# Fourier coefficients... 'F349' # Coeff Disc Reduced form Unreduced form 3 -3 1, 1, 1 1, 122 15007, 245, 1 2 -4 1, 0, 1 1, 136 18497, 272, 1 1 -12 1, 0, 3 1, 151 68404, 906, 3 6 -15 1, 1, 4 1, 110 48511, 881, 4 -7 -15 2, 1, 2 1, 220 97022, 881, 2 3 -16 1, 0, 4 1, 281 315845, 2248, 4 4 -19 1, 1, 5 1, 22 2443, 221, 5 7 -20 1, 0, 5 1, 81 32806, 810, 5 -6 -20 2, 2, 3 1, 251 189507, 1508, 3 0 -23 1, 1, 6 1, 259 402746, 3109, 6 0 -23 2, -1, 3 1, 53 8376, 317, 3 0 -23 2, 1, 3 1, 169 85854, 1015, 3 -2 -27 1, 1, 7 1, 202 285831, 2829, 7 -9 -31 1, 1, 8 1, 54 23383, 865, 8 4 -31 2, -1, 4 1, 21 1745, 167, 4 4 -31 2, 1, 4 1, 108 46766, 865, 4 5 -36 1, 0, 9 1, 278 695557, 5004, 9 -8 -36 2, 2, 5 1, 221 244649, 2212, 5 2 -48 1, 0, 12 1, 99 117613, 2376, 12 -11 -48 3, 0, 4 1, 297 352839, 2376, 4 -4 -51 1, 1, 13 1, 118 181131, 3069, 13 9 -51 3, 3, 5 1, 167 139949, 1673, 5 -6 -56 1, 0, 14 1, 331 1533855, 9268, 14 7 -56 2, 0, 7 1, 313 685785, 4382, 7 7 -56 3, -2, 5 1, 229 261750, 2288, 5 -6 -56 3, 2, 5 1, 89 39786, 892, 5 -10 -60 1, 0, 15 1, 267 1069336, 8010, 15 3 -60 3, 0, 5 1, 103 53048, 1030, 5 -6 -64 1, 0, 16 1, 315 1587601, 10080, 16 -6 -64 4, 4, 5 1, 170 145184, 1704, 5 13 -67 1, 1, 17 1, 190 613891, 6461, 17 4 -68 1, 0, 17 1, 274 1276293, 9316, 17 -9 -68 2, 2, 9 1, 246 545138, 4430, 9 4 -68 3, -2, 6 1, 253 383551, 3034, 6 4 -68 3, 2, 6 1, 20 2443, 242, 6 -5 -75 1, 1, 19 1, 280 1489881, 10641, 19 8 -75 3, 3, 7 1, 12 1047, 171, 7 -3 -76 1, 0, 19 1, 319 1933460, 12122, 19 -3 -76 4, -2, 5 1, 305 464519, 3048, 5 10 -76 4, 2, 5 1, 165 136459, 1652, 5 4 -80 1, 0, 20 1, 215 924501, 8600, 20 4 -80 3, -2, 7 1, 66 30363, 922, 7 4 -80 3, 2, 7 1, 315 695208, 4412, 7 -9 -80 4, 0, 5 1, 162 131224, 1620, 5 5 -83 1, 1, 21 1, 38 30363, 1597, 21 -8 -83 3, -1, 7 1, 164 188111, 2295, 7 5 -83 3, 1, 7 1, 114 91089, 1597, 7 -5 -87 1, 1, 22 1, 115 291066, 5061, 22 -5 -87 2, -1, 11 1, 8 698, 175, 11 -5 -87 2, 1, 11 1, 230 582132, 5061, 11 -5 -87 3, 3, 8 1, 98 77129, 1571, 8 8 -87 4, -3, 6 1, 73 31759, 873, 6 8 -87 4, 3, 6 1, 247 366799, 2967, 6 1 -88 1, 0, 22 1, 255 1430551, 11220, 22 1 -88 2, 0, 11 1, 161 285133, 3542, 11 2 -91 1, 1, 23 1, 108 268381, 4969, 23 2 -91 5, 3, 5 1, 8 349, 83, 5 0 -92 1, 0, 23 1, 229 1206144, 10534, 23 0 -92 3, -2, 8 1, 135 145533, 2158, 8 0 -92 3, 2, 8 1, 222 394719, 3554, 8 6 -95 1, 1, 24 1, 220 1161821, 10561, 24 -7 -95 2, -1, 12 1, 62 46068, 1487, 12 -7 -95 2, 1, 12 1, 91 99465, 2185, 12 -7 -95 3, -1, 8 1, 93 69102, 1487, 8 -7 -95 3, 1, 8 1, 311 774082, 4977, 8 6 -95 4, -1, 6 1, 124 92136, 1487, 6 6 -95 4, 1, 6 1, 182 198930, 2185, 6 6 -95 5, 5, 6 1, 298 534319, 3581, 6 10 -100 1, 0, 25 1, 252 1587601, 12600, 25 -3 -100 2, 2, 13 1, 55 39437, 1432, 13 9 -104 1, 0, 26 1, 193 968475, 10036, 26 -4 -104 2, 0, 13 1, 37 17799, 962, 13 -4 -104 3, -2, 9 1, 325 949978, 5848, 9 -4 -104 3, 2, 9 1, 286 736739, 5150, 9 -4 -104 5, -4, 6 1, 255 389135, 3056, 6 9 -104 5, 4, 6 1, 138 114821, 1660, 6 -5 -108 1, 0, 27 1, 66 117613, 3564, 27 -5 -108 4, -2, 7 1, 155 167869, 2168, 7 8 -108 4, 2, 7 1, 55 21289, 772, 7 -5 -111 1, 1, 28 1, 102 291415, 5713, 28 8 -111 2, -1, 14 1, 229 733947, 6411, 14 8 -111 2, 1, 14 1, 204 582830, 5713, 14 -5 -111 3, 3, 10 1, 111 123546, 2223, 10 -5 -111 4, -1, 7 1, 109 83062, 1525, 7 -5 -111 4, 1, 7 1, 59 24430, 827, 7 8 -111 5, -3, 6 1, 11 698, 129, 6 -5 -111 5, 3, 6 1, 185 205910, 2223, 6 7 -115 1, 1, 29 1, 317 2914499, 18387, 29 7 -115 5, 5, 7 1, 266 496627, 3729, 7 1 -116 1, 0, 29 1, 330 3158101, 19140, 29 1 -116 2, 2, 15 1, 33 16403, 992, 15 -12 -116 3, -2, 10 1, 294 863775, 5878, 10 1 -116 3, 2, 10 1, 224 502211, 4482, 10 1 -116 5, -2, 6 1, 141 119009, 1690, 6 14 -116 5, 2, 6 1, 257 396813, 3086, 6 9 -123 1, 1, 31 1, 150 697651, 9301, 31 9 -123 3, 3, 11 1, 264 767451, 5811, 11 15 -124 1, 0, 31 1, 163 823640, 10106, 31 -11 -124 5, -4, 7 1, 74 38041, 1032, 7 -11 -124 5, 4, 7 1, 223 349000, 3126, 7 -4 -135 1, 1, 34 1, 228 1767685, 15505, 34 9 -135 2, -1, 17 1, 66 73988, 2243, 17 9 -135 2, 1, 17 1, 107 194742, 3639, 17 -4 -135 4, -3, 9 1, 86 66310, 1545, 9 -17 -135 4, 3, 9 1, 202 367846, 3639, 9 9 -135 5, 5, 8 1, 9 698, 149, 8 5 -139 1, 1, 35 1, 104 378665, 7281, 35 -21 -139 5, -1, 7 1, 221 341671, 3093, 7 5 -139 5, 1, 7 1, 171 204863, 2395, 7 -8 -143 1, 1, 36 1, 79 224756, 5689, 36 5 -143 2, -1, 18 1, 255 1170197, 9179, 18 5 -143 2, 1, 18 1, 158 449512, 5689, 18 5 -143 3, -1, 12 1, 208 518963, 4991, 12 5 -143 3, 1, 12 1, 237 674268, 5689, 12 5 -143 4, -1, 9 1, 161 233132, 2897, 9 -8 -143 4, 1, 9 1, 316 899024, 5689, 9 5 -143 6, -5, 7 1, 307 658214, 4293, 7 -8 -143 6, 1, 6 1, 125 93881, 1501, 6 -8 -143 6, 5, 7 1, 57 23034, 803, 7 -12 -144 1, 0, 36 1, 139 695557, 10008, 36 1 -144 4, 0, 9 1, 207 385645, 3726, 9 1 -144 5, -4, 8 1, 15 1745, 236, 8 1 -144 5, 4, 8 1, 189 286529, 3028, 8 6 -147 1, 1, 37 1, 325 3908451, 24051, 37 6 -147 3, 3, 13 1, 39 19893, 1017, 13 -20 -148 1, 0, 37 1, 88 286529, 6512, 37 19 -148 2, 2, 19 1, 6 698, 230, 19 -15 -151 1, 1, 38 1, 214 1740463, 16265, 38 11 -151 2, -1, 19 1, 226 970220, 8587, 19 11 -151 2, 1, 19 1, 79 118660, 3003, 19 -2 -151 4, -3, 10 1, 255 649489, 5097, 10 -15 -151 4, 3, 10 1, 150 225454, 3003, 10 11 -151 5, -3, 8 1, 57 25826, 909, 8 -2 -151 5, 3, 8 1, 13 1396, 211, 8 1 -155 1, 1, 39 1, 173 1167405, 13495, 39 1 -155 3, -1, 13 1, 9 1047, 233, 13 1 -155 3, 1, 13 1, 170 375873, 4421, 13 -12 -155 5, 5, 9 1, 129 150419, 2327, 9 13 -164 1, 0, 41 1, 53 115170, 4346, 41 -13 -164 2, 2, 21 1, 253 1344697, 10628, 21 0 -164 3, -2, 14 1, 255 909843, 7138, 14 0 -164 3, 2, 14 1, 205 588763, 5742, 14 -13 -164 5, -4, 9 1, 9 698, 158, 9 13 -164 5, 4, 9 1, 280 706725, 5044, 9 0 -164 6, -2, 7 1, 161 181131, 2252, 7 0 -164 6, 2, 7 1, 61 26175, 856, 7 -5 -168 1, 0, 42 1, 292 3581089, 24528, 42 8 -168 2, 0, 21 1, 235 1159727, 9870, 21 8 -168 3, 0, 14 1, 178 443579, 4984, 14 -5 -168 6, 0, 7 1, 7 349, 98, 7 -16 -171 1, 1, 43 1, 252 2730925, 21673, 43 -3 -171 5, -3, 9 1, 196 345161, 3525, 9 -3 -171 5, 3, 9 1, 312 877037, 5619, 9 10 -171 7, 5, 7 1, 52 19195, 733, 7 -16 -180 1, 0, 45 1, 27 32806, 2430, 45 10 -180 2, 2, 23 1, 159 581783, 7316, 23 -3 -180 5, 0, 9 1, 135 164030, 2430, 9 10 -180 7, 4, 7 1, 273 522802, 3826, 7 -1 -191 1, 1, 48 1, 255 3121456, 24481, 48 -1 -191 2, -1, 24 1, 321 2472665, 15407, 24 -1 -191 2, 1, 24 1, 161 622267, 7729, 24 -1 -191 3, -1, 16 1, 307 1507680, 9823, 16 12 -191 3, 1, 16 1, 67 71894, 2145, 16 -1 -191 4, -1, 12 1, 293 1029899, 7031, 12 -1 -191 4, 1, 12 1, 322 1244534, 7729, 12 -14 -191 5, -3, 10 1, 247 609354, 4937, 10 12 -191 5, 3, 10 1, 142 202071, 2843, 10 -14 -191 6, -5, 9 1, 197 348302, 3541, 9 -1 -191 6, -1, 8 1, 265 561541, 4239, 8 -1 -191 6, 1, 8 1, 134 143788, 2145, 8 12 -191 6, 5, 9 1, 274 677060, 4937, 9 1 -192 1, 0, 48 1, 125 750001, 12000, 48 1 -192 3, 0, 16 1, 26 10819, 832, 16 1 -192 4, 4, 13 1, 5 349, 134, 13 1 -192 7, 2, 7 1, 159 177292, 2228, 7 -18 -196 1, 0, 49 1, 180 1587601, 17640, 49 21 -196 2, 2, 25 1, 269 1809565, 13452, 25 21 -196 5, -2, 10 1, 219 479177, 4378, 10 -18 -196 5, 2, 10 1, 149 222313, 2982, 10 -10 -204 1, 0, 51 1, 63 202420, 6426, 51 3 -204 3, 0, 17 1, 189 607260, 6426, 17 16 -204 4, -2, 13 1, 113 165775, 2936, 13 -10 -204 4, 2, 13 1, 86 96324, 2238, 13 3 -204 5, -4, 11 1, 324 1153445, 7124, 11 3 -204 5, 4, 11 1, 165 300140, 3634, 11 -13 -207 1, 1, 52 1, 338 5941027, 35153, 52 13 -207 2, -1, 26 1, 72 134714, 3743, 26 13 -207 2, 1, 26 1, 327 2780483, 17005, 26 -13 -207 4, -1, 13 1, 144 269428, 3743, 13 -13 -207 4, 1, 13 1, 305 1209634, 7931, 13 13 -207 8, 7, 8 1, 59 28269, 951, 8 4 -219 1, 1, 55 1, 229 2884485, 25191, 55 4 -219 3, 3, 19 1, 222 937065, 8439, 19 17 -219 5, -1, 11 1, 225 556655, 4949, 11 -9 -219 5, 1, 11 1, 98 105747, 2157, 11 15 -223 1, 1, 56 1, 344 6627161, 38529, 56 -11 -223 2, -1, 28 1, 177 877037, 9911, 28 -11 -223 2, 1, 28 1, 339 3218129, 18985, 28 15 -223 4, -1, 14 1, 5 349, 139, 14 2 -223 4, 1, 14 1, 329 1515707, 9213, 14 2 -223 7, -1, 8 1, 96 73639, 1535, 8 -11 -223 7, 1, 8 1, 314 789089, 5025, 8 4 -224 1, 0, 56 1, 9 4537, 1008, 56 4 -224 3, -2, 19 1, 247 1158680, 9384, 19 4 -224 3, 2, 19 1, 302 1733483, 11478, 19 4 -224 4, 4, 15 1, 80 96324, 2404, 15 -9 -224 5, -4, 12 1, 333 1329341, 7988, 12 4 -224 5, 4, 12 1, 100 120405, 2404, 12 4 -224 7, 0, 8 1, 63 31759, 1008, 8 -9 -224 8, 8, 9 1, 327 964985, 5894, 9 -8 -227 1, 1, 57 1, 197 2212311, 22459, 57 5 -227 3, -1, 19 1, 40 30363, 1519, 19 5 -227 3, 1, 19 1, 242 1112961, 9197, 19 5 -227 7, -5, 9 1, 201 362611, 3613, 9 -8 -227 7, 5, 9 1, 278 696953, 5009, 9 10 -228 1, 0, 57 1, 254 3677413, 28956, 57 -16 -228 2, 2, 29 1, 78 176594, 4526, 29 -16 -228 3, 0, 19 1, 64 77827, 2432, 19 10 -228 6, 6, 11 1, 142 222662, 3130, 11 -9 -231 1, 1, 58 1, 243 3425086, 28189, 58 4 -231 2, -1, 29 1, 125 453002, 7249, 29 4 -231 2, 1, 29 1, 137 544440, 7947, 29 4 -231 3, 3, 20 1, 59 69800, 2363, 20 -9 -231 4, -3, 15 1, 265 1052584, 7947, 15 -9 -231 4, 3, 15 1, 195 570964, 5853, 15 4 -231 5, -3, 12 1, 244 713705, 5853, 12 17 -231 5, 3, 12 1, 331 1315730, 7947, 12 -9 -231 6, -3, 10 1, 223 496627, 4457, 10 -9 -231 6, 3, 10 1, 118 139600, 2363, 10 -9 -231 7, 7, 10 1, 48 23383, 967, 10 17 -231 8, 5, 8 1, 191 292811, 3061, 8 -8 -239 1, 1, 60 1, 142 1209983, 17041, 60 5 -239 2, -1, 30 1, 63 119009, 3779, 30 5 -239 2, 1, 30 1, 284 2419966, 17041, 30 5 -239 3, -1, 20 1, 269 1446954, 10759, 20 5 -239 3, 1, 20 1, 77 118660, 3081, 20 -8 -239 4, -1, 15 1, 126 238018, 3779, 15 5 -239 4, 1, 15 1, 219 719638, 6571, 15 5 -239 5, -1, 12 1, 332 1322361, 7967, 12 5 -239 5, 1, 12 1, 12 1745, 289, 12 -8 -239 6, -5, 11 1, 172 324570, 3779, 11 -8 -239 6, -1, 10 1, 189 357027, 3779, 10 -8 -239 6, 1, 10 1, 154 237320, 3081, 10 5 -239 6, 5, 11 1, 235 608656, 5175, 11 -8 -239 8, -7, 9 1, 94 78874, 1685, 9 5 -239 8, 7, 9 1, 132 157748, 2383, 9 -1 -240 1, 0, 60 1, 41 100861, 4920, 60 12 -240 3, 0, 20 1, 123 302583, 4920, 20 -1 -240 4, 0, 15 1, 164 403444, 4920, 15 -1 -240 5, 0, 12 1, 205 504305, 4920, 12 -12 -243 1, 1, 61 1, 81 400303, 9883, 61 14 -243 7, -3, 9 1, 239 513379, 4299, 9 -12 -243 7, 3, 9 1, 6 349, 111, 9 8 -255 1, 1, 64 1, 66 278851, 8449, 64 -5 -255 2, -1, 32 1, 252 2031878, 16127, 32 -5 -255 2, 1, 32 1, 132 557702, 8449, 32 -5 -255 3, 3, 22 1, 303 2020710, 13335, 22 8 -255 4, -1, 16 1, 155 384249, 4959, 16 8 -255 4, 1, 16 1, 264 1115404, 8449, 16 8 -255 5, 5, 14 1, 152 324221, 4261, 14 8 -255 6, -3, 11 1, 289 917870, 6355, 11 -5 -255 6, 3, 11 1, 257 727316, 5657, 11 -5 -255 7, -5, 10 1, 318 1009657, 6355, 10 -5 -255 7, 5, 10 1, 143 205212, 2865, 10 -5 -255 8, 1, 8 1, 179 256515, 2865, 8 -2 -256 1, 0, 64 1, 17 18497, 2176, 64 -2 -256 4, 4, 17 1, 146 362960, 4968, 17 -2 -256 5, -2, 13 1, 218 617381, 5666, 13 -2 -256 5, 2, 13 1, 191 474640, 4968, 13 6 -263 1, 1, 66 1, 13 11168, 1717, 66 -7 -263 2, -1, 33 1, 301 2989534, 19865, 33 -7 -263 2, 1, 33 1, 26 22336, 1717, 33 -7 -263 3, -1, 22 1, 277 1687764, 12187, 22 6 -263 3, 1, 22 1, 39 33504, 1717, 22 6 -263 4, -3, 17 1, 338 1941138, 11489, 17 6 -263 4, 3, 17 1, 112 213588, 3811, 17 -7 -263 6, -5, 12 1, 159 302583, 3811, 12 6 -263 6, -1, 11 1, 205 462076, 4509, 11 -7 -263 6, 1, 11 1, 78 67008, 1717, 11 6 -263 6, 5, 12 1, 304 1110518, 7301, 12 6 -263 8, -5, 9 1, 212 403444, 3811, 9 -7 -263 8, 5, 9 1, 289 753142, 5207, 9 17 -264 1, 0, 66 1, 65 278851, 8580, 66 -22 -264 2, 0, 33 1, 130 557702, 8580, 33 -9 -264 3, 0, 22 1, 195 836553, 8580, 22 17 -264 5, -4, 14 1, 157 344463, 4392, 14 -22 -264 5, 4, 14 1, 57 45719, 1600, 14 17 -264 6, 0, 11 1, 41 18497, 902, 11 17 -264 7, -4, 10 1, 150 224407, 2996, 10 -9 -264 7, 4, 10 1, 10 1047, 204, 10 13 -268 1, 0, 67 1, 39 101908, 5226, 67 0 -268 4, -2, 17 1, 318 1718476, 10810, 17 0 -268 4, 2, 17 1, 51 44323, 1736, 17 -15 -271 1, 1, 68 1, 278 5255591, 37809, 68 11 -271 2, -1, 34 1, 12 4886, 815, 34 11 -271 2, 1, 34 1, 207 1457075, 14077, 34 -2 -271 4, -1, 17 1, 24 9772, 815, 17 -15 -271 4, 1, 17 1, 65 71894, 2211, 17 -15 -271 5, -3, 14 1, 104 151117, 2909, 14 11 -271 5, 3, 14 1, 29 11866, 815, 14 -15 -271 7, -3, 10 1, 6 349, 117, 10 11 -271 7, 3, 10 1, 250 625757, 5003, 10 24 -271 8, -7, 10 1, 76 57236, 1513, 10 -2 -271 8, 7, 10 1, 180 325268, 3607, 10 -7 -272 1, 0, 68 1, 212 3056193, 28832, 68 6 -272 3, -2, 23 1, 293 1973944, 13476, 23 unknown -272 3, 2, 23 1, 126 365403, 5798, 23 -7 -272 4, 0, 17 1, 150 382504, 5100, 17 unknown -272 7, -6, 11 1, 10 1047, 214, 11 6 -272 7, 6, 11 1, 295 959052, 6496, 11 6 -272 8, -4, 9 1, 206 381108, 3704, 9 -7 -272 8, 4, 9 1, 128 147976, 2308, 9 -12 -276 1, 0, 69 1, 31 66310, 4278, 69 14 -276 2, 2, 35 1, 91 290019, 6372, 35 14 -276 3, 0, 23 1, 93 198930, 4278, 23 1 -276 5, -2, 14 1, 103 148325, 2882, 14 -12 -276 5, 2, 14 1, 53 39437, 1486, 14 -12 -276 6, 6, 13 1, 218 619126, 5674, 13 27 -276 7, -2, 10 1, 214 457539, 4278, 10 unknown -276 7, 2, 10 1, 144 207655, 2882, 10 10 -279 1, 1, 70 1, 141 1391812, 19741, 70 unknown -279 2, -1, 35 1, 292 2983950, 20439, 35 -3 -279 2, 1, 35 1, 282 2783624, 19741, 35 -3 -279 4, -3, 18 1, 277 1380295, 9969, 18 unknown -279 4, 3, 18 1, 335 2021059, 12063, 18 -3 -279 5, -1, 14 1, 32 14309, 895, 14 unknown -279 5, 1, 14 1, 7 698, 197, 14 unknown -279 7, -1, 10 1, 324 1049443, 6479, 10 -3 -279 7, 1, 10 1, 289 835506, 5781, 10 unknown -279 8, -3, 9 1, 205 377618, 3687, 9 10 -279 8, 3, 9 1, 321 928340, 5781, 9 10 -279 9, 9, 10 1, 149 223360, 2989, 10 10 -280 1, 0, 70 1, 56 219521, 7840, 70 -3 -280 2, 0, 35 1, 112 439042, 7840, 35 10 -280 5, 0, 14 1, 280 1097605, 7840, 14 -3 -280 7, 0, 10 1, 43 18497, 860, 10 -1 -283 1, 1, 71 1, 341 8256293, 48423, 71 -1 -283 7, -5, 11 1, 139 211843, 3053, 11 12 -283 7, 5, 11 1, 202 449861, 4449, 11 -2 -292 1, 0, 73 1, 335 8192426, 48910, 73 -2 -292 2, 2, 37 1, 161 959401, 11916, 37 24 -292 7, -4, 11 1, 288 911239, 6332, 11 -28 -292 7, 4, 11 1, 129 183574, 2842, 11 unknown -300 1, 0, 75 1, 100 750001, 15000, 75 -6 -300 3, 0, 25 1, 300 2250003, 15000, 25 -6 -300 4, -2, 19 1, 156 462076, 5926, 19 -6 -300 4, 2, 19 1, 211 846325, 8020, 19 7 -300 7, -6, 12 1, 189 427525, 4530, 12 7 -300 7, 6, 12 1, 14 2443, 342, 12