Hilbert modular form data - 3.3.1369.1-8.1-d

Formats: - HTML - YAML - JSON - 2024-05-05T01:11:26.971843

• 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': 3, 'dimension': 3, 'disc': 1369, 'field_bad_primes': [37], 'field_label': '3.3.1369.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.1369.1-8.1-d', 'label_nsuffix': 3, 'label_suffix': 'd', 'level_bad_primes': [2], 'level_ideal': '[8, 2, 2]', 'level_label': '8.1', 'level_norm': 8, 'parallel_weight': 2, 'short_label': '8.1-d', 'weight': '[2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[8, 2, 2]', -1]], 'hecke_eigenvalues': [1, 'e', '-e^2 - 2*e + 12', 'e^2 + e - 11', 'e^2 + e - 13', '-e^2 - 2*e + 10', 'e - 2', 7, 'e - 3', 'e^2 + e - 14', '-e^2 - 2*e + 9', '2*e + 1', '2*e^2 + 2*e - 21', '-2*e^2 - 4*e + 25', 10, '2*e - 1', '-2*e^2 - 4*e + 23', '2*e^2 + 2*e - 23', '-e^2 - 2*e + 13', 'e + 1', 'e^2 + e - 10', '-e^2 - e + 20', '-e + 9', 'e^2 + 2*e - 3', '2*e - 3', '-2*e^2 - 4*e + 21', '2*e^2 + 2*e - 25', '2*e^2 + 4*e - 24', '-2*e^2 - 2*e + 22', '-2*e', '-3*e^2 - 5*e + 43', '2*e^2 + e - 14', 'e^2 + 4*e - 4', 0, '-e^2 - e', '-e - 11', 'e^2 + 2*e - 23', '2*e^2 + 4*e - 32', '-2*e - 8', '-2*e^2 - 2*e + 14', '-3*e^2 - 5*e + 42', '2*e^2 + e - 15', 'e^2 + 4*e - 5', '4*e^2 + 4*e - 47', '4*e - 3', '-4*e^2 - 8*e + 45', '5*e^2 + 8*e - 62', '-2*e^2 - 7*e + 20', '-3*e^2 - e + 29', 'e^2 - 2*e - 11', '3*e^2 + 7*e - 36', '-4*e^2 - 5*e + 45', '3*e^2 + 4*e - 16', '-e^2 + e + 29', '-2*e^2 - 5*e + 42', '-e^2 - 4*e + 17', '3*e^2 + 5*e - 30', '-2*e^2 - e + 27', '-6*e^2 - 12*e + 73', '6*e^2 + 6*e - 65', '6*e + 1', '4*e + 1', '-4*e^2 - 8*e + 49', '4*e^2 + 4*e - 43', '-6*e^2 - 13*e + 72', '-e^2 + 5*e + 11', '7*e^2 + 8*e - 78', '-5*e^2 - 9*e + 51', 'e^2 + 6*e - 20', '4*e^2 + 3*e - 52', 22, 'e^2 - 4*e - 7', '-6*e^2 - 7*e + 71', '5*e^2 + 11*e - 56', '-e^2 + e + 9', '-2*e^2 - 5*e + 22', '3*e^2 + 4*e - 36', '-4*e^2 - 4*e + 49', '-4*e + 5', '4*e^2 + 8*e - 43', '-5*e^2 - 3*e + 66', '-2*e^2 - 9*e + 35', '7*e^2 + 12*e - 71', '-4*e^2 - 8*e + 51', '4*e^2 + 4*e - 41', '4*e + 3', '5*e^2 + 12*e - 59', '2*e^2 - 3*e - 21', '-7*e^2 - 9*e + 80', '-3*e^2 - 7*e + 22', '-e^2 + 2*e - 3', '4*e^2 + 5*e - 59', '-e^2 - 3*e + 39', '-e^2 + 38', '2*e^2 + 3*e + 4', '-3*e^2 - 5*e + 28', '2*e^2 + e - 29', 'e^2 + 4*e - 19', '6*e^2 + 12*e - 61', '-6*e^2 - 6*e + 77', '-6*e + 11', '8*e^2 + 9*e - 81', '-7*e^2 - 15*e + 92', '-e^2 + 6*e + 19', '-8*e^2 - 12*e + 80', '4*e^2 + 12*e - 60', '4*e^2 - 56', '-4*e^2 - 12*e + 45', '-4*e^2 + 41', '8*e^2 + 12*e - 95', '4*e - 10', '4*e^2 + 4*e - 54', '-4*e^2 - 8*e + 38', '4*e^2 + 13*e - 54', '-9*e^2 - 14*e + 98', '5*e^2 + e - 61', '-4*e^2 - 5*e + 38', 'e^2 - 2*e - 18', '3*e^2 + 7*e - 43', '-e^2 - e + 44', '-e + 33', 'e^2 + 2*e + 21', '3*e^2 + e - 39', '2*e^2 + 7*e - 30', '-5*e^2 - 8*e + 52', '-3*e^2 + 2*e + 26', '8*e^2 + 11*e - 98', '-5*e^2 - 13*e + 53', '-3*e^2 - 5*e + 56', 'e^2 + 4*e + 9', '2*e^2 + e - 1', '12*e^2 + 23*e - 153', '-11*e^2 - 10*e + 111', '-e^2 - 13*e + 2', '7*e^2 + 12*e - 67', '-5*e^2 - 3*e + 70', '-2*e^2 - 9*e + 39', '-4*e^2 - 13*e + 57', '9*e^2 + 14*e - 95', '-5*e^2 - e + 64', '-e^2 + 3*e', '-4*e^2 - 9*e + 37', '5*e^2 + 6*e - 67', '-2*e^2 + e + 16', '5*e^2 + 7*e - 63', '-3*e^2 - 8*e + 30', '11*e^2 + 15*e - 130', '-4*e^2 + 3*e + 39', '-7*e^2 - 18*e + 79', '3*e^2 + e - 53', '2*e^2 + 7*e - 44', '-5*e^2 - 8*e + 38', '-2*e^2 - 11*e + 2', '-7*e^2 - 5*e + 55', '9*e^2 + 16*e - 128', '5*e^2 + 18*e - 58', '-13*e^2 - 21*e + 153', '8*e^2 + 3*e - 86', '-13*e^2 - 21*e + 141', '8*e^2 + 3*e - 98', '5*e^2 + 18*e - 70'], 'hecke_polynomial': 'x^3 - x^2 - 16*x + 29', 'label': '3.3.1369.1-8.1-d'}
• hmf_fields •

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

  
  {'degree': 3, 'discriminant': 1369, 'ideals': ['[1, 1, 1]', '[8, 2, 2]', '[11, 11, w]', '[11, 11, -w^2 + 3*w + 7]', '[11, 11, w^2 - 2*w - 8]', '[23, 23, w^2 - 2*w - 7]', '[23, 23, w^2 - 3*w - 8]', '[23, 23, w - 1]', '[27, 3, 3]', '[29, 29, w^2 - 2*w - 5]', '[29, 29, w^2 - 3*w - 10]', '[29, 29, w - 3]', '[31, 31, w^2 - 2*w - 6]', '[31, 31, -w^2 + 3*w + 9]', '[31, 31, w - 2]', '[37, 37, -w^2 + 4*w + 7]', '[43, 43, 2*w^2 - 6*w - 13]', '[43, 43, 2*w^2 - 4*w - 17]', '[43, 43, w^2 - 2*w - 12]', '[47, 47, w^2 - 4*w - 4]', '[47, 47, w^2 - w - 5]', '[47, 47, 2*w^2 - 5*w - 18]', '[64, 4, 4]', '[73, 73, -2*w^2 + 5*w + 14]', '[73, 73, w^2 - w - 9]', '[73, 73, -w^2 + 4*w + 8]', '[88, 22, 2*w]', '[88, 22, -2*w^2 + 6*w + 14]', '[88, 22, 2*w^2 - 4*w - 16]', '[97, 97, -2*w^2 + 5*w + 10]', '[97, 97, 2*w^2 - 3*w - 15]', '[97, 97, w^2 - 4*w - 12]', '[101, 101, -w - 5]', '[101, 101, w^2 - 3*w - 2]', '[101, 101, w^2 - 2*w - 13]', '[103, 103, w^2 - w - 10]', '[103, 103, w^2 - 4*w - 9]', '[103, 103, -2*w^2 + 5*w + 13]', '[121, 11, 2*w^2 - 5*w - 11]', '[121, 11, -w^2 + 4*w + 11]', '[121, 11, w^2 - w - 12]', '[121, 121, -w^2 + w + 11]', '[121, 121, -w^2 + 4*w + 10]', '[121, 121, -2*w^2 + 5*w + 12]', '[125, 5, -5]', '[137, 137, 2*w - 1]', '[137, 137, 2*w^2 - 6*w - 15]', '[137, 137, -2*w^2 + 4*w + 15]', '[149, 149, 3*w^2 - 7*w - 24]', '[149, 149, -2*w^2 + 3*w + 18]', '[149, 149, 3*w^2 - 8*w - 20]', '[179, 179, 2*w^2 - 6*w - 21]', '[179, 179, -w^2 + 4*w + 15]', '[179, 179, -2*w^2 + 5*w + 7]', '[184, 46, 2*w^2 - 4*w - 14]', '[184, 46, 2*w^2 - 6*w - 16]', '[184, 46, 2*w - 2]', '[191, 191, -w - 6]', '[191, 191, w^2 - 3*w - 1]', '[191, 191, w^2 - 2*w - 14]', '[193, 193, -3*w^2 + 9*w + 20]', '[193, 193, 2*w^2 - 4*w - 23]', '[193, 193, -3*w^2 + 6*w + 25]', '[199, 199, w^2 - 3*w - 14]', '[199, 199, w^2 - 2*w - 1]', '[199, 199, w - 7]', '[211, 211, 2*w^2 - 3*w - 19]', '[211, 211, w^2 - 5*w - 10]', '[211, 211, 3*w^2 - 8*w - 19]', '[216, 6, 6]', '[223, 223, 2*w^2 - 6*w - 17]', '[223, 223, 2*w^2 - 4*w - 13]', '[223, 223, 2*w - 3]', '[232, 58, 2*w^2 - 4*w - 10]', '[232, 58, 2*w^2 - 6*w - 20]', '[232, 58, 2*w - 6]', '[233, 233, -3*w^2 + 7*w + 23]', '[233, 233, w^2 - 8]', '[233, 233, -2*w^2 + 7*w + 14]', '[248, 62, 2*w^2 - 4*w - 12]', '[248, 62, -2*w^2 + 6*w + 18]', '[248, 62, 2*w - 4]', '[251, 251, w^2 - 5*w - 4]', '[251, 251, 3*w^2 - 8*w - 25]', '[251, 251, 2*w^2 - 3*w - 13]', '[253, 253, w^2 - 5*w - 13]', '[253, 253, -2*w^2 + 3*w + 22]', '[253, 253, -w^2 + 5*w + 11]', '[253, 253, 3*w^2 - 8*w - 18]', '[253, 253, -2*w^2 + 3*w + 20]', '[253, 253, 2*w - 5]', '[253, 253, -2*w^2 + 6*w + 19]', '[253, 253, -2*w^2 + 4*w + 11]', '[253, 253, -3*w^2 + 8*w + 16]', '[269, 269, w^2 - 5*w - 12]', '[269, 269, 2*w^2 - 3*w - 21]', '[269, 269, 3*w^2 - 8*w - 17]', '[296, 74, -2*w^2 + 8*w + 14]', '[297, 33, 3*w]', '[297, 33, -3*w^2 + 9*w + 21]', '[297, 33, 3*w^2 - 6*w - 24]', '[307, 307, w^2 - 5*w - 3]', '[307, 307, 2*w^2 - 3*w - 12]', '[307, 307, -3*w^2 + 8*w + 26]', '[319, 319, w + 7]', '[319, 319, -2*w^2 + 8*w + 9]', '[319, 319, w^2 - 3*w]', '[319, 319, -4*w^2 + 10*w + 35]', '[319, 319, 5*w^2 - 14*w - 32]', '[319, 319, -2*w^2 + 2*w + 11]', '[319, 319, -4*w^2 + 7*w + 36]', '[319, 319, w^2 - 2*w - 15]', '[319, 319, -w^2 + 7*w + 11]', '[341, 341, -3*w^2 + 8*w + 27]', '[341, 341, -w^2 + 3*w + 15]', '[341, 341, 4*w^2 - 11*w - 25]', '[341, 341, -w^2 + 5*w + 2]', '[341, 341, 2*w^2 - 3*w - 11]', '[341, 341, 3*w^2 - 5*w - 28]', '[341, 341, w^2 - 2*w]', '[341, 341, -w^2 + 6*w + 11]', '[341, 341, -w + 8]', '[343, 7, -7]', '[344, 86, 4*w^2 - 12*w - 26]', '[344, 86, 4*w^2 - 8*w - 34]', '[344, 86, 2*w^2 - 4*w - 24]', '[347, 347, 2*w^2 - 3*w - 10]', '[347, 347, 3*w^2 - 8*w - 28]', '[347, 347, w^2 - 5*w - 1]', '[359, 359, 3*w^2 - 5*w - 23]', '[359, 359, 2*w^2 - 7*w - 23]', '[359, 359, -3*w^2 + 7*w + 14]', '[376, 94, 2*w^2 - 8*w - 8]', '[376, 94, 2*w^2 - 2*w - 10]', '[376, 94, 4*w^2 - 10*w - 36]', '[397, 397, 2*w^2 - 8*w - 7]', '[397, 397, 4*w^2 - 10*w - 37]', '[397, 397, 2*w^2 - 2*w - 9]', '[401, 401, 2*w^2 - 7*w - 16]', '[401, 401, 3*w^2 - 7*w - 21]', '[401, 401, w^2 - 10]', '[407, 407, 4*w^2 - 12*w - 17]', '[407, 407, 3*w - 1]', '[407, 407, 3*w^2 - 5*w - 11]', '[421, 421, 3*w^2 - 5*w - 29]', '[421, 421, w^2 - 6*w - 12]', '[421, 421, -4*w^2 + 11*w + 24]', '[433, 433, w^2 - 6*w - 15]', '[433, 433, 3*w^2 - 5*w - 32]', '[433, 433, -4*w^2 + 11*w + 21]', '[443, 443, 5*w^2 - 13*w - 36]', '[443, 443, -2*w^2 + 9*w + 15]', '[443, 443, 5*w^2 - 12*w - 40]', '[467, 467, w^2 - 6*w - 13]', '[467, 467, 3*w^2 - 5*w - 30]', '[467, 467, -4*w^2 + 11*w + 23]', '[473, 473, -w^2 + 11]', '[473, 473, -5*w^2 + 17*w + 19]', '[473, 473, 3*w^2 - 5*w - 31]', '[473, 473, -4*w^2 + 11*w + 22]', '[473, 473, -7*w^2 + 15*w + 63]', '[473, 473, -2*w^2 + 7*w + 22]', '[473, 473, -w^2 + 16]', '[473, 473, 5*w^2 - 13*w - 40]', '[473, 473, -7*w^2 + 16*w + 70]', '[487, 487, -3*w^2 + 10*w + 20]', '[487, 487, -4*w^2 + 9*w + 32]', '[487, 487, w^2 + w - 7]', '[491, 491, -w - 8]', '[491, 491, -w^2 + 3*w - 1]', '[491, 491, w^2 - 2*w - 16]', '[512, 8, 8]', '[517, 517, -w^2 + 5*w + 18]', '[517, 517, -3*w^2 + 6*w + 22]', '[517, 517, 3*w^2 - 9*w - 23]', '[517, 517, 2*w^2 - 3*w - 27]', '[517, 517, 7*w + 11]', '[517, 517, -3*w^2 + 8*w + 11]', '[517, 517, 3*w - 2]', '[517, 517, -7*w^2 + 14*w + 67]', '[517, 517, -7*w^2 + 21*w + 38]', '[529, 23, -3*w^2 + 7*w + 19]', '[529, 23, -w^2 + 12]', '[529, 23, -2*w^2 + 7*w + 18]', '[529, 529, -w^2 + 3*w + 16]', '[529, 529, w^2 - 2*w + 1]', '[529, 529, -w + 9]', '[541, 541, 3*w^2 - 7*w - 16]', '[541, 541, 2*w^2 - 7*w - 21]', '[541, 541, w^2 - 15]', '[547, 547, 2*w^2 - 4*w - 25]', '[547, 547, 2*w^2 - 6*w - 5]', '[547, 547, -2*w - 9]', '[563, 563, 3*w^2 - 7*w - 18]', '[563, 563, 2*w^2 - 7*w - 19]', '[563, 563, w^2 - 13]', '[569, 569, w^2 - 14]', '[569, 569, 3*w^2 - 7*w - 17]', '[569, 569, 2*w^2 - 7*w - 20]', '[584, 146, -4*w^2 + 10*w + 28]', '[584, 146, 2*w^2 - 2*w - 18]', '[584, 146, -2*w^2 + 8*w + 16]', '[593, 593, w^2 - w - 18]', '[593, 593, w^2 - 4*w - 17]', '[593, 593, 2*w^2 - 5*w - 5]', '[619, 619, -5*w^2 + 14*w + 30]', '[619, 619, 4*w^2 - 7*w - 38]', '[619, 619, -5*w^2 + 11*w + 42]', '[621, 69, 3*w^2 - 6*w - 21]', '[621, 69, 3*w^2 - 9*w - 24]', '[621, 69, 3*w - 3]', '[643, 643, w^2 + w - 8]', '[643, 643, -3*w^2 + 10*w + 21]', '[643, 643, -4*w^2 + 9*w + 31]', '[667, 667, -4*w^2 + 11*w + 32]', '[667, 667, w^2 - 6*w - 4]', '[667, 667, -2*w^2 + 5*w + 25]', '[667, 667, w^2 - 4*w + 3]', '[667, 667, w^2 - w + 2]', '[667, 667, -3*w^2 + 4*w + 26]', '[667, 667, -2*w^2 + 9*w + 16]', '[667, 667, -3*w^2 + 5*w + 21]', '[667, 667, -5*w^2 + 13*w + 35]', '[677, 677, -2*w^2 + 7*w + 27]', '[677, 677, -3*w^2 + 7*w + 10]', '[677, 677, 3*w^2 - 9*w - 31]', '[704, 44, 4*w]', '[704, 44, -4*w^2 + 12*w + 28]', '[704, 44, 4*w^2 - 8*w - 32]', '[709, 709, w^2 - 7*w - 14]', '[709, 709, 4*w^2 - 7*w - 39]', '[709, 709, 5*w^2 - 14*w - 29]', '[713, 713, w + 9]', '[713, 713, -4*w^2 + 10*w + 27]', '[713, 713, w^2 - 3*w + 2]', '[713, 713, 2*w^2 - 2*w - 19]', '[713, 713, -3*w^2 + 9*w + 25]', '[713, 713, -3*w + 4]', '[713, 713, -2*w^2 + 8*w + 17]', '[713, 713, w^2 - 2*w - 17]', '[713, 713, 3*w^2 - 6*w - 20]', '[729, 9, 9]', '[739, 739, -5*w^2 + 14*w + 27]', '[739, 739, w^2 - 7*w - 16]', '[739, 739, 4*w^2 - 7*w - 41]', '[751, 751, 4*w^2 - 9*w - 43]', '[751, 751, 4*w^2 - 7*w - 40]', '[751, 751, -3*w^2 + 10*w + 9]', '[769, 769, w^2 - 3*w - 17]', '[769, 769, -w^2 + 2*w - 2]', '[769, 769, w - 10]', '[776, 194, -4*w^2 + 10*w + 20]', '[776, 194, 4*w^2 - 6*w - 30]', '[776, 194, 2*w^2 - 8*w - 24]', '[783, 87, 3*w^2 - 6*w - 15]', '[783, 87, 3*w^2 - 9*w - 30]', '[783, 87, 3*w - 9]', '[787, 787, 3*w^2 - 6*w - 19]', '[787, 787, 3*w - 5]', '[787, 787, 3*w^2 - 9*w - 26]', '[803, 803, w^2 + w - 9]', '[803, 803, 3*w^2 - 10*w - 22]', '[803, 803, 3*w^2 - 9*w - 10]', '[803, 803, 3*w^2 - 6*w - 35]', '[803, 803, 2*w^2 - 9*w - 1]', '[803, 803, 3*w + 11]', '[803, 803, -5*w^2 + 13*w + 50]', '[803, 803, 4*w^2 - 9*w - 30]', '[803, 803, 3*w^2 - 4*w - 11]', '[808, 202, -2*w - 10]', '[808, 202, 2*w^2 - 6*w - 4]', '[808, 202, 2*w^2 - 4*w - 26]', '[824, 206, 2*w^2 - 2*w - 20]', '[824, 206, 2*w^2 - 8*w - 18]', '[824, 206, -4*w^2 + 10*w + 26]', '[837, 93, 3*w^2 - 6*w - 18]', '[837, 93, -3*w^2 + 9*w + 27]', '[837, 93, 3*w - 6]', '[841, 29, 4*w^2 - 13*w - 26]', '[841, 29, -5*w^2 + 11*w + 41]', '[841, 29, w^2 + 2*w - 6]', '[841, 841, 3*w^2 - 9*w - 29]', '[841, 841, 3*w - 8]', '[841, 841, 3*w^2 - 6*w - 16]', '[851, 851, 4*w^2 - 9*w - 18]', '[851, 851, -w^2 + 7*w + 6]', '[851, 851, -3*w^2 + 8*w + 10]', '[857, 857, 3*w^2 - 9*w - 28]', '[857, 857, 3*w^2 - 6*w - 17]', '[857, 857, 3*w - 7]', '[859, 859, 4*w^2 - 11*w - 40]', '[859, 859, 3*w^2 - 4*w - 19]', '[859, 859, 5*w^2 - 13*w - 42]', '[877, 877, 6*w^2 - 14*w - 49]', '[877, 877, -3*w^2 + 13*w + 21]', '[877, 877, -4*w^2 + 14*w + 25]', '[887, 887, 2*w^2 - 5*w - 4]', '[887, 887, w^2 - w - 19]', '[887, 887, w^2 - 4*w - 18]', '[899, 899, 4*w^2 - 8*w - 31]', '[899, 899, 2*w^2 - 8*w - 23]', '[899, 899, -3*w^2 + 8*w + 35]', '[899, 899, 5*w^2 - 12*w - 38]', '[899, 899, -3*w^2 + 11*w + 21]', '[899, 899, 4*w - 1]', '[899, 899, 2*w^2 - w - 16]', '[899, 899, -4*w^2 + 12*w + 29]', '[899, 899, 4*w^2 - 5*w - 28]', '[911, 911, 2*w^2 - 2*w - 21]', '[911, 911, 4*w^2 - 10*w - 25]', '[911, 911, 2*w^2 - 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41*w - 62]', '[9647, 9647, 3*w^2 + w - 57]', '[9647, 9647, 10*w^2 - 15*w - 33]', '[9647, 9647, 15*w^2 - 47*w - 67]', '[9647, 9647, -8*w^2 + 23*w + 66]', '[9647, 9647, 10*w^2 - 23*w - 44]', '[9647, 9647, -w^2 + 13*w + 8]', '[9647, 9647, -17*w^2 + 36*w + 172]', '[9647, 9647, -w^2 + 10*w - 2]', '[9649, 9649, 3*w^2 - 8*w - 45]', '[9649, 9649, -2*w^2 + 3*w - 7]', '[9649, 9649, -w^2 + 5*w - 16]', '[9683, 9683, 11*w^2 - 35*w - 68]', '[9683, 9683, -2*w^2 - 7*w + 7]', '[9683, 9683, 2*w^2 - w + 8]', '[9683, 9683, -5*w^2 + 12*w + 62]', '[9683, 9683, -3*w^2 + 11*w - 3]', '[9683, 9683, -6*w^2 + 24*w + 17]', '[9683, 9683, -12*w^2 + 30*w + 115]', '[9683, 9683, -6*w^2 + 6*w + 23]', '[9683, 9683, -13*w^2 + 28*w + 111]', '[9693, 1077, 9*w^2 - 15*w - 69]', '[9693, 1077, 6*w^2 - 21*w - 69]', '[9693, 1077, -9*w^2 + 21*w + 42]', '[9704, 2426, 6*w^2 - 8*w - 32]', '[9704, 2426, 10*w^2 - 26*w - 90]', '[9704, 2426, 4*w^2 - 18*w - 12]', '[9721, 9721, -5*w^2 + 16*w + 65]', '[9721, 9721, 8*w^2 - 11*w - 56]', '[9721, 9721, -5*w^2 + 23*w + 27]', '[9739, 9739, 12*w^2 - 30*w - 107]', '[9739, 9739, 11*w^2 - 28*w - 105]', '[9739, 9739, -5*w^2 + 21*w + 12]', '[9757, 9757, -12*w^2 + 39*w + 71]', '[9757, 9757, -7*w + 11]', '[9757, 9757, -3*w^2 - 6*w + 11]', '[9757, 9757, -15*w^2 + 33*w + 130]', '[9757, 9757, -11*w^2 + 19*w + 89]', '[9757, 9757, 14*w^2 - 39*w - 100]', '[9757, 9757, 7*w^2 - 21*w - 60]', '[9757, 9757, -3*w^2 + 20*w + 22]', '[9757, 9757, 7*w^2 - 14*w - 45]', '[9767, 9767, 3*w^2 - 5*w - 47]', '[9767, 9767, w^2 - 6*w - 30]', '[9767, 9767, 4*w^2 - 11*w - 6]', '[9769, 9769, 3*w^2 - w - 36]', '[9769, 9769, 5*w^2 - 18*w - 47]', '[9769, 9769, 8*w^2 - 19*w - 49]', '[9791, 9791, 5*w^2 - 6*w - 57]', '[9791, 9791, 4*w^2 - 17*w - 45]', '[9791, 9791, 9*w^2 - 23*w - 50]', '[9797, 9797, 4*w^2 - 17*w - 42]', '[9797, 9797, -10*w^2 + 27*w + 82]', '[9797, 9797, 3*w^2 - 16*w - 12]', '[9797, 9797, 7*w^2 - 11*w - 47]', '[9797, 9797, -2*w^2 + 5*w - 7]', '[9797, 9797, w^2 - w - 30]', '[9797, 9797, w^2 - 4*w - 29]', '[9797, 9797, 9*w^2 - 23*w - 53]', '[9797, 9797, 5*w^2 - 6*w - 54]', '[9811, 9811, 10*w^2 - 20*w - 81]', '[9811, 9811, -10*w^2 + 30*w + 69]', '[9811, 9811, -10*w - 1]', '[9832, 2458, 6*w^2 - 8*w - 28]', '[9832, 2458, 10*w^2 - 26*w - 94]', '[9832, 2458, 4*w^2 - 18*w - 8]', '[9848, 2462, 6*w^2 - 8*w - 58]', '[9848, 2462, 10*w^2 - 26*w - 64]', '[9848, 2462, 4*w^2 - 18*w - 38]', '[9871, 9871, -w^2 + 4*w - 15]', '[9871, 9871, -w^2 + w - 14]', '[9871, 9871, 2*w^2 - 5*w - 37]', '[9887, 9887, 8*w^2 - 23*w - 81]', '[9887, 9887, 12*w^2 - 31*w - 100]', '[9887, 9887, 7*w^2 - 9*w - 45]', '[9889, 9889, w^2 - 3*w - 29]', '[9889, 9889, 9*w^2 - 23*w - 51]', '[9889, 9889, 5*w^2 - 6*w - 56]', '[9889, 9889, -6*w^2 + w + 22]', '[9889, 9889, 4*w^2 - w]', '[9889, 9889, -11*w^2 + 23*w + 117]', '[9889, 9889, 8*w^2 - 17*w - 57]', '[9889, 9889, -11*w^2 + 26*w + 116]', '[9889, 9889, w^2 + 8*w + 22]', '[9889, 9889, -10*w^2 + 26*w + 91]', '[9889, 9889, 10*w^2 - 31*w - 40]', '[9889, 9889, -11*w^2 + 32*w + 125]', '[9889, 9889, 5*w^2 - w - 33]', '[9889, 9889, 8*w^2 - 15*w - 33]', '[9889, 9889, 7*w^2 - 25*w - 17]', '[9889, 9889, -9*w^2 + 12*w + 74]', '[9889, 9889, -5*w^2 + 18*w + 52]', '[9889, 9889, 8*w^2 - 19*w - 44]', '[9889, 9889, -w^2 + 11*w - 24]', '[9889, 9889, 3*w^2 - w - 41]', '[9889, 9889, -7*w^2 + 22*w + 55]', '[9889, 9889, -9*w^2 + 26*w + 95]', '[9889, 9889, -4*w^2 + 17*w + 44]', '[9889, 9889, 6*w^2 - 7*w - 53]', '[9889, 9889, 18*w^2 - 35*w - 159]', '[9889, 9889, w^2 + 5*w - 14]', '[9889, 9889, -w^2 + 20*w + 44]', '[9917, 9917, 3*w^2 - 11*w - 47]', '[9917, 9917, 3*w^2 - 17*w - 43]', '[9917, 9917, 2*w^2 - w - 42]', '[9917, 9917, 2*w - 23]', '[9917, 9917, 5*w^2 - 12*w - 12]', '[9917, 9917, -2*w^2 + 4*w - 7]', '[9917, 9917, 2*w^2 - 6*w - 37]', '[9917, 9917, 8*w^2 - 13*w - 86]', '[9917, 9917, -11*w^2 + 30*w + 58]', '[9947, 203, 7*w^2 - 14*w - 35]', '[9947, 203, 7*w^2 - 21*w - 70]', '[9947, 203, 7*w - 21]', '[9953, 9953, 8*w^2 - 19*w - 48]', '[9953, 9953, 5*w^2 - 18*w - 48]', '[9953, 9953, 3*w^2 - w - 37]', '[9959, 9959, -w^2 + 8*w + 32]', '[9959, 9959, 11*w^2 - 38*w - 65]', '[9959, 9959, -9*w^2 + 33*w + 41]', '[9959, 9959, -5*w^2 + 9*w + 65]', '[9959, 9959, -5*w^2 - w + 28]', '[9959, 9959, -16*w^2 + 37*w + 135]', '[9959, 9959, -6*w^2 + 17*w + 18]', '[9959, 9959, -15*w^2 + 36*w + 136]', '[9959, 9959, -6*w^2 + 3*w + 26]', '[9967, 9967, -9*w^2 + 25*w + 74]', '[9967, 9967, 2*w^2 - 13*w - 5]', '[9967, 9967, -7*w^2 + 12*w + 47]', '[9976, 2494, 8*w^2 - 18*w - 54]', '[9976, 2494, 6*w^2 - 8*w - 30]', '[9976, 2494, 6*w^2 - 20*w - 50]', '[9976, 2494, 2*w^2 + 2*w - 24]', '[9976, 2494, 2*w^2 - 2*w - 40]', '[9976, 2494, 2*w^2 - 8*w - 38]', '[9976, 2494, 4*w^2 - 10*w - 6]', '[9976, 2494, 10*w^2 - 26*w - 92]', '[9976, 2494, 4*w^2 - 18*w - 10]', '[9991, 9991, 9*w^2 - 18*w - 70]', '[9991, 9991, -w^2 + 7*w - 20]', '[9991, 9991, 9*w - 2]', '[9991, 9991, 4*w^2 - 7*w - 5]', '[9991, 9991, 5*w^2 - 14*w - 63]', '[9991, 9991, 10*w^2 - 24*w - 73]', '[9991, 9991, 4*w^2 - 2*w - 35]', '[9991, 9991, -9*w^2 + 27*w + 65]', '[9991, 9991, 6*w^2 - 22*w - 45]'], 'label': '3.3.1369.1', 'narrow_class_no': 1, 'primes': ['[8, 2, 2]', '[11, 11, w]', '[11, 11, -w^2 + 3*w + 7]', '[11, 11, w^2 - 2*w - 8]', '[23, 23, w^2 - 2*w - 7]', '[23, 23, w^2 - 3*w - 8]', '[23, 23, w - 1]', '[27, 3, 3]', '[29, 29, w^2 - 2*w - 5]', '[29, 29, w^2 - 3*w - 10]', '[29, 29, w - 3]', '[31, 31, w^2 - 2*w - 6]', '[31, 31, -w^2 + 3*w + 9]', '[31, 31, w - 2]', '[37, 37, -w^2 + 4*w + 7]', '[43, 43, 2*w^2 - 6*w - 13]', '[43, 43, 2*w^2 - 4*w - 17]', '[43, 43, w^2 - 2*w - 12]', '[47, 47, w^2 - 4*w - 4]', '[47, 47, w^2 - w - 5]', '[47, 47, 2*w^2 - 5*w - 18]', '[73, 73, -2*w^2 + 5*w + 14]', '[73, 73, w^2 - w - 9]', '[73, 73, -w^2 + 4*w + 8]', '[97, 97, -2*w^2 + 5*w + 10]', '[97, 97, 2*w^2 - 3*w - 15]', '[97, 97, w^2 - 4*w - 12]', '[101, 101, -w - 5]', '[101, 101, w^2 - 3*w - 2]', '[101, 101, w^2 - 2*w - 13]', '[103, 103, w^2 - w - 10]', '[103, 103, w^2 - 4*w - 9]', '[103, 103, -2*w^2 + 5*w + 13]', '[125, 5, -5]', '[137, 137, 2*w - 1]', '[137, 137, 2*w^2 - 6*w - 15]', '[137, 137, -2*w^2 + 4*w + 15]', '[149, 149, 3*w^2 - 7*w - 24]', '[149, 149, -2*w^2 + 3*w + 18]', '[149, 149, 3*w^2 - 8*w - 20]', '[179, 179, 2*w^2 - 6*w - 21]', '[179, 179, -w^2 + 4*w + 15]', '[179, 179, -2*w^2 + 5*w + 7]', '[191, 191, -w - 6]', '[191, 191, w^2 - 3*w - 1]', '[191, 191, w^2 - 2*w - 14]', '[193, 193, -3*w^2 + 9*w + 20]', '[193, 193, 2*w^2 - 4*w - 23]', '[193, 193, -3*w^2 + 6*w + 25]', '[199, 199, w^2 - 3*w - 14]', '[199, 199, w^2 - 2*w - 1]', '[199, 199, w - 7]', '[211, 211, 2*w^2 - 3*w - 19]', '[211, 211, w^2 - 5*w - 10]', '[211, 211, 3*w^2 - 8*w - 19]', '[223, 223, 2*w^2 - 6*w - 17]', '[223, 223, 2*w^2 - 4*w - 13]', '[223, 223, 2*w - 3]', '[233, 233, -3*w^2 + 7*w + 23]', '[233, 233, w^2 - 8]', '[233, 233, -2*w^2 + 7*w + 14]', '[251, 251, w^2 - 5*w - 4]', '[251, 251, 3*w^2 - 8*w - 25]', '[251, 251, 2*w^2 - 3*w - 13]', '[269, 269, w^2 - 5*w - 12]', '[269, 269, 2*w^2 - 3*w - 21]', '[269, 269, 3*w^2 - 8*w - 17]', '[307, 307, w^2 - 5*w - 3]', '[307, 307, 2*w^2 - 3*w - 12]', '[307, 307, -3*w^2 + 8*w + 26]', '[343, 7, -7]', '[347, 347, 2*w^2 - 3*w - 10]', '[347, 347, 3*w^2 - 8*w - 28]', '[347, 347, w^2 - 5*w - 1]', '[359, 359, 3*w^2 - 5*w - 23]', '[359, 359, 2*w^2 - 7*w - 23]', '[359, 359, -3*w^2 + 7*w + 14]', '[397, 397, 2*w^2 - 8*w - 7]', '[397, 397, 4*w^2 - 10*w - 37]', '[397, 397, 2*w^2 - 2*w - 9]', '[401, 401, 2*w^2 - 7*w - 16]', '[401, 401, 3*w^2 - 7*w - 21]', '[401, 401, w^2 - 10]', '[421, 421, 3*w^2 - 5*w - 29]', '[421, 421, w^2 - 6*w - 12]', '[421, 421, -4*w^2 + 11*w + 24]', '[433, 433, w^2 - 6*w - 15]', '[433, 433, 3*w^2 - 5*w - 32]', '[433, 433, -4*w^2 + 11*w + 21]', '[443, 443, 5*w^2 - 13*w - 36]', '[443, 443, -2*w^2 + 9*w + 15]', '[443, 443, 5*w^2 - 12*w - 40]', '[467, 467, w^2 - 6*w - 13]', '[467, 467, 3*w^2 - 5*w - 30]', '[467, 467, -4*w^2 + 11*w + 23]', '[487, 487, -3*w^2 + 10*w + 20]', '[487, 487, -4*w^2 + 9*w + 32]', '[487, 487, w^2 + w - 7]', '[491, 491, -w - 8]', '[491, 491, -w^2 + 3*w - 1]', '[491, 491, w^2 - 2*w - 16]', '[541, 541, 3*w^2 - 7*w - 16]', '[541, 541, 2*w^2 - 7*w - 21]', '[541, 541, w^2 - 15]', '[547, 547, 2*w^2 - 4*w - 25]', '[547, 547, 2*w^2 - 6*w - 5]', '[547, 547, -2*w - 9]', '[563, 563, 3*w^2 - 7*w - 18]', '[563, 563, 2*w^2 - 7*w - 19]', '[563, 563, w^2 - 13]', '[569, 569, w^2 - 14]', '[569, 569, 3*w^2 - 7*w - 17]', '[569, 569, 2*w^2 - 7*w - 20]', '[593, 593, w^2 - w - 18]', '[593, 593, w^2 - 4*w - 17]', '[593, 593, 2*w^2 - 5*w - 5]', '[619, 619, -5*w^2 + 14*w + 30]', '[619, 619, 4*w^2 - 7*w - 38]', '[619, 619, -5*w^2 + 11*w + 42]', '[643, 643, w^2 + w - 8]', '[643, 643, -3*w^2 + 10*w + 21]', '[643, 643, -4*w^2 + 9*w + 31]', '[677, 677, -2*w^2 + 7*w + 27]', '[677, 677, -3*w^2 + 7*w + 10]', '[677, 677, 3*w^2 - 9*w - 31]', '[709, 709, w^2 - 7*w - 14]', '[709, 709, 4*w^2 - 7*w - 39]', '[709, 709, 5*w^2 - 14*w - 29]', '[739, 739, -5*w^2 + 14*w + 27]', '[739, 739, w^2 - 7*w - 16]', '[739, 739, 4*w^2 - 7*w - 41]', '[751, 751, 4*w^2 - 9*w - 43]', '[751, 751, 4*w^2 - 7*w - 40]', '[751, 751, -3*w^2 + 10*w + 9]', '[769, 769, w^2 - 3*w - 17]', '[769, 769, -w^2 + 2*w - 2]', '[769, 769, w - 10]', '[787, 787, 3*w^2 - 6*w - 19]', '[787, 787, 3*w - 5]', '[787, 787, 3*w^2 - 9*w - 26]', '[857, 857, 3*w^2 - 9*w - 28]', '[857, 857, 3*w^2 - 6*w - 17]', '[857, 857, 3*w - 7]', '[859, 859, 4*w^2 - 11*w - 40]', '[859, 859, 3*w^2 - 4*w - 19]', '[859, 859, 5*w^2 - 13*w - 42]', '[877, 877, 6*w^2 - 14*w - 49]', '[877, 877, -3*w^2 + 13*w + 21]', '[877, 877, -4*w^2 + 14*w + 25]', '[887, 887, 2*w^2 - 5*w - 4]', '[887, 887, w^2 - w - 19]', '[887, 887, w^2 - 4*w - 18]', '[911, 911, 2*w^2 - 2*w - 21]', '[911, 911, 4*w^2 - 10*w - 25]', '[911, 911, 2*w^2 - 8*w - 19]', '[919, 919, 4*w^2 - 11*w - 34]', '[919, 919, 3*w^2 - 5*w - 19]', '[919, 919, w^2 - 6*w - 2]', '[991, 991, -w - 10]', '[991, 991, -w^2 + 3*w - 3]', '[991, 991, w^2 - 2*w - 18]']}
• 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': [-11, -12, -1, 1], 'conductor': 37, 'degree': 3, 'dirichlet_group': [1, 10, 26], 'disc_abs': 1369, 'disc_rad': 37, 'disc_sign': 1, 'frobs': [[2, [[3, 1]]], [3, [[3, 1]]], [5, [[3, 1]]], [7, [[3, 1]]], [11, [[1, 3]]], [13, [[3, 1]]], [17, [[3, 1]]], [19, [[3, 1]]], [23, [[1, 3]]], [29, [[1, 3]]], [31, [[1, 3]]], [37, [0]], [41, [[3, 1]]], [43, [[1, 3]]], [47, [[1, 3]]], [53, [[3, 1]]], [59, [[3, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [2], 'galois_label': '3T1', 'galt': 1, 'grd': 11.103702468586786, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.1369.1', 'local_algs': ['37.3.2.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [37], 'rd': 11.1037024686, 'regulator': {'__RealLiteral__': 0, 'data': '3.12623019091', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - 3 a - 6 \\)', '\\( a^{2} - 3 a - 5 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}