Newspace parameters
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(67.8521965066\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
|
|
Defining polynomial: |
\( x^{5} - x^{4} - 38x^{3} + 38x^{2} + 202x + 101 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.50693\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 5.31348 | 1.02258 | 0.511289 | − | 0.859409i | \(-0.329168\pi\) | ||||
0.511289 | + | 0.859409i | \(0.329168\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −10.6270 | −0.723072 | ||||||||
\(7\) | −34.1697 | −1.84499 | −0.922495 | − | 0.386009i | \(-0.873853\pi\) | ||||
−0.922495 | + | 0.386009i | \(0.873853\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 1.23302 | 0.0456674 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −58.9953 | −1.61707 | −0.808534 | − | 0.588449i | \(-0.799739\pi\) | ||||
−0.808534 | + | 0.588449i | \(0.799739\pi\) | |||||||
\(12\) | 21.2539 | 0.511289 | ||||||||
\(13\) | −57.0300 | −1.21671 | −0.608357 | − | 0.793663i | \(-0.708171\pi\) | ||||
−0.608357 | + | 0.793663i | \(0.708171\pi\) | |||||||
\(14\) | 68.3394 | 1.30460 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 116.881 | 1.66751 | 0.833757 | − | 0.552132i | \(-0.186186\pi\) | ||||
0.833757 | + | 0.552132i | \(0.186186\pi\) | |||||||
\(18\) | −2.46604 | −0.0322917 | ||||||||
\(19\) | −35.0292 | −0.422960 | −0.211480 | − | 0.977382i | \(-0.567828\pi\) | ||||
−0.211480 | + | 0.977382i | \(0.567828\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −181.560 | −1.88665 | ||||||||
\(22\) | 117.991 | 1.14344 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | −42.5078 | −0.361536 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 114.060 | 0.860347 | ||||||||
\(27\) | −136.912 | −0.975880 | ||||||||
\(28\) | −136.679 | −0.922495 | ||||||||
\(29\) | −171.371 | −1.09734 | −0.548670 | − | 0.836039i | \(-0.684866\pi\) | ||||
−0.548670 | + | 0.836039i | \(0.684866\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 131.300 | 0.760717 | 0.380359 | − | 0.924839i | \(-0.375801\pi\) | ||||
0.380359 | + | 0.924839i | \(0.375801\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −313.470 | −1.65358 | ||||||||
\(34\) | −233.761 | −1.17911 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.93208 | 0.0228337 | ||||||||
\(37\) | 325.843 | 1.44779 | 0.723896 | − | 0.689910i | \(-0.242350\pi\) | ||||
0.723896 | + | 0.689910i | \(0.242350\pi\) | |||||||
\(38\) | 70.0584 | 0.299078 | ||||||||
\(39\) | −303.028 | −1.24419 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −72.3772 | −0.275693 | −0.137847 | − | 0.990454i | \(-0.544018\pi\) | ||||
−0.137847 | + | 0.990454i | \(0.544018\pi\) | |||||||
\(42\) | 363.120 | 1.33406 | ||||||||
\(43\) | 59.4075 | 0.210688 | 0.105344 | − | 0.994436i | \(-0.466406\pi\) | ||||
0.105344 | + | 0.994436i | \(0.466406\pi\) | |||||||
\(44\) | −235.981 | −0.808534 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | 479.286 | 1.48747 | 0.743735 | − | 0.668475i | \(-0.233053\pi\) | ||||
0.743735 | + | 0.668475i | \(0.233053\pi\) | |||||||
\(48\) | 85.0156 | 0.255645 | ||||||||
\(49\) | 824.568 | 2.40399 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 621.043 | 1.70516 | ||||||||
\(52\) | −228.120 | −0.608357 | ||||||||
\(53\) | −230.887 | −0.598392 | −0.299196 | − | 0.954192i | \(-0.596718\pi\) | ||||
−0.299196 | + | 0.954192i | \(0.596718\pi\) | |||||||
\(54\) | 273.824 | 0.690052 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 273.358 | 0.652302 | ||||||||
\(57\) | −186.127 | −0.432510 | ||||||||
\(58\) | 342.743 | 0.775937 | ||||||||
\(59\) | 495.740 | 1.09390 | 0.546948 | − | 0.837166i | \(-0.315789\pi\) | ||||
0.546948 | + | 0.837166i | \(0.315789\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 267.995 | 0.562512 | 0.281256 | − | 0.959633i | \(-0.409249\pi\) | ||||
0.281256 | + | 0.959633i | \(0.409249\pi\) | |||||||
\(62\) | −262.601 | −0.537908 | ||||||||
\(63\) | −42.1319 | −0.0842559 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 626.940 | 1.16926 | ||||||||
\(67\) | 11.1110 | 0.0202601 | 0.0101301 | − | 0.999949i | \(-0.496775\pi\) | ||||
0.0101301 | + | 0.999949i | \(0.496775\pi\) | |||||||
\(68\) | 467.523 | 0.833757 | ||||||||
\(69\) | −122.210 | −0.213222 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −353.044 | −0.590121 | −0.295060 | − | 0.955479i | \(-0.595340\pi\) | ||||
−0.295060 | + | 0.955479i | \(0.595340\pi\) | |||||||
\(72\) | −9.86416 | −0.0161459 | ||||||||
\(73\) | 466.427 | 0.747824 | 0.373912 | − | 0.927464i | \(-0.378016\pi\) | ||||
0.373912 | + | 0.927464i | \(0.378016\pi\) | |||||||
\(74\) | −651.686 | −1.02374 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −140.117 | −0.211480 | ||||||||
\(77\) | 2015.85 | 2.98348 | ||||||||
\(78\) | 606.056 | 0.879773 | ||||||||
\(79\) | −773.967 | −1.10225 | −0.551127 | − | 0.834421i | \(-0.685802\pi\) | ||||
−0.551127 | + | 0.834421i | \(0.685802\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −760.771 | −1.04358 | ||||||||
\(82\) | 144.754 | 0.194945 | ||||||||
\(83\) | 22.4688 | 0.0297141 | 0.0148571 | − | 0.999890i | \(-0.495271\pi\) | ||||
0.0148571 | + | 0.999890i | \(0.495271\pi\) | |||||||
\(84\) | −726.239 | −0.943324 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −118.815 | −0.148979 | ||||||||
\(87\) | −910.578 | −1.12212 | ||||||||
\(88\) | 471.962 | 0.571720 | ||||||||
\(89\) | 1172.86 | 1.39688 | 0.698441 | − | 0.715667i | \(-0.253877\pi\) | ||||
0.698441 | + | 0.715667i | \(0.253877\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1948.70 | 2.24483 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | 697.661 | 0.777893 | ||||||||
\(94\) | −958.572 | −1.05180 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −170.031 | −0.180768 | ||||||||
\(97\) | 1318.71 | 1.38035 | 0.690177 | − | 0.723641i | \(-0.257533\pi\) | ||||
0.690177 | + | 0.723641i | \(0.257533\pi\) | |||||||
\(98\) | −1649.14 | −1.69988 | ||||||||
\(99\) | −72.7424 | −0.0738473 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1452.56 | −1.43104 | −0.715522 | − | 0.698590i | \(-0.753811\pi\) | ||||
−0.715522 | + | 0.698590i | \(0.753811\pi\) | |||||||
\(102\) | −1242.09 | −1.20573 | ||||||||
\(103\) | −481.080 | −0.460216 | −0.230108 | − | 0.973165i | \(-0.573908\pi\) | ||||
−0.230108 | + | 0.973165i | \(0.573908\pi\) | |||||||
\(104\) | 456.240 | 0.430174 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 461.774 | 0.423127 | ||||||||
\(107\) | 176.518 | 0.159483 | 0.0797415 | − | 0.996816i | \(-0.474591\pi\) | ||||
0.0797415 | + | 0.996816i | \(0.474591\pi\) | |||||||
\(108\) | −547.649 | −0.487940 | ||||||||
\(109\) | −336.029 | −0.295282 | −0.147641 | − | 0.989041i | \(-0.547168\pi\) | ||||
−0.147641 | + | 0.989041i | \(0.547168\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1731.36 | 1.48048 | ||||||||
\(112\) | −546.715 | −0.461247 | ||||||||
\(113\) | 1140.89 | 0.949790 | 0.474895 | − | 0.880043i | \(-0.342486\pi\) | ||||
0.474895 | + | 0.880043i | \(0.342486\pi\) | |||||||
\(114\) | 372.253 | 0.305831 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −685.486 | −0.548670 | ||||||||
\(117\) | −70.3192 | −0.0555642 | ||||||||
\(118\) | −991.481 | −0.773502 | ||||||||
\(119\) | −3993.78 | −3.07654 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2149.45 | 1.61491 | ||||||||
\(122\) | −535.990 | −0.397756 | ||||||||
\(123\) | −384.575 | −0.281918 | ||||||||
\(124\) | 525.201 | 0.380359 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 84.2638 | 0.0595779 | ||||||||
\(127\) | 1919.42 | 1.34111 | 0.670556 | − | 0.741859i | \(-0.266056\pi\) | ||||
0.670556 | + | 0.741859i | \(0.266056\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 315.660 | 0.215445 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2728.18 | −1.81956 | −0.909778 | − | 0.415094i | \(-0.863749\pi\) | ||||
−0.909778 | + | 0.415094i | \(0.863749\pi\) | |||||||
\(132\) | −1253.88 | −0.826790 | ||||||||
\(133\) | 1196.94 | 0.780358 | ||||||||
\(134\) | −22.2221 | −0.0143261 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −935.045 | −0.589555 | ||||||||
\(137\) | −1498.15 | −0.934271 | −0.467136 | − | 0.884186i | \(-0.654714\pi\) | ||||
−0.467136 | + | 0.884186i | \(0.654714\pi\) | |||||||
\(138\) | 244.420 | 0.150771 | ||||||||
\(139\) | −3070.10 | −1.87340 | −0.936700 | − | 0.350132i | \(-0.886137\pi\) | ||||
−0.936700 | + | 0.350132i | \(0.886137\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2546.68 | 1.52105 | ||||||||
\(142\) | 706.087 | 0.417278 | ||||||||
\(143\) | 3364.51 | 1.96751 | ||||||||
\(144\) | 19.7283 | 0.0114169 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −932.854 | −0.528791 | ||||||||
\(147\) | 4381.32 | 2.45827 | ||||||||
\(148\) | 1303.37 | 0.723896 | ||||||||
\(149\) | −2446.56 | −1.34517 | −0.672585 | − | 0.740020i | \(-0.734816\pi\) | ||||
−0.672585 | + | 0.740020i | \(0.734816\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1398.67 | 0.753789 | 0.376895 | − | 0.926256i | \(-0.376992\pi\) | ||||
0.376895 | + | 0.926256i | \(0.376992\pi\) | |||||||
\(152\) | 280.234 | 0.149539 | ||||||||
\(153\) | 144.116 | 0.0761510 | ||||||||
\(154\) | −4031.70 | −2.10964 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1212.11 | −0.622093 | ||||||||
\(157\) | −1629.82 | −0.828495 | −0.414248 | − | 0.910164i | \(-0.635955\pi\) | ||||
−0.414248 | + | 0.910164i | \(0.635955\pi\) | |||||||
\(158\) | 1547.93 | 0.779412 | ||||||||
\(159\) | −1226.81 | −0.611903 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 785.903 | 0.384707 | ||||||||
\(162\) | 1521.54 | 0.737924 | ||||||||
\(163\) | −209.019 | −0.100439 | −0.0502197 | − | 0.998738i | \(-0.515992\pi\) | ||||
−0.0502197 | + | 0.998738i | \(0.515992\pi\) | |||||||
\(164\) | −289.509 | −0.137847 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −44.9376 | −0.0210111 | ||||||||
\(167\) | 891.381 | 0.413037 | 0.206518 | − | 0.978443i | \(-0.433787\pi\) | ||||
0.206518 | + | 0.978443i | \(0.433787\pi\) | |||||||
\(168\) | 1452.48 | 0.667031 | ||||||||
\(169\) | 1055.43 | 0.480394 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −43.1917 | −0.0193155 | ||||||||
\(172\) | 237.630 | 0.105344 | ||||||||
\(173\) | 1198.99 | 0.526922 | 0.263461 | − | 0.964670i | \(-0.415136\pi\) | ||||
0.263461 | + | 0.964670i | \(0.415136\pi\) | |||||||
\(174\) | 1821.16 | 0.793457 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −943.925 | −0.404267 | ||||||||
\(177\) | 2634.10 | 1.11860 | ||||||||
\(178\) | −2345.71 | −0.987745 | ||||||||
\(179\) | −1993.46 | −0.832392 | −0.416196 | − | 0.909275i | \(-0.636637\pi\) | ||||
−0.416196 | + | 0.909275i | \(0.636637\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1964.42 | −0.806707 | −0.403354 | − | 0.915044i | \(-0.632156\pi\) | ||||
−0.403354 | + | 0.915044i | \(0.632156\pi\) | |||||||
\(182\) | −3897.40 | −1.58733 | ||||||||
\(183\) | 1423.98 | 0.575213 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1395.32 | −0.550054 | ||||||||
\(187\) | −6895.41 | −2.69648 | ||||||||
\(188\) | 1917.14 | 0.743735 | ||||||||
\(189\) | 4678.25 | 1.80049 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1282.64 | −0.485910 | −0.242955 | − | 0.970038i | \(-0.578117\pi\) | ||||
−0.242955 | + | 0.970038i | \(0.578117\pi\) | |||||||
\(192\) | 340.062 | 0.127822 | ||||||||
\(193\) | 561.448 | 0.209399 | 0.104699 | − | 0.994504i | \(-0.466612\pi\) | ||||
0.104699 | + | 0.994504i | \(0.466612\pi\) | |||||||
\(194\) | −2637.41 | −0.976058 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3298.27 | 1.20199 | ||||||||
\(197\) | 4599.35 | 1.66340 | 0.831701 | − | 0.555224i | \(-0.187367\pi\) | ||||
0.831701 | + | 0.555224i | \(0.187367\pi\) | |||||||
\(198\) | 145.485 | 0.0522180 | ||||||||
\(199\) | 331.109 | 0.117948 | 0.0589740 | − | 0.998260i | \(-0.481217\pi\) | ||||
0.0589740 | + | 0.998260i | \(0.481217\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 59.0382 | 0.0207176 | ||||||||
\(202\) | 2905.13 | 1.01190 | ||||||||
\(203\) | 5855.71 | 2.02458 | ||||||||
\(204\) | 2484.17 | 0.852582 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 962.160 | 0.325422 | ||||||||
\(207\) | −28.3595 | −0.00952231 | ||||||||
\(208\) | −912.481 | −0.304179 | ||||||||
\(209\) | 2066.56 | 0.683956 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3949.25 | −1.28852 | −0.644260 | − | 0.764807i | \(-0.722834\pi\) | ||||
−0.644260 | + | 0.764807i | \(0.722834\pi\) | |||||||
\(212\) | −923.549 | −0.299196 | ||||||||
\(213\) | −1875.89 | −0.603445 | ||||||||
\(214\) | −353.037 | −0.112772 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1095.30 | 0.345026 | ||||||||
\(217\) | −4486.49 | −1.40352 | ||||||||
\(218\) | 672.059 | 0.208796 | ||||||||
\(219\) | 2478.35 | 0.764709 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6665.71 | −2.02889 | ||||||||
\(222\) | −3462.72 | −1.04686 | ||||||||
\(223\) | −3592.14 | −1.07869 | −0.539344 | − | 0.842085i | \(-0.681328\pi\) | ||||
−0.539344 | + | 0.842085i | \(0.681328\pi\) | |||||||
\(224\) | 1093.43 | 0.326151 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2281.79 | −0.671603 | ||||||||
\(227\) | −3349.51 | −0.979359 | −0.489680 | − | 0.871902i | \(-0.662886\pi\) | ||||
−0.489680 | + | 0.871902i | \(0.662886\pi\) | |||||||
\(228\) | −744.507 | −0.216255 | ||||||||
\(229\) | 2763.74 | 0.797525 | 0.398763 | − | 0.917054i | \(-0.369440\pi\) | ||||
0.398763 | + | 0.917054i | \(0.369440\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10711.2 | 3.05084 | ||||||||
\(232\) | 1370.97 | 0.387968 | ||||||||
\(233\) | 2085.17 | 0.586285 | 0.293142 | − | 0.956069i | \(-0.405299\pi\) | ||||
0.293142 | + | 0.956069i | \(0.405299\pi\) | |||||||
\(234\) | 140.638 | 0.0392898 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1982.96 | 0.546948 | ||||||||
\(237\) | −4112.45 | −1.12714 | ||||||||
\(238\) | 7987.55 | 2.17545 | ||||||||
\(239\) | 4763.85 | 1.28932 | 0.644660 | − | 0.764469i | \(-0.276999\pi\) | ||||
0.644660 | + | 0.764469i | \(0.276999\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6928.92 | 1.85200 | 0.925998 | − | 0.377528i | \(-0.123226\pi\) | ||||
0.925998 | + | 0.377528i | \(0.123226\pi\) | |||||||
\(242\) | −4298.89 | −1.14191 | ||||||||
\(243\) | −345.709 | −0.0912645 | ||||||||
\(244\) | 1071.98 | 0.281256 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 769.149 | 0.199346 | ||||||||
\(247\) | 1997.72 | 0.514622 | ||||||||
\(248\) | −1050.40 | −0.268954 | ||||||||
\(249\) | 119.387 | 0.0303850 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4718.91 | 1.18667 | 0.593336 | − | 0.804955i | \(-0.297810\pi\) | ||||
0.593336 | + | 0.804955i | \(0.297810\pi\) | |||||||
\(252\) | −168.528 | −0.0421280 | ||||||||
\(253\) | 1356.89 | 0.337182 | ||||||||
\(254\) | −3838.84 | −0.948309 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 7890.24 | 1.91510 | 0.957548 | − | 0.288275i | \(-0.0930817\pi\) | ||||
0.957548 | + | 0.288275i | \(0.0930817\pi\) | |||||||
\(258\) | −631.321 | −0.152342 | ||||||||
\(259\) | −11134.0 | −2.67116 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −211.304 | −0.0501127 | ||||||||
\(262\) | 5456.35 | 1.28662 | ||||||||
\(263\) | 129.509 | 0.0303645 | 0.0151822 | − | 0.999885i | \(-0.495167\pi\) | ||||
0.0151822 | + | 0.999885i | \(0.495167\pi\) | |||||||
\(264\) | 2507.76 | 0.584629 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2393.87 | −0.551796 | ||||||||
\(267\) | 6231.95 | 1.42842 | ||||||||
\(268\) | 44.4441 | 0.0101301 | ||||||||
\(269\) | 5625.75 | 1.27512 | 0.637561 | − | 0.770400i | \(-0.279943\pi\) | ||||
0.637561 | + | 0.770400i | \(0.279943\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5008.19 | 1.12260 | 0.561302 | − | 0.827611i | \(-0.310301\pi\) | ||||
0.561302 | + | 0.827611i | \(0.310301\pi\) | |||||||
\(272\) | 1870.09 | 0.416878 | ||||||||
\(273\) | 10354.4 | 2.29551 | ||||||||
\(274\) | 2996.29 | 0.660630 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −488.840 | −0.106611 | ||||||||
\(277\) | −6191.44 | −1.34299 | −0.671494 | − | 0.741010i | \(-0.734347\pi\) | ||||
−0.671494 | + | 0.741010i | \(0.734347\pi\) | |||||||
\(278\) | 6140.21 | 1.32469 | ||||||||
\(279\) | 161.896 | 0.0347400 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7739.13 | 1.64298 | 0.821491 | − | 0.570221i | \(-0.193142\pi\) | ||||
0.821491 | + | 0.570221i | \(0.193142\pi\) | |||||||
\(282\) | −5093.35 | −1.07555 | ||||||||
\(283\) | 4201.98 | 0.882621 | 0.441310 | − | 0.897354i | \(-0.354514\pi\) | ||||
0.441310 | + | 0.897354i | \(0.354514\pi\) | |||||||
\(284\) | −1412.17 | −0.295060 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6729.01 | −1.39124 | ||||||||
\(287\) | 2473.11 | 0.508651 | ||||||||
\(288\) | −39.4566 | −0.00807293 | ||||||||
\(289\) | 8748.09 | 1.78060 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7006.91 | 1.41152 | ||||||||
\(292\) | 1865.71 | 0.373912 | ||||||||
\(293\) | −3293.70 | −0.656724 | −0.328362 | − | 0.944552i | \(-0.606497\pi\) | ||||
−0.328362 | + | 0.944552i | \(0.606497\pi\) | |||||||
\(294\) | −8762.64 | −1.73826 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2606.74 | −0.511871 | ||||||||
\(297\) | 8077.18 | 1.57807 | ||||||||
\(298\) | 4893.12 | 0.951178 | ||||||||
\(299\) | 1311.69 | 0.253703 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2029.94 | −0.388716 | ||||||||
\(302\) | −2797.34 | −0.533009 | ||||||||
\(303\) | −7718.16 | −1.46336 | ||||||||
\(304\) | −560.467 | −0.105740 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −288.232 | −0.0538469 | ||||||||
\(307\) | 1088.67 | 0.202390 | 0.101195 | − | 0.994867i | \(-0.467733\pi\) | ||||
0.101195 | + | 0.994867i | \(0.467733\pi\) | |||||||
\(308\) | 8063.41 | 1.49174 | ||||||||
\(309\) | −2556.21 | −0.470607 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3853.58 | 0.702625 | 0.351313 | − | 0.936258i | \(-0.385735\pi\) | ||||
0.351313 | + | 0.936258i | \(0.385735\pi\) | |||||||
\(312\) | 2424.22 | 0.439886 | ||||||||
\(313\) | −8534.78 | −1.54126 | −0.770630 | − | 0.637282i | \(-0.780058\pi\) | ||||
−0.770630 | + | 0.637282i | \(0.780058\pi\) | |||||||
\(314\) | 3259.64 | 0.585835 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3095.87 | −0.551127 | ||||||||
\(317\) | 4063.86 | 0.720029 | 0.360015 | − | 0.932947i | \(-0.382772\pi\) | ||||
0.360015 | + | 0.932947i | \(0.382772\pi\) | |||||||
\(318\) | 2453.63 | 0.432681 | ||||||||
\(319\) | 10110.1 | 1.77447 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 937.926 | 0.163084 | ||||||||
\(322\) | −1571.81 | −0.272029 | ||||||||
\(323\) | −4094.23 | −0.705292 | ||||||||
\(324\) | −3043.08 | −0.521791 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 418.038 | 0.0710214 | ||||||||
\(327\) | −1785.48 | −0.301949 | ||||||||
\(328\) | 579.018 | 0.0974723 | ||||||||
\(329\) | −16377.1 | −2.74437 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7528.47 | −1.25016 | −0.625079 | − | 0.780562i | \(-0.714933\pi\) | ||||
−0.625079 | + | 0.780562i | \(0.714933\pi\) | |||||||
\(332\) | 89.8753 | 0.0148571 | ||||||||
\(333\) | 401.771 | 0.0661169 | ||||||||
\(334\) | −1782.76 | −0.292061 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2904.96 | −0.471662 | ||||||||
\(337\) | 5076.22 | 0.820533 | 0.410266 | − | 0.911966i | \(-0.365436\pi\) | ||||
0.410266 | + | 0.911966i | \(0.365436\pi\) | |||||||
\(338\) | −2110.85 | −0.339690 | ||||||||
\(339\) | 6062.11 | 0.971235 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7746.10 | −1.23013 | ||||||||
\(342\) | 86.3834 | 0.0136581 | ||||||||
\(343\) | −16455.0 | −2.59034 | ||||||||
\(344\) | −475.260 | −0.0744893 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2397.98 | −0.372590 | ||||||||
\(347\) | 1637.97 | 0.253404 | 0.126702 | − | 0.991941i | \(-0.459561\pi\) | ||||
0.126702 | + | 0.991941i | \(0.459561\pi\) | |||||||
\(348\) | −3642.31 | −0.561059 | ||||||||
\(349\) | −9786.85 | −1.50108 | −0.750542 | − | 0.660823i | \(-0.770208\pi\) | ||||
−0.750542 | + | 0.660823i | \(0.770208\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7808.11 | 1.18737 | ||||||||
\(352\) | 1887.85 | 0.285860 | ||||||||
\(353\) | −11697.5 | −1.76372 | −0.881860 | − | 0.471512i | \(-0.843708\pi\) | ||||
−0.881860 | + | 0.471512i | \(0.843708\pi\) | |||||||
\(354\) | −5268.21 | −0.790967 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4691.43 | 0.698441 | ||||||||
\(357\) | −21220.8 | −3.14601 | ||||||||
\(358\) | 3986.92 | 0.588590 | ||||||||
\(359\) | 1498.68 | 0.220327 | 0.110164 | − | 0.993913i | \(-0.464863\pi\) | ||||
0.110164 | + | 0.993913i | \(0.464863\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5631.96 | −0.821105 | ||||||||
\(362\) | 3928.84 | 0.570428 | ||||||||
\(363\) | 11421.0 | 1.65137 | ||||||||
\(364\) | 7794.80 | 1.12241 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2847.97 | −0.406737 | ||||||||
\(367\) | 750.417 | 0.106734 | 0.0533671 | − | 0.998575i | \(-0.483005\pi\) | ||||
0.0533671 | + | 0.998575i | \(0.483005\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | −89.2426 | −0.0125902 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7889.34 | 1.10403 | ||||||||
\(372\) | 2790.64 | 0.388947 | ||||||||
\(373\) | −12191.6 | −1.69238 | −0.846190 | − | 0.532882i | \(-0.821109\pi\) | ||||
−0.846190 | + | 0.532882i | \(0.821109\pi\) | |||||||
\(374\) | 13790.8 | 1.90670 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3834.29 | −0.525900 | ||||||||
\(377\) | 9773.32 | 1.33515 | ||||||||
\(378\) | −9356.50 | −1.27314 | ||||||||
\(379\) | 2267.64 | 0.307337 | 0.153668 | − | 0.988122i | \(-0.450891\pi\) | ||||
0.153668 | + | 0.988122i | \(0.450891\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10198.8 | 1.37139 | ||||||||
\(382\) | 2565.29 | 0.343590 | ||||||||
\(383\) | 7320.76 | 0.976693 | 0.488346 | − | 0.872650i | \(-0.337600\pi\) | ||||
0.488346 | + | 0.872650i | \(0.337600\pi\) | |||||||
\(384\) | −680.125 | −0.0903841 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1122.90 | −0.148067 | ||||||||
\(387\) | 73.2507 | 0.00962155 | ||||||||
\(388\) | 5274.82 | 0.690177 | ||||||||
\(389\) | −3099.78 | −0.404024 | −0.202012 | − | 0.979383i | \(-0.564748\pi\) | ||||
−0.202012 | + | 0.979383i | \(0.564748\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2688.26 | −0.347701 | ||||||||
\(392\) | −6596.54 | −0.849938 | ||||||||
\(393\) | −14496.1 | −1.86064 | ||||||||
\(394\) | −9198.70 | −1.17620 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −290.970 | −0.0369237 | ||||||||
\(397\) | 6476.52 | 0.818759 | 0.409380 | − | 0.912364i | \(-0.365745\pi\) | ||||
0.409380 | + | 0.912364i | \(0.365745\pi\) | |||||||
\(398\) | −662.217 | −0.0834019 | ||||||||
\(399\) | 6359.89 | 0.797977 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9038.72 | 1.12562 | 0.562808 | − | 0.826588i | \(-0.309721\pi\) | ||||
0.562808 | + | 0.826588i | \(0.309721\pi\) | |||||||
\(402\) | −118.076 | −0.0146495 | ||||||||
\(403\) | −7488.06 | −0.925576 | ||||||||
\(404\) | −5810.25 | −0.715522 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11711.4 | −1.43160 | ||||||||
\(407\) | −19223.2 | −2.34118 | ||||||||
\(408\) | −4968.34 | −0.602866 | ||||||||
\(409\) | 1463.62 | 0.176948 | 0.0884738 | − | 0.996079i | \(-0.471801\pi\) | ||||
0.0884738 | + | 0.996079i | \(0.471801\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7960.36 | −0.955366 | ||||||||
\(412\) | −1924.32 | −0.230108 | ||||||||
\(413\) | −16939.3 | −2.01823 | ||||||||
\(414\) | 56.7189 | 0.00673329 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1824.96 | 0.215087 | ||||||||
\(417\) | −16312.9 | −1.91570 | ||||||||
\(418\) | −4133.12 | −0.483630 | ||||||||
\(419\) | −3240.74 | −0.377853 | −0.188926 | − | 0.981991i | \(-0.560501\pi\) | ||||
−0.188926 | + | 0.981991i | \(0.560501\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11983.1 | 1.38722 | 0.693608 | − | 0.720352i | \(-0.256020\pi\) | ||||
0.693608 | + | 0.720352i | \(0.256020\pi\) | |||||||
\(422\) | 7898.50 | 0.911121 | ||||||||
\(423\) | 590.969 | 0.0679289 | ||||||||
\(424\) | 1847.10 | 0.211564 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3751.78 | 0.426700 | ||||||||
\(427\) | −9157.30 | −1.03783 | ||||||||
\(428\) | 706.074 | 0.0797415 | ||||||||
\(429\) | 17877.2 | 2.01194 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7554.30 | −0.844265 | −0.422132 | − | 0.906534i | \(-0.638718\pi\) | ||||
−0.422132 | + | 0.906534i | \(0.638718\pi\) | |||||||
\(432\) | −2190.60 | −0.243970 | ||||||||
\(433\) | 13051.5 | 1.44854 | 0.724268 | − | 0.689519i | \(-0.242178\pi\) | ||||
0.724268 | + | 0.689519i | \(0.242178\pi\) | |||||||
\(434\) | 8972.98 | 0.992435 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1344.12 | −0.147641 | ||||||||
\(437\) | 805.671 | 0.0881933 | ||||||||
\(438\) | −4956.70 | −0.540731 | ||||||||
\(439\) | −6821.34 | −0.741606 | −0.370803 | − | 0.928712i | \(-0.620917\pi\) | ||||
−0.370803 | + | 0.928712i | \(0.620917\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1016.71 | 0.109784 | ||||||||
\(442\) | 13331.4 | 1.43464 | ||||||||
\(443\) | 10760.1 | 1.15402 | 0.577008 | − | 0.816739i | \(-0.304220\pi\) | ||||
0.577008 | + | 0.816739i | \(0.304220\pi\) | |||||||
\(444\) | 6925.44 | 0.740240 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7184.28 | 0.762748 | ||||||||
\(447\) | −12999.7 | −1.37554 | ||||||||
\(448\) | −2186.86 | −0.230624 | ||||||||
\(449\) | 7503.52 | 0.788671 | 0.394335 | − | 0.918967i | \(-0.370975\pi\) | ||||
0.394335 | + | 0.918967i | \(0.370975\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4269.92 | 0.445815 | ||||||||
\(452\) | 4563.57 | 0.474895 | ||||||||
\(453\) | 7431.80 | 0.770809 | ||||||||
\(454\) | 6699.01 | 0.692512 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1489.01 | 0.152915 | ||||||||
\(457\) | 18746.2 | 1.91884 | 0.959421 | − | 0.281977i | \(-0.0909903\pi\) | ||||
0.959421 | + | 0.281977i | \(0.0909903\pi\) | |||||||
\(458\) | −5527.48 | −0.563935 | ||||||||
\(459\) | −16002.4 | −1.62729 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3461.92 | −0.349756 | −0.174878 | − | 0.984590i | \(-0.555953\pi\) | ||||
−0.174878 | + | 0.984590i | \(0.555953\pi\) | |||||||
\(462\) | −21422.4 | −2.15727 | ||||||||
\(463\) | −12567.6 | −1.26148 | −0.630741 | − | 0.775993i | \(-0.717249\pi\) | ||||
−0.630741 | + | 0.775993i | \(0.717249\pi\) | |||||||
\(464\) | −2741.94 | −0.274335 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4170.35 | −0.414566 | ||||||||
\(467\) | 15137.8 | 1.49999 | 0.749995 | − | 0.661443i | \(-0.230056\pi\) | ||||
0.749995 | + | 0.661443i | \(0.230056\pi\) | |||||||
\(468\) | −281.277 | −0.0277821 | ||||||||
\(469\) | −379.661 | −0.0373797 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8660.01 | −0.847202 | ||||||||
\(472\) | −3965.92 | −0.386751 | ||||||||
\(473\) | −3504.77 | −0.340696 | ||||||||
\(474\) | 8224.91 | 0.797010 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −15975.1 | −1.53827 | ||||||||
\(477\) | −284.689 | −0.0273270 | ||||||||
\(478\) | −9527.69 | −0.911687 | ||||||||
\(479\) | 10179.6 | 0.971021 | 0.485511 | − | 0.874231i | \(-0.338634\pi\) | ||||
0.485511 | + | 0.874231i | \(0.338634\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18582.8 | −1.76155 | ||||||||
\(482\) | −13857.8 | −1.30956 | ||||||||
\(483\) | 4175.88 | 0.393393 | ||||||||
\(484\) | 8597.79 | 0.807456 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 691.419 | 0.0645337 | ||||||||
\(487\) | 10705.5 | 0.996123 | 0.498061 | − | 0.867142i | \(-0.334045\pi\) | ||||
0.498061 | + | 0.867142i | \(0.334045\pi\) | |||||||
\(488\) | −2143.96 | −0.198878 | ||||||||
\(489\) | −1110.62 | −0.102707 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1389.39 | 0.127704 | 0.0638518 | − | 0.997959i | \(-0.479661\pi\) | ||||
0.0638518 | + | 0.997959i | \(0.479661\pi\) | |||||||
\(492\) | −1538.30 | −0.140959 | ||||||||
\(493\) | −20030.0 | −1.82983 | ||||||||
\(494\) | −3995.43 | −0.363893 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2100.80 | 0.190179 | ||||||||
\(497\) | 12063.4 | 1.08877 | ||||||||
\(498\) | −238.775 | −0.0214855 | ||||||||
\(499\) | 6024.03 | 0.540426 | 0.270213 | − | 0.962801i | \(-0.412906\pi\) | ||||
0.270213 | + | 0.962801i | \(0.412906\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4736.33 | 0.422363 | ||||||||
\(502\) | −9437.82 | −0.839104 | ||||||||
\(503\) | 897.694 | 0.0795749 | 0.0397875 | − | 0.999208i | \(-0.487332\pi\) | ||||
0.0397875 | + | 0.999208i | \(0.487332\pi\) | |||||||
\(504\) | 337.055 | 0.0297890 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2713.78 | −0.238424 | ||||||||
\(507\) | 5607.98 | 0.491241 | ||||||||
\(508\) | 7677.69 | 0.670556 | ||||||||
\(509\) | −2501.06 | −0.217795 | −0.108897 | − | 0.994053i | \(-0.534732\pi\) | ||||
−0.108897 | + | 0.994053i | \(0.534732\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15937.7 | −1.37973 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 4795.92 | 0.412759 | ||||||||
\(514\) | −15780.5 | −1.35418 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1262.64 | 0.107722 | ||||||||
\(517\) | −28275.6 | −2.40534 | ||||||||
\(518\) | 22267.9 | 1.88880 | ||||||||
\(519\) | 6370.80 | 0.538819 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2231.18 | −0.187619 | −0.0938097 | − | 0.995590i | \(-0.529905\pi\) | ||||
−0.0938097 | + | 0.995590i | \(0.529905\pi\) | |||||||
\(522\) | 422.609 | 0.0354350 | ||||||||
\(523\) | 19156.5 | 1.60163 | 0.800816 | − | 0.598910i | \(-0.204399\pi\) | ||||
0.800816 | + | 0.598910i | \(0.204399\pi\) | |||||||
\(524\) | −10912.7 | −0.909778 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −259.018 | −0.0214709 | ||||||||
\(527\) | 15346.5 | 1.26851 | ||||||||
\(528\) | −5015.52 | −0.413395 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 611.258 | 0.0499554 | ||||||||
\(532\) | 4787.75 | 0.390179 | ||||||||
\(533\) | 4127.68 | 0.335440 | ||||||||
\(534\) | −12463.9 | −1.01005 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −88.8883 | −0.00716304 | ||||||||
\(537\) | −10592.2 | −0.851187 | ||||||||
\(538\) | −11251.5 | −0.901648 | ||||||||
\(539\) | −48645.6 | −3.88741 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3507.07 | −0.278708 | −0.139354 | − | 0.990243i | \(-0.544503\pi\) | ||||
−0.139354 | + | 0.990243i | \(0.544503\pi\) | |||||||
\(542\) | −10016.4 | −0.793801 | ||||||||
\(543\) | −10437.9 | −0.824922 | ||||||||
\(544\) | −3740.18 | −0.294777 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −20708.7 | −1.62317 | ||||||||
\(547\) | 18849.4 | 1.47339 | 0.736694 | − | 0.676227i | \(-0.236386\pi\) | ||||
0.736694 | + | 0.676227i | \(0.236386\pi\) | |||||||
\(548\) | −5992.58 | −0.467136 | ||||||||
\(549\) | 330.443 | 0.0256885 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6003.00 | 0.464132 | ||||||||
\(552\) | 977.679 | 0.0753855 | ||||||||
\(553\) | 26446.2 | 2.03365 | ||||||||
\(554\) | 12382.9 | 0.949635 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12280.4 | −0.936700 | ||||||||
\(557\) | 532.356 | 0.0404966 | 0.0202483 | − | 0.999795i | \(-0.493554\pi\) | ||||
0.0202483 | + | 0.999795i | \(0.493554\pi\) | |||||||
\(558\) | −323.792 | −0.0245649 | ||||||||
\(559\) | −3388.01 | −0.256347 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −36638.6 | −2.75737 | ||||||||
\(562\) | −15478.3 | −1.16176 | ||||||||
\(563\) | 820.550 | 0.0614246 | 0.0307123 | − | 0.999528i | \(-0.490222\pi\) | ||||
0.0307123 | + | 0.999528i | \(0.490222\pi\) | |||||||
\(564\) | 10186.7 | 0.760527 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8403.96 | −0.624107 | ||||||||
\(567\) | 25995.3 | 1.92540 | ||||||||
\(568\) | 2824.35 | 0.208639 | ||||||||
\(569\) | 24200.5 | 1.78302 | 0.891508 | − | 0.453006i | \(-0.149648\pi\) | ||||
0.891508 | + | 0.453006i | \(0.149648\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18192.0 | 1.33329 | 0.666646 | − | 0.745374i | \(-0.267729\pi\) | ||||
0.666646 | + | 0.745374i | \(0.267729\pi\) | |||||||
\(572\) | 13458.0 | 0.983756 | ||||||||
\(573\) | −6815.29 | −0.496881 | ||||||||
\(574\) | −4946.21 | −0.359671 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 78.9133 | 0.00570843 | ||||||||
\(577\) | −21178.1 | −1.52800 | −0.763998 | − | 0.645218i | \(-0.776766\pi\) | ||||
−0.763998 | + | 0.645218i | \(0.776766\pi\) | |||||||
\(578\) | −17496.2 | −1.25907 | ||||||||
\(579\) | 2983.24 | 0.214127 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −767.752 | −0.0548223 | ||||||||
\(582\) | −14013.8 | −0.998096 | ||||||||
\(583\) | 13621.3 | 0.967641 | ||||||||
\(584\) | −3731.42 | −0.264396 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6587.40 | 0.464374 | ||||||||
\(587\) | −10093.9 | −0.709745 | −0.354873 | − | 0.934915i | \(-0.615476\pi\) | ||||
−0.354873 | + | 0.934915i | \(0.615476\pi\) | |||||||
\(588\) | 17525.3 | 1.22913 | ||||||||
\(589\) | −4599.34 | −0.321753 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24438.5 | 1.70096 | ||||||||
\(592\) | 5213.49 | 0.361948 | ||||||||
\(593\) | −14438.3 | −0.999851 | −0.499926 | − | 0.866068i | \(-0.666639\pi\) | ||||
−0.499926 | + | 0.866068i | \(0.666639\pi\) | |||||||
\(594\) | −16154.4 | −1.11586 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9786.25 | −0.672585 | ||||||||
\(597\) | 1759.34 | 0.120611 | ||||||||
\(598\) | −2623.38 | −0.179395 | ||||||||
\(599\) | 3466.27 | 0.236440 | 0.118220 | − | 0.992987i | \(-0.462281\pi\) | ||||
0.118220 | + | 0.992987i | \(0.462281\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12108.7 | 0.821839 | 0.410919 | − | 0.911672i | \(-0.365208\pi\) | ||||
0.410919 | + | 0.911672i | \(0.365208\pi\) | |||||||
\(602\) | 4059.87 | 0.274864 | ||||||||
\(603\) | 13.7001 | 0.000925228 0 | ||||||||
\(604\) | 5594.68 | 0.376895 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 15436.3 | 1.03475 | ||||||||
\(607\) | −5997.00 | −0.401006 | −0.200503 | − | 0.979693i | \(-0.564258\pi\) | ||||
−0.200503 | + | 0.979693i | \(0.564258\pi\) | |||||||
\(608\) | 1120.93 | 0.0747695 | ||||||||
\(609\) | 31114.2 | 2.07029 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27333.7 | −1.80983 | ||||||||
\(612\) | 576.465 | 0.0380755 | ||||||||
\(613\) | −7989.11 | −0.526390 | −0.263195 | − | 0.964743i | \(-0.584776\pi\) | ||||
−0.263195 | + | 0.964743i | \(0.584776\pi\) | |||||||
\(614\) | −2177.34 | −0.143111 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −16126.8 | −1.05482 | ||||||||
\(617\) | −53.6752 | −0.00350224 | −0.00175112 | − | 0.999998i | \(-0.500557\pi\) | ||||
−0.00175112 | + | 0.999998i | \(0.500557\pi\) | |||||||
\(618\) | 5112.41 | 0.332769 | ||||||||
\(619\) | −40.1805 | −0.00260903 | −0.00130452 | − | 0.999999i | \(-0.500415\pi\) | ||||
−0.00130452 | + | 0.999999i | \(0.500415\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3148.98 | 0.203485 | ||||||||
\(622\) | −7707.16 | −0.496831 | ||||||||
\(623\) | −40076.2 | −2.57723 | ||||||||
\(624\) | −4848.44 | −0.311047 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17069.6 | 1.08984 | ||||||||
\(627\) | 10980.6 | 0.699399 | ||||||||
\(628\) | −6519.28 | −0.414248 | ||||||||
\(629\) | 38084.8 | 2.41421 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9418.81 | −0.594227 | −0.297113 | − | 0.954842i | \(-0.596024\pi\) | ||||
−0.297113 | + | 0.954842i | \(0.596024\pi\) | |||||||
\(632\) | 6191.74 | 0.389706 | ||||||||
\(633\) | −20984.2 | −1.31761 | ||||||||
\(634\) | −8127.73 | −0.509138 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4907.25 | −0.305952 | ||||||||
\(637\) | −47025.1 | −2.92497 | ||||||||
\(638\) | −20220.2 | −1.25474 | ||||||||
\(639\) | −435.310 | −0.0269493 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 991.573 | 0.0610995 | 0.0305497 | − | 0.999533i | \(-0.490274\pi\) | ||||
0.0305497 | + | 0.999533i | \(0.490274\pi\) | |||||||
\(642\) | −1875.85 | −0.115318 | ||||||||
\(643\) | 23370.9 | 1.43337 | 0.716687 | − | 0.697395i | \(-0.245657\pi\) | ||||
0.716687 | + | 0.697395i | \(0.245657\pi\) | |||||||
\(644\) | 3143.61 | 0.192353 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8188.47 | 0.498717 | ||||||||
\(647\) | 17039.2 | 1.03536 | 0.517682 | − | 0.855573i | \(-0.326795\pi\) | ||||
0.517682 | + | 0.855573i | \(0.326795\pi\) | |||||||
\(648\) | 6086.17 | 0.368962 | ||||||||
\(649\) | −29246.4 | −1.76891 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23838.9 | −1.43520 | ||||||||
\(652\) | −836.075 | −0.0502197 | ||||||||
\(653\) | −31674.7 | −1.89820 | −0.949102 | − | 0.314968i | \(-0.898006\pi\) | ||||
−0.949102 | + | 0.314968i | \(0.898006\pi\) | |||||||
\(654\) | 3570.97 | 0.213510 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1158.04 | −0.0689233 | ||||||||
\(657\) | 575.114 | 0.0341512 | ||||||||
\(658\) | 32754.1 | 1.94056 | ||||||||
\(659\) | 25107.8 | 1.48416 | 0.742080 | − | 0.670311i | \(-0.233839\pi\) | ||||
0.742080 | + | 0.670311i | \(0.233839\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21628.9 | −1.27272 | −0.636358 | − | 0.771394i | \(-0.719560\pi\) | ||||
−0.636358 | + | 0.771394i | \(0.719560\pi\) | |||||||
\(662\) | 15056.9 | 0.883995 | ||||||||
\(663\) | −35418.1 | −2.07470 | ||||||||
\(664\) | −179.751 | −0.0105055 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −803.542 | −0.0467517 | ||||||||
\(667\) | 3941.54 | 0.228811 | ||||||||
\(668\) | 3565.52 | 0.206518 | ||||||||
\(669\) | −19086.8 | −1.10304 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15810.4 | −0.909621 | ||||||||
\(672\) | 5809.91 | 0.333515 | ||||||||
\(673\) | −21063.2 | −1.20643 | −0.603214 | − | 0.797579i | \(-0.706114\pi\) | ||||
−0.603214 | + | 0.797579i | \(0.706114\pi\) | |||||||
\(674\) | −10152.4 | −0.580204 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4221.71 | 0.240197 | ||||||||
\(677\) | −1518.27 | −0.0861921 | −0.0430960 | − | 0.999071i | \(-0.513722\pi\) | ||||
−0.0430960 | + | 0.999071i | \(0.513722\pi\) | |||||||
\(678\) | −12124.2 | −0.686767 | ||||||||
\(679\) | −45059.8 | −2.54674 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17797.5 | −1.00147 | ||||||||
\(682\) | 15492.2 | 0.869834 | ||||||||
\(683\) | −27013.3 | −1.51337 | −0.756687 | − | 0.653777i | \(-0.773183\pi\) | ||||
−0.756687 | + | 0.653777i | \(0.773183\pi\) | |||||||
\(684\) | −172.767 | −0.00965775 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 32910.0 | 1.83165 | ||||||||
\(687\) | 14685.1 | 0.815532 | ||||||||
\(688\) | 950.521 | 0.0526719 | ||||||||
\(689\) | 13167.5 | 0.728073 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29988.3 | −1.65095 | −0.825477 | − | 0.564435i | \(-0.809094\pi\) | ||||
−0.825477 | + | 0.564435i | \(0.809094\pi\) | |||||||
\(692\) | 4795.96 | 0.263461 | ||||||||
\(693\) | 2485.59 | 0.136248 | ||||||||
\(694\) | −3275.95 | −0.179183 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7284.62 | 0.396728 | ||||||||
\(697\) | −8459.50 | −0.459722 | ||||||||
\(698\) | 19573.7 | 1.06143 | ||||||||
\(699\) | 11079.5 | 0.599522 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7127.00 | 0.383999 | 0.191999 | − | 0.981395i | \(-0.438503\pi\) | ||||
0.191999 | + | 0.981395i | \(0.438503\pi\) | |||||||
\(702\) | −15616.2 | −0.839596 | ||||||||
\(703\) | −11414.0 | −0.612358 | ||||||||
\(704\) | −3775.70 | −0.202134 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23394.9 | 1.24714 | ||||||||
\(707\) | 49633.6 | 2.64026 | ||||||||
\(708\) | 10536.4 | 0.559298 | ||||||||
\(709\) | 19983.2 | 1.05851 | 0.529257 | − | 0.848462i | \(-0.322471\pi\) | ||||
0.529257 | + | 0.848462i | \(0.322471\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −954.317 | −0.0503371 | ||||||||
\(712\) | −9382.85 | −0.493873 | ||||||||
\(713\) | −3019.91 | −0.158620 | ||||||||
\(714\) | 42441.7 | 2.22456 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7973.84 | −0.416196 | ||||||||
\(717\) | 25312.6 | 1.31843 | ||||||||
\(718\) | −2997.36 | −0.155795 | ||||||||
\(719\) | −10043.0 | −0.520921 | −0.260460 | − | 0.965485i | \(-0.583874\pi\) | ||||
−0.260460 | + | 0.965485i | \(0.583874\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16438.4 | 0.849093 | ||||||||
\(722\) | 11263.9 | 0.580609 | ||||||||
\(723\) | 36816.7 | 1.89381 | ||||||||
\(724\) | −7857.67 | −0.403354 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −22842.1 | −1.16770 | ||||||||
\(727\) | 6665.79 | 0.340056 | 0.170028 | − | 0.985439i | \(-0.445614\pi\) | ||||
0.170028 | + | 0.985439i | \(0.445614\pi\) | |||||||
\(728\) | −15589.6 | −0.793666 | ||||||||
\(729\) | 18703.9 | 0.950257 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6943.59 | 0.351324 | ||||||||
\(732\) | 5695.94 | 0.287606 | ||||||||
\(733\) | 18197.2 | 0.916955 | 0.458477 | − | 0.888706i | \(-0.348395\pi\) | ||||
0.458477 | + | 0.888706i | \(0.348395\pi\) | |||||||
\(734\) | −1500.83 | −0.0754725 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | −655.499 | −0.0327620 | ||||||||
\(738\) | 178.485 | 0.00890261 | ||||||||
\(739\) | −1847.66 | −0.0919722 | −0.0459861 | − | 0.998942i | \(-0.514643\pi\) | ||||
−0.0459861 | + | 0.998942i | \(0.514643\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10614.8 | 0.526242 | ||||||||
\(742\) | −15778.7 | −0.780665 | ||||||||
\(743\) | 25291.0 | 1.24877 | 0.624385 | − | 0.781117i | \(-0.285350\pi\) | ||||
0.624385 | + | 0.781117i | \(0.285350\pi\) | |||||||
\(744\) | −5581.29 | −0.275027 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 24383.2 | 1.19669 | ||||||||
\(747\) | 27.7045 | 0.00135697 | ||||||||
\(748\) | −27581.6 | −1.34824 | ||||||||
\(749\) | −6031.58 | −0.294245 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15059.5 | 0.731731 | 0.365865 | − | 0.930668i | \(-0.380773\pi\) | ||||
0.365865 | + | 0.930668i | \(0.380773\pi\) | |||||||
\(752\) | 7668.58 | 0.371867 | ||||||||
\(753\) | 25073.8 | 1.21347 | ||||||||
\(754\) | −19546.6 | −0.944094 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 18713.0 | 0.900245 | ||||||||
\(757\) | −23808.2 | −1.14310 | −0.571548 | − | 0.820569i | \(-0.693657\pi\) | ||||
−0.571548 | + | 0.820569i | \(0.693657\pi\) | |||||||
\(758\) | −4535.27 | −0.217320 | ||||||||
\(759\) | 7209.81 | 0.344795 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15673.8 | 0.746614 | 0.373307 | − | 0.927708i | \(-0.378224\pi\) | ||||
0.373307 | + | 0.927708i | \(0.378224\pi\) | |||||||
\(762\) | −20397.6 | −0.969721 | ||||||||
\(763\) | 11482.0 | 0.544793 | ||||||||
\(764\) | −5130.57 | −0.242955 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14641.5 | −0.690626 | ||||||||
\(767\) | −28272.1 | −1.33096 | ||||||||
\(768\) | 1360.25 | 0.0639112 | ||||||||
\(769\) | 24213.5 | 1.13545 | 0.567724 | − | 0.823219i | \(-0.307824\pi\) | ||||
0.567724 | + | 0.823219i | \(0.307824\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 41924.6 | 1.95834 | ||||||||
\(772\) | 2245.79 | 0.104699 | ||||||||
\(773\) | 34754.7 | 1.61713 | 0.808563 | − | 0.588410i | \(-0.200246\pi\) | ||||
0.808563 | + | 0.588410i | \(0.200246\pi\) | |||||||
\(774\) | −146.501 | −0.00680347 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −10549.6 | −0.488029 | ||||||||
\(777\) | −59160.0 | −2.73147 | ||||||||
\(778\) | 6199.56 | 0.285688 | ||||||||
\(779\) | 2535.32 | 0.116607 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20827.9 | 0.954266 | ||||||||
\(782\) | 5376.51 | 0.245861 | ||||||||
\(783\) | 23462.8 | 1.07087 | ||||||||
\(784\) | 13193.1 | 0.600997 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 28992.2 | 1.31567 | ||||||||
\(787\) | −7625.98 | −0.345409 | −0.172704 | − | 0.984974i | \(-0.555251\pi\) | ||||
−0.172704 | + | 0.984974i | \(0.555251\pi\) | |||||||
\(788\) | 18397.4 | 0.831701 | ||||||||
\(789\) | 688.142 | 0.0310501 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −38984.0 | −1.75235 | ||||||||
\(792\) | 581.939 | 0.0261090 | ||||||||
\(793\) | −15283.8 | −0.684417 | ||||||||
\(794\) | −12953.0 | −0.578950 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1324.43 | 0.0589740 | ||||||||
\(797\) | 1536.17 | 0.0682733 | 0.0341367 | − | 0.999417i | \(-0.489132\pi\) | ||||
0.0341367 | + | 0.999417i | \(0.489132\pi\) | |||||||
\(798\) | −12719.8 | −0.564255 | ||||||||
\(799\) | 56019.3 | 2.48038 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1446.16 | 0.0637920 | ||||||||
\(802\) | −18077.4 | −0.795931 | ||||||||
\(803\) | −27517.0 | −1.20928 | ||||||||
\(804\) | 236.153 | 0.0103588 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14976.1 | 0.654481 | ||||||||
\(807\) | 29892.3 | 1.30391 | ||||||||
\(808\) | 11620.5 | 0.505950 | ||||||||
\(809\) | −2722.59 | −0.118320 | −0.0591601 | − | 0.998249i | \(-0.518842\pi\) | ||||
−0.0591601 | + | 0.998249i | \(0.518842\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 828.222 | 0.0358604 | 0.0179302 | − | 0.999839i | \(-0.494292\pi\) | ||||
0.0179302 | + | 0.999839i | \(0.494292\pi\) | |||||||
\(812\) | 23422.8 | 1.01229 | ||||||||
\(813\) | 26610.9 | 1.14795 | ||||||||
\(814\) | 38446.4 | 1.65546 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 9936.68 | 0.426291 | ||||||||
\(817\) | −2081.00 | −0.0891125 | ||||||||
\(818\) | −2927.25 | −0.125121 | ||||||||
\(819\) | 2402.79 | 0.102515 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32894.5 | 1.39832 | 0.699162 | − | 0.714963i | \(-0.253556\pi\) | ||||
0.699162 | + | 0.714963i | \(0.253556\pi\) | |||||||
\(822\) | 15920.7 | 0.675546 | ||||||||
\(823\) | −18307.6 | −0.775412 | −0.387706 | − | 0.921783i | \(-0.626733\pi\) | ||||
−0.387706 | + | 0.921783i | \(0.626733\pi\) | |||||||
\(824\) | 3848.64 | 0.162711 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 33878.6 | 1.42710 | ||||||||
\(827\) | −5237.10 | −0.220208 | −0.110104 | − | 0.993920i | \(-0.535118\pi\) | ||||
−0.110104 | + | 0.993920i | \(0.535118\pi\) | |||||||
\(828\) | −113.438 | −0.00476116 | ||||||||
\(829\) | −2235.56 | −0.0936601 | −0.0468300 | − | 0.998903i | \(-0.514912\pi\) | ||||
−0.0468300 | + | 0.998903i | \(0.514912\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −32898.1 | −1.37331 | ||||||||
\(832\) | −3649.92 | −0.152089 | ||||||||
\(833\) | 96376.0 | 4.00868 | ||||||||
\(834\) | 32625.8 | 1.35460 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8266.23 | 0.341978 | ||||||||
\(837\) | −17976.6 | −0.742369 | ||||||||
\(838\) | 6481.47 | 0.267182 | ||||||||
\(839\) | −23031.3 | −0.947711 | −0.473856 | − | 0.880603i | \(-0.657138\pi\) | ||||
−0.473856 | + | 0.880603i | \(0.657138\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4979.16 | 0.204156 | ||||||||
\(842\) | −23966.1 | −0.980910 | ||||||||
\(843\) | 41121.7 | 1.68008 | ||||||||
\(844\) | −15797.0 | −0.644260 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1181.94 | −0.0480330 | ||||||||
\(847\) | −73445.9 | −2.97949 | ||||||||
\(848\) | −3694.19 | −0.149598 | ||||||||
\(849\) | 22327.1 | 0.902550 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7494.39 | −0.301885 | ||||||||
\(852\) | −7503.55 | −0.301722 | ||||||||
\(853\) | −4326.89 | −0.173681 | −0.0868405 | − | 0.996222i | \(-0.527677\pi\) | ||||
−0.0868405 | + | 0.996222i | \(0.527677\pi\) | |||||||
\(854\) | 18314.6 | 0.733856 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1412.15 | −0.0563858 | ||||||||
\(857\) | −20912.6 | −0.833562 | −0.416781 | − | 0.909007i | \(-0.636842\pi\) | ||||
−0.416781 | + | 0.909007i | \(0.636842\pi\) | |||||||
\(858\) | −35754.4 | −1.42265 | ||||||||
\(859\) | −18002.3 | −0.715054 | −0.357527 | − | 0.933903i | \(-0.616380\pi\) | ||||
−0.357527 | + | 0.933903i | \(0.616380\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13140.8 | 0.520136 | ||||||||
\(862\) | 15108.6 | 0.596985 | ||||||||
\(863\) | −37389.4 | −1.47480 | −0.737399 | − | 0.675457i | \(-0.763946\pi\) | ||||
−0.737399 | + | 0.675457i | \(0.763946\pi\) | |||||||
\(864\) | 4381.19 | 0.172513 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −26103.0 | −1.02427 | ||||||||
\(867\) | 46482.8 | 1.82080 | ||||||||
\(868\) | −17946.0 | −0.701758 | ||||||||
\(869\) | 45660.4 | 1.78242 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −633.663 | −0.0246508 | ||||||||
\(872\) | 2688.23 | 0.104398 | ||||||||
\(873\) | 1625.99 | 0.0630372 | ||||||||
\(874\) | −1611.34 | −0.0623621 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9913.39 | 0.382355 | ||||||||
\(877\) | −3952.88 | −0.152200 | −0.0760999 | − | 0.997100i | \(-0.524247\pi\) | ||||
−0.0760999 | + | 0.997100i | \(0.524247\pi\) | |||||||
\(878\) | 13642.7 | 0.524395 | ||||||||
\(879\) | −17501.0 | −0.671552 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51900.7 | 1.98477 | 0.992383 | − | 0.123188i | \(-0.0393119\pi\) | ||||
0.992383 | + | 0.123188i | \(0.0393119\pi\) | |||||||
\(882\) | −2033.42 | −0.0776289 | ||||||||
\(883\) | 8033.47 | 0.306170 | 0.153085 | − | 0.988213i | \(-0.451079\pi\) | ||||
0.153085 | + | 0.988213i | \(0.451079\pi\) | |||||||
\(884\) | −26662.8 | −1.01444 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21520.2 | −0.816012 | ||||||||
\(887\) | 16089.7 | 0.609062 | 0.304531 | − | 0.952502i | \(-0.401500\pi\) | ||||
0.304531 | + | 0.952502i | \(0.401500\pi\) | |||||||
\(888\) | −13850.9 | −0.523429 | ||||||||
\(889\) | −65586.0 | −2.47434 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 44881.9 | 1.68754 | ||||||||
\(892\) | −14368.6 | −0.539344 | ||||||||
\(893\) | −16789.0 | −0.629141 | ||||||||
\(894\) | 25999.5 | 0.972655 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4373.72 | 0.163076 | ||||||||
\(897\) | 6969.64 | 0.259431 | ||||||||
\(898\) | −15007.0 | −0.557675 | ||||||||
\(899\) | −22501.1 | −0.834766 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26986.2 | −0.997827 | ||||||||
\(902\) | −8539.83 | −0.315239 | ||||||||
\(903\) | −10786.0 | −0.397493 | ||||||||
\(904\) | −9127.15 | −0.335801 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −14863.6 | −0.545044 | ||||||||
\(907\) | 10734.2 | 0.392969 | 0.196485 | − | 0.980507i | \(-0.437047\pi\) | ||||
0.196485 | + | 0.980507i | \(0.437047\pi\) | |||||||
\(908\) | −13398.0 | −0.489680 | ||||||||
\(909\) | −1791.04 | −0.0653521 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7368.29 | 0.267972 | 0.133986 | − | 0.990983i | \(-0.457222\pi\) | ||||
0.133986 | + | 0.990983i | \(0.457222\pi\) | |||||||
\(912\) | −2978.03 | −0.108128 | ||||||||
\(913\) | −1325.55 | −0.0480498 | ||||||||
\(914\) | −37492.4 | −1.35683 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11055.0 | 0.398763 | ||||||||
\(917\) | 93221.0 | 3.35706 | ||||||||
\(918\) | 32004.8 | 1.15067 | ||||||||
\(919\) | −12106.3 | −0.434549 | −0.217275 | − | 0.976111i | \(-0.569717\pi\) | ||||
−0.217275 | + | 0.976111i | \(0.569717\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5784.62 | 0.206960 | ||||||||
\(922\) | 6923.83 | 0.247315 | ||||||||
\(923\) | 20134.1 | 0.718008 | ||||||||
\(924\) | 42844.7 | 1.52542 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 25135.2 | 0.892003 | ||||||||
\(927\) | −593.181 | −0.0210169 | ||||||||
\(928\) | 5483.89 | 0.193984 | ||||||||
\(929\) | 14622.7 | 0.516421 | 0.258210 | − | 0.966089i | \(-0.416867\pi\) | ||||
0.258210 | + | 0.966089i | \(0.416867\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28883.9 | −1.01679 | ||||||||
\(932\) | 8340.70 | 0.293142 | ||||||||
\(933\) | 20475.9 | 0.718490 | ||||||||
\(934\) | −30275.7 | −1.06065 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 562.554 | 0.0196449 | ||||||||
\(937\) | −54950.3 | −1.91585 | −0.957924 | − | 0.287023i | \(-0.907334\pi\) | ||||
−0.957924 | + | 0.287023i | \(0.907334\pi\) | |||||||
\(938\) | 759.321 | 0.0264315 | ||||||||
\(939\) | −45349.4 | −1.57606 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36477.3 | 1.26368 | 0.631841 | − | 0.775098i | \(-0.282299\pi\) | ||||
0.631841 | + | 0.775098i | \(0.282299\pi\) | |||||||
\(942\) | 17320.0 | 0.599062 | ||||||||
\(943\) | 1664.68 | 0.0574860 | ||||||||
\(944\) | 7931.85 | 0.273474 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7009.53 | 0.240909 | ||||||||
\(947\) | 20311.8 | 0.696985 | 0.348492 | − | 0.937312i | \(-0.386694\pi\) | ||||
0.348492 | + | 0.937312i | \(0.386694\pi\) | |||||||
\(948\) | −16449.8 | −0.563571 | ||||||||
\(949\) | −26600.4 | −0.909888 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21593.2 | 0.736287 | ||||||||
\(952\) | 31950.2 | 1.08772 | ||||||||
\(953\) | −4320.54 | −0.146858 | −0.0734292 | − | 0.997300i | \(-0.523394\pi\) | ||||
−0.0734292 | + | 0.997300i | \(0.523394\pi\) | |||||||
\(954\) | 569.377 | 0.0193231 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 19055.4 | 0.644660 | ||||||||
\(957\) | 53719.8 | 1.81454 | ||||||||
\(958\) | −20359.3 | −0.686616 | ||||||||
\(959\) | 51191.2 | 1.72372 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12551.2 | −0.421310 | ||||||||
\(962\) | 37165.7 | 1.24560 | ||||||||
\(963\) | 217.651 | 0.00728318 | ||||||||
\(964\) | 27715.7 | 0.925998 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8351.75 | −0.278171 | ||||||||
\(967\) | −19455.1 | −0.646986 | −0.323493 | − | 0.946231i | \(-0.604857\pi\) | ||||
−0.323493 | + | 0.946231i | \(0.604857\pi\) | |||||||
\(968\) | −17195.6 | −0.570957 | ||||||||
\(969\) | −21754.6 | −0.721217 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19512.5 | −0.644888 | −0.322444 | − | 0.946588i | \(-0.604504\pi\) | ||||
−0.322444 | + | 0.946588i | \(0.604504\pi\) | |||||||
\(972\) | −1382.84 | −0.0456322 | ||||||||
\(973\) | 104904. | 3.45641 | ||||||||
\(974\) | −21411.0 | −0.704365 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4287.92 | 0.140628 | ||||||||
\(977\) | 23683.1 | 0.775526 | 0.387763 | − | 0.921759i | \(-0.373248\pi\) | ||||
0.387763 | + | 0.921759i | \(0.373248\pi\) | |||||||
\(978\) | 2221.23 | 0.0726249 | ||||||||
\(979\) | −69193.1 | −2.25886 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −414.331 | −0.0134848 | ||||||||
\(982\) | −2778.79 | −0.0903001 | ||||||||
\(983\) | −19378.5 | −0.628767 | −0.314384 | − | 0.949296i | \(-0.601798\pi\) | ||||
−0.314384 | + | 0.949296i | \(0.601798\pi\) | |||||||
\(984\) | 3076.60 | 0.0996731 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 40060.0 | 1.29388 | ||||||||
\(987\) | −87019.1 | −2.80633 | ||||||||
\(988\) | 7990.87 | 0.257311 | ||||||||
\(989\) | −1366.37 | −0.0439314 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2734.03 | 0.0876380 | 0.0438190 | − | 0.999039i | \(-0.486048\pi\) | ||||
0.0438190 | + | 0.999039i | \(0.486048\pi\) | |||||||
\(992\) | −4201.61 | −0.134477 | ||||||||
\(993\) | −40002.3 | −1.27838 | ||||||||
\(994\) | −24126.8 | −0.769874 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 477.550 | 0.0151925 | ||||||||
\(997\) | 35626.3 | 1.13169 | 0.565846 | − | 0.824511i | \(-0.308550\pi\) | ||||
0.565846 | + | 0.824511i | \(0.308550\pi\) | |||||||
\(998\) | −12048.1 | −0.382139 | ||||||||
\(999\) | −44611.9 | −1.41287 |
(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 | 1150.4.a.s.1.4 | ✓ | 5 | |
5.2 | odd | 4 | 1150.4.b.p.599.2 | 10 | |||
5.3 | odd | 4 | 1150.4.b.p.599.9 | 10 | |||
5.4 | even | 2 | 1150.4.a.t.1.2 | yes | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1150.4.a.s.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial | |
1150.4.a.t.1.2 | yes | 5 | 5.4 | even | 2 | ||
1150.4.b.p.599.2 | 10 | 5.2 | odd | 4 | |||
1150.4.b.p.599.9 | 10 | 5.3 | odd | 4 |