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hmf_forms • Show schema
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{'deg': 2, 'dimension': 1, 'disc': 213, 'field_bad_primes': [3, 71], 'field_label': '2.2.213.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.213.1-25.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [5], 'level_ideal': '[25, 5, 5]', 'level_label': '25.1', 'level_norm': 25, 'parallel_weight': 2, 'short_label': '25.1-a', 'weight': '[2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[25, 5, 5]', -1]], 'hecke_eigenvalues': [-2, 0, -6, 6, -6, 6, 1, 1, 4, -4, 1, -4, -4, 0, 0, -4, -4, 13, -13, 13, -1, 1, 10, -10, 0, -8, -8, 13, 13, -14, -14, 5, 5, -3, 3, 9, -9, 4, -4, 20, 20, 4, 4, 17, -14, 14, -5, 5, -21, -21, -4, -4, 3, -3, -23, -23, -2, 2, -27, 27, -28, 28, -23, -23, -14, -14, 18, -18, 0, 0, -10, 10, 16, -16, -11, 11, 30, 30, 8, 8, 15, 15, 31, -31, 14, -14, 26, -26, 30, 30, -9, 9, 42, -42, 12, -12, -34, -34, -3, 3, -12, 12, -20, 20, -20, -20, 22, 22, 36, -36, -20, -20, -2, -2, 6, -6, -16, -16, 30, 30, 21, -21, 45, -45, 10, -10, -33, -33, 45, -45, 38, -38, -26, 26, -28, -28, 0, 0, -31, -31, 28, -28, 13, 13, 23, -36, -36, -31, 31, -8, -8, 19, -19, 24, -24, -38, -12, -12], 'hecke_polynomial': 'x', 'label': '2.2.213.1-25.1-a'}
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hmf_fields • Show schema
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{'degree': 2, 'discriminant': 213, 'ideals': ['[1, 1, 1]', '[3, 3, w - 8]', '[4, 2, 2]', '[9, 3, 3]', '[11, 11, -w + 7]', '[11, 11, -w - 6]', '[12, 6, 2*w - 16]', '[16, 4, 4]', '[17, 17, -2*w + 15]', '[17, 17, -2*w - 13]', '[19, 19, -w - 8]', '[19, 19, -w + 9]', '[23, 23, -w - 5]', '[23, 23, -w + 6]', '[25, 5, 5]', '[27, 9, 3*w - 24]', '[33, 33, w + 4]', '[33, 33, w - 5]', '[36, 6, 6]', '[37, 37, -w - 9]', '[37, 37, w - 10]', '[41, 41, -w - 3]', '[41, 41, w - 4]', '[43, 43, -2*w + 17]', '[43, 43, -7*w + 55]', '[44, 22, -2*w + 14]', '[44, 22, -2*w - 12]', '[47, 47, -w - 2]', '[47, 47, w - 3]', '[48, 12, 4*w - 32]', '[49, 7, -7]', '[51, 51, w + 1]', '[51, 51, w - 2]', '[53, 53, -w]', '[53, 53, w - 1]', '[57, 57, -w - 10]', '[57, 57, -w + 11]', '[59, 59, -7*w + 54]', '[59, 59, 3*w - 22]', '[64, 8, 8]', '[68, 34, -4*w + 30]', '[68, 34, -4*w - 26]', '[69, 69, 2*w - 13]', '[69, 69, 2*w + 11]', '[71, 71, -5*w + 38]', '[73, 73, -3*w + 25]', '[73, 73, -8*w + 63]', '[75, 15, 5*w - 40]', '[76, 38, -2*w - 16]', '[76, 38, -2*w + 18]', '[79, 79, -w - 11]', '[79, 79, w - 12]', '[81, 9, 9]', '[92, 46, -2*w - 10]', '[92, 46, -2*w + 12]', '[99, 33, -3*w + 21]', '[99, 33, -3*w - 18]', '[100, 10, 10]', '[103, 103, -w - 12]', '[103, 103, w - 13]', '[108, 18, 6*w - 48]', '[109, 109, -4*w + 33]', '[109, 109, -9*w + 71]', '[111, 111, -2*w + 19]', '[111, 111, -17*w + 133]', '[113, 113, 2*w - 11]', '[113, 113, -2*w - 9]', '[121, 11, 11]', '[121, 121, 3*w + 23]', '[121, 121, -3*w + 26]', '[123, 123, -11*w + 85]', '[123, 123, 4*w - 29]', '[129, 129, -w - 13]', '[129, 129, w - 14]', '[132, 66, 2*w + 8]', '[132, 66, 2*w - 10]', '[137, 137, 3*w - 20]', '[137, 137, -3*w - 17]', '[141, 141, 5*w - 37]', '[141, 141, -10*w + 77]', '[144, 12, 12]', '[147, 21, -7*w + 56]', '[148, 74, -2*w - 18]', '[148, 74, 2*w - 20]', '[149, 149, 2*w - 9]', '[149, 149, -2*w - 7]', '[151, 151, -5*w + 41]', '[151, 151, -10*w + 79]', '[153, 51, -6*w + 45]', '[153, 51, -6*w - 39]', '[157, 157, -w - 14]', '[157, 157, w - 15]', '[159, 159, -8*w + 61]', '[159, 159, 7*w - 53]', '[164, 82, -2*w - 6]', '[164, 82, 2*w - 8]', '[169, 13, -13]', '[171, 57, -3*w - 24]', '[171, 57, -3*w + 27]', '[172, 86, -4*w + 34]', '[172, 86, -14*w + 110]', '[173, 173, -3*w - 16]', '[173, 173, 3*w - 19]', '[176, 44, -4*w + 28]', '[176, 44, -4*w - 24]', '[177, 177, 2*w - 7]', '[177, 177, -2*w - 5]', '[187, 187, w + 15]', '[187, 187, -2*w + 21]', '[187, 187, 2*w + 19]', '[187, 187, -w + 16]', '[188, 94, -2*w - 4]', '[188, 94, 2*w - 6]', '[192, 24, 8*w - 64]', '[196, 14, -14]', '[197, 197, 2*w - 5]', '[197, 197, -2*w - 3]', '[199, 199, -6*w + 49]', '[199, 199, -11*w + 87]', '[204, 102, 2*w + 2]', '[204, 102, 2*w - 4]', '[207, 69, -3*w - 15]', '[207, 69, -3*w + 18]', '[209, 209, -5*w - 31]', '[209, 209, 2*w - 3]', '[209, 209, -2*w - 1]', '[209, 209, 5*w - 36]', '[212, 106, -2*w]', '[212, 106, 2*w - 2]', '[213, 213, 2*w - 1]', '[219, 219, -w - 16]', '[219, 219, w - 17]', '[223, 223, 3*w - 28]', '[223, 223, -3*w - 25]', '[225, 15, 15]', '[227, 227, 4*w - 27]', '[227, 227, -4*w - 23]', '[228, 114, -2*w - 20]', '[228, 114, -2*w + 22]', '[229, 229, -15*w + 118]', '[229, 229, -5*w + 42]', '[236, 118, -14*w + 108]', '[236, 118, 6*w - 44]', '[237, 237, -19*w + 149]', '[237, 237, -4*w + 35]', '[239, 239, 3*w - 17]', '[239, 239, -3*w - 14]', '[243, 27, 9*w - 72]', '[253, 253, w + 17]', '[253, 253, -7*w + 57]', '[253, 253, 7*w + 50]', '[253, 253, -w + 18]', '[256, 16, 16]', '[257, 257, 7*w - 52]', '[257, 257, -13*w + 100]', '[269, 269, -3*w - 13]', '[269, 269, 3*w - 16]', '[271, 271, 2*w - 23]', '[271, 271, -2*w - 21]', '[272, 68, -8*w + 60]', '[272, 68, -8*w - 52]', '[275, 55, -5*w + 35]', '[275, 55, -5*w - 30]', '[276, 138, 4*w - 26]', '[276, 138, 4*w + 22]', '[277, 277, -3*w - 26]', '[277, 277, 3*w - 29]', '[281, 281, -11*w + 84]', '[281, 281, 9*w - 68]', '[284, 142, -10*w + 76]', '[289, 17, 17]', '[289, 289, w + 18]', '[289, 289, -w + 19]', '[292, 146, -6*w + 50]', '[292, 146, -16*w + 126]', '[297, 99, 3*w + 12]', '[297, 99, 3*w - 15]', '[300, 30, 10*w - 80]', '[304, 76, -4*w - 32]', '[304, 76, -4*w + 36]', '[309, 309, -5*w + 43]', '[309, 309, -20*w + 157]', '[313, 313, -8*w + 65]', '[313, 313, -13*w + 103]', '[316, 158, -2*w - 22]', '[316, 158, 2*w - 24]', '[317, 317, -19*w + 147]', '[317, 317, 6*w - 43]', '[323, 323, -4*w - 21]', '[323, 323, 3*w - 14]', '[323, 323, -3*w - 11]', '[323, 323, 4*w - 25]', '[324, 18, 18]', '[327, 327, -w - 19]', '[327, 327, w - 20]', '[333, 111, -3*w - 27]', '[333, 111, 3*w - 30]', '[339, 339, 5*w - 34]', '[339, 339, -25*w + 194]', '[347, 347, -3*w - 10]', '[347, 347, 3*w - 13]', '[353, 353, 7*w - 51]', '[353, 353, -18*w + 139]', '[361, 19, 19]', '[361, 361, 7*w + 51]', '[361, 361, -7*w + 58]', '[363, 33, 11*w - 88]', '[363, 363, 2*w - 25]', '[363, 363, -2*w - 23]', '[367, 367, -w - 20]', '[367, 367, w - 21]', '[368, 92, -4*w - 20]', '[368, 92, -4*w + 24]', '[369, 123, -3*w - 9]', '[369, 123, 3*w - 12]', '[373, 373, 4*w - 37]', '[373, 373, -4*w - 33]', '[379, 379, -9*w + 73]', '[379, 379, -14*w + 111]', '[383, 383, -17*w + 131]', '[383, 383, 8*w - 59]', '[387, 129, -6*w + 51]', '[387, 129, -21*w + 165]', '[389, 389, 3*w - 11]', '[389, 389, -3*w - 8]', '[391, 391, 5*w + 39]', '[391, 391, -3*w + 31]', '[391, 391, 3*w + 28]', '[391, 391, -5*w + 44]', '[396, 66, -6*w + 42]', '[396, 66, -6*w - 36]', '[400, 20, 20]', '[401, 401, -5*w - 28]', '[401, 401, 5*w - 33]', '[407, 407, 16*w + 107]', '[407, 407, 3*w + 7]', '[407, 407, 3*w - 10]', '[407, 407, 16*w - 123]', '[409, 409, -w - 21]', '[409, 409, w - 22]', '[411, 411, 4*w - 23]', '[411, 411, -41*w + 319]', '[412, 206, -2*w - 24]', '[412, 206, 2*w - 26]', '[423, 141, -3*w - 6]', '[423, 141, 3*w - 9]', '[425, 85, -10*w + 75]', '[425, 85, -10*w - 65]', '[432, 36, 12*w - 96]', '[436, 218, -8*w + 66]', '[436, 218, -18*w + 142]', '[437, 437, -11*w - 72]', '[437, 437, -3*w + 8]', '[437, 437, 3*w + 5]', '[437, 437, 11*w - 83]', '[441, 21, -21]', '[443, 443, -12*w + 91]', '[443, 443, -13*w + 99]', '[444, 222, -4*w + 38]', '[444, 222, -34*w + 266]', '[447, 447, -23*w + 178]', '[447, 447, 7*w - 50]', '[449, 449, -3*w - 4]', '[449, 449, 3*w - 7]', '[451, 451, 10*w - 81]', '[451, 451, -3*w - 29]', '[451, 451, -3*w + 32]', '[451, 451, 10*w + 71]', '[452, 226, 4*w - 22]', '[452, 226, -4*w - 18]', '[453, 453, -w - 22]', '[453, 453, w - 23]', '[459, 153, 3*w + 3]', '[459, 153, 3*w - 6]', '[461, 461, 5*w - 32]', '[461, 461, -5*w - 27]', '[463, 463, 2*w - 27]', '[463, 463, -2*w - 25]', '[467, 467, 3*w - 5]', '[467, 467, -3*w - 2]', '[471, 471, -22*w + 173]', '[471, 471, -7*w + 59]', '[473, 473, -6*w + 41]', '[473, 473, -3*w - 1]', '[473, 473, -3*w + 4]', '[473, 473, -6*w - 35]', '[475, 95, -5*w - 40]', '[475, 95, -5*w + 45]', '[477, 159, -3*w]', '[477, 159, 3*w - 3]', '[479, 479, 3*w - 2]', '[479, 479, 3*w - 1]', '[484, 22, 22]', '[484, 242, 6*w + 46]', '[484, 242, -6*w + 52]', '[491, 491, -4*w - 17]', '[491, 491, 4*w - 21]', '[492, 246, -22*w + 170]', '[492, 246, 8*w - 58]', '[499, 499, -w - 23]', '[499, 499, w - 24]', '[507, 39, -13*w + 104]', '[513, 171, -3*w - 30]', '[513, 171, -3*w + 33]', '[516, 258, -2*w - 26]', '[516, 258, 2*w - 28]', '[517, 517, -4*w - 35]', '[517, 517, 9*w + 65]', '[517, 517, 9*w - 74]', '[517, 517, -4*w + 39]', '[519, 519, -40*w + 311]', '[519, 519, 5*w - 31]', '[528, 132, 4*w + 16]', '[528, 132, 4*w - 20]', '[529, 23, 23]', '[529, 529, -11*w + 89]', '[529, 529, 11*w + 78]', '[531, 177, -21*w + 162]', '[531, 177, 9*w - 66]', '[539, 77, 7*w - 49]', '[539, 77, 7*w + 42]', '[547, 547, -w - 24]', '[547, 547, w - 25]', '[548, 274, 6*w - 40]', '[548, 274, -6*w - 34]', '[561, 561, 5*w - 46]', '[561, 561, 8*w - 67]', '[561, 561, -8*w - 59]', '[561, 561, -5*w - 41]', '[563, 563, 4*w - 19]', '[563, 563, -4*w - 15]', '[564, 282, 10*w - 74]', '[564, 282, -20*w + 154]', '[571, 571, 2*w - 29]', '[571, 571, -2*w - 27]', '[575, 115, -5*w - 25]', '[575, 115, -5*w + 30]', '[576, 24, 24]', '[577, 577, 3*w - 34]', '[577, 577, -3*w - 31]', '[583, 583, -6*w - 47]', '[583, 583, 7*w - 60]', '[583, 583, 7*w + 53]', '[583, 583, -6*w + 53]', '[588, 42, -14*w + 112]', '[591, 591, 11*w - 82]', '[591, 591, -19*w + 146]', '[592, 148, -4*w - 36]', '[592, 148, 4*w - 40]', '[596, 298, 4*w - 18]', '[596, 298, -4*w - 14]', '[597, 597, -w - 25]', '[597, 597, w - 26]', '[599, 599, -27*w + 209]', '[599, 599, 8*w - 57]', '[604, 302, -10*w + 82]', '[604, 302, -20*w + 158]', '[612, 102, -12*w + 90]', '[612, 102, -12*w - 78]', '[613, 613, -12*w + 97]', '[613, 613, -17*w + 135]', '[621, 207, 6*w - 39]', '[621, 207, 6*w + 33]', '[625, 25, 25]', '[627, 627, -13*w - 85]', '[627, 627, -4*w - 13]', '[627, 627, 4*w - 17]', '[627, 627, 13*w - 98]', '[628, 314, -2*w - 28]', '[628, 314, 2*w - 30]', '[629, 629, 33*w + 223]', '[629, 629, 5*w - 29]', '[629, 629, 5*w + 24]', '[629, 629, 33*w - 256]', '[636, 318, -16*w + 122]', '[636, 318, 14*w - 106]', '[639, 213, -15*w + 114]', '[643, 643, -3*w - 32]', '[643, 643, 3*w - 35]', '[649, 649, w + 26]', '[649, 649, -5*w - 42]', '[649, 649, -5*w + 47]', '[649, 649, w - 27]', '[653, 653, 9*w - 65]', '[653, 653, -26*w + 201]', '[656, 164, -4*w - 12]', '[656, 164, 4*w - 16]', '[657, 219, -9*w + 75]', '[657, 219, -24*w + 189]', '[669, 669, -4*w + 41]', '[669, 669, -49*w + 383]', '[675, 45, 15*w - 120]', '[676, 26, -26]', '[681, 681, -55*w + 428]', '[681, 681, 5*w - 28]', '[683, 683, 4*w - 15]', '[683, 683, -4*w - 11]', '[684, 114, -6*w - 48]', '[684, 114, -6*w + 54]', '[687, 687, 2*w - 31]', '[687, 687, -2*w - 29]', '[688, 172, -8*w + 68]', '[688, 172, -28*w + 220]', '[692, 346, -6*w - 32]', '[692, 346, 6*w - 38]', '[697, 697, -7*w + 61]', '[697, 697, 21*w - 166]', '[697, 697, 21*w + 145]', '[697, 697, -7*w - 54]', '[701, 701, 10*w - 73]', '[701, 701, -25*w + 193]', '[703, 703, w + 27]', '[703, 703, 18*w + 125]', '[703, 703, 18*w - 143]', '[703, 703, w - 28]', '[704, 88, -8*w + 56]', '[704, 88, -8*w - 48]', '[708, 354, 4*w - 14]', '[708, 354, -4*w - 10]', '[711, 237, -3*w - 33]', '[711, 237, 3*w - 36]', '[717, 717, -38*w + 295]', '[717, 717, 7*w - 47]', '[729, 27, 27]', '[731, 731, -4*w - 9]', '[731, 731, -5*w + 27]', '[731, 731, -5*w - 22]', '[731, 731, -4*w + 13]', '[739, 739, 5*w - 48]', '[739, 739, -5*w - 43]', '[743, 743, -24*w + 185]', '[743, 743, 11*w - 81]', '[748, 374, 2*w + 30]', '[748, 374, -4*w + 42]', '[748, 374, 4*w + 38]', '[748, 374, -2*w + 32]', '[752, 188, -4*w - 8]', '[752, 188, 4*w - 12]', '[759, 759, -w - 28]', '[759, 759, -10*w - 73]', '[759, 759, 10*w - 83]', '[759, 759, w - 29]', '[761, 761, -6*w - 31]', '[761, 761, 6*w - 37]', '[768, 48, 16*w - 128]', '[771, 771, 4*w - 11]', '[771, 771, -4*w - 7]', '[773, 773, -31*w + 240]', '[773, 773, 9*w - 64]', '[779, 779, -5*w - 21]', '[779, 779, 12*w + 77]', '[779, 779, 12*w - 89]', '[779, 779, -5*w + 26]', '[781, 781, -3*w + 37]', '[781, 781, 3*w + 34]', '[784, 28, -28]', '[787, 787, 6*w - 55]', '[787, 787, -6*w - 49]', '[788, 394, 4*w - 10]', '[788, 394, -4*w - 6]', '[796, 398, -12*w + 98]', '[796, 398, -22*w + 174]', '[799, 799, 19*w + 132]', '[799, 799, -9*w - 67]', '[799, 799, -9*w + 76]', '[799, 799, 19*w - 151]', '[803, 803, -4*w - 5]', '[803, 803, -7*w - 39]', '[803, 803, -7*w + 46]', '[803, 803, -4*w + 9]', '[807, 807, 8*w - 55]', '[807, 807, -37*w + 287]', '[809, 809, 13*w - 97]', '[809, 809, -22*w + 169]', '[811, 811, 2*w - 33]', '[811, 811, -2*w - 31]', '[813, 813, -37*w + 290]', '[813, 813, -7*w + 62]', '[816, 204, 4*w + 4]', '[816, 204, 4*w - 8]', '[817, 817, w + 29]', '[817, 817, 8*w + 61]', '[817, 817, 8*w - 69]', '[817, 817, w - 30]', '[825, 165, 5*w + 20]', '[825, 165, 5*w - 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261]', '[9964, 4982, -6*w - 106]', '[9964, 4982, 4*w - 106]', '[9964, 4982, -4*w - 102]', '[9964, 4982, 6*w - 112]', '[9967, 9967, 9*w - 124]', '[9967, 9967, -9*w - 115]', '[9971, 767, -91*w + 702]', '[9971, 767, 39*w - 286]', '[9972, 1662, -18*w - 156]', '[9972, 1662, 18*w - 174]', '[9981, 3327, -69*w + 528]', '[9981, 3327, 51*w - 384]', '[9987, 9987, 17*w - 82]', '[9987, 9987, -17*w - 65]', '[9988, 4994, -2*w - 100]', '[9988, 4994, 102*w + 700]', '[9988, 4994, 102*w - 802]', '[9988, 4994, -2*w + 102]', '[9996, 714, -14*w - 14]', '[9996, 714, -14*w + 28]', '[10000, 100, 100]'], 'label': '2.2.213.1', 'narrow_class_no': 2, 'primes': ['[3, 3, w - 8]', '[4, 2, 2]', '[11, 11, -w + 7]', '[11, 11, -w - 6]', '[17, 17, -2*w + 15]', '[17, 17, -2*w - 13]', '[19, 19, -w - 8]', '[19, 19, -w + 9]', '[23, 23, -w - 5]', '[23, 23, -w + 6]', '[25, 5, 5]', '[37, 37, -w - 9]', '[37, 37, w - 10]', '[41, 41, -w - 3]', '[41, 41, w - 4]', '[43, 43, -2*w + 17]', '[43, 43, -7*w + 55]', '[47, 47, -w - 2]', '[47, 47, w - 3]', '[49, 7, -7]', '[53, 53, -w]', '[53, 53, w - 1]', '[59, 59, -7*w + 54]', '[59, 59, 3*w - 22]', '[71, 71, -5*w + 38]', '[73, 73, -3*w + 25]', '[73, 73, -8*w + 63]', '[79, 79, -w - 11]', '[79, 79, w - 12]', '[103, 103, -w - 12]', '[103, 103, w - 13]', '[109, 109, -4*w + 33]', '[109, 109, -9*w + 71]', '[113, 113, 2*w - 11]', '[113, 113, -2*w - 9]', '[137, 137, 3*w - 20]', '[137, 137, -3*w - 17]', '[149, 149, 2*w - 9]', '[149, 149, -2*w - 7]', '[151, 151, -5*w + 41]', '[151, 151, -10*w + 79]', '[157, 157, -w - 14]', '[157, 157, w - 15]', '[169, 13, -13]', '[173, 173, -3*w - 16]', '[173, 173, 3*w - 19]', '[197, 197, 2*w - 5]', '[197, 197, -2*w - 3]', '[199, 199, -6*w + 49]', '[199, 199, -11*w + 87]', '[223, 223, 3*w - 28]', '[223, 223, -3*w - 25]', '[227, 227, 4*w - 27]', '[227, 227, -4*w - 23]', '[229, 229, -15*w + 118]', '[229, 229, -5*w + 42]', '[239, 239, 3*w - 17]', '[239, 239, -3*w - 14]', '[257, 257, 7*w - 52]', '[257, 257, -13*w + 100]', '[269, 269, -3*w - 13]', '[269, 269, 3*w - 16]', '[271, 271, 2*w - 23]', '[271, 271, -2*w - 21]', '[277, 277, -3*w - 26]', '[277, 277, 3*w - 29]', '[281, 281, -11*w + 84]', '[281, 281, 9*w - 68]', '[313, 313, -8*w + 65]', '[313, 313, -13*w + 103]', '[317, 317, -19*w + 147]', '[317, 317, 6*w - 43]', '[347, 347, -3*w - 10]', '[347, 347, 3*w - 13]', '[353, 353, 7*w - 51]', '[353, 353, -18*w + 139]', '[367, 367, -w - 20]', '[367, 367, w - 21]', '[373, 373, 4*w - 37]', '[373, 373, -4*w - 33]', '[379, 379, -9*w + 73]', '[379, 379, -14*w + 111]', '[383, 383, -17*w + 131]', '[383, 383, 8*w - 59]', '[389, 389, 3*w - 11]', '[389, 389, -3*w - 8]', '[401, 401, -5*w - 28]', '[401, 401, 5*w - 33]', '[409, 409, -w - 21]', '[409, 409, w - 22]', '[443, 443, -12*w + 91]', '[443, 443, -13*w + 99]', '[449, 449, -3*w - 4]', '[449, 449, 3*w - 7]', '[461, 461, 5*w - 32]', '[461, 461, -5*w - 27]', '[463, 463, 2*w - 27]', '[463, 463, -2*w - 25]', '[467, 467, 3*w - 5]', '[467, 467, -3*w - 2]', '[479, 479, 3*w - 2]', '[479, 479, 3*w - 1]', '[491, 491, -4*w - 17]', '[491, 491, 4*w - 21]', '[499, 499, -w - 23]', '[499, 499, w - 24]', '[547, 547, -w - 24]', '[547, 547, w - 25]', '[563, 563, 4*w - 19]', '[563, 563, -4*w - 15]', '[571, 571, 2*w - 29]', '[571, 571, -2*w - 27]', '[577, 577, 3*w - 34]', '[577, 577, -3*w - 31]', '[599, 599, -27*w + 209]', '[599, 599, 8*w - 57]', '[613, 613, -12*w + 97]', '[613, 613, -17*w + 135]', '[643, 643, -3*w - 32]', '[643, 643, 3*w - 35]', '[653, 653, 9*w - 65]', '[653, 653, -26*w + 201]', '[683, 683, 4*w - 15]', '[683, 683, -4*w - 11]', '[701, 701, 10*w - 73]', '[701, 701, -25*w + 193]', '[739, 739, 5*w - 48]', '[739, 739, -5*w - 43]', '[743, 743, -24*w + 185]', '[743, 743, 11*w - 81]', '[761, 761, -6*w - 31]', '[761, 761, 6*w - 37]', '[773, 773, -31*w + 240]', '[773, 773, 9*w - 64]', '[787, 787, 6*w - 55]', '[787, 787, -6*w - 49]', '[809, 809, 13*w - 97]', '[809, 809, -22*w + 169]', '[811, 811, 2*w - 33]', '[811, 811, -2*w - 31]', '[827, 827, 4*w - 7]', '[827, 827, -4*w - 3]', '[829, 829, -4*w - 39]', '[829, 829, 4*w - 43]', '[841, 29, -29]', '[853, 853, -3*w - 35]', '[853, 853, 3*w - 38]', '[863, 863, 16*w - 121]', '[863, 863, -19*w + 145]', '[877, 877, -w - 30]', '[877, 877, w - 31]', '[887, 887, 7*w - 45]', '[887, 887, -7*w - 38]', '[911, 911, -5*w - 18]', '[911, 911, 5*w - 23]', '[961, 31, -31]', '[997, 997, 4*w - 45]', '[997, 997, -4*w - 41]']}
-
nf_fields • Show schema
Hide schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-53, -1, 1], 'conductor': 213, 'degree': 2, 'dirichlet_group': [1, 212], 'disc_abs': 213, 'disc_rad': 213, 'disc_sign': 1, 'frobs': [[2, [[2, 1]]], [3, [0]], [5, [[2, 1]]], [7, [[2, 1]]], [11, [[1, 2]]], [13, [[2, 1]]], [17, [[1, 2]]], [19, [[1, 2]]], [23, [[1, 2]]], [29, [[2, 1]]], [31, [[2, 1]]], [37, [[1, 2]]], [41, [[1, 2]]], [43, [[1, 2]]], [47, [[1, 2]]], [53, [[1, 2]]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 14.594519519326424, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.213.1', 'local_algs': ['3.2.1.2', '71.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [3, 71], 'rd': 14.5945195193, 'regulator': {'__RealLiteral__': 0, 'data': '4.29027173584', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 5 a + 34 \\)'], 'used_grh': False, 'zk': ['1', 'a']}