Artin representation data - 6.984150000.18t51.b

Formats: - HTML - YAML - JSON - 2024-05-22T05:09:50.217502

• 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, 5], 'Baselabel': '6.984150000.18t51.b', 'CharacterField': 1, 'Conductor': 984150000, 'Container': '18t51', 'Dets': ['1.15.2t1.a.a'], 'Dim': 6, 'GalConjSigns': [1], 'Galn': 9, 'GaloisConjugates': [{'Sign': 1, 'Character': [[6], [0], [-2], [0], [-3], [0], [0], [0], [0], [1], [0]], 'GalOrbIndex': 1, 'HardFactors': [12, 13, 13, 2, 6, 3, 2], 'LocalFactors': [[[1], [-6], [15], [-20], [15], [-6], [1]], [[1], [0], [-3], [0], [3], [0], [-1]], [[1], [2], [-1], [-4], [-1], [2], [1]], [[1], [0], [-3], [0], [3], [0], [-1]], [[1], [3], [6], [7], [6], [3], [1]], [[1], [0], [0], [-2], [0], [0], [1]], [[1], [0], [0], [-2], [0], [0], [1]], [[1], [0], [0], [-2], [0], [0], [1]], [[1], [0], [0], [0], [0], [0], [-1]], [[1], [-1], [2], [-1], [2], [-1], [1]], [[1], [0], [0], [0], [0], [0], [-1]], [[1], [-1], [1]], [[1], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T18', 'Galt': 18, 'HardPrimes': [2, 3, 5, 73, 5521, 7127, 93913], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [-11, 9, -27, 30, -18, 27, -3, 9, 0, 1], 'NumBadPrimes': 3, 'Proj_GAP': [108, 17], 'Proj_Polynomial': [-11, 9, -27, 30, -18, 27, -3, 9, 0, 1], 'Proj_nTj': [9, 18]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.15.2t1.a', 'Character': [[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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.5.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [1], [1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.300.6t3.a', 'Character': [[2], [-2], [0], [0], [2], [2], [-1], [-1], [1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.1620.6t3.f', 'Character': [[2], [0], [0], [-2], [2], [-1], [2], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.1620.3t2.a', 'Character': [[2], [0], [0], [2], [2], [-1], [2], [-1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.300.3t2.a', 'Character': [[2], [2], [0], [0], [2], [2], [-1], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.16402500.6t9.a', 'Character': [[4], [0], [0], [0], [4], [-2], [-2], [1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.984150000.18t51.b', 'Character': [[6], [0], [-2], [0], [-3], [0], [0], [0], [0], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.984150000.9t18.b', 'Character': [[6], [0], [2], [0], [-3], [0], [0], [0], [0], [-1], [0]], 'CharacterField': 1}], 'ComplexConjugation': 4, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '9', 'Order': 2, 'Representative': [1, 3, 2, 9, 5, 7, 6, 8, 4]}, {'Size': '9', 'Order': 2, 'Representative': [1, 2, 3, 5, 4, 9, 8, 7, 6]}, {'Size': '9', 'Order': 2, 'Representative': [9, 8, 4, 3, 7, 6, 5, 2, 1]}, {'Size': '2', 'Order': 3, 'Representative': [2, 3, 1, 8, 7, 5, 6, 9, 4]}, {'Size': '6', 'Order': 3, 'Representative': [3, 1, 2, 4, 7, 5, 6, 8, 9]}, {'Size': '6', 'Order': 3, 'Representative': [5, 7, 6, 3, 8, 4, 9, 1, 2]}, {'Size': '12', 'Order': 3, 'Representative': [4, 8, 9, 5, 1, 3, 2, 7, 6]}, {'Size': '18', 'Order': 6, 'Representative': [8, 4, 9, 7, 1, 2, 3, 5, 6]}, {'Size': '18', 'Order': 6, 'Representative': [3, 1, 2, 7, 4, 9, 8, 6, 5]}, {'Size': '18', 'Order': 6, 'Representative': [8, 4, 9, 1, 7, 6, 5, 3, 2]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['2657205', '2657205', '885735', '196830', '65610', '10935', '729', '243', '0', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-816057180', '291702060', '-50913360', '6983820', '-947700', '114210', '-9369', '513', '-27', '1'], 'ConjugacyClass': 3}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 2, 2, 2]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 3, 3]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 2, 2]}, {'Data': 0, 'Classes': 11, 'Algorithm': 'CYC', 'CycleType': [1, 2, 6]}, {'Data': {'Powers': [1, 2], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['9', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-378', '-108', '0', '1'], 'ConjugacyClass': 7}, {'RootOf': ['7464960', '466560', '116640', '2160', '675', '0', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': {'Powers': [1, 5], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-1096736760', '-292883040', '-21257640', '-2274480', '-218700', '0', '162', '162', '0', '1'], 'ConjugacyClass': 9}, {'RootOf': ['816057180', '291702060', '50913360', '6983820', '947700', '114210', '9369', '513', '27', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [3, 6]}], 'Frobs': [10, 2, 3, 9, 11, 9, 3, 8, 10, 11, 8, 2, 11, 9, 10, 10, 11, 7, 9, 11, 2, 5, 10, 11, 9, 11, 2, 10, 8, 10, 2, 11, 10, 6, 4, 8, 9, 9, 10, 10, 11, 8, 11, 9, 3, 7, 8, 9, 3, 7, 10, 4, 8, 4, 10, 10, 11, 5, 9, 4, 9, 3, 9, 11, 9, 3, 6, 9, 10, 6, 10, 11, 9, 9, 7, 10, 4, 9, 4, 7, 4, 6, 11, 9, 8, 3, 11, 2, 11, 2, 10, 11, 9, 11, 8, 10, 4, 4, 9, 8, 2, 10, 3, 11, 8, 9, 10, 10, 11, 8, 2, 2, 3, 7, 8, 11, 2, 3, 10, 4, 6, 2, 3, 10, 1, 11, 7, 11, 9, 2, 6, 10, 1, 9, 11, 8, 10, 9, 10, 11, 8, 11, 9, 10, 6, 11, 9, 10, 6, 10, 9, 11, 9, 3, 2, 11, 8, 11, 9, 4, 10, 10, 2, 11, 10, 10, 8, 2], 'G-Gens': [[3, 1, 2, 4, 7, 5, 6, 8, 9], [1, 2, 3, 9, 7, 5, 6, 4, 8], [4, 8, 9, 5, 1, 3, 2, 7, 6], [1, 3, 2, 8, 7, 6, 5, 4, 9], [1, 2, 3, 5, 4, 9, 8, 7, 6]], 'G-Name': 'He3:C2^2', 'Polynomial': [-11, 9, -27, 30, -18, 27, -3, 9, 0, 1], 'QpRts': [['79987125272195978551446', '0', '0'], ['-6141256228528741128316', '0', '0'], ['-73845869043667237423130', '0', '0'], ['180455494721837409629836', '-41990205091516650216344', '45113873680459352407459'], ['39823623285356802921063', '98341561550373705821427', '-83606808274504478190619'], ['41147364796494186420085', '420710797709314303912', '103849555294967225525906'], ['-80970988081850989341148', '-98762272348083020125339', '-20242747020462747335287'], ['-107061533867792313685234', '5008829129029897596286', '160360044724739279420461'], ['-73393960854045095944602', '36981375962486752620058', '168776937978176083855619']], 'QpRts-minpoly': [137, 6, 0, 1], 'QpRts-p': 139, 'QpRts-prec': 11, 'Size': 108, 'TransitiveDegree': 9}