Artin representation data - 16.19280468196782158498292736.24t1334.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': [2, 3, 89], 'Baselabel': '16.19280468196782158498292736.24t1334.a', 'CharacterField': 1, 'Conductor': 19280468196782158498292736, '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': [12, 13, 8, 14], '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], [0], [0], [0], [0], [0], [-1]], [[1], [0], [-1]], [[1], [0], [-4], [0], [6], [0], [-4], [0], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T26', 'Galt': 26, 'HardPrimes': [2, 3, 41, 89], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [1, 0, 9, -21, 3, 12, -6, 3, -3, 1], 'NumBadPrimes': 3, 'Proj_GAP': [432, 734], 'Proj_Polynomial': [1, 0, 9, -21, 3, 12, -6, 3, -3, 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': '1.267.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [1], [1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.1068.3t2.a', 'Character': [[2], [2], [0], [2], [-1], [-1], [2], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.3204.24t22.d', '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], [0, 0, 0, 0], [1, 0, 0, 0], [0, -1, 0, -1], [0, 1, 0, 1]], 'CharacterField': 8}, {'GalConj': 2, 'Baselabel': '2.3204.24t22.d', '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], [0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 1], [0, -1, 0, -1]], 'CharacterField': 8}, {'GalConj': 1, 'Baselabel': '3.9612.4t5.a', 'Character': [[3], [3], [1], [3], [0], [0], [-1], [1], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.285156.6t8.a', 'Character': [[3], [3], [-1], [3], [0], [0], [-1], [-1], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.2566404.8t23.d', 'Character': [[4], [-4], [0], [4], [1], [1], [0], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.98673100992.9t26.a', 'Character': [[8], [0], [2], [-1], [2], [-1], [0], [-1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.781589632957632.18t157.a', 'Character': [[8], [0], [-2], [-1], [2], [-1], [0], [1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '16.19280468196782158498292736.24t1334.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': [4, 3, 2, 1, 7, 9, 5, 8, 6]}, {'Size': '36', 'Order': 2, 'Representative': [4, 2, 3, 1, 6, 5, 9, 8, 7]}, {'Size': '8', 'Order': 3, 'Representative': [2, 6, 4, 9, 8, 1, 5, 7, 3]}, {'Size': '24', 'Order': 3, 'Representative': [7, 4, 1, 5, 2, 6, 3, 8, 9]}, {'Size': '48', 'Order': 3, 'Representative': [7, 5, 2, 6, 3, 8, 9, 4, 1]}, {'Size': '54', 'Order': 4, 'Representative': [3, 1, 4, 2, 6, 7, 9, 8, 5]}, {'Size': '72', 'Order': 6, 'Representative': [6, 8, 2, 5, 7, 9, 1, 3, 4]}, {'Size': '72', 'Order': 6, 'Representative': [7, 6, 3, 8, 9, 4, 1, 5, 2]}, {'Size': '54', 'Order': 8, 'Representative': [6, 5, 7, 9, 1, 3, 4, 8, 2]}, {'Size': '54', 'Order': 8, 'Representative': [9, 7, 5, 6, 4, 2, 1, 8, 3]}], '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': 9, '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': ['5877690779882950488330059448', '5969234312066894893983057744', '-1601359197899011033966280568', '610226685358949298535466652', '169708082570099474425741620', '3388536654608033170917336', '-3118605447257289358548264', '101434847990278141631574', '60731334500529988856430', '-6082619627445104334591', '764172756962978164308', '-39669269419826668107', '1876820812534427040', '81744082325683245', '-21619685219685714', '1898274793000896', '-153028069373808', '9607311626634', '-315071659656', '-7318928907', '1325597562', '-71012619', '1506114', '124173', '-19494', '1404', '-54', '1'], 'ConjugacyClass': 10}, {'RootOf': ['6343593869213162762826600', '17328073255028449169910120', '14161214700335531667667248', '2821086017318535559142976', '-174556170756100891626048', '239908228875933620269680', '74705476676283820313838', '-1285658431304225468004', '2192961286038681985014', '-607347033792075608373', '136329223831503817536', '-1986259644812662956', '1141617855924303750', '-110558941412335425', '12015446860966752', '-1644260073050133', '146912810972346', '-8833011360327', '493057562238', '-13755709494', '-259395696', '59578254', '-6739362', '549423', '-31266', '1539', '-54', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'RES', 'CycleType': [1, 8]}, {'Data': {'Powers': [1, 2], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-4374', '2916', '162', '9', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-678702930309205465464', '-1059059215672729678314', '-182791228972722629256', '99393992839958240016', '19906490844472596993', '-9416059970010897420', '-2880159023364817374', '20282828866999434', '87438543985574613', '4247251141396176', '-3119884043689368', '-722832735352356', '-63005836367862', '-2636270082468', '-696165061428', '-171220195008', '-17422013790', '-806698278', '-39163824', '-6094764', '-530955', '-13392', '738', '54', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [3, 6]}], 'Frobs': [8, 3, 10, 10, 8, 10, 11, 8, 9, 6, 10, 11, 9, 10, 11, 8, 5, 11, 6, 10, 6, 9, 6, 3, 9, 7, 8, 8, 9, 6, 8, 11, 4, 9, 9, 8, 6, 10, 10, 8, 10, 3, 9, 3, 7, 9, 11, 6, 3, 8, 11, 9, 8, 11, 10, 8, 3, 7, 9, 7, 7, 9, 9, 8, 11, 8, 7, 8, 10, 8, 6, 7, 2, 6, 10, 7, 7, 8, 11, 9, 6, 11, 7, 10, 11, 10, 8, 11, 10, 7, 11, 8, 9, 5, 3, 2, 3, 7, 7, 8, 8, 9, 9, 9, 11, 11, 10, 5, 4, 9, 9, 9, 9, 9, 6, 8, 9, 9, 6, 11, 10, 9, 7, 5, 6, 10, 10, 7, 8, 9, 11, 9, 7, 5, 8, 5, 6, 10, 3, 11, 5, 11, 5, 9, 10, 9, 11, 2, 3, 7, 8, 3, 3, 6, 9, 10, 8, 11, 9, 9, 8, 6, 8, 8, 10, 10, 10, 9], 'G-Gens': [[1, 8, 2, 7, 5, 4, 6, 3, 9], [1, 8, 9, 2, 3, 4, 5, 6, 7], [2, 6, 4, 9, 8, 1, 5, 7, 3], [1, 2, 9, 3, 8, 6, 5, 7, 4], [5, 8, 2, 6, 9, 7, 4, 3, 1], [6, 5, 7, 9, 1, 3, 4, 8, 2]], 'G-Name': 'H432', 'Polynomial': [1, 0, 9, -21, 3, 12, -6, 3, -3, 1], 'QpRts': [['-77154769719431838240215690102082615836440982800622708380307', '0', '0', '0'], ['386671738882618732152786785034367756531679784156731770324623', '-433879642250024110871592519092084289694519123221127813511218', '-277557446271185708738499401169715331969727361427127333342625', '-165490605631687399035175764173060271831676193408585436266277'], ['330830617054768910605218458007087560508591726920077975490308', '79205360650774009578098621884388756878591059576198898733545', '452809747118029255527551424766320283870801065605212297400858', '452409827803977582228845738949726295584483467181598536418871'], ['-17379411495107860145418017960058892644920152163661033473546', '531580039284272870185827332003752622958621897212685762408209', '625673147556011152612526667153899657490434547261673354105331', '-548759820890111594459826626704900860101502102706186567499955'], ['243593512385420060218823547201157461599187610137361174999137', '453785922710532930761939626626205189847957634028133615722154', '125641531505088446272458663777698563118639520726837944634086', '-456371114974016462965803515871604151506028817260355479240126'], ['-199199774914687600574799557820217792041671362765281373431415', '57460986993273738431284141487856149782526470075418414391170', '-571471109251053151513103970645188215613002375126593502963848', '-192277722466548299258950896026386878622141289803313638891'], ['398412970221807904322302641752886227352349747367101911444325', '-293238998282679029658386822048143348412316226243655619853582', '418509379433518864100393977521682791031206860144013537203159', '-582948610708355068829578926034408248787631045826069533321850'], ['221043553427704931321035010425588720811812091778247540282868', '-155161384027522497745518954399524483046629244066976363288161', '223355407966227707639076704661003890092295189292047482201142', '-633406211088640108791261009535789998055582987798229246947878'], ['61030479489812410925789174771049090586794962572849307097011', '-239752285078627910681651426462450598314232467360676894602117', '350888257276269084685118285244075878846735978726740785114898', '586909897878393949566536702956286104709176395904826476143105']], 'QpRts-minpoly': [2, 78, 1, 0, 1], 'QpRts-p': 101, 'QpRts-prec': 30, 'Size': 432, 'TransitiveDegree': 9}