Hilbert modular form data - 4.4.3600.1-59.3-e

Formats: - HTML - YAML - JSON - 2024-05-05T07:22:34.099878

• 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': 3600, 'field_bad_primes': [2, 3, 5], 'field_label': '4.4.3600.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.3600.1-59.3-e', 'label_nsuffix': 4, 'label_suffix': 'e', 'level_bad_primes': [59], 'level_ideal': '[59,59,-3/7*w^3 + 1/7*w^2 + 32/7*w + 13/7]', 'level_label': '59.3', 'level_norm': 59, 'parallel_weight': 2, 'short_label': '59.3-e', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[59,59,-3/7*w^3 + 1/7*w^2 + 32/7*w + 13/7]', 1]], 'hecke_eigenvalues': ['e', '3*e + 6', 5, '-2*e - 3', '2*e + 3', '3*e + 7', 0, '-3*e - 6', '-5*e - 9', '-10*e - 15', '9*e + 11', -1, '2*e + 3', 3, '-3*e - 9', -12, '-4*e - 3', '6*e + 9', '-8*e - 12', 'e - 6', '-3*e + 3', '-3*e + 7', 9, '-6*e - 20', '-15*e - 21', 15, '4*e + 6', '4*e + 6', '-12*e - 18', '-15*e - 24', '15*e + 16', 15, '5*e + 15', '-4*e - 6', '-15*e - 15', '4*e + 18', 'e + 6', '-16*e - 27', '11*e + 6', '-12*e - 18', 15, '-2*e - 18', 15, '2*e - 3', '-3*e - 3', '-2*e - 24', '-6*e - 15', '-6*e + 1', '-9*e - 6', '5*e + 30', '-15*e - 20', '18*e + 19', '-15*e - 18', '-3*e - 5', '6*e + 11', '16*e + 24', '-6*e - 24', '-3*e - 2', '16*e + 24', '-3*e + 9', 6, '-3*e - 7', 15, '-10*e - 15', '-15*e - 5', '6*e + 25', '-12*e - 17', '3*e + 23', '-12*e - 27', '11*e + 9', '-12*e - 8', '9*e + 26', '26*e + 39', '3*e + 25', '-15*e - 37', '15*e + 11', '-12*e - 42', '15*e + 26', '-3*e + 14', '-9*e - 36', '14*e + 21', '5*e + 15', '-3*e - 12', '12*e + 6', '-6*e - 11', '18*e + 30', '18*e + 10', '4*e - 9', '-12*e - 33', 5, '-26*e - 39', '3*e + 27', '-12*e + 2', -15, '-10*e - 45', '12*e + 33', '-7*e - 18', '-13*e - 42', '-6*e - 29', '-16*e - 15', '11*e + 3', '6*e - 18', '30*e + 33', '-24*e - 33', '-5*e - 42', '-17*e - 33', '3*e + 27', '3*e - 23', '5*e + 30', '-2*e + 39', -3, '-7*e + 9', 27, '-4*e + 24', '6*e + 39', '-9*e - 11', '6*e + 24', '10*e - 3', -18, '-32*e - 51', 'e - 24', '11*e + 3', '30*e + 39', '-6*e - 30', '-10*e - 6', '-6*e + 11', '19*e + 36', '-17*e - 18', '21*e + 14', '12*e + 42', '-12*e - 14', '30*e + 49', '27*e + 27', '12*e + 44', '-30*e - 29', '24*e + 17', '-12*e - 2', '-9*e + 14', '28*e + 42', '-24*e - 36', '3*e - 8', -27, '23*e + 30', '24*e + 26', '20*e + 15', '-17*e + 12', '27*e + 23', '6*e + 1', '-9*e - 9', -45, '-3*e - 42', '3*e + 52', '-20*e - 45'], 'hecke_polynomial': 'x^2 + 3*x + 1', 'label': '4.4.3600.1-59.3-e'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 3600, 'ideals': ['[1, 1, 1]', '[4, 2, -2/7*w^3 + 3/7*w^2 + 19/7*w - 17/7]', '[9, 3, -2/7*w^3 + 3/7*w^2 + 19/7*w - 10/7]', '[11, 11, -w - 1]', '[11, 11, 4/7*w^3 - 6/7*w^2 - 31/7*w + 27/7]', '[11, 11, 4/7*w^3 - 6/7*w^2 - 31/7*w + 6/7]', '[11, 11, -w + 2]', '[16, 2, 2]', '[25, 5, 4/7*w^3 - 6/7*w^2 - 24/7*w + 13/7]', '[36, 6, 2/7*w^3 - 3/7*w^2 - 19/7*w + 31/7]', '[44, 22, 3/7*w^3 - 8/7*w^2 - 18/7*w + 15/7]', '[44, 22, 1/7*w^3 + 2/7*w^2 - 6/7*w - 23/7]', '[44, 22, -1/7*w^3 + 5/7*w^2 - 1/7*w - 26/7]', '[44, 22, -3/7*w^3 + 1/7*w^2 + 25/7*w - 8/7]', '[49, 7, 5/7*w^3 - 11/7*w^2 - 23/7*w + 25/7]', '[49, 7, w^3 - w^2 - 7*w + 1]', '[59, 59, 3/7*w^3 - 1/7*w^2 - 32/7*w + 15/7]', '[59, 59, -3/7*w^3 + 8/7*w^2 + 25/7*w - 43/7]', '[59, 59, -3/7*w^3 + 1/7*w^2 + 32/7*w + 13/7]', '[59, 59, 3/7*w^3 - 8/7*w^2 - 25/7*w + 15/7]', '[61, 61, -8/7*w^3 + 12/7*w^2 + 55/7*w - 26/7]', '[61, 61, -4/7*w^3 + 6/7*w^2 + 17/7*w - 6/7]', '[61, 61, 6/7*w^3 - 9/7*w^2 - 50/7*w + 16/7]', '[61, 61, 8/7*w^3 - 12/7*w^2 - 55/7*w + 33/7]', '[64, 4, -4/7*w^3 + 6/7*w^2 + 38/7*w - 34/7]', '[71, 71, -3/7*w^3 + 1/7*w^2 + 25/7*w - 15/7]', '[71, 71, -w^3 + w^2 + 8*w - 2]', '[71, 71, w^3 - 2*w^2 - 7*w + 6]', '[71, 71, -3/7*w^3 + 8/7*w^2 + 18/7*w - 8/7]', '[81, 3, 3]', '[99, 33, 3/7*w^3 - 8/7*w^2 - 25/7*w + 8/7]', '[99, 33, -3/7*w^3 + 8/7*w^2 + 25/7*w - 50/7]', '[99, 33, 3/7*w^3 - 1/7*w^2 - 32/7*w - 20/7]', '[99, 33, -3/7*w^3 + 1/7*w^2 + 32/7*w - 22/7]', '[100, 10, -4/7*w^3 + 13/7*w^2 + 17/7*w - 41/7]', '[109, 109, -6/7*w^3 + 9/7*w^2 + 50/7*w - 30/7]', '[109, 109, -2/7*w^3 + 3/7*w^2 + 26/7*w - 10/7]', '[109, 109, 2/7*w^3 - 3/7*w^2 - 26/7*w + 17/7]', '[109, 109, -6/7*w^3 + 9/7*w^2 + 50/7*w - 23/7]', '[121, 11, -6/7*w^3 + 9/7*w^2 + 36/7*w - 23/7]', '[121, 11, -w^2 + w + 6]', '[121, 11, 6/7*w^3 - 9/7*w^2 - 36/7*w + 16/7]', '[121, 11, 4/7*w^3 - 6/7*w^2 - 38/7*w + 13/7]', '[121, 11, -4/7*w^3 + 6/7*w^2 + 38/7*w - 27/7]', '[121, 11, w^2 - w - 2]', '[121, 121, 2/7*w^3 - 10/7*w^2 - 5/7*w + 45/7]', '[121, 121, 2/7*w^3 - 10/7*w^2 - 5/7*w + 24/7]', '[121, 121, -2/7*w^3 - 4/7*w^2 + 19/7*w + 11/7]', '[121, 121, -2/7*w^3 - 4/7*w^2 + 19/7*w + 32/7]', '[131, 131, 5/7*w^3 - 4/7*w^2 - 37/7*w + 18/7]', '[131, 131, 3/7*w^3 - 1/7*w^2 - 18/7*w - 20/7]', '[131, 131, 5/7*w^3 - 4/7*w^2 - 44/7*w + 18/7]', '[131, 131, 1/7*w^3 - 5/7*w^2 - 13/7*w + 33/7]', '[144, 6, -4/7*w^3 + 6/7*w^2 + 38/7*w - 20/7]', '[169, 13, w^3 - 2*w^2 - 5*w + 3]', '[169, 13, 9/7*w^3 - 10/7*w^2 - 61/7*w + 3/7]', '[176, 22, -2*w - 2]', '[176, 22, 8/7*w^3 - 12/7*w^2 - 62/7*w + 54/7]', '[176, 22, 8/7*w^3 - 12/7*w^2 - 62/7*w + 12/7]', '[176, 22, -2*w + 4]', '[179, 179, 9/7*w^3 - 10/7*w^2 - 75/7*w + 31/7]', '[179, 179, 1/7*w^3 - 5/7*w^2 - 20/7*w + 33/7]', '[179, 179, 3/7*w^3 - 1/7*w^2 - 18/7*w - 34/7]', '[179, 179, 4/7*w^3 + 1/7*w^2 - 31/7*w - 36/7]', '[181, 181, -2/7*w^3 + 10/7*w^2 + 5/7*w - 38/7]', '[181, 181, -2/7*w^3 + 10/7*w^2 + 5/7*w - 31/7]', '[181, 181, 2/7*w^3 + 4/7*w^2 - 19/7*w - 18/7]', '[181, 181, 2/7*w^3 + 4/7*w^2 - 19/7*w - 25/7]', '[191, 191, w^3 - 2*w^2 - 7*w + 5]', '[191, 191, -1/7*w^3 + 5/7*w^2 - 8/7*w - 19/7]', '[191, 191, 1/7*w^3 + 2/7*w^2 + 1/7*w - 23/7]', '[191, 191, -w^3 + w^2 + 8*w - 3]', '[196, 14, w^2 - w - 3]', '[196, 14, w^2 - w - 5]', '[225, 15, w^2 - w - 4]', '[229, 229, 6/7*w^3 - 9/7*w^2 - 43/7*w + 58/7]', '[229, 229, -9/7*w^3 + 17/7*w^2 + 54/7*w - 45/7]', '[229, 229, 9/7*w^3 - 10/7*w^2 - 61/7*w + 17/7]', '[229, 229, 6/7*w^3 - 9/7*w^2 - 43/7*w - 12/7]', '[236, 118, -1/7*w^3 - 2/7*w^2 + 34/7*w - 47/7]', '[236, 118, 13/7*w^3 - 23/7*w^2 - 99/7*w + 114/7]', '[236, 118, -w^3 + 2*w^2 + 6*w - 3]', '[236, 118, -5/7*w^3 + 11/7*w^2 + 23/7*w - 46/7]', '[239, 239, -4/7*w^3 - 1/7*w^2 + 24/7*w + 22/7]', '[239, 239, 2*w - 5]', '[239, 239, -2*w - 3]', '[239, 239, -5/7*w^3 + 4/7*w^2 + 51/7*w + 17/7]', '[241, 241, 9/7*w^3 - 10/7*w^2 - 61/7*w + 10/7]', '[241, 241, w^3 - w^2 - 6*w + 2]', '[241, 241, w^3 - 2*w^2 - 5*w + 4]', '[241, 241, -9/7*w^3 + 17/7*w^2 + 54/7*w - 52/7]', '[244, 122, w^3 - 3*w^2 - 5*w + 12]', '[244, 122, 3/7*w^3 - 15/7*w^2 + 3/7*w + 22/7]', '[244, 122, 3/7*w^3 - 8/7*w^2 - 18/7*w + 57/7]', '[244, 122, -9/7*w^3 + 24/7*w^2 + 54/7*w - 101/7]', '[251, 251, -5/7*w^3 + 4/7*w^2 + 23/7*w + 10/7]', '[251, 251, 11/7*w^3 - 13/7*w^2 - 80/7*w + 34/7]', '[251, 251, -11/7*w^3 + 20/7*w^2 + 73/7*w - 48/7]', '[251, 251, 10/7*w^3 - 15/7*w^2 - 74/7*w + 22/7]', '[256, 4, 4]', '[275, 55, -6/7*w^3 + 2/7*w^2 + 43/7*w - 9/7]', '[275, 55, 6/7*w^3 - 16/7*w^2 - 29/7*w + 65/7]', '[275, 55, -6/7*w^3 + 2/7*w^2 + 43/7*w + 26/7]', '[275, 55, 6/7*w^3 - 16/7*w^2 - 29/7*w + 30/7]', '[284, 142, 2/7*w^3 - 3/7*w^2 - 33/7*w + 45/7]', '[284, 142, 1/7*w^3 - 5/7*w^2 - 13/7*w + 54/7]', '[284, 142, 13/7*w^3 - 30/7*w^2 - 78/7*w + 121/7]', '[284, 142, 4/7*w^3 - 13/7*w^2 - 3/7*w + 27/7]', '[289, 17, -10/7*w^3 + 15/7*w^2 + 67/7*w - 36/7]', '[289, 17, 6/7*w^3 - 9/7*w^2 - 29/7*w + 16/7]', '[311, 311, 5/7*w^3 - 4/7*w^2 - 44/7*w + 32/7]', '[311, 311, 1/7*w^3 + 2/7*w^2 - 20/7*w - 30/7]', '[311, 311, -1/7*w^3 + 5/7*w^2 + 13/7*w - 47/7]', '[311, 311, -5/7*w^3 + 11/7*w^2 + 37/7*w - 11/7]', '[324, 6, -6/7*w^3 + 9/7*w^2 + 57/7*w - 51/7]', '[349, 349, -6/7*w^3 + 16/7*w^2 + 36/7*w - 93/7]', '[349, 349, 11/7*w^3 - 13/7*w^2 - 94/7*w + 6/7]', '[349, 349, 9/7*w^3 - 3/7*w^2 - 75/7*w - 25/7]', '[349, 349, 2*w^3 - 3*w^2 - 14*w + 8]', '[359, 359, w^3 - 2*w^2 - 6*w + 2]', '[359, 359, 2/7*w^3 - 10/7*w^2 - 19/7*w + 52/7]', '[359, 359, 2/7*w^3 + 4/7*w^2 - 33/7*w - 25/7]', '[359, 359, -w^3 + w^2 + 7*w - 5]', '[361, 19, -8/7*w^3 + 12/7*w^2 + 48/7*w - 33/7]', '[361, 19, 8/7*w^3 - 12/7*w^2 - 48/7*w + 19/7]', '[396, 66, -3/7*w^3 + 8/7*w^2 + 4/7*w - 29/7]', '[396, 66, 9/7*w^3 - 10/7*w^2 - 68/7*w + 31/7]', '[396, 66, 9/7*w^3 - 17/7*w^2 - 61/7*w + 38/7]', '[396, 66, -3/7*w^3 + 1/7*w^2 + 11/7*w + 20/7]', '[400, 10, 8/7*w^3 - 12/7*w^2 - 48/7*w + 26/7]', '[409, 409, 1/7*w^3 + 2/7*w^2 - 13/7*w - 44/7]', '[409, 409, -1/7*w^3 - 2/7*w^2 + 13/7*w - 26/7]', '[409, 409, 1/7*w^3 - 5/7*w^2 - 6/7*w - 16/7]', '[409, 409, -1/7*w^3 + 5/7*w^2 + 6/7*w - 54/7]', '[419, 419, -6/7*w^3 + 16/7*w^2 + 36/7*w - 37/7]', '[419, 419, -2/7*w^3 + 10/7*w^2 - 2/7*w - 45/7]', '[419, 419, 2/7*w^3 + 4/7*w^2 - 12/7*w - 39/7]', '[419, 419, 6/7*w^3 - 2/7*w^2 - 50/7*w + 9/7]', '[421, 421, 13/7*w^3 - 16/7*w^2 - 92/7*w + 30/7]', '[421, 421, -3/7*w^3 + 15/7*w^2 + 18/7*w - 71/7]', '[421, 421, -w^3 + 3*w^2 + 6*w - 13]', '[421, 421, -13/7*w^3 + 23/7*w^2 + 85/7*w - 65/7]', '[431, 431, w^2 - 2*w - 7]', '[431, 431, -4/7*w^3 - 1/7*w^2 + 38/7*w - 13/7]', '[431, 431, 4/7*w^3 - 13/7*w^2 - 24/7*w + 20/7]', '[431, 431, w^2 - 8]', '[436, 218, w^3 - 2*w^2 - 8*w + 13]', '[436, 218, 1/7*w^3 + 2/7*w^2 - 20/7*w + 33/7]', '[436, 218, 3/7*w^3 - 1/7*w^2 - 39/7*w + 50/7]', '[436, 218, 5/7*w^3 - 11/7*w^2 - 37/7*w + 74/7]', '[441, 21, -5/7*w^3 + 18/7*w^2 + 16/7*w - 46/7]', '[441, 21, w^3 - 8*w - 4]', '[479, 479, 1/7*w^3 + 2/7*w^2 - 27/7*w - 16/7]', '[479, 479, 9/7*w^3 - 17/7*w^2 - 68/7*w + 38/7]', '[479, 479, 9/7*w^3 - 10/7*w^2 - 75/7*w + 38/7]', '[479, 479, -1/7*w^3 + 5/7*w^2 + 20/7*w - 40/7]', '[484, 22, -2/7*w^3 + 3/7*w^2 + 33/7*w - 17/7]', '[484, 22, -2/7*w^3 + 3/7*w^2 + 19/7*w - 45/7]', '[484, 22, 10/7*w^3 - 15/7*w^2 - 81/7*w + 43/7]', '[484, 22, w^3 - 3*w^2 - 5*w + 10]', '[484, 22, -5/7*w^3 + 18/7*w^2 + 16/7*w - 53/7]', '[484, 22, -2/7*w^3 + 3/7*w^2 + 19/7*w + 25/7]', '[484, 242, -13/7*w^3 + 16/7*w^2 + 92/7*w - 23/7]', '[484, 242, -w^3 + w^2 + 5*w - 2]', '[484, 242, -w^3 + 2*w^2 + 4*w - 3]', '[484, 242, -13/7*w^3 + 23/7*w^2 + 85/7*w - 72/7]', '[491, 491, 10/7*w^3 - 8/7*w^2 - 74/7*w + 15/7]', '[491, 491, 2/7*w^3 - 3/7*w^2 - 33/7*w + 52/7]', '[491, 491, 11/7*w^3 - 6/7*w^2 - 87/7*w - 1/7]', '[491, 491, 5/7*w^3 + 3/7*w^2 - 30/7*w - 31/7]', '[524, 262, -3/7*w^3 + 8/7*w^2 + 32/7*w - 57/7]', '[524, 262, w^3 - w^2 - 9*w + 6]', '[524, 262, -2/7*w^3 + 3/7*w^2 + 33/7*w - 59/7]', '[524, 262, w^3 - 3*w^2 - 3*w + 8]', '[529, 23, -6/7*w^3 + 9/7*w^2 + 57/7*w - 16/7]', '[529, 23, 6/7*w^3 - 9/7*w^2 - 57/7*w + 44/7]', '[531, 177, 2/7*w^3 - 3/7*w^2 + 2/7*w - 32/7]', '[531, 177, 10/7*w^3 - 15/7*w^2 - 74/7*w + 71/7]', '[531, 177, -10/7*w^3 + 15/7*w^2 + 74/7*w - 8/7]', '[531, 177, -2/7*w^3 + 3/7*w^2 - 2/7*w - 31/7]', '[539, 77, -4/7*w^3 - 1/7*w^2 + 38/7*w - 20/7]', '[539, 77, 1/7*w^3 - 5/7*w^2 + 8/7*w + 33/7]', '[539, 77, -w^2 + 2*w + 8]', '[539, 77, w^3 - 2*w^2 - 7*w + 3]', '[539, 77, -w^3 + w^2 + 8*w - 5]', '[539, 77, -w^2 + 9]', '[539, 77, -1/7*w^3 - 2/7*w^2 - 1/7*w + 37/7]', '[539, 77, 4/7*w^3 - 13/7*w^2 - 24/7*w + 13/7]', '[541, 541, 4/7*w^3 - 6/7*w^2 - 45/7*w + 13/7]', '[541, 541, -8/7*w^3 + 12/7*w^2 + 69/7*w - 47/7]', '[541, 541, 8/7*w^3 - 12/7*w^2 - 69/7*w + 26/7]', '[541, 541, 4/7*w^3 - 6/7*w^2 - 45/7*w + 34/7]', '[549, 183, -1/7*w^3 - 9/7*w^2 + 20/7*w + 58/7]', '[549, 183, -1/7*w^3 - 9/7*w^2 + 20/7*w + 16/7]', '[549, 183, -3/7*w^3 + 1/7*w^2 + 32/7*w + 41/7]', '[549, 183, -1/7*w^3 + 12/7*w^2 - 1/7*w - 68/7]', '[576, 12, 4/7*w^3 - 6/7*w^2 - 38/7*w + 62/7]', '[599, 599, -3/7*w^3 + 15/7*w^2 + 4/7*w - 78/7]', '[599, 599, w^3 - 2*w^2 - 5*w + 11]', '[599, 599, -4/7*w^3 + 13/7*w^2 + 31/7*w - 76/7]', '[599, 599, 3/7*w^3 + 6/7*w^2 - 25/7*w - 62/7]', '[601, 601, 11/7*w^3 - 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79/7]', '[9791, 9791, -19/7*w^3 + 18/7*w^2 + 163/7*w - 60/7]', '[9791, 9791, -12/7*w^3 + 4/7*w^2 + 93/7*w - 32/7]', '[9801, 33, -18/7*w^3 + 27/7*w^2 + 108/7*w - 69/7]', '[9801, 33, -3*w^2 + 3*w + 18]', '[9801, 33, 18/7*w^3 - 27/7*w^2 - 108/7*w + 48/7]', '[9801, 33, 12/7*w^3 - 18/7*w^2 - 114/7*w + 39/7]', '[9801, 33, -12/7*w^3 + 18/7*w^2 + 114/7*w - 81/7]', '[9801, 33, 3*w^2 - 3*w - 6]', '[9801, 363, 6/7*w^3 - 30/7*w^2 - 15/7*w + 135/7]', '[9801, 363, 6/7*w^3 - 30/7*w^2 - 15/7*w + 72/7]', '[9801, 363, -6/7*w^3 - 12/7*w^2 + 57/7*w + 33/7]', '[9801, 363, -6/7*w^3 - 12/7*w^2 + 57/7*w + 96/7]', '[9819, 3273, -13/7*w^3 + 2/7*w^2 + 99/7*w + 89/7]', '[9819, 3273, 4*w^3 - 4*w^2 - 31*w + 6]', '[9819, 3273, 11/7*w^3 + 1/7*w^2 - 80/7*w + 27/7]', '[9819, 3273, -13/7*w^3 + 37/7*w^2 + 64/7*w - 177/7]', '[9829, 9829, 16/7*w^3 - 31/7*w^2 - 75/7*w + 52/7]', '[9829, 9829, 24/7*w^3 - 43/7*w^2 - 151/7*w + 134/7]', '[9829, 9829, -24/7*w^3 + 29/7*w^2 + 165/7*w - 36/7]', '[9829, 9829, 16/7*w^3 - 17/7*w^2 - 89/7*w + 38/7]', '[9836, 4918, 5/7*w^3 + 10/7*w^2 - 86/7*w + 53/7]', '[9836, 4918, -3*w^3 + 8*w^2 + 16*w - 33]', '[9836, 4918, 17/7*w^3 - 43/7*w^2 - 123/7*w + 232/7]', '[9836, 4918, 15/7*w^3 - 47/7*w^2 - 55/7*w + 82/7]', '[9839, 9839, -10/7*w^3 + 22/7*w^2 + 39/7*w - 148/7]', '[9839, 9839, 13/7*w^3 - 9/7*w^2 - 148/7*w - 26/7]', '[9839, 9839, 18/7*w^3 - 34/7*w^2 - 115/7*w - 1/7]', '[9839, 9839, 10/7*w^3 - 8/7*w^2 - 53/7*w - 97/7]', '[9851, 9851, 18/7*w^3 - 13/7*w^2 - 150/7*w + 27/7]', '[9851, 9851, 2*w^3 - 2*w^2 - 16*w + 11]', '[9851, 9851, -2*w^3 + 4*w^2 + 14*w - 5]', '[9851, 9851, -18/7*w^3 + 41/7*w^2 + 122/7*w - 118/7]', '[9900, 330, -11/7*w^3 + 6/7*w^2 + 94/7*w - 55/7]', '[9900, 330, 1/7*w^3 - 12/7*w^2 + 22/7*w + 89/7]', '[9900, 330, -1/7*w^3 - 9/7*w^2 - 1/7*w + 100/7]', '[9900, 330, 11/7*w^3 - 27/7*w^2 - 73/7*w + 34/7]', '[9901, 9901, 15/7*w^3 - 26/7*w^2 - 69/7*w + 33/7]', '[9901, 9901, 25/7*w^3 - 41/7*w^2 - 164/7*w + 125/7]', '[9901, 9901, -25/7*w^3 + 34/7*w^2 + 171/7*w - 55/7]', '[9901, 9901, -15/7*w^3 + 19/7*w^2 + 76/7*w - 47/7]', '[9949, 9949, w^3 + w^2 - 10*w - 20]', '[9949, 9949, -12/7*w^3 - 3/7*w^2 + 100/7*w + 59/7]', '[9949, 9949, 17/7*w^3 - 1/7*w^2 - 130/7*w - 55/7]', '[9949, 9949, 8/7*w^3 + 9/7*w^2 - 62/7*w - 44/7]', '[9971, 767, 1/7*w^3 + 2/7*w^2 - 41/7*w - 51/7]', '[9971, 767, 2*w^3 - w^2 - 18*w + 4]', '[9971, 767, -16/7*w^3 + 31/7*w^2 + 110/7*w - 52/7]', '[9971, 767, -17/7*w^3 + 29/7*w^2 + 130/7*w - 29/7]', '[9971, 767, 16/7*w^3 - 17/7*w^2 - 124/7*w + 73/7]', '[9971, 767, 17/7*w^3 - 22/7*w^2 - 137/7*w + 113/7]', '[9971, 767, -1/7*w^3 + 5/7*w^2 + 34/7*w - 89/7]', '[9971, 767, -2*w^3 + 5*w^2 + 14*w - 13]', '[10000, 10, 10]'], 'label': '4.4.3600.1', 'narrow_class_no': 2, 'primes': ['[4, 2, -2/7*w^3 + 3/7*w^2 + 19/7*w - 17/7]', '[9, 3, -2/7*w^3 + 3/7*w^2 + 19/7*w - 10/7]', '[11, 11, -w - 1]', '[11, 11, 4/7*w^3 - 6/7*w^2 - 31/7*w + 27/7]', '[11, 11, 4/7*w^3 - 6/7*w^2 - 31/7*w + 6/7]', '[11, 11, -w + 2]', '[25, 5, 4/7*w^3 - 6/7*w^2 - 24/7*w + 13/7]', '[49, 7, 5/7*w^3 - 11/7*w^2 - 23/7*w + 25/7]', '[49, 7, w^3 - w^2 - 7*w + 1]', '[59, 59, 3/7*w^3 - 1/7*w^2 - 32/7*w + 15/7]', '[59, 59, -3/7*w^3 + 8/7*w^2 + 25/7*w - 43/7]', '[59, 59, -3/7*w^3 + 1/7*w^2 + 32/7*w + 13/7]', '[59, 59, 3/7*w^3 - 8/7*w^2 - 25/7*w + 15/7]', '[61, 61, -8/7*w^3 + 12/7*w^2 + 55/7*w - 26/7]', '[61, 61, -4/7*w^3 + 6/7*w^2 + 17/7*w - 6/7]', '[61, 61, 6/7*w^3 - 9/7*w^2 - 50/7*w + 16/7]', '[61, 61, 8/7*w^3 - 12/7*w^2 - 55/7*w + 33/7]', '[71, 71, -3/7*w^3 + 1/7*w^2 + 25/7*w - 15/7]', '[71, 71, -w^3 + w^2 + 8*w - 2]', '[71, 71, w^3 - 2*w^2 - 7*w + 6]', '[71, 71, -3/7*w^3 + 8/7*w^2 + 18/7*w - 8/7]', '[109, 109, -6/7*w^3 + 9/7*w^2 + 50/7*w - 30/7]', '[109, 109, -2/7*w^3 + 3/7*w^2 + 26/7*w - 10/7]', '[109, 109, 2/7*w^3 - 3/7*w^2 - 26/7*w + 17/7]', '[109, 109, -6/7*w^3 + 9/7*w^2 + 50/7*w - 23/7]', '[131, 131, 5/7*w^3 - 4/7*w^2 - 37/7*w + 18/7]', '[131, 131, 3/7*w^3 - 1/7*w^2 - 18/7*w - 20/7]', '[131, 131, 5/7*w^3 - 4/7*w^2 - 44/7*w + 18/7]', '[131, 131, 1/7*w^3 - 5/7*w^2 - 13/7*w + 33/7]', '[169, 13, w^3 - 2*w^2 - 5*w + 3]', '[169, 13, 9/7*w^3 - 10/7*w^2 - 61/7*w + 3/7]', '[179, 179, 9/7*w^3 - 10/7*w^2 - 75/7*w + 31/7]', '[179, 179, 1/7*w^3 - 5/7*w^2 - 20/7*w + 33/7]', '[179, 179, 3/7*w^3 - 1/7*w^2 - 18/7*w - 34/7]', '[179, 179, 4/7*w^3 + 1/7*w^2 - 31/7*w - 36/7]', '[181, 181, -2/7*w^3 + 10/7*w^2 + 5/7*w - 38/7]', '[181, 181, -2/7*w^3 + 10/7*w^2 + 5/7*w - 31/7]', '[181, 181, 2/7*w^3 + 4/7*w^2 - 19/7*w - 18/7]', '[181, 181, 2/7*w^3 + 4/7*w^2 - 19/7*w - 25/7]', '[191, 191, w^3 - 2*w^2 - 7*w + 5]', '[191, 191, -1/7*w^3 + 5/7*w^2 - 8/7*w - 19/7]', '[191, 191, 1/7*w^3 + 2/7*w^2 + 1/7*w - 23/7]', '[191, 191, -w^3 + w^2 + 8*w - 3]', '[229, 229, 6/7*w^3 - 9/7*w^2 - 43/7*w + 58/7]', '[229, 229, -9/7*w^3 + 17/7*w^2 + 54/7*w - 45/7]', '[229, 229, 9/7*w^3 - 10/7*w^2 - 61/7*w + 17/7]', '[229, 229, 6/7*w^3 - 9/7*w^2 - 43/7*w - 12/7]', '[239, 239, -4/7*w^3 - 1/7*w^2 + 24/7*w + 22/7]', '[239, 239, 2*w - 5]', '[239, 239, -2*w - 3]', '[239, 239, -5/7*w^3 + 4/7*w^2 + 51/7*w + 17/7]', '[241, 241, 9/7*w^3 - 10/7*w^2 - 61/7*w + 10/7]', '[241, 241, w^3 - w^2 - 6*w + 2]', '[241, 241, w^3 - 2*w^2 - 5*w + 4]', '[241, 241, -9/7*w^3 + 17/7*w^2 + 54/7*w - 52/7]', '[251, 251, -5/7*w^3 + 4/7*w^2 + 23/7*w + 10/7]', '[251, 251, 11/7*w^3 - 13/7*w^2 - 80/7*w + 34/7]', '[251, 251, -11/7*w^3 + 20/7*w^2 + 73/7*w - 48/7]', '[251, 251, 10/7*w^3 - 15/7*w^2 - 74/7*w + 22/7]', '[289, 17, -10/7*w^3 + 15/7*w^2 + 67/7*w - 36/7]', '[289, 17, 6/7*w^3 - 9/7*w^2 - 29/7*w + 16/7]', '[311, 311, 5/7*w^3 - 4/7*w^2 - 44/7*w + 32/7]', '[311, 311, 1/7*w^3 + 2/7*w^2 - 20/7*w - 30/7]', '[311, 311, -1/7*w^3 + 5/7*w^2 + 13/7*w - 47/7]', '[311, 311, -5/7*w^3 + 11/7*w^2 + 37/7*w - 11/7]', '[349, 349, -6/7*w^3 + 16/7*w^2 + 36/7*w - 93/7]', '[349, 349, 11/7*w^3 - 13/7*w^2 - 94/7*w + 6/7]', '[349, 349, 9/7*w^3 - 3/7*w^2 - 75/7*w - 25/7]', '[349, 349, 2*w^3 - 3*w^2 - 14*w + 8]', '[359, 359, w^3 - 2*w^2 - 6*w + 2]', '[359, 359, 2/7*w^3 - 10/7*w^2 - 19/7*w + 52/7]', '[359, 359, 2/7*w^3 + 4/7*w^2 - 33/7*w - 25/7]', '[359, 359, -w^3 + w^2 + 7*w - 5]', '[361, 19, -8/7*w^3 + 12/7*w^2 + 48/7*w - 33/7]', '[361, 19, 8/7*w^3 - 12/7*w^2 - 48/7*w + 19/7]', '[409, 409, 1/7*w^3 + 2/7*w^2 - 13/7*w - 44/7]', '[409, 409, -1/7*w^3 - 2/7*w^2 + 13/7*w - 26/7]', '[409, 409, 1/7*w^3 - 5/7*w^2 - 6/7*w - 16/7]', '[409, 409, -1/7*w^3 + 5/7*w^2 + 6/7*w - 54/7]', '[419, 419, -6/7*w^3 + 16/7*w^2 + 36/7*w - 37/7]', '[419, 419, -2/7*w^3 + 10/7*w^2 - 2/7*w - 45/7]', '[419, 419, 2/7*w^3 + 4/7*w^2 - 12/7*w - 39/7]', '[419, 419, 6/7*w^3 - 2/7*w^2 - 50/7*w + 9/7]', '[421, 421, 13/7*w^3 - 16/7*w^2 - 92/7*w + 30/7]', '[421, 421, -3/7*w^3 + 15/7*w^2 + 18/7*w - 71/7]', '[421, 421, -w^3 + 3*w^2 + 6*w - 13]', '[421, 421, -13/7*w^3 + 23/7*w^2 + 85/7*w - 65/7]', '[431, 431, w^2 - 2*w - 7]', '[431, 431, -4/7*w^3 - 1/7*w^2 + 38/7*w - 13/7]', '[431, 431, 4/7*w^3 - 13/7*w^2 - 24/7*w + 20/7]', '[431, 431, w^2 - 8]', '[479, 479, 1/7*w^3 + 2/7*w^2 - 27/7*w - 16/7]', '[479, 479, 9/7*w^3 - 17/7*w^2 - 68/7*w + 38/7]', '[479, 479, 9/7*w^3 - 10/7*w^2 - 75/7*w + 38/7]', '[479, 479, -1/7*w^3 + 5/7*w^2 + 20/7*w - 40/7]', '[491, 491, 10/7*w^3 - 8/7*w^2 - 74/7*w + 15/7]', '[491, 491, 2/7*w^3 - 3/7*w^2 - 33/7*w + 52/7]', '[491, 491, 11/7*w^3 - 6/7*w^2 - 87/7*w - 1/7]', '[491, 491, 5/7*w^3 + 3/7*w^2 - 30/7*w - 31/7]', '[529, 23, -6/7*w^3 + 9/7*w^2 + 57/7*w - 16/7]', '[529, 23, 6/7*w^3 - 9/7*w^2 - 57/7*w + 44/7]', '[541, 541, 4/7*w^3 - 6/7*w^2 - 45/7*w + 13/7]', '[541, 541, -8/7*w^3 + 12/7*w^2 + 69/7*w - 47/7]', '[541, 541, 8/7*w^3 - 12/7*w^2 - 69/7*w + 26/7]', '[541, 541, 4/7*w^3 - 6/7*w^2 - 45/7*w + 34/7]', '[599, 599, -3/7*w^3 + 15/7*w^2 + 4/7*w - 78/7]', '[599, 599, w^3 - 2*w^2 - 5*w + 11]', '[599, 599, -4/7*w^3 + 13/7*w^2 + 31/7*w - 76/7]', '[599, 599, 3/7*w^3 + 6/7*w^2 - 25/7*w - 62/7]', '[601, 601, 11/7*w^3 - 20/7*w^2 - 87/7*w + 83/7]', '[601, 601, -3/7*w^3 + 8/7*w^2 + 39/7*w - 15/7]', '[601, 601, -2/7*w^3 + 10/7*w^2 + 5/7*w - 80/7]', '[601, 601, -11/7*w^3 + 13/7*w^2 + 94/7*w - 13/7]', '[659, 659, -3/7*w^3 + 8/7*w^2 - 3/7*w - 22/7]', '[659, 659, 13/7*w^3 - 23/7*w^2 - 92/7*w + 58/7]', '[659, 659, -13/7*w^3 + 16/7*w^2 + 99/7*w - 44/7]', '[659, 659, 3/7*w^3 - 1/7*w^2 - 4/7*w - 20/7]', '[661, 661, -11/7*w^3 + 13/7*w^2 + 73/7*w - 13/7]', '[661, 661, 9/7*w^3 - 10/7*w^2 - 54/7*w + 24/7]', '[661, 661, 9/7*w^3 - 17/7*w^2 - 47/7*w + 31/7]', '[661, 661, 11/7*w^3 - 20/7*w^2 - 66/7*w + 62/7]', '[709, 709, 11/7*w^3 - 13/7*w^2 - 94/7*w + 34/7]', '[709, 709, -3/7*w^3 + 1/7*w^2 + 46/7*w - 8/7]', '[709, 709, 3/7*w^3 - 8/7*w^2 - 39/7*w + 36/7]', '[709, 709, -11/7*w^3 + 20/7*w^2 + 87/7*w - 62/7]', '[719, 719, 3/7*w^3 - 1/7*w^2 - 39/7*w - 27/7]', '[719, 719, w^3 - 2*w^2 - 8*w + 2]', '[719, 719, -w^3 + w^2 + 9*w - 7]', '[719, 719, -3/7*w^3 + 8/7*w^2 + 32/7*w - 64/7]', '[769, 769, -5/7*w^3 + 11/7*w^2 + 51/7*w - 25/7]', '[769, 769, 9/7*w^3 - 10/7*w^2 - 82/7*w + 10/7]', '[769, 769, -9/7*w^3 + 17/7*w^2 + 75/7*w - 73/7]', '[769, 769, 5/7*w^3 - 4/7*w^2 - 58/7*w + 32/7]', '[829, 829, -11/7*w^3 + 20/7*w^2 + 87/7*w - 69/7]', '[829, 829, -3/7*w^3 + 8/7*w^2 + 39/7*w - 29/7]', '[829, 829, 3/7*w^3 - 1/7*w^2 - 46/7*w + 15/7]', '[829, 829, -11/7*w^3 + 13/7*w^2 + 94/7*w - 27/7]', '[839, 839, 1/7*w^3 + 2/7*w^2 - 27/7*w - 23/7]', '[839, 839, -9/7*w^3 + 10/7*w^2 + 75/7*w - 45/7]', '[839, 839, 9/7*w^3 - 17/7*w^2 - 68/7*w + 31/7]', '[839, 839, -1/7*w^3 + 5/7*w^2 + 20/7*w - 47/7]', '[841, 29, -10/7*w^3 + 15/7*w^2 + 60/7*w - 43/7]', '[841, 29, 10/7*w^3 - 15/7*w^2 - 60/7*w + 22/7]', '[911, 911, 8/7*w^3 - 5/7*w^2 - 76/7*w + 26/7]', '[911, 911, 4/7*w^3 - 13/7*w^2 - 38/7*w + 69/7]', '[911, 911, 4/7*w^3 + 1/7*w^2 - 52/7*w - 22/7]', '[911, 911, 8/7*w^3 - 19/7*w^2 - 62/7*w + 47/7]', '[961, 31, 10/7*w^3 - 15/7*w^2 - 60/7*w + 29/7]', '[961, 31, -10/7*w^3 + 15/7*w^2 + 60/7*w - 36/7]', '[971, 971, -2/7*w^3 + 10/7*w^2 - 2/7*w - 59/7]', '[971, 971, -6/7*w^3 + 2/7*w^2 + 50/7*w - 23/7]', '[971, 971, 6/7*w^3 - 16/7*w^2 - 36/7*w + 23/7]', '[971, 971, 2/7*w^3 + 4/7*w^2 - 12/7*w - 53/7]']}
• 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': [1, 8, -7, -2, 1], 'conductor': 60, 'degree': 4, 'dirichlet_group': [1, 11, 59, 49], 'disc_abs': 3600, 'disc_rad': 30, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[2, 2]]], [11, [[1, 4]]], [13, [[2, 2]]], [17, [[2, 2]]], [19, [[2, 2]]], [23, [[2, 2]]], [29, [[2, 2]]], [31, [[2, 2]]], [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': 7.745966692414834, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.3600.1', 'local_algs': ['2.4.4.1', '3.4.2.1', '5.4.2.1'], 'monogenic': -1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 3, 5], 'rd': 7.74596669241, 'regulator': {'__RealLiteral__': 0, 'data': '2.61534752461', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-3.0.1', '-1.-1.1', '-15.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{2}{7} a^{3} - \\frac{3}{7} a^{2} - \\frac{12}{7} a + \\frac{10}{7} \\)', '\\( \\frac{1}{7} a^{3} - \\frac{5}{7} a^{2} + \\frac{1}{7} a + \\frac{5}{7} \\)', '\\( \\frac{1}{7} a^{3} + \\frac{2}{7} a^{2} - \\frac{6}{7} a - \\frac{2}{7} \\)'], 'unitsGmodule': [[1, 1], [4, 1]], 'unitsType': 'Type II (i)', 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/7*a^3 + 2/7*a^2 + 1/7*a - 2/7']}