Hilbert modular form data - 2.2.357.1-1.1-e

Formats: - HTML - YAML - JSON - 2024-05-19T03:58:15.814879

• 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': 10, 'disc': 357, 'field_bad_primes': [3, 7, 17], 'field_label': '2.2.357.1', 'is_CM': 'yes', 'is_base_change': 'yes', 'label': '2.2.357.1-1.1-e', 'label_nsuffix': 4, 'label_suffix': 'e', 'level_bad_primes': [], 'level_ideal': '[1, 1, 1]', 'level_label': '1.1', 'level_norm': 1, 'parallel_weight': 2, 'short_label': '1.1-e', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [], 'hecke_eigenvalues': ['e', '1/40*e^8 - 3/5*e^6 + 9/2*e^4 - 91/8*e^2 + 15/2', '1/5*e^5 - 3*e^3 + 9*e', 0, 0, 0, 0, 0, '-1/5*e^6 + 4*e^4 - 21*e^2 + 18', 0, 0, '1/10*e^7 - 21/10*e^5 + 23/2*e^3 - 9*e', '1/10*e^7 - 21/10*e^5 + 23/2*e^3 - 9*e', '-1/20*e^6 + 1/4*e^4 + 15/4*e^2 - 9', '-1/20*e^6 + 1/4*e^4 + 15/4*e^2 - 9', 0, 0, 0, 0, '-1/20*e^9 + 27/20*e^7 - 243/20*e^5 + 81/2*e^3 - 32*e', '-1/20*e^9 + 27/20*e^7 - 243/20*e^5 + 81/2*e^3 - 32*e', '-1/20*e^8 + 6/5*e^6 - 9*e^4 + 79/4*e^2 + 3', '-1/20*e^8 + 6/5*e^6 - 9*e^4 + 79/4*e^2 + 3', 0, 0, '-1/20*e^9 + 27/20*e^7 - 243/20*e^5 + 81/2*e^3 - 38*e', '-1/20*e^9 + 27/20*e^7 - 243/20*e^5 + 81/2*e^3 - 38*e', 0, 0, 0, 0, '-1/20*e^7 + 21/20*e^5 - 17/4*e^3 - 9*e', '-1/20*e^7 + 21/20*e^5 - 17/4*e^3 - 9*e', 0, 0, 0, 0, 0, 0, '-1/20*e^8 + 6/5*e^6 - 9*e^4 + 103/4*e^2 - 33', '-1/20*e^8 + 6/5*e^6 - 9*e^4 + 103/4*e^2 - 33', '-1/5*e^7 + 21/5*e^5 - 26*e^3 + 45*e', '-1/5*e^7 + 21/5*e^5 - 26*e^3 + 45*e', '-7/20*e^6 + 31/4*e^4 - 183/4*e^2 + 45', '-7/20*e^6 + 31/4*e^4 - 183/4*e^2 + 45', 26, '-2/5*e^5 + 6*e^3 - 18*e', '-2/5*e^5 + 6*e^3 - 18*e', 0, 0, '1/10*e^9 - 27/10*e^7 + 243/10*e^5 - 81*e^3 + 73*e', '1/10*e^9 - 27/10*e^7 + 243/10*e^5 - 81*e^3 + 73*e', 0, 0, '-7/20*e^7 + 147/20*e^5 - 167/4*e^3 + 45*e', '-7/20*e^7 + 147/20*e^5 - 167/4*e^3 + 45*e', 0, 0, 0, 0, '2/5*e^7 - 42/5*e^5 + 49*e^3 - 63*e', '2/5*e^7 - 42/5*e^5 + 49*e^3 - 63*e', 0, 0, '1/4*e^7 - 21/4*e^5 + 133/4*e^3 - 63*e', '1/4*e^7 - 21/4*e^5 + 133/4*e^3 - 63*e', 0, 0, '1/4*e^8 - 6*e^6 + 45*e^4 - 443/4*e^2 + 57', '1/4*e^8 - 6*e^6 + 45*e^4 - 443/4*e^2 + 57', 0, 0, 0, 0, 38, '1/10*e^9 - 27/10*e^7 + 243/10*e^5 - 81*e^3 + 61*e', '1/10*e^9 - 27/10*e^7 + 243/10*e^5 - 81*e^3 + 61*e', '7/10*e^6 - 25/2*e^4 + 111/2*e^2 - 36', '7/10*e^6 - 25/2*e^4 + 111/2*e^2 - 36', 0, 0, '1/4*e^7 - 21/4*e^5 + 109/4*e^3 - 9*e', '1/4*e^7 - 21/4*e^5 + 109/4*e^3 - 9*e', 0, 0, '-1/2*e^6 + 23/2*e^4 - 141/2*e^2 + 72', '-1/2*e^6 + 23/2*e^4 - 141/2*e^2 + 72', 0, 0, '1/10*e^9 - 27/10*e^7 + 243/10*e^5 - 81*e^3 + 79*e', '1/10*e^9 - 27/10*e^7 + 243/10*e^5 - 81*e^3 + 79*e', 0, 0, '-1/5*e^8 + 24/5*e^6 - 36*e^4 + 94*e^2 - 78', '-1/5*e^8 + 24/5*e^6 - 36*e^4 + 94*e^2 - 78', 0, 0, '11/20*e^6 - 35/4*e^4 + 123/4*e^2 - 9', '11/20*e^6 - 35/4*e^4 + 123/4*e^2 - 9', 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, '-8/5*e^5 + 24*e^3 - 72*e', '-8/5*e^5 + 24*e^3 - 72*e', '-1/2*e^7 + 21/2*e^5 - 127/2*e^3 + 99*e', '-1/2*e^7 + 21/2*e^5 - 127/2*e^3 + 99*e', '1/10*e^8 - 12/5*e^6 + 18*e^4 - 73/2*e^2 - 24', '1/10*e^8 - 12/5*e^6 + 18*e^4 - 73/2*e^2 - 24', 0, 0, '1/5*e^5 - 3*e^3 + 9*e', '1/5*e^5 - 3*e^3 + 9*e', '1/4*e^8 - 6*e^6 + 45*e^4 - 467/4*e^2 + 93', '1/4*e^8 - 6*e^6 + 45*e^4 - 467/4*e^2 + 93', 0, 0, '-1/5*e^9 + 27/5*e^7 - 243/5*e^5 + 162*e^3 - 137*e', '-1/5*e^9 + 27/5*e^7 - 243/5*e^5 + 162*e^3 - 137*e', 0, 0, 0, 0, 0, 0, '-1/5*e^9 + 27/5*e^7 - 243/5*e^5 + 162*e^3 - 143*e', '-1/5*e^9 + 27/5*e^7 - 243/5*e^5 + 162*e^3 - 143*e', '-19/20*e^6 + 67/4*e^4 - 291/4*e^2 + 45', '-19/20*e^6 + 67/4*e^4 - 291/4*e^2 + 45', 0, 0, '-11/10*e^6 + 41/2*e^4 - 195/2*e^2 + 72', '-11/10*e^6 + 41/2*e^4 - 195/2*e^2 + 72', 0, 0, 0, 0, '-e^5 + 15*e^3 - 45*e', '-e^5 + 15*e^3 - 45*e', 0, 0, 0, 0, '-1/5*e^9 + 27/5*e^7 - 243/5*e^5 + 162*e^3 - 131*e', '-1/5*e^9 + 27/5*e^7 - 243/5*e^5 + 162*e^3 - 131*e', 0, 0, 0, 0, '2*e^5 - 30*e^3 + 90*e', '2*e^5 - 30*e^3 + 90*e', '-7/20*e^8 + 42/5*e^6 - 63*e^4 + 601/4*e^2 - 51', '-7/20*e^8 + 42/5*e^6 - 63*e^4 + 601/4*e^2 - 51', 0, 0, '-5/4*e^6 + 97/4*e^4 - 489/4*e^2 + 99', '-5/4*e^6 + 97/4*e^4 - 489/4*e^2 + 99', 0, 0, '23/20*e^6 - 95/4*e^4 + 519/4*e^2 - 117', '23/20*e^6 - 95/4*e^4 + 519/4*e^2 - 117', 0, 0, '1/4*e^9 - 27/4*e^7 + 243/4*e^5 - 405/2*e^3 + 172*e', '1/4*e^9 - 27/4*e^7 + 243/4*e^5 - 405/2*e^3 + 172*e'], 'hecke_polynomial': 'x^10 - 30*x^8 + 315*x^6 - 1350*x^4 + 2025*x^2 - 700', 'label': '2.2.357.1-1.1-e'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 357, 'ideals': ['[1, 1, 1]', '[3, 3, w + 1]', '[4, 2, 2]', '[7, 7, w + 3]', '[9, 3, 3]', '[11, 11, w + 3]', '[11, 11, w + 7]', '[12, 6, 2*w + 2]', '[16, 4, 4]', '[17, 17, w + 8]', '[21, 21, -w - 10]', '[23, 23, w + 4]', '[23, 23, w + 18]', '[25, 5, 5]', '[27, 9, 3*w + 3]', '[28, 14, 2*w + 6]', '[29, 29, w + 1]', '[29, 29, w + 27]', '[31, 31, w + 13]', '[31, 31, w + 17]', '[33, 33, -w - 7]', '[33, 33, -w + 8]', '[36, 6, 6]', '[43, 43, -w - 11]', '[43, 43, w - 12]', '[44, 22, 2*w + 6]', '[44, 22, 2*w + 14]', '[47, 47, -w - 6]', '[47, 47, w - 7]', '[48, 12, 4*w + 4]', '[49, 7, 7]', '[51, 51, w + 25]', '[59, 59, -w - 5]', '[59, 59, w - 6]', '[61, 61, w + 16]', '[61, 61, w + 44]', '[63, 21, 3*w + 9]', '[64, 8, 8]', '[67, 67, -w - 12]', '[67, 67, w - 13]', '[68, 34, 2*w + 16]', '[69, 69, w + 4]', '[69, 69, w - 5]', '[71, 71, w + 29]', '[71, 71, w + 41]', '[73, 73, w + 24]', '[73, 73, w + 48]', '[75, 15, 5*w + 5]', '[77, 77, w + 3]', '[77, 77, w - 4]', '[81, 9, 9]', '[83, 83, -w - 2]', '[83, 83, w - 3]', '[84, 42, -2*w - 20]', '[87, 87, w + 1]', '[87, 87, -w + 2]', '[89, 89, -w]', '[89, 89, w - 1]', '[92, 46, 2*w + 8]', '[92, 46, 2*w + 36]', '[93, 93, w + 13]', '[93, 93, 4*w + 37]', '[97, 97, w + 19]', '[97, 97, w + 77]', '[99, 33, 3*w + 9]', '[99, 33, 3*w + 21]', '[100, 10, 10]', '[101, 101, 2*w - 17]', '[101, 101, -2*w - 15]', '[107, 107, w + 50]', '[107, 107, w + 56]', '[108, 18, 6*w + 6]', '[112, 28, 4*w + 12]', '[113, 113, w + 36]', '[113, 113, w + 76]', '[116, 58, 2*w + 2]', '[116, 58, 2*w + 54]', '[119, 119, w + 59]', '[121, 11, 11]', '[121, 121, w + 14]', '[121, 121, -w + 15]', '[124, 62, 2*w + 26]', '[124, 62, 2*w + 34]', '[127, 127, 2*w - 23]', '[127, 127, 2*w + 21]', '[129, 129, w + 31]', '[129, 129, w + 97]', '[132, 66, -2*w - 14]', '[132, 66, -2*w + 16]', '[139, 139, w + 22]', '[139, 139, w + 116]', '[141, 141, w + 40]', '[141, 141, w + 100]', '[144, 12, 12]', '[147, 21, 7*w + 7]', '[151, 151, -w - 15]', '[151, 151, w - 16]', '[153, 51, 3*w + 24]', '[161, 161, -2*w + 15]', '[161, 161, -2*w - 13]', '[169, 13, -13]', '[172, 86, -2*w - 22]', '[172, 86, 2*w - 24]', '[175, 35, 5*w + 15]', '[176, 44, 4*w + 12]', '[176, 44, 4*w + 28]', '[177, 177, w + 64]', '[177, 177, w + 112]', '[181, 181, w + 75]', '[181, 181, w + 105]', '[183, 183, -w - 16]', '[183, 183, -w + 17]', '[187, 187, w + 25]', '[187, 187, w + 161]', '[188, 94, -2*w - 12]', '[188, 94, 2*w - 14]', '[189, 63, -3*w - 30]', '[192, 24, 8*w + 8]', '[196, 14, 14]', '[197, 197, w + 47]', '[197, 197, w + 149]', '[199, 199, w + 38]', '[199, 199, w + 160]', '[201, 201, w + 79]', '[201, 201, w + 121]', '[203, 203, -3*w + 26]', '[203, 203, 3*w + 23]', '[204, 102, 2*w + 50]', '[207, 69, 3*w + 12]', '[207, 69, 3*w + 54]', '[213, 213, 2*w - 13]', '[213, 213, -2*w - 11]', '[217, 217, -w - 17]', '[217, 217, w - 18]', '[219, 219, 2*w - 25]', '[219, 219, 2*w + 23]', '[225, 15, 15]', '[231, 231, w + 73]', '[231, 231, w + 157]', '[233, 233, w + 51]', '[233, 233, w + 181]', '[236, 118, -2*w - 10]', '[236, 118, 2*w - 12]', '[241, 241, w + 28]', '[241, 241, w + 212]', '[243, 27, 9*w + 9]', '[244, 122, 2*w + 32]', '[244, 122, 2*w + 88]', '[249, 249, w + 85]', '[249, 249, w + 163]', '[251, 251, -3*w - 22]', '[251, 251, 3*w - 25]', '[252, 42, 6*w + 18]', '[253, 253, -w - 18]', '[253, 253, 3*w - 34]', '[253, 253, -3*w - 31]', '[253, 253, w - 19]', '[256, 16, 16]', '[257, 257, 2*w - 11]', '[257, 257, -2*w - 9]', '[261, 87, 3*w + 3]', '[261, 87, 3*w + 81]', '[267, 267, w + 88]', '[267, 267, w + 178]', '[268, 134, -2*w - 24]', '[268, 134, 2*w - 26]', '[272, 68, 4*w + 32]', '[275, 55, 5*w + 15]', '[275, 55, 5*w + 35]', '[276, 138, 2*w + 8]', '[276, 138, 2*w - 10]', '[279, 93, 3*w + 39]', '[279, 93, 3*w + 51]', '[283, 283, w + 45]', '[283, 283, w + 237]', '[284, 142, 2*w + 58]', '[284, 142, 2*w + 82]', '[289, 17, 17]', '[291, 291, -w - 19]', '[291, 291, w - 20]', '[292, 146, 2*w + 48]', '[292, 146, 2*w + 96]', '[293, 293, 2*w - 9]', '[293, 293, -2*w - 7]', '[297, 99, -3*w - 21]', '[297, 99, -3*w + 24]', '[300, 30, 10*w + 10]', '[301, 301, w + 31]', '[301, 301, w + 269]', '[303, 303, w + 58]', '[303, 303, w + 244]', '[308, 154, 2*w + 6]', '[308, 154, 2*w - 8]', '[313, 313, w + 138]', '[313, 313, w + 174]', '[317, 317, w + 127]', '[317, 317, w + 189]', '[319, 319, -3*w - 32]', '[319, 319, 2*w - 27]', '[319, 319, 2*w + 25]', '[319, 319, -3*w + 35]', '[321, 321, 2*w - 7]', '[321, 321, -2*w - 5]', '[324, 18, 18]', '[329, 329, w + 87]', '[329, 329, w + 241]', '[331, 331, -w - 20]', '[331, 331, w - 21]', '[332, 166, -2*w - 4]', '[332, 166, 2*w - 6]', '[336, 84, -4*w - 40]', '[339, 339, 4*w - 35]', '[339, 339, 4*w + 31]', '[341, 341, -3*w + 23]', '[341, 341, -2*w + 5]', '[341, 341, -2*w - 3]', '[341, 341, -3*w - 20]', '[343, 49, 7*w + 21]', '[347, 347, w + 62]', '[347, 347, w + 284]', '[348, 174, 2*w + 2]', '[348, 174, -2*w + 4]', '[353, 353, 2*w - 3]', '[353, 353, -2*w - 1]', '[356, 178, -2*w]', '[356, 178, 2*w - 2]', '[357, 357, -2*w + 1]', '[361, 19, -19]', '[363, 33, 11*w + 11]', '[363, 363, w + 106]', '[363, 363, w + 256]', '[367, 367, w + 34]', '[367, 367, w + 332]', '[368, 92, 4*w + 16]', '[368, 92, 4*w + 72]', '[372, 186, 2*w + 26]', '[372, 186, 8*w + 74]', '[373, 373, -w - 21]', '[373, 373, w - 22]', '[381, 381, w + 52]', '[381, 381, w + 328]', '[383, 383, -3*w - 19]', '[383, 383, 3*w - 22]', '[387, 129, -3*w - 33]', '[387, 129, 3*w - 36]', '[388, 194, 2*w + 38]', '[388, 194, 2*w + 154]', '[391, 391, w + 110]', '[391, 391, w + 280]', '[396, 66, 6*w + 18]', '[396, 66, 6*w + 42]', '[397, 397, w + 170]', '[397, 397, w + 226]', '[400, 20, 20]', '[401, 401, w + 96]', '[401, 401, w + 304]', '[404, 202, 4*w - 34]', '[404, 202, -4*w - 30]', '[413, 413, w + 171]', '[413, 413, w + 241]', '[417, 417, -w - 22]', '[417, 417, w - 23]', '[421, 421, -5*w - 49]', '[421, 421, 5*w - 54]', '[423, 141, -3*w - 18]', '[423, 141, 3*w - 21]', '[425, 85, 5*w + 40]', '[427, 427, 9*w + 83]', '[427, 427, -2*w - 27]', '[428, 214, 2*w + 100]', '[428, 214, 2*w + 112]', '[431, 431, w + 69]', '[431, 431, w + 361]', '[432, 36, 12*w + 12]', '[439, 439, w + 37]', '[439, 439, w + 401]', '[441, 21, 21]', '[448, 56, 8*w + 24]', '[449, 449, w + 114]', '[449, 449, w + 334]', '[452, 226, 2*w + 72]', '[452, 226, 2*w + 152]', '[453, 453, w + 166]', '[453, 453, w + 286]', '[457, 457, 3*w - 37]', '[457, 457, -3*w - 34]', '[459, 153, 3*w + 75]', '[461, 461, 3*w - 20]', '[461, 461, -3*w - 17]', '[463, 463, -w - 23]', '[463, 463, w - 24]', '[464, 116, 4*w + 4]', '[464, 116, 4*w + 108]', '[467, 467, -4*w - 29]', '[467, 467, 4*w - 33]', '[469, 469, w + 213]', '[469, 469, w + 255]', '[473, 473, w + 117]', '[473, 473, w + 183]', '[473, 473, w + 289]', '[473, 473, w + 355]', '[476, 238, 2*w + 118]', '[483, 483, w + 73]', '[483, 483, w + 409]', '[484, 22, 22]', '[484, 242, 2*w + 28]', '[484, 242, -2*w + 30]', '[493, 493, w + 59]', '[493, 493, w + 433]', '[496, 124, 4*w + 52]', '[496, 124, 4*w + 68]', '[497, 497, -3*w - 16]', '[497, 497, 11*w + 96]', '[507, 39, 13*w + 13]', '[508, 254, 4*w - 46]', '[508, 254, 4*w + 42]', '[509, 509, -6*w - 49]', '[509, 509, 6*w - 55]', '[511, 511, w + 24]', '[511, 511, w - 25]', '[516, 258, 2*w + 62]', '[516, 258, 2*w + 194]', '[517, 517, w + 40]', '[517, 517, w + 194]', '[517, 517, w + 322]', '[517, 517, w + 476]', '[525, 105, -5*w - 50]', '[527, 527, w + 110]', '[527, 527, w + 416]', '[528, 132, -4*w - 28]', '[528, 132, -4*w + 32]', '[529, 23, 23]', '[529, 529, 3*w + 35]', '[529, 529, -3*w + 38]', '[531, 177, -3*w - 15]', '[531, 177, 3*w - 18]', '[539, 77, 7*w + 21]', '[539, 77, 7*w + 49]', '[543, 543, 2*w - 31]', '[543, 543, -2*w - 29]', '[549, 183, 3*w + 48]', '[549, 183, 3*w + 132]', '[556, 278, 2*w + 44]', '[556, 278, 2*w + 232]', '[561, 561, -w - 25]', '[561, 561, w - 26]', '[563, 563, 3*w - 17]', '[563, 563, -3*w - 14]', '[564, 282, 2*w + 80]', '[564, 282, 2*w + 200]', '[567, 63, 9*w + 27]', '[575, 115, 5*w + 20]', '[575, 115, 5*w + 90]', '[576, 24, 24]', '[581, 581, w + 80]', '[581, 581, w + 500]', '[587, 587, 4*w - 31]', '[587, 587, -4*w - 27]', '[588, 42, 14*w + 14]', '[591, 591, -5*w - 38]', '[591, 591, 7*w + 58]', '[593, 593, -3*w - 13]', '[593, 593, 3*w - 16]', '[597, 597, 4*w + 43]', '[597, 597, 4*w - 47]', '[601, 601, w + 43]', '[601, 601, w + 557]', '[603, 201, -3*w - 36]', '[603, 201, 3*w - 39]', '[604, 302, -2*w - 30]', '[604, 302, 2*w - 32]', '[607, 607, w + 137]', '[607, 607, w + 469]', '[609, 609, w + 262]', '[609, 609, w + 346]', '[612, 102, 6*w + 48]', '[613, 613, -w - 26]', '[613, 613, w - 27]', '[617, 617, w + 119]', '[617, 617, w + 497]', '[619, 619, w + 66]', '[619, 619, w + 552]', '[621, 207, 3*w + 12]', '[621, 207, 3*w - 15]', '[623, 623, w + 178]', '[623, 623, w + 444]', '[625, 25, 25]', '[631, 631, -6*w - 59]', '[631, 631, 6*w - 65]', '[639, 213, 3*w + 87]', '[639, 213, 3*w + 123]', '[641, 641, w + 84]', '[641, 641, w + 556]', '[643, 643, w + 141]', '[643, 643, w + 501]', '[644, 322, -4*w + 30]', '[644, 322, -4*w - 26]', '[647, 647, 3*w - 14]', '[647, 647, -3*w - 11]', '[649, 649, w + 289]', '[649, 649, w + 300]', '[649, 649, w + 348]', '[649, 649, w + 359]', '[651, 651, w + 199]', '[651, 651, w + 451]', '[653, 653, w + 264]', '[653, 653, w + 388]', '[657, 219, 3*w + 72]', '[657, 219, 3*w + 144]', '[667, 667, -w - 27]', '[667, 667, 2*w - 33]', '[667, 667, 2*w + 31]', '[667, 667, -w + 28]', '[671, 671, -3*w - 10]', '[671, 671, 8*w + 67]', '[671, 671, -8*w + 75]', '[671, 671, 3*w - 13]', '[675, 45, 15*w + 15]', '[676, 26, -26]', '[679, 679, 10*w + 93]', '[679, 679, 3*w + 37]', '[683, 683, w + 270]', '[683, 683, w + 412]', '[688, 172, -4*w - 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2]', '[83, 83, w - 3]', '[89, 89, -w]', '[89, 89, w - 1]', '[97, 97, w + 19]', '[97, 97, w + 77]', '[101, 101, 2*w - 17]', '[101, 101, -2*w - 15]', '[107, 107, w + 50]', '[107, 107, w + 56]', '[113, 113, w + 36]', '[113, 113, w + 76]', '[127, 127, 2*w - 23]', '[127, 127, 2*w + 21]', '[139, 139, w + 22]', '[139, 139, w + 116]', '[151, 151, -w - 15]', '[151, 151, w - 16]', '[169, 13, -13]', '[181, 181, w + 75]', '[181, 181, w + 105]', '[197, 197, w + 47]', '[197, 197, w + 149]', '[199, 199, w + 38]', '[199, 199, w + 160]', '[233, 233, w + 51]', '[233, 233, w + 181]', '[241, 241, w + 28]', '[241, 241, w + 212]', '[251, 251, -3*w - 22]', '[251, 251, 3*w - 25]', '[257, 257, 2*w - 11]', '[257, 257, -2*w - 9]', '[283, 283, w + 45]', '[283, 283, w + 237]', '[293, 293, 2*w - 9]', '[293, 293, -2*w - 7]', '[313, 313, w + 138]', '[313, 313, w + 174]', '[317, 317, w + 127]', '[317, 317, w + 189]', '[331, 331, -w - 20]', '[331, 331, w - 21]', '[347, 347, w + 62]', '[347, 347, w + 284]', '[353, 353, 2*w - 3]', '[353, 353, -2*w - 1]', '[361, 19, -19]', '[367, 367, w + 34]', '[367, 367, w + 332]', '[373, 373, -w - 21]', '[373, 373, w - 22]', '[383, 383, -3*w - 19]', '[383, 383, 3*w - 22]', '[397, 397, w + 170]', '[397, 397, w + 226]', '[401, 401, w + 96]', '[401, 401, w + 304]', '[421, 421, -5*w - 49]', '[421, 421, 5*w - 54]', '[431, 431, w + 69]', '[431, 431, w + 361]', '[439, 439, w + 37]', '[439, 439, w + 401]', '[449, 449, w + 114]', '[449, 449, w + 334]', '[457, 457, 3*w - 37]', '[457, 457, -3*w - 34]', '[461, 461, 3*w - 20]', '[461, 461, -3*w - 17]', '[463, 463, -w - 23]', '[463, 463, w - 24]', '[467, 467, -4*w - 29]', '[467, 467, 4*w - 33]', '[509, 509, -6*w - 49]', '[509, 509, 6*w - 55]', '[563, 563, 3*w - 17]', '[563, 563, -3*w - 14]', '[587, 587, 4*w - 31]', '[587, 587, -4*w - 27]', '[593, 593, -3*w - 13]', '[593, 593, 3*w - 16]', '[601, 601, w + 43]', '[601, 601, w + 557]', '[607, 607, w + 137]', '[607, 607, w + 469]', '[613, 613, -w - 26]', '[613, 613, w - 27]', '[617, 617, w + 119]', '[617, 617, w + 497]', '[619, 619, w + 66]', '[619, 619, w + 552]', '[631, 631, -6*w - 59]', '[631, 631, 6*w - 65]', '[641, 641, w + 84]', '[641, 641, w + 556]', '[643, 643, w + 141]', '[643, 643, w + 501]', '[647, 647, 3*w - 14]', '[647, 647, -3*w - 11]', '[653, 653, w + 264]', '[653, 653, w + 388]', '[683, 683, w + 270]', '[683, 683, w + 412]', '[691, 691, w + 46]', '[691, 691, w + 644]', '[739, 739, -5*w - 52]', '[739, 739, 5*w - 57]', '[743, 743, w + 297]', '[743, 743, w + 445]', '[757, 757, -3*w - 38]', '[757, 757, 3*w - 41]', '[761, 761, 3*w - 8]', '[761, 761, -3*w - 5]', '[773, 773, -3*w - 4]', '[773, 773, 3*w - 7]', '[787, 787, w + 49]', '[787, 787, w + 737]', '[797, 797, -3*w - 1]', '[797, 797, 3*w - 4]', '[809, 809, w + 302]', '[809, 809, w + 506]', '[811, 811, w + 243]', '[811, 811, w + 567]', '[821, 821, w + 95]', '[821, 821, w + 725]', '[827, 827, w + 242]', '[827, 827, w + 584]', '[853, 853, w + 399]', '[853, 853, w + 453]', '[883, 883, -7*w - 69]', '[883, 883, 7*w - 76]', '[911, 911, w + 254]', '[911, 911, w + 656]', '[919, 919, 3*w - 43]', '[919, 919, -3*w - 40]', '[947, 947, w + 102]', '[947, 947, w + 844]', '[967, 967, -w - 32]', '[967, 967, w - 33]', '[971, 971, -5*w - 33]', '[971, 971, 5*w - 38]', '[997, 997, w + 55]', '[997, 997, w + 941]']}
• 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': [-89, -1, 1], 'conductor': 357, 'degree': 2, 'dirichlet_group': [1, 356], 'disc_abs': 357, 'disc_rad': 357, 'disc_sign': 1, 'frobs': [[2, [[2, 1]]], [3, [0]], [5, [[2, 1]]], [7, [0]], [11, [[1, 2]]], [13, [[2, 1]]], [17, [0]], [19, [[2, 1]]], [23, [[1, 2]]], [29, [[1, 2]]], [31, [[1, 2]]], [37, [[2, 1]]], [41, [[2, 1]]], [43, [[1, 2]]], [47, [[1, 2]]], [53, [[2, 1]]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1, 1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 18.894443627691185, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.357.1', 'local_algs': ['3.2.1.2', '7.2.1.1', '17.2.1.1'], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [3, 7, 17], 'rd': 18.8944436277, 'regulator': {'__RealLiteral__': 0, 'data': '2.94165731465', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 9 \\)'], 'used_grh': False, 'zk': ['1', 'a']}