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hmf_forms • Show schema
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{'deg': 3, 'dimension': 1, 'disc': 1300, 'field_bad_primes': [2, 5, 13], 'field_label': '3.3.1300.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.1300.1-14.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [2, 7], 'level_ideal': '[14, 14, -w^2 + 3*w + 4]', 'level_label': '14.1', 'level_norm': 14, 'parallel_weight': 2, 'short_label': '14.1-b', 'weight': '[2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[2, 2, -w - 2]', 1], ['[7, 7, w + 3]', 1]], 'hecke_eigenvalues': [-1, 0, -1, 2, -4, -4, 2, 2, 2, 0, 2, -8, -8, 2, 12, -10, 0, 12, -8, 6, 6, -10, 2, 10, 2, 2, -10, -8, -8, 22, -18, -4, -8, 6, 6, 16, -8, 22, 2, 6, -8, -18, -18, 12, -4, -8, -10, 0, -18, 2, 2, -18, -4, 16, -24, -28, 22, -24, -14, -4, -24, 12, 12, -18, -20, -34, 20, 2, 10, -24, 2, 2, 10, 22, -8, -20, 0, 20, 6, -24, 6, -10, 22, 2, -4, -40, 32, -30, 10, -4, 26, -44, -8, 2, -28, -38, 2, -18, -28, 22, -38, 12, -34, -8, 32, -8, 6, 42, 30, -8, -34, 32, 32, -8, 36, 6, -4, 12, -34, -14, -34, 6, -8, 10, 46, -20, -24, -18, 22, -38, -38, -30, -4, -8, -10, 50, 30, -38, 2, -18, 40, 6, -10, 30, -10, 16, 32, 12, -48, -8, 0, 20, -20, -50, 22, -18, 6, 6, 46, -38, 32, 42, -18, 22, -18, -24], 'hecke_polynomial': 'x', 'label': '3.3.1300.1-14.1-b'}
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hmf_fields • Show schema
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{'degree': 3, 'discriminant': 1300, 'ideals': ['[1, 1, 1]', '[2, 2, -w - 2]', '[4, 2, w^2 - 2*w - 6]', '[5, 5, -w^2 + 2*w + 5]', '[7, 7, w + 3]', '[8, 2, 2]', '[10, 10, w]', '[11, 11, -2*w^2 + 5*w + 9]', '[13, 13, -w^2 + w + 7]', '[13, 13, w - 3]', '[14, 14, -w^2 + 3*w + 4]', '[16, 4, -2*w - 4]', '[17, 17, -w^2 + 2*w + 7]', '[17, 17, -2*w^2 + 5*w + 7]', '[17, 17, -w^2 + 3*w + 3]', '[19, 19, -w + 1]', '[20, 10, w^2 - 2*w - 10]', '[22, 22, -w + 2]', '[25, 5, -w^2 + 5]', '[26, 26, w^2 + w - 4]', '[26, 26, -w^2 + w + 6]', '[27, 3, -3]', '[28, 14, w^2 - 2*w - 8]', '[31, 31, w^2 - 2*w - 9]', '[32, 4, 2*w^2 - 4*w - 12]', '[34, 34, -w - 4]', '[34, 34, -w^2 + w + 4]', '[34, 34, -w^2 + 3*w + 6]', '[35, 35, -w^2 + w + 5]', '[37, 37, w^2 - 7]', '[38, 38, -w^2 - w + 2]', '[40, 10, -2*w^2 + 4*w + 10]', '[41, 41, w^2 - w - 11]', '[44, 22, w^2 - 4]', '[47, 47, w^2 - 3]', '[49, 7, w^2 - 3*w - 1]', '[49, 49, -2*w^2 + 4*w + 9]', '[50, 10, 2*w^2 - 5*w - 10]', '[52, 26, w^2 - 2*w - 2]', '[52, 26, w^2 + 2*w - 2]', '[54, 6, 3*w + 6]', '[55, 55, 2*w^2 - 2*w - 15]', '[56, 14, 2*w + 6]', '[59, 59, w^2 - 4*w + 1]', '[62, 62, 3*w + 8]', '[64, 4, 4]', '[65, 65, 2*w^2 - w - 15]', '[65, 65, -w + 5]', '[67, 67, w^2 - 3*w - 7]', '[68, 34, 3*w^2 - 8*w - 12]', '[68, 34, -w^2 + 8]', '[68, 34, -w^2 + 2*w + 12]', '[70, 70, -2*w^2 + 3*w + 20]', '[71, 71, 4*w + 9]', '[73, 73, -4*w^2 + 8*w + 23]', '[74, 74, -2*w^2 - 3*w + 4]', '[76, 38, -3*w^2 + 6*w + 16]', '[77, 77, 2*w^2 - 3*w - 13]', '[80, 20, 2*w]', '[82, 82, -w^2 + 3*w + 12]', '[83, 83, 2*w^2 - 4*w - 13]', '[85, 85, -w - 5]', '[85, 85, w^2 + w - 5]', '[85, 85, 2*w^2 - 6*w - 5]', '[88, 22, -4*w^2 + 10*w + 18]', '[89, 89, -w^2 + 11]', '[91, 91, w^2 - 9]', '[91, 91, -2*w^2 + 11]', '[94, 94, -2*w^2 - 7*w - 4]', '[95, 95, 3*w^2 - 7*w - 15]', '[97, 97, 2*w^2 - w - 13]', '[98, 14, w^2 - 3*w - 8]', '[98, 98, -w^2 + w + 12]', '[100, 10, w^2 - 10]', '[104, 26, -2*w^2 + 2*w + 14]', '[104, 26, 2*w - 6]', '[108, 6, -3*w^2 + 6*w + 18]', '[109, 109, 2*w^2 - 5*w - 11]', '[110, 110, -4*w^2 + 9*w + 20]', '[112, 28, -2*w^2 + 6*w + 8]', '[118, 118, 2*w^2 - 3*w - 12]', '[119, 119, -w^2 + 3*w + 11]', '[119, 119, 2*w - 1]', '[119, 119, -w^2 + 2*w + 1]', '[121, 11, -3*w^2 + 5*w + 29]', '[121, 121, w^2 - 3*w - 9]', '[124, 62, -w^2 + 14]', '[125, 5, 5]', '[128, 8, -4*w - 8]', '[130, 130, w^2 - 3*w]', '[130, 130, w^2 - 3*w - 10]', '[133, 133, w^2 + 2*w - 3]', '[134, 134, w^2 + 3*w + 4]', '[135, 15, 3*w^2 - 6*w - 15]', '[136, 34, -2*w^2 + 4*w + 14]', '[136, 34, -4*w^2 + 10*w + 14]', '[136, 34, -2*w^2 + 6*w + 6]', '[137, 137, 3*w^2 - 3*w - 23]', '[140, 70, -w^2 + 4*w]', '[142, 142, -3*w^2 + 5*w + 22]', '[143, 143, -2*w - 7]', '[143, 143, 2*w^2 - 6*w - 7]', '[146, 146, w - 6]', '[148, 74, -3*w^2 + 4*w + 22]', '[149, 149, 3*w^2 - 5*w - 19]', '[151, 151, 2*w^2 - 3*w - 11]', '[152, 38, 2*w - 2]', '[154, 154, -w^2 - w + 6]', '[155, 155, 2*w - 5]', '[157, 157, w^2 - 2*w - 13]', '[157, 157, 4*w^2 - 7*w - 27]', '[157, 157, 2*w^2 - 2*w - 13]', '[160, 20, 2*w^2 - 4*w - 20]', '[163, 163, 2*w^2 - 13]', '[164, 82, -5*w^2 + 8*w + 36]', '[166, 166, w + 6]', '[167, 167, w^2 - 4*w - 3]', '[169, 13, -2*w^2 + 3*w + 9]', '[169, 13, w^2 + 3*w - 1]', '[169, 169, -5*w - 11]', '[170, 170, 5*w^2 - 13*w - 20]', '[170, 170, 3*w^2 - 7*w - 10]', '[170, 170, 2*w^2 - 3*w - 10]', '[173, 173, 2*w - 3]', '[173, 173, -5*w^2 + 7*w + 47]', '[173, 173, -2*w^2 + 6*w + 3]', '[175, 35, 2*w^2 - 5*w - 5]', '[176, 44, -2*w + 4]', '[178, 178, 2*w^2 - w - 12]', '[181, 181, w^2 - 4*w - 1]', '[181, 181, -2*w^2 + 3*w + 21]', '[181, 181, 2*w^2 - 2*w - 21]', '[182, 182, -2*w^2 - w + 8]', '[182, 182, 2*w^2 - 5*w - 12]', '[185, 185, 2*w^2 - 4*w - 15]', '[187, 187, -2*w^2 + w + 17]', '[187, 187, -w^2 + w + 13]', '[187, 187, -2*w^2 - 3*w + 3]', '[188, 94, w^2 - 4*w - 2]', '[189, 21, -3*w - 9]', '[190, 190, w^2 - w]', '[193, 193, 3*w^2 - 9*w - 7]', '[194, 194, -3*w^2 - 5*w + 6]', '[196, 14, w^2 + 4*w + 6]', '[196, 98, w^2 - 4*w - 14]', '[197, 197, 5*w^2 - 11*w - 23]', '[200, 10, -2*w^2 + 10]', '[205, 205, 4*w^2 - 7*w - 25]', '[208, 52, 2*w^2 + 2*w - 8]', '[208, 52, -2*w^2 + 2*w + 12]', '[209, 209, 7*w^2 - 16*w - 29]', '[211, 211, w^2 - 4*w - 9]', '[211, 211, -7*w^2 + 16*w + 31]', '[211, 211, -5*w^2 + 10*w + 29]', '[216, 6, -6]', '[217, 217, w^2 - 5*w - 17]', '[218, 218, w^2 + w + 2]', '[220, 110, -w^2 + 2*w]', '[221, 221, 3*w^2 - 6*w - 19]', '[221, 221, -2*w^2 + w + 19]', '[221, 221, 4*w^2 - 8*w - 21]', '[221, 221, -3*w^2 + 2*w + 21]', '[221, 221, -4*w^2 + 10*w + 19]', '[221, 221, -2*w^2 + 4*w + 19]', '[223, 223, 3*w^2 - 5*w - 23]', '[224, 28, 2*w^2 - 4*w - 16]', '[227, 227, w^2 + w - 7]', '[229, 229, 4*w^2 - 11*w - 11]', '[235, 235, -2*w^2 + 4*w + 5]', '[236, 118, -w^2 - 2*w + 4]', '[238, 238, 5*w^2 - 11*w - 22]', '[238, 238, 3*w^2 - 5*w - 28]', '[238, 238, 3*w^2 - 3*w - 22]', '[239, 239, -2*w^2 - 5*w + 1]', '[241, 241, 3*w^2 - 4*w - 21]', '[242, 22, 3*w^2 - 5*w - 18]', '[242, 242, 4*w^2 - 3*w - 32]', '[245, 35, -w^2 + 3*w + 15]', '[245, 245, -2*w^2 - 2*w + 5]', '[247, 247, w^2 - 4*w + 3]', '[247, 247, 2*w^2 - 4*w - 17]', '[248, 62, 2*w^2 - 4*w - 18]', '[250, 10, -5*w - 10]', '[251, 251, 2*w^2 - w - 11]', '[251, 251, 2*w^2 - 2*w - 11]', '[251, 251, w^2 - 3*w + 1]', '[256, 8, 4*w^2 - 8*w - 24]', '[259, 259, 3*w^2 + 3*w - 11]', '[260, 130, w^2 - 4*w - 10]', '[260, 130, 5*w^2 - 4*w - 40]', '[263, 263, -2*w^2 + 5*w + 13]', '[263, 263, w^2 - 4*w - 13]', '[263, 263, w - 7]', '[266, 266, 4*w^2 - 9*w - 14]', '[268, 134, 3*w^2 - 8*w - 8]', '[270, 30, -3*w]', '[271, 271, 5*w + 9]', '[272, 68, -2*w - 8]', '[272, 68, -2*w^2 + 2*w + 8]', '[272, 68, -2*w^2 + 6*w + 12]', '[274, 274, -3*w^2 - w + 16]', '[275, 55, w^2 - 15]', '[280, 70, -2*w^2 + 2*w + 10]', '[281, 281, -2*w^2 - 6*w - 1]', '[283, 283, -w - 7]', '[283, 283, -5*w^2 + 10*w + 27]', '[283, 283, -2*w^2 - w + 7]', '[284, 142, w^2 - 2*w - 14]', '[286, 286, -3*w^2 + 5*w + 24]', '[286, 286, 4*w^2 - 11*w - 16]', '[287, 287, 2*w^2 - 4*w - 23]', '[289, 17, 2*w^2 + w - 11]', '[289, 17, -w^2 + 4*w + 11]', '[289, 17, w^2 - 5*w - 19]', '[289, 289, -2*w + 9]', '[289, 289, -2*w^2 + 9]', '[289, 289, -2*w^2 + 2*w + 9]', '[292, 146, -w^2 + 4*w + 12]', '[293, 293, -w^2 + 4*w + 17]', '[295, 295, -3*w^2 + 2*w + 25]', '[296, 74, 2*w^2 - 14]', '[297, 33, 6*w^2 - 15*w - 27]', '[298, 298, -w^2 - w + 8]', '[302, 302, -w^2 - 3*w + 2]', '[304, 76, -2*w^2 - 2*w + 4]', '[307, 307, 3*w^2 - 5*w - 27]', '[308, 154, -5*w^2 + 12*w + 18]', '[310, 310, -2*w^2 + w + 10]', '[314, 314, 7*w + 16]', '[314, 314, -w^2 + w + 14]', '[314, 314, -2*w^2 - 3*w + 6]', '[317, 317, 3*w^2 - 7*w - 17]', '[320, 20, -4*w^2 + 8*w + 20]', '[323, 323, 7*w^2 - 18*w - 27]', '[323, 323, 3*w^2 - 5*w - 17]', '[323, 323, 4*w^2 - 10*w - 13]', '[325, 65, -2*w^2 + 5*w + 25]', '[325, 65, 3*w^2 - 5*w - 25]', '[326, 326, 4*w^2 + 7*w - 6]', '[328, 82, 2*w^2 - 2*w - 22]', '[329, 329, 3*w^2 + 7*w + 1]', '[331, 331, -w^2 + w - 1]', '[332, 166, 3*w^2 - 10*w - 2]', '[334, 334, 2*w^2 + w - 4]', '[335, 335, -4*w^2 + 11*w + 15]', '[338, 26, -2*w^2 + 3*w + 22]', '[338, 26, -2*w^2 + 7*w + 2]', '[338, 338, -3*w^2 + 5*w + 12]', '[340, 170, -3*w^2 + 6*w + 20]', '[340, 170, -3*w^2 + 4*w + 20]', '[340, 170, 3*w^2 - 4*w - 30]', '[341, 341, -3*w^2 + 7*w + 9]', '[343, 7, 7]', '[343, 343, -2*w^2 + w + 7]', '[346, 346, -2*w^2 + 5*w + 14]', '[346, 346, -2*w^2 - w + 6]', '[346, 346, w^2 + w - 14]', '[349, 349, 2*w^2 - w - 9]', '[350, 70, w^2 - 5*w - 10]', '[351, 39, 3*w^2 - 3*w - 21]', '[351, 39, -3*w + 9]', '[352, 44, 2*w^2 - 8]', '[353, 353, -5*w^2 + 9*w + 33]', '[355, 355, -w^2 - 2*w + 5]', '[356, 178, -3*w^2 - 6*w + 4]', '[359, 359, 3*w - 1]', '[361, 19, w^2 + w - 9]', '[361, 361, -w^2 + 2*w - 1]', '[362, 362, 2*w^2 - w - 8]', '[362, 362, w^2 - 7*w - 22]', '[362, 362, -2*w^2 + 5*w + 22]', '[364, 182, 3*w^2 - 8*w - 16]', '[364, 182, 3*w^2 - 2*w - 26]', '[365, 365, -4*w^2 + 6*w + 35]', '[370, 370, 3*w + 10]', '[374, 374, 3*w^2 + w - 14]', '[374, 374, -4*w^2 + 7*w + 24]', '[374, 374, w^2 - 5*w - 16]', '[376, 94, 2*w^2 - 6]', '[378, 42, 3*w^2 - 9*w - 12]', '[379, 379, 4*w^2 - 8*w - 19]', '[380, 190, -3*w^2 + 2*w + 20]', '[383, 383, 2*w^2 - 7]', '[385, 385, -3*w^2 + 9*w + 5]', '[386, 386, 3*w^2 - 5*w - 16]', '[388, 194, -3*w^2 + 2*w + 28]', '[392, 14, 2*w^2 - 6*w - 2]', '[392, 98, -4*w^2 + 8*w + 18]', '[394, 394, w^2 - 5*w - 4]', '[397, 397, 3*w^2 - 2*w - 27]', '[400, 20, 4*w^2 - 10*w - 20]', '[401, 401, 8*w^2 - 18*w - 39]', '[403, 403, -5*w^2 + 7*w + 37]', '[403, 403, 4*w^2 - 3*w - 33]', '[407, 407, 3*w^2 - 5*w - 13]', '[409, 409, -4*w^2 + 3*w + 29]', '[410, 410, -w^2 - w + 10]', '[413, 413, -w^2 - w + 13]', '[415, 415, -5*w^2 + 14*w + 15]', '[416, 52, 2*w^2 - 4*w - 4]', '[416, 52, 2*w^2 + 4*w - 4]', '[418, 418, -w^2 + 3*w - 2]', '[421, 421, w^2 - 6*w - 19]', '[422, 422, 2*w^2 + 7*w + 8]', '[422, 422, -2*w^2 + 7*w + 8]', '[422, 422, w - 8]', '[425, 85, -2*w^2 + 15]', '[425, 85, 3*w^2 - 5*w - 15]', '[425, 85, 2*w^2 - 5*w - 15]', '[431, 431, -2*w^2 - 2*w + 9]', '[432, 12, 6*w + 12]', '[434, 434, -3*w^2 + 5*w + 14]', '[436, 218, 7*w^2 - 18*w - 24]', '[439, 439, w^2 + w - 11]', '[439, 439, w^2 - 5*w - 11]', '[439, 439, 3*w^2 - 4*w - 19]', '[440, 110, 4*w^2 - 4*w - 30]', '[442, 442, w + 8]', '[442, 442, -w^2 - w + 12]', '[442, 442, 6*w^2 - 13*w - 28]', '[442, 442, 3*w^2 - w - 18]', '[442, 442, -3*w + 2]', '[442, 442, 4*w^2 - 9*w - 22]', '[443, 443, 4*w^2 - 6*w - 27]', '[443, 443, 5*w^2 - 14*w - 13]', '[443, 443, w^2 - 5*w + 3]', '[445, 445, -5*w^2 + 2*w + 35]', '[446, 446, -w^2 + 3*w + 16]', '[448, 28, 4*w + 12]', '[449, 449, -2*w - 9]', '[451, 451, 6*w^2 - 14*w - 29]', '[454, 454, -3*w^2 - 5*w + 4]', '[455, 455, 4*w^2 - 8*w - 25]', '[455, 455, -w^2 + 2*w + 15]', '[457, 457, -7*w^2 + 15*w + 37]', '[458, 458, 3*w^2 - 7*w - 18]', '[459, 51, 3*w^2 - 6*w - 21]', '[459, 51, 6*w^2 - 15*w - 21]', '[459, 51, 3*w^2 - 9*w - 9]', '[461, 461, -w^2 - 2*w + 21]', '[463, 463, w^2 + 3*w - 3]', '[469, 469, -6*w - 11]', '[470, 470, 7*w + 10]', '[472, 118, 2*w^2 - 8*w + 2]', '[475, 95, w^2 - 5*w - 15]', '[476, 238, w^2 - 16]', '[476, 238, -5*w^2 + 10*w + 26]', '[476, 238, -7*w^2 + 16*w + 34]', '[478, 478, -3*w + 8]', '[479, 479, 2*w^2 - 5*w - 21]', '[481, 481, -3*w^2 + 3*w + 31]', '[481, 481, 4*w^2 - 7*w - 39]', '[482, 482, -2*w^2 - w + 12]', '[484, 22, -w^2 - 2*w + 6]', '[484, 242, w^2 - 4*w + 4]', '[485, 485, w^2 - w - 15]', '[487, 487, 2*w^2 - 7*w - 3]', '[490, 70, -3*w^2 + 9*w + 10]', '[490, 490, -5*w^2 + 9*w + 30]', '[494, 494, 2*w^2 - 5*w - 16]', '[494, 494, 5*w + 14]', '[496, 124, 6*w + 16]', '[497, 497, w^2 - 5*w - 3]', '[499, 499, -w^2 - 5*w - 9]', '[500, 10, 5*w^2 - 10*w - 30]', '[502, 502, -3*w^2 - 7*w + 2]', '[502, 502, w^2 - 5*w - 12]', '[502, 502, -2*w^2 - 5*w + 2]', '[509, 509, -4*w^2 + 5*w + 29]', '[511, 511, -4*w^2 + 7*w + 29]', '[512, 8, 8]', '[513, 57, -3*w + 3]', '[517, 517, -5*w^2 + 15*w + 23]', '[518, 518, w^2 - w + 2]', '[520, 130, 4*w^2 - 2*w - 30]', '[520, 130, -2*w + 10]', '[523, 523, -2*w^2 + 27]', '[523, 523, -8*w^2 + 14*w + 53]', '[523, 523, -4*w + 13]', '[526, 526, -w^2 - 3*w - 6]', '[526, 526, -6*w^2 + 13*w + 26]', '[526, 526, -w^2 + 5*w + 14]', '[527, 527, 2*w^2 - 2*w - 23]', '[527, 527, -4*w^2 + 7*w + 23]', '[527, 527, -5*w^2 + 11*w + 27]', '[532, 266, -3*w^2 + 4*w + 18]', '[533, 533, 7*w^2 - 8*w - 57]', '[533, 533, -4*w^2 + 2*w + 43]', '[536, 134, 2*w^2 - 6*w - 14]', '[539, 77, -w^2 - 4*w + 1]', '[539, 539, 3*w^2 - 2*w - 19]', '[540, 30, -3*w^2 + 6*w + 30]', '[541, 541, 2*w^2 - 7*w + 1]', '[542, 542, -6*w^2 + 13*w + 32]', '[544, 68, 6*w^2 - 16*w - 24]', '[544, 68, -2*w^2 + 16]', '[544, 68, -2*w^2 + 4*w + 24]', '[545, 545, -9*w^2 + 23*w + 35]', '[547, 547, -6*w^2 + 9*w + 43]', '[547, 547, 2*w^2 - 5*w - 17]', '[547, 547, 2*w^2 - 3*w - 23]', '[548, 274, -5*w^2 + 4*w + 48]', '[550, 110, -2*w^2 + 5*w + 20]', '[557, 557, 3*w - 7]', '[560, 140, -4*w^2 + 6*w + 40]', '[562, 562, w^2 - 5*w + 2]', '[566, 566, w^2 + 9*w + 14]', '[566, 566, 3*w - 4]', '[566, 566, -6*w^2 + 11*w + 36]', '[568, 142, 8*w + 18]', '[571, 571, 3*w^2 - 4*w - 31]', '[571, 571, w^2 + 6*w + 11]', '[571, 571, 3*w^2 + 2*w - 11]', '[572, 286, -3*w^2 + 6*w + 22]', '[572, 286, w^2 - 4*w - 18]', '[574, 574, 2*w^2 - 7*w - 4]', '[577, 577, -2*w^2 - 3*w + 7]', '[578, 34, -5*w^2 + 3*w + 38]', '[578, 34, 3*w^2 - 7*w - 8]', '[578, 34, w^2 - 5*w - 2]', '[578, 578, 2*w^2 - 5*w - 18]', '[578, 578, 6*w^2 - 15*w - 28]', '[578, 578, -3*w^2 + 5*w + 32]', '[581, 581, 2*w^2 - 5*w - 19]', '[584, 146, -8*w^2 + 16*w + 46]', '[586, 586, -3*w^2 + w + 36]', '[587, 587, -5*w + 17]', '[589, 589, 3*w^2 - 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6]', '[1925, 385, 3*w^2 - 5*w - 35]', '[1927, 1927, 4*w^2 - 3*w - 23]', '[1928, 482, 6*w^2 - 8*w - 42]', '[1930, 1930, -9*w^2 + 23*w + 30]', '[1931, 1931, 5*w^2 - 9*w - 39]', '[1934, 1934, -3*w^2 - 11*w - 4]', '[1936, 44, 6*w^2 - 10*w - 36]', '[1936, 484, 8*w^2 - 6*w - 64]', '[1937, 1937, -14*w^2 + 26*w + 87]', '[1937, 1937, 5*w^2 - 4*w - 53]', '[1940, 970, -11*w^2 + 6*w + 80]', '[1942, 1942, -3*w^2 + 9*w + 2]', '[1942, 1942, -6*w^2 + 11*w + 42]', '[1942, 1942, 2*w^2 + 15*w + 22]', '[1948, 974, -3*w^2 - 10*w - 2]', '[1949, 1949, -w^2 - 9*w - 19]', '[1949, 1949, 5*w^2 - 10*w - 51]', '[1949, 1949, 2*w^2 + 3*w - 11]', '[1951, 1951, -4*w^2 - 7*w + 9]', '[1951, 1951, -w^2 - 3*w + 19]', '[1951, 1951, 4*w^2 - 10*w - 9]', '[1954, 1954, 5*w^2 - 5*w - 34]', '[1958, 1958, -3*w^2 + 11*w + 12]', '[1960, 70, -2*w^2 + 6*w + 30]', '[1960, 490, -4*w^2 - 4*w + 10]', '[1963, 1963, 2*w^2 - 2*w - 27]', '[1963, 1963, -9*w^2 + 18*w + 53]', '[1966, 1966, -w^2 + 9*w + 24]', '[1967, 1967, -5*w^2 + 15*w + 27]', '[1970, 1970, -11*w^2 + 27*w + 50]', '[1971, 219, -12*w^2 + 24*w + 69]', '[1973, 1973, -7*w^2 + 14*w + 43]', '[1973, 1973, 5*w - 3]', '[1973, 1973, -4*w^2 - w + 17]', '[1976, 494, 2*w^2 - 8*w + 6]', '[1976, 494, 4*w^2 - 8*w - 34]', '[1979, 1979, -4*w^2 + 19]', '[1979, 1979, -13*w^2 + 27*w + 71]', '[1979, 1979, 2*w^2 + 7*w - 1]', '[1981, 1981, -w^2 - 10*w - 21]', '[1981, 1981, 6*w^2 - 14*w - 19]', '[1981, 1981, -5*w^2 + 7*w + 31]', '[1984, 124, 4*w^2 - 8*w - 36]', '[1985, 1985, 8*w^2 - 14*w - 55]', '[1987, 1987, 4*w^2 - 4*w - 43]', '[1988, 994, w^2 - 10*w - 32]', '[1991, 1991, 10*w^2 - 23*w - 49]', '[1991, 1991, -5*w^2 + 12*w + 29]', '[1991, 1991, 2*w^2 + 7*w + 11]', '[1996, 998, -3*w^2 + 8*w + 24]', '[1997, 1997, -5*w^2 + 14*w + 27]', '[1998, 222, -6*w^2 - 9*w + 12]', '[2000, 20, -10*w - 20]', '[2002, 2002, 2*w^2 - w - 28]', '[2002, 2002, -4*w^2 + 9*w + 42]', '[2005, 2005, 4*w^2 - 8*w - 35]', '[2006, 2006, -11*w^2 + 25*w + 54]', '[2006, 2006, -17*w^2 + 39*w + 76]', '[2006, 2006, 5*w - 14]', '[2008, 502, 4*w^2 - 2*w - 22]', '[2008, 502, 4*w^2 - 4*w - 22]', '[2008, 502, 2*w^2 - 6*w + 2]', '[2009, 287, w^2 + 4*w - 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10*w + 8]', '[9809, 9809, -2*w^2 + 2*w - 9]', '[9809, 9809, -3*w^2 + 14*w + 9]', '[9809, 9809, -7*w^2 + 3*w + 39]', '[9812, 4906, -5*w^2 + 42]', '[9815, 9815, 13*w^2 - 24*w - 75]', '[9815, 9815, -9*w^2 + 16*w + 85]', '[9817, 9817, -3*w^2 + 5*w - 3]', '[9818, 9818, -w^2 - 19*w - 28]', '[9823, 9823, 11*w^2 - 31*w - 37]', '[9824, 1228, -10*w^2 + 8*w + 104]', '[9826, 34, -17*w - 34]', '[9826, 578, -15*w^2 + 35*w + 74]', '[9826, 578, -11*w^2 + 21*w + 56]', '[9826, 578, 6*w^2 - 7*w - 66]', '[9826, 578, 8*w^2 + 11*w - 16]', '[9826, 578, 6*w^2 + 3*w - 16]', '[9826, 578, 4*w^2 + w - 44]', '[9826, 9826, 5*w - 26]', '[9826, 9826, 10*w^2 - 7*w - 84]', '[9826, 9826, 2*w^2 - w - 36]', '[9827, 9827, 3*w - 23]', '[9828, 546, -9*w^2 + 24*w + 48]', '[9828, 546, -9*w^2 + 6*w + 78]', '[9830, 9830, -w^2 - 7*w + 10]', '[9832, 2458, 12*w^2 - 24*w - 58]', '[9833, 9833, 11*w^2 - 17*w - 93]', '[9835, 9835, 11*w^2 - 6*w - 75]', '[9836, 4918, 5*w^2 - 20*w + 4]', '[9838, 9838, -17*w - 28]', '[9839, 9839, -18*w^2 + 37*w + 101]', '[9841, 9841, -8*w^2 - 9*w + 21]', '[9841, 9841, -9*w^2 + w + 51]', '[9841, 9841, 7*w^2 - 6*w - 41]', '[9841, 9841, 4*w^2 + w - 39]', '[9841, 9841, 4*w^2 - 16*w - 1]', '[9841, 9841, 6*w^2 - 17*w - 39]', '[9842, 9842, 2*w^2 - 13*w - 8]', '[9848, 2462, -2*w - 22]', '[9848, 2462, 4*w^2 - 20*w + 18]', '[9848, 2462, -6*w^2 - 18*w - 2]', '[9850, 1970, -w^2 + 15*w + 30]', '[9851, 9851, -11*w^2 + 22*w + 69]', '[9851, 9851, 4*w^2 - 7*w - 51]', '[9851, 9851, 12*w^2 - 14*w - 91]', '[9853, 9853, 9*w^2 - 4*w - 57]', '[9854, 9854, -3*w^2 + 13*w + 36]', '[9854, 9854, -5*w^2 + 13*w + 6]', '[9855, 1095, -12*w^2 + 18*w + 105]', '[9856, 616, -4*w^2 - 4*w + 24]', '[9857, 9857, 3*w^2 - 13*w - 37]', '[9857, 9857, 7*w^2 + 5*w - 23]', '[9857, 9857, 13*w^2 - 38*w - 33]', '[9859, 9859, 6*w^2 + 2*w - 19]', '[9863, 9863, -18*w - 47]', '[9865, 9865, 13*w^2 - 31*w - 65]', '[9865, 9865, -7*w^2 + 16*w + 75]', '[9865, 9865, w^2 - w + 15]', '[9866, 9866, -8*w^2 - 15*w + 14]', '[9872, 2468, -8*w^2 - 14*w + 8]', '[9877, 9877, 3*w^2 - 3*w - 43]', '[9877, 9877, -13*w^2 + 30*w + 67]', '[9877, 9877, -10*w^2 + 18*w + 53]', '[9878, 9878, 2*w^2 + 5*w - 18]', '[9880, 2470, -6*w^2 + 12*w + 70]', '[9880, 2470, -2*w^2 + 12*w - 10]', '[9881, 9881, 5*w^2 - 14*w - 39]', '[9883, 9883, -9*w^2 + 15*w + 37]', '[9883, 9883, 4*w^2 - 15*w - 33]', '[9883, 9883, 7*w + 27]', '[9884, 4942, 7*w^2 - 22*w - 24]', '[9887, 9887, 6*w^2 - 23]', '[9893, 9893, 19*w^2 - 40*w - 103]', '[9893, 9893, -2*w^2 + 37]', '[9895, 9895, 5*w^2 - 17*w - 35]', '[9895, 9895, -11*w^2 + 17*w + 95]', '[9895, 9895, w^2 - 2*w + 15]', '[9896, 2474, 6*w^2 - 8*w - 66]', '[9901, 9901, -2*w^2 + 9*w + 41]', '[9902, 9902, 2*w^2 + 21*w + 32]', '[9904, 2476, -4*w^2 - 2*w - 4]', '[9905, 9905, 6*w^2 - 2*w - 25]', '[9905, 9905, 8*w^2 - 23*w - 15]', '[9905, 9905, 15*w^2 - 13*w - 125]', '[9908, 4954, 11*w^2 - 12*w - 82]', '[9916, 4958, -w^2 - 6*w + 24]', '[9917, 9917, 6*w^2 - 20*w - 13]', '[9917, 9917, -7*w^2 + 25*w + 3]', '[9917, 9917, 3*w^2 - 5*w - 43]', '[9919, 9919, 4*w^2 + 5*w - 21]', '[9919, 9919, -9*w^2 + 15*w + 49]', '[9920, 620, 8*w - 20]', '[9922, 902, -7*w^2 + 19*w + 42]', '[9922, 9922, -33*w^2 + 35*w + 282]', '[9925, 1985, 12*w^2 - 20*w - 115]', '[9926, 9926, 6*w^2 + w - 16]', '[9928, 2482, -26*w^2 + 66*w + 102]', '[9928, 2482, 6*w^2 - 2*w - 58]', '[9928, 2482, 8*w^2 - 10*w - 82]', '[9929, 9929, 15*w^2 - 32*w - 69]', '[9929, 9929, 2*w^2 - 14*w - 31]', '[9929, 9929, 11*w^2 - 8*w - 91]', '[9935, 9935, 15*w^2 - 26*w - 95]', '[9937, 9937, -2*w^2 - 7*w + 47]', '[9937, 9937, -8*w^2 - 18*w + 7]', '[9937, 9937, -4*w^2 + 17*w - 13]', '[9940, 4970, 7*w^2 - 4*w - 40]', '[9941, 9941, 13*w^2 - 19*w - 109]', '[9941, 9941, -5*w^2 - w + 71]', '[9941, 9941, 6*w^2 + w - 21]', '[9946, 9946, -9*w^2 - w + 54]', '[9955, 9955, -28*w^2 + 32*w + 235]', '[9955, 9955, -7*w^2 + 7*w + 25]', '[9955, 9955, 26*w^2 - 27*w - 215]', '[9958, 9958, -w^2 - 7*w - 22]', '[9958, 9958, 5*w^2 + 33*w + 48]', '[9961, 9961, 2*w^2 - 28*w - 81]', '[9962, 9962, 18*w^2 - 25*w - 162]', '[9962, 9962, 16*w^2 - 17*w - 128]', '[9962, 9962, 14*w^2 - 29*w - 68]', '[9967, 9967, 10*w^2 - 17*w - 77]', '[9967, 9967, 6*w^2 - 2*w - 57]', '[9967, 9967, 7*w^2 - 14*w - 57]', '[9968, 2492, 10*w^2 + 10*w - 32]', '[9971, 767, -2*w^2 + 7*w - 11]', '[9971, 767, -25*w^2 + 57*w + 119]', '[9971, 9971, 9*w^2 - 11*w - 61]', '[9973, 9973, -w^2 + 10*w + 37]', '[9974, 9974, 5*w^2 + 19*w + 24]', '[9979, 9979, 22*w^2 - 52*w - 101]', '[9979, 9979, 12*w^2 - 18*w - 101]', '[9979, 9979, 15*w^2 - 16*w - 119]', '[9980, 4990, 7*w^2 - 22*w - 20]', '[9983, 9983, 5*w^2 - 18*w - 7]', '[9985, 9985, 26*w^2 - 66*w - 105]', '[9988, 4994, -w^2 + 16*w + 38]', '[9990, 1110, 9*w + 30]', '[9994, 9994, -2*w^2 - 13*w - 4]', '[9994, 9994, -6*w^2 + w + 24]', '[9994, 9994, -9*w^2 - 25*w - 4]', '[9997, 9997, 5*w^2 - 15*w - 37]', '[9997, 9997, 14*w^2 - 35*w - 47]', '[9998, 9998, -2*w^2 + 15*w + 52]', '[10000, 100, 10*w]'], 'label': '3.3.1300.1', 'narrow_class_no': 1, 'primes': ['[2, 2, -w - 2]', '[5, 5, -w^2 + 2*w + 5]', '[7, 7, w + 3]', '[11, 11, -2*w^2 + 5*w + 9]', '[13, 13, -w^2 + w + 7]', '[13, 13, w - 3]', '[17, 17, -w^2 + 2*w + 7]', '[17, 17, -2*w^2 + 5*w + 7]', '[17, 17, -w^2 + 3*w + 3]', '[19, 19, -w + 1]', '[27, 3, -3]', '[31, 31, w^2 - 2*w - 9]', '[37, 37, w^2 - 7]', '[41, 41, w^2 - w - 11]', '[47, 47, w^2 - 3]', '[49, 7, w^2 - 3*w - 1]', '[59, 59, w^2 - 4*w + 1]', '[67, 67, w^2 - 3*w - 7]', '[71, 71, 4*w + 9]', '[73, 73, -4*w^2 + 8*w + 23]', '[83, 83, 2*w^2 - 4*w - 13]', '[89, 89, -w^2 + 11]', '[97, 97, 2*w^2 - w - 13]', '[109, 109, 2*w^2 - 5*w - 11]', '[121, 11, -3*w^2 + 5*w + 29]', '[137, 137, 3*w^2 - 3*w - 23]', '[149, 149, 3*w^2 - 5*w - 19]', '[151, 151, 2*w^2 - 3*w - 11]', '[157, 157, w^2 - 2*w - 13]', '[157, 157, 4*w^2 - 7*w - 27]', '[157, 157, 2*w^2 - 2*w - 13]', '[163, 163, 2*w^2 - 13]', '[167, 167, w^2 - 4*w - 3]', '[173, 173, 2*w - 3]', '[173, 173, -5*w^2 + 7*w + 47]', '[173, 173, -2*w^2 + 6*w + 3]', '[181, 181, w^2 - 4*w - 1]', '[181, 181, -2*w^2 + 3*w + 21]', '[181, 181, 2*w^2 - 2*w - 21]', '[193, 193, 3*w^2 - 9*w - 7]', '[197, 197, 5*w^2 - 11*w - 23]', '[211, 211, w^2 - 4*w - 9]', '[211, 211, -7*w^2 + 16*w + 31]', '[211, 211, -5*w^2 + 10*w + 29]', '[223, 223, 3*w^2 - 5*w - 23]', '[227, 227, w^2 + w - 7]', '[229, 229, 4*w^2 - 11*w - 11]', '[239, 239, -2*w^2 - 5*w + 1]', '[241, 241, 3*w^2 - 4*w - 21]', '[251, 251, 2*w^2 - w - 11]', '[251, 251, 2*w^2 - 2*w - 11]', '[251, 251, w^2 - 3*w + 1]', '[263, 263, -2*w^2 + 5*w + 13]', '[263, 263, w^2 - 4*w - 13]', '[263, 263, w - 7]', '[271, 271, 5*w + 9]', '[281, 281, -2*w^2 - 6*w - 1]', '[283, 283, -w - 7]', '[283, 283, -5*w^2 + 10*w + 27]', '[283, 283, -2*w^2 - w + 7]', '[293, 293, -w^2 + 4*w + 17]', '[307, 307, 3*w^2 - 5*w - 27]', '[317, 317, 3*w^2 - 7*w - 17]', '[331, 331, -w^2 + w - 1]', '[349, 349, 2*w^2 - w - 9]', '[353, 353, -5*w^2 + 9*w + 33]', '[359, 359, 3*w - 1]', '[361, 19, w^2 + w - 9]', '[379, 379, 4*w^2 - 8*w - 19]', '[383, 383, 2*w^2 - 7]', '[397, 397, 3*w^2 - 2*w - 27]', '[401, 401, 8*w^2 - 18*w - 39]', '[409, 409, -4*w^2 + 3*w + 29]', '[421, 421, w^2 - 6*w - 19]', '[431, 431, -2*w^2 - 2*w + 9]', '[439, 439, w^2 + w - 11]', '[439, 439, w^2 - 5*w - 11]', '[439, 439, 3*w^2 - 4*w - 19]', '[443, 443, 4*w^2 - 6*w - 27]', '[443, 443, 5*w^2 - 14*w - 13]', '[443, 443, w^2 - 5*w + 3]', '[449, 449, -2*w - 9]', '[457, 457, -7*w^2 + 15*w + 37]', '[461, 461, -w^2 - 2*w + 21]', '[463, 463, w^2 + 3*w - 3]', '[479, 479, 2*w^2 - 5*w - 21]', '[487, 487, 2*w^2 - 7*w - 3]', '[499, 499, -w^2 - 5*w - 9]', '[509, 509, -4*w^2 + 5*w + 29]', '[523, 523, -2*w^2 + 27]', '[523, 523, -8*w^2 + 14*w + 53]', '[523, 523, -4*w + 13]', '[541, 541, 2*w^2 - 7*w + 1]', '[547, 547, -6*w^2 + 9*w + 43]', '[547, 547, 2*w^2 - 5*w - 17]', '[547, 547, 2*w^2 - 3*w - 23]', '[557, 557, 3*w - 7]', '[571, 571, 3*w^2 - 4*w - 31]', '[571, 571, w^2 + 6*w + 11]', '[571, 571, 3*w^2 + 2*w - 11]', '[577, 577, -2*w^2 - 3*w + 7]', '[587, 587, -5*w + 17]', '[593, 593, -2*w^2 + 23]', '[607, 607, -w^2 + 7*w - 13]', '[607, 607, -w^2 - 7*w - 13]', '[607, 607, -w^2 - 3]', '[613, 613, 3*w^2 - 4*w - 17]', '[617, 617, w^2 + 2*w - 7]', '[619, 619, -4*w^2 + 10*w + 21]', '[631, 631, w^2 - 5*w - 1]', '[643, 643, -3*w^2 + w + 17]', '[647, 647, 3*w^2 + w - 13]', '[647, 647, -9*w^2 + 12*w + 83]', '[647, 647, 2*w^2 - 17]', '[653, 653, -4*w^2 + 9*w + 23]', '[653, 653, -6*w^2 + 17*w + 17]', '[653, 653, -3*w^2 + w + 33]', '[661, 661, -6*w^2 + 11*w + 39]', '[673, 673, 3*w^2 - 6*w - 23]', '[673, 673, w^2 - 5*w + 7]', '[673, 673, w^2 + 9*w + 13]', '[683, 683, 2*w^2 + w - 13]', '[691, 691, 3*w^2 - 6*w - 29]', '[709, 709, -w^2 + 7*w + 21]', '[733, 733, w^2 - 17]', '[739, 739, -5*w^2 + 9*w + 29]', '[743, 743, 7*w + 13]', '[757, 757, -3*w + 13]', '[757, 757, 4*w + 13]', '[757, 757, -w^2 + w - 3]', '[761, 761, -4*w^2 + 7*w + 21]', '[769, 769, -2*w^2 + 8*w + 9]', '[773, 773, -4*w^2 + 7*w + 17]', '[787, 787, -w^2 + 2*w - 3]', '[809, 809, -5*w^2 + 10*w + 31]', '[809, 809, -2*w^2 - 7*w - 9]', '[809, 809, 4*w^2 - 7*w - 31]', '[811, 811, 2*w - 11]', '[821, 821, 3*w^2 - 3*w - 11]', '[827, 827, 7*w^2 - 15*w - 33]', '[839, 839, 2*w^2 - 8*w + 1]', '[853, 853, -9*w^2 + 16*w + 57]', '[859, 859, -5*w + 19]', '[859, 859, -w^2 + 7*w - 11]', '[859, 859, 4*w^2 - 7*w - 19]', '[863, 863, -4*w^2 + 5*w + 27]', '[877, 877, -4*w^2 + 8*w + 27]', '[887, 887, 2*w^2 - 6*w - 17]', '[887, 887, 3*w^2 + 4*w - 3]', '[887, 887, -3*w^2 + 37]', '[919, 919, -2*w^2 - 6*w + 1]', '[919, 919, -w^2 + 4*w + 19]', '[919, 919, 4*w^2 - 8*w - 41]', '[929, 929, 3*w^2 - 7*w - 21]', '[941, 941, 9*w^2 - 20*w - 41]', '[947, 947, -3*w^2 + 5*w + 33]', '[953, 953, w^2 - 2*w - 17]', '[953, 953, 7*w^2 - 18*w - 23]', '[953, 953, -6*w - 17]', '[961, 31, -3*w^2 + 8*w + 19]', '[967, 967, 3*w^2 - 3*w - 13]', '[971, 971, -2*w^2 - 8*w - 11]', '[971, 971, -2*w^2 + 10*w - 11]', '[971, 971, -2*w - 11]', '[977, 977, -2*w^2 - w + 27]', '[983, 983, w^2 - w - 17]']}
-
nf_fields • Show schema
Hide schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-10, -10, 0, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 1300, 'disc_rad': 130, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[3, 1]]], [5, [0]], [7, [[2, 1], [1, 1]]], [11, [[2, 1], [1, 1]]], [13, [0]], [17, [[1, 3]]], [19, [[2, 1], [1, 1]]], [23, [[3, 1]]], [29, [[3, 1]]], [31, [[2, 1], [1, 1]]], [37, [[2, 1], [1, 1]]], [41, [[2, 1], [1, 1]]], [43, [[3, 1]]], [47, [[2, 1], [1, 1]]], [53, [[3, 1]]], [59, [[2, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 4, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 16.735486539211966, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.1300.1', 'local_algs': ['2.3.2.1', '5.3.2.1', '13.1.0.1', '13.2.1.1'], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 5, 13], 'rd': 10.9139288306, 'regulator': {'__RealLiteral__': 0, 'data': '6.55000546582', 'prec': 44}, 'res': {'gal': ['1,-3,-4,13,-4,-3,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 1 \\)', '\\( a^{2} + 2 a - 1 \\)'], 'unitsGmodule': [[1, 1], [4, 2]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}