Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,4,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, 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("2151.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(126.913108422\) |
Analytic rank: | \(1\) |
Dimension: | \(59\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.94849 | −1.04245 | −0.521224 | − | 0.853420i | \(-0.674524\pi\) | ||||
−0.521224 | + | 0.853420i | \(0.674524\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.693582 | 0.0866977 | ||||||||
\(5\) | 3.01150 | 0.269356 | 0.134678 | − | 0.990889i | \(-0.457000\pi\) | ||||
0.134678 | + | 0.990889i | \(0.457000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −30.9852 | −1.67305 | −0.836523 | − | 0.547932i | \(-0.815415\pi\) | ||||
−0.836523 | + | 0.547932i | \(0.815415\pi\) | |||||||
\(8\) | 21.5429 | 0.952070 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.87936 | −0.280790 | ||||||||
\(11\) | 60.7325 | 1.66468 | 0.832342 | − | 0.554262i | \(-0.186999\pi\) | ||||
0.832342 | + | 0.554262i | \(0.186999\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.59182 | 0.161969 | 0.0809844 | − | 0.996715i | \(-0.474194\pi\) | ||||
0.0809844 | + | 0.996715i | \(0.474194\pi\) | |||||||
\(14\) | 91.3596 | 1.74406 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −69.0676 | −1.07918 | ||||||||
\(17\) | −11.9021 | −0.169804 | −0.0849022 | − | 0.996389i | \(-0.527058\pi\) | ||||
−0.0849022 | + | 0.996389i | \(0.527058\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.6377 | 0.128445 | 0.0642227 | − | 0.997936i | \(-0.479543\pi\) | ||||
0.0642227 | + | 0.997936i | \(0.479543\pi\) | |||||||
\(20\) | 2.08872 | 0.0233526 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −179.069 | −1.73535 | ||||||||
\(23\) | 110.008 | 0.997319 | 0.498659 | − | 0.866798i | \(-0.333826\pi\) | ||||
0.498659 | + | 0.866798i | \(0.333826\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −115.931 | −0.927447 | ||||||||
\(26\) | −22.3844 | −0.168844 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −21.4908 | −0.145049 | ||||||||
\(29\) | −158.086 | −1.01227 | −0.506137 | − | 0.862453i | \(-0.668927\pi\) | ||||
−0.506137 | + | 0.862453i | \(0.668927\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −48.9384 | −0.283535 | −0.141768 | − | 0.989900i | \(-0.545279\pi\) | ||||
−0.141768 | + | 0.989900i | \(0.545279\pi\) | |||||||
\(32\) | 31.3019 | 0.172920 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 35.0931 | 0.177012 | ||||||||
\(35\) | −93.3120 | −0.450646 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −266.163 | −1.18262 | −0.591310 | − | 0.806445i | \(-0.701389\pi\) | ||||
−0.591310 | + | 0.806445i | \(0.701389\pi\) | |||||||
\(38\) | −31.3652 | −0.133898 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 64.8763 | 0.256446 | ||||||||
\(41\) | 266.974 | 1.01693 | 0.508467 | − | 0.861082i | \(-0.330213\pi\) | ||||
0.508467 | + | 0.861082i | \(0.330213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −494.592 | −1.75406 | −0.877030 | − | 0.480435i | \(-0.840479\pi\) | ||||
−0.877030 | + | 0.480435i | \(0.840479\pi\) | |||||||
\(44\) | 42.1229 | 0.144324 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −324.358 | −1.03965 | ||||||||
\(47\) | −34.2493 | −0.106293 | −0.0531466 | − | 0.998587i | \(-0.516925\pi\) | ||||
−0.0531466 | + | 0.998587i | \(0.516925\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 617.085 | 1.79908 | ||||||||
\(50\) | 341.821 | 0.966815 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.26555 | 0.0140423 | ||||||||
\(53\) | 344.258 | 0.892217 | 0.446109 | − | 0.894979i | \(-0.352810\pi\) | ||||
0.446109 | + | 0.894979i | \(0.352810\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 182.896 | 0.448394 | ||||||||
\(56\) | −667.512 | −1.59286 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 466.116 | 1.05524 | ||||||||
\(59\) | 528.630 | 1.16647 | 0.583235 | − | 0.812304i | \(-0.301787\pi\) | ||||
0.583235 | + | 0.812304i | \(0.301787\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −39.5050 | −0.0829197 | −0.0414598 | − | 0.999140i | \(-0.513201\pi\) | ||||
−0.0414598 | + | 0.999140i | \(0.513201\pi\) | |||||||
\(62\) | 144.294 | 0.295571 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 460.248 | 0.898921 | ||||||||
\(65\) | 22.8628 | 0.0436273 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 541.024 | 0.986516 | 0.493258 | − | 0.869883i | \(-0.335806\pi\) | ||||
0.493258 | + | 0.869883i | \(0.335806\pi\) | |||||||
\(68\) | −8.25506 | −0.0147217 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 275.129 | 0.469775 | ||||||||
\(71\) | −1137.35 | −1.90111 | −0.950556 | − | 0.310553i | \(-0.899486\pi\) | ||||
−0.950556 | + | 0.310553i | \(0.899486\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1164.62 | 1.86724 | 0.933621 | − | 0.358263i | \(-0.116631\pi\) | ||||
0.933621 | + | 0.358263i | \(0.116631\pi\) | |||||||
\(74\) | 784.778 | 1.23282 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.37813 | 0.0111359 | ||||||||
\(77\) | −1881.81 | −2.78509 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −365.495 | −0.520524 | −0.260262 | − | 0.965538i | \(-0.583809\pi\) | ||||
−0.260262 | + | 0.965538i | \(0.583809\pi\) | |||||||
\(80\) | −207.997 | −0.290684 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −787.168 | −1.06010 | ||||||||
\(83\) | 869.830 | 1.15032 | 0.575158 | − | 0.818042i | \(-0.304941\pi\) | ||||
0.575158 | + | 0.818042i | \(0.304941\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −35.8431 | −0.0457379 | ||||||||
\(86\) | 1458.30 | 1.82852 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1308.35 | 1.58490 | ||||||||
\(89\) | 150.942 | 0.179773 | 0.0898864 | − | 0.995952i | \(-0.471350\pi\) | ||||
0.0898864 | + | 0.995952i | \(0.471350\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −235.235 | −0.270981 | ||||||||
\(92\) | 76.2998 | 0.0864652 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 100.984 | 0.110805 | ||||||||
\(95\) | 32.0355 | 0.0345976 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 70.1786 | 0.0734594 | 0.0367297 | − | 0.999325i | \(-0.488306\pi\) | ||||
0.0367297 | + | 0.999325i | \(0.488306\pi\) | |||||||
\(98\) | −1819.47 | −1.87545 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −80.4075 | −0.0804075 | ||||||||
\(101\) | 658.591 | 0.648835 | 0.324417 | − | 0.945914i | \(-0.394832\pi\) | ||||
0.324417 | + | 0.945914i | \(0.394832\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1912.26 | 1.82932 | 0.914661 | − | 0.404221i | \(-0.132457\pi\) | ||||
0.914661 | + | 0.404221i | \(0.132457\pi\) | |||||||
\(104\) | 163.550 | 0.154206 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1015.04 | −0.930090 | ||||||||
\(107\) | 601.859 | 0.543775 | 0.271887 | − | 0.962329i | \(-0.412352\pi\) | ||||
0.271887 | + | 0.962329i | \(0.412352\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −201.258 | −0.176853 | −0.0884266 | − | 0.996083i | \(-0.528184\pi\) | ||||
−0.0884266 | + | 0.996083i | \(0.528184\pi\) | |||||||
\(110\) | −539.266 | −0.467427 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2140.08 | 1.80552 | ||||||||
\(113\) | −1303.00 | −1.08475 | −0.542373 | − | 0.840138i | \(-0.682474\pi\) | ||||
−0.542373 | + | 0.840138i | \(0.682474\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 331.290 | 0.268634 | ||||||||
\(116\) | −109.646 | −0.0877618 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1558.66 | −1.21598 | ||||||||
\(119\) | 368.789 | 0.284091 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2357.43 | 1.77118 | ||||||||
\(122\) | 116.480 | 0.0864394 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −33.9428 | −0.0245819 | ||||||||
\(125\) | −725.563 | −0.519170 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 950.566 | 0.664166 | 0.332083 | − | 0.943250i | \(-0.392249\pi\) | ||||
0.332083 | + | 0.943250i | \(0.392249\pi\) | |||||||
\(128\) | −1607.45 | −1.11000 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −67.4106 | −0.0454792 | ||||||||
\(131\) | −1967.89 | −1.31248 | −0.656241 | − | 0.754551i | \(-0.727855\pi\) | ||||
−0.656241 | + | 0.754551i | \(0.727855\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −329.612 | −0.214895 | ||||||||
\(134\) | −1595.20 | −1.02839 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −256.405 | −0.161666 | ||||||||
\(137\) | −1926.79 | −1.20158 | −0.600790 | − | 0.799407i | \(-0.705147\pi\) | ||||
−0.600790 | + | 0.799407i | \(0.705147\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2076.51 | −1.26710 | −0.633551 | − | 0.773701i | \(-0.718403\pi\) | ||||
−0.633551 | + | 0.773701i | \(0.718403\pi\) | |||||||
\(140\) | −64.7195 | −0.0390699 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3353.47 | 1.98181 | ||||||||
\(143\) | 461.070 | 0.269627 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −476.077 | −0.272662 | ||||||||
\(146\) | −3433.87 | −1.94650 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −184.606 | −0.102530 | ||||||||
\(149\) | 1828.22 | 1.00519 | 0.502596 | − | 0.864522i | \(-0.332378\pi\) | ||||
0.502596 | + | 0.864522i | \(0.332378\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2553.07 | −1.37593 | −0.687966 | − | 0.725743i | \(-0.741496\pi\) | ||||
−0.687966 | + | 0.725743i | \(0.741496\pi\) | |||||||
\(152\) | 229.167 | 0.122289 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5548.50 | 2.90331 | ||||||||
\(155\) | −147.378 | −0.0763721 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1264.56 | −0.642819 | −0.321409 | − | 0.946940i | \(-0.604157\pi\) | ||||
−0.321409 | + | 0.946940i | \(0.604157\pi\) | |||||||
\(158\) | 1077.66 | 0.542619 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 94.2655 | 0.0465772 | ||||||||
\(161\) | −3408.64 | −1.66856 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −655.491 | −0.314982 | −0.157491 | − | 0.987520i | \(-0.550340\pi\) | ||||
−0.157491 | + | 0.987520i | \(0.550340\pi\) | |||||||
\(164\) | 185.168 | 0.0881658 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2564.68 | −1.19914 | ||||||||
\(167\) | −3316.90 | −1.53694 | −0.768472 | − | 0.639883i | \(-0.778983\pi\) | ||||
−0.768472 | + | 0.639883i | \(0.778983\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2139.36 | −0.973766 | ||||||||
\(170\) | 105.683 | 0.0476794 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −343.040 | −0.152073 | ||||||||
\(173\) | 4170.71 | 1.83291 | 0.916455 | − | 0.400138i | \(-0.131038\pi\) | ||||
0.916455 | + | 0.400138i | \(0.131038\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3592.15 | 1.55166 | ||||||||
\(176\) | −4194.65 | −1.79650 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −445.050 | −0.187404 | ||||||||
\(179\) | −743.541 | −0.310474 | −0.155237 | − | 0.987877i | \(-0.549614\pi\) | ||||
−0.155237 | + | 0.987877i | \(0.549614\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2355.82 | 0.967439 | 0.483720 | − | 0.875223i | \(-0.339285\pi\) | ||||
0.483720 | + | 0.875223i | \(0.339285\pi\) | |||||||
\(182\) | 693.586 | 0.282484 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2369.90 | 0.949517 | ||||||||
\(185\) | −801.549 | −0.318546 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −722.842 | −0.282671 | ||||||||
\(188\) | −23.7547 | −0.00921538 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −94.4562 | −0.0360662 | ||||||||
\(191\) | 1069.64 | 0.405217 | 0.202608 | − | 0.979260i | \(-0.435058\pi\) | ||||
0.202608 | + | 0.979260i | \(0.435058\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1458.76 | −0.544060 | −0.272030 | − | 0.962289i | \(-0.587695\pi\) | ||||
−0.272030 | + | 0.962289i | \(0.587695\pi\) | |||||||
\(194\) | −206.921 | −0.0765776 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 427.999 | 0.155976 | ||||||||
\(197\) | 4612.24 | 1.66806 | 0.834032 | − | 0.551716i | \(-0.186027\pi\) | ||||
0.834032 | + | 0.551716i | \(0.186027\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3081.14 | 1.09757 | 0.548785 | − | 0.835964i | \(-0.315091\pi\) | ||||
0.548785 | + | 0.835964i | \(0.315091\pi\) | |||||||
\(200\) | −2497.49 | −0.882995 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1941.85 | −0.676376 | ||||||||
\(203\) | 4898.35 | 1.69358 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 803.990 | 0.273918 | ||||||||
\(206\) | −5638.26 | −1.90697 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −524.349 | −0.174794 | ||||||||
\(209\) | 646.055 | 0.213821 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4592.03 | −1.49824 | −0.749120 | − | 0.662435i | \(-0.769523\pi\) | ||||
−0.749120 | + | 0.662435i | \(0.769523\pi\) | |||||||
\(212\) | 238.771 | 0.0773532 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1774.57 | −0.566857 | ||||||||
\(215\) | −1489.46 | −0.472467 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1516.37 | 0.474368 | ||||||||
\(218\) | 593.406 | 0.184360 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 126.853 | 0.0388747 | ||||||||
\(221\) | −90.3584 | −0.0275030 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −321.155 | −0.0964400 | −0.0482200 | − | 0.998837i | \(-0.515355\pi\) | ||||
−0.0482200 | + | 0.998837i | \(0.515355\pi\) | |||||||
\(224\) | −969.897 | −0.289303 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3841.89 | 1.13079 | ||||||||
\(227\) | 6134.88 | 1.79377 | 0.896886 | − | 0.442261i | \(-0.145824\pi\) | ||||
0.896886 | + | 0.442261i | \(0.145824\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 631.036 | 0.182096 | 0.0910480 | − | 0.995847i | \(-0.470978\pi\) | ||||
0.0910480 | + | 0.995847i | \(0.470978\pi\) | |||||||
\(230\) | −976.804 | −0.280037 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3405.64 | −0.963755 | ||||||||
\(233\) | −2027.27 | −0.570005 | −0.285003 | − | 0.958527i | \(-0.591994\pi\) | ||||
−0.285003 | + | 0.958527i | \(0.591994\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −103.142 | −0.0286308 | ||||||||
\(236\) | 366.648 | 0.101130 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1087.37 | −0.296150 | ||||||||
\(239\) | 239.000 | 0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6461.36 | 1.72702 | 0.863512 | − | 0.504329i | \(-0.168260\pi\) | ||||
0.863512 | + | 0.504329i | \(0.168260\pi\) | |||||||
\(242\) | −6950.87 | −1.84636 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −27.4000 | −0.00718895 | ||||||||
\(245\) | 1858.35 | 0.484594 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 80.7597 | 0.0208041 | ||||||||
\(248\) | −1054.27 | −0.269945 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2139.31 | 0.541208 | ||||||||
\(251\) | 25.1402 | 0.00632206 | 0.00316103 | − | 0.999995i | \(-0.498994\pi\) | ||||
0.00316103 | + | 0.999995i | \(0.498994\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6681.08 | 1.66022 | ||||||||
\(254\) | −2802.73 | −0.692358 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1057.57 | 0.258195 | ||||||||
\(257\) | 703.026 | 0.170636 | 0.0853182 | − | 0.996354i | \(-0.472809\pi\) | ||||
0.0853182 | + | 0.996354i | \(0.472809\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8247.12 | 1.97858 | ||||||||
\(260\) | 15.8572 | 0.00378239 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5802.29 | 1.36819 | ||||||||
\(263\) | 1074.16 | 0.251846 | 0.125923 | − | 0.992040i | \(-0.459811\pi\) | ||||
0.125923 | + | 0.992040i | \(0.459811\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1036.73 | 0.240324 | ||||||||
\(266\) | 971.858 | 0.224017 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 375.244 | 0.0855287 | ||||||||
\(269\) | −1974.09 | −0.447444 | −0.223722 | − | 0.974653i | \(-0.571821\pi\) | ||||
−0.223722 | + | 0.974653i | \(0.571821\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6933.48 | −1.55416 | −0.777082 | − | 0.629399i | \(-0.783301\pi\) | ||||
−0.777082 | + | 0.629399i | \(0.783301\pi\) | |||||||
\(272\) | 822.047 | 0.183250 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5681.11 | 1.25258 | ||||||||
\(275\) | −7040.77 | −1.54391 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4833.19 | −1.04837 | −0.524184 | − | 0.851605i | \(-0.675630\pi\) | ||||
−0.524184 | + | 0.851605i | \(0.675630\pi\) | |||||||
\(278\) | 6122.56 | 1.32089 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2010.21 | −0.429046 | ||||||||
\(281\) | −5582.95 | −1.18523 | −0.592617 | − | 0.805484i | \(-0.701905\pi\) | ||||
−0.592617 | + | 0.805484i | \(0.701905\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5523.03 | −1.16011 | −0.580053 | − | 0.814578i | \(-0.696968\pi\) | ||||
−0.580053 | + | 0.814578i | \(0.696968\pi\) | |||||||
\(284\) | −788.847 | −0.164822 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1359.46 | −0.281072 | ||||||||
\(287\) | −8272.24 | −1.70138 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4771.34 | −0.971166 | ||||||||
\(290\) | 1403.71 | 0.284236 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 807.760 | 0.161886 | ||||||||
\(293\) | 6073.81 | 1.21104 | 0.605522 | − | 0.795829i | \(-0.292964\pi\) | ||||
0.605522 | + | 0.795829i | \(0.292964\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1591.97 | 0.314196 | ||||||||
\(296\) | −5733.92 | −1.12594 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5390.48 | −1.04786 | ||||||||
\(299\) | 835.164 | 0.161534 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15325.1 | 2.93462 | ||||||||
\(302\) | 7527.69 | 1.43434 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −734.722 | −0.138616 | ||||||||
\(305\) | −118.969 | −0.0223349 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9068.44 | −1.68587 | −0.842937 | − | 0.538012i | \(-0.819176\pi\) | ||||
−0.842937 | + | 0.538012i | \(0.819176\pi\) | |||||||
\(308\) | −1305.19 | −0.241461 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 434.542 | 0.0796139 | ||||||||
\(311\) | 5169.60 | 0.942577 | 0.471288 | − | 0.881979i | \(-0.343789\pi\) | ||||
0.471288 | + | 0.881979i | \(0.343789\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8108.59 | −1.46430 | −0.732148 | − | 0.681145i | \(-0.761482\pi\) | ||||
−0.732148 | + | 0.681145i | \(0.761482\pi\) | |||||||
\(314\) | 3728.53 | 0.670105 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −253.501 | −0.0451282 | ||||||||
\(317\) | −752.282 | −0.133288 | −0.0666441 | − | 0.997777i | \(-0.521229\pi\) | ||||
−0.0666441 | + | 0.997777i | \(0.521229\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9600.98 | −1.68512 | ||||||||
\(320\) | 1386.03 | 0.242130 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10050.3 | 1.73939 | ||||||||
\(323\) | −126.611 | −0.0218106 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −880.127 | −0.150217 | ||||||||
\(326\) | 1932.71 | 0.328352 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5751.38 | 0.968192 | ||||||||
\(329\) | 1061.22 | 0.177833 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4543.36 | −0.754459 | −0.377229 | − | 0.926120i | \(-0.623123\pi\) | ||||
−0.377229 | + | 0.926120i | \(0.623123\pi\) | |||||||
\(332\) | 603.298 | 0.0997298 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9779.85 | 1.60219 | ||||||||
\(335\) | 1629.29 | 0.265725 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 635.014 | 0.102645 | 0.0513226 | − | 0.998682i | \(-0.483656\pi\) | ||||
0.0513226 | + | 0.998682i | \(0.483656\pi\) | |||||||
\(338\) | 6307.89 | 1.01510 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −24.8601 | −0.00396537 | ||||||||
\(341\) | −2972.15 | −0.471997 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8492.59 | −1.33690 | ||||||||
\(344\) | −10654.9 | −1.66999 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12297.3 | −1.91071 | ||||||||
\(347\) | −6898.85 | −1.06729 | −0.533645 | − | 0.845709i | \(-0.679178\pi\) | ||||
−0.533645 | + | 0.845709i | \(0.679178\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3737.75 | 0.573287 | 0.286644 | − | 0.958037i | \(-0.407460\pi\) | ||||
0.286644 | + | 0.958037i | \(0.407460\pi\) | |||||||
\(350\) | −10591.4 | −1.61753 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1901.04 | 0.287858 | ||||||||
\(353\) | −3933.96 | −0.593155 | −0.296578 | − | 0.955009i | \(-0.595845\pi\) | ||||
−0.296578 | + | 0.955009i | \(0.595845\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3425.13 | −0.512077 | ||||||||
\(356\) | 104.690 | 0.0155859 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2192.32 | 0.323653 | ||||||||
\(359\) | −1651.18 | −0.242746 | −0.121373 | − | 0.992607i | \(-0.538730\pi\) | ||||
−0.121373 | + | 0.992607i | \(0.538730\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6745.84 | −0.983502 | ||||||||
\(362\) | −6946.10 | −1.00850 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −163.154 | −0.0234934 | ||||||||
\(365\) | 3507.25 | 0.502953 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 304.439 | 0.0433013 | 0.0216506 | − | 0.999766i | \(-0.493108\pi\) | ||||
0.0216506 | + | 0.999766i | \(0.493108\pi\) | |||||||
\(368\) | −7598.01 | −1.07629 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2363.36 | 0.332068 | ||||||||
\(371\) | −10666.9 | −1.49272 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6639.18 | 0.921618 | 0.460809 | − | 0.887499i | \(-0.347559\pi\) | ||||
0.460809 | + | 0.887499i | \(0.347559\pi\) | |||||||
\(374\) | 2131.29 | 0.294670 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −737.830 | −0.101199 | ||||||||
\(377\) | −1200.16 | −0.163957 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12535.4 | −1.69894 | −0.849470 | − | 0.527637i | \(-0.823078\pi\) | ||||
−0.849470 | + | 0.527637i | \(0.823078\pi\) | |||||||
\(380\) | 22.2192 | 0.00299953 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3153.82 | −0.422417 | ||||||||
\(383\) | 9432.96 | 1.25849 | 0.629245 | − | 0.777207i | \(-0.283364\pi\) | ||||
0.629245 | + | 0.777207i | \(0.283364\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5667.07 | −0.750183 | ||||||||
\(386\) | 4301.12 | 0.567154 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 48.6746 | 0.00636876 | ||||||||
\(389\) | −13408.0 | −1.74759 | −0.873793 | − | 0.486298i | \(-0.838347\pi\) | ||||
−0.873793 | + | 0.486298i | \(0.838347\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1309.33 | −0.169349 | ||||||||
\(392\) | 13293.8 | 1.71285 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13599.1 | −1.73887 | ||||||||
\(395\) | −1100.69 | −0.140207 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4323.18 | 0.546535 | 0.273267 | − | 0.961938i | \(-0.411896\pi\) | ||||
0.273267 | + | 0.961938i | \(0.411896\pi\) | |||||||
\(398\) | −9084.70 | −1.14416 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8007.07 | 1.00088 | ||||||||
\(401\) | −9306.73 | −1.15899 | −0.579496 | − | 0.814975i | \(-0.696751\pi\) | ||||
−0.579496 | + | 0.814975i | \(0.696751\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −371.532 | −0.0459239 | ||||||||
\(404\) | 456.787 | 0.0562525 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14442.7 | −1.76547 | ||||||||
\(407\) | −16164.7 | −1.96869 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15210.7 | −1.83892 | −0.919460 | − | 0.393184i | \(-0.871374\pi\) | ||||
−0.919460 | + | 0.393184i | \(0.871374\pi\) | |||||||
\(410\) | −2370.55 | −0.285545 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1326.31 | 0.158598 | ||||||||
\(413\) | −16379.7 | −1.95156 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2619.49 | 0.309845 | ||||||||
\(416\) | 237.638 | 0.0280077 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1904.89 | −0.222897 | ||||||||
\(419\) | 8083.79 | 0.942528 | 0.471264 | − | 0.881992i | \(-0.343798\pi\) | ||||
0.471264 | + | 0.881992i | \(0.343798\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13087.0 | 1.51501 | 0.757506 | − | 0.652829i | \(-0.226418\pi\) | ||||
0.757506 | + | 0.652829i | \(0.226418\pi\) | |||||||
\(422\) | 13539.6 | 1.56184 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7416.32 | 0.849453 | ||||||||
\(425\) | 1379.82 | 0.157485 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1224.07 | 0.138728 | ||||||||
\(428\) | 417.438 | 0.0471440 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4391.66 | 0.492523 | ||||||||
\(431\) | −656.182 | −0.0733345 | −0.0366673 | − | 0.999328i | \(-0.511674\pi\) | ||||
−0.0366673 | + | 0.999328i | \(0.511674\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1520.21 | −0.168722 | −0.0843611 | − | 0.996435i | \(-0.526885\pi\) | ||||
−0.0843611 | + | 0.996435i | \(0.526885\pi\) | |||||||
\(434\) | −4470.99 | −0.494503 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −139.589 | −0.0153328 | ||||||||
\(437\) | 1170.24 | 0.128101 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7687.24 | 0.835745 | 0.417872 | − | 0.908506i | \(-0.362776\pi\) | ||||
0.417872 | + | 0.908506i | \(0.362776\pi\) | |||||||
\(440\) | 3940.10 | 0.426902 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 266.421 | 0.0286705 | ||||||||
\(443\) | −8124.34 | −0.871330 | −0.435665 | − | 0.900109i | \(-0.643487\pi\) | ||||
−0.435665 | + | 0.900109i | \(0.643487\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 454.560 | 0.0484230 | ||||||||
\(446\) | 946.922 | 0.100534 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −14260.9 | −1.50394 | ||||||||
\(449\) | −18128.8 | −1.90545 | −0.952727 | − | 0.303828i | \(-0.901735\pi\) | ||||
−0.952727 | + | 0.303828i | \(0.901735\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16214.0 | 1.69287 | ||||||||
\(452\) | −903.740 | −0.0940450 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −18088.6 | −1.86991 | ||||||||
\(455\) | −708.408 | −0.0729905 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11175.2 | 1.14389 | 0.571943 | − | 0.820294i | \(-0.306190\pi\) | ||||
0.571943 | + | 0.820294i | \(0.306190\pi\) | |||||||
\(458\) | −1860.60 | −0.189826 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 229.777 | 0.0232900 | ||||||||
\(461\) | 3955.48 | 0.399620 | 0.199810 | − | 0.979835i | \(-0.435967\pi\) | ||||
0.199810 | + | 0.979835i | \(0.435967\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7668.34 | 0.769715 | 0.384857 | − | 0.922976i | \(-0.374251\pi\) | ||||
0.384857 | + | 0.922976i | \(0.374251\pi\) | |||||||
\(464\) | 10918.7 | 1.09243 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5977.40 | 0.594201 | ||||||||
\(467\) | −7427.44 | −0.735976 | −0.367988 | − | 0.929831i | \(-0.619953\pi\) | ||||
−0.367988 | + | 0.929831i | \(0.619953\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16763.8 | −1.65049 | ||||||||
\(470\) | 304.112 | 0.0298461 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11388.2 | 1.11056 | ||||||||
\(473\) | −30037.8 | −2.91996 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1233.24 | −0.119126 | ||||||||
\(476\) | 255.785 | 0.0246300 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −704.689 | −0.0674304 | ||||||||
\(479\) | 14201.1 | 1.35463 | 0.677314 | − | 0.735694i | \(-0.263144\pi\) | ||||
0.677314 | + | 0.735694i | \(0.263144\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2020.66 | −0.191547 | ||||||||
\(482\) | −19051.2 | −1.80033 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1635.07 | 0.153557 | ||||||||
\(485\) | 211.343 | 0.0197868 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14212.8 | 1.32247 | 0.661236 | − | 0.750178i | \(-0.270032\pi\) | ||||
0.661236 | + | 0.750178i | \(0.270032\pi\) | |||||||
\(488\) | −851.052 | −0.0789453 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5479.32 | −0.505164 | ||||||||
\(491\) | −15438.9 | −1.41904 | −0.709521 | − | 0.704684i | \(-0.751089\pi\) | ||||
−0.709521 | + | 0.704684i | \(0.751089\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1881.56 | 0.171889 | ||||||||
\(494\) | −238.119 | −0.0216872 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3380.06 | 0.305986 | ||||||||
\(497\) | 35241.2 | 3.18065 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21095.9 | −1.89255 | −0.946276 | − | 0.323361i | \(-0.895187\pi\) | ||||
−0.946276 | + | 0.323361i | \(0.895187\pi\) | |||||||
\(500\) | −503.237 | −0.0450109 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −74.1257 | −0.00659042 | ||||||||
\(503\) | 4997.19 | 0.442970 | 0.221485 | − | 0.975164i | \(-0.428910\pi\) | ||||
0.221485 | + | 0.975164i | \(0.428910\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1983.35 | 0.174768 | ||||||||
\(506\) | −19699.1 | −1.73069 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 659.295 | 0.0575817 | ||||||||
\(509\) | 66.7780 | 0.00581509 | 0.00290755 | − | 0.999996i | \(-0.499074\pi\) | ||||
0.00290755 | + | 0.999996i | \(0.499074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36086.1 | −3.12398 | ||||||||
\(512\) | 9741.38 | 0.840844 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2072.86 | −0.177879 | ||||||||
\(515\) | 5758.75 | 0.492740 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2080.05 | −0.176945 | ||||||||
\(518\) | −24316.5 | −2.06256 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 492.530 | 0.0415363 | ||||||||
\(521\) | −18888.9 | −1.58837 | −0.794184 | − | 0.607678i | \(-0.792101\pi\) | ||||
−0.794184 | + | 0.607678i | \(0.792101\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12882.2 | −1.07706 | −0.538529 | − | 0.842607i | \(-0.681020\pi\) | ||||
−0.538529 | + | 0.842607i | \(0.681020\pi\) | |||||||
\(524\) | −1364.89 | −0.113789 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3167.14 | −0.262536 | ||||||||
\(527\) | 582.468 | 0.0481456 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −65.1627 | −0.00535569 | ||||||||
\(530\) | −3056.79 | −0.250526 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −228.613 | −0.0186309 | ||||||||
\(533\) | 2026.82 | 0.164711 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1812.50 | 0.146469 | ||||||||
\(536\) | 11655.2 | 0.939233 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5820.58 | 0.466437 | ||||||||
\(539\) | 37477.1 | 2.99490 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8225.78 | −0.653704 | −0.326852 | − | 0.945076i | \(-0.605988\pi\) | ||||
−0.326852 | + | 0.945076i | \(0.605988\pi\) | |||||||
\(542\) | 20443.3 | 1.62014 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −372.557 | −0.0293626 | ||||||||
\(545\) | −606.087 | −0.0476366 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11783.2 | −0.921049 | −0.460524 | − | 0.887647i | \(-0.652339\pi\) | ||||
−0.460524 | + | 0.887647i | \(0.652339\pi\) | |||||||
\(548\) | −1336.38 | −0.104174 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 20759.6 | 1.60944 | ||||||||
\(551\) | −1681.68 | −0.130022 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11324.9 | 0.870860 | ||||||||
\(554\) | 14250.6 | 1.09287 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1440.23 | −0.109855 | ||||||||
\(557\) | −8763.38 | −0.666636 | −0.333318 | − | 0.942814i | \(-0.608168\pi\) | ||||
−0.333318 | + | 0.942814i | \(0.608168\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3754.86 | −0.284103 | ||||||||
\(560\) | 6444.83 | 0.486328 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16461.3 | 1.23555 | ||||||||
\(563\) | 17285.5 | 1.29396 | 0.646978 | − | 0.762509i | \(-0.276033\pi\) | ||||
0.646978 | + | 0.762509i | \(0.276033\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3923.99 | −0.292183 | ||||||||
\(566\) | 16284.6 | 1.20935 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −24501.9 | −1.80999 | ||||||||
\(569\) | −16391.4 | −1.20767 | −0.603835 | − | 0.797110i | \(-0.706361\pi\) | ||||
−0.603835 | + | 0.797110i | \(0.706361\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2412.70 | −0.176827 | −0.0884134 | − | 0.996084i | \(-0.528180\pi\) | ||||
−0.0884134 | + | 0.996084i | \(0.528180\pi\) | |||||||
\(572\) | 319.790 | 0.0233760 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 24390.6 | 1.77360 | ||||||||
\(575\) | −12753.4 | −0.924960 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22394.9 | −1.61579 | −0.807897 | − | 0.589324i | \(-0.799394\pi\) | ||||
−0.807897 | + | 0.589324i | \(0.799394\pi\) | |||||||
\(578\) | 14068.2 | 1.01239 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −330.198 | −0.0236392 | ||||||||
\(581\) | −26951.9 | −1.92453 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20907.7 | 1.48526 | ||||||||
\(584\) | 25089.3 | 1.77774 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17908.6 | −1.26245 | ||||||||
\(587\) | 5624.16 | 0.395458 | 0.197729 | − | 0.980257i | \(-0.436643\pi\) | ||||
0.197729 | + | 0.980257i | \(0.436643\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −520.593 | −0.0364188 | ||||||||
\(590\) | −4693.89 | −0.327533 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 18383.2 | 1.27626 | ||||||||
\(593\) | −17933.9 | −1.24192 | −0.620960 | − | 0.783843i | \(-0.713257\pi\) | ||||
−0.620960 | + | 0.783843i | \(0.713257\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1110.61 | 0.0765217 | ||||||||
\(596\) | 1268.02 | 0.0871478 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2462.47 | −0.168391 | ||||||||
\(599\) | 20410.3 | 1.39223 | 0.696113 | − | 0.717932i | \(-0.254911\pi\) | ||||
0.696113 | + | 0.717932i | \(0.254911\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26687.9 | −1.81135 | −0.905675 | − | 0.423973i | \(-0.860635\pi\) | ||||
−0.905675 | + | 0.423973i | \(0.860635\pi\) | |||||||
\(602\) | −45185.7 | −3.05919 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1770.76 | −0.119290 | ||||||||
\(605\) | 7099.41 | 0.477077 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9563.73 | −0.639505 | −0.319753 | − | 0.947501i | \(-0.603600\pi\) | ||||
−0.319753 | + | 0.947501i | \(0.603600\pi\) | |||||||
\(608\) | 332.981 | 0.0222108 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 350.779 | 0.0232830 | ||||||||
\(611\) | −260.015 | −0.0172162 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18801.5 | −1.23880 | −0.619400 | − | 0.785075i | \(-0.712624\pi\) | ||||
−0.619400 | + | 0.785075i | \(0.712624\pi\) | |||||||
\(614\) | 26738.2 | 1.75744 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −40539.6 | −2.65160 | ||||||||
\(617\) | 9903.34 | 0.646181 | 0.323090 | − | 0.946368i | \(-0.395278\pi\) | ||||
0.323090 | + | 0.946368i | \(0.395278\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6474.65 | 0.420417 | 0.210208 | − | 0.977657i | \(-0.432586\pi\) | ||||
0.210208 | + | 0.977657i | \(0.432586\pi\) | |||||||
\(620\) | −102.219 | −0.00662128 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15242.5 | −0.982587 | ||||||||
\(623\) | −4676.96 | −0.300768 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12306.3 | 0.787605 | ||||||||
\(626\) | 23908.1 | 1.52645 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −877.073 | −0.0557309 | ||||||||
\(629\) | 3167.89 | 0.200814 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17350.1 | 1.09461 | 0.547304 | − | 0.836934i | \(-0.315654\pi\) | ||||
0.547304 | + | 0.836934i | \(0.315654\pi\) | |||||||
\(632\) | −7873.82 | −0.495575 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2218.10 | 0.138946 | ||||||||
\(635\) | 2862.63 | 0.178897 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4684.80 | 0.291395 | ||||||||
\(638\) | 28308.4 | 1.75665 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4840.83 | −0.298985 | ||||||||
\(641\) | −22564.0 | −1.39037 | −0.695183 | − | 0.718833i | \(-0.744677\pi\) | ||||
−0.695183 | + | 0.718833i | \(0.744677\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4977.44 | 0.305274 | 0.152637 | − | 0.988282i | \(-0.451224\pi\) | ||||
0.152637 | + | 0.988282i | \(0.451224\pi\) | |||||||
\(644\) | −2364.17 | −0.144660 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 373.311 | 0.0227364 | ||||||||
\(647\) | 13751.2 | 0.835571 | 0.417785 | − | 0.908546i | \(-0.362806\pi\) | ||||
0.417785 | + | 0.908546i | \(0.362806\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32105.0 | 1.94180 | ||||||||
\(650\) | 2595.04 | 0.156594 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −454.636 | −0.0273082 | ||||||||
\(653\) | −11758.0 | −0.704635 | −0.352317 | − | 0.935881i | \(-0.614606\pi\) | ||||
−0.352317 | + | 0.935881i | \(0.614606\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5926.29 | −0.353526 | ||||||||
\(656\) | −18439.2 | −1.09746 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3129.01 | −0.185382 | ||||||||
\(659\) | −9970.21 | −0.589354 | −0.294677 | − | 0.955597i | \(-0.595212\pi\) | ||||
−0.294677 | + | 0.955597i | \(0.595212\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3802.25 | −0.223737 | −0.111869 | − | 0.993723i | \(-0.535684\pi\) | ||||
−0.111869 | + | 0.993723i | \(0.535684\pi\) | |||||||
\(662\) | 13396.1 | 0.786484 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 18738.6 | 1.09518 | ||||||||
\(665\) | −992.627 | −0.0578833 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17390.8 | −1.00956 | ||||||||
\(668\) | −2300.54 | −0.133250 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4803.95 | −0.277004 | ||||||||
\(671\) | −2399.24 | −0.138035 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2812.14 | −0.161070 | −0.0805350 | − | 0.996752i | \(-0.525663\pi\) | ||||
−0.0805350 | + | 0.996752i | \(0.525663\pi\) | |||||||
\(674\) | −1872.33 | −0.107002 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1483.82 | −0.0844233 | ||||||||
\(677\) | 10291.8 | 0.584261 | 0.292131 | − | 0.956378i | \(-0.405636\pi\) | ||||
0.292131 | + | 0.956378i | \(0.405636\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2174.50 | −0.122901 | ||||||||
\(680\) | −772.163 | −0.0435457 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8763.35 | 0.492032 | ||||||||
\(683\) | −617.671 | −0.0346040 | −0.0173020 | − | 0.999850i | \(-0.505508\pi\) | ||||
−0.0173020 | + | 0.999850i | \(0.505508\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5802.51 | −0.323653 | ||||||||
\(686\) | 25040.3 | 1.39365 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 34160.3 | 1.89295 | ||||||||
\(689\) | 2613.55 | 0.144511 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23997.5 | 1.32114 | 0.660569 | − | 0.750766i | \(-0.270315\pi\) | ||||
0.660569 | + | 0.750766i | \(0.270315\pi\) | |||||||
\(692\) | 2892.73 | 0.158909 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20341.2 | 1.11259 | ||||||||
\(695\) | −6253.40 | −0.341302 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3177.54 | −0.172680 | ||||||||
\(698\) | −11020.7 | −0.597622 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2491.45 | 0.134525 | ||||||||
\(701\) | −24153.2 | −1.30136 | −0.650682 | − | 0.759351i | \(-0.725517\pi\) | ||||
−0.650682 | + | 0.759351i | \(0.725517\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2831.37 | −0.151902 | ||||||||
\(704\) | 27952.0 | 1.49642 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11599.2 | 0.618333 | ||||||||
\(707\) | −20406.6 | −1.08553 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2210.49 | −0.117090 | −0.0585450 | − | 0.998285i | \(-0.518646\pi\) | ||||
−0.0585450 | + | 0.998285i | \(0.518646\pi\) | |||||||
\(710\) | 10099.0 | 0.533813 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3251.72 | 0.171156 | ||||||||
\(713\) | −5383.63 | −0.282775 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1388.51 | 0.0726257 | ||||||||
\(716\) | −515.706 | −0.0269174 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4868.48 | 0.253050 | ||||||||
\(719\) | −33927.5 | −1.75978 | −0.879891 | − | 0.475175i | \(-0.842385\pi\) | ||||
−0.879891 | + | 0.475175i | \(0.842385\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −59251.7 | −3.06054 | ||||||||
\(722\) | 19890.0 | 1.02525 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1633.95 | 0.0838747 | ||||||||
\(725\) | 18327.1 | 0.938830 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19140.6 | −0.976461 | −0.488231 | − | 0.872715i | \(-0.662358\pi\) | ||||
−0.488231 | + | 0.872715i | \(0.662358\pi\) | |||||||
\(728\) | −5067.63 | −0.257993 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10341.1 | −0.524303 | ||||||||
\(731\) | 5886.67 | 0.297847 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28268.3 | 1.42444 | 0.712219 | − | 0.701957i | \(-0.247690\pi\) | ||||
0.712219 | + | 0.701957i | \(0.247690\pi\) | |||||||
\(734\) | −897.634 | −0.0451393 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3443.47 | 0.172456 | ||||||||
\(737\) | 32857.7 | 1.64224 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36066.3 | 1.79529 | 0.897645 | − | 0.440719i | \(-0.145277\pi\) | ||||
0.897645 | + | 0.440719i | \(0.145277\pi\) | |||||||
\(740\) | −555.940 | −0.0276172 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 31451.3 | 1.55608 | ||||||||
\(743\) | 19646.9 | 0.970088 | 0.485044 | − | 0.874490i | \(-0.338804\pi\) | ||||
0.485044 | + | 0.874490i | \(0.338804\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5505.67 | 0.270755 | ||||||||
\(746\) | −19575.5 | −0.960739 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −501.350 | −0.0245069 | ||||||||
\(749\) | −18648.7 | −0.909760 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14286.8 | −0.694183 | −0.347092 | − | 0.937831i | \(-0.612831\pi\) | ||||
−0.347092 | + | 0.937831i | \(0.612831\pi\) | |||||||
\(752\) | 2365.52 | 0.114710 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3538.67 | 0.170916 | ||||||||
\(755\) | −7688.56 | −0.370616 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6082.28 | −0.292027 | −0.146013 | − | 0.989283i | \(-0.546644\pi\) | ||||
−0.146013 | + | 0.989283i | \(0.546644\pi\) | |||||||
\(758\) | 36960.4 | 1.77106 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 690.137 | 0.0329393 | ||||||||
\(761\) | 14570.0 | 0.694038 | 0.347019 | − | 0.937858i | \(-0.387194\pi\) | ||||
0.347019 | + | 0.937858i | \(0.387194\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6236.02 | 0.295884 | ||||||||
\(764\) | 741.882 | 0.0351314 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27813.0 | −1.31191 | ||||||||
\(767\) | 4013.26 | 0.188932 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40710.2 | 1.90904 | 0.954518 | − | 0.298153i | \(-0.0963705\pi\) | ||||
0.954518 | + | 0.298153i | \(0.0963705\pi\) | |||||||
\(770\) | 16709.3 | 0.782027 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1011.77 | −0.0471687 | ||||||||
\(773\) | −22309.4 | −1.03805 | −0.519026 | − | 0.854758i | \(-0.673705\pi\) | ||||
−0.519026 | + | 0.854758i | \(0.673705\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5673.47 | 0.262964 | ||||||||
\(776\) | 1511.85 | 0.0699385 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 39533.2 | 1.82177 | ||||||||
\(779\) | 2839.99 | 0.130620 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −69074.3 | −3.16475 | ||||||||
\(782\) | 3860.54 | 0.176538 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −42620.6 | −1.94154 | ||||||||
\(785\) | −3808.21 | −0.173147 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29959.9 | 1.35700 | 0.678499 | − | 0.734602i | \(-0.262631\pi\) | ||||
0.678499 | + | 0.734602i | \(0.262631\pi\) | |||||||
\(788\) | 3198.97 | 0.144617 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3245.36 | 0.146158 | ||||||||
\(791\) | 40373.9 | 1.81483 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −299.915 | −0.0134304 | ||||||||
\(794\) | −12746.8 | −0.569734 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2137.02 | 0.0951567 | ||||||||
\(797\) | −33708.9 | −1.49815 | −0.749077 | − | 0.662483i | \(-0.769503\pi\) | ||||
−0.749077 | + | 0.662483i | \(0.769503\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 407.638 | 0.0180491 | ||||||||
\(800\) | −3628.86 | −0.160374 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 27440.8 | 1.20819 | ||||||||
\(803\) | 70730.3 | 3.10837 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10265.1 | −0.449437 | ||||||||
\(806\) | 1095.46 | 0.0478732 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14188.0 | 0.617736 | ||||||||
\(809\) | 33454.7 | 1.45390 | 0.726951 | − | 0.686690i | \(-0.240937\pi\) | ||||
0.726951 | + | 0.686690i | \(0.240937\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10656.8 | 0.461418 | 0.230709 | − | 0.973023i | \(-0.425895\pi\) | ||||
0.230709 | + | 0.973023i | \(0.425895\pi\) | |||||||
\(812\) | 3397.40 | 0.146829 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 47661.5 | 2.05225 | ||||||||
\(815\) | −1974.01 | −0.0848423 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5261.33 | −0.225301 | ||||||||
\(818\) | 44848.4 | 1.91698 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 557.633 | 0.0237480 | ||||||||
\(821\) | −12361.9 | −0.525497 | −0.262749 | − | 0.964864i | \(-0.584629\pi\) | ||||
−0.262749 | + | 0.964864i | \(0.584629\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4611.71 | −0.195327 | −0.0976634 | − | 0.995220i | \(-0.531137\pi\) | ||||
−0.0976634 | + | 0.995220i | \(0.531137\pi\) | |||||||
\(824\) | 41195.5 | 1.74164 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 48295.4 | 2.03440 | ||||||||
\(827\) | 12793.3 | 0.537927 | 0.268964 | − | 0.963150i | \(-0.413319\pi\) | ||||
0.268964 | + | 0.963150i | \(0.413319\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8373.92 | −0.350830 | −0.175415 | − | 0.984495i | \(-0.556127\pi\) | ||||
−0.175415 | + | 0.984495i | \(0.556127\pi\) | |||||||
\(830\) | −7723.54 | −0.322997 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3494.12 | 0.145597 | ||||||||
\(833\) | −7344.59 | −0.305492 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9988.85 | −0.413986 | ||||||||
\(836\) | 448.092 | 0.0185378 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −23835.0 | −0.982536 | ||||||||
\(839\) | 18047.5 | 0.742633 | 0.371316 | − | 0.928506i | \(-0.378906\pi\) | ||||
0.371316 | + | 0.928506i | \(0.378906\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 602.340 | 0.0246972 | ||||||||
\(842\) | −38586.8 | −1.57932 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3184.95 | −0.129894 | ||||||||
\(845\) | −6442.69 | −0.262290 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −73045.7 | −2.96326 | ||||||||
\(848\) | −23777.1 | −0.962864 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4068.38 | −0.164170 | ||||||||
\(851\) | −29280.1 | −1.17945 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31063.1 | −1.24687 | −0.623436 | − | 0.781875i | \(-0.714264\pi\) | ||||
−0.623436 | + | 0.781875i | \(0.714264\pi\) | |||||||
\(854\) | −3609.16 | −0.144617 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12965.8 | 0.517712 | ||||||||
\(857\) | −653.734 | −0.0260573 | −0.0130287 | − | 0.999915i | \(-0.504147\pi\) | ||||
−0.0130287 | + | 0.999915i | \(0.504147\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 227.597 | 0.00904018 | 0.00452009 | − | 0.999990i | \(-0.498561\pi\) | ||||
0.00452009 | + | 0.999990i | \(0.498561\pi\) | |||||||
\(860\) | −1033.06 | −0.0409618 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1934.75 | 0.0764474 | ||||||||
\(863\) | −41470.6 | −1.63578 | −0.817889 | − | 0.575377i | \(-0.804855\pi\) | ||||
−0.817889 | + | 0.575377i | \(0.804855\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12560.1 | 0.493706 | ||||||||
\(866\) | 4482.33 | 0.175884 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1051.72 | 0.0411266 | ||||||||
\(869\) | −22197.4 | −0.866508 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4107.36 | 0.159785 | ||||||||
\(872\) | −4335.67 | −0.168377 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3450.43 | −0.133539 | ||||||||
\(875\) | 22481.7 | 0.868596 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8502.68 | 0.327383 | 0.163692 | − | 0.986512i | \(-0.447660\pi\) | ||||
0.163692 | + | 0.986512i | \(0.447660\pi\) | |||||||
\(878\) | −22665.7 | −0.871221 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −12632.2 | −0.483898 | ||||||||
\(881\) | 8892.91 | 0.340079 | 0.170040 | − | 0.985437i | \(-0.445610\pi\) | ||||
0.170040 | + | 0.985437i | \(0.445610\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20622.6 | −0.785964 | −0.392982 | − | 0.919546i | \(-0.628557\pi\) | ||||
−0.392982 | + | 0.919546i | \(0.628557\pi\) | |||||||
\(884\) | −62.6710 | −0.00238445 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23954.5 | 0.908316 | ||||||||
\(887\) | −67.3701 | −0.00255024 | −0.00127512 | − | 0.999999i | \(-0.500406\pi\) | ||||
−0.00127512 | + | 0.999999i | \(0.500406\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29453.5 | −1.11118 | ||||||||
\(890\) | −1340.27 | −0.0504784 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −222.747 | −0.00836113 | ||||||||
\(893\) | −364.335 | −0.0136529 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2239.17 | −0.0836282 | ||||||||
\(896\) | 49807.2 | 1.85708 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 53452.4 | 1.98634 | ||||||||
\(899\) | 7736.50 | 0.287015 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4097.39 | −0.151502 | ||||||||
\(902\) | −47806.7 | −1.76473 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −28070.5 | −1.03275 | ||||||||
\(905\) | 7094.53 | 0.260586 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19833.4 | 0.726082 | 0.363041 | − | 0.931773i | \(-0.381738\pi\) | ||||
0.363041 | + | 0.931773i | \(0.381738\pi\) | |||||||
\(908\) | 4255.04 | 0.155516 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2088.73 | 0.0760888 | ||||||||
\(911\) | 27914.0 | 1.01518 | 0.507591 | − | 0.861598i | \(-0.330536\pi\) | ||||
0.507591 | + | 0.861598i | \(0.330536\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 52826.9 | 1.91491 | ||||||||
\(914\) | −32950.1 | −1.19244 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 437.675 | 0.0157873 | ||||||||
\(917\) | 60975.5 | 2.19584 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7309.96 | −0.262387 | −0.131193 | − | 0.991357i | \(-0.541881\pi\) | ||||
−0.131193 | + | 0.991357i | \(0.541881\pi\) | |||||||
\(920\) | 7136.94 | 0.255759 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −11662.7 | −0.416583 | ||||||||
\(923\) | −8634.58 | −0.307921 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30856.5 | 1.09682 | ||||||||
\(926\) | −22610.0 | −0.802387 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4948.41 | −0.175042 | ||||||||
\(929\) | 11015.8 | 0.389037 | 0.194518 | − | 0.980899i | \(-0.437686\pi\) | ||||
0.194518 | + | 0.980899i | \(0.437686\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6564.38 | 0.231084 | ||||||||
\(932\) | −1406.08 | −0.0494181 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 21899.7 | 0.767217 | ||||||||
\(935\) | −2176.84 | −0.0761392 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24322.9 | 0.848018 | 0.424009 | − | 0.905658i | \(-0.360622\pi\) | ||||
0.424009 | + | 0.905658i | \(0.360622\pi\) | |||||||
\(938\) | 49427.7 | 1.72055 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −71.5373 | −0.00248222 | ||||||||
\(941\) | −33881.0 | −1.17374 | −0.586869 | − | 0.809682i | \(-0.699640\pi\) | ||||
−0.586869 | + | 0.809682i | \(0.699640\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29369.3 | 1.01421 | ||||||||
\(944\) | −36511.2 | −1.25883 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 88566.1 | 3.04390 | ||||||||
\(947\) | 7065.40 | 0.242444 | 0.121222 | − | 0.992625i | \(-0.461319\pi\) | ||||
0.121222 | + | 0.992625i | \(0.461319\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8841.60 | 0.302435 | ||||||||
\(950\) | 3636.20 | 0.124183 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7944.77 | 0.270474 | ||||||||
\(953\) | −21167.4 | −0.719495 | −0.359747 | − | 0.933050i | \(-0.617137\pi\) | ||||
−0.359747 | + | 0.933050i | \(0.617137\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3221.22 | 0.109148 | ||||||||
\(956\) | 165.766 | 0.00560801 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −41871.9 | −1.41213 | ||||||||
\(959\) | 59701.9 | 2.01030 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27396.0 | −0.919608 | ||||||||
\(962\) | 5957.90 | 0.199678 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4481.48 | 0.149729 | ||||||||
\(965\) | −4393.04 | −0.146546 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10137.8 | −0.337134 | −0.168567 | − | 0.985690i | \(-0.553914\pi\) | ||||
−0.168567 | + | 0.985690i | \(0.553914\pi\) | |||||||
\(968\) | 50785.9 | 1.68628 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −623.141 | −0.0206267 | ||||||||
\(971\) | 13500.9 | 0.446203 | 0.223101 | − | 0.974795i | \(-0.428382\pi\) | ||||
0.223101 | + | 0.974795i | \(0.428382\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 64341.1 | 2.11992 | ||||||||
\(974\) | −41906.3 | −1.37861 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2728.52 | 0.0894853 | ||||||||
\(977\) | −25825.9 | −0.845695 | −0.422848 | − | 0.906201i | \(-0.638969\pi\) | ||||
−0.422848 | + | 0.906201i | \(0.638969\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9167.06 | 0.299265 | ||||||||
\(980\) | 1288.92 | 0.0420132 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 45521.5 | 1.47928 | ||||||||
\(983\) | −21515.7 | −0.698113 | −0.349056 | − | 0.937102i | \(-0.613498\pi\) | ||||
−0.349056 | + | 0.937102i | \(0.613498\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13889.8 | 0.449304 | ||||||||
\(986\) | −5547.75 | −0.179185 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 56.0135 | 0.00180367 | ||||||||
\(989\) | −54409.3 | −1.74936 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1578.43 | 0.0505957 | 0.0252979 | − | 0.999680i | \(-0.491947\pi\) | ||||
0.0252979 | + | 0.999680i | \(0.491947\pi\) | |||||||
\(992\) | −1531.86 | −0.0490290 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −103908. | −3.31566 | ||||||||
\(995\) | 9278.84 | 0.295637 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42702.0 | −1.35645 | −0.678227 | − | 0.734852i | \(-0.737252\pi\) | ||||
−0.678227 | + | 0.734852i | \(0.737252\pi\) | |||||||
\(998\) | 62201.1 | 1.97289 | ||||||||
\(999\) | 0 | 0 |
(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 | 2151.4.a.g.1.18 | ✓ | 59 | |
3.2 | odd | 2 | 2151.4.a.h.1.42 | yes | 59 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.4.a.g.1.18 | ✓ | 59 | 1.1 | even | 1 | trivial | |
2151.4.a.h.1.42 | yes | 59 | 3.2 | odd | 2 |