Artin representation data - 12.171126940264356241.18t206.a

Formats: - HTML - YAML - JSON - 2023-12-03T18:25:21.901003

• 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': [11, 43], 'Baselabel': '12.171126940264356241.18t206.a', 'CharacterField': 1, 'Conductor': 171126940264356241, 'Container': '18t206', 'Dets': ['1.1.1t1.a.a'], 'Dim': 12, 'GalConjSigns': [1], 'Galn': 9, 'GaloisConjugates': [{'Sign': 1, 'Character': [[12], [4], [0], [0], [0], [3], [-3], [0], [0], [-2], [-2], [1], [0], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [12, 16, 16, 13, 18, 19, 13, 16, 16, 16, 13, 16], 'LocalFactors': [[[1], [-12], [66], [-220], [495], [-792], [924], [-792], [495], [-220], [66], [-12], [1]], [[1], [-4], [2], [12], [-17], [-8], [28], [-8], [-17], [12], [2], [-4], [1]], [[1], [0], [-6], [0], [15], [0], [-20], [0], [15], [0], [-6], [0], [1]], [[1], [0], [-6], [0], [15], [0], [-20], [0], [15], [0], [-6], [0], [1]], [[1], [0], [0], [-4], [0], [0], [6], [0], [0], [-4], [0], [0], [1]], [[1], [-3], [3], [-4], [9], [-9], [6], [-9], [9], [-4], [3], [-3], [1]], [[1], [3], [6], [5], [0], [-9], [-12], [-9], [0], [5], [6], [3], [1]], [[1], [0], [0], [-4], [0], [0], [6], [0], [0], [-4], [0], [0], [1]], [[1], [0], [0], [-4], [0], [0], [6], [0], [0], [-4], [0], [0], [1]], [[1], [2], [2], [0], [-2], [-2], [-2], [-2], [-2], [0], [2], [2], [1]], [[1], [2], [2], [0], [-2], [-2], [-2], [-2], [-2], [0], [2], [2], [1]], [[1], [-1], [2], [-3], [4], [-5], [4], [-5], [4], [-3], [2], [-1], [1]], [[1], [0], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [0], [1]], [[1], [0], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [0], [1]], [[1], [0], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [0], [1]], [[1], [0], [0], [-1], [0], [0], [0], [0], [0], [-1], [0], [0], [1]], [[1], [0], [0], [-1], [0], [0], [0], [0], [0], [-1], [0], [0], [1]], [[1], [1], [1], [0], [0], [0], [-1], [-1], [-1]], [[1], [0], [-2], [0], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T28', 'Galt': 28, 'HardPrimes': [2, 3, 5, 7, 11, 43, 277, 509, 751, 2377, 3121, 4663003], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [4, 9, -4, -10, 8, 3, -4, -3, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [648, 705], 'Proj_Polynomial': [4, 9, -4, -10, 8, 3, -4, -3, 0, 1], 'Proj_nTj': [9, 28]}
• 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': '1.11.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [1], [-1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.473.6t1.b', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, 0], [-1, 0], [-1, 0], [1, 0], [1, 1], [0, -1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.43.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.43.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.473.6t1.b', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [-1, 0], [-1, 0], [-1, 0], [1, 0], [0, -1], [1, 1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '3.20339.6t6.a', 'Character': [[3], [1], [-3], [-1], [3], [3], [3], [0], [0], [1], [1], [1], [-1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.223729.4t4.a', 'Character': [[3], [-1], [3], [-1], [3], [3], [3], [0], [0], [-1], [-1], [-1], [-1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.4550424131.18t197.a', 'Character': [[6], [0], [0], [-2], [3], [-3], [0], [0], [0], [-3], [3], [0], [1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.37606811.9t28.a', 'Character': [[6], [4], [0], [2], [3], [-3], [0], [0], [0], [1], [1], [-2], [-1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.550601319851.18t202.a', 'Character': [[6], [-4], [0], [2], [3], [-3], [0], [0], [0], [-1], [-1], [2], [-1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.4550424131.18t197.b', 'Character': [[6], [0], [0], [-2], [3], [-3], [0], [0], [0], [3], [-3], [0], [1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.50054665441.12t176.a', 'Character': [[8], [0], [0], [0], [-4], [-1], [2], [2], [2], [0], [0], [0], [0], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.92551076400409.24t1539.a', 'Character': [[8, 0], [0, 0], [0, 0], [0, 0], [-4, 0], [-1, 0], [2, 0], [0, 2], [-2, -2], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '8.92551076400409.24t1539.a', 'Character': [[8, 0], [0, 0], [0, 0], [0, 0], [-4, 0], [-1, 0], [2, 0], [-2, -2], [0, 2], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '12.171126940264356241.18t206.a', 'Character': [[12], [4], [0], [0], [0], [3], [-3], [0], [0], [-2], [-2], [1], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.2505469532410439724481.36t1101.a', 'Character': [[12], [-4], [0], [0], [0], [3], [-3], [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, 2, 3, 4, 5, 1, 7, 8, 9]}, {'Size': '27', 'Order': 2, 'Representative': [6, 5, 4, 3, 2, 1, 7, 8, 9]}, {'Size': '27', 'Order': 2, 'Representative': [6, 2, 3, 4, 7, 1, 5, 8, 9]}, {'Size': '6', 'Order': 3, 'Representative': [1, 2, 4, 9, 5, 6, 7, 8, 3]}, {'Size': '8', 'Order': 3, 'Representative': [6, 5, 4, 9, 7, 8, 2, 1, 3]}, {'Size': '12', 'Order': 3, 'Representative': [1, 5, 4, 9, 7, 6, 2, 8, 3]}, {'Size': '36', 'Order': 3, 'Representative': [2, 3, 1, 6, 4, 5, 9, 7, 8]}, {'Size': '36', 'Order': 3, 'Representative': [3, 1, 2, 5, 6, 4, 8, 9, 7]}, {'Size': '18', 'Order': 6, 'Representative': [6, 2, 4, 9, 5, 1, 7, 8, 3]}, {'Size': '18', 'Order': 6, 'Representative': [6, 5, 3, 4, 7, 1, 2, 8, 9]}, {'Size': '36', 'Order': 6, 'Representative': [6, 5, 4, 9, 7, 1, 2, 8, 3]}, {'Size': '54', 'Order': 6, 'Representative': [6, 2, 4, 9, 7, 1, 5, 8, 3]}, {'Size': '108', 'Order': 6, 'Representative': [5, 3, 1, 6, 4, 2, 9, 7, 8]}, {'Size': '108', 'Order': 6, 'Representative': [3, 6, 2, 5, 1, 4, 8, 9, 7]}, {'Size': '72', 'Order': 9, 'Representative': [2, 3, 6, 8, 4, 5, 9, 7, 1]}, {'Size': '72', 'Order': 9, 'Representative': [3, 6, 5, 7, 8, 4, 1, 9, 2]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 2]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 3]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 2, 2]}, {'Data': {'Powers': [1, 5], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['358949902712', '-124199140008', '13564568974', '-42595927', '-59592944', '1323039', '81358', '-2145', '-36', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-301707871672', '-116344278408', '-16489601798', '-907940311', '5580952', '2326143', '39562', '-2145', '-36', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 2, 3]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 2, 2]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 3, 3]}, {'Data': 0, 'Classes': 13, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2, 3]}, {'Data': 0, 'Classes': 12, 'Algorithm': 'CYC', 'CycleType': [1, 2, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['2513620080', '631714128', '106772012', '10835928', '850233', '44712', '1914', '48', '1'], 'ConjugacyClass': 6}, {'RootOf': ['5295200063848446834746990357211', '-1092856675007828576560809705372', '482468480287141907303536457799', '-240089661386506335191065274628', '33224768282754220246620267096', '-9769844414227985234918258472', '3048692963278070477399006331', '-235685379540145175435341782', '60636912066837050007960225', '-17912796693401546480533888', '532043204336866584331335', '-102525106927027160062152', '52824196166929810647155', '-1167643323037901612376', '-157506806983200687885', '-33383344620930635516', '3963097545532749828', '-271579421380219746', '-80253233756799342', '10359767392450686', '2777530022089947', '-606456165788240', '-29434898248668', '3846763729980', '1085162671845', '-78873481314', '2659599513', '1288485250', '-66327084', '-6632598', '1272729', '129726', '2016', '-3030', '-36', '0', '1'], 'ConjugacyClass': 8}, {'RootOf': ['18338245001980162582031786907', '-48665812043995437926134903356', '53067063431405984052226846815', '-31924490355411132631282894116', '13285291726391680586285821296', '-5042171425103914852431611064', '1722157689694113985905127467', '-398590114185367436370411738', '58962095739432902024676945', '-8097258154339342934756848', '137448787879608071653575', '549254741353082836883568', '-131915875302746487317125', '-13151284430049563113800', '9734874769812849730035', '-297146016513771089900', '-270994566574341861300', '62809509501602890626', '5180468439673625970', '-1104010680954663702', '155644180274533347', '38771473308291472', '-1914799625312076', '158916271139892', '96367567909509', '-2019130379406', '80125810569', '96677553310', '-1164893148', '20102910', '46607457', '-330030', '2016', '10902', '-36', '0', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['2570425919896417436960066169275374364484872606608937085358600036803619959412825183228264448', 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'675248851915955763259709463197411162920027713662474685604607639800500', '-11226622485552429872577290802156084405307959830579315410876964319432', '20824716987513754159790496711833249435411443063018611018572679083279', '-2256472348355826462082451908596564048263912646273836377391516177508', '125342310341296078250036611253249539624589508870642705258765122802', '-101554894198689611554833033922435369752230027766662563039249107588', '7293287982672302426667958206233373522142935329984625255632948382', '-787927433293723281606913453272248218952403977542028874131020152', '396794009390545339972719311728766538779029242861991210637365101', '-34181224320205993363794351317965313995464344494320762149648430', '2916963826321677518130748267159614107388738428495938455966981', '-1365630302136467636916184377931870323392307176919778815414042', '180493041519473326845780674655807268347959072132566932723315', '-7246674677463593152756730084216187945794534170218016654254', 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