Hilbert modular form data - 4.4.18496.1-1.1-b

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• hmf_forms •

  Column	Type
  deg	smallint
  dimension	integer
  disc	bigint
  field_bad_primes	integer[]
  field_label	text
  is_CM	text
  is_base_change	text
  label	text
  label_nsuffix	smallint
  label_suffix	text
  level_bad_primes	integer[]
  level_ideal	text
  level_label	text
  level_norm	integer
  parallel_weight	smallint
  short_label	text
  weight	text

  
  {'deg': 4, 'dimension': 2, 'disc': 18496, 'field_bad_primes': [2, 17], 'field_label': '4.4.18496.1', 'is_CM': 'yes', 'is_base_change': 'yes', 'label': '4.4.18496.1-1.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [], 'level_ideal': '[1, 1, 1]', 'level_label': '1.1', 'level_norm': 1, 'parallel_weight': 2, 'short_label': '1.1-b', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [], 'hecke_eigenvalues': ['e', '-2*e + 2', 0, 0, 0, 0, 0, 0, '8*e - 10', '4*e + 4', '8*e - 10', '4*e + 4', '2*e - 10', '2*e - 10', '-2*e - 14', '2*e + 6', '-2*e - 14', '2*e + 6', 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, '-16*e + 14', 26, '-16*e + 18', '-8*e + 24', '-16*e + 18', '-8*e + 24', '-8*e + 6', '-8*e + 6', '8*e - 16', '8*e - 16', '-8*e + 26', '16*e - 24', '-8*e + 26', '16*e - 24', 0, 0, 0, 0, 0, 0, 0, 0, '16*e - 14', '-4*e - 12', '16*e - 14', '-4*e - 12', 0, 0, 0, 0, 0, 0, 0, 0, '-4*e + 36', '-4*e + 36', '-8*e - 18', '-8*e - 18', '16*e - 18', 38, 0, 0, 0, 0, 0, 0, 0, 0, '18*e - 2', '18*e - 2', '-2*e + 34', '-2*e + 34', '-18*e + 26', '-2*e - 30', '-18*e + 26', '-2*e - 30', 0, 0, 0, 0, '-26*e + 18', '-26*e + 18', '16*e + 2', '-32*e + 34', '16*e + 2', '-32*e + 34', 0, 0, 0, 0, '-16*e + 42', '-32*e + 30', '-16*e + 42', '-32*e + 30', 0, 0, 0, 0, '-16*e', '-16*e', '8*e + 18', '8*e + 18', '4*e - 12', '4*e - 12', '-16*e - 10', '-16*e - 10', '8*e - 46', '8*e - 46', '-8*e - 24', '-8*e - 24', 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, '16*e - 54', '16*e - 54', '4*e - 12', '4*e - 12', 0, 0, 0, 0, '26*e - 42', '26*e - 42', '-38*e + 46', '-38*e + 46', '-2*e + 18', '-2*e + 18', '32*e - 24', '32*e - 24', '-16*e + 42', '-16*e + 42', '32*e - 34', '32*e - 34', '16*e + 22', '16*e + 22', '34*e - 50', '38*e - 30', '34*e - 50', '38*e - 30', 0, 0, 0, 0, '-32*e + 16', '-32*e + 16', '-8*e + 34', '-8*e + 34', 0, 0, 0, 0, '-16*e + 50', '32*e - 50', '-16*e + 50', '32*e - 50', 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, '16*e - 54', '16*e - 54', '-16*e - 10', '-16*e - 10', 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, '-4*e - 60', '-16*e - 18', '-4*e - 60', '-16*e - 18', '-26*e - 6', '-26*e - 6', '26*e - 18', '26*e - 18', '-16*e + 32', '-16*e + 32', '-16*e - 2', '-16*e - 2', '-32*e + 58', '4*e + 68', '-32*e + 58', '4*e + 68', '-8*e - 56', '-8*e + 46', '-8*e - 56', '-8*e + 46', '32*e - 66', '-8*e + 40', '32*e - 66', '-8*e + 40', 0, 0, 0, 0, 0, 0, 0, 0, '16*e - 42', '16*e - 42', 0, 0, 0, 0, '16*e + 34', '16*e + 34', '-32*e - 2', '-32*e - 2', '36*e - 68', '36*e - 68', '-32*e + 34', '-32*e + 34', 0, 0, 0, 0, '32*e - 58', '32*e - 58', '52*e - 60', '52*e - 60', '-38*e + 22', '-38*e + 22', '-34*e + 42', '-34*e + 42', '32*e - 40', '32*e - 40', '8*e + 10', '8*e + 10', 86, '-32*e - 6', 0, 0, 0, 0, 0, 0, 0, 0, '50*e - 34', '-38*e + 70', '50*e - 34', '-38*e + 70', 0, 0, 0, 0, 0, 0, 0, 0, '2*e + 6', '18*e - 50', '2*e + 6', '18*e - 50'], 'hecke_polynomial': 'x^2 - 2*x - 1', 'label': '4.4.18496.1-1.1-b'}
• hmf_fields •

  Column	Type
  degree	smallint
  discriminant	bigint
  ideals	jsonb
  label	text
  narrow_class_no	smallint
  primes	jsonb

  
  {'degree': 4, 'discriminant': 18496, 'ideals': ['[1, 1, 1]', '[2, 2, 4/9*w^3 - 2/3*w^2 - 47/9*w + 20/9]', '[2, 2, 5/9*w^3 - 4/3*w^2 - 52/9*w + 79/9]', '[4, 2, 2/9*w^3 - 1/3*w^2 - 28/9*w + 28/9]', '[4, 2, 2/9*w^3 - 1/3*w^2 - 19/9*w + 10/9]', '[4, 2, 2/9*w^3 - 1/3*w^2 - 28/9*w + 1/9]', '[8, 2, w^3 - 2*w^2 - 11*w + 12]', '[8, 2, -1/9*w^3 - 1/3*w^2 + 14/9*w + 40/9]', '[8, 4, -1/9*w^3 + 2/3*w^2 - 4/9*w + 4/9]', '[8, 4, 2/3*w^3 - w^2 - 22/3*w + 13/3]', '[9, 3, 1/3*w^3 - 11/3*w - 1/3]', '[9, 3, w^3 - w^2 - 12*w - 1]', '[16, 2, 2]', '[16, 4, 1/3*w^3 - w^2 - 8/3*w + 14/3]', '[16, 4, 2/9*w^3 - 1/3*w^2 - 28/9*w + 10/9]', '[16, 4, 2/9*w^3 - 1/3*w^2 - 28/9*w + 19/9]', '[16, 4, -1/3*w^3 + 11/3*w + 4/3]', '[17, 17, -1/9*w^3 - 1/3*w^2 + 14/9*w + 49/9]', '[17, 17, -1/9*w^3 + 2/3*w^2 + 5/9*w - 59/9]', '[18, 6, 4/9*w^3 - 2/3*w^2 - 47/9*w + 38/9]', '[18, 6, w + 1]', '[18, 6, 4/9*w^3 - 2/3*w^2 - 47/9*w + 11/9]', '[18, 6, -w + 2]', '[25, 5, -7/9*w^3 + 2/3*w^2 + 89/9*w + 19/9]', '[25, 5, -5/9*w^3 + 1/3*w^2 + 52/9*w + 11/9]', '[32, 4, 8/9*w^3 - 4/3*w^2 - 94/9*w + 40/9]', '[32, 4, 1/3*w^3 - w^2 - 2/3*w + 2/3]', '[32, 4, 1/9*w^3 - 2/3*w^2 - 5/9*w + 68/9]', '[32, 4, 10/9*w^3 - 8/3*w^2 - 104/9*w + 158/9]', '[32, 8, -1/9*w^3 + 2/3*w^2 + 14/9*w + 4/9]', '[32, 8, 4/9*w^3 - 5/3*w^2 - 2/9*w + 11/9]', '[34, 34, w + 2]', '[34, 34, -4/9*w^3 + 2/3*w^2 + 47/9*w - 2/9]', '[34, 34, 4/9*w^3 - 2/3*w^2 - 47/9*w + 47/9]', '[34, 34, w - 3]', '[36, 6, 1/9*w^3 - 2/3*w^2 - 14/9*w + 14/9]', '[36, 6, -2/9*w^3 + 1/3*w^2 + 37/9*w + 8/9]', '[36, 6, 2/9*w^3 - 1/3*w^2 - 10/9*w + 19/9]', '[36, 6, -4/3*w^3 + w^2 + 47/3*w + 10/3]', '[36, 6, 2/3*w^3 - w^2 - 22/3*w + 16/3]', '[36, 6, 1/3*w^3 - w^2 - 11/3*w + 23/3]', '[47, 47, -1/9*w^3 + 2/3*w^2 + 5/9*w - 41/9]', '[47, 47, 1/9*w^3 + 1/3*w^2 - 14/9*w - 13/9]', '[47, 47, -1/9*w^3 + 2/3*w^2 + 5/9*w - 23/9]', '[47, 47, 1/9*w^3 + 1/3*w^2 - 14/9*w - 31/9]', '[49, 7, -4/9*w^3 + 2/3*w^2 + 38/9*w - 29/9]', '[49, 7, 4/9*w^3 - 2/3*w^2 - 38/9*w + 11/9]', '[50, 10, 1/3*w^3 - w^2 - 11/3*w + 26/3]', '[50, 10, 1/9*w^3 + 1/3*w^2 - 23/9*w + 14/9]', '[50, 10, 1/9*w^3 - 2/3*w^2 - 14/9*w + 5/9]', '[50, 10, -1/3*w^3 + 14/3*w + 13/3]', '[64, 4, 4/9*w^3 - 2/3*w^2 - 56/9*w + 56/9]', '[64, 4, 4/9*w^3 - 2/3*w^2 - 38/9*w + 20/9]', '[64, 4, 4/9*w^3 - 2/3*w^2 - 56/9*w + 2/9]', '[64, 8, -1/9*w^3 - 1/3*w^2 + 14/9*w + 22/9]', '[64, 8, 2/9*w^3 - 1/3*w^2 - 28/9*w + 46/9]', '[64, 8, -2/9*w^3 + 1/3*w^2 + 28/9*w + 17/9]', '[64, 8, 1/9*w^3 - 2/3*w^2 - 5/9*w + 32/9]', '[68, 34, 16/9*w^3 - 5/3*w^2 - 188/9*w - 1/9]', '[68, 34, 13/9*w^3 - 8/3*w^2 - 146/9*w + 146/9]', '[68, 34, 10/9*w^3 - 5/3*w^2 - 113/9*w + 50/9]', '[68, 34, -16/9*w^3 + 11/3*w^2 + 170/9*w - 188/9]', '[68, 34, -10/9*w^3 + 5/3*w^2 + 113/9*w - 68/9]', '[68, 34, -13/9*w^3 + 5/3*w^2 + 155/9*w - 11/9]', '[72, 6, -1/3*w^3 + 11/3*w + 10/3]', '[72, 6, 1/3*w^3 - w^2 - 8/3*w + 20/3]', '[72, 6, 1/3*w^3 - 11/3*w + 2/3]', '[72, 6, 1/3*w^3 - w^2 - 8/3*w + 8/3]', '[72, 12, 7/9*w^3 - 2/3*w^2 - 80/9*w + 8/9]', '[72, 12, 1/3*w^3 - w^2 - 5/3*w + 11/3]', '[72, 12, 7/9*w^3 - 5/3*w^2 - 71/9*w + 71/9]', '[72, 12, -1/3*w^3 + 8/3*w + 4/3]', '[81, 3, 3]', '[81, 9, 8/9*w^3 - 4/3*w^2 - 94/9*w + 49/9]', '[81, 9, -2*w + 1]', '[89, 89, 20/9*w^3 - 16/3*w^2 - 208/9*w + 325/9]', '[89, 89, 2/3*w^3 - w^2 - 25/3*w + 7/3]', '[89, 89, -2/3*w^3 + w^2 + 25/3*w - 19/3]', '[89, 89, -2*w^3 + 3*w^2 + 23*w - 11]', '[94, 94, -16/9*w^3 + 8/3*w^2 + 179/9*w - 98/9]', '[94, 94, -w^3 + w^2 + 11*w - 2]', '[94, 94, -8/9*w^3 + 4/3*w^2 + 85/9*w - 58/9]', '[94, 94, -17/9*w^3 + 7/3*w^2 + 193/9*w - 58/9]', '[94, 94, -8/3*w^3 + 6*w^2 + 85/3*w - 121/3]', '[94, 94, -5/9*w^3 + 4/3*w^2 + 52/9*w - 97/9]', '[94, 94, -14/9*w^3 + 10/3*w^2 + 151/9*w - 205/9]', '[94, 94, -5/3*w^3 + 4*w^2 + 52/3*w - 85/3]', '[98, 14, -2/3*w^3 + 25/3*w + 20/3]', '[98, 14, -2/9*w^3 + 4/3*w^2 + 19/9*w - 100/9]', '[98, 14, -23/9*w^3 + 16/3*w^2 + 250/9*w - 295/9]', '[98, 14, 13/9*w^3 - 8/3*w^2 - 146/9*w + 137/9]', '[100, 10, -1/9*w^3 - 1/3*w^2 + 23/9*w + 31/9]', '[100, 10, 1/3*w^3 - 14/3*w + 2/3]', '[100, 10, 2/3*w^3 - w^2 - 25/3*w - 2/3]', '[100, 10, 2/3*w^3 - w^2 - 22/3*w + 4/3]', '[100, 10, 4/3*w^3 - w^2 - 47/3*w - 4/3]', '[100, 10, -2/9*w^3 + 1/3*w^2 + 10/9*w + 17/9]', '[103, 103, 8/9*w^3 - 4/3*w^2 - 94/9*w + 67/9]', '[103, 103, -38/9*w^3 + 28/3*w^2 + 406/9*w - 541/9]', '[103, 103, 20/9*w^3 - 7/3*w^2 - 235/9*w + 19/9]', '[103, 103, -8/9*w^3 + 4/3*w^2 + 94/9*w - 31/9]', '[121, 11, -7/3*w^3 + 2*w^2 + 83/3*w + 7/3]', '[121, 11, -31/9*w^3 + 23/3*w^2 + 326/9*w - 443/9]', '[127, 127, -8/9*w^3 + 7/3*w^2 + 67/9*w - 103/9]', '[127, 127, -2/9*w^3 + 1/3*w^2 + 37/9*w - 55/9]', '[127, 127, -8/9*w^3 + 7/3*w^2 + 67/9*w - 85/9]', '[127, 127, -2/3*w^3 + w^2 + 25/3*w - 25/3]', '[128, 4, 2*w^3 - 4*w^2 - 22*w + 24]', '[128, 4, -2/9*w^3 - 2/3*w^2 + 28/9*w + 80/9]', '[128, 8, -2/9*w^3 + 4/3*w^2 - 8/9*w + 8/9]', '[128, 8, 5/9*w^3 - 1/3*w^2 - 34/9*w - 2/9]', '[128, 8, -1/3*w^3 + 2*w^2 - 7/3*w + 4/3]', '[128, 8, 4/3*w^3 - 2*w^2 - 44/3*w + 26/3]', '[128, 16, 13/9*w^3 - 8/3*w^2 - 146/9*w + 128/9]', '[128, 16, 4/9*w^3 - 5/3*w^2 - 38/9*w + 119/9]', '[136, 34, 5/9*w^3 - 1/3*w^2 - 52/9*w + 16/9]', '[136, 34, 5/9*w^3 - 4/3*w^2 - 43/9*w + 70/9]', '[136, 34, 5/9*w^3 - 1/3*w^2 - 52/9*w - 20/9]', '[136, 34, -5/9*w^3 + 4/3*w^2 + 43/9*w - 34/9]', '[136, 68, 5/9*w^3 - 4/3*w^2 - 52/9*w + 52/9]', '[136, 68, -1/9*w^3 + 2/3*w^2 - 4/9*w - 32/9]', '[136, 68, -1/9*w^3 - 1/3*w^2 + 5/9*w + 31/9]', '[136, 68, -5/9*w^3 + 1/3*w^2 + 61/9*w - 7/9]', '[137, 137, 7/9*w^3 - 2/3*w^2 - 89/9*w + 17/9]', '[137, 137, 1/9*w^3 - 5/3*w^2 + 4/9*w + 167/9]', '[137, 137, -29/9*w^3 + 19/3*w^2 + 316/9*w - 325/9]', '[137, 137, -7/9*w^3 + 5/3*w^2 + 80/9*w - 71/9]', '[144, 6, 2/3*w^3 - 22/3*w - 2/3]', '[144, 6, 2*w^3 - 2*w^2 - 24*w - 2]', '[144, 12, 5/9*w^3 - 4/3*w^2 - 34/9*w + 52/9]', '[144, 12, -1/9*w^3 - 1/3*w^2 - 4/9*w + 22/9]', '[144, 12, -5/9*w^3 + 1/3*w^2 + 43/9*w + 11/9]', '[144, 12, w^3 - 2*w^2 - 11*w + 10]', '[144, 12, w^3 - 2*w^2 - 10*w + 8]', '[144, 12, w^3 - w^2 - 11*w + 3]', '[144, 12, 1/3*w^3 - 11/3*w + 8/3]', '[144, 12, 1/3*w^3 - w^2 - 8/3*w + 26/3]', '[151, 151, 2/9*w^3 + 2/3*w^2 - 28/9*w - 89/9]', '[151, 151, 8/9*w^3 - 7/3*w^2 - 85/9*w + 157/9]', '[151, 151, -4/3*w^3 + 2*w^2 + 44/3*w - 29/3]', '[151, 151, -20/9*w^3 + 13/3*w^2 + 217/9*w - 235/9]', '[153, 51, 14/9*w^3 - 10/3*w^2 - 142/9*w + 169/9]', '[153, 51, 2/3*w^3 - 16/3*w + 1/3]', '[153, 51, 2/3*w^3 - 22/3*w - 5/3]', '[153, 51, -14/9*w^3 + 4/3*w^2 + 160/9*w + 11/9]', '[162, 6, 4/3*w^3 - 2*w^2 - 47/3*w + 20/3]', '[162, 6, 5/3*w^3 - 4*w^2 - 52/3*w + 79/3]', '[162, 18, 5/9*w^3 - 1/3*w^2 - 43/9*w + 16/9]', '[162, 18, w + 4]', '[162, 18, 4/9*w^3 - 2/3*w^2 - 47/9*w + 65/9]', '[162, 18, w^3 - 2*w^2 - 10*w + 11]', '[169, 13, -4/9*w^3 + 2/3*w^2 + 56/9*w - 11/9]', '[169, 13, -4/9*w^3 + 2/3*w^2 + 56/9*w - 47/9]', '[178, 178, 11/9*w^3 - 4/3*w^2 - 136/9*w + 1/9]', '[178, 178, -11/9*w^3 + 1/3*w^2 + 145/9*w + 116/9]', '[178, 178, -5/9*w^3 + 7/3*w^2 + 43/9*w - 196/9]', '[178, 178, -8/9*w^3 + 4/3*w^2 + 85/9*w - 49/9]', '[178, 178, 8/9*w^3 - 4/3*w^2 - 85/9*w + 40/9]', '[178, 178, 26/9*w^3 - 16/3*w^2 - 283/9*w + 265/9]', '[178, 178, -46/9*w^3 + 32/3*w^2 + 491/9*w - 581/9]', '[178, 178, -11/9*w^3 + 7/3*w^2 + 127/9*w - 136/9]', '[188, 94, -4/3*w^3 + 3*w^2 + 38/3*w - 44/3]', '[188, 94, -2/3*w^3 + w^2 + 25/3*w - 16/3]', '[188, 94, -w^3 + w^2 + 11*w - 1]', '[188, 94, -8/9*w^3 + 1/3*w^2 + 76/9*w + 5/9]', '[188, 94, -5/9*w^3 + 4/3*w^2 + 34/9*w - 34/9]', '[188, 94, -2/9*w^3 + 1/3*w^2 + 37/9*w - 10/9]', '[188, 94, -2/9*w^3 + 1/3*w^2 + 37/9*w - 28/9]', '[188, 94, -5/9*w^3 + 1/3*w^2 + 43/9*w - 7/9]', '[188, 94, -8/9*w^3 + 7/3*w^2 + 58/9*w - 76/9]', '[188, 94, -2/3*w^3 + w^2 + 25/3*w - 10/3]', '[188, 94, -4/3*w^3 + w^2 + 44/3*w + 1/3]', '[188, 94, -w^3 + 2*w^2 + 10*w - 10]', '[191, 191, 7/9*w^3 - 2/3*w^2 - 71/9*w - 1/9]', '[191, 191, 7/9*w^3 - 5/3*w^2 - 62/9*w + 53/9]', '[191, 191, -7/9*w^3 + 2/3*w^2 + 71/9*w - 17/9]', '[191, 191, 7/9*w^3 - 5/3*w^2 - 62/9*w + 71/9]', '[196, 14, 4/9*w^3 + 1/3*w^2 - 38/9*w - 25/9]', '[196, 14, -2/9*w^3 + 1/3*w^2 + 19/9*w + 26/9]', '[196, 14, 4/9*w^3 - 5/3*w^2 - 20/9*w + 56/9]', '[196, 14, -8/9*w^3 + 7/3*w^2 + 76/9*w - 112/9]', '[196, 14, -2/9*w^3 + 1/3*w^2 + 19/9*w - 46/9]', '[196, 14, -8/9*w^3 + 1/3*w^2 + 94/9*w + 23/9]', '[200, 10, 1/3*w^3 - w^2 - 2/3*w + 8/3]', '[200, 10, -1/3*w^3 + 5/3*w + 4/3]', '[200, 10, 11/9*w^3 - 4/3*w^2 - 127/9*w + 28/9]', '[200, 10, 11/9*w^3 - 7/3*w^2 - 118/9*w + 100/9]', '[200, 20, -8/9*w^3 + 1/3*w^2 + 94/9*w + 50/9]', '[200, 20, 4/9*w^3 + 1/3*w^2 - 38/9*w + 2/9]', '[200, 20, 4/9*w^3 - 5/3*w^2 - 20/9*w + 29/9]', '[200, 20, 8/9*w^3 - 7/3*w^2 - 76/9*w + 139/9]', '[206, 206, 55/9*w^3 - 38/3*w^2 - 590/9*w + 689/9]', '[206, 206, -8/9*w^3 + 4/3*w^2 + 85/9*w - 76/9]', '[206, 206, -5/9*w^3 + 1/3*w^2 + 79/9*w - 52/9]', '[206, 206, -35/9*w^3 + 22/3*w^2 + 382/9*w - 373/9]', '[206, 206, 4/9*w^3 - 8/3*w^2 - 29/9*w + 236/9]', '[206, 206, -5/9*w^3 + 4/3*w^2 + 70/9*w - 25/9]', '[206, 206, -8/9*w^3 + 4/3*w^2 + 85/9*w - 13/9]', '[206, 206, 4/3*w^3 - 53/3*w - 52/3]', '[223, 223, -59/9*w^3 + 43/3*w^2 + 628/9*w - 835/9]', '[223, 223, 7/9*w^3 - 5/3*w^2 - 80/9*w + 125/9]', '[223, 223, -7/9*w^3 + 2/3*w^2 + 89/9*w + 37/9]', '[223, 223, -41/9*w^3 + 31/3*w^2 + 430/9*w - 601/9]', '[225, 15, 4/9*w^3 - 2/3*w^2 - 20/9*w + 11/9]', '[225, 15, 2/9*w^3 - 1/3*w^2 - 37/9*w + 19/9]', '[225, 15, 4/3*w^3 - 2*w^2 - 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247/9]', '[1097, 1097, -16/9*w^3 + 8/3*w^2 + 188/9*w - 107/9]', '[1097, 1097, 14/9*w^3 - 13/3*w^2 - 151/9*w + 259/9]', '[1097, 1097, 10/9*w^3 - 11/3*w^2 - 95/9*w + 257/9]', '[1103, 1103, 8/9*w^3 - 1/3*w^2 - 85/9*w + 13/9]', '[1103, 1103, 8/9*w^3 - 1/3*w^2 - 85/9*w - 41/9]', '[1103, 1103, 8/9*w^3 - 7/3*w^2 - 67/9*w + 121/9]', '[1103, 1103, 8/9*w^3 - 7/3*w^2 - 67/9*w + 67/9]', '[1223, 1223, 10/9*w^3 - 8/3*w^2 - 104/9*w + 113/9]', '[1223, 1223, -10/9*w^3 + 5/3*w^2 + 113/9*w - 113/9]', '[1223, 1223, 10/9*w^3 - 5/3*w^2 - 113/9*w + 5/9]', '[1223, 1223, -10/9*w^3 + 2/3*w^2 + 122/9*w - 5/9]', '[1249, 1249, -23/9*w^3 + 13/3*w^2 + 268/9*w - 151/9]', '[1249, 1249, 5/3*w^3 - w^2 - 64/3*w - 29/3]', '[1249, 1249, -49/9*w^3 + 35/3*w^2 + 524/9*w - 641/9]', '[1249, 1249, 23/3*w^3 - 16*w^2 - 247/3*w + 301/3]', '[1279, 1279, 22/3*w^3 - 16*w^2 - 236/3*w + 311/3]', '[1279, 1279, 10/9*w^3 + 1/3*w^2 - 113/9*w - 103/9]', '[1279, 1279, -4*w^3 + 8*w^2 + 44*w - 51]', '[1279, 1279, 34/9*w^3 - 11/3*w^2 - 395/9*w + 17/9]', '[1327, 1327, -28/9*w^3 + 17/3*w^2 + 311/9*w - 293/9]', '[1327, 1327, 4*w^3 - 9*w^2 - 43*w + 59]', '[1327, 1327, -22/9*w^3 + 8/3*w^2 + 254/9*w - 47/9]', '[1327, 1327, -4/9*w^3 + 8/3*w^2 + 38/9*w - 209/9]', '[1361, 1361, -14/3*w^3 + 11*w^2 + 145/3*w - 217/3]', '[1361, 1361, 14/9*w^3 - 4/3*w^2 - 178/9*w - 65/9]', '[1361, 1361, 14/9*w^3 - 10/3*w^2 - 160/9*w + 241/9]', '[1361, 1361, -2/9*w^3 - 2/3*w^2 + 64/9*w - 73/9]', '[1369, 37, 13/9*w^3 - 2/3*w^2 - 173/9*w - 115/9]', '[1369, 37, -43/9*w^3 + 32/3*w^2 + 449/9*w - 611/9]', '[1409, 1409, -71/9*w^3 + 52/3*w^2 + 751/9*w - 1003/9]', '[1409, 1409, -61/9*w^3 + 44/3*w^2 + 647/9*w - 809/9]', '[1409, 1409, 7/3*w^3 - 2*w^2 - 89/3*w - 25/3]', '[1409, 1409, -37/9*w^3 + 14/3*w^2 + 437/9*w - 41/9]', '[1447, 1447, -4/3*w^3 + 2*w^2 + 50/3*w - 47/3]', '[1447, 1447, 2/3*w^3 + 2*w^2 - 34/3*w - 101/3]', '[1447, 1447, -70/9*w^3 + 47/3*w^2 + 755/9*w - 827/9]', '[1447, 1447, -20/9*w^3 + 16/3*w^2 + 190/9*w - 271/9]', '[1471, 1471, -5/3*w^3 + 3*w^2 + 52/3*w - 43/3]', '[1471, 1471, 7/9*w^3 - 5/3*w^2 - 62/9*w - 19/9]', '[1471, 1471, -61/9*w^3 + 41/3*w^2 + 656/9*w - 737/9]', '[1471, 1471, -7/9*w^3 + 5/3*w^2 + 62/9*w - 143/9]', '[1481, 1481, 10/9*w^3 - 5/3*w^2 - 131/9*w + 23/9]', '[1481, 1481, 46/9*w^3 - 23/3*w^2 - 527/9*w + 257/9]', '[1481, 1481, -50/9*w^3 + 40/3*w^2 + 520/9*w - 817/9]', '[1481, 1481, -10/9*w^3 + 5/3*w^2 + 131/9*w - 113/9]', '[1487, 1487, 11/9*w^3 - 4/3*w^2 - 145/9*w + 1/9]', '[1487, 1487, -11/9*w^3 + 1/3*w^2 + 136/9*w + 35/9]', '[1487, 1487, -11/9*w^3 + 10/3*w^2 + 109/9*w - 163/9]', '[1487, 1487, -7/9*w^3 + 5/3*w^2 + 116/9*w + 37/9]', '[1511, 1511, -5/3*w^3 + 3*w^2 + 58/3*w - 49/3]', '[1511, 1511, 1/9*w^3 + 7/3*w^2 - 32/9*w - 247/9]', '[1511, 1511, 1/3*w^3 - 2*w^2 - 11/3*w + 23/3]', '[1511, 1511, -5/9*w^3 + 7/3*w^2 + 52/9*w - 151/9]', '[1543, 1543, -1/9*w^3 + 2/3*w^2 - 13/9*w + 49/9]', '[1543, 1543, w^3 - w^2 - 12*w - 5]', '[1543, 1543, -w^3 + 2*w^2 + 11*w - 17]', '[1543, 1543, -1/9*w^3 - 1/3*w^2 - 4/9*w - 41/9]', '[1583, 1583, 1/9*w^3 + 1/3*w^2 - 14/9*w - 85/9]', '[1583, 1583, 1/9*w^3 - 2/3*w^2 - 5/9*w - 31/9]', '[1583, 1583, -1/9*w^3 - 1/3*w^2 + 14/9*w - 41/9]', '[1583, 1583, -1/9*w^3 + 2/3*w^2 + 5/9*w - 95/9]', '[1607, 1607, -20/9*w^3 + 13/3*w^2 + 217/9*w - 199/9]', '[1607, 1607, -32/9*w^3 + 25/3*w^2 + 331/9*w - 511/9]', '[1607, 1607, -28/9*w^3 + 14/3*w^2 + 320/9*w - 149/9]', '[1607, 1607, -2/3*w^3 + 2*w^2 + 16/3*w - 55/3]', '[1657, 1657, 1/9*w^3 + 1/3*w^2 - 32/9*w - 49/9]', '[1657, 1657, -7/9*w^3 + 5/3*w^2 + 80/9*w - 35/9]', '[1657, 1657, -7/9*w^3 + 2/3*w^2 + 89/9*w - 53/9]', '[1657, 1657, -1/9*w^3 + 2/3*w^2 + 23/9*w - 77/9]', '[1681, 41, 10/9*w^3 - 5/3*w^2 - 95/9*w + 23/9]', '[1681, 41, -10/9*w^3 + 5/3*w^2 + 95/9*w - 77/9]', '[1721, 1721, 7/9*w^3 - 8/3*w^2 - 53/9*w + 71/9]', '[1721, 1721, -7/9*w^3 + 8/3*w^2 + 53/9*w - 161/9]', '[1721, 1721, 7/9*w^3 + 1/3*w^2 - 80/9*w - 91/9]', '[1721, 1721, -7/9*w^3 - 1/3*w^2 + 80/9*w + 1/9]', '[1753, 1753, -4/3*w^3 + 4*w^2 + 38/3*w - 101/3]', '[1753, 1753, 2/9*w^3 - 4/3*w^2 - 10/9*w + 145/9]', '[1753, 1753, 2/9*w^3 + 2/3*w^2 - 28/9*w - 125/9]', '[1753, 1753, -32/9*w^3 + 19/3*w^2 + 349/9*w - 295/9]', '[1759, 1759, -19/9*w^3 + 14/3*w^2 + 221/9*w - 221/9]', '[1759, 1759, 37/9*w^3 - 14/3*w^2 - 437/9*w + 59/9]', '[1759, 1759, 67/9*w^3 - 50/3*w^2 - 713/9*w + 965/9]', '[1759, 1759, 1/3*w^3 - 2*w^2 - 5/3*w + 47/3]', '[1777, 1777, -13/9*w^3 + 8/3*w^2 + 155/9*w - 83/9]', '[1777, 1777, 7/9*w^3 + 4/3*w^2 - 107/9*w - 235/9]', '[1777, 1777, 1/3*w^3 - w^2 - 20/3*w + 29/3]', '[1777, 1777, 13/9*w^3 - 5/3*w^2 - 164/9*w + 83/9]', '[1783, 1783, -1/9*w^3 + 5/3*w^2 - 4/9*w - 185/9]', '[1783, 1783, -13/9*w^3 + 11/3*w^2 + 128/9*w - 263/9]', '[1783, 1783, -23/9*w^3 + 13/3*w^2 + 250/9*w - 187/9]', '[1783, 1783, -11/3*w^3 + 7*w^2 + 118/3*w - 121/3]', '[1801, 1801, 14/9*w^3 - 4/3*w^2 - 142/9*w - 11/9]', '[1801, 1801, -14/9*w^3 + 7/3*w^2 + 187/9*w - 187/9]', '[1801, 1801, 14/9*w^3 - 10/3*w^2 - 124/9*w + 97/9]', '[1801, 1801, -14/9*w^3 + 10/3*w^2 + 124/9*w - 151/9]', '[1823, 1823, 7/9*w^3 - 2/3*w^2 - 89/9*w + 107/9]', '[1823, 1823, -1/9*w^3 + 2/3*w^2 + 23/9*w - 131/9]', '[1823, 1823, 1/9*w^3 + 1/3*w^2 - 32/9*w - 103/9]', '[1823, 1823, -7/9*w^3 + 5/3*w^2 + 80/9*w + 19/9]', '[1849, 43, 8/9*w^3 - 4/3*w^2 - 112/9*w + 13/9]', '[1849, 43, -4/3*w^3 + 2*w^2 + 56/3*w + 13/3]', '[1871, 1871, -58/9*w^3 + 38/3*w^2 + 632/9*w - 677/9]', '[1871, 1871, -16/9*w^3 + 11/3*w^2 + 161/9*w - 143/9]', '[1871, 1871, 16/9*w^3 - 5/3*w^2 - 179/9*w + 35/9]', '[1871, 1871, 4/9*w^3 + 7/3*w^2 - 65/9*w - 277/9]', '[1879, 1879, 14/9*w^3 - 1/3*w^2 - 133/9*w - 29/9]', '[1879, 1879, -22/9*w^3 + 5/3*w^2 + 245/9*w + 7/9]', '[1879, 1879, -22/9*w^3 + 17/3*w^2 + 209/9*w - 245/9]', '[1879, 1879, -14/9*w^3 + 13/3*w^2 + 97/9*w - 151/9]', '[1889, 1889, 2/9*w^3 - 1/3*w^2 - 37/9*w + 91/9]', '[1889, 1889, 2/3*w^3 - w^2 - 25/3*w - 11/3]', '[1889, 1889, 2/3*w^3 - w^2 - 25/3*w + 37/3]', '[1889, 1889, 2/9*w^3 - 1/3*w^2 - 37/9*w - 53/9]', '[1913, 1913, 11/9*w^3 - 7/3*w^2 - 118/9*w + 73/9]', '[1913, 1913, 1/3*w^3 - 5/3*w - 13/3]', '[1913, 1913, -1/3*w^3 + w^2 + 2/3*w - 17/3]', '[1913, 1913, -11/9*w^3 + 4/3*w^2 + 127/9*w - 55/9]', '[1951, 1951, -4/3*w^3 + 3*w^2 + 41/3*w - 41/3]', '[1951, 1951, -4/9*w^3 - 1/3*w^2 + 29/9*w + 43/9]', '[1951, 1951, 4/9*w^3 - 5/3*w^2 - 11/9*w + 65/9]', '[1951, 1951, -4/3*w^3 + w^2 + 47/3*w - 5/3]', '[1993, 1993, 38/9*w^3 - 16/3*w^2 - 424/9*w + 163/9]', '[1993, 1993, -58/9*w^3 + 41/3*w^2 + 623/9*w - 803/9]', '[1993, 1993, 44/9*w^3 - 31/3*w^2 - 481/9*w + 589/9]', '[1993, 1993, -46/9*w^3 + 35/3*w^2 + 491/9*w - 725/9]']}
• nf_fields •

  Column	Type
  class_group	jsonb
  class_number	numeric
  cm	boolean
  coeffs	numeric[]
  conductor	numeric
  degree	smallint
  disc_abs	numeric
  disc_rad	numeric
  disc_sign	smallint
  embeddings_gen_imag	double precision[]
  embeddings_gen_real	double precision[]
  gal_is_abelian	boolean
  gal_is_cyclic	boolean
  gal_is_solvable	boolean
  galois_disc_exponents	numeric[]
  galois_label	text
  galt	integer
  grd	double precision
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  is_minimal_sibling	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  minimal_sibling	numeric[]
  monogenic	smallint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  used_grh	boolean
  dirichlet_group	bigint[]
  frobs	jsonb
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [2, 12, -11, -2, 1], 'conductor': 136, 'degree': 4, 'dirichlet_group': [1, 33, 101, 69], 'disc_abs': 18496, 'disc_rad': 34, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[2, 2]]], [5, [[2, 2]]], [7, [[2, 2]]], [11, [[2, 2]]], [13, [[2, 2]]], [17, [0]], [19, [[2, 2]]], [23, [[2, 2]]], [29, [[2, 2]]], [31, [[2, 2]]], [37, [[2, 2]]], [41, [[2, 2]]], [43, [[2, 2]]], [47, [[1, 4]]], [53, [[2, 2]]], [59, [[2, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [6, 2], 'galois_label': '4T2', 'galt': 2, 'grd': 11.661903789690601, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.18496.1', 'local_algs': ['2.2.3.1', '2.2.3.1', '17.2.1.1', '17.2.1.1'], 'monogenic': -1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 17], 'rd': 11.6619037897, 'regulator': {'__RealLiteral__': 0, 'data': '15.6865966151', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-4.-1.1', '-2.0.1', '-34.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{2}{9} a^{3} - \\frac{1}{3} a^{2} - \\frac{19}{9} a + \\frac{19}{9} \\)', '\\( \\frac{4}{9} a^{3} - \\frac{2}{3} a^{2} - \\frac{56}{9} a - \\frac{7}{9} \\)', '\\( \\frac{10}{9} a^{3} - \\frac{5}{3} a^{2} - \\frac{113}{9} a + \\frac{59}{9} \\)'], 'unitsGmodule': [[1, 1], [2, 1], [3, 1]], 'unitsType': 'Type I (ii)', 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/9*a^3 + 1/3*a^2 + 4/9*a - 4/9']}