Artin representation data - 56.11830699888159640166031150777443264511833745828375103599436349035114687411270724335160431657346388003286104975069039098219498658191299929541985480891048058764975516806824835577681040555214913370467598336.105.a

Formats: - HTML - YAML - JSON - 2024-04-25T01:15:43.955136

• 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, 3217], 'Baselabel': '56.11830699888159640166031150777443264511833745828375103599436349035114687411270724335160431657346388003286104975069039098219498658191299929541985480891048058764975516806824835577681040555214913370467598336.105.a', 'CharacterField': 1, 'Conductor': 11830699888159640166031150777443264511833745828375103599436349035114687411270724335160431657346388003286104975069039098219498658191299929541985480891048058764975516806824835577681040555214913370467598336, 'Container': '105', 'Dets': ['1.1.1t1.a.a'], 'Dim': 56, 'GalConjSigns': [1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[56], [8], [0], [-4], [-1], [0], [0], [1], [0], [-1], [0], [0], [1], [1]], 'GalOrbIndex': 1, 'HardFactors': [15, 10, 16], 'LocalFactors': [[[1], [-56], [1540], [-27720], [367290], [-3819816], [32468436], [-231917400], [1420494075], [-7575968400], [35607051480], [-148902215280], [558383307300], [-1889912732400], [5804731963800], [-16253249498640], [41648951840265], [-97997533741800], [212327989773900], [-424655979547800], [785613562163430], [-1346766106565880], [2142582442263900], [-3167295784216200], [4355031703297275], [-5574440580220512], [6646448384109072], [-7384942649010080], [7648690600760440], [-7384942649010080], [6646448384109072], [-5574440580220512], [4355031703297275], [-3167295784216200], [2142582442263900], [-1346766106565880], [785613562163430], [-424655979547800], [212327989773900], [-97997533741800], [41648951840265], [-16253249498640], [5804731963800], [-1889912732400], [558383307300], [-148902215280], [35607051480], [-7575968400], [1420494075], [-231917400], [32468436], [-3819816], [367290], [-27720], [1540], [-56], [1]], [[1], [-8], [4], [136], [-326], [-920], [4052], [2072], [-27397], [13072], [121048], [-143888], [-368092], [724592], [742808], [-2473328], [-713207], [6300712], [-1215412], [-12421288], [7277798], [19112632], [-18859172], [-22524728], [34225403], [18780512], [-47902192], [-7369568], [53429368], [-7369568], [-47902192], [18780512], [34225403], [-22524728], [-18859172], [19112632], [7277798], [-12421288], [-1215412], [6300712], [-713207], [-2473328], [742808], [724592], [-368092], [-143888], [121048], [13072], [-27397], [2072], [4052], [-920], [-326], [136], [4], [-8], [1]], [[1], [0], [-28], [0], [378], [0], [-3276], [0], [20475], [0], [-98280], [0], [376740], [0], [-1184040], [0], [3108105], [0], [-6906900], [0], [13123110], [0], [-21474180], [0], [30421755], [0], [-37442160], [0], [40116600], [0], [-37442160], [0], [30421755], [0], [-21474180], [0], [13123110], [0], [-6906900], [0], [3108105], [0], [-1184040], [0], [376740], [0], [-98280], [0], [20475], [0], [-3276], [0], [378], [0], [-28], [0], [1]], [[1], [4], [10], [0], [-45], [-144], [-126], [180], [945], [1200], [-24], [-3696], [-5940], [-2880], [9360], [19152], [14868], [-15120], [-43680], [-43680], [12012], [73008], [88920], [9360], [-90090], [-133848], [-46332], [80080], [153010], [80080], [-46332], [-133848], [-90090], [9360], [88920], [73008], [12012], [-43680], [-43680], [-15120], [14868], [19152], [9360], [-2880], [-5940], [-3696], [-24], [1200], [945], [180], [-126], [-144], [-45], [0], [10], [4], [1]], [[1], [1], [1], [-18], [-18], [-18], [153], [153], [153], [-816], [-816], [-816], [3060], [3060], [3060], [-8568], [-8568], [-8568], [18564], [18564], [18564], [-31824], [-31824], [-31824], [43758], [43758], [43758], [-48620], [-48620], [-48620], [43758], [43758], [43758], [-31824], [-31824], [-31824], [18564], [18564], [18564], [-8568], [-8568], [-8568], [3060], [3060], [3060], [-816], [-816], [-816], [153], [153], [153], [-18], [-18], [-18], [1], [1], [1]], [[1], [0], [-4], [0], [-6], [0], [44], [0], [-5], [0], [-216], [0], [164], [0], [616], [0], [-759], [0], [-1100], [0], [1958], [0], [1188], [0], [-3333], [0], [-528], [0], [3960], [0], [-528], [0], [-3333], [0], [1188], [0], [1958], [0], [-1100], [0], [-759], [0], [616], [0], [164], [0], [-216], [0], [-5], [0], [44], [0], [-6], [0], [-4], [0], [1]], [[1], [0], [0], [0], [-14], [0], [0], [0], [91], [0], [0], [0], [-364], [0], [0], [0], [1001], [0], [0], [0], [-2002], [0], [0], [0], [3003], [0], [0], [0], [-3432], [0], [0], [0], [3003], [0], [0], [0], [-2002], [0], [0], [0], [1001], [0], [0], [0], [-364], [0], [0], [0], [91], [0], [0], [0], [-14], [0], [0], [0], [1]], [[1], [-1], [0], [0], [0], [-11], [11], [0], [0], [0], [55], [-55], [0], [0], [0], [-165], [165], [0], [0], [0], [330], [-330], [0], [0], [0], [-462], [462], [0], [0], [0], [462], [-462], [0], [0], [0], [-330], [330], [0], [0], [0], [165], [-165], [0], [0], [0], [-55], [55], [0], [0], [0], [11], [-11], [0], [0], [0], [-1], [1]], [[1], [0], [2], [0], [3], [0], [-6], [0], [-15], [0], [-24], [0], [12], [0], [48], [0], [84], [0], [0], [0], [-84], [0], [-168], [0], [-42], [0], [84], [0], [210], [0], [84], [0], [-42], [0], [-168], [0], [-84], [0], [0], [0], [84], [0], [48], [0], [12], [0], [-24], [0], [-15], [0], [-6], [0], [3], [0], [2], [0], [1]], [[1], [1], [1], [-2], [-2], [-2], [-7], [-7], [-7], [16], [16], [16], [20], [20], [20], [-56], [-56], [-56], [-28], [-28], [-28], [112], [112], [112], [14], [14], [14], [-140], [-140], [-140], [14], [14], [14], [112], [112], [112], [-28], [-28], [-28], [-56], [-56], [-56], [20], [20], [20], [16], [16], [16], [-7], [-7], [-7], [-2], [-2], [-2], [1], [1], [1]], [[1], [0], [0], [0], [0], [0], [0], [-8], [0], [0], [0], [0], [0], [0], [28], [0], [0], [0], [0], [0], [0], [-56], [0], [0], [0], [0], [0], [0], [70], [0], [0], [0], [0], [0], [0], [-56], [0], [0], [0], [0], [0], [0], [28], [0], [0], [0], [0], [0], [0], [-8], [0], [0], [0], [0], [0], [0], [1]], [[1], [0], [0], [0], [0], [0], [0], [-8], [0], [0], [0], [0], [0], [0], [28], [0], [0], [0], [0], [0], [0], [-56], [0], [0], [0], [0], [0], [0], [70], [0], [0], [0], [0], [0], [0], [-56], [0], [0], [0], [0], [0], [0], [28], [0], [0], [0], [0], [0], [0], [-8], [0], [0], [0], [0], [0], [0], [1]], [[1], [-1], [0], [0], [0], [1], [-1], [0], [0], [0], [1], [-1], [0], [0], [0], [-3], [3], [0], [0], [0], [-3], [3], [0], [0], [0], [-3], [3], [0], [0], [0], [3], [-3], [0], [0], [0], [3], [-3], [0], [0], [0], [3], [-3], [0], [0], [0], [-1], [1], [0], [0], [0], [-1], [1], [0], [0], [0], [-1], [1]], [[1], [-1], [0], [0], [0], [1], [-1], [0], [0], [0], [1], [-1], [0], [0], [0], [-3], [3], [0], [0], [0], [-3], [3], [0], [0], [0], [-3], [3], [0], [0], [0], [3], [-3], [0], [0], [0], [3], [-3], [0], [0], [0], [3], [-3], [0], [0], [0], [-1], [1], [0], [0], [0], [-1], [1], [0], [0], [0], [-1], [1]], [[1], [-1]], [[1], [1], [1], [-2], [-2], [-2], [1], [1], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T49', 'Galt': 49, 'HardPrimes': [2, 3, 3217], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [3217, 0, 0, 0, 0, 0, 0, -4, 1], 'NumBadPrimes': 2, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [3217, 0, 0, 0, 0, 0, 0, -4, 1], 'Proj_nTj': [8, 49]}
• 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': '7.72641749645773438449680384.8t49.a', 'Character': [[7], [-1], [3], [4], [1], [-1], [1], [2], [0], [-1], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.5153148233983618623516207984986690777239093510144.15t72.a', 'Character': [[14], [6], [2], [-1], [2], [2], [0], [-1], [-1], [0], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '20.374333703900597548061689388732763711301044668124672309503312784525461815296.28t433.a', 'Character': [[20], [4], [4], [5], [-1], [0], [0], [0], [1], [1], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.383317712794211889215169934062350040372269740159664444931392291354072898863104.56.a', 'Character': [[21], [-3], [1], [6], [0], [1], [-1], [1], [-2], [0], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.383317712794211889215169934062350040372269740159664444931392291354072898863104.336.a', 'Character': [[21, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 2, 1, -1, 2, -1, 0, 1], [1, -2, -1, 1, -2, 1, 0, -1]], 'CharacterField': 15}, {'GalConj': 2, 'Baselabel': '21.383317712794211889215169934062350040372269740159664444931392291354072898863104.336.a', 'Character': [[21, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, -2, -1, 1, -2, 1, 0, -1], [-2, 2, 1, -1, 2, -1, 0, 1]], 'CharacterField': 15}, {'GalConj': 1, 'Baselabel': '28.27844869327587626118969435824762107376182451530025240596221458285362436669228656561088342556305770151936.56.a', 'Character': [[28], [-4], [4], [1], [1], [0], [0], [-2], [1], [-1], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.7901171978960531722259074189917547207169107111850162829840025882271512288546266438533605480355005402852491738127396169165307904.70.a', 'Character': [[35], [3], [-5], [5], [2], [-1], [-1], [0], [1], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '45.78269208418970417222195611788482931966767902407795196365318334274494167695863368992567649189381033610686223497464799306084975766507841028352175926648262264498346262528.336.a', 'Character': [[45, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0], [-1, -1, -1, 0, -1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]], 'CharacterField': 7}, {'GalConj': 2, 'Baselabel': '45.78269208418970417222195611788482931966767902407795196365318334274494167695863368992567649189381033610686223497464799306084975766507841028352175926648262264498346262528.336.a', 'Character': [[45, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-1, -1, -1, 0, -1, 0], [0, 1, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]], 'CharacterField': 7}, {'GalConj': 1, 'Baselabel': '56.11830699888159640166031150777443264511833745828375103599436349035114687411270724335160431657346388003286104975069039098219498658191299929541985480891048058764975516806824835577681040555214913370467598336.105.a', 'Character': [[56], [8], [0], [-4], [-1], [0], [0], [1], [0], [-1], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '64.880028405155811736488195248653721168095084447239656248752303904114169825639733001976764081143410486592535510867885958711269152052378069811657814381533221425613808624048207764540403950741493645497637758427313926144412720425206808576.168.a', 'Character': [[64], [0], [0], [4], [-2], [0], [0], [-1], [0], [0], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '70.15981700772124437796021650657450273660711693411476566090088742954124114091265145615650649334529794088074505478035573161031919156110285861515880966634491081193626553981154311796075156939608199132690453733328569086586143020896073904688653408605761311967543296.120.a', 'Character': [[70], [-2], [2], [-5], [1], [-2], [0], [0], [-1], [1], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '105', 'Order': 2, 'Representative': [2, 1, 4, 3, 6, 5, 8, 7]}, {'Size': '210', 'Order': 2, 'Representative': [2, 1, 4, 3, 5, 6, 7, 8]}, {'Size': '112', 'Order': 3, 'Representative': [2, 3, 1, 4, 5, 6, 7, 8]}, {'Size': '1120', 'Order': 3, 'Representative': [2, 3, 1, 5, 6, 4, 7, 8]}, {'Size': '1260', 'Order': 4, 'Representative': [2, 3, 4, 1, 6, 7, 8, 5]}, {'Size': '2520', 'Order': 4, 'Representative': [2, 3, 4, 1, 6, 5, 7, 8]}, {'Size': '1344', 'Order': 5, 'Representative': [2, 3, 4, 5, 1, 6, 7, 8]}, {'Size': '1680', 'Order': 6, 'Representative': [2, 3, 1, 5, 4, 7, 6, 8]}, {'Size': '3360', 'Order': 6, 'Representative': [2, 3, 4, 5, 6, 1, 8, 7]}, {'Size': '2880', 'Order': 7, 'Representative': [2, 3, 4, 5, 6, 7, 1, 8]}, {'Size': '2880', 'Order': 7, 'Representative': [3, 1, 4, 5, 6, 7, 2, 8]}, {'Size': '1344', 'Order': 15, 'Representative': [2, 3, 4, 5, 1, 7, 8, 6]}, {'Size': '1344', 'Order': 15, 'Representative': [3, 1, 4, 5, 2, 7, 8, 6]}], '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, 3]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 5]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 4]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [1, 1, 3, 3]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 3]}, {'Data': [1, 3, 4, 5, 6, 7, 8, 2], 'Classes': [{'RootOf': ['-25569038832384', '1'], 'ConjugacyClass': 12}, {'RootOf': ['25569038832384', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'ALT', 'CycleType': [1, 7]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2]}, {'Data': 0, 'Classes': 10, 'Algorithm': 'CYC', 'CycleType': [2, 6]}, {'Data': [2, 3, 1, 5, 6, 7, 8, 4], 'Classes': [{'RootOf': ['-25569038832384', '1'], 'ConjugacyClass': 14}, {'RootOf': ['25569038832384', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'ALT', 'CycleType': [3, 5]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [4, 4]}], 'Frobs': [3, 10, 12, 11, 14, 11, 11, 9, 11, 10, 10, 13, 6, 7, 12, 12, 7, 5, 9, 12, 11, 9, 12, 14, 13, 10, 11, 13, 9, 6, 7, 11, 10, 12, 12, 12, 5, 10, 9, 11, 3, 7, 10, 9, 9, 8, 14, 7, 4, 10, 11, 11, 6, 9, 12, 12, 12, 5, 12, 13, 10, 12, 5, 7, 3, 11, 12, 7, 11, 13, 7, 11, 7, 12, 6, 6, 11, 10, 11, 10, 7, 12, 8, 10, 6, 8, 7, 14, 7, 14, 12, 14, 10, 9, 5, 12, 12, 9, 11, 12, 8, 13, 7, 7, 6, 11, 11, 7, 13, 8, 11, 11, 14, 12, 3, 6, 8, 10, 5, 8, 12, 10, 12, 11, 7, 12, 7, 11, 10, 10, 14, 12, 9, 10, 12, 10, 7, 6, 11, 7, 12, 11, 7, 8, 10, 14, 10, 9, 6, 13, 12, 10, 8, 9, 12, 13, 12, 8, 13, 9, 9, 14, 6, 11, 10, 9, 5, 12], 'G-Gens': [[2, 1, 4, 5, 6, 7, 8, 3], [2, 3, 1, 4, 5, 6, 7, 8]], 'G-Name': 'A8', 'Polynomial': [3217, 0, 0, 0, 0, 0, 0, -4, 1], 'QpRts': [['-412748255440842519', '0'], ['-40332298513945519', '0'], ['230517902190884958', '0'], ['-384413400660817097', '120672147704040373'], ['-461570693019624925', '179228001309612774'], ['-254618263851273399', '0'], ['-60817027981486033', '-120672147704040373'], ['330021748388390777', '-179228001309612774']], 'QpRts-minpoly': [2, 172, 1], 'QpRts-p': 179, 'QpRts-prec': 8, 'Size': 20160, 'TransitiveDegree': 8}