Hilbert modular form data - 4.4.4225.1-36.1-d

Formats: - HTML - YAML - JSON - 2024-04-27T14:14:31.617348

• 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': 3, 'disc': 4225, 'field_bad_primes': [5, 13], 'field_label': '4.4.4225.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.4225.1-36.1-d', 'label_nsuffix': 3, 'label_suffix': 'd', 'level_bad_primes': [2, 3], 'level_ideal': '[36, 6, -1/2*w^2 - 1/2*w + 5]', 'level_label': '36.1', 'level_norm': 36, 'parallel_weight': 2, 'short_label': '36.1-d', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[4,2,w]', -1], ['[9,3,1/4*w^3-11/4*w-1/2]', -1]], 'hecke_eigenvalues': [1, 'e', 1, 'e^2 - 2*e - 5', '-e - 1', '-e + 3', '-e^2 + 3*e + 8', '2*e^2 - 2*e - 10', '-2*e^2 + 2*e + 6', '-e^2 + 11', '3*e + 3', '-e^2 + 4*e + 3', -2, -2, '-2*e^2 + e + 11', '-3*e^2 + 2*e + 17', '-2*e^2 - 2*e + 12', '2*e^2 + e - 7', '-3*e - 1', '-4*e - 6', '3*e^2 - 4*e - 17', '2*e^2 - 7*e - 9', '-e^2 + 3*e + 16', '-e^2 + 2*e + 9', '-4*e^2 + 2*e + 20', '4*e^2 - 2*e - 22', '-4*e^2 + 4*e + 20', '-2*e^2 + e + 17', 4, '5*e^2 - 6*e - 19', '4*e - 8', 'e^2 - 7*e - 10', 'e^2 - 4*e + 7', '-e^2 + 3', '3*e^2 - 2*e - 13', '-2*e - 2', '2*e^2 - 10*e - 12', '-5*e^2 + 6*e + 19', '3*e + 7', '2*e^2 - 8*e - 20', -10, '-4*e^2 + 26', '-e^2 + 4*e + 5', 'e^2 - 4*e - 5', '4*e^2 - 4*e - 16', '-5*e^2 + e + 24', '-2*e^2 - 6', 'e^2 + e + 10', '2*e^2 - 6*e - 12', 'e^2 - 4*e + 3', '2*e^2 + 3*e - 13', 'e^2 - 5', '2*e^2 - 6*e', '-e^2 - 2*e - 9', '-4*e^2 + 14*e + 26', '3*e^2 - 5*e - 22', '-5*e^2 - e + 30', '-3*e^2 + 12*e + 11', '-2*e^2 - 2*e + 10', 14, '3*e^2 - e - 24', '-2*e^2 + 8*e + 24', '-e^2 + 5*e + 2', '-e^2 + 5*e + 2', '-5*e^2 + 11*e + 30', '7*e^2 - 4*e - 35', '-e^2 - 5*e + 10', '-5*e^2 + 11*e + 30', '8*e^2 - 7*e - 27', 'e^2 + 4*e - 3', '-7*e^2 + 16*e + 37', 'e^2 + 2*e - 29', '4*e^2 - 2*e - 20', '2*e^2 - 3*e + 3', '8*e - 4', '-8*e^2 + 9*e + 31', '5*e^2 - 2*e - 15', '6*e^2 - 6*e - 20', '3*e^2 - 2*e - 9', '-4*e^2 + 11*e + 5', '4*e^2 - 16*e - 28', '-8*e^2 + 6*e + 34', '3*e^2 - 4*e - 11', '-4*e^2 + 2*e + 6', '4*e^2 - 6*e - 26', '5*e^2 - 7*e - 14', '7*e^2 - 16*e - 21', '8*e^2 - 4*e - 42', '-4*e^2 - 3*e + 29', '-3*e^2 + 14*e + 15', '-e^2 + 3*e - 4', '-e^2 - 2*e - 11', '14*e - 12', '6*e^2 - 28', 'e^2 + 3*e - 14', '-e^2 + 3*e + 36', '-3*e^2 - 4*e + 27', '4*e^2 - 4*e - 20', '2*e - 14', '-10*e^2 + 16*e + 38', '-6*e^2 + 2*e + 36', '2*e^2 + 8*e - 2', '-4*e - 20', '-2*e^2 + 10*e + 24', '6*e^2 - 8*e - 20', '5*e^2 - 6*e - 5', '3*e^2 - 4*e - 29', '2*e + 16', 2, '-3*e^2 - 4*e + 33', '-6*e^2 + 5*e + 31', '-2*e^2 + 2*e - 22', '5*e^2 - 41', '2*e^2 + 8*e - 6', 'e^2 - 14*e + 1', '3*e^2 + 8*e - 31', '2*e^2 - e - 15', '9*e^2 - 22*e - 53', '12*e + 2', '-3*e^2 + 12*e + 13', '7*e^2 - 24*e - 39', '8*e^2 - 14*e - 50', '-e^2 - 8*e + 17', '-5*e^2 + 6*e + 47', '-7*e^2 + 16*e + 15', '4*e^2 - 8*e - 12', '-e^2 + 4*e - 11', '8*e^2 - 17*e - 35', '-11*e^2 + 13*e + 28', '4*e^2 - 10*e - 8', '6*e^2 - 8*e - 4', '2*e^2 - 8*e - 32', '11*e - 25', '2*e^2 - 4*e - 32', '6*e^2 - 24', '6*e^2 - 12*e - 28', '-e^2 + 2*e - 21', '-6*e^2 + 20*e + 14', '4*e^2 - 8', '2*e^2 + 7*e - 25', '-6*e^2 + 18*e + 46', '-4*e^2 - 4*e + 42', '6*e^2 - 12*e - 40', '-5*e^2 + 6*e + 17', '-8*e^2 + 8*e + 48', '-9*e^2 + 19*e + 50', '-e^2 + 5*e - 16', '-3*e^2 + 5*e + 34', '8*e^2 - 28*e - 36', '-9*e^2 + 19*e + 58', '6*e^2 + 8*e - 38', '-2*e^2 + 8*e + 34', '-6*e - 32', '-4*e^2 - 4*e - 6', '-5*e^2 + 9', '12*e^2 - 32*e - 64', '-e^2 + 13*e + 4', '-9*e^2 + 6*e + 15', '8*e^2 - 3*e - 57', '4*e^2 - 8*e - 28', '-11*e^2 + 12*e + 55', '5*e^2 + 2*e - 39'], 'hecke_polynomial': 'x^3 - x^2 - 7*x - 1', 'label': '4.4.4225.1-36.1-d'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 4225, 'ideals': ['[1, 1, 1]', '[4, 2, w]', '[4, 2, -1/2*w^3 + 9/2*w]', '[9, 3, 1/4*w^3 - 11/4*w - 1/2]', '[9, 3, 1/4*w^3 - 11/4*w + 1/2]', '[16, 2, 2]', '[16, 4, -1/4*w^3 + 1/2*w^2 + 5/4*w - 5/2]', '[16, 4, w - 2]', '[25, 5, 1/2*w^3 - 7/2*w]', '[29, 29, -1/4*w^3 + 1/2*w^2 + 9/4*w - 1/2]', '[29, 29, -1/2*w^2 - 1/2*w + 4]', '[29, 29, -1/2*w^2 + 1/2*w + 4]', '[29, 29, -1/4*w^3 - 1/2*w^2 + 9/4*w + 1/2]', '[36, 6, -1/2*w^2 - 1/2*w + 5]', '[36, 6, -w^3 - 1/2*w^2 + 17/2*w + 3]', '[36, 6, 1/4*w^3 - 1/2*w^2 - 1/4*w + 3/2]', '[36, 6, -1/4*w^3 - 1/2*w^2 + 1/4*w + 3/2]', '[49, 7, 3/4*w^3 + 1/2*w^2 - 23/4*w - 3/2]', '[49, 7, 1/2*w^3 + 1/2*w^2 - 3*w - 3]', '[61, 61, 1/2*w^3 + 1/2*w^2 - 5*w - 1]', '[61, 61, -1/4*w^3 - 1/2*w^2 + 13/4*w + 7/2]', '[61, 61, -1/4*w^3 + 1/2*w^2 + 13/4*w - 7/2]', '[61, 61, -1/2*w^3 + 1/2*w^2 + 5*w - 1]', '[64, 4, 2*w]', '[64, 4, -w^3 + 9*w]', '[64, 8, -w^3 + 8*w]', '[64, 8, -1/2*w^3 + 5/2*w]', '[79, 79, 3/4*w^3 - 25/4*w - 9/2]', '[79, 79, -1/4*w^3 + 1/2*w^2 - 3/4*w - 3/2]', '[79, 79, 1/4*w^3 - 3/4*w - 9/2]', '[79, 79, 3/2*w^3 + 1/2*w^2 - 13*w - 3]', '[81, 3, 3]', '[81, 9, 1/4*w^3 - 11/4*w + 7/2]', '[81, 9, -1/4*w^3 + 11/4*w + 7/2]', '[100, 10, w^2 - 2]', '[100, 10, w^2 - 7]', '[101, 101, 1/4*w^3 + w^2 - 7/4*w - 5/2]', '[101, 101, 5/4*w^3 - 1/2*w^2 - 45/4*w + 9/2]', '[101, 101, 1/4*w^3 + w^2 - 7/4*w - 13/2]', '[101, 101, 1/4*w^3 - w^2 - 7/4*w + 5/2]', '[116, 58, w^3 + 1/2*w^2 - 15/2*w - 3]', '[116, 58, -1/2*w^3 - 1/2*w^2 + 4*w]', '[116, 58, 3/4*w^3 + 1/2*w^2 - 19/4*w - 3/2]', '[116, 58, -1/4*w^3 - 1/2*w^2 + 5/4*w + 9/2]', '[116, 58, 1/4*w^3 - 1/2*w^2 - 5/4*w + 9/2]', '[116, 58, 3/4*w^3 - 1/2*w^2 - 19/4*w + 3/2]', '[116, 58, -1/2*w^3 + 1/2*w^2 + 4*w]', '[116, 58, w^3 - 1/2*w^2 - 15/2*w + 3]', '[121, 11, 3/4*w^3 - 21/4*w - 1/2]', '[121, 11, 1/4*w^3 - 7/4*w - 7/2]', '[131, 131, -3/4*w^3 + 29/4*w - 1/2]', '[131, 131, 1/4*w^3 - 15/4*w - 1/2]', '[131, 131, 1/4*w^3 - 15/4*w + 1/2]', '[131, 131, 3/4*w^3 - 29/4*w - 1/2]', '[139, 139, w^2 + w + 1]', '[139, 139, 1/2*w^3 + w^2 - 9/2*w - 10]', '[139, 139, 1/2*w^3 - w^2 - 9/2*w + 10]', '[139, 139, w^2 - w + 1]', '[144, 6, 1/2*w^3 - 11/2*w - 1]', '[144, 6, 1/2*w^3 - 11/2*w + 1]', '[144, 12, -1/2*w^3 - 1/2*w^2 + 5*w]', '[144, 12, -3/4*w^3 - 1/2*w^2 + 23/4*w + 1/2]', '[144, 12, -1/2*w^3 + 1/2*w^2 + 5*w]', '[144, 12, 1/4*w^3 - 1/2*w^2 - 13/4*w + 9/2]', '[169, 13, 1/2*w^3 - 11/2*w]', '[179, 179, -3/4*w^3 + w^2 + 21/4*w - 13/2]', '[179, 179, 1/2*w^3 + 1/2*w^2 - 6*w - 5]', '[179, 179, -3/4*w^3 - w^2 + 25/4*w + 7/2]', '[179, 179, -3/2*w^2 + 1/2*w + 2]', '[181, 181, -1/2*w^2 + 1/2*w - 2]', '[181, 181, 1/4*w^3 - 1/2*w^2 - 9/4*w + 13/2]', '[181, 181, 5/4*w^3 - 39/4*w + 3/2]', '[181, 181, 1/2*w^2 + 1/2*w + 2]', '[191, 191, -w^3 + 1/2*w^2 + 19/2*w - 4]', '[191, 191, 1/4*w^3 + 1/2*w^2 - 17/4*w - 1/2]', '[191, 191, 1/2*w^3 + 1/2*w^2 - 6*w - 3]', '[191, 191, -3/4*w^3 + 1/2*w^2 + 31/4*w - 3/2]', '[196, 14, 1/2*w^3 + w^2 - 3/2*w - 3]', '[196, 14, 1/2*w^3 + 3/2*w^2 - 3*w - 2]', '[196, 14, 3/4*w^3 + 3/2*w^2 - 23/4*w - 23/2]', '[196, 14, 3/2*w^3 + w^2 - 25/2*w - 6]', '[199, 199, 1/4*w^3 + 1/2*w^2 - 5/4*w - 15/2]', '[199, 199, -1/4*w^3 + w^2 + 11/4*w - 17/2]', '[199, 199, 1/2*w^3 + 1/2*w^2 - 4*w + 3]', '[199, 199, -1/4*w^3 - w^2 + 11/4*w + 1/2]', '[211, 211, -3/4*w^3 + 1/2*w^2 + 19/4*w - 9/2]', '[211, 211, -w^3 - 1/2*w^2 + 15/2*w]', '[211, 211, -1/4*w^3 + 1/2*w^2 + 13/4*w - 11/2]', '[211, 211, 3/4*w^3 + 1/2*w^2 - 19/4*w - 9/2]', '[225, 15, -1/4*w^3 - w^2 + 7/4*w + 9/2]', '[225, 15, 1/4*w^3 - w^2 - 7/4*w + 9/2]', '[244, 122, 1/2*w^3 - 1/2*w^2 - w - 2]', '[244, 122, -1/2*w^3 + w^2 + 7/2*w + 1]', '[244, 122, 7/4*w^3 - 1/2*w^2 - 59/4*w + 13/2]', '[244, 122, 1/2*w^3 - w^2 - 7/2*w + 10]', '[244, 122, 1/2*w^3 + w^2 - 7/2*w - 10]', '[244, 122, -7/4*w^3 - 1/2*w^2 + 59/4*w + 13/2]', '[244, 122, 1/2*w^3 + w^2 - 7/2*w + 1]', '[244, 122, 1/2*w^3 + 1/2*w^2 - w + 2]', '[251, 251, 3/4*w^3 - 1/2*w^2 - 27/4*w + 1/2]', '[251, 251, 1/2*w^2 - 3/2*w - 4]', '[251, 251, 1/2*w^2 + 3/2*w - 4]', '[251, 251, -3/4*w^3 - 1/2*w^2 + 27/4*w + 1/2]', '[256, 4, 4]', '[256, 8, -1/2*w^3 + w^2 + 5/2*w - 5]', '[256, 8, 2*w - 4]', '[256, 16, -w^2 + 5]', '[256, 16, -w^2 + 4]', '[261, 87, -1/2*w^3 + 1/2*w^2 + 2*w - 3]', '[261, 87, -1/4*w^3 - 1/4*w - 5/2]', '[261, 87, 5/4*w^3 + 1/2*w^2 - 41/4*w - 3/2]', '[261, 87, 5/4*w^3 - 43/4*w + 5/2]', '[261, 87, 5/4*w^3 - 43/4*w - 5/2]', '[261, 87, 5/4*w^3 - 1/2*w^2 - 41/4*w + 3/2]', '[261, 87, 1/2*w^3 + 1/2*w^2 - 2*w - 3]', '[261, 87, 1/4*w^3 + 1/4*w - 5/2]', '[269, 269, -3/4*w^3 + 17/4*w - 1/2]', '[269, 269, 1/2*w^3 + 1/2*w^2 - 4*w - 7]', '[269, 269, -5/4*w^3 + 39/4*w + 1/2]', '[269, 269, 3/4*w^3 - 17/4*w - 1/2]', '[289, 17, -1/4*w^3 + 11/4*w - 9/2]', '[289, 17, 1/4*w^3 - 11/4*w - 9/2]', '[311, 311, 3/4*w^3 + w^2 - 29/4*w - 19/2]', '[311, 311, 3/4*w^3 + w^2 - 25/4*w - 21/2]', '[311, 311, 3/4*w^3 - w^2 - 13/4*w + 7/2]', '[311, 311, -3/4*w^3 + w^2 + 29/4*w - 19/2]', '[316, 158, 1/2*w^2 - 9/2*w - 3]', '[316, 158, -w^3 + w^2 + 5*w]', '[316, 158, 9/4*w^3 + 1/2*w^2 - 81/4*w - 3/2]', '[316, 158, 1/4*w^3 - 3/2*w^2 - 1/4*w + 13/2]', '[316, 158, 9/4*w^3 + 3/2*w^2 - 81/4*w - 25/2]', '[316, 158, 3/4*w^3 - 1/2*w^2 - 23/4*w - 3/2]', '[316, 158, 3/2*w^2 - 9/2*w - 1]', '[316, 158, 1/2*w^3 + 1/2*w^2 - 3*w - 6]', '[324, 6, 3*w]', '[324, 6, -3/2*w^3 + 27/2*w]', '[324, 18, 1/2*w^3 + w^2 - 7/2*w - 9]', '[324, 18, 3/2*w^3 + 1/2*w^2 - 13*w - 2]', '[324, 18, 1/2*w^3 - w^2 - 7/2*w]', '[324, 18, -1/4*w^3 + 1/2*w^2 - 3/4*w - 5/2]', '[361, 19, -1/4*w^3 + 7/4*w - 9/2]', '[361, 19, -w^3 + 7*w - 1]', '[389, 389, 5/4*w^3 - 3/2*w^2 - 41/4*w + 13/2]', '[389, 389, 5/4*w^3 - 47/4*w + 9/2]', '[389, 389, 1/2*w^3 + 3/2*w^2 - 2*w - 7]', '[389, 389, 5/4*w^3 + 3/2*w^2 - 41/4*w - 13/2]', '[400, 10, w^3 - 7*w]', '[400, 20, -3/4*w^3 - 1/2*w^2 + 31/4*w - 3/2]', '[400, 20, -w^3 + w^2 + 7*w - 2]', '[404, 202, 5/4*w^3 + 1/2*w^2 - 37/4*w - 7/2]', '[404, 202, -1/2*w^3 + 9/2*w - 5]', '[404, 202, 13/4*w^3 + 1/2*w^2 - 109/4*w - 7/2]', '[404, 202, 3/2*w^3 - 3/2*w^2 - 11*w + 6]', '[404, 202, -w^3 + 1/2*w^2 + 15/2*w + 1]', '[404, 202, 5/4*w^3 - 3/2*w^2 - 33/4*w + 15/2]', '[404, 202, w^3 + 1/2*w^2 - 13/2*w - 1]', '[404, 202, -5/4*w^3 + 1/2*w^2 + 37/4*w - 7/2]', '[419, 419, 5/4*w^3 - 1/2*w^2 - 37/4*w + 5/2]', '[419, 419, w^3 - 1/2*w^2 - 13/2*w + 2]', '[419, 419, w^3 + 1/2*w^2 - 13/2*w - 2]', '[419, 419, 5/4*w^3 + 1/2*w^2 - 37/4*w - 5/2]', '[439, 439, -1/4*w^3 - 1/2*w^2 - 7/4*w + 5/2]', '[439, 439, 2*w^3 + 1/2*w^2 - 35/2*w - 2]', '[439, 439, 2*w^3 - 1/2*w^2 - 35/2*w + 2]', '[439, 439, -1/4*w^3 + 1/2*w^2 - 7/4*w - 5/2]', '[441, 21, -3/4*w^3 - w^2 + 25/4*w + 5/2]', '[441, 21, -5/4*w^3 - 3/2*w^2 + 37/4*w + 11/2]', '[441, 21, -1/4*w^3 - w^2 + 3/4*w + 13/2]', '[441, 21, -w^3 - 3/2*w^2 + 13/2*w + 8]', '[464, 58, -1/2*w^3 + w^2 + 9/2*w - 1]', '[464, 58, -w^2 - w + 8]', '[464, 58, -w^2 + w + 8]', '[464, 58, -1/2*w^3 - w^2 + 9/2*w + 1]', '[464, 116, -1/2*w^3 + 1/2*w^2 + 5*w - 8]', '[464, 116, 3/4*w^3 + 3/2*w^2 - 23/4*w - 19/2]', '[464, 116, -1/4*w^3 - 1/2*w^2 + 13/4*w - 7/2]', '[464, 116, -1/2*w^3 + 3/2*w^2 + 3*w - 4]', '[464, 116, 1/2*w^3 + 3/2*w^2 - 3*w - 4]', '[464, 116, 1/4*w^3 - 1/2*w^2 - 13/4*w - 7/2]', '[464, 116, -3/4*w^3 + 3/2*w^2 + 23/4*w - 19/2]', '[464, 116, 1/2*w^3 + 1/2*w^2 - 5*w - 8]', '[484, 22, 3/2*w^2 - 1/2*w - 3]', '[484, 22, 1/2*w^2 - 7/2*w - 1]', '[484, 22, 7/4*w^3 + 1/2*w^2 - 63/4*w - 7/2]', '[484, 22, 1/4*w^3 + 3/2*w^2 - 9/4*w - 21/2]', '[491, 491, 1/4*w^3 + 3/2*w^2 - 9/4*w - 7/2]', '[491, 491, -3/2*w^2 + 1/2*w + 10]', '[491, 491, -1/4*w^3 - 5/4*w + 5/2]', '[491, 491, 1/4*w^3 - 3/2*w^2 - 9/4*w + 7/2]', '[521, 521, 1/2*w^2 - 3/2*w - 6]', '[521, 521, -3/4*w^3 - 1/2*w^2 + 27/4*w - 3/2]', '[521, 521, 3/4*w^3 - 1/2*w^2 - 27/4*w - 3/2]', '[521, 521, 1/2*w^2 + 3/2*w - 6]', '[524, 262, 1/2*w^2 - 1/2*w + 3]', '[524, 262, -3/2*w^2 - 1/2*w - 1]', '[524, 262, -1/4*w^3 + 1/2*w^2 + 9/4*w - 15/2]', '[524, 262, 1/4*w^3 + 3/2*w^2 - 9/4*w - 29/2]', '[524, 262, 1/4*w^3 - 3/2*w^2 - 9/4*w + 29/2]', '[524, 262, 1/4*w^3 + 1/2*w^2 - 9/4*w - 15/2]', '[524, 262, -3/2*w^2 + 1/2*w - 1]', '[524, 262, -1/2*w^2 - 1/2*w - 3]', '[529, 23, 1/2*w^3 - 11/2*w - 6]', '[529, 23, -1/2*w^3 + 11/2*w - 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3/2*w - 4]', '[251, 251, 1/2*w^2 + 3/2*w - 4]', '[251, 251, -3/4*w^3 - 1/2*w^2 + 27/4*w + 1/2]', '[269, 269, -3/4*w^3 + 17/4*w - 1/2]', '[269, 269, 1/2*w^3 + 1/2*w^2 - 4*w - 7]', '[269, 269, -5/4*w^3 + 39/4*w + 1/2]', '[269, 269, 3/4*w^3 - 17/4*w - 1/2]', '[289, 17, -1/4*w^3 + 11/4*w - 9/2]', '[289, 17, 1/4*w^3 - 11/4*w - 9/2]', '[311, 311, 3/4*w^3 + w^2 - 29/4*w - 19/2]', '[311, 311, 3/4*w^3 + w^2 - 25/4*w - 21/2]', '[311, 311, 3/4*w^3 - w^2 - 13/4*w + 7/2]', '[311, 311, -3/4*w^3 + w^2 + 29/4*w - 19/2]', '[361, 19, -1/4*w^3 + 7/4*w - 9/2]', '[361, 19, -w^3 + 7*w - 1]', '[389, 389, 5/4*w^3 - 3/2*w^2 - 41/4*w + 13/2]', '[389, 389, 5/4*w^3 - 47/4*w + 9/2]', '[389, 389, 1/2*w^3 + 3/2*w^2 - 2*w - 7]', '[389, 389, 5/4*w^3 + 3/2*w^2 - 41/4*w - 13/2]', '[419, 419, 5/4*w^3 - 1/2*w^2 - 37/4*w + 5/2]', '[419, 419, w^3 - 1/2*w^2 - 13/2*w + 2]', '[419, 419, w^3 + 1/2*w^2 - 13/2*w - 2]', '[419, 419, 5/4*w^3 + 1/2*w^2 - 37/4*w - 5/2]', '[439, 439, -1/4*w^3 - 1/2*w^2 - 7/4*w + 5/2]', '[439, 439, 2*w^3 + 1/2*w^2 - 35/2*w - 2]', '[439, 439, 2*w^3 - 1/2*w^2 - 35/2*w + 2]', '[439, 439, -1/4*w^3 + 1/2*w^2 - 7/4*w - 5/2]', '[491, 491, 1/4*w^3 + 3/2*w^2 - 9/4*w - 7/2]', '[491, 491, -3/2*w^2 + 1/2*w + 10]', '[491, 491, -1/4*w^3 - 5/4*w + 5/2]', '[491, 491, 1/4*w^3 - 3/2*w^2 - 9/4*w + 7/2]', '[521, 521, 1/2*w^2 - 3/2*w - 6]', '[521, 521, -3/4*w^3 - 1/2*w^2 + 27/4*w - 3/2]', '[521, 521, 3/4*w^3 - 1/2*w^2 - 27/4*w - 3/2]', '[521, 521, 1/2*w^2 + 3/2*w - 6]', '[529, 23, 1/2*w^3 - 11/2*w - 6]', '[529, 23, -1/2*w^3 + 11/2*w - 6]', '[569, 569, 3/4*w^3 + w^2 - 33/4*w - 3/2]', '[569, 569, -3/4*w^3 + w^2 + 33/4*w - 15/2]', '[569, 569, 3/4*w^3 + w^2 - 33/4*w - 15/2]', '[569, 569, -3/4*w^3 + w^2 + 33/4*w - 3/2]', '[571, 571, -1/2*w^3 - 3/2*w^2 + 5*w + 9]', '[571, 571, 1/4*w^3 - 19/4*w + 1/2]', '[571, 571, 1/4*w^3 - 19/4*w - 1/2]', '[571, 571, 3/4*w^3 + 3/2*w^2 - 27/4*w - 19/2]', '[599, 599, -3/4*w^3 - w^2 + 21/4*w + 1/2]', '[599, 599, 1/2*w^3 - 3/2*w^2 - 6*w + 9]', '[599, 599, -1/2*w^3 - 3/2*w^2 + 6*w + 9]', '[599, 599, 3/4*w^3 - w^2 - 21/4*w + 1/2]', '[601, 601, 1/2*w^3 - w^2 - 9/2*w]', '[601, 601, -w^2 - w + 9]', '[601, 601, -7/4*w^3 + 57/4*w - 7/2]', '[601, 601, 1/2*w^3 + w^2 - 9/2*w]', '[641, 641, w^3 + 1/2*w^2 - 11/2*w - 2]', '[641, 641, -7/4*w^3 + 1/2*w^2 + 55/4*w - 5/2]', '[641, 641, 7/4*w^3 + 1/2*w^2 - 55/4*w - 5/2]', '[641, 641, -w^3 + 1/2*w^2 + 11/2*w - 2]', '[659, 659, 7/4*w^3 - 1/2*w^2 - 59/4*w + 3/2]', '[659, 659, 5/2*w^3 - w^2 - 41/2*w + 8]', '[659, 659, 5/2*w^3 + w^2 - 41/2*w - 8]', '[659, 659, w^3 + 3/2*w^2 - 19/2*w - 12]', '[701, 701, 1/2*w^3 - 3/2*w^2 - 3*w + 5]', '[701, 701, 3/4*w^3 + 3/2*w^2 - 23/4*w - 17/2]', '[701, 701, 3/4*w^3 - 3/2*w^2 - 23/4*w + 17/2]', '[701, 701, 1/2*w^3 + 3/2*w^2 - 3*w - 5]', '[719, 719, 3/4*w^3 - 3/2*w^2 - 23/4*w + 13/2]', '[719, 719, -1/2*w^3 + 3/2*w^2 + 3*w - 7]', '[719, 719, 1/2*w^3 + 3/2*w^2 - 3*w - 7]', '[719, 719, 3/4*w^3 + 3/2*w^2 - 23/4*w - 13/2]', '[751, 751, 1/2*w^3 - 3/2*w - 4]', '[751, 751, -3/2*w^3 + 25/2*w + 4]', '[751, 751, 3/2*w^3 - 25/2*w + 4]', '[751, 751, -1/2*w^3 + 3/2*w - 4]', '[809, 809, 3/2*w^2 - 1/2*w - 4]', '[809, 809, 1/4*w^3 + 3/2*w^2 - 9/4*w - 19/2]', '[809, 809, 1/4*w^3 - 3/2*w^2 - 9/4*w + 19/2]', '[809, 809, 3/2*w^2 + 1/2*w - 4]', '[829, 829, -3/2*w^3 - 1/2*w^2 + 11*w + 1]', '[829, 829, 5/4*w^3 - 1/2*w^2 - 33/4*w + 7/2]', '[829, 829, 5/4*w^3 + 1/2*w^2 - 33/4*w - 7/2]', '[829, 829, -3/2*w^3 + 1/2*w^2 + 11*w - 1]', '[859, 859, -1/2*w^3 - 1/2*w^2 + 7*w + 3]', '[859, 859, 5/4*w^3 + 1/2*w^2 - 49/4*w - 3/2]', '[859, 859, -5/4*w^3 + 1/2*w^2 + 49/4*w - 3/2]', '[859, 859, 1/2*w^3 - 1/2*w^2 - 7*w + 3]', '[881, 881, 5/4*w^3 + 2*w^2 - 43/4*w - 29/2]', '[881, 881, -1/4*w^3 + 2*w^2 - 1/4*w - 7/2]', '[881, 881, -w^3 + 3/2*w^2 + 15/2*w - 12]', '[881, 881, 5/4*w^3 - 2*w^2 - 43/4*w + 29/2]', '[911, 911, 1/4*w^3 - w^2 - 7/4*w - 5/2]', '[911, 911, -1/4*w^3 + w^2 + 7/4*w - 23/2]', '[911, 911, -9/4*w^3 + 1/2*w^2 + 73/4*w - 9/2]', '[911, 911, 9/4*w^3 + w^2 - 75/4*w - 11/2]', '[919, 919, 5/4*w^3 - 1/2*w^2 - 41/4*w - 1/2]', '[919, 919, -3/4*w^3 - w^2 + 29/4*w + 3/2]', '[919, 919, -3/4*w^3 + w^2 + 29/4*w - 3/2]', '[919, 919, -5/4*w^3 - 1/2*w^2 + 41/4*w - 1/2]', '[961, 31, 1/2*w^3 - 7/2*w - 6]', '[961, 31, 5/4*w^3 - 35/4*w - 1/2]', '[971, 971, -7/4*w^3 + 61/4*w - 7/2]', '[971, 971, -1/4*w^3 - 5/4*w - 7/2]', '[971, 971, 11/4*w^3 + w^2 - 97/4*w - 17/2]', '[971, 971, 1/4*w^3 - 2*w^2 - 7/4*w + 7/2]', '[991, 991, -5/4*w^3 - w^2 + 43/4*w + 7/2]', '[991, 991, w^3 - 1/2*w^2 - 17/2*w - 2]', '[991, 991, -w^3 - 1/2*w^2 + 17/2*w - 2]', '[991, 991, -5/4*w^3 + w^2 + 43/4*w - 7/2]']}
• 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': [4, 0, -9, 0, 1], 'conductor': 65, 'degree': 4, 'dirichlet_group': [64, 1, 51, 14], 'disc_abs': 4225, 'disc_rad': 65, 'disc_sign': 1, 'frobs': [[2, [[2, 2]]], [3, [[2, 2]]], [5, [0]], [7, [[2, 2]]], [11, [[2, 2]]], [13, [0]], [17, [[2, 2]]], [19, [[2, 2]]], [23, [[2, 2]]], [29, [[1, 4]]], [31, [[2, 2]]], [37, [[2, 2]]], [41, [[2, 2]]], [43, [[2, 2]]], [47, [[2, 2]]], [53, [[2, 2]]], [59, [[2, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2, 2], 'galois_label': '4T2', 'galt': 2, 'grd': 8.06225774829855, 'index': 2, 'inessentialp': [2], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.4225.1', 'local_algs': ['5.4.2.1', '13.4.2.1'], 'monogenic': -1, 'num_ram': 2, 'r2': 0, 'ramps': [5, 13], 'rd': 8.0622577483, 'regulator': {'__RealLiteral__': 0, 'data': '3.19257767414', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-3.-1.1', '-1.-1.1', '-16.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{4} a^{3} - \\frac{7}{4} a - \\frac{1}{2} \\)', '\\( \\frac{1}{4} a^{3} - \\frac{11}{4} a - \\frac{3}{2} \\)', '\\( \\frac{1}{4} a^{3} - \\frac{1}{2} a^{2} - \\frac{9}{4} a + \\frac{9}{2} \\)'], 'unitsGmodule': [[14, 1]], 'unitsType': 'Type IV', 'used_grh': False, 'zk': ['1', 'a', '1/2*a^2 - 1/2*a', '1/4*a^3 + 1/4*a - 1/2']}