Hilbert modular form data - 4.4.17424.1-16.2-g

Formats: - HTML - YAML - JSON - 2024-05-19T13:13:14.350578

• 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': 17424, 'field_bad_primes': [2, 3, 11], 'field_label': '4.4.17424.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.17424.1-16.2-g', 'label_nsuffix': 6, 'label_suffix': 'g', 'level_bad_primes': [2], 'level_ideal': '[16, 4, -w^3 + 6*w]', 'level_label': '16.2', 'level_norm': 16, 'parallel_weight': 2, 'short_label': '16.2-g', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2,2,-1/2*w^3+7/2*w-1]', -1]], 'hecke_eigenvalues': [0, 'e', 'e^2 - 3', '-e^3 + e^2 + 4*e - 2', '-e^3 - e^2 + 4*e + 2', 'e^3 - 2*e^2 - 6*e + 3', '-e^3 - 2*e^2 + 6*e + 3', '-2*e^3 + e^2 + 8*e - 3', '-e^2 + 4*e + 1', '-e^2 - 4*e + 1', '2*e^3 + e^2 - 8*e - 3', '-e^3 + e^2 + 6*e - 4', 'e^3 + e^2 - 6*e - 4', '-4*e^2 - 2*e + 12', '2*e^3 - 10*e - 4', '2*e^3 - 10*e + 4', '4*e^2 - 2*e - 12', 'e^3 - 2*e^2 - 2*e + 3', '5*e^3 - 18*e - 9', '-5*e^3 + 18*e - 9', '-e^3 - 2*e^2 + 2*e + 3', '3*e^3 - 5*e^2 - 14*e + 10', '3*e^3 + 3*e^2 - 8*e - 10', '3*e^3 - 3*e^2 - 8*e + 10', '3*e^3 + 5*e^2 - 14*e - 10', '4*e^3 + 2*e^2 - 24*e', '2*e^3 - 6*e - 8', '2*e^3 - 6*e + 8', '4*e^3 - 2*e^2 - 24*e', '-8*e^3 - e^2 + 32*e + 1', '4*e^3 + e^2 - 16*e - 3', '-4*e^3 + e^2 + 16*e - 3', '8*e^3 - e^2 - 32*e + 1', '-4*e^3 + 2*e^2 + 18*e - 4', '-2*e^3 - 2*e^2 + 8*e', '-2*e^3 + 2*e^2 + 8*e', '-4*e^3 - 2*e^2 + 18*e + 4', '5*e^3 + 3*e^2 - 30*e - 8', '-5*e^3 + 3*e^2 + 30*e - 8', '-2*e^3 + e^2 + 4*e - 11', '4*e^3 + e^2 - 24*e + 5', '-4*e^3 + e^2 + 24*e + 5', '2*e^3 + e^2 - 4*e - 11', '3*e^3 + 9*e^2 - 12*e - 22', '-e^3 - e^2 + 2*e - 6', '-e^3 + e^2 + 2*e + 6', '3*e^3 - 9*e^2 - 12*e + 22', '-6*e^3 - e^2 + 24*e - 3', '2*e^3 - 3*e^2 - 16*e + 9', '-2*e^3 - 3*e^2 + 16*e + 9', '6*e^3 - e^2 - 24*e - 3', '6*e^3 - 4*e^2 - 22*e + 12', '4*e^3 - 2*e^2 - 18*e + 16', '4*e^3 + 2*e^2 - 18*e - 16', '6*e^3 + 4*e^2 - 22*e - 12', '-4*e^2 - 4*e + 20', '-2*e^3 - 2*e^2 + 2*e + 4', '-2*e^3 + 2*e^2 + 2*e - 4', '4*e^2 - 4*e - 20', '-2*e^2 - 10', '6*e^2 - 2', '2*e^3 - e^2 + 9', '-4*e^3 + 5*e^2 + 20*e - 19', '4*e^3 + 5*e^2 - 20*e - 19', '-2*e^3 - e^2 + 9', '8*e + 12', '6*e^3 - 2*e^2 - 22*e - 4', '6*e^3 + 2*e^2 - 22*e + 4', '8*e - 12', '-10*e^3 - 4*e^2 + 40*e - 4', '-2*e^3 - 4*e^2 - 2*e + 32', '-2*e^3 + 4*e^2 - 2*e - 32', '-10*e^3 + 4*e^2 + 40*e + 4', '2*e^3 + 4*e^2 - 4*e - 6', '-2*e^3 + 4*e^2 + 4*e - 6', '12*e^3 - 4*e^2 - 56*e - 2', '2*e^3 - 8*e^2 + 4*e + 30', '-2*e^3 - 8*e^2 - 4*e + 30', '-12*e^3 - 4*e^2 + 56*e - 2', '10*e^3 + 4*e^2 - 36*e - 10', '-2*e^3 - 2*e^2 + 4*e - 6', '2*e^3 - 2*e^2 - 4*e - 6', '-10*e^3 + 4*e^2 + 36*e - 10', '-8*e^3 - 4*e^2 + 44*e + 12', '-4*e^3 - 10*e^2 + 14*e + 20', '-4*e^3 + 10*e^2 + 14*e - 20', '-8*e^3 + 4*e^2 + 44*e - 12', '-e^2 - 4*e - 7', '7*e^2 + 4*e - 15', '7*e^2 - 4*e - 15', '-e^2 + 4*e - 7', '10*e^3 + 12*e^2 - 46*e - 16', '8*e^3 - 2*e^2 - 32*e - 16', '8*e^3 + 2*e^2 - 32*e + 16', '10*e^3 - 12*e^2 - 46*e + 16', '-11*e^3 - e^2 + 44*e - 14', '-3*e^3 - 5*e^2 + 18', '-3*e^3 + 5*e^2 - 18', '-11*e^3 + e^2 + 44*e + 14', '14*e^3 - 52*e', '-6*e^3 + 2*e^2 + 24*e - 20', '-6*e^3 - 2*e^2 + 24*e + 20', '14*e^3 - 52*e', '5*e^3 + 6*e^2 - 22*e - 25', '-5*e^3 + 6*e^2 + 22*e - 25', '3*e^3 + e^2 - 22*e + 2', '-3*e^3 + e^2 + 30*e - 6', '-3*e^3 - e^2 + 30*e + 6', '3*e^3 - e^2 - 22*e - 2', '-7*e^3 - 2*e^2 + 26*e + 11', '-7*e^3 + 2*e^2 + 26*e - 21', '7*e^3 + 2*e^2 - 26*e - 21', '7*e^3 - 2*e^2 - 26*e + 11', '7*e^3 - 5*e^2 - 14*e + 14', 'e^3 - e^2 - 2*e - 18', 'e^3 + e^2 - 2*e + 18', '7*e^3 + 5*e^2 - 14*e - 14', '2*e^3 + e^2 + 4*e + 1', '-10*e^3 + 5*e^2 + 36*e - 7', '10*e^3 + 5*e^2 - 36*e - 7', '-2*e^3 + e^2 - 4*e + 1', '-5*e^2 + 4*e + 5', '-6*e^3 - e^2 + 16*e - 11', '6*e^3 - e^2 - 16*e - 11', '-5*e^2 - 4*e + 5', '-10*e^3 + 8*e^2 + 50*e - 4', '-12*e^3 + 4*e^2 + 42*e - 4', '-12*e^3 - 4*e^2 + 42*e + 4', '-10*e^3 - 8*e^2 + 50*e + 4', '4*e^3 - 8*e^2 - 8*e + 14', '8*e^3 + 6*e^2 - 32*e + 2', '-8*e^3 + 6*e^2 + 32*e + 2', '-4*e^3 - 8*e^2 + 8*e + 14', '4*e^3 - 4*e^2 - 16*e + 20', '8*e^3 - 12*e^2 - 30*e + 40', '8*e^3 + 12*e^2 - 30*e - 40', '4*e^3 + 4*e^2 - 16*e - 20', '10*e^3 - 7*e^2 - 32*e + 25', '14*e^3 - 7*e^2 - 64*e + 1', '-14*e^3 - 7*e^2 + 64*e + 1', '-10*e^3 - 7*e^2 + 32*e + 25', '-20*e^2 + 58', '-8*e^2 + 18', '-14*e^3 + 4*e^2 + 62*e - 12', '-4*e^3 - 8*e^2 + 10*e + 44', '-4*e^3 + 8*e^2 + 10*e - 44', '-14*e^3 - 4*e^2 + 62*e + 12', '-9*e^2 + 17', '11*e^2 - 39'], 'hecke_polynomial': 'x^4 - 5*x^2 + 2', 'label': '4.4.17424.1-16.2-g'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 17424, 'ideals': ['[1, 1, 1]', '[2, 2, -1/2*w^3 + 7/2*w - 1]', '[2, 2, -w + 1]', '[4, 2, w]', '[4, 2, -1/2*w^3 + 5/2*w + 1]', '[4, 2, -1/2*w^3 + 7/2*w]', '[8, 2, w^3 - w^2 - 6*w + 6]', '[8, 2, -1/2*w^3 + w^2 + 3/2*w - 1]', '[8, 4, w + 2]', '[8, 4, -1/2*w^3 + 7/2*w + 2]', '[9, 3, 1/2*w^3 - 5/2*w]', '[11, 11, -w^2 + w + 1]', '[11, 11, w^2 + w - 1]', '[16, 2, 2]', '[16, 4, -w^3 + 6*w]', '[16, 4, -1/2*w^3 + 3/2*w]', '[16, 4, -w^2 + w + 2]', '[16, 4, -1/2*w^3 - w^2 + 7/2*w + 5]', '[18, 6, -1/2*w^3 + w^2 + 5/2*w - 5]', '[18, 6, 1/2*w^3 - w^2 - 5/2*w + 2]', '[22, 22, 1/2*w^3 - w^2 - 5/2*w + 4]', '[22, 22, 1/2*w^3 - w^2 - 5/2*w + 3]', '[22, 22, -1/2*w^3 - w^2 + 5/2*w + 3]', '[22, 22, -1/2*w^3 - w^2 + 5/2*w + 4]', '[25, 5, 1/2*w^3 - w^2 - 7/2*w + 4]', '[25, 5, -1/2*w^3 - w^2 + 7/2*w + 4]', '[32, 4, -w^3 - w^2 + 6*w + 4]', '[32, 4, -w^3 + 7*w - 2]', '[32, 4, -1/2*w^3 - w^2 + 3/2*w + 3]', '[32, 4, -2*w + 2]', '[32, 8, -w^2 + 2*w]', '[32, 8, -w^3 - w^2 + 7*w + 7]', '[36, 6, w^2 - 5]', '[36, 6, w^2 - 2]', '[36, 6, 1/2*w^3 - 5/2*w - 3]', '[37, 37, -w^3 + 7*w + 1]', '[37, 37, -2*w + 1]', '[37, 37, 2*w + 1]', '[37, 37, -w^3 + 7*w - 1]', '[44, 22, -1/2*w^3 + 3/2*w + 2]', '[44, 22, 1/2*w^3 - 1/2*w + 1]', '[44, 22, -w^3 + 6*w - 2]', '[44, 22, -w^3 + 6*w + 2]', '[44, 22, -1/2*w^3 + 1/2*w + 1]', '[44, 22, 1/2*w^3 - 3/2*w + 2]', '[49, 7, 1/2*w^3 - 9/2*w + 2]', '[49, 7, -1/2*w^3 + 9/2*w + 2]', '[50, 10, -3/2*w^3 - w^2 + 19/2*w + 5]', '[50, 10, -3/2*w^3 + w^2 + 19/2*w - 5]', '[50, 10, 1/2*w^3 - w^2 - 1/2*w + 2]', '[50, 10, -1/2*w^3 - w^2 + 1/2*w + 2]', '[64, 4, 2*w]', '[64, 4, -w^3 + 5*w + 2]', '[64, 4, -w^3 + 7*w]', '[64, 8, -w^2 + 4]', '[64, 8, -w^2 + 3]', '[64, 8, -w^3 - w^2 + 6*w + 8]', '[64, 8, -1/2*w^3 + w^2 + 3/2*w + 1]', '[72, 6, 1/2*w^3 - w^2 + 1/2*w - 1]', '[72, 6, 2*w^3 - w^2 - 13*w + 8]', '[72, 12, w^3 + w^2 - 5*w - 5]', '[72, 12, w^3 + w^2 - 5*w - 2]', '[74, 74, -1/2*w^3 + w^2 + 5/2*w - 1]', '[74, 74, -1/2*w^3 + 3/2*w - 3]', '[74, 74, 1/2*w^3 - w^2 - 5/2*w + 6]', '[74, 74, -w^3 + 6*w + 3]', '[74, 74, -w^3 + 6*w - 3]', '[74, 74, 1/2*w^3 + w^2 - 5/2*w - 6]', '[74, 74, -1/2*w^3 + 3/2*w + 3]', '[74, 74, -1/2*w^3 - w^2 + 5/2*w + 1]', '[81, 3, 3]', '[83, 83, 1/2*w^3 + w^2 - 7/2*w - 2]', '[83, 83, w^2 + w - 5]', '[83, 83, w^2 - w - 5]', '[83, 83, -1/2*w^3 + w^2 + 7/2*w - 2]', '[88, 22, -3/2*w^3 - w^2 + 17/2*w + 5]', '[88, 22, -w^3 + w^2 + 4*w - 2]', '[88, 22, -3/2*w^3 + w^2 + 17/2*w - 5]', '[88, 22, -w^3 - w^2 + 4*w + 2]', '[88, 44, -2*w^3 + w^2 + 12*w - 5]', '[88, 44, -w^3 - w^2 + 3*w + 2]', '[88, 44, -w^3 + w^2 + 3*w - 2]', '[88, 44, -2*w^3 - w^2 + 12*w + 5]', '[97, 97, -1/2*w^3 + w^2 + 7/2*w - 8]', '[97, 97, 5/2*w^3 - w^2 - 31/2*w + 6]', '[97, 97, -11/2*w^3 + 4*w^2 + 71/2*w - 26]', '[97, 97, -9/2*w^3 + 4*w^2 + 57/2*w - 24]', '[98, 14, 1/2*w^3 + w^2 - 5/2*w - 7]', '[98, 14, 3/2*w^3 - w^2 - 23/2*w + 11]', '[98, 14, -1/2*w^3 - w^2 + 13/2*w - 4]', '[98, 14, 1/2*w^3 + w^2 - 5/2*w]', '[99, 33, -1/2*w^3 + w^2 - 1/2*w - 2]', '[99, 33, 1/2*w^3 + w^2 + 1/2*w - 2]', '[100, 10, -1/2*w^3 + 9/2*w - 1]', '[100, 10, -w^3 + w^2 + 3*w]', '[100, 10, -w^3 + 4*w + 2]', '[100, 10, -1/2*w^3 + 9/2*w + 1]', '[100, 10, -2*w^3 - w^2 + 12*w + 7]', '[100, 10, -2*w^3 + w^2 + 12*w - 7]', '[107, 107, w^3 - 7*w - 3]', '[107, 107, 2*w - 3]', '[107, 107, 1/2*w^3 - w^2 + 1/2*w - 2]', '[107, 107, -w^3 + 7*w - 3]', '[121, 11, -1/2*w^3 + 9/2*w]', '[121, 11, -w^3 + 5*w + 1]', '[121, 11, -w^3 + 5*w - 1]', '[128, 4, 2*w^3 - 2*w^2 - 12*w + 12]', '[128, 4, -w^3 + 2*w^2 + 3*w - 2]', '[128, 8, -w^3 - w^2 + 4*w + 4]', '[128, 8, -3/2*w^3 - w^2 + 17/2*w + 3]', '[128, 8, 2*w + 4]', '[128, 8, -w^3 + 7*w + 4]', '[128, 16, -2*w^3 - w^2 + 12*w + 4]', '[128, 16, -w^3 - w^2 + 3*w + 3]', '[131, 131, -1/2*w^3 + w^2 + 3/2*w - 4]', '[131, 131, -w^3 + w^2 + 6*w - 3]', '[131, 131, w^3 + w^2 - 6*w - 3]', '[131, 131, 1/2*w^3 + w^2 - 3/2*w - 4]', '[144, 6, w^3 - 5*w]', '[144, 12, -w^2 - 1]', '[144, 12, w^2 - 8]', '[144, 12, w^2 - 3*w - 2]', '[144, 12, 3/2*w^3 + w^2 - 21/2*w - 5]', '[148, 74, w + 4]', '[148, 74, -w^3 - w^2 + 3*w + 1]', '[148, 74, -3/2*w^3 - 2*w^2 + 19/2*w + 11]', '[148, 74, 2*w^3 - w^2 - 12*w + 6]', '[148, 74, -1/2*w^3 + 7/2*w - 4]', '[148, 74, -1/2*w^3 + 2*w^2 + 1/2*w - 3]', '[148, 74, -1/2*w^3 + 7/2*w + 4]', '[148, 74, -1/2*w^3 - 2*w^2 + 1/2*w + 3]', '[148, 74, -2*w^3 - w^2 + 12*w + 6]', '[148, 74, -w^3 + w^2 + 3*w - 1]', '[148, 74, 3/2*w^3 - 2*w^2 - 19/2*w + 11]', '[148, 74, -w + 4]', '[157, 157, w^3 - w^2 - 8*w + 3]', '[157, 157, -w^2 + 3*w + 1]', '[157, 157, -3/2*w^3 + 2*w^2 + 11/2*w - 4]', '[157, 157, -w^3 - w^2 + 8*w + 3]', '[162, 6, -3/2*w^3 + 21/2*w - 3]', '[162, 6, -3*w + 3]', '[166, 166, 1/2*w^3 - 3/2*w - 5]', '[166, 166, -w^3 + 6*w - 5]', '[166, 166, 5/2*w^3 - w^2 - 29/2*w + 3]', '[166, 166, -3/2*w^3 + w^2 + 11/2*w - 4]', '[166, 166, -1/2*w^3 + w^2 - 3/2*w]', '[166, 166, 5/2*w^3 - w^2 - 33/2*w + 7]', '[166, 166, -w^3 + 2*w^2 + 4*w - 5]', '[166, 166, 3/2*w^3 - 2*w^2 - 17/2*w + 9]', '[167, 167, -1/2*w^3 + 1/2*w - 2]', '[167, 167, 3/2*w^3 - 19/2*w + 2]', '[167, 167, -9/2*w^3 + 3*w^2 + 59/2*w - 22]', '[167, 167, -1/2*w^3 + 1/2*w + 2]', '[169, 13, w^3 - 5*w - 5]', '[169, 13, 1/2*w^3 - 5/2*w - 4]', '[176, 22, -2*w^2 + 2*w + 2]', '[176, 22, 2*w^2 + 2*w - 2]', '[176, 44, -1/2*w^3 + w^2 + 7/2*w - 1]', '[176, 44, -w^3 - w^2 + 7*w + 3]', '[176, 44, -w^2 + w + 6]', '[176, 44, -w^2 - 2*w + 4]', '[176, 44, -w^2 + 2*w + 4]', '[176, 44, -w^2 - w + 6]', '[176, 44, -w^3 + w^2 + 7*w - 3]', '[176, 44, -1/2*w^3 - w^2 + 7/2*w + 1]', '[181, 181, 1/2*w^3 - 2*w^2 - 1/2*w]', '[181, 181, -3/2*w^3 + 2*w^2 + 19/2*w - 14]', '[181, 181, -3/2*w^3 - 2*w^2 + 19/2*w + 14]', '[181, 181, 1/2*w^3 + 2*w^2 - 1/2*w]', '[194, 194, 1/2*w^3 + w^2 - 9/2*w - 6]', '[194, 194, 3/2*w^3 + w^2 - 19/2*w - 4]', '[194, 194, -1/2*w^3 - w^2 + 9/2*w + 1]', '[194, 194, -1/2*w^3 + w^2 + 1/2*w - 3]', '[194, 194, 3/2*w^3 - 13/2*w - 5]', '[194, 194, 3/2*w^3 - 17/2*w - 5]', '[194, 194, -3/2*w^3 + w^2 + 19/2*w - 4]', '[194, 194, -1/2*w^3 + w^2 + 9/2*w - 6]', '[196, 14, w^2 - 2*w + 2]', '[196, 14, 3/2*w^3 + 2*w^2 - 19/2*w - 9]', '[196, 14, 1/2*w^3 - 2*w^2 - 1/2*w + 5]', '[196, 14, -w^2 - 2*w - 2]', '[196, 14, w^3 - w^2 - 7*w + 9]', '[196, 14, w^3 + w^2 - 7*w - 9]', '[198, 66, w^3 - 8*w + 3]', '[198, 66, 1/2*w^3 - 11/2*w + 3]', '[198, 66, 1/2*w^3 - 11/2*w - 3]', '[198, 66, w^3 - 8*w - 3]', '[200, 10, -w^2 + w + 8]', '[200, 10, -w^2 - w + 8]', '[200, 10, -1/2*w^3 - w^2 + 7/2*w - 1]', '[200, 10, -1/2*w^3 + w^2 + 7/2*w + 1]', '[200, 20, w^3 - w^2 - 5*w + 6]', '[200, 20, -w^3 + w^2 + 5*w - 1]', '[200, 20, -w^3 - w^2 + 5*w + 6]', '[200, 20, -w^3 - w^2 + 5*w + 1]', '[214, 214, w^3 - 4*w + 1]', '[214, 214, 3/2*w^3 - 17/2*w + 1]', '[214, 214, 3*w^3 + 2*w^2 - 20*w - 11]', '[214, 214, 5/2*w^3 - 2*w^2 - 35/2*w + 17]', '[214, 214, 1/2*w^3 + 2*w^2 - 7/2*w - 11]', '[214, 214, 5/2*w^3 + w^2 - 33/2*w - 6]', '[214, 214, 3/2*w^3 - 17/2*w - 1]', '[214, 214, -w^3 + 10*w - 7]', '[225, 15, w^3 - w^2 - 8*w + 5]', '[225, 15, w^3 + w^2 - 8*w - 5]', '[227, 227, -2*w^3 + 2*w^2 + 12*w - 13]', '[227, 227, -3/2*w^3 + 3*w^2 + 9/2*w - 4]', '[227, 227, -w^3 + 2*w^2 + 3*w - 1]', '[227, 227, -3*w^3 + 3*w^2 + 18*w - 17]', '[229, 229, -3/2*w^3 + w^2 + 21/2*w - 10]', '[229, 229, 1/2*w^3 - 2*w^2 - 1/2*w + 4]', '[229, 229, -w^2 + 3*w - 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4*w^2 + 7/2*w + 3]', '[1964, 982, w^3 - 2*w^2 - 8*w + 14]', '[1964, 982, 3/2*w^3 + 2*w^2 - 15/2*w - 17]', '[1964, 982, 1/2*w^3 + 2*w^2 - 11/2*w]', '[1979, 1979, 3/2*w^3 + w^2 - 21/2*w + 6]', '[1979, 1979, 3/2*w^3 - 2*w^2 - 23/2*w + 16]', '[1979, 1979, w^2 + 3*w - 13]', '[1979, 1979, -1/2*w^3 - 2*w^2 + 13/2*w - 2]', '[1991, 1991, -3/2*w^3 + w^2 + 13/2*w - 8]', '[1991, 1991, 3/2*w^3 + w^2 - 21/2*w]', '[1991, 1991, w^2 + 3*w - 7]', '[1991, 1991, 5/2*w^3 - 3*w^2 - 35/2*w + 12]', '[1991, 1991, -5/2*w^3 - 3*w^2 + 35/2*w + 12]', '[1991, 1991, -w^2 + 3*w + 7]', '[1991, 1991, -3/2*w^3 + w^2 + 21/2*w]', '[1991, 1991, -3*w^2 - 5*w + 9]', '[2012, 1006, -w^3 - w^2 + w + 4]', '[2012, 1006, -1/2*w^3 - 2*w^2 + 13/2*w + 9]', '[2012, 1006, -1/2*w^3 - 2*w^2 + 3/2*w + 12]', '[2012, 1006, w^3 + 2*w^2 - 6*w - 2]', '[2012, 1006, 3/2*w^3 + 2*w^2 - 23/2*w - 5]', '[2012, 1006, 3*w^3 - w^2 - 19*w + 3]', '[2012, 1006, 5/2*w^3 - 29/2*w - 7]', '[2012, 1006, 3*w^3 + w^2 - 19*w - 3]', '[2012, 1006, w^3 - 2*w^2 - 6*w + 2]', '[2012, 1006, -1/2*w^3 + 2*w^2 + 3/2*w - 12]', '[2012, 1006, 3/2*w^3 - 11/2*w - 7]', '[2012, 1006, -w^3 + w^2 + w - 4]', '[2017, 2017, 7*w^3 - 4*w^2 - 47*w + 31]', '[2017, 2017, w^3 - 4*w^2 + 7*w - 3]', '[2017, 2017, -5/2*w^3 + 3*w^2 + 11/2*w]', '[2017, 2017, -6*w^3 + 3*w^2 + 37*w - 21]', '[2025, 15, 3/2*w^3 - 3*w^2 - 21/2*w + 12]', '[2025, 15, -3/2*w^3 - 3*w^2 + 21/2*w + 12]', '[2029, 2029, w^2 - 5*w - 1]', '[2029, 2029, -5/2*w^3 + w^2 + 35/2*w - 6]', '[2029, 2029, 5/2*w^3 + w^2 - 35/2*w - 6]', '[2029, 2029, 7/2*w^3 - 6*w^2 - 19/2*w + 8]', '[2038, 2038, -3/2*w^3 + 5*w^2 + 3/2*w - 6]', '[2038, 2038, -9/2*w^3 + 4*w^2 + 59/2*w - 29]', '[2038, 2038, 2*w^3 - 2*w^2 - 7*w + 3]', '[2038, 2038, 9/2*w^3 - 3*w^2 - 61/2*w + 21]', '[2038, 2038, 7/2*w^3 - w^2 - 35/2*w - 5]', '[2038, 2038, -1/2*w^3 + 3*w^2 - 11/2*w]', '[2038, 2038, -9/2*w^3 + 5*w^2 + 57/2*w - 29]', '[2038, 2038, -5/2*w^3 - w^2 + 29/2*w - 10]', '[2042, 2042, -3/2*w^3 + 3*w^2 + 3/2*w - 5]', '[2042, 2042, -3/2*w^3 - w^2 + 23/2*w - 1]', '[2042, 2042, 9/2*w^3 + 3*w^2 - 57/2*w - 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1/2*w + 4]', '[229, 229, -w^2 + 3*w - 3]', '[229, 229, -3/2*w^3 + 2*w^2 + 19/2*w - 10]', '[239, 239, 1/2*w^3 + w^2 - 7/2*w]', '[239, 239, w^2 - w - 7]', '[239, 239, w^2 + w - 7]', '[239, 239, 1/2*w^3 - w^2 - 7/2*w]', '[263, 263, 4*w^3 - 3*w^2 - 25*w + 17]', '[263, 263, -3/2*w^3 + 3*w^2 + 5/2*w - 4]', '[263, 263, -w^3 + 2*w^2 + w - 3]', '[263, 263, -3*w^3 + 2*w^2 + 19*w - 11]', '[289, 17, 2*w^2 - 11]', '[289, 17, 2*w^2 - 3]', '[313, 313, -3/2*w^3 - w^2 + 17/2*w + 10]', '[313, 313, w^3 - w^2 - 4*w - 3]', '[313, 313, -1/2*w^3 + w^2 + 3/2*w + 2]', '[313, 313, -w^3 - w^2 + 6*w + 9]', '[347, 347, 2*w^3 - 12*w - 3]', '[347, 347, w^3 - 3*w - 3]', '[347, 347, -w^3 + 3*w - 3]', '[347, 347, -2*w^3 + 12*w - 3]', '[359, 359, 3/2*w^3 - 19/2*w - 6]', '[359, 359, 1/2*w^3 - 1/2*w - 6]', '[359, 359, -1/2*w^3 + 1/2*w - 6]', '[359, 359, -3/2*w^3 + 19/2*w - 6]', '[361, 19, 3/2*w^3 - w^2 - 13/2*w]', '[361, 19, 2*w^3 + w^2 - 11*w - 7]', '[397, 397, 1/2*w^3 + 2*w^2 - 9/2*w - 8]', '[397, 397, 2*w^2 - 2*w - 5]', '[397, 397, 1/2*w^3 + 2*w^2 - 9/2*w - 6]', '[397, 397, w^3 + 2*w^2 - 7*w - 9]', '[421, 421, 7/2*w^3 - 2*w^2 - 43/2*w + 12]', '[421, 421, -w^3 + 3*w^2 - 2*w - 1]', '[421, 421, 3/2*w^3 - 2*w^2 - 7/2*w + 2]', '[421, 421, -9/2*w^3 + 3*w^2 + 59/2*w - 20]', '[431, 431, 1/2*w^3 + w^2 - 3/2*w - 10]', '[431, 431, -11/2*w^3 + 5*w^2 + 69/2*w - 32]', '[431, 431, -7/2*w^3 + 4*w^2 + 43/2*w - 24]', '[431, 431, -1/2*w^3 + w^2 + 3/2*w - 10]', '[433, 433, 2*w^3 - w^2 - 11*w + 3]', '[433, 433, 3/2*w^3 - w^2 - 13/2*w + 4]', '[433, 433, -w^3 + 4*w^2 - 3*w - 3]', '[433, 433, -5*w^3 + 4*w^2 + 33*w - 25]', '[479, 479, 3/2*w^3 - 19/2*w - 4]', '[479, 479, w^3 + 2*w^2 - 9*w - 9]', '[479, 479, -1/2*w^3 + 1/2*w + 4]', '[479, 479, w^3 + 2*w^2 - 9*w - 5]', '[491, 491, 5/2*w^3 + w^2 - 31/2*w - 4]', '[491, 491, w^3 + w^2 - 2*w - 3]', '[491, 491, w^3 - w^2 - 2*w + 3]', '[491, 491, 5/2*w^3 - w^2 - 31/2*w + 4]', '[503, 503, -w^3 - w^2 + 6*w + 1]', '[503, 503, -1/2*w^3 + w^2 + 3/2*w - 6]', '[503, 503, 1/2*w^3 + w^2 - 3/2*w - 6]', '[503, 503, w^3 - w^2 - 6*w + 1]', '[529, 23, -3/2*w^3 + 15/2*w + 2]', '[529, 23, 3/2*w^3 - 15/2*w + 2]', '[563, 563, -w^3 + 3*w^2 - 5]', '[563, 563, 2*w^3 - w^2 - 11*w + 1]', '[563, 563, -2*w^3 - w^2 + 11*w + 1]', '[563, 563, 3/2*w^3 - 2*w^2 - 11/2*w + 6]', '[577, 577, -1/2*w^3 + 3*w^2 - 1/2*w - 4]', '[577, 577, -2*w^3 + 3*w^2 + 13*w - 17]', '[577, 577, -5*w^3 + 4*w^2 + 33*w - 29]', '[577, 577, -w^3 + 4*w^2 - 3*w + 1]', '[659, 659, 2*w^2 - 2*w - 9]', '[659, 659, 2*w^3 - 3*w^2 - 9*w + 7]', '[659, 659, 3/2*w^3 - 2*w^2 - 11/2*w]', '[659, 659, -5/2*w^3 - 2*w^2 + 29/2*w + 14]', '[661, 661, -w^3 + 3*w^2 + 2*w - 5]', '[661, 661, -5/2*w^3 + 3*w^2 + 31/2*w - 16]', '[661, 661, -5/2*w^3 + 2*w^2 + 33/2*w - 16]', '[661, 661, -1/2*w^3 + 2*w^2 - 3/2*w + 2]', '[709, 709, 3/2*w^3 - w^2 - 13/2*w + 2]', '[709, 709, -2*w^3 - w^2 + 11*w + 5]', '[709, 709, 2*w^3 - w^2 - 11*w + 5]', '[709, 709, -3/2*w^3 - w^2 + 13/2*w + 2]', '[743, 743, w^3 - 2*w^2 - 5*w + 3]', '[743, 743, w^3 - 2*w^2 - 5*w + 11]', '[743, 743, w^3 + 2*w^2 - 5*w - 11]', '[743, 743, -w^3 - 2*w^2 + 5*w + 3]', '[757, 757, 8*w^3 - 6*w^2 - 50*w + 37]', '[757, 757, -w^3 + 3*w^2 + 6*w - 17]', '[757, 757, w^3 + 3*w^2 - 6*w - 17]', '[757, 757, -3*w^3 + w^2 + 20*w - 7]', '[827, 827, w^3 - w^2 - 6*w - 1]', '[827, 827, 1/2*w^3 + w^2 - 3/2*w - 8]', '[827, 827, -1/2*w^3 + w^2 + 3/2*w - 8]', '[827, 827, -w^3 - w^2 + 6*w - 1]', '[829, 829, -1/2*w^3 + 2*w^2 + 5/2*w - 8]', '[829, 829, 1/2*w^3 + 2*w^2 - 5/2*w - 6]', '[829, 829, -1/2*w^3 + 2*w^2 + 5/2*w - 6]', '[829, 829, 1/2*w^3 + 2*w^2 - 5/2*w - 8]', '[841, 29, 2*w^2 - 9]', '[841, 29, 2*w^2 - 5]', '[887, 887, 2*w^3 - w^2 - 13*w + 3]', '[887, 887, 1/2*w^3 - w^2 + 1/2*w + 4]', '[887, 887, 1/2*w^3 + w^2 + 1/2*w - 4]', '[887, 887, 2*w^3 + w^2 - 13*w - 3]', '[961, 31, 2*w^2 - 15]', '[961, 31, 7/2*w^3 - 43/2*w]']}
• 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, -7, 0, 1], 'conductor': 132, 'degree': 4, 'dirichlet_group': [23, 1, 43, 65], 'disc_abs': 17424, 'disc_rad': 66, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[2, 2]]], [7, [[2, 2]]], [11, [0]], [13, [[2, 2]]], [17, [[2, 2]]], [19, [[2, 2]]], [23, [[2, 2]]], [29, [[2, 2]]], [31, [[2, 2]]], [37, [[1, 4]]], [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': [4, 2, 2], 'galois_label': '4T2', 'galt': 2, 'grd': 11.489125293076057, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.17424.1', 'local_algs': ['2.2.2.2', '2.2.2.2', '3.4.2.1', '11.2.1.1', '11.2.1.1'], 'monogenic': -1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 3, 11], 'rd': 11.4891252931, 'regulator': {'__RealLiteral__': 0, 'data': '15.0904428273', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-3.0.1', '-11.0.1', '-8.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{3} - \\frac{5}{2} a - 2 \\)', '\\( a^{3} + a^{2} - 6 a - 5 \\)', '\\( \\frac{1}{2} a^{3} - \\frac{1}{2} a \\)'], 'unitsGmodule': [[1, 1], [4, 1]], 'unitsType': 'Type II (ii)', 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2*a']}