# Fourier coefficients... 'F461' # Coeff Disc Reduced form Unreduced form 2 -4 1, 0, 1 1, 48 2305, 96, 1 1 -16 1, 0, 4 1, 24 2305, 192, 4 -1 -19 1, 1, 5 1, 202 204223, 2021, 5 -3 -20 1, 0, 5 1, 44 9681, 440, 5 4 -20 2, 2, 3 1, 73 16135, 440, 3 -2 -23 1, 1, 6 1, 104 65001, 1249, 6 -2 -23 2, -1, 3 1, 362 392772, 2171, 3 5 -23 2, 1, 3 1, 208 130002, 1249, 3 -1 -24 1, 0, 6 1, 98 57625, 1176, 6 -1 -24 2, 0, 3 1, 196 115250, 1176, 3 2 -36 1, 0, 9 1, 16 2305, 288, 9 2 -36 2, 2, 5 1, 213 227273, 2132, 5 4 -39 1, 1, 10 1, 374 1399135, 7481, 10 -3 -39 2, -1, 5 1, 195 189932, 1949, 5 4 -39 2, 1, 5 1, 287 412134, 2871, 5 -3 -39 3, 3, 4 1, 128 65923, 1027, 4 4 -43 1, 1, 11 1, 388 1656373, 8537, 11 0 -56 1, 0, 14 1, 299 1251615, 8372, 14 0 -56 2, 0, 7 1, 137 131385, 1918, 7 0 -56 3, -2, 5 1, 192 183939, 1918, 5 0 -56 3, 2, 5 1, 376 707635, 3762, 5 4 -59 1, 1, 15 1, 284 1210125, 8521, 15 -3 -59 3, -1, 5 1, 299 446709, 2989, 5 -3 -59 3, 1, 5 1, 391 764799, 3911, 5 0 -64 1, 0, 16 1, 12 2305, 384, 16 0 -64 4, 4, 5 1, 38 7376, 384, 5 2 -67 1, 1, 17 1, 358 2179147, 12173, 17 -2 -68 1, 0, 17 1, 385 2519826, 13090, 17 5 -68 2, 2, 9 1, 10 922, 182, 9 -2 -68 3, -2, 6 1, 169 171031, 2026, 6 -2 -68 3, 2, 6 1, 15 1383, 182, 6 2 -76 1, 0, 19 1, 349 2314220, 13262, 19 -5 -76 4, -2, 5 1, 220 241564, 2198, 5 2 -76 4, 2, 5 1, 404 816892, 4042, 5 2 -80 1, 0, 20 1, 439 3854421, 17560, 20 2 -80 3, -2, 7 1, 69 33192, 964, 7 2 -80 3, 2, 7 1, 398 1109627, 5574, 7 -5 -80 4, 0, 5 1, 373 695649, 3730, 5 5 -84 1, 0, 21 1, 30 18901, 1260, 21 -2 -84 2, 2, 11 1, 141 218975, 3104, 11 -2 -84 3, 0, 7 1, 90 56703, 1260, 7 5 -84 5, 4, 5 1, 310 481745, 3104, 5 2 -87 1, 1, 22 1, 303 2020102, 13333, 22 2 -87 2, -1, 11 1, 187 384474, 4113, 11 -5 -87 2, 1, 11 1, 145 231422, 3191, 11 2 -87 3, 3, 8 1, 84 56703, 1347, 8 -5 -87 4, -3, 6 1, 343 704869, 4113, 6 2 -87 4, 3, 6 1, 112 75604, 1347, 6 -1 -88 1, 0, 22 1, 169 628343, 7436, 22 -1 -88 2, 0, 11 1, 338 1256686, 7436, 11 -2 -91 1, 1, 23 1, 109 273373, 5015, 23 -2 -91 5, 3, 5 1, 409 837637, 4093, 5 1 -92 1, 0, 23 1, 86 170109, 3956, 23 1 -92 3, -2, 8 1, 305 743593, 4878, 8 1 -92 3, 2, 8 1, 420 1412043, 6722, 8 -4 -95 1, 1, 24 1, 293 2060670, 14065, 24 -4 -95 2, -1, 12 1, 394 1862440, 9455, 12 -4 -95 2, 1, 12 1, 125 187627, 3001, 12 3 -95 3, -1, 8 1, 130 135073, 2079, 8 3 -95 3, 1, 8 1, 418 1398213, 6689, 8 3 -95 4, -1, 6 1, 327 641251, 3923, 6 3 -95 4, 1, 6 1, 250 375254, 3001, 6 3 -95 5, 5, 6 1, 96 55781, 1157, 6 -4 -96 1, 0, 24 1, 412 4073857, 19776, 24 3 -96 3, 0, 8 1, 314 788771, 5024, 8 3 -96 4, 4, 7 1, 161 182095, 2258, 7 -4 -96 5, 2, 5 1, 410 841325, 4102, 5 -5 -100 1, 0, 25 1, 267 1782226, 13350, 25 2 -100 2, 2, 13 1, 407 2154253, 10584, 13 -4 -103 1, 1, 26 1, 93 224968, 4837, 26 -4 -103 2, -1, 13 1, 257 858382, 6681, 13 -4 -103 2, 1, 13 1, 186 449936, 4837, 13 3 -103 4, -3, 7 1, 214 319934, 2993, 7 3 -103 4, 3, 7 1, 16 1844, 227, 7 -2 -104 1, 0, 26 1, 411 4391947, 21372, 26 5 -104 2, 0, 13 1, 361 1694175, 9386, 13 5 -104 3, -2, 9 1, 163 238798, 2932, 9 -2 -104 3, 2, 9 1, 214 412595, 3854, 9 -2 -104 5, -4, 6 1, 91 49327, 1088, 6 -2 -104 5, 4, 6 1, 244 358197, 2932, 6 0 -107 1, 1, 27 1, 278 2086947, 15013, 27 0 -107 3, -1, 9 1, 117 123087, 2105, 9 0 -107 3, 1, 9 1, 373 1252537, 6715, 9 3 -111 1, 1, 28 1, 68 129541, 3809, 28 3 -111 2, -1, 14 1, 169 399687, 4731, 14 -4 -111 2, 1, 14 1, 136 259082, 3809, 14 -4 -111 3, 3, 10 1, 52 27199, 1043, 10 3 -111 4, -1, 7 1, 338 799374, 4731, 7 -4 -111 4, 1, 7 1, 272 518164, 3809, 7 -4 -111 5, -3, 6 1, 164 160889, 1965, 6 3 -111 5, 3, 6 1, 394 932603, 4731, 6 0 -115 1, 1, 29 1, 306 2715751, 17749, 29 7 -115 5, 5, 7 1, 82 47483, 1153, 7 4 -120 1, 0, 30 1, 448 6021121, 26880, 30 -3 -120 2, 0, 15 1, 435 2838377, 13050, 15 -3 -120 3, 0, 10 1, 422 1780843, 8440, 10 4 -120 5, 0, 6 1, 396 940901, 4752, 6 -5 -132 1, 0, 33 1, 424 5932609, 27984, 33 -5 -132 2, 2, 17 1, 362 2228474, 12310, 17 2 -132 3, 0, 11 1, 350 1347503, 7700, 11 2 -132 6, 6, 7 1, 352 869446, 4934, 7 1 -139 1, 1, 35 1, 186 1211047, 13021, 35 8 -139 5, -1, 7 1, 74 38263, 1035, 7 1 -139 5, 1, 7 1, 8 461, 113, 7 0 -143 1, 1, 36 1, 401 5789238, 28873, 36 0 -143 2, -1, 18 1, 213 816431, 7667, 18 -7 -143 2, 1, 18 1, 341 2093401, 12277, 18 0 -143 3, -1, 12 1, 89 94966, 2135, 12 0 -143 3, 1, 12 1, 281 947816, 6745, 12 -7 -143 4, -1, 9 1, 426 1632862, 7667, 9 7 -143 4, 1, 9 1, 221 439794, 3979, 9 0 -143 6, -5, 7 1, 87 52554, 1213, 7 0 -143 6, 1, 6 1, 101 61313, 1213, 6 7 -143 6, 5, 7 1, 218 333764, 3057, 7 1 -144 1, 0, 36 1, 453 7387525, 32616, 36 1 -144 4, 0, 9 1, 429 1656373, 7722, 9 1 -144 5, -4, 8 1, 310 767565, 4956, 8 1 -144 5, 4, 8 1, 79 50249, 1268, 8 -3 -151 1, 1, 38 1, 268 2729581, 20369, 38 -3 -151 2, -1, 19 1, 439 3661262, 16681, 19 -3 -151 2, 1, 19 1, 75 106952, 2851, 19 4 -151 4, -3, 10 1, 281 788771, 5617, 10 -3 -151 4, 3, 10 1, 419 1756871, 8383, 10 -3 -151 5, -3, 8 1, 236 444865, 3773, 8 4 -151 5, 3, 8 1, 178 254011, 2851, 8 -2 -156 1, 0, 39 1, 180 1263601, 14040, 39 5 -156 3, 0, 13 1, 79 81136, 2054, 13 -2 -156 5, -2, 8 1, 359 1030335, 5742, 8 5 -156 5, 2, 8 1, 13 1383, 210, 8 -3 -163 1, 1, 41 1, 439 7902001, 35999, 41 -4 -164 1, 0, 41 1, 262 2814405, 21484, 41 3 -164 2, 2, 21 1, 270 1531442, 11342, 21 10 -164 3, -2, 14 1, 10 1383, 278, 14 -4 -164 3, 2, 14 1, 405 2297163, 11342, 14 -4 -164 5, -4, 9 1, 323 937674, 5810, 9 3 -164 5, 4, 9 1, 425 1627330, 7654, 9 -4 -164 6, -2, 7 1, 20 2766, 278, 7 -4 -164 6, 2, 7 1, 349 853311, 4888, 7 -5 -167 1, 1, 42 1, 178 1330907, 14953, 42 9 -167 2, -1, 21 1, 378 3000188, 15875, 21 2 -167 2, 1, 21 1, 356 2661814, 14953, 21 2 -167 3, -1, 14 1, 106 157201, 2967, 14 9 -167 3, 1, 14 1, 73 74682, 2045, 14 -5 -167 4, -3, 11 1, 135 200074, 2967, 11 9 -167 4, 3, 11 1, 9 922, 201, 11 -5 -167 6, -5, 8 1, 301 723309, 4811, 8 -5 -167 6, -1, 7 1, 212 314402, 2967, 7 -5 -167 6, 1, 7 1, 146 149364, 2045, 7 -5 -167 6, 5, 8 1, 358 1027108, 5733, 8 -1 -171 1, 1, 43 1, 294 3717043, 25285, 43 -1 -171 5, -3, 9 1, 278 694727, 5001, 9 -1 -171 5, 3, 9 1, 124 138761, 2235, 9 -1 -171 7, 5, 7 1, 291 594229, 4079, 7 6 -172 1, 0, 43 1, 434 8099309, 37324, 43 -1 -172 4, -2, 11 1, 146 234188, 3210, 11 -1 -172 4, 2, 11 1, 62 42412, 1366, 11 3 -180 1, 0, 45 1, 322 4665781, 28980, 45 3 -180 2, 2, 23 1, 189 821963, 8696, 23 3 -180 5, 0, 9 1, 227 463766, 4086, 9 3 -180 7, 4, 7 1, 94 62235, 1320, 7 1 -191 1, 1, 48 1, 148 1051541, 14209, 48 1 -191 2, -1, 24 1, 200 959802, 9599, 24 1 -191 2, 1, 24 1, 296 2103082, 14209, 24 -6 -191 3, -1, 16 1, 300 1439703, 9599, 16 8 -191 3, 1, 16 1, 444 3154623, 14209, 16 -6 -191 4, -1, 12 1, 400 1919604, 9599, 12 1 -191 4, 1, 12 1, 131 206067, 3145, 12 8 -191 5, -3, 10 1, 434 1882263, 8677, 10 1 -191 5, 3, 10 1, 111 123548, 2223, 10 1 -191 6, -5, 9 1, 175 274756, 3145, 9 1 -191 6, -1, 8 1, 139 154435, 2223, 8 -6 -191 6, 1, 8 1, 427 1459065, 6833, 8 -6 -191 6, 5, 9 1, 72 47022, 1301, 9 -4 -195 1, 1, 49 1, 48 112945, 4705, 49 3 -195 3, 3, 17 1, 301 1541123, 10237, 17 -4 -195 5, 5, 11 1, 46 23511, 1017, 11 3 -195 7, 1, 7 1, 336 790615, 4705, 7 0 -196 1, 0, 49 1, 59 170570, 5782, 49 0 -196 2, 2, 25 1, 300 2250602, 15002, 25 0 -196 5, -2, 10 1, 197 387701, 3938, 10 0 -196 5, 2, 10 1, 289 835793, 5782, 10 -1 -199 1, 1, 50 1, 105 551356, 10501, 50 6 -199 2, -1, 25 1, 376 3534026, 18799, 25 -1 -199 2, 1, 25 1, 210 1102712, 10501, 25 -1 -199 4, -3, 13 1, 404 2120600, 10501, 13 -1 -199 4, 3, 13 1, 191 474830, 4969, 13 -1 -199 5, -1, 10 1, 18 3227, 359, 10 -1 -199 5, 1, 10 1, 64 41029, 1281, 10 6 -199 7, -5, 8 1, 138 151669, 2203, 8 -1 -199 7, 5, 8 1, 195 305182, 3125, 8 3 -203 1, 1, 51 1, 299 4559751, 30499, 51 3 -203 3, -1, 17 1, 192 626499, 6527, 17 -4 -203 3, 1, 17 1, 436 3232071, 14825, 17 -4 -203 7, 7, 9 1, 311 872673, 5605, 9 2 -207 1, 1, 52 1, 169 1485342, 17577, 52 2 -207 2, -1, 26 1, 143 531533, 7435, 26 2 -207 2, 1, 26 1, 338 2970684, 17577, 26 2 -207 4, -1, 13 1, 286 1063066, 7435, 13 2 -207 4, 1, 13 1, 215 601144, 5591, 13 2 -207 8, 7, 8 1, 349 976859, 5591, 8 -3 -212 1, 0, 53 1, 36 68689, 3816, 53 4 -212 2, 2, 27 1, 156 657386, 8426, 27 4 -212 3, -2, 18 1, 439 3468103, 15802, 18 4 -212 3, 2, 18 1, 234 986079, 8426, 18 -3 -212 6, -2, 9 1, 417 1564173, 7504, 9 -3 -212 6, 2, 9 1, 7 461, 128, 9 -4 -215 1, 1, 54 1, 61 200996, 6589, 54 3 -215 2, -1, 27 1, 344 3194730, 18575, 27 -4 -215 2, 1, 27 1, 122 401992, 6589, 27 3 -215 3, -1, 18 1, 55 54398, 1979, 18 3 -215 3, 1, 18 1, 183 602988, 6589, 18 -4 -215 4, -3, 14 1, 433 2623551, 12121, 14 3 -215 4, 3, 14 1, 334 1562790, 9355, 14 -4 -215 5, 5, 12 1, 428 2200353, 10277, 12 -4 -215 6, -5, 10 1, 7 461, 135, 10 -4 -215 6, -1, 9 1, 110 108796, 1979, 9 3 -215 6, 1, 9 1, 366 1205976, 6589, 9 -4 -215 6, 5, 10 1, 237 562881, 4745, 10 10 -215 7, -3, 8 1, 412 1356723, 6589, 8 3 -215 7, 3, 8 1, 354 1003597, 5667, 8 0 -216 1, 0, 54 1, 121 790615, 13068, 54 0 -216 2, 0, 27 1, 242 1581230, 13068, 27 -7 -216 5, -2, 11 1, 175 336530, 3848, 11 0 -216 5, 2, 11 1, 91 91278, 2004, 11 0 -216 7, -6, 9 1, 419 1577542, 7536, 9 -7 -216 7, 6, 9 1, 111 111562, 2004, 9 7 -223 1, 1, 56 1, 398 8871023, 44577, 56 -7 -223 2, -1, 28 1, 121 409829, 6775, 28 7 -223 2, 1, 28 1, 335 3142637, 18761, 28 0 -223 4, -1, 14 1, 242 819658, 6775, 14 -7 -223 4, 1, 14 1, 209 611747, 5853, 14 0 -223 7, -1, 8 1, 193 297806, 3087, 8 0 -223 7, 1, 8 1, 20 3227, 321, 8 0 -224 1, 0, 56 1, 380 8086401, 42560, 56 -7 -224 3, -2, 19 1, 101 193620, 3836, 19 0 -224 3, 2, 19 1, 295 1654068, 11212, 19 0 -224 4, 4, 15 1, 97 141527, 2914, 15 7 -224 5, -4, 12 1, 160 306565, 3836, 12 0 -224 5, 4, 12 1, 6 461, 148, 12 -7 -224 7, 0, 8 1, 355 1008207, 5680, 8 7 -224 8, 8, 9 1, 59 31809, 1070, 9 5 -227 1, 1, 57 1, 28 44717, 3193, 57 -9 -227 3, -1, 19 1, 448 3812931, 17023, 19 5 -227 3, 1, 19 1, 84 134151, 3193, 19 5 -227 7, -5, 9 1, 24 5071, 427, 9 -9 -227 7, 5, 9 1, 382 1315233, 6881, 9 5 -232 1, 0, 58 1, 392 8912513, 45472, 58 5 -232 2, 0, 29 1, 323 3025543, 18734, 29 6 -236 1, 0, 59 1, 246 3570445, 29028, 59 -8 -236 3, -2, 20 1, 380 2887243, 15198, 20 -8 -236 3, 2, 20 1, 426 3630375, 17042, 20 -1 -236 4, -2, 15 1, 353 1868433, 10588, 15 -1 -236 4, 2, 15 1, 107 171953, 3212, 15 -1 -236 5, -2, 12 1, 326 1274665, 7822, 12 -1 -236 5, 2, 12 1, 249 744515, 5978, 12 6 -236 7, -4, 9 1, 25 5532, 446, 9 6 -236 7, 4, 9 1, 127 145676, 2290, 9 6 -244 1, 0, 61 1, 23 32270, 2806, 61 -1 -244 2, 2, 31 1, 417 5391395, 25856, 31 -1 -244 5, -4, 13 1, 179 415822, 4650, 13 -1 -244 5, 4, 13 1, 356 1648997, 9260, 13 6 -244 7, -6, 10 1, 325 1054307, 6494, 10 6 -244 7, 6, 10 1, 140 196847, 2806, 10 -9 -248 1, 0, 62 1, 328 6670209, 40672, 62 5 -248 2, 0, 31 1, 195 1178777, 12090, 31 5 -248 3, -2, 21 1, 244 1249771, 10246, 21 5 -248 3, 2, 21 1, 200 840403, 8402, 21 -2 -248 6, -4, 11 1, 424 1975846, 9324, 11 -9 -248 6, 4, 11 1, 256 721926, 5636, 11 5 -248 7, -2, 9 1, 262 617279, 4714, 9 -2 -248 7, 2, 9 1, 313 882354, 5636, 9 unknown -256 1, 0, 64 1, 455 13249601, 58240, 64 -2 -256 4, 4, 17 1, 140 333764, 4764, 17 unknown -256 5, -2, 13 1, 6 461, 154, 13 -2 -256 5, 2, 13 1, 325 1373780, 8452, 13 -1 -259 1, 1, 65 1, 343 7647529, 44591, 65 -1 -259 5, -1, 13 1, 403 2110919, 10477, 13 -1 -259 5, 1, 13 1, 332 1433249, 8633, 13 -1 -259 7, 7, 11 1, 434 2074961, 9555, 11 6 -263 1, 1, 66 1, 134 1185231, 17689, 66 -8 -263 2, -1, 33 1, 282 2624012, 18611, 33 -1 -263 2, 1, 33 1, 268 2370462, 17689, 33 -8 -263 3, -1, 22 1, 423 3936018, 18611, 22 -1 -263 3, 1, 22 1, 402 3555693, 17689, 22 -1 -263 4, -3, 17 1, 439 3274944, 14923, 17 unknown -263 4, 3, 17 1, 249 1054768, 8469, 17 6 -263 6, -5, 12 1, 161 310253, 3859, 12 6 -263 6, -1, 11 1, 385 1630096, 8469, 11 -1 -263 6, 1, 11 1, 343 1294488, 7547, 11 unknown -263 6, 5, 12 1, 199 476213, 4781, 12 6 -263 8, -5, 9 1, 61 33192, 1093, 9 -1 -263 8, 5, 9 1, 419 1582152, 7547, 9 unknown -268 1, 0, 67 1, 106 752813, 14204, 67 unknown -268 4, -2, 17 1, 228 883276, 7750, 17 10 -268 4, 2, 17 1, 255 1105939, 8672, 17 -1 -272 1, 0, 68 1, 423 12167173, 57528, 68 -8 -272 3, -2, 23 1, 28 17979, 1286, 23 6 -272 3, 2, 23 1, 68 106491, 3130, 23 -1 -272 4, 0, 17 1, 309 1623181, 10506, 17 6 -272 7, -6, 11 1, 394 1705239, 8662, 11 -8 -272 7, 6, 11 1, 142 222663, 3130, 11 13 -272 8, -4, 9 1, 379 1291261, 6818, 9 -8 -272 8, 4, 9 1, 20 3688, 364, 9 1 -280 1, 0, 70 1, 82 470681, 11480, 70 1 -280 2, 0, 35 1, 164 941362, 11480, 35 1 -280 5, 0, 14 1, 410 2353405, 11480, 14 1 -280 7, 0, 10 1, 113 127697, 2260, 10 -2 -292 1, 0, 73 1, 142 1471973, 20732, 73 -2 -292 2, 2, 37 1, 168 1044626, 12434, 37 -2 -292 7, -4, 11 1, 272 812743, 5980, 11 -2 -292 7, 4, 11 1, 104 119399, 2292, 11 unknown -295 1, 1, 74 1, 152 1709849, 22497, 74 3 -295 2, -1, 37 1, 5 922, 369, 37 -4 -295 2, 1, 37 1, 304 3419698, 22497, 37 3 -295 4, -3, 19 1, 398 3008486, 15121, 19 unknown -295 4, 3, 19 1, 228 988384, 8667, 19 3 -295 5, 5, 16 1, 69 76526, 2213, 16 -4 -295 8, -5, 10 1, 157 245713, 3135, 10 3 -295 8, 5, 10 1, 387 1499633, 7745, 10 unknown -296 1, 0, 74 1, 432 13810177, 63936, 74 unknown -296 2, 0, 37 1, 403 6009135, 29822, 37 1 -296 3, -2, 25 1, 283 2001662, 14148, 25 -6 -296 3, 2, 25 1, 412 4244427, 20602, 25 1 -296 5, -2, 15 1, 318 1516229, 9538, 15 1 -296 5, 2, 15 1, 72 77909, 2162, 15 1 -296 6, -4, 13 1, 367 1749495, 9538, 13 -6 -296 6, 4, 13 1, 83 89895, 2162, 13 1 -296 9, -8, 10 1, 339 1146507, 6772, 10 1 -296 9, 8, 10 1, 246 607137, 4928, 10