Hilbert modular form data - 4.4.11025.1-20.3-e

Formats: - HTML - YAML - JSON - 2024-05-04T08:18:06.080662

• 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': 11025, 'field_bad_primes': [3, 5, 7], 'field_label': '4.4.11025.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.11025.1-20.3-e', 'label_nsuffix': 4, 'label_suffix': 'e', 'level_bad_primes': [2, 5], 'level_ideal': '[20,10,1/4*w^3 - 13/4*w - 2]', 'level_label': '20.3', 'level_norm': 20, 'parallel_weight': 2, 'short_label': '20.3-e', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[4,2,-1/8*w^3 + 1/2*w^2 + 5/8*w - 3/2]', 1], ['[5,5,1/8*w^3 - 1/8*w - 1/2]', -1]], 'hecke_eigenvalues': ['e', -1, 1, '-e - 3', '-3*e - 3', '-3*e + 5', '2*e', '2*e + 2', '2*e - 2', '6*e + 4', -4, '-e + 5', '-2*e + 4', '2*e - 2', 'e + 5', '6*e + 4', '-8*e - 10', 'e + 5', '-3*e - 11', '6*e + 2', '2*e - 12', '-2*e - 2', '4*e - 6', '4*e - 4', '-e + 9', '-6*e - 16', 8, '-3*e - 9', '10*e + 8', '4*e + 10', '-4*e', '6*e - 2', '2*e', '-9*e - 13', '-2*e - 10', '10*e + 6', '2*e + 2', '-9*e - 11', '13*e + 7', '4*e - 4', '-e - 5', '4*e + 18', '11*e - 1', '-10*e - 6', '-2*e - 2', '6*e + 14', '7*e + 1', '4*e', '4*e + 4', '-12*e', '3*e - 1', '6*e + 10', '8*e - 10', '2*e - 14', '-7*e + 11', '-6*e - 20', '6*e + 18', '-4*e - 20', '-7*e - 17', '6*e - 12', '-9*e - 27', '-4*e + 4', '-e - 5', '5*e + 15', '4*e - 10', -12, 'e + 5', '6*e + 6', '-3*e - 9', '-19*e - 19', '-12*e - 30', '7*e - 9', '-12*e - 32', '9*e + 11', '-4*e - 18', '-4*e + 16', '6*e + 14', '-e + 15', '-24*e - 24', '12*e + 16', '3*e + 23', '-19*e - 15', '7*e + 13', '21*e + 17', '-14*e - 24', '18*e + 24', -4, '4*e - 16', 24, '-e + 13', '12*e + 20', '-9*e - 11', '-14*e - 4', '-26*e - 20', '-11*e + 11', '28*e + 28', '-e - 39', '4*e - 18', '6*e + 6', '4*e - 8', 'e + 31', '-2*e', '-4*e + 6', '-3*e - 13', '-2*e - 4', 30, '-6*e - 8', '10*e + 30', '-13*e - 35', '6*e - 6', '4*e + 28', '13*e + 27', '-4*e - 42', '-15*e - 9', '-8*e - 2', '6*e - 16', '-8*e + 10', '2*e - 24', '7*e + 11', '12*e + 20', '-26*e - 12', '8*e + 32', '-6*e + 4', '20*e + 32', '-2*e + 20', '-10*e - 6', '11*e - 13', '-6*e - 24', '-34*e - 38', '2*e - 46', '-20*e - 26', '-8*e + 10', '17*e - 1', -4, '-12*e + 12', '-10*e + 8', '-3*e + 19', '-e - 43', '10*e + 8', '7*e - 7', '12*e + 20', '-36*e - 42', '-16*e - 8', '-8*e', '2*e + 40', '-2*e - 22', '-24*e - 34', '14*e + 12', '-16*e - 34', -34, '-24*e - 42', '6*e - 4', '12*e + 6', '-10*e + 4', '10*e - 32', '5*e + 53', '-2*e - 10', '12*e + 4', '15*e - 15', '17*e - 7', '-32*e - 26', '-15*e + 1', '12*e + 4', '-24*e - 22', '-16*e + 12', '20*e - 2', '-24*e - 38', '22*e + 38', -10, '21*e + 11', '-6*e - 28', '-4*e + 22', '2*e - 10', '-8*e - 52', '2*e + 30', '-15*e - 43', '-2*e + 10', '-3*e - 21', '-12*e - 18', '14*e - 4', '-2*e + 48', '8*e + 38', '-19*e - 33', 28, '-16*e - 30', '-18*e - 24', '-3*e - 13', '23*e + 49', '-10*e - 2', '-10*e - 34', -48, '-4*e - 26', '-36*e - 30', '-22*e - 18', '-4*e - 16', '24*e', '-20*e - 42', '-6*e + 24', '40*e + 42', '-26*e - 44', '8*e + 6', '-4*e - 14', 44, '-20*e - 50', '3*e + 33', '-8*e + 8', '10*e - 14', '38*e + 40', '3*e + 11', '-12*e - 34', '-30*e - 22', '-4*e + 20', '-15*e - 35', '4*e - 40', '10*e - 2', '6*e - 36', '-8*e + 12', '11*e + 55', '38*e + 22', '5*e + 53', '-13*e + 1', '-18*e - 12', '-17*e - 49', '-24*e - 54', '18*e - 26', '34*e + 36', '-24*e + 10', '-32*e - 16', '-12*e - 6', '35*e + 29', '28*e + 2', '-2*e + 54', '-9*e - 9', -54, '-10*e + 6', '-24*e - 16', '-9*e + 17', '-30*e - 12', '-22*e + 2', '17*e + 1', '25*e + 33', '12*e + 54', '-16*e - 48', '-4*e + 6', '-39*e - 17', '15*e - 5', '8*e + 42', '15*e - 37', '-38*e - 34', '-19*e - 37', '21*e + 39', '11*e + 11', '5*e - 55', '-12*e + 12', '32*e + 22', '-34*e - 38', '8*e + 18', '-12*e + 30', '-8*e - 30', '4*e - 50', '-38*e - 50', '-5*e - 25', '-2*e + 12', '12*e + 22', '14*e - 16', '34*e + 32', '12*e - 4', '-28*e', '-e + 17', -24, '-12*e - 32', '9*e - 13', '-12*e + 22', '-8*e - 2', '15*e - 17', '18*e + 16', '19*e - 29', '-14*e', '52*e + 48', -48, '16*e - 14', '-14*e + 6', '-8*e - 52', '-24*e - 30', '12*e + 16', '23*e + 23', '26*e + 42', -20, '-4*e - 38', '12*e + 16', '40*e + 38', '32*e + 24', '34*e + 64', '-6*e - 22', '10*e - 4', '-24*e - 24', '20*e + 2', '-8*e + 48', '-10*e - 36', '4*e - 18', '36*e + 34', '-36*e - 16', '-40*e - 36', '-2*e + 46', '-18*e - 52', '-2*e - 10', '-9*e - 3', '24*e + 32', '38*e + 28', '-42*e - 56', '-16*e + 48', '-18*e', '-4*e + 64', '32*e + 68', '2*e - 30', '-51*e - 67', '14*e - 40', '-8*e + 38', 42, '28*e + 54', '-23*e + 9', '-55*e - 41', '10*e + 2', '23*e - 17', '-16*e + 34', '12*e - 22', '32*e + 42', '7*e + 73', '43*e + 21', '-28*e - 16', '-16*e - 16', '-5*e - 17', '-16*e - 40', '2*e + 14', '32*e + 46', '28*e + 30', '-18*e + 14', '-12*e - 46', '8*e - 12', '-9*e + 47', '-6*e - 30', '-26*e - 60', '26*e + 20', '-29*e - 25', '32*e + 16', '-12*e - 6', -2, '-6*e - 2', '29*e + 45', '24*e + 56', 'e + 29', '8*e - 22', '-26*e + 10', '-11*e - 19', '32*e + 74', '21*e - 27', '-32*e - 24', '-40*e - 64', 'e - 57', '3*e - 41', '-40*e - 44', '-8*e - 48', '-16*e - 46', '-40*e - 42', '29*e + 19', '-3*e + 19', '18*e + 6', '-20*e - 66', '-20*e + 4', '-32*e + 16', '-58*e - 48', '-30*e + 28', '-e - 47', '37*e + 13', '-60*e - 56', '20*e + 24', -42, -30, '38*e + 68', '11*e - 43', '-4*e + 8', '52*e + 54', '2*e - 16', '-46*e - 74', '32*e', '16*e - 44', '28*e + 68', 10, '-20*e - 56', '6*e + 92', '11*e - 13', '-18*e - 62', '34*e', '-20*e - 2', '35*e + 33', '-20*e - 76', '5*e + 17', '7*e + 61', '68*e + 72', '26*e - 40', '48*e + 56', '28*e + 46', '-20*e - 46', '-26*e - 6', '-20*e + 2', '-6*e - 28', '43*e + 15', '-10*e - 10', '-16*e + 18', '56*e + 52', '8*e - 56', '-24*e - 28', '-25*e - 15', '-42*e - 28', '-30*e - 8', '-8*e - 54', '8*e + 46', '-33*e - 61', '-20*e - 88', '-4*e + 40', '15*e - 39', '-12*e - 28', '-10*e - 74', '10*e + 20', '-8*e - 50', '-38*e - 4', '-2*e + 28', '-8*e - 36', '-14*e - 60', '35*e + 11', '-28*e - 32', '-28*e + 18', '42*e + 32', '-21*e - 51', '42*e + 40', '23*e + 61', '-24*e - 58', '39*e + 77', '37*e + 83', '-4*e - 90', 22, '6*e - 52', '-33*e - 75', '44*e + 86', '11*e + 95', '42*e + 70', '-4*e + 26', '-28*e - 72', '-30*e - 36', '44*e + 76', '-40*e - 46', '-52*e - 68', '-18*e - 60', '14*e - 38', '-20*e - 90', '-6*e - 40', '33*e + 23', '-24*e - 28', '-28*e - 12', '-40*e - 86', '-64*e - 44', '32*e + 30', '-16*e - 78', '-60*e - 56', '-9*e - 49', '-8*e - 26', '42*e + 48', '18*e + 38', '-35*e - 23', '36*e + 80', '-4*e + 18', '-44*e - 38', '38*e - 10', '-57*e - 63', '18*e + 62', '6*e + 58', '-35*e + 15', '-17*e + 11', '-62*e - 68', '-48*e - 18', '-14*e + 66', '-12*e - 78', '-12*e - 92', '-36*e - 8', '42*e + 22', '-28*e - 6', '-24*e + 8', '-24*e - 34', '23*e + 59', '28*e + 48', '-e + 67', '8*e + 16', '-8*e + 56', 74, '-60*e - 82', '-16*e - 32', '23*e + 27', '-13*e - 51', '40*e + 82', '24*e', '40*e + 26', '33*e + 29', '-32*e + 28', '14*e - 64', '-44*e - 30', -16, '42*e + 40', '16*e - 28', '-14*e - 58', '-37*e - 53', '-20*e - 76', '48*e + 36', '62*e + 92', '-29*e - 55', '22*e + 76', '3*e + 7', '-16*e - 34', '-3*e + 13', '32*e + 68', '-5*e + 13', '-2*e - 92', '10*e - 80', '-2*e + 110', '-22*e - 4', '42*e + 56', '4*e + 28', '-21*e + 23', '56*e + 42', '15*e + 69', '67*e + 53', '32*e + 42', '-2*e - 66', '56*e + 40', '28*e + 12', '-4*e + 4', '30*e - 6', '20*e - 4', '42*e - 6', '-40*e - 66', '20*e - 58', '-37*e - 3', '-30*e - 60', '-17*e - 1', '45*e + 77', '-50*e - 62', '12*e - 40', '8*e + 24', '12*e + 28', '-12*e + 72', '-60*e - 80', '-32*e - 44', '-73*e - 67', '-64*e - 82', '35*e + 91', '46*e + 60', '-10*e + 70', '28*e + 40', '40*e + 22', '22*e + 102', '-13*e - 45', '24*e + 54', '11*e + 51'], 'hecke_polynomial': 'x^2 + 2*x - 1', 'label': '4.4.11025.1-20.3-e'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 11025, 'ideals': ['[1, 1, 1]', '[4, 2, 1/4*w^3 - 1/2*w^2 - 11/4*w + 5]', '[4, 2, 1/8*w^3 - 1/2*w^2 - 5/8*w + 3/2]', '[5, 5, -3/8*w^3 + 35/8*w - 1/2]', '[5, 5, 3/8*w^3 - 35/8*w - 1/2]', '[9, 3, -1/8*w^3 + 17/8*w + 3/2]', '[16, 2, 2]', '[16, 4, -w]', '[16, 4, 1/4*w^3 - 13/4*w]', '[20, 10, -w - 2]', '[20, 10, 1/4*w^3 - 13/4*w + 2]', '[20, 10, -1/4*w^3 + 13/4*w + 2]', '[20, 10, -w + 2]', '[25, 5, 1/8*w^3 - 17/8*w - 1/2]', '[25, 5, 1/8*w^3 - 17/8*w + 1/2]', '[25, 5, -1/4*w^3 + 9/4*w]', '[36, 6, -1/2*w^3 + 11/2*w]', '[36, 6, -1/4*w^3 + 5/4*w]', '[41, 41, 1/8*w^3 - 1/8*w + 3/2]', '[41, 41, 3/8*w^3 - 35/8*w + 3/2]', '[41, 41, 3/8*w^3 - 35/8*w - 3/2]', '[41, 41, -1/8*w^3 + 1/8*w + 3/2]', '[45, 15, 1/4*w^3 + w^2 - 5/4*w - 2]', '[45, 15, -1/4*w^3 + w^2 + 5/4*w - 2]', '[49, 7, 1/8*w^3 - 17/8*w + 7/2]', '[59, 59, 5/8*w^3 - 53/8*w - 5/2]', '[59, 59, -7/8*w^3 + 3/2*w^2 + 83/8*w - 35/2]', '[59, 59, -3/4*w^3 + 3/2*w^2 + 33/4*w - 16]', '[59, 59, 5/8*w^3 - 53/8*w + 5/2]', '[64, 4, 1/2*w^3 - w^2 - 11/2*w + 10]', '[64, 4, 1/4*w^3 - w^2 - 5/4*w + 3]', '[64, 8, 1/2*w^3 - 1/2*w^2 - 5*w + 4]', '[64, 8, 3/8*w^3 + 1/2*w^2 - 23/8*w - 5/2]', '[79, 79, 3/8*w^3 - w^2 - 35/8*w + 21/2]', '[79, 79, -1/2*w^3 + 3/2*w^2 + 3*w - 5]', '[79, 79, 7/8*w^3 - 79/8*w - 1/2]', '[79, 79, -3/8*w^3 - w^2 + 35/8*w + 21/2]', '[80, 10, -3/4*w^3 + 35/4*w - 1]', '[80, 10, 3/4*w^3 - 35/4*w - 1]', '[80, 20, 1/8*w^3 - 1/2*w^2 - 13/8*w + 1/2]', '[80, 20, -1/2*w^2 + 1/2*w + 6]', '[80, 20, 1/2*w^2 + 1/2*w - 6]', '[80, 20, -1/8*w^3 - 1/2*w^2 + 13/8*w + 1/2]', '[81, 3, 3]', '[89, 89, 1/8*w^3 - 1/8*w - 5/2]', '[89, 89, 3/8*w^3 - 35/8*w + 5/2]', '[89, 89, 3/8*w^3 - 35/8*w - 5/2]', '[89, 89, -1/8*w^3 + 1/8*w - 5/2]', '[100, 10, 3/4*w^3 - 1/2*w^2 - 33/4*w + 5]', '[100, 10, 3/4*w^3 + 1/2*w^2 - 33/4*w - 5]', '[100, 10, -3/4*w^3 + 1/2*w^2 + 37/4*w - 7]', '[100, 10, 3/8*w^3 - 1/2*w^2 - 15/8*w + 3/2]', '[100, 10, 1/8*w^3 - 1/2*w^2 + 11/8*w - 1/2]', '[100, 10, 3/8*w^3 + 1/2*w^2 - 15/8*w - 3/2]', '[101, 101, -3/8*w^3 + 1/2*w^2 + 31/8*w - 5/2]', '[101, 101, 1/4*w^3 + 1/2*w^2 - 7/4*w - 4]', '[101, 101, -1/4*w^3 + 1/2*w^2 + 7/4*w - 4]', '[101, 101, 3/8*w^3 + 1/2*w^2 - 31/8*w - 5/2]', '[109, 109, 1/8*w^3 - w^2 + 15/8*w - 3/2]', '[109, 109, 1/8*w^3 + 1/2*w^2 - 13/8*w - 15/2]', '[109, 109, -1/8*w^3 + 1/2*w^2 + 13/8*w - 15/2]', '[109, 109, -1/2*w^2 + 1/2*w - 1]', '[121, 11, -1/8*w^3 + 9/8*w - 7/2]', '[121, 11, 3/8*w^3 - 27/8*w + 1/2]', '[125, 5, 1/8*w^3 - w^2 - 9/8*w + 23/2]', '[125, 5, 1/8*w^3 + w^2 - 9/8*w - 23/2]', '[125, 25, -w^2 + w + 1]', '[125, 25, -w^2 - w + 1]', '[131, 131, 1/2*w^3 - 13/2*w + 3]', '[131, 131, 2*w - 3]', '[131, 131, -1/8*w^3 - 1/2*w^2 + 21/8*w - 3/2]', '[131, 131, 1/2*w^3 - 13/2*w - 3]', '[144, 6, -1/4*w^3 + 17/4*w + 3]', '[144, 12, -1/2*w^2 - 3/2*w - 2]', '[144, 12, 3/8*w^3 + 1/2*w^2 - 39/8*w - 17/2]', '[151, 151, 1/8*w^3 - 25/8*w - 5/2]', '[151, 151, 3/8*w^3 - 43/8*w + 5/2]', '[151, 151, -3/8*w^3 + 43/8*w + 5/2]', '[151, 151, -1/8*w^3 + 25/8*w - 5/2]', '[164, 82, 1/4*w^3 - 1/2*w^2 - 15/4*w + 7]', '[164, 82, 1/4*w^3 + 1/2*w^2 + 1/4*w + 1]', '[164, 82, 1/8*w^3 + 1/2*w^2 - 21/8*w + 1/2]', '[164, 82, 7/8*w^3 + 1/2*w^2 - 83/8*w - 15/2]', '[164, 82, 7/8*w^3 - 1/2*w^2 - 83/8*w + 15/2]', '[164, 82, 1/8*w^3 - 1/2*w^2 - 21/8*w - 1/2]', '[164, 82, -1/4*w^3 + 1/2*w^2 - 1/4*w + 1]', '[164, 82, -1/4*w^3 - 1/2*w^2 + 15/4*w + 7]', '[169, 13, -5/8*w^3 + w^2 + 61/8*w - 27/2]', '[169, 13, 1/8*w^3 - w^2 + 7/8*w - 1/2]', '[180, 30, 1/4*w^3 - 1/2*w^2 - 11/4*w + 1]', '[180, 30, 1/8*w^3 + 1/2*w^2 - 5/8*w - 11/2]', '[180, 30, 1/8*w^3 - 1/2*w^2 - 5/8*w + 11/2]', '[180, 30, -1/4*w^3 - 1/2*w^2 + 11/4*w + 1]', '[196, 14, -w^2 + 10]', '[196, 14, -w^2 + 3]', '[205, 205, 1/2*w^3 - 13/2*w - 1]', '[205, 205, 5/8*w^3 - 53/8*w - 1/2]', '[205, 205, -3/8*w^3 + 19/8*w + 1/2]', '[205, 205, 2*w - 1]', '[205, 205, -2*w - 1]', '[205, 205, 3/8*w^3 - 19/8*w + 1/2]', '[205, 205, -5/8*w^3 + 53/8*w - 1/2]', '[205, 205, -1/2*w^3 + 13/2*w - 1]', '[211, 211, 13/8*w^3 - w^2 - 149/8*w + 23/2]', '[211, 211, -3/4*w^3 + 1/2*w^2 + 37/4*w - 6]', '[211, 211, -5/8*w^3 + 1/2*w^2 + 65/8*w - 7/2]', '[211, 211, -13/8*w^3 - w^2 + 149/8*w + 23/2]', '[225, 15, -1/8*w^3 + 17/8*w - 9/2]', '[225, 15, 1/8*w^3 - 17/8*w - 9/2]', '[225, 15, 3/8*w^3 - w^2 - 27/8*w + 13/2]', '[236, 118, 7/4*w^3 - 1/2*w^2 - 85/4*w + 9]', '[236, 118, -1/4*w^3 + 1/2*w^2 + 15/4*w - 1]', '[236, 118, 1/8*w^3 + 1/2*w^2 - 5/8*w - 15/2]', '[236, 118, 1/2*w^3 - w^2 - 13/2*w + 7]', '[236, 118, -1/8*w^3 + 3/2*w^2 - 27/8*w - 1/2]', '[236, 118, -1/8*w^3 + 1/2*w^2 + 5/8*w - 15/2]', '[236, 118, -1/4*w^3 - 1/2*w^2 + 15/4*w + 1]', '[236, 118, 3*w^3 - 3*w^2 - 35*w + 34]', '[245, 35, 1/2*w^3 + w^2 - 3/2*w - 3]', '[245, 35, 5/4*w^3 - w^2 - 57/4*w + 10]', '[251, 251, 1/2*w^3 + 1/2*w^2 - 6*w - 3]', '[251, 251, 1/8*w^3 + 1/2*w^2 + 3/8*w - 7/2]', '[251, 251, -1/8*w^3 + 1/2*w^2 - 3/8*w - 7/2]', '[251, 251, -1/2*w^3 + 1/2*w^2 + 6*w - 3]', '[256, 4, 4]', '[256, 8, -2*w]', '[256, 8, 1/2*w^3 - 13/2*w]', '[256, 16, w^2]', '[256, 16, -w^2 + 13]', '[269, 269, w^2 - w - 9]', '[269, 269, 3/8*w^3 - 2*w^2 + 13/8*w + 3/2]', '[269, 269, -1/4*w^3 + w^2 + 13/4*w - 4]', '[269, 269, 13/8*w^3 - 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9/8*w - 39/2]', '[3571, 3571, -1/8*w^3 + 2*w^2 + 9/8*w - 39/2]', '[3571, 3571, -23/8*w^3 - w^2 + 263/8*w + 23/2]', '[3659, 3659, 7/8*w^3 - 87/8*w + 15/2]', '[3659, 3659, 7/8*w^3 - 3/2*w^2 - 75/8*w + 17/2]', '[3659, 3659, -7/8*w^3 - 3/2*w^2 + 75/8*w + 17/2]', '[3659, 3659, 7/8*w^3 - 87/8*w - 15/2]', '[3671, 3671, 11/8*w^3 - 123/8*w + 9/2]', '[3671, 3671, 7/2*w^2 + 1/2*w - 41]', '[3671, 3671, -7/2*w^2 + 1/2*w + 41]', '[3671, 3671, 11/8*w^3 - 123/8*w - 9/2]', '[3691, 3691, -5/4*w^3 + 1/2*w^2 + 51/4*w - 2]', '[3691, 3691, 7/8*w^3 - 1/2*w^2 - 51/8*w + 9/2]', '[3691, 3691, -11/8*w^3 + 3*w^2 + 59/8*w - 17/2]', '[3691, 3691, 5/8*w^3 + w^2 - 61/8*w - 33/2]', '[3701, 3701, 3/4*w^3 - 3/2*w^2 - 25/4*w + 4]', '[3701, 3701, 1/8*w^3 + 2*w^2 + 15/8*w - 27/2]', '[3701, 3701, -7/8*w^3 + 3/2*w^2 + 67/8*w - 31/2]', '[3701, 3701, 7/8*w^3 + 2*w^2 - 87/8*w - 25/2]', '[3721, 61, 3/8*w^3 - 27/8*w - 17/2]', '[3721, 61, -3/8*w^3 + 27/8*w - 17/2]', '[3739, 3739, -7/8*w^3 - 1/2*w^2 + 59/8*w + 3/2]', '[3739, 3739, w^3 + 1/2*w^2 - 19/2*w - 5]', '[3739, 3739, w^3 - 1/2*w^2 - 19/2*w + 5]', '[3739, 3739, -3/8*w^3 + 35/8*w - 17/2]', '[3779, 3779, 1/2*w^2 - 5/2*w - 9]', '[3779, 3779, -5/8*w^3 - 1/2*w^2 + 65/8*w - 5/2]', '[3779, 3779, 5/8*w^3 - 1/2*w^2 - 65/8*w - 5/2]', '[3779, 3779, 1/2*w^2 + 5/2*w - 9]', '[3821, 3821, -3/8*w^3 - 7/2*w^2 + 39/8*w + 81/2]', '[3821, 3821, 11/8*w^3 + w^2 - 131/8*w - 15/2]', '[3821, 3821, 11/8*w^3 - w^2 - 131/8*w + 15/2]', '[3821, 3821, -3/8*w^3 + 7/2*w^2 + 39/8*w - 81/2]', '[3881, 3881, 1/8*w^3 - w^2 - 25/8*w + 29/2]', '[3881, 3881, -5/4*w^3 + 3*w^2 + 33/4*w - 10]', '[3881, 3881, 3/8*w^3 + w^2 - 43/8*w + 3/2]', '[3881, 3881, -2*w^3 + 3*w^2 + 21*w - 29]', '[3889, 3889, 5/8*w^3 + 2*w^2 - 61/8*w - 37/2]', '[3889, 3889, -1/8*w^3 + 2*w^2 + 25/8*w - 17/2]', '[3889, 3889, 1/8*w^3 + 2*w^2 - 25/8*w - 17/2]', '[3889, 3889, -3/8*w^3 - 2*w^2 + 43/8*w + 35/2]', '[3911, 3911, 1/8*w^3 + w^2 - 25/8*w - 27/2]', '[3911, 3911, -3/8*w^3 - w^2 + 43/8*w - 1/2]', '[3911, 3911, -3/8*w^3 + w^2 + 43/8*w + 1/2]', '[3911, 3911, -1/8*w^3 + w^2 + 25/8*w - 27/2]', '[3931, 3931, -13/8*w^3 + 141/8*w + 5/2]', '[3931, 3931, 21/8*w^3 - 1/2*w^2 - 249/8*w + 13/2]', '[3931, 3931, -21/8*w^3 - 1/2*w^2 + 249/8*w + 13/2]', '[3931, 3931, -13/8*w^3 + 141/8*w - 5/2]', '[3989, 3989, -3/8*w^3 + w^2 + 59/8*w - 23/2]', '[3989, 3989, -5/8*w^3 + w^2 + 77/8*w - 3/2]', '[3989, 3989, -5/8*w^3 + 3/2*w^2 + 41/8*w - 27/2]', '[3989, 3989, 3/8*w^3 + w^2 - 59/8*w - 23/2]']}
• 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': [16, 0, -13, 0, 1], 'conductor': 105, 'degree': 4, 'dirichlet_group': [64, 1, 104, 41], 'disc_abs': 11025, 'disc_rad': 105, 'disc_sign': 1, 'frobs': [[2, [[2, 2]]], [3, [0]], [5, [0]], [7, [0]], [11, [[2, 2]]], [13, [[2, 2]]], [17, [[2, 2]]], [19, [[2, 2]]], [23, [[2, 2]]], [29, [[2, 2]]], [31, [[2, 2]]], [37, [[2, 2]]], [41, [[1, 4]]], [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': [2, 2, 2], 'galois_label': '4T2', 'galt': 2, 'grd': 10.246950765959598, 'index': 2, 'inessentialp': [2], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.11025.1', 'local_algs': ['3.4.2.1', '5.2.1.1', '5.2.1.1', '7.4.2.1'], 'monogenic': -1, 'num_ram': 3, 'r2': 0, 'ramps': [3, 5, 7], 'rd': 10.246950766, 'regulator': {'__RealLiteral__': 0, 'data': '6.64477622728', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-26.-1.1', '-1.-1.1', '-5.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{8} a^{3} - \\frac{9}{8} a - \\frac{1}{2} \\)', '\\( \\frac{1}{8} a^{3} - \\frac{17}{8} a - \\frac{5}{2} \\)', '\\( \\frac{1}{4} a^{3} - \\frac{1}{4} a \\)'], 'unitsGmodule': [[1, 1], [2, 1], [3, 1]], 'unitsType': 'Type I (ii)', 'used_grh': False, 'zk': ['1', 'a', '1/2*a^2 - 1/2*a', '1/8*a^3 - 1/8*a - 1/2']}