Artin representation data - 2.2016.12t18.c

Formats: - HTML - YAML - JSON - 2026-04-21T02:49:31.679046

• 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, 7], 'Baselabel': '2.2016.12t18.c', 'CharacterField': 3, 'Conductor': 2016, 'Container': '12t18', 'Dets': ['1.504.6t1.f.b', '1.504.6t1.f.a'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 12, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [-2, -2], [0, 2], [0, -1], [1, 1], [-1], [2, 2], [0, -2], [-1, -1], [0, 1], [1], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [19, 20, 21, 16, 3, 15, 15, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [2, 2], [0, 1]], [[1], [0, -2], [-1, -1]], [[1], [0, 1], [-1, -1]], [[1], [-1, -1], [0, 1]], [[1], [1], [1]], [[1], [-2, -2], [0, 1]], [[1], [0, 2], [-1, -1]], [[1], [1, 1], [0, 1]], [[1], [0, -1], [-1, -1]], [[1], [-1], [1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1]], [[1], [-1]], [[1], [0, 1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, 2], [-2, -2], [1, 1], [0, -1], [-1], [0, -2], [2, 2], [0, 1], [-1, -1], [1], [0], [0], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [19, 20, 21, 16, 3, 15, 15, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, -2], [-1, -1]], [[1], [2, 2], [0, 1]], [[1], [-1, -1], [0, 1]], [[1], [0, 1], [-1, -1]], [[1], [1], [1]], [[1], [0, 2], [-1, -1]], [[1], [-2, -2], [0, 1]], [[1], [0, -1], [-1, -1]], [[1], [1, 1], [0, 1]], [[1], [-1], [1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1]], [[1], [-1]], [[1], [-1, -1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '12T18', 'Galt': 18, 'HardPrimes': [2, 3, 7, 11, 53, 67, 167, 1801], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [9, 12, -12, -12, 107, -140, 170, -132, 108, -48, 22, -4, 1], 'NumBadPrimes': 3, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-26, -3, 0, 1], 'Proj_nTj': [3, 2]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.28.2t1.a', 'Character': [[1], [-1], [1], [-1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.56.2t1.b', 'Character': [[1], [1], [-1], [-1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.8.2t1.b', 'Character': [[1], [-1], [-1], [1], [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, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.252.6t1.i', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [0, -1], [1, 1], [0, -1], [1, 1], [-1, 0], [0, -1], [1, 1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.504.6t1.f', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.504.6t1.f', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.72.6t1.a', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [0, -1], [1, 1], [0, -1], [1, 1], [-1, 0], [0, 1], [-1, -1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.252.6t1.i', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [1, 1], [0, -1], [1, 1], [0, -1], [-1, 0], [1, 1], [0, -1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.72.6t1.a', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [1, 1], [0, -1], [1, 1], [0, -1], [-1, 0], [-1, -1], [0, 1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.4536.3t2.a', 'Character': [[2], [2], [0], [0], [2], [2], [-1], [-1], [-1], [2], [2], [-1], [-1], [-1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.18144.6t3.g', 'Character': [[2], [-2], [0], [0], [2], [2], [-1], [-1], [-1], [-2], [-2], [1], [1], [1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.504.6t5.b', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [1, 1], [0, -1], [-1, 0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.2016.12t18.c', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [0, -1], [1, 1], [-1, 0], [2, 2], [0, -2], [-1, -1], [0, 1], [1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.2016.12t18.c', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [1, 1], [0, -1], [-1, 0], [0, -2], [2, 2], [0, 1], [-1, -1], [1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.504.6t5.b', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [0, -1], [1, 1], [-1, 0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]}, {'Size': '1', 'Order': 2, 'Representative': [10, 3, 2, 7, 12, 11, 4, 9, 8, 1, 6, 5]}, {'Size': '3', 'Order': 2, 'Representative': [7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6]}, {'Size': '3', 'Order': 2, 'Representative': [4, 9, 8, 1, 6, 5, 10, 3, 2, 7, 12, 11]}, {'Size': '1', 'Order': 3, 'Representative': [5, 7, 4, 6, 8, 3, 11, 1, 10, 12, 2, 9]}, {'Size': '1', 'Order': 3, 'Representative': [8, 11, 6, 3, 1, 4, 2, 5, 12, 9, 7, 10]}, {'Size': '2', 'Order': 3, 'Representative': [5, 2, 3, 4, 8, 6, 7, 1, 10, 12, 11, 9]}, {'Size': '2', 'Order': 3, 'Representative': [8, 2, 3, 4, 1, 6, 7, 5, 12, 9, 11, 10]}, {'Size': '2', 'Order': 3, 'Representative': [5, 11, 6, 3, 8, 4, 2, 1, 10, 12, 7, 9]}, {'Size': '1', 'Order': 6, 'Representative': [12, 4, 7, 11, 9, 2, 6, 10, 1, 5, 3, 8]}, {'Size': '1', 'Order': 6, 'Representative': [9, 6, 11, 2, 10, 7, 3, 12, 5, 8, 4, 1]}, {'Size': '2', 'Order': 6, 'Representative': [9, 3, 2, 7, 10, 11, 4, 12, 5, 8, 6, 1]}, {'Size': '2', 'Order': 6, 'Representative': [12, 3, 2, 7, 9, 11, 4, 10, 1, 5, 6, 8]}, {'Size': '2', 'Order': 6, 'Representative': [9, 4, 7, 11, 10, 2, 6, 12, 5, 8, 3, 1]}, {'Size': '3', 'Order': 6, 'Representative': [3, 9, 8, 1, 4, 5, 10, 6, 11, 2, 12, 7]}, {'Size': '3', 'Order': 6, 'Representative': [4, 10, 1, 5, 6, 8, 12, 3, 2, 7, 9, 11]}, {'Size': '3', 'Order': 6, 'Representative': [11, 1, 10, 12, 2, 9, 5, 7, 4, 6, 8, 3]}, {'Size': '3', 'Order': 6, 'Representative': [2, 5, 12, 9, 7, 10, 8, 11, 6, 3, 1, 4]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['2496', '80', '1'], 'ConjugacyClass': 7}, {'RootOf': ['1380', '44', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['48', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-5408', '36', '-12', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-5376', '36', '12', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['1092', '28', '1'], 'ConjugacyClass': 12}, {'RootOf': ['1920', '64', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['24', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-12', '1'], 'ConjugacyClass': 6}, {'RootOf': ['36', '12', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['16', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-20', '1'], 'ConjugacyClass': 11}, {'RootOf': ['4', '-4', '1'], 'ConjugacyClass': 14}, {'RootOf': ['37824', '1764', '12', '1'], 'ConjugacyClass': 15}, {'RootOf': ['4992', '864', '12', '1'], 'ConjugacyClass': 16}, {'RootOf': ['23968', '1764', '-12', '1'], 'ConjugacyClass': 17}, {'RootOf': ['-1664', '864', '-12', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [6, 6]}], 'Frobs': [6, 1, 12, 18, 16, 10, 4, 9, 12, 18, 17, 3, 15, 16, 18, 3, 5, 13, 15, 14, 4, 13, 6, 4, 16, 13, 17, 4, 3, 8, 14, 8, 6, 8, 17, 13, 12, 4, 17, 11, 4, 14, 13, 8, 3, 3, 15, 18, 7, 12, 9, 12, 16, 9, 15, 13, 14, 3, 18, 7, 8, 12, 9, 17, 16, 18, 16, 5, 15, 11, 16, 14, 18, 17, 4, 17, 18, 2, 8, 15, 8, 18, 2, 4, 18, 16, 9, 7, 13, 12, 1, 18, 14, 15, 15, 3, 10, 4, 9, 3, 16, 3, 8, 6, 15, 4, 7, 4, 10, 16, 17, 3, 5, 7, 14, 7, 5, 3, 17, 16, 12, 7, 11, 4, 7, 3, 18, 3, 18, 12, 4, 10, 12, 3, 15, 15, 14, 5, 12, 1, 1, 18, 10, 4, 2, 18, 13, 16, 5, 14, 17, 4, 4, 17, 16, 13, 14, 16, 4, 12, 16, 1, 12, 9, 5, 18, 2, 13], 'G-Gens': [[10, 3, 2, 7, 12, 11, 4, 9, 8, 1, 6, 5], [9, 3, 2, 7, 10, 11, 4, 12, 5, 8, 6, 1], [7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6], [5, 7, 4, 6, 8, 3, 11, 1, 10, 12, 2, 9]], 'G-Name': 'C6*S3', 'Polynomial': [9, 12, -12, -12, 107, -140, 170, -132, 108, -48, 22, -4, 1], 'QpRts': [['-120441336', '4251889501', '8047656545', '4336350690', '921281367', '6714147218'], ['-2460272333', '5922326322', '6475169160', '438556816', '-7521379785', '7111441386'], ['4072821890', '2809474899', '-7298607958', '3737436099', '-5462652710', '4049764730'], ['4125137932', '3939666486', '-5619230913', '5433094900', '2485306990', '4325417808'], ['-6344998858', '-3456986970', '1333088785', '8119151059', '4169664240', '-3272860335'], ['-55152371', '6010941725', '-2310242887', '2645016096', '7679819704', '-392334481'], ['-2407956291', '7052517909', '8154546205', '2134215617', '426579915', '7387094464'], ['672039105', '-5643663601', '-974242308', '2875465314', '-3617238366', '-3359288599'], ['-5861055118', '-2530812178', '-4450341499', '-423413969', '-5675965441', '-297611943'], ['-6653535559', '7364740924', '4571557354', '1037471407', '-1137445708', '-7474052435'], ['-6588246594', '-8126083161', '-5786342078', '-653863187', '5621092629', '2669342175'], ['4371783228', '-344135547', '-2143010406', '4820271776', '2110937165', '-211183679']], 'QpRts-minpoly': [2, 13, 17, 25, 1, 0, 1], 'QpRts-p': 29, 'QpRts-prec': 7, 'Size': 36, 'TransitiveDegree': 12}