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hmf_forms • Show schema
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{'deg': 3, 'dimension': 1, 'disc': 1076, 'field_bad_primes': [2, 269], 'field_label': '3.3.1076.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.1076.1-16.1-e', 'label_nsuffix': 4, 'label_suffix': 'e', 'level_bad_primes': [2], 'level_ideal': '[16, 4, -2*w - 4]', 'level_label': '16.1', 'level_norm': 16, 'parallel_weight': 2, 'short_label': '16.1-e', 'weight': '[2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[2, 2, -w - 2]', -1]], 'hecke_eigenvalues': [0, 0, 0, -4, -4, 2, -4, -4, -4, -4, 8, -4, -4, 0, 6, 6, 10, 0, 16, 8, 16, 12, 0, 12, -4, -2, -4, 0, 0, -6, 16, -6, -4, -20, -20, 16, 0, 0, 12, 12, 6, 16, -4, -22, -4, 12, -26, -4, 28, -20, -30, 12, -16, -20, 6, -12, 16, -16, -20, 10, 6, -22, 20, 28, -4, 0, -4, -28, 32, 32, 28, 20, 28, -12, -8, -38, 16, -6, 16, 0, -4, -4, 10, -8, -12, 28, 12, 22, 28, 16, 28, 0, -36, -16, 12, 22, -16, 30, 16, 32, -12, 12, 42, -32, -2, -20, 24, -20, 8, -48, -16, -4, -2, 12, 32, 0, -16, 36, 22, -34, 10, 28, 0, 18, -26, 24, -20, 12, 48, 48, 0, 22, 28, -4, 42, 12, -16, -48, 12, 12, -38, -52, -36, -6, -8, 16, 32, -52, -24, -20, -38, 44, 30, 48, -32, 48, 0, 12, 16, -32, 32, 32, -36, 12, 14, 16, -6, -2, 48, 28, 44, -18, -32], 'hecke_polynomial': 'x', 'label': '3.3.1076.1-16.1-e'}
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hmf_fields • Show schema
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{'degree': 3, 'discriminant': 1076, 'ideals': ['[1, 1, 1]', '[2, 2, -w - 2]', '[3, 3, -w^2 + 2*w + 3]', '[4, 2, w^2 - 2*w - 4]', '[6, 6, w]', '[7, 7, -2*w^2 + 5*w + 5]', '[8, 2, 2]', '[9, 3, -w^2 + 5]', '[9, 9, -w - 3]', '[12, 6, -w^2 + 6]', '[13, 13, -w^2 + 3*w + 1]', '[13, 13, 2*w + 5]', '[13, 13, w - 1]', '[14, 14, -w + 2]', '[16, 4, -2*w - 4]', '[17, 17, w^2 - w - 5]', '[18, 6, w^2 - 3*w - 2]', '[18, 18, -w^2 + 3*w]', '[19, 19, w^2 - 2*w - 5]', '[21, 21, -w^2 + w + 9]', '[24, 6, -2*w^2 + 4*w + 6]', '[26, 26, -w^2 - w + 2]', '[26, 26, -w^2 + w + 4]', '[26, 26, -w + 4]', '[27, 3, 3]', '[27, 27, w^2 - w - 3]', '[28, 14, w^2 - 4]', '[29, 29, w^2 - 7]', '[31, 31, 2*w^2 - 3*w - 11]', '[32, 4, 2*w^2 - 4*w - 8]', '[34, 34, -w^2 - w + 4]', '[36, 6, w^2 - 8]', '[36, 18, -w^2 + 2*w + 6]', '[38, 38, w + 4]', '[39, 39, -w^2 + 3]', '[39, 39, 3*w^2 - 7*w - 9]', '[39, 39, -w^2 + 2*w + 9]', '[42, 42, w^2 - 3*w - 12]', '[48, 12, 2*w]', '[49, 7, -2*w^2 - 4*w + 1]', '[49, 49, w^2 - 2*w - 7]', '[51, 51, -2*w^2 + 5*w + 3]', '[52, 26, w^2 + 2*w - 2]', '[52, 26, w^2 - 2*w - 8]', '[52, 26, -3*w^2 + 6*w + 10]', '[54, 6, -3*w - 6]', '[54, 54, -2*w^2 + w + 12]', '[56, 14, -4*w^2 + 10*w + 10]', '[57, 57, -4*w^2 + 10*w + 9]', '[58, 58, -2*w^2 - w + 8]', '[59, 59, w^2 - 2*w - 11]', '[62, 62, -w^2 + w + 10]', '[63, 21, w^2 - 3*w - 5]', '[63, 63, -2*w^2 + 3*w + 9]', '[64, 4, 4]', '[68, 34, -3*w^2 + 6*w + 8]', '[71, 71, -2*w + 7]', '[72, 6, -2*w^2 + 10]', '[72, 18, -2*w - 6]', '[73, 73, w^2 - 3*w - 13]', '[73, 73, 2*w^2 - 2*w - 17]', '[73, 73, -w^2 - 4*w - 5]', '[76, 38, 3*w^2 - 8*w - 4]', '[78, 78, -2*w^2 + 3*w + 12]', '[78, 78, 3*w^2 - 7*w - 6]', '[78, 78, 3*w^2 - w - 18]', '[79, 79, 2*w - 1]', '[79, 79, w^2 + w - 5]', '[79, 79, w - 5]', '[81, 9, -3*w^2 + 6*w + 9]', '[81, 9, -w^2 + 3*w - 1]', '[81, 81, -4*w^2 + 9*w + 9]', '[83, 83, -2*w + 5]', '[84, 42, -w^2 + 2*w]', '[87, 87, 2*w^2 - 4*w - 9]', '[91, 91, -w - 5]', '[91, 91, 3*w^2 - 4*w - 25]', '[91, 91, 2*w^2 - 2*w - 11]', '[93, 93, -5*w^2 + 13*w + 9]', '[96, 12, -2*w^2 + 12]', '[98, 14, 2*w^2 - 3*w - 8]', '[98, 98, 3*w + 8]', '[101, 101, -3*w^2 + 5*w + 13]', '[102, 102, -w^2 + 3*w + 6]', '[104, 26, -2*w^2 + 6*w + 2]', '[104, 26, 4*w + 10]', '[104, 26, 2*w - 2]', '[107, 107, -4*w^2 + 7*w + 17]', '[108, 6, 3*w^2 - 6*w - 12]', '[108, 54, 3*w^2 - 8*w - 6]', '[109, 109, 2*w^2 - w - 11]', '[112, 28, -2*w + 4]', '[113, 113, -7*w^2 + 14*w + 25]', '[114, 114, -2*w^2 + 3*w + 6]', '[116, 58, -3*w^2 + 4*w + 16]', '[117, 39, 2*w^2 - 3*w - 13]', '[117, 39, 2*w^2 - 3*w - 7]', '[117, 39, w^2 - 3*w - 11]', '[117, 117, -w^2 - 2*w + 3]', '[117, 117, 2*w^2 - 4*w - 3]', '[117, 117, -2*w + 3]', '[118, 118, 3*w^2 - 7*w - 10]', '[119, 119, -5*w - 11]', '[124, 62, 3*w^2 - 10*w + 2]', '[125, 5, -5]', '[126, 42, -2*w^2 + 3*w + 16]', '[126, 126, w^2 + w - 6]', '[128, 8, -4*w - 8]', '[131, 131, w^2 - w - 11]', '[131, 131, w^2 - 4*w + 1]', '[131, 131, -3*w^2 + 2*w + 19]', '[133, 133, -11*w^2 + 25*w + 29]', '[136, 34, 2*w^2 - 2*w - 10]', '[137, 137, w^2 - 3*w - 7]', '[139, 139, 3*w^2 - 17]', '[142, 142, 2*w^2 - 3*w - 14]', '[144, 12, 2*w^2 - 6*w - 4]', '[144, 36, -2*w^2 + 6*w]', '[146, 146, 2*w^2 - 5*w - 8]', '[146, 146, -2*w^2 + 5*w + 22]', '[146, 146, -2*w^2 + 5*w + 2]', '[147, 21, -w^2 - 2*w - 3]', '[147, 147, -2*w^2 + 6*w + 3]', '[149, 149, -4*w^2 + 9*w + 13]', '[149, 149, -4*w^2 + 8*w + 13]', '[149, 149, w^2 - 4*w - 1]', '[152, 38, 2*w^2 - 4*w - 10]', '[153, 51, 2*w^2 - 3*w - 19]', '[153, 153, -2*w^2 + 9]', '[156, 78, -w^2 + 4*w]', '[156, 78, w^2 - 2*w - 12]', '[156, 78, w^2 - 4*w - 6]', '[157, 157, -2*w^2 - w + 7]', '[158, 158, -w^2 + 3*w + 10]', '[158, 158, -2*w^2 - 3*w + 2]', '[158, 158, -3*w^2 - 5*w + 4]', '[162, 18, 3*w]', '[162, 18, -w^2 + 3*w + 8]', '[162, 162, -w + 6]', '[163, 163, 6*w^2 - 13*w - 17]', '[166, 166, 2*w^2 - w - 10]', '[167, 167, -2*w - 7]', '[168, 42, -2*w^2 + 2*w + 18]', '[169, 13, 2*w^2 + 3*w - 5]', '[169, 13, w^2 + w - 7]', '[169, 13, 4*w^2 - 10*w - 7]', '[169, 169, -w^2 + w - 1]', '[169, 169, -4*w - 7]', '[169, 169, w^2 - 2*w + 1]', '[171, 57, 2*w^2 - 13]', '[171, 171, -w^2 + 3*w + 9]', '[174, 174, w + 6]', '[177, 177, 2*w^2 - 2*w - 9]', '[179, 179, -w^2 + 5*w - 5]', '[181, 181, -w^2 - w + 11]', '[182, 182, -w^2 + 3*w - 2]', '[182, 182, -4*w^2 + 5*w + 34]', '[182, 182, -2*w^2 - w + 10]', '[186, 186, -3*w^2 + 5*w + 12]', '[189, 21, -6*w^2 + 15*w + 15]', '[189, 189, 2*w^2 - 4*w - 21]', '[192, 12, -4*w^2 + 8*w + 12]', '[193, 193, -5*w^2 + 10*w + 17]', '[196, 14, -w^2 - 2*w + 4]', '[196, 98, w^2 - 4*w + 4]', '[197, 197, 2*w^2 - 4*w - 19]', '[202, 202, w^2 + w - 8]', '[203, 203, 3*w^2 - 7*w - 5]', '[204, 102, 3*w^2 - 4*w - 24]', '[208, 52, -2*w^2 - 2*w + 4]', '[208, 52, -2*w^2 + 2*w + 8]', '[208, 52, -2*w + 8]', '[213, 213, 5*w^2 - 3*w - 33]', '[214, 214, w^2 + w - 10]', '[216, 6, 6]', '[216, 54, 2*w^2 - 2*w - 6]', '[217, 217, -15*w^2 + 34*w + 41]', '[218, 218, -3*w^2 - 3*w + 10]', '[219, 219, 2*w^2 - w - 9]', '[219, 219, 3*w^2 - 4*w - 15]', '[219, 219, 2*w^2 - 3]', '[221, 221, 3*w^2 + w - 13]', '[221, 221, -2*w^2 + 4*w + 11]', '[221, 221, 5*w^2 - 11*w - 11]', '[223, 223, 2*w^2 - 2*w - 7]', '[224, 28, 2*w^2 - 8]', '[226, 226, 3*w - 8]', '[227, 227, -3*w^2 + 6*w + 13]', '[228, 114, 3*w^2 - 2*w - 18]', '[229, 229, w^2 - 4*w - 7]', '[232, 58, 2*w^2 - 14]', '[233, 233, 2*w^2 + 5*w - 1]', '[233, 233, 3*w - 1]', '[233, 233, -3*w^2 + 7*w + 11]', '[234, 78, -4*w^2 + 9*w + 8]', '[234, 78, -w^2 + 3*w + 14]', '[234, 78, -w^2 - 3*w + 2]', '[234, 234, 4*w^2 - 11*w - 6]', '[234, 234, w^2 - w - 12]', '[234, 234, 2*w^2 + w - 6]', '[236, 118, -3*w^2 + 4*w + 20]', '[237, 237, 5*w^2 - 12*w - 15]', '[237, 237, 2*w^2 - 5*w - 9]', '[237, 237, 7*w^2 - 15*w - 21]', '[238, 238, 3*w^2 - 5*w - 16]', '[241, 241, 4*w^2 - w - 25]', '[243, 9, -3*w^2 + 15]', '[243, 27, -3*w - 9]', '[243, 243, -3*w^2 + w + 21]', '[247, 247, w^2 - 4*w - 13]', '[247, 247, -3*w^2 + 5*w + 11]', '[247, 247, -8*w^2 + 17*w + 25]', '[248, 62, 4*w^2 - 6*w - 22]', '[249, 249, 3*w^2 - 5*w - 27]', '[250, 10, 5*w + 10]', '[251, 251, 6*w + 13]', '[252, 42, 5*w^2 - 12*w - 10]', '[252, 126, -3*w^2 - 4*w + 6]', '[256, 8, 4*w^2 - 8*w - 16]', '[257, 257, 3*w^2 - 3*w - 17]', '[261, 87, 4*w^2 - 6*w - 35]', '[261, 261, -3*w^2 - w + 15]', '[262, 262, -w^2 + 5*w + 16]', '[262, 262, 2*w^2 - w - 8]', '[262, 262, 4*w^2 + w - 20]', '[266, 266, 4*w^2 - 7*w - 16]', '[269, 269, 3*w^2 - 4*w - 23]', '[269, 269, -4*w^2 + w + 23]', '[271, 271, 2*w^2 - w - 5]', '[272, 68, -2*w^2 - 2*w + 8]', '[273, 273, 2*w^2 - 15]', '[273, 273, 3*w^2 - 5*w - 9]', '[273, 273, -3*w^2 + 8*w + 3]', '[274, 274, w^2 + 5*w + 8]', '[277, 277, -2*w^2 + 7*w - 1]', '[278, 278, 3*w^2 - 5*w - 10]', '[279, 93, 5*w^2 - 3*w - 37]', '[279, 279, -3*w^2 + 4*w + 21]', '[281, 281, w - 7]', '[283, 283, -4*w^2 + 7*w + 19]', '[283, 283, 2*w^2 + w - 5]', '[283, 283, w^2 + 2*w - 5]', '[284, 142, -w^2 + 4*w + 16]', '[288, 12, 2*w^2 - 16]', '[288, 36, -2*w^2 + 4*w + 12]', '[289, 17, 2*w^2 - w - 7]', '[289, 289, -w^2 + 13]', '[292, 146, -3*w^2 + 4*w + 22]', '[292, 146, -5*w^2 + 6*w + 32]', '[292, 146, -w^2 + 4*w + 8]', '[293, 293, -w - 7]', '[293, 293, 2*w^2 - 5*w - 1]', '[293, 293, w^2 - 2*w - 13]', '[294, 42, -w^2 + 5*w + 18]', '[294, 294, -2*w^2 + w + 6]', '[298, 298, -w^2 + w - 2]', '[298, 298, 2*w^2 + w - 4]', '[298, 298, 3*w - 2]', '[303, 303, 3*w^2 - 4*w - 27]', '[304, 76, 2*w + 8]', '[306, 102, 4*w^2 - 9*w - 14]', '[306, 306, 5*w^2 - 13*w - 12]', '[307, 307, -6*w^2 + 14*w + 13]', '[307, 307, 4*w + 11]', '[307, 307, 2*w^2 - 2*w - 19]', '[311, 311, 2*w^2 + w - 11]', '[312, 78, -2*w^2 + 6]', '[312, 78, 6*w^2 - 14*w - 18]', '[312, 78, -2*w^2 + 4*w + 18]', '[314, 314, -5*w^2 + 9*w + 20]', '[316, 158, -5*w^2 + 10*w + 16]', '[316, 158, -3*w^2 + 4*w + 14]', '[316, 158, -7*w^2 + 14*w + 26]', '[317, 317, 2*w^2 - 5]', '[321, 321, 4*w^2 - 4*w - 33]', '[323, 323, -3*w + 7]', '[324, 18, -3*w^2 + 18]', '[324, 18, -w^2 - 6*w - 10]', '[324, 162, w^2 - 4*w - 12]', '[326, 326, w^2 - 5*w - 2]', '[327, 327, -w^2 + 3*w - 3]', '[331, 331, w^2 - 5*w + 7]', '[331, 331, -4*w^2 + 6*w + 19]', '[331, 331, 5*w^2 - 13*w - 11]', '[332, 166, -3*w^2 - 4*w + 8]', '[334, 334, 2*w^2 + 11*w + 14]', '[336, 84, 2*w^2 - 6*w - 24]', '[337, 337, 3*w^2 - 2*w - 17]', '[338, 26, -w^2 + 5*w - 4]', '[338, 26, -3*w^2 - 3*w + 8]', '[338, 26, 2*w^2 - 5*w - 10]', '[338, 338, -2*w^2 + 3*w + 20]', '[338, 338, 6*w^2 - 13*w - 20]', '[338, 338, 3*w^2 - 3*w - 26]', '[339, 339, 4*w^2 - 3*w - 33]', '[342, 114, 7*w^2 - 15*w - 20]', '[342, 342, -9*w^2 + 19*w + 30]', '[343, 7, 7]', '[343, 343, -7*w^2 + 15*w + 19]', '[347, 347, -5*w^2 + 11*w + 17]', '[347, 347, 5*w + 13]', '[347, 347, 2*w^2 - 4*w - 13]', '[348, 174, 5*w^2 - 6*w - 42]', '[351, 39, -3*w^2 + 9*w + 3]', '[351, 39, 6*w + 15]', '[351, 39, 3*w - 3]', '[351, 351, 5*w^2 - 2*w - 33]', '[351, 351, -2*w^2 + 6*w + 9]', '[351, 351, -7*w^2 + 16*w + 21]', '[354, 354, -2*w^2 - 3*w + 6]', '[357, 357, w^2 + 3*w - 3]', '[358, 358, -3*w^2 + 3*w + 16]', '[359, 359, 3*w^2 - 5*w - 17]', '[361, 19, w^2 - 4*w - 11]', '[361, 361, 2*w^2 - 6*w + 1]', '[362, 362, 3*w^2 - w - 16]', '[364, 182, -3*w^2 + 6*w + 14]', '[364, 182, -w^2 + 4*w + 10]', '[364, 182, -5*w^2 + 10*w + 14]', '[367, 367, 3*w^2 - 6*w - 31]', '[372, 186, 7*w^2 - 6*w - 48]', '[373, 373, 3*w^2 - 5*w - 29]', '[375, 15, 5*w^2 - 10*w - 15]', '[377, 377, 5*w^2 + 2*w - 23]', '[377, 377, -w^2 + w + 13]', '[377, 377, -3*w + 11]', '[378, 42, -3*w + 6]', '[378, 378, 3*w^2 - 7*w - 12]', '[379, 379, 4*w^2 - 3*w - 25]', '[383, 383, 2*w^2 - 4*w - 17]', '[384, 24, 4*w]', '[386, 386, 3*w - 4]', '[392, 14, 4*w^2 + 8*w - 2]', '[392, 98, 2*w^2 - 4*w - 14]', '[393, 393, 2*w^2 - 5*w - 21]', '[393, 393, 4*w^2 - 7*w - 15]', '[393, 393, -2*w + 9]', '[394, 394, -3*w^2 + 7*w + 4]', '[397, 397, 3*w - 5]', '[399, 399, 4*w^2 - 5*w - 27]', '[401, 401, -3*w^2 + 4*w + 13]', '[403, 403, 4*w^2 - 5*w - 31]', '[403, 403, -12*w^2 + 24*w + 43]', '[403, 403, -5*w^2 + 8*w + 23]', '[404, 202, -3*w^2 - 2*w + 10]', '[406, 406, 2*w^2 - w - 20]', '[408, 102, -4*w^2 + 10*w + 6]', '[409, 409, -w^2 + 4*w - 5]', '[411, 411, -4*w^2 + 11*w + 9]', '[413, 413, w^2 - 5*w - 1]', '[416, 52, 2*w^2 + 4*w - 4]', '[416, 52, 2*w^2 - 4*w - 16]', '[416, 52, -6*w^2 + 12*w + 20]', '[417, 417, 2*w^2 - 4*w - 15]', '[426, 426, -2*w^2 + 7*w]', '[428, 214, -3*w^2 + 14]', '[431, 431, 2*w^2 - 4*w - 1]', '[432, 12, -6*w - 12]', '[432, 108, -4*w^2 + 2*w + 24]', '[434, 434, 7*w^2 - 11*w - 34]', '[436, 218, -w^2 - 2*w + 14]', '[438, 438, -3*w^2 - 5*w + 6]', '[438, 438, -3*w^2 - w + 12]', '[438, 438, -2*w^2 - w + 12]', '[441, 21, 2*w^2 - 3*w - 1]', '[441, 63, -w^2 + 5*w - 3]', '[441, 147, 4*w^2 - 23]', '[441, 441, -w^2 + 5*w + 15]', '[442, 442, -2*w^2 + 7*w + 4]', '[442, 442, -3*w - 10]', '[442, 442, w - 8]', '[443, 443, 2*w^2 - 5*w - 11]', '[446, 446, -2*w^2 - 5*w + 2]', '[447, 447, -12*w^2 + 28*w + 33]', '[447, 447, 2*w^2 + 2*w - 9]', '[447, 447, w^2 - 3*w - 15]', '[448, 28, -8*w^2 + 20*w + 20]', '[452, 226, -3*w^2 + 2*w + 16]', '[454, 454, -w - 8]', '[456, 114, -8*w^2 + 20*w + 18]', '[457, 457, -3*w^2 - 4*w + 5]', '[457, 457, w^2 + 2*w - 7]', '[457, 457, -6*w^2 + 12*w + 23]', '[458, 458, 2*w^2 + 7*w + 8]', '[459, 51, 3*w^2 - 3*w - 15]', '[459, 459, w^2 - 2*w + 3]', '[461, 461, 4*w - 11]', '[463, 463, -4*w^2 + 8*w + 17]', '[464, 116, -4*w^2 - 2*w + 16]', '[466, 466, -w^2 - w - 4]', '[466, 466, -3*w^2 + 9*w + 4]', '[466, 466, -3*w^2 - 5*w + 2]', '[467, 467, -6*w^2 + 10*w + 29]', '[468, 78, -5*w^2 + 12*w + 16]', '[468, 78, 5*w^2 - 28]', '[468, 78, -w^2 + 14]', '[468, 234, 3*w^2 - 4*w - 12]', '[468, 234, -w^2 + 6*w + 18]', '[468, 234, 7*w^2 - 14*w - 24]', '[471, 471, w^2 - w + 3]', '[472, 118, 2*w^2 - 4*w - 22]', '[474, 474, 2*w^2 - w]', '[474, 474, w^2 + 3*w + 6]', '[474, 474, w^2 - 5*w]', '[476, 238, -w^2 + 2*w + 14]', '[479, 479, 4*w^2 - 12*w - 1]', '[482, 482, 4*w^2 - 7*w - 14]', '[486, 18, 3*w^2 - 9*w - 6]', '[486, 54, -3*w^2 + 9*w]', '[486, 486, -8*w^2 + 17*w + 24]', '[489, 489, 2*w + 9]', '[493, 493, -4*w^2 + 5*w + 29]', '[494, 494, w^2 + 3*w - 4]', '[494, 494, 6*w^2 - 11*w - 26]', '[494, 494, -w^2 + 5*w - 2]', '[496, 124, -2*w^2 + 2*w + 20]', '[497, 497, -3*w^2 + 19]', '[498, 498, -2*w^2 + 5*w]', '[499, 499, 3*w^2 - 6*w - 29]', '[500, 10, -5*w^2 + 10*w + 20]', '[501, 501, 3*w^2 - 4*w - 9]', '[502, 502, -4*w^2 + 7*w + 20]', '[503, 503, -w^2 + 5*w - 1]', '[504, 42, 2*w^2 - 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33]', '[1893, 1893, -2*w^2 + 9*w + 3]', '[1893, 1893, 2*w^2 - 3*w + 3]', '[1894, 1894, -6*w^2 + w + 32]', '[1896, 474, 10*w^2 - 24*w - 30]', '[1896, 474, 4*w^2 - 10*w - 18]', '[1896, 474, 14*w^2 - 30*w - 42]', '[1897, 1897, -17*w^2 + 42*w + 47]', '[1898, 1898, 6*w^2 + w - 28]', '[1898, 1898, 10*w^2 - 7*w - 80]', '[1898, 1898, 7*w^2 + w - 34]', '[1898, 1898, 7*w^2 - 5*w - 44]', '[1898, 1898, -3*w - 14]', '[1898, 1898, 7*w^2 - 19*w - 14]', '[1898, 1898, -9*w - 16]', '[1898, 1898, -7*w^2 + 13*w + 20]', '[1898, 1898, 5*w^2 + 9*w - 2]', '[1901, 1901, 3*w^2 - 8*w + 1]', '[1902, 1902, 11*w + 12]', '[1904, 476, 6*w^2 - 10*w - 32]', '[1906, 1906, -3*w^2 + 5*w + 32]', '[1911, 273, 4*w^2 - 13*w - 51]', '[1911, 273, -5*w^2 + 4*w + 27]', '[1911, 273, 4*w^2 - 13*w - 9]', '[1911, 1911, 8*w^2 - 19*w - 15]', '[1911, 1911, 4*w^2 - 6*w - 39]', '[1911, 1911, 2*w^2 + 4*w - 9]', '[1916, 958, -w^2 + 4*w + 20]', '[1917, 213, -6*w + 21]', '[1917, 1917, 9*w^2 - 17*w - 33]', '[1918, 1918, 5*w^2 - 7*w - 20]', '[1919, 1919, 6*w^2 - 19*w - 1]', '[1921, 1921, 21*w^2 - 48*w - 59]', '[1922, 62, -11*w^2 + 25*w + 34]', '[1922, 1922, -w^2 + 3*w - 8]', '[1923, 1923, 4*w^2 - 7*w - 27]', '[1923, 1923, -9*w^2 + 10*w + 69]', '[1923, 1923, -7*w^2 + 19*w + 15]', '[1926, 642, 7*w^2 - 9*w - 56]', '[1926, 1926, -4*w^2 - w + 24]', '[1928, 482, 8*w^2 - 2*w - 50]', '[1931, 1931, 3*w^2 - 4*w - 31]', '[1933, 1933, -2*w^2 - 2*w + 29]', '[1934, 1934, -5*w^2 - 11*w + 4]', '[1937, 1937, -4*w^2 + 2*w + 17]', '[1937, 1937, -5*w^2 + 11*w + 7]', '[1937, 1937, 13*w^2 - 28*w - 37]', '[1937, 1937, -18*w^2 + 43*w + 41]', '[1937, 1937, -3*w^2 - 10*w - 1]', '[1937, 1937, 12*w^2 - 27*w - 37]', '[1937, 1937, 2*w^2 + 7*w + 11]', '[1937, 1937, -3*w^2 - 6*w + 7]', '[1937, 1937, -2*w^2 + 7*w + 17]', '[1938, 1938, -3*w^2 + 7*w]', '[1939, 1939, w^2 - 3*w - 19]', '[1941, 1941, -w^2 + 4*w - 9]', '[1944, 18, -6*w^2 + 30]', '[1944, 54, -6*w - 18]', '[1944, 486, -6*w^2 + 2*w + 42]', '[1946, 1946, 6*w^2 - 7*w - 52]', '[1949, 1949, 5*w^2 - w - 35]', '[1949, 1949, 6*w^2 - 11*w - 29]', '[1949, 1949, 3*w^2 + w - 23]', '[1951, 1951, w^2 + 5*w - 5]', '[1953, 651, 4*w^2 - 12*w + 1]', '[1953, 1953, -w^2 + 12*w - 27]', '[1954, 1954, 5*w^2 - 7*w - 14]', '[1954, 1954, 4*w^2 - 3*w - 16]', '[1954, 1954, 9*w + 14]', '[1956, 978, -5*w^2 + 6*w + 6]', '[1962, 654, 4*w^2 - 9*w - 20]', '[1962, 1962, -8*w^2 + 11*w + 42]', '[1967, 1967, 19*w^2 - 46*w - 47]', '[1971, 219, 3*w^2 - 9*w - 39]', '[1971, 219, 6*w^2 - 6*w - 51]', '[1971, 219, -3*w^2 - 12*w - 15]', '[1971, 1971, -4*w^2 - 2*w + 21]', '[1971, 1971, -5*w^2 - 4*w + 15]', '[1971, 1971, -5*w^2 + 3*w + 27]', '[1972, 986, 5*w^2 - 12*w - 20]', '[1973, 1973, w^2 - 7*w + 7]', '[1976, 494, 2*w^2 - 8*w - 26]', '[1976, 494, -6*w^2 + 10*w + 22]', '[1976, 494, -16*w^2 + 34*w + 50]', '[1977, 1977, -4*w^2 + 2*w + 9]', '[1977, 1977, -3*w^2 + 10*w + 15]', '[1977, 1977, w^2 + 2*w + 9]', '[1981, 1981, -5*w^2 + w + 25]', '[1981, 1981, -7*w^2 + 20*w + 23]', '[1981, 1981, 9*w^2 - 19*w - 19]', '[1982, 1982, 7*w^2 - 13*w - 22]', '[1983, 1983, -11*w^2 + 28*w + 27]', '[1984, 124, 8*w^2 - 12*w - 44]', '[1986, 1986, -5*w^2 + 15*w + 6]', '[1986, 1986, -13*w^2 + 29*w + 30]', '[1986, 1986, 6*w^2 - 13*w - 24]', '[1987, 1987, -7*w^2 + 14*w + 29]', '[1988, 994, 7*w^2 - 8*w - 40]', '[1989, 663, 2*w^2 - 6*w + 5]', '[1989, 663, -5*w^2 + 31]', '[1989, 663, -4*w^2 + 3*w + 11]', '[1989, 1989, 5*w^2 - 9*w - 27]', '[1989, 1989, 2*w^2 - 7*w - 21]', '[1989, 1989, 7*w^2 - 13*w - 21]', '[1992, 498, 6*w^2 - 10*w - 54]', '[1993, 1993, 8*w^2 - 3*w - 53]', '[1996, 998, -5*w^2 + 4*w + 44]', '[1997, 1997, -w^2 - 4*w + 25]', '[1999, 1999, -w^2 - 4*w - 11]', '[2000, 20, 10*w + 20]', '[2004, 1002, 7*w^2 + 4*w - 30]', '[2006, 2006, 6*w^2 - 17*w - 10]', '[2007, 669, w^2 - 6*w - 23]', '[2007, 2007, -4*w^2 - 3*w + 9]', '[2008, 502, 12*w + 26]', '[2011, 2011, 3*w^2 - 11*w + 1]', '[2012, 1006, -15*w^2 + 32*w + 46]', '[2016, 84, 10*w^2 - 24*w - 20]', '[2016, 252, -6*w^2 - 8*w + 12]', '[2017, 2017, -12*w^2 + 31*w + 23]', '[2018, 2018, -2*w^2 + 5*w - 4]', '[2018, 2018, -5*w^2 - w + 28]', '[2018, 2018, -w^2 + 7*w - 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3*w + 37]', '[9939, 9939, w^2 - w - 27]', '[9941, 9941, -15*w^2 + 22*w + 83]', '[9947, 203, -7*w^2 + 49]', '[9947, 9947, 12*w^2 - 27*w - 43]', '[9948, 4974, -11*w^2 + 26*w + 18]', '[9949, 9949, -3*w^2 + 14*w + 43]', '[9949, 9949, 3*w^2 - 15*w - 23]', '[9949, 9949, -w^2 + 11*w - 29]', '[9951, 9951, -3*w^2 + 2*w + 39]', '[9952, 1244, -10*w^2 + 12*w + 52]', '[9954, 3318, 13*w^2 - 3*w - 74]', '[9954, 3318, 13*w^2 - 15*w - 92]', '[9954, 3318, 8*w^2 - 3*w - 40]', '[9954, 9954, -4*w^2 - 3*w + 36]', '[9954, 9954, -2*w^2 + 11*w + 42]', '[9954, 9954, w^2 + 3*w + 18]', '[9956, 4978, 7*w^2 - 22*w - 10]', '[9956, 4978, 5*w^2 - 22*w + 22]', '[9956, 4978, -7*w^2 - 4*w + 20]', '[9957, 9957, 13*w^2 - 7*w - 81]', '[9958, 9958, 9*w^2 + 13*w - 22]', '[9958, 9958, 12*w^2 - 15*w - 80]', '[9958, 9958, 5*w^2 + 3*w - 32]', '[9961, 9961, -6*w^2 - 15*w + 5]', '[9961, 9961, 11*w^2 - 32*w - 29]', '[9961, 9961, 14*w^2 - 37*w - 31]', '[9962, 9962, 8*w^2 + 11*w - 22]', '[9962, 9962, -2*w^2 - 7*w + 14]', '[9962, 9962, 11*w^2 + 7*w - 46]', '[9967, 9967, 6*w^2 + w - 43]', '[9967, 9967, 8*w^2 - 5*w - 41]', '[9967, 9967, -2*w^2 - 5*w + 41]', '[9969, 9969, 11*w^2 - 26*w - 39]', '[9971, 767, -12*w^2 + w + 71]', '[9971, 767, -7*w^2 + 22*w + 11]', '[9971, 767, w^2 + 4*w - 31]', '[9971, 9971, 20*w^2 - 47*w - 59]', '[9971, 9971, 2*w^2 - 6*w - 35]', '[9971, 9971, 9*w + 29]', '[9972, 1662, -13*w^2 + 30*w + 44]', '[9972, 4986, 19*w^2 - 36*w - 72]', '[9974, 9974, 3*w^2 + 5*w - 38]', '[9981, 3327, 10*w^2 - 59]', '[9981, 9981, -3*w^2 + 13*w + 39]', '[9984, 312, -4*w^2 + 16*w]', '[9984, 312, 4*w^2 - 8*w - 48]', '[9984, 312, 4*w^2 - 16*w - 24]', '[9986, 9986, 16*w^2 - 33*w - 34]', '[9986, 9986, 2*w^2 - 13*w - 26]', '[9986, 9986, -3*w^2 + 9*w + 44]', '[9987, 9987, 2*w^2 - w - 33]', '[9989, 9989, -9*w^2 + 4*w + 49]', '[9992, 2498, -2*w - 22]', '[9992, 2498, 4*w^2 - 16*w - 2]', '[9992, 2498, 6*w^2 + 2*w - 38]', '[9993, 9993, -17*w^2 + 44*w + 27]', '[9993, 9993, -6*w^2 + 20*w + 9]', '[9993, 9993, -5*w^2 + 17*w - 9]', '[9996, 714, -5*w^2 + 18*w + 6]', '[9996, 4998, w^2 + 18*w + 30]', '[9998, 9998, -2*w^2 + 19*w + 52]'], 'label': '3.3.1076.1', 'narrow_class_no': 2, 'primes': ['[2, 2, -w - 2]', '[3, 3, -w^2 + 2*w + 3]', '[7, 7, -2*w^2 + 5*w + 5]', '[9, 3, -w^2 + 5]', '[13, 13, -w^2 + 3*w + 1]', '[13, 13, 2*w + 5]', '[13, 13, w - 1]', '[17, 17, w^2 - w - 5]', '[19, 19, w^2 - 2*w - 5]', '[29, 29, w^2 - 7]', '[31, 31, 2*w^2 - 3*w - 11]', '[49, 7, -2*w^2 - 4*w + 1]', '[59, 59, w^2 - 2*w - 11]', '[71, 71, -2*w + 7]', '[73, 73, w^2 - 3*w - 13]', '[73, 73, 2*w^2 - 2*w - 17]', '[73, 73, -w^2 - 4*w - 5]', '[79, 79, 2*w - 1]', '[79, 79, w^2 + w - 5]', '[79, 79, w - 5]', '[83, 83, -2*w + 5]', '[101, 101, -3*w^2 + 5*w + 13]', '[107, 107, -4*w^2 + 7*w + 17]', '[109, 109, 2*w^2 - w - 11]', '[113, 113, -7*w^2 + 14*w + 25]', '[125, 5, -5]', '[131, 131, w^2 - w - 11]', '[131, 131, w^2 - 4*w + 1]', '[131, 131, -3*w^2 + 2*w + 19]', '[137, 137, w^2 - 3*w - 7]', '[139, 139, 3*w^2 - 17]', '[149, 149, -4*w^2 + 9*w + 13]', '[149, 149, -4*w^2 + 8*w + 13]', '[149, 149, w^2 - 4*w - 1]', '[157, 157, -2*w^2 - w + 7]', '[163, 163, 6*w^2 - 13*w - 17]', '[167, 167, -2*w - 7]', '[179, 179, -w^2 + 5*w - 5]', '[181, 181, -w^2 - w + 11]', '[193, 193, -5*w^2 + 10*w + 17]', '[197, 197, 2*w^2 - 4*w - 19]', '[223, 223, 2*w^2 - 2*w - 7]', '[227, 227, -3*w^2 + 6*w + 13]', '[229, 229, w^2 - 4*w - 7]', '[233, 233, 2*w^2 + 5*w - 1]', '[233, 233, 3*w - 1]', '[233, 233, -3*w^2 + 7*w + 11]', '[241, 241, 4*w^2 - w - 25]', '[251, 251, 6*w + 13]', '[257, 257, 3*w^2 - 3*w - 17]', '[269, 269, 3*w^2 - 4*w - 23]', '[269, 269, -4*w^2 + w + 23]', '[271, 271, 2*w^2 - w - 5]', '[277, 277, -2*w^2 + 7*w - 1]', '[281, 281, w - 7]', '[283, 283, -4*w^2 + 7*w + 19]', '[283, 283, 2*w^2 + w - 5]', '[283, 283, w^2 + 2*w - 5]', '[289, 17, 2*w^2 - w - 7]', '[293, 293, -w - 7]', '[293, 293, 2*w^2 - 5*w - 1]', '[293, 293, w^2 - 2*w - 13]', '[307, 307, -6*w^2 + 14*w + 13]', '[307, 307, 4*w + 11]', '[307, 307, 2*w^2 - 2*w - 19]', '[311, 311, 2*w^2 + w - 11]', '[317, 317, 2*w^2 - 5]', '[331, 331, w^2 - 5*w + 7]', '[331, 331, -4*w^2 + 6*w + 19]', '[331, 331, 5*w^2 - 13*w - 11]', '[337, 337, 3*w^2 - 2*w - 17]', '[347, 347, -5*w^2 + 11*w + 17]', '[347, 347, 5*w + 13]', '[347, 347, 2*w^2 - 4*w - 13]', '[359, 359, 3*w^2 - 5*w - 17]', '[361, 19, w^2 - 4*w - 11]', '[367, 367, 3*w^2 - 6*w - 31]', '[373, 373, 3*w^2 - 5*w - 29]', '[379, 379, 4*w^2 - 3*w - 25]', '[383, 383, 2*w^2 - 4*w - 17]', '[397, 397, 3*w - 5]', '[401, 401, -3*w^2 + 4*w + 13]', '[409, 409, -w^2 + 4*w - 5]', '[431, 431, 2*w^2 - 4*w - 1]', '[443, 443, 2*w^2 - 5*w - 11]', '[457, 457, -3*w^2 - 4*w + 5]', '[457, 457, w^2 + 2*w - 7]', '[457, 457, -6*w^2 + 12*w + 23]', '[461, 461, 4*w - 11]', '[463, 463, -4*w^2 + 8*w + 17]', '[467, 467, -6*w^2 + 10*w + 29]', '[479, 479, 4*w^2 - 12*w - 1]', '[499, 499, 3*w^2 - 6*w - 29]', '[503, 503, -w^2 + 5*w - 1]', '[509, 509, 3*w^2 - 9*w - 5]', '[521, 521, -4*w^2 + 5*w + 35]', '[523, 523, -9*w^2 + 17*w + 35]', '[541, 541, 6*w + 11]', '[547, 547, w^2 + 2*w - 13]', '[547, 547, -3*w^2 - 3*w + 7]', '[547, 547, -3*w^2 + 7*w + 13]', '[557, 557, 2*w^2 + w - 13]', '[569, 569, 5*w^2 - 13*w - 7]', '[571, 571, -6*w^2 + 12*w + 19]', '[577, 577, 3*w^2 - 5*w - 19]', '[601, 601, 3*w^2 - 13]', '[607, 607, 3*w^2 - 5*w - 25]', '[613, 613, 8*w^2 - 17*w - 23]', '[631, 631, w^2 - 5*w - 13]', '[631, 631, -3*w^2 - w + 11]', '[631, 631, 5*w^2 - 14*w - 7]', '[641, 641, -w^2 + 7*w - 11]', '[641, 641, 2*w^2 - 5*w - 13]', '[641, 641, 5*w^2 - w - 31]', '[647, 647, 4*w^2 - 2*w - 23]', '[659, 659, -2*w^2 - 4*w + 5]', '[659, 659, -4*w^2 - 4*w + 11]', '[659, 659, w^2 + 6*w + 11]', '[661, 661, 2*w^2 - 6*w - 11]', '[673, 673, 2*w^2 - 6*w - 23]', '[677, 677, 8*w^2 - 19*w - 17]', '[683, 683, w^2 - 5*w - 19]', '[691, 691, 6*w^2 - 16*w - 11]', '[701, 701, -3*w - 11]', '[709, 709, -w^2 - w - 5]', '[719, 719, 8*w + 17]', '[733, 733, 5*w^2 - 7*w - 25]', '[739, 739, 4*w^2 - 10*w - 5]', '[743, 743, 3*w^2 - 3*w - 11]', '[743, 743, -w^2 + 7*w + 23]', '[743, 743, -7*w^2 + 14*w + 23]', '[757, 757, w^2 + 7*w + 13]', '[761, 761, -9*w^2 + 4*w + 59]', '[773, 773, 3*w^2 - w - 13]', '[773, 773, -w^2 + 3*w - 5]', '[773, 773, 3*w^2 - 2*w - 13]', '[787, 787, -4*w^2 - 3*w + 13]', '[787, 787, 5*w^2 - 4*w - 31]', '[787, 787, -10*w^2 + 20*w + 37]', '[797, 797, 3*w^2 + 3*w - 5]', '[809, 809, 6*w^2 - 17*w - 5]', '[821, 821, -5*w^2 + 9*w + 17]', '[821, 821, 2*w^2 + 2*w - 11]', '[821, 821, 2*w^2 - 5*w - 17]', '[823, 823, -2*w^2 + 4*w + 23]', '[823, 823, 2*w^2 + w - 25]', '[823, 823, 3*w^2 - 6*w - 17]', '[829, 829, -3*w^2 - 5*w + 7]', '[839, 839, 2*w^2 - 7*w - 11]', '[841, 29, w^2 - 6*w - 1]', '[853, 853, 3*w^2 - 7*w - 31]', '[857, 857, 4*w^2 - 5*w - 19]', '[881, 881, -w^2 - 5]', '[883, 883, -4*w^2 - 7*w + 7]', '[887, 887, 3*w^2 - 11]', '[887, 887, 3*w^2 + 2*w - 7]', '[887, 887, 2*w^2 - 8*w + 7]', '[907, 907, 3*w^2 - 8*w - 1]', '[907, 907, 4*w^2 - 19]', '[907, 907, 3*w^2 - 2*w - 11]', '[911, 911, -6*w^2 + 9*w + 29]', '[919, 919, -9*w^2 + 18*w + 31]', '[929, 929, w^2 + 3*w - 7]', '[937, 937, 4*w - 7]', '[941, 941, -2*w^2 + 8*w + 11]', '[947, 947, 3*w^2 - 25]', '[953, 953, 5*w^2 - 7*w - 31]', '[961, 31, -3*w^2 + 4*w + 29]', '[967, 967, 3*w^2 - w - 11]', '[977, 977, 5*w^2 + 4*w - 19]', '[977, 977, 3*w^2 - 10*w - 1]', '[977, 977, -2*w^2 + 4*w - 1]', '[991, 991, 5*w^2 - 29]']}
-
nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-6, -8, 0, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 1076, 'disc_rad': 538, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[2, 1], [1, 1]]], [5, [[3, 1]]], [7, [[2, 1], [1, 1]]], [11, [[3, 1]]], [13, [[1, 3]]], [17, [[2, 1], [1, 1]]], [19, [[2, 1], [1, 1]]], [23, [[3, 1]]], [29, [[2, 1], [1, 1]]], [31, [[2, 1], [1, 1]]], [37, [[3, 1]]], [41, [[3, 1]]], [43, [[3, 1]]], [47, [[3, 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, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 26.035313035249676, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.1076.1', 'local_algs': ['2.3.2.1', 'm269.1.1.0', 'm269.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 269], 'rd': 10.2471735217, 'regulator': {'__RealLiteral__': 0, 'data': '6.93232675724', 'prec': 44}, 'res': {'gal': ['-169,-141,114,53,-24,-3,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 1 \\)', '\\( 3 a + 7 \\)'], 'unitsGmodule': [[4, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}