-
hmf_forms • Show schema
{'deg': 2, 'dimension': 12, 'disc': 357, 'field_bad_primes': [3, 7, 17], 'field_label': '2.2.357.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '2.2.357.1-1.1-f', 'label_nsuffix': 5, 'label_suffix': 'f', 'level_bad_primes': [], 'level_ideal': '[1, 1, 1]', 'level_label': '1.1', 'level_norm': 1, 'parallel_weight': 2, 'short_label': '1.1-f', 'weight': '[2, 2]'} -
hmf_hecke • Show schema
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13849213625/8394325232*e^6 + 194505637271/8394325232*e^4 - 98935066335/1049290654*e^2 + 47311150952/524645327', '-3393591/8394325232*e^10 + 375828577/8394325232*e^8 - 13849213625/8394325232*e^6 + 194505637271/8394325232*e^4 - 98935066335/1049290654*e^2 + 47311150952/524645327', '3436607/8394325232*e^10 - 370244531/8394325232*e^8 + 12722098477/8394325232*e^6 - 143346695321/8394325232*e^4 + 6773982909/1049290654*e^2 + 14240243896/524645327', '3436607/8394325232*e^10 - 370244531/8394325232*e^8 + 12722098477/8394325232*e^6 - 143346695321/8394325232*e^4 + 6773982909/1049290654*e^2 + 14240243896/524645327', '226376591/1393457988512*e^11 - 27343782281/1393457988512*e^9 + 1150231164747/1393457988512*e^7 - 19948270792347/1393457988512*e^5 + 61341186259545/696728994256*e^3 - 7856841340803/87091124282*e', '226376591/1393457988512*e^11 - 27343782281/1393457988512*e^9 + 1150231164747/1393457988512*e^7 - 19948270792347/1393457988512*e^5 + 61341186259545/696728994256*e^3 - 7856841340803/87091124282*e'], 'hecke_polynomial': 'x^12 - 140*x^10 + 7246*x^8 - 168516*x^6 + 1618137*x^4 - 3479624*x^2 + 1763584', 'label': '2.2.357.1-1.1-f'} -
hmf_fields • Show schema
{'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 - 44]', '[688, 172, 4*w - 48]', '[691, 691, w + 46]', '[691, 691, w + 644]', '[693, 231, 3*w + 9]', '[693, 231, 3*w - 12]', '[699, 699, 4*w + 25]', '[699, 699, -11*w - 95]', '[700, 70, 10*w + 30]', '[704, 88, 8*w + 24]', '[704, 88, 8*w + 56]', '[707, 707, w + 143]', '[707, 707, w + 563]', '[708, 354, 2*w + 128]', '[708, 354, 2*w + 224]', '[713, 713, 7*w + 57]', '[713, 713, 3*w - 11]', '[713, 713, 3*w + 8]', '[713, 713, 7*w - 64]', '[723, 723, -w - 28]', '[723, 723, w - 29]', '[724, 362, 2*w + 150]', '[724, 362, 2*w + 210]', '[725, 145, 5*w + 5]', '[725, 145, 5*w + 135]', '[729, 27, 27]', '[731, 731, -3*w - 7]', '[731, 731, -20*w - 177]', '[732, 366, -2*w - 32]', '[732, 366, -2*w + 34]', '[737, 737, w + 146]', '[737, 737, w + 322]', '[737, 737, w + 414]', '[737, 737, w + 590]', '[739, 739, -5*w - 52]', '[739, 739, 5*w - 57]', '[743, 743, w + 297]', '[743, 743, w + 445]', '[747, 249, -3*w - 6]', '[747, 249, 3*w - 9]', '[748, 374, 2*w + 50]', '[748, 374, 2*w + 322]', '[749, 749, -5*w - 36]', '[749, 749, 9*w + 76]', '[752, 188, -4*w - 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101]', '[9643, 9643, -2*w - 99]', '[9648, 804, -12*w - 144]', '[9648, 804, 12*w - 156]', '[9649, 9649, w + 1652]', '[9649, 9649, w + 7996]', '[9651, 9651, w + 3274]', '[9651, 9651, w + 6376]', '[9653, 1379, 7*w + 329]', '[9653, 1379, 7*w + 1043]', '[9664, 1208, -8*w - 120]', '[9664, 1208, 8*w - 128]', '[9667, 9667, w + 1739]', '[9667, 9667, w + 7927]', '[9668, 4834, 2*w + 1500]', '[9668, 4834, 2*w + 3332]', '[9669, 9669, -7*w - 115]', '[9669, 9669, 23*w + 227]', '[9669, 9669, 23*w - 250]', '[9669, 9669, -7*w + 122]', '[9675, 645, -15*w - 165]', '[9675, 645, 15*w - 180]', '[9677, 9677, -11*w - 28]', '[9677, 9677, 11*w - 39]', '[9679, 9679, w + 3043]', '[9679, 9679, w + 6635]', '[9681, 9681, 50*w + 437]', '[9681, 9681, -13*w - 67]', '[9683, 9683, w + 326]', '[9683, 9683, w + 1168]', '[9683, 9683, w + 8514]', '[9683, 9683, w + 9356]', '[9687, 9687, w + 2131]', '[9687, 9687, w + 7555]', '[9700, 970, 10*w + 190]', '[9700, 970, 10*w + 770]', '[9703, 9703, 22*w + 219]', '[9703, 9703, -3*w - 101]', '[9703, 9703, 3*w - 104]', '[9703, 9703, 22*w - 241]', '[9708, 4854, -22*w - 172]', '[9708, 4854, 26*w + 212]', '[9712, 2428, 4*w + 548]', '[9712, 2428, 4*w + 1876]', '[9713, 9713, w + 1019]', '[9713, 9713, w + 3395]', '[9713, 9713, w + 6317]', '[9713, 9713, w + 8693]', '[9716, 4858, 12*w + 50]', '[9716, 4858, -12*w + 62]', '[9721, 9721, w + 2098]', '[9721, 9721, w + 7622]', '[9723, 9723, 34*w + 319]', '[9723, 9723, 13*w + 151]', '[9729, 3243, 3*w + 261]', '[9729, 3243, 3*w + 1530]', '[9729, 3243, 3*w + 1710]', '[9729, 3243, 3*w + 2979]', '[9732, 4866, 14*w + 158]', '[9732, 4866, 14*w - 172]', '[9739, 9739, -17*w - 180]', '[9739, 9739, 17*w - 197]', '[9743, 9743, 11*w - 38]', '[9743, 9743, -11*w - 27]', '[9744, 2436, 4*w + 1048]', '[9744, 2436, 4*w + 1384]', '[9747, 171, 57*w + 57]', '[9749, 9749, 14*w - 95]', '[9749, 9749, -14*w - 81]', '[9751, 1393, 7*w + 266]', '[9751, 1393, 7*w + 1120]', '[9753, 9753, w + 4639]', '[9753, 9753, w + 5113]', '[9759, 9759, -5*w - 107]', '[9759, 9759, 5*w - 112]', '[9771, 9771, -23*w - 182]', '[9771, 9771, -25*w - 202]', '[9775, 1955, 5*w + 550]', '[9775, 1955, 5*w + 1400]', '[9779, 9779, 15*w + 94]', '[9779, 9779, 29*w + 241]', '[9779, 9779, -29*w + 270]', '[9779, 9779, -15*w + 109]', '[9783, 3261, 6*w - 117]', '[9783, 3261, -6*w - 111]', '[9791, 9791, 17*w - 135]', '[9791, 9791, -17*w - 118]', '[9792, 408, 24*w + 192]', '[9793, 9793, 39*w + 362]', '[9793, 9793, 11*w + 138]', '[9797, 9797, w + 2987]', '[9797, 9797, w + 3375]', '[9797, 9797, w + 6421]', '[9797, 9797, w + 6809]', '[9801, 99, 99]', '[9801, 1089, 9*w + 126]', '[9801, 1089, -9*w + 135]', '[9807, 9807, -11*w - 26]', '[9807, 9807, 73*w + 646]', '[9808, 2452, -4*w - 104]', '[9808, 2452, 4*w - 108]', '[9811, 9811, -w - 99]', '[9811, 9811, w - 100]', '[9821, 9821, w + 1053]', '[9821, 9821, w + 3615]', '[9821, 9821, w + 6205]', '[9821, 9821, w + 8767]', '[9827, 9827, -13*w - 66]', '[9827, 9827, -12*w - 49]', '[9827, 9827, 12*w - 61]', '[9827, 9827, 13*w - 79]', '[9831, 9831, w + 262]', '[9831, 9831, w + 3652]', '[9831, 9831, w + 6178]', '[9831, 9831, w + 9568]', '[9836, 4918, 2*w + 1798]', '[9836, 4918, 2*w + 3118]', '[9844, 4922, 2*w + 100]', '[9844, 4922, -10*w + 142]', '[9844, 4922, -10*w - 132]', '[9844, 4922, 2*w - 102]', '[9849, 1407, 7*w + 553]', '[9849, 1407, 7*w + 847]', '[9852, 4926, -16*w + 122]', '[9852, 4926, 16*w + 106]', '[9857, 9857, w + 3175]', '[9857, 9857, w + 6681]', '[9869, 9869, -11*w - 25]', '[9869, 9869, 19*w - 159]', '[9869, 9869, -19*w - 140]', '[9869, 9869, 11*w - 36]', '[9872, 2468, 4*w + 476]', '[9872, 2468, 4*w + 1988]', '[9873, 3291, -18*w - 129]', '[9873, 3291, 18*w - 147]', '[9877, 9877, w + 3986]', '[9877, 9877, w + 5890]', '[9883, 9883, w + 776]', '[9883, 9883, w + 9106]', '[9884, 4942, 2*w + 1056]', '[9884, 4942, 2*w + 3884]', '[9889, 9889, w + 172]', '[9889, 9889, w + 1129]', '[9889, 9889, w + 4264]', '[9889, 9889, w + 4667]', '[9889, 9889, w + 5221]', '[9889, 9889, w + 5624]', '[9889, 9889, w + 8759]', '[9889, 9889, w + 9716]', '[9892, 4946, -18*w - 188]', '[9892, 4946, 18*w - 206]', '[9900, 330, 30*w + 90]', '[9900, 330, 30*w + 210]', '[9901, 9901, w + 2262]', '[9901, 9901, w + 7638]', '[9904, 2476, 4*w + 264]', '[9904, 2476, 4*w + 2208]', '[9907, 9907, 7*w - 123]', '[9907, 9907, -7*w - 116]', '[9909, 3303, -3*w - 102]', '[9909, 3303, 3*w - 105]', '[9913, 9913, -8*w + 129]', '[9913, 9913, -16*w + 189]', '[9913, 9913, 16*w + 173]', '[9913, 9913, 8*w + 121]', '[9923, 9923, w + 4175]', '[9923, 9923, w + 5747]', '[9924, 4962, -14*w - 80]', '[9924, 4962, 14*w - 94]', '[9925, 1985, 5*w + 850]', '[9925, 1985, 5*w + 1130]', '[9929, 9929, 11*w - 35]', '[9929, 9929, -11*w - 24]', '[9931, 9931, w + 851]', '[9931, 9931, w + 9079]', '[9933, 9933, w + 1774]', '[9933, 9933, w + 4546]', '[9933, 9933, w + 5386]', '[9933, 9933, w + 8158]', '[9936, 828, 12*w + 48]', '[9936, 828, 12*w - 60]', '[9939, 9939, w + 4543]', '[9939, 9939, w + 5395]', '[9947, 1421, -21*w + 182]', '[9947, 1421, 21*w + 161]', '[9949, 9949, 12*w - 157]', '[9949, 9949, -12*w - 145]', '[9951, 9951, w + 478]', '[9951, 9951, w + 2404]', '[9951, 9951, w + 7546]', '[9951, 9951, w + 9472]', '[9957, 9957, w + 1342]', '[9957, 9957, w + 8614]', '[9967, 9967, w + 2447]', '[9967, 9967, w + 7519]', '[9968, 2492, 4*w + 712]', '[9968, 2492, 4*w + 1776]', '[9969, 9969, w + 4054]', '[9969, 9969, w + 5914]', '[9971, 767, -13*w - 65]', '[9971, 767, 13*w - 78]', '[9973, 9973, w + 4899]', '[9973, 9973, w + 5073]', '[9979, 9979, -63*w - 572]', '[9979, 9979, 5*w + 108]', '[9981, 3327, -15*w - 93]', '[9981, 3327, 15*w - 108]', '[9987, 9987, -11*w - 23]', '[9987, 9987, 11*w - 34]', '[9989, 9989, w + 4637]', '[9989, 9989, w + 5351]', '[9996, 714, 14*w + 350]', '[9999, 3333, 3*w + 174]', '[9999, 3333, 3*w + 780]', '[9999, 3333, 3*w + 2550]', '[9999, 3333, 3*w + 3156]', '[10000, 100, 100]'], 'label': '2.2.357.1', 'narrow_class_no': 4, 'primes': ['[3, 3, w + 1]', '[4, 2, 2]', '[7, 7, w + 3]', '[11, 11, w + 3]', '[11, 11, w + 7]', '[17, 17, w + 8]', '[23, 23, w + 4]', '[23, 23, w + 18]', '[25, 5, 5]', '[29, 29, w + 1]', '[29, 29, w + 27]', '[31, 31, w + 13]', '[31, 31, w + 17]', '[43, 43, -w - 11]', '[43, 43, w - 12]', '[47, 47, -w - 6]', '[47, 47, w - 7]', '[59, 59, -w - 5]', '[59, 59, w - 6]', '[61, 61, w + 16]', '[61, 61, w + 44]', '[67, 67, -w - 12]', '[67, 67, w - 13]', '[71, 71, w + 29]', '[71, 71, w + 41]', '[73, 73, w + 24]', '[73, 73, w + 48]', '[83, 83, -w - 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 • Show schema
{'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']}
Hilbert modular form data - 2.2.357.1-1.1-f