Hilbert modular form data - 4.4.19600.1-25.1-k

Formats: - HTML - YAML - JSON - 2024-04-28T01:21:39.154364

• 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': 19600, 'field_bad_primes': [2, 5, 7], 'field_label': '4.4.19600.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.19600.1-25.1-k', 'label_nsuffix': 10, 'label_suffix': 'k', 'level_bad_primes': [5], 'level_ideal': '[25, 5, -4/23*w^3 + 6/23*w^2 + 40/23*w - 21/23]', 'level_label': '25.1', 'level_norm': 25, 'parallel_weight': 2, 'short_label': '25.1-k', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[25,5,-4/23*w^3+6/23*w^2+40/23*w-21/23]', -1]], 'hecke_eigenvalues': [2, '-e - 2', 'e', 4, -4, '-e + 3', '-e - 5', 1, 'e + 4', '-e - 6', '-e + 2', 'e - 4', 'e + 5', '2*e - 2', 'e - 3', '2*e + 6', 2, '-3*e - 7', 'e + 5', '-3*e + 1', 'e - 3', '-e - 10', '-e - 18', 'e - 8', 'e - 16', -13, 3, '-2*e - 10', '-3*e + 5', '-2*e + 6', '-3*e - 11', '3*e + 11', '-3*e - 11', '3*e - 5', '-3*e + 5', -10, -10, '-4*e + 2', '4*e + 10', '-3*e - 8', '3*e - 2', '-4*e - 8', '-4*e', '2*e - 10', '2*e + 14', '7*e + 15', '-e + 7', '7*e - 1', '-e - 9', '-e - 1', '-e - 1', '4*e + 20', '4*e - 12', '4*e - 13', '6*e + 13', '-4*e - 21', '-6*e + 1', '3*e + 14', '-3*e + 8', '-5*e - 9', '-5*e - 1', 20, -20, '5*e + 16', '-3*e + 8', '-5*e + 6', '3*e + 14', '6*e - 7', '-6*e - 19', '2*e - 11', '-2*e - 15', '10*e - 2', -20, '10*e + 22', 20, '6*e + 13', '-6*e + 1', '-4*e - 13', '4*e - 5', 'e - 31', 'e + 33', '13*e + 13', '13*e + 13', '-7*e', '5*e + 4', '7*e + 14', '-5*e - 6', '-8*e - 8', '-e + 7', '-8*e - 8', '-e - 9', '-8*e - 6', '8*e + 10', '-4*e - 29', '4*e - 21', '4*e + 19', '-4*e + 11', '12*e + 6', '-12*e - 18', '8*e - 6', '-8*e - 22', '-7*e - 31', '-7*e + 17', '-10*e + 6', '-10*e - 26', '12*e + 6', '-8*e - 14', '-12*e - 18', '8*e + 2', 'e + 9', '5*e - 19', 'e - 7', '5*e + 29', '4*e + 23', '-4*e + 15', '-14*e - 19', '14*e + 9', '9*e - 4', '-9*e - 22', '-e + 18', 'e + 20', '5*e + 37', '-2*e + 6', '5*e - 27', '-2*e - 10', '-15*e - 8', '7*e + 30', '15*e + 22', '-7*e + 16', '-8*e - 8', '-2*e - 34', '-8*e - 8', '-2*e + 30', '8*e + 11', '-8*e - 5', '-2*e - 23', '2*e - 19', '8*e + 24', '8*e - 8', '-e - 9', '-e + 7', '6*e + 30', '6*e - 18', 8, -8, '7*e + 43', -20, '7*e - 29', 20], 'hecke_polynomial': 'x^2 + 2*x - 7', 'label': '4.4.19600.1-25.1-k'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 19600, 'ideals': ['[1, 1, 1]', '[4, 2, -2/23*w^3 + 3/23*w^2 - 3/23*w + 1/23]', '[9, 3, -2/23*w^3 + 3/23*w^2 + 43/23*w + 24/23]', '[9, 3, -2/23*w^3 + 3/23*w^2 + 43/23*w - 68/23]', '[16, 2, 2]', '[19, 19, -2/23*w^3 + 3/23*w^2 - 3/23*w + 24/23]', '[19, 19, -6/23*w^3 + 9/23*w^2 + 83/23*w - 20/23]', '[19, 19, 6/23*w^3 - 9/23*w^2 - 83/23*w + 66/23]', '[19, 19, -2/23*w^3 + 3/23*w^2 - 3/23*w - 22/23]', '[25, 5, -4/23*w^3 + 6/23*w^2 + 40/23*w - 21/23]', '[29, 29, w]', '[29, 29, -4/23*w^3 + 6/23*w^2 + 63/23*w - 21/23]', '[29, 29, 4/23*w^3 - 6/23*w^2 - 63/23*w + 44/23]', '[29, 29, -w + 1]', '[31, 31, w + 2]', '[31, 31, -4/23*w^3 + 6/23*w^2 + 63/23*w + 25/23]', '[31, 31, 4/23*w^3 - 6/23*w^2 - 63/23*w + 90/23]', '[31, 31, -w + 3]', '[36, 6, 2/23*w^3 - 3/23*w^2 - 43/23*w + 45/23]', '[36, 6, 2/23*w^3 - 3/23*w^2 - 43/23*w - 1/23]', '[49, 7, -2/23*w^3 + 3/23*w^2 + 43/23*w - 22/23]', '[59, 59, -20/23*w^3 + 30/23*w^2 + 269/23*w - 128/23]', '[59, 59, -8/23*w^3 + 12/23*w^2 + 103/23*w - 88/23]', '[59, 59, -8/23*w^3 + 12/23*w^2 + 103/23*w - 19/23]', '[59, 59, -4/23*w^3 + 6/23*w^2 + 17/23*w - 44/23]', '[64, 4, -4/23*w^3 + 6/23*w^2 - 6/23*w + 2/23]', '[76, 38, 6/23*w^3 - 9/23*w^2 - 83/23*w + 89/23]', '[76, 38, -2/23*w^3 + 3/23*w^2 - 3/23*w - 45/23]', '[76, 38, -2/23*w^3 + 3/23*w^2 - 3/23*w + 47/23]', '[76, 38, -6/23*w^3 + 9/23*w^2 + 83/23*w + 3/23]', '[81, 3, 3]', '[81, 9, 2/23*w^3 - 3/23*w^2 - 43/23*w + 114/23]', '[81, 9, -2/23*w^3 + 3/23*w^2 + 43/23*w + 70/23]', '[100, 10, w^2 - w - 13]', '[109, 109, -9/23*w^3 + 2/23*w^2 + 113/23*w + 62/23]', '[109, 109, 4/23*w^3 - 6/23*w^2 - 63/23*w - 71/23]', '[109, 109, 7/23*w^3 - 22/23*w^2 - 47/23*w + 100/23]', '[109, 109, 9/23*w^3 - 25/23*w^2 - 90/23*w + 168/23]', '[116, 58, 3/23*w^3 + 7/23*w^2 - 53/23*w - 174/23]', '[116, 58, -1/23*w^3 - 10/23*w^2 + 10/23*w - 11/23]', '[116, 58, -1/23*w^3 + 13/23*w^2 - 13/23*w + 12/23]', '[116, 58, 3/23*w^3 - 16/23*w^2 - 30/23*w + 217/23]', '[121, 11, -2/23*w^3 + 3/23*w^2 + 20/23*w - 91/23]', '[121, 11, 2/23*w^3 - 3/23*w^2 - 20/23*w - 70/23]', '[124, 62, -5/23*w^3 + 19/23*w^2 + 27/23*w - 124/23]', '[124, 62, 7/23*w^3 - 22/23*w^2 - 70/23*w + 123/23]', '[124, 62, -7/23*w^3 - 1/23*w^2 + 93/23*w + 38/23]', '[124, 62, 5/23*w^3 + 4/23*w^2 - 50/23*w - 83/23]', '[131, 131, -5/23*w^3 + 19/23*w^2 + 50/23*w - 101/23]', '[131, 131, -3/23*w^3 + 16/23*w^2 + 7/23*w - 125/23]', '[131, 131, 3/23*w^3 + 7/23*w^2 - 30/23*w - 105/23]', '[131, 131, 5/23*w^3 + 4/23*w^2 - 73/23*w - 37/23]', '[139, 139, -2/23*w^3 - 20/23*w^2 + 43/23*w + 323/23]', '[139, 139, 17/23*w^3 - 37/23*w^2 - 216/23*w + 302/23]', '[139, 139, 17/23*w^3 - 14/23*w^2 - 239/23*w - 66/23]', '[139, 139, -2/23*w^3 + 26/23*w^2 - 3/23*w - 344/23]', '[144, 6, -4/23*w^3 + 6/23*w^2 + 86/23*w + 48/23]', '[144, 6, -4/23*w^3 + 6/23*w^2 + 86/23*w - 136/23]', '[149, 149, -1/23*w^3 - 10/23*w^2 + 33/23*w - 34/23]', '[149, 149, 1/23*w^3 + 10/23*w^2 - 33/23*w - 196/23]', '[149, 149, -1/23*w^3 + 13/23*w^2 + 10/23*w - 218/23]', '[149, 149, 1/23*w^3 - 13/23*w^2 - 10/23*w - 12/23]', '[169, 13, 6/23*w^3 - 9/23*w^2 - 37/23*w + 20/23]', '[169, 13, -10/23*w^3 + 15/23*w^2 + 123/23*w - 64/23]', '[171, 57, 5/23*w^3 - 19/23*w^2 - 73/23*w + 239/23]', '[171, 57, -1/23*w^3 - 10/23*w^2 + 10/23*w + 150/23]', '[171, 57, -1/23*w^3 + 13/23*w^2 + 33/23*w - 11/23]', '[171, 57, -3/23*w^3 + 16/23*w^2 + 30/23*w - 56/23]', '[171, 57, 3/23*w^3 + 7/23*w^2 - 53/23*w - 13/23]', '[171, 57, 1/23*w^3 + 10/23*w^2 - 56/23*w + 34/23]', '[171, 57, -1/23*w^3 + 13/23*w^2 - 13/23*w - 149/23]', '[171, 57, 5/23*w^3 + 4/23*w^2 - 96/23*w - 152/23]', '[196, 14, -w^2 + w + 1]', '[199, 199, -1/23*w^3 + 13/23*w^2 - 13/23*w - 195/23]', '[199, 199, 3/23*w^3 + 7/23*w^2 - 53/23*w + 33/23]', '[199, 199, 3/23*w^3 - 16/23*w^2 - 30/23*w + 10/23]', '[199, 199, 1/23*w^3 + 10/23*w^2 - 10/23*w - 196/23]', '[225, 15, 8/23*w^3 - 35/23*w^2 - 57/23*w + 226/23]', '[225, 15, -8/23*w^3 - 11/23*w^2 + 103/23*w + 142/23]', '[236, 118, -1/23*w^3 + 13/23*w^2 - 13/23*w - 172/23]', '[236, 118, 3/23*w^3 + 7/23*w^2 - 7/23*w - 82/23]', '[236, 118, -3/23*w^3 + 16/23*w^2 - 16/23*w - 79/23]', '[236, 118, 3/23*w^3 + 53/23*w^2 - 53/23*w - 128/23]', '[251, 251, 6/23*w^3 - 9/23*w^2 - 14/23*w + 43/23]', '[251, 251, 14/23*w^3 - 21/23*w^2 - 186/23*w + 62/23]', '[251, 251, 4/23*w^3 - 6/23*w^2 - 109/23*w + 228/23]', '[251, 251, 6/23*w^3 - 9/23*w^2 - 14/23*w - 26/23]', '[256, 4, 4]', '[261, 87, -1/23*w^3 + 13/23*w^2 - 36/23*w + 58/23]', '[261, 87, -10/23*w^3 + 15/23*w^2 + 146/23*w - 87/23]', '[261, 87, 7/23*w^3 - 22/23*w^2 - 93/23*w + 284/23]', '[261, 87, 2/23*w^3 - 3/23*w^2 + 26/23*w - 24/23]', '[261, 87, 7/23*w^3 + 1/23*w^2 - 116/23*w - 176/23]', '[261, 87, -2/23*w^3 + 3/23*w^2 - 26/23*w + 1/23]', '[261, 87, -1/23*w^3 - 10/23*w^2 - 13/23*w - 34/23]', '[261, 87, 10/23*w^3 - 15/23*w^2 - 146/23*w + 64/23]', '[271, 271, -8/23*w^3 + 12/23*w^2 + 126/23*w + 27/23]', '[271, 271, 8/23*w^3 - 35/23*w^2 - 80/23*w + 226/23]', '[271, 271, 13/23*w^3 - 31/23*w^2 - 153/23*w + 189/23]', '[271, 271, 8/23*w^3 - 12/23*w^2 - 126/23*w + 157/23]', '[279, 93, -5/23*w^3 + 19/23*w^2 + 50/23*w - 78/23]', '[279, 93, -10/23*w^3 + 38/23*w^2 + 77/23*w - 202/23]', '[279, 93, 3/23*w^3 - 16/23*w^2 - 7/23*w + 148/23]', '[279, 93, 10/23*w^3 - 38/23*w^2 - 77/23*w + 271/23]', '[279, 93, 3/23*w^3 + 7/23*w^2 - 30/23*w - 128/23]', '[279, 93, 10/23*w^3 + 8/23*w^2 - 123/23*w - 166/23]', '[279, 93, -5/23*w^3 - 4/23*w^2 + 73/23*w + 14/23]', '[279, 93, -10/23*w^3 - 8/23*w^2 + 123/23*w + 97/23]', '[281, 281, -w^2 + 2*w + 9]', '[281, 281, 13/23*w^3 - 8/23*w^2 - 153/23*w + 28/23]', '[281, 281, -13/23*w^3 + 31/23*w^2 + 130/23*w - 120/23]', '[281, 281, 11/23*w^3 - 28/23*w^2 - 87/23*w + 190/23]', '[289, 17, -11/23*w^3 + 51/23*w^2 + 110/23*w - 581/23]', '[289, 17, -8/23*w^3 + 35/23*w^2 + 80/23*w - 410/23]', '[304, 38, -4/23*w^3 + 6/23*w^2 - 6/23*w + 48/23]', '[304, 38, -12/23*w^3 + 18/23*w^2 + 166/23*w - 40/23]', '[304, 38, 12/23*w^3 - 18/23*w^2 - 166/23*w + 132/23]', '[304, 38, -4/23*w^3 + 6/23*w^2 - 6/23*w - 44/23]', '[311, 311, 5/23*w^3 + 4/23*w^2 - 50/23*w - 106/23]', '[311, 311, -7/23*w^3 + 22/23*w^2 + 70/23*w - 100/23]', '[311, 311, 7/23*w^3 + 1/23*w^2 - 93/23*w - 15/23]', '[311, 311, -5/23*w^3 + 19/23*w^2 + 27/23*w - 147/23]', '[324, 6, -6/23*w^3 + 9/23*w^2 - 9/23*w + 3/23]', '[324, 18, 2/23*w^3 - 3/23*w^2 - 43/23*w - 93/23]', '[324, 18, -2/23*w^3 + 3/23*w^2 + 43/23*w - 137/23]', '[361, 19, w^2 - w - 12]', '[361, 19, -8/23*w^3 + 12/23*w^2 + 80/23*w - 19/23]', '[361, 19, 4/23*w^3 - 6/23*w^2 - 86/23*w - 25/23]', '[361, 19, w^2 - w - 4]', '[361, 19, 4/23*w^3 - 6/23*w^2 - 86/23*w + 113/23]', '[361, 19, -8/23*w^3 + 12/23*w^2 + 80/23*w - 65/23]', '[361, 361, 1/23*w^3 - 13/23*w^2 + 59/23*w - 35/23]', '[361, 361, -11/23*w^3 + 5/23*w^2 + 179/23*w + 109/23]', '[361, 361, -11/23*w^3 + 28/23*w^2 + 156/23*w - 282/23]', '[361, 361, 1/23*w^3 + 10/23*w^2 + 36/23*w - 12/23]', '[389, 389, -8/23*w^3 + 35/23*w^2 + 80/23*w - 295/23]', '[389, 389, -4/23*w^3 + 29/23*w^2 - 6/23*w - 136/23]', '[389, 389, -4/23*w^3 - 17/23*w^2 + 40/23*w + 117/23]', '[389, 389, 2/23*w^3 + 20/23*w^2 - 20/23*w - 185/23]', '[400, 10, -8/23*w^3 + 12/23*w^2 + 80/23*w - 42/23]', '[401, 401, 11/23*w^3 - 5/23*w^2 - 179/23*w - 17/23]', '[401, 401, 2/23*w^3 + 20/23*w^2 - 43/23*w - 93/23]', '[401, 401, 1/23*w^3 + 10/23*w^2 + 36/23*w - 104/23]', '[401, 401, 11/23*w^3 - 28/23*w^2 - 156/23*w + 190/23]', '[419, 419, -6/23*w^3 - 14/23*w^2 + 83/23*w + 72/23]', '[419, 419, 3/23*w^3 + 7/23*w^2 - 76/23*w + 79/23]', '[419, 419, -6/23*w^3 + 32/23*w^2 + 37/23*w - 296/23]', '[419, 419, -1/23*w^3 + 13/23*w^2 + 56/23*w - 172/23]', '[421, 421, -8/23*w^3 + 12/23*w^2 + 57/23*w - 65/23]', '[421, 421, -12/23*w^3 + 18/23*w^2 + 143/23*w - 109/23]', '[421, 421, 12/23*w^3 - 18/23*w^2 - 143/23*w + 40/23]', '[421, 421, 8/23*w^3 - 12/23*w^2 - 57/23*w - 4/23]', '[436, 218, 7/23*w^3 + 24/23*w^2 - 70/23*w - 107/23]', '[436, 218, 9/23*w^3 - 2/23*w^2 + 2/23*w + 7/23]', '[436, 218, 11/23*w^3 - 74/23*w^2 + 28/23*w + 167/23]', '[436, 218, 7/23*w^3 - 45/23*w^2 - 1/23*w + 146/23]', '[439, 439, 7/23*w^3 - 22/23*w^2 - 93/23*w + 123/23]', '[439, 439, 1/23*w^3 + 10/23*w^2 + 13/23*w - 127/23]', '[439, 439, 5/23*w^3 + 4/23*w^2 - 73/23*w + 9/23]', '[439, 439, 7/23*w^3 + 1/23*w^2 - 116/23*w - 15/23]', '[441, 21, -4/23*w^3 + 6/23*w^2 + 86/23*w + 117/23]', '[441, 21, 4/23*w^3 - 6/23*w^2 - 86/23*w + 205/23]', '[449, 449, -11/23*w^3 + 5/23*w^2 + 133/23*w + 63/23]', '[449, 449, -9/23*w^3 + 2/23*w^2 + 90/23*w + 16/23]', '[449, 449, 9/23*w^3 - 25/23*w^2 - 67/23*w + 99/23]', '[449, 449, -11/23*w^3 + 28/23*w^2 + 110/23*w - 190/23]', '[464, 58, 2*w]', '[464, 58, -8/23*w^3 + 12/23*w^2 + 126/23*w - 42/23]', '[464, 58, 8/23*w^3 - 12/23*w^2 - 126/23*w + 88/23]', '[464, 58, -2*w + 2]', '[475, 95, -4/23*w^3 + 29/23*w^2 + 17/23*w - 90/23]', '[475, 95, -4/23*w^3 - 17/23*w^2 + 63/23*w + 278/23]', '[475, 95, -4/23*w^3 + 29/23*w^2 + 17/23*w - 320/23]', '[475, 95, 4/23*w^3 + 17/23*w^2 - 63/23*w - 48/23]', '[479, 479, 10/23*w^3 - 15/23*w^2 - 123/23*w - 74/23]', '[479, 479, 6/23*w^3 - 9/23*w^2 - 37/23*w + 158/23]', '[479, 479, -6/23*w^3 + 9/23*w^2 + 37/23*w + 118/23]', '[479, 479, 10/23*w^3 - 15/23*w^2 - 123/23*w + 202/23]', '[484, 22, 7/23*w^3 - 22/23*w^2 + 22/23*w + 31/23]', '[484, 22, 7/23*w^3 + 1/23*w^2 - 1/23*w - 38/23]', '[496, 62, 2*w + 4]', '[496, 62, -8/23*w^3 + 12/23*w^2 + 126/23*w + 50/23]', '[496, 62, 8/23*w^3 - 12/23*w^2 - 126/23*w + 180/23]', '[496, 62, -2*w + 6]', '[524, 262, 11/23*w^3 - 28/23*w^2 - 18/23*w + 75/23]', '[524, 262, -7/23*w^3 + 45/23*w^2 + 1/23*w - 100/23]', '[524, 262, -7/23*w^3 - 24/23*w^2 + 70/23*w + 61/23]', '[524, 262, -11/23*w^3 + 5/23*w^2 + 41/23*w + 40/23]', '[529, 23, -4/23*w^3 + 29/23*w^2 + 40/23*w - 274/23]', '[529, 23, w^2 - 6]', '[531, 177, -10/23*w^3 + 15/23*w^2 + 146/23*w + 5/23]', '[531, 177, -11/23*w^3 + 28/23*w^2 + 133/23*w - 167/23]', '[531, 177, -13/23*w^3 - 15/23*w^2 + 176/23*w + 294/23]', '[531, 177, 19/23*w^3 - 63/23*w^2 - 236/23*w + 646/23]', '[531, 177, -19/23*w^3 - 6/23*w^2 + 305/23*w + 366/23]', '[531, 177, 13/23*w^3 - 54/23*w^2 - 107/23*w + 442/23]', '[531, 177, -5/23*w^3 - 27/23*w^2 + 4/23*w + 60/23]', '[531, 177, 11/23*w^3 - 51/23*w^2 - 64/23*w + 236/23]', '[541, 541, 6/23*w^3 + 14/23*w^2 - 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255/23]', '[9956, 4978, w^3 - 4*w^2 - 10*w + 33]', '[9956, 4978, -3/23*w^3 - 7/23*w^2 + 53/23*w + 312/23]', '[9956, 4978, -31/23*w^3 + 81/23*w^2 + 333/23*w - 548/23]', '[9956, 4978, -1/23*w^3 - 10/23*w^2 + 10/23*w - 149/23]', '[9956, 4978, 21/23*w^3 - 66/23*w^2 - 118/23*w + 277/23]', '[9956, 4978, -1/23*w^3 + 13/23*w^2 - 105/23*w - 34/23]', '[9956, 4978, -13/23*w^3 - 38/23*w^2 + 130/23*w + 271/23]', '[9971, 767, -15/23*w^3 + 34/23*w^2 + 173/23*w - 4/23]', '[9971, 767, -3/23*w^3 - 53/23*w^2 + 76/23*w + 772/23]', '[9971, 767, 54/23*w^3 - 58/23*w^2 - 747/23*w + 111/23]', '[9971, 767, 14/23*w^3 + 2/23*w^2 - 209/23*w - 7/23]', '[9971, 767, 15/23*w^3 + 58/23*w^2 - 265/23*w - 1054/23]', '[9971, 767, -14/23*w^3 + 44/23*w^2 + 163/23*w - 200/23]', '[9971, 767, 15/23*w^3 - 11/23*w^2 - 196/23*w + 188/23]', '[9971, 767, 42/23*w^3 - 86/23*w^2 - 535/23*w + 692/23]', '[10000, 10, 10]'], 'label': '4.4.19600.1', 'narrow_class_no': 2, 'primes': ['[4, 2, -2/23*w^3 + 3/23*w^2 - 3/23*w + 1/23]', '[9, 3, -2/23*w^3 + 3/23*w^2 + 43/23*w + 24/23]', '[9, 3, -2/23*w^3 + 3/23*w^2 + 43/23*w - 68/23]', '[19, 19, -2/23*w^3 + 3/23*w^2 - 3/23*w + 24/23]', '[19, 19, -6/23*w^3 + 9/23*w^2 + 83/23*w - 20/23]', '[19, 19, 6/23*w^3 - 9/23*w^2 - 83/23*w + 66/23]', '[19, 19, -2/23*w^3 + 3/23*w^2 - 3/23*w - 22/23]', '[25, 5, -4/23*w^3 + 6/23*w^2 + 40/23*w - 21/23]', '[29, 29, w]', '[29, 29, -4/23*w^3 + 6/23*w^2 + 63/23*w - 21/23]', '[29, 29, 4/23*w^3 - 6/23*w^2 - 63/23*w + 44/23]', '[29, 29, -w + 1]', '[31, 31, w + 2]', '[31, 31, -4/23*w^3 + 6/23*w^2 + 63/23*w + 25/23]', '[31, 31, 4/23*w^3 - 6/23*w^2 - 63/23*w + 90/23]', '[31, 31, -w + 3]', '[49, 7, -2/23*w^3 + 3/23*w^2 + 43/23*w - 22/23]', '[59, 59, -20/23*w^3 + 30/23*w^2 + 269/23*w - 128/23]', '[59, 59, -8/23*w^3 + 12/23*w^2 + 103/23*w - 88/23]', '[59, 59, -8/23*w^3 + 12/23*w^2 + 103/23*w - 19/23]', '[59, 59, -4/23*w^3 + 6/23*w^2 + 17/23*w - 44/23]', '[109, 109, -9/23*w^3 + 2/23*w^2 + 113/23*w + 62/23]', '[109, 109, 4/23*w^3 - 6/23*w^2 - 63/23*w - 71/23]', '[109, 109, 7/23*w^3 - 22/23*w^2 - 47/23*w + 100/23]', '[109, 109, 9/23*w^3 - 25/23*w^2 - 90/23*w + 168/23]', '[121, 11, -2/23*w^3 + 3/23*w^2 + 20/23*w - 91/23]', '[121, 11, 2/23*w^3 - 3/23*w^2 - 20/23*w - 70/23]', '[131, 131, -5/23*w^3 + 19/23*w^2 + 50/23*w - 101/23]', '[131, 131, -3/23*w^3 + 16/23*w^2 + 7/23*w - 125/23]', '[131, 131, 3/23*w^3 + 7/23*w^2 - 30/23*w - 105/23]', '[131, 131, 5/23*w^3 + 4/23*w^2 - 73/23*w - 37/23]', '[139, 139, -2/23*w^3 - 20/23*w^2 + 43/23*w + 323/23]', '[139, 139, 17/23*w^3 - 37/23*w^2 - 216/23*w + 302/23]', '[139, 139, 17/23*w^3 - 14/23*w^2 - 239/23*w - 66/23]', '[139, 139, -2/23*w^3 + 26/23*w^2 - 3/23*w - 344/23]', '[149, 149, -1/23*w^3 - 10/23*w^2 + 33/23*w - 34/23]', '[149, 149, 1/23*w^3 + 10/23*w^2 - 33/23*w - 196/23]', '[149, 149, -1/23*w^3 + 13/23*w^2 + 10/23*w - 218/23]', '[149, 149, 1/23*w^3 - 13/23*w^2 - 10/23*w - 12/23]', '[169, 13, 6/23*w^3 - 9/23*w^2 - 37/23*w + 20/23]', '[169, 13, -10/23*w^3 + 15/23*w^2 + 123/23*w - 64/23]', '[199, 199, -1/23*w^3 + 13/23*w^2 - 13/23*w - 195/23]', '[199, 199, 3/23*w^3 + 7/23*w^2 - 53/23*w + 33/23]', '[199, 199, 3/23*w^3 - 16/23*w^2 - 30/23*w + 10/23]', '[199, 199, 1/23*w^3 + 10/23*w^2 - 10/23*w - 196/23]', '[251, 251, 6/23*w^3 - 9/23*w^2 - 14/23*w + 43/23]', '[251, 251, 14/23*w^3 - 21/23*w^2 - 186/23*w + 62/23]', '[251, 251, 4/23*w^3 - 6/23*w^2 - 109/23*w + 228/23]', '[251, 251, 6/23*w^3 - 9/23*w^2 - 14/23*w - 26/23]', '[271, 271, -8/23*w^3 + 12/23*w^2 + 126/23*w + 27/23]', '[271, 271, 8/23*w^3 - 35/23*w^2 - 80/23*w + 226/23]', '[271, 271, 13/23*w^3 - 31/23*w^2 - 153/23*w + 189/23]', '[271, 271, 8/23*w^3 - 12/23*w^2 - 126/23*w + 157/23]', '[281, 281, -w^2 + 2*w + 9]', '[281, 281, 13/23*w^3 - 8/23*w^2 - 153/23*w + 28/23]', '[281, 281, -13/23*w^3 + 31/23*w^2 + 130/23*w - 120/23]', '[281, 281, 11/23*w^3 - 28/23*w^2 - 87/23*w + 190/23]', '[289, 17, -11/23*w^3 + 51/23*w^2 + 110/23*w - 581/23]', '[289, 17, -8/23*w^3 + 35/23*w^2 + 80/23*w - 410/23]', '[311, 311, 5/23*w^3 + 4/23*w^2 - 50/23*w - 106/23]', '[311, 311, -7/23*w^3 + 22/23*w^2 + 70/23*w - 100/23]', '[311, 311, 7/23*w^3 + 1/23*w^2 - 93/23*w - 15/23]', '[311, 311, -5/23*w^3 + 19/23*w^2 + 27/23*w - 147/23]', '[389, 389, -8/23*w^3 + 35/23*w^2 + 80/23*w - 295/23]', '[389, 389, -4/23*w^3 + 29/23*w^2 - 6/23*w - 136/23]', '[389, 389, -4/23*w^3 - 17/23*w^2 + 40/23*w + 117/23]', '[389, 389, 2/23*w^3 + 20/23*w^2 - 20/23*w - 185/23]', '[401, 401, 11/23*w^3 - 5/23*w^2 - 179/23*w - 17/23]', '[401, 401, 2/23*w^3 + 20/23*w^2 - 43/23*w - 93/23]', '[401, 401, 1/23*w^3 + 10/23*w^2 + 36/23*w - 104/23]', '[401, 401, 11/23*w^3 - 28/23*w^2 - 156/23*w + 190/23]', '[419, 419, -6/23*w^3 - 14/23*w^2 + 83/23*w + 72/23]', '[419, 419, 3/23*w^3 + 7/23*w^2 - 76/23*w + 79/23]', '[419, 419, -6/23*w^3 + 32/23*w^2 + 37/23*w - 296/23]', '[419, 419, -1/23*w^3 + 13/23*w^2 + 56/23*w - 172/23]', '[421, 421, -8/23*w^3 + 12/23*w^2 + 57/23*w - 65/23]', '[421, 421, -12/23*w^3 + 18/23*w^2 + 143/23*w - 109/23]', '[421, 421, 12/23*w^3 - 18/23*w^2 - 143/23*w + 40/23]', '[421, 421, 8/23*w^3 - 12/23*w^2 - 57/23*w - 4/23]', '[439, 439, 7/23*w^3 - 22/23*w^2 - 93/23*w + 123/23]', '[439, 439, 1/23*w^3 + 10/23*w^2 + 13/23*w - 127/23]', '[439, 439, 5/23*w^3 + 4/23*w^2 - 73/23*w + 9/23]', '[439, 439, 7/23*w^3 + 1/23*w^2 - 116/23*w - 15/23]', '[449, 449, -11/23*w^3 + 5/23*w^2 + 133/23*w + 63/23]', '[449, 449, -9/23*w^3 + 2/23*w^2 + 90/23*w + 16/23]', '[449, 449, 9/23*w^3 - 25/23*w^2 - 67/23*w + 99/23]', '[449, 449, -11/23*w^3 + 28/23*w^2 + 110/23*w - 190/23]', '[479, 479, 10/23*w^3 - 15/23*w^2 - 123/23*w - 74/23]', '[479, 479, 6/23*w^3 - 9/23*w^2 - 37/23*w + 158/23]', '[479, 479, -6/23*w^3 + 9/23*w^2 + 37/23*w + 118/23]', '[479, 479, 10/23*w^3 - 15/23*w^2 - 123/23*w + 202/23]', '[529, 23, -4/23*w^3 + 29/23*w^2 + 40/23*w - 274/23]', '[529, 23, w^2 - 6]', '[541, 541, 6/23*w^3 + 14/23*w^2 - 83/23*w - 141/23]', '[541, 541, -6/23*w^3 + 32/23*w^2 + 37/23*w - 227/23]', '[541, 541, 6/23*w^3 + 14/23*w^2 - 83/23*w - 164/23]', '[541, 541, -6/23*w^3 + 32/23*w^2 + 37/23*w - 204/23]', '[569, 569, -5/23*w^3 - 4/23*w^2 + 50/23*w - 78/23]', '[569, 569, -7/23*w^3 + 22/23*w^2 + 70/23*w - 284/23]', '[569, 569, -5/23*w^3 + 19/23*w^2 + 50/23*w - 262/23]', '[569, 569, 5/23*w^3 - 19/23*w^2 - 27/23*w - 37/23]', '[619, 619, -2/23*w^3 - 43/23*w^2 + 66/23*w + 622/23]', '[619, 619, 17/23*w^3 - 37/23*w^2 - 216/23*w + 233/23]', '[619, 619, 17/23*w^3 - 14/23*w^2 - 239/23*w + 3/23]', '[619, 619, -2/23*w^3 + 49/23*w^2 - 26/23*w - 643/23]', '[641, 641, -1/23*w^3 + 13/23*w^2 - 59/23*w + 127/23]', '[641, 641, -14/23*w^3 + 44/23*w^2 + 117/23*w - 246/23]', '[641, 641, -11/23*w^3 + 5/23*w^2 + 179/23*w + 201/23]', '[641, 641, -1/23*w^3 - 10/23*w^2 - 36/23*w - 80/23]', '[691, 691, 5/23*w^3 - 65/23*w^2 - 4/23*w + 837/23]', '[691, 691, -2/23*w^3 + 26/23*w^2 + 20/23*w - 321/23]', '[691, 691, -2/23*w^3 - 20/23*w^2 + 66/23*w + 277/23]', '[691, 691, -5/23*w^3 - 50/23*w^2 + 119/23*w + 773/23]', '[701, 701, 2/23*w^3 + 20/23*w^2 - 66/23*w - 185/23]', '[701, 701, w^2 - 7]', '[701, 701, -2/23*w^3 + 26/23*w^2 + 20/23*w - 183/23]', '[701, 701, -2/23*w^3 + 26/23*w^2 + 20/23*w - 229/23]', '[709, 709, -18/23*w^3 + 27/23*w^2 + 226/23*w - 152/23]', '[709, 709, -33/23*w^3 + 38/23*w^2 + 445/23*w - 41/23]', '[709, 709, -33/23*w^3 + 61/23*w^2 + 422/23*w - 409/23]', '[709, 709, 18/23*w^3 - 27/23*w^2 - 226/23*w + 83/23]', '[719, 719, -4/23*w^3 + 29/23*w^2 + 40/23*w - 136/23]', '[719, 719, 12/23*w^3 - 18/23*w^2 - 166/23*w + 155/23]', '[719, 719, w^2 - 12]', '[719, 719, 4/23*w^3 + 17/23*w^2 - 86/23*w - 71/23]', '[809, 809, -10/23*w^3 + 15/23*w^2 + 123/23*w - 248/23]', '[809, 809, 7/23*w^3 - 22/23*w^2 - 93/23*w + 307/23]', '[809, 809, 7/23*w^3 + 1/23*w^2 - 116/23*w - 199/23]', '[809, 809, 10/23*w^3 - 15/23*w^2 - 123/23*w - 120/23]', '[811, 811, -7/23*w^3 - 1/23*w^2 + 93/23*w - 31/23]', '[811, 811, -7/23*w^3 + 22/23*w^2 + 93/23*w - 100/23]', '[811, 811, 7/23*w^3 + 1/23*w^2 - 116/23*w + 8/23]', '[811, 811, 1/23*w^3 + 10/23*w^2 + 13/23*w - 150/23]', '[821, 821, -4/23*w^3 + 29/23*w^2 + 17/23*w - 182/23]', '[821, 821, 4/23*w^3 + 17/23*w^2 - 63/23*w - 186/23]', '[821, 821, -4/23*w^3 + 29/23*w^2 + 17/23*w - 228/23]', '[821, 821, 4/23*w^3 + 17/23*w^2 - 63/23*w - 140/23]', '[839, 839, -16/23*w^3 + 70/23*w^2 + 160/23*w - 751/23]', '[839, 839, 22/23*w^3 - 33/23*w^2 - 289/23*w + 196/23]', '[839, 839, -22/23*w^3 + 33/23*w^2 + 289/23*w - 104/23]', '[839, 839, -16/23*w^3 - 22/23*w^2 + 252/23*w + 537/23]', '[859, 859, -7/23*w^3 + 22/23*w^2 + 47/23*w - 192/23]', '[859, 859, -9/23*w^3 + 2/23*w^2 + 113/23*w - 30/23]', '[859, 859, -9/23*w^3 + 25/23*w^2 + 90/23*w - 76/23]', '[859, 859, 7/23*w^3 + 1/23*w^2 - 70/23*w - 130/23]', '[971, 971, -10/23*w^3 + 15/23*w^2 + 146/23*w + 97/23]', '[971, 971, -14/23*w^3 - 2/23*w^2 + 186/23*w + 99/23]', '[971, 971, 14/23*w^3 - 44/23*w^2 - 140/23*w + 269/23]', '[971, 971, -10/23*w^3 + 15/23*w^2 + 146/23*w - 248/23]']}
• 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': [29, 16, -15, -2, 1], 'conductor': 140, 'degree': 4, 'dirichlet_group': [1, 139, 29, 111], 'disc_abs': 19600, 'disc_rad': 70, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[2, 2]]], [5, [0]], [7, [0]], [11, [[2, 2]]], [13, [[2, 2]]], [17, [[2, 2]]], [19, [[1, 4]]], [23, [[2, 2]]], [29, [[1, 4]]], [31, [[1, 4]]], [37, [[2, 2]]], [41, [[2, 2]]], [43, [[2, 2]]], [47, [[2, 2]]], [53, [[2, 2]]], [59, [[1, 4]]]], 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 2, 2], 'galois_label': '4T2', 'galt': 2, 'grd': 11.832159566199232, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.19600.1', 'local_algs': ['2.4.4.1', '5.4.2.1', '7.4.2.1'], 'monogenic': -1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 5, 7], 'rd': 11.8321595662, 'regulator': {'__RealLiteral__': 0, 'data': '6.60263997027', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-35.0.1', '-1.-1.1', '-7.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{2}{23} a^{3} - \\frac{3}{23} a^{2} - \\frac{20}{23} a + \\frac{22}{23} \\)', '\\( \\frac{9}{23} a^{3} - \\frac{2}{23} a^{2} - \\frac{136}{23} a - \\frac{108}{23} \\)', '\\( \\frac{3}{23} a^{3} + \\frac{7}{23} a^{2} - \\frac{7}{23} a - \\frac{13}{23} \\)'], 'unitsGmodule': [[1, 1], [4, 1]], 'unitsType': 'Type II (i)', 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/23*a^3 + 10/23*a^2 - 10/23*a + 11/23']}