Artin representation data - 2.288.16t60.a

Formats: - HTML - YAML - JSON - 2025-09-22T05:43:01.430651

• 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], 'Baselabel': '2.288.16t60.a', 'CharacterField': 12, 'Conductor': 288, 'Container': '16t60', 'Dets': ['1.36.6t1.b.a', '1.36.6t1.b.a', '1.36.6t1.b.b', '1.36.6t1.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': [15, 16, 5, 11, 8, 1], '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': 2, 'HardFactors': [15, 16, 5, 11, 8, 1], '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': 3, 'HardFactors': [15, 16, 5, 11, 8, 1], '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], [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, 16, 5, 11, 8, 1], '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, 5, 7, 17, 233], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, -4, 10, -28, 58, -92, 150, -180, 212, -176, 146, -88, 58, -28, 14, -4, 1], 'NumBadPrimes': 2, 'Proj_GAP': [12, 3], 'Proj_Polynomial': [2, -4, 6, -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': '1.9.3t1.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': '1.36.6t1.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': '1.9.3t1.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': '1.36.6t1.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': '2.2592.24t21.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': '2.2592.24t21.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': '2.288.16t60.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': '2.288.16t60.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': '2.288.16t60.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': '2.288.16t60.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': '3.5184.6t6.a', 'Character': [[3], [3], [1], [0], [0], [-3], [-3], [-1], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.5184.4t4.b', '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': [5, 4, 15, 2, 1, 8, 11, 6, 13, 12, 7, 10, 9, 16, 3, 14]}, {'Size': '4', 'Order': 3, 'Representative': [10, 15, 12, 16, 5, 6, 1, 3, 2, 7, 4, 8, 13, 14, 9, 11]}, {'Size': '4', 'Order': 3, 'Representative': [7, 9, 8, 11, 5, 6, 10, 12, 15, 1, 16, 3, 13, 14, 2, 4]}, {'Size': '1', 'Order': 4, 'Representative': [16, 3, 10, 15, 14, 5, 4, 1, 8, 11, 2, 7, 6, 13, 12, 9]}, {'Size': '1', 'Order': 4, 'Representative': [8, 11, 2, 7, 6, 13, 12, 9, 16, 3, 10, 15, 14, 5, 4, 1]}, {'Size': '6', 'Order': 4, 'Representative': [15, 6, 5, 16, 11, 10, 1, 4, 7, 14, 13, 8, 3, 2, 9, 12]}, {'Size': '4', 'Order': 6, 'Representative': [15, 1, 16, 3, 13, 14, 2, 4, 7, 9, 8, 11, 5, 6, 10, 12]}, {'Size': '4', 'Order': 6, 'Representative': [2, 7, 4, 8, 13, 14, 9, 11, 10, 15, 12, 16, 5, 6, 1, 3]}, {'Size': '4', 'Order': 12, 'Representative': [3, 4, 15, 1, 6, 13, 8, 2, 11, 12, 7, 9, 14, 5, 16, 10]}, {'Size': '4', 'Order': 12, 'Representative': [12, 16, 9, 10, 6, 13, 3, 15, 4, 8, 1, 2, 14, 5, 11, 7]}, {'Size': '4', 'Order': 12, 'Representative': [11, 12, 7, 9, 14, 5, 16, 10, 3, 4, 15, 1, 6, 13, 8, 2]}, {'Size': '4', 'Order': 12, 'Representative': [4, 8, 1, 2, 14, 5, 11, 7, 12, 16, 9, 10, 6, 13, 3, 15]}], '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': ['9664', '2240', '384', '32', '1'], 'ConjugacyClass': 4}, {'RootOf': ['1136', '-272', '72', '-4', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['16', '1'], 'ConjugacyClass': 2}, {'RootOf': ['327168', '-80640', '35136', '-2368', '-288', '12', '1'], 'ConjugacyClass': 3}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['1136', '944', '264', '28', '1'], 'ConjugacyClass': 9}, {'RootOf': ['2752', '-896', '96', '-8', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [2, 2, 6, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['12', '1'], 'ConjugacyClass': 6}, {'RootOf': ['0', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-100864', '-28416', '4032', '1152', '-96', '-12', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [4, 4, 4, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['15552', '1728', '0', '0', '1'], 'ConjugacyClass': 11}, {'RootOf': ['432', '80', '72', '12', '1'], 'ConjugacyClass': 12}, {'RootOf': ['5568', '1664', '288', '24', '1'], 'ConjugacyClass': 13}, {'RootOf': ['432', '144', '72', '12', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [4, 12]}], 'Frobs': [4, 13, 5, 11, 13, 9, 8, 3, 12, 10, 12, 8, 9, 11, 11, 8, 14, 10, 12, 6, 8, 13, 11, 8, 10, 4, 14, 3, 8, 5, 3, 14, 10, 14, 9, 13, 5, 3, 14, 4, 3, 8, 11, 9, 2, 7, 12, 11, 13, 5, 1, 12, 4, 3, 5, 13, 8, 3, 4, 10, 14, 5, 3, 12, 4, 10, 13, 5, 12, 4, 10, 3, 13, 9, 7, 14, 4, 8, 9, 5, 12, 10, 3, 8, 13, 11, 8, 10, 10, 12, 3, 13, 3, 14, 14, 7, 9, 2, 6, 2, 13, 8, 12, 4, 12, 8, 11, 8, 14, 10, 14, 8, 9, 13, 3, 4, 12, 3, 5, 13, 5, 10, 4, 3, 11, 8, 4, 3, 13, 9, 6, 14, 14, 1, 9, 5, 8, 14, 9, 8, 3, 10, 12, 3, 8, 11, 10, 10, 12, 3, 9, 8, 3, 12, 11, 13, 3, 10, 8, 5, 13, 8, 12, 7, 5, 13, 3, 4], 'G-Gens': [[14, 2, 3, 8, 4, 7, 9, 5, 6, 10, 11, 16, 12, 15, 1, 13], [15, 6, 5, 16, 11, 10, 1, 4, 7, 14, 13, 8, 3, 2, 9, 12], [3, 4, 15, 1, 6, 13, 8, 2, 11, 12, 7, 9, 14, 5, 16, 10], [9, 10, 11, 12, 13, 14, 15, 16, 1, 2, 3, 4, 5, 6, 7, 8], [6, 7, 4, 11, 8, 9, 10, 13, 14, 15, 12, 3, 16, 1, 2, 5]], 'G-Name': 'SL2(F3):C2', 'Polynomial': [1, -4, 10, -28, 58, -92, 150, -180, 212, -176, 146, -88, 58, -28, 14, -4, 1], 'QpRts': [['20566142230200', '-119411092901647', '-158292031622888', '57694708513855', '103954466495243', '-172901897850387'], ['14157774540516', '-38089830126304', '196453319170149', '-155793780779296', '64446588485770', '-14989324073292'], ['61120628547836', '32590534148009', '189627705738736', '-1797210882750', '-112299659807309', '39571451424721'], ['95070707170886', '72956546529831', '-42621200086125', '-137929904055970', '194252149665235', '123911143356379'], ['134032308664805', '-98608676132796', '142458903840304', '95226799452953', '-153646680366539', '-82811974664205'], ['-174817626161994', '-109556520900188', '-70585707696156', '178216567898371', '-10689449417063', '-69801662379808'], ['81959872009699', '158139081539508', '-40216610879426', '-94885587315198', '70951638294220', '87470695124992'], ['112152953938227', '-8338091594225', '-58084238447815', '-28110506127550', '-24710818126016', '159785133089586'], ['-35734133996643', '61757025145105', '-109596686767716', '-151826795472973', '-176687591377716', '-91172411316012'], ['159100846485963', '154574230235311', '-152592140513622', '-69038796381905', '200138002285462', '-14803172562673'], ['-24318357735503', '118699890964324', '7980160230744', '-13103470811863', '-115841912843852', '185302234716277'], ['93579083252492', '-72956546529831', '42621200086125', '137929904055970', '-194252149665235', '-123911143356379'], ['66766628235714', '-88147150564898', '194449364996826', '-95403175037746', '-149977353636888', '-105261770531739'], ['-70142219709399', '50726188547723', '-126093985869968', '140748096221948', '-181162016471696', '-57038765118029'], ['4909344601660', '-158139081539508', '40216610879426', '94885587315198', '-70951638294220', '-87470695124992'], ['-117696718774254', '43803493179586', '-55724663058594', '43187563406956', '135769191480403', '-196585074034640']], 'QpRts-minpoly': [2, 13, 17, 25, 1, 0, 1], 'QpRts-p': 29, 'QpRts-prec': 10, 'Size': 48, 'TransitiveDegree': 16}