Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [855,2,Mod(64,855)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(855, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("855.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 855 = 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 855.be (of order \(6\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(6.82720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6x^{10} + 29x^{8} - 40x^{6} + 43x^{4} - 7x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 334.3 | ||
Root | \(-1.83525 - 1.05958i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 855.334 |
Dual form | 855.2.be.d.64.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(191\) | \(496\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.408663 | − | 0.235942i | −0.288969 | − | 0.166836i | 0.348508 | − | 0.937306i | \(-0.386688\pi\) |
−0.637477 | + | 0.770470i | \(0.720022\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.888663 | − | 1.53921i | −0.444331 | − | 0.769605i | ||||
\(5\) | −1.47848 | − | 1.67752i | −0.661197 | − | 0.750212i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.17540i | 0.444259i | 0.975017 | + | 0.222129i | \(0.0713007\pi\) | ||||
−0.975017 | + | 0.222129i | \(0.928699\pi\) | |||||||
\(8\) | 1.78246i | 0.630194i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.208403 | + | 1.03438i | 0.0659029 | + | 0.327099i | ||||
\(11\) | −0.713538 | −0.215140 | −0.107570 | − | 0.994198i | \(-0.534307\pi\) | ||||
−0.107570 | + | 0.994198i | \(0.534307\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.55344 | + | 2.05158i | −0.985546 | + | 0.569005i | −0.903940 | − | 0.427659i | \(-0.859338\pi\) |
−0.0816060 | + | 0.996665i | \(0.526005\pi\) | |||||||
\(14\) | 0.277326 | − | 0.480342i | 0.0741184 | − | 0.128377i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.35677 | + | 2.34999i | −0.339192 | + | 0.587498i | ||||
\(17\) | 2.21038 | + | 1.27616i | 0.536096 | + | 0.309515i | 0.743495 | − | 0.668741i | \(-0.233167\pi\) |
−0.207399 | + | 0.978256i | \(0.566500\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.57031 | − | 4.06622i | −0.360253 | − | 0.932855i | ||||
\(20\) | −1.26819 | + | 3.76645i | −0.283576 | + | 0.842203i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.291597 | + | 0.168353i | 0.0621686 | + | 0.0358931i | ||||
\(23\) | −0.525730 | + | 0.303530i | −0.109622 | + | 0.0632904i | −0.553809 | − | 0.832644i | \(-0.686826\pi\) |
0.444186 | + | 0.895934i | \(0.353493\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.628179 | + | 4.96038i | −0.125636 | + | 0.992076i | ||||
\(26\) | 1.93621 | 0.379722 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.80918 | − | 1.04453i | 0.341904 | − | 0.197398i | ||||
\(29\) | 0.429693 | + | 0.744250i | 0.0797920 | + | 0.138204i | 0.903160 | − | 0.429304i | \(-0.141241\pi\) |
−0.823368 | + | 0.567508i | \(0.807908\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.50914 | 0.450654 | 0.225327 | − | 0.974283i | \(-0.427655\pi\) | ||||
0.225327 | + | 0.974283i | \(0.427655\pi\) | |||||||
\(32\) | 4.19623 | − | 2.42270i | 0.741796 | − | 0.428276i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.602201 | − | 1.04304i | −0.103277 | − | 0.178880i | ||||
\(35\) | 1.97176 | − | 1.73781i | 0.333288 | − | 0.293743i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.38171i | 1.54234i | 0.636627 | + | 0.771172i | \(0.280329\pi\) | ||||
−0.636627 | + | 0.771172i | \(0.719671\pi\) | |||||||
\(38\) | −0.317665 | + | 2.03222i | −0.0515320 | + | 0.329669i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.99012 | − | 2.63533i | 0.472779 | − | 0.416683i | ||||
\(41\) | −2.06117 | + | 3.57005i | −0.321901 | + | 0.557548i | −0.980880 | − | 0.194612i | \(-0.937655\pi\) |
0.658979 | + | 0.752161i | \(0.270988\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.76759 | + | 5.06197i | 1.33705 | + | 0.771944i | 0.986368 | − | 0.164553i | \(-0.0526181\pi\) |
0.350677 | + | 0.936496i | \(0.385951\pi\) | |||||||
\(44\) | 0.634095 | + | 1.09828i | 0.0955934 | + | 0.165573i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.286462 | 0.0422365 | ||||||||
\(47\) | −9.10919 | + | 5.25919i | −1.32871 | + | 0.767132i | −0.985100 | − | 0.171980i | \(-0.944984\pi\) |
−0.343611 | + | 0.939112i | \(0.611650\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.61844 | 0.802634 | ||||||||
\(50\) | 1.42708 | − | 1.87891i | 0.201819 | − | 0.265718i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.31561 | + | 3.64632i | 0.875818 | + | 0.505654i | ||||
\(53\) | 4.31330 | − | 2.49028i | 0.592477 | − | 0.342067i | −0.173599 | − | 0.984816i | \(-0.555540\pi\) |
0.766076 | + | 0.642750i | \(0.222206\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.05495 | + | 1.19698i | 0.142250 | + | 0.161400i | ||||
\(56\) | −2.09510 | −0.279969 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 0.405530i | − | 0.0532488i | ||||||
\(59\) | 3.12496 | − | 5.41259i | 0.406835 | − | 0.704659i | −0.587698 | − | 0.809080i | \(-0.699966\pi\) |
0.994533 | + | 0.104421i | \(0.0332991\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.27733 | + | 3.94444i | 0.291582 | + | 0.505034i | 0.974184 | − | 0.225756i | \(-0.0724852\pi\) |
−0.682602 | + | 0.730790i | \(0.739152\pi\) | |||||||
\(62\) | −1.02539 | − | 0.592010i | −0.130225 | − | 0.0751854i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.14061 | 0.392577 | ||||||||
\(65\) | 8.69527 | + | 2.92776i | 1.07851 | + | 0.363144i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.48783 | + | 2.59105i | −0.548276 | + | 0.316547i | −0.748426 | − | 0.663218i | \(-0.769190\pi\) |
0.200151 | + | 0.979765i | \(0.435857\pi\) | |||||||
\(68\) | − | 4.53632i | − | 0.550109i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.21581 | + | 0.244957i | −0.145317 | + | 0.0292779i | ||||
\(71\) | −6.58393 | + | 11.4037i | −0.781368 | + | 1.35337i | 0.149776 | + | 0.988720i | \(0.452145\pi\) |
−0.931145 | + | 0.364650i | \(0.881189\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.7199 | − | 6.18914i | −1.25467 | − | 0.724384i | −0.282637 | − | 0.959227i | \(-0.591209\pi\) |
−0.972033 | + | 0.234842i | \(0.924543\pi\) | |||||||
\(74\) | 2.21354 | − | 3.83396i | 0.257319 | − | 0.445689i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.86329 | + | 6.03053i | −0.557857 | + | 0.691749i | ||||
\(77\) | − | 0.838691i | − | 0.0955777i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.98173 | + | 5.16450i | −0.335471 | + | 0.581052i | −0.983575 | − | 0.180499i | \(-0.942229\pi\) |
0.648105 | + | 0.761551i | \(0.275562\pi\) | |||||||
\(80\) | 5.94813 | − | 1.19841i | 0.665021 | − | 0.133986i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.68465 | − | 0.972633i | 0.186038 | − | 0.107409i | ||||
\(83\) | 13.8603i | 1.52136i | 0.649124 | + | 0.760682i | \(0.275136\pi\) | ||||
−0.649124 | + | 0.760682i | \(0.724864\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.12721 | − | 5.59475i | −0.122263 | − | 0.606836i | ||||
\(86\) | −2.38866 | − | 4.13729i | −0.257576 | − | 0.446135i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 1.27185i | − | 0.135580i | ||||||
\(89\) | −7.98173 | − | 13.8248i | −0.846061 | − | 1.46542i | −0.884696 | − | 0.466168i | \(-0.845634\pi\) |
0.0386349 | − | 0.999253i | \(-0.487699\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.41142 | − | 4.17670i | −0.252786 | − | 0.437837i | ||||
\(92\) | 0.934393 | + | 0.539472i | 0.0974172 | + | 0.0562439i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.96345 | 0.511941 | ||||||||
\(95\) | −4.49951 | + | 8.64606i | −0.461640 | + | 0.887067i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.4643 | − | 8.35099i | −1.46863 | − | 0.847915i | −0.469249 | − | 0.883066i | \(-0.655475\pi\) |
−0.999382 | + | 0.0351512i | \(0.988809\pi\) | |||||||
\(98\) | −2.29605 | − | 1.32563i | −0.231936 | − | 0.133908i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.19331 | − | 3.44121i | 0.819331 | − | 0.344121i | ||||
\(101\) | 7.01362 | + | 12.1479i | 0.697881 | + | 1.20877i | 0.969200 | + | 0.246276i | \(0.0792071\pi\) |
−0.271318 | + | 0.962490i | \(0.587460\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 3.55382i | − | 0.350169i | −0.984553 | − | 0.175084i | \(-0.943980\pi\) | ||
0.984553 | − | 0.175084i | \(-0.0560198\pi\) | |||||||
\(104\) | −3.65685 | − | 6.33385i | −0.358584 | − | 0.621085i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.35025 | −0.228276 | ||||||||
\(107\) | − | 3.63127i | − | 0.351048i | −0.984475 | − | 0.175524i | \(-0.943838\pi\) | ||
0.984475 | − | 0.175524i | \(-0.0561620\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.11134 | + | 5.38899i | −0.298012 | + | 0.516172i | −0.975681 | − | 0.219195i | \(-0.929657\pi\) |
0.677669 | + | 0.735367i | \(0.262990\pi\) | |||||||
\(110\) | −0.148704 | − | 0.738069i | −0.0141783 | − | 0.0703721i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.76218 | − | 1.59474i | −0.261001 | − | 0.150689i | ||||
\(113\) | − | 12.2707i | − | 1.15433i | −0.816626 | − | 0.577167i | \(-0.804158\pi\) | ||
0.816626 | − | 0.577167i | \(-0.195842\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.28646 | + | 0.433161i | 0.119963 | + | 0.0403925i | ||||
\(116\) | 0.763705 | − | 1.32278i | 0.0709082 | − | 0.122817i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.55411 | + | 1.47462i | −0.235125 | + | 0.135750i | ||||
\(119\) | −1.50000 | + | 2.59808i | −0.137505 | + | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4909 | −0.953715 | ||||||||
\(122\) | − | 2.14927i | − | 0.194585i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.22978 | − | 3.86209i | −0.200240 | − | 0.346826i | ||||
\(125\) | 9.24992 | − | 6.28005i | 0.827338 | − | 0.561705i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.86879 | − | 1.07894i | 0.165828 | − | 0.0957408i | −0.414789 | − | 0.909918i | \(-0.636145\pi\) |
0.580617 | + | 0.814177i | \(0.302811\pi\) | |||||||
\(128\) | −9.67592 | − | 5.58639i | −0.855239 | − | 0.493772i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.86266 | − | 3.24804i | −0.251072 | − | 0.284872i | ||||
\(131\) | −8.77471 | + | 15.1982i | −0.766650 | + | 1.32788i | 0.172720 | + | 0.984971i | \(0.444744\pi\) |
−0.939370 | + | 0.342906i | \(0.888589\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.77943 | − | 1.84574i | 0.414429 | − | 0.160046i | ||||
\(134\) | 2.44535 | 0.211246 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.27471 | + | 3.93991i | −0.195055 | + | 0.337845i | ||||
\(137\) | −4.39469 | + | 2.53728i | −0.375464 | + | 0.216774i | −0.675843 | − | 0.737046i | \(-0.736220\pi\) |
0.300379 | + | 0.953820i | \(0.402887\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.99086 | + | 5.18033i | 0.253682 | + | 0.439390i | 0.964537 | − | 0.263949i | \(-0.0850251\pi\) |
−0.710855 | + | 0.703339i | \(0.751692\pi\) | |||||||
\(140\) | −4.42708 | − | 1.49063i | −0.374156 | − | 0.125981i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.38122 | − | 3.10685i | 0.451582 | − | 0.260721i | ||||
\(143\) | 2.53551 | − | 1.46388i | 0.212030 | − | 0.122416i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.613205 | − | 1.82118i | 0.0509239 | − | 0.151241i | ||||
\(146\) | 2.92056 | + | 5.05855i | 0.241707 | + | 0.418649i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 14.4404 | − | 8.33718i | 1.18699 | − | 0.685312i | ||||
\(149\) | −4.80008 | + | 8.31399i | −0.393238 | + | 0.681108i | −0.992875 | − | 0.119164i | \(-0.961979\pi\) |
0.599636 | + | 0.800273i | \(0.295312\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.53638 | 0.613302 | 0.306651 | − | 0.951822i | \(-0.400792\pi\) | ||||
0.306651 | + | 0.951822i | \(0.400792\pi\) | |||||||
\(152\) | 7.24787 | − | 2.79901i | 0.587880 | − | 0.227029i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.197882 | + | 0.342742i | −0.0159458 | + | 0.0276190i | ||||
\(155\) | −3.70971 | − | 4.20914i | −0.297971 | − | 0.338086i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.53560 | + | 4.92803i | 0.681215 | + | 0.393300i | 0.800313 | − | 0.599583i | \(-0.204667\pi\) |
−0.119098 | + | 0.992883i | \(0.538000\pi\) | |||||||
\(158\) | 2.43705 | − | 1.40703i | 0.193881 | − | 0.111937i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −10.2682 | − | 3.45737i | −0.811772 | − | 0.273329i | ||||
\(161\) | −0.356769 | − | 0.617942i | −0.0281173 | − | 0.0487007i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.0688234i | 0.00539067i | 0.999996 | + | 0.00269533i | \(0.000857952\pi\) | ||||
−0.999996 | + | 0.00269533i | \(0.999142\pi\) | |||||||
\(164\) | 7.32674 | 0.572122 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.27022 | − | 5.66419i | 0.253819 | − | 0.439627i | ||||
\(167\) | 14.4143 | − | 8.32212i | 1.11542 | − | 0.643985i | 0.175189 | − | 0.984535i | \(-0.443946\pi\) |
0.940227 | + | 0.340550i | \(0.110613\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.91794 | − | 3.32197i | 0.147534 | − | 0.255536i | ||||
\(170\) | −0.859386 | + | 2.55233i | −0.0659119 | + | 0.195755i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 17.9935i | − | 1.37200i | ||||||
\(173\) | −10.5097 | − | 6.06778i | −0.799038 | − | 0.461325i | 0.0440965 | − | 0.999027i | \(-0.485959\pi\) |
−0.843135 | + | 0.537702i | \(0.819292\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.83042 | − | 0.738361i | −0.440739 | − | 0.0558148i | ||||
\(176\) | 0.968106 | − | 1.67681i | 0.0729737 | − | 0.126394i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.53290i | 0.564614i | ||||||||
\(179\) | 11.7538 | 0.878522 | 0.439261 | − | 0.898360i | \(-0.355240\pi\) | ||||
0.439261 | + | 0.898360i | \(0.355240\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.41794 | + | 7.65210i | 0.328383 | + | 0.568776i | 0.982191 | − | 0.187884i | \(-0.0601631\pi\) |
−0.653808 | + | 0.756660i | \(0.726830\pi\) | |||||||
\(182\) | 2.27582i | 0.168695i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.541030 | − | 0.937092i | −0.0398853 | − | 0.0690833i | ||||
\(185\) | 15.7380 | − | 13.8707i | 1.15708 | − | 1.01979i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.57719 | − | 0.910591i | −0.115336 | − | 0.0665890i | ||||
\(188\) | 16.1900 | + | 9.34730i | 1.18078 | + | 0.681722i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.87875 | − | 2.47171i | 0.281394 | − | 0.179316i | ||||
\(191\) | −14.2447 | −1.03071 | −0.515355 | − | 0.856977i | \(-0.672340\pi\) | ||||
−0.515355 | + | 0.856977i | \(0.672340\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.8924 | − | 9.75283i | −1.21594 | − | 0.702024i | −0.251894 | − | 0.967755i | \(-0.581053\pi\) |
−0.964047 | + | 0.265731i | \(0.914387\pi\) | |||||||
\(194\) | 3.94070 | + | 6.82549i | 0.282926 | + | 0.490041i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.99290 | − | 8.64795i | −0.356636 | − | 0.617711i | ||||
\(197\) | − | 4.33232i | − | 0.308665i | −0.988019 | − | 0.154332i | \(-0.950677\pi\) | ||
0.988019 | − | 0.154332i | \(-0.0493226\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.31574 | − | 10.9392i | −0.447711 | − | 0.775458i | 0.550526 | − | 0.834818i | \(-0.314427\pi\) |
−0.998237 | + | 0.0593602i | \(0.981094\pi\) | |||||||
\(200\) | −8.84168 | − | 1.11970i | −0.625201 | − | 0.0791750i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 6.61923i | − | 0.465727i | ||||||
\(203\) | −0.874790 | + | 0.505060i | −0.0613983 | + | 0.0354483i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.03626 | − | 1.82059i | 0.631119 | − | 0.127156i | ||||
\(206\) | −0.838496 | + | 1.45232i | −0.0584208 | + | 0.101188i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 11.1341i | − | 0.772009i | ||||||
\(209\) | 1.12047 | + | 2.90140i | 0.0775048 | + | 0.200694i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.1223 | + | 19.2645i | −0.765694 | + | 1.32622i | 0.174186 | + | 0.984713i | \(0.444271\pi\) |
−0.939879 | + | 0.341507i | \(0.889063\pi\) | |||||||
\(212\) | −7.66614 | − | 4.42605i | −0.526512 | − | 0.303982i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.856769 | + | 1.48397i | −0.0585675 | + | 0.101442i | ||||
\(215\) | −4.47115 | − | 22.1919i | −0.304930 | − | 1.51347i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.94923i | 0.200207i | ||||||||
\(218\) | 2.54298 | − | 1.46819i | 0.172232 | − | 0.0994383i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.904901 | − | 2.68750i | 0.0610084 | − | 0.181191i | ||||
\(221\) | −10.4726 | −0.704463 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.7974 | − | 6.81125i | −0.790015 | − | 0.456115i | 0.0499529 | − | 0.998752i | \(-0.484093\pi\) |
−0.839968 | + | 0.542636i | \(0.817426\pi\) | |||||||
\(224\) | 2.84763 | + | 4.93224i | 0.190265 | + | 0.329549i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.89518 | + | 5.01460i | −0.192585 | + | 0.333566i | ||||
\(227\) | 6.58913i | 0.437336i | 0.975799 | + | 0.218668i | \(0.0701711\pi\) | ||||
−0.975799 | + | 0.218668i | \(0.929829\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.585962 | 0.0387215 | 0.0193607 | − | 0.999813i | \(-0.493837\pi\) | ||||
0.0193607 | + | 0.999813i | \(0.493837\pi\) | |||||||
\(230\) | −0.423529 | − | 0.480547i | −0.0279267 | − | 0.0316863i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.32660 | + | 0.765910i | −0.0870953 | + | 0.0502845i | ||||
\(233\) | 6.19855 | + | 3.57873i | 0.406080 | + | 0.234451i | 0.689104 | − | 0.724662i | \(-0.258004\pi\) |
−0.283024 | + | 0.959113i | \(0.591338\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.2902 | + | 7.50527i | 1.45405 | + | 0.489590i | ||||
\(236\) | −11.1081 | −0.723078 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.22599 | − | 0.707826i | 0.0794691 | − | 0.0458815i | ||||
\(239\) | 3.65498 | 0.236421 | 0.118211 | − | 0.992989i | \(-0.462284\pi\) | ||||
0.118211 | + | 0.992989i | \(0.462284\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.63148 | − | 14.9502i | −0.556002 | − | 0.963024i | −0.997825 | − | 0.0659218i | \(-0.979001\pi\) |
0.441822 | − | 0.897103i | \(-0.354332\pi\) | |||||||
\(242\) | 4.28723 | + | 2.47523i | 0.275594 | + | 0.159114i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.04755 | − | 7.01056i | 0.259118 | − | 0.448805i | ||||
\(245\) | −8.30676 | − | 9.42507i | −0.530700 | − | 0.602146i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.9221 | + | 11.2274i | 0.885845 | + | 0.714385i | ||||
\(248\) | 4.47243i | 0.284000i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.26183 | + | 0.383984i | −0.332787 | + | 0.0242853i | ||||
\(251\) | −9.70702 | − | 16.8130i | −0.612702 | − | 1.06123i | −0.990783 | − | 0.135458i | \(-0.956749\pi\) |
0.378082 | − | 0.925772i | \(-0.376584\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.375128 | − | 0.216580i | 0.0235841 | − | 0.0136163i | ||||
\(254\) | −1.01827 | −0.0638921 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.504485 | − | 0.873793i | −0.0315303 | − | 0.0546121i | ||||
\(257\) | −12.0316 | + | 6.94643i | −0.750509 | + | 0.433306i | −0.825878 | − | 0.563849i | \(-0.809320\pi\) |
0.0753689 | + | 0.997156i | \(0.475987\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.0272 | −0.685199 | ||||||||
\(260\) | −3.22073 | − | 15.9856i | −0.199741 | − | 0.991386i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.17180 | − | 4.14064i | 0.443076 | − | 0.255810i | ||||
\(263\) | −12.9803 | − | 7.49417i | −0.800399 | − | 0.462110i | 0.0432118 | − | 0.999066i | \(-0.486241\pi\) |
−0.843611 | + | 0.536955i | \(0.819574\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.5547 | − | 3.55382i | −0.648367 | − | 0.218310i | ||||
\(266\) | −2.38866 | − | 0.373382i | −0.146458 | − | 0.0228935i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.97633 | + | 4.60514i | 0.487232 | + | 0.281304i | ||||
\(269\) | −9.68613 | + | 16.7769i | −0.590574 | + | 1.02290i | 0.403582 | + | 0.914944i | \(0.367765\pi\) |
−0.994155 | + | 0.107960i | \(0.965568\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.95897 | + | 10.3212i | −0.361982 | + | 0.626971i | −0.988287 | − | 0.152607i | \(-0.951233\pi\) |
0.626305 | + | 0.779578i | \(0.284566\pi\) | |||||||
\(272\) | −5.99795 | + | 3.46292i | −0.363679 | + | 0.209970i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.39460 | 0.144663 | ||||||||
\(275\) | 0.448230 | − | 3.53942i | 0.0270293 | − | 0.213435i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 10.9824i | − | 0.659866i | −0.944004 | − | 0.329933i | \(-0.892974\pi\) | ||
0.944004 | − | 0.329933i | \(-0.107026\pi\) | |||||||
\(278\) | − | 2.82268i | − | 0.169293i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.09757 | + | 3.51458i | 0.185115 | + | 0.210036i | ||||
\(281\) | 7.32488 | + | 12.6871i | 0.436965 | + | 0.756846i | 0.997454 | − | 0.0713160i | \(-0.0227199\pi\) |
−0.560488 | + | 0.828162i | \(0.689387\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.3927 | + | 9.46435i | 0.974447 | + | 0.562597i | 0.900589 | − | 0.434672i | \(-0.143136\pi\) |
0.0738576 | + | 0.997269i | \(0.476469\pi\) | |||||||
\(284\) | 23.4036 | 1.38875 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.38156 | −0.0816934 | ||||||||
\(287\) | −4.19623 | − | 2.42270i | −0.247696 | − | 0.143007i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.24281 | − | 9.08082i | −0.308401 | − | 0.534166i | ||||
\(290\) | −0.680287 | + | 0.599570i | −0.0399478 | + | 0.0352079i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 22.0002i | 1.28747i | ||||||||
\(293\) | − | 5.59625i | − | 0.326937i | −0.986549 | − | 0.163468i | \(-0.947732\pi\) | ||
0.986549 | − | 0.163468i | \(-0.0522681\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.6999 | + | 2.76022i | −0.797642 | + | 0.160706i | ||||
\(296\) | −16.7225 | −0.971976 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.92324 | − | 2.26508i | 0.227267 | − | 0.131213i | ||||
\(299\) | 1.24543 | − | 2.15715i | 0.0720252 | − | 0.124751i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.94983 | + | 10.3054i | −0.342943 | + | 0.593994i | ||||
\(302\) | −3.07984 | − | 1.77815i | −0.177225 | − | 0.102321i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 11.6861 | + | 1.82671i | 0.670245 | + | 0.104769i | ||||
\(305\) | 3.24992 | − | 9.65206i | 0.186090 | − | 0.552675i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.8678 | − | 10.3160i | −1.01977 | − | 0.588764i | −0.105732 | − | 0.994395i | \(-0.533718\pi\) |
−0.914037 | + | 0.405631i | \(0.867052\pi\) | |||||||
\(308\) | −1.29092 | + | 0.745314i | −0.0735571 | + | 0.0424682i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.522912 | + | 2.59540i | 0.0296994 | + | 0.147409i | ||||
\(311\) | 24.6587 | 1.39827 | 0.699134 | − | 0.714991i | \(-0.253569\pi\) | ||||
0.699134 | + | 0.714991i | \(0.253569\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.02985 | + | 1.74928i | −0.171257 | + | 0.0988753i | −0.583178 | − | 0.812344i | \(-0.698191\pi\) |
0.411921 | + | 0.911219i | \(0.364858\pi\) | |||||||
\(314\) | −2.32546 | − | 4.02781i | −0.131233 | − | 0.227303i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.5990 | 0.596240 | ||||||||
\(317\) | −27.1680 | + | 15.6854i | −1.52590 | + | 0.880982i | −0.526377 | + | 0.850251i | \(0.676450\pi\) |
−0.999528 | + | 0.0307305i | \(0.990217\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.306602 | − | 0.531051i | −0.0171664 | − | 0.0297331i | ||||
\(320\) | −4.64334 | − | 5.26846i | −0.259571 | − | 0.294516i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.336707i | 0.0187639i | ||||||||
\(323\) | 1.71818 | − | 10.9919i | 0.0956024 | − | 0.611603i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.94441 | − | 18.9152i | −0.440677 | − | 1.04922i | ||||
\(326\) | 0.0162383 | − | 0.0281256i | 0.000899358 | − | 0.00155773i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.36347 | − | 3.67395i | −0.351364 | − | 0.202860i | ||||
\(329\) | −6.18164 | − | 10.7069i | −0.340805 | − | 0.590292i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 35.7497 | 1.96498 | 0.982492 | − | 0.186305i | \(-0.0596512\pi\) | ||||
0.982492 | + | 0.186305i | \(0.0596512\pi\) | |||||||
\(332\) | 21.3339 | − | 12.3171i | 1.17085 | − | 0.675990i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.85415 | −0.429760 | ||||||||
\(335\) | 10.9817 | + | 3.69762i | 0.599996 | + | 0.202023i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.9403 | − | 13.2446i | −1.24964 | − | 0.721480i | −0.278602 | − | 0.960407i | \(-0.589871\pi\) |
−0.971038 | + | 0.238927i | \(0.923204\pi\) | |||||||
\(338\) | −1.56758 | + | 0.905045i | −0.0852653 | + | 0.0492279i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.60978 | + | 6.70686i | −0.412698 | + | 0.363731i | ||||
\(341\) | −1.79036 | −0.0969536 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.8317i | 0.800836i | ||||||||
\(344\) | −9.02276 | + | 15.6279i | −0.486474 | + | 0.842599i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.86329 | + | 4.95936i | 0.153931 | + | 0.266617i | ||||
\(347\) | 29.7392 | + | 17.1699i | 1.59648 | + | 0.921729i | 0.992158 | + | 0.124990i | \(0.0398898\pi\) |
0.604323 | + | 0.796739i | \(0.293444\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.4308 | 1.14717 | 0.573583 | − | 0.819148i | \(-0.305553\pi\) | ||||
0.573583 | + | 0.819148i | \(0.305553\pi\) | |||||||
\(350\) | 2.20847 | + | 1.67738i | 0.118048 | + | 0.0896599i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.99417 | + | 1.72869i | −0.159590 | + | 0.0921393i | ||||
\(353\) | 19.5659i | 1.04139i | 0.853744 | + | 0.520693i | \(0.174326\pi\) | ||||
−0.853744 | + | 0.520693i | \(0.825674\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 28.8642 | − | 5.81546i | 1.53195 | − | 0.308653i | ||||
\(356\) | −14.1861 | + | 24.5711i | −0.751863 | + | 1.30227i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.80335 | − | 2.77322i | −0.253865 | − | 0.146569i | ||||
\(359\) | 8.23630 | − | 14.2657i | 0.434695 | − | 0.752914i | −0.562576 | − | 0.826746i | \(-0.690189\pi\) |
0.997271 | + | 0.0738319i | \(0.0235228\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.0683 | + | 12.7704i | −0.740435 | + | 0.672128i | ||||
\(362\) | − | 4.16951i | − | 0.219144i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.28588 | + | 7.42336i | −0.224641 | + | 0.389090i | ||||
\(365\) | 5.46676 | + | 27.1335i | 0.286143 | + | 1.42023i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.0286 | − | 6.36735i | 0.575687 | − | 0.332373i | −0.183730 | − | 0.982977i | \(-0.558817\pi\) |
0.759418 | + | 0.650603i | \(0.225484\pi\) | |||||||
\(368\) | − | 1.64728i | − | 0.0858705i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.70424 | + | 1.95518i | −0.504499 | + | 0.101645i | ||||
\(371\) | 2.92708 | + | 5.06984i | 0.151966 | + | 0.263213i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.3342i | 1.00109i | 0.865711 | + | 0.500544i | \(0.166867\pi\) | ||||
−0.865711 | + | 0.500544i | \(0.833133\pi\) | |||||||
\(374\) | 0.429693 | + | 0.744250i | 0.0222189 | + | 0.0384843i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.37429 | − | 16.2368i | −0.483442 | − | 0.837346i | ||||
\(377\) | −3.05377 | − | 1.76310i | −0.157277 | − | 0.0908041i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.85789 | −0.506366 | −0.253183 | − | 0.967418i | \(-0.581477\pi\) | ||||
−0.253183 | + | 0.967418i | \(0.581477\pi\) | |||||||
\(380\) | 17.3066 | − | 0.757744i | 0.887812 | − | 0.0388714i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.82128 | + | 3.36092i | 0.297843 | + | 0.171959i | ||||
\(383\) | 17.6091 | + | 10.1666i | 0.899784 | + | 0.519490i | 0.877130 | − | 0.480253i | \(-0.159455\pi\) |
0.0226536 | + | 0.999743i | \(0.492789\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.40693 | + | 1.23999i | −0.0717036 | + | 0.0631958i | ||||
\(386\) | 4.60220 | + | 7.97125i | 0.234246 | + | 0.405726i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 29.6849i | 1.50702i | ||||||||
\(389\) | 0.502617 | + | 0.870559i | 0.0254837 | + | 0.0441391i | 0.878486 | − | 0.477768i | \(-0.158554\pi\) |
−0.853002 | + | 0.521907i | \(0.825221\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.54942 | −0.0783574 | ||||||||
\(392\) | 10.0146i | 0.505816i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.02217 | + | 1.77046i | −0.0514964 | + | 0.0891944i | ||||
\(395\) | 13.0720 | − | 2.63371i | 0.657724 | − | 0.132516i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.54093 | + | 4.93111i | 0.428657 | + | 0.247485i | 0.698774 | − | 0.715342i | \(-0.253729\pi\) |
−0.270117 | + | 0.962827i | \(0.587063\pi\) | |||||||
\(398\) | 5.96059i | 0.298777i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.8046 | − | 8.20631i | −0.540228 | − | 0.410315i | ||||
\(401\) | 14.9159 | − | 25.8351i | 0.744865 | − | 1.29014i | −0.205393 | − | 0.978680i | \(-0.565847\pi\) |
0.950258 | − | 0.311464i | \(-0.100819\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.91606 | + | 5.14769i | −0.444140 | + | 0.256425i | ||||
\(404\) | 12.4655 | − | 21.5909i | 0.620181 | − | 1.07419i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.476660 | 0.0236562 | ||||||||
\(407\) | − | 6.69420i | − | 0.331819i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.8221 | + | 23.9406i | 0.683458 | + | 1.18378i | 0.973919 | + | 0.226898i | \(0.0728583\pi\) |
−0.290460 | + | 0.956887i | \(0.593808\pi\) | |||||||
\(410\) | −4.12234 | − | 1.38802i | −0.203588 | − | 0.0685495i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.47008 | + | 3.15815i | −0.269491 | + | 0.155591i | ||||
\(413\) | 6.36194 | + | 3.67307i | 0.313051 | + | 0.180740i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.2510 | − | 20.4922i | 1.14135 | − | 1.00592i | ||||
\(416\) | −9.94070 | + | 17.2178i | −0.487383 | + | 0.844172i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.226666 | − | 1.45006i | 0.0110866 | − | 0.0709249i | ||||
\(419\) | −11.2902 | −0.551562 | −0.275781 | − | 0.961220i | \(-0.588936\pi\) | ||||
−0.275781 | + | 0.961220i | \(0.588936\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.27471 | + | 3.93991i | −0.110863 | + | 0.192019i | −0.916118 | − | 0.400908i | \(-0.868695\pi\) |
0.805256 | + | 0.592928i | \(0.202028\pi\) | |||||||
\(422\) | 9.09059 | − | 5.24845i | 0.442523 | − | 0.255491i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.43883 | + | 7.68828i | 0.215569 | + | 0.373376i | ||||
\(425\) | −7.71877 | + | 10.1627i | −0.374415 | + | 0.492962i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.63629 | + | 2.67676i | −0.224366 | + | 0.129538i | ||||
\(428\) | −5.58929 | + | 3.22698i | −0.270168 | + | 0.155982i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.40880 | + | 10.1239i | −0.164387 | + | 0.488220i | ||||
\(431\) | 16.4517 | + | 28.4952i | 0.792451 | + | 1.37256i | 0.924445 | + | 0.381314i | \(0.124528\pi\) |
−0.131995 | + | 0.991250i | \(0.542138\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.3204 | − | 11.1547i | 0.928481 | − | 0.536059i | 0.0421503 | − | 0.999111i | \(-0.486579\pi\) |
0.886331 | + | 0.463052i | \(0.153246\pi\) | |||||||
\(434\) | 0.695848 | − | 1.20524i | 0.0334018 | − | 0.0578536i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.0597 | 0.529664 | ||||||||
\(437\) | 2.05978 | + | 1.66110i | 0.0985325 | + | 0.0794611i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.85287 | − | 4.94131i | 0.136160 | − | 0.235836i | −0.789880 | − | 0.613261i | \(-0.789857\pi\) |
0.926040 | + | 0.377425i | \(0.123191\pi\) | |||||||
\(440\) | −2.13356 | + | 1.88041i | −0.101714 | + | 0.0896451i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.27976 | + | 2.47092i | 0.203568 | + | 0.117530i | ||||
\(443\) | −10.0265 | + | 5.78881i | −0.476374 | + | 0.275034i | −0.718904 | − | 0.695109i | \(-0.755356\pi\) |
0.242530 | + | 0.970144i | \(0.422023\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.3905 | + | 33.8292i | −0.539963 | + | 1.60366i | ||||
\(446\) | 3.21412 | + | 5.56702i | 0.152193 | + | 0.263606i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.69147i | 0.174406i | ||||||||
\(449\) | −25.4726 | −1.20213 | −0.601063 | − | 0.799202i | \(-0.705256\pi\) | ||||
−0.601063 | + | 0.799202i | \(0.705256\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.47072 | − | 2.54737i | 0.0692537 | − | 0.119951i | ||||
\(452\) | −18.8872 | + | 10.9046i | −0.888381 | + | 0.512907i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.55465 | − | 2.69274i | 0.0729634 | − | 0.126376i | ||||
\(455\) | −3.44128 | + | 10.2204i | −0.161330 | + | 0.479140i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.92830i | 0.324092i | 0.986783 | + | 0.162046i | \(0.0518094\pi\) | ||||
−0.986783 | + | 0.162046i | \(0.948191\pi\) | |||||||
\(458\) | −0.239461 | − | 0.138253i | −0.0111893 | − | 0.00646014i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.476506 | − | 2.36507i | −0.0222172 | − | 0.110272i | ||||
\(461\) | 16.2473 | − | 28.1411i | 0.756712 | − | 1.31066i | −0.187806 | − | 0.982206i | \(-0.560138\pi\) |
0.944519 | − | 0.328458i | \(-0.106529\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.5062i | 0.999477i | 0.866176 | + | 0.499738i | \(0.166571\pi\) | ||||
−0.866176 | + | 0.499738i | \(0.833429\pi\) | |||||||
\(464\) | −2.33198 | −0.108259 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.68875 | − | 2.92499i | −0.0782296 | − | 0.135498i | ||||
\(467\) | − | 16.9509i | − | 0.784392i | −0.919882 | − | 0.392196i | \(-0.871715\pi\) | ||
0.919882 | − | 0.392196i | \(-0.128285\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.04551 | − | 5.27499i | −0.140629 | − | 0.243576i | ||||
\(470\) | −7.33838 | − | 8.32632i | −0.338494 | − | 0.384064i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.64771 | + | 5.57011i | 0.444072 | + | 0.256385i | ||||
\(473\) | −6.25601 | − | 3.61191i | −0.287652 | − | 0.166076i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.1564 | − | 5.23501i | 0.970724 | − | 0.240199i | ||||
\(476\) | 5.33198 | 0.244391 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.49366 | − | 0.862364i | −0.0683183 | − | 0.0394436i | ||||
\(479\) | −4.42894 | − | 7.67115i | −0.202364 | − | 0.350504i | 0.746926 | − | 0.664907i | \(-0.231529\pi\) |
−0.949290 | + | 0.314403i | \(0.898196\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.2473 | − | 33.3373i | −0.877601 | − | 1.52005i | ||||
\(482\) | 8.14611i | 0.371045i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.32284 | + | 16.1476i | 0.423765 | + | 0.733983i | ||||
\(485\) | 7.37628 | + | 36.6111i | 0.334940 | + | 1.66242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.0628i | 1.36227i | 0.732156 | + | 0.681137i | \(0.238514\pi\) | ||||
−0.732156 | + | 0.681137i | \(0.761486\pi\) | |||||||
\(488\) | −7.03081 | + | 4.05924i | −0.318270 | + | 0.183753i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.17090 | + | 5.81159i | 0.0528959 | + | 0.262541i | ||||
\(491\) | 1.55017 | − | 2.68497i | 0.0699580 | − | 0.121171i | −0.828925 | − | 0.559360i | \(-0.811047\pi\) |
0.898883 | + | 0.438190i | \(0.144380\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.19343i | 0.0987873i | ||||||||
\(494\) | −3.04045 | − | 7.87306i | −0.136796 | − | 0.354226i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.40432 | + | 5.89645i | −0.152858 | + | 0.264759i | ||||
\(497\) | −13.4039 | − | 7.73874i | −0.601246 | − | 0.347130i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.0696 | − | 27.8333i | 0.719372 | − | 1.24599i | −0.241877 | − | 0.970307i | \(-0.577763\pi\) |
0.961249 | − | 0.275682i | \(-0.0889037\pi\) | |||||||
\(500\) | −17.8864 | − | 8.65671i | −0.799903 | − | 0.387140i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.16117i | 0.408883i | ||||||||
\(503\) | 7.29040 | − | 4.20911i | 0.325063 | − | 0.187675i | −0.328584 | − | 0.944475i | \(-0.606571\pi\) |
0.653647 | + | 0.756800i | \(0.273238\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0090 | − | 29.7261i | 0.445393 | − | 1.32279i | ||||
\(506\) | −0.204402 | −0.00908676 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.32144 | − | 1.91764i | −0.147365 | − | 0.0850813i | ||||
\(509\) | −10.1725 | − | 17.6193i | −0.450888 | − | 0.780962i | 0.547553 | − | 0.836771i | \(-0.315559\pi\) |
−0.998441 | + | 0.0558093i | \(0.982226\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.27471 | − | 12.6002i | 0.321814 | − | 0.557398i | ||||
\(512\) | 22.8217i | 1.00859i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.55582 | 0.289165 | ||||||||
\(515\) | −5.96163 | + | 5.25427i | −0.262701 | + | 0.231531i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.49975 | − | 3.75263i | 0.285859 | − | 0.165041i | ||||
\(518\) | 4.50643 | + | 2.60179i | 0.198001 | + | 0.114316i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.21861 | + | 15.4990i | −0.228851 | + | 0.679674i | ||||
\(521\) | −15.3502 | −0.672507 | −0.336253 | − | 0.941772i | \(-0.609160\pi\) | ||||
−0.336253 | + | 0.941772i | \(0.609160\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.4633 | + | 6.61835i | −0.501256 | + | 0.289400i | −0.729232 | − | 0.684267i | \(-0.760122\pi\) |
0.227976 | + | 0.973667i | \(0.426789\pi\) | |||||||
\(524\) | 31.1910 | 1.36259 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.53638 | + | 6.12519i | 0.154193 | + | 0.267071i | ||||
\(527\) | 5.54614 | + | 3.20207i | 0.241594 | + | 0.139484i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.3157 | + | 19.5994i | −0.491989 | + | 0.852149i | ||||
\(530\) | 3.47480 | + | 3.94260i | 0.150936 | + | 0.171256i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.08827 | − | 5.71630i | −0.307316 | − | 0.247833i | ||||
\(533\) | − | 16.9146i | − | 0.732653i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.09155 | + | 5.36877i | −0.263361 | + | 0.232112i | ||||
\(536\) | −4.61844 | − | 7.99937i | −0.199486 | − | 0.345520i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.91673 | − | 4.57073i | 0.341315 | − | 0.197058i | ||||
\(539\) | −4.00897 | −0.172679 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.8704 | + | 24.0242i | 0.596335 | + | 1.03288i | 0.993357 | + | 0.115073i | \(0.0367102\pi\) |
−0.397022 | + | 0.917809i | \(0.629956\pi\) | |||||||
\(542\) | 4.87043 | − | 2.81194i | 0.209203 | − | 0.120783i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 12.3670 | 0.530232 | ||||||||
\(545\) | 13.6402 | − | 2.74819i | 0.584283 | − | 0.117719i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.7745 | − | 8.53008i | 0.631714 | − | 0.364720i | −0.149702 | − | 0.988731i | \(-0.547831\pi\) |
0.781415 | + | 0.624011i | \(0.214498\pi\) | |||||||
\(548\) | 7.81080 | + | 4.50957i | 0.333661 | + | 0.192639i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.01827 | + | 1.34068i | −0.0434193 | + | 0.0571666i | ||||
\(551\) | 2.35153 | − | 2.91593i | 0.100179 | − | 0.124223i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.07035 | − | 3.50472i | −0.258137 | − | 0.149036i | ||||
\(554\) | −2.59120 | + | 4.48808i | −0.110089 | + | 0.190680i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.31574 | − | 9.20713i | 0.225438 | − | 0.390469i | ||||
\(557\) | 22.9856 | − | 13.2708i | 0.973932 | − | 0.562300i | 0.0734992 | − | 0.997295i | \(-0.476583\pi\) |
0.900433 | + | 0.434995i | \(0.143250\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.5401 | −1.75696 | ||||||||
\(560\) | 1.40861 | + | 6.99142i | 0.0595246 | + | 0.295441i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 6.91298i | − | 0.291606i | ||||||
\(563\) | 35.5594i | 1.49865i | 0.662203 | + | 0.749325i | \(0.269622\pi\) | ||||
−0.662203 | + | 0.749325i | \(0.730378\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.5845 | + | 18.1421i | −0.865995 | + | 0.763243i | ||||
\(566\) | −4.46607 | − | 7.73546i | −0.187723 | − | 0.325146i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −20.3266 | − | 11.7356i | −0.852886 | − | 0.492414i | ||||
\(569\) | −14.9713 | −0.627628 | −0.313814 | − | 0.949485i | \(-0.601607\pi\) | ||||
−0.313814 | + | 0.949485i | \(0.601607\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.92724 | 0.248047 | 0.124024 | − | 0.992279i | \(-0.460420\pi\) | ||||
0.124024 | + | 0.992279i | \(0.460420\pi\) | |||||||
\(572\) | −4.50643 | − | 2.60179i | −0.188423 | − | 0.108786i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.14323 | + | 1.98013i | 0.0477175 | + | 0.0826492i | ||||
\(575\) | −1.17537 | − | 2.79849i | −0.0490165 | − | 0.116705i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.5559i | 0.605970i | 0.952995 | + | 0.302985i | \(0.0979832\pi\) | ||||
−0.952995 | + | 0.302985i | \(0.902017\pi\) | |||||||
\(578\) | 4.94800i | 0.205810i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.34811 | + | 0.674566i | −0.139023 | + | 0.0280098i | ||||
\(581\) | −16.2914 | −0.675880 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.07770 | + | 1.77691i | −0.127465 | + | 0.0735922i | ||||
\(584\) | 11.0319 | − | 19.1078i | 0.456503 | − | 0.790686i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.32039 | + | 2.28698i | −0.0545448 | + | 0.0944744i | ||||
\(587\) | −17.8262 | − | 10.2919i | −0.735765 | − | 0.424794i | 0.0847626 | − | 0.996401i | \(-0.472987\pi\) |
−0.820527 | + | 0.571607i | \(0.806320\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.94011 | − | 10.2027i | −0.162350 | − | 0.420395i | ||||
\(590\) | 6.24992 | + | 2.10439i | 0.257305 | + | 0.0866364i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −22.0469 | − | 12.7288i | −0.906124 | − | 0.523151i | ||||
\(593\) | −12.4120 | + | 7.16609i | −0.509701 | + | 0.294276i | −0.732711 | − | 0.680540i | \(-0.761745\pi\) |
0.223010 | + | 0.974816i | \(0.428412\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.57606 | − | 1.32492i | 0.269592 | − | 0.0543165i | ||||
\(596\) | 17.0626 | 0.698912 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.01792 | + | 0.587699i | −0.0416260 | + | 0.0240328i | ||||
\(599\) | −1.25008 | − | 2.16521i | −0.0510770 | − | 0.0884680i | 0.839356 | − | 0.543581i | \(-0.182932\pi\) |
−0.890434 | + | 0.455113i | \(0.849599\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.5259 | 0.592524 | 0.296262 | − | 0.955107i | \(-0.404260\pi\) | ||||
0.296262 | + | 0.955107i | \(0.404260\pi\) | |||||||
\(602\) | 4.86296 | − | 2.80763i | 0.198199 | − | 0.114430i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.69730 | − | 11.6001i | −0.272509 | − | 0.472000i | ||||
\(605\) | 15.5106 | + | 17.5987i | 0.630594 | + | 0.715488i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 31.8704i | − | 1.29358i | −0.762669 | − | 0.646789i | \(-0.776111\pi\) | ||
0.762669 | − | 0.646789i | \(-0.223889\pi\) | |||||||
\(608\) | −16.4406 | − | 13.2584i | −0.666754 | − | 0.537700i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.60545 | + | 3.17765i | −0.145980 | + | 0.128659i | ||||
\(611\) | 21.5793 | − | 37.3764i | 0.873004 | − | 1.51209i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.3628 | + | 10.0244i | 0.701277 | + | 0.404882i | 0.807823 | − | 0.589425i | \(-0.200646\pi\) |
−0.106546 | + | 0.994308i | \(0.533979\pi\) | |||||||
\(614\) | 4.86794 | + | 8.43152i | 0.196454 | + | 0.340268i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.49493 | 0.0602325 | ||||||||
\(617\) | 17.3914 | − | 10.0410i | 0.700153 | − | 0.404234i | −0.107251 | − | 0.994232i | \(-0.534205\pi\) |
0.807404 | + | 0.589998i | \(0.200872\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.62217 | −0.225974 | −0.112987 | − | 0.993596i | \(-0.536042\pi\) | ||||
−0.112987 | + | 0.993596i | \(0.536042\pi\) | |||||||
\(620\) | −3.18206 | + | 9.45053i | −0.127795 | + | 0.379542i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.0771 | − | 5.81803i | −0.404056 | − | 0.233282i | ||||
\(623\) | 16.2496 | − | 9.38171i | 0.651026 | − | 0.375870i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.2108 | − | 6.23202i | −0.968431 | − | 0.249281i | ||||
\(626\) | 1.65092 | 0.0659839 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 17.5174i | − | 0.699022i | ||||||
\(629\) | −11.9726 | + | 20.7371i | −0.477378 | + | 0.826844i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.42184 | + | 4.19475i | 0.0964120 | + | 0.166990i | 0.910197 | − | 0.414176i | \(-0.135930\pi\) |
−0.813785 | + | 0.581166i | \(0.802597\pi\) | |||||||
\(632\) | −9.20551 | − | 5.31481i | −0.366176 | − | 0.211412i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.8034 | 0.587918 | ||||||||
\(635\) | −4.57292 | − | 1.53974i | −0.181471 | − | 0.0611025i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.9648 | + | 11.5267i | −0.791033 | + | 0.456703i | ||||
\(638\) | 0.289361i | 0.0114559i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.93436 | + | 24.4910i | 0.195048 | + | 0.968091i | ||||
\(641\) | −12.6503 | + | 21.9110i | −0.499658 | + | 0.865433i | −1.00000 | 0.000394734i | \(-0.999874\pi\) | |
0.500342 | + | 0.865828i | \(0.333208\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.0773 | + | 6.97283i | 0.476282 | + | 0.274981i | 0.718866 | − | 0.695149i | \(-0.244662\pi\) |
−0.242584 | + | 0.970130i | \(0.577995\pi\) | |||||||
\(644\) | −0.634095 | + | 1.09828i | −0.0249868 | + | 0.0432785i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.29560 | + | 4.08658i | −0.129664 | + | 0.160784i | ||||
\(647\) | 2.51360i | 0.0988200i | 0.998779 | + | 0.0494100i | \(0.0157341\pi\) | ||||
−0.998779 | + | 0.0494100i | \(0.984266\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.22978 | + | 3.86209i | −0.0875264 | + | 0.151600i | ||||
\(650\) | −1.21629 | + | 9.60435i | −0.0477068 | + | 0.376714i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.105934 | − | 0.0611608i | 0.00414868 | − | 0.00239524i | ||||
\(653\) | 1.92873i | 0.0754770i | 0.999288 | + | 0.0377385i | \(0.0120154\pi\) | ||||
−0.999288 | + | 0.0377385i | \(0.987985\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 38.4687 | − | 7.75054i | 1.50310 | − | 0.302839i | ||||
\(656\) | −5.59306 | − | 9.68747i | −0.218372 | − | 0.378232i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.83404i | 0.227434i | ||||||||
\(659\) | −7.90042 | − | 13.6839i | −0.307757 | − | 0.533050i | 0.670115 | − | 0.742258i | \(-0.266245\pi\) |
−0.977871 | + | 0.209208i | \(0.932912\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.20178 | − | 14.2059i | −0.319012 | − | 0.552546i | 0.661270 | − | 0.750148i | \(-0.270018\pi\) |
−0.980282 | + | 0.197602i | \(0.936685\pi\) | |||||||
\(662\) | −14.6096 | − | 8.43486i | −0.567819 | − | 0.327830i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −24.7054 | −0.958755 | ||||||||
\(665\) | −10.1626 | − | 5.28872i | −0.394087 | − | 0.205088i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.451805 | − | 0.260850i | −0.0174940 | − | 0.0101001i | ||||
\(668\) | −25.6190 | − | 14.7911i | −0.991228 | − | 0.572286i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.61541 | − | 4.10213i | −0.139675 | − | 0.158479i | ||||
\(671\) | −1.62496 | − | 2.81451i | −0.0627308 | − | 0.108653i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 17.0878i | − | 0.658686i | −0.944210 | − | 0.329343i | \(-0.893173\pi\) | ||
0.944210 | − | 0.329343i | \(-0.106827\pi\) | |||||||
\(674\) | 6.24992 | + | 10.8252i | 0.240738 | + | 0.416970i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.81761 | −0.262216 | ||||||||
\(677\) | 4.57680i | 0.175901i | 0.996125 | + | 0.0879504i | \(0.0280317\pi\) | ||||
−0.996125 | + | 0.0879504i | \(0.971968\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.81574 | − | 17.0014i | 0.376693 | − | 0.652452i | ||||
\(680\) | 9.97241 | − | 2.00921i | 0.382425 | − | 0.0770496i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.731656 | + | 0.422422i | 0.0280166 | + | 0.0161754i | ||||
\(683\) | − | 29.0692i | − | 1.11230i | −0.831082 | − | 0.556151i | \(-0.812278\pi\) | ||
0.831082 | − | 0.556151i | \(-0.187722\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.7538 | + | 3.62089i | 0.410882 | + | 0.138347i | ||||
\(686\) | 3.49942 | − | 6.06117i | 0.133608 | − | 0.231416i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −23.7912 | + | 13.7359i | −0.907031 | + | 0.523675i | ||||
\(689\) | −10.2180 | + | 17.6981i | −0.389276 | + | 0.674245i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.07833 | −0.231230 | −0.115615 | − | 0.993294i | \(-0.536884\pi\) | ||||
−0.115615 | + | 0.993294i | \(0.536884\pi\) | |||||||
\(692\) | 21.5689i | 0.819925i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.10220 | − | 14.0334i | −0.307555 | − | 0.532701i | ||||
\(695\) | 4.26819 | − | 12.6763i | 0.161902 | − | 0.480838i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.11194 | + | 5.26078i | −0.345139 | + | 0.199266i | ||||
\(698\) | −8.75799 | − | 5.05643i | −0.331495 | − | 0.191389i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.04479 | + | 9.63040i | 0.152879 | + | 0.363995i | ||||
\(701\) | 5.20569 | − | 9.01651i | 0.196616 | − | 0.340549i | −0.750813 | − | 0.660515i | \(-0.770338\pi\) |
0.947429 | + | 0.319966i | \(0.103671\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 38.1481 | − | 14.7322i | 1.43878 | − | 0.555634i | ||||
\(704\) | −2.24095 | −0.0844589 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.61640 | − | 7.99585i | 0.173741 | − | 0.300928i | ||||
\(707\) | −14.2787 | + | 8.24380i | −0.537005 | + | 0.310040i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.265572 | − | 0.459984i | −0.00997377 | − | 0.0172751i | 0.860995 | − | 0.508613i | \(-0.169841\pi\) |
−0.870969 | + | 0.491338i | \(0.836508\pi\) | |||||||
\(710\) | −13.1679 | − | 4.43371i | −0.494181 | − | 0.166394i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 24.6421 | − | 14.2271i | 0.923500 | − | 0.533183i | ||||
\(713\) | −1.31913 | + | 0.761599i | −0.0494017 | + | 0.0285221i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.20440 | − | 2.08907i | −0.232031 | − | 0.0781266i | ||||
\(716\) | −10.4452 | − | 18.0916i | −0.390355 | − | 0.676114i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.73174 | + | 3.88657i | −0.251226 | + | 0.145046i | ||||
\(719\) | −11.2135 | + | 19.4224i | −0.418194 | + | 0.724334i | −0.995758 | − | 0.0920118i | \(-0.970670\pi\) |
0.577564 | + | 0.816346i | \(0.304004\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.17716 | 0.155566 | ||||||||
\(722\) | 8.76227 | − | 1.89951i | 0.326098 | − | 0.0706924i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.85212 | − | 13.6003i | 0.291822 | − | 0.505450i | ||||
\(725\) | −3.96169 | + | 1.66392i | −0.147133 | + | 0.0617964i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.8141 | + | 22.9867i | 1.47662 | + | 0.852529i | 0.999652 | − | 0.0263888i | \(-0.00840080\pi\) |
0.476972 | + | 0.878918i | \(0.341734\pi\) | |||||||
\(728\) | 7.44480 | − | 4.29826i | 0.275923 | − | 0.159304i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.16786 | − | 12.3783i | 0.154259 | − | 0.458141i | ||||
\(731\) | 12.9198 | + | 22.3778i | 0.477856 | + | 0.827671i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 42.5178i | − | 1.57043i | −0.619223 | − | 0.785215i | \(-0.712552\pi\) | ||
0.619223 | − | 0.785215i | \(-0.287448\pi\) | |||||||
\(734\) | −6.00930 | −0.221807 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.47072 | + | 2.54737i | −0.0542116 | + | 0.0938972i | ||||
\(737\) | 3.20224 | − | 1.84881i | 0.117956 | − | 0.0681019i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.70889 | + | 2.95988i | −0.0628624 | + | 0.108881i | −0.895744 | − | 0.444571i | \(-0.853356\pi\) |
0.832881 | + | 0.553452i | \(0.186690\pi\) | |||||||
\(740\) | −35.3357 | − | 11.8978i | −1.29897 | − | 0.437371i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 2.76248i | − | 0.101414i | ||||||
\(743\) | 8.41853 | + | 4.86044i | 0.308846 | + | 0.178312i | 0.646410 | − | 0.762990i | \(-0.276270\pi\) |
−0.337564 | + | 0.941303i | \(0.609603\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.0438 | − | 4.23983i | 0.770984 | − | 0.155335i | ||||
\(746\) | 4.56175 | − | 7.90119i | 0.167018 | − | 0.289283i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.23683i | 0.118350i | ||||||||
\(749\) | 4.26819 | 0.155956 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.69265 | + | 9.85996i | 0.207728 | + | 0.359795i | 0.950998 | − | 0.309196i | \(-0.100060\pi\) |
−0.743271 | + | 0.668991i | \(0.766727\pi\) | |||||||
\(752\) | − | 28.5420i | − | 1.04082i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.831977 | + | 1.44103i | 0.0302988 | + | 0.0524791i | ||||
\(755\) | −11.1424 | − | 12.6425i | −0.405514 | − | 0.460106i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.7317 | − | 11.3921i | −0.717160 | − | 0.414053i | 0.0965464 | − | 0.995328i | \(-0.469220\pi\) |
−0.813707 | + | 0.581276i | \(0.802554\pi\) | |||||||
\(758\) | 4.02856 | + | 2.32589i | 0.146324 | + | 0.0844801i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −15.4112 | − | 8.02020i | −0.559025 | − | 0.290923i | ||||
\(761\) | 36.7665 | 1.33279 | 0.666393 | − | 0.745601i | \(-0.267837\pi\) | ||||
0.666393 | + | 0.745601i | \(0.267837\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.33421 | − | 3.65706i | −0.229314 | − | 0.132394i | ||||
\(764\) | 12.6587 | + | 21.9255i | 0.457976 | + | 0.793238i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.79747 | − | 8.30945i | −0.173339 | − | 0.300233i | ||||
\(767\) | 25.6444i | 0.925965i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.4004 | − | 18.0140i | −0.375049 | − | 0.649603i | 0.615286 | − | 0.788304i | \(-0.289041\pi\) |
−0.990334 | + | 0.138701i | \(0.955707\pi\) | |||||||
\(770\) | 0.867524 | − | 0.174786i | 0.0312634 | − | 0.00629885i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 34.6679i | 1.24772i | ||||||||
\(773\) | 18.1944 | − | 10.5046i | 0.654409 | − | 0.377823i | −0.135735 | − | 0.990745i | \(-0.543339\pi\) |
0.790143 | + | 0.612922i | \(0.210006\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.57619 | + | 12.4463i | −0.0566183 | + | 0.447083i | ||||
\(776\) | 14.8853 | − | 25.7821i | 0.534351 | − | 0.925523i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 0.474354i | − | 0.0170064i | ||||||
\(779\) | 17.7533 | + | 2.77509i | 0.636077 | + | 0.0994280i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.69788 | − | 8.13697i | 0.168103 | − | 0.291164i | ||||
\(782\) | 0.633190 | + | 0.365572i | 0.0226428 | + | 0.0130728i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.62292 | + | 13.2033i | −0.272247 | + | 0.471546i | ||||
\(785\) | −4.35284 | − | 21.6047i | −0.155360 | − | 0.771104i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 18.0606i | − | 0.643791i | −0.946775 | − | 0.321896i | \(-0.895680\pi\) | ||
0.946775 | − | 0.321896i | \(-0.104320\pi\) | |||||||
\(788\) | −6.66834 | + | 3.84997i | −0.237550 | + | 0.137149i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.96345 | − | 2.00794i | −0.212170 | − | 0.0714392i | ||||
\(791\) | 14.4230 | 0.512823 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.1847 | − | 9.34422i | −0.574734 | − | 0.331823i | ||||
\(794\) | −2.32691 | − | 4.03033i | −0.0825789 | − | 0.143031i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.2251 | + | 19.4425i | −0.397864 | + | 0.689121i | ||||
\(797\) | − | 24.2571i | − | 0.859229i | −0.903012 | − | 0.429615i | \(-0.858649\pi\) | ||
0.903012 | − | 0.429615i | \(-0.141351\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.8463 | −0.949756 | ||||||||
\(800\) | 9.38151 | + | 22.3368i | 0.331687 | + | 0.789725i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.1912 | + | 7.03857i | −0.430485 | + | 0.248541i | ||||
\(803\) | 7.64906 | + | 4.41619i | 0.269930 | + | 0.155844i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.509136 | + | 1.51211i | −0.0179447 | + | 0.0532947i | ||||
\(806\) | 4.85822 | 0.171124 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −21.6532 | + | 12.5015i | −0.761758 | + | 0.439801i | ||||
\(809\) | −4.27192 | −0.150193 | −0.0750964 | − | 0.997176i | \(-0.523926\pi\) | ||||
−0.0750964 | + | 0.997176i | \(0.523926\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.09120 | − | 8.81821i | −0.178776 | − | 0.309649i | 0.762685 | − | 0.646770i | \(-0.223880\pi\) |
−0.941462 | + | 0.337120i | \(0.890547\pi\) | |||||||
\(812\) | 1.55479 | + | 0.897657i | 0.0545623 | + | 0.0315016i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.57944 | + | 2.73568i | −0.0553595 | + | 0.0958854i | ||||
\(815\) | 0.115453 | − | 0.101754i | 0.00404414 | − | 0.00356430i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.81528 | − | 43.5998i | 0.238436 | − | 1.52536i | ||||
\(818\) | − | 13.0448i | − | 0.456102i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.8325 | − | 12.2908i | −0.378286 | − | 0.429213i | ||||
\(821\) | −28.0108 | − | 48.5162i | −0.977585 | − | 1.69323i | −0.671127 | − | 0.741343i | \(-0.734189\pi\) |
−0.306458 | − | 0.951884i | \(-0.599144\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.0479 | − | 16.7708i | 1.01255 | − | 0.584593i | 0.100610 | − | 0.994926i | \(-0.467921\pi\) |
0.911936 | + | 0.410333i | \(0.134587\pi\) | |||||||
\(824\) | 6.33455 | 0.220674 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.73326 | − | 3.00210i | −0.0603079 | − | 0.104456i | ||||
\(827\) | −0.0313960 | + | 0.0181265i | −0.00109175 | + | 0.000630320i | −0.500546 | − | 0.865710i | \(-0.666867\pi\) |
0.499454 | + | 0.866340i | \(0.333534\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.5662 | −1.37419 | −0.687095 | − | 0.726567i | \(-0.741115\pi\) | ||||
−0.687095 | + | 0.726567i | \(0.741115\pi\) | |||||||
\(830\) | −14.3368 | + | 2.88853i | −0.497637 | + | 0.100262i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −11.1600 | + | 6.44321i | −0.386902 | + | 0.223378i | ||||
\(833\) | 12.4189 | + | 7.17005i | 0.430289 | + | 0.248427i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.2719 | − | 11.8763i | −1.22064 | − | 0.410996i | ||||
\(836\) | 3.47014 | − | 4.30301i | 0.120017 | − | 0.148823i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.61389 | + | 2.66383i | 0.159384 | + | 0.0920205i | ||||
\(839\) | −20.0811 | + | 34.7816i | −0.693278 | + | 1.20079i | 0.277480 | + | 0.960732i | \(0.410501\pi\) |
−0.970758 | + | 0.240061i | \(0.922832\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.1307 | − | 24.4751i | 0.487266 | − | 0.843970i | ||||
\(842\) | 1.85918 | − | 1.07340i | 0.0640716 | − | 0.0369917i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 39.5360 | 1.36089 | ||||||||
\(845\) | −8.40832 | + | 1.69408i | −0.289255 | + | 0.0582782i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 12.3309i | − | 0.423696i | ||||||
\(848\) | 13.5150i | 0.464106i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.55218 | − | 2.33193i | 0.190438 | − | 0.0799845i | ||||
\(851\) | −2.84763 | − | 4.93224i | −0.0976156 | − | 0.169075i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.2563 | − | 8.23086i | −0.488126 | − | 0.281819i | 0.235671 | − | 0.971833i | \(-0.424271\pi\) |
−0.723796 | + | 0.690014i | \(0.757605\pi\) | |||||||
\(854\) | 2.52624 | 0.0864463 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.47259 | 0.221229 | ||||||||
\(857\) | −4.85549 | − | 2.80332i | −0.165860 | − | 0.0957595i | 0.414772 | − | 0.909925i | \(-0.363861\pi\) |
−0.580632 | + | 0.814166i | \(0.697195\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.5149 | + | 21.6765i | 0.427003 | + | 0.739591i | 0.996605 | − | 0.0823296i | \(-0.0262360\pi\) |
−0.569602 | + | 0.821921i | \(0.692903\pi\) | |||||||
\(860\) | −30.1846 | + | 26.6031i | −1.02929 | + | 0.907160i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 15.5266i | − | 0.528837i | ||||||
\(863\) | 42.4307i | 1.44436i | 0.691707 | + | 0.722178i | \(0.256859\pi\) | ||||
−0.691707 | + | 0.722178i | \(0.743141\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.35956 | + | 26.6014i | 0.182231 | + | 0.904475i | ||||
\(866\) | −10.5274 | −0.357736 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.53949 | − | 2.62087i | 0.154080 | − | 0.0889583i | ||||
\(869\) | 2.12758 | − | 3.68507i | 0.0721731 | − | 0.125007i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.6315 | − | 18.4143i | 0.360234 | − | 0.623943i | ||||
\(872\) | −9.60566 | − | 5.54583i | −0.325289 | − | 0.187806i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.449833 | − | 1.16482i | −0.0152158 | − | 0.0394005i | ||||
\(875\) | 7.38156 | + | 10.8723i | 0.249542 | + | 0.367552i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.482588 | + | 0.278622i | 0.0162958 | + | 0.00940841i | 0.508126 | − | 0.861283i | \(-0.330338\pi\) |
−0.491830 | + | 0.870691i | \(0.663672\pi\) | |||||||
\(878\) | −2.33172 | + | 1.34622i | −0.0786919 | + | 0.0454328i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.24422 | + | 0.855111i | −0.143073 | + | 0.0288258i | ||||
\(881\) | −8.35432 | −0.281464 | −0.140732 | − | 0.990048i | \(-0.544946\pi\) | ||||
−0.140732 | + | 0.990048i | \(0.544946\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.8738 | − | 9.74209i | 0.567848 | − | 0.327847i | −0.188441 | − | 0.982084i | \(-0.560343\pi\) |
0.756289 | + | 0.654237i | \(0.227010\pi\) | |||||||
\(884\) | 9.30660 | + | 16.1195i | 0.313015 | + | 0.542158i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.46329 | 0.183543 | ||||||||
\(887\) | 31.1226 | − | 17.9686i | 1.04499 | − | 0.603328i | 0.123751 | − | 0.992313i | \(-0.460508\pi\) |
0.921244 | + | 0.388985i | \(0.127174\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.26819 | + | 2.19657i | 0.0425337 | + | 0.0736705i | ||||
\(890\) | 12.6366 | − | 11.1373i | 0.423580 | − | 0.373322i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 24.2116i | 0.810666i | ||||||||
\(893\) | 35.6892 | + | 28.7814i | 1.19429 | + | 0.963133i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.3778 | − | 19.7173i | −0.580876 | − | 0.659077i | ||||
\(896\) | 6.56624 | − | 11.3731i | 0.219363 | − | 0.379947i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.4097 | + | 6.01005i | 0.347377 | + | 0.200558i | ||||
\(899\) | 1.07816 | + | 1.86743i | 0.0359586 | + | 0.0622821i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.7120 | 0.423499 | ||||||||
\(902\) | −1.20206 | + | 0.694011i | −0.0400243 | + | 0.0231080i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 21.8721 | 0.727455 | ||||||||
\(905\) | 6.30473 | − | 18.7247i | 0.209576 | − | 0.622430i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.3922 | + | 24.4751i | 1.40761 | + | 0.812683i | 0.995157 | − | 0.0982962i | \(-0.0313393\pi\) |
0.412452 | + | 0.910980i | \(0.364673\pi\) | |||||||
\(908\) | 10.1420 | − | 5.85551i | 0.336576 | − | 0.194322i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.81775 | − | 3.36476i | 0.126557 | − | 0.111541i | ||||
\(911\) | 19.7811 | 0.655376 | 0.327688 | − | 0.944786i | \(-0.393731\pi\) | ||||
0.327688 | + | 0.944786i | \(0.393731\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 9.88984i | − | 0.327306i | ||||||
\(914\) | 1.63468 | − | 2.83134i | 0.0540703 | − | 0.0936525i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.520723 | − | 0.901919i | −0.0172052 | − | 0.0298002i | ||||
\(917\) | −17.8640 | − | 10.3138i | −0.589921 | − | 0.340591i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.0582 | −0.859581 | −0.429791 | − | 0.902929i | \(-0.641413\pi\) | ||||
−0.429791 | + | 0.902929i | \(0.641413\pi\) | |||||||
\(920\) | −0.772091 | + | 2.29307i | −0.0254551 | + | 0.0756001i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −13.2794 | + | 7.66684i | −0.437332 | + | 0.252494i | ||||
\(923\) | − | 54.0298i | − | 1.77841i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −46.5369 | − | 5.89340i | −1.53012 | − | 0.193774i | ||||
\(926\) | 5.07421 | − | 8.78879i | 0.166749 | − | 0.288817i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.60618 | + | 2.08203i | 0.118379 | + | 0.0683460i | ||||
\(929\) | 3.98900 | − | 6.90914i | 0.130875 | − | 0.226682i | −0.793139 | − | 0.609040i | \(-0.791555\pi\) |
0.924014 | + | 0.382359i | \(0.124888\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.82267 | − | 22.8458i | −0.289151 | − | 0.748741i | ||||
\(932\) | − | 12.7211i | − | 0.416695i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.99942 | + | 6.92719i | −0.130865 | + | 0.226665i | ||||
\(935\) | 0.804308 | + | 3.99207i | 0.0263037 | + | 0.130555i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.4037 | − | 23.3271i | 1.31993 | − | 0.762063i | 0.336215 | − | 0.941785i | \(-0.390853\pi\) |
0.983717 | + | 0.179722i | \(0.0575198\pi\) | |||||||
\(938\) | 2.87426i | 0.0938479i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.25630 | − | 40.9789i | −0.269291 | − | 1.33659i | ||||
\(941\) | −0.700500 | − | 1.21330i | −0.0228356 | − | 0.0395525i | 0.854382 | − | 0.519646i | \(-0.173936\pi\) |
−0.877217 | + | 0.480093i | \(0.840603\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.50251i | − | 0.0814930i | ||||||
\(944\) | 8.47969 | + | 14.6873i | 0.275990 | + | 0.478030i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.70440 | + | 2.95211i | 0.0554149 | + | 0.0959814i | ||||
\(947\) | 33.1255 | + | 19.1250i | 1.07643 | + | 0.621480i | 0.929932 | − | 0.367730i | \(-0.119865\pi\) |
0.146502 | + | 0.989210i | \(0.453198\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 50.7900 | 1.64871 | ||||||||
\(950\) | −9.88102 | − | 2.85233i | −0.320583 | − | 0.0925419i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.63096 | − | 2.67369i | −0.150090 | − | 0.0866547i | ||||
\(953\) | −47.1455 | − | 27.2195i | −1.52719 | − | 0.881726i | −0.999478 | − | 0.0323042i | \(-0.989715\pi\) |
−0.527715 | − | 0.849421i | \(-0.676951\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.0605 | + | 23.8958i | 0.681502 | + | 0.773250i | ||||
\(956\) | −3.24805 | − | 5.62579i | −0.105049 | − | 0.181951i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.17989i | 0.135046i | ||||||||
\(959\) | −2.98231 | − | 5.16551i | −0.0963038 | − | 0.166803i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.7042 | −0.796911 | ||||||||
\(962\) | 18.1650i | 0.585662i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15.3409 | + | 26.5713i | −0.494099 | + | 0.855804i | ||||
\(965\) | 8.61449 | + | 42.7568i | 0.277310 | + | 1.37639i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.32077 | − | 2.49460i | −0.138946 | − | 0.0802208i | 0.428915 | − | 0.903345i | \(-0.358896\pi\) |
−0.567862 | + | 0.823124i | \(0.692229\pi\) | |||||||
\(968\) | − | 18.6995i | − | 0.601026i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.62367 | − | 16.7020i | 0.180565 | − | 0.536268i | ||||
\(971\) | −7.27006 | + | 12.5921i | −0.233307 | + | 0.404100i | −0.958779 | − | 0.284152i | \(-0.908288\pi\) |
0.725472 | + | 0.688252i | \(0.241621\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.08895 | + | 3.51546i | −0.195203 | + | 0.112700i | ||||
\(974\) | 7.09306 | − | 12.2855i | 0.227276 | − | 0.393654i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.3592 | −0.395609 | ||||||||
\(977\) | − | 26.1353i | − | 0.836141i | −0.908415 | − | 0.418071i | \(-0.862706\pi\) | ||
0.908415 | − | 0.418071i | \(-0.137294\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.69527 | + | 9.86449i | 0.182021 | + | 0.315270i | ||||
\(980\) | −7.12524 | + | 21.1616i | −0.227608 | + | 0.675981i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.26699 | + | 0.731499i | −0.0404314 | + | 0.0233431i | ||||
\(983\) | −39.9376 | − | 23.0580i | −1.27381 | − | 0.735436i | −0.298109 | − | 0.954532i | \(-0.596356\pi\) |
−0.975703 | + | 0.219096i | \(0.929689\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.26757 | + | 6.40525i | −0.231564 | + | 0.204088i | ||||
\(986\) | 0.517523 | − | 0.896376i | 0.0164813 | − | 0.0285464i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.90929 | − | 31.4065i | 0.156185 | − | 0.999174i | ||||
\(989\) | −6.14585 | −0.195427 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.6640 | − | 27.1308i | 0.497582 | − | 0.861837i | −0.502414 | − | 0.864627i | \(-0.667555\pi\) |
0.999996 | + | 0.00278993i | \(0.000888065\pi\) | |||||||
\(992\) | 10.5289 | − | 6.07887i | 0.334294 | − | 0.193004i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.65178 | + | 6.32508i | 0.115828 | + | 0.200619i | ||||
\(995\) | −9.01304 | + | 26.7682i | −0.285733 | + | 0.848609i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.7186 | + | 10.8072i | −0.592826 | + | 0.342268i | −0.766214 | − | 0.642586i | \(-0.777862\pi\) |
0.173388 | + | 0.984854i | \(0.444528\pi\) | |||||||
\(998\) | −13.1341 | + | 7.58296i | −0.415752 | + | 0.240035i | ||||
\(999\) | 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 | 855.2.be.d.334.3 | 12 | ||
3.2 | odd | 2 | 95.2.i.b.49.4 | yes | 12 | ||
5.4 | even | 2 | inner | 855.2.be.d.334.4 | 12 | ||
15.2 | even | 4 | 475.2.e.g.201.3 | 12 | |||
15.8 | even | 4 | 475.2.e.g.201.4 | 12 | |||
15.14 | odd | 2 | 95.2.i.b.49.3 | ✓ | 12 | ||
19.7 | even | 3 | inner | 855.2.be.d.64.4 | 12 | ||
57.8 | even | 6 | 1805.2.b.g.1084.4 | 6 | |||
57.11 | odd | 6 | 1805.2.b.f.1084.3 | 6 | |||
57.26 | odd | 6 | 95.2.i.b.64.3 | yes | 12 | ||
95.64 | even | 6 | inner | 855.2.be.d.64.3 | 12 | ||
285.8 | odd | 12 | 9025.2.a.bt.1.4 | 6 | |||
285.68 | even | 12 | 9025.2.a.bu.1.3 | 6 | |||
285.83 | even | 12 | 475.2.e.g.26.4 | 12 | |||
285.122 | odd | 12 | 9025.2.a.bt.1.3 | 6 | |||
285.179 | even | 6 | 1805.2.b.g.1084.3 | 6 | |||
285.182 | even | 12 | 9025.2.a.bu.1.4 | 6 | |||
285.197 | even | 12 | 475.2.e.g.26.3 | 12 | |||
285.239 | odd | 6 | 1805.2.b.f.1084.4 | 6 | |||
285.254 | odd | 6 | 95.2.i.b.64.4 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.i.b.49.3 | ✓ | 12 | 15.14 | odd | 2 | ||
95.2.i.b.49.4 | yes | 12 | 3.2 | odd | 2 | ||
95.2.i.b.64.3 | yes | 12 | 57.26 | odd | 6 | ||
95.2.i.b.64.4 | yes | 12 | 285.254 | odd | 6 | ||
475.2.e.g.26.3 | 12 | 285.197 | even | 12 | |||
475.2.e.g.26.4 | 12 | 285.83 | even | 12 | |||
475.2.e.g.201.3 | 12 | 15.2 | even | 4 | |||
475.2.e.g.201.4 | 12 | 15.8 | even | 4 | |||
855.2.be.d.64.3 | 12 | 95.64 | even | 6 | inner | ||
855.2.be.d.64.4 | 12 | 19.7 | even | 3 | inner | ||
855.2.be.d.334.3 | 12 | 1.1 | even | 1 | trivial | ||
855.2.be.d.334.4 | 12 | 5.4 | even | 2 | inner | ||
1805.2.b.f.1084.3 | 6 | 57.11 | odd | 6 | |||
1805.2.b.f.1084.4 | 6 | 285.239 | odd | 6 | |||
1805.2.b.g.1084.3 | 6 | 285.179 | even | 6 | |||
1805.2.b.g.1084.4 | 6 | 57.8 | even | 6 | |||
9025.2.a.bt.1.3 | 6 | 285.122 | odd | 12 | |||
9025.2.a.bt.1.4 | 6 | 285.8 | odd | 12 | |||
9025.2.a.bu.1.3 | 6 | 285.68 | even | 12 | |||
9025.2.a.bu.1.4 | 6 | 285.182 | even | 12 |