# Fourier coefficients... 'F523' # Coeff Disc Reduced form Unreduced form -3 -3 1, 1, 1 1, 60 3661, 121, 1 -2 -8 1, 0, 2 1, 28 1569, 112, 2 -1 -12 1, 0, 3 1, 389 453964, 2334, 3 1 -20 1, 0, 5 1, 124 76881, 1240, 5 1 -20 2, 2, 3 1, 32 3138, 194, 3 2 -27 1, 1, 7 1, 250 437751, 3501, 7 -2 -32 1, 0, 8 1, 14 1569, 224, 8 -2 -32 3, 2, 3 1, 37 4184, 224, 3 -2 -35 1, 1, 9 1, 353 1121835, 6355, 9 -2 -35 3, 1, 3 1, 13 523, 79, 3 3 -39 1, 1, 10 1, 25 6276, 501, 10 3 -39 2, -1, 5 1, 364 662118, 3639, 5 3 -39 2, 1, 5 1, 50 12552, 501, 5 -7 -39 3, 3, 4 1, 193 149578, 1547, 4 7 -47 1, 1, 12 1, 225 607726, 5401, 12 -3 -47 2, -1, 6 1, 363 790253, 4355, 6 -3 -47 2, 1, 6 1, 450 1215452, 5401, 6 -3 -47 3, -1, 4 1, 283 320076, 2263, 4 -3 -47 3, 1, 4 1, 152 92571, 1217, 4 0 -48 1, 0, 12 1, 456 2495233, 10944, 12 0 -48 3, 0, 4 1, 322 414739, 2576, 4 5 -51 1, 1, 13 1, 47 28765, 1223, 13 -5 -51 3, 3, 5 1, 122 74789, 1223, 5 4 -55 1, 1, 14 1, 90 113491, 2521, 14 4 -55 2, -1, 7 1, 479 1605610, 6705, 7 -6 -55 2, 1, 7 1, 180 226982, 2521, 7 -6 -55 4, 3, 4 1, 184 135980, 1475, 4 0 -56 1, 0, 14 1, 41 23535, 1148, 14 0 -56 2, 0, 7 1, 82 47070, 1148, 7 0 -56 3, -2, 5 1, 115 65898, 1148, 5 0 -56 3, 2, 5 1, 10 523, 102, 5 -4 -59 1, 1, 15 1, 144 311185, 4321, 15 -4 -59 3, -1, 5 1, 223 248425, 2229, 5 6 -59 3, 1, 5 1, 432 933555, 4321, 5 5 -67 1, 1, 17 1, 432 3173041, 14689, 17 0 -72 1, 0, 18 1, 358 2306953, 12888, 18 0 -72 2, 0, 9 1, 193 335243, 3474, 9 -3 -75 1, 1, 19 1, 452 3882229, 17177, 19 -3 -75 3, 3, 7 1, 106 78973, 1487, 7 -8 -79 1, 1, 20 1, 324 2099845, 12961, 20 -8 -79 2, -1, 10 1, 282 794960, 5639, 10 2 -79 2, 1, 10 1, 125 156377, 2501, 10 2 -79 4, -1, 5 1, 41 8368, 409, 5 12 -79 4, 1, 5 1, 250 312754, 2501, 5 6 -80 1, 0, 20 1, 62 76881, 2480, 20 -4 -80 3, -2, 7 1, 252 444027, 3526, 7 6 -80 3, 2, 7 1, 177 219660, 2480, 7 -4 -80 4, 0, 5 1, 248 307524, 2480, 5 1 -83 1, 1, 21 1, 484 4919861, 20329, 21 1 -83 3, -1, 7 1, 182 231689, 2547, 7 1 -83 3, 1, 7 1, 406 1154261, 5685, 7 6 -84 1, 0, 21 1, 383 3080470, 16086, 21 -4 -84 2, 2, 11 1, 113 140687, 2488, 11 6 -84 3, 0, 7 1, 103 74266, 1442, 7 -4 -84 5, 4, 5 1, 353 624462, 3534, 5 -3 -87 1, 1, 22 1, 216 1026649, 9505, 22 -3 -87 2, -1, 11 1, 337 1248924, 7413, 11 7 -87 2, 1, 11 1, 432 2053298, 9505, 11 -3 -87 3, 3, 8 1, 267 571116, 4275, 8 -3 -87 4, -3, 6 1, 95 53869, 1137, 6 -3 -87 4, 3, 6 1, 356 761488, 4275, 6 2 -88 1, 0, 22 1, 49 52823, 2156, 22 2 -88 2, 0, 11 1, 98 105646, 2156, 11 -5 -95 1, 1, 24 1, 177 752074, 8497, 24 5 -95 2, -1, 12 1, 49 28765, 1175, 12 5 -95 2, 1, 12 1, 354 1504148, 8497, 12 -5 -95 3, -1, 8 1, 335 897468, 5359, 8 -5 -95 3, 1, 8 1, 8 523, 129, 8 5 -95 4, -1, 6 1, 98 57530, 1175, 6 -5 -95 4, 1, 6 1, 185 205539, 2221, 6 5 -95 5, 5, 6 1, 359 775086, 4313, 6 7 -103 1, 1, 26 1, 447 5195482, 23245, 26 -13 -103 2, -1, 13 1, 9 1046, 233, 13 -3 -103 2, 1, 13 1, 371 1789706, 9647, 13 -3 -103 4, -3, 7 1, 241 405848, 3371, 7 7 -103 4, 3, 7 1, 390 1065874, 5463, 7 -4 -104 1, 0, 26 1, 369 3540187, 19188, 26 -4 -104 2, 0, 13 1, 215 600927, 5590, 13 -4 -104 3, -2, 9 1, 485 2116058, 8728, 9 -4 -104 3, 2, 9 1, 78 54915, 1406, 9 6 -104 5, -4, 6 1, 379 860335, 4544, 6 6 -104 5, 4, 6 1, 204 250517, 2452, 6 4 -108 1, 0, 27 1, 219 1294948, 11826, 27 -6 -108 4, -2, 7 1, 23 3661, 320, 7 4 -108 4, 2, 7 1, 471 1553833, 6596, 7 3 -115 1, 1, 29 1, 459 6110209, 26623, 29 3 -115 5, 5, 7 1, 407 1161583, 5703, 7 -6 -120 1, 0, 30 1, 301 2718031, 18060, 30 4 -120 2, 0, 15 1, 79 93617, 2370, 15 -6 -120 3, 0, 10 1, 380 1444003, 7600, 10 4 -120 5, 0, 6 1, 459 1264091, 5508, 6 -1 -123 1, 1, 31 1, 413 5288053, 25607, 31 -1 -123 3, 3, 11 1, 308 1044431, 6779, 11 -4 -127 1, 1, 32 1, 202 1305931, 12929, 32 6 -127 2, -1, 16 1, 306 1497872, 9791, 16 -4 -127 2, 1, 16 1, 404 2611862, 12929, 16 6 -127 4, -1, 8 1, 89 63283, 1423, 8 -4 -127 4, 1, 8 1, 285 650089, 4561, 8 2 -128 1, 0, 32 1, 7 1569, 448, 32 2 -128 3, -2, 11 1, 68 50731, 1494, 11 2 -128 3, 2, 11 1, 258 732723, 5678, 11 2 -128 4, 4, 9 1, 199 357209, 3586, 9 4 -132 1, 0, 33 1, 496 8118529, 32736, 33 -6 -132 2, 2, 17 1, 409 2844597, 13908, 17 -6 -132 3, 0, 11 1, 442 2149007, 9724, 11 4 -132 6, 6, 7 1, 470 1549126, 6586, 7 6 -136 1, 0, 34 1, 37 46547, 2516, 34 6 -136 2, 0, 17 1, 74 93094, 2516, 17 6 -136 5, -2, 7 1, 404 1141709, 5654, 7 -14 -136 5, 2, 7 1, 329 758350, 4608, 7 4 -139 1, 1, 35 1, 483 8165599, 33811, 35 -6 -139 5, -1, 7 1, 99 68513, 1385, 7 -6 -139 5, 1, 7 1, 323 730631, 4523, 7 -4 -140 1, 0, 35 1, 331 3834636, 23170, 35 -4 -140 3, -2, 12 1, 181 392773, 4342, 12 6 -140 3, 2, 12 1, 268 862427, 6434, 12 6 -140 4, -2, 9 1, 67 40271, 1204, 9 -4 -140 4, 2, 9 1, 183 301771, 3296, 9 -4 -140 5, 0, 7 1, 86 51777, 1204, 7 1 -147 1, 1, 37 1, 455 7660381, 33671, 37 1 -147 3, 3, 13 1, 88 100939, 2291, 13 0 -148 1, 0, 37 1, 48 85249, 3552, 37 0 -148 2, 2, 19 1, 176 588898, 6690, 19 -8 -152 1, 0, 38 1, 17 10983, 1292, 38 2 -152 2, 0, 19 1, 34 21966, 1292, 19 2 -152 3, -2, 13 1, 90 105123, 2338, 13 -8 -152 3, 2, 13 1, 291 1101438, 7568, 13 2 -152 6, -4, 7 1, 242 408986, 3384, 7 2 -152 6, 4, 7 1, 92 59622, 1292, 7 -5 -155 1, 1, 39 1, 271 2864471, 21139, 39 5 -155 3, -1, 13 1, 451 2643765, 11725, 13 -5 -155 3, 1, 13 1, 290 1093593, 7541, 13 5 -155 5, 5, 9 1, 70 44455, 1265, 9 -5 -156 1, 0, 39 1, 309 3723760, 24102, 39 5 -156 3, 0, 13 1, 404 2121811, 10504, 13 5 -156 5, -2, 8 1, 199 316415, 3182, 8 5 -156 5, 2, 8 1, 68 37133, 1090, 8 7 -159 1, 1, 40 1, 422 7123783, 33761, 40 -3 -159 2, -1, 20 1, 138 380744, 5519, 20 -3 -159 2, 1, 20 1, 321 2061143, 12841, 20 -3 -159 3, 3, 14 1, 197 543920, 5519, 14 7 -159 4, -1, 10 1, 276 761488, 5519, 10 -3 -159 4, 1, 10 1, 119 141733, 2381, 10 -3 -159 5, -1, 8 1, 345 951860, 5519, 8 -13 -159 5, 1, 8 1, 18 2615, 289, 8 7 -159 6, -3, 7 1, 245 419446, 3427, 7 7 -159 6, 3, 7 1, 394 1087840, 5519, 7 9 -163 1, 1, 41 1, 336 4629073, 27553, 41 -2 -167 1, 1, 42 1, 391 6421394, 32845, 42 -2 -167 2, -1, 21 1, 10 2092, 419, 21 -2 -167 2, 1, 21 1, 259 1408962, 10879, 21 -2 -167 3, -1, 14 1, 15 3138, 419, 14 -2 -167 3, 1, 14 1, 127 225936, 3557, 14 -2 -167 4, -3, 11 1, 352 1361892, 7741, 11 8 -167 4, 3, 11 1, 114 143302, 2511, 11 8 -167 6, -5, 8 1, 288 662118, 4603, 8 -2 -167 6, -1, 7 1, 30 6276, 419, 7 -2 -167 6, 1, 7 1, 254 451872, 3557, 7 -2 -167 6, 5, 8 1, 222 395388, 3557, 8 -5 -180 1, 0, 45 1, 133 796006, 11970, 45 5 -180 2, 2, 23 1, 101 234827, 4648, 23 5 -180 5, 0, 9 1, 142 181481, 2556, 9 -5 -180 7, 4, 7 1, 257 463378, 3602, 7 6 -184 1, 0, 46 1, 138 876025, 12696, 46 -4 -184 2, 0, 23 1, 276 1752050, 12696, 23 -4 -184 5, -4, 10 1, 112 124997, 2236, 10 6 -184 5, 4, 10 1, 7 523, 144, 10 -5 -188 1, 0, 47 1, 471 10426528, 44274, 47 -5 -188 3, -2, 16 1, 403 2597741, 12894, 16 -5 -188 3, 2, 16 1, 76 92571, 2434, 16 -5 -188 7, -6, 8 1, 414 1368691, 6618, 8 -5 -188 7, 6, 8 1, 21 3661, 342, 8 2 -192 1, 0, 48 1, 295 4177201, 28320, 48 2 -192 3, 0, 16 1, 362 2096707, 11584, 16 2 -192 4, 4, 13 1, 204 541828, 5308, 13 2 -192 7, 2, 7 1, 379 1006252, 5308, 7 unknown -199 1, 1, 50 1, 277 3836728, 27701, 50 1 -199 2, -1, 25 1, 303 2294924, 15149, 25 1 -199 2, 1, 25 1, 31 24058, 1551, 25 -9 -199 4, -3, 13 1, 100 129704, 2597, 13 -9 -199 4, 3, 13 1, 140 255224, 3643, 13 -9 -199 5, -1, 10 1, 496 2459669, 9919, 10 -9 -199 5, 1, 10 1, 339 1149554, 6781, 10 11 -199 7, -5, 8 1, 228 414739, 3643, 8 11 -199 7, 5, 8 1, 162 210769, 2597, 8 -2 -200 1, 0, 50 1, 99 490051, 9900, 50 -2 -200 2, 0, 25 1, 198 980102, 9900, 25 -2 -200 3, -2, 17 1, 322 1761987, 10946, 17 -2 -200 3, 2, 17 1, 45 34518, 1532, 17 -2 -200 6, -4, 9 1, 434 1693474, 7808, 9 -2 -200 6, 4, 9 1, 143 184619, 2578, 9