Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(136,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 2, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.136");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.et (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 273) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 514.5 | ||
Character | \(\chi\) | \(=\) | 819.514 |
Dual form | 819.2.et.c.145.5 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.111217 | − | 0.111217i | −0.0786424 | − | 0.0786424i | 0.666691 | − | 0.745334i | \(-0.267710\pi\) |
−0.745334 | + | 0.666691i | \(0.767710\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.97526i | − | 0.987631i | ||||||
\(5\) | 2.13060 | + | 0.570893i | 0.952834 | + | 0.255311i | 0.701564 | − | 0.712606i | \(-0.252485\pi\) |
0.251270 | + | 0.967917i | \(0.419152\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.399954 | + | 2.61535i | −0.151168 | + | 0.988508i | ||||
\(8\) | −0.442117 | + | 0.442117i | −0.156312 | + | 0.156312i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.173466 | − | 0.300452i | −0.0548548 | − | 0.0950114i | ||||
\(11\) | 5.42348 | + | 1.45322i | 1.63524 | + | 0.438162i | 0.955428 | − | 0.295223i | \(-0.0953940\pi\) |
0.679814 | + | 0.733385i | \(0.262061\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.34030 | − | 3.34718i | −0.371734 | − | 0.928339i | ||||
\(14\) | 0.335353 | − | 0.246390i | 0.0896268 | − | 0.0658504i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.85218 | −0.963045 | ||||||||
\(17\) | 3.59112 | 0.870974 | 0.435487 | − | 0.900195i | \(-0.356576\pi\) | ||||
0.435487 | + | 0.900195i | \(0.356576\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.24688 | + | 4.65341i | 0.286053 | + | 1.06757i | 0.948066 | + | 0.318073i | \(0.103036\pi\) |
−0.662013 | + | 0.749493i | \(0.730298\pi\) | |||||||
\(20\) | 1.12766 | − | 4.20850i | 0.252153 | − | 0.941048i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.441561 | − | 0.764807i | −0.0941412 | − | 0.163057i | ||||
\(23\) | 4.45466i | 0.928860i | 0.885610 | + | 0.464430i | \(0.153741\pi\) | ||||
−0.885610 | + | 0.464430i | \(0.846259\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.116582 | − | 0.0673085i | −0.0233164 | − | 0.0134617i | ||||
\(26\) | −0.223198 | + | 0.521328i | −0.0437728 | + | 0.102241i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.16599 | + | 0.790013i | 0.976281 | + | 0.149298i | ||||
\(29\) | −1.02264 | + | 1.77127i | −0.189900 | + | 0.328917i | −0.945217 | − | 0.326443i | \(-0.894150\pi\) |
0.755317 | + | 0.655360i | \(0.227483\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.643610 | + | 2.40198i | 0.115596 | + | 0.431409i | 0.999331 | − | 0.0365784i | \(-0.0116459\pi\) |
−0.883735 | + | 0.467988i | \(0.844979\pi\) | |||||||
\(32\) | 1.31266 | + | 1.31266i | 0.232048 | + | 0.232048i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.399394 | − | 0.399394i | −0.0684955 | − | 0.0684955i | ||||
\(35\) | −2.34523 | + | 5.34393i | −0.396415 | + | 0.903289i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.22320 | − | 7.22320i | 1.18749 | − | 1.18749i | 0.209727 | − | 0.977760i | \(-0.432743\pi\) |
0.977760 | − | 0.209727i | \(-0.0672574\pi\) | |||||||
\(38\) | 0.378865 | − | 0.656213i | 0.0614600 | − | 0.106452i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.19438 | + | 0.689574i | −0.188848 | + | 0.109031i | ||||
\(41\) | −1.34422 | − | 5.01671i | −0.209932 | − | 0.783479i | −0.987889 | − | 0.155161i | \(-0.950410\pi\) |
0.777957 | − | 0.628318i | \(-0.216256\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.12300 | − | 2.38042i | 0.628752 | − | 0.363010i | −0.151517 | − | 0.988455i | \(-0.548416\pi\) |
0.780268 | + | 0.625445i | \(0.215082\pi\) | |||||||
\(44\) | 2.87049 | − | 10.7128i | 0.432742 | − | 1.61502i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.495434 | − | 0.495434i | 0.0730477 | − | 0.0730477i | ||||
\(47\) | 1.22397 | − | 4.56791i | 0.178534 | − | 0.666298i | −0.817389 | − | 0.576087i | \(-0.804579\pi\) |
0.995923 | − | 0.0902113i | \(-0.0287542\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.68007 | − | 2.09204i | −0.954296 | − | 0.298862i | ||||
\(50\) | 0.00548003 | + | 0.0204517i | 0.000774993 | + | 0.00289231i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.61155 | + | 2.64745i | −0.916857 | + | 0.367136i | ||||
\(53\) | −0.201475 | + | 0.348965i | −0.0276747 | + | 0.0479340i | −0.879531 | − | 0.475841i | \(-0.842144\pi\) |
0.851856 | + | 0.523776i | \(0.175477\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.7257 | + | 6.19246i | 1.44625 | + | 0.834991i | ||||
\(56\) | −0.979463 | − | 1.33312i | −0.130886 | − | 0.178145i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.310731 | − | 0.0832601i | 0.0408010 | − | 0.0109326i | ||||
\(59\) | 1.93268 | + | 1.93268i | 0.251614 | + | 0.251614i | 0.821632 | − | 0.570018i | \(-0.193064\pi\) |
−0.570018 | + | 0.821632i | \(0.693064\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.61092 | + | 0.930065i | 0.206257 | + | 0.119083i | 0.599571 | − | 0.800322i | \(-0.295338\pi\) |
−0.393314 | + | 0.919404i | \(0.628671\pi\) | |||||||
\(62\) | 0.195561 | − | 0.338722i | 0.0248363 | − | 0.0430178i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.41238i | 0.926548i | ||||||||
\(65\) | −0.944776 | − | 7.89667i | −0.117185 | − | 0.979461i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.78441 | − | 6.65951i | 0.218000 | − | 0.813589i | −0.767088 | − | 0.641542i | \(-0.778295\pi\) |
0.985089 | − | 0.172047i | \(-0.0550381\pi\) | |||||||
\(68\) | − | 7.09340i | − | 0.860201i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.855166 | − | 0.333507i | 0.102212 | − | 0.0398617i | ||||
\(71\) | 3.63562 | − | 13.5683i | 0.431469 | − | 1.61026i | −0.317909 | − | 0.948121i | \(-0.602981\pi\) |
0.749378 | − | 0.662142i | \(-0.230353\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.45744 | + | 1.19437i | −0.521704 | + | 0.139790i | −0.510055 | − | 0.860142i | \(-0.670375\pi\) |
−0.0116493 | + | 0.999932i | \(0.503708\pi\) | |||||||
\(74\) | −1.60669 | −0.186773 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.19171 | − | 2.46291i | 1.05436 | − | 0.282515i | ||||
\(77\) | −5.96981 | + | 13.6031i | −0.680323 | + | 1.55021i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.45889 | − | 4.25893i | −0.276647 | − | 0.479167i | 0.693902 | − | 0.720069i | \(-0.255890\pi\) |
−0.970549 | + | 0.240902i | \(0.922557\pi\) | |||||||
\(80\) | −8.20746 | − | 2.19918i | −0.917622 | − | 0.245876i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.408443 | + | 0.707445i | −0.0451050 | + | 0.0781242i | ||||
\(83\) | −10.3390 | + | 10.3390i | −1.13485 | + | 1.13485i | −0.145496 | + | 0.989359i | \(0.546478\pi\) |
−0.989359 | + | 0.145496i | \(0.953522\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.65124 | + | 2.05014i | 0.829894 | + | 0.222369i | ||||
\(86\) | −0.723291 | − | 0.193805i | −0.0779945 | − | 0.0208986i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.04031 | + | 1.75532i | −0.324098 | + | 0.187118i | ||||
\(89\) | 12.7764 | + | 12.7764i | 1.35430 | + | 1.35430i | 0.880787 | + | 0.473513i | \(0.157014\pi\) |
0.473513 | + | 0.880787i | \(0.342986\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.29008 | − | 2.16664i | 0.973865 | − | 0.227126i | ||||
\(92\) | 8.79911 | 0.917371 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.644155 | + | 0.371903i | −0.0664396 | + | 0.0383589i | ||||
\(95\) | 10.6264i | 1.09025i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.52628 | − | 0.944864i | −0.358040 | − | 0.0959365i | 0.0753153 | − | 0.997160i | \(-0.476004\pi\) |
−0.433355 | + | 0.901223i | \(0.642670\pi\) | |||||||
\(98\) | 0.510268 | + | 0.975608i | 0.0515449 | + | 0.0985513i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.132952 | + | 0.230280i | −0.0132952 | + | 0.0230280i | ||||
\(101\) | 4.85620 | + | 8.41119i | 0.483210 | + | 0.836945i | 0.999814 | − | 0.0192798i | \(-0.00613733\pi\) |
−0.516604 | + | 0.856225i | \(0.672804\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.12086 | − | 5.40548i | −0.307507 | − | 0.532618i | 0.670309 | − | 0.742082i | \(-0.266161\pi\) |
−0.977816 | + | 0.209464i | \(0.932828\pi\) | |||||||
\(104\) | 2.07241 | + | 0.887272i | 0.203217 | + | 0.0870042i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.0612184 | − | 0.0164034i | 0.00594605 | − | 0.00159324i | ||||
\(107\) | 4.47949 | 0.433049 | 0.216525 | − | 0.976277i | \(-0.430528\pi\) | ||||
0.216525 | + | 0.976277i | \(0.430528\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.4448 | + | 3.60252i | −1.28778 | + | 0.345059i | −0.836815 | − | 0.547485i | \(-0.815585\pi\) |
−0.450961 | + | 0.892544i | \(0.648919\pi\) | |||||||
\(110\) | −0.504169 | − | 1.88158i | −0.0480706 | − | 0.179402i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.54069 | − | 10.0748i | 0.145582 | − | 0.951978i | ||||
\(113\) | −4.28714 | − | 7.42555i | −0.403301 | − | 0.698537i | 0.590821 | − | 0.806802i | \(-0.298804\pi\) |
−0.994122 | + | 0.108265i | \(0.965470\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.54313 | + | 9.49110i | −0.237148 | + | 0.885049i | ||||
\(116\) | 3.49872 | + | 2.01999i | 0.324848 | + | 0.187551i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 0.429895i | − | 0.0395750i | ||||||
\(119\) | −1.43628 | + | 9.39202i | −0.131664 | + | 0.860965i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.7761 | + | 10.2630i | 1.61601 | + | 0.933001i | ||||
\(122\) | −0.0757227 | − | 0.282601i | −0.00685561 | − | 0.0255855i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.74455 | − | 1.27130i | 0.426073 | − | 0.114166i | ||||
\(125\) | −8.00851 | − | 8.00851i | −0.716303 | − | 0.716303i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.25421 | − | 4.76557i | −0.732443 | − | 0.422876i | 0.0868725 | − | 0.996219i | \(-0.472313\pi\) |
−0.819315 | + | 0.573344i | \(0.805646\pi\) | |||||||
\(128\) | 3.44971 | − | 3.44971i | 0.304914 | − | 0.304914i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.773169 | + | 0.983320i | −0.0678114 | + | 0.0862428i | ||||
\(131\) | −3.05542 | + | 1.76405i | −0.266954 | + | 0.154126i | −0.627502 | − | 0.778615i | \(-0.715923\pi\) |
0.360549 | + | 0.932740i | \(0.382589\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.6690 | + | 1.39987i | −1.09854 | + | 0.121384i | ||||
\(134\) | −0.939108 | + | 0.542194i | −0.0811266 | + | 0.0468385i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.58769 | + | 1.58769i | −0.136144 | + | 0.136144i | ||||
\(137\) | −7.14511 | + | 7.14511i | −0.610448 | + | 0.610448i | −0.943063 | − | 0.332615i | \(-0.892069\pi\) |
0.332615 | + | 0.943063i | \(0.392069\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.05971 | + | 5.23063i | −0.768435 | + | 0.443656i | −0.832316 | − | 0.554302i | \(-0.812985\pi\) |
0.0638813 | + | 0.997958i | \(0.479652\pi\) | |||||||
\(140\) | 10.5557 | + | 4.63243i | 0.892116 | + | 0.391512i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.91337 | + | 1.10469i | −0.160567 | + | 0.0927032i | ||||
\(143\) | −2.40494 | − | 20.1011i | −0.201111 | − | 1.68094i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.19005 | + | 3.19005i | −0.264919 | + | 0.264919i | ||||
\(146\) | 0.628578 | + | 0.362909i | 0.0520214 | + | 0.0300346i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −14.2677 | − | 14.2677i | −1.17280 | − | 1.17280i | ||||
\(149\) | −0.428100 | + | 0.114709i | −0.0350713 | + | 0.00939732i | −0.276312 | − | 0.961068i | \(-0.589112\pi\) |
0.241241 | + | 0.970465i | \(0.422446\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.55428 | + | 9.53270i | 0.207864 | + | 0.775760i | 0.988557 | + | 0.150845i | \(0.0481996\pi\) |
−0.780693 | + | 0.624915i | \(0.785134\pi\) | |||||||
\(152\) | −2.60862 | − | 1.50609i | −0.211587 | − | 0.122160i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.17684 | − | 0.848949i | 0.175415 | − | 0.0684102i | ||||
\(155\) | 5.48511i | 0.440574i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.2252 | − | 11.0997i | −1.53434 | − | 0.885852i | −0.999154 | − | 0.0411178i | \(-0.986908\pi\) |
−0.535186 | − | 0.844734i | \(-0.679759\pi\) | |||||||
\(158\) | −0.200195 | + | 0.747137i | −0.0159266 | + | 0.0594390i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.04737 | + | 3.54615i | 0.161859 | + | 0.280348i | ||||
\(161\) | −11.6505 | − | 1.78166i | −0.918185 | − | 0.140414i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.722700 | − | 2.69715i | −0.0566062 | − | 0.211257i | 0.931830 | − | 0.362895i | \(-0.118212\pi\) |
−0.988436 | + | 0.151638i | \(0.951545\pi\) | |||||||
\(164\) | −9.90932 | + | 2.65519i | −0.773788 | + | 0.207336i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.29975 | 0.178495 | ||||||||
\(167\) | −2.34772 | + | 0.629070i | −0.181672 | + | 0.0486789i | −0.348508 | − | 0.937306i | \(-0.613312\pi\) |
0.166836 | + | 0.985985i | \(0.446645\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.40717 | + | 8.97247i | −0.723628 | + | 0.690190i | ||||
\(170\) | −0.622938 | − | 1.07896i | −0.0477772 | − | 0.0827525i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.70194 | − | 8.14400i | −0.358520 | − | 0.620974i | ||||
\(173\) | −5.37379 | + | 9.30768i | −0.408562 | + | 0.707650i | −0.994729 | − | 0.102540i | \(-0.967303\pi\) |
0.586167 | + | 0.810190i | \(0.300636\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.222662 | − | 0.277981i | 0.0168317 | − | 0.0210134i | ||||
\(176\) | −20.8922 | − | 5.59806i | −1.57481 | − | 0.421970i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 2.84192i | − | 0.213011i | ||||||
\(179\) | −16.5020 | + | 9.52742i | −1.23342 | + | 0.712113i | −0.967740 | − | 0.251950i | \(-0.918928\pi\) |
−0.265675 | + | 0.964063i | \(0.585595\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.5472 | −1.52726 | −0.763632 | − | 0.645652i | \(-0.776586\pi\) | ||||
−0.763632 | + | 0.645652i | \(0.776586\pi\) | |||||||
\(182\) | −1.27418 | − | 0.792248i | −0.0944488 | − | 0.0587253i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.96948 | − | 1.96948i | −0.145192 | − | 0.145192i | ||||
\(185\) | 19.5134 | − | 11.2661i | 1.43466 | − | 0.828299i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.4764 | + | 5.21868i | 1.42425 | + | 0.381628i | ||||
\(188\) | −9.02281 | − | 2.41766i | −0.658056 | − | 0.176326i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.18184 | − | 1.18184i | 0.0857395 | − | 0.0857395i | ||||
\(191\) | 9.70429 | − | 16.8083i | 0.702178 | − | 1.21621i | −0.265522 | − | 0.964105i | \(-0.585544\pi\) |
0.967700 | − | 0.252103i | \(-0.0811222\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.4662 | − | 4.68005i | −1.25724 | − | 0.336877i | −0.432112 | − | 0.901820i | \(-0.642232\pi\) |
−0.825130 | + | 0.564943i | \(0.808898\pi\) | |||||||
\(194\) | 0.287098 | + | 0.497268i | 0.0206124 | + | 0.0357018i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.13232 | + | 13.1949i | −0.295165 | + | 0.942492i | ||||
\(197\) | 12.0770 | − | 3.23603i | 0.860453 | − | 0.230558i | 0.198498 | − | 0.980101i | \(-0.436394\pi\) |
0.661955 | + | 0.749544i | \(0.269727\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.9422 | 1.48455 | 0.742276 | − | 0.670094i | \(-0.233746\pi\) | ||||
0.742276 | + | 0.670094i | \(0.233746\pi\) | |||||||
\(200\) | 0.0813010 | − | 0.0217845i | 0.00574885 | − | 0.00154040i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.395375 | − | 1.47556i | 0.0278185 | − | 0.103820i | ||||
\(203\) | −4.22348 | − | 3.38299i | −0.296430 | − | 0.237440i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 11.4560i | − | 0.800123i | ||||||
\(206\) | −0.254089 | + | 0.948274i | −0.0177032 | + | 0.0660694i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.16310 | + | 12.8939i | 0.357996 | + | 0.894033i | ||||
\(209\) | 27.0497i | 1.87107i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.85575 | − | 15.3386i | 0.609655 | − | 1.05595i | −0.381642 | − | 0.924310i | \(-0.624641\pi\) |
0.991297 | − | 0.131643i | \(-0.0420253\pi\) | |||||||
\(212\) | 0.689297 | + | 0.397966i | 0.0473411 | + | 0.0273324i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.498196 | − | 0.498196i | −0.0340560 | − | 0.0340560i | ||||
\(215\) | 10.1434 | − | 2.71792i | 0.691776 | − | 0.185361i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.53944 | + | 0.722580i | −0.443926 | + | 0.0490519i | ||||
\(218\) | 1.89595 | + | 1.09463i | 0.128410 | + | 0.0741375i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 12.2317 | − | 21.1860i | 0.824663 | − | 1.42836i | ||||
\(221\) | −4.81319 | − | 12.0201i | −0.323770 | − | 0.808560i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.51328 | + | 13.1117i | 0.235267 | + | 0.878027i | 0.978029 | + | 0.208471i | \(0.0668487\pi\) |
−0.742762 | + | 0.669556i | \(0.766485\pi\) | |||||||
\(224\) | −3.95807 | + | 2.90806i | −0.264460 | + | 0.194303i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.349045 | + | 1.30265i | −0.0232181 | + | 0.0866511i | ||||
\(227\) | 5.69257 | − | 5.69257i | 0.377829 | − | 0.377829i | −0.492489 | − | 0.870319i | \(-0.663913\pi\) |
0.870319 | + | 0.492489i | \(0.163913\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.157795 | − | 0.588900i | 0.0104274 | − | 0.0389156i | −0.960516 | − | 0.278224i | \(-0.910254\pi\) |
0.970944 | + | 0.239309i | \(0.0769208\pi\) | |||||||
\(230\) | 1.33841 | − | 0.772732i | 0.0882523 | − | 0.0509525i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.330981 | − | 1.23524i | −0.0217299 | − | 0.0810973i | ||||
\(233\) | −20.5734 | + | 11.8780i | −1.34781 | + | 0.778157i | −0.987939 | − | 0.154846i | \(-0.950512\pi\) |
−0.359868 | + | 0.933003i | \(0.617178\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.21557 | − | 9.03364i | 0.340227 | − | 0.589290i | ||||
\(236\) | 3.81755 | − | 3.81755i | 0.248502 | − | 0.248502i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.20429 | − | 0.884814i | 0.0780627 | − | 0.0573540i | ||||
\(239\) | −8.02410 | − | 8.02410i | −0.519036 | − | 0.519036i | 0.398244 | − | 0.917280i | \(-0.369620\pi\) |
−0.917280 | + | 0.398244i | \(0.869620\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.76834 | + | 9.76834i | 0.629234 | + | 0.629234i | 0.947875 | − | 0.318641i | \(-0.103227\pi\) |
−0.318641 | + | 0.947875i | \(0.603227\pi\) | |||||||
\(242\) | −0.835579 | − | 3.11842i | −0.0537131 | − | 0.200460i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.83712 | − | 3.18199i | 0.117610 | − | 0.203706i | ||||
\(245\) | −13.0382 | − | 8.27090i | −0.832983 | − | 0.528409i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.9046 | − | 10.4105i | 0.884728 | − | 0.662405i | ||||
\(248\) | −1.34651 | − | 0.777407i | −0.0855034 | − | 0.0493654i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.78137i | 0.112663i | ||||||||
\(251\) | 10.1546 | + | 17.5882i | 0.640950 | + | 1.11016i | 0.985221 | + | 0.171287i | \(0.0547927\pi\) |
−0.344271 | + | 0.938870i | \(0.611874\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.47359 | + | 24.1598i | −0.406991 | + | 1.51891i | ||||
\(254\) | 0.387996 | + | 1.44802i | 0.0243450 | + | 0.0908570i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.0574 | 0.878589 | ||||||||
\(257\) | 24.6914 | 1.54021 | 0.770105 | − | 0.637917i | \(-0.220204\pi\) | ||||
0.770105 | + | 0.637917i | \(0.220204\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.0022 | + | 21.7801i | 0.994330 | + | 1.35335i | ||||
\(260\) | −15.5980 | + | 1.86618i | −0.967346 | + | 0.115736i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.536008 | + | 0.143623i | 0.0331147 | + | 0.00887305i | ||||
\(263\) | −15.1818 | − | 26.2956i | −0.936148 | − | 1.62146i | −0.772573 | − | 0.634925i | \(-0.781031\pi\) |
−0.163575 | − | 0.986531i | \(-0.552302\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.628485 | + | 0.628485i | −0.0386075 | + | 0.0386075i | ||||
\(266\) | 1.56470 | + | 1.25332i | 0.0959377 | + | 0.0768458i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.1543 | − | 3.52468i | −0.803525 | − | 0.215304i | ||||
\(269\) | 5.95292i | 0.362956i | 0.983395 | + | 0.181478i | \(0.0580882\pi\) | ||||
−0.983395 | + | 0.181478i | \(0.941912\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.55925 | − | 9.55925i | −0.580683 | − | 0.580683i | 0.354408 | − | 0.935091i | \(-0.384683\pi\) |
−0.935091 | + | 0.354408i | \(0.884683\pi\) | |||||||
\(272\) | −13.8336 | −0.838788 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.58932 | 0.0960141 | ||||||||
\(275\) | −0.534466 | − | 0.534466i | −0.0322295 | − | 0.0322295i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.5559i | 0.694326i | 0.937805 | + | 0.347163i | \(0.112855\pi\) | ||||
−0.937805 | + | 0.347163i | \(0.887145\pi\) | |||||||
\(278\) | 1.58933 | + | 0.425860i | 0.0953216 | + | 0.0255414i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.32578 | − | 3.39951i | −0.0792304 | − | 0.203159i | ||||
\(281\) | −22.1034 | + | 22.1034i | −1.31858 | + | 1.31858i | −0.403672 | + | 0.914904i | \(0.632266\pi\) |
−0.914904 | + | 0.403672i | \(0.867734\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.2897 | + | 19.5544i | 0.671105 | + | 1.16239i | 0.977591 | + | 0.210513i | \(0.0675136\pi\) |
−0.306486 | + | 0.951875i | \(0.599153\pi\) | |||||||
\(284\) | −26.8010 | − | 7.18130i | −1.59035 | − | 0.426132i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.96812 | + | 2.50306i | −0.116377 | + | 0.148009i | ||||
\(287\) | 13.6581 | − | 1.50916i | 0.806210 | − | 0.0890828i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.10387 | −0.241404 | ||||||||
\(290\) | 0.709577 | 0.0416678 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.35919 | + | 8.80461i | 0.138061 | + | 0.515251i | ||||
\(293\) | 0.143904 | − | 0.537058i | 0.00840697 | − | 0.0313752i | −0.961595 | − | 0.274473i | \(-0.911497\pi\) |
0.970002 | + | 0.243097i | \(0.0781634\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.01442 | + | 5.22113i | 0.175506 | + | 0.303986i | ||||
\(296\) | 6.38700i | 0.371237i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.0603696 | + | 0.0348544i | 0.00349712 | + | 0.00201906i | ||||
\(299\) | 14.9105 | − | 5.97059i | 0.862297 | − | 0.345288i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.57660 | + | 11.7351i | 0.263791 | + | 0.676402i | ||||
\(302\) | 0.776119 | − | 1.34428i | 0.0446607 | − | 0.0773545i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.80320 | − | 17.9258i | −0.275482 | − | 1.02811i | ||||
\(305\) | 2.90126 | + | 2.90126i | 0.166126 | + | 0.166126i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.01312 | − | 5.01312i | −0.286114 | − | 0.286114i | 0.549427 | − | 0.835541i | \(-0.314846\pi\) |
−0.835541 | + | 0.549427i | \(0.814846\pi\) | |||||||
\(308\) | 26.8696 | + | 11.7919i | 1.53104 | + | 0.671908i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.610037 | − | 0.610037i | 0.0346478 | − | 0.0346478i | ||||
\(311\) | −0.404846 | + | 0.701214i | −0.0229567 | + | 0.0397622i | −0.877276 | − | 0.479987i | \(-0.840641\pi\) |
0.854319 | + | 0.519749i | \(0.173975\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.914764 | − | 0.528139i | 0.0517055 | − | 0.0298522i | −0.473924 | − | 0.880566i | \(-0.657163\pi\) |
0.525630 | + | 0.850713i | \(0.323830\pi\) | |||||||
\(314\) | 0.903699 | + | 3.37265i | 0.0509987 | + | 0.190330i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.41250 | + | 4.85696i | −0.473240 | + | 0.273225i | ||||
\(317\) | 8.45663 | − | 31.5606i | 0.474972 | − | 1.77262i | −0.146531 | − | 0.989206i | \(-0.546811\pi\) |
0.621503 | − | 0.783412i | \(-0.286522\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.12033 | + | 8.12033i | −0.454651 | + | 0.454651i | ||||
\(320\) | −4.23168 | + | 15.7928i | −0.236558 | + | 0.882846i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.09758 | + | 1.49388i | 0.0611658 | + | 0.0832508i | ||||
\(323\) | 4.47769 | + | 16.7110i | 0.249145 | + | 0.929822i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.0690384 | + | 0.480434i | −0.00382956 | + | 0.0266497i | ||||
\(326\) | −0.219593 | + | 0.380346i | −0.0121621 | + | 0.0210654i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.81228 | + | 1.62367i | 0.155282 | + | 0.0896521i | ||||
\(329\) | 11.4571 | + | 5.02805i | 0.631652 | + | 0.277205i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.2335 | + | 6.22540i | −1.27703 | + | 0.342179i | −0.832720 | − | 0.553695i | \(-0.813217\pi\) |
−0.444309 | + | 0.895874i | \(0.646551\pi\) | |||||||
\(332\) | 20.4223 | + | 20.4223i | 1.12082 | + | 1.12082i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.331070 | + | 0.191143i | 0.0181153 | + | 0.0104589i | ||||
\(335\) | 7.60374 | − | 13.1701i | 0.415436 | − | 0.719557i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 26.8501i | − | 1.46262i | −0.682046 | − | 0.731310i | \(-0.738909\pi\) | ||
0.682046 | − | 0.731310i | \(-0.261091\pi\) | |||||||
\(338\) | 2.04413 | + | 0.0483460i | 0.111186 | + | 0.00262968i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.04957 | − | 15.1132i | 0.219619 | − | 0.819629i | ||||
\(341\) | 13.9624i | 0.756108i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.14312 | − | 16.6340i | 0.439687 | − | 0.898151i | ||||
\(344\) | −0.770426 | + | 2.87527i | −0.0415386 | + | 0.155024i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.63283 | − | 0.437516i | 0.0877815 | − | 0.0235210i | ||||
\(347\) | −23.0516 | −1.23747 | −0.618737 | − | 0.785598i | \(-0.712355\pi\) | ||||
−0.618737 | + | 0.785598i | \(0.712355\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.97543 | − | 1.60111i | 0.319858 | − | 0.0857056i | −0.0953181 | − | 0.995447i | \(-0.530387\pi\) |
0.415176 | + | 0.909741i | \(0.363720\pi\) | |||||||
\(350\) | −0.0556802 | + | 0.00615242i | −0.00297623 | + | 0.000328861i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.21162 | + | 9.02679i | 0.277780 | + | 0.481129i | ||||
\(353\) | −27.1270 | − | 7.26865i | −1.44382 | − | 0.386871i | −0.549952 | − | 0.835196i | \(-0.685354\pi\) |
−0.893871 | + | 0.448325i | \(0.852021\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.4921 | − | 26.8331i | 0.822236 | − | 1.42416i | ||||
\(356\) | 25.2368 | − | 25.2368i | 1.33755 | − | 1.33755i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.89491 | + | 0.775689i | 0.153001 | + | 0.0409965i | ||||
\(359\) | 7.64083 | + | 2.04735i | 0.403268 | + | 0.108055i | 0.454751 | − | 0.890619i | \(-0.349728\pi\) |
−0.0514834 | + | 0.998674i | \(0.516395\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.64506 | + | 2.10447i | −0.191845 | + | 0.110762i | ||||
\(362\) | 2.28520 | + | 2.28520i | 0.120108 | + | 0.120108i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.27969 | − | 18.3503i | −0.224317 | − | 0.961819i | ||||
\(365\) | −10.1789 | −0.532787 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.92031 | + | 4.57279i | −0.413437 | + | 0.238698i | −0.692265 | − | 0.721643i | \(-0.743387\pi\) |
0.278829 | + | 0.960341i | \(0.410054\pi\) | |||||||
\(368\) | − | 17.1601i | − | 0.894534i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.42321 | − | 0.917246i | −0.177964 | − | 0.0476854i | ||||
\(371\) | −0.832084 | − | 0.666497i | −0.0431996 | − | 0.0346028i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.4024 | − | 28.4099i | 0.849286 | − | 1.47101i | −0.0325601 | − | 0.999470i | \(-0.510366\pi\) |
0.881846 | − | 0.471537i | \(-0.156301\pi\) | |||||||
\(374\) | −1.58570 | − | 2.74651i | −0.0819946 | − | 0.142019i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.47841 | + | 2.56069i | 0.0762433 | + | 0.132057i | ||||
\(377\) | 7.29941 | + | 1.04893i | 0.375939 | + | 0.0540224i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.9754 | + | 4.54854i | −0.871967 | + | 0.233643i | −0.666938 | − | 0.745113i | \(-0.732395\pi\) |
−0.205029 | + | 0.978756i | \(0.565729\pi\) | |||||||
\(380\) | 20.9899 | 1.07676 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.94866 | + | 0.790090i | −0.150866 | + | 0.0404245i | ||||
\(383\) | 7.96025 | + | 29.7081i | 0.406750 | + | 1.51801i | 0.800806 | + | 0.598924i | \(0.204405\pi\) |
−0.394056 | + | 0.919087i | \(0.628928\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.4852 | + | 25.5746i | −1.04402 | + | 1.30340i | ||||
\(386\) | 1.42204 | + | 2.46304i | 0.0723797 | + | 0.125365i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.86635 | + | 6.96533i | −0.0947498 | + | 0.353611i | ||||
\(389\) | 13.1147 | + | 7.57176i | 0.664940 | + | 0.383903i | 0.794157 | − | 0.607713i | \(-0.207913\pi\) |
−0.129217 | + | 0.991616i | \(0.541246\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.9972i | 0.809013i | ||||||||
\(392\) | 3.87830 | − | 2.02845i | 0.195884 | − | 0.102452i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.70307 | − | 0.983270i | −0.0857996 | − | 0.0495364i | ||||
\(395\) | −2.80753 | − | 10.4778i | −0.141262 | − | 0.527198i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.79662 | − | 2.08910i | 0.391301 | − | 0.104849i | −0.0578036 | − | 0.998328i | \(-0.518410\pi\) |
0.449105 | + | 0.893479i | \(0.351743\pi\) | |||||||
\(398\) | −2.32913 | − | 2.32913i | −0.116749 | − | 0.116749i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.449094 | + | 0.259285i | 0.0224547 | + | 0.0129642i | ||||
\(401\) | 12.1510 | − | 12.1510i | 0.606791 | − | 0.606791i | −0.335315 | − | 0.942106i | \(-0.608843\pi\) |
0.942106 | + | 0.335315i | \(0.108843\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.17723 | − | 5.37367i | 0.357523 | − | 0.267681i | ||||
\(404\) | 16.6143 | − | 9.59227i | 0.826592 | − | 0.477233i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.0934760 | + | 0.845969i | 0.00463914 | + | 0.0419848i | ||||
\(407\) | 49.6718 | − | 28.6780i | 2.46214 | − | 1.42152i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.6885 | − | 21.6885i | 1.07243 | − | 1.07243i | 0.0752633 | − | 0.997164i | \(-0.476020\pi\) |
0.997164 | − | 0.0752633i | \(-0.0239797\pi\) | |||||||
\(410\) | −1.27411 | + | 1.27411i | −0.0629236 | + | 0.0629236i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.6772 | + | 6.16451i | −0.526030 | + | 0.303703i | ||||
\(413\) | −5.82762 | + | 4.28165i | −0.286758 | + | 0.210686i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −27.9308 | + | 16.1259i | −1.37107 | + | 0.791587i | ||||
\(416\) | 2.63434 | − | 6.15308i | 0.129159 | − | 0.301679i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.00839 | − | 3.00839i | 0.147145 | − | 0.147145i | ||||
\(419\) | 15.2013 | + | 8.77646i | 0.742631 | + | 0.428758i | 0.823025 | − | 0.568005i | \(-0.192285\pi\) |
−0.0803942 | + | 0.996763i | \(0.525618\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.5736 | + | 15.5736i | 0.759010 | + | 0.759010i | 0.976142 | − | 0.217132i | \(-0.0696702\pi\) |
−0.217132 | + | 0.976142i | \(0.569670\pi\) | |||||||
\(422\) | −2.69083 | + | 0.721005i | −0.130987 | + | 0.0350980i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.0652078 | − | 0.243359i | −0.00316677 | − | 0.0118186i | ||||
\(425\) | −0.418659 | − | 0.241713i | −0.0203079 | − | 0.0117248i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.07674 | + | 3.84113i | −0.148894 | + | 0.185885i | ||||
\(428\) | − | 8.84817i | − | 0.427693i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.43040 | − | 0.825843i | −0.0689801 | − | 0.0398257i | ||||
\(431\) | −1.12224 | + | 4.18826i | −0.0540564 | + | 0.201741i | −0.987673 | − | 0.156533i | \(-0.949968\pi\) |
0.933616 | + | 0.358275i | \(0.116635\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.6114 | − | 25.3077i | −0.702181 | − | 1.21621i | −0.967699 | − | 0.252107i | \(-0.918876\pi\) |
0.265519 | − | 0.964106i | \(-0.414457\pi\) | |||||||
\(434\) | 0.807660 | + | 0.646934i | 0.0387689 | + | 0.0310538i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.11591 | + | 26.5570i | 0.340791 | + | 1.27185i | ||||
\(437\) | −20.7293 | + | 5.55441i | −0.991619 | + | 0.265704i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.0638652 | −0.00304812 | −0.00152406 | − | 0.999999i | \(-0.500485\pi\) | ||||
−0.00152406 | + | 0.999999i | \(0.500485\pi\) | |||||||
\(440\) | −7.47978 | + | 2.00420i | −0.356585 | + | 0.0955466i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.801532 | + | 1.87215i | −0.0381250 | + | 0.0890491i | ||||
\(443\) | −8.77423 | − | 15.1974i | −0.416876 | − | 0.722051i | 0.578747 | − | 0.815507i | \(-0.303542\pi\) |
−0.995623 | + | 0.0934562i | \(0.970208\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.9275 | + | 34.5155i | 0.944655 | + | 1.63619i | ||||
\(446\) | 1.06751 | − | 1.84899i | 0.0505482 | − | 0.0875520i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −19.3859 | − | 2.96461i | −0.915900 | − | 0.140065i | ||||
\(449\) | 1.21603 | + | 0.325835i | 0.0573881 | + | 0.0153771i | 0.287399 | − | 0.957811i | \(-0.407209\pi\) |
−0.230011 | + | 0.973188i | \(0.573876\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 29.1615i | − | 1.37316i | ||||||
\(452\) | −14.6674 | + | 8.46823i | −0.689897 | + | 0.398312i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.26622 | −0.0594268 | ||||||||
\(455\) | 21.0304 | + | 0.687386i | 0.985920 | + | 0.0322252i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.23927 | − | 5.23927i | −0.245083 | − | 0.245083i | 0.573866 | − | 0.818949i | \(-0.305443\pi\) |
−0.818949 | + | 0.573866i | \(0.805443\pi\) | |||||||
\(458\) | −0.0830452 | + | 0.0479462i | −0.00388045 | + | 0.00224038i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 18.7474 | + | 5.02335i | 0.874102 | + | 0.234215i | ||||
\(461\) | −17.9390 | − | 4.80674i | −0.835502 | − | 0.223872i | −0.184390 | − | 0.982853i | \(-0.559031\pi\) |
−0.651113 | + | 0.758981i | \(0.725697\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.9354 | − | 10.9354i | 0.508209 | − | 0.508209i | −0.405767 | − | 0.913976i | \(-0.632996\pi\) |
0.913976 | + | 0.405767i | \(0.132996\pi\) | |||||||
\(464\) | 3.93941 | − | 6.82326i | 0.182882 | − | 0.316762i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.60915 | + | 0.967070i | 0.167191 | + | 0.0447986i | ||||
\(467\) | 8.85362 | + | 15.3349i | 0.409697 | + | 0.709616i | 0.994856 | − | 0.101303i | \(-0.0323011\pi\) |
−0.585159 | + | 0.810919i | \(0.698968\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.7032 | + | 7.33035i | 0.771284 | + | 0.338484i | ||||
\(470\) | −1.58476 | + | 0.424634i | −0.0730993 | + | 0.0195869i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.70894 | −0.0786605 | ||||||||
\(473\) | 25.8203 | − | 6.91853i | 1.18722 | − | 0.318114i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.167851 | − | 0.626429i | 0.00770153 | − | 0.0287425i | ||||
\(476\) | 18.5517 | + | 2.83703i | 0.850316 | + | 0.130035i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.78483i | 0.0816364i | ||||||||
\(479\) | −4.37332 | + | 16.3215i | −0.199822 | + | 0.745747i | 0.791143 | + | 0.611631i | \(0.209486\pi\) |
−0.990966 | + | 0.134116i | \(0.957181\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33.8586 | − | 14.4960i | −1.54382 | − | 0.660962i | ||||
\(482\) | − | 2.17281i | − | 0.0989689i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 20.2721 | − | 35.1124i | 0.921461 | − | 1.59602i | ||||
\(485\) | −6.97369 | − | 4.02626i | −0.316659 | − | 0.182823i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.58169 | − | 1.58169i | −0.0716733 | − | 0.0716733i | 0.670361 | − | 0.742035i | \(-0.266139\pi\) |
−0.742035 | + | 0.670361i | \(0.766139\pi\) | |||||||
\(488\) | −1.12341 | + | 0.301017i | −0.0508545 | + | 0.0136264i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.530210 | + | 2.36994i | 0.0239525 | + | 0.107063i | ||||
\(491\) | 28.4705 | + | 16.4375i | 1.28486 | + | 0.741812i | 0.977732 | − | 0.209858i | \(-0.0673000\pi\) |
0.307124 | + | 0.951669i | \(0.400633\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.67243 | + | 6.36084i | −0.165398 | + | 0.286478i | ||||
\(494\) | −2.70425 | − | 0.388602i | −0.121670 | − | 0.0174840i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.47930 | − | 9.25288i | −0.111324 | − | 0.415467i | ||||
\(497\) | 34.0318 | + | 14.9351i | 1.52653 | + | 0.669931i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.97619 | − | 29.7675i | 0.357063 | − | 1.33258i | −0.520805 | − | 0.853676i | \(-0.674368\pi\) |
0.877868 | − | 0.478902i | \(-0.158965\pi\) | |||||||
\(500\) | −15.8189 | + | 15.8189i | −0.707443 | + | 0.707443i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.826749 | − | 3.08547i | 0.0368996 | − | 0.137711i | ||||
\(503\) | 9.25091 | − | 5.34101i | 0.412478 | − | 0.238144i | −0.279376 | − | 0.960182i | \(-0.590128\pi\) |
0.691854 | + | 0.722038i | \(0.256794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.54475 | + | 20.6933i | 0.246738 | + | 0.920838i | ||||
\(506\) | 3.40695 | − | 1.96700i | 0.151457 | − | 0.0874440i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.41325 | + | 16.3042i | −0.417645 | + | 0.723383i | ||||
\(509\) | 16.6654 | − | 16.6654i | 0.738681 | − | 0.738681i | −0.233641 | − | 0.972323i | \(-0.575064\pi\) |
0.972323 | + | 0.233641i | \(0.0750642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.34091 | − | 12.1354i | −0.0593186 | − | 0.536840i | ||||
\(512\) | −8.46284 | − | 8.46284i | −0.374008 | − | 0.374008i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.74611 | − | 2.74611i | −0.121126 | − | 0.121126i | ||||
\(515\) | −3.56335 | − | 13.2986i | −0.157020 | − | 0.586006i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.2763 | − | 22.9953i | 0.583893 | − | 1.01133i | ||||
\(518\) | 0.642600 | − | 4.20204i | 0.0282342 | − | 0.184627i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.90895 | + | 3.07355i | 0.171419 | + | 0.134784i | ||||
\(521\) | −27.2035 | − | 15.7059i | −1.19180 | − | 0.688089i | −0.233089 | − | 0.972455i | \(-0.574883\pi\) |
−0.958716 | + | 0.284367i | \(0.908217\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.66261i | 0.335062i | 0.985867 | + | 0.167531i | \(0.0535795\pi\) | ||||
−0.985867 | + | 0.167531i | \(0.946420\pi\) | |||||||
\(524\) | 3.48446 | + | 6.03526i | 0.152219 | + | 0.263652i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.23605 | + | 4.61299i | −0.0538942 | + | 0.201136i | ||||
\(527\) | 2.31128 | + | 8.62581i | 0.100681 | + | 0.375746i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.15604 | 0.137219 | ||||||||
\(530\) | 0.139797 | 0.00607237 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.76511 | + | 25.0245i | 0.119883 | + | 1.08495i | ||||
\(533\) | −14.9901 | + | 11.2233i | −0.649295 | + | 0.486134i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.54402 | + | 2.55731i | 0.412624 | + | 0.110562i | ||||
\(536\) | 2.15536 | + | 3.73320i | 0.0930976 | + | 0.161250i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.662067 | − | 0.662067i | 0.0285437 | − | 0.0285437i | ||||
\(539\) | −33.1891 | − | 21.0537i | −1.42956 | − | 0.906848i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.5302 | + | 5.76899i | 0.925654 | + | 0.248028i | 0.690001 | − | 0.723809i | \(-0.257610\pi\) |
0.235654 | + | 0.971837i | \(0.424277\pi\) | |||||||
\(542\) | 2.12630i | 0.0913326i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.71393 | + | 4.71393i | 0.202108 | + | 0.202108i | ||||
\(545\) | −30.7021 | −1.31513 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.1017 | 0.773971 | 0.386986 | − | 0.922086i | \(-0.373516\pi\) | ||||
0.386986 | + | 0.922086i | \(0.373516\pi\) | |||||||
\(548\) | 14.1135 | + | 14.1135i | 0.602897 | + | 0.602897i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.118883i | 0.00506920i | ||||||||
\(551\) | −9.51756 | − | 2.55022i | −0.405462 | − | 0.108643i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.1220 | − | 4.72749i | 0.515481 | − | 0.201033i | ||||
\(554\) | 1.28521 | − | 1.28521i | 0.0546035 | − | 0.0546035i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.3319 | + | 17.8953i | 0.438168 | + | 0.758930i | ||||
\(557\) | −0.603665 | − | 0.161752i | −0.0255781 | − | 0.00685364i | 0.246007 | − | 0.969268i | \(-0.420881\pi\) |
−0.271585 | + | 0.962414i | \(0.587548\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.4937 | − | 10.6099i | −0.570724 | − | 0.448752i | ||||
\(560\) | 9.03423 | − | 20.5858i | 0.381766 | − | 0.869908i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.91654 | 0.207392 | ||||||||
\(563\) | 6.32497 | 0.266566 | 0.133283 | − | 0.991078i | \(-0.457448\pi\) | ||||
0.133283 | + | 0.991078i | \(0.457448\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.89500 | − | 18.2684i | −0.205934 | − | 0.768557i | ||||
\(566\) | 0.919172 | − | 3.43040i | 0.0386357 | − | 0.144190i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.39142 | + | 7.60615i | 0.184260 | + | 0.319147i | ||||
\(569\) | 7.32323i | 0.307006i | 0.988148 | + | 0.153503i | \(0.0490554\pi\) | ||||
−0.988148 | + | 0.153503i | \(0.950945\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.3352 | + | 14.0500i | 1.01840 | + | 0.587972i | 0.913639 | − | 0.406526i | \(-0.133260\pi\) |
0.104758 | + | 0.994498i | \(0.466593\pi\) | |||||||
\(572\) | −39.7049 | + | 4.75039i | −1.66015 | + | 0.198624i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.68685 | − | 1.35117i | −0.0704079 | − | 0.0563966i | ||||
\(575\) | 0.299836 | − | 0.519332i | 0.0125040 | − | 0.0216576i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.18425 | − | 34.2761i | −0.382345 | − | 1.42693i | −0.842309 | − | 0.538995i | \(-0.818804\pi\) |
0.459964 | − | 0.887938i | \(-0.347862\pi\) | |||||||
\(578\) | 0.456420 | + | 0.456420i | 0.0189846 | + | 0.0189846i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.30119 | + | 6.30119i | 0.261643 | + | 0.261643i | ||||
\(581\) | −22.9050 | − | 31.1753i | −0.950259 | − | 1.29337i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.59982 | + | 1.59982i | −0.0662578 | + | 0.0662578i | ||||
\(584\) | 1.44266 | − | 2.49876i | 0.0596977 | − | 0.103399i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.0757346 | + | 0.0437254i | −0.00312857 | + | 0.00180628i | ||||
\(587\) | 4.40846 | + | 16.4526i | 0.181957 | + | 0.679071i | 0.995262 | + | 0.0972337i | \(0.0309994\pi\) |
−0.813305 | + | 0.581838i | \(0.802334\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.3749 | + | 5.98996i | −0.427491 | + | 0.246812i | ||||
\(590\) | 0.245424 | − | 0.915934i | 0.0101039 | − | 0.0377084i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −27.8251 | + | 27.8251i | −1.14360 | + | 1.14360i | ||||
\(593\) | 3.60164 | − | 13.4415i | 0.147901 | − | 0.551976i | −0.851708 | − | 0.524017i | \(-0.824433\pi\) |
0.999609 | − | 0.0279585i | \(-0.00890063\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.42198 | + | 19.1907i | −0.345268 | + | 0.786742i | ||||
\(596\) | 0.226580 | + | 0.845609i | 0.00928109 | + | 0.0346375i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.32234 | − | 0.994272i | −0.0949674 | − | 0.0406588i | ||||
\(599\) | 8.84405 | − | 15.3183i | 0.361358 | − | 0.625890i | −0.626827 | − | 0.779159i | \(-0.715647\pi\) |
0.988185 | + | 0.153268i | \(0.0489799\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.8753 | + | 13.7844i | 0.973894 | + | 0.562278i | 0.900421 | − | 0.435019i | \(-0.143258\pi\) |
0.0734732 | + | 0.997297i | \(0.476592\pi\) | |||||||
\(602\) | 0.796151 | − | 1.81414i | 0.0324487 | − | 0.0739389i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 18.8296 | − | 5.04537i | 0.766164 | − | 0.205293i | ||||
\(605\) | 32.0146 | + | 32.0146i | 1.30158 | + | 1.30158i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.6565 | + | 10.1940i | 0.716657 | + | 0.413762i | 0.813521 | − | 0.581536i | \(-0.197548\pi\) |
−0.0968642 | + | 0.995298i | \(0.530881\pi\) | |||||||
\(608\) | −4.47163 | + | 7.74509i | −0.181348 | + | 0.314105i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 0.645339i | − | 0.0261290i | ||||||
\(611\) | −16.9301 | + | 2.02555i | −0.684918 | + | 0.0819451i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.69586 | − | 21.2573i | 0.230054 | − | 0.858572i | −0.750263 | − | 0.661140i | \(-0.770073\pi\) |
0.980316 | − | 0.197433i | \(-0.0632603\pi\) | |||||||
\(614\) | 1.11509i | 0.0450014i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.37479 | − | 8.65350i | −0.135974 | − | 0.348660i | ||||
\(617\) | −2.77212 | + | 10.3457i | −0.111602 | + | 0.416503i | −0.999010 | − | 0.0444809i | \(-0.985837\pi\) |
0.887409 | + | 0.460984i | \(0.152503\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −46.3466 | + | 12.4185i | −1.86283 | + | 0.499143i | −0.999980 | − | 0.00631894i | \(-0.997989\pi\) |
−0.862849 | + | 0.505462i | \(0.831322\pi\) | |||||||
\(620\) | 10.8345 | 0.435125 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.123013 | − | 0.0329612i | 0.00493236 | − | 0.00132162i | ||||
\(623\) | −38.5248 | + | 28.3048i | −1.54346 | + | 1.13401i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.1544 | − | 21.0520i | −0.486176 | − | 0.842081i | ||||
\(626\) | −0.160476 | − | 0.0429993i | −0.00641389 | − | 0.00171860i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −21.9248 | + | 37.9749i | −0.874895 | + | 1.51536i | ||||
\(629\) | 25.9394 | − | 25.9394i | 1.03427 | − | 1.03427i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.4576 | − | 7.62520i | −1.13288 | − | 0.303554i | −0.356795 | − | 0.934183i | \(-0.616131\pi\) |
−0.776085 | + | 0.630628i | \(0.782797\pi\) | |||||||
\(632\) | 2.97006 | + | 0.795826i | 0.118143 | + | 0.0316563i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.45060 | + | 2.56955i | −0.176756 | + | 0.102050i | ||||
\(635\) | −14.8658 | − | 14.8658i | −0.589931 | − | 0.589931i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.95092 | + | 25.1633i | 0.0772984 | + | 0.997008i | ||||
\(638\) | 1.80624 | 0.0715097 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.31937 | − | 5.38054i | 0.368380 | − | 0.212685i | ||||
\(641\) | 3.78962i | 0.149681i | 0.997196 | + | 0.0748405i | \(0.0238448\pi\) | ||||
−0.997196 | + | 0.0748405i | \(0.976155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.08002 | − | 2.43298i | −0.358081 | − | 0.0959475i | 0.0752936 | − | 0.997161i | \(-0.476011\pi\) |
−0.433375 | + | 0.901214i | \(0.642677\pi\) | |||||||
\(644\) | −3.51924 | + | 23.0127i | −0.138677 | + | 0.906828i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.36055 | − | 2.35654i | 0.0535301 | − | 0.0927168i | ||||
\(647\) | −14.8089 | − | 25.6498i | −0.582199 | − | 1.00840i | −0.995218 | − | 0.0976755i | \(-0.968859\pi\) |
0.413020 | − | 0.910722i | \(-0.364474\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.67327 | + | 13.2905i | 0.301202 | + | 0.521697i | ||||
\(650\) | 0.0611107 | − | 0.0457542i | 0.00239696 | − | 0.00179463i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.32758 | + | 1.42752i | −0.208644 | + | 0.0559060i | ||||
\(653\) | −42.5984 | −1.66700 | −0.833502 | − | 0.552516i | \(-0.813668\pi\) | ||||
−0.833502 | + | 0.552516i | \(0.813668\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.51697 | + | 2.01417i | −0.293712 | + | 0.0787000i | ||||
\(656\) | 5.17819 | + | 19.3253i | 0.202174 | + | 0.754525i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.715024 | − | 1.83343i | −0.0278745 | − | 0.0714747i | ||||
\(659\) | −0.832186 | − | 1.44139i | −0.0324173 | − | 0.0561485i | 0.849362 | − | 0.527811i | \(-0.176987\pi\) |
−0.881779 | + | 0.471663i | \(0.843654\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.43629 | + | 9.09235i | −0.0947606 | + | 0.353651i | −0.996983 | − | 0.0776197i | \(-0.975268\pi\) |
0.902222 | + | 0.431271i | \(0.141935\pi\) | |||||||
\(662\) | 3.27633 | + | 1.89159i | 0.127338 | + | 0.0735188i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 9.14211i | − | 0.354783i | ||||||
\(665\) | −27.7917 | − | 4.25007i | −1.07772 | − | 0.164811i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.89040 | − | 4.55552i | −0.305518 | − | 0.176391i | ||||
\(668\) | 1.24258 | + | 4.63736i | 0.0480768 | + | 0.179425i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.31040 | + | 0.619070i | −0.0892586 | + | 0.0239168i | ||||
\(671\) | 7.38521 | + | 7.38521i | 0.285103 | + | 0.285103i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.15591 | + | 1.24472i | 0.0831043 | + | 0.0479803i | 0.540976 | − | 0.841038i | \(-0.318055\pi\) |
−0.457872 | + | 0.889018i | \(0.651388\pi\) | |||||||
\(674\) | −2.98619 | + | 2.98619i | −0.115024 | + | 0.115024i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.7230 | + | 18.5816i | 0.681653 | + | 0.714678i | ||||
\(677\) | −18.2860 | + | 10.5574i | −0.702789 | + | 0.405756i | −0.808385 | − | 0.588654i | \(-0.799658\pi\) |
0.105596 | + | 0.994409i | \(0.466325\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.88150 | − | 8.84455i | 0.148958 | − | 0.339423i | ||||
\(680\) | −4.28915 | + | 2.47634i | −0.164481 | + | 0.0949633i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.55286 | − | 1.55286i | 0.0594621 | − | 0.0594621i | ||||
\(683\) | −3.90071 | + | 3.90071i | −0.149257 | + | 0.149257i | −0.777786 | − | 0.628529i | \(-0.783657\pi\) |
0.628529 | + | 0.777786i | \(0.283657\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.3025 | + | 11.1443i | −0.737510 | + | 0.425801i | ||||
\(686\) | −2.75564 | + | 0.944330i | −0.105211 | + | 0.0360547i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −15.8825 | + | 9.16979i | −0.605516 | + | 0.349595i | ||||
\(689\) | 1.43809 | + | 0.206653i | 0.0547867 | + | 0.00787285i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.4634 | + | 11.4634i | −0.436089 | + | 0.436089i | −0.890694 | − | 0.454604i | \(-0.849781\pi\) |
0.454604 | + | 0.890694i | \(0.349781\pi\) | |||||||
\(692\) | 18.3851 | + | 10.6146i | 0.698897 | + | 0.403508i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.56373 | + | 2.56373i | 0.0973179 | + | 0.0973179i | ||||
\(695\) | −22.2888 | + | 5.97226i | −0.845461 | + | 0.226541i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.82727 | − | 18.0156i | −0.182846 | − | 0.682390i | ||||
\(698\) | −0.842641 | − | 0.486499i | −0.0318944 | − | 0.0184143i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.549086 | − | 0.439817i | −0.0207535 | − | 0.0166235i | ||||
\(701\) | − | 11.5049i | − | 0.434534i | −0.976112 | − | 0.217267i | \(-0.930286\pi\) | ||
0.976112 | − | 0.217267i | \(-0.0697142\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 42.6190 | + | 24.6061i | 1.60741 | + | 0.928036i | ||||
\(704\) | −10.7718 | + | 40.2009i | −0.405978 | + | 1.51513i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.20858 | + | 3.82538i | 0.0831212 | + | 0.143970i | ||||
\(707\) | −23.9404 | + | 9.33657i | −0.900373 | + | 0.351138i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.0992239 | − | 0.370309i | −0.00372643 | − | 0.0139072i | 0.964038 | − | 0.265766i | \(-0.0856248\pi\) |
−0.967764 | + | 0.251859i | \(0.918958\pi\) | |||||||
\(710\) | −4.70729 | + | 1.26132i | −0.176662 | + | 0.0473363i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.2974 | −0.423387 | ||||||||
\(713\) | −10.7000 | + | 2.86706i | −0.400719 | + | 0.107372i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.35161 | − | 44.2004i | 0.237537 | − | 1.65300i | ||||
\(716\) | 18.8191 | + | 32.5957i | 0.703304 | + | 1.21816i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.622090 | − | 1.07749i | −0.0232162 | − | 0.0402116i | ||||
\(719\) | 11.9136 | − | 20.6350i | 0.444304 | − | 0.769557i | −0.553699 | − | 0.832717i | \(-0.686784\pi\) |
0.998003 | + | 0.0631593i | \(0.0201176\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3854 | − | 6.00018i | 0.572982 | − | 0.223458i | ||||
\(722\) | 0.639446 | + | 0.171339i | 0.0237977 | + | 0.00637658i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 40.5862i | 1.50837i | ||||||||
\(725\) | 0.238443 | − | 0.137665i | 0.00885556 | − | 0.00511276i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.135408 | −0.00502200 | −0.00251100 | − | 0.999997i | \(-0.500799\pi\) | ||||
−0.00251100 | + | 0.999997i | \(0.500799\pi\) | |||||||
\(728\) | −3.14939 | + | 5.06521i | −0.116724 | + | 0.187729i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.13207 | + | 1.13207i | 0.0418996 | + | 0.0418996i | ||||
\(731\) | 14.8062 | − | 8.54835i | 0.547626 | − | 0.316172i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.2352 | − | 9.97714i | −1.37531 | − | 0.368514i | −0.505897 | − | 0.862594i | \(-0.668838\pi\) |
−0.869417 | + | 0.494080i | \(0.835505\pi\) | |||||||
\(734\) | 1.38945 | + | 0.372301i | 0.0512854 | + | 0.0137419i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.84746 | + | 5.84746i | −0.215540 | + | 0.215540i | ||||
\(737\) | 19.3554 | − | 33.5246i | 0.712967 | − | 1.23489i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.9013 | − | 10.6915i | −1.46779 | − | 0.393294i | −0.565620 | − | 0.824666i | \(-0.691363\pi\) |
−0.902174 | + | 0.431372i | \(0.858030\pi\) | |||||||
\(740\) | −22.2535 | − | 38.5441i | −0.818054 | − | 1.41691i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.0184161 | + | 0.166668i | 0.000676076 | + | 0.00611857i | ||||
\(743\) | 29.7830 | − | 7.98032i | 1.09263 | − | 0.292769i | 0.332870 | − | 0.942973i | \(-0.391983\pi\) |
0.759760 | + | 0.650203i | \(0.225316\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.977597 | −0.0358164 | ||||||||
\(746\) | −4.98389 | + | 1.33543i | −0.182473 | + | 0.0488936i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.3083 | − | 38.4709i | 0.376907 | − | 1.40664i | ||||
\(749\) | −1.79159 | + | 11.7154i | −0.0654633 | + | 0.428072i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.6954i | 1.19307i | 0.802586 | + | 0.596536i | \(0.203457\pi\) | ||||
−0.802586 | + | 0.596536i | \(0.796543\pi\) | |||||||
\(752\) | −4.71494 | + | 17.5964i | −0.171936 | + | 0.641675i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.695160 | − | 0.928477i | −0.0253162 | − | 0.0338131i | ||||
\(755\) | 21.7686i | 0.792241i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.04055 | − | 6.99844i | 0.146856 | − | 0.254363i | −0.783208 | − | 0.621760i | \(-0.786418\pi\) |
0.930064 | + | 0.367398i | \(0.119751\pi\) | |||||||
\(758\) | 2.39383 | + | 1.38208i | 0.0869477 | + | 0.0501993i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.69811 | − | 4.69811i | −0.170418 | − | 0.170418i | ||||
\(761\) | 13.8024 | − | 3.69833i | 0.500335 | − | 0.134064i | 0.000179461 | − | 1.00000i | \(-0.499943\pi\) |
0.500155 | + | 0.865936i | \(0.333276\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.04454 | − | 36.6036i | −0.146422 | − | 1.32514i | ||||
\(764\) | −33.2008 | − | 19.1685i | −1.20116 | − | 0.693493i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.41873 | − | 4.18936i | 0.0873922 | − | 0.151368i | ||||
\(767\) | 3.87865 | − | 9.05941i | 0.140050 | − | 0.327116i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.992641 | + | 3.70459i | 0.0357955 | + | 0.133591i | 0.981511 | − | 0.191404i | \(-0.0613041\pi\) |
−0.945716 | + | 0.324995i | \(0.894637\pi\) | |||||||
\(770\) | 5.12264 | − | 0.566029i | 0.184607 | − | 0.0203983i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.24431 | + | 34.5003i | −0.332710 | + | 1.24169i | ||||
\(773\) | 0.986845 | − | 0.986845i | 0.0354943 | − | 0.0354943i | −0.689137 | − | 0.724631i | \(-0.742010\pi\) |
0.724631 | + | 0.689137i | \(0.242010\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.0866409 | − | 0.323348i | 0.00311223 | − | 0.0116150i | ||||
\(776\) | 1.97677 | − | 1.14129i | 0.0709619 | − | 0.0409699i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.616466 | − | 2.30068i | −0.0221014 | − | 0.0824835i | ||||
\(779\) | 21.6687 | − | 12.5105i | 0.776363 | − | 0.448234i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 39.4355 | − | 68.3042i | 1.41111 | − | 2.44412i | ||||
\(782\) | 1.77916 | − | 1.77916i | 0.0636227 | − | 0.0636227i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 25.7329 | + | 8.05890i | 0.919031 | + | 0.287818i | ||||
\(785\) | −34.6246 | − | 34.6246i | −1.23580 | − | 1.23580i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.6123 | − | 23.6123i | −0.841686 | − | 0.841686i | 0.147392 | − | 0.989078i | \(-0.452912\pi\) |
−0.989078 | + | 0.147392i | \(0.952912\pi\) | |||||||
\(788\) | −6.39201 | − | 23.8553i | −0.227706 | − | 0.849809i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.853070 | + | 1.47756i | −0.0303509 | + | 0.0525693i | ||||
\(791\) | 21.1351 | − | 8.24249i | 0.751476 | − | 0.293069i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.953968 | − | 6.63860i | 0.0338764 | − | 0.235744i | ||||
\(794\) | −1.09946 | − | 0.634774i | −0.0390184 | − | 0.0225273i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 41.3663i | − | 1.46619i | ||||||
\(797\) | 13.5213 | + | 23.4196i | 0.478950 | + | 0.829566i | 0.999709 | − | 0.0241380i | \(-0.00768412\pi\) |
−0.520758 | + | 0.853704i | \(0.674351\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.39541 | − | 16.4039i | 0.155498 | − | 0.580328i | ||||
\(800\) | −0.0646792 | − | 0.241386i | −0.00228675 | − | 0.00853428i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.70279 | −0.0954389 | ||||||||
\(803\) | −25.9105 | −0.914363 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −23.8054 | − | 10.4472i | −0.839029 | − | 0.368214i | ||||
\(806\) | −1.39587 | − | 0.200587i | −0.0491676 | − | 0.00706539i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.86574 | − | 1.57172i | −0.206356 | − | 0.0552929i | ||||
\(809\) | 4.12773 | + | 7.14944i | 0.145123 | + | 0.251361i | 0.929419 | − | 0.369026i | \(-0.120309\pi\) |
−0.784296 | + | 0.620387i | \(0.786975\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.4673 | − | 17.4673i | 0.613359 | − | 0.613359i | −0.330461 | − | 0.943820i | \(-0.607204\pi\) |
0.943820 | + | 0.330461i | \(0.107204\pi\) | |||||||
\(812\) | −6.68230 | + | 8.34247i | −0.234503 | + | 0.292763i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.71384 | − | 2.33487i | −0.305420 | − | 0.0818370i | ||||
\(815\) | − | 6.15914i | − | 0.215745i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.2179 | + | 16.2179i | 0.567394 | + | 0.567394i | ||||
\(818\) | −4.82426 | −0.168676 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22.6286 | −0.790226 | ||||||||
\(821\) | 25.3099 | + | 25.3099i | 0.883322 | + | 0.883322i | 0.993871 | − | 0.110549i | \(-0.0352608\pi\) |
−0.110549 | + | 0.993871i | \(0.535261\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 4.02596i | − | 0.140336i | −0.997535 | − | 0.0701681i | \(-0.977646\pi\) | ||
0.997535 | − | 0.0701681i | \(-0.0223536\pi\) | |||||||
\(824\) | 3.76964 | + | 1.01007i | 0.131322 | + | 0.0351875i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.12432 | + | 0.171938i | 0.0391202 | + | 0.00598249i | ||||
\(827\) | −1.28533 | + | 1.28533i | −0.0446954 | + | 0.0446954i | −0.729101 | − | 0.684406i | \(-0.760062\pi\) |
0.684406 | + | 0.729101i | \(0.260062\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.96119 | + | 17.2533i | 0.345967 | + | 0.599232i | 0.985529 | − | 0.169508i | \(-0.0542177\pi\) |
−0.639562 | + | 0.768739i | \(0.720884\pi\) | |||||||
\(830\) | 4.89985 | + | 1.31291i | 0.170076 | + | 0.0455718i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 24.8105 | − | 9.93485i | 0.860151 | − | 0.344429i | ||||
\(833\) | −23.9889 | − | 7.51275i | −0.831167 | − | 0.260301i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.36119 | −0.185532 | ||||||||
\(836\) | 53.4302 | 1.84792 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.714549 | − | 2.66673i | −0.0246837 | − | 0.0921208i | ||||
\(839\) | 13.3275 | − | 49.7391i | 0.460118 | − | 1.71718i | −0.212471 | − | 0.977167i | \(-0.568151\pi\) |
0.672589 | − | 0.740016i | \(-0.265182\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.4084 | + | 21.4920i | 0.427876 | + | 0.741103i | ||||
\(842\) | − | 3.46410i | − | 0.119381i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −30.2978 | − | 17.4924i | −1.04289 | − | 0.602114i | ||||
\(845\) | −25.1652 | + | 13.7463i | −0.865711 | + | 0.472886i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −33.9509 | + | 42.3858i | −1.16657 | + | 1.45639i | ||||
\(848\) | 0.776119 | − | 1.34428i | 0.0266520 | − | 0.0461627i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.0196794 | + | 0.0734446i | 0.000674999 | + | 0.00251913i | ||||
\(851\) | 32.1769 | + | 32.1769i | 1.10301 | + | 1.10301i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.4061 | + | 11.4061i | 0.390537 | + | 0.390537i | 0.874879 | − | 0.484342i | \(-0.160941\pi\) |
−0.484342 | + | 0.874879i | \(0.660941\pi\) | |||||||
\(854\) | 0.769385 | − | 0.0850137i | 0.0263278 | − | 0.00290911i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.98046 | + | 1.98046i | −0.0676907 | + | 0.0676907i | ||||
\(857\) | −5.11355 | + | 8.85693i | −0.174676 | + | 0.302547i | −0.940049 | − | 0.341040i | \(-0.889221\pi\) |
0.765373 | + | 0.643586i | \(0.222554\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.0305 | + | 11.5646i | −0.683433 | + | 0.394580i | −0.801147 | − | 0.598467i | \(-0.795777\pi\) |
0.117714 | + | 0.993048i | \(0.462443\pi\) | |||||||
\(860\) | −5.36861 | − | 20.0359i | −0.183068 | − | 0.683220i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.590618 | − | 0.340994i | 0.0201165 | − | 0.0116143i | ||||
\(863\) | −2.58806 | + | 9.65877i | −0.0880986 | + | 0.328788i | −0.995883 | − | 0.0906489i | \(-0.971106\pi\) |
0.907784 | + | 0.419437i | \(0.137773\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.7631 | + | 16.7631i | −0.569963 | + | 0.569963i | ||||
\(866\) | −1.18961 | + | 4.43969i | −0.0404247 | + | 0.150867i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.42728 | + | 12.9171i | 0.0484452 | + | 0.438435i | ||||
\(869\) | −7.14662 | − | 26.6715i | −0.242432 | − | 0.904770i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.6822 | + | 2.95304i | −0.836324 | + | 0.100060i | ||||
\(872\) | 4.35143 | − | 7.53690i | 0.147358 | − | 0.255232i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.92320 | + | 1.68771i | 0.0988788 | + | 0.0570877i | ||||
\(875\) | 24.1481 | − | 17.7420i | 0.816353 | − | 0.599789i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.23964 | − | 1.93986i | 0.244465 | − | 0.0655043i | −0.134506 | − | 0.990913i | \(-0.542945\pi\) |
0.378971 | + | 0.925409i | \(0.376278\pi\) | |||||||
\(878\) | 0.00710290 | + | 0.00710290i | 0.000239711 | + | 0.000239711i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −41.3172 | − | 23.8545i | −1.39280 | − | 0.804134i | ||||
\(881\) | −10.1686 | + | 17.6125i | −0.342589 | + | 0.593381i | −0.984913 | − | 0.173052i | \(-0.944637\pi\) |
0.642324 | + | 0.766433i | \(0.277970\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.9023i | 1.07360i | 0.843710 | + | 0.536799i | \(0.180367\pi\) | ||||
−0.843710 | + | 0.536799i | \(0.819633\pi\) | |||||||
\(884\) | −23.7429 | + | 9.50731i | −0.798558 | + | 0.319766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.714368 | + | 2.66606i | −0.0239996 | + | 0.0895679i | ||||
\(887\) | 43.1400i | 1.44850i | 0.689538 | + | 0.724249i | \(0.257814\pi\) | ||||
−0.689538 | + | 0.724249i | \(0.742186\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.7649 | − | 19.6816i | 0.528738 | − | 0.660100i | ||||
\(890\) | 1.62243 | − | 6.05499i | 0.0543840 | − | 0.202964i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 25.8991 | − | 6.93964i | 0.867166 | − | 0.232356i | ||||
\(893\) | 22.7825 | 0.762387 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −40.5983 | + | 10.8783i | −1.35705 | + | 0.363620i | ||||
\(896\) | 7.64246 | + | 10.4019i | 0.255317 | + | 0.347503i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.0990052 | − | 0.171482i | −0.00330385 | − | 0.00572243i | ||||
\(899\) | −4.91275 | − | 1.31637i | −0.163849 | − | 0.0439033i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.723521 | + | 1.25318i | −0.0241040 | + | 0.0417493i | ||||
\(902\) | −3.24326 | + | 3.24326i | −0.107989 | + | 0.107989i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.17838 | + | 1.38754i | 0.172230 | + | 0.0461490i | ||||
\(905\) | −43.7780 | − | 11.7303i | −1.45523 | − | 0.389927i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.7355 | − | 22.3639i | 1.28619 | − | 0.742583i | 0.308218 | − | 0.951316i | \(-0.400267\pi\) |
0.977973 | + | 0.208733i | \(0.0669340\pi\) | |||||||
\(908\) | −11.2443 | − | 11.2443i | −0.373156 | − | 0.373156i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.26249 | − | 2.41539i | −0.0750008 | − | 0.0800693i | ||||
\(911\) | −19.2491 | −0.637751 | −0.318875 | − | 0.947797i | \(-0.603305\pi\) | ||||
−0.318875 | + | 0.947797i | \(0.603305\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −71.0984 | + | 41.0487i | −2.35301 | + | 1.35851i | ||||
\(914\) | 1.16539i | 0.0385478i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.16323 | − | 0.311687i | −0.0384342 | − | 0.0102984i | ||||
\(917\) | −3.39157 | − | 8.69653i | −0.112000 | − | 0.287185i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.95449 | − | 5.11733i | 0.0974596 | − | 0.168805i | −0.813173 | − | 0.582022i | \(-0.802262\pi\) |
0.910632 | + | 0.413217i | \(0.135595\pi\) | |||||||
\(920\) | −3.07181 | − | 5.32054i | −0.101275 | − | 0.175413i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.46053 | + | 2.52971i | 0.0481000 | + | 0.0833117i | ||||
\(923\) | −50.2884 | + | 6.01662i | −1.65526 | + | 0.198039i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.32828 | + | 0.355911i | −0.0436735 | + | 0.0117023i | ||||
\(926\) | −2.43240 | −0.0799335 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.66747 | + | 0.982694i | −0.120390 | + | 0.0322585i | ||||
\(929\) | −6.93438 | − | 25.8795i | −0.227510 | − | 0.849077i | −0.981384 | − | 0.192058i | \(-0.938484\pi\) |
0.753874 | − | 0.657019i | \(-0.228183\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.40587 | − | 33.6937i | 0.0460754 | − | 1.10426i | ||||
\(932\) | 23.4623 | + | 40.6378i | 0.768532 | + | 1.33114i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.720832 | − | 2.69018i | 0.0235863 | − | 0.0880254i | ||||
\(935\) | 38.5171 | + | 22.2379i | 1.25964 | + | 0.727256i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.5545i | 1.09618i | 0.836420 | + | 0.548089i | \(0.184644\pi\) | ||||
−0.836420 | + | 0.548089i | \(0.815356\pi\) | |||||||
\(938\) | −1.04243 | − | 2.67295i | −0.0340364 | − | 0.0872748i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −17.8438 | − | 10.3021i | −0.582001 | − | 0.336018i | ||||
\(941\) | 0.902282 | + | 3.36736i | 0.0294135 | + | 0.109773i | 0.979072 | − | 0.203514i | \(-0.0652364\pi\) |
−0.949658 | + | 0.313287i | \(0.898570\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.3477 | − | 5.98805i | 0.727742 | − | 0.194998i | ||||
\(944\) | −7.44504 | − | 7.44504i | −0.242316 | − | 0.242316i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.64112 | − | 2.10220i | −0.118383 | − | 0.0683484i | ||||
\(947\) | 4.56102 | − | 4.56102i | 0.148213 | − | 0.148213i | −0.629106 | − | 0.777319i | \(-0.716579\pi\) |
0.777319 | + | 0.629106i | \(0.216579\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.97208 | + | 13.3190i | 0.323708 | + | 0.432354i | ||||
\(950\) | −0.0883375 | + | 0.0510017i | −0.00286605 | + | 0.00165471i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.51737 | − | 4.78738i | −0.113999 | − | 0.155160i | ||||
\(953\) | −21.7137 | + | 12.5364i | −0.703376 | + | 0.406094i | −0.808604 | − | 0.588354i | \(-0.799776\pi\) |
0.105228 | + | 0.994448i | \(0.466443\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.2717 | − | 30.2717i | 0.979570 | − | 0.979570i | ||||
\(956\) | −15.8497 | + | 15.8497i | −0.512616 | + | 0.512616i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.30161 | − | 1.32884i | 0.0743618 | − | 0.0429328i | ||||
\(959\) | −15.8292 | − | 21.5447i | −0.511152 | − | 0.695713i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.4915 | − | 12.4081i | 0.693274 | − | 0.400262i | ||||
\(962\) | 2.15345 | + | 5.37786i | 0.0694300 | + | 0.173389i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 19.2950 | − | 19.2950i | 0.621451 | − | 0.621451i | ||||
\(965\) | −34.5416 | − | 19.9426i | −1.11193 | − | 0.641976i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.8740 | + | 15.8740i | 0.510473 | + | 0.510473i | 0.914671 | − | 0.404199i | \(-0.132450\pi\) |
−0.404199 | + | 0.914671i | \(0.632450\pi\) | |||||||
\(968\) | −12.3966 | + | 3.32165i | −0.398440 | + | 0.106762i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.327804 | + | 1.22338i | 0.0105252 | + | 0.0392804i | ||||
\(971\) | −32.4502 | − | 18.7352i | −1.04138 | − | 0.601240i | −0.121155 | − | 0.992634i | \(-0.538660\pi\) |
−0.920223 | + | 0.391394i | \(0.871993\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.0564 | − | 25.7863i | −0.322394 | − | 0.826670i | ||||
\(974\) | 0.351822i | 0.0112731i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.20555 | − | 3.58278i | −0.198635 | − | 0.114682i | ||||
\(977\) | −6.13522 | + | 22.8970i | −0.196283 | + | 0.732539i | 0.795648 | + | 0.605759i | \(0.207131\pi\) |
−0.991931 | + | 0.126779i | \(0.959536\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 50.7259 | + | 87.8598i | 1.62121 | + | 2.80801i | ||||
\(980\) | −16.3372 | + | 25.7540i | −0.521873 | + | 0.822680i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.33828 | − | 4.99453i | −0.0427063 | − | 0.159382i | ||||
\(983\) | −5.27840 | + | 1.41434i | −0.168355 | + | 0.0451105i | −0.342012 | − | 0.939696i | \(-0.611108\pi\) |
0.173657 | + | 0.984806i | \(0.444442\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.5788 | 0.878732 | ||||||||
\(986\) | 1.11587 | − | 0.298997i | 0.0355366 | − | 0.00952200i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −20.5635 | − | 27.4652i | −0.654211 | − | 0.873785i | ||||
\(989\) | 10.6039 | + | 18.3665i | 0.337185 | + | 0.584022i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.31507 | + | 7.47392i | 0.137073 | + | 0.237417i | 0.926387 | − | 0.376572i | \(-0.122897\pi\) |
−0.789315 | + | 0.613989i | \(0.789564\pi\) | |||||||
\(992\) | −2.30815 | + | 3.99784i | −0.0732839 | + | 0.126931i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.12388 | − | 5.44595i | −0.0673653 | − | 0.172735i | ||||
\(995\) | 44.6195 | + | 11.9558i | 1.41453 | + | 0.379023i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.6402i | 0.495330i | 0.968846 | + | 0.247665i | \(0.0796633\pi\) | ||||
−0.968846 | + | 0.247665i | \(0.920337\pi\) | |||||||
\(998\) | −4.19775 | + | 2.42357i | −0.132877 | + | 0.0767168i | ||||
\(999\) | 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 | 819.2.et.c.514.5 | 36 | ||
3.2 | odd | 2 | 273.2.bt.a.241.5 | yes | 36 | ||
7.5 | odd | 6 | 819.2.gh.c.397.5 | 36 | |||
13.2 | odd | 12 | 819.2.gh.c.262.5 | 36 | |||
21.5 | even | 6 | 273.2.cg.a.124.5 | yes | 36 | ||
39.2 | even | 12 | 273.2.cg.a.262.5 | yes | 36 | ||
91.54 | even | 12 | inner | 819.2.et.c.145.5 | 36 | ||
273.236 | odd | 12 | 273.2.bt.a.145.5 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.bt.a.145.5 | ✓ | 36 | 273.236 | odd | 12 | ||
273.2.bt.a.241.5 | yes | 36 | 3.2 | odd | 2 | ||
273.2.cg.a.124.5 | yes | 36 | 21.5 | even | 6 | ||
273.2.cg.a.262.5 | yes | 36 | 39.2 | even | 12 | ||
819.2.et.c.145.5 | 36 | 91.54 | even | 12 | inner | ||
819.2.et.c.514.5 | 36 | 1.1 | even | 1 | trivial | ||
819.2.gh.c.262.5 | 36 | 13.2 | odd | 12 | |||
819.2.gh.c.397.5 | 36 | 7.5 | odd | 6 |