Hilbert modular form data - 4.4.8000.1-20.1-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': 4, 'disc': 8000, 'field_bad_primes': [2, 5], 'field_label': '4.4.8000.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.8000.1-20.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [2, 5], 'level_ideal': '[20, 10, w]', 'level_label': '20.1', 'level_norm': 20, 'parallel_weight': 2, 'short_label': '20.1-b', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[4, 2, 1/2*w^3 - 3*w + 2]', -1], ['[5, 5, w^2 - w - 5]', -1]], 'hecke_eigenvalues': [1, 1, 'e', '-1/2*e^3 + 3/2*e^2 + 9/2*e - 9', '-1/2*e^3 + 5/2*e^2 + 7/2*e - 18', 'e^3 - 4*e^2 - 9*e + 34', '3/2*e^3 - 11/2*e^2 - 29/2*e + 44', '-e^2 + 10', '-e^3 + 5*e^2 + 8*e - 42', '-1/2*e^3 + 3/2*e^2 + 13/2*e - 15', '5/2*e^3 - 21/2*e^2 - 45/2*e + 87', '-1/2*e^3 + 7/2*e^2 + 3/2*e - 26', '-3/2*e^3 + 9/2*e^2 + 29/2*e - 33', '-1/2*e^3 + 5/2*e^2 + 13/2*e - 24', '5/2*e^3 - 21/2*e^2 - 37/2*e + 77', '-5/2*e^3 + 19/2*e^2 + 39/2*e - 72', '-7/2*e^3 + 29/2*e^2 + 57/2*e - 115', '7/2*e^3 - 27/2*e^2 - 59/2*e + 102', 0, 'e^3 - 3*e^2 - 12*e + 24', '3/2*e^3 - 15/2*e^2 - 25/2*e + 60', '-1/2*e^3 + 7/2*e^2 + 9/2*e - 35', '-2*e^3 + 7*e^2 + 20*e - 60', '3*e^3 - 10*e^2 - 27*e + 74', '-9/2*e^3 + 37/2*e^2 + 79/2*e - 150', '-1/2*e^3 + 3/2*e^2 + 1/2*e - 5', '2*e^3 - 10*e^2 - 13*e + 76', '-1/2*e^3 + 1/2*e^2 + 7/2*e - 2', '-e^2 + 4*e', '3*e^3 - 11*e^2 - 28*e + 84', '-5/2*e^3 + 23/2*e^2 + 41/2*e - 97', '-5/2*e^3 + 15/2*e^2 + 41/2*e - 45', '6*e^3 - 23*e^2 - 54*e + 188', 'e^3 - 5*e^2 - 2*e + 36', '-9/2*e^3 + 41/2*e^2 + 71/2*e - 158', '-3*e^3 + 13*e^2 + 30*e - 116', '1/2*e^3 + 3/2*e^2 - 19/2*e - 16', '-3/2*e^3 + 5/2*e^2 + 35/2*e - 21', '4*e^3 - 17*e^2 - 38*e + 140', '-6*e^3 + 24*e^2 + 50*e - 182', '5*e^3 - 19*e^2 - 41*e + 148', '5*e^3 - 21*e^2 - 39*e + 166', '-4*e^3 + 16*e^2 + 30*e - 114', '7/2*e^3 - 33/2*e^2 - 53/2*e + 125', '-1/2*e^3 + 5/2*e^2 - 3/2*e - 17', '-11/2*e^3 + 43/2*e^2 + 99/2*e - 178', '5/2*e^3 - 15/2*e^2 - 43/2*e + 46', '-1/2*e^3 + 3/2*e^2 + 21/2*e - 15', '-3*e^3 + 15*e^2 + 22*e - 114', '-2*e^3 + 5*e^2 + 18*e - 26', '11/2*e^3 - 43/2*e^2 - 101/2*e + 180', '6*e^3 - 24*e^2 - 52*e + 196', '-4*e^3 + 14*e^2 + 34*e - 98', '-4*e^3 + 18*e^2 + 30*e - 134', '2*e^3 - 8*e^2 - 12*e + 60', '3/2*e^3 - 7/2*e^2 - 33/2*e + 20', '2*e^3 - 9*e^2 - 20*e + 72', '-3*e^3 + 13*e^2 + 28*e - 116', '-1/2*e^3 - 1/2*e^2 + 17/2*e - 3', '2*e^3 - 10*e^2 - 16*e + 98', '-3*e^3 + 11*e^2 + 29*e - 74', 'e^3 - 3*e^2 - 13*e + 44', '2*e^2 - 6', '-5*e^3 + 18*e^2 + 45*e - 146', '3/2*e^3 - 9/2*e^2 - 19/2*e + 19', '11/2*e^3 - 47/2*e^2 - 93/2*e + 182', '-2*e^3 + 10*e^2 + 11*e - 80', '5*e^3 - 20*e^2 - 39*e + 142', '-11/2*e^3 + 45/2*e^2 + 87/2*e - 181', '-11/2*e^3 + 43/2*e^2 + 89/2*e - 172', '6*e^3 - 24*e^2 - 49*e + 176', '9/2*e^3 - 39/2*e^2 - 79/2*e + 171', '-7/2*e^3 + 23/2*e^2 + 67/2*e - 78', '-1/2*e^3 + 9/2*e^2 - 3/2*e - 21', '-1/2*e^3 + 7/2*e^2 + 15/2*e - 26', '6*e^3 - 24*e^2 - 48*e + 176', '-6*e^3 + 24*e^2 + 48*e - 190', '7/2*e^3 - 27/2*e^2 - 65/2*e + 120', '-e^3 + 2*e^2 + 9*e', '-2*e^3 + 10*e^2 + 15*e - 70', '-1/2*e^3 + 3/2*e^2 + 17/2*e - 7', '9/2*e^3 - 31/2*e^2 - 87/2*e + 136', '1/2*e^3 - 9/2*e^2 - 13/2*e + 59', '-9/2*e^3 + 41/2*e^2 + 77/2*e - 156', '-1/2*e^3 - 1/2*e^2 + 23/2*e + 11', '-7/2*e^3 + 27/2*e^2 + 71/2*e - 105', '-1/2*e^3 + 11/2*e^2 + 3/2*e - 39', '1/2*e^3 - 11/2*e^2 - 3/2*e + 58', '7/2*e^3 - 27/2*e^2 - 71/2*e + 124', '7/2*e^3 - 25/2*e^2 - 79/2*e + 109', '3*e^3 - 17*e^2 - 22*e + 140', '5*e^2 - 2*e - 52', '-13/2*e^3 + 49/2*e^2 + 127/2*e - 204', '-1/2*e^3 + 1/2*e^2 + 11/2*e - 12', '-e^3 + 4*e^2 + 11*e - 46', '2*e^3 - 8*e^2 - 19*e + 56', '-1/2*e^3 + 7/2*e^2 + 5/2*e - 39', '-9/2*e^3 + 29/2*e^2 + 79/2*e - 98', 'e^3 - 4*e^2 - e + 26', '8*e^3 - 32*e^2 - 71*e + 264', '-9/2*e^3 + 43/2*e^2 + 65/2*e - 161', '-4*e^3 + 16*e^2 + 36*e - 140', '2*e^3 - 6*e^2 - 18*e + 32', '2*e^3 - 10*e^2 - 14*e + 68', '-4*e - 4', '-2*e^3 + 6*e^2 + 23*e - 64', '-5/2*e^3 + 25/2*e^2 + 43/2*e - 118', '3/2*e^3 - 17/2*e^2 - 27/2*e + 63', '3*e^3 - 10*e^2 - 31*e + 70', '4*e^2 - 8*e - 44', '6*e^3 - 26*e^2 - 54*e + 200', '-2*e^3 + 10*e^2 + 22*e - 108', '-4*e^3 + 12*e^2 + 40*e - 108', '-7/2*e^3 + 33/2*e^2 + 37/2*e - 130', '19/2*e^3 - 83/2*e^2 - 155/2*e + 317', '9/2*e^3 - 29/2*e^2 - 69/2*e + 84', '-21/2*e^3 + 79/2*e^2 + 187/2*e - 323', '-2*e^3 + 4*e^2 + 22*e - 22', '-3*e^3 + 13*e^2 + 31*e - 108', '5*e^3 - 21*e^2 - 47*e + 182', '4*e^2 - 6*e - 26', '-e^3 + 4*e^2 + 5*e - 20', '5/2*e^3 - 17/2*e^2 - 43/2*e + 68', '5/2*e^3 - 23/2*e^2 - 37/2*e + 95', '-4*e^3 + 16*e^2 + 35*e - 122', '7/2*e^3 - 41/2*e^2 - 51/2*e + 175', '5*e^3 - 18*e^2 - 55*e + 160', '-8*e^3 + 30*e^2 + 79*e - 246', '-1/2*e^3 + 17/2*e^2 + 3/2*e - 78', '-17/2*e^3 + 67/2*e^2 + 159/2*e - 292', '7/2*e^3 - 39/2*e^2 - 47/2*e + 140', '5/2*e^3 - 9/2*e^2 - 49/2*e + 7', '5/2*e^3 - 19/2*e^2 - 63/2*e + 73', '1/2*e^3 - 5/2*e^2 - 5/2*e + 1', '-3/2*e^3 + 13/2*e^2 + 25/2*e - 69', '-1/2*e^3 + 3/2*e^2 + 7/2*e - 26', '3/2*e^3 - 11/2*e^2 - 27/2*e + 26', '-3/2*e^3 + 21/2*e^2 + 7/2*e - 77', '-e^3 + 6*e^2 + 15*e - 62', '8*e^3 - 34*e^2 - 71*e + 280', '-11/2*e^3 + 35/2*e^2 + 105/2*e - 132', '-5/2*e^3 + 13/2*e^2 + 59/2*e - 76', '-4*e^3 + 19*e^2 + 36*e - 182', '3*e^3 - 15*e^2 - 28*e + 110', '7/2*e^3 - 21/2*e^2 - 75/2*e + 65', '6*e^3 - 22*e^2 - 50*e + 144', '-8*e^3 + 32*e^2 + 68*e - 272', '-4*e^3 + 16*e^2 + 28*e - 136', '6*e^3 - 26*e^2 - 46*e + 180', '7/2*e^3 - 25/2*e^2 - 85/2*e + 96', '3/2*e^3 + 1/2*e^2 - 31/2*e - 38', '9/2*e^3 - 49/2*e^2 - 65/2*e + 181', '-19/2*e^3 + 73/2*e^2 + 181/2*e - 319', '-5*e^3 + 27*e^2 + 41*e - 232', '8*e^3 - 28*e^2 - 82*e + 230', '-6*e^3 + 20*e^2 + 66*e - 174', '3*e^3 - 19*e^2 - 25*e + 166', '-4*e^3 + 16*e^2 + 32*e - 144', '4*e^3 - 16*e^2 - 32*e + 100', 'e^3 - 5*e^2 - 6*e + 36', '-5/2*e^3 + 21/2*e^2 + 43/2*e - 86', '-1/2*e^3 + 3/2*e^2 + 5/2*e - 9', '2*e^3 - 7*e^2 - 18*e + 52'], 'hecke_polynomial': 'x^4 - 7*x^3 + 3*x^2 + 58*x - 92', 'label': '4.4.8000.1-20.1-b'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 8000, 'ideals': ['[1, 1, 1]', '[4, 2, 1/2*w^3 - 3*w + 2]', '[5, 5, w^2 - w - 5]', '[11, 11, -1/2*w^3 - 1/2*w^2 + 3*w + 3]', '[11, 11, -1/2*w^2 + w + 2]', '[11, 11, -1/2*w^2 - w + 2]', '[11, 11, 1/2*w^3 - 1/2*w^2 - 3*w + 3]', '[16, 2, 2]', '[20, 10, w]', '[25, 5, -w^2 + 5]', '[29, 29, -1/2*w^2 - w + 4]', '[29, 29, -1/2*w^3 + 1/2*w^2 + 3*w - 1]', '[29, 29, -1/2*w^3 - 1/2*w^2 + 3*w + 1]', '[29, 29, -1/2*w^2 + w + 4]', '[41, 41, w^3 - 1/2*w^2 - 6*w + 6]', '[41, 41, -1/2*w^3 + 5/2*w^2 + 5*w - 14]', '[41, 41, 1/2*w^3 - 1/2*w^2 - 3*w + 6]', '[41, 41, -3/2*w^2 - 2*w + 6]', '[44, 22, -w^2 + w + 6]', '[44, 22, -1/2*w^3 - w^2 + 3*w + 4]', '[44, 22, 1/2*w^3 - w^2 - 3*w + 4]', '[44, 22, w^2 + w - 6]', '[55, 55, -1/2*w^2 + w + 5]', '[55, 55, 1/2*w^3 + 1/2*w^2 - 3*w]', '[55, 55, -1/2*w^3 + 1/2*w^2 + 3*w]', '[55, 55, 1/2*w^2 + w - 5]', '[64, 4, w^3 - 6*w + 4]', '[79, 79, -w^3 - w^2 + 4*w - 1]', '[79, 79, -3/2*w^2 - w + 9]', '[79, 79, -w^3 + 7/2*w^2 + 9*w - 21]', '[79, 79, w^3 - w^2 - 6*w + 9]', '[80, 10, 2*w^2 + 2*w - 10]', '[81, 3, -3]', '[100, 10, 1/2*w^3 - 2*w^2 - 5*w + 10]', '[109, 109, w^2 - w - 7]', '[109, 109, -1/2*w^3 + 1/2*w^2 + 4*w - 1]', '[109, 109, 1/2*w^3 + 1/2*w^2 - 4*w - 1]', '[109, 109, w^2 + w - 7]', '[116, 58, -w - 4]', '[116, 58, 1/2*w^3 - 3*w - 4]', '[116, 58, -1/2*w^3 + 3*w - 4]', '[116, 58, w - 4]', '[121, 11, 3/2*w^2 - 8]', '[121, 11, -w^2 - 2*w + 3]', '[121, 11, w^2 - 2*w - 3]', '[121, 11, 3/2*w^2 - 7]', '[121, 11, -w^3 + w^2 + 6*w - 7]', '[121, 11, -w^3 - w^2 + 6*w + 7]', '[121, 121, -w^3 + 1/2*w^2 + 5*w + 1]', '[121, 121, -1/2*w^3 + 1/2*w^2 + 5*w - 6]', '[121, 121, -1/2*w^3 - 1/2*w^2 + 5*w + 6]', '[121, 121, -w^3 - 1/2*w^2 + 5*w - 1]', '[125, 5, w^3 - 5*w - 5]', '[131, 131, -1/2*w^3 - 1/2*w^2 + 4*w + 7]', '[131, 131, -1/2*w^3 + 7/2*w^2 + 6*w - 18]', '[131, 131, 1/2*w^3 + 1/2*w^2 - 2*w + 2]', '[131, 131, 1/2*w^3 - 1/2*w^2 - 4*w + 7]', '[145, 145, w^3 + 1/2*w^2 - 6*w - 5]', '[145, 145, 1/2*w^2 - 2*w]', '[145, 145, -1/2*w^2 - 2*w]', '[145, 145, w^3 - 1/2*w^2 - 6*w + 5]', '[149, 149, w^3 + w^2 - 5*w - 7]', '[149, 149, 1/2*w^3 - w^2 - 5*w + 3]', '[149, 149, -1/2*w^3 - w^2 + 5*w + 3]', '[149, 149, -w^3 + w^2 + 5*w - 7]', '[164, 82, 1/2*w^3 - w^2 - 2*w + 6]', '[164, 82, 1/2*w^3 + w^2 - 4*w - 4]', '[164, 82, -1/2*w^3 + w^2 + 4*w - 4]', '[164, 82, -1/2*w^3 - w^2 + 2*w + 6]', '[176, 22, -w^3 - w^2 + 6*w + 6]', '[176, 22, -w^2 + 2*w + 4]', '[176, 22, -w^2 - 2*w + 4]', '[176, 22, w^3 - w^2 - 6*w + 6]', '[199, 199, -w^3 - w^2 + 6*w + 3]', '[199, 199, -w^2 + 2*w + 7]', '[199, 199, -w^2 - 2*w + 7]', '[199, 199, w^3 - w^2 - 6*w + 3]', '[205, 205, -1/2*w^3 + 3/2*w^2 + 3*w - 5]', '[205, 205, 1/2*w^3 - 1/2*w^2 - 2*w + 5]', '[205, 205, 1/2*w^3 + 1/2*w^2 - 2*w - 5]', '[205, 205, -1/2*w^3 - 3/2*w^2 + 3*w + 5]', '[211, 211, 1/2*w^3 - 2*w^2 - 3*w + 11]', '[211, 211, -1/2*w^3 - 1/2*w^2 + 3*w + 7]', '[211, 211, 1/2*w^3 - 1/2*w^2 - 3*w + 7]', '[211, 211, 1/2*w^3 + 2*w^2 - 3*w - 11]', '[220, 110, -1/2*w^3 + 2*w^2 + 3*w - 10]', '[220, 110, 2*w^2 + w - 10]', '[220, 110, -2*w^2 + w + 10]', '[220, 110, -1/2*w^3 - 2*w^2 + 3*w + 10]', '[229, 229, -1/2*w^3 - 1/2*w^2 + 4*w - 2]', '[229, 229, 1/2*w^3 + 1/2*w^2 - 2*w - 7]', '[229, 229, 1/2*w^3 - 1/2*w^2 - 2*w + 7]', '[229, 229, 1/2*w^3 - 1/2*w^2 - 4*w - 2]', '[239, 239, 1/2*w^2 + 2*w - 6]', '[239, 239, -w^3 - 1/2*w^2 + 6*w - 1]', '[239, 239, w^3 - 1/2*w^2 - 6*w - 1]', '[239, 239, 1/2*w^2 - 2*w - 6]', '[241, 241, -w^3 + 1/2*w^2 + 6*w - 2]', '[241, 241, -w^3 - 1/2*w^2 + 6*w + 4]', '[241, 241, w^3 - 1/2*w^2 - 6*w + 4]', '[241, 241, w^3 + 1/2*w^2 - 6*w - 2]', '[251, 251, 1/2*w^3 + w^2 - 5*w - 7]', '[251, 251, w^3 + w^2 - 5*w - 3]', '[251, 251, -w^3 + w^2 + 5*w - 3]', '[251, 251, -1/2*w^3 + w^2 + 5*w - 7]', '[256, 4, 4]', '[269, 269, 1/2*w^3 + 1/2*w^2 - 2*w - 6]', '[269, 269, 1/2*w^3 - 1/2*w^2 - 4*w - 1]', '[269, 269, -1/2*w^3 - 1/2*w^2 + 4*w - 1]', '[269, 269, -1/2*w^3 + 1/2*w^2 + 2*w - 6]', '[275, 55, -1/2*w^3 - 1/2*w^2 + 5*w + 5]', '[275, 55, -w^3 + 1/2*w^2 + 5*w]', '[275, 55, w^3 + 1/2*w^2 - 5*w]', '[275, 55, 1/2*w^3 - 1/2*w^2 - 5*w + 5]', '[281, 281, w^3 - 6*w + 1]', '[281, 281, w^3 - 1/2*w^2 - 6*w + 3]', '[281, 281, -w^3 - 1/2*w^2 + 6*w + 3]', '[281, 281, -w^3 + 6*w + 1]', '[316, 158, 1/2*w^3 + w^2 - 5*w - 6]', '[316, 158, w^3 - w^2 - 5*w + 4]', '[316, 158, -w^3 - w^2 + 5*w + 4]', '[316, 158, -1/2*w^3 + w^2 + 5*w - 6]', '[319, 319, 1/2*w^3 - 3/2*w^2 - 5*w + 12]', '[319, 319, 1/2*w^3 + w^2 - 4*w - 3]', '[319, 319, -3/2*w^2 + 2*w + 9]', '[319, 319, -w^3 + 3/2*w^2 + 5*w - 3]', '[319, 319, -w^3 + 3/2*w^2 + 6*w - 6]', '[319, 319, -1/2*w^3 + w^2 + 2*w - 7]', '[319, 319, w^3 - 2*w^2 - 6*w + 9]', '[319, 319, 2*w^2 - 2*w - 11]', '[319, 319, -2*w^2 - 2*w + 11]', '[319, 319, -w^3 - 2*w^2 + 6*w + 9]', '[319, 319, -1/2*w^3 - w^2 + 2*w + 7]', '[319, 319, w^3 + 3/2*w^2 - 6*w - 6]', '[319, 319, w^3 + 3/2*w^2 - 5*w - 3]', '[319, 319, 3/2*w^2 + 2*w - 9]', '[319, 319, -1/2*w^3 + w^2 + 4*w - 3]', '[319, 319, 1/2*w^3 + 3/2*w^2 - 5*w - 12]', '[320, 20, 2*w]', '[324, 6, -3/2*w^3 + 9*w - 6]', '[331, 331, 3/2*w^3 + w^2 - 7*w + 1]', '[331, 331, -1/2*w^3 + 3*w^2 + 5*w - 17]', '[331, 331, -3/2*w^3 + w^2 + 9*w - 13]', '[331, 331, 1/2*w^3 + 3*w^2 + w - 11]', '[349, 349, 1/2*w^3 + 3/2*w^2 - 2*w - 9]', '[349, 349, -1/2*w^3 + 3/2*w^2 + 4*w - 6]', '[349, 349, 1/2*w^3 + 3/2*w^2 - 4*w - 6]', '[349, 349, -1/2*w^3 + 3/2*w^2 + 2*w - 9]', '[359, 359, -w^3 + 7/2*w^2 + 9*w - 19]', '[359, 359, w^3 - 2*w^2 - 8*w + 11]', '[359, 359, w^3 - 1/2*w^2 - 6*w - 2]', '[359, 359, -5/2*w^2 - 3*w + 9]', '[361, 19, 2*w^2 - 11]', '[361, 19, -1/2*w^2 + 7]', '[389, 389, -1/2*w^3 + 5/2*w^2 + 6*w - 11]', '[389, 389, 5/2*w^3 - 3/2*w^2 - 16*w + 17]', '[389, 389, 3/2*w^3 - 1/2*w^2 - 10*w + 7]', '[389, 389, -3/2*w^3 + 7/2*w^2 + 12*w - 21]', '[395, 395, -1/2*w^3 - 5/2*w^2 + 2*w + 10]', '[395, 395, 1/2*w^3 - 3*w + 5]', '[395, 395, 1/2*w^3 - 3*w - 5]', '[395, 395, -1/2*w^3 + 5/2*w^2 + 2*w - 10]', '[400, 10, -2*w^2 + 10]', '[401, 401, -w^3 + 1/2*w^2 + 5*w - 1]', '[401, 401, 1/2*w^3 + 1/2*w^2 - 5*w - 4]', '[401, 401, -1/2*w^3 + 1/2*w^2 + 5*w - 4]', '[401, 401, w^3 + 1/2*w^2 - 5*w - 1]', '[405, 15, -3*w^2 + 3*w + 15]', '[436, 218, 3/2*w^3 - 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7/2*w^2 + w + 24]', '[9799, 9799, 1/2*w^3 - 7/2*w^2 - w + 24]', '[9799, 9799, 3/2*w^3 + 3/2*w^2 - 11*w - 2]', '[9799, 9799, 2*w^3 + 5/2*w^2 - 10*w - 18]', '[9799, 9799, w^3 - 9/2*w^2 - 12*w + 18]', '[9799, 9799, 2*w^3 + 7/2*w^2 - 14*w - 17]', '[9799, 9799, w^3 - 7/2*w^2 - 2*w + 18]', '[9799, 9799, -w^3 - 5/2*w^2 + 10*w + 7]', '[9799, 9799, -3/2*w^3 - 9/2*w^2 + 13*w + 22]', '[9801, 33, -9/2*w^2 + 24]', '[9801, 33, 3*w^2 + 6*w - 9]', '[9801, 33, -3*w^2 + 6*w + 9]', '[9801, 33, -9/2*w^2 + 21]', '[9801, 33, 3*w^3 - 3*w^2 - 18*w + 21]', '[9801, 33, 3*w^3 + 3*w^2 - 18*w - 21]', '[9801, 363, 3*w^3 - 3/2*w^2 - 15*w - 3]', '[9801, 363, 3/2*w^3 - 3/2*w^2 - 15*w + 18]', '[9801, 363, 3/2*w^3 + 3/2*w^2 - 15*w - 18]', '[9801, 363, 3*w^3 + 3/2*w^2 - 15*w + 3]', '[9811, 9811, 7/2*w^3 + 3/2*w^2 - 17*w + 13]', '[9811, 9811, 3*w^3 - 9*w^2 - 27*w + 53]', '[9811, 9811, 3*w^3 + w^2 - 17*w + 3]', '[9811, 9811, 3/2*w^3 - 13/2*w^2 - 13*w + 37]', '[9820, 4910, 5/2*w^3 + 3*w^2 - 11*w - 10]', '[9820, 4910, 5/2*w^3 + w^2 - 14*w - 10]', '[9820, 4910, 5/2*w^3 - w^2 - 14*w + 10]', '[9820, 4910, 5/2*w^3 - 3*w^2 - 11*w + 10]', '[9829, 9829, -5/2*w^3 - 11/2*w^2 + 17*w + 29]', '[9829, 9829, w^3 - 11/2*w^2 - w + 26]', '[9829, 9829, -w^3 - 11/2*w^2 + w + 26]', '[9829, 9829, 5/2*w^3 - 11/2*w^2 - 17*w + 29]', '[9839, 9839, -3/2*w^3 + 3*w^2 + 12*w - 13]', '[9839, 9839, 5/2*w^2 + 3*w - 21]', '[9839, 9839, 5/2*w^2 - 3*w - 21]', '[9839, 9839, 3/2*w^3 + 3*w^2 - 12*w - 13]', '[9851, 9851, 9/2*w^2 + 7*w - 16]', '[9851, 9851, 2*w^3 - 5/2*w^2 - 13*w + 26]', '[9851, 9851, -w^3 + 21/2*w^2 + 15*w - 54]', '[9851, 9851, -5*w^3 + 7/2*w^2 + 31*w - 36]', '[9875, 395, 1/2*w^3 + 5/2*w^2]', '[9875, 395, 1/2*w^3 + 5*w^2 - 5*w - 25]', '[9875, 395, 1/2*w^3 - 5*w^2 - 5*w + 25]', '[9875, 395, 1/2*w^3 - 5/2*w^2]', '[9881, 9881, -5/2*w^3 - 2*w^2 + 14*w + 13]', '[9881, 9881, -1/2*w^3 + 5*w^2 + 10*w - 21]', '[9881, 9881, -w^3 + 13/2*w^2 + 10*w - 37]', '[9881, 9881, 3/2*w^3 + 15/2*w^2 + w - 26]', '[9881, 9881, 1/2*w^3 + 2*w^2 - 8*w - 7]', '[9881, 9881, -2*w^3 - 13/2*w^2 + 14*w + 34]', '[9881, 9881, -2*w^3 + 3/2*w^2 + 12*w - 21]', '[9881, 9881, w^3 - 13/2*w^2 - 2*w + 31]', '[9881, 9881, -w^3 - 13/2*w^2 + 2*w + 31]', '[9881, 9881, 2*w^3 + 3/2*w^2 - 12*w - 21]', '[9881, 9881, -2*w^3 + 13/2*w^2 + 14*w - 34]', '[9881, 9881, -1/2*w^3 + 2*w^2 + 8*w - 7]', '[9881, 9881, 7/2*w^3 + 3/2*w^2 - 17*w + 6]', '[9881, 9881, -4*w^3 + 5/2*w^2 + 24*w - 33]', '[9881, 9881, 9/2*w^3 - 3*w^2 - 28*w + 31]', '[9881, 9881, 5/2*w^3 - 2*w^2 - 14*w + 13]', '[9931, 9931, -7/2*w^3 + 8*w^2 + 29*w - 51]', '[9931, 9931, 1/2*w^3 - 11/2*w^2 - 6*w + 29]', '[9931, 9931, 9/2*w^3 + 1/2*w^2 - 24*w + 21]', '[9931, 9931, -7/2*w^3 - 2*w^2 + 19*w - 1]', '[9949, 9949, -3/2*w^3 - 11/2*w^2 + 8*w + 19]', '[9949, 9949, -1/2*w^3 + 11/2*w^2 + 6*w - 36]', '[9949, 9949, 1/2*w^3 + 11/2*w^2 - 6*w - 36]', '[9949, 9949, 3/2*w^3 - 11/2*w^2 - 8*w + 19]', '[9995, 9995, -5/2*w^3 + 17/2*w^2 + 8*w - 30]', '[9995, 9995, -7/2*w^3 - 7/2*w^2 + 23*w + 25]', '[9995, 9995, 1/2*w^3 + 25/2*w^2 - 17*w - 55]', '[9995, 9995, 11/2*w^3 + 1/2*w^2 - 32*w - 30]', '[10000, 10, 10]'], 'label': '4.4.8000.1', 'narrow_class_no': 2, 'primes': ['[4, 2, 1/2*w^3 - 3*w + 2]', '[5, 5, w^2 - w - 5]', '[11, 11, -1/2*w^3 - 1/2*w^2 + 3*w + 3]', '[11, 11, -1/2*w^2 + w + 2]', '[11, 11, -1/2*w^2 - w + 2]', '[11, 11, 1/2*w^3 - 1/2*w^2 - 3*w + 3]', '[29, 29, -1/2*w^2 - w + 4]', '[29, 29, -1/2*w^3 + 1/2*w^2 + 3*w - 1]', '[29, 29, -1/2*w^3 - 1/2*w^2 + 3*w + 1]', '[29, 29, -1/2*w^2 + w + 4]', '[41, 41, w^3 - 1/2*w^2 - 6*w + 6]', '[41, 41, -1/2*w^3 + 5/2*w^2 + 5*w - 14]', '[41, 41, 1/2*w^3 - 1/2*w^2 - 3*w + 6]', '[41, 41, -3/2*w^2 - 2*w + 6]', '[79, 79, -w^3 - w^2 + 4*w - 1]', '[79, 79, -3/2*w^2 - w + 9]', '[79, 79, -w^3 + 7/2*w^2 + 9*w - 21]', '[79, 79, w^3 - w^2 - 6*w + 9]', '[81, 3, -3]', '[109, 109, w^2 - w - 7]', '[109, 109, -1/2*w^3 + 1/2*w^2 + 4*w - 1]', '[109, 109, 1/2*w^3 + 1/2*w^2 - 4*w - 1]', '[109, 109, w^2 + w - 7]', '[131, 131, -1/2*w^3 - 1/2*w^2 + 4*w + 7]', '[131, 131, -1/2*w^3 + 7/2*w^2 + 6*w - 18]', '[131, 131, 1/2*w^3 + 1/2*w^2 - 2*w + 2]', '[131, 131, 1/2*w^3 - 1/2*w^2 - 4*w + 7]', '[149, 149, w^3 + w^2 - 5*w - 7]', '[149, 149, 1/2*w^3 - w^2 - 5*w + 3]', '[149, 149, -1/2*w^3 - w^2 + 5*w + 3]', '[149, 149, -w^3 + w^2 + 5*w - 7]', '[199, 199, -w^3 - w^2 + 6*w + 3]', '[199, 199, -w^2 + 2*w + 7]', '[199, 199, -w^2 - 2*w + 7]', '[199, 199, w^3 - w^2 - 6*w + 3]', '[211, 211, 1/2*w^3 - 2*w^2 - 3*w + 11]', '[211, 211, -1/2*w^3 - 1/2*w^2 + 3*w + 7]', '[211, 211, 1/2*w^3 - 1/2*w^2 - 3*w + 7]', '[211, 211, 1/2*w^3 + 2*w^2 - 3*w - 11]', '[229, 229, -1/2*w^3 - 1/2*w^2 + 4*w - 2]', '[229, 229, 1/2*w^3 + 1/2*w^2 - 2*w - 7]', '[229, 229, 1/2*w^3 - 1/2*w^2 - 2*w + 7]', '[229, 229, 1/2*w^3 - 1/2*w^2 - 4*w - 2]', '[239, 239, 1/2*w^2 + 2*w - 6]', '[239, 239, -w^3 - 1/2*w^2 + 6*w - 1]', '[239, 239, w^3 - 1/2*w^2 - 6*w - 1]', '[239, 239, 1/2*w^2 - 2*w - 6]', '[241, 241, -w^3 + 1/2*w^2 + 6*w - 2]', '[241, 241, -w^3 - 1/2*w^2 + 6*w + 4]', '[241, 241, w^3 - 1/2*w^2 - 6*w + 4]', '[241, 241, w^3 + 1/2*w^2 - 6*w - 2]', '[251, 251, 1/2*w^3 + w^2 - 5*w - 7]', '[251, 251, w^3 + w^2 - 5*w - 3]', '[251, 251, -w^3 + w^2 + 5*w - 3]', '[251, 251, -1/2*w^3 + w^2 + 5*w - 7]', '[269, 269, 1/2*w^3 + 1/2*w^2 - 2*w - 6]', '[269, 269, 1/2*w^3 - 1/2*w^2 - 4*w - 1]', '[269, 269, -1/2*w^3 - 1/2*w^2 + 4*w - 1]', '[269, 269, -1/2*w^3 + 1/2*w^2 + 2*w - 6]', '[281, 281, w^3 - 6*w + 1]', '[281, 281, w^3 - 1/2*w^2 - 6*w + 3]', '[281, 281, -w^3 - 1/2*w^2 + 6*w + 3]', '[281, 281, -w^3 + 6*w + 1]', '[331, 331, 3/2*w^3 + w^2 - 7*w + 1]', '[331, 331, -1/2*w^3 + 3*w^2 + 5*w - 17]', '[331, 331, -3/2*w^3 + w^2 + 9*w - 13]', '[331, 331, 1/2*w^3 + 3*w^2 + w - 11]', '[349, 349, 1/2*w^3 + 3/2*w^2 - 2*w - 9]', '[349, 349, -1/2*w^3 + 3/2*w^2 + 4*w - 6]', '[349, 349, 1/2*w^3 + 3/2*w^2 - 4*w - 6]', '[349, 349, -1/2*w^3 + 3/2*w^2 + 2*w - 9]', '[359, 359, -w^3 + 7/2*w^2 + 9*w - 19]', '[359, 359, w^3 - 2*w^2 - 8*w + 11]', '[359, 359, w^3 - 1/2*w^2 - 6*w - 2]', '[359, 359, -5/2*w^2 - 3*w + 9]', '[361, 19, 2*w^2 - 11]', '[361, 19, -1/2*w^2 + 7]', '[389, 389, -1/2*w^3 + 5/2*w^2 + 6*w - 11]', '[389, 389, 5/2*w^3 - 3/2*w^2 - 16*w + 17]', '[389, 389, 3/2*w^3 - 1/2*w^2 - 10*w + 7]', '[389, 389, -3/2*w^3 + 7/2*w^2 + 12*w - 21]', '[401, 401, -w^3 + 1/2*w^2 + 5*w - 1]', '[401, 401, 1/2*w^3 + 1/2*w^2 - 5*w - 4]', '[401, 401, -1/2*w^3 + 1/2*w^2 + 5*w - 4]', '[401, 401, w^3 + 1/2*w^2 - 5*w - 1]', '[439, 439, -2*w^3 + 3/2*w^2 + 12*w - 16]', '[439, 439, -w^3 + 1/2*w^2 + 5*w - 7]', '[439, 439, w^3 + 1/2*w^2 - 5*w - 7]', '[439, 439, w^3 + 1/2*w^2 - 4*w + 4]', '[479, 479, -w^3 + 9/2*w^2 + 10*w - 26]', '[479, 479, -3/2*w^3 + 3/2*w^2 + 9*w - 14]', '[479, 479, -3/2*w^3 - 1/2*w^2 + 7*w - 6]', '[479, 479, -5/2*w^2 - 2*w + 14]', '[491, 491, 1/2*w^3 + 5/2*w^2 - 4*w - 14]', '[491, 491, 1/2*w^3 + 5/2*w^2 - 2*w - 11]', '[491, 491, -1/2*w^3 + 5/2*w^2 + 2*w - 11]', '[491, 491, -1/2*w^3 + 5/2*w^2 + 4*w - 14]', '[509, 509, 1/2*w^3 - 1/2*w^2 - 5*w - 3]', '[509, 509, -w^3 + 1/2*w^2 + 5*w - 8]', '[509, 509, w^3 + 1/2*w^2 - 5*w - 8]', '[509, 509, -7/2*w^2 - 3*w + 18]', '[521, 521, -9/2*w^2 - 4*w + 21]', '[521, 521, -5/2*w^3 + 2*w^2 + 16*w - 19]', '[521, 521, -1/2*w^3 + 2*w^2 + 6*w - 9]', '[521, 521, w^3 - 7/2*w^2 - 8*w + 22]', '[571, 571, 1/2*w^3 - 1/2*w^2 - 4*w - 4]', '[571, 571, 3/2*w^3 - 3/2*w^2 - 9*w + 7]', '[571, 571, -3/2*w^3 - 3/2*w^2 + 9*w + 7]', '[571, 571, -1/2*w^3 - 1/2*w^2 + 4*w - 4]', '[599, 599, 1/2*w^3 + w^2 - 2*w - 9]', '[599, 599, -1/2*w^3 + w^2 + 4*w - 1]', '[599, 599, 1/2*w^3 + w^2 - 4*w - 1]', '[599, 599, -1/2*w^3 + w^2 + 2*w - 9]', '[601, 601, 5/2*w^2 + w - 11]', '[601, 601, 1/2*w^3 - 5/2*w^2 - 3*w + 14]', '[601, 601, -1/2*w^3 - 5/2*w^2 + 3*w + 14]', '[601, 601, 5/2*w^2 - w - 11]', '[641, 641, 5/2*w^2 + w - 13]', '[641, 641, -1/2*w^3 + 5/2*w^2 + 3*w - 12]', '[641, 641, 1/2*w^3 + 5/2*w^2 - 3*w - 12]', '[641, 641, 5/2*w^2 - w - 13]', '[691, 691, 1/2*w^3 + 5/2*w^2 - 3*w - 13]', '[691, 691, -1/2*w^3 - w^2 + 3*w + 11]', '[691, 691, 1/2*w^3 - w^2 - 3*w + 11]', '[691, 691, -1/2*w^3 + 5/2*w^2 + 3*w - 13]', '[709, 709, 3/2*w^3 - 3/2*w^2 - 8*w + 2]', '[709, 709, -1/2*w^3 + 3/2*w^2 + 6*w - 13]', '[709, 709, 1/2*w^3 + 3/2*w^2 - 6*w - 13]', '[709, 709, -3/2*w^3 - 3/2*w^2 + 8*w + 2]', '[719, 719, w^2 + 2*w - 9]', '[719, 719, w^3 + w^2 - 6*w - 1]', '[719, 719, -w^3 + w^2 + 6*w - 1]', '[719, 719, w^2 - 2*w - 9]', '[761, 761, 1/2*w^3 + w^2 - 6*w - 9]', '[761, 761, 3/2*w^3 + w^2 - 8*w - 1]', '[761, 761, 3/2*w^3 - 5*w^2 - 14*w + 29]', '[761, 761, -1/2*w^3 + w^2 + 6*w - 9]', '[811, 811, 3/2*w^3 - 1/2*w^2 - 8*w + 12]', '[811, 811, w^3 - 2*w^2 - 9*w + 11]', '[811, 811, -w^3 - 2*w^2 + 9*w + 11]', '[811, 811, -3/2*w^3 + 9/2*w^2 + 12*w - 28]', '[829, 829, w^3 + w^2 - 5*w - 9]', '[829, 829, 1/2*w^3 - w^2 - 5*w + 1]', '[829, 829, -1/2*w^3 - w^2 + 5*w + 1]', '[829, 829, -w^3 + w^2 + 5*w - 9]', '[839, 839, w^3 - 5/2*w^2 - 8*w + 13]', '[839, 839, 2*w^3 - 1/2*w^2 - 13*w - 1]', '[839, 839, -2*w^3 - 1/2*w^2 + 13*w - 1]', '[839, 839, w^3 + 5/2*w^2 - 8*w - 13]', '[881, 881, -w^3 + 9/2*w^2 + 9*w - 27]', '[881, 881, -2*w^3 + 1/2*w^2 + 12*w - 9]', '[881, 881, w^3 - 7/2*w^2 - 10*w + 19]', '[881, 881, 2*w^3 - 5/2*w^2 - 13*w + 23]', '[919, 919, 1/2*w^3 + 2*w^2 - 4*w - 7]', '[919, 919, 1/2*w^3 + 2*w^2 - 2*w - 13]', '[919, 919, -1/2*w^3 + 2*w^2 + 2*w - 13]', '[919, 919, -1/2*w^3 + 2*w^2 + 4*w - 7]', '[961, 31, -w^2 + 11]', '[961, 31, 5/2*w^2 - 13]', '[971, 971, 1/2*w^3 + 7/2*w^2 - 5*w - 17]', '[971, 971, 2*w^3 - 13*w - 3]', '[971, 971, -2*w^3 + 13*w - 3]', '[971, 971, -1/2*w^3 + 7/2*w^2 + 5*w - 17]']}
• 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': [20, 0, -10, 0, 1], 'conductor': 40, 'degree': 4, 'dirichlet_group': [3, 1, 27, 9], 'disc_abs': 8000, 'disc_rad': 10, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 1]]], [5, [0]], [7, [[4, 1]]], [11, [[1, 4]]], [13, [[4, 1]]], [17, [[4, 1]]], [19, [[2, 2]]], [23, [[4, 1]]], [29, [[1, 4]]], [31, [[2, 2]]], [37, [[4, 1]]], [41, [[1, 4]]], [43, [[4, 1]]], [47, [[4, 1]]], [53, [[4, 1]]], [59, [[2, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [6, 3], 'galois_label': '4T1', 'galt': 1, 'grd': 9.457416090031758, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.8000.1', 'local_algs': ['2.4.6.4', '5.4.3.1'], 'monogenic': -1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 5], 'rd': 9.45741609003, 'regulator': {'__RealLiteral__': 0, 'data': '4.50325854125', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{2} - 3 \\)', '\\( \\frac{1}{2} a^{3} - a^{2} - 4 a + 7 \\)', '\\( \\frac{1}{2} a^{3} + a^{2} - 2 a - 3 \\)'], 'used_grh': False, 'zk': ['1', 'a', '1/2*a^2', '1/2*a^3']}