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hmf_forms • Show schema
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{'deg': 3, 'dimension': 1, 'disc': 1620, 'field_bad_primes': [2, 3, 5], 'field_label': '3.3.1620.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.1620.1-10.1-g', 'label_nsuffix': 6, 'label_suffix': 'g', 'level_bad_primes': [2, 5], 'level_ideal': '[10, 10, w^2 - w - 10]', 'level_label': '10.1', 'level_norm': 10, 'parallel_weight': 2, 'short_label': '10.1-g', 'weight': '[2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[2, 2, -w - 2]', 1], ['[5, 5, -2*w^2 + 3*w + 19]', -1]], 'hecke_eigenvalues': [-1, -2, 2, 1, -5, -1, 4, 1, -2, -2, 9, -5, -13, 6, -2, -4, 10, -14, 8, 4, 10, -2, 2, -11, 8, -4, -5, -10, 0, 20, -2, 21, -8, 0, -11, -21, 14, -3, 24, 14, -2, 0, 24, 28, 6, -26, -8, -20, -6, 24, -9, -5, 5, 22, -7, 32, 10, 8, 17, -11, -23, 25, 16, 14, 19, -2, 4, 11, -10, 10, 26, 32, 34, -19, -11, -13, 9, 16, -36, 16, -14, 13, 11, 31, 21, -29, -25, -16, 12, -12, 40, -4, -16, -9, -18, 35, 28, -18, 10, -42, -39, -17, -25, -22, -15, -22, -11, -30, -22, -30, -2, 28, -5, 18, 5, -7, -7, 16, 16, -30, 37, 37, 5, 22, 45, 12, -35, 17, 47, 6, 34, -30, -33, -22, 24, -20, -16, 34, 27, 6, -22, -18, -40, -2, -2, 10, 21, 33, -20, 29, -22, 44, 42, -10, -46, 24, 26, -24, 2, 56, -17], 'hecke_polynomial': 'x', 'label': '3.3.1620.1-10.1-g'}
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hmf_fields • Show schema
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{'degree': 3, 'discriminant': 1620, 'ideals': ['[1, 1, 1]', '[2, 2, -w - 2]', '[3, 3, w + 1]', '[4, 2, w^2 - 2*w - 8]', '[5, 5, -w - 3]', '[5, 5, -2*w^2 + 3*w + 19]', '[6, 6, 2*w^2 - 3*w - 20]', '[7, 7, -w^2 + 2*w + 7]', '[8, 2, 2]', '[9, 3, w^2 - w - 11]', '[10, 10, w^2 - w - 10]', '[10, 10, w^2 - w - 12]', '[12, 6, -w^2 + 2*w + 6]', '[13, 13, w^2 - 3*w - 5]', '[14, 14, w]', '[15, 15, w^2 - 2*w - 9]', '[15, 15, 2*w^2 - 4*w - 15]', '[16, 4, -2*w - 4]', '[17, 17, w^2 - w - 3]', '[18, 6, -w^2 + w + 8]', '[20, 10, -w^2 + 2*w + 10]', '[20, 10, w^2 - 2*w - 4]', '[21, 21, w^2 - 3*w - 7]', '[23, 23, -w + 3]', '[24, 6, 2*w + 2]', '[25, 5, -w^2 + 3*w + 3]', '[25, 5, -w^2 - w + 1]', '[25, 25, w - 1]', '[26, 26, w^2 - w - 4]', '[27, 3, 3]', '[28, 14, -w^2 - 2*w]', '[30, 30, w + 4]', '[30, 30, -w + 2]', '[32, 4, 2*w^2 - 4*w - 16]', '[34, 34, -2*w^2 + 3*w + 18]', '[35, 35, -w^2 + 4*w + 7]', '[35, 35, w^2 - w - 7]', '[36, 6, w^2 - 4*w - 8]', '[37, 37, 3*w + 5]', '[39, 39, w^2 + w - 3]', '[40, 10, -2*w - 6]', '[40, 10, -4*w^2 + 6*w + 38]', '[42, 42, w^2 + w]', '[43, 43, w^2 + 3*w + 3]', '[45, 15, -2*w^2 + 5*w + 13]', '[45, 15, -w^2 + w + 5]', '[46, 46, w^2 - w - 6]', '[47, 47, -w^2 + 3]', '[48, 12, 4*w^2 - 6*w - 40]', '[49, 7, -w^2 + 5]', '[49, 49, -5*w^2 + 7*w + 49]', '[50, 10, -w^2 + 3*w + 8]', '[50, 10, -2*w^2 + 3*w + 22]', '[50, 50, -w^2 - w + 2]', '[51, 51, -w + 5]', '[52, 26, 3*w^2 - 4*w - 32]', '[53, 53, -w^2 + w + 13]', '[54, 6, -3*w - 6]', '[56, 14, -2*w^2 + 4*w + 14]', '[60, 30, -w^2 + 16]', '[60, 30, w^2 - 4]', '[61, 61, -w^2 + 15]', '[61, 61, w^2 - 2*w - 13]', '[61, 61, -4*w - 5]', '[63, 21, 4*w^2 - 7*w - 35]', '[64, 4, 4]', '[65, 65, 2*w + 1]', '[65, 65, -w^2 - 4*w - 5]', '[67, 67, -2*w^2 + 6*w + 13]', '[68, 34, w^2 - 8]', '[69, 69, -w^2 + 2*w + 3]', '[70, 70, 3*w^2 - 5*w - 28]', '[70, 70, -w^2 - 3*w]', '[72, 6, 2*w^2 - 2*w - 22]', '[73, 73, 2*w^2 - 2*w - 17]', '[74, 74, -3*w^2 + 7*w + 20]', '[75, 15, -w^2 + 3*w + 13]', '[75, 15, -2*w^2 + 3*w + 17]', '[75, 75, w^2 - 1]', '[78, 78, 3*w^2 - 5*w - 26]', '[79, 79, -w - 5]', '[79, 79, 2*w^2 - 4*w - 17]', '[79, 79, w^2 - 3*w - 9]', '[80, 20, 2*w^2 - 2*w - 20]', '[80, 20, 2*w^2 - 2*w - 24]', '[81, 9, 3*w + 3]', '[83, 83, 2*w^2 - 4*w - 11]', '[84, 42, -3*w^2 + 4*w + 28]', '[85, 85, -2*w^2 + 4*w + 13]', '[85, 85, -4*w^2 + 5*w + 41]', '[86, 86, -4*w^2 + 5*w + 38]', '[90, 30, w^2 + 5*w + 4]', '[90, 30, -w^2 + w + 2]', '[91, 91, -2*w^2 + 2*w + 21]', '[92, 46, -w^2 - 4*w - 2]', '[94, 94, -4*w^2 + 9*w + 26]', '[96, 12, -2*w^2 + 4*w + 12]', '[97, 97, -3*w^2 + 5*w + 31]', '[98, 14, -4*w^2 + 7*w + 34]', '[98, 98, 2*w^2 - 5*w - 14]', '[100, 10, -w^2 - 2*w - 2]', '[100, 10, -w^2 + 4*w + 6]', '[100, 50, -3*w^2 + 6*w + 22]', '[102, 102, w^2 - 3*w - 10]', '[103, 103, -4*w - 9]', '[104, 26, 2*w^2 - 6*w - 10]', '[105, 105, 4*w + 7]', '[105, 105, 2*w - 7]', '[106, 106, w^2 - 3*w - 12]', '[107, 107, -w^2 + 4*w + 9]', '[108, 6, 3*w^2 - 6*w - 24]', '[111, 111, -3*w^2 + 5*w + 29]', '[112, 28, 2*w]', '[113, 113, w^2 - 3*w - 11]', '[115, 115, w^2 - 9]', '[115, 115, 2*w^2 - 3*w - 9]', '[117, 39, -w^2 + 4*w - 1]', '[119, 119, 2*w + 7]', '[120, 30, 2*w^2 - 4*w - 18]', '[120, 30, 4*w^2 - 8*w - 30]', '[122, 122, 2*w^2 - 3*w - 16]', '[122, 122, 5*w + 12]', '[122, 122, -3*w^2 + 5*w + 30]', '[125, 5, 5]', '[125, 25, w^2 - 4*w - 1]', '[125, 25, -w^2 - 2*w + 3]', '[125, 125, 5*w^2 - 8*w - 47]', '[126, 42, -w^2 + w + 14]', '[127, 127, 6*w^2 - 9*w - 59]', '[128, 8, -4*w - 8]', '[129, 129, -2*w^2 + 3*w + 23]', '[130, 130, -2*w^2 - 5*w - 2]', '[130, 130, w - 6]', '[134, 134, -2*w^2 - w + 2]', '[135, 15, -3*w - 9]', '[135, 15, -6*w^2 + 9*w + 57]', '[136, 34, 2*w^2 - 2*w - 6]', '[137, 137, -w^2 - w + 19]', '[138, 138, 5*w + 8]', '[140, 70, -w^2 + 2*w + 14]', '[140, 70, -w^2 + 14]', '[141, 141, -4*w^2 + 6*w + 37]', '[144, 12, -2*w^2 + 2*w + 16]', '[146, 146, -2*w^2 - 3*w + 6]', '[147, 21, -10*w^2 + 14*w + 99]', '[147, 147, 2*w^2 - 4*w - 21]', '[148, 74, -w^2 + 2*w + 2]', '[149, 149, -7*w^2 + 11*w + 65]', '[149, 149, 2*w^2 - 4*w - 19]', '[149, 149, -3*w^2 + 4*w + 33]', '[150, 30, 2*w^2 - w - 6]', '[150, 30, w^2 + w - 6]', '[150, 150, -5*w^2 + 7*w + 48]', '[153, 51, -w^2 + 4*w + 5]', '[156, 78, -w^2 + 10]', '[157, 157, w^2 + w + 1]', '[158, 158, w + 6]', '[158, 158, w^2 + 3*w + 4]', '[158, 158, w^2 + 7*w + 10]', '[159, 159, 2*w - 1]', '[160, 20, -2*w^2 + 4*w + 20]', '[160, 20, 2*w^2 - 4*w - 8]', '[161, 161, -5*w^2 + 11*w + 35]', '[162, 18, 6*w^2 - 9*w - 60]', '[163, 163, 2*w^2 - 5*w - 15]', '[166, 166, -5*w - 6]', '[167, 167, -3*w^2 + 4*w + 27]', '[168, 42, 2*w^2 - 6*w - 14]', '[169, 13, 2*w^2 - w - 17]', '[169, 169, -2*w^2 + 3*w + 15]', '[170, 170, 3*w + 2]', '[170, 170, -2*w^2 + 5*w + 8]', '[172, 86, w^2 - 4*w - 10]', '[173, 173, 3*w^2 - 5*w - 25]', '[175, 35, 6*w^2 - 8*w - 63]', '[175, 35, 2*w^2 - 3*w - 7]', '[175, 175, 3*w^2 - 7*w - 21]', '[180, 30, 7*w^2 - 10*w - 68]', '[180, 30, -w^2 + 4*w + 2]', '[182, 182, 2*w^2 - w - 14]', '[183, 183, -w^2 + 3*w + 1]', '[183, 183, -w^2 - 3*w + 1]', '[183, 183, -w^2 + 13]', '[184, 46, -2*w + 6]', '[185, 185, -w^2 + 11]', '[185, 185, -2*w + 9]', '[188, 94, -w^2 + 4*w + 4]', '[189, 21, -3*w^2 + 6*w + 21]', '[192, 12, 4*w + 4]', '[193, 193, 5*w^2 - 9*w - 43]', '[194, 194, w^2 - 5*w - 20]', '[195, 195, 4*w^2 - 9*w - 25]', '[195, 195, 5*w^2 - 6*w - 53]', '[196, 14, w^2 - 12]', '[196, 98, w^2]', '[197, 197, -w^2 + 4*w + 15]', '[199, 199, 4*w^2 - 10*w - 25]', '[199, 199, w^2 - w - 1]', '[199, 199, w^2 - 4*w - 3]', '[200, 10, -2*w^2 + 6*w + 6]', '[200, 10, -2*w^2 - 2*w + 2]', '[200, 50, 2*w - 2]', '[201, 201, -5*w^2 + 10*w + 39]', '[204, 102, w^2 + 4*w + 6]', '[206, 206, 4*w^2 - 7*w - 36]', '[207, 69, w^2 - 7*w - 11]', '[208, 52, 2*w^2 - 2*w - 8]', '[210, 210, -4*w^2 + 9*w + 28]', '[210, 210, -2*w^2 + 3*w + 14]', '[212, 106, -3*w^2 + 4*w + 12]', '[214, 214, 2*w^2 + 5*w + 4]', '[215, 215, -3*w^2 + 6*w + 25]', '[215, 215, -2*w^2 + 2*w + 15]', '[216, 6, 6]', '[219, 219, 5*w + 11]', '[221, 221, 5*w + 9]', '[222, 222, w^2 - 3*w - 16]', '[223, 223, 3*w^2 - 8*w - 13]', '[224, 28, -2*w^2 - 4*w]', '[225, 15, w^2 - 4*w - 11]', '[225, 15, 2*w^2 + 4*w - 1]', '[225, 75, -2*w^2 + 2*w + 25]', '[226, 226, w^2 + 5*w + 8]', '[227, 227, 2*w - 5]', '[229, 229, -w^2 + 17]', '[229, 229, w^2 + 4*w + 1]', '[229, 229, 2*w - 3]', '[230, 230, -2*w^2 - 3*w + 4]', '[230, 230, 4*w^2 - 5*w - 44]', '[233, 233, 5*w^2 - 8*w - 45]', '[234, 78, -2*w^2 + 5*w + 16]', '[235, 235, -w^2 + w + 15]', '[235, 235, -3*w + 11]', '[237, 237, -2*w^2 + 3*w + 11]', '[237, 237, -w^2 - 6*w - 5]', '[237, 237, -2*w^2 + 5]', '[238, 238, -2*w^2 + w + 28]', '[239, 239, 2*w^2 - 3*w - 13]', '[239, 239, 7*w + 9]', '[239, 239, 2*w^2 + 3*w - 1]', '[240, 60, 2*w + 8]', '[240, 60, -2*w + 4]', '[243, 9, 3*w^2 - 3*w - 33]', '[244, 122, -w^2 - 2*w + 4]', '[244, 122, -5*w^2 + 8*w + 48]', '[244, 122, 3*w^2 - 6*w - 16]', '[245, 35, -6*w^2 + 7*w + 65]', '[245, 35, -5*w^2 + 7*w + 53]', '[245, 245, w^2 + w - 7]', '[245, 245, w - 7]', '[249, 249, -2*w^2 + 9*w + 17]', '[250, 10, -5*w - 10]', '[250, 50, -2*w^2 + w + 26]', '[250, 50, 2*w^2 - 3*w - 12]', '[250, 250, -2*w^2 + 3*w + 24]', '[251, 251, w^2 + 2*w + 3]', '[251, 251, -2*w^2 - w + 9]', '[251, 251, -w^2 - 5*w - 3]', '[252, 42, w^2 - 4*w - 14]', '[254, 254, -3*w^2 + 5*w + 34]', '[255, 255, w^2 - 2*w - 15]', '[255, 255, 2*w^2 - 7*w - 15]', '[256, 8, 4*w^2 - 8*w - 32]', '[257, 257, -3*w^2 - 10*w - 9]', '[258, 258, w^2 - 5*w - 18]', '[259, 259, w^2 - 5*w - 7]', '[260, 130, -3*w^2 + 6*w + 20]', '[260, 130, -w^2 + 4*w + 12]', '[263, 263, w^2 - 2*w - 1]', '[265, 265, w^2 - 5*w - 11]', '[265, 265, 4*w^2 - 9*w - 23]', '[268, 134, 3*w^2 - 4*w - 26]', '[270, 30, 3*w^2 - 3*w - 30]', '[270, 30, 3*w^2 - 3*w - 36]', '[271, 271, -4*w^2 + 7*w + 33]', '[271, 271, w^2 - 4*w - 13]', '[271, 271, -3*w - 1]', '[272, 68, -4*w^2 + 6*w + 36]', '[273, 273, -w - 7]', '[274, 274, 3*w^2 - 5*w - 24]', '[276, 138, -5*w^2 + 6*w + 50]', '[277, 277, -6*w^2 + 10*w + 53]', '[280, 70, -2*w^2 + 8*w + 14]', '[280, 70, 2*w^2 - 2*w - 14]', '[281, 281, 2*w^2 - 6*w - 15]', '[281, 281, -7*w - 17]', '[281, 281, -w^2 + 5*w - 5]', '[282, 282, 2*w^2 - w - 18]', '[283, 283, -2*w^2 + w + 13]', '[288, 12, 2*w^2 - 8*w - 16]', '[289, 17, -2*w^2 - 10*w - 9]', '[289, 289, 5*w^2 - 8*w - 51]', '[291, 291, 2*w^2 - 11]', '[292, 146, -5*w^2 + 6*w + 52]', '[293, 293, 4*w^2 - 8*w - 29]', '[294, 42, 3*w^2 - 7*w - 22]', '[294, 294, -3*w^2 + 5*w + 14]', '[296, 74, 6*w + 10]', '[298, 298, 3*w^2 - 3*w - 32]', '[298, 298, 2*w^2 - 5*w - 24]', '[298, 298, 3*w + 10]', '[299, 299, -5*w^2 + 7*w + 47]', '[300, 30, 3*w^2 - 2*w - 38]', '[300, 30, 3*w^2 - 4*w - 34]', '[300, 150, 3*w^2 - 8*w - 20]', '[301, 301, -2*w^2 + w + 7]', '[305, 305, 15*w^2 - 21*w - 149]', '[305, 305, -5*w^2 + 11*w + 33]', '[305, 305, 3*w^2 - 3*w - 31]', '[305, 305, -2*w^2 + 5*w + 17]', '[305, 305, 3*w^2 - 6*w - 17]', '[305, 305, -w^2 + 7*w + 25]', '[306, 102, -2*w^2 - w + 4]', '[307, 307, 3*w^2 - 6*w - 19]', '[309, 309, -4*w^2 - 13*w - 9]', '[312, 78, 2*w^2 + 2*w - 6]', '[313, 313, -2*w^2 - 3*w + 3]', '[314, 314, -3*w^2 + 9*w + 10]', '[315, 105, 2*w^2 - 5*w - 7]', '[315, 105, -5*w^2 + 8*w + 49]', '[316, 158, -3*w^2 + 6*w + 26]', '[316, 158, -3*w^2 + 12*w + 22]', '[316, 158, w^2 - 4*w + 2]', '[317, 317, -5*w^2 + 6*w + 51]', '[318, 318, -2*w^2 - 3*w + 2]', '[320, 20, -4*w - 12]', '[320, 20, -8*w^2 + 12*w + 76]', '[321, 321, -3*w^2 - w + 5]', '[322, 322, -w^2 + 3*w]', '[324, 18, -3*w^2 + 6*w + 18]', '[325, 65, 4*w^2 - 7*w - 37]', '[325, 65, -2*w^2 - 7*w - 3]', '[325, 325, 3*w^2 - 3*w - 25]', '[326, 326, w^2 + w + 2]', '[329, 329, 2*w^2 - 4*w - 7]', '[332, 166, 5*w^2 - 14*w - 24]', '[333, 111, 2*w^2 - 2*w - 13]', '[334, 334, 2*w^2 + w - 12]', '[335, 335, 2*w^2 - 7*w - 5]', '[335, 335, -7*w - 11]', '[336, 84, 2*w^2 + 2*w]', '[337, 337, 6*w^2 - 17*w - 27]', '[338, 26, -3*w^2 - 5*w + 6]', '[338, 338, w^2 + 3*w - 2]', '[339, 339, -2*w^2 - 2*w + 3]', '[340, 170, 11*w^2 - 16*w - 110]', '[340, 170, -w^2 + 6*w + 12]', '[343, 7, 7]', '[343, 343, 6*w + 7]', '[344, 86, 2*w^2 + 6*w + 6]', '[345, 345, w^2 + 3*w + 5]', '[345, 345, 5*w^2 - 9*w - 41]', '[346, 346, -w^2 - w + 8]', '[347, 347, -4*w - 3]', '[350, 70, -6*w^2 + 9*w + 56]', '[350, 70, 3*w^2 - 9*w - 14]', '[350, 350, w^2 - w]', '[351, 39, 3*w^2 - 9*w - 15]', '[353, 353, -2*w^2 + 15]', '[357, 357, 2*w^2 + 9*w + 7]', '[360, 30, -4*w^2 + 10*w + 26]', '[360, 30, -2*w^2 + 2*w + 10]', '[364, 182, -w^2 + 8*w + 14]', '[365, 365, 18*w^2 - 25*w - 183]', '[365, 365, -4*w^2 - w + 23]', '[366, 366, -16*w^2 + 23*w + 162]', '[366, 366, -w^2 + 5*w + 12]', '[366, 366, 2*w^2 - w - 12]', '[367, 367, -6*w^2 + 13*w + 41]', '[368, 92, 2*w^2 - 2*w - 12]', '[370, 370, 2*w^2 + w - 8]', '[370, 370, 2*w^2 - 5*w - 18]', '[371, 371, -6*w^2 + 11*w + 49]', '[373, 373, -5*w^2 + 10*w + 37]', '[375, 15, 5*w + 5]', '[375, 75, -6*w^2 + 13*w + 43]', '[375, 75, -3*w^2 + 7*w + 13]', '[375, 375, -3*w^2 + 5*w + 23]', '[376, 94, -2*w^2 + 6]', '[378, 42, 3*w]', '[379, 379, 2*w^2 - 2*w - 11]', '[379, 379, -2*w^2 - 4*w - 3]', '[379, 379, w^2 - 7*w - 13]', '[381, 381, -3*w^2 + 4*w + 25]', '[383, 383, -2*w^2 + w + 19]', '[384, 24, 8*w^2 - 12*w - 80]', '[386, 386, -w^2 + w + 16]', '[387, 129, w^2 + 2*w - 5]', '[388, 194, 9*w^2 - 12*w - 94]', '[389, 389, 2*w^2 + 2*w - 5]', '[389, 389, 3*w^2 + 4*w - 1]', '[389, 389, 2*w^2 - 7*w - 11]', '[390, 390, w^2 - 5*w - 6]', '[390, 390, -4*w^2 + 5*w + 36]', '[391, 391, -w^2 + 5*w + 17]', '[392, 14, -2*w^2 + 10]', '[392, 98, -10*w^2 + 14*w + 98]', '[394, 394, -2*w^2 - 11*w - 16]', '[395, 395, 6*w + 13]', '[395, 395, 7*w^2 - 10*w - 67]', '[395, 395, w^2 + 8*w + 15]', '[395, 395, 2*w^2 - 2*w - 5]', '[395, 395, 5*w^2 - 14*w - 27]', '[395, 395, 4*w^2 - 4*w - 45]', '[397, 397, 6*w + 11]', '[398, 398, 2*w^2 - 3*w - 6]', '[398, 398, -w^2 - 9*w - 12]', '[398, 398, 2*w^2 - w - 8]', '[400, 20, -2*w^2 + 6*w + 16]', '[400, 20, -4*w^2 + 6*w + 44]', '[400, 100, -2*w^2 - 2*w + 4]', '[401, 401, -4*w^2 + 9*w + 29]', '[401, 401, 2*w^2 - w - 25]', '[401, 401, -4*w + 15]', '[402, 402, w - 8]', '[405, 45, 3*w^2 - 6*w - 27]', '[405, 45, 6*w^2 - 12*w - 45]', '[408, 102, -2*w + 10]', '[409, 409, -2*w - 9]', '[409, 409, 4*w^2 - 11*w - 17]', '[409, 409, w^2 - 3*w - 17]', '[411, 411, -2*w^2 + 6*w + 5]', '[412, 206, -w^2 + 2*w + 16]', '[414, 138, -4*w^2 + 7*w + 38]', '[415, 415, 3*w - 13]', '[415, 415, -2*w^2 - w + 5]', '[416, 52, 6*w^2 - 8*w - 64]', '[419, 419, -9*w^2 + 13*w + 87]', '[419, 419, 2*w^2 - 3*w - 25]', '[419, 419, -6*w^2 + 11*w + 51]', '[420, 210, -w^2 + 2*w]', '[420, 210, w^2 + 4*w]', '[423, 141, 2*w^2 - 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1]', '[1831, 1831, 5*w^2 - 12*w - 37]', '[1831, 1831, 6*w^2 - 13*w - 27]', '[1832, 458, -2*w^2 + 34]', '[1832, 458, 2*w^2 + 8*w + 2]', '[1832, 458, 4*w - 6]', '[1833, 1833, -9*w^2 + 19*w + 67]', '[1835, 1835, 5*w^2 - 8*w - 39]', '[1835, 1835, 2*w^2 - 8*w - 29]', '[1836, 102, 3*w^2 - 24]', '[1839, 1839, -3*w^2 + 8*w + 29]', '[1840, 460, -4*w^2 - 6*w + 8]', '[1840, 460, 8*w^2 - 10*w - 88]', '[1841, 1841, -8*w^2 + 18*w + 49]', '[1842, 1842, -8*w^2 + 9*w + 86]', '[1847, 1847, 10*w^2 - 15*w - 93]', '[1849, 43, -6*w^2 + 5*w + 75]', '[1849, 1849, 5*w^2 - 3*w - 43]', '[1850, 370, -w^2 + 9*w + 26]', '[1850, 370, 11*w^2 - 13*w - 118]', '[1850, 1850, 9*w^2 - 13*w - 96]', '[1851, 1851, -w^2 - 7*w - 3]', '[1852, 926, -7*w^2 + 20*w + 34]', '[1854, 618, 2*w^2 - 11*w - 22]', '[1855, 1855, 7*w^2 - 10*w - 63]', '[1855, 1855, -4*w^2 + 13*w + 21]', '[1857, 1857, 7*w^2 - 12*w - 67]', '[1857, 1857, -w^2 + 3*w - 5]', '[1857, 1857, -w^2 + 9*w + 19]', '[1861, 1861, -8*w^2 + 19*w + 53]', '[1861, 1861, 6*w^2 - 14*w - 43]', '[1861, 1861, -4*w^2 + 2*w + 13]', '[1863, 207, -3*w^2 + 6*w + 9]', '[1864, 466, 10*w^2 - 16*w - 90]', '[1865, 1865, 5*w^2 - 7*w - 41]', '[1865, 1865, -5*w^2 + 16*w + 29]', '[1867, 1867, 3*w^2 - 7*w - 9]', '[1868, 934, -9*w^2 + 10*w + 102]', '[1872, 156, -4*w^2 + 10*w + 32]', '[1873, 1873, 6*w^2 - 18*w - 25]', '[1874, 1874, -3*w^2 - 17*w - 16]', '[1875, 75, 5*w^2 - 10*w - 45]', '[1875, 75, 2*w^2 + 2*w + 3]', '[1875, 75, 10*w^2 - 20*w - 75]', '[1875, 375, 4*w^2 - 2*w - 27]', '[1875, 1875, -w^2 + 11*w + 15]', '[1876, 938, 3*w^2 - 2*w - 42]', '[1877, 1877, -w^2 - 13*w - 19]', '[1878, 1878, 4*w^2 - 11*w - 30]', '[1880, 470, -2*w^2 + 2*w + 30]', '[1880, 470, -6*w + 22]', '[1882, 1882, -w^2 + 7*w + 6]', '[1882, 1882, 8*w^2 - 11*w - 74]', '[1882, 1882, -3*w^2 + 9*w + 26]', '[1884, 942, 5*w^2 - 6*w - 20]', '[1887, 1887, -3*w^2 + 10*w + 25]', '[1889, 1889, -w^2 - 17*w - 23]', '[1889, 1889, 4*w^2 - 10*w - 15]', '[1889, 1889, w^2 - 10*w + 23]', '[1890, 210, 9*w^2 - 15*w - 84]', '[1890, 210, -3*w^2 - 9*w]', '[1894, 1894, 6*w^2 + 29*w + 36]', '[1895, 1895, 6*w^2 - 7*w - 69]', '[1895, 1895, 4*w^2 - 5*w - 29]', '[1895, 1895, -4*w^2 - 7*w + 5]', '[1895, 1895, 7*w^2 - 15*w - 53]', '[1895, 1895, 4*w - 9]', '[1895, 1895, -5*w^2 + 16*w + 13]', '[1896, 474, -4*w^2 + 6*w + 22]', '[1896, 474, -2*w^2 - 12*w - 10]', '[1896, 474, -4*w^2 + 10]', '[1897, 1897, -5*w^2 + 13*w + 35]', '[1897, 1897, -2*w^2 - 15*w - 21]', '[1897, 1897, 4*w - 7]', '[1898, 1898, w^2 + 5*w + 12]', '[1902, 1902, w^2 + 13*w + 24]', '[1904, 476, -4*w^2 + 2*w + 56]', '[1905, 1905, 5*w^2 - w - 33]', '[1905, 1905, -23*w^2 + 31*w + 237]', '[1906, 1906, 4*w^2 - 9*w - 36]', '[1907, 1907, 4*w^2 - w - 25]', '[1908, 318, 5*w^2 - 14*w - 34]', '[1909, 1909, 10*w^2 - 25*w - 61]', '[1911, 273, -13*w^2 + 21*w + 121]', '[1911, 1911, 5*w^2 - 9*w - 35]', '[1912, 478, 4*w^2 - 6*w - 26]', '[1912, 478, 14*w + 18]', '[1912, 478, 4*w^2 + 6*w - 2]', '[1913, 1913, -9*w^2 + 17*w + 75]', '[1915, 1915, 5*w^2 + 2*w - 29]', '[1915, 1915, -25*w^2 + 36*w + 249]', '[1918, 1918, -w^2 + 7*w - 14]', '[1920, 120, 4*w + 16]', '[1920, 120, -4*w + 8]', '[1921, 1921, w^2 - 14*w - 23]', '[1924, 962, 3*w^2 - 8*w - 34]', '[1926, 642, w^2 + 5*w - 2]', '[1929, 1929, -17*w^2 + 25*w + 171]', '[1930, 1930, 2*w^2 - 7*w - 34]', '[1930, 1930, -24*w^2 + 35*w + 234]', '[1932, 966, -13*w^2 + 20*w + 126]', '[1933, 1933, w^2 + 3*w + 9]', '[1934, 1934, -2*w^2 - w + 32]', '[1935, 645, -5*w^2 - 13*w + 1]', '[1935, 645, 11*w^2 - 17*w - 109]', '[1937, 1937, 7*w^2 - 15*w - 45]', '[1937, 1937, -5*w + 17]', '[1937, 1937, -17*w^2 + 36*w + 123]', '[1939, 1939, -10*w - 21]', '[1940, 970, -3*w^2 + 8*w + 30]', '[1940, 970, -15*w^2 + 22*w + 156]', '[1941, 1941, -10*w - 19]', '[1944, 18, 6*w^2 - 6*w - 66]', '[1945, 1945, w^2 + 8*w + 5]', '[1945, 1945, 6*w^2 - 9*w - 67]', '[1945, 1945, -w^2 + w - 5]', '[1945, 1945, 7*w^2 - 7*w - 79]', '[1945, 1945, -4*w^2 + 13*w + 15]', '[1945, 1945, -9*w^2 + 18*w + 71]', '[1948, 974, -3*w^2 - 2*w + 18]', '[1950, 390, 2*w^2 + 9*w + 4]', '[1950, 390, -2*w^2 + 3*w + 2]', '[1950, 1950, -8*w^2 + 15*w + 68]', '[1952, 244, -2*w^2 - 4*w + 8]', '[1952, 244, -10*w^2 + 16*w + 96]', '[1952, 244, 6*w^2 - 12*w - 32]', '[1954, 1954, -8*w^2 + 17*w + 60]', '[1955, 1955, 11*w + 13]', '[1955, 1955, -10*w^2 + 23*w + 67]', '[1956, 978, -7*w^2 + 20*w + 36]', '[1959, 1959, 7*w^2 - 14*w - 57]', '[1960, 70, -12*w^2 + 14*w + 130]', '[1960, 70, -10*w^2 + 14*w + 106]', '[1960, 490, 2*w^2 + 2*w - 14]', '[1960, 490, 2*w - 14]', '[1961, 1961, 2*w^2 - 8*w - 23]', '[1966, 1966, -4*w^2 - w + 26]', '[1967, 1967, -7*w^2 + 20*w + 35]', '[1967, 1967, -w^2 - 9*w - 7]', '[1967, 1967, 3*w^2 + w - 21]', '[1970, 1970, 9*w^2 - 9*w - 80]', '[1970, 1970, 11*w^2 - 17*w - 110]', '[1971, 219, 6*w^2 - 6*w - 51]', '[1973, 1973, -5*w^2 + 16*w + 17]', '[1974, 1974, 6*w^2 - 11*w - 56]', '[1975, 395, 6*w^2 + 16*w + 9]', '[1975, 395, 2*w^2 - 6*w - 1]', '[1975, 395, -w^2 + 9*w + 11]', '[1975, 395, -4*w^2 - 13*w - 13]', '[1975, 395, w^2 + 16*w + 19]', '[1975, 395, -9*w^2 + 22*w + 57]', '[1975, 1975, -w^2 - 4*w + 5]', '[1975, 1975, -4*w^2 + 6*w + 23]', '[1975, 1975, -6*w^2 + 11*w + 45]', '[1977, 1977, -2*w^2 + 12*w + 23]', '[1977, 1977, -4*w^2 + 6*w + 25]', '[1977, 1977, -14*w^2 + 18*w + 143]', '[1978, 1978, -17*w^2 + 25*w + 170]', '[1981, 1981, -w^2 + w + 21]', '[1985, 1985, -3*w^2 + w + 45]', '[1985, 1985, -4*w^2 + 3*w + 41]', '[1987, 1987, -7*w - 5]', '[1989, 663, 4*w^2 - 4*w - 29]', '[1990, 1990, 3*w^2 - 3*w - 40]', '[1990, 1990, 3*w - 16]', '[1990, 1990, -3*w^2 - 9*w - 10]', '[1990, 1990, 2*w^2 + w - 18]', '[1990, 1990, w^2 + 5*w - 34]', '[1990, 1990, -7*w^2 + 13*w + 54]', '[1992, 498, -4*w^2 + 18*w + 34]', '[1993, 1993, 3*w^2 - w - 39]', '[1994, 1994, -2*w^2 - 11*w - 8]', '[1997, 1997, w^2 - 10*w - 13]', '[1998, 222, -9*w^2 + 21*w + 60]', '[2000, 20, -10*w - 20]', '[2000, 100, -4*w^2 + 2*w + 52]', '[2000, 100, 4*w^2 - 6*w - 24]', '[2000, 500, -4*w^2 + 6*w + 48]', '[2003, 2003, 3*w^2 - 8*w - 33]', '[2004, 1002, -w^2 + 22]', '[2005, 2005, 3*w^2 - 8*w - 31]', '[2005, 2005, 4*w^2 + 4*w - 13]', '[2005, 2005, -5*w^2 + 4*w + 47]', '[2005, 2005, 4*w^2 - 3*w - 45]', '[2005, 2005, 37*w^2 - 54*w - 363]', '[2005, 2005, 8*w^2 - 18*w - 45]', '[2007, 669, 10*w^2 - 16*w - 41]', '[2008, 502, 2*w^2 + 4*w + 6]', '[2008, 502, -4*w^2 - 2*w + 18]', '[2008, 502, -2*w^2 - 10*w - 6]', '[2010, 2010, -2*w^2 + 13*w + 24]', '[2010, 2010, -10*w^2 + 23*w + 54]', '[2012, 1006, 7*w^2 - 12*w - 68]', '[2016, 84, 2*w^2 - 8*w - 28]', '[2017, 2017, -3*w^2 - 3*w - 1]', '[2019, 2019, 2*w^2 - 27*w - 41]', '[2021, 2021, 7*w^2 - 12*w - 71]', '[2022, 2022, -6*w^2 + 19*w + 40]', '[2023, 119, -w^2 + 12*w + 21]', '[2023, 2023, 10*w^2 - 12*w - 105]', '[2025, 45, -3*w^2 + 9*w + 39]', '[2025, 45, -6*w^2 + 9*w + 51]', '[2025, 225, 3*w^2 - 3]', '[2026, 2026, -6*w^2 - 15*w + 2]', '[2027, 2027, w - 13]', '[2028, 78, 3*w^2 - 8*w - 32]', '[2028, 1014, 3*w^2 - 8*w - 8]', '[2031, 2031, -2*w^2 - 3*w + 11]', '[2032, 508, -6*w^2 + 10*w + 68]', '[2034, 678, 4*w^2 - w - 32]', '[2036, 1018, 9*w^2 - 20*w - 58]', '[2036, 1018, -11*w^2 + 24*w + 78]', '[2036, 1018, -11*w^2 + 16*w + 104]', '[2037, 2037, w^2 - 2*w - 21]', '[2040, 510, 2*w^2 - 4*w - 30]', '[2040, 510, 4*w^2 - 14*w - 30]', '[2041, 2041, -5*w^2 + 18*w + 33]', '[2043, 681, -7*w^2 + 7*w + 83]', '[2044, 1022, -3*w^2 - 18*w - 28]', '[2045, 2045, 12*w^2 - 17*w - 115]', '[2045, 2045, 20*w^2 - 28*w - 197]', '[2045, 2045, 2*w^2 + 15*w + 27]', '[2045, 2045, 10*w^2 - 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w - 17]', '[173, 173, 3*w^2 - 5*w - 25]', '[193, 193, 5*w^2 - 9*w - 43]', '[197, 197, -w^2 + 4*w + 15]', '[199, 199, 4*w^2 - 10*w - 25]', '[199, 199, w^2 - w - 1]', '[199, 199, w^2 - 4*w - 3]', '[223, 223, 3*w^2 - 8*w - 13]', '[227, 227, 2*w - 5]', '[229, 229, -w^2 + 17]', '[229, 229, w^2 + 4*w + 1]', '[229, 229, 2*w - 3]', '[233, 233, 5*w^2 - 8*w - 45]', '[239, 239, 2*w^2 - 3*w - 13]', '[239, 239, 7*w + 9]', '[239, 239, 2*w^2 + 3*w - 1]', '[251, 251, w^2 + 2*w + 3]', '[251, 251, -2*w^2 - w + 9]', '[251, 251, -w^2 - 5*w - 3]', '[257, 257, -3*w^2 - 10*w - 9]', '[263, 263, w^2 - 2*w - 1]', '[271, 271, -4*w^2 + 7*w + 33]', '[271, 271, w^2 - 4*w - 13]', '[271, 271, -3*w - 1]', '[277, 277, -6*w^2 + 10*w + 53]', '[281, 281, 2*w^2 - 6*w - 15]', '[281, 281, -7*w - 17]', '[281, 281, -w^2 + 5*w - 5]', '[283, 283, -2*w^2 + w + 13]', '[289, 17, -2*w^2 - 10*w - 9]', '[293, 293, 4*w^2 - 8*w - 29]', '[307, 307, 3*w^2 - 6*w - 19]', '[313, 313, -2*w^2 - 3*w + 3]', '[317, 317, -5*w^2 + 6*w + 51]', '[337, 337, 6*w^2 - 17*w - 27]', '[347, 347, -4*w - 3]', '[353, 353, -2*w^2 + 15]', '[367, 367, -6*w^2 + 13*w + 41]', '[373, 373, -5*w^2 + 10*w + 37]', '[379, 379, 2*w^2 - 2*w - 11]', '[379, 379, -2*w^2 - 4*w - 3]', '[379, 379, w^2 - 7*w - 13]', '[383, 383, -2*w^2 + w + 19]', '[389, 389, 2*w^2 + 2*w - 5]', '[389, 389, 3*w^2 + 4*w - 1]', '[389, 389, 2*w^2 - 7*w - 11]', '[397, 397, 6*w + 11]', '[401, 401, -4*w^2 + 9*w + 29]', '[401, 401, 2*w^2 - w - 25]', '[401, 401, -4*w + 15]', '[409, 409, -2*w - 9]', '[409, 409, 4*w^2 - 11*w - 17]', '[409, 409, w^2 - 3*w - 17]', '[419, 419, -9*w^2 + 13*w + 87]', '[419, 419, 2*w^2 - 3*w - 25]', '[419, 419, -6*w^2 + 11*w + 51]', '[433, 433, -6*w^2 + 12*w + 47]', '[443, 443, w^2 - 5*w - 13]', '[457, 457, 2*w^2 - 9]', '[463, 463, -3*w^2 + 5*w + 15]', '[467, 467, 4*w^2 - 7*w - 39]', '[487, 487, -3*w^2 + 5]', '[503, 503, -w^2 + 4*w + 19]', '[509, 509, w^2 - 5*w - 5]', '[509, 509, -w^2 + 3*w - 1]', '[509, 509, 3*w^2 - 2*w - 27]', '[521, 521, 4*w^2 - 4*w - 39]', '[521, 521, 3*w + 11]', '[521, 521, -3*w^2 + 6*w + 31]', '[523, 523, 3*w^2 - 6*w - 29]', '[529, 23, w^2 + 3*w - 3]', '[547, 547, -2*w^2 + w + 23]', '[557, 557, 4*w^2 - 10*w - 27]', '[563, 563, -2*w^2 - 5*w - 5]', '[577, 577, -3*w^2 + 3*w + 37]', '[587, 587, -2*w^2 + w + 29]', '[593, 593, -4*w^2 + 7*w + 19]', '[607, 607, w - 9]', '[613, 613, 6*w^2 - 9*w - 55]', '[617, 617, w^2 - 2*w - 17]', '[619, 619, -8*w - 13]', '[619, 619, -3*w^2 + 2*w + 37]', '[619, 619, 3*w^2 - 4*w - 23]', '[643, 643, 7*w + 15]', '[647, 647, -3*w^2 + 3*w + 23]', '[653, 653, -12*w^2 + 19*w + 111]', '[659, 659, 5*w^2 - 9*w - 45]', '[659, 659, -w^2 - 4*w + 1]', '[659, 659, 3*w^2 - 5*w - 19]', '[673, 673, -4*w^2 + 6*w + 15]', '[677, 677, 4*w^2 - 6*w - 45]', '[683, 683, 2*w^2 - 2*w - 27]', '[691, 691, 8*w^2 - 12*w - 75]', '[691, 691, -10*w^2 + 15*w + 99]', '[691, 691, -2*w + 11]', '[709, 709, -7*w^2 + 15*w + 51]', '[709, 709, w^2 + 9*w + 9]', '[709, 709, -5*w^2 + 6*w + 45]', '[727, 727, -4*w^2 + 2*w + 55]', '[733, 733, 2*w^2 - 6*w - 19]', '[743, 743, 3*w^2 - 7*w - 39]', '[751, 751, 2*w^2 - 6*w - 25]', '[751, 751, -6*w^2 + 10*w + 57]', '[751, 751, 4*w^2 - 8*w - 17]', '[757, 757, w^2 + 2*w + 5]', '[773, 773, 2*w^2 - 5*w - 5]', '[787, 787, -5*w^2 + 7*w + 55]', '[797, 797, -3*w^2 + w + 9]', '[823, 823, -12*w^2 + 17*w + 117]', '[827, 827, 9*w^2 - 12*w - 95]', '[853, 853, 2*w^2 + 2*w - 11]', '[857, 857, -w^2 - 7*w - 5]', '[863, 863, -7*w^2 + 16*w + 43]', '[877, 877, -5*w - 3]', '[883, 883, -2*w^2 - 7*w - 9]', '[887, 887, w^2 - 8*w - 11]', '[907, 907, 5*w^2 - 9*w - 39]', '[937, 937, 3*w^2 - 3*w - 13]', '[941, 941, -3*w^2 - w + 3]', '[941, 941, -2*w^2 + 7*w + 1]', '[941, 941, -6*w^2 + 13*w + 39]', '[947, 947, w^2 - 8*w - 25]', '[953, 953, -w^2 - 2*w + 25]', '[967, 967, -2*w^2 - 6*w + 1]', '[977, 977, 8*w + 15]', '[983, 983, 6*w^2 - 8*w - 55]', '[997, 997, 3*w^2 - 4*w - 17]']}
-
nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-14, -12, 0, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 1620, 'disc_rad': 30, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[2, 1], [1, 1]]], [11, [[3, 1]]], [13, [[2, 1], [1, 1]]], [17, [[2, 1], [1, 1]]], [19, [[3, 1]]], [23, [[2, 1], [1, 1]]], [29, [[3, 1]]], [31, [[3, 1]]], [37, [[2, 1], [1, 1]]], [41, [[3, 1]]], [43, [[2, 1], [1, 1]]], [47, [[2, 1], [1, 1]]], [53, [[2, 1], [1, 1]]], [59, [[3, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 8, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 15.357953166968596, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.1620.1', 'local_algs': ['2.3.2.1', '3.3.4.4', '5.1.0.1', '5.2.1.1'], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 3, 5], 'rd': 11.7446029235, 'regulator': {'__RealLiteral__': 0, 'data': '10.1679428335', 'prec': 44}, 'res': {'gal': ['-20,0,36,0,-12,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - a - 9 \\)', '\\( a^{2} + 5 a + 5 \\)'], 'unitsGmodule': [[1, 1], [4, 2]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}