Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,4,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1859.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(109.684550701\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 5 x^{10} - 64 x^{9} + 268 x^{8} + 1564 x^{7} - 4963 x^{6} - 16942 x^{5} + 37082 x^{4} + 68209 x^{3} - 90926 x^{2} - 1672 x + 16256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 143) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.778412\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.221588 | −0.0783432 | −0.0391716 | − | 0.999232i | \(-0.512472\pi\) | ||||
−0.0391716 | + | 0.999232i | \(0.512472\pi\) | |||||||
\(3\) | −7.13795 | −1.37370 | −0.686849 | − | 0.726800i | \(-0.741007\pi\) | ||||
−0.686849 | + | 0.726800i | \(0.741007\pi\) | |||||||
\(4\) | −7.95090 | −0.993862 | ||||||||
\(5\) | −6.37060 | −0.569803 | −0.284902 | − | 0.958557i | \(-0.591961\pi\) | ||||
−0.284902 | + | 0.958557i | \(0.591961\pi\) | |||||||
\(6\) | 1.58168 | 0.107620 | ||||||||
\(7\) | 23.0480 | 1.24448 | 0.622239 | − | 0.782828i | \(-0.286223\pi\) | ||||
0.622239 | + | 0.782828i | \(0.286223\pi\) | |||||||
\(8\) | 3.53453 | 0.156206 | ||||||||
\(9\) | 23.9503 | 0.887048 | ||||||||
\(10\) | 1.41165 | 0.0446402 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 56.7531 | 1.36527 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −5.10717 | −0.0974963 | ||||||||
\(15\) | 45.4730 | 0.782738 | ||||||||
\(16\) | 62.8240 | 0.981625 | ||||||||
\(17\) | 73.4783 | 1.04830 | 0.524150 | − | 0.851626i | \(-0.324383\pi\) | ||||
0.524150 | + | 0.851626i | \(0.324383\pi\) | |||||||
\(18\) | −5.30710 | −0.0694942 | ||||||||
\(19\) | 12.9866 | 0.156807 | 0.0784037 | − | 0.996922i | \(-0.475018\pi\) | ||||
0.0784037 | + | 0.996922i | \(0.475018\pi\) | |||||||
\(20\) | 50.6520 | 0.566306 | ||||||||
\(21\) | −164.516 | −1.70954 | ||||||||
\(22\) | 2.43747 | 0.0236214 | ||||||||
\(23\) | 132.964 | 1.20543 | 0.602715 | − | 0.797957i | \(-0.294086\pi\) | ||||
0.602715 | + | 0.797957i | \(0.294086\pi\) | |||||||
\(24\) | −25.2293 | −0.214579 | ||||||||
\(25\) | −84.4155 | −0.675324 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 21.7686 | 0.155162 | ||||||||
\(28\) | −183.253 | −1.23684 | ||||||||
\(29\) | 283.903 | 1.81791 | 0.908957 | − | 0.416890i | \(-0.136880\pi\) | ||||
0.908957 | + | 0.416890i | \(0.136880\pi\) | |||||||
\(30\) | −10.0763 | −0.0613222 | ||||||||
\(31\) | 225.356 | 1.30565 | 0.652825 | − | 0.757509i | \(-0.273584\pi\) | ||||
0.652825 | + | 0.757509i | \(0.273584\pi\) | |||||||
\(32\) | −42.1973 | −0.233109 | ||||||||
\(33\) | 78.5174 | 0.414186 | ||||||||
\(34\) | −16.2819 | −0.0821271 | ||||||||
\(35\) | −146.830 | −0.709107 | ||||||||
\(36\) | −190.426 | −0.881604 | ||||||||
\(37\) | 89.8050 | 0.399023 | 0.199511 | − | 0.979895i | \(-0.436064\pi\) | ||||
0.199511 | + | 0.979895i | \(0.436064\pi\) | |||||||
\(38\) | −2.87768 | −0.0122848 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −22.5170 | −0.0890065 | ||||||||
\(41\) | 127.456 | 0.485495 | 0.242747 | − | 0.970090i | \(-0.421951\pi\) | ||||
0.242747 | + | 0.970090i | \(0.421951\pi\) | |||||||
\(42\) | 36.4547 | 0.133931 | ||||||||
\(43\) | −477.108 | −1.69205 | −0.846027 | − | 0.533140i | \(-0.821012\pi\) | ||||
−0.846027 | + | 0.533140i | \(0.821012\pi\) | |||||||
\(44\) | 87.4599 | 0.299661 | ||||||||
\(45\) | −152.578 | −0.505443 | ||||||||
\(46\) | −29.4632 | −0.0944372 | ||||||||
\(47\) | −402.605 | −1.24949 | −0.624745 | − | 0.780829i | \(-0.714797\pi\) | ||||
−0.624745 | + | 0.780829i | \(0.714797\pi\) | |||||||
\(48\) | −448.434 | −1.34846 | ||||||||
\(49\) | 188.212 | 0.548723 | ||||||||
\(50\) | 18.7055 | 0.0529070 | ||||||||
\(51\) | −524.484 | −1.44005 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 533.370 | 1.38234 | 0.691169 | − | 0.722693i | \(-0.257096\pi\) | ||||
0.691169 | + | 0.722693i | \(0.257096\pi\) | |||||||
\(54\) | −4.82366 | −0.0121559 | ||||||||
\(55\) | 70.0766 | 0.171802 | ||||||||
\(56\) | 81.4639 | 0.194394 | ||||||||
\(57\) | −92.6980 | −0.215406 | ||||||||
\(58\) | −62.9095 | −0.142421 | ||||||||
\(59\) | −1.69034 | −0.00372988 | −0.00186494 | − | 0.999998i | \(-0.500594\pi\) | ||||
−0.00186494 | + | 0.999998i | \(0.500594\pi\) | |||||||
\(60\) | −361.551 | −0.777934 | ||||||||
\(61\) | 522.467 | 1.09664 | 0.548320 | − | 0.836269i | \(-0.315268\pi\) | ||||
0.548320 | + | 0.836269i | \(0.315268\pi\) | |||||||
\(62\) | −49.9362 | −0.102289 | ||||||||
\(63\) | 552.007 | 1.10391 | ||||||||
\(64\) | −493.241 | −0.963362 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −17.3985 | −0.0324486 | ||||||||
\(67\) | −873.364 | −1.59251 | −0.796257 | − | 0.604959i | \(-0.793190\pi\) | ||||
−0.796257 | + | 0.604959i | \(0.793190\pi\) | |||||||
\(68\) | −584.218 | −1.04187 | ||||||||
\(69\) | −949.089 | −1.65590 | ||||||||
\(70\) | 32.5357 | 0.0555537 | ||||||||
\(71\) | 253.773 | 0.424188 | 0.212094 | − | 0.977249i | \(-0.431972\pi\) | ||||
0.212094 | + | 0.977249i | \(0.431972\pi\) | |||||||
\(72\) | 84.6530 | 0.138562 | ||||||||
\(73\) | −542.512 | −0.869811 | −0.434905 | − | 0.900476i | \(-0.643218\pi\) | ||||
−0.434905 | + | 0.900476i | \(0.643218\pi\) | |||||||
\(74\) | −19.8997 | −0.0312607 | ||||||||
\(75\) | 602.553 | 0.927692 | ||||||||
\(76\) | −103.255 | −0.155845 | ||||||||
\(77\) | −253.528 | −0.375224 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −139.158 | −0.198183 | −0.0990914 | − | 0.995078i | \(-0.531594\pi\) | ||||
−0.0990914 | + | 0.995078i | \(0.531594\pi\) | |||||||
\(80\) | −400.226 | −0.559333 | ||||||||
\(81\) | −802.041 | −1.10019 | ||||||||
\(82\) | −28.2427 | −0.0380352 | ||||||||
\(83\) | 454.213 | 0.600678 | 0.300339 | − | 0.953832i | \(-0.402900\pi\) | ||||
0.300339 | + | 0.953832i | \(0.402900\pi\) | |||||||
\(84\) | 1308.05 | 1.69904 | ||||||||
\(85\) | −468.100 | −0.597325 | ||||||||
\(86\) | 105.721 | 0.132561 | ||||||||
\(87\) | −2026.49 | −2.49727 | ||||||||
\(88\) | −38.8798 | −0.0470977 | ||||||||
\(89\) | −430.013 | −0.512149 | −0.256074 | − | 0.966657i | \(-0.582429\pi\) | ||||
−0.256074 | + | 0.966657i | \(0.582429\pi\) | |||||||
\(90\) | 33.8094 | 0.0395980 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1057.18 | −1.19803 | ||||||||
\(93\) | −1608.58 | −1.79357 | ||||||||
\(94\) | 89.2125 | 0.0978890 | ||||||||
\(95\) | −82.7326 | −0.0893494 | ||||||||
\(96\) | 301.202 | 0.320222 | ||||||||
\(97\) | −1490.83 | −1.56053 | −0.780263 | − | 0.625452i | \(-0.784915\pi\) | ||||
−0.780263 | + | 0.625452i | \(0.784915\pi\) | |||||||
\(98\) | −41.7055 | −0.0429887 | ||||||||
\(99\) | −263.453 | −0.267455 | ||||||||
\(100\) | 671.179 | 0.671179 | ||||||||
\(101\) | 1293.51 | 1.27435 | 0.637173 | − | 0.770720i | \(-0.280104\pi\) | ||||
0.637173 | + | 0.770720i | \(0.280104\pi\) | |||||||
\(102\) | 116.219 | 0.112818 | ||||||||
\(103\) | 584.488 | 0.559139 | 0.279569 | − | 0.960125i | \(-0.409808\pi\) | ||||
0.279569 | + | 0.960125i | \(0.409808\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1048.06 | 0.974100 | ||||||||
\(106\) | −118.188 | −0.108297 | ||||||||
\(107\) | 1700.46 | 1.53635 | 0.768174 | − | 0.640241i | \(-0.221165\pi\) | ||||
0.768174 | + | 0.640241i | \(0.221165\pi\) | |||||||
\(108\) | −173.080 | −0.154209 | ||||||||
\(109\) | 714.703 | 0.628038 | 0.314019 | − | 0.949417i | \(-0.398324\pi\) | ||||
0.314019 | + | 0.949417i | \(0.398324\pi\) | |||||||
\(110\) | −15.5281 | −0.0134595 | ||||||||
\(111\) | −641.023 | −0.548137 | ||||||||
\(112\) | 1447.97 | 1.22161 | ||||||||
\(113\) | −1022.39 | −0.851132 | −0.425566 | − | 0.904927i | \(-0.639925\pi\) | ||||
−0.425566 | + | 0.904927i | \(0.639925\pi\) | |||||||
\(114\) | 20.5408 | 0.0168756 | ||||||||
\(115\) | −847.059 | −0.686858 | ||||||||
\(116\) | −2257.29 | −1.80676 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.374558 | 0.000292211 0 | ||||||||
\(119\) | 1693.53 | 1.30458 | ||||||||
\(120\) | 160.726 | 0.122268 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −115.772 | −0.0859142 | ||||||||
\(123\) | −909.775 | −0.666924 | ||||||||
\(124\) | −1791.78 | −1.29764 | ||||||||
\(125\) | 1334.10 | 0.954605 | ||||||||
\(126\) | −122.318 | −0.0864839 | ||||||||
\(127\) | 1021.58 | 0.713784 | 0.356892 | − | 0.934146i | \(-0.383836\pi\) | ||||
0.356892 | + | 0.934146i | \(0.383836\pi\) | |||||||
\(128\) | 446.874 | 0.308582 | ||||||||
\(129\) | 3405.57 | 2.32437 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −225.024 | −0.150080 | −0.0750398 | − | 0.997181i | \(-0.523908\pi\) | ||||
−0.0750398 | + | 0.997181i | \(0.523908\pi\) | |||||||
\(132\) | −624.284 | −0.411644 | ||||||||
\(133\) | 299.317 | 0.195143 | ||||||||
\(134\) | 193.527 | 0.124763 | ||||||||
\(135\) | −138.679 | −0.0884117 | ||||||||
\(136\) | 259.711 | 0.163750 | ||||||||
\(137\) | −1654.80 | −1.03197 | −0.515983 | − | 0.856599i | \(-0.672573\pi\) | ||||
−0.515983 | + | 0.856599i | \(0.672573\pi\) | |||||||
\(138\) | 210.307 | 0.129728 | ||||||||
\(139\) | −699.725 | −0.426978 | −0.213489 | − | 0.976945i | \(-0.568483\pi\) | ||||
−0.213489 | + | 0.976945i | \(0.568483\pi\) | |||||||
\(140\) | 1167.43 | 0.704755 | ||||||||
\(141\) | 2873.78 | 1.71642 | ||||||||
\(142\) | −56.2331 | −0.0332323 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1504.65 | 0.870748 | ||||||||
\(145\) | −1808.63 | −1.03585 | ||||||||
\(146\) | 120.214 | 0.0681438 | ||||||||
\(147\) | −1343.45 | −0.753781 | ||||||||
\(148\) | −714.030 | −0.396574 | ||||||||
\(149\) | −1244.63 | −0.684325 | −0.342162 | − | 0.939641i | \(-0.611159\pi\) | ||||
−0.342162 | + | 0.939641i | \(0.611159\pi\) | |||||||
\(150\) | −133.519 | −0.0726783 | ||||||||
\(151\) | −1148.93 | −0.619197 | −0.309598 | − | 0.950867i | \(-0.600195\pi\) | ||||
−0.309598 | + | 0.950867i | \(0.600195\pi\) | |||||||
\(152\) | 45.9016 | 0.0244942 | ||||||||
\(153\) | 1759.83 | 0.929892 | ||||||||
\(154\) | 56.1789 | 0.0293962 | ||||||||
\(155\) | −1435.65 | −0.743964 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2141.94 | 1.08883 | 0.544413 | − | 0.838817i | \(-0.316752\pi\) | ||||
0.544413 | + | 0.838817i | \(0.316752\pi\) | |||||||
\(158\) | 30.8356 | 0.0155263 | ||||||||
\(159\) | −3807.17 | −1.89892 | ||||||||
\(160\) | 268.822 | 0.132826 | ||||||||
\(161\) | 3064.56 | 1.50013 | ||||||||
\(162\) | 177.723 | 0.0861927 | ||||||||
\(163\) | 2952.91 | 1.41895 | 0.709477 | − | 0.704728i | \(-0.248931\pi\) | ||||
0.709477 | + | 0.704728i | \(0.248931\pi\) | |||||||
\(164\) | −1013.39 | −0.482515 | ||||||||
\(165\) | −500.203 | −0.236004 | ||||||||
\(166\) | −100.648 | −0.0470591 | ||||||||
\(167\) | −898.670 | −0.416414 | −0.208207 | − | 0.978085i | \(-0.566763\pi\) | ||||
−0.208207 | + | 0.978085i | \(0.566763\pi\) | |||||||
\(168\) | −581.485 | −0.267039 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 103.725 | 0.0467963 | ||||||||
\(171\) | 311.034 | 0.139096 | ||||||||
\(172\) | 3793.44 | 1.68167 | ||||||||
\(173\) | −2344.10 | −1.03017 | −0.515083 | − | 0.857140i | \(-0.672239\pi\) | ||||
−0.515083 | + | 0.857140i | \(0.672239\pi\) | |||||||
\(174\) | 449.045 | 0.195644 | ||||||||
\(175\) | −1945.61 | −0.840425 | ||||||||
\(176\) | −691.064 | −0.295971 | ||||||||
\(177\) | 12.0655 | 0.00512373 | ||||||||
\(178\) | 95.2857 | 0.0401234 | ||||||||
\(179\) | 1418.35 | 0.592247 | 0.296123 | − | 0.955150i | \(-0.404306\pi\) | ||||
0.296123 | + | 0.955150i | \(0.404306\pi\) | |||||||
\(180\) | 1213.13 | 0.502341 | ||||||||
\(181\) | −3048.87 | −1.25205 | −0.626025 | − | 0.779803i | \(-0.715319\pi\) | ||||
−0.626025 | + | 0.779803i | \(0.715319\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3729.34 | −1.50645 | ||||||||
\(184\) | 469.965 | 0.188295 | ||||||||
\(185\) | −572.111 | −0.227365 | ||||||||
\(186\) | 356.442 | 0.140514 | ||||||||
\(187\) | −808.261 | −0.316074 | ||||||||
\(188\) | 3201.07 | 1.24182 | ||||||||
\(189\) | 501.723 | 0.193095 | ||||||||
\(190\) | 18.3326 | 0.00699991 | ||||||||
\(191\) | 1481.95 | 0.561412 | 0.280706 | − | 0.959794i | \(-0.409431\pi\) | ||||
0.280706 | + | 0.959794i | \(0.409431\pi\) | |||||||
\(192\) | 3520.73 | 1.32337 | ||||||||
\(193\) | 4950.57 | 1.84637 | 0.923187 | − | 0.384352i | \(-0.125575\pi\) | ||||
0.923187 | + | 0.384352i | \(0.125575\pi\) | |||||||
\(194\) | 330.350 | 0.122257 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1496.46 | −0.545356 | ||||||||
\(197\) | −787.234 | −0.284711 | −0.142356 | − | 0.989816i | \(-0.545468\pi\) | ||||
−0.142356 | + | 0.989816i | \(0.545468\pi\) | |||||||
\(198\) | 58.3781 | 0.0209533 | ||||||||
\(199\) | −37.2673 | −0.0132754 | −0.00663770 | − | 0.999978i | \(-0.502113\pi\) | ||||
−0.00663770 | + | 0.999978i | \(0.502113\pi\) | |||||||
\(200\) | −298.369 | −0.105489 | ||||||||
\(201\) | 6234.03 | 2.18763 | ||||||||
\(202\) | −286.626 | −0.0998364 | ||||||||
\(203\) | 6543.41 | 2.26235 | ||||||||
\(204\) | 4170.12 | 1.43121 | ||||||||
\(205\) | −811.971 | −0.276637 | ||||||||
\(206\) | −129.516 | −0.0438047 | ||||||||
\(207\) | 3184.53 | 1.06927 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −142.853 | −0.0472792 | ||||||||
\(210\) | −232.238 | −0.0763141 | ||||||||
\(211\) | 3594.70 | 1.17284 | 0.586420 | − | 0.810007i | \(-0.300537\pi\) | ||||
0.586420 | + | 0.810007i | \(0.300537\pi\) | |||||||
\(212\) | −4240.77 | −1.37385 | ||||||||
\(213\) | −1811.42 | −0.582707 | ||||||||
\(214\) | −376.801 | −0.120362 | ||||||||
\(215\) | 3039.46 | 0.964138 | ||||||||
\(216\) | 76.9417 | 0.0242371 | ||||||||
\(217\) | 5194.02 | 1.62485 | ||||||||
\(218\) | −158.370 | −0.0492025 | ||||||||
\(219\) | 3872.42 | 1.19486 | ||||||||
\(220\) | −557.172 | −0.170748 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 142.043 | 0.0429428 | ||||||||
\(223\) | 5262.76 | 1.58036 | 0.790180 | − | 0.612874i | \(-0.209987\pi\) | ||||
0.790180 | + | 0.612874i | \(0.209987\pi\) | |||||||
\(224\) | −972.564 | −0.290099 | ||||||||
\(225\) | −2021.78 | −0.599045 | ||||||||
\(226\) | 226.548 | 0.0666804 | ||||||||
\(227\) | 645.666 | 0.188786 | 0.0943928 | − | 0.995535i | \(-0.469909\pi\) | ||||
0.0943928 | + | 0.995535i | \(0.469909\pi\) | |||||||
\(228\) | 737.032 | 0.214084 | ||||||||
\(229\) | 2614.26 | 0.754391 | 0.377195 | − | 0.926134i | \(-0.376889\pi\) | ||||
0.377195 | + | 0.926134i | \(0.376889\pi\) | |||||||
\(230\) | 187.698 | 0.0538107 | ||||||||
\(231\) | 1809.67 | 0.515445 | ||||||||
\(232\) | 1003.46 | 0.283968 | ||||||||
\(233\) | 5317.46 | 1.49510 | 0.747551 | − | 0.664205i | \(-0.231230\pi\) | ||||
0.747551 | + | 0.664205i | \(0.231230\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2564.84 | 0.711964 | ||||||||
\(236\) | 13.4397 | 0.00370699 | ||||||||
\(237\) | 993.299 | 0.272244 | ||||||||
\(238\) | −375.266 | −0.102205 | ||||||||
\(239\) | −3337.77 | −0.903357 | −0.451678 | − | 0.892181i | \(-0.649175\pi\) | ||||
−0.451678 | + | 0.892181i | \(0.649175\pi\) | |||||||
\(240\) | 2856.79 | 0.768355 | ||||||||
\(241\) | −3795.52 | −1.01449 | −0.507243 | − | 0.861803i | \(-0.669335\pi\) | ||||
−0.507243 | + | 0.861803i | \(0.669335\pi\) | |||||||
\(242\) | −26.8121 | −0.00712211 | ||||||||
\(243\) | 5137.18 | 1.35617 | ||||||||
\(244\) | −4154.08 | −1.08991 | ||||||||
\(245\) | −1199.02 | −0.312664 | ||||||||
\(246\) | 201.595 | 0.0522489 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 796.527 | 0.203950 | ||||||||
\(249\) | −3242.15 | −0.825151 | ||||||||
\(250\) | −295.621 | −0.0747868 | ||||||||
\(251\) | −2238.10 | −0.562820 | −0.281410 | − | 0.959588i | \(-0.590802\pi\) | ||||
−0.281410 | + | 0.959588i | \(0.590802\pi\) | |||||||
\(252\) | −4388.96 | −1.09714 | ||||||||
\(253\) | −1462.60 | −0.363451 | ||||||||
\(254\) | −226.370 | −0.0559201 | ||||||||
\(255\) | 3341.28 | 0.820544 | ||||||||
\(256\) | 3846.91 | 0.939187 | ||||||||
\(257\) | −5554.35 | −1.34814 | −0.674068 | − | 0.738670i | \(-0.735454\pi\) | ||||
−0.674068 | + | 0.738670i | \(0.735454\pi\) | |||||||
\(258\) | −754.634 | −0.182099 | ||||||||
\(259\) | 2069.83 | 0.496575 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6799.57 | 1.61258 | ||||||||
\(262\) | 49.8626 | 0.0117577 | ||||||||
\(263\) | 2945.49 | 0.690595 | 0.345297 | − | 0.938493i | \(-0.387778\pi\) | ||||
0.345297 | + | 0.938493i | \(0.387778\pi\) | |||||||
\(264\) | 277.522 | 0.0646981 | ||||||||
\(265\) | −3397.88 | −0.787661 | ||||||||
\(266\) | −66.3250 | −0.0152881 | ||||||||
\(267\) | 3069.41 | 0.703538 | ||||||||
\(268\) | 6944.03 | 1.58274 | ||||||||
\(269\) | −4153.67 | −0.941463 | −0.470731 | − | 0.882277i | \(-0.656010\pi\) | ||||
−0.470731 | + | 0.882277i | \(0.656010\pi\) | |||||||
\(270\) | 30.7296 | 0.00692645 | ||||||||
\(271\) | 6141.93 | 1.37674 | 0.688369 | − | 0.725361i | \(-0.258327\pi\) | ||||
0.688369 | + | 0.725361i | \(0.258327\pi\) | |||||||
\(272\) | 4616.20 | 1.02904 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 366.685 | 0.0808475 | ||||||||
\(275\) | 928.571 | 0.203618 | ||||||||
\(276\) | 7546.11 | 1.64573 | ||||||||
\(277\) | 3715.68 | 0.805969 | 0.402984 | − | 0.915207i | \(-0.367973\pi\) | ||||
0.402984 | + | 0.915207i | \(0.367973\pi\) | |||||||
\(278\) | 155.051 | 0.0334508 | ||||||||
\(279\) | 5397.35 | 1.15817 | ||||||||
\(280\) | −518.974 | −0.110766 | ||||||||
\(281\) | 635.949 | 0.135009 | 0.0675045 | − | 0.997719i | \(-0.478496\pi\) | ||||
0.0675045 | + | 0.997719i | \(0.478496\pi\) | |||||||
\(282\) | −636.794 | −0.134470 | ||||||||
\(283\) | 4253.77 | 0.893500 | 0.446750 | − | 0.894659i | \(-0.352581\pi\) | ||||
0.446750 | + | 0.894659i | \(0.352581\pi\) | |||||||
\(284\) | −2017.73 | −0.421585 | ||||||||
\(285\) | 590.541 | 0.122739 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2937.61 | 0.604187 | ||||||||
\(288\) | −1010.64 | −0.206779 | ||||||||
\(289\) | 486.053 | 0.0989321 | ||||||||
\(290\) | 400.771 | 0.0811521 | ||||||||
\(291\) | 10641.5 | 2.14369 | ||||||||
\(292\) | 4313.46 | 0.864472 | ||||||||
\(293\) | 3946.01 | 0.786787 | 0.393394 | − | 0.919370i | \(-0.371301\pi\) | ||||
0.393394 | + | 0.919370i | \(0.371301\pi\) | |||||||
\(294\) | 297.692 | 0.0590536 | ||||||||
\(295\) | 10.7684 | 0.00212530 | ||||||||
\(296\) | 317.418 | 0.0623296 | ||||||||
\(297\) | −239.454 | −0.0467830 | ||||||||
\(298\) | 275.796 | 0.0536122 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4790.84 | −0.921998 | ||||||||
\(301\) | −10996.4 | −2.10572 | ||||||||
\(302\) | 254.589 | 0.0485099 | ||||||||
\(303\) | −9233.00 | −1.75057 | ||||||||
\(304\) | 815.873 | 0.153926 | ||||||||
\(305\) | −3328.42 | −0.624869 | ||||||||
\(306\) | −389.956 | −0.0728507 | ||||||||
\(307\) | −5882.41 | −1.09357 | −0.546786 | − | 0.837272i | \(-0.684149\pi\) | ||||
−0.546786 | + | 0.837272i | \(0.684149\pi\) | |||||||
\(308\) | 2015.78 | 0.372921 | ||||||||
\(309\) | −4172.04 | −0.768088 | ||||||||
\(310\) | 318.123 | 0.0582845 | ||||||||
\(311\) | −2040.41 | −0.372029 | −0.186015 | − | 0.982547i | \(-0.559557\pi\) | ||||
−0.186015 | + | 0.982547i | \(0.559557\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4695.38 | 0.847918 | 0.423959 | − | 0.905681i | \(-0.360640\pi\) | ||||
0.423959 | + | 0.905681i | \(0.360640\pi\) | |||||||
\(314\) | −474.629 | −0.0853021 | ||||||||
\(315\) | −3516.62 | −0.629012 | ||||||||
\(316\) | 1106.43 | 0.196966 | ||||||||
\(317\) | −10244.2 | −1.81504 | −0.907522 | − | 0.420004i | \(-0.862029\pi\) | ||||
−0.907522 | + | 0.420004i | \(0.862029\pi\) | |||||||
\(318\) | 843.622 | 0.148767 | ||||||||
\(319\) | −3122.94 | −0.548122 | ||||||||
\(320\) | 3142.24 | 0.548927 | ||||||||
\(321\) | −12137.8 | −2.11048 | ||||||||
\(322\) | −679.069 | −0.117525 | ||||||||
\(323\) | 954.236 | 0.164381 | ||||||||
\(324\) | 6376.95 | 1.09344 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −654.329 | −0.111165 | ||||||||
\(327\) | −5101.51 | −0.862735 | ||||||||
\(328\) | 450.497 | 0.0758370 | ||||||||
\(329\) | −9279.26 | −1.55496 | ||||||||
\(330\) | 110.839 | 0.0184893 | ||||||||
\(331\) | 6762.25 | 1.12292 | 0.561460 | − | 0.827504i | \(-0.310240\pi\) | ||||
0.561460 | + | 0.827504i | \(0.310240\pi\) | |||||||
\(332\) | −3611.40 | −0.596992 | ||||||||
\(333\) | 2150.86 | 0.353953 | ||||||||
\(334\) | 199.135 | 0.0326232 | ||||||||
\(335\) | 5563.85 | 0.907420 | ||||||||
\(336\) | −10335.5 | −1.67812 | ||||||||
\(337\) | 3074.22 | 0.496923 | 0.248462 | − | 0.968642i | \(-0.420075\pi\) | ||||
0.248462 | + | 0.968642i | \(0.420075\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7297.73 | 1.16920 | ||||||||
\(340\) | 3721.82 | 0.593659 | ||||||||
\(341\) | −2478.92 | −0.393668 | ||||||||
\(342\) | −68.9214 | −0.0108972 | ||||||||
\(343\) | −3567.56 | −0.561603 | ||||||||
\(344\) | −1686.35 | −0.264308 | ||||||||
\(345\) | 6046.27 | 0.943536 | ||||||||
\(346\) | 519.424 | 0.0807064 | ||||||||
\(347\) | −6003.78 | −0.928819 | −0.464409 | − | 0.885621i | \(-0.653733\pi\) | ||||
−0.464409 | + | 0.885621i | \(0.653733\pi\) | |||||||
\(348\) | 16112.4 | 2.48194 | ||||||||
\(349\) | 3081.09 | 0.472570 | 0.236285 | − | 0.971684i | \(-0.424070\pi\) | ||||
0.236285 | + | 0.971684i | \(0.424070\pi\) | |||||||
\(350\) | 431.124 | 0.0658416 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 464.170 | 0.0702851 | ||||||||
\(353\) | −5235.28 | −0.789365 | −0.394683 | − | 0.918817i | \(-0.629145\pi\) | ||||
−0.394683 | + | 0.918817i | \(0.629145\pi\) | |||||||
\(354\) | −2.67358 | −0.000401410 0 | ||||||||
\(355\) | −1616.69 | −0.241704 | ||||||||
\(356\) | 3418.99 | 0.509006 | ||||||||
\(357\) | −12088.3 | −1.79211 | ||||||||
\(358\) | −314.289 | −0.0463985 | ||||||||
\(359\) | −6812.64 | −1.00155 | −0.500776 | − | 0.865577i | \(-0.666952\pi\) | ||||
−0.500776 | + | 0.865577i | \(0.666952\pi\) | |||||||
\(360\) | −539.290 | −0.0789530 | ||||||||
\(361\) | −6690.35 | −0.975411 | ||||||||
\(362\) | 675.593 | 0.0980895 | ||||||||
\(363\) | −863.692 | −0.124882 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3456.12 | 0.495621 | ||||||||
\(366\) | 826.377 | 0.118020 | ||||||||
\(367\) | 3729.39 | 0.530443 | 0.265222 | − | 0.964187i | \(-0.414555\pi\) | ||||
0.265222 | + | 0.964187i | \(0.414555\pi\) | |||||||
\(368\) | 8353.32 | 1.18328 | ||||||||
\(369\) | 3052.61 | 0.430657 | ||||||||
\(370\) | 126.773 | 0.0178125 | ||||||||
\(371\) | 12293.1 | 1.72029 | ||||||||
\(372\) | 12789.7 | 1.78256 | ||||||||
\(373\) | 4450.76 | 0.617833 | 0.308916 | − | 0.951089i | \(-0.400034\pi\) | ||||
0.308916 | + | 0.951089i | \(0.400034\pi\) | |||||||
\(374\) | 179.101 | 0.0247623 | ||||||||
\(375\) | −9522.75 | −1.31134 | ||||||||
\(376\) | −1423.02 | −0.195177 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −111.176 | −0.0151277 | ||||||||
\(379\) | −3667.51 | −0.497065 | −0.248532 | − | 0.968624i | \(-0.579948\pi\) | ||||
−0.248532 | + | 0.968624i | \(0.579948\pi\) | |||||||
\(380\) | 657.799 | 0.0888010 | ||||||||
\(381\) | −7291.98 | −0.980524 | ||||||||
\(382\) | −328.381 | −0.0439828 | ||||||||
\(383\) | −10896.7 | −1.45378 | −0.726889 | − | 0.686755i | \(-0.759035\pi\) | ||||
−0.726889 | + | 0.686755i | \(0.759035\pi\) | |||||||
\(384\) | −3189.77 | −0.423899 | ||||||||
\(385\) | 1615.13 | 0.213804 | ||||||||
\(386\) | −1096.99 | −0.144651 | ||||||||
\(387\) | −11426.9 | −1.50093 | ||||||||
\(388\) | 11853.4 | 1.55095 | ||||||||
\(389\) | −6688.53 | −0.871778 | −0.435889 | − | 0.900000i | \(-0.643566\pi\) | ||||
−0.435889 | + | 0.900000i | \(0.643566\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9769.95 | 1.26365 | ||||||||
\(392\) | 665.241 | 0.0857136 | ||||||||
\(393\) | 1606.21 | 0.206164 | ||||||||
\(394\) | 174.442 | 0.0223052 | ||||||||
\(395\) | 886.516 | 0.112925 | ||||||||
\(396\) | 2094.69 | 0.265814 | ||||||||
\(397\) | 2533.80 | 0.320322 | 0.160161 | − | 0.987091i | \(-0.448799\pi\) | ||||
0.160161 | + | 0.987091i | \(0.448799\pi\) | |||||||
\(398\) | 8.25798 | 0.00104004 | ||||||||
\(399\) | −2136.51 | −0.268068 | ||||||||
\(400\) | −5303.32 | −0.662915 | ||||||||
\(401\) | 14014.4 | 1.74525 | 0.872625 | − | 0.488391i | \(-0.162416\pi\) | ||||
0.872625 | + | 0.488391i | \(0.162416\pi\) | |||||||
\(402\) | −1381.39 | −0.171386 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −10284.6 | −1.26653 | ||||||||
\(405\) | 5109.48 | 0.626894 | ||||||||
\(406\) | −1449.94 | −0.177240 | ||||||||
\(407\) | −987.855 | −0.120310 | ||||||||
\(408\) | −1853.80 | −0.224943 | ||||||||
\(409\) | 6090.96 | 0.736378 | 0.368189 | − | 0.929751i | \(-0.379978\pi\) | ||||
0.368189 | + | 0.929751i | \(0.379978\pi\) | |||||||
\(410\) | 179.923 | 0.0216726 | ||||||||
\(411\) | 11811.9 | 1.41761 | ||||||||
\(412\) | −4647.20 | −0.555707 | ||||||||
\(413\) | −38.9589 | −0.00464175 | ||||||||
\(414\) | −705.653 | −0.0837704 | ||||||||
\(415\) | −2893.60 | −0.342269 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4994.60 | 0.586539 | ||||||||
\(418\) | 31.6545 | 0.00370400 | ||||||||
\(419\) | −454.104 | −0.0529462 | −0.0264731 | − | 0.999650i | \(-0.508428\pi\) | ||||
−0.0264731 | + | 0.999650i | \(0.508428\pi\) | |||||||
\(420\) | −8333.04 | −0.968121 | ||||||||
\(421\) | −3809.92 | −0.441055 | −0.220528 | − | 0.975381i | \(-0.570778\pi\) | ||||
−0.220528 | + | 0.975381i | \(0.570778\pi\) | |||||||
\(422\) | −796.542 | −0.0918840 | ||||||||
\(423\) | −9642.52 | −1.10836 | ||||||||
\(424\) | 1885.21 | 0.215929 | ||||||||
\(425\) | −6202.70 | −0.707942 | ||||||||
\(426\) | 401.389 | 0.0456511 | ||||||||
\(427\) | 12041.8 | 1.36474 | ||||||||
\(428\) | −13520.2 | −1.52692 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −673.508 | −0.0755336 | ||||||||
\(431\) | −12074.5 | −1.34944 | −0.674721 | − | 0.738073i | \(-0.735736\pi\) | ||||
−0.674721 | + | 0.738073i | \(0.735736\pi\) | |||||||
\(432\) | 1367.59 | 0.152311 | ||||||||
\(433\) | 7121.85 | 0.790426 | 0.395213 | − | 0.918590i | \(-0.370671\pi\) | ||||
0.395213 | + | 0.918590i | \(0.370671\pi\) | |||||||
\(434\) | −1150.93 | −0.127296 | ||||||||
\(435\) | 12909.9 | 1.42295 | ||||||||
\(436\) | −5682.53 | −0.624183 | ||||||||
\(437\) | 1726.75 | 0.189020 | ||||||||
\(438\) | −858.082 | −0.0936090 | ||||||||
\(439\) | −9344.80 | −1.01595 | −0.507976 | − | 0.861371i | \(-0.669606\pi\) | ||||
−0.507976 | + | 0.861371i | \(0.669606\pi\) | |||||||
\(440\) | 247.688 | 0.0268365 | ||||||||
\(441\) | 4507.74 | 0.486744 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9584.79 | 1.02796 | 0.513981 | − | 0.857802i | \(-0.328170\pi\) | ||||
0.513981 | + | 0.857802i | \(0.328170\pi\) | |||||||
\(444\) | 5096.71 | 0.544773 | ||||||||
\(445\) | 2739.44 | 0.291824 | ||||||||
\(446\) | −1166.16 | −0.123810 | ||||||||
\(447\) | 8884.14 | 0.940056 | ||||||||
\(448\) | −11368.2 | −1.19888 | ||||||||
\(449\) | −4321.80 | −0.454251 | −0.227125 | − | 0.973866i | \(-0.572933\pi\) | ||||
−0.227125 | + | 0.973866i | \(0.572933\pi\) | |||||||
\(450\) | 448.001 | 0.0469311 | ||||||||
\(451\) | −1402.02 | −0.146382 | ||||||||
\(452\) | 8128.88 | 0.845908 | ||||||||
\(453\) | 8201.01 | 0.850590 | ||||||||
\(454\) | −143.072 | −0.0147901 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −327.644 | −0.0336476 | ||||||||
\(457\) | −16281.7 | −1.66658 | −0.833291 | − | 0.552834i | \(-0.813546\pi\) | ||||
−0.833291 | + | 0.552834i | \(0.813546\pi\) | |||||||
\(458\) | −579.290 | −0.0591014 | ||||||||
\(459\) | 1599.52 | 0.162656 | ||||||||
\(460\) | 6734.88 | 0.682642 | ||||||||
\(461\) | 6835.80 | 0.690618 | 0.345309 | − | 0.938489i | \(-0.387774\pi\) | ||||
0.345309 | + | 0.938489i | \(0.387774\pi\) | |||||||
\(462\) | −401.002 | −0.0403816 | ||||||||
\(463\) | 614.185 | 0.0616492 | 0.0308246 | − | 0.999525i | \(-0.490187\pi\) | ||||
0.0308246 | + | 0.999525i | \(0.490187\pi\) | |||||||
\(464\) | 17835.9 | 1.78451 | ||||||||
\(465\) | 10247.6 | 1.02198 | ||||||||
\(466\) | −1178.29 | −0.117131 | ||||||||
\(467\) | −17077.5 | −1.69218 | −0.846092 | − | 0.533037i | \(-0.821051\pi\) | ||||
−0.846092 | + | 0.533037i | \(0.821051\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20129.3 | −1.98185 | ||||||||
\(470\) | −568.337 | −0.0557775 | ||||||||
\(471\) | −15289.1 | −1.49572 | ||||||||
\(472\) | −5.97454 | −0.000582628 0 | ||||||||
\(473\) | 5248.19 | 0.510173 | ||||||||
\(474\) | −220.103 | −0.0213284 | ||||||||
\(475\) | −1096.27 | −0.105896 | ||||||||
\(476\) | −13465.1 | −1.29658 | ||||||||
\(477\) | 12774.4 | 1.22620 | ||||||||
\(478\) | 739.609 | 0.0707719 | ||||||||
\(479\) | −15654.5 | −1.49326 | −0.746632 | − | 0.665237i | \(-0.768331\pi\) | ||||
−0.746632 | + | 0.665237i | \(0.768331\pi\) | |||||||
\(480\) | −1918.84 | −0.182463 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 841.042 | 0.0794780 | ||||||||
\(483\) | −21874.6 | −2.06073 | ||||||||
\(484\) | −962.059 | −0.0903511 | ||||||||
\(485\) | 9497.48 | 0.889193 | ||||||||
\(486\) | −1138.34 | −0.106247 | ||||||||
\(487\) | −14358.5 | −1.33603 | −0.668014 | − | 0.744149i | \(-0.732855\pi\) | ||||
−0.668014 | + | 0.744149i | \(0.732855\pi\) | |||||||
\(488\) | 1846.67 | 0.171301 | ||||||||
\(489\) | −21077.7 | −1.94922 | ||||||||
\(490\) | 265.689 | 0.0244951 | ||||||||
\(491\) | 9150.12 | 0.841017 | 0.420508 | − | 0.907289i | \(-0.361852\pi\) | ||||
0.420508 | + | 0.907289i | \(0.361852\pi\) | |||||||
\(492\) | 7233.53 | 0.662830 | ||||||||
\(493\) | 20860.7 | 1.90572 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1678.35 | 0.152397 | ||||||||
\(496\) | 14157.8 | 1.28166 | ||||||||
\(497\) | 5848.98 | 0.527892 | ||||||||
\(498\) | 718.421 | 0.0646450 | ||||||||
\(499\) | 11822.2 | 1.06059 | 0.530296 | − | 0.847813i | \(-0.322081\pi\) | ||||
0.530296 | + | 0.847813i | \(0.322081\pi\) | |||||||
\(500\) | −10607.3 | −0.948746 | ||||||||
\(501\) | 6414.66 | 0.572028 | ||||||||
\(502\) | 495.936 | 0.0440931 | ||||||||
\(503\) | −4441.37 | −0.393700 | −0.196850 | − | 0.980434i | \(-0.563071\pi\) | ||||
−0.196850 | + | 0.980434i | \(0.563071\pi\) | |||||||
\(504\) | 1951.09 | 0.172437 | ||||||||
\(505\) | −8240.43 | −0.726127 | ||||||||
\(506\) | 324.095 | 0.0284739 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8122.48 | −0.709403 | ||||||||
\(509\) | 9760.01 | 0.849912 | 0.424956 | − | 0.905214i | \(-0.360290\pi\) | ||||
0.424956 | + | 0.905214i | \(0.360290\pi\) | |||||||
\(510\) | −740.387 | −0.0642841 | ||||||||
\(511\) | −12503.8 | −1.08246 | ||||||||
\(512\) | −4427.42 | −0.382161 | ||||||||
\(513\) | 282.701 | 0.0243305 | ||||||||
\(514\) | 1230.78 | 0.105617 | ||||||||
\(515\) | −3723.54 | −0.318599 | ||||||||
\(516\) | −27077.4 | −2.31011 | ||||||||
\(517\) | 4428.66 | 0.376735 | ||||||||
\(518\) | −458.649 | −0.0389033 | ||||||||
\(519\) | 16732.1 | 1.41514 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15982.5 | 1.34397 | 0.671984 | − | 0.740566i | \(-0.265442\pi\) | ||||
0.671984 | + | 0.740566i | \(0.265442\pi\) | |||||||
\(522\) | −1506.70 | −0.126334 | ||||||||
\(523\) | 502.803 | 0.0420383 | 0.0210191 | − | 0.999779i | \(-0.493309\pi\) | ||||
0.0210191 | + | 0.999779i | \(0.493309\pi\) | |||||||
\(524\) | 1789.14 | 0.149158 | ||||||||
\(525\) | 13887.7 | 1.15449 | ||||||||
\(526\) | −652.684 | −0.0541034 | ||||||||
\(527\) | 16558.8 | 1.36871 | ||||||||
\(528\) | 4932.78 | 0.406575 | ||||||||
\(529\) | 5512.40 | 0.453061 | ||||||||
\(530\) | 752.930 | 0.0617079 | ||||||||
\(531\) | −40.4840 | −0.00330858 | ||||||||
\(532\) | −2379.84 | −0.193945 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −680.144 | −0.0551174 | ||||||||
\(535\) | −10832.9 | −0.875417 | ||||||||
\(536\) | −3086.93 | −0.248759 | ||||||||
\(537\) | −10124.1 | −0.813569 | ||||||||
\(538\) | 920.403 | 0.0737572 | ||||||||
\(539\) | −2070.33 | −0.165446 | ||||||||
\(540\) | 1102.62 | 0.0878691 | ||||||||
\(541\) | −16867.2 | −1.34044 | −0.670220 | − | 0.742163i | \(-0.733800\pi\) | ||||
−0.670220 | + | 0.742163i | \(0.733800\pi\) | |||||||
\(542\) | −1360.98 | −0.107858 | ||||||||
\(543\) | 21762.7 | 1.71994 | ||||||||
\(544\) | −3100.58 | −0.244368 | ||||||||
\(545\) | −4553.08 | −0.357858 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9104.87 | 0.711693 | 0.355846 | − | 0.934544i | \(-0.384193\pi\) | ||||
0.355846 | + | 0.934544i | \(0.384193\pi\) | |||||||
\(548\) | 13157.2 | 1.02563 | ||||||||
\(549\) | 12513.2 | 0.972772 | ||||||||
\(550\) | −205.760 | −0.0159521 | ||||||||
\(551\) | 3686.95 | 0.285062 | ||||||||
\(552\) | −3354.58 | −0.258660 | ||||||||
\(553\) | −3207.31 | −0.246634 | ||||||||
\(554\) | −823.349 | −0.0631422 | ||||||||
\(555\) | 4083.70 | 0.312330 | ||||||||
\(556\) | 5563.44 | 0.424357 | ||||||||
\(557\) | 5185.09 | 0.394433 | 0.197217 | − | 0.980360i | \(-0.436810\pi\) | ||||
0.197217 | + | 0.980360i | \(0.436810\pi\) | |||||||
\(558\) | −1195.99 | −0.0907351 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −9224.43 | −0.696077 | ||||||||
\(561\) | 5769.32 | 0.434191 | ||||||||
\(562\) | −140.919 | −0.0105770 | ||||||||
\(563\) | 3523.48 | 0.263760 | 0.131880 | − | 0.991266i | \(-0.457899\pi\) | ||||
0.131880 | + | 0.991266i | \(0.457899\pi\) | |||||||
\(564\) | −22849.1 | −1.70589 | ||||||||
\(565\) | 6513.20 | 0.484978 | ||||||||
\(566\) | −942.585 | −0.0699996 | ||||||||
\(567\) | −18485.5 | −1.36917 | ||||||||
\(568\) | 896.969 | 0.0662605 | ||||||||
\(569\) | 14692.9 | 1.08253 | 0.541265 | − | 0.840852i | \(-0.317945\pi\) | ||||
0.541265 | + | 0.840852i | \(0.317945\pi\) | |||||||
\(570\) | −130.857 | −0.00961577 | ||||||||
\(571\) | −20772.1 | −1.52239 | −0.761196 | − | 0.648522i | \(-0.775387\pi\) | ||||
−0.761196 | + | 0.648522i | \(0.775387\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10578.0 | −0.771212 | ||||||||
\(574\) | −650.940 | −0.0473340 | ||||||||
\(575\) | −11224.2 | −0.814056 | ||||||||
\(576\) | −11813.3 | −0.854549 | ||||||||
\(577\) | 19163.9 | 1.38267 | 0.691336 | − | 0.722533i | \(-0.257022\pi\) | ||||
0.691336 | + | 0.722533i | \(0.257022\pi\) | |||||||
\(578\) | −107.704 | −0.00775066 | ||||||||
\(579\) | −35336.9 | −2.53636 | ||||||||
\(580\) | 14380.3 | 1.02950 | ||||||||
\(581\) | 10468.7 | 0.747531 | ||||||||
\(582\) | −2358.02 | −0.167944 | ||||||||
\(583\) | −5867.07 | −0.416791 | ||||||||
\(584\) | −1917.52 | −0.135869 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −874.390 | −0.0616394 | ||||||||
\(587\) | 25419.4 | 1.78734 | 0.893672 | − | 0.448722i | \(-0.148121\pi\) | ||||
0.893672 | + | 0.448722i | \(0.148121\pi\) | |||||||
\(588\) | 10681.6 | 0.749154 | ||||||||
\(589\) | 2926.62 | 0.204736 | ||||||||
\(590\) | −2.38616 | −0.000166503 0 | ||||||||
\(591\) | 5619.24 | 0.391107 | ||||||||
\(592\) | 5641.91 | 0.391691 | ||||||||
\(593\) | −22771.2 | −1.57690 | −0.788451 | − | 0.615098i | \(-0.789116\pi\) | ||||
−0.788451 | + | 0.615098i | \(0.789116\pi\) | |||||||
\(594\) | 53.0602 | 0.00366513 | ||||||||
\(595\) | −10788.8 | −0.743357 | ||||||||
\(596\) | 9895.96 | 0.680125 | ||||||||
\(597\) | 266.012 | 0.0182364 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14844.0 | −1.01253 | −0.506267 | − | 0.862377i | \(-0.668975\pi\) | ||||
−0.506267 | + | 0.862377i | \(0.668975\pi\) | |||||||
\(600\) | 2129.74 | 0.144911 | ||||||||
\(601\) | 1152.87 | 0.0782475 | 0.0391237 | − | 0.999234i | \(-0.487543\pi\) | ||||
0.0391237 | + | 0.999234i | \(0.487543\pi\) | |||||||
\(602\) | 2436.67 | 0.164969 | ||||||||
\(603\) | −20917.3 | −1.41264 | ||||||||
\(604\) | 9135.04 | 0.615396 | ||||||||
\(605\) | −770.842 | −0.0518003 | ||||||||
\(606\) | 2045.92 | 0.137145 | ||||||||
\(607\) | −10559.8 | −0.706112 | −0.353056 | − | 0.935602i | \(-0.614858\pi\) | ||||
−0.353056 | + | 0.935602i | \(0.614858\pi\) | |||||||
\(608\) | −548.001 | −0.0365532 | ||||||||
\(609\) | −46706.5 | −3.10779 | ||||||||
\(610\) | 737.539 | 0.0489542 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −13992.2 | −0.924185 | ||||||||
\(613\) | 26620.7 | 1.75400 | 0.876998 | − | 0.480495i | \(-0.159543\pi\) | ||||
0.876998 | + | 0.480495i | \(0.159543\pi\) | |||||||
\(614\) | 1303.47 | 0.0856739 | ||||||||
\(615\) | 5795.81 | 0.380015 | ||||||||
\(616\) | −896.103 | −0.0586121 | ||||||||
\(617\) | 12506.8 | 0.816053 | 0.408026 | − | 0.912970i | \(-0.366217\pi\) | ||||
0.408026 | + | 0.912970i | \(0.366217\pi\) | |||||||
\(618\) | 924.475 | 0.0601745 | ||||||||
\(619\) | 11013.3 | 0.715121 | 0.357561 | − | 0.933890i | \(-0.383609\pi\) | ||||
0.357561 | + | 0.933890i | \(0.383609\pi\) | |||||||
\(620\) | 11414.7 | 0.739398 | ||||||||
\(621\) | 2894.44 | 0.187037 | ||||||||
\(622\) | 452.130 | 0.0291459 | ||||||||
\(623\) | −9910.95 | −0.637358 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2052.92 | 0.131387 | ||||||||
\(626\) | −1040.44 | −0.0664286 | ||||||||
\(627\) | 1019.68 | 0.0649474 | ||||||||
\(628\) | −17030.4 | −1.08214 | ||||||||
\(629\) | 6598.71 | 0.418296 | ||||||||
\(630\) | 779.240 | 0.0492788 | ||||||||
\(631\) | −3315.53 | −0.209174 | −0.104587 | − | 0.994516i | \(-0.533352\pi\) | ||||
−0.104587 | + | 0.994516i | \(0.533352\pi\) | |||||||
\(632\) | −491.856 | −0.0309573 | ||||||||
\(633\) | −25658.8 | −1.61113 | ||||||||
\(634\) | 2269.98 | 0.142196 | ||||||||
\(635\) | −6508.07 | −0.406716 | ||||||||
\(636\) | 30270.4 | 1.88726 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 692.005 | 0.0429416 | ||||||||
\(639\) | 6077.95 | 0.376275 | ||||||||
\(640\) | −2846.86 | −0.175831 | ||||||||
\(641\) | 18082.3 | 1.11421 | 0.557103 | − | 0.830443i | \(-0.311913\pi\) | ||||
0.557103 | + | 0.830443i | \(0.311913\pi\) | |||||||
\(642\) | 2689.58 | 0.165342 | ||||||||
\(643\) | 16694.9 | 1.02392 | 0.511961 | − | 0.859009i | \(-0.328919\pi\) | ||||
0.511961 | + | 0.859009i | \(0.328919\pi\) | |||||||
\(644\) | −24366.0 | −1.49092 | ||||||||
\(645\) | −21695.5 | −1.32443 | ||||||||
\(646\) | −211.447 | −0.0128781 | ||||||||
\(647\) | 17734.1 | 1.07759 | 0.538795 | − | 0.842437i | \(-0.318880\pi\) | ||||
0.538795 | + | 0.842437i | \(0.318880\pi\) | |||||||
\(648\) | −2834.84 | −0.171856 | ||||||||
\(649\) | 18.5937 | 0.00112460 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −37074.6 | −2.23206 | ||||||||
\(652\) | −23478.3 | −1.41025 | ||||||||
\(653\) | 19094.7 | 1.14431 | 0.572153 | − | 0.820147i | \(-0.306108\pi\) | ||||
0.572153 | + | 0.820147i | \(0.306108\pi\) | |||||||
\(654\) | 1130.43 | 0.0675894 | ||||||||
\(655\) | 1433.54 | 0.0855159 | ||||||||
\(656\) | 8007.30 | 0.476574 | ||||||||
\(657\) | −12993.3 | −0.771564 | ||||||||
\(658\) | 2056.17 | 0.121821 | ||||||||
\(659\) | −5756.24 | −0.340260 | −0.170130 | − | 0.985422i | \(-0.554419\pi\) | ||||
−0.170130 | + | 0.985422i | \(0.554419\pi\) | |||||||
\(660\) | 3977.06 | 0.234556 | ||||||||
\(661\) | 30596.6 | 1.80041 | 0.900205 | − | 0.435466i | \(-0.143417\pi\) | ||||
0.900205 | + | 0.435466i | \(0.143417\pi\) | |||||||
\(662\) | −1498.43 | −0.0879732 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1605.43 | 0.0938293 | ||||||||
\(665\) | −1906.83 | −0.111193 | ||||||||
\(666\) | −476.604 | −0.0277298 | ||||||||
\(667\) | 37748.9 | 2.19137 | ||||||||
\(668\) | 7145.24 | 0.413859 | ||||||||
\(669\) | −37565.3 | −2.17094 | ||||||||
\(670\) | −1232.88 | −0.0710902 | ||||||||
\(671\) | −5747.13 | −0.330649 | ||||||||
\(672\) | 6942.11 | 0.398509 | ||||||||
\(673\) | −19024.1 | −1.08963 | −0.544817 | − | 0.838555i | \(-0.683401\pi\) | ||||
−0.544817 | + | 0.838555i | \(0.683401\pi\) | |||||||
\(674\) | −681.209 | −0.0389306 | ||||||||
\(675\) | −1837.61 | −0.104784 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14655.3 | 0.831976 | 0.415988 | − | 0.909370i | \(-0.363436\pi\) | ||||
0.415988 | + | 0.909370i | \(0.363436\pi\) | |||||||
\(678\) | −1617.09 | −0.0915988 | ||||||||
\(679\) | −34360.7 | −1.94204 | ||||||||
\(680\) | −1654.51 | −0.0933054 | ||||||||
\(681\) | −4608.73 | −0.259335 | ||||||||
\(682\) | 549.298 | 0.0308412 | ||||||||
\(683\) | −5137.72 | −0.287832 | −0.143916 | − | 0.989590i | \(-0.545970\pi\) | ||||
−0.143916 | + | 0.989590i | \(0.545970\pi\) | |||||||
\(684\) | −2473.00 | −0.138242 | ||||||||
\(685\) | 10542.1 | 0.588018 | ||||||||
\(686\) | 790.528 | 0.0439978 | ||||||||
\(687\) | −18660.5 | −1.03631 | ||||||||
\(688\) | −29973.8 | −1.66096 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1339.78 | −0.0739196 | ||||||||
\(691\) | 18074.2 | 0.995046 | 0.497523 | − | 0.867451i | \(-0.334243\pi\) | ||||
0.497523 | + | 0.867451i | \(0.334243\pi\) | |||||||
\(692\) | 18637.7 | 1.02384 | ||||||||
\(693\) | −6072.08 | −0.332842 | ||||||||
\(694\) | 1330.37 | 0.0727666 | ||||||||
\(695\) | 4457.67 | 0.243293 | ||||||||
\(696\) | −7162.67 | −0.390087 | ||||||||
\(697\) | 9365.25 | 0.508944 | ||||||||
\(698\) | −682.732 | −0.0370226 | ||||||||
\(699\) | −37955.8 | −2.05382 | ||||||||
\(700\) | 15469.4 | 0.835267 | ||||||||
\(701\) | 17200.1 | 0.926733 | 0.463366 | − | 0.886167i | \(-0.346641\pi\) | ||||
0.463366 | + | 0.886167i | \(0.346641\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1166.26 | 0.0625697 | ||||||||
\(704\) | 5425.66 | 0.290465 | ||||||||
\(705\) | −18307.7 | −0.978023 | ||||||||
\(706\) | 1160.08 | 0.0618414 | ||||||||
\(707\) | 29812.9 | 1.58590 | ||||||||
\(708\) | −95.9318 | −0.00509228 | ||||||||
\(709\) | 22222.6 | 1.17713 | 0.588565 | − | 0.808450i | \(-0.299693\pi\) | ||||
0.588565 | + | 0.808450i | \(0.299693\pi\) | |||||||
\(710\) | 358.239 | 0.0189359 | ||||||||
\(711\) | −3332.86 | −0.175798 | ||||||||
\(712\) | −1519.89 | −0.0800005 | ||||||||
\(713\) | 29964.2 | 1.57387 | ||||||||
\(714\) | 2678.63 | 0.140399 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11277.1 | −0.588612 | ||||||||
\(717\) | 23824.8 | 1.24094 | ||||||||
\(718\) | 1509.60 | 0.0784648 | ||||||||
\(719\) | 23179.8 | 1.20231 | 0.601154 | − | 0.799133i | \(-0.294708\pi\) | ||||
0.601154 | + | 0.799133i | \(0.294708\pi\) | |||||||
\(720\) | −9585.54 | −0.496155 | ||||||||
\(721\) | 13471.3 | 0.695836 | ||||||||
\(722\) | 1482.50 | 0.0764168 | ||||||||
\(723\) | 27092.2 | 1.39360 | ||||||||
\(724\) | 24241.3 | 1.24436 | ||||||||
\(725\) | −23965.8 | −1.22768 | ||||||||
\(726\) | 191.384 | 0.00978363 | ||||||||
\(727\) | −27170.8 | −1.38612 | −0.693059 | − | 0.720880i | \(-0.743738\pi\) | ||||
−0.693059 | + | 0.720880i | \(0.743738\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15013.8 | −0.762779 | ||||||||
\(730\) | −765.835 | −0.0388285 | ||||||||
\(731\) | −35057.1 | −1.77378 | ||||||||
\(732\) | 29651.6 | 1.49721 | ||||||||
\(733\) | −17639.9 | −0.888872 | −0.444436 | − | 0.895811i | \(-0.646596\pi\) | ||||
−0.444436 | + | 0.895811i | \(0.646596\pi\) | |||||||
\(734\) | −826.389 | −0.0415566 | ||||||||
\(735\) | 8558.57 | 0.429507 | ||||||||
\(736\) | −5610.71 | −0.280997 | ||||||||
\(737\) | 9607.01 | 0.480161 | ||||||||
\(738\) | −676.422 | −0.0337391 | ||||||||
\(739\) | −7869.41 | −0.391720 | −0.195860 | − | 0.980632i | \(-0.562750\pi\) | ||||
−0.195860 | + | 0.980632i | \(0.562750\pi\) | |||||||
\(740\) | 4548.80 | 0.225969 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2724.01 | −0.134773 | ||||||||
\(743\) | −16096.4 | −0.794779 | −0.397389 | − | 0.917650i | \(-0.630084\pi\) | ||||
−0.397389 | + | 0.917650i | \(0.630084\pi\) | |||||||
\(744\) | −5685.57 | −0.280166 | ||||||||
\(745\) | 7929.06 | 0.389931 | ||||||||
\(746\) | −986.235 | −0.0484030 | ||||||||
\(747\) | 10878.5 | 0.532831 | ||||||||
\(748\) | 6426.40 | 0.314134 | ||||||||
\(749\) | 39192.2 | 1.91195 | ||||||||
\(750\) | 2110.13 | 0.102735 | ||||||||
\(751\) | −10069.4 | −0.489263 | −0.244632 | − | 0.969616i | \(-0.578667\pi\) | ||||
−0.244632 | + | 0.969616i | \(0.578667\pi\) | |||||||
\(752\) | −25293.3 | −1.22653 | ||||||||
\(753\) | 15975.4 | 0.773144 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7319.38 | 0.352820 | ||||||||
\(756\) | −3989.15 | −0.191910 | ||||||||
\(757\) | −35438.8 | −1.70151 | −0.850757 | − | 0.525559i | \(-0.823856\pi\) | ||||
−0.850757 | + | 0.525559i | \(0.823856\pi\) | |||||||
\(758\) | 812.677 | 0.0389416 | ||||||||
\(759\) | 10440.0 | 0.499272 | ||||||||
\(760\) | −292.421 | −0.0139569 | ||||||||
\(761\) | 21534.0 | 1.02577 | 0.512883 | − | 0.858458i | \(-0.328577\pi\) | ||||
0.512883 | + | 0.858458i | \(0.328577\pi\) | |||||||
\(762\) | 1615.82 | 0.0768174 | ||||||||
\(763\) | 16472.5 | 0.781578 | ||||||||
\(764\) | −11782.8 | −0.557967 | ||||||||
\(765\) | −11211.1 | −0.529856 | ||||||||
\(766\) | 2414.59 | 0.113894 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −27459.0 | −1.29016 | ||||||||
\(769\) | −24991.8 | −1.17195 | −0.585974 | − | 0.810330i | \(-0.699288\pi\) | ||||
−0.585974 | + | 0.810330i | \(0.699288\pi\) | |||||||
\(770\) | −357.893 | −0.0167501 | ||||||||
\(771\) | 39646.7 | 1.85193 | ||||||||
\(772\) | −39361.5 | −1.83504 | ||||||||
\(773\) | 16709.6 | 0.777493 | 0.388746 | − | 0.921345i | \(-0.372908\pi\) | ||||
0.388746 | + | 0.921345i | \(0.372908\pi\) | |||||||
\(774\) | 2532.06 | 0.117588 | ||||||||
\(775\) | −19023.5 | −0.881737 | ||||||||
\(776\) | −5269.38 | −0.243763 | ||||||||
\(777\) | −14774.3 | −0.682144 | ||||||||
\(778\) | 1482.10 | 0.0682979 | ||||||||
\(779\) | 1655.23 | 0.0761292 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2791.51 | −0.127898 | ||||||||
\(782\) | −2164.90 | −0.0989985 | ||||||||
\(783\) | 6180.17 | 0.282071 | ||||||||
\(784\) | 11824.2 | 0.538640 | ||||||||
\(785\) | −13645.5 | −0.620417 | ||||||||
\(786\) | −355.917 | −0.0161516 | ||||||||
\(787\) | 39178.5 | 1.77454 | 0.887270 | − | 0.461251i | \(-0.152599\pi\) | ||||
0.887270 | + | 0.461251i | \(0.152599\pi\) | |||||||
\(788\) | 6259.22 | 0.282964 | ||||||||
\(789\) | −21024.7 | −0.948669 | ||||||||
\(790\) | −196.441 | −0.00884693 | ||||||||
\(791\) | −23564.0 | −1.05921 | ||||||||
\(792\) | −931.183 | −0.0417780 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −561.459 | −0.0250950 | ||||||||
\(795\) | 24253.9 | 1.08201 | ||||||||
\(796\) | 296.308 | 0.0131939 | ||||||||
\(797\) | −43194.1 | −1.91972 | −0.959858 | − | 0.280487i | \(-0.909504\pi\) | ||||
−0.959858 | + | 0.280487i | \(0.909504\pi\) | |||||||
\(798\) | 473.424 | 0.0210013 | ||||||||
\(799\) | −29582.7 | −1.30984 | ||||||||
\(800\) | 3562.10 | 0.157424 | ||||||||
\(801\) | −10298.9 | −0.454301 | ||||||||
\(802\) | −3105.42 | −0.136728 | ||||||||
\(803\) | 5967.63 | 0.262258 | ||||||||
\(804\) | −49566.1 | −2.17421 | ||||||||
\(805\) | −19523.1 | −0.854779 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 29648.7 | 1.29329 | ||||||||
\(808\) | 4571.95 | 0.199060 | ||||||||
\(809\) | 30480.9 | 1.32466 | 0.662330 | − | 0.749212i | \(-0.269568\pi\) | ||||
0.662330 | + | 0.749212i | \(0.269568\pi\) | |||||||
\(810\) | −1132.20 | −0.0491129 | ||||||||
\(811\) | −38120.8 | −1.65056 | −0.825279 | − | 0.564725i | \(-0.808982\pi\) | ||||
−0.825279 | + | 0.564725i | \(0.808982\pi\) | |||||||
\(812\) | −52026.0 | −2.24847 | ||||||||
\(813\) | −43840.8 | −1.89122 | ||||||||
\(814\) | 218.897 | 0.00942546 | ||||||||
\(815\) | −18811.8 | −0.808525 | ||||||||
\(816\) | −32950.2 | −1.41359 | ||||||||
\(817\) | −6196.03 | −0.265326 | ||||||||
\(818\) | −1349.68 | −0.0576902 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6455.90 | 0.274939 | ||||||||
\(821\) | 27818.9 | 1.18257 | 0.591284 | − | 0.806464i | \(-0.298621\pi\) | ||||
0.591284 | + | 0.806464i | \(0.298621\pi\) | |||||||
\(822\) | −2617.38 | −0.111060 | ||||||||
\(823\) | 37786.8 | 1.60044 | 0.800222 | − | 0.599704i | \(-0.204715\pi\) | ||||
0.800222 | + | 0.599704i | \(0.204715\pi\) | |||||||
\(824\) | 2065.89 | 0.0873406 | ||||||||
\(825\) | −6628.09 | −0.279710 | ||||||||
\(826\) | 8.63283 | 0.000363650 0 | ||||||||
\(827\) | −43364.7 | −1.82338 | −0.911692 | − | 0.410873i | \(-0.865224\pi\) | ||||
−0.911692 | + | 0.410873i | \(0.865224\pi\) | |||||||
\(828\) | −25319.8 | −1.06271 | ||||||||
\(829\) | 1244.35 | 0.0521327 | 0.0260664 | − | 0.999660i | \(-0.491702\pi\) | ||||
0.0260664 | + | 0.999660i | \(0.491702\pi\) | |||||||
\(830\) | 641.188 | 0.0268144 | ||||||||
\(831\) | −26522.3 | −1.10716 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13829.5 | 0.575227 | ||||||||
\(834\) | −1106.74 | −0.0459513 | ||||||||
\(835\) | 5725.07 | 0.237274 | ||||||||
\(836\) | 1135.81 | 0.0469890 | ||||||||
\(837\) | 4905.68 | 0.202587 | ||||||||
\(838\) | 100.624 | 0.00414797 | ||||||||
\(839\) | −23769.0 | −0.978064 | −0.489032 | − | 0.872266i | \(-0.662650\pi\) | ||||
−0.489032 | + | 0.872266i | \(0.662650\pi\) | |||||||
\(840\) | 3704.41 | 0.152160 | ||||||||
\(841\) | 56212.0 | 2.30481 | ||||||||
\(842\) | 844.233 | 0.0345537 | ||||||||
\(843\) | −4539.37 | −0.185462 | ||||||||
\(844\) | −28581.1 | −1.16564 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2136.67 | 0.0868323 | ||||||||
\(847\) | 2788.81 | 0.113134 | ||||||||
\(848\) | 33508.4 | 1.35694 | ||||||||
\(849\) | −30363.2 | −1.22740 | ||||||||
\(850\) | 1374.44 | 0.0554624 | ||||||||
\(851\) | 11940.8 | 0.480994 | ||||||||
\(852\) | 14402.4 | 0.579130 | ||||||||
\(853\) | 42511.5 | 1.70641 | 0.853204 | − | 0.521577i | \(-0.174656\pi\) | ||||
0.853204 | + | 0.521577i | \(0.174656\pi\) | |||||||
\(854\) | −2668.33 | −0.106918 | ||||||||
\(855\) | −1981.47 | −0.0792572 | ||||||||
\(856\) | 6010.31 | 0.239986 | ||||||||
\(857\) | 15326.8 | 0.610915 | 0.305457 | − | 0.952206i | \(-0.401191\pi\) | ||||
0.305457 | + | 0.952206i | \(0.401191\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18415.6 | 0.731471 | 0.365736 | − | 0.930719i | \(-0.380817\pi\) | ||||
0.365736 | + | 0.930719i | \(0.380817\pi\) | |||||||
\(860\) | −24166.5 | −0.958220 | ||||||||
\(861\) | −20968.5 | −0.829971 | ||||||||
\(862\) | 2675.57 | 0.105720 | ||||||||
\(863\) | 2893.68 | 0.114139 | 0.0570695 | − | 0.998370i | \(-0.481824\pi\) | ||||
0.0570695 | + | 0.998370i | \(0.481824\pi\) | |||||||
\(864\) | −918.575 | −0.0361696 | ||||||||
\(865\) | 14933.3 | 0.586992 | ||||||||
\(866\) | −1578.12 | −0.0619245 | ||||||||
\(867\) | −3469.42 | −0.135903 | ||||||||
\(868\) | −41297.1 | −1.61488 | ||||||||
\(869\) | 1530.73 | 0.0597544 | ||||||||
\(870\) | −2860.68 | −0.111478 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 2526.14 | 0.0981030 | ||||||||
\(873\) | −35705.8 | −1.38426 | ||||||||
\(874\) | −382.628 | −0.0148085 | ||||||||
\(875\) | 30748.4 | 1.18798 | ||||||||
\(876\) | −30789.2 | −1.18752 | ||||||||
\(877\) | −43023.3 | −1.65655 | −0.828275 | − | 0.560323i | \(-0.810677\pi\) | ||||
−0.828275 | + | 0.560323i | \(0.810677\pi\) | |||||||
\(878\) | 2070.70 | 0.0795929 | ||||||||
\(879\) | −28166.4 | −1.08081 | ||||||||
\(880\) | 4402.49 | 0.168645 | ||||||||
\(881\) | −30466.0 | −1.16507 | −0.582534 | − | 0.812806i | \(-0.697939\pi\) | ||||
−0.582534 | + | 0.812806i | \(0.697939\pi\) | |||||||
\(882\) | −998.860 | −0.0381331 | ||||||||
\(883\) | 39398.2 | 1.50153 | 0.750767 | − | 0.660567i | \(-0.229684\pi\) | ||||
0.750767 | + | 0.660567i | \(0.229684\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −76.8646 | −0.00291952 | ||||||||
\(886\) | −2123.87 | −0.0805338 | ||||||||
\(887\) | 6077.46 | 0.230058 | 0.115029 | − | 0.993362i | \(-0.463304\pi\) | ||||
0.115029 | + | 0.993362i | \(0.463304\pi\) | |||||||
\(888\) | −2265.71 | −0.0856221 | ||||||||
\(889\) | 23545.4 | 0.888288 | ||||||||
\(890\) | −607.026 | −0.0228624 | ||||||||
\(891\) | 8822.45 | 0.331721 | ||||||||
\(892\) | −41843.7 | −1.57066 | ||||||||
\(893\) | −5228.49 | −0.195929 | ||||||||
\(894\) | −1968.62 | −0.0736470 | ||||||||
\(895\) | −9035.71 | −0.337464 | ||||||||
\(896\) | 10299.6 | 0.384023 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 957.660 | 0.0355874 | ||||||||
\(899\) | 63979.3 | 2.37356 | ||||||||
\(900\) | 16074.9 | 0.595368 | ||||||||
\(901\) | 39191.1 | 1.44911 | ||||||||
\(902\) | 310.670 | 0.0114681 | ||||||||
\(903\) | 78491.8 | 2.89263 | ||||||||
\(904\) | −3613.65 | −0.132952 | ||||||||
\(905\) | 19423.1 | 0.713422 | ||||||||
\(906\) | −1817.25 | −0.0666379 | ||||||||
\(907\) | 10979.6 | 0.401954 | 0.200977 | − | 0.979596i | \(-0.435588\pi\) | ||||
0.200977 | + | 0.979596i | \(0.435588\pi\) | |||||||
\(908\) | −5133.62 | −0.187627 | ||||||||
\(909\) | 30979.9 | 1.13041 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2625.11 | −0.0954706 | −0.0477353 | − | 0.998860i | \(-0.515200\pi\) | ||||
−0.0477353 | + | 0.998860i | \(0.515200\pi\) | |||||||
\(912\) | −5823.66 | −0.211448 | ||||||||
\(913\) | −4996.34 | −0.181111 | ||||||||
\(914\) | 3607.84 | 0.130565 | ||||||||
\(915\) | 23758.1 | 0.858382 | ||||||||
\(916\) | −20785.8 | −0.749760 | ||||||||
\(917\) | −5186.36 | −0.186771 | ||||||||
\(918\) | −354.434 | −0.0127430 | ||||||||
\(919\) | 27772.9 | 0.996892 | 0.498446 | − | 0.866921i | \(-0.333904\pi\) | ||||
0.498446 | + | 0.866921i | \(0.333904\pi\) | |||||||
\(920\) | −2993.95 | −0.107291 | ||||||||
\(921\) | 41988.3 | 1.50224 | ||||||||
\(922\) | −1514.73 | −0.0541052 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −14388.5 | −0.512281 | ||||||||
\(925\) | −7580.93 | −0.269470 | ||||||||
\(926\) | −136.096 | −0.00482980 | ||||||||
\(927\) | 13998.7 | 0.495983 | ||||||||
\(928\) | −11979.9 | −0.423772 | ||||||||
\(929\) | −41116.0 | −1.45207 | −0.726034 | − | 0.687658i | \(-0.758639\pi\) | ||||
−0.726034 | + | 0.687658i | \(0.758639\pi\) | |||||||
\(930\) | −2270.75 | −0.0800653 | ||||||||
\(931\) | 2444.24 | 0.0860439 | ||||||||
\(932\) | −42278.6 | −1.48593 | ||||||||
\(933\) | 14564.3 | 0.511056 | ||||||||
\(934\) | 3784.16 | 0.132571 | ||||||||
\(935\) | 5149.10 | 0.180100 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13015.6 | 0.453790 | 0.226895 | − | 0.973919i | \(-0.427143\pi\) | ||||
0.226895 | + | 0.973919i | \(0.427143\pi\) | |||||||
\(938\) | 4460.42 | 0.155264 | ||||||||
\(939\) | −33515.3 | −1.16478 | ||||||||
\(940\) | −20392.7 | −0.707594 | ||||||||
\(941\) | 40088.4 | 1.38878 | 0.694392 | − | 0.719597i | \(-0.255673\pi\) | ||||
0.694392 | + | 0.719597i | \(0.255673\pi\) | |||||||
\(942\) | 3387.88 | 0.117179 | ||||||||
\(943\) | 16947.1 | 0.585230 | ||||||||
\(944\) | −106.194 | −0.00366134 | ||||||||
\(945\) | −3196.28 | −0.110026 | ||||||||
\(946\) | −1162.94 | −0.0399686 | ||||||||
\(947\) | −44753.7 | −1.53569 | −0.767846 | − | 0.640634i | \(-0.778671\pi\) | ||||
−0.767846 | + | 0.640634i | \(0.778671\pi\) | |||||||
\(948\) | −7897.62 | −0.270573 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 242.921 | 0.00829621 | ||||||||
\(951\) | 73122.2 | 2.49332 | ||||||||
\(952\) | 5985.83 | 0.203783 | ||||||||
\(953\) | 2835.36 | 0.0963762 | 0.0481881 | − | 0.998838i | \(-0.484655\pi\) | ||||
0.0481881 | + | 0.998838i | \(0.484655\pi\) | |||||||
\(954\) | −2830.65 | −0.0960645 | ||||||||
\(955\) | −9440.87 | −0.319895 | ||||||||
\(956\) | 26538.3 | 0.897812 | ||||||||
\(957\) | 22291.3 | 0.752954 | ||||||||
\(958\) | 3468.86 | 0.116987 | ||||||||
\(959\) | −38140.0 | −1.28426 | ||||||||
\(960\) | −22429.2 | −0.754060 | ||||||||
\(961\) | 20994.4 | 0.704722 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 40726.4 | 1.36282 | ||||||||
\(964\) | 30177.8 | 1.00826 | ||||||||
\(965\) | −31538.1 | −1.05207 | ||||||||
\(966\) | 4847.16 | 0.161444 | ||||||||
\(967\) | −24439.5 | −0.812741 | −0.406371 | − | 0.913708i | \(-0.633206\pi\) | ||||
−0.406371 | + | 0.913708i | \(0.633206\pi\) | |||||||
\(968\) | 427.678 | 0.0142005 | ||||||||
\(969\) | −6811.28 | −0.225810 | ||||||||
\(970\) | −2104.53 | −0.0696622 | ||||||||
\(971\) | −1845.66 | −0.0609989 | −0.0304994 | − | 0.999535i | \(-0.509710\pi\) | ||||
−0.0304994 | + | 0.999535i | \(0.509710\pi\) | |||||||
\(972\) | −40845.2 | −1.34785 | ||||||||
\(973\) | −16127.3 | −0.531364 | ||||||||
\(974\) | 3181.67 | 0.104669 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32823.4 | 1.07649 | ||||||||
\(977\) | 25442.8 | 0.833151 | 0.416575 | − | 0.909101i | \(-0.363230\pi\) | ||||
0.416575 | + | 0.909101i | \(0.363230\pi\) | |||||||
\(978\) | 4670.57 | 0.152708 | ||||||||
\(979\) | 4730.14 | 0.154419 | ||||||||
\(980\) | 9533.31 | 0.310745 | ||||||||
\(981\) | 17117.3 | 0.557100 | ||||||||
\(982\) | −2027.56 | −0.0658879 | ||||||||
\(983\) | −44900.2 | −1.45686 | −0.728430 | − | 0.685121i | \(-0.759749\pi\) | ||||
−0.728430 | + | 0.685121i | \(0.759749\pi\) | |||||||
\(984\) | −3215.62 | −0.104177 | ||||||||
\(985\) | 5015.15 | 0.162229 | ||||||||
\(986\) | −4622.48 | −0.149300 | ||||||||
\(987\) | 66234.9 | 2.13605 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −63438.1 | −2.03965 | ||||||||
\(990\) | −371.903 | −0.0119393 | ||||||||
\(991\) | 8954.53 | 0.287033 | 0.143517 | − | 0.989648i | \(-0.454159\pi\) | ||||
0.143517 | + | 0.989648i | \(0.454159\pi\) | |||||||
\(992\) | −9509.41 | −0.304359 | ||||||||
\(993\) | −48268.6 | −1.54255 | ||||||||
\(994\) | −1296.06 | −0.0413568 | ||||||||
\(995\) | 237.415 | 0.00756437 | ||||||||
\(996\) | 25778.0 | 0.820087 | ||||||||
\(997\) | 270.402 | 0.00858950 | 0.00429475 | − | 0.999991i | \(-0.498633\pi\) | ||||
0.00429475 | + | 0.999991i | \(0.498633\pi\) | |||||||
\(998\) | −2619.66 | −0.0830901 | ||||||||
\(999\) | 1954.93 | 0.0619131 |
(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 | 1859.4.a.e.1.7 | 11 | ||
13.12 | even | 2 | 143.4.a.d.1.5 | ✓ | 11 | ||
39.38 | odd | 2 | 1287.4.a.m.1.7 | 11 | |||
52.51 | odd | 2 | 2288.4.a.u.1.10 | 11 | |||
143.142 | odd | 2 | 1573.4.a.f.1.7 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.4.a.d.1.5 | ✓ | 11 | 13.12 | even | 2 | ||
1287.4.a.m.1.7 | 11 | 39.38 | odd | 2 | |||
1573.4.a.f.1.7 | 11 | 143.142 | odd | 2 | |||
1859.4.a.e.1.7 | 11 | 1.1 | even | 1 | trivial | ||
2288.4.a.u.1.10 | 11 | 52.51 | odd | 2 |