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hmf_forms • Show schema
Hide schema
{'deg': 2, 'dimension': 1, 'disc': 12, 'field_bad_primes': [2, 3], 'field_label': '2.2.12.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '2.2.12.1-1734.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [2, 3, 17], 'level_ideal': '[1734, 102, -17*w + 51]', 'level_label': '1734.1', 'level_norm': 1734, 'parallel_weight': 2, 'short_label': '1734.1-b', 'weight': '[2, 2]'}
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hmf_hecke • Show schema
Hide schema
{'AL_eigenvalues': [['[2, 2, -w + 1]', 1], ['[3, 3, w]', 1], ['[289, 17, -17]', -1]], 'hecke_eigenvalues': [-1, -1, 4, 4, -2, -2, 0, 0, -6, -2, -2, 0, 0, -14, -12, -12, -10, -10, 0, 0, 10, 10, -4, -4, -14, -14, 4, 4, -10, -10, 12, 12, -2, -2, -16, -16, 12, 12, 14, 14, 16, 16, 18, 18, -4, -4, -26, -26, 0, 0, 2, 2, -28, -28, 8, 8, 30, 30, 1, 0, 0, 10, 10, -14, -14, -28, -28, 14, 14, 24, 24, -22, 6, 6, 16, 16, -26, -26, 26, 26, -4, -4, 22, 22, 8, 8, -14, -14, 4, 4, 10, 10, 12, 12, -24, -24, -12, -12, 0, 0, -10, -10, -36, -36, 2, 2, 20, 20, 8, 8, -6, -6, 38, 38, 40, 40, -36, -36, 6, 6, -46, -46, 20, 20, 46, 46, -40, -40, 46, 46, 16, 16, -10, -10, -30, -30, 20, 20, -34, -34, 0, 0, 42, -2, -2, 32, 32, 22, 22, 48, 48, -8, -8, -22, -22, 28, 28, 2, 4, 4, -48, -48, -2, -2, 34, 34, -12, -12, -50, -50, -32, -32, -54, -54, -18, -18, 12, 12, -2, -2, -32, -32, 22, 22, 26, 26, -8, -8, -62, -62, -44, -44, -4, -4, -46, -46, -42, -42, 56, 56, 22, 22, -30, -30, 36, 36, -36, -36, 2, 2, -28, -28, -32, -32, 26, 26, 16, 16, -26, -26, 12, 12, -58, -58, 56, 56, 52, 52, -34, -34, 16, 16, -30, -30, -12, -12, -40, -40, 76, 76, -50, -50, 0, 0, -68, -68, 16, 16, -2, -2, 72, 72, 10, 10, 12, 12, 14, 14, -6, -6, 44, 44, 30, 30, 18, 70, 70, -10, -10, 26, 26, -14, -14, 20, 20, -18, -18, 74, 74, -36, -36, 48, 48, -80, -80, 58, 54, 54, 48, 48, 2, 2, 44, 44, -28, -28, -26, -26, 4, 4, -22, -22, 12, 12, -14, -14, -60, -60, -58, -58, 40, 40, -58, -58, -24, -24, 88, 88, 42, 42, -84, -84, -8, -8, 34, 34, -22, -22, -46, -46, -24, -24, 22, 22, 76, 76, -12, -12, 78, 78, 10, 10, 6, 6, -36, -36, -66, -66, 40, 40, 26, 26, 22, 22, -32, -32, 20, 20, -40, -40, -66, -66, 32, 32, 36, 36, -86, -86, -22, -22, 12, 12, 72, 72, -58, -58, 12, 12, -24, -24, 34, 34, 58, 58, -64, -64, 86, 86, -64, -64, -62, -62, 36, 36, -72, -72, -54, -54, 54, 54, -50, -50, -70, 92, 92, -46, -46, -76, -76, 42, 42, 24, 24, 56, 56, 14, 14, -40, -40, 4, 4, 26, 26, -36, -36, -16, -16, 58, 58, 28, 28, 40, 40, -58, -58, 10, 10, -26, -26, 84, 84, 38, 38, 48, 48, 50, 50, -104, -104, 50, 50, 14, 14, -16, -16, 44, 44, -46, -46, -82, -82, 92, 92, 30, 30, -4, -4, 62, 62, 50, 50, 36, 36, 28, 28, -24, -24, 34, 34, -12, -12, -58, -58, -8, -8, 74, 74, -46, -46, -76, -76, 30, 30, -52, -52, -50, -50, 8, 8, 10, 10, 44, 44, -98, -98, -34, -34, 24, 24, 22, 22, 36, 36, -24, -24, 90, 90, -14, -14, -90, -90, 72, 72, 62, 62, -48, -48, 10, 10, 12, 12, -46, -46, -108, -108, -108, -108, 70, 70, 88, 88, -58, -58, 50, 50, -88, -88, -84, -84, 36, 36, -64, -64, -68, -68, 38, 38, -70, -70, 0, 0, -92, -92, 94, 94, 0, 0, 2, 2, 36, 36, -70, -70, 114, 114, -22, -22, -52, -52, 12, 12, -82, -82, 48, 48, 82, 82, 20, 20, -54, -54, -98, -98, -16, -16, 122, 122, -84, -84, 0, 0, 10, 34, 34, 36, 36, -36, -36, 94, 94, 66, 66, -16, -16, 62, 62, -42, -42, -84, -84, -14, -14, -72, -72, -132, -132, 120, 120, 10, 10, 64, 64, 12, 12, 46, 46, -40, -40, 98, 98, -114, -114, -18, -18, -24, -24, -2, -2, -64, -64, 92, 92, -34, -34, -48, -48, -74, -74, 80, 80, -38, -38, -94, -94, 36, 36, -24, -24, -60, -60, 30, 30, -64, -64, -44, -44, -18, -18, -134, -134, -76, -76, 28, 28, 22, 22, 122, 122, 72, 72, 18, 18, 64, 64, 82, 82, 88, 88, 72, 72, 132, 132, -48, -48, -18, -18, -74, -74, 74, 74, -88, -88, 4, 4, -36, -36, -88, -88, 50, 50, -92, -92, -26, -26, 2, 2, -10, -10, -24, -24, 96, 96, -38, -38, -52, -52, 6, 6, -6, -6, -98, -98, 96, 96, -22, -22, 62, 62, -80, -80, -40, -40, -26, -26, -84, -84, 98, 98, -124, -124, -50, -50, -48, -48, 58, 58, -96, -96, 128, 128, -100, -100, 114, 114, 108, 108, -28, -28, 70, 70, -72, -72, 26, 26, 42, 42, 44, 44, 22, 22, -56, -56, 4, 4, -70, -70, 110, 110, -94, 144, 144, -90, -90, -88, -88, 132, 132, 70, 70, 72, 72, -36, -36, -158, -158, 72, 72, -102, -102, 70, 70, 118, 118, 62, 62, -106, -106, 82, 82, 100, 100, -62, -62, 112, 112, -38, -38, 92, 92, -78, -78, -160, -160, -26, -26, 60, 60, -82, -82, -14, -14, 14, 14, -144, -144, -82, -82, -108, -108, -98, -98, -24, -24, 10, 10, 140, 140, -44, -44, 22, 22, -38, -38, -72, -72, 44, 44, 160, 160, -148, -148, 118, 118, 120, 120, 18, 18, -76, -76, -24, -24, 14, 14, -44, -44, -36, -36, 18, 18, -10, -10, 48, 48, 24, 24, 152, 152, -134, -134, 120, 120, -70, -70, 108, 108, -12, -12, 38, 38, 142, 142, 120, 120, 108, 108, 98, 98, 100, 100, 62, 62, -22, -22, 28, 28, -34, -34, 10, 10, -30, -30, -54, -54, 84, 84, 14, 14, -136, -136, 66, 66, 20, 20, -4, -4, 34, 34, -156, -156, 62, 62, -144, -144, -118, -118, -42, -42, -128, -128, 104, 104, 14, 14, -76, -76, 38, 38, -78, -78, -60, -60, -72, -72, -26, -26, -144, -144, 118, 118, -54, -54, -106, -106, 24, 24, 130, 130, 148, 148, 140, 140, -24, -24, -142, -74, -74, -38, -38, 34, 34, -104, -104, -146, -146, 64, 64, 10, 10, -10, -10, -160, -160, 116, 116, -132, -132, -30, -30, 36, 36, 82, 82, 4, 4, -106, -106, 48, 48, -86, -86, -180, -180, -154, -154, 60, 60, 14, 14, 94, 94, -150, -150, 114, 114, 20, 20, 58, 58, 156, 156, -154, -154, -168, -168, 48, 48, 118, 118, 10, 10, 16, 16, -42, -42, -84, -84, -130, -130, -46, -46, -48, -48, 94, 94, 146, 146, 52, 52, 138, 138, 130, 130, -172, -172, -134, -134, -72, -72, -8, -8, 12, 12, 54, 54, 48, 48, -52, -52, -82, -82, 2, 2, -178, -178, -152, -152, 124, 124, -96, -96, 42, 42, 12, 12, 62, 62, 74, 74, 12, 12, -50, -50, 94, 94, -50, -50, 14, 14, -180, -180, 36, 36, 168, 168, 26, 26, 134, 134, -120, -120, -92, -92, -6, -6, -10, -10, -60, -60, -58, -58, 116, 116, -26, -26, 24, 24, 122, 122, -108, -108, -160, -160, -116, -116, -132, -132, 152, 152, 124, 124, -62, -62, -130, -130, 88, 88, 82, 82, 54, 54, 162, 162, 192, 192, 90, 90, -42, -42, 0, 0, -104, -104, 42, 42, 62, 62, 0, 0, 84, 84, 122, 122, -34, -34, 16, 16, 148, 148, -88, -88, 134, 134, -52, -52, -146, -146, -130, -130], 'hecke_polynomial': 'x', 'label': '2.2.12.1-1734.1-b'}
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hmf_fields • Show schema
Hide schema
{'degree': 2, 'discriminant': 12, 'ideals': ['[1, 1, 1]', '[2, 2, -w + 1]', '[3, 3, w]', '[4, 2, 2]', '[6, 6, w - 3]', '[8, 4, -2*w + 2]', '[9, 3, 3]', '[11, 11, -2*w + 1]', '[11, 11, 2*w + 1]', '[12, 6, 2*w]', '[13, 13, w + 4]', '[13, 13, -w + 4]', '[16, 4, 4]', '[18, 6, -3*w + 3]', '[22, 22, w + 5]', '[22, 22, w - 5]', '[23, 23, -3*w + 2]', '[23, 23, 3*w + 2]', '[24, 12, 2*w - 6]', '[25, 5, 5]', '[26, 26, -3*w - 1]', '[26, 26, -3*w + 1]', '[27, 9, 3*w]', '[32, 8, -4*w + 4]', '[33, 33, w + 6]', '[33, 33, w - 6]', '[36, 6, 6]', '[37, 37, 2*w - 7]', '[37, 37, -2*w - 7]', '[39, 39, 4*w - 3]', '[39, 39, 4*w + 3]', '[44, 22, -4*w + 2]', '[44, 22, 4*w + 2]', '[46, 46, w + 7]', '[46, 46, w - 7]', '[47, 47, -4*w - 1]', '[47, 47, 4*w - 1]', '[48, 12, 4*w]', '[49, 7, -7]', '[50, 10, -5*w + 5]', '[52, 26, 2*w + 8]', '[52, 26, -2*w + 8]', '[54, 18, 3*w - 9]', '[59, 59, 5*w - 4]', '[59, 59, -5*w - 4]', '[61, 61, -w - 8]', '[61, 61, w - 8]', '[64, 8, 8]', '[66, 66, 5*w + 3]', '[66, 66, -5*w + 3]', '[69, 69, 2*w - 9]', '[69, 69, 2*w + 9]', '[71, 71, 5*w - 2]', '[71, 71, -5*w - 2]', '[72, 12, -6*w + 6]', '[73, 73, 3*w - 10]', '[73, 73, -3*w - 10]', '[74, 74, 9*w - 13]', '[74, 74, 5*w - 1]', '[75, 15, 5*w]', '[78, 78, -w - 9]', '[78, 78, w - 9]', '[81, 9, 9]', '[83, 83, 6*w - 5]', '[83, 83, -6*w - 5]', '[88, 44, 2*w + 10]', '[88, 44, 2*w - 10]', '[92, 46, -6*w + 4]', '[92, 46, 6*w + 4]', '[94, 94, 5*w - 13]', '[94, 94, -3*w + 11]', '[96, 24, 4*w - 12]', '[97, 97, -w - 10]', '[97, 97, w - 10]', '[98, 14, 7*w - 7]', '[99, 33, -6*w + 3]', '[99, 33, 6*w + 3]', '[100, 10, 10]', '[104, 52, -6*w - 2]', '[104, 52, -6*w + 2]', '[107, 107, -6*w - 1]', '[107, 107, 6*w - 1]', '[108, 18, 6*w]', '[109, 109, 2*w - 11]', '[109, 109, -2*w - 11]', '[111, 111, -7*w + 6]', '[111, 111, -7*w - 6]', '[117, 39, 3*w + 12]', '[117, 39, -3*w + 12]', '[118, 118, 9*w - 19]', '[118, 118, -w + 11]', '[121, 11, 11]', '[121, 121, -4*w + 13]', '[121, 121, 4*w + 13]', '[122, 122, 9*w - 11]', '[122, 122, 7*w - 5]', '[128, 16, -8*w + 8]', '[131, 131, -7*w - 4]', '[131, 131, 7*w - 4]', '[132, 66, 2*w + 12]', '[132, 66, 2*w - 12]', '[138, 138, -7*w + 3]', '[138, 138, 7*w + 3]', '[141, 141, -w - 12]', '[141, 141, -w + 12]', '[142, 142, -3*w + 13]', '[142, 142, 7*w - 17]', '[143, 143, 8*w - 7]', '[143, 143, 7*w - 2]', '[143, 143, -7*w - 2]', '[143, 143, -8*w - 7]', '[144, 12, 12]', '[146, 146, 13*w - 19]', '[146, 146, 7*w - 1]', '[147, 21, -7*w]', '[148, 74, 4*w - 14]', '[148, 74, -4*w - 14]', '[150, 30, 5*w - 15]', '[156, 78, 8*w - 6]', '[156, 78, 8*w + 6]', '[157, 157, 2*w - 13]', '[157, 157, -2*w - 13]', '[162, 18, -9*w + 9]', '[166, 166, 11*w - 23]', '[166, 166, -w + 13]', '[167, 167, 8*w - 5]', '[167, 167, -8*w - 5]', '[169, 13, 13]', '[169, 169, 3*w + 14]', '[169, 169, -3*w + 14]', '[176, 44, -8*w + 4]', '[176, 44, 8*w + 4]', '[177, 177, -4*w - 15]', '[177, 177, -4*w + 15]', '[179, 179, 9*w - 8]', '[179, 179, -9*w - 8]', '[181, 181, 5*w - 16]', '[181, 181, -5*w - 16]', '[183, 183, -8*w - 3]', '[183, 183, -8*w + 3]', '[184, 92, 2*w + 14]', '[184, 92, 2*w - 14]', '[188, 94, -8*w - 2]', '[188, 94, 8*w - 2]', '[191, 191, -8*w - 1]', '[191, 191, 8*w - 1]', '[192, 24, 8*w]', '[193, 193, -w - 14]', '[193, 193, w - 14]', '[194, 194, 11*w - 13]', '[194, 194, 9*w - 7]', '[196, 14, -14]', '[198, 66, 3*w + 15]', '[198, 66, 3*w - 15]', '[200, 20, -10*w + 10]', '[207, 69, -9*w + 6]', '[207, 69, 9*w + 6]', '[208, 52, 4*w + 16]', '[208, 52, -4*w + 16]', '[213, 213, -2*w + 15]', '[213, 213, -2*w - 15]', '[214, 214, 7*w - 19]', '[214, 214, -5*w + 17]', '[216, 36, 6*w - 18]', '[218, 218, 13*w - 17]', '[218, 218, 9*w - 5]', '[219, 219, -10*w + 9]', '[219, 219, -10*w - 9]', '[222, 222, -13*w + 27]', '[222, 222, -w + 15]', '[225, 15, 15]', '[227, 227, 9*w - 4]', '[227, 227, -9*w - 4]', '[229, 229, 3*w - 16]', '[229, 229, -3*w - 16]', '[234, 78, -9*w - 3]', '[234, 78, -9*w + 3]', '[236, 118, 10*w - 8]', '[236, 118, -10*w - 8]', '[239, 239, 9*w - 2]', '[239, 239, -9*w - 2]', '[241, 241, 4*w - 17]', '[241, 241, -4*w - 17]', '[242, 22, 11*w - 11]', '[242, 242, -9*w - 1]', '[242, 242, -9*w + 1]', '[243, 27, 9*w]', '[244, 122, -2*w - 16]', '[244, 122, 2*w - 16]', '[249, 249, -5*w + 18]', '[249, 249, -5*w - 18]', '[251, 251, -10*w - 7]', '[251, 251, 10*w - 7]', '[253, 253, -w - 16]', '[253, 253, -6*w + 19]', '[253, 253, 6*w + 19]', '[253, 253, w - 16]', '[256, 16, 16]', '[262, 262, 11*w - 25]', '[262, 262, -3*w + 17]', '[263, 263, 11*w - 10]', '[263, 263, -11*w - 10]', '[264, 132, 10*w + 6]', '[264, 132, -10*w + 6]', '[275, 55, -10*w + 5]', '[275, 55, 10*w + 5]', '[276, 138, 4*w - 18]', '[276, 138, 4*w + 18]', '[277, 277, 2*w - 17]', '[277, 277, -2*w - 17]', '[282, 282, -13*w + 15]', '[282, 282, 11*w - 9]', '[284, 142, 10*w - 4]', '[284, 142, -10*w - 4]', '[286, 286, -w - 17]', '[286, 286, -5*w - 19]', '[286, 286, -5*w + 19]', '[286, 286, -w + 17]', '[288, 24, -12*w + 12]', '[289, 17, -17]', '[291, 291, -10*w + 3]', '[291, 291, -10*w - 3]', '[292, 146, 6*w - 20]', '[292, 146, -6*w - 20]', '[294, 42, -7*w + 21]', '[296, 148, 18*w - 26]', '[296, 148, 10*w - 2]', '[297, 99, 3*w + 18]', '[297, 99, 3*w - 18]', '[299, 299, -10*w - 1]', '[299, 299, 11*w - 8]', '[299, 299, -11*w - 8]', '[299, 299, 10*w - 1]', '[300, 30, 10*w]', '[311, 311, 12*w - 11]', '[311, 311, -12*w - 11]', '[312, 156, -2*w - 18]', '[312, 156, 2*w - 18]', '[313, 313, -4*w - 19]', '[313, 313, 4*w - 19]', '[314, 314, 11*w - 7]', '[314, 314, 15*w - 19]', '[321, 321, -w - 18]', '[321, 321, -w + 18]', '[324, 18, 18]', '[325, 65, 5*w + 20]', '[325, 65, -5*w + 20]', '[327, 327, -11*w - 6]', '[327, 327, -11*w + 6]', '[332, 166, 12*w - 10]', '[332, 166, -12*w - 10]', '[333, 111, 6*w - 21]', '[333, 111, -6*w - 21]', '[334, 334, -3*w + 19]', '[334, 334, 13*w - 29]', '[337, 337, 7*w - 22]', '[337, 337, -7*w - 22]', '[338, 26, -13*w + 13]', '[338, 338, -11*w + 5]', '[338, 338, -11*w - 5]', '[347, 347, -11*w - 4]', '[347, 347, 11*w - 4]', '[349, 349, 2*w - 19]', '[349, 349, -2*w - 19]', '[351, 117, 12*w - 9]', '[351, 117, 12*w + 9]', '[352, 88, 4*w + 20]', '[352, 88, 4*w - 20]', '[354, 354, -19*w + 27]', '[354, 354, 11*w - 3]', '[358, 358, 17*w - 35]', '[358, 358, -w + 19]', '[359, 359, 11*w - 2]', '[359, 359, -11*w - 2]', '[361, 19, -19]', '[362, 362, 21*w - 31]', '[362, 362, 11*w - 1]', '[363, 33, -11*w]', '[363, 363, 13*w - 12]', '[363, 363, 13*w + 12]', '[366, 366, -5*w + 21]', '[366, 366, -11*w + 27]', '[368, 92, -12*w + 8]', '[368, 92, 12*w + 8]', '[373, 373, -3*w - 20]', '[373, 373, 3*w - 20]', '[376, 188, 10*w - 26]', '[376, 188, -6*w + 22]', '[382, 382, 9*w - 25]', '[382, 382, -7*w + 23]', '[383, 383, 12*w - 7]', '[383, 383, -12*w - 7]', '[384, 48, 8*w - 24]', '[386, 386, 15*w - 17]', '[386, 386, 13*w - 11]', '[388, 194, -2*w - 20]', '[388, 194, 2*w - 20]', '[392, 28, 14*w - 14]', '[393, 393, -4*w + 21]', '[393, 393, -4*w - 21]', '[396, 66, -12*w + 6]', '[396, 66, 12*w + 6]', '[397, 397, -w - 20]', '[397, 397, w - 20]', '[400, 20, 20]', '[407, 407, 16*w - 19]', '[407, 407, 12*w + 5]', '[407, 407, -12*w + 5]', '[407, 407, -16*w - 19]', '[409, 409, -5*w - 22]', '[409, 409, 5*w - 22]', '[414, 138, 3*w + 21]', '[414, 138, 3*w - 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104]', '[9973, 9973, 3*w - 100]', '[9973, 9973, -3*w - 100]']}
-
nf_fields • Show schema
Hide schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-3, 0, 1], 'conductor': 12, 'degree': 2, 'dirichlet_group': [1, 11], 'disc_abs': 12, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[2, 1]]], [7, [[2, 1]]], [11, [[1, 2]]], [13, [[1, 2]]], [17, [[2, 1]]], [19, [[2, 1]]], [23, [[1, 2]]], [29, [[2, 1]]], [31, [[2, 1]]], [37, [[1, 2]]], [41, [[2, 1]]], [43, [[2, 1]]], [47, [[1, 2]]], [53, [[2, 1]]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [2, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 3.4641016151377544, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.12.1', 'local_algs': ['2.2.2.2', '3.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 3], 'rd': 3.46410161514, 'regulator': {'__RealLiteral__': 0, 'data': '1.31695789692', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a']}