Artin representation data - 9.4335087698497294968384.18t273.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, 673], 'Baselabel': '9.4335087698497294968384.18t273.a', 'CharacterField': 1, 'Conductor': 4335087698497294968384, 'Container': '18t273', 'Dets': ['1.1.1t1.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, 11, 10, 12, 3, 22, 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], [0], [0], [1]], [[1], [0], [0], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T47', 'Galt': 47, 'HardPrimes': [2, 3, 7, 23, 37, 661, 673, 1051], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [432, 0, -196, -98, 65, 16, -4, -4, 1], 'NumBadPrimes': 3, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [432, 0, -196, -98, 65, 16, -4, -4, 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': '1.3.2t1.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': '1.2019.2t1.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': '1.673.2t1.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': '2.2019.4t3.a', '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': '4.43894255248.12t34.b', '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': '4.48916332.12t34.b', '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': '4.96912.6t13.b', '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': '4.5435148.6t13.b', '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': '6.98762074308.12t201.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': '6.296286222924.12t202.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': '6.3657854604.8t47.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': '6.10973563812.12t200.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': '9.526731062976.16t1294.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': '9.14221738700352.18t272.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': '9.4335087698497294968384.18t273.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': '9.160558803648047961792.18t274.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': '12.208084209527870158482432.36t1763.a', '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': '12.23120467725318906498048.24t2821.a', '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': '18.2283425351523661576557520632950784.36t1758.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, 6, 3, 7, 5, 2, 4, 8]}, {'Size': '9', 'Order': 2, 'Representative': [5, 6, 8, 7, 1, 2, 4, 3]}, {'Size': '12', 'Order': 2, 'Representative': [3, 2, 1, 4, 5, 6, 7, 8]}, {'Size': '24', 'Order': 2, 'Representative': [2, 1, 4, 3, 6, 5, 8, 7]}, {'Size': '36', 'Order': 2, 'Representative': [3, 4, 1, 2, 5, 6, 7, 8]}, {'Size': '36', 'Order': 2, 'Representative': [3, 6, 1, 7, 5, 2, 4, 8]}, {'Size': '16', 'Order': 3, 'Representative': [5, 2, 3, 4, 8, 6, 7, 1]}, {'Size': '64', 'Order': 3, 'Representative': [5, 2, 3, 6, 8, 7, 4, 1]}, {'Size': '12', 'Order': 4, 'Representative': [1, 4, 3, 6, 5, 7, 2, 8]}, {'Size': '36', 'Order': 4, 'Representative': [3, 4, 5, 6, 8, 7, 2, 1]}, {'Size': '36', 'Order': 4, 'Representative': [3, 6, 5, 7, 8, 2, 4, 1]}, {'Size': '72', 'Order': 4, 'Representative': [2, 5, 4, 8, 6, 1, 3, 7]}, {'Size': '72', 'Order': 4, 'Representative': [3, 4, 1, 6, 5, 7, 2, 8]}, {'Size': '144', 'Order': 4, 'Representative': [4, 1, 2, 3, 6, 5, 8, 7]}, {'Size': '48', 'Order': 6, 'Representative': [8, 6, 3, 7, 1, 2, 4, 5]}, {'Size': '96', 'Order': 6, 'Representative': [3, 2, 1, 7, 5, 4, 6, 8]}, {'Size': '192', 'Order': 6, 'Representative': [4, 3, 2, 5, 6, 8, 1, 7]}, {'Size': '144', 'Order': 8, 'Representative': [2, 3, 4, 5, 6, 8, 1, 7]}, {'Size': '96', 'Order': 12, 'Representative': [5, 4, 3, 6, 8, 7, 2, 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': ['233619456', '-67272704', '7464704', '-413472', '12080', '-176', '1'], 'ConjugacyClass': 2}, {'RootOf': ['9447274175067474612466545970676299309366866560782696448', '-6076746505702106298718327916629204680275562556974694400', '3666546110637007890935873417122673593083676082351112192', '-1493293884200837732080477926968964370334805330191450112', '405449912252201568151305194561913169845315116417941504', '-79482879458832728421650282553541031572316033327824896', '11988287323698369481344535414418092896081494488907776', '-1453562154555237236661481251057356661589790005657600', '146079151976528246737375257808291315816511251152896', '-12439518464873834348470542068232239651166560976896', '912480871893952590406877177858353549275775893504', '-58388317280545924990739353789778783560544550912', '3291549333491183638272645236952484865174929408', '-164761228350650799626991778946932697198493696', '7369054454656171895885299092464937470001152', '-295960576904171993291037903733119602655232', '10715440149174042720781666490201971621888', '-350760056836070438223373872636580855808', '10402123859724478520966834781464559616', '-279816904615146219180696516731863040', '6830390738369692032086320516825088', '-151240419710418944008214415409152', '3033977265696094546723799040000', '-55025914064901593235269877760', '899497676942282295873847296', '-13197761488014129790976000', '172861232588237399777280', '-2006978011358310596608', '20470658792136786944', '-181319360969838592', '1373821615927296', '-8726532708352', '45192098832', '-183183936', '544760', '-1056', '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': ['141710295040', '-23124492288', '-5249146880', '213711872', '37282816', '-257280', '-96864', '-1456', '48', '1'], 'ConjugacyClass': 3}, {'RootOf': ['405897782611205847877266700691832832', '-66177125794960666402171385169313792', '1692252067217936998021721577488384', '292347425935687828928401963483136', '3954683112757105559051113070592', '-229123079583976802800034119680', '-6609726027765930098766643200', '659359047889250992097591296', '-4116682880432907119296512', '-343881315034467743039488', '-11317772183297439432704', '821136476911071395840', '23683982868014022656', '-3763295816585543680', '181144247597948928', '-2905302762045440', '-118812826251520', '7876751688704', '-177738702080', '332544000', '86653984', '-2505152', '36272', '-288', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1, 3], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-96208728678564403060146176', '-55890090638990810047053824', '-13046904141357311076597760', '-1562020217650826656612352', '-89785495537777501011968', '-349730690670580989952', '255320906346828660736', '12085332934282706944', '-21632298691592192', '-16582097102143488', '-356871977418752', '6102719750144', '308151229440', '1386279936', '-88914176', '-1245088', '5008', '192', '1'], 'ConjugacyClass': 12}, {'RootOf': ['58166231390522758278696750913194560738375686361997458187037010729247534175318644336058194482604075363412488116890903773184', '-8684914928442628050285826405810060837998211500856668913662509325384248725477904037860221454249490967461371264035343826944', '401786882185688565689257359359068583755265820405323659717796398805466939513118640057834980405233325329906195934392352768', '-3453524240395271792432640262709830224042808826495729452838815845375131358837816308226888244911773974356276611821600768', 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