Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(37,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(12))
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("432.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.y (of order \(12\), degree \(4\), 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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 37.18 | ||
Character | \(\chi\) | \(=\) | 432.37 |
Dual form | 432.2.y.e.397.18 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.40500 | + | 0.161164i | 0.993485 | + | 0.113960i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.94805 | + | 0.452871i | 0.974026 | + | 0.226435i | ||||
\(5\) | 0.846545 | − | 0.226831i | 0.378587 | − | 0.101442i | −0.0645072 | − | 0.997917i | \(-0.520548\pi\) |
0.443094 | + | 0.896475i | \(0.353881\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.567074 | + | 0.327400i | −0.214334 | + | 0.123746i | −0.603324 | − | 0.797496i | \(-0.706157\pi\) |
0.388990 | + | 0.921242i | \(0.372824\pi\) | |||||||
\(8\) | 2.66403 | + | 0.950239i | 0.941876 | + | 0.335960i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.22595 | − | 0.182265i | 0.387681 | − | 0.0576374i | ||||
\(11\) | 1.54155 | − | 5.75313i | 0.464794 | − | 1.73463i | −0.192778 | − | 0.981242i | \(-0.561750\pi\) |
0.657572 | − | 0.753392i | \(-0.271584\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.19068 | + | 4.44367i | 0.330234 | + | 1.23245i | 0.908944 | + | 0.416918i | \(0.136890\pi\) |
−0.578710 | + | 0.815534i | \(0.696444\pi\) | |||||||
\(14\) | −0.849504 | + | 0.368606i | −0.227039 | + | 0.0985140i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.58982 | + | 1.76443i | 0.897454 | + | 0.441108i | ||||
\(17\) | −2.75816 | −0.668953 | −0.334477 | − | 0.942404i | \(-0.608559\pi\) | ||||
−0.334477 | + | 0.942404i | \(0.608559\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.73499 | + | 1.73499i | −0.398034 | + | 0.398034i | −0.877539 | − | 0.479505i | \(-0.840816\pi\) |
0.479505 | + | 0.877539i | \(0.340816\pi\) | |||||||
\(20\) | 1.75184 | − | 0.0585035i | 0.391723 | − | 0.0130818i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.09307 | − | 7.83471i | 0.659445 | − | 1.67037i | ||||
\(23\) | 3.50762 | + | 2.02512i | 0.731389 | + | 0.422268i | 0.818930 | − | 0.573893i | \(-0.194568\pi\) |
−0.0875410 | + | 0.996161i | \(0.527901\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.66494 | + | 2.11595i | −0.732988 | + | 0.423191i | ||||
\(26\) | 0.956743 | + | 6.43525i | 0.187633 | + | 1.26206i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.25296 | + | 0.380982i | −0.236787 | + | 0.0719988i | ||||
\(29\) | −2.47312 | − | 0.662669i | −0.459246 | − | 0.123055i | 0.0217764 | − | 0.999763i | \(-0.493068\pi\) |
−0.481022 | + | 0.876708i | \(0.659734\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.08801 | − | 3.61654i | 0.375018 | − | 0.649550i | −0.615312 | − | 0.788284i | \(-0.710970\pi\) |
0.990330 | + | 0.138734i | \(0.0443033\pi\) | |||||||
\(32\) | 4.75933 | + | 3.05758i | 0.841339 | + | 0.540508i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.87522 | − | 0.444516i | −0.664595 | − | 0.0762339i | ||||
\(35\) | −0.405789 | + | 0.405789i | −0.0685909 | + | 0.0685909i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.30563 | − | 4.30563i | −0.707841 | − | 0.707841i | 0.258240 | − | 0.966081i | \(-0.416858\pi\) |
−0.966081 | + | 0.258240i | \(0.916858\pi\) | |||||||
\(38\) | −2.71728 | + | 2.15804i | −0.440801 | + | 0.350081i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.47076 | + | 0.200136i | 0.390662 | + | 0.0316443i | ||||
\(41\) | −6.15806 | − | 3.55536i | −0.961728 | − | 0.555254i | −0.0650233 | − | 0.997884i | \(-0.520712\pi\) |
−0.896704 | + | 0.442630i | \(0.854046\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.225483 | − | 0.841515i | 0.0343859 | − | 0.128330i | −0.946599 | − | 0.322412i | \(-0.895506\pi\) |
0.980985 | + | 0.194082i | \(0.0621729\pi\) | |||||||
\(44\) | 5.60844 | − | 10.5093i | 0.845504 | − | 1.58433i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.60183 | + | 3.41060i | 0.678503 | + | 0.502866i | ||||
\(47\) | −4.65521 | − | 8.06305i | −0.679032 | − | 1.17612i | −0.975273 | − | 0.221004i | \(-0.929067\pi\) |
0.296241 | − | 0.955113i | \(-0.404267\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.28562 | + | 5.69086i | −0.469374 | + | 0.812980i | ||||
\(50\) | −5.49026 | + | 2.38226i | −0.776440 | + | 0.336903i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.307095 | + | 9.19572i | 0.0425865 | + | 1.27522i | ||||
\(53\) | 7.64584 | + | 7.64584i | 1.05024 | + | 1.05024i | 0.998669 | + | 0.0515677i | \(0.0164218\pi\) |
0.0515677 | + | 0.998669i | \(0.483578\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.21996i | − | 0.703859i | ||||||
\(56\) | −1.82181 | + | 0.333348i | −0.243449 | + | 0.0445455i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.36793 | − | 1.32963i | −0.442231 | − | 0.174589i | ||||
\(59\) | −6.83351 | + | 1.83103i | −0.889647 | + | 0.238380i | −0.674565 | − | 0.738216i | \(-0.735669\pi\) |
−0.215082 | + | 0.976596i | \(0.569002\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.77755 | − | 1.01219i | −0.483666 | − | 0.129598i | 0.00874306 | − | 0.999962i | \(-0.497217\pi\) |
−0.492409 | + | 0.870364i | \(0.663884\pi\) | |||||||
\(62\) | 3.51651 | − | 4.74473i | 0.446597 | − | 0.602581i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.19409 | + | 5.06293i | 0.774261 | + | 0.632866i | ||||
\(65\) | 2.01592 | + | 3.49168i | 0.250045 | + | 0.433090i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.11705 | + | 11.6330i | 0.380809 | + | 1.42120i | 0.844669 | + | 0.535289i | \(0.179797\pi\) |
−0.463860 | + | 0.885908i | \(0.653536\pi\) | |||||||
\(68\) | −5.37305 | − | 1.24909i | −0.651578 | − | 0.151475i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.635532 | + | 0.504735i | −0.0759606 | + | 0.0603274i | ||||
\(71\) | − | 4.34835i | − | 0.516054i | −0.966138 | − | 0.258027i | \(-0.916928\pi\) | ||
0.966138 | − | 0.258027i | \(-0.0830723\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.656583i | − | 0.0768472i | −0.999262 | − | 0.0384236i | \(-0.987766\pi\) | ||
0.999262 | − | 0.0384236i | \(-0.0122336\pi\) | |||||||
\(74\) | −5.35550 | − | 6.74332i | −0.622564 | − | 0.783896i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.16557 | + | 2.59412i | −0.477824 | + | 0.297566i | ||||
\(77\) | 1.00941 | + | 3.76715i | 0.115032 | + | 0.429307i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.16172 | − | 14.1365i | −0.918266 | − | 1.59048i | −0.802048 | − | 0.597259i | \(-0.796256\pi\) |
−0.116217 | − | 0.993224i | \(-0.537077\pi\) | |||||||
\(80\) | 3.43917 | + | 0.679389i | 0.384511 | + | 0.0759580i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.07908 | − | 5.98774i | −0.892186 | − | 0.661235i | ||||
\(83\) | −5.36845 | − | 1.43847i | −0.589264 | − | 0.157893i | −0.0481470 | − | 0.998840i | \(-0.515332\pi\) |
−0.541117 | + | 0.840948i | \(0.681998\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.33491 | + | 0.625638i | −0.253257 | + | 0.0678599i | ||||
\(86\) | 0.452426 | − | 1.14599i | 0.0487863 | − | 0.123575i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.57357 | − | 13.8617i | 1.02055 | − | 1.47766i | ||||
\(89\) | − | 5.11081i | − | 0.541744i | −0.962615 | − | 0.270872i | \(-0.912688\pi\) | ||
0.962615 | − | 0.270872i | \(-0.0873121\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.13006 | − | 2.13006i | −0.223291 | − | 0.223291i | ||||
\(92\) | 5.91591 | + | 5.53355i | 0.616776 | + | 0.576912i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.24109 | − | 12.0788i | −0.540578 | − | 1.24584i | ||||
\(95\) | −1.07520 | + | 1.86230i | −0.110313 | + | 0.191068i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.05669 | + | 5.29434i | 0.310360 | + | 0.537559i | 0.978440 | − | 0.206530i | \(-0.0662171\pi\) |
−0.668080 | + | 0.744089i | \(0.732884\pi\) | |||||||
\(98\) | −5.53346 | + | 7.46613i | −0.558963 | + | 0.754193i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.09775 | + | 2.46225i | −0.809775 | + | 0.246225i | ||||
\(101\) | −3.30688 | + | 12.3415i | −0.329047 | + | 1.22802i | 0.581133 | + | 0.813809i | \(0.302610\pi\) |
−0.910180 | + | 0.414213i | \(0.864057\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.82866 | + | 1.05577i | 0.180183 | + | 0.104029i | 0.587379 | − | 0.809312i | \(-0.300160\pi\) |
−0.407196 | + | 0.913341i | \(0.633493\pi\) | |||||||
\(104\) | −1.05055 | + | 12.9695i | −0.103015 | + | 1.27176i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.51018 | + | 11.9746i | 0.923710 | + | 1.16308i | ||||
\(107\) | −7.26738 | − | 7.26738i | −0.702564 | − | 0.702564i | 0.262396 | − | 0.964960i | \(-0.415487\pi\) |
−0.964960 | + | 0.262396i | \(0.915487\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.73169 | − | 5.73169i | 0.548996 | − | 0.548996i | −0.377154 | − | 0.926150i | \(-0.623097\pi\) |
0.926150 | + | 0.377154i | \(0.123097\pi\) | |||||||
\(110\) | 0.841268 | − | 7.33404i | 0.0802118 | − | 0.699273i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.61337 | + | 0.174744i | −0.246940 | + | 0.0165118i | ||||
\(113\) | −0.907975 | + | 1.57266i | −0.0854151 | + | 0.147943i | −0.905568 | − | 0.424201i | \(-0.860555\pi\) |
0.820153 | + | 0.572144i | \(0.193888\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.42872 | + | 0.918723i | 0.319730 | + | 0.0856713i | ||||
\(116\) | −4.51766 | − | 2.41092i | −0.419454 | − | 0.223848i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.89618 | + | 1.47129i | −0.911017 | + | 0.135443i | ||||
\(119\) | 1.56408 | − | 0.903023i | 0.143379 | − | 0.0827800i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −21.1959 | − | 12.2374i | −1.92690 | − | 1.11249i | ||||
\(122\) | −5.14433 | − | 2.03094i | −0.465746 | − | 0.183872i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.70538 | − | 6.09961i | 0.512358 | − | 0.547761i | ||||
\(125\) | −5.72115 | + | 5.72115i | −0.511715 | + | 0.511715i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.2026 | 1.70395 | 0.851976 | − | 0.523581i | \(-0.175404\pi\) | ||||
0.851976 | + | 0.523581i | \(0.175404\pi\) | |||||||
\(128\) | 7.88674 | + | 8.11168i | 0.697096 | + | 0.716978i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.26964 | + | 5.23071i | 0.199061 | + | 0.458764i | ||||
\(131\) | 3.12885 | + | 11.6770i | 0.273369 | + | 1.02023i | 0.956927 | + | 0.290330i | \(0.0937650\pi\) |
−0.683558 | + | 0.729896i | \(0.739568\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.415831 | − | 1.55190i | 0.0360571 | − | 0.134567i | ||||
\(134\) | 2.50464 | + | 16.8467i | 0.216368 | + | 1.45534i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.34783 | − | 2.62092i | −0.630071 | − | 0.224742i | ||||
\(137\) | 2.88080 | − | 1.66323i | 0.246123 | − | 0.142099i | −0.371865 | − | 0.928287i | \(-0.621281\pi\) |
0.617988 | + | 0.786188i | \(0.287948\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.4536 | − | 2.80104i | 0.886666 | − | 0.237582i | 0.213385 | − | 0.976968i | \(-0.431551\pi\) |
0.673281 | + | 0.739387i | \(0.264884\pi\) | |||||||
\(140\) | −0.974268 | + | 0.606728i | −0.0823407 | + | 0.0512779i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.700796 | − | 6.10943i | 0.0588095 | − | 0.512692i | ||||
\(143\) | 27.4005 | 2.29134 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.24392 | −0.186347 | ||||||||
\(146\) | 0.105817 | − | 0.922499i | 0.00875751 | − | 0.0763466i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.43770 | − | 10.3375i | −0.529176 | − | 0.849736i | ||||
\(149\) | 19.1223 | − | 5.12380i | 1.56656 | − | 0.419758i | 0.631827 | − | 0.775110i | \(-0.282305\pi\) |
0.934733 | + | 0.355351i | \(0.115639\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.09441 | − | 2.94126i | 0.414577 | − | 0.239356i | −0.278177 | − | 0.960530i | \(-0.589730\pi\) |
0.692754 | + | 0.721174i | \(0.256397\pi\) | |||||||
\(152\) | −6.27071 | + | 2.97340i | −0.508622 | + | 0.241175i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.811086 | + | 5.45553i | 0.0653592 | + | 0.439619i | ||||
\(155\) | 0.947251 | − | 3.53519i | 0.0760851 | − | 0.283953i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.09096 | + | 18.9997i | 0.406303 | + | 1.51634i | 0.801640 | + | 0.597808i | \(0.203961\pi\) |
−0.395336 | + | 0.918536i | \(0.629372\pi\) | |||||||
\(158\) | −9.18893 | − | 21.1772i | −0.731032 | − | 1.68477i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.72254 | + | 1.50881i | 0.373350 | + | 0.119282i | ||||
\(161\) | −2.65210 | −0.209015 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.00716 | − | 5.00716i | 0.392191 | − | 0.392191i | −0.483277 | − | 0.875468i | \(-0.660554\pi\) |
0.875468 | + | 0.483277i | \(0.160554\pi\) | |||||||
\(164\) | −10.3861 | − | 9.71483i | −0.811019 | − | 0.758601i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.31084 | − | 2.88625i | −0.567431 | − | 0.224017i | ||||
\(167\) | −14.5023 | − | 8.37292i | −1.12222 | − | 0.647916i | −0.180255 | − | 0.983620i | \(-0.557692\pi\) |
−0.941967 | + | 0.335704i | \(0.891026\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.07014 | + | 4.08195i | −0.543857 | + | 0.313996i | ||||
\(170\) | −3.38138 | + | 0.502718i | −0.259340 | + | 0.0385567i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.820350 | − | 1.53720i | 0.0625511 | − | 0.117210i | ||||
\(173\) | 16.2848 | + | 4.36351i | 1.23811 | + | 0.331751i | 0.817733 | − | 0.575597i | \(-0.195230\pi\) |
0.420379 | + | 0.907349i | \(0.361897\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.38553 | − | 2.39980i | 0.104736 | − | 0.181408i | ||||
\(176\) | 15.6849 | − | 17.9327i | 1.18229 | − | 1.35173i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.823677 | − | 7.18068i | 0.0617372 | − | 0.538215i | ||||
\(179\) | −6.56566 | + | 6.56566i | −0.490740 | + | 0.490740i | −0.908539 | − | 0.417799i | \(-0.862802\pi\) |
0.417799 | + | 0.908539i | \(0.362802\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.4877 | + | 15.4877i | 1.15119 | + | 1.15119i | 0.986315 | + | 0.164875i | \(0.0527219\pi\) |
0.164875 | + | 0.986315i | \(0.447278\pi\) | |||||||
\(182\) | −2.64945 | − | 3.33602i | −0.196390 | − | 0.247282i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.42004 | + | 8.72807i | 0.547013 | + | 0.643442i | ||||
\(185\) | −4.62156 | − | 2.66826i | −0.339784 | − | 0.196174i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.25184 | + | 15.8681i | −0.310925 | + | 1.16039i | ||||
\(188\) | −5.41707 | − | 17.8155i | −0.395080 | − | 1.29933i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.81079 | + | 2.44324i | −0.131368 | + | 0.177252i | ||||
\(191\) | 1.73038 | + | 2.99710i | 0.125206 | + | 0.216863i | 0.921813 | − | 0.387634i | \(-0.126708\pi\) |
−0.796608 | + | 0.604497i | \(0.793374\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.93395 | − | 8.54585i | 0.355153 | − | 0.615144i | −0.631991 | − | 0.774976i | \(-0.717762\pi\) |
0.987144 | + | 0.159832i | \(0.0510953\pi\) | |||||||
\(194\) | 3.44139 | + | 7.93118i | 0.247078 | + | 0.569426i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.97778 | + | 9.59813i | −0.641270 | + | 0.685581i | ||||
\(197\) | −4.95292 | − | 4.95292i | −0.352881 | − | 0.352881i | 0.508299 | − | 0.861180i | \(-0.330274\pi\) |
−0.861180 | + | 0.508299i | \(0.830274\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.3983i | 1.37511i | 0.726132 | + | 0.687556i | \(0.241316\pi\) | ||||
−0.726132 | + | 0.687556i | \(0.758684\pi\) | |||||||
\(200\) | −11.7742 | + | 2.15439i | −0.832559 | + | 0.152339i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.63517 | + | 16.8068i | −0.466849 | + | 1.18252i | ||||
\(203\) | 1.61940 | − | 0.433916i | 0.113659 | − | 0.0304549i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.01954 | − | 1.61293i | −0.420423 | − | 0.112652i | ||||
\(206\) | 2.39911 | + | 1.77808i | 0.167154 | + | 0.123884i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.56623 | + | 18.0528i | −0.247274 | + | 1.25174i | ||||
\(209\) | 7.30705 | + | 12.6562i | 0.505439 | + | 0.875446i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.499784 | − | 1.86522i | −0.0344066 | − | 0.128407i | 0.946586 | − | 0.322450i | \(-0.104506\pi\) |
−0.980993 | + | 0.194043i | \(0.937840\pi\) | |||||||
\(212\) | 11.4319 | + | 18.3571i | 0.785148 | + | 1.26077i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.03943 | − | 11.3819i | −0.617923 | − | 0.778051i | ||||
\(215\) | − | 0.763527i | − | 0.0520721i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.73446i | 0.185627i | ||||||||
\(218\) | 8.97677 | − | 7.12928i | 0.607983 | − | 0.482856i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.36396 | − | 10.1687i | 0.159378 | − | 0.685577i | ||||
\(221\) | −3.28408 | − | 12.2564i | −0.220911 | − | 0.824452i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.56173 | − | 11.3653i | −0.439406 | − | 0.761074i | 0.558237 | − | 0.829681i | \(-0.311478\pi\) |
−0.997644 | + | 0.0686072i | \(0.978144\pi\) | |||||||
\(224\) | −3.69994 | − | 0.175665i | −0.247213 | − | 0.0117371i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.52916 | + | 2.06325i | −0.101718 | + | 0.137246i | ||||
\(227\) | −4.02317 | − | 1.07800i | −0.267027 | − | 0.0715497i | 0.122821 | − | 0.992429i | \(-0.460806\pi\) |
−0.389848 | + | 0.920879i | \(0.627473\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.9787 | − | 7.22892i | 1.78280 | − | 0.477701i | 0.791713 | − | 0.610894i | \(-0.209190\pi\) |
0.991090 | + | 0.133193i | \(0.0425231\pi\) | |||||||
\(230\) | 4.66929 | + | 1.84339i | 0.307884 | + | 0.121550i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.95876 | − | 4.11542i | −0.391211 | − | 0.270191i | ||||
\(233\) | − | 6.78106i | − | 0.444242i | −0.975019 | − | 0.222121i | \(-0.928702\pi\) | ||
0.975019 | − | 0.222121i | \(-0.0712980\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.76980 | − | 5.76980i | −0.376380 | − | 0.376380i | ||||
\(236\) | −14.1412 | + | 0.472253i | −0.920517 | + | 0.0307411i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.34307 | − | 1.01667i | 0.151879 | − | 0.0659012i | ||||
\(239\) | 4.09048 | − | 7.08492i | 0.264591 | − | 0.458286i | −0.702865 | − | 0.711323i | \(-0.748096\pi\) |
0.967456 | + | 0.253038i | \(0.0814296\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.259428 | − | 0.449343i | −0.0167112 | − | 0.0289447i | 0.857549 | − | 0.514403i | \(-0.171986\pi\) |
−0.874260 | + | 0.485458i | \(0.838653\pi\) | |||||||
\(242\) | −27.8080 | − | 20.6096i | −1.78756 | − | 1.32484i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.90048 | − | 3.68255i | −0.441758 | − | 0.235751i | ||||
\(245\) | −1.49056 | + | 5.56285i | −0.0952285 | + | 0.355397i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.77552 | − | 5.64390i | −0.622002 | − | 0.359113i | ||||
\(248\) | 8.99909 | − | 7.65045i | 0.571443 | − | 0.485804i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.96025 | + | 7.11617i | −0.566696 | + | 0.450066i | ||||
\(251\) | 13.9609 | + | 13.9609i | 0.881207 | + | 0.881207i | 0.993657 | − | 0.112450i | \(-0.0358699\pi\) |
−0.112450 | + | 0.993657i | \(0.535870\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.0580 | − | 17.0580i | 1.07243 | − | 1.07243i | ||||
\(254\) | 26.9796 | + | 3.09476i | 1.69285 | + | 0.194183i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.77357 | + | 12.6680i | 0.610848 | + | 0.791748i | ||||
\(257\) | 8.72443 | − | 15.1112i | 0.544215 | − | 0.942609i | −0.454441 | − | 0.890777i | \(-0.650161\pi\) |
0.998656 | − | 0.0518315i | \(-0.0165059\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.85127 | + | 1.03195i | 0.239307 | + | 0.0641220i | ||||
\(260\) | 2.34585 | + | 7.71494i | 0.145483 | + | 0.478460i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.51412 | + | 16.9105i | 0.155323 | + | 1.04473i | ||||
\(263\) | 9.06417 | − | 5.23320i | 0.558921 | − | 0.322693i | −0.193791 | − | 0.981043i | \(-0.562079\pi\) |
0.752712 | + | 0.658350i | \(0.228745\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.20687 | + | 4.73824i | 0.504144 | + | 0.291068i | ||||
\(266\) | 0.834353 | − | 2.11341i | 0.0511575 | − | 0.129581i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.803940 | + | 24.0733i | 0.0491084 | + | 1.47051i | ||||
\(269\) | −14.8881 | + | 14.8881i | −0.907746 | + | 0.907746i | −0.996090 | − | 0.0883440i | \(-0.971843\pi\) |
0.0883440 | + | 0.996090i | \(0.471843\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.64797 | −0.100107 | −0.0500534 | − | 0.998747i | \(-0.515939\pi\) | ||||
−0.0500534 | + | 0.998747i | \(0.515939\pi\) | |||||||
\(272\) | −9.90130 | − | 4.86659i | −0.600355 | − | 0.295080i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.31558 | − | 1.87256i | 0.260714 | − | 0.113125i | ||||
\(275\) | 6.52368 | + | 24.3467i | 0.393393 | + | 1.46816i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.13780 | − | 11.7104i | 0.188532 | − | 0.703612i | −0.805315 | − | 0.592848i | \(-0.798004\pi\) |
0.993847 | − | 0.110764i | \(-0.0353298\pi\) | |||||||
\(278\) | 15.1388 | − | 2.25072i | 0.907965 | − | 0.134989i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.46663 | + | 0.695437i | −0.0876479 | + | 0.0415603i | ||||
\(281\) | −2.28116 | + | 1.31703i | −0.136083 | + | 0.0785674i | −0.566496 | − | 0.824065i | \(-0.691701\pi\) |
0.430413 | + | 0.902632i | \(0.358368\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.3823 | + | 2.78192i | −0.617162 | + | 0.165368i | −0.553837 | − | 0.832625i | \(-0.686837\pi\) |
−0.0633245 | + | 0.997993i | \(0.520170\pi\) | |||||||
\(284\) | 1.96924 | − | 8.47081i | 0.116853 | − | 0.502650i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 38.4977 | + | 4.41597i | 2.27642 | + | 0.261122i | ||||
\(287\) | 4.65610 | 0.274841 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.39253 | −0.552502 | ||||||||
\(290\) | −3.15271 | − | 0.361639i | −0.185133 | − | 0.0212361i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.297347 | − | 1.27906i | 0.0174009 | − | 0.0748512i | ||||
\(293\) | −3.95963 | + | 1.06098i | −0.231324 | + | 0.0619831i | −0.372619 | − | 0.927984i | \(-0.621540\pi\) |
0.141295 | + | 0.989968i | \(0.454873\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.36954 | + | 3.10010i | −0.312627 | + | 0.180495i | ||||
\(296\) | −7.37894 | − | 15.5617i | −0.428892 | − | 0.904505i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 27.6926 | − | 4.11712i | 1.60419 | − | 0.238499i | ||||
\(299\) | −4.82254 | + | 17.9980i | −0.278895 | + | 1.04085i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.147646 | + | 0.551024i | 0.00851020 | + | 0.0317605i | ||||
\(302\) | 7.63167 | − | 3.31143i | 0.439153 | − | 0.190552i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.28956 | + | 3.16702i | −0.532793 | + | 0.181641i | ||||
\(305\) | −3.42747 | −0.196256 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.40346 | − | 5.40346i | 0.308392 | − | 0.308392i | −0.535894 | − | 0.844286i | \(-0.680025\pi\) |
0.844286 | + | 0.535894i | \(0.180025\pi\) | |||||||
\(308\) | 0.260342 | + | 7.79574i | 0.0148344 | + | 0.444203i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.90063 | − | 4.81428i | 0.107949 | − | 0.273433i | ||||
\(311\) | 13.4939 | + | 7.79068i | 0.765167 | + | 0.441769i | 0.831148 | − | 0.556052i | \(-0.187684\pi\) |
−0.0659811 | + | 0.997821i | \(0.521018\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.4594 | − | 14.6990i | 1.43905 | − | 0.830835i | 0.441265 | − | 0.897377i | \(-0.354530\pi\) |
0.997784 | + | 0.0665417i | \(0.0211965\pi\) | |||||||
\(314\) | 4.09074 | + | 27.5151i | 0.230854 | + | 1.55277i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.49745 | − | 31.2349i | −0.534273 | − | 1.75710i | ||||
\(317\) | −5.27629 | − | 1.41378i | −0.296346 | − | 0.0794057i | 0.107583 | − | 0.994196i | \(-0.465689\pi\) |
−0.403929 | + | 0.914790i | \(0.632356\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.62485 | + | 13.2066i | −0.426909 | + | 0.739429i | ||||
\(320\) | 6.39201 | + | 2.88098i | 0.357324 | + | 0.161052i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.72621 | − | 0.427423i | −0.207653 | − | 0.0238194i | ||||
\(323\) | 4.78538 | − | 4.78538i | 0.266266 | − | 0.266266i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.7664 | − | 13.7664i | −0.763620 | − | 0.763620i | ||||
\(326\) | 7.84203 | − | 6.22808i | 0.434330 | − | 0.344942i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −13.0268 | − | 15.3232i | −0.719285 | − | 0.846083i | ||||
\(329\) | 5.27969 | + | 3.04823i | 0.291079 | + | 0.168054i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.68483 | + | 24.9481i | −0.367432 | + | 1.37127i | 0.496663 | + | 0.867944i | \(0.334559\pi\) |
−0.864094 | + | 0.503330i | \(0.832108\pi\) | |||||||
\(332\) | −9.80658 | − | 5.23343i | −0.538206 | − | 0.287222i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.0263 | − | 14.1012i | −1.04108 | − | 0.771583i | ||||
\(335\) | 5.27746 | + | 9.14082i | 0.288338 | + | 0.499416i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.97680 | + | 3.42392i | −0.107683 | + | 0.186513i | −0.914831 | − | 0.403836i | \(-0.867677\pi\) |
0.807148 | + | 0.590349i | \(0.201010\pi\) | |||||||
\(338\) | −10.5914 | + | 4.59569i | −0.576097 | + | 0.249972i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.83186 | + | 0.161362i | −0.262045 | + | 0.00875110i | ||||
\(341\) | −17.5877 | − | 17.5877i | −0.952425 | − | 0.952425i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 8.88645i | − | 0.479823i | ||||||
\(344\) | 1.40033 | − | 2.02756i | 0.0755009 | − | 0.109318i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.1769 | + | 8.75525i | 1.19224 | + | 0.470685i | ||||
\(347\) | −4.56059 | + | 1.22201i | −0.244825 | + | 0.0656008i | −0.379145 | − | 0.925337i | \(-0.623782\pi\) |
0.134320 | + | 0.990938i | \(0.457115\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.74559 | − | 2.07543i | −0.414612 | − | 0.111095i | 0.0454819 | − | 0.998965i | \(-0.485518\pi\) |
−0.460094 | + | 0.887870i | \(0.652184\pi\) | |||||||
\(350\) | 2.33343 | − | 3.14843i | 0.124727 | − | 0.168291i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 24.9274 | − | 22.6677i | 1.32863 | − | 1.20819i | ||||
\(353\) | −6.95793 | − | 12.0515i | −0.370333 | − | 0.641436i | 0.619283 | − | 0.785168i | \(-0.287423\pi\) |
−0.989617 | + | 0.143731i | \(0.954090\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.986340 | − | 3.68107i | −0.0523495 | − | 0.195371i | ||||
\(356\) | 2.31453 | − | 9.95612i | 0.122670 | − | 0.527673i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.2829 | + | 8.16660i | −0.543468 | + | 0.431618i | ||||
\(359\) | − | 0.491573i | − | 0.0259443i | −0.999916 | − | 0.0129721i | \(-0.995871\pi\) | ||
0.999916 | − | 0.0129721i | \(-0.00412927\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.9796i | 0.683138i | ||||||||
\(362\) | 19.2641 | + | 24.2562i | 1.01250 | + | 1.27488i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.18483 | − | 5.11411i | −0.166930 | − | 0.268052i | ||||
\(365\) | −0.148933 | − | 0.555827i | −0.00779553 | − | 0.0290933i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.97080 | + | 6.87763i | 0.207274 | + | 0.359010i | 0.950855 | − | 0.309637i | \(-0.100207\pi\) |
−0.743581 | + | 0.668646i | \(0.766874\pi\) | |||||||
\(368\) | 9.01852 | + | 13.4588i | 0.470123 | + | 0.701587i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.06327 | − | 4.49374i | −0.315214 | − | 0.233618i | ||||
\(371\) | −6.83901 | − | 1.83251i | −0.355064 | − | 0.0951390i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.8895 | − | 5.86527i | 1.13340 | − | 0.303692i | 0.357103 | − | 0.934065i | \(-0.383765\pi\) |
0.776293 | + | 0.630373i | \(0.217098\pi\) | |||||||
\(374\) | −8.53120 | + | 21.6094i | −0.441138 | + | 1.11740i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.73977 | − | 25.9038i | −0.244435 | − | 1.33588i | ||||
\(377\) | − | 11.7787i | − | 0.606635i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.5680 | − | 24.5680i | −1.26197 | − | 1.26197i | −0.950135 | − | 0.311839i | \(-0.899055\pi\) |
−0.311839 | − | 0.950135i | \(-0.600945\pi\) | |||||||
\(380\) | −2.93792 | + | 3.14093i | −0.150712 | + | 0.161126i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.94816 | + | 4.48980i | 0.0996764 | + | 0.229718i | ||||
\(383\) | −3.67713 | + | 6.36897i | −0.187892 | + | 0.325439i | −0.944547 | − | 0.328375i | \(-0.893499\pi\) |
0.756655 | + | 0.653814i | \(0.226832\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.70901 | + | 2.96010i | 0.0870995 | + | 0.150861i | ||||
\(386\) | 8.30948 | − | 11.2117i | 0.422941 | − | 0.570663i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.55694 | + | 11.6979i | 0.180576 | + | 0.593873i | ||||
\(389\) | 4.98406 | − | 18.6007i | 0.252702 | − | 0.943095i | −0.716653 | − | 0.697430i | \(-0.754327\pi\) |
0.969355 | − | 0.245665i | \(-0.0790065\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.67459 | − | 5.58563i | −0.489265 | − | 0.282477i | ||||
\(392\) | −14.1607 | + | 12.0385i | −0.715221 | + | 0.608035i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.16062 | − | 7.75709i | −0.310368 | − | 0.390796i | ||||
\(395\) | −10.1159 | − | 10.1159i | −0.508985 | − | 0.508985i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.3235 | + | 23.3235i | −1.17057 | + | 1.17057i | −0.188500 | + | 0.982073i | \(0.560362\pi\) |
−0.982073 | + | 0.188500i | \(0.939638\pi\) | |||||||
\(398\) | −3.12631 | + | 27.2547i | −0.156708 | + | 1.36615i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −16.8899 | + | 1.12935i | −0.844496 | + | 0.0564676i | ||||
\(401\) | 4.61036 | − | 7.98538i | 0.230231 | − | 0.398771i | −0.727645 | − | 0.685954i | \(-0.759385\pi\) |
0.957876 | + | 0.287183i | \(0.0927186\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.5568 | + | 4.97229i | 0.924382 | + | 0.247687i | ||||
\(404\) | −12.0311 | + | 22.5442i | −0.598568 | + | 1.12162i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.34519 | − | 0.348664i | 0.116390 | − | 0.0173039i | ||||
\(407\) | −31.4082 | + | 18.1335i | −1.55685 | + | 0.898845i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.2773 | − | 9.97503i | −0.854306 | − | 0.493234i | 0.00779552 | − | 0.999970i | \(-0.497519\pi\) |
−0.862101 | + | 0.506736i | \(0.830852\pi\) | |||||||
\(410\) | −8.19752 | − | 3.23630i | −0.404846 | − | 0.159830i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.08419 | + | 2.88485i | 0.151947 | + | 0.142126i | ||||
\(413\) | 3.27562 | − | 3.27562i | 0.161183 | − | 0.161183i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.87092 | −0.239104 | ||||||||
\(416\) | −7.92002 | + | 24.7895i | −0.388311 | + | 1.21540i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.22669 | + | 18.9596i | 0.402380 | + | 0.927343i | ||||
\(419\) | −7.85913 | − | 29.3307i | −0.383943 | − | 1.43290i | −0.839826 | − | 0.542856i | \(-0.817343\pi\) |
0.455882 | − | 0.890040i | \(-0.349324\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.70420 | + | 10.0922i | −0.131795 | + | 0.491864i | −0.999991 | − | 0.00435733i | \(-0.998613\pi\) |
0.868196 | + | 0.496222i | \(0.165280\pi\) | |||||||
\(422\) | −0.401591 | − | 2.70118i | −0.0195491 | − | 0.131491i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.1034 | + | 27.6341i | 0.636356 | + | 1.34203i | ||||
\(425\) | 10.1085 | − | 5.83615i | 0.490335 | − | 0.283095i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.47354 | − | 0.662784i | 0.119703 | − | 0.0320744i | ||||
\(428\) | −10.8660 | − | 17.4484i | −0.525230 | − | 0.843401i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.123053 | − | 1.07276i | 0.00593414 | − | 0.0517329i | ||||
\(431\) | −11.3639 | −0.547382 | −0.273691 | − | 0.961818i | \(-0.588244\pi\) | ||||
−0.273691 | + | 0.961818i | \(0.588244\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.65126 | −0.463810 | −0.231905 | − | 0.972738i | \(-0.574496\pi\) | ||||
−0.231905 | + | 0.972738i | \(0.574496\pi\) | |||||||
\(434\) | −0.440696 | + | 3.84192i | −0.0211541 | + | 0.184418i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.7613 | − | 8.56992i | 0.659049 | − | 0.410425i | ||||
\(437\) | −9.59925 | + | 2.57211i | −0.459194 | + | 0.123041i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.6132 | + | 7.85957i | −0.649722 | + | 0.375117i | −0.788350 | − | 0.615228i | \(-0.789064\pi\) |
0.138628 | + | 0.990345i | \(0.455731\pi\) | |||||||
\(440\) | 4.96021 | − | 13.9061i | 0.236469 | − | 0.662948i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.63886 | − | 17.7495i | −0.125518 | − | 0.844256i | ||||
\(443\) | 4.97116 | − | 18.5526i | 0.236187 | − | 0.881461i | −0.741424 | − | 0.671037i | \(-0.765849\pi\) |
0.977610 | − | 0.210424i | \(-0.0674843\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.15929 | − | 4.32653i | −0.0549556 | − | 0.205097i | ||||
\(446\) | −7.38757 | − | 17.0257i | −0.349812 | − | 0.806191i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.17011 | − | 0.843106i | −0.244265 | − | 0.0398330i | ||||
\(449\) | −35.3101 | −1.66639 | −0.833194 | − | 0.552982i | \(-0.813490\pi\) | ||||
−0.833194 | + | 0.552982i | \(0.813490\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.9474 | + | 29.9474i | −1.41017 | + | 1.41017i | ||||
\(452\) | −2.48099 | + | 2.65243i | −0.116696 | + | 0.124760i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.47882 | − | 2.16299i | −0.257134 | − | 0.101514i | ||||
\(455\) | −2.28636 | − | 1.32003i | −0.107186 | − | 0.0618839i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.565406 | − | 0.326437i | 0.0264486 | − | 0.0152701i | −0.486717 | − | 0.873559i | \(-0.661806\pi\) |
0.513166 | + | 0.858289i | \(0.328473\pi\) | |||||||
\(458\) | 39.0701 | − | 5.80865i | 1.82563 | − | 0.271420i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.26326 | + | 3.34249i | 0.292026 | + | 0.155844i | ||||
\(461\) | 3.91317 | + | 1.04853i | 0.182255 | + | 0.0488350i | 0.348792 | − | 0.937200i | \(-0.386592\pi\) |
−0.166537 | + | 0.986035i | \(0.553259\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.0971 | + | 36.5413i | −0.980466 | + | 1.69822i | −0.319894 | + | 0.947453i | \(0.603647\pi\) |
−0.660571 | + | 0.750763i | \(0.729686\pi\) | |||||||
\(464\) | −7.70880 | − | 6.74250i | −0.357872 | − | 0.313013i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.09286 | − | 9.52739i | 0.0506258 | − | 0.441348i | ||||
\(467\) | 0.180878 | − | 0.180878i | 0.00837005 | − | 0.00837005i | −0.702909 | − | 0.711279i | \(-0.748116\pi\) |
0.711279 | + | 0.702909i | \(0.248116\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.57625 | − | 5.57625i | −0.257487 | − | 0.257487i | ||||
\(470\) | −7.17668 | − | 9.03645i | −0.331036 | − | 0.416820i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −19.9446 | − | 1.61554i | −0.918023 | − | 0.0743613i | ||||
\(473\) | −4.49375 | − | 2.59447i | −0.206623 | − | 0.119294i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.68747 | − | 10.0298i | 0.123310 | − | 0.460198i | ||||
\(476\) | 3.45587 | − | 1.05081i | 0.158399 | − | 0.0481638i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.88896 | − | 9.29508i | 0.315094 | − | 0.425147i | ||||
\(479\) | −6.98122 | − | 12.0918i | −0.318980 | − | 0.552490i | 0.661295 | − | 0.750126i | \(-0.270007\pi\) |
−0.980276 | + | 0.197636i | \(0.936674\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.0062 | − | 24.2594i | 0.638627 | − | 1.10613i | ||||
\(482\) | −0.292079 | − | 0.673138i | −0.0133038 | − | 0.0306606i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −35.7487 | − | 33.4381i | −1.62494 | − | 1.51992i | ||||
\(485\) | 3.78855 | + | 3.78855i | 0.172029 | + | 0.172029i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.93338i | 0.132924i | 0.997789 | + | 0.0664621i | \(0.0211712\pi\) | ||||
−0.997789 | + | 0.0664621i | \(0.978829\pi\) | |||||||
\(488\) | −9.10168 | − | 6.28609i | −0.412014 | − | 0.284558i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.99077 | + | 7.57558i | −0.135109 | + | 0.342230i | ||||
\(491\) | −17.7814 | + | 4.76452i | −0.802465 | + | 0.215020i | −0.636666 | − | 0.771140i | \(-0.719687\pi\) |
−0.165799 | + | 0.986160i | \(0.553020\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.82126 | + | 1.82775i | 0.307214 | + | 0.0823178i | ||||
\(494\) | −12.8250 | − | 9.50515i | −0.577025 | − | 0.427657i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.8767 | − | 9.29856i | 0.623082 | − | 0.417518i | ||||
\(497\) | 1.42365 | + | 2.46583i | 0.0638594 | + | 0.110608i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.74054 | − | 17.6919i | −0.212216 | − | 0.791999i | −0.987128 | − | 0.159931i | \(-0.948873\pi\) |
0.774913 | − | 0.632068i | \(-0.217794\pi\) | |||||||
\(500\) | −13.7360 | + | 8.55415i | −0.614294 | + | 0.382553i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 17.3651 | + | 21.8651i | 0.775044 | + | 0.975889i | ||||
\(503\) | 7.01136i | 0.312621i | 0.987708 | + | 0.156311i | \(0.0499601\pi\) | ||||
−0.987708 | + | 0.156311i | \(0.950040\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.1977i | 0.498292i | ||||||||
\(506\) | 26.7156 | − | 21.2173i | 1.18765 | − | 0.943225i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 37.4076 | + | 8.69628i | 1.65969 | + | 0.385835i | ||||
\(509\) | −1.25064 | − | 4.66745i | −0.0554336 | − | 0.206881i | 0.932654 | − | 0.360771i | \(-0.117486\pi\) |
−0.988088 | + | 0.153890i | \(0.950820\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.214965 | + | 0.372331i | 0.00950950 | + | 0.0164709i | ||||
\(512\) | 11.6902 | + | 19.3736i | 0.516641 | + | 0.856202i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.6932 | − | 19.8251i | 0.648090 | − | 0.874449i | ||||
\(515\) | 1.78752 | + | 0.478965i | 0.0787676 | + | 0.0211057i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −53.5640 | + | 14.3524i | −2.35574 | + | 0.631219i | ||||
\(518\) | 5.24473 | + | 2.07057i | 0.230440 | + | 0.0909756i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.05255 | + | 11.2176i | 0.0900101 | + | 0.491922i | ||||
\(521\) | 28.0687i | 1.22971i | 0.788640 | + | 0.614855i | \(0.210785\pi\) | ||||
−0.788640 | + | 0.614855i | \(0.789215\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.5264 | + | 14.5264i | 0.635193 | + | 0.635193i | 0.949366 | − | 0.314173i | \(-0.101727\pi\) |
−0.314173 | + | 0.949366i | \(0.601727\pi\) | |||||||
\(524\) | 0.806982 | + | 24.1644i | 0.0352532 | + | 1.05563i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.5786 | − | 5.89183i | 0.592054 | − | 0.256896i | ||||
\(527\) | −5.75907 | + | 9.97501i | −0.250869 | + | 0.434518i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.29774 | − | 5.71185i | −0.143380 | − | 0.248341i | ||||
\(530\) | 10.7670 | + | 7.97988i | 0.467689 | + | 0.346624i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.51287 | − | 2.83487i | 0.0655913 | − | 0.122907i | ||||
\(533\) | 8.46657 | − | 31.5977i | 0.366728 | − | 1.36865i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.80063 | − | 4.50370i | −0.337251 | − | 0.194712i | ||||
\(536\) | −2.75021 | + | 33.9526i | −0.118791 | + | 1.46653i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −23.3173 | + | 18.5184i | −1.00528 | + | 0.798386i | ||||
\(539\) | 27.6753 | + | 27.6753i | 1.19206 | + | 1.19206i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.4081 | − | 18.4081i | 0.791427 | − | 0.791427i | −0.190299 | − | 0.981726i | \(-0.560946\pi\) |
0.981726 | + | 0.190299i | \(0.0609458\pi\) | |||||||
\(542\) | −2.31539 | − | 0.265593i | −0.0994547 | − | 0.0114082i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −13.1270 | − | 8.43329i | −0.562816 | − | 0.361575i | ||||
\(545\) | 3.55201 | − | 6.15226i | 0.152151 | − | 0.263534i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.9583 | − | 4.27602i | −0.682328 | − | 0.182829i | −0.0990263 | − | 0.995085i | \(-0.531573\pi\) |
−0.583302 | + | 0.812256i | \(0.698239\pi\) | |||||||
\(548\) | 6.36518 | − | 1.93543i | 0.271907 | − | 0.0826775i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.24197 | + | 35.2585i | 0.223518 | + | 1.50343i | ||||
\(551\) | 5.44055 | − | 3.14110i | 0.231775 | − | 0.133816i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.25660 | + | 5.34430i | 0.393631 | + | 0.227263i | ||||
\(554\) | 6.29591 | − | 15.9475i | 0.267488 | − | 0.677543i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 21.6328 | − | 0.722436i | 0.917433 | − | 0.0306381i | ||||
\(557\) | 15.4219 | − | 15.4219i | 0.653447 | − | 0.653447i | −0.300375 | − | 0.953821i | \(-0.597112\pi\) |
0.953821 | + | 0.300375i | \(0.0971117\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.00789 | 0.169516 | ||||||||
\(560\) | −2.17270 | + | 0.740721i | −0.0918131 | + | 0.0313012i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.41729 | + | 1.48279i | −0.144150 | + | 0.0625476i | ||||
\(563\) | −1.67165 | − | 6.23868i | −0.0704516 | − | 0.262929i | 0.921712 | − | 0.387875i | \(-0.126791\pi\) |
−0.992164 | + | 0.124946i | \(0.960124\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.411914 | + | 1.53728i | −0.0173293 | + | 0.0646740i | ||||
\(566\) | −15.0354 | + | 2.23535i | −0.631986 | + | 0.0939589i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.13197 | − | 11.5841i | 0.173374 | − | 0.486059i | ||||
\(569\) | −7.90864 | + | 4.56605i | −0.331547 | + | 0.191419i | −0.656528 | − | 0.754302i | \(-0.727976\pi\) |
0.324981 | + | 0.945721i | \(0.394642\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.5804 | − | 7.39016i | 1.15421 | − | 0.309268i | 0.369556 | − | 0.929208i | \(-0.379510\pi\) |
0.784649 | + | 0.619940i | \(0.212843\pi\) | |||||||
\(572\) | 53.3776 | + | 12.4089i | 2.23183 | + | 0.518841i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.54182 | + | 0.750395i | 0.273050 | + | 0.0313209i | ||||
\(575\) | −17.1403 | −0.714799 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.350515 | 0.0145921 | 0.00729607 | − | 0.999973i | \(-0.497678\pi\) | ||||
0.00729607 | + | 0.999973i | \(0.497678\pi\) | |||||||
\(578\) | −13.1965 | − | 1.51374i | −0.548902 | − | 0.0629631i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.37127 | − | 1.01620i | −0.181507 | − | 0.0421956i | ||||
\(581\) | 3.51526 | − | 0.941911i | 0.145838 | − | 0.0390771i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 55.7739 | − | 32.2011i | 2.30992 | − | 1.33363i | ||||
\(584\) | 0.623910 | − | 1.74915i | 0.0258176 | − | 0.0723805i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.73427 | + | 0.852527i | −0.236881 | + | 0.0352176i | ||||
\(587\) | −0.259943 | + | 0.970122i | −0.0107290 | + | 0.0400412i | −0.971083 | − | 0.238743i | \(-0.923265\pi\) |
0.960354 | + | 0.278784i | \(0.0899314\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.65198 | + | 9.89733i | 0.109273 | + | 0.407812i | ||||
\(590\) | −8.04383 | + | 3.49027i | −0.331159 | + | 0.143692i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.85943 | − | 23.0534i | −0.323021 | − | 0.947489i | ||||
\(593\) | −7.12791 | −0.292708 | −0.146354 | − | 0.989232i | \(-0.546754\pi\) | ||||
−0.146354 | + | 0.989232i | \(0.546754\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.11923 | − | 1.11923i | 0.0458841 | − | 0.0458841i | ||||
\(596\) | 39.5717 | − | 1.32151i | 1.62092 | − | 0.0541313i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.67629 | + | 24.5099i | −0.395693 | + | 1.00229i | ||||
\(599\) | 1.83973 | + | 1.06217i | 0.0751695 | + | 0.0433991i | 0.537114 | − | 0.843510i | \(-0.319515\pi\) |
−0.461944 | + | 0.886909i | \(0.652848\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.6223 | − | 18.8345i | 1.33069 | − | 0.768275i | 0.345286 | − | 0.938497i | \(-0.387782\pi\) |
0.985406 | + | 0.170222i | \(0.0544485\pi\) | |||||||
\(602\) | 0.118638 | + | 0.797984i | 0.00483533 | + | 0.0325234i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.2562 | − | 3.42262i | 0.458007 | − | 0.139264i | ||||
\(605\) | −20.7191 | − | 5.55166i | −0.842351 | − | 0.225707i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.2096 | − | 17.6835i | 0.414393 | − | 0.717750i | −0.580971 | − | 0.813924i | \(-0.697327\pi\) |
0.995365 | + | 0.0961740i | \(0.0306605\pi\) | |||||||
\(608\) | −13.5622 | + | 2.95253i | −0.550022 | + | 0.119741i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.81559 | − | 0.552384i | −0.194978 | − | 0.0223654i | ||||
\(611\) | 30.2867 | − | 30.2867i | 1.22527 | − | 1.22527i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.2801 | − | 10.2801i | −0.415208 | − | 0.415208i | 0.468340 | − | 0.883548i | \(-0.344852\pi\) |
−0.883548 | + | 0.468340i | \(0.844852\pi\) | |||||||
\(614\) | 8.46271 | − | 6.72103i | 0.341527 | − | 0.271239i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.890610 | + | 10.9950i | −0.0358837 | + | 0.443000i | ||||
\(617\) | 41.2817 | + | 23.8340i | 1.66194 | + | 0.959521i | 0.971788 | + | 0.235856i | \(0.0757895\pi\) |
0.690152 | + | 0.723665i | \(0.257544\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.41291 | + | 5.27305i | −0.0567896 | + | 0.211942i | −0.988490 | − | 0.151286i | \(-0.951659\pi\) |
0.931700 | + | 0.363228i | \(0.118325\pi\) | |||||||
\(620\) | 3.44628 | − | 6.45775i | 0.138406 | − | 0.259350i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.7033 | + | 13.1206i | 0.709838 | + | 0.526090i | ||||
\(623\) | 1.67328 | + | 2.89820i | 0.0670385 | + | 0.116114i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.03430 | − | 12.1838i | 0.281372 | − | 0.487350i | ||||
\(626\) | 38.1394 | − | 16.5489i | 1.52436 | − | 0.661428i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.31304 | + | 39.3180i | 0.0523961 | + | 1.56896i | ||||
\(629\) | 11.8756 | + | 11.8756i | 0.473513 | + | 0.473513i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.7362i | 0.825496i | 0.910845 | + | 0.412748i | \(0.135431\pi\) | ||||
−0.910845 | + | 0.412748i | \(0.864569\pi\) | |||||||
\(632\) | −8.30999 | − | 45.4157i | −0.330554 | − | 1.80654i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.18534 | − | 2.83671i | −0.285366 | − | 0.112660i | ||||
\(635\) | 16.2558 | − | 4.35574i | 0.645094 | − | 0.172852i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29.2004 | − | 7.82422i | −1.15696 | − | 0.310007i | ||||
\(638\) | −12.8413 | + | 17.3265i | −0.508394 | + | 0.685961i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8.51647 | + | 5.07794i | 0.336643 | + | 0.200723i | ||||
\(641\) | −3.67059 | − | 6.35766i | −0.144980 | − | 0.251112i | 0.784386 | − | 0.620273i | \(-0.212978\pi\) |
−0.929365 | + | 0.369161i | \(0.879645\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.23207 | − | 8.33019i | −0.0880241 | − | 0.328511i | 0.907846 | − | 0.419305i | \(-0.137726\pi\) |
−0.995870 | + | 0.0907942i | \(0.971059\pi\) | |||||||
\(644\) | −5.16644 | − | 1.20106i | −0.203586 | − | 0.0473284i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.49470 | − | 5.95223i | 0.294875 | − | 0.234188i | ||||
\(647\) | 11.6387i | 0.457566i | 0.973477 | + | 0.228783i | \(0.0734746\pi\) | ||||
−0.973477 | + | 0.228783i | \(0.926525\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 42.1367i | 1.65401i | ||||||||
\(650\) | −17.1231 | − | 21.5604i | −0.671623 | − | 0.845668i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.0218 | − | 7.48661i | 0.470810 | − | 0.293198i | ||||
\(653\) | 5.20569 | + | 19.4279i | 0.203715 | + | 0.760273i | 0.989838 | + | 0.142203i | \(0.0454186\pi\) |
−0.786123 | + | 0.618070i | \(0.787915\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.29742 | + | 9.17541i | 0.206988 | + | 0.358513i | ||||
\(656\) | −15.8331 | − | 23.6286i | −0.618180 | − | 0.922540i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.92670 | + | 5.13366i | 0.270031 | + | 0.200131i | ||||
\(659\) | 14.5489 | + | 3.89836i | 0.566744 | + | 0.151859i | 0.530803 | − | 0.847495i | \(-0.321890\pi\) |
0.0359413 | + | 0.999354i | \(0.488557\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.83468 | + | 2.63519i | −0.382525 | + | 0.102497i | −0.444957 | − | 0.895552i | \(-0.646781\pi\) |
0.0624321 | + | 0.998049i | \(0.480114\pi\) | |||||||
\(662\) | −13.4129 | + | 33.9748i | −0.521308 | + | 1.32047i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.9348 | − | 8.93344i | −0.501968 | − | 0.346685i | ||||
\(665\) | − | 1.40808i | − | 0.0546030i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.33276 | − | 7.33276i | −0.283926 | − | 0.283926i | ||||
\(668\) | −24.4594 | − | 22.8786i | −0.946364 | − | 0.885198i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.94166 | + | 13.6934i | 0.229546 | + | 0.529022i | ||||
\(671\) | −11.6465 | + | 20.1724i | −0.449610 | + | 0.778747i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.1240 | + | 27.9276i | 0.621534 | + | 1.07653i | 0.989200 | + | 0.146571i | \(0.0468236\pi\) |
−0.367666 | + | 0.929958i | \(0.619843\pi\) | |||||||
\(674\) | −3.32922 | + | 4.49202i | −0.128237 | + | 0.173026i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.6216 | + | 4.74999i | −0.600831 | + | 0.182692i | ||||
\(677\) | −9.43821 | + | 35.2239i | −0.362740 | + | 1.35376i | 0.507719 | + | 0.861523i | \(0.330489\pi\) |
−0.870459 | + | 0.492241i | \(0.836178\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.46674 | − | 2.00152i | −0.133041 | − | 0.0768113i | ||||
\(680\) | −6.81477 | − | 0.552008i | −0.261335 | − | 0.0211685i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −21.8762 | − | 27.5452i | −0.837682 | − | 1.05476i | ||||
\(683\) | 1.95185 | + | 1.95185i | 0.0746855 | + | 0.0746855i | 0.743463 | − | 0.668777i | \(-0.233182\pi\) |
−0.668777 | + | 0.743463i | \(0.733182\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.06146 | − | 2.06146i | 0.0787642 | − | 0.0787642i | ||||
\(686\) | 1.43217 | − | 12.4855i | 0.0546807 | − | 0.476697i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.29424 | − | 2.62303i | 0.0874670 | − | 0.100002i | ||||
\(689\) | −24.8719 | + | 43.0793i | −0.947542 | + | 1.64119i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.50428 | + | 0.403069i | 0.0572253 | + | 0.0153335i | 0.287318 | − | 0.957835i | \(-0.407236\pi\) |
−0.230093 | + | 0.973169i | \(0.573903\pi\) | |||||||
\(692\) | 29.7476 | + | 15.8753i | 1.13083 | + | 0.603487i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.60458 | + | 0.981917i | −0.250706 | + | 0.0372731i | ||||
\(695\) | 8.21412 | − | 4.74242i | 0.311579 | − | 0.179890i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.9849 | + | 9.80626i | 0.643351 | + | 0.371439i | ||||
\(698\) | −10.5481 | − | 4.16428i | −0.399251 | − | 0.157620i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.78588 | − | 4.04748i | 0.143093 | − | 0.152980i | ||||
\(701\) | 21.5819 | − | 21.5819i | 0.815136 | − | 0.815136i | −0.170263 | − | 0.985399i | \(-0.554462\pi\) |
0.985399 | + | 0.170263i | \(0.0544617\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.9404 | 0.563489 | ||||||||
\(704\) | 38.6762 | − | 27.8307i | 1.45766 | − | 1.04891i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.83363 | − | 18.0537i | −0.294823 | − | 0.679461i | ||||
\(707\) | −2.16535 | − | 8.08119i | −0.0814363 | − | 0.303925i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.51773 | + | 20.5925i | −0.207223 | + | 0.773366i | 0.781538 | + | 0.623858i | \(0.214436\pi\) |
−0.988760 | + | 0.149508i | \(0.952231\pi\) | |||||||
\(710\) | −0.792553 | − | 5.33087i | −0.0297440 | − | 0.200064i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.85649 | − | 13.6153i | 0.182005 | − | 0.510256i | ||||
\(713\) | 14.6479 | − | 8.45696i | 0.548568 | − | 0.316716i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.1958 | − | 6.21528i | 0.867472 | − | 0.232438i | ||||
\(716\) | −15.7636 | + | 9.81685i | −0.589115 | + | 0.366873i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.0792239 | − | 0.690661i | 0.00295661 | − | 0.0257752i | ||||
\(719\) | −28.4354 | −1.06046 | −0.530230 | − | 0.847854i | \(-0.677894\pi\) | ||||
−0.530230 | + | 0.847854i | \(0.677894\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.38264 | −0.0514923 | ||||||||
\(722\) | −2.09185 | + | 18.2364i | −0.0778505 | + | 0.678688i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 23.1569 | + | 37.1847i | 0.860619 | + | 1.38196i | ||||
\(725\) | 10.4660 | − | 2.80436i | 0.388697 | − | 0.104151i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.2100 | − | 13.4003i | 0.860812 | − | 0.496990i | −0.00347239 | − | 0.999994i | \(-0.501105\pi\) |
0.864284 | + | 0.503004i | \(0.167772\pi\) | |||||||
\(728\) | −3.65047 | − | 7.69860i | −0.135296 | − | 0.285329i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.119672 | − | 0.804940i | −0.00442927 | − | 0.0297922i | ||||
\(731\) | −0.621920 | + | 2.32104i | −0.0230025 | + | 0.0858466i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.44950 | − | 24.0699i | −0.238218 | − | 0.889041i | −0.976672 | − | 0.214737i | \(-0.931110\pi\) |
0.738454 | − | 0.674304i | \(-0.235556\pi\) | |||||||
\(734\) | 4.47055 | + | 10.3030i | 0.165011 | + | 0.380292i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.5019 | + | 20.3630i | 0.387107 | + | 0.750592i | ||||
\(737\) | 71.7313 | 2.64226 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.91976 | + | 9.91976i | −0.364904 | + | 0.364904i | −0.865615 | − | 0.500711i | \(-0.833072\pi\) |
0.500711 | + | 0.865615i | \(0.333072\pi\) | |||||||
\(740\) | −7.79467 | − | 7.29088i | −0.286538 | − | 0.268018i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.31347 | − | 3.67687i | −0.341908 | − | 0.134982i | ||||
\(743\) | 15.1283 | + | 8.73432i | 0.555003 | + | 0.320431i | 0.751137 | − | 0.660146i | \(-0.229506\pi\) |
−0.196134 | + | 0.980577i | \(0.562839\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.0257 | − | 8.67507i | 0.550497 | − | 0.317830i | ||||
\(746\) | 31.7000 | − | 4.71292i | 1.16062 | − | 0.172552i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −15.4690 | + | 28.9863i | −0.565602 | + | 1.05984i | ||||
\(749\) | 6.50048 | + | 1.74180i | 0.237522 | + | 0.0636439i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.95134 | + | 3.37983i | −0.0712056 | + | 0.123332i | −0.899430 | − | 0.437065i | \(-0.856018\pi\) |
0.828224 | + | 0.560397i | \(0.189351\pi\) | |||||||
\(752\) | −2.48463 | − | 37.1587i | −0.0906052 | − | 1.35504i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.89831 | − | 16.5491i | 0.0691322 | − | 0.602683i | ||||
\(755\) | 3.64548 | − | 3.64548i | 0.132673 | − | 0.132673i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.8568 | + | 16.8568i | 0.612670 | + | 0.612670i | 0.943641 | − | 0.330971i | \(-0.107376\pi\) |
−0.330971 | + | 0.943641i | \(0.607376\pi\) | |||||||
\(758\) | −30.5586 | − | 38.4775i | −1.10994 | − | 1.39757i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.63398 | + | 3.93951i | −0.168092 | + | 0.142901i | ||||
\(761\) | −34.1207 | − | 19.6996i | −1.23688 | − | 0.714111i | −0.268422 | − | 0.963302i | \(-0.586502\pi\) |
−0.968454 | + | 0.249191i | \(0.919835\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.37373 | + | 5.12685i | −0.0497325 | + | 0.185604i | ||||
\(764\) | 2.01357 | + | 6.62215i | 0.0728483 | + | 0.239581i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.19281 | + | 8.35579i | −0.223755 | + | 0.301907i | ||||
\(767\) | −16.2730 | − | 28.1857i | −0.587584 | − | 1.01773i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.1180 | − | 17.5249i | 0.364866 | − | 0.631966i | −0.623889 | − | 0.781513i | \(-0.714448\pi\) |
0.988755 | + | 0.149547i | \(0.0477816\pi\) | |||||||
\(770\) | 1.92411 | + | 4.43437i | 0.0693399 | + | 0.159804i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.4818 | − | 14.4133i | 0.485219 | − | 0.518747i | ||||
\(773\) | 2.34590 | + | 2.34590i | 0.0843761 | + | 0.0843761i | 0.748035 | − | 0.663659i | \(-0.230997\pi\) |
−0.663659 | + | 0.748035i | \(0.730997\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.6725i | 0.634816i | ||||||||
\(776\) | 3.11222 | + | 17.0089i | 0.111722 | + | 0.610582i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.0004 | − | 25.3308i | 0.358531 | − | 0.908153i | ||||
\(779\) | 16.8527 | − | 4.51566i | 0.603810 | − | 0.161790i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.0166 | − | 6.70318i | −0.895164 | − | 0.239859i | ||||
\(782\) | −12.6926 | − | 9.40700i | −0.453886 | − | 0.336394i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −21.8359 | + | 14.6319i | −0.779853 | + | 0.522567i | ||||
\(785\) | 8.61946 | + | 14.9293i | 0.307642 | + | 0.532851i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.00353 | − | 29.8696i | −0.285295 | − | 1.06474i | −0.948623 | − | 0.316407i | \(-0.897523\pi\) |
0.663328 | − | 0.748328i | \(-0.269143\pi\) | |||||||
\(788\) | −7.40552 | − | 11.8916i | −0.263811 | − | 0.423620i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.5825 | − | 15.8431i | −0.447665 | − | 0.563673i | ||||
\(791\) | − | 1.18908i | − | 0.0422790i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 17.9914i | − | 0.638893i | ||||||
\(794\) | −36.5284 | + | 29.0106i | −1.29635 | + | 1.02955i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.78493 | + | 37.7890i | −0.311374 | + | 1.33939i | ||||
\(797\) | −5.59514 | − | 20.8814i | −0.198190 | − | 0.739655i | −0.991418 | − | 0.130730i | \(-0.958268\pi\) |
0.793228 | − | 0.608925i | \(-0.208399\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.8398 | + | 22.2392i | 0.454240 | + | 0.786767i | ||||
\(800\) | −23.9124 | − | 1.13530i | −0.845429 | − | 0.0401390i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.76452 | − | 10.4764i | 0.274175 | − | 0.369936i | ||||
\(803\) | −3.77741 | − | 1.01215i | −0.133302 | − | 0.0357181i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.24513 | + | 0.601580i | −0.0791303 | + | 0.0212029i | ||||
\(806\) | 25.2710 | + | 9.97676i | 0.890134 | + | 0.351417i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −20.5370 | + | 29.7357i | −0.722488 | + | 1.04610i | ||||
\(809\) | 16.4138i | 0.577078i | 0.957468 | + | 0.288539i | \(0.0931695\pi\) | ||||
−0.957468 | + | 0.288539i | \(0.906831\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.03580 | + | 2.03580i | 0.0714865 | + | 0.0714865i | 0.741946 | − | 0.670460i | \(-0.233903\pi\) |
−0.670460 | + | 0.741946i | \(0.733903\pi\) | |||||||
\(812\) | 3.35118 | − | 0.111914i | 0.117603 | − | 0.00392742i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −47.0510 | + | 20.4157i | −1.64914 | + | 0.715571i | ||||
\(815\) | 3.10301 | − | 5.37456i | 0.108694 | − | 0.188263i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.06881 | + | 1.85123i | 0.0373928 | + | 0.0647663i | ||||
\(818\) | −22.6670 | − | 16.7994i | −0.792531 | − | 0.587377i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.9959 | − | 5.86815i | −0.383995 | − | 0.204925i | ||||
\(821\) | −2.92634 | + | 10.9213i | −0.102130 | + | 0.381155i | −0.998004 | − | 0.0631541i | \(-0.979884\pi\) |
0.895874 | + | 0.444309i | \(0.146551\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.22371 | − | 5.32531i | −0.321518 | − | 0.185629i | 0.330551 | − | 0.943788i | \(-0.392766\pi\) |
−0.652069 | + | 0.758159i | \(0.726099\pi\) | |||||||
\(824\) | 3.86835 | + | 4.55027i | 0.134760 | + | 0.158516i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.13016 | − | 4.07434i | 0.178501 | − | 0.141764i | ||||
\(827\) | −25.0775 | − | 25.0775i | −0.872029 | − | 0.872029i | 0.120665 | − | 0.992693i | \(-0.461497\pi\) |
−0.992693 | + | 0.120665i | \(0.961497\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.3779 | − | 21.3779i | 0.742484 | − | 0.742484i | −0.230571 | − | 0.973055i | \(-0.574059\pi\) |
0.973055 | + | 0.230571i | \(0.0740594\pi\) | |||||||
\(830\) | −6.84365 | − | 0.785017i | −0.237547 | − | 0.0272483i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −15.1228 | + | 33.5528i | −0.524289 | + | 1.16323i | ||||
\(833\) | 9.06227 | − | 15.6963i | 0.313989 | − | 0.543845i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.1761 | − | 3.79848i | −0.490584 | − | 0.131452i | ||||
\(836\) | 8.50290 | + | 27.9641i | 0.294079 | + | 0.967157i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.31503 | − | 42.4762i | −0.218149 | − | 1.46732i | ||||
\(839\) | 26.6311 | − | 15.3755i | 0.919407 | − | 0.530820i | 0.0359612 | − | 0.999353i | \(-0.488551\pi\) |
0.883446 | + | 0.468533i | \(0.155217\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.4376 | − | 11.2223i | −0.670261 | − | 0.386975i | ||||
\(842\) | −5.42590 | + | 13.7437i | −0.186989 | + | 0.473641i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.128903 | − | 3.85988i | −0.00443701 | − | 0.132863i | ||||
\(845\) | −5.05928 | + | 5.05928i | −0.174045 | + | 0.174045i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.0262 | 0.550665 | ||||||||
\(848\) | 13.9566 | + | 40.9377i | 0.479272 | + | 1.40581i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 15.1430 | − | 6.57067i | 0.519402 | − | 0.225372i | ||||
\(851\) | −6.38307 | − | 23.8220i | −0.218809 | − | 0.816606i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.3808 | + | 38.7416i | −0.355431 | + | 1.32649i | 0.524511 | + | 0.851404i | \(0.324248\pi\) |
−0.879942 | + | 0.475082i | \(0.842418\pi\) | |||||||
\(854\) | 3.58215 | − | 0.532566i | 0.122579 | − | 0.0182240i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.4548 | − | 26.2662i | −0.425695 | − | 0.897762i | ||||
\(857\) | −47.6428 | + | 27.5066i | −1.62745 | + | 0.939606i | −0.642594 | + | 0.766206i | \(0.722142\pi\) |
−0.984851 | + | 0.173400i | \(0.944525\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.6273 | − | 8.20655i | 1.04499 | − | 0.280004i | 0.304809 | − | 0.952413i | \(-0.401407\pi\) |
0.740179 | + | 0.672409i | \(0.234741\pi\) | |||||||
\(860\) | 0.345779 | − | 1.48739i | 0.0117910 | − | 0.0507196i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.9663 | − | 1.83146i | −0.543815 | − | 0.0623796i | ||||
\(863\) | −3.26635 | −0.111188 | −0.0555940 | − | 0.998453i | \(-0.517705\pi\) | ||||
−0.0555940 | + | 0.998453i | \(0.517705\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.7756 | 0.502386 | ||||||||
\(866\) | −13.5600 | − | 1.55543i | −0.460788 | − | 0.0528558i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.23836 | + | 5.32687i | −0.0420325 | + | 0.180806i | ||||
\(869\) | −93.9109 | + | 25.1634i | −3.18571 | + | 0.853608i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −47.9818 | + | 27.7023i | −1.62580 | + | 0.938657i | ||||
\(872\) | 20.7159 | − | 9.82291i | 0.701527 | − | 0.332646i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −13.9015 | + | 2.06676i | −0.470225 | + | 0.0699094i | ||||
\(875\) | 1.37121 | − | 5.11741i | 0.0463553 | − | 0.173000i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.53436 | + | 35.5827i | 0.321952 | + | 1.20154i | 0.917340 | + | 0.398104i | \(0.130332\pi\) |
−0.595388 | + | 0.803439i | \(0.703002\pi\) | |||||||
\(878\) | −20.3932 | + | 8.84875i | −0.688237 | + | 0.298631i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.21025 | − | 18.7387i | 0.310478 | − | 0.631681i | ||||
\(881\) | 24.2794 | 0.817994 | 0.408997 | − | 0.912536i | \(-0.365879\pi\) | ||||
0.408997 | + | 0.912536i | \(0.365879\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.8136 | − | 17.8136i | 0.599475 | − | 0.599475i | −0.340698 | − | 0.940173i | \(-0.610663\pi\) |
0.940173 | + | 0.340698i | \(0.110663\pi\) | |||||||
\(884\) | −0.847019 | − | 25.3633i | −0.0284883 | − | 0.853060i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.97448 | − | 25.2652i | 0.335099 | − | 0.848803i | ||||
\(887\) | −3.04467 | − | 1.75784i | −0.102230 | − | 0.0590225i | 0.448013 | − | 0.894027i | \(-0.352132\pi\) |
−0.550243 | + | 0.835004i | \(0.685465\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.8893 | + | 6.28692i | −0.365214 | + | 0.210857i | ||||
\(890\) | −0.931523 | − | 6.26561i | −0.0312247 | − | 0.210024i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.63561 | − | 25.1117i | −0.255659 | − | 0.840803i | ||||
\(893\) | 22.0660 | + | 5.91258i | 0.738412 | + | 0.197857i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.06883 | + | 7.04742i | −0.136006 | + | 0.235569i | ||||
\(896\) | −7.12813 | − | 2.01780i | −0.238134 | − | 0.0674099i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −49.6107 | − | 5.69071i | −1.65553 | − | 0.189902i | ||||
\(899\) | −7.56046 | + | 7.56046i | −0.252155 | + | 0.252155i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.0885 | − | 21.0885i | −0.702559 | − | 0.702559i | ||||
\(902\) | −46.9025 | + | 37.2496i | −1.56168 | + | 1.24028i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.91327 | + | 3.32681i | −0.130153 | + | 0.110648i | ||||
\(905\) | 16.6241 | + | 9.59793i | 0.552604 | + | 0.319046i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.82207 | − | 29.1924i | 0.259727 | − | 0.969316i | −0.705672 | − | 0.708539i | \(-0.749355\pi\) |
0.965399 | − | 0.260777i | \(-0.0839788\pi\) | |||||||
\(908\) | −7.34915 | − | 3.92198i | −0.243890 | − | 0.130156i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.99959 | − | 2.22312i | −0.0994354 | − | 0.0736956i | ||||
\(911\) | 25.9833 | + | 45.0044i | 0.860866 | + | 1.49106i | 0.871094 | + | 0.491116i | \(0.163411\pi\) |
−0.0102283 | + | 0.999948i | \(0.503256\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.5514 | + | 28.6679i | −0.547772 | + | 0.948769i | ||||
\(914\) | 0.847006 | − | 0.367522i | 0.0280165 | − | 0.0121565i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 55.8297 | − | 1.86446i | 1.84466 | − | 0.0616034i | ||||
\(917\) | −5.59735 | − | 5.59735i | −0.184841 | − | 0.184841i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 24.7771i | − | 0.817322i | −0.912686 | − | 0.408661i | \(-0.865996\pi\) | ||
0.912686 | − | 0.408661i | \(-0.134004\pi\) | |||||||
\(920\) | 8.26120 | + | 5.70561i | 0.272364 | + | 0.188108i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.32902 | + | 2.10385i | 0.175502 | + | 0.0692866i | ||||
\(923\) | 19.3226 | − | 5.17748i | 0.636011 | − | 0.170419i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.8904 | + | 6.66936i | 0.818391 | + | 0.219287i | ||||
\(926\) | −35.5306 | + | 47.9404i | −1.16761 | + | 1.57542i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.74422 | − | 10.7156i | −0.319870 | − | 0.351757i | ||||
\(929\) | −18.9049 | − | 32.7442i | −0.620249 | − | 1.07430i | −0.989439 | − | 0.144949i | \(-0.953698\pi\) |
0.369190 | − | 0.929354i | \(-0.379635\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.17306 | − | 15.5741i | −0.136767 | − | 0.510420i | ||||
\(932\) | 3.07094 | − | 13.2099i | 0.100592 | − | 0.432703i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.283285 | − | 0.224983i | 0.00926937 | − | 0.00736167i | ||||
\(935\) | 14.3975i | 0.470849i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.8873i | 0.617022i | 0.951221 | + | 0.308511i | \(0.0998307\pi\) | ||||
−0.951221 | + | 0.308511i | \(0.900169\pi\) | |||||||
\(938\) | −6.93594 | − | 8.73332i | −0.226466 | − | 0.285153i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.62689 | − | 13.8528i | −0.281378 | − | 0.451830i | ||||
\(941\) | −2.22556 | − | 8.30590i | −0.0725511 | − | 0.270765i | 0.920116 | − | 0.391647i | \(-0.128094\pi\) |
−0.992667 | + | 0.120882i | \(0.961428\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.4001 | − | 24.9417i | −0.468931 | − | 0.812213i | ||||
\(944\) | −27.7618 | − | 5.48418i | −0.903568 | − | 0.178495i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.89559 | − | 4.36946i | −0.191682 | − | 0.142063i | ||||
\(947\) | 29.3101 | + | 7.85363i | 0.952452 | + | 0.255209i | 0.701402 | − | 0.712766i | \(-0.252558\pi\) |
0.251049 | + | 0.967974i | \(0.419224\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.91764 | − | 0.781778i | 0.0947105 | − | 0.0253776i | ||||
\(950\) | 5.39234 | − | 13.6587i | 0.174951 | − | 0.443148i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.02485 | − | 0.919428i | 0.162856 | − | 0.0297988i | ||||
\(953\) | 53.9237i | 1.74676i | 0.487038 | + | 0.873381i | \(0.338077\pi\) | ||||
−0.487038 | + | 0.873381i | \(0.661923\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.14468 | + | 2.14468i | 0.0694002 | + | 0.0694002i | ||||
\(956\) | 11.1770 | − | 11.9493i | 0.361491 | − | 0.386469i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.85985 | − | 18.1141i | −0.253940 | − | 0.585241i | ||||
\(959\) | −1.08908 | + | 1.88635i | −0.0351684 | + | 0.0609134i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.78043 | + | 11.7441i | 0.218724 | + | 0.378840i | ||||
\(962\) | 23.5884 | − | 31.8272i | 0.760521 | − | 1.02615i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.301886 | − | 0.992831i | −0.00972309 | − | 0.0319769i | ||||
\(965\) | 2.23835 | − | 8.35362i | 0.0720549 | − | 0.268913i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.5688 | + | 10.1433i | 0.564973 | + | 0.326187i | 0.755139 | − | 0.655565i | \(-0.227569\pi\) |
−0.190166 | + | 0.981752i | \(0.560903\pi\) | |||||||
\(968\) | −44.8379 | − | 52.7420i | −1.44114 | − | 1.69519i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.71233 | + | 5.93349i | 0.151304 | + | 0.190513i | ||||
\(971\) | −8.82647 | − | 8.82647i | −0.283255 | − | 0.283255i | 0.551151 | − | 0.834406i | \(-0.314189\pi\) |
−0.834406 | + | 0.551151i | \(0.814189\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.01092 | + | 5.01092i | −0.160643 | + | 0.160643i | ||||
\(974\) | −0.472755 | + | 4.12140i | −0.0151481 | + | 0.132058i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.7748 | − | 10.2988i | −0.376901 | − | 0.329657i | ||||
\(977\) | −21.4183 | + | 37.0976i | −0.685233 | + | 1.18686i | 0.288131 | + | 0.957591i | \(0.406966\pi\) |
−0.973364 | + | 0.229267i | \(0.926367\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29.4031 | − | 7.87854i | −0.939728 | − | 0.251799i | ||||
\(980\) | −5.42294 | + | 10.1617i | −0.173230 | + | 0.324603i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −25.7508 | + | 3.82843i | −0.821741 | + | 0.122170i | ||||
\(983\) | 16.9469 | − | 9.78431i | 0.540523 | − | 0.312071i | −0.204768 | − | 0.978811i | \(-0.565644\pi\) |
0.745291 | + | 0.666740i | \(0.232311\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.31635 | − | 3.06940i | −0.169393 | − | 0.0977991i | ||||
\(986\) | 9.28931 | + | 3.66733i | 0.295832 | + | 0.116792i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16.4873 | − | 15.4217i | −0.524530 | − | 0.490628i | ||||
\(989\) | 2.49508 | − | 2.49508i | 0.0793390 | − | 0.0793390i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.7726 | −0.850459 | −0.425230 | − | 0.905086i | \(-0.639807\pi\) | ||||
−0.425230 | + | 0.905086i | \(0.639807\pi\) | |||||||
\(992\) | 20.9954 | − | 10.8281i | 0.666604 | − | 0.343791i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.60282 | + | 3.69394i | 0.0508385 | + | 0.117165i | ||||
\(995\) | 4.40015 | + | 16.4216i | 0.139494 | + | 0.520599i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.37990 | − | 8.88189i | 0.0753720 | − | 0.281292i | −0.917945 | − | 0.396707i | \(-0.870153\pi\) |
0.993317 | + | 0.115415i | \(0.0368196\pi\) | |||||||
\(998\) | −3.80916 | − | 25.6212i | −0.120577 | − | 0.811024i | ||||
\(999\) | 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 | 432.2.y.e.37.18 | 72 | ||
3.2 | odd | 2 | 144.2.x.e.85.1 | yes | 72 | ||
4.3 | odd | 2 | 1728.2.bc.e.1009.12 | 72 | |||
9.2 | odd | 6 | 144.2.x.e.133.11 | yes | 72 | ||
9.7 | even | 3 | inner | 432.2.y.e.181.8 | 72 | ||
12.11 | even | 2 | 576.2.bb.e.49.17 | 72 | |||
16.3 | odd | 4 | 1728.2.bc.e.145.7 | 72 | |||
16.13 | even | 4 | inner | 432.2.y.e.253.8 | 72 | ||
36.7 | odd | 6 | 1728.2.bc.e.1585.7 | 72 | |||
36.11 | even | 6 | 576.2.bb.e.241.9 | 72 | |||
48.29 | odd | 4 | 144.2.x.e.13.11 | ✓ | 72 | ||
48.35 | even | 4 | 576.2.bb.e.337.9 | 72 | |||
144.29 | odd | 12 | 144.2.x.e.61.1 | yes | 72 | ||
144.61 | even | 12 | inner | 432.2.y.e.397.18 | 72 | ||
144.83 | even | 12 | 576.2.bb.e.529.17 | 72 | |||
144.115 | odd | 12 | 1728.2.bc.e.721.12 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.e.13.11 | ✓ | 72 | 48.29 | odd | 4 | ||
144.2.x.e.61.1 | yes | 72 | 144.29 | odd | 12 | ||
144.2.x.e.85.1 | yes | 72 | 3.2 | odd | 2 | ||
144.2.x.e.133.11 | yes | 72 | 9.2 | odd | 6 | ||
432.2.y.e.37.18 | 72 | 1.1 | even | 1 | trivial | ||
432.2.y.e.181.8 | 72 | 9.7 | even | 3 | inner | ||
432.2.y.e.253.8 | 72 | 16.13 | even | 4 | inner | ||
432.2.y.e.397.18 | 72 | 144.61 | even | 12 | inner | ||
576.2.bb.e.49.17 | 72 | 12.11 | even | 2 | |||
576.2.bb.e.241.9 | 72 | 36.11 | even | 6 | |||
576.2.bb.e.337.9 | 72 | 48.35 | even | 4 | |||
576.2.bb.e.529.17 | 72 | 144.83 | even | 12 | |||
1728.2.bc.e.145.7 | 72 | 16.3 | odd | 4 | |||
1728.2.bc.e.721.12 | 72 | 144.115 | odd | 12 | |||
1728.2.bc.e.1009.12 | 72 | 4.3 | odd | 2 | |||
1728.2.bc.e.1585.7 | 72 | 36.7 | odd | 6 |