/************************************************************/ /* Author : Gonzalo Tornaria * Date : December 2003 */ /* * Data about real quadratic twists for elliptic curves of prime conductor * less than 300, and congruent to 3 mod 4 (except 179A for now). * * [ell, vec, qfs, aut] * * ell : elliptic curve data, as given in * vec : vector of coefficients * qfs : vector of ternary quadratic forms [a1,a2,a3,a23,a13,a12] * aut : vector of number of automorphisms of forms in qfs * * For the explicit formula for the central value of the L-series of * the (real) quadratic twists, see the file * * Based on joint work with Ariel Pacetti, in preparation. * * For PARI/GP routines to compute this data, see * * * TODO: more conductors, maybe up to 500 (a *LOT* of quadratic forms!) */ { tw_11A_r = [ /* ell */ ell_11A, /* vec */ [-2,-1,3,-3,2,1], /* qfs */ [[36,36,5,4,4,28], [121,12,4,4,0,0], [45,33,4,0,-4,-22], [124,9,5,-2,-4,-8], [25,16,16,-12,-4,-4], [132,44,1,0,0,44]], /* aut */ [2,4,2,2,2,4] ]; tw_19A_r = [ /* ell */ ell_19A, /* vec */ [-2,2,1,-2,-2,-2,1,2,2,-1,-1,2], /* qfs */ [[92,76,5,0,-4,-76], [45,36,20,12,16,20], [365,16,5,4,2,16], [36,36,25,-16,-16,-4], [92,61,5,2,4,16], [77,44,9,8,6,28], [361,20,4,4,0,0], [73,24,20,20,8,4], [44,44,17,16,16,12], [96,77,4,4,4,40], [380,76,1,0,0,76], [77,24,16,4,8,20]], /* aut */ [2,1,2,2,1,1,4,2,2,2,4,1] ]; tw_43A_r = [ /* ell */ ell_43A, /* vec */ [1,1,1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,1,-1,1,1,1,1], /* qfs */ [[932,29,12,-4,-4,-28], [276,241,5,2,4,104], [929,69,5,-2,-2,-34], [113,77,45,10,-42,-62], [389,108,8,4,8,88], [237,45,37,-34,-26,-2], [376,33,28,16,12,28], [80,77,69,-58,-8,-44], [161,77,29,26,10,46], [104,93,37,-2,-16,-60], [377,32,28,12,16,28], [624,65,8,4,4,44], [76,77,69,-58,-32,-4], [157,69,32,24,12,26], [104,89,37,10,16,44], [157,77,29,26,18,14], [108,77,48,-32,-28,-48], [621,29,20,16,12,22], [104,77,48,-32,-4,-56], [89,80,61,16,-42,-76], [277,61,20,8,12,54], [373,73,12,8,4,30]], /* aut */ [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] ]; tw_67A_r = [ /* ell */ ell_67A, /* vec */ [2, -2, 2, -2, -2, 2, -2, 2, 2, -2, -2, -1, 2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 2, 2, -2, 2, -2, 2, -2, -2, 2, -2, 2, -2, 2, -2, 2, -2, -2, 2, -2, 2, 2, -2, -2, 2, 2, 1, 2, -2, 1, -2, 2, -2, 2, -2, 2, 2, 2, -2, 2, -2, -2, -2, -2, 2, -1, -2, -2, 2], /* qfs */ [[216, 205, 29, 14, 20, 88], [149, 140, 68, 52, 44, 72], [301, 68, 65, -40, -2, -20], [236, 173, 33, 18, 8, 124], [224, 205, 29, 14, 16, 124], [181, 92, 73, 8, 18, 12], [265, 236, 24, 12, 28, 208], [760, 56, 29, -8, -16, -44], [248, 248, 25, 12, 12, 228], [260, 104, 49, -4, -24, -92], [464, 77, 37, -26, 8, -68], [4493, 17, 16, 4, 16, 2], [148, 132, 77, 56, 52, 92], [304, 68, 65, -40, -28, -12], [157, 149, 65, 58, 34, 110], [277, 84, 60, -44, 4, -64], [237, 173, 33, -18, -14, -118], [224, 224, 29, 16, 16, 180], [241, 96, 68, 60, 48, 100], [196, 93, 81, -74, -16, 4], [157, 129, 77, 66, 74, 70], [240, 77, 73, 46, 20, 32], [509, 68, 36, 12, 20, 48], [173, 96, 88, 52, 44, 80], [189, 189, 37, 10, 10, 110], [216, 173, 36, -16, 4, -120], [173, 93, 93, -82, -6, -6], [293, 116, 37, -4, -22, -64], [140, 140, 65, 32, 32, 12], [332, 237, 17, -6, -8, -172], [157, 132, 77, 56, 74, 100], [504, 89, 29, 26, 24, 20], [132, 132, 73, -32, -32, -4], [277, 77, 60, -16, -4, -62], [265, 84, 68, 68, 16, 8], [160, 140, 65, -32, -44, -84], [149, 149, 65, 58, 58, 30], [148, 149, 89, -106, 48, -140], [193, 84, 77, 12, 22, 40], [189, 188, 37, 32, 10, 84], [160, 129, 64, -44, -36, 4], [217, 96, 68, -60, -8, -28], [149, 104, 104, -60, -64, -64], [508, 269, 9, 6, 8, 92], [237, 77, 68, 24, 12, 10], [193, 93, 93, -82, -46, -46], [173, 116, 84, 60, 88, 108], [4489, 68, 4, 4, 0, 0], [157, 96, 96, -76, -16, -16], [308, 217, 21, 2, -12, -192], [1140, 269, 4, 4, 4, 136], [173, 93, 76, -20, -8, -6], [293, 144, 33, 28, 34, 120], [332, 268, 17, 0, -8, -268], [153, 116, 84, 60, 32, 88], [149, 104, 100, 44, 96, 64], [753, 77, 21, -6, -2, -38], [272, 76, 77, -72, -48, 12], [220, 89, 77, -70, -36, -8], [181, 92, 92, -84, -12, -12], [237, 149, 40, -16, -20, -130], [301, 89, 60, 56, 76, 98], [328, 157, 24, 8, 20, 48], [132, 132, 89, -72, -72, -4], [449, 77, 40, 40, 4, 2], [188, 93, 76, 20, 68, 16], [4556, 268, 1, 0, 0, 268], [308, 220, 21, 16, 12, 196], [173, 88, 92, 36, 76, 44], [457, 77, 40, 40, 36, 18]], /* aut */ [1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 4, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 4, 1, 1, 2] ]; tw_79A_r = [ /* ell */ ell_79A, /* vec */ [1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1], /* qfs */ [[185, 140, 96, -44, -16, -128], [185, 172, 68, -4, -32, -92], [201, 136, 96, 20, -80, -140], [372, 96, 61, -44, -32, -4], [544, 116, 33, 12, 32, 92], [161, 120, 108, -4, -36, -52], [201, 137, 77, -22, -50, -38], [161, 145, 93, 46, 22, 70], [236, 216, 41, 36, 28, 20], [188, 161, 113, 110, 108, 184], [193, 161, 69, -14, -38, -74], [376, 153, 37, -34, -36, 8], [249, 113, 77, -26, -46, -62], [284, 113, 68, 20, 12, 104], [276, 185, 41, -2, -32, -84], [265, 185, 41, -2, -22, -38], [896, 133, 17, -14, -16, -12], [145, 140, 153, 132, 134, 64], [161, 145, 108, 104, 36, 70], [425, 116, 41, -8, -38, -4], [1044, 56, 41, -40, -24, 4], [461, 185, 24, 8, 4, 106], [449, 264, 17, -16, -14, -12], [377, 96, 56, -4, -32, -44], [385, 192, 28, -4, -12, -112], [216, 157, 60, -32, -4, -20], [153, 164, 132, 140, 100, 144], [233, 201, 53, -30, -10, -182], [233, 113, 85, 42, 46, 82], [185, 113, 116, -56, -100, -14], [149, 132, 137, 108, 98, 64], [449, 369, 12, 4, 8, 54], [2088, 33, 29, -6, -28, -8], [185, 137, 116, 96, 100, 134], [217, 137, 69, 34, 22, 10], [224, 193, 48, -20, -36, -32], [377, 112, 48, 4, 40, 28], [229, 217, 41, -14, -30, -18], [521, 224, 17, 8, 6, 20], [185, 112, 116, 12, -100, -76]], /* aut */ [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] ]; tw_83A_r = [ /* ell */ ell_83A, /* vec */ [1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1], /* qfs */ [[384, 136, 45, -24, -8, -20], [3453, 133, 5, -2, -2, -66], [168, 145, 117, 90, 40, 92], [185, 172, 88, -28, -52, -120], [224, 133, 80, -8, -36, -48], [1381, 128, 13, -4, -10, -24], [200, 165, 88, -48, 4, -152], [205, 141, 97, -54, -62, -82], [512, 88, 53, 8, 48, 60], [141, 157, 125, 110, 38, 30], [488, 460, 13, 4, -12, -436], [352, 128, 53, 24, 16, 60], [224, 165, 88, 48, 92, 176], [157, 141, 133, 118, 62, 30], [325, 133, 60, 52, 48, 54], [556, 85, 60, 56, 68, 76], [461, 85, 73, -70, -22, 6], [288, 157, 52, 28, 12, 16], [213, 137, 85, 10, 58, 62], [205, 117, 101, -46, -22, -18], [1176, 156, 13, -12, -8, -124], [345, 141, 53, -26, 10, -134], [305, 157, 52, 28, 32, 98], [389, 89, 72, -20, -56, -66], [181, 137, 136, 132, 104, 70], [237, 128, 85, -32, -30, -92], [208, 157, 72, 8, 12, 56], [240, 128, 101, -96, -4, -100], [325, 141, 53, -26, -50, 6], [541, 85, 57, 46, 50, 26], [208, 141, 105, 46, 108, 128], [541, 96, 45, 4, 42, 24], [412, 85, 76, 44, 84, 68], [1413, 208, 8, 4, 8, 168], [321, 165, 45, 22, 26, 58], [541, 184, 24, 20, 12, 88], [469, 97, 52, -16, -44, -6], [180, 165, 85, -18, -64, -44], [165, 133, 140, 64, 124, 90], [320, 133, 56, -24, -36, -16], [533, 216, 20, -4, -12, -32], [533, 76, 72, -68, -28, 4]], /* aut */ [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] ]; /* NOTE: ellquadtwist(ell_131A, -131) has rank 2, thus the following is a NONTRIVIAL linear relation between theta series !!! */ tw_131A_r = [ /* ell */ ell_131A, /* vec */ [1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1], /* qfs */ [[357, 228, 133, 120, 74, 124], [341, 204, 181, -168, -170, 76], [348, 253, 116, -4, -92, -152], [628, 224, 73, 68, 32, 180], [309, 264, 148, -108, -24, -232], [517, 281, 69, 2, -66, -206], [332, 241, 124, 8, -108, -88], [596, 228, 73, -40, 8, -196], [1236, 92, 85, -44, -56, -4], [264, 241, 157, 82, 48, 116], [796, 217, 56, 20, 12, 208], [276, 229, 157, -74, -88, -36], [224, 221, 201, 110, 44, 72], [796, 124, 93, -4, -24, -84], [340, 280, 137, 68, 144, 292], [600, 160, 97, -36, -12, -68], [316, 253, 141, -66, 8, -236], [792, 168, 69, 16, 52, 44], [412, 253, 88, -32, -20, -44], [264, 249, 173, -82, -104, -148], [332, 284, 141, 116, 124, 300], [444, 181, 116, 12, 52, 84], [564, 185, 88, 12, 60, 16], [316, 221, 133, -14, -68, -24], [640, 141, 124, 84, 148, 160], [433, 309, 69, 38, 6, 70], [737, 148, 85, -4, -34, -104], [925, 141, 72, -28, -48, -78], [796, 213, 56, -40, -12, -108], [344, 181, 157, -22, -12, -136], [1233, 88, 85, -24, -46, -12], [229, 216, 197, -68, -14, -96], [1720, 181, 29, -6, -20, -16], [669, 380, 40, -4, -12, -340], [476, 217, 96, -76, -68, 16], [1000, 133, 76, 52, 92, 128], [581, 141, 120, -52, -80, -70], [309, 228, 160, -36, -140, -148], [564, 149, 128, -96, -100, -28], [964, 261, 37, 30, 12, 104], [669, 341, 40, 8, 12, 106], [581, 137, 120, -28, -80, -78], [465, 204, 96, -28, -20, -8], [1720, 85, 69, -50, -32, 4], [596, 141, 124, -84, -92, -28], [724, 340, 37, 4, 16, 100], [489, 272, 72, 28, 20, 164], [561, 133, 128, -32, -92, -54], [316, 213, 168, -52, -132, -148], [229, 224, 201, -44, -42, -144], [268, 197, 209, 126, 144, 76], [293, 261, 173, 146, 150, 242], [309, 304, 133, -104, -30, -268], [765, 149, 97, 98, 74, 86], [509, 217, 92, 48, 84, 170], [465, 253, 93, 78, 86, 222], [348, 197, 149, -6, -64, -164], [284, 249, 141, 2, -116, -64], [672, 472, 29, 16, 20, 132], [597, 148, 104, -28, -32, -36], [949, 276, 37, 32, 46, 204], [816, 312, 37, 8, 36, 188], [469, 228, 88, -52, -40, -12], [481, 264, 76, 52, 40, 124], [280, 213, 181, 126, 60, 128], [261, 264, 141, -92, -22, -56]], /* aut */ [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] ]; tw_139A_r = [ /* ell */ ell_139A, /* vec */ [2, -2, -2, -2, -2, 2, 2, 2, -2, 2, 2, -2, 2, 2, 2, -2, -2, 2, -2, -2, -2, 2, 2, 2, 2, 2, -2, 2, 2, -2, 2, 2, -2, -2, -2, -2, -2, 2, 2, -2, 2, -2, 2, -2, -2, -2, -2, 2, 2, -2, -2, -2, 2, -2, 2, 2, 2, -2, 2, -2, -2, 2, -2, -2, 2, -2, 2, -2, -2, -2, -2, 2, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, -2, -2, 2, -2, -2, -2, 2, -2, 2, 2, 2, 2, -2, -2, 2, 2, -2, 2, -2, 2, -1, 2, 2, 2, -2, 2, 2, 2, 2, 2, -2, 2, -2, 2, -2, -2, 2, 2, 2, -2, 2, -2, 2, -2, -2, 2, 2, -2, 2, -2, -2, 2, -2, -2, 2, -2, 2, -2, -2, 2, -2, 2, 2, 2, -2, 2, 2, 2, 2, -2, -1, 2, 2, -2, 2, 2, -2, 2, 2, 2, 2, 2, -2, 2, -1, -2, 2, -2, -2, -2, 2, 2, -2, -2, 2, 2, 2, -2, -2, -2, -2, -2, 2, -1, -2, -2, -2, -2, 1, 2, 2, -2, 1, 2, 2, 2, -2, -2, 2, -2, -2, -2, 2, -2, 1, -2, 2, 2, 2, -2, -2, 1], /* qfs */ [[464, 333, 81, 58, 76, 240], [560, 261, 81, 82, 36, 80], [349, 205, 181, 78, 174, 102], [529, 356, 69, 20, 38, 352], [309, 264, 152, -84, -120, -40], [565, 332, 64, 52, 48, 228], [676, 652, 29, -4, -24, -516], [437, 196, 148, 84, 144, 116], [285, 257, 184, -116, -136, -78], [537, 152, 136, 20, 28, 92], [548, 452, 45, -36, -28, -100], [308, 204, 185, -80, -88, 4], [620, 572, 37, -12, -24, -492], [309, 285, 152, 124, 120, 166], [325, 264, 152, 84, 148, 136], [565, 173, 121, 38, 66, 162], [453, 205, 125, 14, 114, 82], [701, 180, 96, 68, 48, 156], [576, 169, 116, -24, -84, -68], [557, 428, 49, 40, 14, 244], [701, 676, 24, 20, 24, 288], [341, 205, 208, -168, -180, 62], [645, 173, 100, -16, -4, -122], [569, 533, 44, -20, 8, -482], [437, 176, 144, 36, 20, 72], [445, 176, 164, -124, 24, -104], [652, 152, 125, -84, -36, -108], [441, 205, 125, 14, 18, 130], [481, 180, 148, -124, -48, -40], [405, 284, 100, 68, 64, 44], [1781, 136, 45, 4, 18, 112], [308, 309, 129, -122, -32, -84], [276, 228, 217, -200, -40, -20], [533, 316, 69, 52, 18, 176], [480, 289, 80, 36, 12, 100], [341, 225, 196, 136, 212, 170], [529, 164, 152, 132, 60, 48], [2156, 80, 77, 68, 36, 52], [820, 125, 116, -68, -68, -28], [700, 421, 37, 6, 36, 48], [2765, 137, 29, 18, 22, 26], [524, 181, 137, 130, 16, 36], [453, 228, 125, 24, -114, -220], [808, 669, 20, -12, -12, -52], [341, 333, 113, -102, -26, -190], [320, 309, 129, 122, 108, 64], [980, 384, 29, -8, -16, -132], [608, 309, 65, 50, 68, 240], [260, 261, 180, 100, 84, 116], [3221, 120, 29, 24, 2, 20], [260, 261, 205, 190, 104, 116], [396, 245, 129, 114, 80, 100], [700, 245, 69, -30, -44, -208], [332, 308, 125, 108, 112, 124], [324, 261, 140, 40, 36, 164], [701, 672, 24, 4, -24, -280], [333, 216, 185, -44, -162, -128], [369, 204, 164, 84, 64, 152], [561, 164, 125, 44, 50, 120], [1212, 173, 52, -20, -28, -16], [620, 508, 41, 32, 40, 436], [309, 260, 176, 172, 140, 100], [384, 204, 173, 120, 88, 188], [396, 193, 176, 164, 28, 32], [276, 252, 261, 268, 224, 164], [669, 129, 125, -2, -30, -22], [333, 320, 120, -12, -44, -248], [593, 261, 77, -18, -50, -218], [260, 284, 169, -144, -8, -92], [561, 176, 117, 48, 106, 36], [581, 169, 116, 24, 52, 130], [685, 541, 36, -8, -28, -522], [3869, 120, 24, 20, 4, 48], [309, 260, 152, 68, 120, 100], [677, 152, 120, -92, -16, -68], [1208, 308, 29, 12, 4, 20], [669, 204, 80, 28, 24, 32], [673, 140, 136, 108, 60, 32], [1764, 125, 49, 6, 32, 36], [776, 125, 124, -80, -12, -32], [268, 245, 188, 64, 60, 164], [276, 245, 220, -156, -212, 60], [377, 181, 173, 98, 26, 62], [513, 204, 124, 100, 56, 184], [813, 284, 49, 8, 38, 196], [973, 869, 16, -4, 0, -834], [544, 452, 45, -36, -8, -108], [1780, 1224, 5, -4, -4, -332], [741, 332, 49, -24, -26, -300], [845, 325, 44, 40, 44, 298], [453, 205, 136, -96, -92, -82], [533, 312, 69, -40, -18, -164], [421, 177, 148, -16, -12, -82], [405, 245, 116, 16, 100, 74], [428, 181, 152, -88, -4, -72], [405, 276, 116, 36, 100, 236], [980, 164, 69, -28, -60, -12], [333, 204, 185, -80, -162, 20], [329, 344, 120, -108, 4, -252], [405, 205, 137, 58, 42, 86], [437, 284, 89, 32, 46, 52], [3877, 96, 29, -4, -22, -56], [19328, 28, 25, 24, 12, 28], [636, 557, 36, -12, -20, -460], [332, 312, 125, 96, 112, 172], [276, 256, 177, -100, -104, -68], [693, 541, 29, 22, 18, 26], [488, 309, 80, -32, -52, -212], [341, 284, 113, -40, -26, -20], [320, 285, 129, -50, -108, 8], [537, 173, 117, -30, -2, -14], [1004, 309, 36, -4, -4, -216], [341, 276, 140, 100, 104, 196], [1004, 256, 45, 40, 24, 196], [737, 576, 28, -4, -16, -396], [428, 245, 121, -98, -96, -76], [557, 541, 36, 8, 12, 94], [1001, 256, 45, -40, 6, -188], [3241, 120, 29, 24, 10, 100], [369, 261, 125, -102, -66, -22], [276, 260, 181, -112, -148, 12], [693, 245, 69, -30, 2, -218], [569, 184, 112, 12, 60, 172], [333, 216, 217, 172, 226, 128], [469, 324, 80, 60, 88, 172], [500, 185, 144, 124, 100, 128], [2148, 80, 65, 28, 16, 12], [325, 329, 116, 112, 92, 54], [692, 421, 41, 10, 8, 340], [396, 261, 125, -102, -8, -188], [396, 173, 164, -8, -92, -52], [1792, 680, 9, -4, -4, -308], [704, 145, 117, -58, -96, -76], [452, 181, 144, -80, 12, -96], [285, 260, 188, 124, 128, 196], [441, 176, 144, 36, 52, 76], [285, 245, 184, 68, 136, 146], [276, 264, 173, -96, -80, -116], [349, 324, 144, 124, 152, 328], [445, 324, 80, -60, -8, -136], [569, 437, 44, -36, -8, -22], [845, 316, 44, 4, -44, -280], [864, 461, 29, 10, 12, 328], [441, 196, 125, 12, 18, 32], [676, 140, 129, 88, 64, 52], [2152, 77, 65, -2, -36, -8], [672, 257, 64, 36, 28, 60], [4832, 77, 29, 6, 8, 20], [396, 260, 113, -64, -88, 20], [529, 184, 117, -40, -98, 12], [676, 581, 29, 26, 24, 260], [484, 324, 77, -44, -8, -236], [3893, 696, 4, 4, 4, 280], [3869, 64, 44, 12, 20, 28], [324, 285, 144, 140, 124, 68], [357, 196, 193, 48, 194, 148], [245, 268, 225, -208, 18, -164], [692, 140, 117, 32, 60, 108], [2165, 125, 41, 22, 38, 78], [276, 245, 180, 136, 28, 60], [1508, 113, 64, 4, 36, 88], [500, 405, 57, 34, 24, 212], [529, 312, 69, 40, 38, 148], [693, 144, 112, -4, -76, -88], [677, 364, 45, 32, 42, 52], [3336, 668, 5, -4, 0, -556], [1808, 1529, 4, 0, -4, -556], [464, 309, 77, -42, -24, -44], [669, 252, 64, -4, -4, -52], [557, 329, 64, 44, 16, 214], [513, 181, 117, -14, -46, -2], [409, 260, 116, -108, -72, -24], [1757, 100, 69, -56, -10, -4], [464, 356, 69, -20, -36, -164], [424, 309, 89, 74, 44, 112], [656, 245, 69, -30, -56, -12], [333, 245, 148, -52, -112, -78], [341, 356, 120, 132, 76, 292], [437, 344, 89, -12, -46, -328], [732, 584, 29, 32, 20, 452], [585, 181, 125, -122, 34, -110], [341, 289, 144, 148, 136, 178], [488, 324, 77, -44, -36, -228], [1004, 176, 69, 64, 76, 140], [677, 285, 57, -22, -30, -82], [19321, 28, 20, 4, 0, 0], [469, 320, 81, 60, 86, 176], [488, 204, 113, 32, 20, 116], [685, 140, 120, 52, 64, 88], [1757, 245, 25, -6, -2, -22], [19332, 44, 13, 8, 4, 44], [257, 268, 176, 132, 28, 80], [285, 256, 168, -28, -16, -184], [585, 260, 77, 4, 6, 224], [3892, 2780, 1, 0, 0, 556], [1781, 81, 77, -22, -38, -74], [445, 216, 116, 12, 64, 80], [285, 256, 177, 100, 62, 184], [1256, 245, 37, 26, 36, 208], [977, 309, 36, 4, 24, 94], [2149, 116, 44, 20, 12, 28], [309, 217, 173, -34, -18, -130], [544, 513, 45, -34, -8, -380], [576, 437, 44, 36, 36, 40], [1229, 116, 77, 12, 70, 56], [285, 228, 176, 84, 52, 44], [19349, 112, 5, 4, 2, 112], [701, 169, 96, -20, -48, -134], [261, 268, 176, 132, 60, 92], [553, 173, 124, -36, -72, -142], [1236, 125, 77, 54, 84, 80], [2176, 113, 45, -18, -16, -108], [572, 517, 37, 30, 12, 80], [2781, 973, 4, 0, -4, -278]], /* aut */ [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2] ]; tw_163A_r = [ /* ell */ ell_163A, /* vec */ [1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1], /* qfs */ [[13289, 45, 29, -2, -14, -22], [2348, 1565, 5, -2, -4, -912], [3912, 913, 5, -2, 0, -652], [1333, 292, 45, -20, -2, -72], [1497, 269, 44, 20, 8, 150], [1504, 269, 44, -20, -36, -140], [1168, 337, 45, 26, 40, 84], [2217, 1565, 5, -2, -2, -130], [405, 317, 149, 34, 38, 210], [393, 293, 200, 176, 188, 174], [920, 464, 45, -8, -36, -388], [405, 317, 180, -140, -112, -210], [317, 272, 229, -96, -118, -92], [1496, 117, 101, -18, -44, -80], [13312, 109, 12, -4, -4, -108], [396, 269, 176, -40, -124, -60], [1573, 252, 44, -4, -20, -88], [2429, 249, 29, -14, -10, -110], [1549, 1469, 8, 8, 4, 654], [320, 261, 252, -176, -132, -16], [392, 293, 181, 118, 168, 116], [344, 285, 236, 116, 140, 272], [2048, 124, 73, 48, 28, 36], [344, 293, 205, -18, -116, -208], [293, 288, 236, -92, -12, -180], [305, 293, 264, -232, -36, -162], [860, 181, 128, -96, -100, -44], [433, 405, 112, 64, 60, 250], [2057, 424, 20, 4, 16, 132], [428, 392, 125, 20, 12, 340], [356, 293, 229, -210, -52, -184], [473, 420, 109, -76, -14, -360], [609, 288, 109, -104, -46, 4], [1572, 125, 112, 108, 52, 60], [432, 233, 200, -108, -140, -60], [972, 181, 101, 10, 64, 100], [1480, 125, 108, 84, 20, 44], [412, 317, 168, -132, -116, -164], [2045, 193, 44, 8, 4, 30], [741, 236, 109, -80, -70, -76], [616, 213, 157, 58, 156, 224], [432, 245, 192, -104, -76, -156], [2429, 116, 73, -72, -50, -20], [2420, 149, 52, -48, 4, -52], [2081, 112, 76, 12, 64, 108], [404, 293, 176, -136, -12, -188], [8861, 68, 29, -8, -18, -20], [665, 261, 117, 86, 78, 246], [333, 273, 229, 134, 50, 194], [533, 213, 157, 58, 30, 18], [728, 193, 125, -2, -64, -36], [488, 273, 148, -88, -68, -156], [541, 453, 72, -8, -44, -70], [552, 245, 149, 102, 104, 180], [1413, 148, 89, 56, 70, 44], [317, 280, 293, 244, 242, 192], [405, 272, 205, -120, -118, -204], [860, 229, 89, 26, 32, 12], [392, 317, 168, -132, -4, -208], [1333, 205, 68, -60, -8, -54], [953, 269, 68, 12, 32, 22], [3328, 117, 48, -40, 4, -56], [512, 245, 149, -102, 4, -32], [389, 344, 157, -100, -66, -224], [305, 264, 245, -56, -174, -36], [605, 293, 108, 96, 76, 70], [329, 333, 205, -182, -34, -198], [392, 269, 208, -160, -12, -196], [777, 320, 76, 28, 64, 252], [357, 233, 229, -86, -94, -82], [917, 148, 128, -12, -8, -20], [404, 357, 148, -52, -84, -276], [453, 385, 124, 24, 20, 370], [565, 300, 117, -100, -94, -88], [3361, 261, 20, -4, -16, -194], [665, 277, 117, 122, 78, 258], [917, 512, 37, -12, -10, -16], [977, 157, 125, -74, -106, -26], [732, 205, 128, -92, -84, 20], [300, 277, 269, -230, -68, -80], [1045, 881, 20, -8, -12, -454], [556, 269, 128, -112, -20, -32], [508, 329, 117, 10, -116, -200], [464, 245, 181, 6, -112, -236], [425, 405, 112, -64, 4, -234], [3328, 180, 29, 4, 8, 68], [996, 697, 29, 2, -28, -608], [989, 433, 44, 24, 44, 338], [396, 257, 200, -100, -108, -136], [517, 301, 125, 122, 54, 42], [637, 236, 125, 92, 18, 64], [637, 320, 92, 20, 48, 232], [357, 349, 148, 24, 52, 154], [293, 301, 236, -144, 12, -186], [453, 404, 117, 36, 58, 360], [496, 428, 101, 28, -100, -356], [344, 293, 272, 212, 300, 208], [317, 337, 236, -184, 44, -310], [3521, 1044, 5, -4, -2, -912], [1592, 108, 105, -32, -60, -84], [285, 301, 252, -200, 20, -158], [860, 181, 116, -56, -4, -44], [989, 432, 44, 20, 44, 336], [741, 208, 128, -100, -108, 32], [453, 356, 117, -48, -58, -172], [368, 269, 213, -70, -24, -244], [488, 261, 176, 80, 196, 252], [1581, 241, 48, -44, -32, -94], [1352, 117, 112, -16, -92, -40], [261, 293, 272, -212, -48, -58], [557, 285, 116, 84, 16, 62], [2420, 424, 17, 12, 16, 44], [392, 277, 200, 88, 92, 268], [392, 257, 200, -100, -92, -140], [408, 393, 125, -30, -24, -284], [453, 277, 165, 74, 110, 242], [5325, 72, 48, -28, -8, -52], [1020, 261, 68, 24, 60, 164], [725, 368, 68, 60, 40, 56], [425, 245, 192, -104, 20, -182], [893, 148, 137, -16, -110, -84], [344, 285, 252, 20, -204, -272], [453, 301, 165, 146, 110, 266], [917, 564, 37, -4, -10, -440], [1172, 153, 120, -116, -84, 8], [485, 293, 149, -50, -86, -270], [857, 165, 141, -98, -78, -70], [832, 192, 117, -80, -28, 4], [932, 213, 89, -14, -24, -108], [500, 249, 157, 50, 148, 144], [488, 269, 153, 18, -140, -200], [285, 252, 264, -52, -148, -20], [293, 288, 252, 164, 92, 180], [1348, 357, 37, 26, 36, 136], [453, 404, 124, -100, -20, -360], [757, 304, 80, 28, 48, 204], [968, 229, 80, 16, 68, 72], [357, 272, 229, -96, -94, -228], [300, 312, 269, -264, 68, -220], [488, 353, 117, -30, -64, -276], [488, 269, 168, -164, 44, -200], [1160, 137, 120, 76, 36, 44], [957, 157, 125, 74, 62, 34], [468, 425, 101, 86, 36, 280], [468, 393, 101, -70, -36, -136], [997, 153, 116, -24, -60, -50], [2217, 125, 68, -52, -24, -10], [393, 344, 149, -40, -46, -252], [917, 213, 92, 12, 32, 158], [897, 213, 92, -12, -64, -10], [732, 205, 124, -72, -76, -20], [588, 245, 141, 114, 116, 144], [1629, 300, 37, 8, 34, 268], [320, 277, 288, 236, 252, 144], [2076, 305, 28, 16, 20, 192], [389, 293, 157, -38, -66, -46], [932, 193, 108, -88, -60, -48], [537, 317, 112, 80, 92, 126], [453, 269, 165, 14, -110, -222], [1405, 953, 13, -2, -6, -150], [5332, 73, 45, -10, -4, -72], [741, 208, 116, -4, -100, -32], [917, 592, 32, -12, -4, -40], [833, 192, 109, -16, -26, -28], [408, 272, 205, 120, 128, 276], [516, 293, 128, -120, -28, -48], [404, 245, 181, 6, 20, 112], [569, 300, 117, -100, -90, -112], [2048, 236, 37, 32, 24, 28], [996, 401, 45, 42, 44, 64], [3821, 89, 52, 16, 44, 82], [952, 153, 124, 16, 12, 148], [353, 293, 264, 232, 228, 278], [1565, 556, 20, -12, -4, -64], [349, 293, 200, -176, -12, -86], [317, 268, 261, -128, -222, -28], [741, 464, 52, -4, -16, -200], [1413, 337, 37, -18, -22, -118], [517, 293, 128, 120, 36, 78], [997, 245, 72, 12, 16, 110], [456, 269, 165, 14, -148, -192], [508, 320, 141, 56, 152, 340], [277, 292, 264, -212, -116, 12], [5324, 105, 32, -20, -28, -32], [832, 720, 29, 8, 4, 68], [968, 157, 137, 102, 148, 136], [1581, 153, 80, -68, -72, -2], [637, 293, 101, 94, 42, 26], [325, 304, 213, 164, 146, 96], [492, 272, 193, 140, 232, 324], [581, 272, 125, -104, -94, -60], [305, 277, 269, -230, -86, -82], [1005, 153, 125, -78, -42, -86], [317, 273, 236, 160, 44, 142], [1576, 925, 12, -8, -4, -216], [977, 176, 124, 108, 112, 196], [541, 325, 108, -100, -40, -66], [325, 269, 288, -168, -220, -126], [368, 317, 213, -214, 24, -260], [556, 293, 117, 82, 68, 152], [5317, 252, 13, 8, 6, 52], [453, 292, 165, -124, -110, -176], [272, 261, 257, -70, -76, -48], [376, 357, 137, -6, -4, -176], [2452, 101, 72, 20, 68, 100], [405, 293, 149, -50, -38, 2], [617, 272, 108, 12, 56, 148], [2436, 109, 72, -52, 4, -92], [613, 257, 117, -54, -2, -150], [453, 277, 176, -68, -128, -242], [5333, 68, 48, 4, 40, 56], [613, 368, 80, -20, -76, -72], [5333, 120, 28, 20, 8, 96], [1020, 269, 68, -12, -60, -244], [5332, 192, 17, 4, 8, 116], [432, 325, 137, 58, 68, 200], [521, 317, 112, 80, 36, 106], [488, 337, 117, 62, 64, 212], [833, 208, 101, -24, -10, -44], [8884, 245, 8, 4, 4, 164], [764, 325, 76, -48, 12, -244], [989, 149, 137, -106, -46, -6], [412, 293, 149, 50, 20, 104], [665, 293, 101, -94, 6, -190], [857, 148, 141, -4, -78, -96], [488, 273, 141, 10, -96, -156], [389, 245, 208, -116, -16, -146], [757, 277, 89, 46, 78, 174], [1592, 112, 105, 52, 60, 108], [269, 293, 272, -212, 24, -134], [596, 245, 128, -16, 4, -204], [449, 405, 116, -12, -48, -346], [648, 288, 101, 40, 60, 212], [5321, 108, 32, -28, -20, -32], [2221, 245, 32, 8, 4, 82], [428, 425, 101, -86, -28, -72], [325, 257, 272, -76, -248, -90], [389, 229, 208, -12, -16, -150], [328, 300, 213, -4, -20, -260], [917, 277, 73, 6, -66, -226], [857, 165, 128, -32, -92, -70], [581, 268, 125, -60, -94, -160], [969, 181, 101, -10, -90, -2], [916, 389, 52, -8, -12, -300], [424, 277, 165, 74, 28, 192], [597, 252, 128, 108, 56, 44]], /* aut */ [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] ]; tw_179A_r = [ /* ell */ ell_179A, [],[],[] ]; /************************************************************/ /* List of available data (rank 0) */ tw_real = [tw_11A_r, tw_19A_r, tw_43A_r, tw_67A_r, tw_79A_r, tw_83A_r, tw_139A_r, tw_163A_r]; \\, tw_179A_r]; /* List of available data (rank 2) */ tw_real_2 = [tw_131A_r]; } /************************************************************/