Hilbert modular form data - 4.4.19525.1-5.2-a

Formats: - HTML - YAML - JSON - 2024-04-30T13:49:49.785111

• 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': 19525, 'field_bad_primes': [5, 11, 71], 'field_label': '4.4.19525.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.19525.1-5.2-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [5], 'level_ideal': '[5,5,2/3*w^2 - 5/3*w - 4]', 'level_label': '5.2', 'level_norm': 5, 'parallel_weight': 2, 'short_label': '5.2-a', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[5,5,2/3*w^2 - 5/3*w - 4]', 1]], 'hecke_eigenvalues': ['e', -1, '2*e^3 - 8*e^2 + 2*e + 8', '-e^3 + 5*e^2 - 4*e - 4', 'e^2 - 3*e', '-e^2 + 3*e - 1', '-e^3 + 5*e^2 - 3*e', '2*e^3 - 8*e^2 + 2*e + 6', '2*e^3 - 7*e^2 - 3*e + 12', '-2*e^2 + 3*e + 6', '-2*e^2 + 6*e + 6', '2*e^3 - 7*e^2 - e + 6', '-e^3 + 3*e^2 - e', '-e^3 + 4*e^2 + 4*e - 6', '2*e^3 - 10*e^2 + 8*e + 6', '-e^3 + 3*e^2 + 2*e - 6', 'e^3 - 3*e^2 + 2*e - 2', '-e^3 + 2*e^2 + 3*e', '-e^3 + 2*e^2 + 4*e + 6', '-e^3 + e^2 + 4*e + 4', '-2*e^3 + 10*e^2 - 6*e - 12', '-e^3 + 2*e^2 + 6*e - 6', '-e^3 + e^2 + 3*e + 12', '-3*e^3 + 15*e^2 - 12*e - 12', '-2*e^3 + 8*e^2 + 4*e - 18', '-4*e + 4', '-4*e + 4', '-2*e^2 + 8*e - 8', '-e^3 + 3*e^2 + 2*e - 6', 'e^3 - 3*e^2 - 8*e + 12', '2*e^3 - 9*e^2 - e + 12', '-5*e^3 + 25*e^2 - 25*e - 18', 'e^3 + 2*e^2 - 16*e', '-e^3 + 6*e^2 - 14*e + 6', '-3*e^3 + 12*e^2 - 2*e - 12', '8*e - 12', '-e^3 + 12*e^2 - 26*e - 6', '-e^3 + 8*e^2 - 6*e - 12', '-2*e^3 + 4*e^2 + 8*e', '-5*e^3 + 22*e^2 - 13*e - 12', '-2*e^3 + 12*e^2 - 12*e - 2', '3*e^3 - 7*e^2 - 18*e + 16', '-2*e^3 + 12*e^2 - 12*e - 2', '-3*e^3 + 9*e^2 + 6*e - 2', '5*e^3 - 25*e^2 + 10*e + 30', '5*e^2 - 14*e + 6', '6*e^3 - 30*e^2 + 18*e + 34', '-4*e^3 + 17*e^2 - 10*e + 4', '-5*e^3 + 13*e^2 + 16*e - 24', '4*e^3 - 19*e^2 + 21*e + 6', '-5*e^3 + 18*e^2 - 4*e', 'e^3 - 3*e^2 - 6*e + 6', 'e^3 - 2*e^2 - 6*e', '-2*e^3 + 12*e^2 - 6*e - 12', '-5*e^3 + 22*e^2 - 5*e - 18', '-2*e^3 + 8*e^2 - e + 18', '-2*e^3 + 8*e^2 - 4*e - 6', '-5*e^3 + 21*e^2 - 10*e - 18', '2*e^3 - 12*e^2 + 14*e + 8', '-7*e^3 + 25*e^2 - 24', '6*e^3 - 25*e^2 + 2*e + 36', '-4*e^3 + 15*e^2 + e - 24', 'e^3 - 5*e^2 - 5*e + 30', '5*e^3 - 16*e^2 - 4*e + 18', '-5*e^3 + 21*e^2 + e - 24', '-e^3 - 6*e^2 + 22*e + 12', '-7*e^3 + 31*e^2 - 19*e - 12', '-6*e^3 + 22*e^2 - 4*e - 6', '8*e^2 - 20*e - 12', '-2*e^3 + 4*e^2 + 14*e - 30', '-3*e^3 + e^2 + 35*e - 12', '-3*e^3 + 17*e^2 - 26*e', '-e^3 + 4*e^2 + 4*e - 6', '-7*e^3 + 32*e^2 - 54', '7*e^3 - 31*e^2 + 54', '-9*e^3 + 43*e^2 - 28*e - 42', '-2*e^3 + 16*e^2 - 22*e - 18', '9*e^3 - 40*e^2 + 17*e + 48', '4*e^3 - 6*e^2 - 22*e + 6', '6*e^3 - 18*e^2 - 4*e + 6', '-2*e^3 + 14*e + 18', '-2*e^3 + 14*e^2 - 6*e - 36', '-10*e^3 + 42*e^2 - 23*e - 24', 'e^3 - 9*e^2 + 20*e - 16', '-e^3 + 11*e^2 - 30*e - 4', '8*e^3 - 38*e^2 + 22*e + 26', '2*e^3 - 7*e^2 + 2*e + 20', '-8*e^3 + 34*e^2 - 6*e - 30', '-7*e^3 + 33*e^2 - 28*e - 24', '-e^2 - 4*e + 6', '-3*e^3 + 17*e^2 - 6*e - 48', '4*e^2 - 24', '-4*e^3 + 11*e^2 + 13*e - 12', '5*e^3 - 17*e^2 + e + 18', '-5*e^3 + 8*e^2 + 20*e + 12', '3*e^3 - 8*e^2 - 13*e + 18', '-10*e^3 + 40*e^2 - 6*e - 38', '-4*e^3 + 12*e^2 - 2*e + 10', 'e^3 - 14*e^2 + 25*e + 30', 'e^3 - 6*e^2 + 12*e + 24', '-e^3 - 2*e^2 + 13*e + 24', '8*e^3 - 36*e^2 + 29*e + 24', '6*e^3 - 22*e^2 - 4*e + 30', '8*e^3 - 29*e^2 + 5*e + 6', '-e^3 - 2*e^2 + 18*e + 18', '2*e^3 - 22*e^2 + 42*e + 8', '9*e^3 - 36*e^2 + 14*e + 24', '-4*e^3 + 11*e^2 + e + 6', '2*e^3 - 11*e^2 + 14*e + 14', '-10*e^2 + 28*e + 18', '-2*e^3 + 6*e^2 + 7*e + 24', '2*e^3 - 12*e^2 + 14*e + 4', '5*e^3 - 13*e^2 - 6*e - 2', '-3*e^3 + 6*e^2 + 13*e - 18', '6*e^3 - 23*e^2 - e + 36', '-8*e^3 + 38*e^2 - 16*e - 52', '-2*e^3 + 10*e^2 - 12*e - 4', '5*e^2 - 22*e + 16', '2*e^3 - 30*e + 10', '-11*e^3 + 45*e^2 - 2*e - 72', '-e^3 + 7*e^2 - 11*e', '2*e^3 - 4*e^2 + 2*e - 18', '6*e^3 - 28*e^2 + 14*e + 54', '-e^3 - 4*e^2 + 10*e + 24', '6*e^3 - 26*e^2 + 6*e + 24', '5*e^3 - 2*e^2 - 50*e + 12', '-10*e^2 + 31*e - 6', '-2*e^3 - 5*e^2 + 39*e', '15*e^3 - 70*e^2 + 43*e + 48', '-9*e^3 + 29*e^2 + 10*e - 22', '-6*e^3 + 28*e^2 - 10*e - 28', '4*e^3 - 12*e^2 - 10*e + 2', '-5*e^3 + 27*e^2 - 28*e - 34', 'e^3 - 10*e^2 + 26*e - 12', '5*e^3 - 25*e^2 + 16*e + 36', '-e^3 + 3*e^2 + 12*e - 12', '-4*e^3 + 18*e^2 - 8*e - 24', '2*e^3 + e^2 - 17*e - 12', '-8*e^3 + 22*e^2 + 12*e - 4', '3*e^3 + e^2 - 34*e + 2', '4*e^2 - 17*e + 18', '-10*e^2 + 30*e - 20', '2*e^3 - 18*e^2 + 16*e + 46', '-5*e^3 + 26*e^2 - 10*e - 60', '9*e^3 - 33*e^2 + e + 24', '15*e^3 - 71*e^2 + 48*e + 48', '15*e^3 - 61*e^2 + 16*e + 54', '4*e^3 - 18*e^2 + 2*e + 36', '-10*e^3 + 39*e^2 - 18*e - 18', '-15*e^3 + 65*e^2 - 28*e - 52', '10*e^3 - 42*e^2 + 15*e + 42', '5*e^3 - 15*e^2 - 25*e + 30', '-14*e^3 + 60*e^2 - 13*e - 78', '5*e^3 - 18*e^2 - 5*e + 42', '4*e^3 - 11*e^2 - 14*e + 14', '-2*e^3 + 5*e^2 - 5*e', '-14*e^3 + 48*e^2 + 11*e - 54', '5*e^3 - 29*e^2 + 30*e + 2', '-5*e^3 + 24*e^2 - 10*e - 42', '9*e^3 - 44*e^2 + 38*e + 18', '-6*e^3 + 31*e^2 - 8*e - 70', '9*e^3 - 41*e^2 + 25*e + 30', '-4*e^3 + 24*e^2 - 31*e - 24', '-e^3 + 10*e^2 - 30*e - 6', '8*e^3 - 31*e^2 + 21*e', '-3*e^3 + 18*e^2 - 34*e', '7*e^3 - 38*e^2 + 34*e + 24', '-10*e^3 + 47*e^2 - 8*e - 80', '6*e^3 - 18*e^2 - 10*e + 4', '4*e^3 - 24*e^2 + 6*e + 54', '3*e^3 - 23*e^2 + 38*e - 6', 'e^3 - 15*e^2 + 25*e + 30', '4*e^3 - 11*e^2 - 3*e - 12', '5*e^3 - 21*e^2 + 5*e + 42', '-3*e^3 + 21*e^2 - 9*e - 54', '6*e^3 - 28*e^2 + 26*e + 36', '-8*e^3 + 29*e^2 + 2*e - 54', '13*e^3 - 55*e^2 + 36*e + 36', '-2*e^3 + 16*e^2 - 48*e + 6', 'e^3 - 4*e^2 + 20*e - 36', '2*e^3 - 3*e^2 - 7*e - 18', '4*e^3 - 16*e^2 - 14*e + 24', '10*e^3 - 40*e^2 + 10*e + 48', '-17*e^3 + 79*e^2 - 35*e - 72', '-8*e^3 + 16*e^2 + 34*e - 6', '2*e^3 + 2*e^2 - 36*e', '-2*e^2 + 12*e', '-14*e^3 + 42*e^2 + 30*e - 66', '-18*e^3 + 83*e^2 - 53*e - 54', '6*e^3 - 25*e^2 - 7*e + 54', '3*e^3 - 10*e^2 - 8*e', '10*e^3 - 40*e^2 + 12*e + 52', '14*e^3 - 59*e^2 + 36*e + 34', '8*e^3 - 34*e^2 + 21*e + 12', '3*e^3 - 15*e^2 + 8*e + 10', '8*e^3 - 20*e^2 - 14*e - 2', '-5*e^3 + 14*e^2 + 10*e - 30', '8*e^3 - 42*e^2 + 35*e + 36', '8*e^3 - 42*e^2 + 36*e + 42', '23*e^3 - 89*e^2 + 16*e + 92', '-6*e^3 + 25*e^2 + 3*e - 60', '2*e^3 - 6*e^2 + 7*e - 42', '-12*e^3 + 60*e^2 - 40*e - 58', '5*e^3 - 20*e^2 + 22*e', '7*e^3 - 28*e^2 + 7*e + 60', '4*e^3 - 26*e^2 + 44*e + 8', '-2*e^3 + 14*e^2 - 8*e - 26', '12*e^3 - 44*e^2 + 4*e + 28', '10*e^3 - 32*e^2 - 14*e + 32', '11*e^3 - 36*e^2 - 8*e + 42', '-2*e^3 - 2*e^2 + 22*e - 18', '-15*e^3 + 69*e^2 - 40*e - 54', '2*e^3 - 6*e^2 + 6*e - 48', '3*e^3 - 8*e^2 - 26*e + 18', '12*e^3 - 36*e^2 - 36*e + 60', '-2*e^3 + 13*e^2 - 17*e - 18', '2*e^3 - 30*e^2 + 62*e + 18', '-7*e^3 + 22*e^2 + 6*e + 6', '-e^3 + 11*e^2 - 44*e + 6', '2*e^3 - 10*e^2 + 6*e', '-12*e^3 + 45*e^2 + 23*e - 90', '12*e^3 - 42*e^2 - 22*e + 84', '-15*e^3 + 54*e^2 - 12*e - 24', '-3*e^3 + 23*e^2 - 32*e - 22', '2*e^3 - 2*e^2 + 14*e - 46', '16*e^3 - 66*e^2 + 22*e + 66', '-4*e^3 + 30*e^2 - 29*e - 36', '5*e^3 - 19*e^2 + 6*e - 22', '-2*e^3 + 5*e^2 + 20*e - 34', '8*e^3 - 30*e^2 + 10*e - 14', '8*e^3 - 44*e^2 + 32*e + 52', '14*e^3 - 68*e^2 + 34*e + 60', '10*e^3 - 54*e^2 + 68*e + 36', '18*e^3 - 66*e^2 + 78', '12*e^3 - 50*e^2 + 24*e + 60', '-15*e^3 + 62*e^2 - 26*e - 72', '2*e^3 - 31*e^2 + 66*e + 34', '-3*e^3 + 21*e^2 - 18*e - 2', '13*e^3 - 42*e^2 - 22*e + 54', '15*e^3 - 57*e^2 + 14*e + 20', '-4*e^3 + 15*e^2 - 5*e - 54', '-21*e^3 + 96*e^2 - 52*e - 84', '5*e^3 - 33*e^2 + 48*e + 50', '15*e^3 - 48*e^2 - 15*e + 48', '5*e^3 - 22*e^2 + 20*e + 12', '-13*e^3 + 48*e^2 + e - 90', '-10*e^3 + 34*e^2 + 5*e - 54', '6*e^3 - 20*e^2 + 2*e - 12', 'e^3 - 2*e^2 - 11*e + 42', '-5*e^3 + 23*e^2 - 29*e + 18', '-7*e^3 + 38*e^2 - 36*e - 6', '6*e^3 - 31*e^2 + 18*e + 66', '-e^3 - 3*e^2 + 26*e - 42', '-2*e^3 - 6*e^2 + 48*e - 18', '8*e^3 - 44*e^2 + 50*e + 18', '-20*e^3 + 84*e^2 - 33*e - 78', '-22*e^3 + 98*e^2 - 58*e - 66', '-12*e^3 + 62*e^2 - 62*e - 54', '-17*e^3 + 72*e^2 - 21*e - 66', '-5*e^3 + 21*e^2 - 4*e + 14', '6*e^3 - 22*e^2 - 28', '3*e^3 - 20*e^2 + 24*e + 42', 'e^3 + 6*e^2 - 40*e', '-11*e^3 + 64*e^2 - 69*e - 54', '10*e^2 - 19*e + 6', '-5*e^3 + 15*e^2 + 2*e - 26', '-12*e^3 + 42*e^2 + 28*e - 74', '30*e - 46', '-18*e^3 + 66*e^2 - 20*e - 14', '-2*e^3 - 3*e^2 + 24*e - 8', '10*e^3 - 28*e^2 + 6*e - 44', '-10*e^3 + 36*e^2 + 20*e - 54', '4*e^3 - 12*e^2 + 18', '7*e^3 - 33*e^2 - 8*e + 76', '-4*e^3 + 23*e^2 - 31*e', '-6*e^3 + 28*e^2 - 21*e + 18', '-2*e^3 + e^2 + 32*e - 2', '12*e^2 - 24*e - 24', '11*e^3 - 55*e^2 + 48*e + 66', '-9*e^3 + 32*e^2 - 4*e - 42', '4*e^3 + 6*e^2 - 53*e - 12', '2*e^3 + 6*e^2 - 40*e + 32', '12*e^3 - 60*e^2 + 56*e + 14', '-13*e^3 + 55*e^2 - 25*e - 6', '25*e^3 - 116*e^2 + 76*e + 84', '7*e^3 - 27*e^2 + 9*e', '7*e^3 - 17*e^2 - 35*e + 6', '6*e^3 - 31*e^2 + 27*e + 12', '-10*e^3 + 22*e^2 + 57*e - 42', '2*e^3 - 16*e^2 + 28*e - 30', '-10*e^3 + 21*e^2 + 25*e + 18', 'e^3 - 11*e^2 + 4*e + 60', '-5*e^3 + 15*e^2 - 4*e + 60', '2*e^3 - 10*e^2 - 16*e + 72', '-2*e^3 - 6*e^2 + 16*e + 30', '-4*e^3 + 32*e + 48', '13*e^3 - 58*e^2 + 50*e + 12', '-10*e^3 + 40*e^2 - 16*e - 30', '-7*e^3 + 25*e^2 - 20*e - 6', '-11*e^3 + 59*e^2 - 58*e - 38', '9*e^3 - 25*e^2 - 36*e + 28', '22*e^3 - 84*e^2 + 16*e + 84', '-2*e^3 - 8*e^2 + 58*e + 14', '-14*e^3 + 56*e^2 + 4*e - 76', '2*e^3 + 8*e^2 - 56*e'], 'hecke_polynomial': 'x^4 - 6*x^3 + 8*x^2 + 4*x - 6', 'label': '4.4.19525.1-5.2-a'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 19525, 'ideals': ['[1, 1, 1]', '[5, 5, 2/3*w^2 + 1/3*w - 5]', '[5, 5, 2/3*w^2 - 5/3*w - 4]', '[9, 3, -w + 3]', '[9, 3, w + 2]', '[11, 11, 2/3*w^2 + 1/3*w - 4]', '[16, 2, 2]', '[19, 19, 1/3*w^3 - 10/3*w - 3]', '[19, 19, 1/3*w^3 - w^2 - 7/3*w + 6]', '[25, 5, -2/3*w^2 + 5/3*w + 5]', '[25, 5, 2/3*w^2 - 2/3*w - 5]', '[25, 5, 1/3*w^3 - w^2 - 7/3*w + 8]', '[29, 29, -1/3*w^3 + 2/3*w^2 + 8/3*w - 2]', '[29, 29, 1/3*w^3 - 1/3*w^2 - 3*w + 1]', '[31, 31, -1/3*w^3 + 1/3*w^2 + 3*w + 1]', '[31, 31, -1/3*w^3 + 2/3*w^2 + 8/3*w - 4]', '[45, 15, -1/3*w^3 + 1/3*w^2 + 3*w]', '[45, 15, -1/3*w^3 + 2/3*w^2 + 8/3*w]', '[45, 15, 1/3*w^3 - 1/3*w^2 - 3*w + 3]', '[45, 15, 1/3*w^3 - 2/3*w^2 - 8/3*w + 3]', '[49, 7, 1/3*w^3 - 10/3*w - 1]', '[49, 7, -1/3*w^3 + w^2 + 7/3*w - 4]', '[55, 55, -1/3*w^2 - 2/3*w + 5]', '[55, 55, 1/3*w^2 - 4/3*w - 4]', '[59, 59, -1/3*w^3 + 5/3*w^2 + 5/3*w - 11]', '[59, 59, -2/3*w^3 + 5/3*w^2 + 5*w - 13]', '[61, 61, -1/3*w^3 + 5/3*w^2 + 2/3*w - 9]', '[61, 61, -1/3*w^3 + 1/3*w^2 + 4*w + 2]', '[61, 61, 2/3*w^2 - 5/3*w - 1]', '[61, 61, -1/3*w^2 + 4/3*w + 6]', '[71, 71, -4/3*w^2 + 7/3*w + 11]', '[79, 79, -1/3*w^2 + 7/3*w - 3]', '[79, 79, -2/3*w^3 + 1/3*w^2 + 16/3*w - 4]', '[80, 10, 4/3*w^2 + 2/3*w - 10]', '[80, 10, 4/3*w^2 - 10/3*w - 8]', '[81, 3, 3]', '[81, 9, 1/3*w^3 - 1/3*w^2 - 2*w + 3]', '[81, 9, -1/3*w^3 + 2/3*w^2 + 5/3*w + 1]', '[95, 95, 1/3*w^3 - w^2 - 4/3*w]', '[95, 95, -1/3*w^2 - 2/3*w + 6]', '[95, 95, 1/3*w^2 - 4/3*w - 5]', '[95, 95, 1/3*w^3 - 7/3*w + 2]', '[99, 33, -1/3*w^3 + 2/3*w^2 + 11/3*w - 7]', '[99, 33, -1/3*w^3 + 1/3*w^2 + 4*w + 3]', '[101, 101, 2/3*w^2 - 5/3*w - 6]', '[101, 101, -2/3*w^2 - 1/3*w + 7]', '[109, 109, -4/3*w^2 + 1/3*w + 9]', '[109, 109, 1/3*w^3 - 1/3*w^2 - 3*w - 4]', '[121, 11, -w^2 + w + 8]', '[121, 11, -1/3*w^2 + 1/3*w + 6]', '[125, 5, 2/3*w^3 - 2/3*w^2 - 5*w + 5]', '[125, 5, -2/3*w^3 + 4/3*w^2 + 13/3*w]', '[125, 25, -1/3*w^3 + 10/3*w]', '[125, 25, 1/3*w^3 - w^2 - 7/3*w + 3]', '[131, 131, -2/3*w^3 + 2/3*w^2 + 5*w - 7]', '[131, 131, 2/3*w^3 - 4/3*w^2 - 13/3*w - 2]', '[144, 6, -2*w + 6]', '[144, 6, 2*w + 4]', '[145, 145, 8/3*w^2 - 17/3*w - 17]', '[145, 145, -1/3*w^3 - w^2 + 16/3*w + 11]', '[145, 145, 1/3*w^3 - 2*w^2 - 7/3*w + 15]', '[145, 145, 8/3*w^2 + 1/3*w - 20]', '[151, 151, -1/3*w^3 - 2/3*w^2 + 5*w + 7]', '[151, 151, 1/3*w^3 - 10/3*w + 2]', '[155, 155, 4/3*w^2 - 7/3*w - 9]', '[155, 155, 1/3*w^3 + 7/3*w^2 - 26/3*w - 19]', '[155, 155, 1/3*w^3 - 10/3*w^2 - 3*w + 25]', '[155, 155, -4/3*w^2 + 1/3*w + 10]', '[169, 13, 5/3*w^2 + 1/3*w - 11]', '[169, 13, 5/3*w^2 - 11/3*w - 9]', '[171, 57, 1/3*w^3 + 1/3*w^2 - 11/3*w - 3]', '[171, 57, w^2 - 3*w - 4]', '[171, 57, -w^2 - w + 6]', '[171, 57, 1/3*w^3 - 4/3*w^2 - 2*w + 6]', '[176, 22, 4/3*w^2 + 2/3*w - 8]', '[181, 181, -1/3*w^3 + 4/3*w^2 + 3*w - 8]', '[181, 181, -1/3*w^3 - 1/3*w^2 + 14/3*w + 4]', '[191, 191, -2/3*w^3 + w^2 + 17/3*w - 9]', '[191, 191, 1/3*w^3 - 2*w^2 - 7/3*w + 13]', '[191, 191, 2/3*w^3 - 1/3*w^2 - 22/3*w - 7]', '[191, 191, 2/3*w^3 - w^2 - 17/3*w - 3]', '[199, 199, 1/3*w^3 + w^2 - 13/3*w - 9]', '[199, 199, 2/3*w^2 - 5/3*w - 7]', '[199, 199, 1/3*w^3 - w^2 - 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4/3*w^2 - 10*w + 10]', '[2000, 10, -4/3*w^3 + 8/3*w^2 + 26/3*w]', '[2000, 50, -2/3*w^3 + 20/3*w]', '[2000, 50, 2/3*w^3 - 2*w^2 - 14/3*w + 6]', '[2005, 2005, 1/3*w^3 - 1/3*w^2 - 3*w - 7]', '[2005, 2005, 8/3*w^3 - 4*w^2 - 62/3*w + 35]', '[2005, 2005, -8/3*w^3 + 4*w^2 + 62/3*w + 13]', '[2005, 2005, -1/3*w^3 + 2/3*w^2 + 8/3*w - 10]', '[2011, 2011, 1/3*w^3 + 1/3*w^2 + 1/3*w - 8]', '[2011, 2011, -1/3*w^3 + 4/3*w^2 - 2*w - 7]', '[2025, 15, -2*w^2 + 5*w + 15]', '[2025, 15, 2*w^2 - 2*w - 15]', '[2025, 15, w^3 - 3*w^2 - 7*w + 24]', '[2025, 45, 1/3*w^3 + 5/3*w^2 - 2*w - 15]', '[2025, 45, -1/3*w^3 - 5/3*w^2 + 5*w + 15]', '[2025, 45, w^3 - 5*w^2 - 3*w + 27]', '[2025, 45, -w^3 - 2*w^2 + 10*w + 20]', '[2025, 45, 1/3*w^3 - 8/3*w^2 - 2/3*w + 18]', '[2025, 45, -1/3*w^3 + 8/3*w^2 - 7/3*w - 15]', '[2029, 2029, -1/3*w^3 + 3*w^2 + 7/3*w - 27]', '[2029, 2029, 1/3*w^3 - 7/3*w^2 + 2*w + 13]', '[2039, 2039, -w^3 + w^2 + 9*w - 7]', '[2039, 2039, -w^3 + 2*w^2 + 8*w - 2]', '[2045, 2045, 7/3*w^2 + 2/3*w - 20]', '[2045, 2045, -5/3*w^3 + 8/3*w^2 + 12*w + 7]', '[2045, 2045, 5/3*w^3 - 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23/3*w + 9]', '[1451, 1451, -1/3*w^3 + 2*w^2 - 2/3*w - 12]', '[1451, 1451, -1/3*w^3 - w^2 + 7/3*w + 11]', '[1451, 1451, 1/3*w^3 - 8/3*w^2 + 10/3*w + 12]', '[1459, 1459, -2/3*w^3 + 8/3*w^2 + 5*w - 16]', '[1459, 1459, -1/3*w^3 + 8/3*w^2 + 2/3*w - 16]', '[1459, 1459, -1/3*w^3 - 5/3*w^2 + 5*w + 13]', '[1459, 1459, 2/3*w^3 + 2/3*w^2 - 25/3*w - 9]', '[1471, 1471, -2/3*w^3 + 3*w^2 + 5/3*w - 16]', '[1471, 1471, -13/3*w^2 - 5/3*w + 33]', '[1471, 1471, -13/3*w^2 + 31/3*w + 27]', '[1471, 1471, 2/3*w^3 + w^2 - 17/3*w - 12]', '[1489, 1489, 1/3*w^3 - 7/3*w^2 - 4*w + 17]', '[1489, 1489, 1/3*w^3 + 4/3*w^2 - 23/3*w - 11]', '[1531, 1531, -w^3 + 3*w^2 + 7*w - 17]', '[1531, 1531, w^3 - 10*w - 8]', '[1549, 1549, w^3 + 2/3*w^2 - 35/3*w - 13]', '[1549, 1549, -2/3*w^3 + 5*w^2 + 17/3*w - 36]', '[1549, 1549, -2/3*w^3 - 3*w^2 + 41/3*w + 26]', '[1549, 1549, -w^3 + 11/3*w^2 + 22/3*w - 23]', '[1571, 1571, -w^3 + 3*w^2 + 7*w - 23]', '[1571, 1571, -1/3*w^3 - 2*w^2 + 4/3*w + 17]', '[1571, 1571, -1/3*w^3 + 1/3*w^2 + 6*w - 13]', '[1571, 1571, -2/3*w^3 + 4*w^2 + 8/3*w - 23]', '[1601, 1601, -w^3 + 4/3*w^2 + 26/3*w - 11]', '[1601, 1601, -w^3 + 8/3*w^2 + 25/3*w - 24]', '[1601, 1601, -1/3*w^3 - 7/3*w^2 + 23/3*w + 18]', '[1601, 1601, -w^3 + 5/3*w^2 + 25/3*w + 2]', '[1609, 1609, -5/3*w^3 + 2/3*w^2 + 12*w - 8]', '[1609, 1609, 2/3*w^3 + 4/3*w^2 - 7*w - 17]', '[1619, 1619, w^3 - 4/3*w^2 - 23/3*w - 3]', '[1619, 1619, -w^3 + 5/3*w^2 + 22/3*w - 11]', '[1621, 1621, 7/3*w^2 - 13/3*w - 11]', '[1621, 1621, -2/3*w^3 + 8/3*w^2 + 6*w - 17]', '[1669, 1669, 5/3*w^2 + 1/3*w - 16]', '[1669, 1669, 5/3*w^2 - 11/3*w - 14]', '[1681, 41, 2*w^2 - 2*w - 17]', '[1681, 41, 2*w^2 - 2*w - 13]', '[1699, 1699, 1/3*w^3 - 2*w^2 + 5/3*w + 11]', '[1699, 1699, -1/3*w^3 - w^2 + 4/3*w + 11]', '[1721, 1721, 1/3*w^2 + 8/3*w - 11]', '[1721, 1721, 1/3*w^2 - 10/3*w - 8]', '[1789, 1789, -2/3*w^2 - 7/3*w - 4]', '[1789, 1789, -w^3 + 2*w^2 + 8*w - 13]', '[1789, 1789, 4/3*w^2 - 13/3*w - 8]', '[1789, 1789, 2/3*w^2 - 11/3*w + 7]', '[1811, 1811, 2/3*w^2 - 11/3*w - 9]', '[1811, 1811, 2/3*w^2 + 7/3*w - 12]', '[1831, 1831, 4/3*w^2 + 5/3*w - 9]', '[1831, 1831, -w^3 + 5/3*w^2 + 25/3*w - 2]', '[1861, 1861, 14/3*w^2 + 1/3*w - 33]', '[1861, 1861, 14/3*w^2 - 29/3*w - 28]', '[1871, 1871, -w^3 + 2/3*w^2 + 28/3*w - 3]', '[1871, 1871, 1/3*w^3 + w^2 - 22/3*w - 7]', '[1871, 1871, -1/3*w^3 + 2*w^2 + 13/3*w - 13]', '[1871, 1871, -w^3 + 7/3*w^2 + 23/3*w - 6]', '[1879, 1879, -w^3 + 8/3*w^2 + 22/3*w - 13]', '[1879, 1879, -w^3 + 1/3*w^2 + 29/3*w + 4]', '[1889, 1889, -5/3*w^3 + 2*w^2 + 38/3*w - 16]', '[1889, 1889, 5/3*w^3 - 3*w^2 - 35/3*w - 3]', '[1901, 1901, w^2 - 3*w - 11]', '[1901, 1901, w^2 + w - 13]', '[1931, 1931, 2/3*w^3 + 2*w^2 - 38/3*w - 21]', '[1931, 1931, w^3 - 2/3*w^2 - 25/3*w - 9]', '[1931, 1931, -w^3 + 7/3*w^2 + 20/3*w - 17]', '[1931, 1931, -2/3*w^3 + 4*w^2 + 20/3*w - 31]', '[1949, 1949, 2/3*w^3 + 5/3*w^2 - 28/3*w - 21]', '[1949, 1949, -1/3*w^3 + 3*w^2 + 1/3*w - 17]', '[1951, 1951, -1/3*w^3 + 8/3*w^2 + 2/3*w - 19]', '[1951, 1951, 1/3*w^3 + 5/3*w^2 - 5*w - 16]', '[1999, 1999, -5/3*w^3 + 3*w^2 + 38/3*w - 23]', '[1999, 1999, -1/3*w^3 - 5/3*w^2 + 4*w + 19]', '[1999, 1999, 1/3*w^3 - 8/3*w^2 + 1/3*w + 21]', '[1999, 1999, 5/3*w^3 - 2*w^2 - 41/3*w - 9]']}
• 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': [45, 15, -14, -2, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 19525, 'disc_rad': 3905, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[2, 2]]], [5, [0]], [7, [[2, 2]]], [11, [0]], [13, [[2, 2]]], [17, [[2, 2]]], [19, [[2, 1], [1, 2]]], [23, [[4, 1]]], [29, [[2, 1], [1, 2]]], [31, [[2, 1], [1, 2]]], [37, [[2, 2]]], [41, [[2, 2]]], [43, [[4, 1]]], [47, [[4, 1]]], [53, [[4, 1]]], [59, [[2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 4, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 62.489999199871974, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.19525.1', 'local_algs': ['5.2.1.1', '5.2.1.1', '11.2.1.2', '11.2.0.1', '71.2.1.1', '71.2.0.1'], 'monogenic': -1, 'num_ram': 3, 'r2': 0, 'ramps': [5, 11, 71], 'rd': 11.8208242574, 'regulator': {'__RealLiteral__': 0, 'data': '7.25243027109', 'prec': 44}, 'res': {'gal': ['45,195,-179,-782,703,126,-62,-2,1'], 'sib': ['45,0,-31,0,1', '45,195,-179,-782,703,126,-62,-2,1']}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{3} a^{2} - \\frac{1}{3} a - 3 \\)', '\\( \\frac{1}{3} a^{3} + \\frac{1}{3} a^{2} - \\frac{14}{3} a - 7 \\)', '\\( \\frac{1}{3} a^{3} + a^{2} - \\frac{7}{3} a - 7 \\)'], 'used_grh': False, 'zk': ['1', 'a', '1/3*a^2 - 1/3*a', '1/3*a^3 - 1/3*a']}