Artin representation data - 1.45.12t1.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': [3, 5], 'Baselabel': '1.45.12t1.a', 'CharacterField': 12, 'Conductor': 45, 'Container': '12t1', 'Dets': ['45.7', '45.43', '45.22', '45.13'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 12, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [-1, 0, 1], [0, 0, 0, 1], [0, 0, 0, -1], [1, 0, -1], [0, 0, 1], [0, 1], [0, -1, 0, 1], [0, -1], [0, 1, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [12, 13, 13, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [1, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [-1, 0, 1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [0, 1, 0, -1]], [[1], [0, 1]], [[1], [0, -1, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [-1, 0, 1], [0, 0, 0, -1], [0, 0, 0, 1], [1, 0, -1], [0, 0, 1], [0, -1], [0, 1, 0, -1], [0, 1], [0, -1, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [12, 13, 13, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [1, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [-1, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 1]], [[1], [0, -1, 0, 1]], [[1], [0, -1]], [[1], [0, 1, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, 0, 1], [0, 0, -1], [0, 0, 0, 1], [0, 0, 0, -1], [0, 0, 1], [1, 0, -1], [0, -1, 0, 1], [0, 1], [0, 1, 0, -1], [0, -1]], 'GalOrbIndex': 3, 'HardFactors': [12, 13, 13, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, -1]], [[1], [-1, 0, 1]], [[1], [0, 1, 0, -1]], [[1], [0, -1]], [[1], [0, -1, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, 0, 1], [0, 0, -1], [0, 0, 0, -1], [0, 0, 0, 1], [0, 0, 1], [1, 0, -1], [0, 1, 0, -1], [0, -1], [0, -1, 0, 1], [0, 1]], 'GalOrbIndex': 4, 'HardFactors': [12, 13, 13, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [-1, 0, 1]], [[1], [0, -1, 0, 1]], [[1], [0, 1]], [[1], [0, 1, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '12T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 701], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 3, 9, 26, 75, 18, 28, 9, 9, -1, 3, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.5.4t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [1, 0], [0, 1], [0, -1], [-1, 0], [-1, 0], [0, -1], [0, -1], [0, 1], [0, 1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '1.5.2t1.a', 'Character': [[1], [1], [1], [1], [-1], [-1], [1], [1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 2, 'Baselabel': '1.5.4t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [1, 0], [0, -1], [0, 1], [-1, 0], [-1, 0], [0, 1], [0, 1], [0, -1], [0, -1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.45.12t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, -1, 0], [-1, 0, 1, 0], [0, 0, 0, 1], [0, 0, 0, -1], [1, 0, -1, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, -1, 0, 1], [0, -1, 0, 0], [0, 1, 0, -1]], 'CharacterField': 12}, {'GalConj': 1, 'Baselabel': '1.45.6t1.a', 'Character': [[1, 0], [1, 0], [-1, -1], [0, 1], [-1, 0], [-1, 0], [0, 1], [-1, -1], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.45.12t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, -1, 0], [-1, 0, 1, 0], [0, 0, 0, -1], [0, 0, 0, 1], [1, 0, -1, 0], [0, 0, 1, 0], [0, -1, 0, 0], [0, 1, 0, -1], [0, 1, 0, 0], [0, -1, 0, 1]], 'CharacterField': 12}, {'GalConj': 2, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 3, 'Baselabel': '1.45.12t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [-1, 0, 1, 0], [0, 0, -1, 0], [0, 0, 0, 1], [0, 0, 0, -1], [0, 0, 1, 0], [1, 0, -1, 0], [0, -1, 0, 1], [0, 1, 0, 0], [0, 1, 0, -1], [0, -1, 0, 0]], 'CharacterField': 12}, {'GalConj': 2, 'Baselabel': '1.45.6t1.a', 'Character': [[1, 0], [1, 0], [0, 1], [-1, -1], [-1, 0], [-1, 0], [-1, -1], [0, 1], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 4, 'Baselabel': '1.45.12t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [-1, 0, 1, 0], [0, 0, -1, 0], [0, 0, 0, -1], [0, 0, 0, 1], [0, 0, 1, 0], [1, 0, -1, 0], [0, 1, 0, -1], [0, -1, 0, 0], [0, -1, 0, 1], [0, 1, 0, 0]], 'CharacterField': 12}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]}, {'Size': '1', 'Order': 2, 'Representative': [6, 4, 12, 2, 9, 1, 11, 10, 5, 8, 7, 3]}, {'Size': '1', 'Order': 3, 'Representative': [5, 8, 4, 10, 7, 9, 1, 12, 11, 3, 6, 2]}, {'Size': '1', 'Order': 3, 'Representative': [7, 12, 10, 3, 1, 11, 5, 2, 6, 4, 9, 8]}, {'Size': '1', 'Order': 4, 'Representative': [10, 7, 9, 11, 3, 8, 4, 1, 12, 6, 2, 5]}, {'Size': '1', 'Order': 4, 'Representative': [8, 11, 5, 7, 12, 10, 2, 6, 3, 1, 4, 9]}, {'Size': '1', 'Order': 6, 'Representative': [11, 3, 8, 12, 6, 7, 9, 4, 1, 2, 5, 10]}, {'Size': '1', 'Order': 6, 'Representative': [9, 10, 2, 8, 11, 5, 6, 3, 7, 12, 1, 4]}, {'Size': '1', 'Order': 12, 'Representative': [2, 9, 1, 5, 8, 4, 12, 11, 10, 7, 3, 6]}, {'Size': '1', 'Order': 12, 'Representative': [12, 6, 7, 1, 2, 3, 8, 9, 4, 5, 10, 11]}, {'Size': '1', 'Order': 12, 'Representative': [4, 5, 6, 9, 10, 2, 3, 7, 8, 11, 12, 1]}, {'Size': '1', 'Order': 12, 'Representative': [3, 1, 11, 6, 4, 12, 10, 5, 2, 9, 8, 7]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['6', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-3', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-3', '1'], 'ConjugacyClass': 5}, {'RootOf': ['12', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [4, 4, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-3', '1'], 'ConjugacyClass': 7}, {'RootOf': ['6', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [6, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['12', '1'], 'ConjugacyClass': 9}, {'RootOf': ['-24', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-3', '1'], 'ConjugacyClass': 11}, {'RootOf': ['6', '1'], 'ConjugacyClass': 12}], 'Algorithm': 'RES', 'CycleType': [12]}], 'Frobs': [12, 6, 4, 12, 3, 9, 5, 2, 9, 8, 4, 5, 4, 10, 12, 6, 7, 3, 11, 1, 6, 8, 10, 2, 12, 3, 9, 5, 2, 9, 5, 4, 12, 7, 7, 3, 11, 6, 11, 10, 2, 1, 3, 9, 5, 2, 4, 10, 12, 7, 6, 7, 3, 1, 11, 10, 2, 1, 12, 3, 9, 9, 5, 4, 10, 12, 3, 11, 11, 8, 10, 2, 12, 9, 2, 9, 8, 5, 4, 7, 7, 3, 1, 6, 8, 10, 2, 12, 3, 9, 5, 8, 5, 4, 7, 6, 7, 1, 6, 1, 12, 5, 9, 8, 4, 5, 12, 6, 7, 3, 11, 6, 11, 8, 1, 3, 9, 5, 9, 8, 4, 10, 12, 6, 3, 1, 8, 2, 12, 9, 2, 9, 4, 5, 4, 7, 6, 11, 11, 2, 1, 3, 9, 5, 2, 8, 10, 12, 7, 6, 11, 1, 6, 11, 12, 3, 2, 8, 5, 4, 12, 6, 11, 1, 11, 10, 1, 12], 'G-Gens': [[10, 7, 9, 11, 3, 8, 4, 1, 12, 6, 2, 5], [11, 3, 8, 12, 6, 7, 9, 4, 1, 2, 5, 10]], 'G-Name': 'C12', 'Polynomial': [1, 3, 9, 26, 75, 18, 28, 9, 9, -1, 3, 0, 1], 'QpRts': [['-706719', '361471', '367046', '22254'], ['-619537', '-287754', '-679268', '-465771'], ['70713', '119368', '-361715', '-261299'], ['-361024', '-311035', '162109', '27969'], ['206932', '-688449', '69151', '-254893'], ['401791', '-145055', '147640', '-295498'], ['499787', '326978', '-436197', '232639'], ['-99381', '-408083', '705565', '39914'], ['-589444', '-126756', '318861', '90335'], ['290311', '191667', '199606', '233330'], ['187653', '271811', '-466501', '205163'], ['-700939', '695837', '-26297', '425857']], 'QpRts-minpoly': [3, 10, 7, 0, 1], 'QpRts-p': 17, 'QpRts-prec': 5, 'Size': 12, 'TransitiveDegree': 12}