Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,2,Mod(107,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.l (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: | \(5.17430605098\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 16.0.534694406811304329216.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 539.3 | ||
Root | \(-0.841995 - 1.13624i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.539 |
Dual form | 648.2.l.f.107.3 |
$q$-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 \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(487\) | \(569\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.841995 | + | 1.13624i | −0.595380 | + | 0.803444i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.582088 | − | 1.91342i | −0.291044 | − | 0.956710i | ||||
\(5\) | −1.53819 | + | 2.66422i | −0.687899 | + | 1.19148i | 0.284617 | + | 0.958641i | \(0.408133\pi\) |
−0.972516 | + | 0.232835i | \(0.925200\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.45632 | − | 1.99551i | 1.30637 | − | 0.754231i | 0.324879 | − | 0.945756i | \(-0.394677\pi\) |
0.981488 | + | 0.191525i | \(0.0613432\pi\) | |||||||
\(8\) | 2.66422 | + | 0.949697i | 0.941945 | + | 0.335768i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.73205 | − | 3.99102i | −0.547723 | − | 1.26207i | ||||
\(11\) | 1.64492 | − | 0.949697i | 0.495963 | − | 0.286344i | −0.231082 | − | 0.972934i | \(-0.574227\pi\) |
0.727045 | + | 0.686590i | \(0.240893\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.926118 | − | 0.534695i | −0.256859 | − | 0.148298i | 0.366042 | − | 0.930598i | \(-0.380713\pi\) |
−0.622901 | + | 0.782301i | \(0.714046\pi\) | |||||||
\(14\) | −0.642827 | + | 5.60742i | −0.171803 | + | 1.49865i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.32235 | + | 2.22756i | −0.830587 | + | 0.556890i | ||||
\(17\) | − | 7.08863i | − | 1.71925i | −0.510929 | − | 0.859623i | \(-0.670698\pi\) | ||
0.510929 | − | 0.859623i | \(-0.329302\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.73205 | 0.856191 | 0.428096 | − | 0.903733i | \(-0.359185\pi\) | ||||
0.428096 | + | 0.903733i | \(0.359185\pi\) | |||||||
\(20\) | 5.99313 | + | 1.39239i | 1.34011 | + | 0.311347i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.305932 | + | 2.66867i | −0.0652250 | + | 0.568962i | ||||
\(23\) | 0.412157 | − | 0.713876i | 0.0859406 | − | 0.148853i | −0.819851 | − | 0.572577i | \(-0.805944\pi\) |
0.905792 | + | 0.423723i | \(0.139277\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.23205 | − | 3.86603i | −0.446410 | − | 0.773205i | ||||
\(26\) | 1.38733 | − | 0.602084i | 0.272078 | − | 0.118078i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.83013 | − | 5.45183i | −1.10179 | − | 1.03030i | ||||
\(29\) | 2.25207 | + | 3.90069i | 0.418198 | + | 0.724340i | 0.995758 | − | 0.0920079i | \(-0.0293285\pi\) |
−0.577560 | + | 0.816348i | \(0.695995\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.06040 | + | 2.92163i | 0.908876 | + | 0.524740i | 0.880069 | − | 0.474845i | \(-0.157496\pi\) |
0.0288063 | + | 0.999585i | \(0.490829\pi\) | |||||||
\(32\) | 0.266355 | − | 5.65058i | 0.0470854 | − | 0.998891i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.05440 | + | 5.96859i | 1.38132 | + | 1.02361i | ||||
\(35\) | 12.2779i | 2.07534i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.91264i | 1.13643i | 0.822880 | + | 0.568216i | \(0.192366\pi\) | ||||
−0.822880 | + | 0.568216i | \(0.807634\pi\) | |||||||
\(38\) | −3.14237 | + | 4.24051i | −0.509759 | + | 0.687902i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.62828 | + | 5.63726i | −1.04802 | + | 0.891330i | ||||
\(41\) | 3.28985 | + | 1.89939i | 0.513788 | + | 0.296635i | 0.734389 | − | 0.678729i | \(-0.237469\pi\) |
−0.220602 | + | 0.975364i | \(0.570802\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | − | 1.73205i | −0.152499 | − | 0.264135i | 0.779647 | − | 0.626219i | \(-0.215399\pi\) |
−0.932145 | + | 0.362084i | \(0.882065\pi\) | |||||||
\(44\) | −2.77466 | − | 2.59462i | −0.418296 | − | 0.391154i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.464102 | + | 1.06939i | 0.0684280 | + | 0.157673i | ||||
\(47\) | 3.48853 | + | 6.04232i | 0.508855 | + | 0.881363i | 0.999947 | + | 0.0102553i | \(0.00326442\pi\) |
−0.491092 | + | 0.871108i | \(0.663402\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.46410 | − | 7.73205i | 0.637729 | − | 1.10458i | ||||
\(50\) | 6.27211 | + | 0.719026i | 0.887011 | + | 0.101686i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.484012 | + | 2.08329i | −0.0671204 | + | 0.288901i | ||||
\(53\) | 10.6569 | 1.46384 | 0.731918 | − | 0.681393i | \(-0.238625\pi\) | ||||
0.731918 | + | 0.681393i | \(0.238625\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.84325i | 0.787904i | ||||||||
\(56\) | 11.1035 | − | 2.03402i | 1.48377 | − | 0.271807i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.32835 | − | 0.725474i | −0.830954 | − | 0.0952593i | ||||
\(59\) | −1.64492 | − | 0.949697i | −0.214151 | − | 0.123640i | 0.389088 | − | 0.921201i | \(-0.372790\pi\) |
−0.603239 | + | 0.797561i | \(0.706123\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.926118 | + | 0.534695i | −0.118577 | + | 0.0684606i | −0.558116 | − | 0.829763i | \(-0.688475\pi\) |
0.439538 | + | 0.898224i | \(0.355142\pi\) | |||||||
\(62\) | −7.58051 | + | 3.28985i | −0.962725 | + | 0.417811i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.19615 | + | 5.06040i | 0.774519 | + | 0.632551i | ||||
\(65\) | 2.84909 | − | 1.64492i | 0.353386 | − | 0.204028i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.59808 | − | 7.96410i | 0.561744 | − | 0.972970i | −0.435600 | − | 0.900140i | \(-0.643464\pi\) |
0.997344 | − | 0.0728295i | \(-0.0232029\pi\) | |||||||
\(68\) | −13.5635 | + | 4.12621i | −1.64482 | + | 0.500377i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −13.9506 | − | 10.3379i | −1.66742 | − | 1.23562i | ||||
\(71\) | −10.6569 | −1.26474 | −0.632370 | − | 0.774667i | \(-0.717918\pi\) | ||||
−0.632370 | + | 0.774667i | \(0.717918\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.92820 | 0.693844 | 0.346922 | − | 0.937894i | \(-0.387227\pi\) | ||||
0.346922 | + | 0.937894i | \(0.387227\pi\) | |||||||
\(74\) | −7.85443 | − | 5.82041i | −0.913059 | − | 0.676609i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.17238 | − | 7.14098i | −0.249190 | − | 0.819126i | ||||
\(77\) | 3.79025 | − | 6.56491i | 0.431940 | − | 0.748141i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.30856 | + | 3.06490i | −0.597259 | + | 0.344828i | −0.767963 | − | 0.640495i | \(-0.778729\pi\) |
0.170703 | + | 0.985322i | \(0.445396\pi\) | |||||||
\(80\) | −0.824313 | − | 12.2779i | −0.0921610 | − | 1.37271i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.92820 | + | 2.13878i | −0.544229 | + | 0.236189i | ||||
\(83\) | −8.98803 | + | 5.18924i | −0.986564 | + | 0.569593i | −0.904245 | − | 0.427013i | \(-0.859566\pi\) |
−0.0823186 | + | 0.996606i | \(0.526232\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.8857 | + | 10.9037i | 2.04844 | + | 1.18267i | ||||
\(86\) | 2.81002 | + | 0.322137i | 0.303013 | + | 0.0347369i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.28436 | − | 0.968024i | 0.563315 | − | 0.103192i | ||||
\(89\) | − | 13.6683i | − | 1.44884i | −0.689359 | − | 0.724420i | \(-0.742108\pi\) | ||
0.689359 | − | 0.724420i | \(-0.257892\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.26795 | −0.447403 | ||||||||
\(92\) | −1.60586 | − | 0.373089i | −0.167422 | − | 0.0388972i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.80286 | − | 1.12379i | −1.01109 | − | 0.115910i | ||||
\(95\) | −5.74060 | + | 9.94301i | −0.588973 | + | 1.02013i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.69615 | + | 9.86603i | 0.578357 | + | 1.00174i | 0.995668 | + | 0.0929795i | \(0.0296391\pi\) |
−0.417311 | + | 0.908764i | \(0.637028\pi\) | |||||||
\(98\) | 5.02672 | + | 11.5826i | 0.507776 | + | 1.17002i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.09808 | + | 6.52122i | −0.609808 | + | 0.652122i | ||||
\(101\) | −3.07638 | − | 5.32844i | −0.306111 | − | 0.530200i | 0.671397 | − | 0.741098i | \(-0.265695\pi\) |
−0.977508 | + | 0.210898i | \(0.932361\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.45632 | + | 1.99551i | 0.340561 | + | 0.196623i | 0.660520 | − | 0.750808i | \(-0.270336\pi\) |
−0.319959 | + | 0.947431i | \(0.603669\pi\) | |||||||
\(104\) | −1.95959 | − | 2.30408i | −0.192153 | − | 0.225933i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.97305 | + | 12.1088i | −0.871539 | + | 1.17611i | ||||
\(107\) | 8.47908i | 0.819704i | 0.912152 | + | 0.409852i | \(0.134420\pi\) | ||||
−0.912152 | + | 0.409852i | \(0.865580\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.1208i | − | 0.969398i | −0.874681 | − | 0.484699i | \(-0.838929\pi\) | ||
0.874681 | − | 0.484699i | \(-0.161071\pi\) | |||||||
\(110\) | −6.63934 | − | 4.91999i | −0.633037 | − | 0.469103i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.03798 | + | 14.3289i | −0.665027 | + | 1.35396i | ||||
\(113\) | −9.42878 | − | 5.44371i | −0.886985 | − | 0.512101i | −0.0140300 | − | 0.999902i | \(-0.504466\pi\) |
−0.872955 | + | 0.487800i | \(0.837799\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.26795 | + | 2.19615i | 0.118237 | + | 0.204792i | ||||
\(116\) | 6.15276 | − | 6.57969i | 0.571269 | − | 0.610909i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.46410 | − | 1.06939i | 0.226839 | − | 0.0984453i | ||||
\(119\) | −14.1454 | − | 24.5006i | −1.29671 | − | 2.24597i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.69615 | + | 6.40192i | −0.336014 | + | 0.581993i | ||||
\(122\) | 0.172245 | − | 1.50250i | 0.0155943 | − | 0.136030i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.64469 | − | 11.3833i | 0.237500 | − | 1.02225i | ||||
\(125\) | −1.64863 | −0.147458 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | −10.9670 | + | 2.77949i | −0.969352 | + | 0.245674i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.529891 | + | 4.62227i | −0.0464745 | + | 0.405400i | ||||
\(131\) | 8.98803 | + | 5.18924i | 0.785287 | + | 0.453386i | 0.838301 | − | 0.545208i | \(-0.183549\pi\) |
−0.0530134 | + | 0.998594i | \(0.516883\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.8992 | − | 7.44734i | 1.11850 | − | 0.645766i | ||||
\(134\) | 5.17758 | + | 11.9303i | 0.447275 | + | 1.03062i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.73205 | − | 18.8857i | 0.577269 | − | 1.61943i | ||||
\(137\) | 15.1270 | − | 8.73356i | 1.29238 | − | 0.746158i | 0.313307 | − | 0.949652i | \(-0.398563\pi\) |
0.979076 | + | 0.203494i | \(0.0652297\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.59808 | − | 2.76795i | 0.135547 | − | 0.234774i | −0.790259 | − | 0.612773i | \(-0.790054\pi\) |
0.925806 | + | 0.377998i | \(0.123387\pi\) | |||||||
\(140\) | 23.4927 | − | 7.14681i | 1.98550 | − | 0.604015i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.97305 | − | 12.1088i | 0.753001 | − | 1.01615i | ||||
\(143\) | −2.03119 | −0.169857 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.8564 | −1.15071 | ||||||||
\(146\) | −4.99152 | + | 6.73587i | −0.413101 | + | 0.557465i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 13.2268 | − | 4.02377i | 1.08723 | − | 0.330752i | ||||
\(149\) | 3.07638 | − | 5.32844i | 0.252027 | − | 0.436523i | −0.712057 | − | 0.702122i | \(-0.752236\pi\) |
0.964084 | + | 0.265599i | \(0.0855696\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.51673 | + | 4.91713i | −0.693081 | + | 0.400151i | −0.804765 | − | 0.593593i | \(-0.797709\pi\) |
0.111684 | + | 0.993744i | \(0.464376\pi\) | |||||||
\(152\) | 9.94301 | + | 3.54432i | 0.806485 | + | 0.287482i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.26795 | + | 9.83427i | 0.343921 | + | 0.792468i | ||||
\(155\) | −15.5677 | + | 8.98803i | −1.25043 | + | 0.721936i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.8857 | − | 10.9037i | −1.50724 | − | 0.870207i | −0.999965 | − | 0.00842371i | \(-0.997319\pi\) |
−0.507277 | − | 0.861783i | \(-0.669348\pi\) | |||||||
\(158\) | 0.987317 | − | 8.61243i | 0.0785467 | − | 0.685168i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 14.6447 | + | 9.40129i | 1.15776 | + | 0.743237i | ||||
\(161\) | − | 3.28985i | − | 0.259276i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.80385 | 0.689571 | 0.344785 | − | 0.938682i | \(-0.387952\pi\) | ||||
0.344785 | + | 0.938682i | \(0.387952\pi\) | |||||||
\(164\) | 1.71935 | − | 7.40047i | 0.134259 | − | 0.577880i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.67165 | − | 14.5819i | 0.129745 | − | 1.13177i | ||||
\(167\) | 11.0690 | − | 19.1721i | 0.856548 | − | 1.48359i | −0.0186530 | − | 0.999826i | \(-0.505938\pi\) |
0.875201 | − | 0.483759i | \(-0.160729\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.92820 | − | 10.2679i | −0.456016 | − | 0.789842i | ||||
\(170\) | −28.2908 | + | 12.2779i | −2.16981 | + | 0.941670i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.73205 | + | 2.92163i | −0.208317 | + | 0.222772i | ||||
\(173\) | 0.824313 | + | 1.42775i | 0.0626714 | + | 0.108550i | 0.895659 | − | 0.444742i | \(-0.146705\pi\) |
−0.832987 | + | 0.553292i | \(0.813371\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.4294 | − | 8.90815i | −1.16635 | − | 0.673393i | ||||
\(176\) | −3.34950 | + | 6.81938i | −0.252478 | + | 0.514030i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 15.5305 | + | 11.5087i | 1.16406 | + | 0.862611i | ||||
\(179\) | − | 3.79879i | − | 0.283935i | −0.989871 | − | 0.141967i | \(-0.954657\pi\) | ||
0.989871 | − | 0.141967i | \(-0.0453428\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.20817i | 0.238461i | 0.992867 | + | 0.119231i | \(0.0380428\pi\) | ||||
−0.992867 | + | 0.119231i | \(0.961957\pi\) | |||||||
\(182\) | 3.59359 | − | 4.84942i | 0.266375 | − | 0.359463i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.77604 | − | 1.51050i | 0.130932 | − | 0.111356i | ||||
\(185\) | −18.4168 | − | 10.6329i | −1.35403 | − | 0.781750i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.73205 | − | 11.6603i | −0.492296 | − | 0.852682i | ||||
\(188\) | 9.53085 | − | 10.1922i | 0.695109 | − | 0.743342i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.46410 | − | 14.8947i | −0.468955 | − | 1.08057i | ||||
\(191\) | 3.48853 | + | 6.04232i | 0.252421 | + | 0.437207i | 0.964192 | − | 0.265205i | \(-0.0854397\pi\) |
−0.711770 | + | 0.702412i | \(0.752106\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.69615 | − | 4.66987i | 0.194073 | − | 0.336145i | −0.752523 | − | 0.658566i | \(-0.771163\pi\) |
0.946596 | + | 0.322421i | \(0.104497\pi\) | |||||||
\(194\) | −16.0063 | − | 1.83494i | −1.14919 | − | 0.131741i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −17.3932 | − | 4.04096i | −1.24237 | − | 0.288640i | ||||
\(197\) | −17.0305 | −1.21337 | −0.606687 | − | 0.794941i | \(-0.707502\pi\) | ||||
−0.606687 | + | 0.794941i | \(0.707502\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 15.6775i | − | 1.11135i | −0.831400 | − | 0.555675i | \(-0.812460\pi\) | ||
0.831400 | − | 0.555675i | \(-0.187540\pi\) | |||||||
\(200\) | −2.27513 | − | 12.4197i | −0.160876 | − | 0.878207i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.64469 | + | 0.991015i | 0.608238 | + | 0.0697276i | ||||
\(203\) | 15.5677 | + | 8.98803i | 1.09264 | + | 0.630836i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.1208 | + | 5.84325i | −0.706868 | + | 0.408110i | ||||
\(206\) | −5.17758 | + | 2.24701i | −0.360739 | + | 0.156556i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.26795 | − | 0.286542i | 0.295929 | − | 0.0198681i | ||||
\(209\) | 6.13894 | − | 3.54432i | 0.424639 | − | 0.245165i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.5263 | + | 18.2321i | −0.724659 | + | 1.25515i | 0.234455 | + | 0.972127i | \(0.424669\pi\) |
−0.959114 | + | 0.283019i | \(0.908664\pi\) | |||||||
\(212\) | −6.20325 | − | 20.3911i | −0.426041 | − | 1.40047i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.63429 | − | 7.13935i | −0.658586 | − | 0.488036i | ||||
\(215\) | 6.15276 | 0.419614 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.3205 | 1.58310 | ||||||||
\(218\) | 11.4997 | + | 8.52167i | 0.778857 | + | 0.577160i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 11.1806 | − | 3.40129i | 0.753795 | − | 0.229315i | ||||
\(221\) | −3.79025 | + | 6.56491i | −0.254960 | + | 0.441604i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.5902 | − | 13.0424i | 1.51275 | − | 0.873386i | 0.512860 | − | 0.858472i | \(-0.328586\pi\) |
0.999889 | − | 0.0149140i | \(-0.00474744\pi\) | |||||||
\(224\) | −10.3552 | − | 20.0617i | −0.691884 | − | 1.34043i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.1244 | − | 6.12979i | 0.939538 | − | 0.407748i | ||||
\(227\) | −3.28985 | + | 1.89939i | −0.218355 | + | 0.126067i | −0.605188 | − | 0.796082i | \(-0.706902\pi\) |
0.386833 | + | 0.922150i | \(0.373569\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.1208 | − | 5.84325i | −0.668802 | − | 0.386133i | 0.126821 | − | 0.991926i | \(-0.459523\pi\) |
−0.795623 | + | 0.605793i | \(0.792856\pi\) | |||||||
\(230\) | −3.56297 | − | 0.408453i | −0.234935 | − | 0.0269326i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.29553 | + | 12.5311i | 0.150709 | + | 0.822706i | ||||
\(233\) | 14.1773i | 0.928784i | 0.885630 | + | 0.464392i | \(0.153727\pi\) | ||||
−0.885630 | + | 0.464392i | \(0.846273\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.4641 | −1.40016 | ||||||||
\(236\) | −0.859677 | + | 3.70023i | −0.0559602 | + | 0.240865i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 39.7490 | + | 4.55676i | 2.57654 | + | 0.295371i | ||||
\(239\) | −6.15276 | + | 10.6569i | −0.397989 | + | 0.689337i | −0.993478 | − | 0.114027i | \(-0.963625\pi\) |
0.595489 | + | 0.803363i | \(0.296958\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.69615 | + | 4.66987i | 0.173674 | + | 0.300813i | 0.939702 | − | 0.341995i | \(-0.111103\pi\) |
−0.766027 | + | 0.642808i | \(0.777769\pi\) | |||||||
\(242\) | −4.16199 | − | 9.59011i | −0.267543 | − | 0.616476i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.56218 | + | 1.46081i | 0.100008 | + | 0.0935190i | ||||
\(245\) | 13.7333 | + | 23.7867i | 0.877386 | + | 1.51968i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.45632 | − | 1.99551i | −0.219920 | − | 0.126971i | ||||
\(248\) | 10.7074 | + | 12.5897i | 0.679919 | + | 0.799447i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.38814 | − | 1.87324i | 0.0877934 | − | 0.118474i | ||||
\(251\) | 14.1773i | 0.894861i | 0.894319 | + | 0.447431i | \(0.147661\pi\) | ||||
−0.894319 | + | 0.447431i | \(0.852339\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1.56569i | − | 0.0984344i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.07597 | − | 14.8014i | 0.379748 | − | 0.925090i | ||||
\(257\) | 3.28985 | + | 1.89939i | 0.205215 | + | 0.118481i | 0.599086 | − | 0.800685i | \(-0.295531\pi\) |
−0.393871 | + | 0.919166i | \(0.628864\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.7942 | + | 23.8923i | 0.857132 | + | 1.48460i | ||||
\(260\) | −4.80585 | − | 4.49401i | −0.298046 | − | 0.278707i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.4641 | + | 5.84325i | −0.831815 | + | 0.360997i | ||||
\(263\) | −1.64863 | − | 2.85550i | −0.101659 | − | 0.176078i | 0.810710 | − | 0.585449i | \(-0.199082\pi\) |
−0.912368 | + | 0.409371i | \(0.865748\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.3923 | + | 28.3923i | −1.00697 | + | 1.74413i | ||||
\(266\) | −2.39906 | + | 20.9272i | −0.147096 | + | 1.28313i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −17.9152 | − | 4.16224i | −1.09434 | − | 0.254249i | ||||
\(269\) | 19.8860 | 1.21247 | 0.606236 | − | 0.795285i | \(-0.292679\pi\) | ||||
0.606236 | + | 0.795285i | \(0.292679\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.9730i | 0.727311i | 0.931534 | + | 0.363655i | \(0.118471\pi\) | ||||
−0.931534 | + | 0.363655i | \(0.881529\pi\) | |||||||
\(272\) | 15.7903 | + | 23.5509i | 0.957430 | + | 1.42798i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.81340 | + | 24.5415i | −0.169964 | + | 1.48261i | ||||
\(275\) | −7.34310 | − | 4.23954i | −0.442806 | − | 0.255654i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.8857 | + | 10.9037i | −1.13473 | + | 0.655137i | −0.945120 | − | 0.326722i | \(-0.894056\pi\) |
−0.189611 | + | 0.981859i | \(0.560723\pi\) | |||||||
\(278\) | 1.79949 | + | 4.14640i | 0.107926 | + | 0.248685i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −11.6603 | + | 32.7110i | −0.696833 | + | 1.95485i | ||||
\(281\) | −8.98803 | + | 5.18924i | −0.536181 | + | 0.309564i | −0.743530 | − | 0.668703i | \(-0.766850\pi\) |
0.207349 | + | 0.978267i | \(0.433516\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.9282 | + | 24.1244i | −0.827946 | + | 1.43404i | 0.0717013 | + | 0.997426i | \(0.477157\pi\) |
−0.899647 | + | 0.436618i | \(0.856176\pi\) | |||||||
\(284\) | 6.20325 | + | 20.3911i | 0.368095 | + | 1.20999i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.71025 | − | 2.30792i | 0.101129 | − | 0.136470i | ||||
\(287\) | 15.1610 | 0.894926 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −33.2487 | −1.95581 | ||||||||
\(290\) | 11.6670 | − | 15.7442i | 0.685111 | − | 0.924532i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.45074 | − | 11.3431i | −0.201939 | − | 0.663807i | ||||
\(293\) | 3.79025 | − | 6.56491i | 0.221429 | − | 0.383526i | −0.733813 | − | 0.679351i | \(-0.762261\pi\) |
0.955242 | + | 0.295825i | \(0.0955946\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.06040 | − | 2.92163i | 0.294628 | − | 0.170104i | ||||
\(296\) | −6.56491 | + | 18.4168i | −0.381578 | + | 1.07046i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.46410 | + | 7.98203i | 0.200670 | + | 0.462387i | ||||
\(299\) | −0.763411 | + | 0.440756i | −0.0441492 | + | 0.0254896i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.91264 | − | 3.99102i | −0.398438 | − | 0.230038i | ||||
\(302\) | 1.58399 | − | 13.8173i | 0.0911484 | − | 0.795094i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −12.3992 | + | 8.31336i | −0.711141 | + | 0.476804i | ||||
\(305\) | − | 3.28985i | − | 0.188376i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.9282 | 1.19444 | 0.597218 | − | 0.802079i | \(-0.296273\pi\) | ||||
0.597218 | + | 0.802079i | \(0.296273\pi\) | |||||||
\(308\) | −14.7677 | − | 3.43098i | −0.841467 | − | 0.195499i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.89538 | − | 25.2566i | 0.164446 | − | 1.43448i | ||||
\(311\) | −10.2447 | + | 17.7444i | −0.580925 | + | 1.00619i | 0.414445 | + | 0.910075i | \(0.363976\pi\) |
−0.995370 | + | 0.0961176i | \(0.969357\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.69615 | − | 8.13397i | −0.265442 | − | 0.459759i | 0.702237 | − | 0.711943i | \(-0.252185\pi\) |
−0.967679 | + | 0.252184i | \(0.918851\pi\) | |||||||
\(314\) | 28.2908 | − | 12.2779i | 1.59654 | − | 0.692880i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.95448 | + | 8.37345i | 0.503729 | + | 0.471044i | ||||
\(317\) | −8.40482 | − | 14.5576i | −0.472062 | − | 0.817635i | 0.527427 | − | 0.849600i | \(-0.323157\pi\) |
−0.999489 | + | 0.0319652i | \(0.989823\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.40895 | + | 4.27756i | 0.414821 | + | 0.239497i | ||||
\(320\) | −23.0129 | + | 8.72406i | −1.28646 | + | 0.487690i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.73806 | + | 2.77003i | 0.208314 | + | 0.154368i | ||||
\(323\) | − | 26.4551i | − | 1.47200i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.77386i | 0.264806i | ||||||||
\(326\) | −7.41280 | + | 10.0033i | −0.410557 | + | 0.554031i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.96103 | + | 8.18476i | 0.384359 | + | 0.451928i | ||||
\(329\) | 24.1150 | + | 13.9228i | 1.32950 | + | 0.767589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.937822 | − | 1.62436i | −0.0515474 | − | 0.0892827i | 0.839100 | − | 0.543977i | \(-0.183082\pi\) |
−0.890648 | + | 0.454694i | \(0.849749\pi\) | |||||||
\(332\) | 15.1610 | + | 14.1773i | 0.832069 | + | 0.778079i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.4641 | + | 28.7200i | 0.682005 | + | 1.57149i | ||||
\(335\) | 14.1454 | + | 24.5006i | 0.772847 | + | 1.33861i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.69615 | − | 9.86603i | 0.310289 | − | 0.537437i | −0.668136 | − | 0.744039i | \(-0.732907\pi\) |
0.978425 | + | 0.206603i | \(0.0662408\pi\) | |||||||
\(338\) | 16.6584 | + | 1.90969i | 0.906097 | + | 0.103874i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.87013 | − | 42.4831i | 0.535283 | − | 2.30397i | ||||
\(341\) | 11.0986 | 0.601025 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 7.69549i | − | 0.415517i | ||||||
\(344\) | −1.01930 | − | 5.56426i | −0.0549569 | − | 0.300005i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.31634 | − | 0.265542i | −0.124527 | − | 0.0142756i | ||||
\(347\) | −6.57969 | − | 3.79879i | −0.353216 | − | 0.203930i | 0.312885 | − | 0.949791i | \(-0.398705\pi\) |
−0.666101 | + | 0.745862i | \(0.732038\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.28205 | − | 1.31754i | 0.122155 | − | 0.0705264i | −0.437677 | − | 0.899132i | \(-0.644199\pi\) |
0.559833 | + | 0.828606i | \(0.310865\pi\) | |||||||
\(350\) | 23.1133 | − | 10.0309i | 1.23546 | − | 0.536172i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.92820 | − | 9.54773i | −0.262674 | − | 0.508895i | ||||
\(353\) | 6.57969 | − | 3.79879i | 0.350202 | − | 0.202189i | −0.314572 | − | 0.949233i | \(-0.601861\pi\) |
0.664774 | + | 0.747044i | \(0.268528\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.3923 | − | 28.3923i | 0.870013 | − | 1.50691i | ||||
\(356\) | −26.1532 | + | 7.95617i | −1.38612 | + | 0.421676i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.31634 | + | 3.19856i | 0.228126 | + | 0.169049i | ||||
\(359\) | −23.7867 | −1.25541 | −0.627707 | − | 0.778449i | \(-0.716007\pi\) | ||||
−0.627707 | + | 0.778449i | \(0.716007\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.07180 | −0.266937 | ||||||||
\(362\) | −3.64525 | − | 2.70126i | −0.191590 | − | 0.141975i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.48432 | + | 8.16638i | 0.130214 | + | 0.428034i | ||||
\(365\) | −9.11870 | + | 15.7940i | −0.477294 | + | 0.826698i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.4628 | + | 18.7424i | −1.69455 | + | 0.978346i | −0.743785 | + | 0.668419i | \(0.766971\pi\) |
−0.950760 | + | 0.309927i | \(0.899695\pi\) | |||||||
\(368\) | 0.220874 | + | 3.28985i | 0.0115139 | + | 0.171495i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 27.5885 | − | 11.9730i | 1.43426 | − | 0.622449i | ||||
\(371\) | 36.8336 | − | 21.2659i | 1.91231 | − | 1.10407i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.1073 | − | 9.29957i | −0.834006 | − | 0.481514i | 0.0212163 | − | 0.999775i | \(-0.493246\pi\) |
−0.855222 | + | 0.518261i | \(0.826579\pi\) | |||||||
\(374\) | 18.9172 | + | 2.16864i | 0.978186 | + | 0.112138i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.55586 | + | 19.4111i | 0.183379 | + | 1.00105i | ||||
\(377\) | − | 4.81667i | − | 0.248071i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.2679 | −1.34929 | −0.674647 | − | 0.738141i | \(-0.735704\pi\) | ||||
−0.674647 | + | 0.738141i | \(0.735704\pi\) | |||||||
\(380\) | 22.3667 | + | 5.19646i | 1.14739 | + | 0.266573i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.80286 | − | 1.12379i | −0.501558 | − | 0.0574979i | ||||
\(383\) | −0.824313 | + | 1.42775i | −0.0421204 | + | 0.0729547i | −0.886317 | − | 0.463079i | \(-0.846745\pi\) |
0.844197 | + | 0.536034i | \(0.180078\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.6603 | + | 20.1962i | 0.594262 | + | 1.02929i | ||||
\(386\) | 3.03596 | + | 6.99549i | 0.154526 | + | 0.356061i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 15.5622 | − | 16.6420i | 0.790050 | − | 0.844871i | ||||
\(389\) | −7.69095 | − | 13.3211i | −0.389946 | − | 0.675407i | 0.602496 | − | 0.798122i | \(-0.294173\pi\) |
−0.992442 | + | 0.122715i | \(0.960840\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.06040 | − | 2.92163i | −0.255916 | − | 0.147753i | ||||
\(392\) | 19.2365 | − | 16.3604i | 0.971588 | − | 0.826323i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.3396 | − | 19.3508i | 0.722419 | − | 0.974878i | ||||
\(395\) | − | 18.8576i | − | 0.948827i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 10.1208i | − | 0.507949i | −0.967211 | − | 0.253974i | \(-0.918262\pi\) | ||
0.967211 | − | 0.253974i | \(-0.0817379\pi\) | |||||||
\(398\) | 17.8134 | + | 13.2004i | 0.892907 | + | 0.661676i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.0274 | + | 7.87225i | 0.801372 | + | 0.393613i | ||||
\(401\) | 13.1594 | + | 7.59757i | 0.657148 | + | 0.379405i | 0.791190 | − | 0.611571i | \(-0.209462\pi\) |
−0.134041 | + | 0.990976i | \(0.542795\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.12436 | − | 5.41154i | −0.155635 | − | 0.269568i | ||||
\(404\) | −8.40482 | + | 8.98803i | −0.418155 | + | 0.447171i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −23.3205 | + | 10.1208i | −1.15738 | + | 0.502287i | ||||
\(407\) | 6.56491 | + | 11.3708i | 0.325411 | + | 0.563628i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.30385 | − | 7.45448i | 0.212812 | − | 0.368600i | −0.739782 | − | 0.672847i | \(-0.765071\pi\) |
0.952593 | + | 0.304246i | \(0.0984046\pi\) | |||||||
\(410\) | 1.88233 | − | 16.4197i | 0.0929615 | − | 0.810910i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.80636 | − | 7.77495i | 0.0889929 | − | 0.383044i | ||||
\(413\) | −7.58051 | −0.373012 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 31.9281i | − | 1.56729i | ||||||
\(416\) | −3.26801 | + | 5.09069i | −0.160227 | + | 0.249591i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.14176 | + | 9.95961i | −0.0558451 | + | 0.487140i | ||||
\(419\) | −22.9108 | − | 13.2276i | −1.11927 | − | 0.646209i | −0.178053 | − | 0.984021i | \(-0.556980\pi\) |
−0.941214 | + | 0.337812i | \(0.890313\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.13429 | + | 2.38693i | −0.201493 | + | 0.116332i | −0.597352 | − | 0.801979i | \(-0.703780\pi\) |
0.395859 | + | 0.918311i | \(0.370447\pi\) | |||||||
\(422\) | −11.8529 | − | 27.3117i | −0.576992 | − | 1.32951i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 28.3923 | + | 10.1208i | 1.37885 | + | 0.491510i | ||||
\(425\) | −27.4048 | + | 15.8222i | −1.32933 | + | 0.767489i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.13397 | + | 3.69615i | −0.103270 | + | 0.178869i | ||||
\(428\) | 16.2240 | − | 4.93558i | 0.784219 | − | 0.238570i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.18059 | + | 6.99102i | −0.249830 | + | 0.337137i | ||||
\(431\) | 0.382565 | 0.0184275 | 0.00921375 | − | 0.999958i | \(-0.497067\pi\) | ||||
0.00921375 | + | 0.999958i | \(0.497067\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.53590 | 0.217981 | 0.108991 | − | 0.994043i | \(-0.465238\pi\) | ||||
0.108991 | + | 0.994043i | \(0.465238\pi\) | |||||||
\(434\) | −19.6358 | + | 26.4977i | −0.942546 | + | 1.27193i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −19.3654 | + | 5.89121i | −0.927432 | + | 0.282138i | ||||
\(437\) | 1.53819 | − | 2.66422i | 0.0735816 | − | 0.127447i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.4694 | + | 7.19918i | −0.595130 | + | 0.343598i | −0.767123 | − | 0.641500i | \(-0.778313\pi\) |
0.171994 | + | 0.985098i | \(0.444979\pi\) | |||||||
\(440\) | −5.54932 | + | 15.5677i | −0.264553 | + | 0.742162i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.26795 | − | 9.83427i | −0.203006 | − | 0.467768i | ||||
\(443\) | 23.6742 | − | 13.6683i | 1.12480 | − | 0.649402i | 0.182176 | − | 0.983266i | \(-0.441686\pi\) |
0.942621 | + | 0.333864i | \(0.108353\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 36.4154 | + | 21.0245i | 1.72626 | + | 0.996655i | ||||
\(446\) | −4.20145 | + | 36.6495i | −0.198944 | + | 1.73541i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 31.5140 | + | 5.12591i | 1.48889 | + | 0.242177i | ||||
\(449\) | 24.0468i | 1.13484i | 0.823429 | + | 0.567419i | \(0.192058\pi\) | ||||
−0.823429 | + | 0.567419i | \(0.807942\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.21539 | 0.339759 | ||||||||
\(452\) | −4.92771 | + | 21.2099i | −0.231780 | + | 0.997631i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.611865 | − | 5.33734i | 0.0287162 | − | 0.250494i | ||||
\(455\) | 6.56491 | − | 11.3708i | 0.307768 | − | 0.533070i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.19615 | − | 5.53590i | −0.149510 | − | 0.258958i | 0.781537 | − | 0.623859i | \(-0.214436\pi\) |
−0.931046 | + | 0.364901i | \(0.881103\pi\) | |||||||
\(458\) | 15.1610 | − | 6.57969i | 0.708428 | − | 0.307449i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.46410 | − | 3.70447i | 0.161515 | − | 0.172722i | ||||
\(461\) | 2.96594 | + | 5.13716i | 0.138138 | + | 0.239261i | 0.926792 | − | 0.375576i | \(-0.122555\pi\) |
−0.788654 | + | 0.614837i | \(0.789222\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.10039 | − | 1.21266i | −0.0976134 | − | 0.0563571i | 0.450399 | − | 0.892828i | \(-0.351282\pi\) |
−0.548012 | + | 0.836470i | \(0.684615\pi\) | |||||||
\(464\) | −16.1712 | − | 7.94284i | −0.750727 | − | 0.368737i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.1088 | − | 11.9372i | −0.746225 | − | 0.552980i | ||||
\(467\) | 19.8754i | 0.919726i | 0.887990 | + | 0.459863i | \(0.152101\pi\) | ||||
−0.887990 | + | 0.459863i | \(0.847899\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 36.7020i | − | 1.69474i | ||||||
\(470\) | 18.0727 | − | 24.3884i | 0.833630 | − | 1.12495i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.48052 | − | 4.09238i | −0.160204 | − | 0.188367i | ||||
\(473\) | −3.28985 | − | 1.89939i | −0.151267 | − | 0.0873342i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.33013 | − | 14.4282i | −0.382212 | − | 0.662011i | ||||
\(476\) | −38.6460 | + | 41.3276i | −1.77134 | + | 1.89425i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.92820 | − | 15.9641i | −0.316889 | − | 0.730179i | ||||
\(479\) | −3.07638 | − | 5.32844i | −0.140563 | − | 0.243463i | 0.787146 | − | 0.616767i | \(-0.211558\pi\) |
−0.927709 | + | 0.373304i | \(0.878225\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.69615 | − | 6.40192i | 0.168530 | − | 0.291903i | ||||
\(482\) | −7.57625 | − | 0.868531i | −0.345089 | − | 0.0395605i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.4011 | + | 3.34580i | 0.654593 | + | 0.152082i | ||||
\(485\) | −35.0470 | −1.59140 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.2073i | 1.50477i | 0.658726 | + | 0.752383i | \(0.271096\pi\) | ||||
−0.658726 | + | 0.752383i | \(0.728904\pi\) | |||||||
\(488\) | −2.97518 | + | 0.545014i | −0.134680 | + | 0.0246716i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −38.5908 | − | 4.42399i | −1.74335 | − | 0.199856i | ||||
\(491\) | −28.6090 | − | 16.5174i | −1.29111 | − | 0.745420i | −0.312256 | − | 0.949998i | \(-0.601085\pi\) |
−0.978850 | + | 0.204578i | \(0.934418\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.6506 | − | 15.9641i | 1.24532 | − | 0.718985i | ||||
\(494\) | 5.17758 | − | 2.24701i | 0.232950 | − | 0.101098i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −23.3205 | + | 1.56569i | −1.04712 | + | 0.0703018i | ||||
\(497\) | −36.8336 | + | 21.2659i | −1.65221 | + | 0.953906i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.80385 | − | 4.85641i | 0.125517 | − | 0.217403i | −0.796418 | − | 0.604747i | \(-0.793274\pi\) |
0.921935 | + | 0.387344i | \(0.126608\pi\) | |||||||
\(500\) | 0.959646 | + | 3.15451i | 0.0429167 | + | 0.141074i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16.1088 | − | 11.9372i | −0.718971 | − | 0.532783i | ||||
\(503\) | 29.4977 | 1.31524 | 0.657619 | − | 0.753351i | \(-0.271564\pi\) | ||||
0.657619 | + | 0.753351i | \(0.271564\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.9282 | 0.842294 | ||||||||
\(506\) | 1.77901 | + | 1.31831i | 0.0790865 | + | 0.0586059i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.110437 | + | 0.191282i | −0.00489503 | + | 0.00847845i | −0.868463 | − | 0.495755i | \(-0.834891\pi\) |
0.863568 | + | 0.504233i | \(0.168225\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.4898 | − | 11.8298i | 0.906414 | − | 0.523318i | ||||
\(512\) | 11.7021 | + | 19.3665i | 0.517163 | + | 0.855887i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.92820 | + | 2.13878i | −0.217374 | + | 0.0943375i | ||||
\(515\) | −10.6329 | + | 6.13894i | −0.468544 | + | 0.270514i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.4767 | + | 6.62610i | 0.504746 | + | 0.291416i | ||||
\(518\) | −38.7621 | − | 4.44363i | −1.70311 | − | 0.195242i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.15278 | − | 1.67667i | 0.401376 | − | 0.0735267i | ||||
\(521\) | − | 7.08863i | − | 0.310559i | −0.987871 | − | 0.155279i | \(-0.950372\pi\) | ||
0.987871 | − | 0.155279i | \(-0.0496278\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.5885 | −1.64363 | −0.821814 | − | 0.569756i | \(-0.807038\pi\) | ||||
−0.821814 | + | 0.569756i | \(0.807038\pi\) | |||||||
\(524\) | 4.69736 | − | 20.2185i | 0.205205 | − | 0.883247i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.63268 | + | 0.531084i | 0.201994 | + | 0.0231563i | ||||
\(527\) | 20.7103 | − | 35.8713i | 0.902156 | − | 1.56258i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.1603 | + | 19.3301i | 0.485228 | + | 0.840440i | ||||
\(530\) | −18.4583 | − | 42.5318i | −0.801776 | − | 1.84746i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −21.7583 | − | 20.3465i | −0.943343 | − | 0.882133i | ||||
\(533\) | −2.03119 | − | 3.51813i | −0.0879806 | − | 0.152387i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.5902 | − | 13.0424i | −0.976658 | − | 0.563874i | ||||
\(536\) | 19.8138 | − | 16.8514i | 0.855825 | − | 0.727868i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16.7439 | + | 22.5953i | −0.721882 | + | 0.974153i | ||||
\(539\) | − | 16.9582i | − | 0.730440i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.5632i | 1.48599i | 0.669298 | + | 0.742994i | \(0.266595\pi\) | ||||
−0.669298 | + | 0.742994i | \(0.733405\pi\) | |||||||
\(542\) | −13.6043 | − | 10.0812i | −0.584353 | − | 0.433027i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −40.0549 | − | 1.88809i | −1.71734 | − | 0.0809514i | ||||
\(545\) | 26.9641 | + | 15.5677i | 1.15501 | + | 0.666848i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.7942 | + | 27.3564i | 0.675312 | + | 1.16968i | 0.976377 | + | 0.216072i | \(0.0693245\pi\) |
−0.301065 | + | 0.953604i | \(0.597342\pi\) | |||||||
\(548\) | −25.5162 | − | 23.8605i | −1.09000 | − | 1.01927i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.0000 | − | 4.77386i | 0.469042 | − | 0.203558i | ||||
\(551\) | 8.40482 | + | 14.5576i | 0.358057 | + | 0.620174i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.2321 | + | 21.1865i | −0.520160 | + | 0.900943i | ||||
\(554\) | 3.51247 | − | 30.6395i | 0.149231 | − | 1.30175i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.22647 | − | 1.44660i | −0.264061 | − | 0.0613494i | ||||
\(557\) | −14.9401 | −0.633034 | −0.316517 | − | 0.948587i | \(-0.602513\pi\) | ||||
−0.316517 | + | 0.948587i | \(0.602513\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.13878i | 0.0904607i | ||||||||
\(560\) | −27.3497 | − | 40.7913i | −1.15573 | − | 1.72375i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.67165 | − | 14.5819i | 0.0705141 | − | 0.615099i | ||||
\(563\) | 30.2539 | + | 17.4671i | 1.27505 | + | 0.736151i | 0.975934 | − | 0.218066i | \(-0.0699747\pi\) |
0.299117 | + | 0.954217i | \(0.403308\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 29.0065 | − | 16.7469i | 1.22031 | − | 0.704548i | ||||
\(566\) | −15.6836 | − | 36.1384i | −0.659231 | − | 1.51901i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −28.3923 | − | 10.1208i | −1.19131 | − | 0.424660i | ||||
\(569\) | 5.25742 | − | 3.03538i | 0.220403 | − | 0.127250i | −0.385734 | − | 0.922610i | \(-0.626052\pi\) |
0.606137 | + | 0.795360i | \(0.292718\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.59808 | − | 2.76795i | 0.0668774 | − | 0.115835i | −0.830648 | − | 0.556798i | \(-0.812030\pi\) |
0.897525 | + | 0.440963i | \(0.145363\pi\) | |||||||
\(572\) | 1.18233 | + | 3.88652i | 0.0494358 | + | 0.162504i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.7655 | + | 17.2266i | −0.532822 | + | 0.719023i | ||||
\(575\) | −3.67982 | −0.153459 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.9282 | 0.496578 | 0.248289 | − | 0.968686i | \(-0.420132\pi\) | ||||
0.248289 | + | 0.968686i | \(0.420132\pi\) | |||||||
\(578\) | 27.9953 | − | 37.7786i | 1.16445 | − | 1.57138i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.06565 | + | 26.5131i | 0.334908 | + | 1.10090i | ||||
\(581\) | −20.7103 | + | 35.8713i | −0.859209 | + | 1.48819i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.5298 | − | 10.1208i | 0.726008 | − | 0.419161i | ||||
\(584\) | 15.7940 | + | 5.62999i | 0.653562 | + | 0.232971i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.26795 | + | 9.83427i | 0.176307 | + | 0.406250i | ||||
\(587\) | 28.6090 | − | 16.5174i | 1.18082 | − | 0.681747i | 0.224616 | − | 0.974447i | \(-0.427887\pi\) |
0.956204 | + | 0.292701i | \(0.0945540\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.8857 | + | 10.9037i | 0.778171 | + | 0.449277i | ||||
\(590\) | −0.941164 | + | 8.20984i | −0.0387471 | + | 0.337994i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −15.3983 | − | 22.9662i | −0.632867 | − | 0.943904i | ||||
\(593\) | 38.7330i | 1.59057i | 0.606233 | + | 0.795287i | \(0.292680\pi\) | ||||
−0.606233 | + | 0.795287i | \(0.707320\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 87.0333 | 3.56802 | ||||||||
\(596\) | −11.9863 | − | 2.78478i | −0.490977 | − | 0.114069i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.141984 | − | 1.23853i | 0.00580615 | − | 0.0506474i | ||||
\(599\) | 11.2603 | − | 19.5035i | 0.460084 | − | 0.796890i | −0.538880 | − | 0.842382i | \(-0.681152\pi\) |
0.998965 | + | 0.0454928i | \(0.0144858\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.1962 | − | 26.3205i | −0.619864 | − | 1.07364i | −0.989510 | − | 0.144463i | \(-0.953854\pi\) |
0.369646 | − | 0.929173i | \(-0.379479\pi\) | |||||||
\(602\) | 10.3552 | − | 4.49401i | 0.422045 | − | 0.183162i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.3660 | + | 13.4339i | 0.584545 | + | 0.546616i | ||||
\(605\) | −11.3708 | − | 19.6947i | −0.462287 | − | 0.800705i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.6106 | + | 17.6730i | 1.24245 | + | 0.717326i | 0.969591 | − | 0.244729i | \(-0.0786992\pi\) |
0.272854 | + | 0.962056i | \(0.412032\pi\) | |||||||
\(608\) | 0.994051 | − | 21.0883i | 0.0403141 | − | 0.855242i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.73806 | + | 2.77003i | 0.151350 | + | 0.112155i | ||||
\(611\) | − | 7.46120i | − | 0.301848i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 6.91264i | − | 0.279199i | −0.990208 | − | 0.139599i | \(-0.955418\pi\) | ||
0.990208 | − | 0.139599i | \(-0.0445815\pi\) | |||||||
\(614\) | −17.6214 | + | 23.7795i | −0.711144 | + | 0.959662i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16.3328 | − | 13.8908i | 0.658065 | − | 0.559676i | ||||
\(617\) | −24.9965 | − | 14.4317i | −1.00632 | − | 0.581000i | −0.0962087 | − | 0.995361i | \(-0.530672\pi\) |
−0.910112 | + | 0.414361i | \(0.864005\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.5981 | − | 32.2128i | −0.747520 | − | 1.29474i | −0.949008 | − | 0.315251i | \(-0.897911\pi\) |
0.201488 | − | 0.979491i | \(-0.435422\pi\) | |||||||
\(620\) | 26.2597 | + | 24.5557i | 1.05461 | + | 0.986182i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.5359 | − | 26.5812i | −0.462547 | − | 1.06581i | ||||
\(623\) | −27.2752 | − | 47.2421i | −1.09276 | − | 1.89272i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.6962 | − | 23.7224i | 0.547846 | − | 0.948897i | ||||
\(626\) | 13.1963 | + | 1.51280i | 0.527430 | + | 0.0604638i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.87013 | + | 42.4831i | −0.393861 | + | 1.69526i | ||||
\(629\) | 49.0012 | 1.95380 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.0939i | 0.879542i | 0.898110 | + | 0.439771i | \(0.144940\pi\) | ||||
−0.898110 | + | 0.439771i | \(0.855060\pi\) | |||||||
\(632\) | −17.0539 | + | 3.12405i | −0.678368 | + | 0.124268i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 23.6177 | + | 2.70750i | 0.937980 | + | 0.107529i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.26857 | + | 4.77386i | −0.327613 | + | 0.189147i | ||||
\(638\) | −11.0986 | + | 4.81667i | −0.439399 | + | 0.190694i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.46410 | − | 33.4938i | 0.374101 | − | 1.32396i | ||||
\(641\) | −30.2539 | + | 17.4671i | −1.19496 | + | 0.689909i | −0.959427 | − | 0.281957i | \(-0.909016\pi\) |
−0.235531 | + | 0.971867i | \(0.575683\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.39230 | − | 16.2679i | 0.370396 | − | 0.641545i | −0.619230 | − | 0.785210i | \(-0.712555\pi\) |
0.989626 | + | 0.143664i | \(0.0458885\pi\) | |||||||
\(644\) | −6.29485 | + | 1.91498i | −0.248052 | + | 0.0754608i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 30.0594 | + | 22.2751i | 1.18267 | + | 0.876402i | ||||
\(647\) | 39.7720 | 1.56360 | 0.781800 | − | 0.623529i | \(-0.214302\pi\) | ||||
0.781800 | + | 0.623529i | \(0.214302\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.60770 | −0.141614 | ||||||||
\(650\) | −5.42426 | − | 4.01957i | −0.212757 | − | 0.157660i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.12462 | − | 16.8455i | −0.200696 | − | 0.659719i | ||||
\(653\) | 16.2062 | − | 28.0700i | 0.634198 | − | 1.09846i | −0.352487 | − | 0.935817i | \(-0.614664\pi\) |
0.986685 | − | 0.162646i | \(-0.0520028\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.6506 | + | 15.9641i | −1.08040 | + | 0.623767i | ||||
\(656\) | −15.1610 | + | 1.01788i | −0.591938 | + | 0.0397416i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −36.1244 | + | 15.6775i | −1.40827 | + | 0.611173i | ||||
\(659\) | −18.8576 | + | 10.8874i | −0.734586 | + | 0.424114i | −0.820098 | − | 0.572224i | \(-0.806081\pi\) |
0.0855113 | + | 0.996337i | \(0.472748\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.1938 | − | 22.6285i | −1.52446 | − | 0.880149i | −0.999580 | − | 0.0289735i | \(-0.990776\pi\) |
−0.524882 | − | 0.851175i | \(-0.675891\pi\) | |||||||
\(662\) | 2.63530 | + | 0.302107i | 0.102424 | + | 0.0117417i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −28.8743 | + | 5.28938i | −1.12054 | + | 0.205268i | ||||
\(665\) | 45.8216i | 1.77689i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.71281 | 0.143761 | ||||||||
\(668\) | −43.1275 | − | 10.0198i | −1.66865 | − | 0.387679i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −39.7490 | − | 4.55676i | −1.53564 | − | 0.176043i | ||||
\(671\) | −1.01560 | + | 1.75906i | −0.0392066 | + | 0.0679079i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.6244 | − | 30.5263i | −0.679369 | − | 1.17670i | −0.975171 | − | 0.221452i | \(-0.928920\pi\) |
0.295802 | − | 0.955249i | \(-0.404413\pi\) | |||||||
\(674\) | 6.41405 | + | 14.7793i | 0.247060 | + | 0.569279i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16.1962 | + | 17.3200i | −0.622929 | + | 0.666154i | ||||
\(677\) | −22.2485 | − | 38.5356i | −0.855080 | − | 1.48104i | −0.876571 | − | 0.481273i | \(-0.840174\pi\) |
0.0214905 | − | 0.999769i | \(-0.493159\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 39.3755 | + | 22.7334i | 1.51109 | + | 0.872429i | ||||
\(680\) | 39.9605 | + | 46.9854i | 1.53241 | + | 1.80181i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.34500 | + | 12.6107i | −0.357838 | + | 0.482890i | ||||
\(683\) | − | 39.7509i | − | 1.52103i | −0.649323 | − | 0.760513i | \(-0.724948\pi\) | ||
0.649323 | − | 0.760513i | \(-0.275052\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 53.7354i | 2.05313i | ||||||||
\(686\) | 8.74393 | + | 6.47956i | 0.333845 | + | 0.247391i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.18059 | + | 3.52691i | 0.273757 | + | 0.134462i | ||||
\(689\) | −9.86954 | − | 5.69818i | −0.375999 | − | 0.217083i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.92820 | − | 3.33975i | −0.0733523 | − | 0.127050i | 0.827016 | − | 0.562178i | \(-0.190036\pi\) |
−0.900369 | + | 0.435128i | \(0.856703\pi\) | |||||||
\(692\) | 2.25207 | − | 2.40833i | 0.0856107 | − | 0.0915511i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.85641 | − | 4.27756i | 0.374144 | − | 0.162374i | ||||
\(695\) | 4.91629 | + | 8.51526i | 0.186485 | + | 0.323002i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.4641 | − | 23.3205i | 0.509989 | − | 0.883327i | ||||
\(698\) | −0.424429 | + | 3.70232i | −0.0160649 | + | 0.140135i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.06377 | + | 34.7082i | −0.304782 | + | 1.31185i | ||||
\(701\) | −51.8567 | −1.95860 | −0.979300 | − | 0.202415i | \(-0.935121\pi\) | ||||
−0.979300 | + | 0.202415i | \(0.935121\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.7983i | 0.973002i | ||||||||
\(704\) | 14.9980 | + | 2.43951i | 0.565260 | + | 0.0919425i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.22373 | + | 10.6747i | −0.0460557 | + | 0.401747i | ||||
\(707\) | −21.2659 | − | 12.2779i | −0.799786 | − | 0.461757i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.4289 | + | 17.5681i | −1.14278 | + | 0.659786i | −0.947118 | − | 0.320885i | \(-0.896020\pi\) |
−0.195664 | + | 0.980671i | \(0.562686\pi\) | |||||||
\(710\) | 18.4583 | + | 42.5318i | 0.692726 | + | 1.59619i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.9808 | − | 36.4154i | 0.486475 | − | 1.36473i | ||||
\(713\) | 4.17136 | − | 2.40833i | 0.156219 | − | 0.0901928i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.12436 | − | 5.41154i | 0.116844 | − | 0.202380i | ||||
\(716\) | −7.26867 | + | 2.21123i | −0.271643 | + | 0.0826375i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 20.0283 | − | 27.0274i | 0.747449 | − | 1.00866i | ||||
\(719\) | −7.80138 | −0.290942 | −0.145471 | − | 0.989362i | \(-0.546470\pi\) | ||||
−0.145471 | + | 0.989362i | \(0.546470\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.9282 | 0.593197 | ||||||||
\(722\) | 4.27043 | − | 5.76278i | 0.158929 | − | 0.214469i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.13857 | − | 1.86744i | 0.228138 | − | 0.0694028i | ||||
\(725\) | 10.0534 | − | 17.4131i | 0.373376 | − | 0.646706i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.5902 | − | 13.0424i | 0.837823 | − | 0.483717i | −0.0187009 | − | 0.999825i | \(-0.505953\pi\) |
0.856524 | + | 0.516108i | \(0.172620\pi\) | |||||||
\(728\) | −11.3708 | − | 4.05326i | −0.421428 | − | 0.150224i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.2679 | − | 23.6595i | −0.380034 | − | 0.875679i | ||||
\(731\) | −12.2779 | + | 7.08863i | −0.454113 | + | 0.262183i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.4767 | + | 6.62610i | 0.423903 | + | 0.244741i | 0.696746 | − | 0.717318i | \(-0.254631\pi\) |
−0.272843 | + | 0.962059i | \(0.587964\pi\) | |||||||
\(734\) | 6.03763 | − | 52.6666i | 0.222853 | − | 1.94396i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.92403 | − | 2.51907i | −0.144642 | − | 0.0928541i | ||||
\(737\) | − | 17.4671i | − | 0.643409i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.6410 | −0.759292 | −0.379646 | − | 0.925132i | \(-0.623954\pi\) | ||||
−0.379646 | + | 0.925132i | \(0.623954\pi\) | |||||||
\(740\) | −9.62508 | + | 41.4284i | −0.353825 | + | 1.52294i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.85053 | + | 59.7577i | −0.251491 | + | 2.19377i | ||||
\(743\) | −25.8475 | + | 44.7692i | −0.948253 | + | 1.64242i | −0.199148 | + | 0.979969i | \(0.563818\pi\) |
−0.749104 | + | 0.662452i | \(0.769516\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.46410 | + | 16.3923i | 0.346738 | + | 0.600568i | ||||
\(746\) | 24.1289 | − | 10.4716i | 0.883420 | − | 0.383393i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −18.3923 | + | 19.6685i | −0.672489 | + | 0.719153i | ||||
\(749\) | 16.9201 | + | 29.3064i | 0.618246 | + | 1.07083i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.2816 | − | 9.97754i | −0.630615 | − | 0.364086i | 0.150375 | − | 0.988629i | \(-0.451952\pi\) |
−0.780990 | + | 0.624543i | \(0.785285\pi\) | |||||||
\(752\) | −25.0497 | − | 12.3038i | −0.913470 | − | 0.448672i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.47290 | + | 4.05561i | 0.199311 | + | 0.147697i | ||||
\(755\) | − | 30.2539i | − | 1.10105i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 52.0930i | 1.89335i | 0.322189 | + | 0.946675i | \(0.395581\pi\) | ||||
−0.322189 | + | 0.946675i | \(0.604419\pi\) | |||||||
\(758\) | 22.1175 | − | 29.8467i | 0.803343 | − | 1.08408i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −24.7371 | + | 21.0386i | −0.897308 | + | 0.763149i | ||||
\(761\) | 37.2744 | + | 21.5204i | 1.35119 | + | 0.780113i | 0.988417 | − | 0.151763i | \(-0.0484950\pi\) |
0.362778 | + | 0.931876i | \(0.381828\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.1962 | − | 34.9808i | −0.731150 | − | 1.26639i | ||||
\(764\) | 9.53085 | − | 10.1922i | 0.344814 | − | 0.368741i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.928203 | − | 2.13878i | −0.0335373 | − | 0.0772772i | ||||
\(767\) | 1.01560 | + | 1.75906i | 0.0366710 | + | 0.0635161i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.03590 | + | 3.52628i | −0.0734164 | + | 0.127161i | −0.900397 | − | 0.435070i | \(-0.856724\pi\) |
0.826980 | + | 0.562231i | \(0.190057\pi\) | |||||||
\(770\) | −32.7656 | − | 3.75620i | −1.18079 | − | 0.135364i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.5048 | − | 2.44059i | −0.378077 | − | 0.0878388i | ||||
\(773\) | −44.7179 | −1.60839 | −0.804196 | − | 0.594364i | \(-0.797404\pi\) | ||||
−0.804196 | + | 0.594364i | \(0.797404\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 26.0849i | − | 0.936996i | ||||||
\(776\) | 5.80608 | + | 31.6949i | 0.208426 | + | 1.13778i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 21.6117 | + | 2.47754i | 0.774818 | + | 0.0888241i | ||||
\(779\) | 12.2779 | + | 7.08863i | 0.439900 | + | 0.253977i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.5298 | + | 10.1208i | −0.627264 | + | 0.362151i | ||||
\(782\) | 7.58051 | − | 3.28985i | 0.271078 | − | 0.117645i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.39230 | + | 35.6326i | 0.0854395 | + | 1.27259i | ||||
\(785\) | 58.0995 | − | 33.5438i | 2.07366 | − | 1.19723i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.72243 | + | 6.44744i | −0.132690 | + | 0.229826i | −0.924713 | − | 0.380666i | \(-0.875695\pi\) |
0.792022 | + | 0.610492i | \(0.209028\pi\) | |||||||
\(788\) | 9.91327 | + | 32.5865i | 0.353146 | + | 1.16085i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 21.4267 | + | 15.8780i | 0.762329 | + | 0.564913i | ||||
\(791\) | −43.4519 | −1.54497 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.14359 | 0.0406102 | ||||||||
\(794\) | 11.4997 | + | 8.52167i | 0.408108 | + | 0.302423i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −29.9977 | + | 9.12570i | −1.06324 | + | 0.323452i | ||||
\(797\) | 13.7333 | − | 23.7867i | 0.486457 | − | 0.842569i | −0.513422 | − | 0.858136i | \(-0.671622\pi\) |
0.999879 | + | 0.0155679i | \(0.00495563\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.8318 | − | 24.7289i | 1.51528 | − | 0.874847i | ||||
\(800\) | −22.4398 | + | 11.5826i | −0.793367 | + | 0.409508i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.7128 | + | 8.55511i | −0.696084 | + | 0.302092i | ||||
\(803\) | 9.75144 | − | 5.62999i | 0.344121 | − | 0.198678i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.76488 | + | 5.06040i | 0.308921 | + | 0.178356i | ||||
\(806\) | 8.77951 | + | 1.00647i | 0.309245 | + | 0.0354514i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.13575 | − | 17.1178i | −0.110315 | − | 0.602201i | ||||
\(809\) | 14.1773i | 0.498446i | 0.968446 | + | 0.249223i | \(0.0801752\pi\) | ||||
−0.968446 | + | 0.249223i | \(0.919825\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.0718 | −0.950619 | −0.475310 | − | 0.879819i | \(-0.657664\pi\) | ||||
−0.475310 | + | 0.879819i | \(0.657664\pi\) | |||||||
\(812\) | 8.13607 | − | 35.0194i | 0.285520 | − | 1.22894i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −18.4476 | − | 2.11480i | −0.646586 | − | 0.0741238i | ||||
\(815\) | −13.5420 | + | 23.4554i | −0.474355 | + | 0.821607i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.73205 | − | 6.46410i | −0.130568 | − | 0.226150i | ||||
\(818\) | 4.84627 | + | 11.1668i | 0.169446 | + | 0.390440i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17.0718 | + | 15.9641i | 0.596173 | + | 0.557489i | ||||
\(821\) | 5.43888 | + | 9.42042i | 0.189818 | + | 0.328775i | 0.945190 | − | 0.326522i | \(-0.105877\pi\) |
−0.755371 | + | 0.655297i | \(0.772543\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.9861 | + | 12.1163i | 0.731529 | + | 0.422348i | 0.818981 | − | 0.573820i | \(-0.194539\pi\) |
−0.0874525 | + | 0.996169i | \(0.527873\pi\) | |||||||
\(824\) | 7.31328 | + | 8.59893i | 0.254770 | + | 0.299558i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.38275 | − | 8.61329i | 0.222084 | − | 0.299695i | ||||
\(827\) | − | 40.6324i | − | 1.41293i | −0.707749 | − | 0.706464i | \(-0.750289\pi\) | ||
0.707749 | − | 0.706464i | \(-0.249711\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 34.5632i | − | 1.20043i | −0.799839 | − | 0.600215i | \(-0.795082\pi\) | ||
0.799839 | − | 0.600215i | \(-0.204918\pi\) | |||||||
\(830\) | 36.2781 | + | 26.8833i | 1.25923 | + | 0.933134i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.03260 | − | 7.99958i | −0.105136 | − | 0.277336i | ||||
\(833\) | −54.8097 | − | 31.6444i | −1.89904 | − | 1.09641i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 34.0526 | + | 58.9808i | 1.17844 | + | 2.04111i | ||||
\(836\) | −10.3552 | − | 9.68325i | −0.358141 | − | 0.334902i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 34.3205 | − | 14.8947i | 1.18558 | − | 0.514528i | ||||
\(839\) | 12.5264 | + | 21.6963i | 0.432459 | + | 0.749041i | 0.997084 | − | 0.0763065i | \(-0.0243127\pi\) |
−0.564626 | + | 0.825347i | \(0.690979\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.35641 | − | 7.54552i | 0.150221 | − | 0.260190i | ||||
\(842\) | 0.768919 | − | 6.70733i | 0.0264987 | − | 0.231150i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 41.0128 | + | 9.52852i | 1.41172 | + | 0.327985i | ||||
\(845\) | 36.4748 | 1.25477 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.5028i | 1.01373i | ||||||||
\(848\) | −35.4059 | + | 23.7388i | −1.21584 | + | 0.815195i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.09691 | − | 44.4607i | 0.174823 | − | 1.52499i | ||||
\(851\) | 4.93477 | + | 2.84909i | 0.169162 | + | 0.0976655i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.8992 | + | 7.44734i | −0.441659 | + | 0.254992i | −0.704301 | − | 0.709901i | \(-0.748739\pi\) |
0.262642 | + | 0.964893i | \(0.415406\pi\) | |||||||
\(854\) | −2.40292 | − | 5.53685i | −0.0822264 | − | 0.189467i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.05256 | + | 22.5902i | −0.275231 | + | 0.772116i | ||||
\(857\) | 0.881512 | − | 0.508941i | 0.0301119 | − | 0.0173851i | −0.484869 | − | 0.874587i | \(-0.661133\pi\) |
0.514980 | + | 0.857202i | \(0.327799\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.79423 | + | 10.0359i | −0.197697 | + | 0.342420i | −0.947781 | − | 0.318921i | \(-0.896679\pi\) |
0.750085 | + | 0.661342i | \(0.230013\pi\) | |||||||
\(860\) | −3.58145 | − | 11.7728i | −0.122126 | − | 0.401449i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.322118 | + | 0.434686i | −0.0109714 | + | 0.0148055i | ||||
\(863\) | −15.9853 | −0.544147 | −0.272073 | − | 0.962276i | \(-0.587709\pi\) | ||||
−0.272073 | + | 0.962276i | \(0.587709\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.07180 | −0.172446 | ||||||||
\(866\) | −3.81920 | + | 5.15387i | −0.129782 | + | 0.175136i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −13.5746 | − | 44.6219i | −0.460752 | − | 1.51457i | ||||
\(869\) | −5.82145 | + | 10.0830i | −0.197479 | + | 0.342044i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.51673 | + | 4.91713i | −0.288578 | + | 0.166611i | ||||
\(872\) | 9.61170 | − | 26.9641i | 0.325493 | − | 0.913119i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.73205 | + | 3.99102i | 0.0585875 | + | 0.134998i | ||||
\(875\) | −5.69818 | + | 3.28985i | −0.192634 | + | 0.111217i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.6036 | + | 9.58611i | 0.560665 | + | 0.323700i | 0.753412 | − | 0.657548i | \(-0.228406\pi\) |
−0.192747 | + | 0.981248i | \(0.561740\pi\) | |||||||
\(878\) | 2.31912 | − | 20.2299i | 0.0782666 | − | 0.682725i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −13.0162 | − | 19.4133i | −0.438776 | − | 0.654422i | ||||
\(881\) | 6.07075i | 0.204529i | 0.994757 | + | 0.102264i | \(0.0326088\pi\) | ||||
−0.994757 | + | 0.102264i | \(0.967391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.1244 | 1.48490 | 0.742451 | − | 0.669900i | \(-0.233663\pi\) | ||||
0.742451 | + | 0.669900i | \(0.233663\pi\) | |||||||
\(884\) | 14.7677 | + | 3.43098i | 0.496691 | + | 0.115397i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.40307 | + | 38.4083i | −0.147924 | + | 1.29035i | ||||
\(887\) | −12.9090 | + | 22.3590i | −0.433440 | + | 0.750740i | −0.997167 | − | 0.0752210i | \(-0.976034\pi\) |
0.563727 | + | 0.825961i | \(0.309367\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −54.5505 | + | 23.6742i | −1.82854 | + | 0.793562i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −38.1051 | − | 35.6326i | −1.27585 | − | 1.19307i | ||||
\(893\) | 13.0194 | + | 22.5502i | 0.435677 | + | 0.754615i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.1208 | + | 5.84325i | 0.338301 | + | 0.195318i | ||||
\(896\) | −32.3589 | + | 31.4915i | −1.08103 | + | 1.05206i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −27.3230 | − | 20.2473i | −0.911779 | − | 0.675661i | ||||
\(899\) | 26.3188i | 0.877780i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 75.5427i | − | 2.51669i | ||||||
\(902\) | −6.07532 | + | 8.19842i | −0.202286 | + | 0.272978i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.9505 | − | 23.4577i | −0.663543 | − | 0.780193i | ||||
\(905\) | −8.54727 | − | 4.93477i | −0.284121 | − | 0.164037i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.1865 | + | 40.1603i | 0.769896 | + | 1.33350i | 0.937619 | + | 0.347665i | \(0.113025\pi\) |
−0.167723 | + | 0.985834i | \(0.553641\pi\) | |||||||
\(908\) | 5.54932 | + | 5.18924i | 0.184161 | + | 0.172211i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.39230 | + | 17.0335i | 0.245053 | + | 0.564653i | ||||
\(911\) | −0.220874 | − | 0.382565i | −0.00731788 | − | 0.0126749i | 0.862343 | − | 0.506324i | \(-0.168996\pi\) |
−0.869661 | + | 0.493649i | \(0.835663\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.85641 | + | 17.0718i | −0.326199 | + | 0.564994i | ||||
\(914\) | 8.98126 | + | 1.02960i | 0.297074 | + | 0.0340561i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.28938 | + | 22.7666i | −0.174766 | + | 0.752231i | ||||
\(917\) | 41.4207 | 1.36783 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 58.0130i | − | 1.91367i | −0.290628 | − | 0.956836i | \(-0.593864\pi\) | ||
0.290628 | − | 0.956836i | \(-0.406136\pi\) | |||||||
\(920\) | 1.29242 | + | 7.05520i | 0.0426098 | + | 0.232603i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −8.33436 | − | 0.955439i | −0.274478 | − | 0.0314657i | ||||
\(923\) | 9.86954 | + | 5.69818i | 0.324860 | + | 0.187558i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26.7244 | − | 15.4294i | 0.878694 | − | 0.507314i | ||||
\(926\) | 3.14639 | − | 1.36549i | 0.103397 | − | 0.0448729i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 22.6410 | − | 11.6865i | 0.743228 | − | 0.383628i | ||||
\(929\) | 17.9761 | − | 10.3785i | 0.589775 | − | 0.340507i | −0.175233 | − | 0.984527i | \(-0.556068\pi\) |
0.765009 | + | 0.644020i | \(0.222735\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.6603 | − | 28.8564i | 0.546018 | − | 0.945731i | ||||
\(932\) | 27.1271 | − | 8.25242i | 0.888576 | − | 0.270317i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −22.5833 | − | 16.7350i | −0.738948 | − | 0.547587i | ||||
\(935\) | 41.4207 | 1.35460 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.3923 | −0.764193 | −0.382097 | − | 0.924122i | \(-0.624798\pi\) | ||||
−0.382097 | + | 0.924122i | \(0.624798\pi\) | |||||||
\(938\) | 41.7023 | + | 30.9029i | 1.36163 | + | 1.00902i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12.4940 | + | 41.0698i | 0.407510 | + | 1.33955i | ||||
\(941\) | −9.33957 | + | 16.1766i | −0.304461 | + | 0.527342i | −0.977141 | − | 0.212591i | \(-0.931810\pi\) |
0.672680 | + | 0.739934i | \(0.265143\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.71186 | − | 1.56569i | 0.0883104 | − | 0.0509860i | ||||
\(944\) | 7.58051 | − | 0.508941i | 0.246725 | − | 0.0165646i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.92820 | − | 2.13878i | 0.160230 | − | 0.0695377i | ||||
\(947\) | −25.3192 | + | 14.6180i | −0.822762 | + | 0.475022i | −0.851368 | − | 0.524569i | \(-0.824227\pi\) |
0.0286060 | + | 0.999591i | \(0.490893\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.49022 | − | 3.16978i | −0.178220 | − | 0.102895i | ||||
\(950\) | 23.4078 | + | 2.68344i | 0.759451 | + | 0.0870624i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −14.4184 | − | 78.7088i | −0.467303 | − | 2.55097i | ||||
\(953\) | 15.7041i | 0.508705i | 0.967112 | + | 0.254353i | \(0.0818624\pi\) | ||||
−0.967112 | + | 0.254353i | \(0.918138\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.4641 | −0.694562 | ||||||||
\(956\) | 23.9725 | + | 5.56955i | 0.775327 | + | 0.180132i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.64469 | + | 0.991015i | 0.279297 | + | 0.0320183i | ||||
\(959\) | 34.8558 | − | 60.3719i | 1.12555 | − | 1.94951i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.57180 | + | 2.72243i | 0.0507031 | + | 0.0878204i | ||||
\(962\) | 4.16199 | + | 9.59011i | 0.134188 | + | 0.309198i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.36603 | − | 7.87715i | 0.237244 | − | 0.253706i | ||||
\(965\) | 8.29438 | + | 14.3663i | 0.267006 | + | 0.462467i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.51673 | − | 4.91713i | −0.273879 | − | 0.158124i | 0.356770 | − | 0.934192i | \(-0.383878\pi\) |
−0.630649 | + | 0.776068i | \(0.717211\pi\) | |||||||
\(968\) | −15.9273 | + | 13.5459i | −0.511921 | + | 0.435382i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 29.5094 | − | 39.8219i | 0.947491 | − | 1.27860i | ||||
\(971\) | 55.8275i | 1.79159i | 0.444466 | + | 0.895796i | \(0.353393\pi\) | ||||
−0.444466 | + | 0.895796i | \(0.646607\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 12.7559i | − | 0.408935i | ||||||
\(974\) | −37.7315 | − | 27.9604i | −1.20899 | − | 0.895908i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.88582 | − | 3.83942i | 0.0603637 | − | 0.122897i | ||||
\(977\) | 20.3844 | + | 11.7689i | 0.652154 | + | 0.376521i | 0.789281 | − | 0.614032i | \(-0.210453\pi\) |
−0.137127 | + | 0.990554i | \(0.543787\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.9808 | − | 22.4833i | −0.414867 | − | 0.718571i | ||||
\(980\) | 37.5200 | − | 40.1235i | 1.19853 | − | 1.28170i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 42.8564 | − | 18.5991i | 1.36760 | − | 0.593523i | ||||
\(983\) | 27.6578 | + | 47.9047i | 0.882147 | + | 1.52792i | 0.848949 | + | 0.528475i | \(0.177236\pi\) |
0.0331982 | + | 0.999449i | \(0.489431\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.1962 | − | 45.3731i | 0.834679 | − | 1.44571i | ||||
\(986\) | −5.14262 | + | 44.8594i | −0.163774 | + | 1.42861i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.80636 | + | 7.77495i | −0.0574679 | + | 0.247354i | ||||
\(989\) | −1.64863 | −0.0524233 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 25.7983i | − | 0.819511i | −0.912195 | − | 0.409755i | \(-0.865614\pi\) | ||
0.912195 | − | 0.409755i | \(-0.134386\pi\) | |||||||
\(992\) | 17.8567 | − | 27.8160i | 0.566952 | − | 0.883160i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.85053 | − | 59.7577i | 0.217286 | − | 1.89540i | ||||
\(995\) | 41.7684 | + | 24.1150i | 1.32415 | + | 0.764497i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.35593 | + | 0.782847i | −0.0429428 | + | 0.0247930i | −0.521318 | − | 0.853363i | \(-0.674559\pi\) |
0.478375 | + | 0.878156i | \(0.341226\pi\) | |||||||
\(998\) | 3.15722 | + | 7.27492i | 0.0999402 | + | 0.230284i | ||||
\(999\) | 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 | 648.2.l.f.539.3 | 16 | ||
3.2 | odd | 2 | inner | 648.2.l.f.539.6 | 16 | ||
4.3 | odd | 2 | 2592.2.p.f.2159.1 | 16 | |||
8.3 | odd | 2 | inner | 648.2.l.f.539.1 | 16 | ||
8.5 | even | 2 | 2592.2.p.f.2159.8 | 16 | |||
9.2 | odd | 6 | inner | 648.2.l.f.107.1 | 16 | ||
9.4 | even | 3 | 216.2.f.a.107.3 | ✓ | 8 | ||
9.5 | odd | 6 | 216.2.f.a.107.6 | yes | 8 | ||
9.7 | even | 3 | inner | 648.2.l.f.107.8 | 16 | ||
12.11 | even | 2 | 2592.2.p.f.2159.7 | 16 | |||
24.5 | odd | 2 | 2592.2.p.f.2159.2 | 16 | |||
24.11 | even | 2 | inner | 648.2.l.f.539.8 | 16 | ||
36.7 | odd | 6 | 2592.2.p.f.431.2 | 16 | |||
36.11 | even | 6 | 2592.2.p.f.431.8 | 16 | |||
36.23 | even | 6 | 864.2.f.a.431.1 | 8 | |||
36.31 | odd | 6 | 864.2.f.a.431.7 | 8 | |||
72.5 | odd | 6 | 864.2.f.a.431.8 | 8 | |||
72.11 | even | 6 | inner | 648.2.l.f.107.3 | 16 | ||
72.13 | even | 6 | 864.2.f.a.431.2 | 8 | |||
72.29 | odd | 6 | 2592.2.p.f.431.1 | 16 | |||
72.43 | odd | 6 | inner | 648.2.l.f.107.6 | 16 | ||
72.59 | even | 6 | 216.2.f.a.107.4 | yes | 8 | ||
72.61 | even | 6 | 2592.2.p.f.431.7 | 16 | |||
72.67 | odd | 6 | 216.2.f.a.107.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.f.a.107.3 | ✓ | 8 | 9.4 | even | 3 | ||
216.2.f.a.107.4 | yes | 8 | 72.59 | even | 6 | ||
216.2.f.a.107.5 | yes | 8 | 72.67 | odd | 6 | ||
216.2.f.a.107.6 | yes | 8 | 9.5 | odd | 6 | ||
648.2.l.f.107.1 | 16 | 9.2 | odd | 6 | inner | ||
648.2.l.f.107.3 | 16 | 72.11 | even | 6 | inner | ||
648.2.l.f.107.6 | 16 | 72.43 | odd | 6 | inner | ||
648.2.l.f.107.8 | 16 | 9.7 | even | 3 | inner | ||
648.2.l.f.539.1 | 16 | 8.3 | odd | 2 | inner | ||
648.2.l.f.539.3 | 16 | 1.1 | even | 1 | trivial | ||
648.2.l.f.539.6 | 16 | 3.2 | odd | 2 | inner | ||
648.2.l.f.539.8 | 16 | 24.11 | even | 2 | inner | ||
864.2.f.a.431.1 | 8 | 36.23 | even | 6 | |||
864.2.f.a.431.2 | 8 | 72.13 | even | 6 | |||
864.2.f.a.431.7 | 8 | 36.31 | odd | 6 | |||
864.2.f.a.431.8 | 8 | 72.5 | odd | 6 | |||
2592.2.p.f.431.1 | 16 | 72.29 | odd | 6 | |||
2592.2.p.f.431.2 | 16 | 36.7 | odd | 6 | |||
2592.2.p.f.431.7 | 16 | 72.61 | even | 6 | |||
2592.2.p.f.431.8 | 16 | 36.11 | even | 6 | |||
2592.2.p.f.2159.1 | 16 | 4.3 | odd | 2 | |||
2592.2.p.f.2159.2 | 16 | 24.5 | odd | 2 | |||
2592.2.p.f.2159.7 | 16 | 12.11 | even | 2 | |||
2592.2.p.f.2159.8 | 16 | 8.5 | even | 2 |