1], [0], [0], [0], [1], [0]], 'GalOrbIndex': 1, 'HardFactors': [21, 21, 16, 21, 3], 'LocalFactors': [[[1], [-9], [36], [-84], [126], [-126], [84], [-36], [9], [-1]], [[1], [3], [0], [-8], [-6], [6], [8], [0], [-3], [-1]], [[1], [-1], [-4], [4], [6], [-6], [-4], [4], [1], [-1]], [[1], [-3], [0], [8], [-6], [-6], [8], [0], [-3], [1]], [[1], [3], [0], [-8], [-6], [6], [8], [0], [-3], [-1]], [[1], [-1], [-4], [4], [6], [-6], [-4], [4], [1], [-1]], [[1], [1], [-4], [-4], [6], [6], [-4], [-4], [1], [1]], [[1], [0], [0], [-3], [0], [0], [3], [0], [0], [-1]], [[1], [0], [0], [-3], [0], [0], [3], [0], [0], [-1]], [[1], [3], [6], [10], [12], [12], [10], [6], [3], [1]], [[1], [-1], [0], [0], [-2], [2], [0], [0], [1], [-1]], [[1], [-1], [2], [-2], [0], [0], [-2], [2], [-1], [1]], [[1], [-1], [0], [0], [-2], [2], [0], [0], [1], [-1]], [[1], [1], [2], [2], [0], [0], [-2], [-2], [-1], [-1]], [[1], [1], [0], [0], [-2], [-2], [0], [0], [1], [1]], [[1], [0], [0], [1], [0], [0], [-1], [0], [0], [-1]], [[1], [0], [0], [-1], [0], [0], [-1], [0], [0], [1]], [[1], [0], [0], [1], [0], [0], [-1], [0], [0], [-1]], [[1], [-1], [0], [0], [0], [0], [0], [0], [-1], [1]], [[1], [0], [0], [1], [0], [0], [1], [0], [0], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T47', 'Galt': 47, 'HardPrimes': [2, 3, 5, 13, 32363], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [4, -32, -8, 4, 4, 4, -2, -2, 1], 'NumBadPrimes': 3, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [4, -32, -8, 4, 4, 4, -2, -2, 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': '1.39.2t1.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': '1.52.2t1.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': '1.12.2t1.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': '2.468.4t3.d', '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': '4.657072.6t13.c', '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': '4.34167744.12t34.h', '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': '4.2628288.12t34.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': '4.202176.6t13.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': '6.10809580833792.12t201.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': '6.277168739328.12t202.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': '6.1640051712.8t47.e', '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': '6.378473472.12t200.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': '9.2564854101918830592.16t1294.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': '9.3502304190148608.18t272.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': '9.18678955680792576.18t273.c', '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': '9.123112996892103868416.18t274.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': '12.944109135929979961344.36t1763.b', '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': '12.159554443972166613467136.24t2821.c', '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': '18.431179164876967932510707234717564928.36t1758.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': 7, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '6', 'Order': 2, 'Representative': [1, 4, 5, 2, 3, 6, 7, 8]}, {'Size': '9', 'Order': 2, 'Representative': [7, 4, 5, 2, 3, 8, 1, 6]}, {'Size': '12', 'Order': 2, 'Representative': [6, 2, 3, 4, 5, 1, 7, 8]}, {'Size': '24', 'Order': 2, 'Representative': [2, 1, 6, 7, 8, 3, 4, 5]}, {'Size': '36', 'Order': 2, 'Representative': [6, 3, 2, 4, 5, 1, 7, 8]}, {'Size': '36', 'Order': 2, 'Representative': [6, 4, 5, 2, 3, 1, 7, 8]}, {'Size': '16', 'Order': 3, 'Representative': [7, 2, 3, 4, 5, 6, 8, 1]}, {'Size': '64', 'Order': 3, 'Representative': [7, 2, 4, 5, 3, 6, 8, 1]}, {'Size': '12', 'Order': 4, 'Representative': [1, 3, 4, 5, 2, 6, 7, 8]}, {'Size': '36', 'Order': 4, 'Representative': [6, 3, 4, 5, 2, 7, 8, 1]}, {'Size': '36', 'Order': 4, 'Representative': [6, 4, 5, 2, 3, 7, 8, 1]}, {'Size': '72', 'Order': 4, 'Representative': [2, 7, 8, 1, 6, 3, 4, 5]}, {'Size': '72', 'Order': 4, 'Representative': [6, 3, 4, 5, 2, 1, 7, 8]}, {'Size': '144', 'Order': 4, 'Representative': [3, 1, 6, 7, 8, 2, 4, 5]}, {'Size': '48', 'Order': 6, 'Representative': [8, 4, 5, 2, 3, 6, 1, 7]}, {'Size': '96', 'Order': 6, 'Representative': [6, 2, 5, 3, 4, 1, 7, 8]}, {'Size': '192', 'Order': 6, 'Representative': [3, 6, 7, 8, 1, 2, 4, 5]}, {'Size': '144', 'Order': 8, 'Representative': [2, 6, 7, 8, 1, 3, 4, 5]}, {'Size': '96', 'Order': 12, 'Representative': [7, 3, 4, 5, 2, 6, 8, 1]}], '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': ['6016', '-3072', '-1344', '1040', '-120', '-12', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-970523354003798264363726662591840256', '2061253623322993037256725399095738368', '325938273680553312606201401629999104', '66280584599219113781854397867753472', '23250260846860290798613942732062720', '743819244466029729257715841105920', '62486431607407568413555609829376', '-7584842262458804827007326617600', '17364805898505817998788671832064', '1428217051318145583303979171840', '502476236473549736618886168576', '1548764269909904530675335168', '4509654459128932365571719168', '-437689370382790915604348928', '23143420438655285273296896', '-5233749613904508594683904', '298347608756110793637888', '-43588694410866689310720', '4773505223169058799616', '-481208716424694988800', '55340539818357030912', '-4863022740703936512', '505918010500448256', '-47286210835316736', '4343556186980352', '-395130642259968', '31119291666432', '-2415742865408', '168935301120', '-11034565632', '688163328', '-37886592', '1889280', '-79680', '2712', '-72', '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': ['-71757824', '-67153920', '-13865472', '3323520', '721536', '-44352', '-8976', '48', '36', '1'], 'ConjugacyClass': 3}, {'RootOf': ['118788278137547181260800', '71642766713952663502848', '48704626490341142298624', '21612071287852579684352', '6520252307613690101760', '1295791404223637225472', '173923110007544479744', '9805376925440409600', '-880992191092359168', '-154087224477220864', '22119345367842816', '3230854890258432', '-174360351506432', '-52045778350080', '5594547081216', '128161538048', '-30197180160', '-3468222720', '984610048', '-100825344', '6245088', '-257056', '7056', '-120', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1, 3], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['2472924351463161856', '-13677917282072788992', '-10868135937142947840', '-2521993804518260736', '4624064267943936', '81644968269840384', '8909888331399168', '-556283994832896', '-149738527309824', '-4605924220928', '718078009344', '55133779968', '-332689536', '-159454848', '-4681152', '82896', '7152', '144', '1'], 'ConjugacyClass': 12}, {'RootOf': ['214187798375203916392082623091572323654413009325008131558291832745528027469534568906752', '103869862918226412364432603567871419585440268737128000887235711485816401372823330750464', '49622983884093873052804587359062339535029955976557290281784339997562595947979091214336', '13663039550897941305941794006949691871483118360378725665942363106607745082494157848576', '1256104338024874559366470769826909017740918445635535260723700180710795923096109842432', '-74115901572448343636320911206020149603056964551568191299752385134128335894490382336', '3579455344687119085355584959915005908005869967102574580939841252732379593695035392', '8704938337657719790992277853848235659929812281318655444474891128081611844302667776', '858293116895560744089365891559272012322158519766998948822604007039144940022005760', '-142204069508676318003704107095293621974982422548245400339840711293708115856326656', '-15604228489335162275837631570541888366962320840660201978945370104695003457519616', '3142305924617191121745479899441350941515722731574256195869647310235950768979968', '379849521528513110388835008046535702856846052657550994546547369921344304054272', '-57356873439585404355627040827306474118447664497207326249336567591257839239168', '-7163454746533060539059492047664624701481367877982236783912817335927761272832', '1008004693015167405482075053832657036446411213376805667234449502037361033216', '101345490742824131035583710591204902276750206852834140845811212964218273792', '-14109050543845709957180807653229584851543014704815849844501873481629040640', '-1397099086808328673868502480797978718133955448451549981841480514189393920', '198500783313106320566215925354589963410867450321157753669156341356167168', '16529805548166725634703725452017209338091744186931621816613781425356800', '-2778850748215544298548568914673272652161073611714984523958823008862208', '-110692631094764566528764143871472286518850143207683515447274312302592', '27762168152055672667198788087305728799986002978647401369542309445632', '766611581971417599741327971144431290234763411299945450127195373568', '-275695174082325749565581437577855968048316099791428082665139470336', '-3628613705766200095566925703927531533085172935149168164775919616', '3049963646351276482918997020769863663572146382719622573293830144', '-116238482449343391139023563549380497118124272135358293915729920', '-16778216801310846230041861126208495206459617905348522627039232', '1311223217946856123481713831188797146494308186841479399866368', '66095320936843343337521789914586537722849507039820252184576', '-8220455065436127944746154704319189674919204645454993162240', '-629749592180420076596746669639725743401579784302636302336', '124477433020428683134692399992081011479277277198250147840', '-3774395440600775573382413596184478322328100680729886720', '-524834004400529931079873795122162107983802274116796416', '46225305860895466253576481193096567204052025716244480', '582376315942990911820355481687846364183265732984832', '-198794907976846061563646381316690415079594806738944', '-10955152386114174470156910869449567160870463602688', '3943857181752330339665387482060916693663962103808', '-369327852767632219427738533379908011821390364672', '14963446755072145654350883217339617474454224896', '319833370974579740289738919684311439544156160', '-85880946731033177656805989036464760049106944', '6603774180056889223692985626436903725170688', '-465820868805033599715212647987135547179008', '50728757256330307937920736447633559650304', '-6288822041946748488007175487798286221312', '652536838699794191083334199701554593792', '-54556143770819898965733818952509816832', '3763273208186722680768041055871303680', '-219559477890220490524935656445050880', '11035131265783916917678350049214464', '-483917609224757381760316798402560', '18675354516718947586733098598400', '-637810431261014039012901126144', '19340176683724694460311273472', '-521416604275188262780796928', '12495903153017440758251520', '-265732699692380847194112', '4997716292138752106496', '-82708401847019307008', '1195885397403400704', '-14961500770931712', '159837156965376', '-1431890927616', '10482973632', '-60356352', '256848', '-720', '1'], 'ConjugacyClass': 15}], 'Algorithm': 'RES', 'CycleType': [2, 2, 4]}, {'Data': 0, 'Classes': 18, 'Algorithm': 'CYC', 'CycleType': [2, 6]}, 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