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hmf_forms • Show schema
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{'deg': 4, 'dimension': 1, 'disc': 12400, 'field_bad_primes': [2, 5, 31], 'field_label': '4.4.12400.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.12400.1-19.2-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [19], 'level_ideal': '[19,19,-1/2*w^2 - w + 5/2]', 'level_label': '19.2', 'level_norm': 19, 'parallel_weight': 2, 'short_label': '19.2-b', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[19,19,-1/2*w^2 - w + 5/2]', 1]], 'hecke_eigenvalues': [-2, 0, 0, -2, 4, 4, -1, 6, 6, 8, 0, 6, -8, -2, 12, 0, 8, -8, 10, -16, 6, 6, -10, -2, -2, 8, -14, 10, 12, -12, -12, -18, 12, -12, -2, 22, 6, -18, 20, -4, 10, 22, 10, 16, 12, 12, 12, -12, -12, 24, -20, -8, -20, 10, 0, 24, 18, 0, -12, 6, 10, -28, 20, -14, -22, -2, 10, 2, 24, 36, -22, 22, -2, 30, 6, -6, -30, 22, -14, -36, 12, 24, 12, 26, 8, -18, 18, 6, -30, -12, -18, 12, 12, -36, -24, 38, -4, 20, -4, -18, -6, 16, 4, -12, 24, 8, 32, 20, 14, 0, 12, 8, -4, -8, 2, 20, -44, 16, -20, -2, 16, 0, -42, -24, -12, 38, 32, -10, 14, -8, 22, 14, -10, 16, -8, 42, 6, -34, -14, 10, 50, -54, -30, 44, -34, 6, 42, -28, -10, 0, -48, -38, -28, -16, -40, -40, -6, -36, -8, 16, 6, 6, 18, -30, 26, 0, 30, 56, -40, -52, 20], 'hecke_polynomial': 'x', 'label': '4.4.12400.1-19.2-b'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 12400, 'ideals': ['[1, 1, 1]', '[4, 2, -1/2*w^3 - 1/2*w^2 + 7/2*w + 11/2]', '[5, 5, -1/2*w^3 + w^2 + 5/2*w - 4]', '[5, 5, -1/2*w^2 - w + 3/2]', '[9, 3, -1/2*w^3 + 1/2*w^2 + 7/2*w - 9/2]', '[9, 3, -1/2*w^3 - 1/2*w^2 + 7/2*w + 9/2]', '[16, 2, 2]', '[19, 19, -1/2*w^2 + w + 5/2]', '[19, 19, 1/2*w^2 + w - 5/2]', '[20, 10, -1/2*w^3 - 1/2*w^2 + 7/2*w + 7/2]', '[20, 10, -w + 1]', '[25, 5, w^2 - 6]', '[25, 5, -1/2*w^3 - w^2 + 7/2*w + 8]', '[25, 5, 1/2*w^3 - w^2 - 7/2*w + 8]', '[29, 29, -3/2*w^2 - w + 17/2]', '[29, 29, -3/2*w^2 + w + 17/2]', '[31, 31, 1/2*w^3 - 7/2*w]', '[36, 6, -1/2*w^3 + 1/2*w^2 + 7/2*w - 3/2]', '[36, 6, -1/2*w^3 - 1/2*w^2 + 7/2*w + 3/2]', '[45, 15, -w^2 + w + 7]', '[45, 15, -1/2*w^3 - 3/2*w^2 + 5/2*w + 17/2]', '[45, 15, w^2 + w - 7]', '[45, 15, -1/2*w^3 + 3/2*w^2 + 5/2*w - 17/2]', '[59, 59, 1/2*w^2 + w - 11/2]', '[59, 59, 1/2*w^2 - w - 11/2]', '[61, 61, -1/2*w^3 + w^2 + 7/2*w - 5]', '[61, 61, 1/2*w^3 + w^2 - 7/2*w - 5]', '[64, 4, -w^3 - w^2 + 7*w + 11]', '[71, 71, -1/2*w^3 - 2*w^2 + 11/2*w + 13]', '[71, 71, 3/2*w^3 + 2*w^2 - 23/2*w - 18]', '[76, 38, -1/2*w^3 - 3/2*w^2 + 9/2*w + 19/2]', '[76, 38, -1/2*w^3 + 3/2*w^2 + 9/2*w - 19/2]', '[79, 79, 1/2*w^3 + 1/2*w^2 - 7/2*w - 1/2]', '[79, 79, -2*w^2 + w + 10]', '[79, 79, 2*w^2 + w - 10]', '[79, 79, 1/2*w^3 - 1/2*w^2 - 7/2*w + 1/2]', '[80, 10, -w^3 + 2*w^2 + 5*w - 8]', '[80, 10, -w^2 - 2*w + 3]', '[81, 3, 3]', '[81, 9, 1/2*w^3 - 5/2*w + 4]', '[81, 9, -1/2*w^3 + 5/2*w + 4]', '[89, 89, 1/2*w^3 - 2*w^2 - 5/2*w + 11]', '[89, 89, -1/2*w^2 + w + 15/2]', '[95, 95, -w - 4]', '[95, 95, 1/2*w^3 - 5/2*w - 3]', '[95, 95, 1/2*w^3 - 5/2*w + 3]', '[95, 95, -w + 4]', '[100, 10, 1/2*w^3 + 5/2*w^2 - 11/2*w - 35/2]', '[100, 10, -1/2*w^3 + 1/2*w^2 + 5/2*w + 3/2]', '[100, 10, 1/2*w^3 + 1/2*w^2 - 5/2*w + 3/2]', '[109, 109, -w^3 + 7*w + 3]', '[109, 109, 1/2*w^3 - 2*w^2 - 9/2*w + 12]', '[109, 109, w^3 + w^2 - 8*w - 11]', '[109, 109, w^3 - 7*w + 3]', '[116, 58, -w^2 + w + 8]', '[116, 58, -w^2 - w + 8]', '[121, 11, 3/2*w^2 - 19/2]', '[121, 11, -1/2*w^2 + 13/2]', '[124, 62, 3/2*w^3 + 3/2*w^2 - 23/2*w - 31/2]', '[125, 5, -1/2*w^3 + 2*w^2 + 1/2*w - 7]', '[125, 5, -w^3 - 3/2*w^2 + 6*w + 13/2]', '[125, 25, -w^3 - 1/2*w^2 + 7*w + 13/2]', '[125, 25, -3/2*w^2 - 2*w + 17/2]', '[131, 131, -1/2*w^3 + 3/2*w^2 + 7/2*w - 15/2]', '[131, 131, -1/2*w^3 + 9/2*w + 3]', '[144, 6, -w^3 + w^2 + 7*w - 9]', '[144, 6, -w^3 - w^2 + 7*w + 9]', '[145, 145, -1/2*w^3 - w^2 + 7/2*w + 4]', '[145, 145, -1/2*w^3 + 9/2*w + 4]', '[145, 145, 1/2*w^3 - 9/2*w + 4]', '[145, 145, 1/2*w^3 - w^2 - 7/2*w + 4]', '[155, 155, 1/2*w^3 - w^2 - 3/2*w]', '[155, 155, -1/2*w^3 - 5/2*w^2 + 5/2*w + 31/2]', '[171, 57, 1/2*w^3 - 2*w^2 - 7/2*w + 12]', '[171, 57, w^3 + 1/2*w^2 - 6*w + 7/2]', '[171, 57, -w^3 + 1/2*w^2 + 6*w + 7/2]', '[171, 57, -1/2*w^3 - 2*w^2 + 7/2*w + 12]', '[179, 179, -w^3 - 5/2*w^2 + 9*w + 35/2]', '[179, 179, 1/2*w^3 + 2*w^2 - 7/2*w - 13]', '[179, 179, -1/2*w^3 + 2*w^2 + 7/2*w - 13]', '[179, 179, 3/2*w^3 + 4*w^2 - 27/2*w - 29]', '[180, 30, 1/2*w^3 - 1/2*w^2 - 7/2*w + 15/2]', '[180, 30, 1/2*w^3 - 3/2*w^2 - 5/2*w + 19/2]', '[180, 30, 1/2*w^3 + 1/2*w^2 - 7/2*w - 15/2]', '[180, 30, 1/2*w^3 + 3/2*w^2 - 5/2*w - 19/2]', '[181, 181, -1/2*w^3 + w^2 + 5/2*w - 7]', '[181, 181, 1/2*w^3 + w^2 - 5/2*w - 7]', '[191, 191, 2*w^2 + w - 12]', '[191, 191, 2*w^2 - w - 12]', '[211, 211, w^3 - w^2 - 7*w + 4]', '[211, 211, -w^3 - w^2 + 7*w + 4]', '[225, 15, 1/2*w^3 + 3/2*w^2 - 11/2*w - 23/2]', '[225, 15, 1/2*w^3 - 3/2*w^2 - 11/2*w + 23/2]', '[225, 15, -w^2 + 2*w + 4]', '[225, 15, -1/2*w^3 - w^2 + 9/2*w + 5]', '[225, 15, -1/2*w^3 - w^2 + 7/2*w + 3]', '[225, 15, w^2 + 2*w - 4]', '[229, 229, 3/2*w^2 + w - 23/2]', '[229, 229, 3/2*w^2 - w - 23/2]', '[236, 118, w^3 - 6*w - 7]', '[236, 118, 2*w^3 + 5*w^2 - 17*w - 38]', '[241, 241, 1/2*w^3 + 3/2*w^2 - 9/2*w - 17/2]', '[241, 241, -1/2*w^3 + 3/2*w^2 + 9/2*w - 17/2]', '[244, 122, -3/2*w^3 + 1/2*w^2 + 19/2*w + 7/2]', '[244, 122, 3/2*w^3 + 7/2*w^2 - 27/2*w - 55/2]', '[251, 251, w^3 - 5*w + 3]', '[251, 251, 3/2*w^3 - 23/2*w + 2]', '[251, 251, 5/2*w^2 + 3*w - 23/2]', '[251, 251, w^3 + 3*w^2 - 9*w - 24]', '[256, 4, 4]', '[261, 87, 1/2*w^2 + 2*w - 1/2]', '[261, 87, -w^3 + 1/2*w^2 + 6*w + 1/2]', '[261, 87, -w^3 - 1/2*w^2 + 6*w - 1/2]', '[261, 87, -1/2*w^2 + 2*w + 1/2]', '[269, 269, 1/2*w^2 + 2*w - 9/2]', '[269, 269, 1/2*w^2 - 2*w - 9/2]', '[271, 271, 1/2*w^3 - 1/2*w^2 - 3/2*w - 3/2]', '[271, 271, w^3 + 3/2*w^2 - 6*w - 15/2]', '[271, 271, 1/2*w^3 + 3*w^2 - 9/2*w - 16]', '[271, 271, -1/2*w^3 - 2*w^2 + 5/2*w + 13]', '[279, 93, -w^3 + 3/2*w^2 + 8*w - 31/2]', '[279, 93, w^3 + 3/2*w^2 - 8*w - 31/2]', '[281, 281, w^3 - 5/2*w^2 - 8*w + 33/2]', '[281, 281, w^2 + 2*w - 6]', '[281, 281, w^2 - 2*w - 6]', '[281, 281, w^3 + 5/2*w^2 - 8*w - 33/2]', '[284, 142, -1/2*w^3 - 1/2*w^2 + 9/2*w + 1/2]', '[284, 142, 1/2*w^3 - 1/2*w^2 - 9/2*w + 1/2]', '[295, 295, 2*w^2 - 2*w - 9]', '[295, 295, 2*w^3 - 5*w^2 - 10*w + 22]', '[295, 295, 3/2*w^2 + 4*w - 1/2]', '[295, 295, -w^3 - 1/2*w^2 + 7*w - 1/2]', '[304, 38, -w^2 + 2*w + 5]', '[304, 38, w^2 + 2*w - 5]', '[305, 305, -1/2*w^3 + 1/2*w^2 + 5/2*w - 15/2]', '[305, 305, -3/2*w^3 - 9/2*w^2 + 15/2*w + 47/2]', '[305, 305, -3/2*w^3 + 4*w^2 + 9/2*w - 11]', '[305, 305, -1/2*w^3 + 2*w^2 + 3/2*w - 11]', '[311, 311, -5/2*w^3 - 3*w^2 + 37/2*w + 30]', '[311, 311, 2*w^2 - 2*w - 13]', '[316, 158, -1/2*w^3 - 13/2*w^2 + 19/2*w + 79/2]', '[316, 158, -5/2*w^3 - 3/2*w^2 + 35/2*w + 41/2]', '[316, 158, 1/2*w^3 + 3/2*w^2 - 11/2*w - 21/2]', '[316, 158, -1/2*w^3 + 3/2*w^2 + 3/2*w - 17/2]', '[320, 20, -w^3 - w^2 + 7*w + 7]', '[320, 20, -2*w + 2]', '[324, 6, -3/2*w^3 - 3/2*w^2 + 21/2*w + 33/2]', '[324, 18, -1/2*w^3 - 1/2*w^2 + 9/2*w + 17/2]', '[324, 18, 1/2*w^3 - 1/2*w^2 - 9/2*w + 17/2]', '[331, 331, -1/2*w^3 + 7/2*w - 5]', '[331, 331, -w^3 + 5/2*w^2 + 7*w - 29/2]', '[331, 331, w^3 + 5/2*w^2 - 7*w - 29/2]', '[331, 331, 1/2*w^3 - 7/2*w - 5]', '[349, 349, 1/2*w^3 - 2*w^2 - 11/2*w + 16]', '[349, 349, w^3 + 3*w^2 - 6*w - 19]', '[349, 349, 1/2*w^3 - w^2 - 1/2*w - 1]', '[349, 349, 1/2*w^3 + 2*w^2 - 11/2*w - 16]', '[355, 355, 1/2*w^2 + 2*w - 15/2]', '[355, 355, -3/2*w^2 + w + 25/2]', '[355, 355, 1/2*w^3 - w^2 - 5/2*w + 8]', '[355, 355, w^3 + 5/2*w^2 - 7*w - 37/2]', '[356, 178, 1/2*w^3 - 11/2*w^2 + 3/2*w + 59/2]', '[356, 178, -w + 5]', '[359, 359, 1/2*w^3 + 3/2*w^2 - 11/2*w - 15/2]', '[359, 359, w^3 - 4*w^2 - 2*w + 16]', '[361, 19, -2*w^2 + 13]', '[361, 19, -1/2*w^2 + 15/2]', '[361, 361, -3*w^2 - 2*w + 18]', '[361, 361, -3*w^2 + 2*w + 18]', '[379, 379, 1/2*w^3 + 5/2*w^2 - 11/2*w - 37/2]', '[379, 379, -w^3 + 1/2*w^2 + 6*w - 15/2]', '[380, 190, -1/2*w^3 - 5/2*w^2 + 9/2*w + 33/2]', '[380, 190, -1/2*w^3 - 5/2*w^2 + 5/2*w + 29/2]', '[380, 190, -1/2*w^3 + 5/2*w^2 + 5/2*w - 29/2]', '[380, 190, -1/2*w^3 + 5/2*w^2 + 9/2*w - 33/2]', '[389, 389, w^3 - 1/2*w^2 - 7*w + 5/2]', '[389, 389, w^3 + 1/2*w^2 - 7*w - 5/2]', '[395, 395, -w^3 + 5/2*w^2 + 5*w - 27/2]', '[395, 395, 3*w^3 - 19/2*w^2 - 10*w + 75/2]', '[395, 395, -w^3 + 5/2*w^2 + 2*w - 13/2]', '[395, 395, -2*w^3 + 9/2*w^2 + 8*w - 27/2]', '[395, 395, -w^3 - 9/2*w^2 + 3*w + 45/2]', '[395, 395, 3/2*w^3 + 3*w^2 - 17/2*w - 16]', '[395, 395, -5/2*w^3 - 5*w^2 + 23/2*w + 16]', '[395, 395, 1/2*w^2 - 2*w - 17/2]', '[400, 10, 2*w^2 - 12]', '[400, 10, -w^3 - 2*w^2 + 7*w + 16]', '[400, 10, w^3 - 2*w^2 - 7*w + 16]', '[401, 401, 1/2*w^3 + 3/2*w^2 - 5/2*w - 21/2]', '[401, 401, -1/2*w^3 + 3/2*w^2 + 5/2*w - 21/2]', '[405, 15, -3/2*w^3 + 3*w^2 + 15/2*w - 12]', '[405, 15, -3/2*w^2 - 3*w + 9/2]', '[405, 45, -1/2*w^3 - 1/2*w^2 + 9/2*w - 1/2]', '[405, 45, 1/2*w^2 + 2*w - 7/2]', '[405, 45, w^3 + 1/2*w^2 - 7*w - 9/2]', '[405, 45, 1/2*w^3 - 1/2*w^2 - 9/2*w - 1/2]', '[409, 409, -2*w^3 - 5*w^2 + 18*w + 38]', '[409, 409, 1/2*w^3 - w^2 - 13/2*w + 1]', '[419, 419, -1/2*w^3 + 1/2*w^2 + 5/2*w - 19/2]', '[419, 419, 1/2*w^3 + 1/2*w^2 - 5/2*w - 19/2]', '[431, 431, 1/2*w^3 - 3/2*w^2 - 7/2*w + 11/2]', '[431, 431, 1/2*w^3 + 3/2*w^2 - 7/2*w - 11/2]', '[436, 218, w^3 - w^2 - 6*w + 4]', '[436, 218, 3/2*w^3 + 3/2*w^2 - 25/2*w - 29/2]', '[436, 218, -9/2*w^3 - 9/2*w^2 + 67/2*w + 95/2]', '[436, 218, 1/2*w^3 - 1/2*w^2 - 11/2*w + 3/2]', '[439, 439, -1/2*w^3 + 5/2*w^2 + 5/2*w - 27/2]', '[439, 439, -1/2*w^3 - 5/2*w^2 + 5/2*w + 27/2]', '[445, 445, 3/2*w^3 + 3*w^2 - 25/2*w - 22]', '[445, 445, w^3 - 7*w + 1]', '[445, 445, -w^3 + 7*w + 1]', '[445, 445, 3*w^3 - 19/2*w^2 - 9*w + 67/2]', '[449, 449, w^3 - 1/2*w^2 - 7*w + 7/2]', '[449, 449, w^3 + 1/2*w^2 - 7*w - 7/2]', '[461, 461, w^3 - 7/2*w^2 - 5*w + 37/2]', '[461, 461, -1/2*w^2 + 2*w + 21/2]', '[464, 58, -3*w^2 - 2*w + 17]', '[464, 58, -3*w^2 + 2*w + 17]', '[475, 95, -w^3 + 2*w^2 + 7*w - 11]', '[475, 95, w^3 - 1/2*w^2 - 6*w + 1/2]', '[475, 95, -w^3 - 3*w^2 + 9*w + 20]', '[475, 95, -w^3 + 3*w^2 + 9*w - 20]', '[475, 95, w^3 + 1/2*w^2 - 6*w - 1/2]', '[475, 95, -w^3 - 2*w^2 + 7*w + 11]', '[479, 479, -w^3 + 4*w^2 + 4*w - 20]', '[479, 479, 1/2*w^3 - 3/2*w + 8]', '[484, 22, w^3 + 4*w^2 - 10*w - 29]', '[484, 22, -2*w^3 - 3*w^2 + 15*w + 28]', '[491, 491, 1/2*w^3 - 5/2*w^2 - 3/2*w + 29/2]', '[491, 491, 1/2*w^3 + 1/2*w^2 - 1/2*w - 7/2]', '[491, 491, 1/2*w^3 + w^2 - 11/2*w - 8]', '[491, 491, -1/2*w^3 + w^2 + 5/2*w - 12]', '[496, 62, w^3 - 7*w]', '[499, 499, 3*w^2 - w - 21]', '[499, 499, 1/2*w^3 + 5/2*w^2 - 11/2*w - 29/2]', '[499, 499, w^3 + 5*w^2 - 11*w - 32]', '[499, 499, 3*w^2 + w - 21]', '[500, 10, 1/2*w^3 + 1/2*w^2 - 11/2*w - 11/2]', '[500, 10, -w^3 + w^2 + 6*w - 6]', '[500, 50, -1/2*w^3 + 3/2*w^2 + 9/2*w - 15/2]', '[500, 50, 1/2*w^3 + 3/2*w^2 - 9/2*w - 15/2]', '[509, 509, -w^3 + 3/2*w^2 + 4*w - 3/2]', '[509, 509, 1/2*w^3 + 3*w^2 - 3/2*w - 18]', '[524, 262, -7/2*w^3 - 11/2*w^2 + 55/2*w + 95/2]', '[524, 262, -3/2*w^3 + 3/2*w^2 + 17/2*w - 5/2]', '[529, 23, 1/2*w^3 - 2*w^2 - 11/2*w + 11]', '[529, 23, 1/2*w^3 + 2*w^2 - 11/2*w - 11]', '[531, 177, w^3 - 1/2*w^2 - 7*w - 3/2]', '[531, 177, 2*w^3 - 9/2*w^2 - 16*w + 65/2]', '[531, 177, w^3 + 1/2*w^2 - 7*w + 3/2]', '[531, 177, 2*w^3 + 9/2*w^2 - 16*w - 65/2]', '[545, 545, 1/2*w^3 - 3/2*w^2 + 3/2*w - 3/2]', '[545, 545, -1/2*w^3 + w^2 + 9/2*w - 12]', '[545, 545, -5/2*w^3 + 5*w^2 + 21/2*w - 12]', '[545, 545, 2*w^3 + 3/2*w^2 - 11*w + 5/2]', '[545, 545, -2*w - 7]', '[545, 545, -w^3 - 13/2*w^2 + 2*w + 71/2]', '[545, 545, w^3 + 7/2*w^2 - 8*w - 53/2]', '[545, 545, 1/2*w^3 - 1/2*w^2 - 7/2*w + 17/2]', '[549, 183, w^3 - 5/2*w^2 - 10*w + 45/2]', '[549, 183, -w^3 - 1/2*w^2 + 6*w + 17/2]', '[549, 183, -w^3 + 1/2*w^2 + 6*w - 17/2]', '[549, 183, w^3 + 5/2*w^2 - 10*w - 45/2]', '[551, 551, -w^3 + 6*w - 2]', '[551, 551, -3/2*w^2 + 3*w + 5/2]', '[551, 551, 3/2*w^2 + 3*w - 5/2]', '[551, 551, -w^3 + 6*w + 2]', '[569, 569, 1/2*w^3 + w^2 - 11/2*w - 3]', '[569, 569, -1/2*w^3 + w^2 + 11/2*w - 3]', '[571, 571, 5/2*w^2 + 2*w - 33/2]', '[571, 571, 2*w^3 - 5/2*w^2 - 16*w + 49/2]', '[571, 571, 2*w^3 + 5/2*w^2 - 16*w - 49/2]', '[571, 571, 5/2*w^2 - 2*w - 33/2]', '[576, 12, -w^3 + w^2 + 7*w - 3]', '[576, 12, -w^3 - w^2 + 7*w + 3]', '[580, 290, 2*w^2 + 3*w - 9]', '[580, 290, w^3 - 3*w^2 - 10*w + 22]', '[580, 290, -w^3 - 3*w^2 + 10*w + 22]', '[580, 290, 2*w^2 - 3*w - 9]', '[589, 589, 5/2*w^2 + w - 31/2]', '[589, 589, 5/2*w^2 - w - 31/2]', '[599, 599, 1/2*w^3 - 1/2*w^2 - 11/2*w - 3/2]', '[599, 599, -1/2*w^3 - 1/2*w^2 + 11/2*w - 3/2]', '[601, 601, 2*w^3 + 3/2*w^2 - 15*w - 35/2]', '[601, 601, 5/2*w^3 + 3*w^2 - 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2*w^2 + 1/2*w + 7]', '[1811, 1811, 2*w^3 + 15/2*w^2 - 20*w - 107/2]', '[1811, 1811, 7/2*w^2 - 3*w - 45/2]', '[1811, 1811, -w^3 + 1/2*w^2 + 10*w - 1/2]', '[1829, 1829, 3/2*w^3 + 5/2*w^2 - 23/2*w - 31/2]', '[1829, 1829, -w^3 + 7/2*w^2 + 6*w - 31/2]', '[1831, 1831, -1/2*w^3 + 4*w^2 + 11/2*w - 27]', '[1831, 1831, -1/2*w^3 - 4*w^2 + 11/2*w + 27]', '[1844, 922, -1/2*w^3 - 7/2*w^2 + 7/2*w + 49/2]', '[1844, 922, -w + 7]', '[1849, 43, -3/2*w^3 + 3*w^2 + 23/2*w - 19]', '[1849, 43, -1/2*w^2 - 4*w + 17/2]', '[1856, 116, -2*w^2 + 2*w + 16]', '[1856, 116, -2*w^2 - 2*w + 16]', '[1871, 1871, -1/2*w^3 - 2*w^2 + 5/2*w + 22]', '[1871, 1871, w^3 + 3/2*w^2 - 9*w - 15/2]', '[1871, 1871, -w^3 + 3/2*w^2 + 9*w - 15/2]', '[1871, 1871, 1/2*w^3 - 2*w^2 - 5/2*w + 22]', '[1879, 1879, 1/2*w^3 + 2*w^2 - 5/2*w - 17]', '[1879, 1879, -1/2*w^3 + 2*w^2 + 5/2*w - 17]', '[1889, 1889, 1/2*w^3 + 2*w^2 - 11/2*w - 9]', '[1889, 1889, -1/2*w^3 + 2*w^2 + 11/2*w - 9]', '[1891, 1891, w^3 + 5/2*w^2 - 5*w - 31/2]', '[1891, 1891, 3/2*w^2 + 2*w - 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4*w^2 + 5/2*w + 27]', '[1949, 1949, 3*w^2 + 3*w - 13]', '[1949, 1949, 3/2*w^3 + 2*w^2 - 27/2*w - 12]', '[1951, 1951, 3/2*w^3 + w^2 - 21/2*w - 6]', '[1951, 1951, 2*w^3 - 5*w^2 - 6*w + 12]', '[1951, 1951, 3/2*w^3 + 11/2*w^2 - 27/2*w - 81/2]', '[1951, 1951, 3/2*w^3 - w^2 - 21/2*w + 6]', '[1964, 982, -1/2*w^3 - 19/2*w^2 + 23/2*w + 113/2]', '[1964, 982, 4*w^3 + 10*w^2 - 35*w - 75]', '[1964, 982, 1/2*w^3 - 9/2*w^2 + 1/2*w + 39/2]', '[1964, 982, 5/2*w^3 + 13/2*w^2 - 41/2*w - 101/2]', '[1975, 395, 1/2*w^3 - 13/2*w - 4]', '[1975, 395, -1/2*w^3 + 5/2*w^2 + 11/2*w - 25/2]', '[1975, 395, 5/2*w^3 - 3*w^2 - 37/2*w + 27]', '[1975, 395, -w^3 - 9/2*w^2 + 12*w + 67/2]', '[1975, 395, w^3 - 2*w^2 - 6*w + 2]', '[1975, 395, -w^3 + 1/2*w^2 + 4*w + 5/2]', '[1975, 395, -w^3 - 1/2*w^2 + 4*w - 5/2]', '[1975, 395, w^3 + 2*w^2 - 6*w - 2]', '[1975, 395, -w^3 + 9/2*w^2 + 12*w - 67/2]', '[1975, 395, 1/2*w^3 + 5/2*w^2 - 11/2*w - 25/2]', '[1975, 395, -5/2*w^3 - 3*w^2 + 37/2*w + 27]', '[1975, 395, -1/2*w^3 + 13/2*w - 4]', '[1979, 1979, 1/2*w^3 - 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49/2]', '[9995, 9995, 5/2*w^3 + 8*w^2 - 31/2*w - 50]', '[10000, 10, 10]', '[10000, 50, -w^3 + 3*w + 8]', '[10000, 50, w^3 - 3*w + 8]', '[10000, 50, -w^3 + 4*w^2 + 11*w - 34]', '[10000, 50, w^3 + 4*w^2 - 11*w - 34]'], 'label': '4.4.12400.1', 'narrow_class_no': 2, 'primes': ['[4, 2, -1/2*w^3 - 1/2*w^2 + 7/2*w + 11/2]', '[5, 5, -1/2*w^3 + w^2 + 5/2*w - 4]', '[5, 5, -1/2*w^2 - w + 3/2]', '[9, 3, -1/2*w^3 + 1/2*w^2 + 7/2*w - 9/2]', '[9, 3, -1/2*w^3 - 1/2*w^2 + 7/2*w + 9/2]', '[19, 19, -1/2*w^2 + w + 5/2]', '[19, 19, 1/2*w^2 + w - 5/2]', '[29, 29, -3/2*w^2 - w + 17/2]', '[29, 29, -3/2*w^2 + w + 17/2]', '[31, 31, 1/2*w^3 - 7/2*w]', '[59, 59, 1/2*w^2 + w - 11/2]', '[59, 59, 1/2*w^2 - w - 11/2]', '[61, 61, -1/2*w^3 + w^2 + 7/2*w - 5]', '[61, 61, 1/2*w^3 + w^2 - 7/2*w - 5]', '[71, 71, -1/2*w^3 - 2*w^2 + 11/2*w + 13]', '[71, 71, 3/2*w^3 + 2*w^2 - 23/2*w - 18]', '[79, 79, 1/2*w^3 + 1/2*w^2 - 7/2*w - 1/2]', '[79, 79, -2*w^2 + w + 10]', '[79, 79, 2*w^2 + w - 10]', '[79, 79, 1/2*w^3 - 1/2*w^2 - 7/2*w + 1/2]', '[89, 89, 1/2*w^3 - 2*w^2 - 5/2*w + 11]', '[89, 89, -1/2*w^2 + w + 15/2]', '[109, 109, -w^3 + 7*w + 3]', '[109, 109, 1/2*w^3 - 2*w^2 - 9/2*w + 12]', '[109, 109, w^3 + w^2 - 8*w - 11]', '[109, 109, w^3 - 7*w + 3]', '[121, 11, 3/2*w^2 - 19/2]', '[121, 11, -1/2*w^2 + 13/2]', '[131, 131, -1/2*w^3 + 3/2*w^2 + 7/2*w - 15/2]', '[131, 131, -1/2*w^3 + 9/2*w + 3]', '[179, 179, -w^3 - 5/2*w^2 + 9*w + 35/2]', '[179, 179, 1/2*w^3 + 2*w^2 - 7/2*w - 13]', '[179, 179, -1/2*w^3 + 2*w^2 + 7/2*w - 13]', '[179, 179, 3/2*w^3 + 4*w^2 - 27/2*w - 29]', '[181, 181, -1/2*w^3 + w^2 + 5/2*w - 7]', '[181, 181, 1/2*w^3 + w^2 - 5/2*w - 7]', '[191, 191, 2*w^2 + w - 12]', '[191, 191, 2*w^2 - w - 12]', '[211, 211, w^3 - w^2 - 7*w + 4]', '[211, 211, -w^3 - w^2 + 7*w + 4]', '[229, 229, 3/2*w^2 + w - 23/2]', '[229, 229, 3/2*w^2 - w - 23/2]', '[241, 241, 1/2*w^3 + 3/2*w^2 - 9/2*w - 17/2]', '[241, 241, -1/2*w^3 + 3/2*w^2 + 9/2*w - 17/2]', '[251, 251, w^3 - 5*w + 3]', '[251, 251, 3/2*w^3 - 23/2*w + 2]', '[251, 251, 5/2*w^2 + 3*w - 23/2]', '[251, 251, w^3 + 3*w^2 - 9*w - 24]', '[269, 269, 1/2*w^2 + 2*w - 9/2]', '[269, 269, 1/2*w^2 - 2*w - 9/2]', '[271, 271, 1/2*w^3 - 1/2*w^2 - 3/2*w - 3/2]', '[271, 271, w^3 + 3/2*w^2 - 6*w - 15/2]', '[271, 271, 1/2*w^3 + 3*w^2 - 9/2*w - 16]', '[271, 271, -1/2*w^3 - 2*w^2 + 5/2*w + 13]', '[281, 281, w^3 - 5/2*w^2 - 8*w + 33/2]', '[281, 281, w^2 + 2*w - 6]', '[281, 281, w^2 - 2*w - 6]', '[281, 281, w^3 + 5/2*w^2 - 8*w - 33/2]', '[311, 311, -5/2*w^3 - 3*w^2 + 37/2*w + 30]', '[311, 311, 2*w^2 - 2*w - 13]', '[331, 331, -1/2*w^3 + 7/2*w - 5]', '[331, 331, -w^3 + 5/2*w^2 + 7*w - 29/2]', '[331, 331, w^3 + 5/2*w^2 - 7*w - 29/2]', '[331, 331, 1/2*w^3 - 7/2*w - 5]', '[349, 349, 1/2*w^3 - 2*w^2 - 11/2*w + 16]', '[349, 349, w^3 + 3*w^2 - 6*w - 19]', '[349, 349, 1/2*w^3 - w^2 - 1/2*w - 1]', '[349, 349, 1/2*w^3 + 2*w^2 - 11/2*w - 16]', '[359, 359, 1/2*w^3 + 3/2*w^2 - 11/2*w - 15/2]', '[359, 359, w^3 - 4*w^2 - 2*w + 16]', '[361, 19, -1/2*w^2 + 15/2]', '[379, 379, 1/2*w^3 + 5/2*w^2 - 11/2*w - 37/2]', '[379, 379, -w^3 + 1/2*w^2 + 6*w - 15/2]', '[389, 389, w^3 - 1/2*w^2 - 7*w + 5/2]', '[389, 389, w^3 + 1/2*w^2 - 7*w - 5/2]', '[401, 401, 1/2*w^3 + 3/2*w^2 - 5/2*w - 21/2]', '[401, 401, -1/2*w^3 + 3/2*w^2 + 5/2*w - 21/2]', '[409, 409, -2*w^3 - 5*w^2 + 18*w + 38]', '[409, 409, 1/2*w^3 - w^2 - 13/2*w + 1]', '[419, 419, -1/2*w^3 + 1/2*w^2 + 5/2*w - 19/2]', '[419, 419, 1/2*w^3 + 1/2*w^2 - 5/2*w - 19/2]', '[431, 431, 1/2*w^3 - 3/2*w^2 - 7/2*w + 11/2]', '[431, 431, 1/2*w^3 + 3/2*w^2 - 7/2*w - 11/2]', '[439, 439, -1/2*w^3 + 5/2*w^2 + 5/2*w - 27/2]', '[439, 439, -1/2*w^3 - 5/2*w^2 + 5/2*w + 27/2]', '[449, 449, w^3 - 1/2*w^2 - 7*w + 7/2]', '[449, 449, w^3 + 1/2*w^2 - 7*w - 7/2]', '[461, 461, w^3 - 7/2*w^2 - 5*w + 37/2]', '[461, 461, -1/2*w^2 + 2*w + 21/2]', '[479, 479, -w^3 + 4*w^2 + 4*w - 20]', '[479, 479, 1/2*w^3 - 3/2*w + 8]', '[491, 491, 1/2*w^3 - 5/2*w^2 - 3/2*w + 29/2]', '[491, 491, 1/2*w^3 + 1/2*w^2 - 1/2*w - 7/2]', '[491, 491, 1/2*w^3 + w^2 - 11/2*w - 8]', '[491, 491, -1/2*w^3 + w^2 + 5/2*w - 12]', '[499, 499, 3*w^2 - w - 21]', '[499, 499, 1/2*w^3 + 5/2*w^2 - 11/2*w - 29/2]', '[499, 499, w^3 + 5*w^2 - 11*w - 32]', '[499, 499, 3*w^2 + w - 21]', '[509, 509, -w^3 + 3/2*w^2 + 4*w - 3/2]', '[509, 509, 1/2*w^3 + 3*w^2 - 3/2*w - 18]', '[529, 23, 1/2*w^3 - 2*w^2 - 11/2*w + 11]', '[529, 23, 1/2*w^3 + 2*w^2 - 11/2*w - 11]', '[569, 569, 1/2*w^3 + w^2 - 11/2*w - 3]', '[569, 569, -1/2*w^3 + w^2 + 11/2*w - 3]', '[571, 571, 5/2*w^2 + 2*w - 33/2]', '[571, 571, 2*w^3 - 5/2*w^2 - 16*w + 49/2]', '[571, 571, 2*w^3 + 5/2*w^2 - 16*w - 49/2]', '[571, 571, 5/2*w^2 - 2*w - 33/2]', '[599, 599, 1/2*w^3 - 1/2*w^2 - 11/2*w - 3/2]', '[599, 599, -1/2*w^3 - 1/2*w^2 + 11/2*w - 3/2]', '[601, 601, 2*w^3 + 3/2*w^2 - 15*w - 35/2]', '[601, 601, 5/2*w^3 + 3*w^2 - 39/2*w - 29]', '[619, 619, 5/2*w^3 + 5/2*w^2 - 37/2*w - 51/2]', '[619, 619, w^3 - 1/2*w^2 - 5*w + 11/2]', '[619, 619, 3/2*w^2 - 2*w - 23/2]', '[619, 619, w^3 + 3*w^2 - 10*w - 21]', '[631, 631, -5/2*w^3 + 33/2*w + 13]', '[631, 631, 3/2*w^3 - 5*w^2 - 13/2*w + 22]', '[631, 631, -2*w^3 - 2*w^2 + 14*w + 23]', '[631, 631, -5/2*w^2 - 5*w + 13/2]', '[641, 641, -1/2*w^3 + 1/2*w^2 + 11/2*w - 5/2]', '[641, 641, 1/2*w^3 + 1/2*w^2 - 11/2*w - 5/2]', '[659, 659, -3/2*w^3 - w^2 + 23/2*w + 14]', '[659, 659, 3/2*w^3 + 5/2*w^2 - 19/2*w - 27/2]', '[661, 661, -1/2*w^3 + 1/2*w^2 + 11/2*w - 9/2]', '[661, 661, w^3 + w^2 - 8*w - 5]', '[661, 661, -1/2*w^3 + 2*w^2 + 7/2*w - 8]', '[661, 661, -1/2*w^3 - 1/2*w^2 + 11/2*w + 9/2]', '[691, 691, 1/2*w^3 - 3/2*w^2 - 3/2*w + 19/2]', '[691, 691, 1/2*w^3 + 3/2*w^2 - 3/2*w - 19/2]', '[709, 709, 1/2*w^3 - 2*w^2 - 3/2*w + 12]', '[709, 709, 1/2*w^3 + 2*w^2 - 3/2*w - 12]', '[751, 751, 3/2*w^3 - w^2 - 21/2*w + 11]', '[751, 751, 3/2*w^3 + w^2 - 21/2*w - 11]', '[761, 761, 2*w^3 + 11/2*w^2 - 17*w - 85/2]', '[761, 761, -3/2*w^3 - 4*w^2 + 17/2*w + 23]', '[769, 769, w^3 - 7/2*w^2 - 8*w + 45/2]', '[769, 769, -1/2*w^3 - 5/2*w^2 + 5/2*w + 35/2]', '[769, 769, -1/2*w^3 + 5/2*w^2 + 5/2*w - 35/2]', '[769, 769, w^3 + 7/2*w^2 - 8*w - 45/2]', '[809, 809, w^3 - 7/2*w^2 - 7*w + 41/2]', '[809, 809, w^3 + 7/2*w^2 - 7*w - 41/2]', '[811, 811, -1/2*w^3 - 9/2*w^2 + 13/2*w + 59/2]', '[811, 811, 3*w^3 + 5*w^2 - 24*w - 45]', '[821, 821, -2*w^3 - 7/2*w^2 + 12*w + 33/2]', '[821, 821, w^3 - 4*w^2 - w + 13]', '[829, 829, -w^3 + 1/2*w^2 + 8*w - 1/2]', '[829, 829, w^3 + 1/2*w^2 - 8*w - 1/2]', '[839, 839, w^3 - 3/2*w^2 - 7*w + 13/2]', '[839, 839, w^3 + 3/2*w^2 - 7*w - 13/2]', '[841, 29, 5/2*w^2 - 27/2]', '[859, 859, 1/2*w^3 - 7/2*w - 6]', '[859, 859, -3/2*w^3 + 2*w^2 + 21/2*w - 15]', '[859, 859, 3/2*w^3 + 2*w^2 - 21/2*w - 15]', '[859, 859, 1/2*w^3 - 7/2*w + 6]', '[881, 881, -3/2*w^3 + 21/2*w + 8]', '[881, 881, -2*w^3 + 1/2*w^2 + 13*w + 15/2]', '[919, 919, -3/2*w^3 + 5/2*w^2 + 15/2*w - 19/2]', '[919, 919, 3/2*w^3 + w^2 - 21/2*w - 4]', '[929, 929, 1/2*w^3 + w^2 - 9/2*w - 1]', '[929, 929, 1/2*w^3 - w^2 - 9/2*w + 1]', '[941, 941, 2*w^3 + 7*w^2 - 19*w - 51]', '[941, 941, 5/2*w^2 - 3*w - 33/2]', '[961, 31, -w^2 + 12]', '[971, 971, 3/2*w^2 - 3*w - 25/2]', '[971, 971, w^3 + 7/2*w^2 - 6*w - 39/2]', '[991, 991, 1/2*w^3 - 3/2*w^2 - 13/2*w + 13/2]', '[991, 991, w^3 + 5/2*w^2 - 5*w - 29/2]', '[991, 991, w^3 - 5/2*w^2 - 5*w + 29/2]', '[991, 991, -3/2*w^3 + 2*w^2 + 17/2*w - 7]']}
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nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [31, 0, -12, 0, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 12400, 'disc_rad': 310, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[2, 2]]], [5, [0]], [7, [[4, 1]]], [11, [[2, 2]]], [13, [[4, 1]]], [17, [[4, 1]]], [19, [[2, 1], [1, 2]]], [23, [[2, 2]]], [29, [[2, 1], [1, 2]]], [31, [0]], [37, [[4, 1]]], [41, [[2, 2]]], [43, [[2, 2]]], [47, [[4, 1]]], [53, [[4, 1]]], [59, [[2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 4, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 35.21363372331802, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.12400.1', 'local_algs': ['2.4.4.3', '5.2.1.1', '5.2.1.1', '31.2.1.2', '31.2.0.1'], 'monogenic': -1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 5, 31], 'rd': 10.5525014692, 'regulator': {'__RealLiteral__': 0, 'data': '6.39680161249', 'prec': 44}, 'res': {'gal': ['-1091,-2294,-550,1178,555,-62,-48,0,1'], 'sib': ['25,-10,-20,-2,1', '-1091,-2294,-550,1178,555,-62,-48,0,1']}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{2} - \\frac{7}{2} \\)', '\\( \\frac{1}{2} a^{3} + a^{2} - \\frac{7}{2} a - 7 \\)', '\\( \\frac{1}{2} a^{3} - 2 a^{2} - \\frac{3}{2} a + 9 \\)'], 'used_grh': False, 'zk': ['1', 'a', '1/2*a^2 - 1/2', '1/2*a^3 - 1/2*a']}