Artin representation data - 2.448.16t60.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, 7], 'Baselabel': '2.448.16t60.a', 'CharacterField': 12, 'Conductor': 448, 'Container': '16t60', 'Dets': ['1.28.6t1.a.b', '1.28.6t1.a.a', '1.28.6t1.a.a', '1.28.6t1.a.b'], 'Dim': 2, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 16, 'GaloisConjugates': [{'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': 1, 'HardFactors': [15, 14, 16, 13, 8, 8, 8], '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]], [[1], [0, 0, 0, -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': [15, 14, 16, 13, 8, 8, 8], '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]], [[1], [0, 0, 0, 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': 3, 'HardFactors': [15, 14, 16, 13, 8, 8, 8], '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]], [[1], [0, 0, 0, -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': [15, 14, 16, 13, 8, 8, 8], '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]], [[1], [0, 0, 0, 1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '16T60', 'Galt': 60, 'HardPrimes': [2, 3, 7, 19, 6089, 8233, 7352437], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 0, 4, 0, 4, 0, 4, 0, 10, 0, -4, 0, 4, 0, -4, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [12, 3], 'Proj_Polynomial': [2, 0, 2, -2, 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': '1.4.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [-1], [-1], [1], [1], [1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.7.3t1.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': '1.28.6t1.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': 2, 'Baselabel': '1.7.3t1.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': '1.28.6t1.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': 1, 'Baselabel': '2.3136.24t21.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': '2.3136.24t21.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': '2.448.16t60.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': 2, 'Baselabel': '2.448.16t60.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': '2.448.16t60.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': 4, 'Baselabel': '2.448.16t60.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': '3.3136.6t6.a', 'Character': [[3], [3], [1], [0], [0], [-3], [-3], [-1], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.3136.4t4.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': [13, 14, 4, 3, 9, 10, 16, 15, 5, 6, 12, 11, 1, 2, 8, 7]}, {'Size': '4', 'Order': 3, 'Representative': [14, 5, 3, 10, 12, 15, 1, 8, 6, 13, 11, 2, 4, 7, 9, 16]}, {'Size': '4', 'Order': 3, 'Representative': [7, 12, 3, 13, 2, 9, 14, 8, 15, 4, 11, 5, 10, 1, 6, 16]}, {'Size': '1', 'Order': 4, 'Representative': [10, 1, 8, 15, 14, 5, 4, 11, 2, 9, 16, 7, 6, 13, 12, 3]}, {'Size': '1', 'Order': 4, 'Representative': [2, 9, 16, 7, 6, 13, 12, 3, 10, 1, 8, 15, 14, 5, 4, 11]}, {'Size': '6', 'Order': 4, 'Representative': [14, 5, 7, 16, 10, 1, 11, 4, 6, 13, 15, 8, 2, 9, 3, 12]}, {'Size': '4', 'Order': 6, 'Representative': [15, 4, 11, 5, 10, 1, 6, 16, 7, 12, 3, 13, 2, 9, 14, 8]}, {'Size': '4', 'Order': 6, 'Representative': [6, 13, 11, 2, 4, 7, 9, 16, 14, 5, 3, 10, 12, 15, 1, 8]}, {'Size': '4', 'Order': 12, 'Representative': [13, 14, 8, 9, 7, 12, 10, 11, 5, 6, 16, 1, 15, 4, 2, 3]}, {'Size': '4', 'Order': 12, 'Representative': [4, 7, 8, 6, 1, 2, 13, 11, 12, 15, 16, 14, 9, 10, 5, 3]}, {'Size': '4', 'Order': 12, 'Representative': [5, 6, 16, 1, 15, 4, 2, 3, 13, 14, 8, 9, 7, 12, 10, 11]}, {'Size': '4', 'Order': 12, 'Representative': [12, 15, 16, 14, 9, 10, 5, 3, 4, 7, 8, 6, 1, 2, 13, 11]}], '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': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['54234368', '-1024256', '18208', '-144', '1'], 'ConjugacyClass': 4}, {'RootOf': ['48558336', '-562688', '12576', '-64', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['-24', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-191102976', '0', '-2654208', '0', '-2880', '0', '1'], 'ConjugacyClass': 3}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['48558336', '562688', '12576', '64', '1'], 'ConjugacyClass': 9}, {'RootOf': ['54234368', '1024256', '18208', '144', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [2, 2, 6, 6]}, {'Data': {'Powers': [1], 'Resolvent': [16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['9824', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-9824', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-1299445497492107620777984', '0', '-12814202293977088', '0', '133283840', '0', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [4, 4, 4, 4]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['30512384', '-72192', '-736', '128', '1'], 'ConjugacyClass': 11}, {'RootOf': ['16355584', '50688', '1952', '-128', '1'], 'ConjugacyClass': 12}, {'RootOf': ['30512384', '72192', '-736', '-128', '1'], 'ConjugacyClass': 13}, {'RootOf': ['16355584', '-50688', '1952', '128', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [4, 12]}], 'Frobs': [4, 14, 4, 11, 12, 8, 9, 13, 13, 8, 14, 10, 8, 3, 11, 9, 14, 10, 14, 3, 5, 13, 3, 4, 8, 5, 13, 13, 5, 8, 3, 11, 9, 3, 4, 14, 9, 11, 7, 10, 12, 1, 11, 9, 8, 14, 3, 3, 12, 4, 10, 6, 5, 7, 10, 12, 9, 13, 9, 8, 12, 2, 3, 12, 4, 10, 11, 8, 14, 8, 9, 11, 12, 10, 6, 11, 5, 4, 10, 9, 3, 8, 14, 8, 11, 13, 8, 4, 8, 3, 11, 12, 12, 6, 11, 3, 4, 5, 13, 4, 7, 5, 14, 4, 12, 5, 3, 10, 12, 8, 11, 5, 8, 14, 3, 5, 3, 12, 10, 3, 9, 8, 4, 12, 11, 2, 10, 13, 3, 10, 12, 3, 11, 8, 10, 8, 5, 14, 8, 5, 3, 4, 12, 3, 5, 3, 8, 5, 13, 13, 4, 2, 3, 11, 14, 3, 11, 4, 1, 9, 11, 8, 3, 11, 9, 14, 12, 9], 'G-Gens': [[10, 1, 8, 15, 14, 5, 4, 11, 2, 9, 16, 7, 6, 13, 12, 3], [7, 12, 6, 2, 16, 11, 9, 5, 15, 4, 14, 10, 8, 3, 1, 13], [11, 8, 7, 2, 5, 6, 9, 4, 3, 16, 15, 10, 13, 14, 1, 12], [9, 10, 11, 12, 13, 14, 15, 16, 1, 2, 3, 4, 5, 6, 7, 8], [14, 5, 7, 16, 10, 1, 11, 4, 6, 13, 15, 8, 2, 9, 3, 12]], 'G-Name': 'SL2(F3):C2', 'Polynomial': [1, 0, 4, 0, 4, 0, 4, 0, 10, 0, -4, 0, 4, 0, -4, 0, 1], 'QpRts': [['-2965314006374572725228562503897477566', '3453164925917881610145875184254562615', '1067717933759113017088197026592886742', '-3972780680174827053634387335989341714', '3914782952865044238608977313386738703', '-1628921625182921380460094781749917875'], ['2920912213462048049410648028089766435', '1808765381569194258945592913107045827', '-302796804943252829221878488075384891', '1716305620898506653262971138874475378', '3737344957331283679153737476008413987', '-1261581391727208170268545788233794728'], ['2889510395872422557989102423557206254', '-866946392003385919087689198627759609', '-98301874511194061208941703105159845', '3256344139171547722848147174582050280', '-2822241472836223671495553522062088071', '-444434877157883247408528022889357914'], ['3494719396270155122553179015772769552', '-1975150833347990021568330290703696151', '-3301825238197688806736091322571334058', '-2270314180791124435997342738062918146', '-1800432782478828309994362986677148977', '-435474822669532986437663825794393692'], ['2597997294446318991770224950882579860', '3221539533717918826609032961963475622', '1411814124216699298043294156513507016', '-1784878259305014867145877830669068650', '-2059031241383012845990940786235879501', '-1499457447713977256565982273781135404'], ['-3325749265084778452414463294949201168', '450364647483039927299202078060093985', '951228523480118466090964139306871733', '-712810336641569894270876846107851510', '434490667804827219256866894979766323', '2405205365209951627594375486190316891'], ['3722196896512528413038408548357735483', '-2767861793372711557198120607981765442', '-1166157167975906761673133319227838064', '3887292928747526465859419116163679160', '859639460233983593387638601083818054', '512187536620405872871503357411187085'], ['1256505199607155407044898439544293433', '3579701283854500169891428226855464399', '3911825612137400523659577316522739872', '220470316486381184631707997262549370', '-3639171462013174008057124422885686925', '-3701606598852027501708063844821839618'], ['2965314006374572725228562503897477566', '-3453164925917881610145875184254562615', '-1067717933759113017088197026592886742', '3972780680174827053634387335989341714', '-3914782952865044238608977313386738703', '1628921625182921380460094781749917875'], ['-2920912213462048049410648028089766435', '-1808765381569194258945592913107045827', '302796804943252829221878488075384891', '-1716305620898506653262971138874475378', '-3737344957331283679153737476008413987', '1261581391727208170268545788233794728'], ['-2889510395872422557989102423557206254', '866946392003385919087689198627759609', '98301874511194061208941703105159845', '-3256344139171547722848147174582050280', '2822241472836223671495553522062088071', '444434877157883247408528022889357914'], ['-3494719396270155122553179015772769552', '1975150833347990021568330290703696151', '3301825238197688806736091322571334058', '2270314180791124435997342738062918146', '1800432782478828309994362986677148977', '435474822669532986437663825794393692'], ['-2597997294446318991770224950882579860', '-3221539533717918826609032961963475622', '-1411814124216699298043294156513507016', '1784878259305014867145877830669068650', '2059031241383012845990940786235879501', '1499457447713977256565982273781135404'], ['3325749265084778452414463294949201168', '-450364647483039927299202078060093985', '-951228523480118466090964139306871733', '712810336641569894270876846107851510', '-434490667804827219256866894979766323', '-2405205365209951627594375486190316891'], ['-3722196896512528413038408548357735483', '2767861793372711557198120607981765442', '1166157167975906761673133319227838064', '-3887292928747526465859419116163679160', '-859639460233983593387638601083818054', '-512187536620405872871503357411187085'], ['-1256505199607155407044898439544293433', '-3579701283854500169891428226855464399', '-3911825612137400523659577316522739872', '-220470316486381184631707997262549370', '3639171462013174008057124422885686925', '3701606598852027501708063844821839618']], 'QpRts-minpoly': [3, 3, 10, 0, 2, 0, 1], 'QpRts-p': 17, 'QpRts-prec': 30, 'Size': 48, 'TransitiveDegree': 16}