Artin representation data - 2.777.16t60.a

Formats: - HTML - YAML - JSON - 2025-09-26T13:45:52.778742

• 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, 7, 37], 'Baselabel': '2.777.16t60.a', 'CharacterField': 12, 'Conductor': 777, 'Container': '16t60', 'Dets': ['1.777.6t1.b.a', '1.777.6t1.b.a', '1.777.6t1.b.b', '1.777.6t1.b.b'], 'Dim': 2, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 16, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [1, 0, -1], [0, 0, 1], [0, 0, 0, -2], [0, 0, 0, 2], [0], [0, 0, -1], [-1, 0, 1], [0, 1], [0, -1, 0, 1], [0, -1], [0, 1, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [3, 15, 11, 16, 9, 12, 17, 8, 12, 4, 8, 12], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [-1, 0, 1], [0, 0, -1]], [[1], [0, 0, -1], [-1, 0, 1]], [[1], [0, 0, 0, 2], [-1]], [[1], [0, 0, 0, -2], [-1]], [[1], [0], [1]], [[1], [0, 0, 1], [-1, 0, 1]], [[1], [1, 0, -1], [0, 0, -1]], [[1], [0, -1], [0, 0, 1]], [[1], [0, 1, 0, -1], [1, 0, -1]], [[1], [0, 1], [0, 0, 1]], [[1], [0, -1, 0, 1], [1, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [1]], [[1], [-1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [1, 0, -1], [0, 0, 1], [0, 0, 0, 2], [0, 0, 0, -2], [0], [0, 0, -1], [-1, 0, 1], [0, -1], [0, 1, 0, -1], [0, 1], [0, -1, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [3, 15, 11, 16, 9, 12, 17, 8, 12, 4, 8, 12], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [-1, 0, 1], [0, 0, -1]], [[1], [0, 0, -1], [-1, 0, 1]], [[1], [0, 0, 0, -2], [-1]], [[1], [0, 0, 0, 2], [-1]], [[1], [0], [1]], [[1], [0, 0, 1], [-1, 0, 1]], [[1], [1, 0, -1], [0, 0, -1]], [[1], [0, 1], [0, 0, 1]], [[1], [0, -1, 0, 1], [1, 0, -1]], [[1], [0, -1], [0, 0, 1]], [[1], [0, 1, 0, -1], [1, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [1]], [[1], [-1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0, 0, 1], [1, 0, -1], [0, 0, 0, 2], [0, 0, 0, -2], [0], [-1, 0, 1], [0, 0, -1], [0, 1, 0, -1], [0, -1], [0, -1, 0, 1], [0, 1]], 'GalOrbIndex': 3, 'HardFactors': [3, 15, 11, 16, 9, 12, 17, 8, 12, 4, 8, 12], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0, 0, -1], [-1, 0, 1]], [[1], [-1, 0, 1], [0, 0, -1]], [[1], [0, 0, 0, -2], [-1]], [[1], [0, 0, 0, 2], [-1]], [[1], [0], [1]], [[1], [1, 0, -1], [0, 0, -1]], [[1], [0, 0, 1], [-1, 0, 1]], [[1], [0, -1, 0, 1], [1, 0, -1]], [[1], [0, 1], [0, 0, 1]], [[1], [0, 1, 0, -1], [1, 0, -1]], [[1], [0, -1], [0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [1]], [[1], [-1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0, 0, 1], [1, 0, -1], [0, 0, 0, -2], [0, 0, 0, 2], [0], [-1, 0, 1], [0, 0, -1], [0, -1, 0, 1], [0, 1], [0, 1, 0, -1], [0, -1]], 'GalOrbIndex': 4, 'HardFactors': [3, 15, 11, 16, 9, 12, 17, 8, 12, 4, 8, 12], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0, 0, -1], [-1, 0, 1]], [[1], [-1, 0, 1], [0, 0, -1]], [[1], [0, 0, 0, 2], [-1]], [[1], [0, 0, 0, -2], [-1]], [[1], [0], [1]], [[1], [1, 0, -1], [0, 0, -1]], [[1], [0, 0, 1], [-1, 0, 1]], [[1], [0, 1, 0, -1], [1, 0, -1]], [[1], [0, -1], [0, 0, 1]], [[1], [0, -1, 0, 1], [1, 0, -1]], [[1], [0, 1], [0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [1]], [[1], [-1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '16T60', 'Galt': 60, 'HardPrimes': [2, 3, 5, 7, 13, 23, 37, 97, 569, 601, 3463, 4733], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [76, -626, 1659, -1912, 3832, -3438, 2625, -2560, 1077, -242, 357, -132, -79, 32, 14, -8, 1], 'NumBadPrimes': 3, 'Proj_GAP': [12, 3], 'Proj_Polynomial': [127, -6, -17, 0, 1], 'Proj_nTj': [4, 4]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.3.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [-1], [-1], [1], [1], [1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.259.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.777.6t1.b', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, -1], [0, 1], [-1, 0], [-1, 0], [1, 0], [0, 1], [-1, -1], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.259.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.777.6t1.b', 'Character': [[1, 0], [1, 0], [-1, 0], [0, 1], [-1, -1], [-1, 0], [-1, 0], [1, 0], [-1, -1], [0, 1], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.201243.24t21.a', 'Character': [[2, 0], [-2, 0], [0, 0], [-1, 0], [-1, 0], [0, 2], [0, -2], [0, 0], [1, 0], [1, 0], [0, 1], [0, 1], [0, -1], [0, -1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '2.201243.24t21.a', 'Character': [[2, 0], [-2, 0], [0, 0], [-1, 0], [-1, 0], [0, -2], [0, 2], [0, 0], [1, 0], [1, 0], [0, -1], [0, -1], [0, 1], [0, 1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '2.777.16t60.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [1, 0, -1, 0], [0, 0, 1, 0], [0, 0, 0, -2], [0, 0, 0, 2], [0, 0, 0, 0], [0, 0, -1, 0], [-1, 0, 1, 0], [0, 1, 0, 0], [0, -1, 0, 1], [0, -1, 0, 0], [0, 1, 0, -1]], 'CharacterField': 12}, {'GalConj': 2, 'Baselabel': '2.777.16t60.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [1, 0, -1, 0], [0, 0, 1, 0], [0, 0, 0, 2], [0, 0, 0, -2], [0, 0, 0, 0], [0, 0, -1, 0], [-1, 0, 1, 0], [0, -1, 0, 0], [0, 1, 0, -1], [0, 1, 0, 0], [0, -1, 0, 1]], 'CharacterField': 12}, {'GalConj': 3, 'Baselabel': '2.777.16t60.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [1, 0, -1, 0], [0, 0, 0, 2], [0, 0, 0, -2], [0, 0, 0, 0], [-1, 0, 1, 0], [0, 0, -1, 0], [0, 1, 0, -1], [0, -1, 0, 0], [0, -1, 0, 1], [0, 1, 0, 0]], 'CharacterField': 12}, {'GalConj': 4, 'Baselabel': '2.777.16t60.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [1, 0, -1, 0], [0, 0, 0, -2], [0, 0, 0, 2], [0, 0, 0, 0], [-1, 0, 1, 0], [0, 0, -1, 0], [0, -1, 0, 1], [0, 1, 0, 0], [0, 1, 0, -1], [0, -1, 0, 0]], 'CharacterField': 12}, {'GalConj': 1, 'Baselabel': '3.201243.6t6.a', 'Character': [[3], [3], [1], [0], [0], [-3], [-3], [-1], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.603729.4t4.a', 'Character': [[3], [3], [-1], [0], [0], [3], [3], [-1], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]}, {'Size': '1', 'Order': 2, 'Representative': [9, 10, 11, 12, 13, 14, 15, 16, 1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '6', 'Order': 2, 'Representative': [8, 3, 2, 15, 14, 13, 12, 1, 16, 11, 10, 7, 6, 5, 4, 9]}, {'Size': '4', 'Order': 3, 'Representative': [1, 6, 4, 8, 5, 7, 2, 3, 9, 14, 12, 16, 13, 15, 10, 11]}, {'Size': '4', 'Order': 3, 'Representative': [1, 7, 8, 3, 5, 2, 6, 4, 9, 15, 16, 11, 13, 10, 14, 12]}, {'Size': '1', 'Order': 4, 'Representative': [5, 4, 15, 10, 9, 8, 3, 14, 13, 12, 7, 2, 1, 16, 11, 6]}, {'Size': '1', 'Order': 4, 'Representative': [13, 12, 7, 2, 1, 16, 11, 6, 5, 4, 15, 10, 9, 8, 3, 14]}, {'Size': '6', 'Order': 4, 'Representative': [14, 15, 4, 11, 16, 1, 2, 5, 6, 7, 12, 3, 8, 9, 10, 13]}, {'Size': '4', 'Order': 6, 'Representative': [9, 15, 16, 11, 13, 10, 14, 12, 1, 7, 8, 3, 5, 2, 6, 4]}, {'Size': '4', 'Order': 6, 'Representative': [9, 14, 12, 16, 13, 15, 10, 11, 1, 6, 4, 8, 5, 7, 2, 3]}, {'Size': '4', 'Order': 12, 'Representative': [13, 16, 2, 6, 1, 11, 12, 7, 5, 8, 10, 14, 9, 3, 4, 15]}, {'Size': '4', 'Order': 12, 'Representative': [13, 11, 6, 7, 1, 12, 16, 2, 5, 3, 14, 15, 9, 4, 8, 10]}, {'Size': '4', 'Order': 12, 'Representative': [5, 8, 10, 14, 9, 3, 4, 15, 13, 16, 2, 6, 1, 11, 12, 7]}, {'Size': '4', 'Order': 12, 'Representative': [5, 3, 14, 15, 9, 4, 8, 10, 13, 11, 6, 7, 1, 12, 16, 2]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['249316', '-47974', '3183', '-82', '1'], 'ConjugacyClass': 4}, {'RootOf': ['539676', '-49122', '4597', '-124', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-48', '1'], 'ConjugacyClass': 2}, {'RootOf': ['703980864', '10029840', '-3184791', '18904', '5030', '-136', '1'], 'ConjugacyClass': 3}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['1181601', '30114', '-1025', '-50', '1'], 'ConjugacyClass': 9}, {'RootOf': ['58227', '-20874', '2671', '-92', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [2, 2, 6, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['37', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-15', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-82996416', '-8442912', '330684', '38758', '-733', '-46', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [4, 4, 4, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['134140', '-28366', '2415', '-82', '1'], 'ConjugacyClass': 11}, {'RootOf': ['920655', '60894', '291', '-84', '1'], 'ConjugacyClass': 12}, {'RootOf': ['56943', '-8874', '847', '-32', '1'], 'ConjugacyClass': 13}, {'RootOf': ['645724', '-2184', '-551', '-30', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [4, 12]}], 'Frobs': [3, 8, 11, 2, 11, 9, 12, 4, 12, 6, 10, 1, 12, 8, 12, 14, 14, 10, 8, 12, 4, 10, 11, 3, 8, 13, 9, 11, 9, 13, 4, 3, 13, 10, 12, 8, 5, 8, 14, 3, 11, 5, 12, 10, 11, 10, 8, 8, 3, 4, 12, 13, 8, 3, 3, 7, 13, 8, 8, 11, 8, 14, 8, 12, 8, 3, 8, 5, 13, 10, 14, 14, 2, 10, 10, 13, 3, 5, 14, 5, 13, 8, 3, 8, 10, 12, 14, 10, 13, 5, 14, 14, 10, 3, 4, 11, 3, 7, 4, 9, 8, 14, 13, 12, 9, 9, 14, 14, 3, 4, 8, 5, 11, 4, 4, 12, 1, 6, 13, 14, 1, 5, 14, 12, 8, 13, 9, 3, 9, 10, 10, 14, 9, 4, 3, 8, 3, 4, 11, 3, 5, 11, 5, 12, 9, 13, 10, 11, 5, 6, 9, 12, 9, 14, 8, 3, 9, 13, 4, 14, 3, 11, 5, 3, 12, 12, 4, 9], 'G-Gens': [[10, 1, 16, 5, 12, 7, 14, 3, 2, 9, 8, 13, 4, 15, 6, 11], [14, 15, 4, 11, 16, 1, 2, 5, 6, 7, 12, 3, 8, 9, 10, 13], [8, 3, 2, 15, 14, 13, 12, 1, 16, 11, 10, 7, 6, 5, 4, 9], [7, 2, 16, 4, 3, 9, 14, 13, 15, 10, 8, 12, 11, 1, 6, 5], [9, 10, 11, 12, 13, 14, 15, 16, 1, 2, 3, 4, 5, 6, 7, 8]], 'G-Name': 'SL2(F3):C2', 'Polynomial': [76, -626, 1659, -1912, 3832, -3438, 2625, -2560, 1077, -242, 357, -132, -79, 32, 14, -8, 1], 'QpRts': [['-279847351595810789', '-361583602524489989', '-287604829167603687', '360310214511245378', '-40299220249961454', '-221472009252509706'], ['157478552430557092', '-198850666709110552', '-264010850024403316', '54444499273241533', '141733821742225670', '-1297089739777642'], ['-298799615769474490', '-42863884257524333', '-81855601836705447', '-107505300244247391', '85489354315214359', '-182328439191590400'], ['-223026640520366984', '284975138682313525', '193471676541063658', '257459496950971902', '234101560419318805', '36070051466994577'], ['142955278232468645', '69631824920536350', '80960903024508016', '107973912989638810', '-180174155938571158', '-293247798225032764'], ['-288211191033675879', '240673661266516171', '238252117805202893', '101614518727996032', '-244397132780970166', '-206763237560305452'], ['-359682470170375089', '27394847369113898', '-272935387860504186', '-50954263118047159', '101092779160955765', '175730800597128253'], ['215469950215982256', '-251869922777564572', '87655166152568701', '269139472521395428', '-323663023432469896', '150577986074478111'], ['-162413470122633495', '361583602524489989', '287604829167603687', '-360310214511245378', '40299220249961454', '221472009252509706'], ['319869130253739103', '73414280730700595', '186998768291665530', '41387592713236142', '-156020559439189059', '340850472319547212'], ['77413746705184673', '274590832658684416', '-162885719549324117', '100308880477285682', '-134759177305679808', '225739552165560673'], ['234415911226854267', '-385814445357958788', '-360788757231356799', '309940534457252271', '-349715625950092267', '156654100590422449'], ['-193611107926262022', '-69631824920536350', '-80960903024508016', '-107973912989638810', '180174155938571158', '293247798225032764'], ['95402524603023273', '176274562813135884', '-14749436234219473', '-230372904476417210', '92192505383587701', '218532007871898072'], ['-75123718946333875', '-318906685470355996', '126444788022258552', '83880556879990662', '65398585933390089', '260609830300059318'], ['-149952311371426439', '120982281052049752', '324403235923754004', '-41680300374108131', '-299115871834840954', '-386713251105865410']], 'QpRts-minpoly': [3, 8, 16, 19, 0, 0, 1], 'QpRts-p': 31, 'QpRts-prec': 12, 'Size': 48, 'TransitiveDegree': 16}