Hilbert modular form data - 2.2.476.1-4.1-c

Formats: - HTML - YAML - JSON - 2024-05-15T09:13:08.157373

• 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': 2, 'dimension': 4, 'disc': 476, 'field_bad_primes': [2, 7, 17], 'field_label': '2.2.476.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.476.1-4.1-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [2], 'level_ideal': '[4, 2, 2]', 'level_label': '4.1', 'level_norm': 4, 'parallel_weight': 2, 'short_label': '4.1-c', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2, 2, -w + 11]', -1]], 'hecke_eigenvalues': [0, '2/43*e^3 - 9/43*e^2 - 18/43*e + 105/43', '2/43*e^3 - 9/43*e^2 - 18/43*e + 105/43', 0, '-6/43*e^3 + 27/43*e^2 + 54/43*e - 229/43', '-2/43*e^3 + 9/43*e^2 + 61/43*e - 105/43', '2/43*e^3 - 9/43*e^2 - 61/43*e + 105/43', '-8/43*e^3 + 36/43*e^2 + 72/43*e - 162/43', '-1/43*e^3 + 26/43*e^2 - 34/43*e - 289/43', '1/43*e^3 - 26/43*e^2 + 34/43*e + 289/43', '-1/43*e^3 + 26/43*e^2 - 34/43*e - 289/43', '1/43*e^3 - 26/43*e^2 + 34/43*e + 289/43', '2/43*e^3 - 9/43*e^2 - 18/43*e - 24/43', '2/43*e^3 - 9/43*e^2 - 18/43*e - 24/43', '2/43*e^3 - 9/43*e^2 - 61/43*e + 105/43', '-2/43*e^3 + 9/43*e^2 + 61/43*e - 105/43', '-6/43*e^3 + 27/43*e^2 + 54/43*e - 57/43', '-6/43*e^3 + 27/43*e^2 + 54/43*e - 57/43', '-4/43*e^3 + 18/43*e^2 + 122/43*e - 210/43', '4/43*e^3 - 18/43*e^2 - 122/43*e + 210/43', '18/43*e^3 - 81/43*e^2 - 162/43*e + 300/43', '18/43*e^3 - 81/43*e^2 - 162/43*e + 300/43', '-3/43*e^3 - 8/43*e^2 + 156/43*e + 79/43', '3/43*e^3 + 8/43*e^2 - 156/43*e - 79/43', '-6/43*e^3 + 27/43*e^2 + 54/43*e - 444/43', '-6/43*e^3 + 27/43*e^2 + 54/43*e - 444/43', '-e^2 + 3*e + 11', 'e^2 - 3*e - 11', '-1/43*e^3 + 69/43*e^2 - 163/43*e - 762/43', '1/43*e^3 - 69/43*e^2 + 163/43*e + 762/43', '-6/43*e^3 + 27/43*e^2 + 54/43*e - 315/43', '-6/43*e^3 + 27/43*e^2 + 54/43*e - 315/43', '-5/43*e^3 + 1/43*e^2 + 217/43*e - 26/43', '5/43*e^3 - 1/43*e^2 - 217/43*e + 26/43', '7/43*e^3 - 53/43*e^2 - 149/43*e + 604/43', '-7/43*e^3 + 53/43*e^2 + 149/43*e - 604/43', '30/43*e^3 - 135/43*e^2 - 270/43*e + 414/43', '30/43*e^3 - 135/43*e^2 - 270/43*e + 414/43', '-18/43*e^3 + 81/43*e^2 + 162/43*e - 558/43', '-18/43*e^3 + 81/43*e^2 + 162/43*e - 558/43', '-9/43*e^3 + 19/43*e^2 + 339/43*e - 236/43', '9/43*e^3 - 19/43*e^2 - 339/43*e + 236/43', '24/43*e^3 - 108/43*e^2 - 216/43*e + 830/43', '-14/43*e^3 + 63/43*e^2 + 126/43*e - 864/43', '-14/43*e^3 + 63/43*e^2 + 126/43*e - 864/43', -6, -6, 0, 0, '-11/43*e^3 + 28/43*e^2 + 400/43*e - 341/43', '11/43*e^3 - 28/43*e^2 - 400/43*e + 341/43', '-30/43*e^3 + 135/43*e^2 + 270/43*e - 543/43', '-30/43*e^3 + 135/43*e^2 + 270/43*e - 543/43', '-5/43*e^3 - 42/43*e^2 + 346/43*e + 447/43', '5/43*e^3 + 42/43*e^2 - 346/43*e - 447/43', '-16/43*e^3 + 72/43*e^2 + 144/43*e + 450/43', '-16/43*e^3 + 72/43*e^2 + 144/43*e + 450/43', '-3/43*e^3 - 94/43*e^2 + 414/43*e + 1025/43', '3/43*e^3 + 94/43*e^2 - 414/43*e - 1025/43', '18/43*e^3 - 81/43*e^2 - 162/43*e - 345/43', '18/43*e^3 - 81/43*e^2 - 162/43*e - 345/43', '5/43*e^3 - 87/43*e^2 + 41/43*e + 972/43', '-5/43*e^3 + 87/43*e^2 - 41/43*e - 972/43', '-30/43*e^3 + 135/43*e^2 + 270/43*e - 27/43', '-30/43*e^3 + 135/43*e^2 + 270/43*e - 27/43', '2*e^2 - 6*e - 22', '-2*e^2 + 6*e + 22', '-18/43*e^3 + 81/43*e^2 + 162/43*e - 730/43', '-18/43*e^3 + 81/43*e^2 + 162/43*e - 730/43', '-6/43*e^3 + 113/43*e^2 - 75/43*e - 1261/43', '6/43*e^3 - 113/43*e^2 + 75/43*e + 1261/43', '-10/43*e^3 + 45/43*e^2 + 305/43*e - 525/43', '10/43*e^3 - 45/43*e^2 - 305/43*e + 525/43', '-6/43*e^3 + 27/43*e^2 + 54/43*e - 573/43', '-6/43*e^3 + 27/43*e^2 + 54/43*e - 573/43', '-6/43*e^3 + 27/43*e^2 + 54/43*e + 201/43', '-6/43*e^3 + 27/43*e^2 + 54/43*e + 201/43', '-18/43*e^3 + 81/43*e^2 + 162/43*e + 130/43', '-18/43*e^3 + 81/43*e^2 + 162/43*e + 130/43', '3/43*e^3 - 35/43*e^2 - 27/43*e + 394/43', '-3/43*e^3 + 35/43*e^2 + 27/43*e - 394/43', '18/43*e^3 - 81/43*e^2 - 162/43*e - 517/43', '18/43*e^3 - 81/43*e^2 - 162/43*e - 517/43', '18/43*e^3 - 81/43*e^2 - 549/43*e + 945/43', '-18/43*e^3 + 81/43*e^2 + 549/43*e - 945/43', '3/43*e^3 - 207/43*e^2 + 489/43*e + 2286/43', '-3/43*e^3 + 207/43*e^2 - 489/43*e - 2286/43', '9/43*e^3 - 191/43*e^2 + 177/43*e + 2128/43', '-9/43*e^3 + 191/43*e^2 - 177/43*e - 2128/43', '2/43*e^3 - 9/43*e^2 - 18/43*e + 1008/43', '2/43*e^3 - 9/43*e^2 - 18/43*e + 1008/43', '-9/43*e^3 - 24/43*e^2 + 468/43*e + 237/43', '9/43*e^3 + 24/43*e^2 - 468/43*e - 237/43', '-18/43*e^3 - 5/43*e^2 + 807/43*e + 1/43', '18/43*e^3 + 5/43*e^2 - 807/43*e - 1/43', '24/43*e^3 - 108/43*e^2 - 216/43*e - 30/43', '24/43*e^3 - 108/43*e^2 - 216/43*e - 30/43', '6/43*e^3 - 27/43*e^2 - 183/43*e + 315/43', '-6/43*e^3 + 27/43*e^2 + 183/43*e - 315/43', '30/43*e^3 - 135/43*e^2 - 270/43*e + 1446/43', '30/43*e^3 - 135/43*e^2 - 270/43*e + 1446/43', '3/43*e^3 + 8/43*e^2 - 156/43*e - 79/43', '-3/43*e^3 - 8/43*e^2 + 156/43*e + 79/43', '-6/43*e^3 + 27/43*e^2 + 183/43*e - 315/43', '6/43*e^3 - 27/43*e^2 - 183/43*e + 315/43', 30, 30, '-6/43*e^3 + 27/43*e^2 + 54/43*e - 401/43', '-6/43*e^3 + 27/43*e^2 + 54/43*e - 401/43', '3*e^2 - 9*e - 33', '-3*e^2 + 9*e + 33', '16/43*e^3 - 72/43*e^2 - 144/43*e - 966/43', '16/43*e^3 - 72/43*e^2 - 144/43*e - 966/43', '5/43*e^3 - 87/43*e^2 + 41/43*e + 972/43', '-5/43*e^3 + 87/43*e^2 - 41/43*e - 972/43', '-24/43*e^3 + 108/43*e^2 + 216/43*e - 2034/43', '-24/43*e^3 + 108/43*e^2 + 216/43*e - 2034/43', '-17/43*e^3 + 141/43*e^2 + 325/43*e - 1602/43', '17/43*e^3 - 141/43*e^2 - 325/43*e + 1602/43', '6/43*e^3 + 102/43*e^2 - 570/43*e - 1104/43', '-6/43*e^3 - 102/43*e^2 + 570/43*e + 1104/43', '-3/43*e^3 - 180/43*e^2 + 672/43*e + 1971/43', '3/43*e^3 + 180/43*e^2 - 672/43*e - 1971/43', '30/43*e^3 - 135/43*e^2 - 270/43*e + 1790/43', '30/43*e^3 - 135/43*e^2 - 270/43*e + 1790/43', '6/43*e^3 + 16/43*e^2 - 312/43*e - 158/43', '-6/43*e^3 - 16/43*e^2 + 312/43*e + 158/43', '-7/43*e^3 + 139/43*e^2 - 109/43*e - 1550/43', '7/43*e^3 - 139/43*e^2 + 109/43*e + 1550/43', -2, '24/43*e^3 - 108/43*e^2 - 216/43*e + 2034/43', '24/43*e^3 - 108/43*e^2 - 216/43*e + 2034/43', '50/43*e^3 - 225/43*e^2 - 450/43*e + 45/43', '50/43*e^3 - 225/43*e^2 - 450/43*e + 45/43', '-6/43*e^3 - 231/43*e^2 + 957/43*e + 2523/43', '6/43*e^3 + 231/43*e^2 - 957/43*e - 2523/43', '2/43*e^3 - 9/43*e^2 - 18/43*e - 927/43', '2/43*e^3 - 9/43*e^2 - 18/43*e - 927/43', '6/43*e^3 + 188/43*e^2 - 828/43*e - 2050/43', '-6/43*e^3 - 188/43*e^2 + 828/43*e + 2050/43', '-7/43*e^3 + 10/43*e^2 + 278/43*e - 131/43', '7/43*e^3 - 10/43*e^2 - 278/43*e + 131/43', '-14/43*e^3 + 63/43*e^2 + 126/43*e + 813/43', '-14/43*e^3 + 63/43*e^2 + 126/43*e + 813/43', '34/43*e^3 - 153/43*e^2 - 306/43*e + 108/43', '34/43*e^3 - 153/43*e^2 - 306/43*e + 108/43', '-12/43*e^3 + 183/43*e^2 - 21/43*e - 2049/43', '12/43*e^3 - 183/43*e^2 + 21/43*e + 2049/43', '42/43*e^3 - 189/43*e^2 - 378/43*e + 1431/43', '42/43*e^3 - 189/43*e^2 - 378/43*e + 1431/43', '-18/43*e^3 + 81/43*e^2 + 162/43*e - 2450/43', '-20/43*e^3 - 39/43*e^2 + 997/43*e + 369/43', '20/43*e^3 + 39/43*e^2 - 997/43*e - 369/43', '-78/43*e^3 + 351/43*e^2 + 702/43*e - 1773/43', '-78/43*e^3 + 351/43*e^2 + 702/43*e - 1773/43', '30/43*e^3 - 178/43*e^2 - 786/43*e + 2048/43', '-30/43*e^3 + 178/43*e^2 + 786/43*e - 2048/43', '-30/43*e^3 + 135/43*e^2 + 270/43*e + 360/43', '-30/43*e^3 + 135/43*e^2 + 270/43*e + 360/43'], 'hecke_polynomial': 'x^4 - 6*x^3 - 13*x^2 + 66*x + 61', 'label': '2.2.476.1-4.1-c'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 476, 'ideals': ['[1, 1, 1]', '[2, 2, -w + 11]', '[4, 2, 2]', '[5, 5, w + 2]', '[5, 5, w + 3]', '[7, 7, w]', '[8, 4, -2*w + 22]', '[9, 3, 3]', '[10, 10, w + 3]', '[10, 10, w + 7]', '[11, 11, w + 3]', '[11, 11, w + 8]', '[14, 14, w + 7]', '[16, 4, 4]', '[17, 17, w]', '[18, 6, -3*w + 33]', '[19, 19, w - 10]', '[19, 19, -w - 10]', '[20, 10, 2*w + 4]', '[20, 10, 2*w + 6]', '[22, 22, w + 3]', '[22, 22, w + 19]', '[23, 23, w + 2]', '[23, 23, w + 21]', '[25, 5, 5]', '[25, 25, w + 12]', '[25, 25, -w + 12]', '[28, 14, 2*w]', '[32, 8, -4*w + 44]', '[34, 34, w + 17]', '[35, 35, -2*w + 21]', '[35, 35, -2*w - 21]', '[36, 6, 6]', '[38, 38, w + 9]', '[38, 38, -w + 9]', '[40, 20, 2*w + 6]', '[40, 20, 2*w + 14]', '[41, 41, w + 18]', '[41, 41, w + 23]', '[44, 22, 2*w + 6]', '[44, 22, 2*w + 16]', '[45, 15, 3*w + 6]', '[45, 15, 3*w + 9]', '[46, 46, w + 21]', '[46, 46, w + 25]', '[47, 47, -3*w + 32]', '[47, 47, 8*w - 87]', '[49, 7, 7]', '[50, 10, -5*w + 55]', '[50, 50, w + 13]', '[50, 50, -w + 13]', '[53, 53, -2*w + 23]', '[53, 53, -13*w + 142]', '[55, 55, 4*w - 43]', '[55, 55, w + 8]', '[55, 55, w - 8]', '[55, 55, 4*w + 43]', '[56, 28, 2*w + 14]', '[59, 59, -5*w + 54]', '[59, 59, 6*w - 65]', '[61, 61, w + 27]', '[61, 61, w + 34]', '[63, 21, 3*w]', '[64, 8, 8]', '[68, 34, 2*w]', '[70, 70, -w - 7]', '[70, 70, -w + 7]', '[71, 71, w + 30]', '[71, 71, w + 41]', '[72, 12, -6*w + 66]', '[73, 73, w + 22]', '[73, 73, w + 51]', '[76, 38, 2*w - 20]', '[76, 38, -2*w - 20]', '[77, 77, -w - 14]', '[77, 77, w - 14]', '[79, 79, w + 35]', '[79, 79, w + 44]', '[80, 20, 4*w + 8]', '[80, 20, 4*w + 12]', '[81, 9, 9]', '[82, 82, w + 23]', '[82, 82, w + 59]', '[83, 83, -w - 6]', '[83, 83, w - 6]', '[85, 85, 3*w - 34]', '[85, 85, -3*w - 34]', '[88, 44, 2*w + 6]', '[88, 44, 2*w + 38]', '[90, 30, 3*w + 9]', '[90, 30, 3*w + 21]', '[92, 46, 2*w + 4]', '[92, 46, 2*w + 42]', '[94, 94, -w - 5]', '[94, 94, w - 5]', '[95, 95, w + 28]', '[95, 95, w + 47]', '[95, 95, w + 48]', '[95, 95, w + 67]', '[97, 97, w + 33]', '[97, 97, w + 64]', '[98, 14, -7*w + 77]', '[99, 33, 3*w + 9]', '[99, 33, 3*w + 24]', '[100, 10, 10]', '[100, 50, 2*w + 24]', '[100, 50, -2*w + 24]', '[103, 103, -w - 4]', '[103, 103, w - 4]', '[106, 106, w + 15]', '[106, 106, -w + 15]', '[107, 107, w + 36]', '[107, 107, w + 71]', '[110, 110, w + 3]', '[110, 110, 3*w + 31]', '[110, 110, 3*w - 31]', '[110, 110, w - 3]', '[112, 28, 4*w]', '[115, 115, -w - 2]', '[115, 115, -2*w + 19]', '[115, 115, 2*w + 19]', '[115, 115, w - 2]', '[118, 118, -w - 1]', '[118, 118, w - 1]', '[119, 119, w]', '[121, 11, 11]', '[121, 121, -4*w + 45]', '[121, 121, 4*w + 45]', '[122, 122, w + 27]', '[122, 122, w + 95]', '[125, 25, 5*w + 10]', '[125, 25, 5*w + 15]', '[125, 125, w + 37]', '[125, 125, w + 88]', '[126, 42, 3*w + 21]', '[128, 16, -8*w + 88]', '[133, 133, w + 28]', '[133, 133, w + 105]', '[136, 68, 2*w + 34]', '[137, 137, -w - 16]', '[137, 137, w - 16]', '[140, 70, -4*w + 42]', '[140, 70, -4*w - 42]', '[142, 142, w + 41]', '[142, 142, w + 101]', '[144, 12, 12]', '[146, 146, w + 51]', '[146, 146, w + 95]', '[149, 149, 2*w - 25]', '[149, 149, -2*w - 25]', '[152, 76, 2*w + 18]', '[152, 76, -2*w + 18]', '[153, 51, 3*w]', '[154, 154, -3*w - 35]', '[154, 154, 3*w - 35]', '[158, 158, w + 35]', '[158, 158, w + 123]', '[160, 40, 4*w + 12]', '[160, 40, 4*w + 28]', '[161, 161, 5*w - 56]', '[161, 161, 5*w + 56]', '[162, 18, -9*w + 99]', '[163, 163, w + 49]', '[163, 163, w + 114]', '[164, 82, 2*w + 36]', '[164, 82, 2*w + 46]', '[166, 166, 17*w - 185]', '[166, 166, -5*w + 53]', '[169, 13, -13]', '[170, 170, -w - 17]', '[170, 170, w - 17]', '[171, 57, 3*w - 30]', '[171, 57, -3*w - 30]', '[173, 173, w + 43]', '[173, 173, w + 130]', '[175, 35, 5*w]', '[175, 175, w + 63]', '[175, 175, w + 112]', '[176, 44, 4*w + 12]', '[176, 44, 4*w + 32]', '[180, 30, 6*w + 12]', '[180, 30, 6*w + 18]', '[181, 181, w + 32]', '[181, 181, w + 149]', '[184, 92, 2*w + 42]', '[184, 92, 2*w + 50]', '[187, 187, -2*w + 17]', '[187, 187, -2*w - 17]', '[188, 94, -6*w + 64]', '[188, 94, 16*w - 174]', '[190, 190, w + 47]', '[190, 190, w + 67]', '[190, 190, w + 123]', '[190, 190, w + 143]', '[194, 194, w + 33]', '[194, 194, w + 161]', '[196, 14, 14]', '[198, 66, 3*w + 9]', '[198, 66, 3*w + 57]', '[200, 20, -10*w + 110]', '[200, 100, 2*w + 26]', '[200, 100, -2*w + 26]', '[205, 205, -w - 18]', '[205, 205, 6*w - 67]', '[205, 205, -6*w - 67]', '[205, 205, w - 18]', '[206, 206, 15*w - 163]', '[206, 206, -7*w + 75]', '[207, 69, 3*w + 6]', '[207, 69, 3*w + 63]', '[209, 209, w + 47]', '[209, 209, w + 85]', '[209, 209, w + 124]', '[209, 209, w + 162]', '[211, 211, w + 69]', '[211, 211, w + 142]', '[212, 106, -4*w + 46]', '[212, 106, -26*w + 284]', '[214, 214, w + 71]', '[214, 214, w + 143]', '[220, 110, 8*w - 86]', '[220, 110, 2*w + 16]', '[220, 110, 2*w - 16]', '[220, 110, 8*w + 86]', '[223, 223, 29*w - 316]', '[223, 223, -4*w + 41]', '[224, 56, 4*w + 28]', '[225, 15, 15]', '[225, 75, 3*w + 36]', '[225, 75, -3*w + 36]', '[230, 230, 3*w - 29]', '[230, 230, 13*w - 141]', '[230, 230, -9*w + 97]', '[230, 230, -3*w - 29]', '[235, 235, w + 42]', '[235, 235, w + 52]', '[235, 235, w + 183]', '[235, 235, w + 193]', '[236, 118, -10*w + 108]', '[236, 118, 12*w - 130]', '[238, 238, 11*w - 119]', '[241, 241, w + 100]', '[241, 241, w + 141]', '[242, 22, -11*w + 121]', '[242, 242, w + 19]', '[242, 242, -w + 19]', '[244, 122, 2*w + 54]', '[244, 122, 2*w + 68]', '[245, 35, 7*w + 14]', '[245, 35, 7*w + 21]', '[250, 50, 5*w + 15]', '[250, 50, 5*w + 35]', '[250, 250, w + 37]', '[250, 250, w + 213]', '[251, 251, 2*w - 15]', '[251, 251, -2*w - 15]', '[252, 42, 6*w]', '[253, 253, 7*w - 78]', '[253, 253, -2*w + 27]', '[253, 253, -2*w - 27]', '[253, 253, 7*w + 78]', '[256, 16, 16]', '[265, 265, w + 38]', '[265, 265, w + 68]', '[265, 265, w + 197]', '[265, 265, w + 227]', '[266, 266, w + 105]', '[266, 266, w + 161]', '[269, 269, w + 53]', '[269, 269, w + 216]', '[271, 271, -5*w + 52]', '[271, 271, 28*w - 305]', '[272, 68, 4*w]', '[274, 274, 27*w - 295]', '[274, 274, 5*w - 57]', '[275, 55, 5*w + 15]', '[275, 55, 5*w + 40]', '[275, 275, w + 63]', '[275, 275, w + 113]', '[275, 275, w + 162]', '[275, 275, w + 212]', '[280, 140, -2*w - 14]', '[280, 140, -2*w + 14]', '[281, 281, -w - 20]', '[281, 281, w - 20]', '[284, 142, 2*w + 60]', '[284, 142, 2*w + 82]', '[287, 287, 3*w + 28]', '[287, 287, 3*w - 28]', '[288, 24, -12*w + 132]', '[289, 17, 17]', '[292, 146, 2*w + 44]', '[292, 146, 2*w + 102]', '[295, 295, w + 58]', '[295, 295, w + 117]', '[295, 295, w + 178]', '[295, 295, w + 237]', '[298, 298, 3*w - 37]', '[298, 298, 47*w - 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99]', '[9682, 9682, -9*w - 139]', '[9682, 9682, 9*w - 139]', '[9682, 9682, w - 99]', '[9683, 9683, w + 3337]', '[9683, 9683, w + 3820]', '[9683, 9683, w + 5863]', '[9683, 9683, w + 6346]', '[9684, 1614, 6*w + 318]', '[9684, 1614, 6*w + 1296]', '[9688, 4844, 26*w - 266]', '[9688, 4844, 26*w + 266]', '[9689, 9689, 88*w - 965]', '[9689, 9689, 55*w - 608]', '[9691, 9691, -85*w - 922]', '[9691, 9691, -10*w - 47]', '[9691, 9691, -10*w + 47]', '[9691, 9691, -85*w + 922]', '[9700, 970, 10*w + 330]', '[9700, 970, 10*w + 640]', '[9700, 4850, 2*w + 1424]', '[9700, 4850, 2*w + 1874]', '[9700, 4850, 2*w + 2976]', '[9700, 4850, 2*w + 3426]', '[9702, 462, 21*w + 63]', '[9702, 462, 21*w + 399]', '[9706, 9706, 51*w - 565]', '[9706, 9706, -15*w - 191]', '[9706, 9706, 15*w - 191]', '[9706, 9706, 95*w - 1041]', '[9707, 9707, 13*w + 102]', '[9707, 9707, 13*w - 102]', '[9709, 9709, 17*w - 210]', '[9709, 9709, 10*w - 147]', '[9709, 9709, 10*w + 147]', '[9709, 9709, 17*w + 210]', '[9710, 9710, w + 327]', '[9710, 9710, w + 3557]', '[9710, 9710, w + 6153]', '[9710, 9710, w + 9383]', '[9716, 4858, 44*w + 490]', '[9716, 4858, 44*w - 490]', '[9721, 9721, w + 4212]', '[9721, 9721, w + 5509]', '[9725, 1945, 25*w - 290]', '[9725, 1945, 190*w - 2075]', '[9725, 9725, 41*w - 458]', '[9725, 9725, 2*w - 101]', '[9725, 9725, -2*w - 101]', '[9725, 9725, -41*w - 458]', '[9727, 9727, w + 669]', '[9727, 9727, w + 2313]', '[9727, 9727, w + 7414]', '[9727, 9727, w + 9058]', '[9728, 608, 16*w + 144]', '[9728, 608, -16*w + 144]', '[9729, 3243, 3*w + 408]', '[9729, 3243, 3*w + 972]', '[9729, 3243, 3*w + 2271]', '[9729, 3243, 3*w + 2835]', '[9736, 4868, 2*w + 1298]', '[9736, 4868, 2*w + 3570]', '[9740, 4870, -12*w - 86]', '[9740, 4870, 46*w - 492]', '[9740, 4870, -108*w + 1174]', '[9740, 4870, 12*w - 86]', '[9742, 9742, 17*w - 157]', '[9742, 9742, -17*w - 157]', '[9743, 9743, 84*w - 911]', '[9743, 9743, -59*w + 636]', '[9745, 9745, -3*w - 104]', '[9745, 9745, 28*w - 321]', '[9745, 9745, -28*w - 321]', '[9745, 9745, 3*w - 104]', '[9752, 4876, 2*w + 878]', '[9752, 4876, 2*w + 1514]', '[9752, 4876, 2*w + 3362]', '[9752, 4876, 2*w + 3998]', '[9755, 9755, w + 1177]', '[9755, 9755, w + 3128]', '[9755, 9755, w + 6627]', '[9755, 9755, w + 8578]', '[9756, 1626, -30*w + 312]', '[9756, 1626, 168*w - 1830]', '[9758, 9758, w + 2975]', '[9758, 9758, w + 6783]', '[9760, 2440, -4*w - 108]', '[9760, 2440, 12*w + 164]', '[9760, 2440, 12*w - 164]', '[9760, 2440, -4*w + 108]', '[9764, 4882, 2*w + 408]', '[9764, 4882, 2*w + 4474]', '[9770, 9770, w + 633]', '[9770, 9770, w + 2587]', '[9770, 9770, w + 7183]', '[9770, 9770, w + 9137]', '[9775, 1955, -40*w + 425]', '[9775, 1955, 40*w + 425]', '[9775, 9775, 28*w - 289]', '[9775, 9775, -11*w + 68]', '[9775, 9775, 11*w + 68]', '[9775, 9775, -28*w - 289]', '[9778, 9778, w + 3517]', '[9778, 9778, w + 6261]', '[9784, 4892, -10*w - 46]', '[9784, 4892, 10*w - 46]', '[9785, 9785, w + 313]', '[9785, 9785, w + 408]', '[9785, 9785, w + 4227]', '[9785, 9785, w + 4322]', '[9785, 9785, w + 5463]', '[9785, 9785, w + 5558]', '[9785, 9785, w + 9377]', '[9785, 9785, w + 9472]', '[9787, 9787, w + 2364]', '[9787, 9787, w + 7423]', '[9791, 9791, 83*w - 900]', '[9791, 9791, -60*w + 647]', '[9792, 408, 24*w]', '[9794, 9794, -7*w - 125]', '[9794, 9794, 5*w - 113]', '[9794, 9794, -5*w - 113]', '[9794, 9794, 7*w - 125]', '[9800, 140, -70*w + 770]', '[9800, 700, 14*w + 182]', '[9800, 700, -14*w + 182]', '[9801, 99, 99]', '[9801, 1089, -36*w + 405]', '[9801, 1089, 36*w + 405]', '[9808, 2452, 8*w - 132]', '[9808, 2452, -8*w - 132]', '[9812, 4906, 2*w + 314]', '[9812, 4906, 2*w + 578]', '[9812, 4906, 2*w + 4328]', '[9812, 4906, 2*w + 4592]', '[9814, 9814, w + 2765]', '[9814, 9814, w + 7049]', '[9818, 9818, 343*w - 3743]', '[9818, 9818, 13*w - 173]', '[9821, 9821, w + 3199]', '[9821, 9821, w + 4487]', '[9821, 9821, w + 5334]', '[9821, 9821, w + 6622]', '[9823, 9823, w + 371]', '[9823, 9823, w + 465]', '[9823, 9823, w + 2214]', '[9823, 9823, w + 3050]', '[9823, 9823, w + 6773]', '[9823, 9823, w + 7609]', '[9823, 9823, w + 9358]', '[9823, 9823, w + 9452]', '[9824, 2456, 140*w - 1524]', '[9824, 2456, -36*w + 380]', '[9826, 578, 17*w + 289]', '[9833, 9833, w + 222]', '[9833, 9833, w + 9611]', '[9835, 9835, 61*w + 658]', '[9835, 9835, 19*w + 182]', '[9835, 9835, 19*w - 182]', '[9835, 9835, 61*w - 658]', '[9836, 4918, 2*w + 2326]', '[9836, 4918, 2*w + 2592]', '[9844, 4922, 60*w - 662]', '[9844, 4922, 260*w - 2838]', '[9844, 4922, 18*w - 220]', '[9844, 4922, 82*w - 900]', '[9846, 3282, 3*w + 477]', '[9846, 3282, 3*w + 2805]', '[9856, 1232, -24*w - 280]', '[9856, 1232, 24*w - 280]', '[9859, 9859, 25*w - 254]', '[9859, 9859, -25*w - 254]', '[9862, 9862, 107*w - 1163]', '[9862, 9862, -47*w + 503]', '[9863, 9863, w + 4039]', '[9863, 9863, w + 5824]', '[9864, 1644, 162*w - 1770]', '[9864, 1644, 30*w - 342]', '[9866, 9866, w + 3659]', '[9866, 9866, w + 6207]', '[9868, 4934, 14*w - 116]', '[9868, 4934, -14*w - 116]', '[9871, 9871, w + 2041]', '[9871, 9871, w + 7830]', '[9875, 1975, -15*w + 130]', '[9875, 1975, 10*w - 45]', '[9875, 1975, -10*w - 45]', '[9875, 1975, 15*w + 130]', '[9875, 9875, 33*w - 346]', '[9875, 9875, 81*w - 878]', '[9875, 9875, -81*w - 878]', '[9875, 9875, -33*w - 346]', '[9877, 9877, -6*w - 119]', '[9877, 9877, -6*w + 119]', '[9881, 9881, -w - 100]', '[9881, 9881, 65*w - 716]', '[9881, 9881, 76*w - 835]', '[9881, 9881, w - 100]', '[9882, 1098, 9*w + 243]', '[9882, 1098, 9*w + 855]', '[9892, 4946, 34*w - 384]', '[9892, 4946, 144*w - 1574]', '[9899, 9899, w + 2157]', '[9899, 9899, w + 4095]', '[9899, 9899, w + 5804]', '[9899, 9899, w + 7742]', '[9900, 330, 30*w + 90]', '[9900, 330, 30*w + 240]', '[9900, 1650, 6*w + 378]', '[9900, 1650, 6*w + 678]', '[9900, 1650, 6*w + 972]', '[9900, 1650, 6*w + 1272]', '[9901, 9901, w + 3683]', '[9901, 9901, w + 6218]', '[9908, 4954, 2*w + 1574]', '[9908, 4954, 2*w + 3380]', '[9910, 9910, 11*w + 67]', '[9910, 9910, 13*w + 101]', '[9910, 9910, 13*w - 101]', '[9910, 9910, 11*w - 67]', '[9911, 9911, -12*w - 85]', '[9911, 9911, -63*w - 680]', '[9911, 9911, -63*w + 680]', '[9911, 9911, -12*w + 85]', '[9913, 9913, 32*w - 363]', '[9913, 9913, 103*w - 1128]', '[9913, 9913, 48*w - 533]', '[9913, 9913, 153*w - 1672]', '[9917, 9917, w + 1546]', '[9917, 9917, w + 2674]', '[9917, 9917, w + 7243]', '[9917, 9917, w + 8371]', '[9922, 902, 11*w + 253]', '[9922, 902, 11*w + 649]', '[9922, 9922, w + 223]', '[9922, 9922, w + 2401]', '[9922, 9922, w + 7521]', '[9922, 9922, w + 9699]', '[9923, 9923, w + 3197]', '[9923, 9923, w + 6726]', '[9925, 1985, 5*w + 780]', '[9925, 1985, 5*w + 1205]', '[9925, 9925, w + 638]', '[9925, 9925, w + 2538]', '[9925, 9925, w + 7387]', '[9925, 9925, w + 9287]', '[9928, 4964, 2*w + 102]', '[9928, 4964, -2*w + 102]', '[9934, 9934, w + 4733]', '[9934, 9934, w + 5201]', '[9935, 9935, w + 1712]', '[9935, 9935, w + 2262]', '[9935, 9935, w + 7673]', '[9935, 9935, w + 8223]', '[9937, 9937, -16*w - 201]', '[9937, 9937, 11*w + 156]', '[9937, 9937, -11*w + 156]', '[9937, 9937, 16*w - 201]', '[9938, 9938, w + 4811]', '[9938, 9938, w + 5127]', '[9940, 4970, 2*w + 224]', '[9940, 4970, 2*w + 1764]', '[9940, 4970, 2*w + 3206]', '[9940, 4970, 2*w + 4746]', '[9941, 9941, 250*w - 2729]', '[9941, 9941, 19*w - 230]', '[9943, 9943, -64*w + 691]', '[9943, 9943, -41*w + 436]', '[9943, 9943, 124*w - 1349]', '[9943, 9943, 79*w - 856]', '[9949, 9949, -23*w - 270]', '[9949, 9949, 23*w - 270]', '[9954, 3318, -3*w - 105]', '[9954, 3318, -3*w + 105]', '[9955, 9955, w + 2747]', '[9955, 9955, w + 3407]', '[9955, 9955, w + 4557]', '[9955, 9955, w + 4738]', '[9955, 9955, w + 5217]', '[9955, 9955, w + 5398]', '[9955, 9955, w + 6548]', '[9955, 9955, w + 7208]', '[9961, 9961, -9*w + 140]', '[9961, 9961, 9*w + 140]', '[9964, 4982, 266*w - 2900]', '[9964, 4982, 10*w - 44]', '[9964, 4982, -10*w - 44]', '[9964, 4982, -20*w + 194]', '[9970, 9970, -27*w + 311]', '[9970, 9970, 39*w - 437]', '[9970, 9970, 39*w + 437]', '[9970, 9970, -27*w - 311]', '[9971, 767, -65*w + 702]', '[9971, 767, 78*w - 845]', '[9973, 9973, w + 1391]', '[9973, 9973, w + 8582]', '[9977, 9977, 4*w - 109]', '[9977, 9977, -89*w - 976]', '[9977, 9977, -89*w + 976]', '[9977, 9977, 4*w + 109]', '[9979, 9979, w + 1377]', '[9979, 9979, w + 8602]', '[9980, 4990, -24*w - 242]', '[9980, 4990, -48*w + 514]', '[9980, 4990, 106*w - 1152]', '[9980, 4990, 24*w - 242]', '[9985, 9985, w + 2043]', '[9985, 9985, w + 3948]', '[9985, 9985, w + 6037]', '[9985, 9985, w + 7942]', '[9989, 9989, w + 854]', '[9989, 9989, w + 9135]', '[9991, 9991, w + 1034]', '[9991, 9991, w + 2167]', '[9991, 9991, w + 7824]', '[9991, 9991, w + 8957]', '[9995, 9995, -77*w + 834]', '[9995, 9995, -18*w + 169]', '[9995, 9995, -18*w - 169]', '[9995, 9995, -77*w - 834]', '[10000, 100, 100]', '[10000, 500, 20*w + 240]', '[10000, 500, -20*w + 240]', '[10000, 2500, -52*w + 576]', '[10000, 2500, 52*w + 576]'], 'label': '2.2.476.1', 'narrow_class_no': 4, 'primes': ['[2, 2, -w + 11]', '[5, 5, w + 2]', '[5, 5, w + 3]', '[7, 7, w]', '[9, 3, 3]', '[11, 11, w + 3]', '[11, 11, w + 8]', '[17, 17, w]', '[19, 19, w - 10]', '[19, 19, -w - 10]', '[23, 23, w + 2]', '[23, 23, w + 21]', '[41, 41, w + 18]', '[41, 41, w + 23]', '[47, 47, -3*w + 32]', '[47, 47, 8*w - 87]', '[53, 53, -2*w + 23]', '[53, 53, -13*w + 142]', '[59, 59, -5*w + 54]', '[59, 59, 6*w - 65]', '[61, 61, w + 27]', '[61, 61, w + 34]', '[71, 71, w + 30]', '[71, 71, w + 41]', '[73, 73, w + 22]', '[73, 73, w + 51]', '[79, 79, w + 35]', '[79, 79, w + 44]', '[83, 83, -w - 6]', '[83, 83, w - 6]', '[97, 97, w + 33]', '[97, 97, w + 64]', '[103, 103, -w - 4]', '[103, 103, w - 4]', '[107, 107, w + 36]', '[107, 107, w + 71]', '[137, 137, -w - 16]', '[137, 137, w - 16]', '[149, 149, 2*w - 25]', '[149, 149, -2*w - 25]', '[163, 163, w + 49]', '[163, 163, w + 114]', '[169, 13, -13]', '[173, 173, w + 43]', '[173, 173, w + 130]', '[181, 181, w + 32]', '[181, 181, w + 149]', '[211, 211, w + 69]', '[211, 211, w + 142]', '[223, 223, 29*w - 316]', '[223, 223, -4*w + 41]', '[241, 241, w + 100]', '[241, 241, w + 141]', '[251, 251, 2*w - 15]', '[251, 251, -2*w - 15]', '[269, 269, w + 53]', '[269, 269, w + 216]', '[271, 271, -5*w + 52]', '[271, 271, 28*w - 305]', '[281, 281, -w - 20]', '[281, 281, w - 20]', '[307, 307, 2*w - 13]', '[307, 307, -2*w - 13]', '[313, 313, w + 57]', '[313, 313, w + 256]', '[347, 347, w + 90]', '[347, 347, w + 257]', '[373, 373, -3*w - 38]', '[373, 373, 3*w - 38]', '[379, 379, w + 94]', '[379, 379, w + 285]', '[383, 383, -4*w + 39]', '[383, 383, 51*w - 556]', '[389, 389, 5*w - 58]', '[389, 389, 38*w - 415]', '[397, 397, w + 156]', '[397, 397, w + 241]', '[421, 421, 10*w - 111]', '[421, 421, 21*w - 230]', '[431, 431, w + 56]', '[431, 431, w + 375]', '[457, 457, -w - 24]', '[457, 457, w - 24]', '[467, 467, 2*w - 3]', '[467, 467, -2*w - 3]', '[487, 487, w + 74]', '[487, 487, w + 413]', '[499, 499, w + 218]', '[499, 499, w + 281]', '[521, 521, w + 73]', '[521, 521, w + 448]', '[523, 523, -14*w + 151]', '[523, 523, 19*w - 206]', '[547, 547, w + 159]', '[547, 547, w + 388]', '[557, 557, -w - 26]', '[557, 557, w - 26]', '[563, 563, -6*w - 61]', '[563, 563, 6*w - 61]', '[569, 569, 40*w - 437]', '[569, 569, 7*w - 80]', '[571, 571, w + 80]', '[571, 571, w + 491]', '[587, 587, -3*w - 22]', '[587, 587, 3*w - 22]', '[601, 601, w + 271]', '[601, 601, w + 330]', '[613, 613, 2*w - 33]', '[613, 613, -2*w - 33]', '[647, 647, -7*w + 72]', '[647, 647, 48*w - 523]', '[677, 677, w + 83]', '[677, 677, w + 594]', '[683, 683, w + 70]', '[683, 683, w + 613]', '[701, 701, 14*w - 155]', '[701, 701, 25*w - 274]', '[727, 727, 47*w - 512]', '[727, 727, -8*w + 83]', '[743, 743, w + 325]', '[743, 743, w + 418]', '[751, 751, w + 129]', '[751, 751, w + 622]', '[757, 757, -6*w - 71]', '[757, 757, 6*w - 71]', '[823, 823, w + 135]', '[823, 823, w + 688]', '[827, 827, w + 96]', '[827, 827, w + 731]', '[841, 29, -29]', '[853, 853, w + 93]', '[853, 853, w + 760]', '[857, 857, w + 394]', '[857, 857, w + 463]', '[859, 859, -5*w - 46]', '[859, 859, 5*w - 46]', '[881, 881, w + 269]', '[881, 881, w + 612]', '[907, 907, w + 254]', '[907, 907, w + 653]', '[911, 911, w + 205]', '[911, 911, w + 706]', '[929, 929, w + 97]', '[929, 929, w + 832]', '[941, 941, w + 339]', '[941, 941, w + 602]', '[947, 947, w + 209]', '[947, 947, w + 738]', '[953, 953, 17*w - 188]', '[953, 953, 28*w - 307]', '[961, 31, -31]', '[971, 971, -3*w - 10]', '[971, 971, 3*w - 10]', '[977, 977, 11*w - 124]', '[977, 977, 44*w - 481]', '[991, 991, w + 84]', '[991, 991, w + 907]', '[997, 997, w + 270]', '[997, 997, w + 727]']}
• 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': [2], 'class_number': 2, 'cm': False, 'coeffs': [-119, 0, 1], 'conductor': 476, 'degree': 2, 'dirichlet_group': [1, 475], 'disc_abs': 476, 'disc_rad': 238, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[2, 1]]], [5, [[1, 2]]], [7, [0]], [11, [[1, 2]]], [13, [[2, 1]]], [17, [0]], [19, [[1, 2]]], [23, [[1, 2]]], [29, [[2, 1]]], [31, [[2, 1]]], [37, [[2, 1]]], [41, [[1, 2]]], [43, [[2, 1]]], [47, [[1, 2]]], [53, [[1, 2]]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [2, 1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 21.817424229271428, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.476.1', 'local_algs': ['2.2.2.1', '7.2.1.2', '17.2.1.2'], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 7, 17], 'rd': 21.8174242293, 'regulator': {'__RealLiteral__': 0, 'data': '5.48062156178', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 11 a - 120 \\)'], 'used_grh': False, 'zk': ['1', 'a']}