Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,2,Mod(724,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("975.724");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.bb (of order \(6\), degree \(2\), not 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: | \(7.78541419707\) |
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: | \( x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 195) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 874.2 | ||
Root | \(2.23871 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 975.874 |
Dual form | 975.2.bb.k.724.2 |
$q$-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 \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.95878 | + | 1.13090i | −1.38507 | + | 0.799668i | −0.992754 | − | 0.120165i | \(-0.961658\pi\) |
−0.392311 | + | 0.919832i | \(0.628324\pi\) | |||||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 1.55787 | − | 2.69832i | 0.778937 | − | 1.34916i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.13090 | + | 1.95878i | −0.461688 | + | 0.799668i | ||||
\(7\) | 1.09275 | + | 0.630901i | 0.413022 | + | 0.238458i | 0.692087 | − | 0.721814i | \(-0.256691\pi\) |
−0.279066 | + | 0.960272i | \(0.590025\pi\) | |||||||
\(8\) | 2.52360i | 0.892229i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.26180 | − | 3.91756i | −0.681959 | − | 1.18119i | −0.974382 | − | 0.224899i | \(-0.927795\pi\) |
0.292423 | − | 0.956289i | \(-0.405538\pi\) | |||||||
\(12\) | − | 3.11575i | − | 0.899439i | ||||||
\(13\) | −1.04571 | + | 3.45058i | −0.290028 | + | 0.957018i | ||||
\(14\) | −2.85395 | −0.762749 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.261802 | + | 0.453455i | 0.0654506 | + | 0.113364i | ||||
\(17\) | 3.89131 | + | 2.24665i | 0.943782 | + | 0.544893i | 0.891144 | − | 0.453721i | \(-0.149904\pi\) |
0.0526381 | + | 0.998614i | \(0.483237\pi\) | |||||||
\(18\) | 2.26180i | 0.533112i | ||||||||
\(19\) | 2.55787 | − | 4.43037i | 0.586817 | − | 1.01640i | −0.407830 | − | 0.913058i | \(-0.633714\pi\) |
0.994646 | − | 0.103338i | \(-0.0329524\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.26180 | 0.275348 | ||||||||
\(22\) | 8.86074 | + | 5.11575i | 1.88912 | + | 1.09068i | ||||
\(23\) | −1.93253 | + | 1.11575i | −0.402961 | + | 0.232650i | −0.687761 | − | 0.725937i | \(-0.741406\pi\) |
0.284800 | + | 0.958587i | \(0.408073\pi\) | |||||||
\(24\) | 1.26180 | + | 2.18551i | 0.257564 | + | 0.446114i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.85395 | − | 7.94151i | −0.363589 | − | 1.55746i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 3.40474 | − | 1.96573i | 0.643436 | − | 0.371488i | ||||
\(29\) | −0.688776 | − | 1.19299i | −0.127902 | − | 0.221534i | 0.794961 | − | 0.606660i | \(-0.207491\pi\) |
−0.922864 | + | 0.385127i | \(0.874158\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.87085 | 1.59325 | 0.796626 | − | 0.604472i | \(-0.206616\pi\) | ||||
0.796626 | + | 0.604472i | \(0.206616\pi\) | |||||||
\(32\) | −5.39664 | − | 3.11575i | −0.954000 | − | 0.550792i | ||||
\(33\) | −3.91756 | − | 2.26180i | −0.681959 | − | 0.393729i | ||||
\(34\) | −10.1630 | −1.74293 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.55787 | − | 2.69832i | −0.259646 | − | 0.449720i | ||||
\(37\) | −0.200484 | + | 0.115749i | −0.0329593 | + | 0.0190291i | −0.516389 | − | 0.856354i | \(-0.672724\pi\) |
0.483430 | + | 0.875383i | \(0.339391\pi\) | |||||||
\(38\) | 11.5708i | 1.87703i | ||||||||
\(39\) | 0.819677 | + | 3.51114i | 0.131253 | + | 0.562233i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.573026 | − | 0.992511i | −0.0894917 | − | 0.155004i | 0.817805 | − | 0.575496i | \(-0.195191\pi\) |
−0.907296 | + | 0.420492i | \(0.861858\pi\) | |||||||
\(42\) | −2.47159 | + | 1.42697i | −0.381375 | + | 0.220187i | ||||
\(43\) | 5.52312 | + | 3.18878i | 0.842268 | + | 0.486284i | 0.858035 | − | 0.513592i | \(-0.171685\pi\) |
−0.0157664 | + | 0.999876i | \(0.505019\pi\) | |||||||
\(44\) | −14.0944 | −2.12481 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.52360 | − | 4.37101i | 0.372085 | − | 0.644470i | ||||
\(47\) | − | 10.7854i | − | 1.57321i | −0.617454 | − | 0.786607i | \(-0.711836\pi\) | ||
0.617454 | − | 0.786607i | \(-0.288164\pi\) | |||||||
\(48\) | 0.453455 | + | 0.261802i | 0.0654506 | + | 0.0377879i | ||||
\(49\) | −2.70393 | − | 4.68334i | −0.386275 | − | 0.669049i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.49330 | 0.629188 | ||||||||
\(52\) | 7.68167 | + | 8.19723i | 1.06526 | + | 1.13675i | ||||
\(53\) | − | 4.52360i | − | 0.621365i | −0.950514 | − | 0.310682i | \(-0.899442\pi\) | ||
0.950514 | − | 0.310682i | \(-0.100558\pi\) | |||||||
\(54\) | 1.13090 | + | 1.95878i | 0.153896 | + | 0.266556i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.59214 | + | 2.75768i | −0.212759 | + | 0.368510i | ||||
\(57\) | − | 5.11575i | − | 0.677598i | ||||||
\(58\) | 2.69832 | + | 1.55787i | 0.354307 | + | 0.204559i | ||||
\(59\) | −0.426974 | + | 0.739540i | −0.0555872 | + | 0.0962799i | −0.892480 | − | 0.451087i | \(-0.851036\pi\) |
0.836893 | + | 0.547367i | \(0.184370\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.31968 | + | 4.01780i | −0.297004 | + | 0.514426i | −0.975449 | − | 0.220225i | \(-0.929321\pi\) |
0.678445 | + | 0.734651i | \(0.262654\pi\) | |||||||
\(62\) | −17.3760 | + | 10.0321i | −2.20676 | + | 1.27407i | ||||
\(63\) | 1.09275 | − | 0.630901i | 0.137674 | − | 0.0794861i | ||||
\(64\) | 13.0472 | 1.63090 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 10.2315 | 1.25941 | ||||||||
\(67\) | 11.3732 | − | 6.56633i | 1.38946 | − | 0.802205i | 0.396205 | − | 0.918162i | \(-0.370327\pi\) |
0.993254 | + | 0.115958i | \(0.0369937\pi\) | |||||||
\(68\) | 12.1244 | − | 7.00000i | 1.47029 | − | 0.848875i | ||||
\(69\) | −1.11575 | + | 1.93253i | −0.134320 | + | 0.232650i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.80453 | − | 8.32168i | 0.570192 | − | 0.987602i | −0.426354 | − | 0.904557i | \(-0.640202\pi\) |
0.996546 | − | 0.0830453i | \(-0.0264646\pi\) | |||||||
\(72\) | 2.18551 | + | 1.26180i | 0.257564 | + | 0.148705i | ||||
\(73\) | − | 13.7854i | − | 1.61346i | −0.590920 | − | 0.806730i | \(-0.701235\pi\) | ||
0.590920 | − | 0.806730i | \(-0.298765\pi\) | |||||||
\(74\) | 0.261802 | − | 0.453455i | 0.0304339 | − | 0.0527130i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.96970 | − | 13.8039i | −0.914187 | − | 1.58342i | ||||
\(77\) | − | 5.70789i | − | 0.650475i | ||||||
\(78\) | −5.57632 | − | 5.95058i | −0.631394 | − | 0.673770i | ||||
\(79\) | 8.87085 | 0.998049 | 0.499024 | − | 0.866588i | \(-0.333692\pi\) | ||||
0.499024 | + | 0.866588i | \(0.333692\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 2.24486 | + | 1.29607i | 0.247904 | + | 0.143127i | ||||
\(83\) | 8.23150i | 0.903524i | 0.892138 | + | 0.451762i | \(0.149204\pi\) | ||||
−0.892138 | + | 0.451762i | \(0.850796\pi\) | |||||||
\(84\) | 1.96573 | − | 3.40474i | 0.214479 | − | 0.371488i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −14.4248 | −1.55546 | ||||||||
\(87\) | −1.19299 | − | 0.688776i | −0.127902 | − | 0.0738445i | ||||
\(88\) | 9.88636 | − | 5.70789i | 1.05389 | − | 0.608464i | ||||
\(89\) | 3.31122 | + | 5.73521i | 0.350989 | + | 0.607931i | 0.986423 | − | 0.164224i | \(-0.0525121\pi\) |
−0.635434 | + | 0.772155i | \(0.719179\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.31968 | + | 3.11089i | −0.347997 | + | 0.326110i | ||||
\(92\) | 6.95279i | 0.724879i | ||||||||
\(93\) | 7.68238 | − | 4.43543i | 0.796626 | − | 0.459932i | ||||
\(94\) | 12.1972 | + | 21.1262i | 1.25805 | + | 2.17900i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −6.23150 | −0.636000 | ||||||||
\(97\) | −9.24019 | − | 5.33483i | −0.938200 | − | 0.541670i | −0.0488041 | − | 0.998808i | \(-0.515541\pi\) |
−0.889395 | + | 0.457139i | \(0.848874\pi\) | |||||||
\(98\) | 10.5928 | + | 6.11575i | 1.07003 | + | 0.617784i | ||||
\(99\) | −4.52360 | −0.454639 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.52360 | + | 14.7633i | 0.848130 | + | 1.46900i | 0.882875 | + | 0.469609i | \(0.155605\pi\) |
−0.0347444 | + | 0.999396i | \(0.511062\pi\) | |||||||
\(102\) | −8.80138 | + | 5.08148i | −0.871466 | + | 0.503141i | ||||
\(103\) | 13.9484i | 1.37437i | 0.726481 | + | 0.687187i | \(0.241155\pi\) | ||||
−0.726481 | + | 0.687187i | \(0.758845\pi\) | |||||||
\(104\) | −8.70789 | − | 2.63896i | −0.853879 | − | 0.258771i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.11575 | + | 8.86074i | 0.496886 | + | 0.860631i | ||||
\(107\) | 10.8195 | − | 6.24665i | 1.04596 | − | 0.603886i | 0.124446 | − | 0.992226i | \(-0.460285\pi\) |
0.921516 | + | 0.388340i | \(0.126951\pi\) | |||||||
\(108\) | −2.69832 | − | 1.55787i | −0.259646 | − | 0.149907i | ||||
\(109\) | 2.27871 | 0.218261 | 0.109130 | − | 0.994027i | \(-0.465193\pi\) | ||||
0.109130 | + | 0.994027i | \(0.465193\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.115749 | + | 0.200484i | −0.0109864 | + | 0.0190291i | ||||
\(112\) | 0.660685i | 0.0624289i | ||||||||
\(113\) | −1.27860 | − | 0.738198i | −0.120280 | − | 0.0694438i | 0.438653 | − | 0.898657i | \(-0.355456\pi\) |
−0.558933 | + | 0.829213i | \(0.688789\pi\) | |||||||
\(114\) | 5.78541 | + | 10.0206i | 0.541853 | + | 0.938517i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.29211 | −0.398512 | ||||||||
\(117\) | 2.46543 | + | 2.63090i | 0.227929 | + | 0.243227i | ||||
\(118\) | − | 1.93146i | − | 0.177805i | ||||||
\(119\) | 2.83483 | + | 4.91007i | 0.259868 | + | 0.450105i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.73150 | + | 8.19520i | −0.430136 | + | 0.745018i | ||||
\(122\) | − | 10.4933i | − | 0.950019i | ||||||
\(123\) | −0.992511 | − | 0.573026i | −0.0894917 | − | 0.0516681i | ||||
\(124\) | 13.8197 | − | 23.9364i | 1.24104 | − | 2.14955i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.42697 | + | 2.47159i | −0.127125 | + | 0.220187i | ||||
\(127\) | −15.4026 | + | 8.89270i | −1.36676 | + | 0.789100i | −0.990513 | − | 0.137419i | \(-0.956119\pi\) |
−0.376248 | + | 0.926519i | \(0.622786\pi\) | |||||||
\(128\) | −14.7633 | + | 8.52360i | −1.30491 | + | 0.753387i | ||||
\(129\) | 6.37755 | 0.561512 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.6697 | 1.01958 | 0.509791 | − | 0.860298i | \(-0.329723\pi\) | ||||
0.509791 | + | 0.860298i | \(0.329723\pi\) | |||||||
\(132\) | −12.2061 | + | 7.04721i | −1.06241 | + | 0.613381i | ||||
\(133\) | 5.59025 | − | 3.22753i | 0.484736 | − | 0.279863i | ||||
\(134\) | −14.8517 | + | 25.7240i | −1.28299 | + | 2.22221i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.66966 | + | 9.82013i | −0.486169 | + | 0.842070i | ||||
\(137\) | 17.3760 | + | 10.0321i | 1.48453 | + | 0.857096i | 0.999845 | − | 0.0175898i | \(-0.00559931\pi\) |
0.484689 | + | 0.874686i | \(0.338933\pi\) | |||||||
\(138\) | − | 5.04721i | − | 0.429647i | ||||||
\(139\) | 8.16966 | − | 14.1503i | 0.692941 | − | 1.20021i | −0.277928 | − | 0.960602i | \(-0.589648\pi\) |
0.970870 | − | 0.239608i | \(-0.0770188\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.39270 | − | 9.34044i | −0.454148 | − | 0.786607i | ||||
\(142\) | 21.7338i | 1.82386i | ||||||||
\(143\) | 15.8830 | − | 3.70789i | 1.32821 | − | 0.310070i | ||||
\(144\) | 0.523604 | 0.0436337 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 15.5899 | + | 27.0026i | 1.29023 | + | 2.23475i | ||||
\(147\) | −4.68334 | − | 2.70393i | −0.386275 | − | 0.223016i | ||||
\(148\) | 0.721292i | 0.0592899i | ||||||||
\(149\) | −1.62245 | + | 2.81016i | −0.132916 | + | 0.230218i | −0.924799 | − | 0.380455i | \(-0.875767\pi\) |
0.791883 | + | 0.610672i | \(0.209101\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.69996 | 0.463856 | 0.231928 | − | 0.972733i | \(-0.425497\pi\) | ||||
0.231928 | + | 0.972733i | \(0.425497\pi\) | |||||||
\(152\) | 11.1805 | + | 6.45506i | 0.906858 | + | 0.523575i | ||||
\(153\) | 3.89131 | − | 2.24665i | 0.314594 | − | 0.181631i | ||||
\(154\) | 6.45506 | + | 11.1805i | 0.520164 | + | 0.900950i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.7511 | + | 3.25817i | 0.860780 | + | 0.260863i | ||||
\(157\) | − | 3.85395i | − | 0.307578i | −0.988104 | − | 0.153789i | \(-0.950852\pi\) | ||
0.988104 | − | 0.153789i | \(-0.0491477\pi\) | |||||||
\(158\) | −17.3760 | + | 10.0321i | −1.38236 | + | 0.798108i | ||||
\(159\) | −2.26180 | − | 3.91756i | −0.179373 | − | 0.310682i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.81571 | −0.221909 | ||||||||
\(162\) | 1.95878 | + | 1.13090i | 0.153896 | + | 0.0888520i | ||||
\(163\) | −8.42192 | − | 4.86240i | −0.659656 | − | 0.380853i | 0.132490 | − | 0.991184i | \(-0.457703\pi\) |
−0.792146 | + | 0.610332i | \(0.791036\pi\) | |||||||
\(164\) | −3.57081 | −0.278834 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.30901 | − | 16.1237i | −0.722519 | − | 1.25144i | ||||
\(167\) | −16.6959 | + | 9.63935i | −1.29196 | + | 0.745916i | −0.979002 | − | 0.203850i | \(-0.934654\pi\) |
−0.312962 | + | 0.949766i | \(0.601321\pi\) | |||||||
\(168\) | 3.18429i | 0.245673i | ||||||||
\(169\) | −10.8130 | − | 7.21661i | −0.831768 | − | 0.555124i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.55787 | − | 4.43037i | −0.195606 | − | 0.338799i | ||||
\(172\) | 17.2087 | − | 9.93543i | 1.31215 | − | 0.757569i | ||||
\(173\) | −2.61272 | − | 1.50845i | −0.198641 | − | 0.114686i | 0.397380 | − | 0.917654i | \(-0.369919\pi\) |
−0.596022 | + | 0.802968i | \(0.703253\pi\) | |||||||
\(174\) | 3.11575 | 0.236204 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.18429 | − | 2.05125i | 0.0892692 | − | 0.154619i | ||||
\(177\) | 0.853947i | 0.0641866i | ||||||||
\(178\) | −12.9719 | − | 7.48933i | −0.972286 | − | 0.561349i | ||||
\(179\) | −2.65847 | − | 4.60461i | −0.198704 | − | 0.344165i | 0.749405 | − | 0.662112i | \(-0.230340\pi\) |
−0.948108 | + | 0.317947i | \(0.897006\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.8709 | 1.92297 | 0.961483 | − | 0.274866i | \(-0.0886333\pi\) | ||||
0.961483 | + | 0.274866i | \(0.0886333\pi\) | |||||||
\(182\) | 2.98440 | − | 9.84777i | 0.221219 | − | 0.729965i | ||||
\(183\) | 4.63935i | 0.342951i | ||||||||
\(184\) | −2.81571 | − | 4.87695i | −0.207577 | − | 0.359534i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −10.0321 | + | 17.3760i | −0.735586 | + | 1.27407i | ||||
\(187\) | − | 20.3259i | − | 1.48638i | ||||||
\(188\) | −29.1025 | − | 16.8023i | −2.12251 | − | 1.22543i | ||||
\(189\) | 0.630901 | − | 1.09275i | 0.0458913 | − | 0.0794861i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.32813 | + | 9.22859i | −0.385530 | + | 0.667757i | −0.991843 | − | 0.127469i | \(-0.959315\pi\) |
0.606313 | + | 0.795226i | \(0.292648\pi\) | |||||||
\(192\) | 11.2992 | − | 6.52360i | 0.815451 | − | 0.470801i | ||||
\(193\) | −6.91356 | + | 3.99155i | −0.497649 | + | 0.287318i | −0.727742 | − | 0.685851i | \(-0.759430\pi\) |
0.230093 | + | 0.973169i | \(0.426097\pi\) | |||||||
\(194\) | 24.1327 | 1.73262 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −16.8495 | −1.20354 | ||||||||
\(197\) | 15.0163 | − | 8.66966i | 1.06987 | − | 0.617688i | 0.141721 | − | 0.989907i | \(-0.454736\pi\) |
0.928145 | + | 0.372219i | \(0.121403\pi\) | |||||||
\(198\) | 8.86074 | − | 5.11575i | 0.629705 | − | 0.363560i | ||||
\(199\) | −0.615749 | + | 1.06651i | −0.0436493 | + | 0.0756028i | −0.887025 | − | 0.461722i | \(-0.847232\pi\) |
0.843375 | + | 0.537325i | \(0.180565\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.56633 | − | 11.3732i | 0.463153 | − | 0.802205i | ||||
\(202\) | −33.3917 | − | 19.2787i | −2.34943 | − | 1.35645i | ||||
\(203\) | − | 1.73820i | − | 0.121998i | ||||||
\(204\) | 7.00000 | − | 12.1244i | 0.490098 | − | 0.848875i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −15.7742 | − | 27.3218i | −1.09904 | − | 1.90360i | ||||
\(207\) | 2.23150i | 0.155100i | ||||||||
\(208\) | −1.83845 | + | 0.429187i | −0.127474 | + | 0.0297587i | ||||
\(209\) | −23.1416 | −1.60074 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.16966 | − | 8.95411i | −0.355894 | − | 0.616426i | 0.631377 | − | 0.775476i | \(-0.282490\pi\) |
−0.987271 | + | 0.159050i | \(0.949157\pi\) | |||||||
\(212\) | −12.2061 | − | 7.04721i | −0.838320 | − | 0.484004i | ||||
\(213\) | − | 9.60905i | − | 0.658401i | ||||||
\(214\) | −14.1287 | + | 24.4716i | −0.965817 | + | 1.67284i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.52360 | 0.171710 | ||||||||
\(217\) | 9.69365 | + | 5.59663i | 0.658048 | + | 0.379924i | ||||
\(218\) | −4.46348 | + | 2.57699i | −0.302305 | + | 0.174536i | ||||
\(219\) | −6.89270 | − | 11.9385i | −0.465766 | − | 0.806730i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.8214 | + | 11.0779i | −0.795195 | + | 0.745182i | ||||
\(222\) | − | 0.523604i | − | 0.0351420i | ||||||
\(223\) | −18.6809 | + | 10.7854i | −1.25096 | + | 0.722244i | −0.971301 | − | 0.237854i | \(-0.923556\pi\) |
−0.279663 | + | 0.960098i | \(0.590223\pi\) | |||||||
\(224\) | −3.93146 | − | 6.80949i | −0.262682 | − | 0.454978i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.33931 | 0.222128 | ||||||||
\(227\) | −4.71645 | − | 2.72305i | −0.313042 | − | 0.180735i | 0.335245 | − | 0.942131i | \(-0.391181\pi\) |
−0.648287 | + | 0.761396i | \(0.724514\pi\) | |||||||
\(228\) | −13.8039 | − | 7.96970i | −0.914187 | − | 0.527806i | ||||
\(229\) | −21.9315 | −1.44927 | −0.724636 | − | 0.689132i | \(-0.757992\pi\) | ||||
−0.724636 | + | 0.689132i | \(0.757992\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.85395 | − | 4.94318i | −0.187776 | − | 0.325237i | ||||
\(232\) | 3.01065 | − | 1.73820i | 0.197659 | − | 0.114118i | ||||
\(233\) | − | 25.3125i | − | 1.65828i | −0.559042 | − | 0.829139i | \(-0.688831\pi\) | ||
0.559042 | − | 0.829139i | \(-0.311169\pi\) | |||||||
\(234\) | −7.80453 | − | 2.36519i | −0.510198 | − | 0.154617i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.33034 | + | 2.30422i | 0.0865979 | + | 0.149992i | ||||
\(237\) | 7.68238 | − | 4.43543i | 0.499024 | − | 0.288112i | ||||
\(238\) | −11.1056 | − | 6.41182i | −0.719869 | − | 0.415617i | ||||
\(239\) | −22.5236 | −1.45693 | −0.728465 | − | 0.685083i | \(-0.759766\pi\) | ||||
−0.728465 | + | 0.685083i | \(0.759766\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.55787 | + | 9.62652i | −0.358014 | + | 0.620099i | −0.987629 | − | 0.156809i | \(-0.949879\pi\) |
0.629615 | + | 0.776907i | \(0.283213\pi\) | |||||||
\(242\) | − | 21.4034i | − | 1.37586i | ||||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 7.22753 | + | 12.5185i | 0.462695 | + | 0.801412i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.59214 | 0.165269 | ||||||||
\(247\) | 12.6125 | + | 13.4590i | 0.802516 | + | 0.856378i | ||||
\(248\) | 22.3865i | 1.42155i | ||||||||
\(249\) | 4.11575 | + | 7.12869i | 0.260825 | + | 0.451762i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.52360 | + | 9.56716i | −0.348647 | + | 0.603874i | −0.986009 | − | 0.166690i | \(-0.946692\pi\) |
0.637363 | + | 0.770564i | \(0.280025\pi\) | |||||||
\(252\) | − | 3.93146i | − | 0.247659i | ||||||
\(253\) | 8.74202 | + | 5.04721i | 0.549606 | + | 0.317315i | ||||
\(254\) | 20.1135 | − | 34.8377i | 1.26204 | − | 2.18591i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.23150 | − | 10.7933i | 0.389469 | − | 0.674580i | ||||
\(257\) | −1.75829 | + | 1.01515i | −0.109679 | + | 0.0633234i | −0.553836 | − | 0.832626i | \(-0.686837\pi\) |
0.444157 | + | 0.895949i | \(0.353503\pi\) | |||||||
\(258\) | −12.4922 | + | 7.21238i | −0.777731 | + | 0.449023i | ||||
\(259\) | −0.292106 | −0.0181506 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.37755 | −0.0852683 | ||||||||
\(262\) | −22.8583 | + | 13.1972i | −1.41219 | + | 0.815328i | ||||
\(263\) | −2.81320 | + | 1.62420i | −0.173469 | + | 0.100153i | −0.584221 | − | 0.811595i | \(-0.698600\pi\) |
0.410751 | + | 0.911747i | \(0.365266\pi\) | |||||||
\(264\) | 5.70789 | − | 9.88636i | 0.351297 | − | 0.608464i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.30004 | + | 12.6440i | −0.447594 | + | 0.775256i | ||||
\(267\) | 5.73521 | + | 3.31122i | 0.350989 | + | 0.202644i | ||||
\(268\) | − | 40.9181i | − | 2.49947i | ||||||
\(269\) | 13.4742 | − | 23.3380i | 0.821535 | − | 1.42294i | −0.0830032 | − | 0.996549i | \(-0.526451\pi\) |
0.904539 | − | 0.426392i | \(-0.140216\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.92476 | + | 17.1902i | 0.602886 | + | 1.04423i | 0.992382 | + | 0.123201i | \(0.0393161\pi\) |
−0.389495 | + | 0.921028i | \(0.627351\pi\) | |||||||
\(272\) | 2.35271i | 0.142654i | ||||||||
\(273\) | −1.31948 | + | 4.35395i | −0.0798586 | + | 0.263513i | ||||
\(274\) | −45.3811 | −2.74157 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.47640 | + | 6.02129i | 0.209254 | + | 0.362439i | ||||
\(277\) | −13.9382 | − | 8.04721i | −0.837464 | − | 0.483510i | 0.0189376 | − | 0.999821i | \(-0.493972\pi\) |
−0.856401 | + | 0.516311i | \(0.827305\pi\) | |||||||
\(278\) | 36.9563i | 2.21649i | ||||||||
\(279\) | 4.43543 | − | 7.68238i | 0.265542 | − | 0.459932i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.37755 | −0.320798 | −0.160399 | − | 0.987052i | \(-0.551278\pi\) | ||||
−0.160399 | + | 0.987052i | \(0.551278\pi\) | |||||||
\(282\) | 21.1262 | + | 12.1972i | 1.25805 | + | 0.726334i | ||||
\(283\) | −23.2670 | + | 13.4332i | −1.38308 | + | 0.798522i | −0.992523 | − | 0.122057i | \(-0.961051\pi\) |
−0.390557 | + | 0.920579i | \(0.627718\pi\) | |||||||
\(284\) | −14.9697 | − | 25.9283i | −0.888288 | − | 1.53856i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −26.9181 | + | 25.2251i | −1.59170 | + | 1.49159i | ||||
\(287\) | − | 1.44609i | − | 0.0853601i | ||||||
\(288\) | −5.39664 | + | 3.11575i | −0.318000 | + | 0.183597i | ||||
\(289\) | 1.59488 | + | 2.76241i | 0.0938163 | + | 0.162495i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.6697 | −0.625466 | ||||||||
\(292\) | −37.1974 | − | 21.4759i | −2.17681 | − | 1.25678i | ||||
\(293\) | 18.5497 | + | 10.7096i | 1.08368 | + | 0.625664i | 0.931887 | − | 0.362748i | \(-0.118161\pi\) |
0.151795 | + | 0.988412i | \(0.451495\pi\) | |||||||
\(294\) | 12.2315 | 0.713355 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.292106 | − | 0.505942i | −0.0169783 | − | 0.0294073i | ||||
\(297\) | −3.91756 | + | 2.26180i | −0.227320 | + | 0.131243i | ||||
\(298\) | − | 7.33931i | − | 0.425155i | ||||||
\(299\) | −1.82911 | − | 7.83511i | −0.105780 | − | 0.453116i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.02360 | + | 6.96909i | 0.231917 | + | 0.401692i | ||||
\(302\) | −11.1650 | + | 6.44609i | −0.642471 | + | 0.370931i | ||||
\(303\) | 14.7633 | + | 8.52360i | 0.848130 | + | 0.489668i | ||||
\(304\) | 2.67863 | 0.153630 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.08148 | + | 8.80138i | −0.290489 | + | 0.503141i | ||||
\(307\) | − | 7.85395i | − | 0.448248i | −0.974561 | − | 0.224124i | \(-0.928048\pi\) | ||
0.974561 | − | 0.224124i | \(-0.0719521\pi\) | |||||||
\(308\) | −15.4017 | − | 8.89218i | −0.877594 | − | 0.506679i | ||||
\(309\) | 6.97418 | + | 12.0796i | 0.396747 | + | 0.687187i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.8744 | −1.58061 | −0.790305 | − | 0.612714i | \(-0.790078\pi\) | ||||
−0.790305 | + | 0.612714i | \(0.790078\pi\) | |||||||
\(312\) | −8.86074 | + | 2.06854i | −0.501641 | + | 0.117108i | ||||
\(313\) | − | 7.88776i | − | 0.445842i | −0.974836 | − | 0.222921i | \(-0.928441\pi\) | ||
0.974836 | − | 0.222921i | \(-0.0715593\pi\) | |||||||
\(314\) | 4.35843 | + | 7.54903i | 0.245961 | + | 0.426016i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.8197 | − | 23.9364i | 0.777418 | − | 1.34653i | ||||
\(317\) | 13.2181i | 0.742403i | 0.928552 | + | 0.371201i | \(0.121054\pi\) | ||||
−0.928552 | + | 0.371201i | \(0.878946\pi\) | |||||||
\(318\) | 8.86074 | + | 5.11575i | 0.496886 | + | 0.286877i | ||||
\(319\) | −3.11575 | + | 5.39664i | −0.174448 | + | 0.302154i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.24665 | − | 10.8195i | 0.348654 | − | 0.603886i | ||||
\(322\) | 5.51535 | − | 3.18429i | 0.307359 | − | 0.177454i | ||||
\(323\) | 19.9070 | − | 11.4933i | 1.10765 | − | 0.639504i | ||||
\(324\) | −3.11575 | −0.173097 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 21.9956 | 1.21822 | ||||||||
\(327\) | 1.97342 | − | 1.13935i | 0.109130 | − | 0.0630064i | ||||
\(328\) | 2.50470 | − | 1.44609i | 0.138299 | − | 0.0798471i | ||||
\(329\) | 6.80453 | − | 11.7858i | 0.375146 | − | 0.649771i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.9248 | − | 20.6543i | 0.655444 | − | 1.13526i | −0.326338 | − | 0.945253i | \(-0.605815\pi\) |
0.981782 | − | 0.190009i | \(-0.0608519\pi\) | |||||||
\(332\) | 22.2112 | + | 12.8236i | 1.21900 | + | 0.703789i | ||||
\(333\) | 0.231499i | 0.0126861i | ||||||||
\(334\) | 21.8023 | − | 37.7627i | 1.19297 | − | 2.06628i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.330343 | + | 0.572170i | 0.0180217 | + | 0.0312144i | ||||
\(337\) | 5.68306i | 0.309576i | 0.987948 | + | 0.154788i | \(0.0494694\pi\) | ||||
−0.987948 | + | 0.154788i | \(0.950531\pi\) | |||||||
\(338\) | 29.3415 | + | 1.90734i | 1.59597 | + | 0.103745i | ||||
\(339\) | −1.47640 | −0.0801868 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.0641 | − | 34.7521i | −1.08653 | − | 1.88193i | ||||
\(342\) | 10.0206 | + | 5.78541i | 0.541853 | + | 0.312839i | ||||
\(343\) | − | 15.6563i | − | 0.845359i | ||||||
\(344\) | −8.04721 | + | 13.9382i | −0.433876 | + | 0.751496i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.82364 | 0.366841 | ||||||||
\(347\) | 18.5759 | + | 10.7248i | 0.997206 | + | 0.575737i | 0.907421 | − | 0.420224i | \(-0.138048\pi\) |
0.0897859 | + | 0.995961i | \(0.471382\pi\) | |||||||
\(348\) | −3.71707 | + | 2.14605i | −0.199256 | + | 0.115041i | ||||
\(349\) | 3.43543 | + | 5.95033i | 0.183894 | + | 0.318514i | 0.943203 | − | 0.332216i | \(-0.107796\pi\) |
−0.759309 | + | 0.650730i | \(0.774463\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.45058 | + | 1.04571i | 0.184178 | + | 0.0558159i | ||||
\(352\) | 28.1888i | 1.50247i | ||||||||
\(353\) | −29.8751 | + | 17.2484i | −1.59009 | + | 0.918040i | −0.596802 | + | 0.802389i | \(0.703562\pi\) |
−0.993290 | + | 0.115651i | \(0.963104\pi\) | |||||||
\(354\) | −0.965730 | − | 1.67269i | −0.0513280 | − | 0.0889026i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 20.6339 | 1.09359 | ||||||||
\(357\) | 4.91007 | + | 2.83483i | 0.259868 | + | 0.150035i | ||||
\(358\) | 10.4147 | + | 6.01294i | 0.550435 | + | 0.317794i | ||||
\(359\) | 8.15945 | 0.430639 | 0.215320 | − | 0.976544i | \(-0.430921\pi\) | ||||
0.215320 | + | 0.976544i | \(0.430921\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.58545 | − | 6.21017i | −0.188708 | − | 0.326851i | ||||
\(362\) | −50.6753 | + | 29.2574i | −2.66343 | + | 1.53773i | ||||
\(363\) | 9.46300i | 0.496679i | ||||||||
\(364\) | 3.22253 | + | 13.8039i | 0.168906 | + | 0.723522i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.24665 | − | 9.08747i | −0.274247 | − | 0.475009i | ||||
\(367\) | −5.92409 | + | 3.42027i | −0.309235 | + | 0.178537i | −0.646584 | − | 0.762843i | \(-0.723803\pi\) |
0.337349 | + | 0.941380i | \(0.390470\pi\) | |||||||
\(368\) | −1.01188 | − | 0.584211i | −0.0527481 | − | 0.0304541i | ||||
\(369\) | −1.14605 | −0.0596611 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.85395 | − | 4.94318i | 0.148170 | − | 0.256637i | ||||
\(372\) | − | 27.6394i | − | 1.43303i | ||||||
\(373\) | 11.9678 | + | 6.90961i | 0.619669 | + | 0.357766i | 0.776740 | − | 0.629821i | \(-0.216872\pi\) |
−0.157071 | + | 0.987587i | \(0.550205\pi\) | |||||||
\(374\) | 22.9866 | + | 39.8140i | 1.18861 | + | 2.05873i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 27.2181 | 1.40367 | ||||||||
\(377\) | 4.83678 | − | 1.12915i | 0.249107 | − | 0.0581540i | ||||
\(378\) | 2.85395i | 0.146791i | ||||||||
\(379\) | 5.75784 | + | 9.97286i | 0.295760 | + | 0.512272i | 0.975161 | − | 0.221495i | \(-0.0710938\pi\) |
−0.679401 | + | 0.733767i | \(0.737760\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.89270 | + | 15.4026i | −0.455587 | + | 0.789100i | ||||
\(382\) | − | 24.1024i | − | 1.23318i | ||||||
\(383\) | 19.8145 | + | 11.4399i | 1.01247 | + | 0.584552i | 0.911915 | − | 0.410379i | \(-0.134604\pi\) |
0.100559 | + | 0.994931i | \(0.467937\pi\) | |||||||
\(384\) | −8.52360 | + | 14.7633i | −0.434968 | + | 0.753387i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.02809 | − | 15.6371i | 0.459518 | − | 0.795908i | ||||
\(387\) | 5.52312 | − | 3.18878i | 0.280756 | − | 0.162095i | ||||
\(388\) | −28.7901 | + | 16.6220i | −1.46160 | + | 0.843854i | ||||
\(389\) | 4.35271 | 0.220691 | 0.110346 | − | 0.993893i | \(-0.464804\pi\) | ||||
0.110346 | + | 0.993893i | \(0.464804\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.0268 | −0.507077 | ||||||||
\(392\) | 11.8189 | − | 6.82364i | 0.596944 | − | 0.344646i | ||||
\(393\) | 10.1062 | − | 5.83483i | 0.509791 | − | 0.294328i | ||||
\(394\) | −19.6091 | + | 33.9639i | −0.987890 | + | 1.71108i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.04721 | + | 12.2061i | −0.354136 | + | 0.613381i | ||||
\(397\) | −6.60123 | − | 3.81122i | −0.331306 | − | 0.191280i | 0.325115 | − | 0.945675i | \(-0.394597\pi\) |
−0.656421 | + | 0.754395i | \(0.727930\pi\) | |||||||
\(398\) | − | 2.78541i | − | 0.139620i | ||||||
\(399\) | 3.22753 | − | 5.59025i | 0.161579 | − | 0.279863i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.4248 | − | 18.0562i | −0.520588 | − | 0.901684i | −0.999713 | − | 0.0239381i | \(-0.992380\pi\) |
0.479126 | − | 0.877746i | \(-0.340954\pi\) | |||||||
\(402\) | 29.7035i | 1.48147i | ||||||||
\(403\) | −9.27635 | + | 30.6096i | −0.462088 | + | 1.52477i | ||||
\(404\) | 53.1148 | 2.64256 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.96573 | + | 3.40474i | 0.0975575 | + | 0.168975i | ||||
\(407\) | 0.906910 | + | 0.523604i | 0.0449538 | + | 0.0259541i | ||||
\(408\) | 11.3393i | 0.561380i | ||||||||
\(409\) | −8.48264 | + | 14.6924i | −0.419439 | + | 0.726490i | −0.995883 | − | 0.0906466i | \(-0.971107\pi\) |
0.576444 | + | 0.817137i | \(0.304440\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.0641 | 0.989690 | ||||||||
\(412\) | 37.6371 | + | 21.7298i | 1.85425 | + | 1.07055i | ||||
\(413\) | −0.933153 | + | 0.538756i | −0.0459175 | + | 0.0265105i | ||||
\(414\) | −2.52360 | − | 4.37101i | −0.124028 | − | 0.214823i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 16.3945 | − | 15.3633i | 0.803804 | − | 0.753250i | ||||
\(417\) | − | 16.3393i | − | 0.800140i | ||||||
\(418\) | 45.3293 | − | 26.1709i | 2.21713 | − | 1.28006i | ||||
\(419\) | 1.04942 | + | 1.81765i | 0.0512676 | + | 0.0887981i | 0.890520 | − | 0.454943i | \(-0.150341\pi\) |
−0.839253 | + | 0.543742i | \(0.817007\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −39.6598 | −1.93290 | −0.966449 | − | 0.256857i | \(-0.917313\pi\) | ||||
−0.966449 | + | 0.256857i | \(0.917313\pi\) | |||||||
\(422\) | 20.2524 | + | 11.6927i | 0.985873 | + | 0.569194i | ||||
\(423\) | −9.34044 | − | 5.39270i | −0.454148 | − | 0.262202i | ||||
\(424\) | 11.4158 | 0.554400 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.8669 | + | 18.8220i | 0.526502 | + | 0.911929i | ||||
\(427\) | −5.06967 | + | 2.92697i | −0.245338 | + | 0.141646i | ||||
\(428\) | − | 38.9260i | − | 1.88156i | ||||||
\(429\) | 11.9012 | − | 11.1526i | 0.574593 | − | 0.538455i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.0641 | + | 19.1636i | 0.532940 | + | 0.923079i | 0.999260 | + | 0.0384626i | \(0.0122461\pi\) |
−0.466320 | + | 0.884616i | \(0.654421\pi\) | |||||||
\(432\) | 0.453455 | − | 0.261802i | 0.0218169 | − | 0.0125960i | ||||
\(433\) | −27.1553 | − | 15.6781i | −1.30500 | − | 0.753442i | −0.323743 | − | 0.946145i | \(-0.604941\pi\) |
−0.981257 | + | 0.192703i | \(0.938275\pi\) | |||||||
\(434\) | −25.3169 | −1.21525 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.54994 | − | 6.14868i | 0.170011 | − | 0.294468i | ||||
\(437\) | 11.4158i | 0.546091i | ||||||||
\(438\) | 27.0026 | + | 15.5899i | 1.29023 | + | 0.744916i | ||||
\(439\) | 2.15672 | + | 3.73555i | 0.102935 | + | 0.178288i | 0.912892 | − | 0.408200i | \(-0.133843\pi\) |
−0.809958 | + | 0.586488i | \(0.800510\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.40786 | −0.257517 | ||||||||
\(442\) | 10.6275 | − | 35.0681i | 0.505499 | − | 1.66802i | ||||
\(443\) | − | 0.493301i | − | 0.0234374i | −0.999931 | − | 0.0117187i | \(-0.996270\pi\) | ||
0.999931 | − | 0.0117187i | \(-0.00373027\pi\) | |||||||
\(444\) | 0.360646 | + | 0.624657i | 0.0171155 | + | 0.0296449i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 24.3945 | − | 42.2524i | 1.15511 | − | 2.00071i | ||||
\(447\) | 3.24490i | 0.153478i | ||||||||
\(448\) | 14.2574 | + | 8.23150i | 0.673598 | + | 0.388902i | ||||
\(449\) | −11.6563 | + | 20.1892i | −0.550093 | + | 0.952789i | 0.448174 | + | 0.893946i | \(0.352074\pi\) |
−0.998267 | + | 0.0588427i | \(0.981259\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.59214 | + | 4.48973i | −0.122059 | + | 0.211413i | ||||
\(452\) | −3.98378 | + | 2.30004i | −0.187381 | + | 0.108185i | ||||
\(453\) | 4.93631 | − | 2.84998i | 0.231928 | − | 0.133904i | ||||
\(454\) | 12.3180 | 0.578112 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.9101 | 0.604572 | ||||||||
\(457\) | 5.77609 | − | 3.33483i | 0.270194 | − | 0.155997i | −0.358782 | − | 0.933422i | \(-0.616808\pi\) |
0.628976 | + | 0.777425i | \(0.283474\pi\) | |||||||
\(458\) | 42.9589 | − | 24.8023i | 2.00734 | − | 1.15894i | ||||
\(459\) | 2.24665 | − | 3.89131i | 0.104865 | − | 0.181631i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.5596 | + | 25.2180i | −0.678110 | + | 1.17452i | 0.297440 | + | 0.954740i | \(0.403867\pi\) |
−0.975550 | + | 0.219780i | \(0.929466\pi\) | |||||||
\(462\) | 11.1805 | + | 6.45506i | 0.520164 | + | 0.300317i | ||||
\(463\) | 1.79334i | 0.0833436i | 0.999131 | + | 0.0416718i | \(0.0132684\pi\) | ||||
−0.999131 | + | 0.0416718i | \(0.986732\pi\) | |||||||
\(464\) | 0.360646 | − | 0.624657i | 0.0167426 | − | 0.0289990i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 28.6260 | + | 49.5816i | 1.32607 | + | 2.29682i | ||||
\(467\) | 16.8192i | 0.778301i | 0.921174 | + | 0.389150i | \(0.127231\pi\) | ||||
−0.921174 | + | 0.389150i | \(0.872769\pi\) | |||||||
\(468\) | 10.9398 | − | 2.55391i | 0.505694 | − | 0.118054i | ||||
\(469\) | 16.5708 | 0.765169 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.92697 | − | 3.33762i | −0.0887903 | − | 0.153789i | ||||
\(472\) | −1.86631 | − | 1.07751i | −0.0859037 | − | 0.0495965i | ||||
\(473\) | − | 28.8495i | − | 1.32650i | ||||||
\(474\) | −10.0321 | + | 17.3760i | −0.460788 | + | 0.798108i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 17.6652 | 0.809685 | ||||||||
\(477\) | −3.91756 | − | 2.26180i | −0.179373 | − | 0.103561i | ||||
\(478\) | 44.1187 | − | 25.4720i | 2.01794 | − | 1.16506i | ||||
\(479\) | 17.5765 | + | 30.4434i | 0.803092 | + | 1.39100i | 0.917571 | + | 0.397571i | \(0.130147\pi\) |
−0.114479 | + | 0.993426i | \(0.536520\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.189754 | − | 0.812826i | −0.00865205 | − | 0.0370617i | ||||
\(482\) | − | 25.1416i | − | 1.14517i | ||||||
\(483\) | −2.43848 | + | 1.40786i | −0.110955 | + | 0.0640596i | ||||
\(484\) | 14.7422 | + | 25.5342i | 0.670098 | + | 1.16064i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.26180 | 0.102597 | ||||||||
\(487\) | 7.47030 | + | 4.31298i | 0.338511 | + | 0.195440i | 0.659614 | − | 0.751605i | \(-0.270720\pi\) |
−0.321102 | + | 0.947045i | \(0.604053\pi\) | |||||||
\(488\) | −10.1393 | − | 5.85395i | −0.458986 | − | 0.264996i | ||||
\(489\) | −9.72480 | −0.439771 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.6068 | + | 20.1036i | 0.523809 | + | 0.907264i | 0.999616 | + | 0.0277143i | \(0.00882287\pi\) |
−0.475807 | + | 0.879550i | \(0.657844\pi\) | |||||||
\(492\) | −3.09242 | + | 1.78541i | −0.139417 | + | 0.0804924i | ||||
\(493\) | − | 6.18975i | − | 0.278773i | ||||||
\(494\) | −39.9260 | − | 12.0997i | −1.79636 | − | 0.544392i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.32241 | + | 4.02253i | 0.104279 | + | 0.180617i | ||||
\(497\) | 10.5003 | − | 6.06236i | 0.471004 | − | 0.271934i | ||||
\(498\) | −16.1237 | − | 9.30901i | −0.722519 | − | 0.417147i | ||||
\(499\) | −29.0393 | −1.29998 | −0.649988 | − | 0.759944i | \(-0.725226\pi\) | ||||
−0.649988 | + | 0.759944i | \(0.725226\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.63935 | + | 16.6959i | −0.430655 | + | 0.745916i | ||||
\(502\) | − | 24.9866i | − | 1.11521i | ||||||
\(503\) | −15.0688 | − | 8.69996i | −0.671883 | − | 0.387912i | 0.124906 | − | 0.992169i | \(-0.460137\pi\) |
−0.796790 | + | 0.604256i | \(0.793470\pi\) | |||||||
\(504\) | 1.59214 | + | 2.75768i | 0.0709198 | + | 0.122837i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −22.8316 | −1.01499 | ||||||||
\(507\) | −12.9726 | − | 0.843281i | −0.576134 | − | 0.0374514i | ||||
\(508\) | 55.4149i | 2.45864i | ||||||||
\(509\) | −11.4382 | − | 19.8115i | −0.506987 | − | 0.878128i | −0.999967 | − | 0.00808731i | \(-0.997426\pi\) |
0.492980 | − | 0.870041i | \(-0.335908\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.69723 | − | 15.0640i | 0.384743 | − | 0.666394i | ||||
\(512\) | − | 5.90558i | − | 0.260992i | ||||||
\(513\) | −4.43037 | − | 2.55787i | −0.195606 | − | 0.112933i | ||||
\(514\) | 2.29607 | − | 3.97691i | 0.101275 | − | 0.175414i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.93543 | − | 17.2087i | 0.437383 | − | 0.757569i | ||||
\(517\) | −42.2524 | + | 24.3945i | −1.85826 | + | 1.07287i | ||||
\(518\) | 0.572170 | − | 0.330343i | 0.0251397 | − | 0.0145144i | ||||
\(519\) | −3.01691 | −0.132427 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.3642 | −1.15503 | −0.577517 | − | 0.816378i | \(-0.695978\pi\) | ||||
−0.577517 | + | 0.816378i | \(0.695978\pi\) | |||||||
\(522\) | 2.69832 | − | 1.55787i | 0.118102 | − | 0.0681863i | ||||
\(523\) | 22.7696 | − | 13.1461i | 0.995646 | − | 0.574837i | 0.0886892 | − | 0.996059i | \(-0.471732\pi\) |
0.906957 | + | 0.421223i | \(0.138399\pi\) | |||||||
\(524\) | 18.1799 | − | 31.4884i | 0.794191 | − | 1.37558i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.67362 | − | 6.36290i | 0.160178 | − | 0.277436i | ||||
\(527\) | 34.5193 | + | 19.9297i | 1.50368 | + | 0.868152i | ||||
\(528\) | − | 2.36858i | − | 0.103079i | ||||||
\(529\) | −9.01021 | + | 15.6061i | −0.391748 | + | 0.678528i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.426974 | + | 0.739540i | 0.0185291 | + | 0.0320933i | ||||
\(532\) | − | 20.1124i | − | 0.871981i | ||||||
\(533\) | 4.02396 | − | 0.939393i | 0.174297 | − | 0.0406896i | ||||
\(534\) | −14.9787 | −0.648190 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 16.5708 | + | 28.7015i | 0.715750 | + | 1.23972i | ||||
\(537\) | −4.60461 | − | 2.65847i | −0.198704 | − | 0.114722i | ||||
\(538\) | 60.9519i | 2.62782i | ||||||||
\(539\) | −12.2315 | + | 21.1856i | −0.526848 | + | 0.912527i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.107816 | −0.00463537 | −0.00231768 | − | 0.999997i | \(-0.500738\pi\) | ||||
−0.00231768 | + | 0.999997i | \(0.500738\pi\) | |||||||
\(542\) | −38.8808 | − | 22.4478i | −1.67007 | − | 0.964218i | ||||
\(543\) | 22.4048 | − | 12.9354i | 0.961483 | − | 0.555112i | ||||
\(544\) | −14.0000 | − | 24.2487i | −0.600245 | − | 1.03965i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.33931 | − | 10.0206i | −0.100113 | − | 0.428843i | ||||
\(547\) | 12.1193i | 0.518182i | 0.965853 | + | 0.259091i | \(0.0834230\pi\) | ||||
−0.965853 | + | 0.259091i | \(0.916577\pi\) | |||||||
\(548\) | 54.1394 | − | 31.2574i | 2.31272 | − | 1.33525i | ||||
\(549\) | 2.31968 | + | 4.01780i | 0.0990014 | + | 0.171475i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.04721 | −0.300221 | ||||||||
\(552\) | −4.87695 | − | 2.81571i | −0.207577 | − | 0.119845i | ||||
\(553\) | 9.69365 | + | 5.59663i | 0.412216 | + | 0.237993i | ||||
\(554\) | 36.4024 | 1.54659 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −25.4546 | − | 44.0887i | −1.07952 | − | 1.86978i | ||||
\(557\) | 32.9150 | − | 19.0035i | 1.39466 | − | 0.805204i | 0.400829 | − | 0.916153i | \(-0.368722\pi\) |
0.993826 | + | 0.110948i | \(0.0353889\pi\) | |||||||
\(558\) | 20.0641i | 0.849382i | ||||||||
\(559\) | −16.7787 | + | 15.7234i | −0.709664 | + | 0.665030i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.1630 | − | 17.6028i | −0.429080 | − | 0.743189i | ||||
\(562\) | 10.5334 | − | 6.08148i | 0.444326 | − | 0.256532i | ||||
\(563\) | 13.4322 | + | 7.75510i | 0.566101 | + | 0.326839i | 0.755591 | − | 0.655044i | \(-0.227350\pi\) |
−0.189490 | + | 0.981883i | \(0.560683\pi\) | |||||||
\(564\) | −33.6046 | −1.41501 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 30.3833 | − | 52.6254i | 1.27710 | − | 2.21201i | ||||
\(567\) | − | 1.26180i | − | 0.0529907i | ||||||
\(568\) | 21.0006 | + | 12.1247i | 0.881167 | + | 0.508742i | ||||
\(569\) | 9.62024 | + | 16.6627i | 0.403301 | + | 0.698538i | 0.994122 | − | 0.108265i | \(-0.0345293\pi\) |
−0.590821 | + | 0.806803i | \(0.701196\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.7338 | 1.16062 | 0.580311 | − | 0.814395i | \(-0.302931\pi\) | ||||
0.580311 | + | 0.814395i | \(0.302931\pi\) | |||||||
\(572\) | 14.7387 | − | 48.6339i | 0.616255 | − | 2.03349i | ||||
\(573\) | 10.6563i | 0.445172i | ||||||||
\(574\) | 1.63539 | + | 2.83257i | 0.0682597 | + | 0.118229i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.52360 | − | 11.2992i | 0.271817 | − | 0.470801i | ||||
\(577\) | 26.9866i | 1.12347i | 0.827318 | + | 0.561733i | \(0.189865\pi\) | ||||
−0.827318 | + | 0.561733i | \(0.810135\pi\) | |||||||
\(578\) | −6.24802 | − | 3.60730i | −0.259883 | − | 0.150044i | ||||
\(579\) | −3.99155 | + | 6.91356i | −0.165883 | + | 0.287318i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.19326 | + | 8.99499i | −0.215453 | + | 0.373175i | ||||
\(582\) | 20.8995 | − | 12.0663i | 0.866312 | − | 0.500165i | ||||
\(583\) | −17.7215 | + | 10.2315i | −0.733949 | + | 0.423745i | ||||
\(584\) | 34.7889 | 1.43958 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −48.4462 | −2.00129 | ||||||||
\(587\) | −26.7195 | + | 15.4265i | −1.10283 | + | 0.636720i | −0.936963 | − | 0.349427i | \(-0.886376\pi\) |
−0.165869 | + | 0.986148i | \(0.553043\pi\) | |||||||
\(588\) | −14.5921 | + | 8.42476i | −0.601769 | + | 0.347431i | ||||
\(589\) | 22.6905 | − | 39.3012i | 0.934947 | − | 1.61938i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.66966 | − | 15.0163i | 0.356622 | − | 0.617688i | ||||
\(592\) | −0.104974 | − | 0.0606069i | −0.00431441 | − | 0.00249093i | ||||
\(593\) | − | 4.29211i | − | 0.176256i | −0.996109 | − | 0.0881278i | \(-0.971912\pi\) | ||
0.996109 | − | 0.0881278i | \(-0.0280884\pi\) | |||||||
\(594\) | 5.11575 | − | 8.86074i | 0.209902 | − | 0.363560i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.05514 | + | 8.75576i | 0.207067 | + | 0.358650i | ||||
\(597\) | 1.23150i | 0.0504019i | ||||||||
\(598\) | 12.4436 | + | 13.2787i | 0.508855 | + | 0.543007i | ||||
\(599\) | 24.0224 | 0.981527 | 0.490764 | − | 0.871293i | \(-0.336718\pi\) | ||||
0.490764 | + | 0.871293i | \(0.336718\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.26577 | − | 2.19238i | −0.0516318 | − | 0.0894289i | 0.839054 | − | 0.544048i | \(-0.183109\pi\) |
−0.890686 | + | 0.454619i | \(0.849776\pi\) | |||||||
\(602\) | −15.7627 | − | 9.10060i | −0.642440 | − | 0.370913i | ||||
\(603\) | − | 13.1327i | − | 0.534803i | ||||||
\(604\) | 8.87982 | − | 15.3803i | 0.361315 | − | 0.625816i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −38.5574 | −1.56629 | ||||||||
\(607\) | −9.90877 | − | 5.72083i | −0.402185 | − | 0.232201i | 0.285242 | − | 0.958456i | \(-0.407926\pi\) |
−0.687426 | + | 0.726254i | \(0.741260\pi\) | |||||||
\(608\) | −27.6078 | + | 15.9394i | −1.11965 | + | 0.646428i | ||||
\(609\) | −0.869099 | − | 1.50532i | −0.0352177 | − | 0.0609988i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 37.2159 | + | 11.2784i | 1.50559 | + | 0.456276i | ||||
\(612\) | − | 14.0000i | − | 0.565916i | ||||||
\(613\) | 6.22955 | − | 3.59663i | 0.251609 | − | 0.145267i | −0.368892 | − | 0.929472i | \(-0.620263\pi\) |
0.620501 | + | 0.784206i | \(0.286929\pi\) | |||||||
\(614\) | 8.88204 | + | 15.3841i | 0.358450 | + | 0.620853i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.4045 | 0.580373 | ||||||||
\(617\) | −22.1450 | − | 12.7854i | −0.891523 | − | 0.514721i | −0.0170827 | − | 0.999854i | \(-0.505438\pi\) |
−0.874440 | + | 0.485133i | \(0.838771\pi\) | |||||||
\(618\) | −27.3218 | − | 15.7742i | −1.09904 | − | 0.634532i | ||||
\(619\) | −5.98660 | −0.240622 | −0.120311 | − | 0.992736i | \(-0.538389\pi\) | ||||
−0.120311 | + | 0.992736i | \(0.538389\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.11575 | + | 1.93253i | 0.0447735 | + | 0.0775499i | ||||
\(622\) | 54.5997 | − | 31.5231i | 2.18925 | − | 1.26396i | ||||
\(623\) | 8.35622i | 0.334785i | ||||||||
\(624\) | −1.37755 | + | 1.29091i | −0.0551462 | + | 0.0516778i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.92027 | + | 15.4504i | 0.356526 | + | 0.617521i | ||||
\(627\) | −20.0412 | + | 11.5708i | −0.800370 | + | 0.462094i | ||||
\(628\) | −10.3992 | − | 6.00397i | −0.414972 | − | 0.239584i | ||||
\(629\) | −1.04019 | −0.0414752 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.5129 | − | 37.2615i | 0.856417 | − | 1.48336i | −0.0189080 | − | 0.999821i | \(-0.506019\pi\) |
0.875325 | − | 0.483536i | \(-0.160648\pi\) | |||||||
\(632\) | 22.3865i | 0.890488i | ||||||||
\(633\) | −8.95411 | − | 5.16966i | −0.355894 | − | 0.205475i | ||||
\(634\) | −14.9484 | − | 25.8913i | −0.593675 | − | 1.02828i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −14.0944 | −0.558880 | ||||||||
\(637\) | 18.9878 | − | 4.43269i | 0.752322 | − | 0.175630i | ||||
\(638\) | − | 14.0944i | − | 0.558003i | ||||||
\(639\) | −4.80453 | − | 8.32168i | −0.190064 | − | 0.329201i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.34725 | − | 5.79760i | 0.132208 | − | 0.228992i | −0.792319 | − | 0.610107i | \(-0.791127\pi\) |
0.924528 | + | 0.381115i | \(0.124460\pi\) | |||||||
\(642\) | 28.2574i | 1.11523i | ||||||||
\(643\) | 7.08477 | + | 4.09039i | 0.279396 | + | 0.161309i | 0.633150 | − | 0.774029i | \(-0.281762\pi\) |
−0.353754 | + | 0.935338i | \(0.615095\pi\) | |||||||
\(644\) | −4.38652 | + | 7.59768i | −0.172853 | + | 0.299391i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −25.9956 | + | 45.0257i | −1.02278 | + | 1.77151i | ||||
\(647\) | −9.76765 | + | 5.63935i | −0.384006 | + | 0.221706i | −0.679560 | − | 0.733620i | \(-0.737829\pi\) |
0.295554 | + | 0.955326i | \(0.404496\pi\) | |||||||
\(648\) | 2.18551 | − | 1.26180i | 0.0858548 | − | 0.0495683i | ||||
\(649\) | 3.86292 | 0.151633 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.1933 | 0.438699 | ||||||||
\(652\) | −26.2406 | + | 15.1500i | −1.02766 | + | 0.593321i | ||||
\(653\) | −23.5978 | + | 13.6242i | −0.923454 | + | 0.533156i | −0.884735 | − | 0.466094i | \(-0.845661\pi\) |
−0.0387184 | + | 0.999250i | \(0.512328\pi\) | |||||||
\(654\) | −2.57699 | + | 4.46348i | −0.100768 | + | 0.174536i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.300039 | − | 0.519683i | 0.0117146 | − | 0.0202902i | ||||
\(657\) | −11.9385 | − | 6.89270i | −0.465766 | − | 0.268910i | ||||
\(658\) | 30.7810i | 1.19997i | ||||||||
\(659\) | 3.37755 | − | 5.85009i | 0.131571 | − | 0.227887i | −0.792711 | − | 0.609597i | \(-0.791331\pi\) |
0.924282 | + | 0.381710i | \(0.124665\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.2551 | + | 22.9585i | 0.515564 | + | 0.892983i | 0.999837 | + | 0.0180657i | \(0.00575081\pi\) |
−0.484273 | + | 0.874917i | \(0.660916\pi\) | |||||||
\(662\) | 53.9429i | 2.09655i | ||||||||
\(663\) | −4.69869 | + | 15.5045i | −0.182482 | + | 0.602144i | ||||
\(664\) | −20.7730 | −0.806151 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.261802 | − | 0.453455i | −0.0101446 | − | 0.0175710i | ||||
\(667\) | 2.66217 | + | 1.53700i | 0.103079 | + | 0.0595130i | ||||
\(668\) | 60.0676i | 2.32409i | ||||||||
\(669\) | −10.7854 | + | 18.6809i | −0.416988 | + | 0.722244i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.9866 | 0.810179 | ||||||||
\(672\) | −6.80949 | − | 3.93146i | −0.262682 | − | 0.151659i | ||||
\(673\) | 0.586811 | − | 0.338795i | 0.0226199 | − | 0.0130596i | −0.488647 | − | 0.872481i | \(-0.662510\pi\) |
0.511267 | + | 0.859422i | \(0.329176\pi\) | |||||||
\(674\) | −6.42697 | − | 11.1318i | −0.247558 | − | 0.428783i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −36.3180 | + | 17.9343i | −1.39685 | + | 0.689780i | ||||
\(677\) | − | 10.4630i | − | 0.402126i | −0.979578 | − | 0.201063i | \(-0.935560\pi\) | ||
0.979578 | − | 0.201063i | \(-0.0644395\pi\) | |||||||
\(678\) | 2.89193 | − | 1.66966i | 0.111064 | − | 0.0641228i | ||||
\(679\) | −6.73150 | − | 11.6593i | −0.258331 | − | 0.447443i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.44609 | −0.208695 | ||||||||
\(682\) | 78.6023 | + | 45.3811i | 3.00984 | + | 1.73773i | ||||
\(683\) | −16.2394 | − | 9.37580i | −0.621382 | − | 0.358755i | 0.156025 | − | 0.987753i | \(-0.450132\pi\) |
−0.777407 | + | 0.628998i | \(0.783465\pi\) | |||||||
\(684\) | −15.9394 | −0.609458 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17.7057 | + | 30.6671i | 0.676006 | + | 1.17088i | ||||
\(687\) | −18.9932 | + | 10.9657i | −0.724636 | + | 0.418369i | ||||
\(688\) | 3.33931i | 0.127310i | ||||||||
\(689\) | 15.6091 | + | 4.73038i | 0.594657 | + | 0.180213i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.7827 | − | 37.7287i | −0.828652 | − | 1.43527i | −0.899096 | − | 0.437752i | \(-0.855775\pi\) |
0.0704440 | − | 0.997516i | \(-0.477558\pi\) | |||||||
\(692\) | −8.14057 | + | 4.69996i | −0.309458 | + | 0.178666i | ||||
\(693\) | −4.94318 | − | 2.85395i | −0.187776 | − | 0.108412i | ||||
\(694\) | −48.5148 | −1.84159 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.73820 | − | 3.01065i | 0.0658862 | − | 0.114118i | ||||
\(697\) | − | 5.14956i | − | 0.195054i | ||||||
\(698\) | −13.4585 | − | 7.77026i | −0.509411 | − | 0.294108i | ||||
\(699\) | −12.6563 | − | 21.9213i | −0.478704 | − | 0.829139i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.0810 | −0.720680 | −0.360340 | − | 0.932821i | \(-0.617339\pi\) | ||||
−0.360340 | + | 0.932821i | \(0.617339\pi\) | |||||||
\(702\) | −7.94151 | + | 1.85395i | −0.299733 | + | 0.0699727i | ||||
\(703\) | 1.18429i | 0.0446663i | ||||||||
\(704\) | −29.5102 | − | 51.1132i | −1.11221 | − | 1.92640i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 39.0125 | − | 67.5716i | 1.46825 | − | 2.54309i | ||||
\(707\) | 21.5102i | 0.808975i | ||||||||
\(708\) | 2.30422 | + | 1.33034i | 0.0865979 | + | 0.0499973i | ||||
\(709\) | 22.3023 | − | 38.6287i | 0.837581 | − | 1.45073i | −0.0543307 | − | 0.998523i | \(-0.517303\pi\) |
0.891912 | − | 0.452210i | \(-0.149364\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.43543 | − | 7.68238i | 0.166341 | − | 0.288112i | ||||
\(712\) | −14.4734 | + | 8.35622i | −0.542414 | + | 0.313163i | ||||
\(713\) | −17.1432 | + | 9.89765i | −0.642019 | + | 0.370670i | ||||
\(714\) | −12.8236 | −0.479913 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16.5663 | −0.619110 | ||||||||
\(717\) | −19.5060 | + | 11.2618i | −0.728465 | + | 0.420580i | ||||
\(718\) | −15.9826 | + | 9.22753i | −0.596464 | + | 0.344368i | ||||
\(719\) | −6.49109 | + | 11.2429i | −0.242077 | + | 0.419289i | −0.961306 | − | 0.275484i | \(-0.911162\pi\) |
0.719229 | + | 0.694773i | \(0.244495\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.80004 | + | 15.2421i | −0.327731 | + | 0.567646i | ||||
\(722\) | 14.0462 | + | 8.10957i | 0.522745 | + | 0.301807i | ||||
\(723\) | 11.1157i | 0.413399i | ||||||||
\(724\) | 40.3035 | − | 69.8078i | 1.49787 | − | 2.59439i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −10.7017 | − | 18.5359i | −0.397178 | − | 0.687932i | ||||
\(727\) | 17.3980i | 0.645255i | 0.946526 | + | 0.322627i | \(0.104566\pi\) | ||||
−0.946526 | + | 0.322627i | \(0.895434\pi\) | |||||||
\(728\) | −7.85065 | − | 8.37755i | −0.290965 | − | 0.310493i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.3281 | + | 24.8170i | 0.529945 | + | 0.917892i | ||||
\(732\) | 12.5185 | + | 7.22753i | 0.462695 | + | 0.267137i | ||||
\(733\) | − | 45.8272i | − | 1.69266i | −0.532655 | − | 0.846332i | \(-0.678806\pi\) | ||
0.532655 | − | 0.846332i | \(-0.321194\pi\) | |||||||
\(734\) | 7.73598 | − | 13.3991i | 0.285540 | − | 0.494570i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.9056 | 0.512567 | ||||||||
\(737\) | −51.4479 | − | 29.7035i | −1.89511 | − | 1.09414i | ||||
\(738\) | 2.24486 | − | 1.29607i | 0.0826346 | − | 0.0477091i | ||||
\(739\) | 8.78541 | + | 15.2168i | 0.323176 | + | 0.559758i | 0.981142 | − | 0.193290i | \(-0.0619159\pi\) |
−0.657965 | + | 0.753048i | \(0.728583\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.6523 | + | 5.34959i | 0.648473 | + | 0.196522i | ||||
\(742\) | 12.9101i | 0.473946i | ||||||||
\(743\) | 26.2893 | − | 15.1781i | 0.964459 | − | 0.556831i | 0.0669167 | − | 0.997759i | \(-0.478684\pi\) |
0.897543 | + | 0.440928i | \(0.145350\pi\) | |||||||
\(744\) | 11.1933 | + | 19.3873i | 0.410365 | + | 0.710773i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −31.2563 | −1.14438 | ||||||||
\(747\) | 7.12869 | + | 4.11575i | 0.260825 | + | 0.150587i | ||||
\(748\) | −54.8458 | − | 31.6652i | −2.00536 | − | 1.15780i | ||||
\(749\) | 15.7641 | 0.576007 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.90162 | − | 3.29369i | −0.0693909 | − | 0.120189i | 0.829242 | − | 0.558889i | \(-0.188772\pi\) |
−0.898633 | + | 0.438700i | \(0.855439\pi\) | |||||||
\(752\) | 4.89069 | − | 2.82364i | 0.178345 | − | 0.102968i | ||||
\(753\) | 11.0472i | 0.402583i | ||||||||
\(754\) | −8.19723 | + | 7.68167i | −0.298525 | + | 0.279750i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.96573 | − | 3.40474i | −0.0714929 | − | 0.123829i | ||||
\(757\) | −2.95129 | + | 1.70393i | −0.107266 | + | 0.0619303i | −0.552673 | − | 0.833398i | \(-0.686392\pi\) |
0.445407 | + | 0.895328i | \(0.353059\pi\) | |||||||
\(758\) | −22.5566 | − | 13.0231i | −0.819294 | − | 0.473020i | ||||
\(759\) | 10.0944 | 0.366404 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.62245 | + | 6.27426i | −0.131314 | + | 0.227442i | −0.924183 | − | 0.381949i | \(-0.875253\pi\) |
0.792870 | + | 0.609391i | \(0.208586\pi\) | |||||||
\(762\) | − | 40.2271i | − | 1.45727i | ||||||
\(763\) | 2.49006 | + | 1.43764i | 0.0901464 | + | 0.0520460i | ||||
\(764\) | 16.6011 | + | 28.7540i | 0.600607 | + | 1.04028i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −51.7496 | −1.86979 | ||||||||
\(767\) | −2.10535 | − | 2.24665i | −0.0760198 | − | 0.0811218i | ||||
\(768\) | − | 12.4630i | − | 0.449720i | ||||||
\(769\) | 15.5882 | + | 26.9995i | 0.562124 | + | 0.973627i | 0.997311 | + | 0.0732873i | \(0.0233490\pi\) |
−0.435187 | + | 0.900340i | \(0.643318\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.01515 | + | 1.75829i | −0.0365598 | + | 0.0633234i | ||||
\(772\) | 24.8733i | 0.895210i | ||||||||
\(773\) | 16.8533 | + | 9.73026i | 0.606172 | + | 0.349973i | 0.771466 | − | 0.636271i | \(-0.219524\pi\) |
−0.165294 | + | 0.986244i | \(0.552857\pi\) | |||||||
\(774\) | −7.21238 | + | 12.4922i | −0.259244 | + | 0.449023i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 13.4630 | − | 23.3186i | 0.483293 | − | 0.837089i | ||||
\(777\) | −0.252971 | + | 0.146053i | −0.00907528 | + | 0.00523962i | ||||
\(778\) | −8.52600 | + | 4.92249i | −0.305672 | + | 0.176480i | ||||
\(779\) | −5.86292 | −0.210061 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43.4675 | −1.55539 | ||||||||
\(782\) | 19.6403 | − | 11.3393i | 0.702335 | − | 0.405493i | ||||
\(783\) | −1.19299 | + | 0.688776i | −0.0426342 | + | 0.0246148i | ||||
\(784\) | 1.41579 | − | 2.45222i | 0.0505639 | − | 0.0875792i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −13.1972 | + | 22.8583i | −0.470730 | + | 0.815328i | ||||
\(787\) | −12.4737 | − | 7.20171i | −0.444641 | − | 0.256713i | 0.260923 | − | 0.965359i | \(-0.415973\pi\) |
−0.705564 | + | 0.708646i | \(0.749306\pi\) | |||||||
\(788\) | − | 54.0250i | − | 1.92456i | ||||||
\(789\) | −1.62420 | + | 2.81320i | −0.0578231 | + | 0.100153i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.931460 | − | 1.61334i | −0.0331189 | − | 0.0573636i | ||||
\(792\) | − | 11.4158i | − | 0.405642i | ||||||
\(793\) | −11.4380 | − | 12.2057i | −0.406176 | − | 0.433436i | ||||
\(794\) | 17.2405 | 0.611841 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.91852 | + | 3.32298i | 0.0680002 | + | 0.117780i | ||||
\(797\) | 20.4392 | + | 11.8006i | 0.723992 | + | 0.417997i | 0.816220 | − | 0.577741i | \(-0.196066\pi\) |
−0.0922279 | + | 0.995738i | \(0.529399\pi\) | |||||||
\(798\) | 14.6001i | 0.516837i | ||||||||
\(799\) | 24.2310 | − | 41.9694i | 0.857233 | − | 1.48477i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.62245 | 0.233993 | ||||||||
\(802\) | 40.8396 | + | 23.5787i | 1.44210 | + | 0.832595i | ||||
\(803\) | −54.0051 | + | 31.1799i | −1.90580 | + | 1.10031i | ||||
\(804\) | −20.4590 | − | 35.4361i | −0.721534 | − | 1.24973i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16.4461 | − | 70.4480i | −0.579289 | − | 2.48142i | ||||
\(807\) | − | 26.9484i | − | 0.948627i | ||||||
\(808\) | −37.2568 | + | 21.5102i | −1.31069 | + | 0.756726i | ||||
\(809\) | 13.3776 | + | 23.1706i | 0.470330 | + | 0.814635i | 0.999424 | − | 0.0339280i | \(-0.0108017\pi\) |
−0.529095 | + | 0.848563i | \(0.677468\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.58421 | −0.125859 | −0.0629293 | − | 0.998018i | \(-0.520044\pi\) | ||||
−0.0629293 | + | 0.998018i | \(0.520044\pi\) | |||||||
\(812\) | −4.69021 | − | 2.70789i | −0.164594 | − | 0.0950285i | ||||
\(813\) | 17.1902 | + | 9.92476i | 0.602886 | + | 0.348077i | ||||
\(814\) | −2.36858 | −0.0830187 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.17636 | + | 2.03751i | 0.0411807 | + | 0.0713271i | ||||
\(817\) | 28.2549 | − | 16.3130i | 0.988514 | − | 0.570719i | ||||
\(818\) | − | 38.3721i | − | 1.34165i | ||||||
\(819\) | 1.03427 | + | 4.43037i | 0.0361403 | + | 0.154810i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.91806 | − | 13.7145i | −0.276342 | − | 0.478639i | 0.694131 | − | 0.719849i | \(-0.255789\pi\) |
−0.970473 | + | 0.241210i | \(0.922456\pi\) | |||||||
\(822\) | −39.3012 | + | 22.6905i | −1.37079 | + | 0.791423i | ||||
\(823\) | 6.42226 | + | 3.70789i | 0.223866 | + | 0.129249i | 0.607739 | − | 0.794137i | \(-0.292077\pi\) |
−0.383873 | + | 0.923386i | \(0.625410\pi\) | |||||||
\(824\) | −35.2002 | −1.22626 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.21856 | − | 2.11061i | 0.0423991 | − | 0.0734374i | ||||
\(827\) | − | 16.6036i | − | 0.577363i | −0.957425 | − | 0.288682i | \(-0.906783\pi\) | ||
0.957425 | − | 0.288682i | \(-0.0932169\pi\) | |||||||
\(828\) | 6.02129 | + | 3.47640i | 0.209254 | + | 0.120813i | ||||
\(829\) | −14.6421 | − | 25.3608i | −0.508541 | − | 0.880818i | −0.999951 | − | 0.00989015i | \(-0.996852\pi\) |
0.491410 | − | 0.870928i | \(-0.336482\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.0944 | −0.558309 | ||||||||
\(832\) | −13.6436 | + | 45.0204i | −0.473007 | + | 1.56080i | ||||
\(833\) | − | 24.2991i | − | 0.841915i | ||||||
\(834\) | 18.4781 | + | 32.0051i | 0.639846 | + | 1.10825i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −36.0518 | + | 62.4435i | −1.24688 | + | 2.15965i | ||||
\(837\) | − | 8.87085i | − | 0.306622i | ||||||
\(838\) | −4.11117 | − | 2.37358i | −0.142018 | − | 0.0819941i | ||||
\(839\) | −15.0810 | + | 26.1211i | −0.520655 | + | 0.901800i | 0.479057 | + | 0.877784i | \(0.340979\pi\) |
−0.999712 | + | 0.0240164i | \(0.992355\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.5512 | − | 23.4713i | 0.467282 | − | 0.809356i | ||||
\(842\) | 77.6847 | − | 44.8513i | 2.67719 | − | 1.54568i | ||||
\(843\) | −4.65710 | + | 2.68878i | −0.160399 | + | 0.0926064i | ||||
\(844\) | −32.2147 | −1.10888 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 24.3945 | 0.838699 | ||||||||
\(847\) | −10.3407 | + | 5.97022i | −0.355311 | + | 0.205139i | ||||
\(848\) | 2.05125 | − | 1.18429i | 0.0704402 | − | 0.0406687i | ||||
\(849\) | −13.4332 | + | 23.2670i | −0.461027 | + | 0.798522i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.258295 | − | 0.447379i | 0.00885423 | − | 0.0153360i | ||||
\(852\) | −25.9283 | − | 14.9697i | −0.888288 | − | 0.512853i | ||||
\(853\) | 2.50670i | 0.0858277i | 0.999079 | + | 0.0429139i | \(0.0136641\pi\) | ||||
−0.999079 | + | 0.0429139i | \(0.986336\pi\) | |||||||
\(854\) | 6.62024 | − | 11.4666i | 0.226540 | − | 0.392378i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.7641 | + | 27.3042i | 0.538805 | + | 0.933238i | ||||
\(857\) | − | 24.4327i | − | 0.834605i | −0.908768 | − | 0.417302i | \(-0.862976\pi\) | ||
0.908768 | − | 0.417302i | \(-0.137024\pi\) | |||||||
\(858\) | −10.6992 | + | 35.3046i | −0.365264 | + | 1.20528i | ||||
\(859\) | 7.10235 | 0.242329 | 0.121165 | − | 0.992632i | \(-0.461337\pi\) | ||||
0.121165 | + | 0.992632i | \(0.461337\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.723046 | − | 1.25235i | −0.0246413 | − | 0.0426801i | ||||
\(862\) | −43.3443 | − | 25.0248i | −1.47631 | − | 0.852349i | ||||
\(863\) | 3.24490i | 0.110458i | 0.998474 | + | 0.0552288i | \(0.0175888\pi\) | ||||
−0.998474 | + | 0.0552288i | \(0.982411\pi\) | |||||||
\(864\) | −3.11575 | + | 5.39664i | −0.106000 | + | 0.183597i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 70.9216 | 2.41001 | ||||||||
\(867\) | 2.76241 | + | 1.59488i | 0.0938163 | + | 0.0541649i | ||||
\(868\) | 30.2030 | − | 17.4377i | 1.02516 | − | 0.591874i | ||||
\(869\) | −20.0641 | − | 34.7521i | −0.680628 | − | 1.17888i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.7645 | + | 46.1106i | 0.364742 | + | 1.56240i | ||||
\(872\) | 5.75056i | 0.194738i | ||||||||
\(873\) | −9.24019 | + | 5.33483i | −0.312733 | + | 0.180557i | ||||
\(874\) | −12.9101 | − | 22.3610i | −0.436692 | − | 0.756372i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −42.9519 | −1.45121 | ||||||||
\(877\) | −16.4429 | − | 9.49330i | −0.555237 | − | 0.320566i | 0.195995 | − | 0.980605i | \(-0.437206\pi\) |
−0.751231 | + | 0.660039i | \(0.770540\pi\) | |||||||
\(878\) | −8.44907 | − | 4.87807i | −0.285142 | − | 0.164627i | ||||
\(879\) | 21.4193 | 0.722455 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.73820 | + | 16.8671i | 0.328088 | + | 0.568265i | 0.982132 | − | 0.188191i | \(-0.0602623\pi\) |
−0.654044 | + | 0.756456i | \(0.726929\pi\) | |||||||
\(882\) | 10.5928 | − | 6.11575i | 0.356678 | − | 0.205928i | ||||
\(883\) | 50.5664i | 1.70169i | 0.525413 | + | 0.850847i | \(0.323911\pi\) | ||||
−0.525413 | + | 0.850847i | \(0.676089\pi\) | |||||||
\(884\) | 11.4755 | + | 49.1560i | 0.385962 | + | 1.65330i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.557875 | + | 0.966267i | 0.0187422 | + | 0.0324624i | ||||
\(887\) | −10.8488 | + | 6.26356i | −0.364267 | + | 0.210310i | −0.670951 | − | 0.741502i | \(-0.734114\pi\) |
0.306684 | + | 0.951811i | \(0.400781\pi\) | |||||||
\(888\) | −0.505942 | − | 0.292106i | −0.0169783 | − | 0.00980243i | ||||
\(889\) | −22.4417 | −0.752669 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.26180 | + | 3.91756i | −0.0757732 | + | 0.131243i | ||||
\(892\) | 67.2092i | 2.25033i | ||||||||
\(893\) | −47.7833 | − | 27.5877i | −1.59901 | − | 0.923188i | ||||
\(894\) | −3.66966 | − | 6.35603i | −0.122732 | − | 0.212578i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −21.5102 | −0.718606 | ||||||||
\(897\) | −5.50161 | − | 5.87085i | −0.183693 | − | 0.196022i | ||||
\(898\) | − | 52.7283i | − | 1.75957i | ||||||
\(899\) | −6.11003 | − | 10.5829i | −0.203781 | − | 0.352959i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.1630 | − | 17.6028i | 0.338577 | − | 0.586433i | ||||
\(902\) | − | 11.7258i | − | 0.390428i | ||||||
\(903\) | 6.96909 | + | 4.02360i | 0.231917 | + | 0.133897i | ||||
\(904\) | 1.86292 | − | 3.22667i | 0.0619598 | − | 0.107317i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.44609 | + | 11.1650i | −0.214157 | + | 0.370931i | ||||
\(907\) | 24.2849 | − | 14.0209i | 0.806366 | − | 0.465555i | −0.0393265 | − | 0.999226i | \(-0.512521\pi\) |
0.845692 | + | 0.533671i | \(0.179188\pi\) | |||||||
\(908\) | −14.6953 | + | 8.48433i | −0.487680 | + | 0.281562i | ||||
\(909\) | 17.0472 | 0.565420 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.1977 | 0.536653 | 0.268327 | − | 0.963328i | \(-0.413529\pi\) | ||||
0.268327 | + | 0.963328i | \(0.413529\pi\) | |||||||
\(912\) | 2.31976 | − | 1.33931i | 0.0768150 | − | 0.0443491i | ||||
\(913\) | 32.2474 | − | 18.6180i | 1.06723 | − | 0.616167i | ||||
\(914\) | −7.54272 | + | 13.0644i | −0.249491 | + | 0.432131i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −34.1665 | + | 59.1781i | −1.12889 | + | 1.95530i | ||||
\(917\) | 12.7521 | + | 7.36240i | 0.421110 | + | 0.243128i | ||||
\(918\) | 10.1630i | 0.335428i | ||||||||
\(919\) | −21.6389 | + | 37.4797i | −0.713801 | + | 1.23634i | 0.249619 | + | 0.968344i | \(0.419695\pi\) |
−0.963420 | + | 0.267996i | \(0.913639\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.92697 | − | 6.80172i | −0.129398 | − | 0.224124i | ||||
\(922\) | − | 65.8620i | − | 2.16905i | ||||||
\(923\) | 23.6905 | + | 25.2805i | 0.779781 | + | 0.832117i | ||||
\(924\) | −17.7844 | −0.585063 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.02809 | − | 3.51276i | −0.0666472 | − | 0.115436i | ||||
\(927\) | 12.0796 | + | 6.97418i | 0.396747 | + | 0.229062i | ||||
\(928\) | 8.58421i | 0.281791i | ||||||||
\(929\) | 6.88425 | − | 11.9239i | 0.225865 | − | 0.391210i | −0.730714 | − | 0.682684i | \(-0.760813\pi\) |
0.956579 | + | 0.291475i | \(0.0941459\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.6652 | −0.906691 | ||||||||
\(932\) | −68.3012 | − | 39.4337i | −2.23728 | − | 1.29169i | ||||
\(933\) | −24.1399 | + | 13.9372i | −0.790305 | + | 0.456283i | ||||
\(934\) | −19.0209 | − | 32.9451i | −0.622382 | − | 1.07800i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.63935 | + | 6.22178i | −0.217014 | + | 0.203365i | ||||
\(937\) | − | 38.1888i | − | 1.24757i | −0.781594 | − | 0.623787i | \(-0.785593\pi\) | ||
0.781594 | − | 0.623787i | \(-0.214407\pi\) | |||||||
\(938\) | −32.4585 | + | 18.7400i | −1.05981 | + | 0.611881i | ||||
\(939\) | −3.94388 | − | 6.83100i | −0.128704 | − | 0.222921i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.9618 | −0.455140 | −0.227570 | − | 0.973762i | \(-0.573078\pi\) | ||||
−0.227570 | + | 0.973762i | \(0.573078\pi\) | |||||||
\(942\) | 7.54903 | + | 4.35843i | 0.245961 | + | 0.142005i | ||||
\(943\) | 2.21479 | + | 1.27871i | 0.0721234 | + | 0.0416405i | ||||
\(944\) | −0.447131 | −0.0145529 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 32.6260 | + | 56.5098i | 1.06076 | + | 1.83729i | ||||
\(947\) | 6.38228 | − | 3.68481i | 0.207396 | − | 0.119740i | −0.392705 | − | 0.919665i | \(-0.628461\pi\) |
0.600101 | + | 0.799924i | \(0.295127\pi\) | |||||||
\(948\) | − | 27.6394i | − | 0.897684i | ||||||
\(949\) | 47.5676 | + | 14.4155i | 1.54411 | + | 0.467948i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.60905 | + | 11.4472i | 0.214313 | + | 0.371201i | ||||
\(952\) | −12.3911 | + | 7.15399i | −0.401597 | + | 0.231862i | ||||
\(953\) | 20.1075 | + | 11.6091i | 0.651345 | + | 0.376054i | 0.788971 | − | 0.614430i | \(-0.210614\pi\) |
−0.137627 | + | 0.990484i | \(0.543947\pi\) | |||||||
\(954\) | 10.2315 | 0.331257 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −35.0890 | + | 60.7759i | −1.13486 | + | 1.96563i | ||||
\(957\) | 6.23150i | 0.201436i | ||||||||
\(958\) | −68.8571 | − | 39.7546i | −2.22467 | − | 1.28441i | ||||
\(959\) | 12.6585 | + | 21.9251i | 0.408763 | + | 0.707999i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 47.6920 | 1.53845 | ||||||||
\(962\) | 1.29091 | + | 1.37755i | 0.0416207 | + | 0.0444140i | ||||
\(963\) | − | 12.4933i | − | 0.402591i | ||||||
\(964\) | 17.3169 | + | 29.9938i | 0.557741 | + | 0.966036i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.18429 | − | 5.51535i | 0.102453 | − | 0.177454i | ||||
\(967\) | − | 7.54402i | − | 0.242599i | −0.992616 | − | 0.121300i | \(-0.961294\pi\) | ||
0.992616 | − | 0.121300i | \(-0.0387062\pi\) | |||||||
\(968\) | −20.6814 | − | 11.9404i | −0.664726 | − | 0.383780i | ||||
\(969\) | 11.4933 | − | 19.9070i | 0.369218 | − | 0.639504i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.2921 | − | 26.4867i | 0.490747 | − | 0.849999i | −0.509196 | − | 0.860650i | \(-0.670057\pi\) |
0.999943 | + | 0.0106517i | \(0.00339059\pi\) | |||||||
\(972\) | −2.69832 | + | 1.55787i | −0.0865486 | + | 0.0499689i | ||||
\(973\) | 17.8548 | − | 10.3085i | 0.572400 | − | 0.330475i | ||||
\(974\) | −19.5102 | −0.625147 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.42919 | −0.0777564 | ||||||||
\(977\) | −30.9007 | + | 17.8405i | −0.988602 | + | 0.570770i | −0.904856 | − | 0.425717i | \(-0.860022\pi\) |
−0.0837460 | + | 0.996487i | \(0.526688\pi\) | |||||||
\(978\) | 19.0487 | − | 10.9978i | 0.609111 | − | 0.351670i | ||||
\(979\) | 14.9787 | − | 25.9438i | 0.478720 | − | 0.829168i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.13935 | − | 1.97342i | 0.0363768 | − | 0.0630064i | ||||
\(982\) | −45.4704 | − | 26.2524i | −1.45102 | − | 0.837747i | ||||
\(983\) | − | 12.9866i | − | 0.414208i | −0.978319 | − | 0.207104i | \(-0.933596\pi\) | ||
0.978319 | − | 0.207104i | \(-0.0664039\pi\) | |||||||
\(984\) | 1.44609 | − | 2.50470i | 0.0460997 | − | 0.0798471i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.00000 | + | 12.1244i | 0.222925 | + | 0.386118i | ||||
\(987\) | − | 13.6091i | − | 0.433181i | ||||||
\(988\) | 55.9655 | − | 13.0652i | 1.78050 | − | 0.415658i | ||||
\(989\) | −14.2315 | −0.452535 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.3736 | + | 19.6996i | 0.361294 | + | 0.625779i | 0.988174 | − | 0.153336i | \(-0.0490018\pi\) |
−0.626880 | + | 0.779116i | \(0.715668\pi\) | |||||||
\(992\) | −47.8728 | − | 27.6394i | −1.51996 | − | 0.877550i | ||||
\(993\) | − | 23.8495i | − | 0.756842i | ||||||
\(994\) | −13.7119 | + | 23.7496i | −0.434914 | + | 0.753293i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 25.6473 | 0.812665 | ||||||||
\(997\) | 11.9910 | + | 6.92301i | 0.379759 | + | 0.219254i | 0.677713 | − | 0.735326i | \(-0.262971\pi\) |
−0.297955 | + | 0.954580i | \(0.596304\pi\) | |||||||
\(998\) | 56.8815 | − | 32.8405i | 1.80055 | − | 1.03955i | ||||
\(999\) | 0.115749 | + | 0.200484i | 0.00366215 | + | 0.00634303i |
(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 | 975.2.bb.k.874.2 | 12 | ||
5.2 | odd | 4 | 975.2.i.l.601.1 | 6 | |||
5.3 | odd | 4 | 195.2.i.d.16.3 | ✓ | 6 | ||
5.4 | even | 2 | inner | 975.2.bb.k.874.5 | 12 | ||
13.9 | even | 3 | inner | 975.2.bb.k.724.5 | 12 | ||
15.8 | even | 4 | 585.2.j.f.406.1 | 6 | |||
65.3 | odd | 12 | 2535.2.a.bb.1.1 | 3 | |||
65.9 | even | 6 | inner | 975.2.bb.k.724.2 | 12 | ||
65.22 | odd | 12 | 975.2.i.l.451.1 | 6 | |||
65.23 | odd | 12 | 2535.2.a.ba.1.3 | 3 | |||
65.48 | odd | 12 | 195.2.i.d.61.3 | yes | 6 | ||
195.23 | even | 12 | 7605.2.a.bw.1.1 | 3 | |||
195.68 | even | 12 | 7605.2.a.bv.1.3 | 3 | |||
195.113 | even | 12 | 585.2.j.f.451.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.i.d.16.3 | ✓ | 6 | 5.3 | odd | 4 | ||
195.2.i.d.61.3 | yes | 6 | 65.48 | odd | 12 | ||
585.2.j.f.406.1 | 6 | 15.8 | even | 4 | |||
585.2.j.f.451.1 | 6 | 195.113 | even | 12 | |||
975.2.i.l.451.1 | 6 | 65.22 | odd | 12 | |||
975.2.i.l.601.1 | 6 | 5.2 | odd | 4 | |||
975.2.bb.k.724.2 | 12 | 65.9 | even | 6 | inner | ||
975.2.bb.k.724.5 | 12 | 13.9 | even | 3 | inner | ||
975.2.bb.k.874.2 | 12 | 1.1 | even | 1 | trivial | ||
975.2.bb.k.874.5 | 12 | 5.4 | even | 2 | inner | ||
2535.2.a.ba.1.3 | 3 | 65.23 | odd | 12 | |||
2535.2.a.bb.1.1 | 3 | 65.3 | odd | 12 | |||
7605.2.a.bv.1.3 | 3 | 195.68 | even | 12 | |||
7605.2.a.bw.1.1 | 3 | 195.23 | even | 12 |