Newspace parameters
Level: | \( N \) | \(=\) | \( 841 = 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 841.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(49.6206063148\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | no (minimal twist has level 29) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 841.1 |
$q$-expansion
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.62919 | −0.576007 | −0.288004 | − | 0.957629i | \(-0.592991\pi\) | ||||
−0.288004 | + | 0.957629i | \(0.592991\pi\) | |||||||
\(3\) | 5.65337 | 1.08799 | 0.543996 | − | 0.839088i | \(-0.316911\pi\) | ||||
0.543996 | + | 0.839088i | \(0.316911\pi\) | |||||||
\(4\) | −5.34573 | −0.668216 | ||||||||
\(5\) | 13.9077 | 1.24394 | 0.621969 | − | 0.783042i | \(-0.286333\pi\) | ||||
0.621969 | + | 0.783042i | \(0.286333\pi\) | |||||||
\(6\) | −9.21044 | −0.626691 | ||||||||
\(7\) | −14.2629 | −0.770127 | −0.385063 | − | 0.922890i | \(-0.625820\pi\) | ||||
−0.385063 | + | 0.922890i | \(0.625820\pi\) | |||||||
\(8\) | 21.7428 | 0.960904 | ||||||||
\(9\) | 4.96064 | 0.183727 | ||||||||
\(10\) | −22.6583 | −0.716517 | ||||||||
\(11\) | 54.7123 | 1.49967 | 0.749835 | − | 0.661624i | \(-0.230133\pi\) | ||||
0.749835 | + | 0.661624i | \(0.230133\pi\) | |||||||
\(12\) | −30.2214 | −0.727014 | ||||||||
\(13\) | 14.8603 | 0.317038 | 0.158519 | − | 0.987356i | \(-0.449328\pi\) | ||||
0.158519 | + | 0.987356i | \(0.449328\pi\) | |||||||
\(14\) | 23.2371 | 0.443598 | ||||||||
\(15\) | 78.6252 | 1.35340 | ||||||||
\(16\) | 7.34260 | 0.114728 | ||||||||
\(17\) | 118.208 | 1.68645 | 0.843226 | − | 0.537559i | \(-0.180653\pi\) | ||||
0.843226 | + | 0.537559i | \(0.180653\pi\) | |||||||
\(18\) | −8.08185 | −0.105828 | ||||||||
\(19\) | −61.3862 | −0.741209 | −0.370604 | − | 0.928791i | \(-0.620849\pi\) | ||||
−0.370604 | + | 0.928791i | \(0.620849\pi\) | |||||||
\(20\) | −74.3465 | −0.831219 | ||||||||
\(21\) | −80.6338 | −0.837892 | ||||||||
\(22\) | −89.1370 | −0.863821 | ||||||||
\(23\) | −5.65413 | −0.0512595 | −0.0256297 | − | 0.999672i | \(-0.508159\pi\) | ||||
−0.0256297 | + | 0.999672i | \(0.508159\pi\) | |||||||
\(24\) | 122.920 | 1.04546 | ||||||||
\(25\) | 68.4228 | 0.547383 | ||||||||
\(26\) | −24.2102 | −0.182616 | ||||||||
\(27\) | −124.597 | −0.888098 | ||||||||
\(28\) | 76.2458 | 0.514611 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | −128.096 | −0.779565 | ||||||||
\(31\) | −158.134 | −0.916184 | −0.458092 | − | 0.888905i | \(-0.651467\pi\) | ||||
−0.458092 | + | 0.888905i | \(0.651467\pi\) | |||||||
\(32\) | −185.905 | −1.02699 | ||||||||
\(33\) | 309.309 | 1.63163 | ||||||||
\(34\) | −192.584 | −0.971409 | ||||||||
\(35\) | −198.364 | −0.957990 | ||||||||
\(36\) | −26.5182 | −0.122770 | ||||||||
\(37\) | 415.980 | 1.84829 | 0.924144 | − | 0.382044i | \(-0.124780\pi\) | ||||
0.924144 | + | 0.382044i | \(0.124780\pi\) | |||||||
\(38\) | 100.010 | 0.426942 | ||||||||
\(39\) | 84.0106 | 0.344935 | ||||||||
\(40\) | 302.391 | 1.19531 | ||||||||
\(41\) | 4.49844 | 0.0171351 | 0.00856753 | − | 0.999963i | \(-0.497273\pi\) | ||||
0.00856753 | + | 0.999963i | \(0.497273\pi\) | |||||||
\(42\) | 131.368 | 0.482632 | ||||||||
\(43\) | 200.555 | 0.711263 | 0.355631 | − | 0.934626i | \(-0.384266\pi\) | ||||
0.355631 | + | 0.934626i | \(0.384266\pi\) | |||||||
\(44\) | −292.477 | −1.00210 | ||||||||
\(45\) | 68.9909 | 0.228546 | ||||||||
\(46\) | 9.21168 | 0.0295258 | ||||||||
\(47\) | 151.533 | 0.470284 | 0.235142 | − | 0.971961i | \(-0.424444\pi\) | ||||
0.235142 | + | 0.971961i | \(0.424444\pi\) | |||||||
\(48\) | 41.5105 | 0.124823 | ||||||||
\(49\) | −139.568 | −0.406905 | ||||||||
\(50\) | −111.474 | −0.315296 | ||||||||
\(51\) | 668.275 | 1.83485 | ||||||||
\(52\) | −79.4389 | −0.211850 | ||||||||
\(53\) | −89.7911 | −0.232712 | −0.116356 | − | 0.993208i | \(-0.537121\pi\) | ||||
−0.116356 | + | 0.993208i | \(0.537121\pi\) | |||||||
\(54\) | 202.992 | 0.511551 | ||||||||
\(55\) | 760.920 | 1.86550 | ||||||||
\(56\) | −310.116 | −0.740018 | ||||||||
\(57\) | −347.039 | −0.806430 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 73.5684 | 0.162335 | 0.0811677 | − | 0.996700i | \(-0.474135\pi\) | ||||
0.0811677 | + | 0.996700i | \(0.474135\pi\) | |||||||
\(60\) | −420.309 | −0.904360 | ||||||||
\(61\) | 51.0266 | 0.107103 | 0.0535516 | − | 0.998565i | \(-0.482946\pi\) | ||||
0.0535516 | + | 0.998565i | \(0.482946\pi\) | |||||||
\(62\) | 257.631 | 0.527729 | ||||||||
\(63\) | −70.7534 | −0.141493 | ||||||||
\(64\) | 244.134 | 0.476824 | ||||||||
\(65\) | 206.671 | 0.394376 | ||||||||
\(66\) | −503.925 | −0.939831 | ||||||||
\(67\) | 848.107 | 1.54646 | 0.773229 | − | 0.634126i | \(-0.218640\pi\) | ||||
0.773229 | + | 0.634126i | \(0.218640\pi\) | |||||||
\(68\) | −631.909 | −1.12691 | ||||||||
\(69\) | −31.9649 | −0.0557699 | ||||||||
\(70\) | 323.174 | 0.551809 | ||||||||
\(71\) | 867.748 | 1.45046 | 0.725230 | − | 0.688506i | \(-0.241733\pi\) | ||||
0.725230 | + | 0.688506i | \(0.241733\pi\) | |||||||
\(72\) | 107.858 | 0.176545 | ||||||||
\(73\) | −602.515 | −0.966014 | −0.483007 | − | 0.875617i | \(-0.660455\pi\) | ||||
−0.483007 | + | 0.875617i | \(0.660455\pi\) | |||||||
\(74\) | −677.712 | −1.06463 | ||||||||
\(75\) | 386.820 | 0.595548 | ||||||||
\(76\) | 328.154 | 0.495288 | ||||||||
\(77\) | −780.359 | −1.15494 | ||||||||
\(78\) | −136.870 | −0.198685 | ||||||||
\(79\) | −633.273 | −0.901883 | −0.450942 | − | 0.892553i | \(-0.648912\pi\) | ||||
−0.450942 | + | 0.892553i | \(0.648912\pi\) | |||||||
\(80\) | 102.118 | 0.142715 | ||||||||
\(81\) | −838.329 | −1.14997 | ||||||||
\(82\) | −7.32883 | −0.00986992 | ||||||||
\(83\) | 851.856 | 1.12655 | 0.563273 | − | 0.826271i | \(-0.309542\pi\) | ||||
0.563273 | + | 0.826271i | \(0.309542\pi\) | |||||||
\(84\) | 431.046 | 0.559893 | ||||||||
\(85\) | 1644.00 | 2.09784 | ||||||||
\(86\) | −326.742 | −0.409692 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1189.60 | 1.44104 | ||||||||
\(89\) | −1201.61 | −1.43113 | −0.715564 | − | 0.698547i | \(-0.753830\pi\) | ||||
−0.715564 | + | 0.698547i | \(0.753830\pi\) | |||||||
\(90\) | −112.400 | −0.131644 | ||||||||
\(91\) | −211.951 | −0.244159 | ||||||||
\(92\) | 30.2254 | 0.0342524 | ||||||||
\(93\) | −893.991 | −0.996802 | ||||||||
\(94\) | −246.877 | −0.270887 | ||||||||
\(95\) | −853.739 | −0.922018 | ||||||||
\(96\) | −1050.99 | −1.11736 | ||||||||
\(97\) | 1716.07 | 1.79629 | 0.898146 | − | 0.439698i | \(-0.144915\pi\) | ||||
0.898146 | + | 0.439698i | \(0.144915\pi\) | |||||||
\(98\) | 227.384 | 0.234380 | ||||||||
\(99\) | 271.408 | 0.275531 | ||||||||
\(100\) | −365.770 | −0.365770 | ||||||||
\(101\) | −1623.25 | −1.59920 | −0.799600 | − | 0.600533i | \(-0.794955\pi\) | ||||
−0.799600 | + | 0.600533i | \(0.794955\pi\) | |||||||
\(102\) | −1088.75 | −1.05689 | ||||||||
\(103\) | 1406.01 | 1.34503 | 0.672515 | − | 0.740084i | \(-0.265214\pi\) | ||||
0.672515 | + | 0.740084i | \(0.265214\pi\) | |||||||
\(104\) | 323.103 | 0.304643 | ||||||||
\(105\) | −1121.43 | −1.04229 | ||||||||
\(106\) | 146.287 | 0.134044 | ||||||||
\(107\) | 520.276 | 0.470065 | 0.235033 | − | 0.971987i | \(-0.424480\pi\) | ||||
0.235033 | + | 0.971987i | \(0.424480\pi\) | |||||||
\(108\) | 666.060 | 0.593441 | ||||||||
\(109\) | 1055.28 | 0.927312 | 0.463656 | − | 0.886015i | \(-0.346537\pi\) | ||||
0.463656 | + | 0.886015i | \(0.346537\pi\) | |||||||
\(110\) | −1239.69 | −1.07454 | ||||||||
\(111\) | 2351.69 | 2.01092 | ||||||||
\(112\) | −104.727 | −0.0883552 | ||||||||
\(113\) | 294.227 | 0.244943 | 0.122471 | − | 0.992472i | \(-0.460918\pi\) | ||||
0.122471 | + | 0.992472i | \(0.460918\pi\) | |||||||
\(114\) | 565.395 | 0.464509 | ||||||||
\(115\) | −78.6357 | −0.0637636 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 73.7164 | 0.0582486 | ||||||||
\(118\) | −119.857 | −0.0935063 | ||||||||
\(119\) | −1686.00 | −1.29878 | ||||||||
\(120\) | 1709.53 | 1.30048 | ||||||||
\(121\) | 1662.44 | 1.24901 | ||||||||
\(122\) | −83.1323 | −0.0616921 | ||||||||
\(123\) | 25.4313 | 0.0186428 | ||||||||
\(124\) | 845.341 | 0.612209 | ||||||||
\(125\) | −786.856 | −0.563028 | ||||||||
\(126\) | 115.271 | 0.0815012 | ||||||||
\(127\) | 955.074 | 0.667316 | 0.333658 | − | 0.942694i | \(-0.391717\pi\) | ||||
0.333658 | + | 0.942694i | \(0.391717\pi\) | |||||||
\(128\) | 1089.50 | 0.752334 | ||||||||
\(129\) | 1133.81 | 0.773848 | ||||||||
\(130\) | −336.708 | −0.227163 | ||||||||
\(131\) | 2129.89 | 1.42053 | 0.710265 | − | 0.703934i | \(-0.248575\pi\) | ||||
0.710265 | + | 0.703934i | \(0.248575\pi\) | |||||||
\(132\) | −1653.48 | −1.09028 | ||||||||
\(133\) | 875.549 | 0.570825 | ||||||||
\(134\) | −1381.73 | −0.890771 | ||||||||
\(135\) | −1732.85 | −1.10474 | ||||||||
\(136\) | 2570.17 | 1.62052 | ||||||||
\(137\) | −32.8073 | −0.0204592 | −0.0102296 | − | 0.999948i | \(-0.503256\pi\) | ||||
−0.0102296 | + | 0.999948i | \(0.503256\pi\) | |||||||
\(138\) | 52.0771 | 0.0321239 | ||||||||
\(139\) | −1888.16 | −1.15217 | −0.576085 | − | 0.817390i | \(-0.695420\pi\) | ||||
−0.576085 | + | 0.817390i | \(0.695420\pi\) | |||||||
\(140\) | 1060.40 | 0.640144 | ||||||||
\(141\) | 856.673 | 0.511666 | ||||||||
\(142\) | −1413.73 | −0.835476 | ||||||||
\(143\) | 813.039 | 0.475453 | ||||||||
\(144\) | 36.4240 | 0.0210787 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 981.614 | 0.556431 | ||||||||
\(147\) | −789.033 | −0.442710 | ||||||||
\(148\) | −2223.71 | −1.23506 | ||||||||
\(149\) | 400.418 | 0.220158 | 0.110079 | − | 0.993923i | \(-0.464890\pi\) | ||||
0.110079 | + | 0.993923i | \(0.464890\pi\) | |||||||
\(150\) | −630.205 | −0.343040 | ||||||||
\(151\) | 2464.12 | 1.32799 | 0.663996 | − | 0.747736i | \(-0.268859\pi\) | ||||
0.663996 | + | 0.747736i | \(0.268859\pi\) | |||||||
\(152\) | −1334.71 | −0.712231 | ||||||||
\(153\) | 586.389 | 0.309848 | ||||||||
\(154\) | 1271.36 | 0.665252 | ||||||||
\(155\) | −2199.27 | −1.13968 | ||||||||
\(156\) | −449.098 | −0.230491 | ||||||||
\(157\) | −603.365 | −0.306712 | −0.153356 | − | 0.988171i | \(-0.549008\pi\) | ||||
−0.153356 | + | 0.988171i | \(0.549008\pi\) | |||||||
\(158\) | 1031.72 | 0.519491 | ||||||||
\(159\) | −507.623 | −0.253189 | ||||||||
\(160\) | −2585.50 | −1.27751 | ||||||||
\(161\) | 80.6446 | 0.0394763 | ||||||||
\(162\) | 1365.80 | 0.662392 | ||||||||
\(163\) | −518.585 | −0.249195 | −0.124597 | − | 0.992207i | \(-0.539764\pi\) | ||||
−0.124597 | + | 0.992207i | \(0.539764\pi\) | |||||||
\(164\) | −24.0474 | −0.0114499 | ||||||||
\(165\) | 4301.76 | 2.02965 | ||||||||
\(166\) | −1387.84 | −0.648899 | ||||||||
\(167\) | −1178.17 | −0.545925 | −0.272963 | − | 0.962025i | \(-0.588004\pi\) | ||||
−0.272963 | + | 0.962025i | \(0.588004\pi\) | |||||||
\(168\) | −1753.20 | −0.805134 | ||||||||
\(169\) | −1976.17 | −0.899487 | ||||||||
\(170\) | −2678.39 | −1.20837 | ||||||||
\(171\) | −304.515 | −0.136180 | ||||||||
\(172\) | −1072.11 | −0.475277 | ||||||||
\(173\) | 116.569 | 0.0512288 | 0.0256144 | − | 0.999672i | \(-0.491846\pi\) | ||||
0.0256144 | + | 0.999672i | \(0.491846\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −975.911 | −0.421554 | ||||||||
\(176\) | 401.731 | 0.172054 | ||||||||
\(177\) | 415.910 | 0.176620 | ||||||||
\(178\) | 1957.66 | 0.824340 | ||||||||
\(179\) | 376.234 | 0.157101 | 0.0785504 | − | 0.996910i | \(-0.474971\pi\) | ||||
0.0785504 | + | 0.996910i | \(0.474971\pi\) | |||||||
\(180\) | −368.806 | −0.152718 | ||||||||
\(181\) | −362.124 | −0.148710 | −0.0743549 | − | 0.997232i | \(-0.523690\pi\) | ||||
−0.0743549 | + | 0.997232i | \(0.523690\pi\) | |||||||
\(182\) | 345.309 | 0.140638 | ||||||||
\(183\) | 288.473 | 0.116527 | ||||||||
\(184\) | −122.937 | −0.0492554 | ||||||||
\(185\) | 5785.30 | 2.29916 | ||||||||
\(186\) | 1456.48 | 0.574165 | ||||||||
\(187\) | 6467.44 | 2.52912 | ||||||||
\(188\) | −810.054 | −0.314251 | ||||||||
\(189\) | 1777.12 | 0.683948 | ||||||||
\(190\) | 1390.91 | 0.531089 | ||||||||
\(191\) | 87.3223 | 0.0330807 | 0.0165404 | − | 0.999863i | \(-0.494735\pi\) | ||||
0.0165404 | + | 0.999863i | \(0.494735\pi\) | |||||||
\(192\) | 1380.18 | 0.518781 | ||||||||
\(193\) | 4135.28 | 1.54230 | 0.771150 | − | 0.636654i | \(-0.219682\pi\) | ||||
0.771150 | + | 0.636654i | \(0.219682\pi\) | |||||||
\(194\) | −2795.81 | −1.03468 | ||||||||
\(195\) | 1168.39 | 0.429078 | ||||||||
\(196\) | 746.095 | 0.271900 | ||||||||
\(197\) | 3849.76 | 1.39231 | 0.696153 | − | 0.717893i | \(-0.254894\pi\) | ||||
0.696153 | + | 0.717893i | \(0.254894\pi\) | |||||||
\(198\) | −442.177 | −0.158708 | ||||||||
\(199\) | 3008.75 | 1.07178 | 0.535891 | − | 0.844287i | \(-0.319976\pi\) | ||||
0.535891 | + | 0.844287i | \(0.319976\pi\) | |||||||
\(200\) | 1487.70 | 0.525982 | ||||||||
\(201\) | 4794.67 | 1.68254 | ||||||||
\(202\) | 2644.59 | 0.921150 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3572.42 | −1.22607 | ||||||||
\(205\) | 62.5627 | 0.0213150 | ||||||||
\(206\) | −2290.66 | −0.774747 | ||||||||
\(207\) | −28.0481 | −0.00941778 | ||||||||
\(208\) | 109.113 | 0.0363732 | ||||||||
\(209\) | −3358.58 | −1.11157 | ||||||||
\(210\) | 1827.02 | 0.600364 | ||||||||
\(211\) | −829.766 | −0.270727 | −0.135364 | − | 0.990796i | \(-0.543220\pi\) | ||||
−0.135364 | + | 0.990796i | \(0.543220\pi\) | |||||||
\(212\) | 479.999 | 0.155502 | ||||||||
\(213\) | 4905.70 | 1.57809 | ||||||||
\(214\) | −847.630 | −0.270761 | ||||||||
\(215\) | 2789.24 | 0.884767 | ||||||||
\(216\) | −2709.08 | −0.853377 | ||||||||
\(217\) | 2255.46 | 0.705578 | ||||||||
\(218\) | −1719.25 | −0.534138 | ||||||||
\(219\) | −3406.24 | −1.05102 | ||||||||
\(220\) | −4067.67 | −1.24656 | ||||||||
\(221\) | 1756.60 | 0.534670 | ||||||||
\(222\) | −3831.36 | −1.15831 | ||||||||
\(223\) | −5325.02 | −1.59906 | −0.799529 | − | 0.600628i | \(-0.794917\pi\) | ||||
−0.799529 | + | 0.600628i | \(0.794917\pi\) | |||||||
\(224\) | 2651.55 | 0.790911 | ||||||||
\(225\) | 339.421 | 0.100569 | ||||||||
\(226\) | −479.353 | −0.141089 | ||||||||
\(227\) | 1411.72 | 0.412771 | 0.206385 | − | 0.978471i | \(-0.433830\pi\) | ||||
0.206385 | + | 0.978471i | \(0.433830\pi\) | |||||||
\(228\) | 1855.18 | 0.538869 | ||||||||
\(229\) | 960.471 | 0.277160 | 0.138580 | − | 0.990351i | \(-0.455746\pi\) | ||||
0.138580 | + | 0.990351i | \(0.455746\pi\) | |||||||
\(230\) | 128.113 | 0.0367283 | ||||||||
\(231\) | −4411.66 | −1.25656 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1798.72 | −0.505744 | −0.252872 | − | 0.967500i | \(-0.581375\pi\) | ||||
−0.252872 | + | 0.967500i | \(0.581375\pi\) | |||||||
\(234\) | −120.098 | −0.0335516 | ||||||||
\(235\) | 2107.47 | 0.585005 | ||||||||
\(236\) | −393.276 | −0.108475 | ||||||||
\(237\) | −3580.13 | −0.981242 | ||||||||
\(238\) | 2746.82 | 0.748108 | ||||||||
\(239\) | 3313.26 | 0.896723 | 0.448361 | − | 0.893852i | \(-0.352008\pi\) | ||||
0.448361 | + | 0.893852i | \(0.352008\pi\) | |||||||
\(240\) | 577.313 | 0.155273 | ||||||||
\(241\) | −372.620 | −0.0995956 | −0.0497978 | − | 0.998759i | \(-0.515858\pi\) | ||||
−0.0497978 | + | 0.998759i | \(0.515858\pi\) | |||||||
\(242\) | −2708.43 | −0.719440 | ||||||||
\(243\) | −1375.28 | −0.363062 | ||||||||
\(244\) | −272.774 | −0.0715680 | ||||||||
\(245\) | −1941.07 | −0.506165 | ||||||||
\(246\) | −41.4326 | −0.0107384 | ||||||||
\(247\) | −912.215 | −0.234991 | ||||||||
\(248\) | −3438.27 | −0.880365 | ||||||||
\(249\) | 4815.86 | 1.22567 | ||||||||
\(250\) | 1281.94 | 0.324308 | ||||||||
\(251\) | −113.182 | −0.0284620 | −0.0142310 | − | 0.999899i | \(-0.504530\pi\) | ||||
−0.0142310 | + | 0.999899i | \(0.504530\pi\) | |||||||
\(252\) | 378.228 | 0.0945481 | ||||||||
\(253\) | −309.351 | −0.0768724 | ||||||||
\(254\) | −1556.00 | −0.384379 | ||||||||
\(255\) | 9294.14 | 2.28244 | ||||||||
\(256\) | −3728.07 | −0.910174 | ||||||||
\(257\) | −1696.91 | −0.411869 | −0.205934 | − | 0.978566i | \(-0.566023\pi\) | ||||
−0.205934 | + | 0.978566i | \(0.566023\pi\) | |||||||
\(258\) | −1847.20 | −0.445742 | ||||||||
\(259\) | −5933.10 | −1.42342 | ||||||||
\(260\) | −1104.81 | −0.263528 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3470.01 | −0.818236 | ||||||||
\(263\) | −134.322 | −0.0314929 | −0.0157464 | − | 0.999876i | \(-0.505012\pi\) | ||||
−0.0157464 | + | 0.999876i | \(0.505012\pi\) | |||||||
\(264\) | 6725.24 | 1.56784 | ||||||||
\(265\) | −1248.78 | −0.289480 | ||||||||
\(266\) | −1426.44 | −0.328799 | ||||||||
\(267\) | −6793.15 | −1.55706 | ||||||||
\(268\) | −4533.75 | −1.03337 | ||||||||
\(269\) | −3099.06 | −0.702427 | −0.351214 | − | 0.936295i | \(-0.614231\pi\) | ||||
−0.351214 | + | 0.936295i | \(0.614231\pi\) | |||||||
\(270\) | 2823.15 | 0.636338 | ||||||||
\(271\) | 2281.66 | 0.511442 | 0.255721 | − | 0.966751i | \(-0.417687\pi\) | ||||
0.255721 | + | 0.966751i | \(0.417687\pi\) | |||||||
\(272\) | 867.956 | 0.193484 | ||||||||
\(273\) | −1198.24 | −0.265644 | ||||||||
\(274\) | 53.4494 | 0.0117847 | ||||||||
\(275\) | 3743.57 | 0.820894 | ||||||||
\(276\) | 170.876 | 0.0372663 | ||||||||
\(277\) | 289.918 | 0.0628862 | 0.0314431 | − | 0.999506i | \(-0.489990\pi\) | ||||
0.0314431 | + | 0.999506i | \(0.489990\pi\) | |||||||
\(278\) | 3076.18 | 0.663658 | ||||||||
\(279\) | −784.446 | −0.168328 | ||||||||
\(280\) | −4312.99 | −0.920537 | ||||||||
\(281\) | −5428.45 | −1.15243 | −0.576217 | − | 0.817297i | \(-0.695472\pi\) | ||||
−0.576217 | + | 0.817297i | \(0.695472\pi\) | |||||||
\(282\) | −1395.69 | −0.294723 | ||||||||
\(283\) | 3063.67 | 0.643521 | 0.321761 | − | 0.946821i | \(-0.395725\pi\) | ||||
0.321761 | + | 0.946821i | \(0.395725\pi\) | |||||||
\(284\) | −4638.74 | −0.969221 | ||||||||
\(285\) | −4826.50 | −1.00315 | ||||||||
\(286\) | −1324.60 | −0.273864 | ||||||||
\(287\) | −64.1609 | −0.0131962 | ||||||||
\(288\) | −922.207 | −0.188686 | ||||||||
\(289\) | 9060.18 | 1.84412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9701.57 | 1.95435 | ||||||||
\(292\) | 3220.88 | 0.645506 | ||||||||
\(293\) | 1436.15 | 0.286351 | 0.143176 | − | 0.989697i | \(-0.454269\pi\) | ||||
0.143176 | + | 0.989697i | \(0.454269\pi\) | |||||||
\(294\) | 1285.49 | 0.255004 | ||||||||
\(295\) | 1023.16 | 0.201935 | ||||||||
\(296\) | 9044.56 | 1.77603 | ||||||||
\(297\) | −6816.97 | −1.33186 | ||||||||
\(298\) | −652.359 | −0.126813 | ||||||||
\(299\) | −84.0219 | −0.0162512 | ||||||||
\(300\) | −2067.83 | −0.397955 | ||||||||
\(301\) | −2860.50 | −0.547762 | ||||||||
\(302\) | −4014.52 | −0.764933 | ||||||||
\(303\) | −9176.83 | −1.73992 | ||||||||
\(304\) | −450.735 | −0.0850375 | ||||||||
\(305\) | 709.661 | 0.133230 | ||||||||
\(306\) | −955.341 | −0.178475 | ||||||||
\(307\) | −6595.85 | −1.22621 | −0.613103 | − | 0.790003i | \(-0.710079\pi\) | ||||
−0.613103 | + | 0.790003i | \(0.710079\pi\) | |||||||
\(308\) | 4171.58 | 0.771747 | ||||||||
\(309\) | 7948.69 | 1.46338 | ||||||||
\(310\) | 3583.04 | 0.656462 | ||||||||
\(311\) | 6486.49 | 1.18269 | 0.591343 | − | 0.806421i | \(-0.298598\pi\) | ||||
0.591343 | + | 0.806421i | \(0.298598\pi\) | |||||||
\(312\) | 1826.62 | 0.331449 | ||||||||
\(313\) | −115.663 | −0.0208871 | −0.0104436 | − | 0.999945i | \(-0.503324\pi\) | ||||
−0.0104436 | + | 0.999945i | \(0.503324\pi\) | |||||||
\(314\) | 982.999 | 0.176668 | ||||||||
\(315\) | −984.013 | −0.176009 | ||||||||
\(316\) | 3385.30 | 0.602653 | ||||||||
\(317\) | −9397.64 | −1.66506 | −0.832530 | − | 0.553979i | \(-0.813109\pi\) | ||||
−0.832530 | + | 0.553979i | \(0.813109\pi\) | |||||||
\(318\) | 827.016 | 0.145839 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3395.33 | 0.593140 | ||||||||
\(321\) | 2941.31 | 0.511427 | ||||||||
\(322\) | −131.386 | −0.0227386 | ||||||||
\(323\) | −7256.36 | −1.25001 | ||||||||
\(324\) | 4481.48 | 0.768429 | ||||||||
\(325\) | 1016.78 | 0.173541 | ||||||||
\(326\) | 844.876 | 0.143538 | ||||||||
\(327\) | 5965.87 | 1.00891 | ||||||||
\(328\) | 97.8085 | 0.0164652 | ||||||||
\(329\) | −2161.31 | −0.362178 | ||||||||
\(330\) | −7008.41 | −1.16909 | ||||||||
\(331\) | −9526.26 | −1.58191 | −0.790953 | − | 0.611877i | \(-0.790415\pi\) | ||||
−0.790953 | + | 0.611877i | \(0.790415\pi\) | |||||||
\(332\) | −4553.79 | −0.752776 | ||||||||
\(333\) | 2063.53 | 0.339581 | ||||||||
\(334\) | 1919.47 | 0.314457 | ||||||||
\(335\) | 11795.2 | 1.92370 | ||||||||
\(336\) | −592.062 | −0.0961298 | ||||||||
\(337\) | −3596.56 | −0.581357 | −0.290678 | − | 0.956821i | \(-0.593881\pi\) | ||||
−0.290678 | + | 0.956821i | \(0.593881\pi\) | |||||||
\(338\) | 3219.57 | 0.518111 | ||||||||
\(339\) | 1663.38 | 0.266496 | ||||||||
\(340\) | −8788.37 | −1.40181 | ||||||||
\(341\) | −8651.88 | −1.37397 | ||||||||
\(342\) | 496.114 | 0.0784409 | ||||||||
\(343\) | 6882.85 | 1.08349 | ||||||||
\(344\) | 4360.61 | 0.683455 | ||||||||
\(345\) | −444.557 | −0.0693744 | ||||||||
\(346\) | −189.913 | −0.0295081 | ||||||||
\(347\) | −3544.68 | −0.548381 | −0.274190 | − | 0.961675i | \(-0.588410\pi\) | ||||
−0.274190 | + | 0.961675i | \(0.588410\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8579.96 | −1.31597 | −0.657987 | − | 0.753029i | \(-0.728592\pi\) | ||||
−0.657987 | + | 0.753029i | \(0.728592\pi\) | |||||||
\(350\) | 1589.95 | 0.242818 | ||||||||
\(351\) | −1851.54 | −0.281561 | ||||||||
\(352\) | −10171.3 | −1.54014 | ||||||||
\(353\) | −1804.92 | −0.272142 | −0.136071 | − | 0.990699i | \(-0.543448\pi\) | ||||
−0.136071 | + | 0.990699i | \(0.543448\pi\) | |||||||
\(354\) | −677.597 | −0.101734 | ||||||||
\(355\) | 12068.3 | 1.80428 | ||||||||
\(356\) | 6423.48 | 0.956303 | ||||||||
\(357\) | −9531.57 | −1.41307 | ||||||||
\(358\) | −612.958 | −0.0904912 | ||||||||
\(359\) | −3681.07 | −0.541169 | −0.270584 | − | 0.962696i | \(-0.587217\pi\) | ||||
−0.270584 | + | 0.962696i | \(0.587217\pi\) | |||||||
\(360\) | 1500.05 | 0.219610 | ||||||||
\(361\) | −3090.73 | −0.450609 | ||||||||
\(362\) | 589.970 | 0.0856579 | ||||||||
\(363\) | 9398.37 | 1.35892 | ||||||||
\(364\) | 1133.03 | 0.163151 | ||||||||
\(365\) | −8379.57 | −1.20166 | ||||||||
\(366\) | −469.978 | −0.0671206 | ||||||||
\(367\) | 1468.37 | 0.208851 | 0.104426 | − | 0.994533i | \(-0.466700\pi\) | ||||
0.104426 | + | 0.994533i | \(0.466700\pi\) | |||||||
\(368\) | −41.5160 | −0.00588091 | ||||||||
\(369\) | 22.3151 | 0.00314818 | ||||||||
\(370\) | −9425.38 | −1.32433 | ||||||||
\(371\) | 1280.69 | 0.179218 | ||||||||
\(372\) | 4779.03 | 0.666079 | ||||||||
\(373\) | −5580.95 | −0.774720 | −0.387360 | − | 0.921928i | \(-0.626613\pi\) | ||||
−0.387360 | + | 0.921928i | \(0.626613\pi\) | |||||||
\(374\) | −10536.7 | −1.45679 | ||||||||
\(375\) | −4448.39 | −0.612570 | ||||||||
\(376\) | 3294.75 | 0.451898 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2895.27 | −0.393959 | ||||||||
\(379\) | −6117.61 | −0.829130 | −0.414565 | − | 0.910020i | \(-0.636066\pi\) | ||||
−0.414565 | + | 0.910020i | \(0.636066\pi\) | |||||||
\(380\) | 4563.85 | 0.616107 | ||||||||
\(381\) | 5399.39 | 0.726035 | ||||||||
\(382\) | −142.265 | −0.0190547 | ||||||||
\(383\) | 2667.05 | 0.355822 | 0.177911 | − | 0.984047i | \(-0.443066\pi\) | ||||
0.177911 | + | 0.984047i | \(0.443066\pi\) | |||||||
\(384\) | 6159.33 | 0.818534 | ||||||||
\(385\) | −10853.0 | −1.43667 | ||||||||
\(386\) | −6737.17 | −0.888376 | ||||||||
\(387\) | 994.880 | 0.130678 | ||||||||
\(388\) | −9173.63 | −1.20031 | ||||||||
\(389\) | −7781.12 | −1.01419 | −0.507093 | − | 0.861891i | \(-0.669280\pi\) | ||||
−0.507093 | + | 0.861891i | \(0.669280\pi\) | |||||||
\(390\) | −1903.53 | −0.247152 | ||||||||
\(391\) | −668.365 | −0.0864467 | ||||||||
\(392\) | −3034.61 | −0.390997 | ||||||||
\(393\) | 12041.1 | 1.54553 | ||||||||
\(394\) | −6272.01 | −0.801978 | ||||||||
\(395\) | −8807.34 | −1.12189 | ||||||||
\(396\) | −1450.87 | −0.184114 | ||||||||
\(397\) | 2454.12 | 0.310249 | 0.155125 | − | 0.987895i | \(-0.450422\pi\) | ||||
0.155125 | + | 0.987895i | \(0.450422\pi\) | |||||||
\(398\) | −4901.84 | −0.617354 | ||||||||
\(399\) | 4949.80 | 0.621053 | ||||||||
\(400\) | 502.402 | 0.0628002 | ||||||||
\(401\) | −5487.12 | −0.683326 | −0.341663 | − | 0.939823i | \(-0.610990\pi\) | ||||
−0.341663 | + | 0.939823i | \(0.610990\pi\) | |||||||
\(402\) | −7811.44 | −0.969152 | ||||||||
\(403\) | −2349.91 | −0.290465 | ||||||||
\(404\) | 8677.44 | 1.06861 | ||||||||
\(405\) | −11659.2 | −1.43049 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22759.2 | 2.77182 | ||||||||
\(408\) | 14530.2 | 1.76311 | ||||||||
\(409\) | 256.848 | 0.0310521 | 0.0155261 | − | 0.999879i | \(-0.495058\pi\) | ||||
0.0155261 | + | 0.999879i | \(0.495058\pi\) | |||||||
\(410\) | −101.927 | −0.0122776 | ||||||||
\(411\) | −185.472 | −0.0222595 | ||||||||
\(412\) | −7516.13 | −0.898770 | ||||||||
\(413\) | −1049.30 | −0.125019 | ||||||||
\(414\) | 45.6958 | 0.00542471 | ||||||||
\(415\) | 11847.3 | 1.40135 | ||||||||
\(416\) | −2762.59 | −0.325594 | ||||||||
\(417\) | −10674.5 | −1.25355 | ||||||||
\(418\) | 5471.78 | 0.640272 | ||||||||
\(419\) | −5193.75 | −0.605564 | −0.302782 | − | 0.953060i | \(-0.597915\pi\) | ||||
−0.302782 | + | 0.953060i | \(0.597915\pi\) | |||||||
\(420\) | 5994.84 | 0.696472 | ||||||||
\(421\) | 10429.9 | 1.20742 | 0.603710 | − | 0.797204i | \(-0.293688\pi\) | ||||
0.603710 | + | 0.797204i | \(0.293688\pi\) | |||||||
\(422\) | 1351.85 | 0.155941 | ||||||||
\(423\) | 751.701 | 0.0864041 | ||||||||
\(424\) | −1952.31 | −0.223614 | ||||||||
\(425\) | 8088.14 | 0.923135 | ||||||||
\(426\) | −7992.34 | −0.908991 | ||||||||
\(427\) | −727.790 | −0.0824829 | ||||||||
\(428\) | −2781.25 | −0.314105 | ||||||||
\(429\) | 4596.41 | 0.517289 | ||||||||
\(430\) | −4544.22 | −0.509632 | ||||||||
\(431\) | −12985.3 | −1.45123 | −0.725616 | − | 0.688100i | \(-0.758445\pi\) | ||||
−0.725616 | + | 0.688100i | \(0.758445\pi\) | |||||||
\(432\) | −914.864 | −0.101890 | ||||||||
\(433\) | 3663.82 | 0.406632 | 0.203316 | − | 0.979113i | \(-0.434828\pi\) | ||||
0.203316 | + | 0.979113i | \(0.434828\pi\) | |||||||
\(434\) | −3674.58 | −0.406418 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5641.21 | −0.619645 | ||||||||
\(437\) | 347.086 | 0.0379940 | ||||||||
\(438\) | 5549.43 | 0.605393 | ||||||||
\(439\) | −12233.9 | −1.33005 | −0.665025 | − | 0.746821i | \(-0.731579\pi\) | ||||
−0.665025 | + | 0.746821i | \(0.731579\pi\) | |||||||
\(440\) | 16544.5 | 1.79256 | ||||||||
\(441\) | −692.349 | −0.0747596 | ||||||||
\(442\) | −2861.85 | −0.307974 | ||||||||
\(443\) | −1596.82 | −0.171258 | −0.0856291 | − | 0.996327i | \(-0.527290\pi\) | ||||
−0.0856291 | + | 0.996327i | \(0.527290\pi\) | |||||||
\(444\) | −12571.5 | −1.34373 | ||||||||
\(445\) | −16711.6 | −1.78024 | ||||||||
\(446\) | 8675.49 | 0.921068 | ||||||||
\(447\) | 2263.71 | 0.239530 | ||||||||
\(448\) | −3482.07 | −0.367215 | ||||||||
\(449\) | −13784.2 | −1.44882 | −0.724408 | − | 0.689372i | \(-0.757887\pi\) | ||||
−0.724408 | + | 0.689372i | \(0.757887\pi\) | |||||||
\(450\) | −552.983 | −0.0579286 | ||||||||
\(451\) | 246.120 | 0.0256970 | ||||||||
\(452\) | −1572.86 | −0.163675 | ||||||||
\(453\) | 13930.6 | 1.44485 | ||||||||
\(454\) | −2299.96 | −0.237759 | ||||||||
\(455\) | −2947.74 | −0.303719 | ||||||||
\(456\) | −7545.60 | −0.774902 | ||||||||
\(457\) | −657.534 | −0.0673045 | −0.0336523 | − | 0.999434i | \(-0.510714\pi\) | ||||
−0.0336523 | + | 0.999434i | \(0.510714\pi\) | |||||||
\(458\) | −1564.79 | −0.159646 | ||||||||
\(459\) | −14728.4 | −1.49774 | ||||||||
\(460\) | 420.365 | 0.0426079 | ||||||||
\(461\) | 2230.20 | 0.225316 | 0.112658 | − | 0.993634i | \(-0.464064\pi\) | ||||
0.112658 | + | 0.993634i | \(0.464064\pi\) | |||||||
\(462\) | 7187.45 | 0.723789 | ||||||||
\(463\) | −4959.02 | −0.497765 | −0.248883 | − | 0.968534i | \(-0.580063\pi\) | ||||
−0.248883 | + | 0.968534i | \(0.580063\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12433.3 | −1.23996 | ||||||||
\(466\) | 2930.47 | 0.291312 | ||||||||
\(467\) | 8429.37 | 0.835256 | 0.417628 | − | 0.908618i | \(-0.362862\pi\) | ||||
0.417628 | + | 0.908618i | \(0.362862\pi\) | |||||||
\(468\) | −394.068 | −0.0389226 | ||||||||
\(469\) | −12096.5 | −1.19097 | ||||||||
\(470\) | −3433.47 | −0.336967 | ||||||||
\(471\) | −3411.05 | −0.333700 | ||||||||
\(472\) | 1599.58 | 0.155989 | ||||||||
\(473\) | 10972.8 | 1.06666 | ||||||||
\(474\) | 5832.73 | 0.565202 | ||||||||
\(475\) | −4200.22 | −0.405725 | ||||||||
\(476\) | 9012.88 | 0.867867 | ||||||||
\(477\) | −445.422 | −0.0427557 | ||||||||
\(478\) | −5397.94 | −0.516519 | ||||||||
\(479\) | 26.7718 | 0.00255373 | 0.00127686 | − | 0.999999i | \(-0.499594\pi\) | ||||
0.00127686 | + | 0.999999i | \(0.499594\pi\) | |||||||
\(480\) | −14616.8 | −1.38992 | ||||||||
\(481\) | 6181.57 | 0.585978 | ||||||||
\(482\) | 607.070 | 0.0573678 | ||||||||
\(483\) | 455.914 | 0.0429499 | ||||||||
\(484\) | −8886.93 | −0.834610 | ||||||||
\(485\) | 23866.5 | 2.23448 | ||||||||
\(486\) | 2240.59 | 0.209126 | ||||||||
\(487\) | 3924.73 | 0.365188 | 0.182594 | − | 0.983188i | \(-0.441551\pi\) | ||||
0.182594 | + | 0.983188i | \(0.441551\pi\) | |||||||
\(488\) | 1109.46 | 0.102916 | ||||||||
\(489\) | −2931.76 | −0.271122 | ||||||||
\(490\) | 3162.38 | 0.291555 | ||||||||
\(491\) | −20977.8 | −1.92814 | −0.964070 | − | 0.265650i | \(-0.914413\pi\) | ||||
−0.964070 | + | 0.265650i | \(0.914413\pi\) | |||||||
\(492\) | −135.949 | −0.0124574 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 1486.18 | 0.135357 | ||||||||
\(495\) | 3774.65 | 0.342743 | ||||||||
\(496\) | −1161.12 | −0.105112 | ||||||||
\(497\) | −12376.6 | −1.11704 | ||||||||
\(498\) | −7845.97 | −0.705997 | ||||||||
\(499\) | −1063.31 | −0.0953914 | −0.0476957 | − | 0.998862i | \(-0.515188\pi\) | ||||
−0.0476957 | + | 0.998862i | \(0.515188\pi\) | |||||||
\(500\) | 4206.32 | 0.376224 | ||||||||
\(501\) | −6660.64 | −0.593963 | ||||||||
\(502\) | 184.395 | 0.0163943 | ||||||||
\(503\) | −1339.19 | −0.118711 | −0.0593556 | − | 0.998237i | \(-0.518905\pi\) | ||||
−0.0593556 | + | 0.998237i | \(0.518905\pi\) | |||||||
\(504\) | −1538.37 | −0.135962 | ||||||||
\(505\) | −22575.6 | −1.98931 | ||||||||
\(506\) | 503.992 | 0.0442790 | ||||||||
\(507\) | −11172.0 | −0.978635 | ||||||||
\(508\) | −5105.57 | −0.445911 | ||||||||
\(509\) | −14925.8 | −1.29975 | −0.649876 | − | 0.760040i | \(-0.725179\pi\) | ||||
−0.649876 | + | 0.760040i | \(0.725179\pi\) | |||||||
\(510\) | −15142.0 | −1.31470 | ||||||||
\(511\) | 8593.63 | 0.743953 | ||||||||
\(512\) | −2642.21 | −0.228067 | ||||||||
\(513\) | 7648.53 | 0.658266 | ||||||||
\(514\) | 2764.59 | 0.237239 | ||||||||
\(515\) | 19554.3 | 1.67313 | ||||||||
\(516\) | −6061.04 | −0.517098 | ||||||||
\(517\) | 8290.72 | 0.705272 | ||||||||
\(518\) | 9666.17 | 0.819898 | ||||||||
\(519\) | 659.008 | 0.0557365 | ||||||||
\(520\) | 4493.61 | 0.378957 | ||||||||
\(521\) | 16074.0 | 1.35166 | 0.675829 | − | 0.737058i | \(-0.263786\pi\) | ||||
0.675829 | + | 0.737058i | \(0.263786\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4739.93 | −0.396295 | −0.198148 | − | 0.980172i | \(-0.563493\pi\) | ||||
−0.198148 | + | 0.980172i | \(0.563493\pi\) | |||||||
\(524\) | −11385.8 | −0.949221 | ||||||||
\(525\) | −5517.19 | −0.458647 | ||||||||
\(526\) | 218.836 | 0.0181401 | ||||||||
\(527\) | −18692.7 | −1.54510 | ||||||||
\(528\) | 2271.13 | 0.187194 | ||||||||
\(529\) | −12135.0 | −0.997372 | ||||||||
\(530\) | 2034.51 | 0.166743 | ||||||||
\(531\) | 364.946 | 0.0298255 | ||||||||
\(532\) | −4680.44 | −0.381434 | ||||||||
\(533\) | 66.8479 | 0.00543247 | ||||||||
\(534\) | 11067.4 | 0.896876 | ||||||||
\(535\) | 7235.82 | 0.584732 | ||||||||
\(536\) | 18440.2 | 1.48600 | ||||||||
\(537\) | 2126.99 | 0.170925 | ||||||||
\(538\) | 5048.97 | 0.404603 | ||||||||
\(539\) | −7636.11 | −0.610224 | ||||||||
\(540\) | 9263.33 | 0.738204 | ||||||||
\(541\) | −818.479 | −0.0650446 | −0.0325223 | − | 0.999471i | \(-0.510354\pi\) | ||||
−0.0325223 | + | 0.999471i | \(0.510354\pi\) | |||||||
\(542\) | −3717.27 | −0.294594 | ||||||||
\(543\) | −2047.22 | −0.161795 | ||||||||
\(544\) | −21975.5 | −1.73197 | ||||||||
\(545\) | 14676.4 | 1.15352 | ||||||||
\(546\) | 1952.16 | 0.153013 | ||||||||
\(547\) | −369.700 | −0.0288980 | −0.0144490 | − | 0.999896i | \(-0.504599\pi\) | ||||
−0.0144490 | + | 0.999896i | \(0.504599\pi\) | |||||||
\(548\) | 175.379 | 0.0136712 | ||||||||
\(549\) | 253.125 | 0.0196778 | ||||||||
\(550\) | −6099.00 | −0.472841 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −695.006 | −0.0535896 | ||||||||
\(553\) | 9032.34 | 0.694564 | ||||||||
\(554\) | −472.333 | −0.0362229 | ||||||||
\(555\) | 32706.5 | 2.50147 | ||||||||
\(556\) | 10093.6 | 0.769898 | ||||||||
\(557\) | 19844.9 | 1.50961 | 0.754806 | − | 0.655948i | \(-0.227731\pi\) | ||||
0.754806 | + | 0.655948i | \(0.227731\pi\) | |||||||
\(558\) | 1278.02 | 0.0969583 | ||||||||
\(559\) | 2980.29 | 0.225497 | ||||||||
\(560\) | −1456.51 | −0.109908 | ||||||||
\(561\) | 36562.9 | 2.75167 | ||||||||
\(562\) | 8844.00 | 0.663810 | ||||||||
\(563\) | 14158.5 | 1.05988 | 0.529938 | − | 0.848036i | \(-0.322215\pi\) | ||||
0.529938 | + | 0.848036i | \(0.322215\pi\) | |||||||
\(564\) | −4579.54 | −0.341903 | ||||||||
\(565\) | 4092.01 | 0.304694 | ||||||||
\(566\) | −4991.32 | −0.370673 | ||||||||
\(567\) | 11957.0 | 0.885624 | ||||||||
\(568\) | 18867.2 | 1.39375 | ||||||||
\(569\) | −15174.2 | −1.11799 | −0.558993 | − | 0.829173i | \(-0.688812\pi\) | ||||
−0.558993 | + | 0.829173i | \(0.688812\pi\) | |||||||
\(570\) | 7863.31 | 0.577821 | ||||||||
\(571\) | −20125.3 | −1.47499 | −0.737493 | − | 0.675355i | \(-0.763990\pi\) | ||||
−0.737493 | + | 0.675355i | \(0.763990\pi\) | |||||||
\(572\) | −4346.28 | −0.317705 | ||||||||
\(573\) | 493.665 | 0.0359916 | ||||||||
\(574\) | 104.531 | 0.00760109 | ||||||||
\(575\) | −386.872 | −0.0280585 | ||||||||
\(576\) | 1211.06 | 0.0876058 | ||||||||
\(577\) | −24675.7 | −1.78035 | −0.890177 | − | 0.455614i | \(-0.849420\pi\) | ||||
−0.890177 | + | 0.455614i | \(0.849420\pi\) | |||||||
\(578\) | −14760.8 | −1.06223 | ||||||||
\(579\) | 23378.3 | 1.67801 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12150.0 | −0.867583 | ||||||||
\(582\) | −15805.7 | −1.12572 | ||||||||
\(583\) | −4912.68 | −0.348992 | ||||||||
\(584\) | −13100.3 | −0.928247 | ||||||||
\(585\) | 1025.22 | 0.0724577 | ||||||||
\(586\) | −2339.77 | −0.164940 | ||||||||
\(587\) | 5450.22 | 0.383228 | 0.191614 | − | 0.981470i | \(-0.438628\pi\) | ||||
0.191614 | + | 0.981470i | \(0.438628\pi\) | |||||||
\(588\) | 4217.95 | 0.295826 | ||||||||
\(589\) | 9707.26 | 0.679084 | ||||||||
\(590\) | −1666.93 | −0.116316 | ||||||||
\(591\) | 21764.2 | 1.51482 | ||||||||
\(592\) | 3054.38 | 0.212051 | ||||||||
\(593\) | 17788.4 | 1.23184 | 0.615922 | − | 0.787807i | \(-0.288784\pi\) | ||||
0.615922 | + | 0.787807i | \(0.288784\pi\) | |||||||
\(594\) | 11106.2 | 0.767158 | ||||||||
\(595\) | −23448.3 | −1.61560 | ||||||||
\(596\) | −2140.53 | −0.147113 | ||||||||
\(597\) | 17009.6 | 1.16609 | ||||||||
\(598\) | 136.888 | 0.00936081 | ||||||||
\(599\) | −17037.8 | −1.16218 | −0.581089 | − | 0.813840i | \(-0.697373\pi\) | ||||
−0.581089 | + | 0.813840i | \(0.697373\pi\) | |||||||
\(600\) | 8410.54 | 0.572265 | ||||||||
\(601\) | 2105.40 | 0.142897 | 0.0714484 | − | 0.997444i | \(-0.477238\pi\) | ||||
0.0714484 | + | 0.997444i | \(0.477238\pi\) | |||||||
\(602\) | 4660.31 | 0.315515 | ||||||||
\(603\) | 4207.15 | 0.284127 | ||||||||
\(604\) | −13172.5 | −0.887386 | ||||||||
\(605\) | 23120.6 | 1.55370 | ||||||||
\(606\) | 14950.8 | 1.00220 | ||||||||
\(607\) | 14072.9 | 0.941025 | 0.470513 | − | 0.882393i | \(-0.344069\pi\) | ||||
0.470513 | + | 0.882393i | \(0.344069\pi\) | |||||||
\(608\) | 11412.0 | 0.761213 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1156.17 | −0.0767412 | ||||||||
\(611\) | 2251.82 | 0.149098 | ||||||||
\(612\) | −3134.67 | −0.207045 | ||||||||
\(613\) | 26905.0 | 1.77273 | 0.886364 | − | 0.462989i | \(-0.153223\pi\) | ||||
0.886364 | + | 0.462989i | \(0.153223\pi\) | |||||||
\(614\) | 10745.9 | 0.706303 | ||||||||
\(615\) | 353.690 | 0.0231905 | ||||||||
\(616\) | −16967.2 | −1.10978 | ||||||||
\(617\) | 3978.90 | 0.259618 | 0.129809 | − | 0.991539i | \(-0.458564\pi\) | ||||
0.129809 | + | 0.991539i | \(0.458564\pi\) | |||||||
\(618\) | −12950.0 | −0.842919 | ||||||||
\(619\) | 14188.1 | 0.921274 | 0.460637 | − | 0.887589i | \(-0.347621\pi\) | ||||
0.460637 | + | 0.887589i | \(0.347621\pi\) | |||||||
\(620\) | 11756.7 | 0.761550 | ||||||||
\(621\) | 704.486 | 0.0455235 | ||||||||
\(622\) | −10567.7 | −0.681235 | ||||||||
\(623\) | 17138.5 | 1.10215 | ||||||||
\(624\) | 616.857 | 0.0395738 | ||||||||
\(625\) | −19496.2 | −1.24775 | ||||||||
\(626\) | 188.438 | 0.0120311 | ||||||||
\(627\) | −18987.3 | −1.20938 | ||||||||
\(628\) | 3225.43 | 0.204950 | ||||||||
\(629\) | 49172.2 | 3.11705 | ||||||||
\(630\) | 1603.15 | 0.101382 | ||||||||
\(631\) | 13764.1 | 0.868368 | 0.434184 | − | 0.900824i | \(-0.357037\pi\) | ||||
0.434184 | + | 0.900824i | \(0.357037\pi\) | |||||||
\(632\) | −13769.1 | −0.866623 | ||||||||
\(633\) | −4690.98 | −0.294549 | ||||||||
\(634\) | 15310.6 | 0.959087 | ||||||||
\(635\) | 13282.8 | 0.830100 | ||||||||
\(636\) | 2713.61 | 0.169185 | ||||||||
\(637\) | −2074.02 | −0.129004 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4304.59 | 0.266490 | ||||||||
\(640\) | 15152.3 | 0.935857 | ||||||||
\(641\) | 6823.67 | 0.420466 | 0.210233 | − | 0.977651i | \(-0.432578\pi\) | ||||
0.210233 | + | 0.977651i | \(0.432578\pi\) | |||||||
\(642\) | −4791.97 | −0.294586 | ||||||||
\(643\) | 7965.35 | 0.488527 | 0.244264 | − | 0.969709i | \(-0.421454\pi\) | ||||
0.244264 | + | 0.969709i | \(0.421454\pi\) | |||||||
\(644\) | −431.104 | −0.0263787 | ||||||||
\(645\) | 15768.6 | 0.962620 | ||||||||
\(646\) | 11822.0 | 0.720017 | ||||||||
\(647\) | 3344.19 | 0.203205 | 0.101602 | − | 0.994825i | \(-0.467603\pi\) | ||||
0.101602 | + | 0.994825i | \(0.467603\pi\) | |||||||
\(648\) | −18227.6 | −1.10501 | ||||||||
\(649\) | 4025.09 | 0.243450 | ||||||||
\(650\) | −1656.53 | −0.0999609 | ||||||||
\(651\) | 12750.9 | 0.767663 | ||||||||
\(652\) | 2772.21 | 0.166516 | ||||||||
\(653\) | 18155.4 | 1.08802 | 0.544009 | − | 0.839079i | \(-0.316906\pi\) | ||||
0.544009 | + | 0.839079i | \(0.316906\pi\) | |||||||
\(654\) | −9719.55 | −0.581139 | ||||||||
\(655\) | 29621.8 | 1.76705 | ||||||||
\(656\) | 33.0302 | 0.00196587 | ||||||||
\(657\) | −2988.86 | −0.177483 | ||||||||
\(658\) | 3521.19 | 0.208617 | ||||||||
\(659\) | −10927.7 | −0.645954 | −0.322977 | − | 0.946407i | \(-0.604684\pi\) | ||||
−0.322977 | + | 0.946407i | \(0.604684\pi\) | |||||||
\(660\) | −22996.1 | −1.35624 | ||||||||
\(661\) | 12431.0 | 0.731483 | 0.365741 | − | 0.930716i | \(-0.380815\pi\) | ||||
0.365741 | + | 0.930716i | \(0.380815\pi\) | |||||||
\(662\) | 15520.1 | 0.911189 | ||||||||
\(663\) | 9930.74 | 0.581717 | ||||||||
\(664\) | 18521.7 | 1.08250 | ||||||||
\(665\) | 12176.8 | 0.710071 | ||||||||
\(666\) | −3361.89 | −0.195601 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 6298.17 | 0.364796 | ||||||||
\(669\) | −30104.3 | −1.73976 | ||||||||
\(670\) | −19216.6 | −1.10806 | ||||||||
\(671\) | 2791.78 | 0.160619 | ||||||||
\(672\) | 14990.2 | 0.860505 | ||||||||
\(673\) | −24349.2 | −1.39464 | −0.697319 | − | 0.716761i | \(-0.745624\pi\) | ||||
−0.697319 | + | 0.716761i | \(0.745624\pi\) | |||||||
\(674\) | 5859.50 | 0.334866 | ||||||||
\(675\) | −8525.26 | −0.486130 | ||||||||
\(676\) | 10564.1 | 0.601051 | ||||||||
\(677\) | −2495.14 | −0.141649 | −0.0708244 | − | 0.997489i | \(-0.522563\pi\) | ||||
−0.0708244 | + | 0.997489i | \(0.522563\pi\) | |||||||
\(678\) | −2709.96 | −0.153504 | ||||||||
\(679\) | −24476.2 | −1.38337 | ||||||||
\(680\) | 35745.1 | 2.01583 | ||||||||
\(681\) | 7980.96 | 0.449091 | ||||||||
\(682\) | 14095.6 | 0.791419 | ||||||||
\(683\) | 24024.9 | 1.34596 | 0.672978 | − | 0.739662i | \(-0.265015\pi\) | ||||
0.672978 | + | 0.739662i | \(0.265015\pi\) | |||||||
\(684\) | 1627.85 | 0.0909979 | ||||||||
\(685\) | −456.272 | −0.0254500 | ||||||||
\(686\) | −11213.5 | −0.624101 | ||||||||
\(687\) | 5429.90 | 0.301548 | ||||||||
\(688\) | 1472.59 | 0.0816019 | ||||||||
\(689\) | −1334.32 | −0.0737787 | ||||||||
\(690\) | 724.270 | 0.0399601 | ||||||||
\(691\) | 35630.3 | 1.96156 | 0.980781 | − | 0.195111i | \(-0.0625067\pi\) | ||||
0.980781 | + | 0.195111i | \(0.0625067\pi\) | |||||||
\(692\) | −623.146 | −0.0342319 | ||||||||
\(693\) | −3871.08 | −0.212194 | ||||||||
\(694\) | 5774.97 | 0.315871 | ||||||||
\(695\) | −26259.9 | −1.43323 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 531.752 | 0.0288975 | ||||||||
\(698\) | 13978.4 | 0.758010 | ||||||||
\(699\) | −10168.9 | −0.550245 | ||||||||
\(700\) | 5216.95 | 0.281689 | ||||||||
\(701\) | −19555.8 | −1.05365 | −0.526827 | − | 0.849973i | \(-0.676618\pi\) | ||||
−0.526827 | + | 0.849973i | \(0.676618\pi\) | |||||||
\(702\) | 3016.52 | 0.162181 | ||||||||
\(703\) | −25535.4 | −1.36997 | ||||||||
\(704\) | 13357.1 | 0.715080 | ||||||||
\(705\) | 11914.3 | 0.636481 | ||||||||
\(706\) | 2940.56 | 0.156756 | ||||||||
\(707\) | 23152.3 | 1.23159 | ||||||||
\(708\) | −2223.34 | −0.118020 | ||||||||
\(709\) | 4929.02 | 0.261090 | 0.130545 | − | 0.991442i | \(-0.458327\pi\) | ||||
0.130545 | + | 0.991442i | \(0.458327\pi\) | |||||||
\(710\) | −19661.7 | −1.03928 | ||||||||
\(711\) | −3141.44 | −0.165701 | ||||||||
\(712\) | −26126.3 | −1.37518 | ||||||||
\(713\) | 894.111 | 0.0469631 | ||||||||
\(714\) | 15528.8 | 0.813936 | ||||||||
\(715\) | 11307.5 | 0.591434 | ||||||||
\(716\) | −2011.24 | −0.104977 | ||||||||
\(717\) | 18731.1 | 0.975627 | ||||||||
\(718\) | 5997.18 | 0.311717 | ||||||||
\(719\) | −18112.0 | −0.939447 | −0.469723 | − | 0.882814i | \(-0.655646\pi\) | ||||
−0.469723 | + | 0.882814i | \(0.655646\pi\) | |||||||
\(720\) | 506.573 | 0.0262206 | ||||||||
\(721\) | −20053.8 | −1.03584 | ||||||||
\(722\) | 5035.40 | 0.259554 | ||||||||
\(723\) | −2106.56 | −0.108359 | ||||||||
\(724\) | 1935.82 | 0.0993702 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −15311.8 | −0.782746 | ||||||||
\(727\) | −4624.52 | −0.235920 | −0.117960 | − | 0.993018i | \(-0.537636\pi\) | ||||
−0.117960 | + | 0.993018i | \(0.537636\pi\) | |||||||
\(728\) | −4608.40 | −0.234614 | ||||||||
\(729\) | 14859.9 | 0.754963 | ||||||||
\(730\) | 13651.9 | 0.692166 | ||||||||
\(731\) | 23707.2 | 1.19951 | ||||||||
\(732\) | −1542.10 | −0.0778654 | ||||||||
\(733\) | −27052.1 | −1.36316 | −0.681578 | − | 0.731745i | \(-0.738706\pi\) | ||||
−0.681578 | + | 0.731745i | \(0.738706\pi\) | |||||||
\(734\) | −2392.27 | −0.120300 | ||||||||
\(735\) | −10973.6 | −0.550703 | ||||||||
\(736\) | 1051.13 | 0.0526429 | ||||||||
\(737\) | 46401.9 | 2.31918 | ||||||||
\(738\) | −36.3557 | −0.00181338 | ||||||||
\(739\) | −35147.3 | −1.74954 | −0.874772 | − | 0.484534i | \(-0.838989\pi\) | ||||
−0.874772 | + | 0.484534i | \(0.838989\pi\) | |||||||
\(740\) | −30926.7 | −1.53633 | ||||||||
\(741\) | −5157.10 | −0.255669 | ||||||||
\(742\) | −2086.49 | −0.103231 | ||||||||
\(743\) | 1467.33 | 0.0724510 | 0.0362255 | − | 0.999344i | \(-0.488467\pi\) | ||||
0.0362255 | + | 0.999344i | \(0.488467\pi\) | |||||||
\(744\) | −19437.8 | −0.957831 | ||||||||
\(745\) | 5568.88 | 0.273863 | ||||||||
\(746\) | 9092.45 | 0.446245 | ||||||||
\(747\) | 4225.75 | 0.206978 | ||||||||
\(748\) | −34573.2 | −1.69000 | ||||||||
\(749\) | −7420.67 | −0.362010 | ||||||||
\(750\) | 7247.29 | 0.352845 | ||||||||
\(751\) | 7477.83 | 0.363342 | 0.181671 | − | 0.983359i | \(-0.441849\pi\) | ||||
0.181671 | + | 0.983359i | \(0.441849\pi\) | |||||||
\(752\) | 1112.65 | 0.0539548 | ||||||||
\(753\) | −639.859 | −0.0309665 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 34270.1 | 1.65194 | ||||||||
\(756\) | −9499.98 | −0.457025 | ||||||||
\(757\) | −9561.20 | −0.459059 | −0.229530 | − | 0.973302i | \(-0.573719\pi\) | ||||
−0.229530 | + | 0.973302i | \(0.573719\pi\) | |||||||
\(758\) | 9966.77 | 0.477585 | ||||||||
\(759\) | −1748.87 | −0.0836365 | ||||||||
\(760\) | −18562.7 | −0.885971 | ||||||||
\(761\) | 9454.04 | 0.450340 | 0.225170 | − | 0.974319i | \(-0.427706\pi\) | ||||
0.225170 | + | 0.974319i | \(0.427706\pi\) | |||||||
\(762\) | −8796.66 | −0.418201 | ||||||||
\(763\) | −15051.3 | −0.714148 | ||||||||
\(764\) | −466.801 | −0.0221051 | ||||||||
\(765\) | 8155.29 | 0.385432 | ||||||||
\(766\) | −4345.14 | −0.204956 | ||||||||
\(767\) | 1093.24 | 0.0514665 | ||||||||
\(768\) | −21076.2 | −0.990263 | ||||||||
\(769\) | −35952.4 | −1.68592 | −0.842962 | − | 0.537973i | \(-0.819190\pi\) | ||||
−0.842962 | + | 0.537973i | \(0.819190\pi\) | |||||||
\(770\) | 17681.6 | 0.827532 | ||||||||
\(771\) | −9593.26 | −0.448110 | ||||||||
\(772\) | −22106.1 | −1.03059 | ||||||||
\(773\) | −4101.58 | −0.190845 | −0.0954226 | − | 0.995437i | \(-0.530420\pi\) | ||||
−0.0954226 | + | 0.995437i | \(0.530420\pi\) | |||||||
\(774\) | −1620.85 | −0.0752717 | ||||||||
\(775\) | −10820.0 | −0.501503 | ||||||||
\(776\) | 37312.1 | 1.72606 | ||||||||
\(777\) | −33542.0 | −1.54867 | ||||||||
\(778\) | 12677.0 | 0.584178 | ||||||||
\(779\) | −276.142 | −0.0127007 | ||||||||
\(780\) | −6245.90 | −0.286717 | ||||||||
\(781\) | 47476.5 | 2.17521 | ||||||||
\(782\) | 1088.90 | 0.0497939 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1024.80 | −0.0466835 | ||||||||
\(785\) | −8391.40 | −0.381531 | ||||||||
\(786\) | −19617.2 | −0.890234 | ||||||||
\(787\) | 10136.2 | 0.459106 | 0.229553 | − | 0.973296i | \(-0.426274\pi\) | ||||
0.229553 | + | 0.973296i | \(0.426274\pi\) | |||||||
\(788\) | −20579.8 | −0.930361 | ||||||||
\(789\) | −759.370 | −0.0342640 | ||||||||
\(790\) | 14348.9 | 0.646215 | ||||||||
\(791\) | −4196.54 | −0.188637 | ||||||||
\(792\) | 5901.17 | 0.264759 | ||||||||
\(793\) | 758.269 | 0.0339558 | ||||||||
\(794\) | −3998.24 | −0.178706 | ||||||||
\(795\) | −7059.84 | −0.314952 | ||||||||
\(796\) | −16084.0 | −0.716182 | ||||||||
\(797\) | −26581.1 | −1.18137 | −0.590685 | − | 0.806903i | \(-0.701142\pi\) | ||||
−0.590685 | + | 0.806903i | \(0.701142\pi\) | |||||||
\(798\) | −8064.19 | −0.357731 | ||||||||
\(799\) | 17912.4 | 0.793112 | ||||||||
\(800\) | −12720.1 | −0.562156 | ||||||||
\(801\) | −5960.76 | −0.262938 | ||||||||
\(802\) | 8939.59 | 0.393601 | ||||||||
\(803\) | −32965.0 | −1.44870 | ||||||||
\(804\) | −25631.0 | −1.12430 | ||||||||
\(805\) | 1121.58 | 0.0491061 | ||||||||
\(806\) | 3828.46 | 0.167310 | ||||||||
\(807\) | −17520.1 | −0.764236 | ||||||||
\(808\) | −35293.9 | −1.53668 | ||||||||
\(809\) | −44869.4 | −1.94997 | −0.974985 | − | 0.222273i | \(-0.928652\pi\) | ||||
−0.974985 | + | 0.222273i | \(0.928652\pi\) | |||||||
\(810\) | 18995.1 | 0.823975 | ||||||||
\(811\) | −10490.1 | −0.454199 | −0.227100 | − | 0.973872i | \(-0.572924\pi\) | ||||
−0.227100 | + | 0.973872i | \(0.572924\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12899.1 | 0.556446 | ||||||||
\(814\) | −37079.2 | −1.59659 | ||||||||
\(815\) | −7212.30 | −0.309983 | ||||||||
\(816\) | 4906.88 | 0.210509 | ||||||||
\(817\) | −12311.3 | −0.527194 | ||||||||
\(818\) | −418.455 | −0.0178862 | ||||||||
\(819\) | −1051.41 | −0.0448588 | ||||||||
\(820\) | −334.443 | −0.0142430 | ||||||||
\(821\) | 1522.68 | 0.0647281 | 0.0323640 | − | 0.999476i | \(-0.489696\pi\) | ||||
0.0323640 | + | 0.999476i | \(0.489696\pi\) | |||||||
\(822\) | 302.170 | 0.0128216 | ||||||||
\(823\) | −9450.65 | −0.400278 | −0.200139 | − | 0.979767i | \(-0.564139\pi\) | ||||
−0.200139 | + | 0.979767i | \(0.564139\pi\) | |||||||
\(824\) | 30570.5 | 1.29244 | ||||||||
\(825\) | 21163.8 | 0.893126 | ||||||||
\(826\) | 1709.52 | 0.0720117 | ||||||||
\(827\) | 30862.6 | 1.29770 | 0.648850 | − | 0.760916i | \(-0.275250\pi\) | ||||
0.648850 | + | 0.760916i | \(0.275250\pi\) | |||||||
\(828\) | 149.938 | 0.00629311 | ||||||||
\(829\) | −12584.4 | −0.527229 | −0.263614 | − | 0.964628i | \(-0.584915\pi\) | ||||
−0.263614 | + | 0.964628i | \(0.584915\pi\) | |||||||
\(830\) | −19301.6 | −0.807190 | ||||||||
\(831\) | 1639.01 | 0.0684197 | ||||||||
\(832\) | 3627.90 | 0.151171 | ||||||||
\(833\) | −16498.1 | −0.686226 | ||||||||
\(834\) | 17390.8 | 0.722055 | ||||||||
\(835\) | −16385.6 | −0.679097 | ||||||||
\(836\) | 17954.1 | 0.742768 | ||||||||
\(837\) | 19703.0 | 0.813662 | ||||||||
\(838\) | 8461.63 | 0.348809 | ||||||||
\(839\) | −18688.9 | −0.769026 | −0.384513 | − | 0.923120i | \(-0.625631\pi\) | ||||
−0.384513 | + | 0.923120i | \(0.625631\pi\) | |||||||
\(840\) | −24382.9 | −1.00154 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | −16992.4 | −0.695483 | ||||||||
\(843\) | −30689.0 | −1.25384 | ||||||||
\(844\) | 4435.70 | 0.180904 | ||||||||
\(845\) | −27483.9 | −1.11891 | ||||||||
\(846\) | −1224.67 | −0.0497694 | ||||||||
\(847\) | −23711.2 | −0.961898 | ||||||||
\(848\) | −659.301 | −0.0266987 | ||||||||
\(849\) | 17320.1 | 0.700146 | ||||||||
\(850\) | −13177.1 | −0.531732 | ||||||||
\(851\) | −2352.01 | −0.0947423 | ||||||||
\(852\) | −26224.5 | −1.05450 | ||||||||
\(853\) | 34110.3 | 1.36919 | 0.684593 | − | 0.728926i | \(-0.259980\pi\) | ||||
0.684593 | + | 0.728926i | \(0.259980\pi\) | |||||||
\(854\) | 1185.71 | 0.0475108 | ||||||||
\(855\) | −4235.09 | −0.169400 | ||||||||
\(856\) | 11312.2 | 0.451688 | ||||||||
\(857\) | −14542.6 | −0.579656 | −0.289828 | − | 0.957079i | \(-0.593598\pi\) | ||||
−0.289828 | + | 0.957079i | \(0.593598\pi\) | |||||||
\(858\) | −7488.45 | −0.297962 | ||||||||
\(859\) | 26425.8 | 1.04964 | 0.524818 | − | 0.851214i | \(-0.324133\pi\) | ||||
0.524818 | + | 0.851214i | \(0.324133\pi\) | |||||||
\(860\) | −14910.5 | −0.591215 | ||||||||
\(861\) | −362.726 | −0.0143573 | ||||||||
\(862\) | 21155.6 | 0.835920 | ||||||||
\(863\) | 14687.6 | 0.579342 | 0.289671 | − | 0.957126i | \(-0.406454\pi\) | ||||
0.289671 | + | 0.957126i | \(0.406454\pi\) | |||||||
\(864\) | 23163.1 | 0.912067 | ||||||||
\(865\) | 1621.20 | 0.0637254 | ||||||||
\(866\) | −5969.07 | −0.234223 | ||||||||
\(867\) | 51220.6 | 2.00639 | ||||||||
\(868\) | −12057.1 | −0.471478 | ||||||||
\(869\) | −34647.8 | −1.35253 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12603.1 | 0.490286 | ||||||||
\(872\) | 22944.6 | 0.891058 | ||||||||
\(873\) | 8512.80 | 0.330028 | ||||||||
\(874\) | −565.470 | −0.0218848 | ||||||||
\(875\) | 11222.9 | 0.433603 | ||||||||
\(876\) | 18208.8 | 0.702305 | ||||||||
\(877\) | −22840.6 | −0.879444 | −0.439722 | − | 0.898134i | \(-0.644923\pi\) | ||||
−0.439722 | + | 0.898134i | \(0.644923\pi\) | |||||||
\(878\) | 19931.4 | 0.766118 | ||||||||
\(879\) | 8119.11 | 0.311548 | ||||||||
\(880\) | 5587.13 | 0.214025 | ||||||||
\(881\) | −21209.1 | −0.811072 | −0.405536 | − | 0.914079i | \(-0.632915\pi\) | ||||
−0.405536 | + | 0.914079i | \(0.632915\pi\) | |||||||
\(882\) | 1127.97 | 0.0430621 | ||||||||
\(883\) | 15870.5 | 0.604854 | 0.302427 | − | 0.953173i | \(-0.402203\pi\) | ||||
0.302427 | + | 0.953173i | \(0.402203\pi\) | |||||||
\(884\) | −9390.33 | −0.357275 | ||||||||
\(885\) | 5784.33 | 0.219704 | ||||||||
\(886\) | 2601.53 | 0.0986459 | ||||||||
\(887\) | 25122.6 | 0.950997 | 0.475498 | − | 0.879717i | \(-0.342268\pi\) | ||||
0.475498 | + | 0.879717i | \(0.342268\pi\) | |||||||
\(888\) | 51132.3 | 1.93231 | ||||||||
\(889\) | −13622.2 | −0.513918 | ||||||||
\(890\) | 27226.4 | 1.02543 | ||||||||
\(891\) | −45866.9 | −1.72458 | ||||||||
\(892\) | 28466.1 | 1.06852 | ||||||||
\(893\) | −9302.04 | −0.348579 | ||||||||
\(894\) | −3688.03 | −0.137971 | ||||||||
\(895\) | 5232.53 | 0.195424 | ||||||||
\(896\) | −15539.4 | −0.579393 | ||||||||
\(897\) | −475.007 | −0.0176812 | ||||||||
\(898\) | 22457.2 | 0.834528 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −1814.45 | −0.0672020 | ||||||||
\(901\) | −10614.0 | −0.392459 | ||||||||
\(902\) | −400.977 | −0.0148016 | ||||||||
\(903\) | −16171.5 | −0.595961 | ||||||||
\(904\) | 6397.31 | 0.235367 | ||||||||
\(905\) | −5036.29 | −0.184986 | ||||||||
\(906\) | −22695.6 | −0.832241 | ||||||||
\(907\) | −47430.9 | −1.73640 | −0.868201 | − | 0.496213i | \(-0.834724\pi\) | ||||
−0.868201 | + | 0.496213i | \(0.834724\pi\) | |||||||
\(908\) | −7546.65 | −0.275820 | ||||||||
\(909\) | −8052.35 | −0.293817 | ||||||||
\(910\) | 4802.44 | 0.174944 | ||||||||
\(911\) | −30167.2 | −1.09713 | −0.548565 | − | 0.836108i | \(-0.684826\pi\) | ||||
−0.548565 | + | 0.836108i | \(0.684826\pi\) | |||||||
\(912\) | −2548.17 | −0.0925202 | ||||||||
\(913\) | 46607.0 | 1.68945 | ||||||||
\(914\) | 1071.25 | 0.0387679 | ||||||||
\(915\) | 4011.98 | 0.144953 | ||||||||
\(916\) | −5134.41 | −0.185203 | ||||||||
\(917\) | −30378.5 | −1.09399 | ||||||||
\(918\) | 23995.4 | 0.862707 | ||||||||
\(919\) | −13387.0 | −0.480517 | −0.240259 | − | 0.970709i | \(-0.577232\pi\) | ||||
−0.240259 | + | 0.970709i | \(0.577232\pi\) | |||||||
\(920\) | −1709.76 | −0.0612707 | ||||||||
\(921\) | −37288.8 | −1.33410 | ||||||||
\(922\) | −3633.43 | −0.129784 | ||||||||
\(923\) | 12895.0 | 0.459851 | ||||||||
\(924\) | 23583.5 | 0.839655 | ||||||||
\(925\) | 28462.5 | 1.01172 | ||||||||
\(926\) | 8079.21 | 0.286716 | ||||||||
\(927\) | 6974.70 | 0.247119 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 40008.9 | 1.41297 | 0.706486 | − | 0.707727i | \(-0.250280\pi\) | ||||
0.706486 | + | 0.707727i | \(0.250280\pi\) | |||||||
\(930\) | 20256.3 | 0.714226 | ||||||||
\(931\) | 8567.58 | 0.301602 | ||||||||
\(932\) | 9615.48 | 0.337946 | ||||||||
\(933\) | 36670.6 | 1.28675 | ||||||||
\(934\) | −13733.1 | −0.481113 | ||||||||
\(935\) | 89947.0 | 3.14607 | ||||||||
\(936\) | 1602.80 | 0.0559713 | ||||||||
\(937\) | −16407.0 | −0.572032 | −0.286016 | − | 0.958225i | \(-0.592331\pi\) | ||||
−0.286016 | + | 0.958225i | \(0.592331\pi\) | |||||||
\(938\) | 19707.5 | 0.686007 | ||||||||
\(939\) | −653.887 | −0.0227250 | ||||||||
\(940\) | −11265.9 | −0.390909 | ||||||||
\(941\) | 38360.3 | 1.32892 | 0.664458 | − | 0.747325i | \(-0.268662\pi\) | ||||
0.664458 | + | 0.747325i | \(0.268662\pi\) | |||||||
\(942\) | 5557.26 | 0.192214 | ||||||||
\(943\) | −25.4348 | −0.000878335 0 | ||||||||
\(944\) | 540.183 | 0.0186244 | ||||||||
\(945\) | 24715.5 | 0.850789 | ||||||||
\(946\) | −17876.8 | −0.614404 | ||||||||
\(947\) | −30441.9 | −1.04459 | −0.522296 | − | 0.852764i | \(-0.674925\pi\) | ||||
−0.522296 | + | 0.852764i | \(0.674925\pi\) | |||||||
\(948\) | 19138.4 | 0.655681 | ||||||||
\(949\) | −8953.53 | −0.306263 | ||||||||
\(950\) | 6842.97 | 0.233700 | ||||||||
\(951\) | −53128.4 | −1.81157 | ||||||||
\(952\) | −36658.3 | −1.24801 | ||||||||
\(953\) | −21635.8 | −0.735418 | −0.367709 | − | 0.929941i | \(-0.619858\pi\) | ||||
−0.367709 | + | 0.929941i | \(0.619858\pi\) | |||||||
\(954\) | 725.678 | 0.0246276 | ||||||||
\(955\) | 1214.45 | 0.0411504 | ||||||||
\(956\) | −17711.8 | −0.599204 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −43.6165 | −0.00147097 | ||||||||
\(959\) | 467.928 | 0.0157562 | ||||||||
\(960\) | 19195.1 | 0.645332 | ||||||||
\(961\) | −4784.62 | −0.160606 | ||||||||
\(962\) | −10071.0 | −0.337527 | ||||||||
\(963\) | 2580.90 | 0.0863639 | ||||||||
\(964\) | 1991.92 | 0.0665514 | ||||||||
\(965\) | 57512.0 | 1.91853 | ||||||||
\(966\) | −742.772 | −0.0247394 | ||||||||
\(967\) | 46.7093 | 0.00155333 | 0.000776665 | − | 1.00000i | \(-0.499753\pi\) | ||||
0.000776665 | 1.00000i | \(0.499753\pi\) | ||||||||
\(968\) | 36146.0 | 1.20018 | ||||||||
\(969\) | −41022.9 | −1.36001 | ||||||||
\(970\) | −38883.1 | −1.28707 | ||||||||
\(971\) | 12150.1 | 0.401560 | 0.200780 | − | 0.979636i | \(-0.435652\pi\) | ||||
0.200780 | + | 0.979636i | \(0.435652\pi\) | |||||||
\(972\) | 7351.86 | 0.242604 | ||||||||
\(973\) | 26930.7 | 0.887316 | ||||||||
\(974\) | −6394.15 | −0.210351 | ||||||||
\(975\) | 5748.24 | 0.188811 | ||||||||
\(976\) | 374.668 | 0.0122877 | ||||||||
\(977\) | −41772.5 | −1.36788 | −0.683942 | − | 0.729537i | \(-0.739736\pi\) | ||||
−0.683942 | + | 0.729537i | \(0.739736\pi\) | |||||||
\(978\) | 4776.40 | 0.156168 | ||||||||
\(979\) | −65742.9 | −2.14622 | ||||||||
\(980\) | 10376.4 | 0.338227 | ||||||||
\(981\) | 5234.84 | 0.170373 | ||||||||
\(982\) | 34177.0 | 1.11062 | ||||||||
\(983\) | −4488.99 | −0.145653 | −0.0728264 | − | 0.997345i | \(-0.523202\pi\) | ||||
−0.0728264 | + | 0.997345i | \(0.523202\pi\) | |||||||
\(984\) | 552.948 | 0.0179140 | ||||||||
\(985\) | 53541.2 | 1.73194 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12218.7 | −0.394047 | ||||||||
\(988\) | 4876.45 | 0.157025 | ||||||||
\(989\) | −1133.96 | −0.0364590 | ||||||||
\(990\) | −6149.64 | −0.197423 | ||||||||
\(991\) | 17506.2 | 0.561152 | 0.280576 | − | 0.959832i | \(-0.409475\pi\) | ||||
0.280576 | + | 0.959832i | \(0.409475\pi\) | |||||||
\(992\) | 29397.9 | 0.940911 | ||||||||
\(993\) | −53855.5 | −1.72110 | ||||||||
\(994\) | 20163.9 | 0.643422 | ||||||||
\(995\) | 41844.7 | 1.33323 | ||||||||
\(996\) | −25744.3 | −0.819015 | ||||||||
\(997\) | 14604.7 | 0.463928 | 0.231964 | − | 0.972724i | \(-0.425485\pi\) | ||||
0.231964 | + | 0.972724i | \(0.425485\pi\) | |||||||
\(998\) | 1732.34 | 0.0549461 | ||||||||
\(999\) | −51829.7 | −1.64146 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 841.4.a.i.1.7 | 21 | ||
29.4 | even | 14 | 29.4.d.a.16.3 | ✓ | 42 | ||
29.22 | even | 14 | 29.4.d.a.20.3 | yes | 42 | ||
29.28 | even | 2 | 841.4.a.h.1.15 | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.4.d.a.16.3 | ✓ | 42 | 29.4 | even | 14 | ||
29.4.d.a.20.3 | yes | 42 | 29.22 | even | 14 | ||
841.4.a.h.1.15 | 21 | 29.28 | even | 2 | |||
841.4.a.i.1.7 | 21 | 1.1 | even | 1 | trivial |