Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,2,Mod(8,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(36))
chi = DirichletCharacter(H, H._module([2, 27]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.r (of order \(36\), degree \(12\), 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: | \(3.23394128186\) |
Analytic rank: | \(0\) |
Dimension: | \(192\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{36})\) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{36}]$ |
Embedding invariants
Embedding label | 197.3 | ||
Character | \(\chi\) | \(=\) | 405.197 |
Dual form | 405.2.r.a.368.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{13}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.98905 | + | 0.174019i | −1.40647 | + | 0.123050i | −0.764966 | − | 0.644071i | \(-0.777244\pi\) |
−0.641503 | + | 0.767121i | \(0.721689\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.95641 | − | 0.344968i | 0.978205 | − | 0.172484i | ||||
\(5\) | −0.840902 | − | 2.07193i | −0.376063 | − | 0.926594i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.15499 | − | 0.808730i | 0.436543 | − | 0.305671i | −0.334567 | − | 0.942372i | \(-0.608590\pi\) |
0.771111 | + | 0.636701i | \(0.219701\pi\) | |||||||
\(8\) | 0.0258608 | − | 0.00692938i | 0.00914317 | − | 0.00244991i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.03315 | + | 3.97483i | 0.642938 | + | 1.25695i | ||||
\(11\) | 1.21986 | + | 3.35154i | 0.367801 | + | 1.01053i | 0.976196 | + | 0.216891i | \(0.0695917\pi\) |
−0.608394 | + | 0.793635i | \(0.708186\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.265789 | − | 3.03799i | 0.0737167 | − | 0.842586i | −0.865869 | − | 0.500271i | \(-0.833234\pi\) |
0.939585 | − | 0.342315i | \(-0.111211\pi\) | |||||||
\(14\) | −2.15659 | + | 1.80959i | −0.576372 | + | 0.483633i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.78380 | + | 1.37719i | −0.945951 | + | 0.344298i | ||||
\(17\) | −3.91899 | − | 1.05009i | −0.950495 | − | 0.254684i | −0.249922 | − | 0.968266i | \(-0.580405\pi\) |
−0.700572 | + | 0.713582i | \(0.747072\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.42357 | − | 0.821896i | −0.326588 | − | 0.188556i | 0.327737 | − | 0.944769i | \(-0.393714\pi\) |
−0.654325 | + | 0.756213i | \(0.727047\pi\) | |||||||
\(20\) | −2.35990 | − | 3.76346i | −0.527689 | − | 0.841534i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.00959 | − | 6.45408i | −0.641646 | − | 1.37602i | ||||
\(23\) | 3.67339 | − | 5.24614i | 0.765954 | − | 1.09390i | −0.226824 | − | 0.973936i | \(-0.572834\pi\) |
0.992779 | − | 0.119960i | \(-0.0382767\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.58577 | + | 3.48458i | −0.717153 | + | 0.696916i | ||||
\(26\) | 6.08895i | 1.19414i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.98064 | − | 1.98064i | 0.374306 | − | 0.374306i | ||||
\(29\) | 2.12205 | + | 1.78061i | 0.394054 | + | 0.330651i | 0.818190 | − | 0.574948i | \(-0.194978\pi\) |
−0.424136 | + | 0.905599i | \(0.639422\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.13538 | − | 6.43905i | −0.203920 | − | 1.15649i | −0.899130 | − | 0.437681i | \(-0.855800\pi\) |
0.695211 | − | 0.718806i | \(-0.255311\pi\) | |||||||
\(32\) | 7.23797 | − | 3.37512i | 1.27951 | − | 0.596643i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.97779 | + | 1.40670i | 1.36818 | + | 0.241247i | ||||
\(35\) | −2.64686 | − | 1.71298i | −0.447401 | − | 0.289547i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.751675 | − | 2.80529i | 0.123575 | − | 0.461186i | −0.876210 | − | 0.481929i | \(-0.839936\pi\) |
0.999785 | + | 0.0207425i | \(0.00660301\pi\) | |||||||
\(38\) | 2.97456 | + | 1.38706i | 0.482538 | + | 0.225011i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.0361036 | − | 0.0477548i | −0.00570848 | − | 0.00755069i | ||||
\(41\) | −5.92728 | − | 7.06386i | −0.925686 | − | 1.10319i | −0.994414 | − | 0.105554i | \(-0.966339\pi\) |
0.0687280 | − | 0.997635i | \(-0.478106\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.41117 | − | 5.17078i | 0.367701 | − | 0.788536i | −0.632205 | − | 0.774801i | \(-0.717850\pi\) |
0.999906 | − | 0.0137353i | \(-0.00437223\pi\) | |||||||
\(44\) | 3.54272 | + | 6.13617i | 0.534085 | + | 0.925062i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.39361 | + | 11.0741i | −0.942687 | + | 1.63278i | ||||
\(47\) | −4.56850 | − | 6.52449i | −0.666384 | − | 0.951695i | −0.999960 | − | 0.00897134i | \(-0.997144\pi\) |
0.333576 | − | 0.942723i | \(-0.391745\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.71419 | + | 4.70971i | −0.244885 | + | 0.672815i | ||||
\(50\) | 6.52587 | − | 7.55498i | 0.922898 | − | 1.06844i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.528015 | − | 6.03524i | −0.0732225 | − | 0.836937i | ||||
\(53\) | −8.37726 | − | 8.37726i | −1.15070 | − | 1.15070i | −0.986412 | − | 0.164293i | \(-0.947466\pi\) |
−0.164293 | − | 0.986412i | \(-0.552534\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.91836 | − | 5.34577i | 0.798031 | − | 0.720824i | ||||
\(56\) | 0.0242649 | − | 0.0289177i | 0.00324253 | − | 0.00386429i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.53071 | − | 3.17244i | −0.594911 | − | 0.416561i | ||||
\(59\) | 13.4607 | + | 4.89929i | 1.75243 | + | 0.637833i | 0.999788 | − | 0.0205964i | \(-0.00655651\pi\) |
0.752643 | + | 0.658429i | \(0.228779\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.11559 | − | 6.32681i | 0.142836 | − | 0.810066i | −0.826242 | − | 0.563315i | \(-0.809526\pi\) |
0.969079 | − | 0.246751i | \(-0.0793630\pi\) | |||||||
\(62\) | 3.37884 | + | 12.6100i | 0.429113 | + | 1.60147i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.83499 | + | 3.94619i | −0.854374 | + | 0.493273i | ||||
\(65\) | −6.51799 | + | 2.00395i | −0.808457 | + | 0.248560i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.6234 | − | 1.01692i | −1.42002 | − | 0.124236i | −0.648877 | − | 0.760893i | \(-0.724761\pi\) |
−0.771147 | + | 0.636658i | \(0.780317\pi\) | |||||||
\(68\) | −8.02940 | − | 0.702481i | −0.973708 | − | 0.0851884i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.56282 | + | 2.94660i | 0.664884 | + | 0.352186i | ||||
\(71\) | −0.966172 | + | 0.557819i | −0.114663 | + | 0.0662010i | −0.556235 | − | 0.831025i | \(-0.687755\pi\) |
0.441571 | + | 0.897226i | \(0.354421\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.19579 | + | 8.19480i | 0.256998 | + | 0.959129i | 0.966968 | + | 0.254898i | \(0.0820417\pi\) |
−0.709970 | + | 0.704232i | \(0.751292\pi\) | |||||||
\(74\) | −1.00694 | + | 5.71065i | −0.117055 | + | 0.663850i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.06861 | − | 1.11688i | −0.351993 | − | 0.128115i | ||||
\(77\) | 4.11941 | + | 2.88444i | 0.469450 | + | 0.328712i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.51532 | + | 4.18939i | −0.395504 | + | 0.471344i | −0.926644 | − | 0.375941i | \(-0.877320\pi\) |
0.531139 | + | 0.847284i | \(0.321764\pi\) | |||||||
\(80\) | 6.03525 | + | 6.68168i | 0.674761 | + | 0.747035i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 13.0189 | + | 13.0189i | 1.43770 | + | 1.43770i | ||||
\(83\) | −0.529499 | − | 6.05220i | −0.0581201 | − | 0.664315i | −0.968249 | − | 0.249989i | \(-0.919573\pi\) |
0.910129 | − | 0.414326i | \(-0.135983\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.11978 | + | 9.00288i | 0.121457 | + | 0.976500i | ||||
\(86\) | −3.89612 | + | 10.7045i | −0.420130 | + | 1.15430i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.0547706 | + | 0.0782205i | 0.00583856 | + | 0.00833833i | ||||
\(89\) | 0.0742532 | − | 0.128610i | 0.00787082 | − | 0.0136327i | −0.862063 | − | 0.506801i | \(-0.830828\pi\) |
0.869934 | + | 0.493168i | \(0.164161\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.14993 | − | 3.72378i | −0.225374 | − | 0.390358i | ||||
\(92\) | 5.37690 | − | 11.5308i | 0.560581 | − | 1.20217i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.2223 | + | 12.1825i | 1.05435 | + | 1.25653i | ||||
\(95\) | −0.505829 | + | 3.64066i | −0.0518970 | + | 0.373524i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.6922 | + | 5.45218i | 1.18717 | + | 0.553585i | 0.912946 | − | 0.408081i | \(-0.133802\pi\) |
0.274222 | + | 0.961667i | \(0.411580\pi\) | |||||||
\(98\) | 2.59003 | − | 9.66613i | 0.261633 | − | 0.976427i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.81316 | + | 8.05424i | −0.581316 | + | 0.805424i | ||||
\(101\) | 5.20108 | + | 0.917090i | 0.517526 | + | 0.0912539i | 0.426310 | − | 0.904577i | \(-0.359813\pi\) |
0.0912166 | + | 0.995831i | \(0.470924\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.92471 | + | 1.36382i | −0.288181 | + | 0.134381i | −0.561333 | − | 0.827590i | \(-0.689711\pi\) |
0.273153 | + | 0.961971i | \(0.411934\pi\) | |||||||
\(104\) | −0.0141778 | − | 0.0804065i | −0.00139025 | − | 0.00788451i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 18.1206 | + | 15.2050i | 1.76002 | + | 1.47684i | ||||
\(107\) | −9.12902 | + | 9.12902i | −0.882536 | + | 0.882536i | −0.993792 | − | 0.111256i | \(-0.964513\pi\) |
0.111256 | + | 0.993792i | \(0.464513\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.32304i | − | 0.701420i | −0.936484 | − | 0.350710i | \(-0.885940\pi\) | ||
0.936484 | − | 0.350710i | \(-0.114060\pi\) | |||||||
\(110\) | −10.8416 | + | 11.6629i | −1.03371 | + | 1.11201i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.25646 | + | 4.65071i | −0.307707 | + | 0.439451i | ||||
\(113\) | 6.43209 | + | 13.7937i | 0.605081 | + | 1.29760i | 0.935354 | + | 0.353714i | \(0.115081\pi\) |
−0.330273 | + | 0.943885i | \(0.607141\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.9586 | − | 3.19950i | −1.30164 | − | 0.298355i | ||||
\(116\) | 4.76585 | + | 2.75156i | 0.442498 | + | 0.255476i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −27.6265 | − | 7.40249i | −2.54322 | − | 0.681455i | ||||
\(119\) | −5.37561 | + | 1.95656i | −0.492782 | + | 0.179358i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.31824 | + | 1.10614i | −0.119840 | + | 0.100558i | ||||
\(122\) | −1.11797 | + | 12.7785i | −0.101216 | + | 1.15691i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.44253 | − | 12.2057i | −0.398951 | − | 1.09611i | ||||
\(125\) | 10.2351 | + | 4.49926i | 0.915453 | + | 0.402426i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.42251 | − | 1.72091i | 0.569905 | − | 0.152706i | 0.0376522 | − | 0.999291i | \(-0.488012\pi\) |
0.532253 | + | 0.846585i | \(0.321345\pi\) | |||||||
\(128\) | −0.175446 | + | 0.122848i | −0.0155074 | + | 0.0108584i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 12.6159 | − | 5.12021i | 1.10648 | − | 0.449072i | ||||
\(131\) | −11.6386 | + | 2.05219i | −1.01687 | + | 0.179301i | −0.657149 | − | 0.753761i | \(-0.728238\pi\) |
−0.359717 | + | 0.933062i | \(0.617127\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.30889 | + | 0.202002i | −0.200206 | + | 0.0175158i | ||||
\(134\) | 23.2964 | 2.01251 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.108625 | −0.00931449 | ||||||||
\(137\) | 12.0706 | − | 1.05604i | 1.03126 | − | 0.0902237i | 0.441059 | − | 0.897478i | \(-0.354603\pi\) |
0.590203 | + | 0.807255i | \(0.299048\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.8272 | − | 2.26177i | 1.08799 | − | 0.191841i | 0.399242 | − | 0.916846i | \(-0.369273\pi\) |
0.688744 | + | 0.725005i | \(0.258162\pi\) | |||||||
\(140\) | −5.76927 | − | 2.43822i | −0.487592 | − | 0.206067i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.82469 | − | 1.27766i | 0.153125 | − | 0.107219i | ||||
\(143\) | 10.5061 | − | 2.81511i | 0.878568 | − | 0.235412i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.90486 | − | 5.89404i | 0.158190 | − | 0.489474i | ||||
\(146\) | −5.79358 | − | 15.9177i | −0.479480 | − | 1.31736i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.502850 | − | 5.74760i | 0.0413340 | − | 0.472450i | ||||
\(149\) | −2.75179 | + | 2.30902i | −0.225435 | + | 0.189162i | −0.748509 | − | 0.663125i | \(-0.769230\pi\) |
0.523074 | + | 0.852288i | \(0.324785\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.415850 | − | 0.151357i | 0.0338414 | − | 0.0123173i | −0.325044 | − | 0.945699i | \(-0.605379\pi\) |
0.358885 | + | 0.933382i | \(0.383157\pi\) | |||||||
\(152\) | −0.0425098 | − | 0.0113905i | −0.00344800 | − | 0.000923888i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.69564 | − | 5.02043i | −0.700715 | − | 0.404558i | ||||
\(155\) | −12.3865 | + | 7.76703i | −0.994907 | + | 0.623863i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.538818 | − | 1.15550i | −0.0430024 | − | 0.0922189i | 0.883633 | − | 0.468180i | \(-0.155090\pi\) |
−0.926635 | + | 0.375961i | \(0.877312\pi\) | |||||||
\(158\) | 6.26310 | − | 8.94463i | 0.498265 | − | 0.711597i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −13.0794 | − | 12.1584i | −1.03402 | − | 0.961207i | ||||
\(161\) | − | 9.02999i | − | 0.711663i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.53097 | + | 2.53097i | −0.198241 | + | 0.198241i | −0.799245 | − | 0.601005i | \(-0.794767\pi\) |
0.601005 | + | 0.799245i | \(0.294767\pi\) | |||||||
\(164\) | −14.0330 | − | 11.7751i | −1.09579 | − | 0.919479i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.10640 | + | 11.9460i | 0.163488 | + | 0.927187i | ||||
\(167\) | 10.9336 | − | 5.09841i | 0.846066 | − | 0.394527i | 0.0492772 | − | 0.998785i | \(-0.484308\pi\) |
0.796789 | + | 0.604258i | \(0.206530\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.64378 | + | 0.642497i | 0.280291 | + | 0.0494228i | ||||
\(170\) | −3.79396 | − | 17.7123i | −0.290984 | − | 1.35847i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.93349 | − | 10.9479i | 0.223677 | − | 0.834773i | ||||
\(173\) | 5.26639 | + | 2.45576i | 0.400397 | + | 0.186708i | 0.612377 | − | 0.790566i | \(-0.290214\pi\) |
−0.211980 | + | 0.977274i | \(0.567991\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.32343 | + | 6.92455i | −0.100042 | + | 0.523447i | ||||
\(176\) | −9.23141 | − | 11.0016i | −0.695844 | − | 0.829274i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.125312 | + | 0.268733i | −0.00939256 | + | 0.0201424i | ||||
\(179\) | −9.76891 | − | 16.9203i | −0.730163 | − | 1.26468i | −0.956813 | − | 0.290703i | \(-0.906111\pi\) |
0.226651 | − | 0.973976i | \(-0.427222\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.30360 | − | 9.18610i | 0.394213 | − | 0.682797i | −0.598787 | − | 0.800908i | \(-0.704350\pi\) |
0.993000 | + | 0.118111i | \(0.0376838\pi\) | |||||||
\(182\) | 4.92432 | + | 7.03265i | 0.365015 | + | 0.521295i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.0586442 | − | 0.161124i | 0.00432331 | − | 0.0118782i | ||||
\(185\) | −6.44444 | + | 0.801558i | −0.473804 | + | 0.0589317i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.26120 | − | 14.4156i | −0.0922282 | − | 1.05417i | ||||
\(188\) | −11.1886 | − | 11.1886i | −0.816012 | − | 0.816012i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.372574 | − | 7.32947i | 0.0270293 | − | 0.531735i | ||||
\(191\) | 3.07377 | − | 3.66318i | 0.222410 | − | 0.265058i | −0.643288 | − | 0.765624i | \(-0.722430\pi\) |
0.865698 | + | 0.500566i | \(0.166875\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.45676 | − | 3.12066i | −0.320804 | − | 0.224630i | 0.402070 | − | 0.915609i | \(-0.368291\pi\) |
−0.722875 | + | 0.690979i | \(0.757180\pi\) | |||||||
\(194\) | −24.2052 | − | 8.80997i | −1.73783 | − | 0.632519i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.72897 | + | 9.80546i | −0.123498 | + | 0.700390i | ||||
\(197\) | 2.07911 | + | 7.75934i | 0.148130 | + | 0.552830i | 0.999596 | + | 0.0284197i | \(0.00904750\pi\) |
−0.851466 | + | 0.524410i | \(0.824286\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.5312 | − | 6.08020i | 0.746539 | − | 0.431014i | −0.0779033 | − | 0.996961i | \(-0.524823\pi\) |
0.824442 | + | 0.565947i | \(0.191489\pi\) | |||||||
\(200\) | −0.0685848 | + | 0.114961i | −0.00484968 | + | 0.00812898i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.5048 | − | 0.919049i | −0.739114 | − | 0.0646641i | ||||
\(203\) | 3.89096 | + | 0.340415i | 0.273092 | + | 0.0238925i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.65154 | + | 18.2209i | −0.674092 | + | 1.27260i | ||||
\(206\) | 5.58006 | − | 3.22165i | 0.388781 | − | 0.224463i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.17819 | + | 11.8612i | 0.220368 | + | 0.822425i | ||||
\(209\) | 1.01806 | − | 5.77373i | 0.0704210 | − | 0.399377i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.80282 | + | 1.02014i | 0.192954 | + | 0.0702295i | 0.436690 | − | 0.899612i | \(-0.356151\pi\) |
−0.243736 | + | 0.969842i | \(0.578373\pi\) | |||||||
\(212\) | −19.2792 | − | 13.4995i | −1.32410 | − | 0.927147i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 16.5694 | − | 19.7467i | 1.13266 | − | 1.34985i | ||||
\(215\) | −12.7410 | − | 0.647657i | −0.868932 | − | 0.0441698i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.51879 | − | 6.51879i | −0.442524 | − | 0.442524i | ||||
\(218\) | 1.27435 | + | 14.5659i | 0.0863097 | + | 0.986525i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.73461 | − | 12.5002i | 0.656307 | − | 0.842761i | ||||
\(221\) | −4.23179 | + | 11.6267i | −0.284661 | + | 0.782099i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.64364 | + | 6.63181i | 0.310961 | + | 0.444099i | 0.943963 | − | 0.330052i | \(-0.107066\pi\) |
−0.633002 | + | 0.774151i | \(0.718177\pi\) | |||||||
\(224\) | 5.63019 | − | 9.75178i | 0.376183 | − | 0.651568i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.1941 | − | 26.3170i | −1.01070 | − | 1.75058i | ||||
\(227\) | 3.25781 | − | 6.98639i | 0.216228 | − | 0.463703i | −0.768036 | − | 0.640407i | \(-0.778766\pi\) |
0.984264 | + | 0.176704i | \(0.0565435\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.93595 | + | 3.49893i | 0.194013 | + | 0.231216i | 0.854277 | − | 0.519818i | \(-0.174000\pi\) |
−0.660264 | + | 0.751033i | \(0.729556\pi\) | |||||||
\(230\) | 28.3211 | + | 3.93490i | 1.86743 | + | 0.259459i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.0672163 | + | 0.0313435i | 0.00441297 | + | 0.00205780i | ||||
\(233\) | −5.18153 | + | 19.3377i | −0.339454 | + | 1.26686i | 0.559506 | + | 0.828826i | \(0.310991\pi\) |
−0.898960 | + | 0.438032i | \(0.855676\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.67661 | + | 14.9521i | −0.631232 | + | 0.975364i | ||||
\(236\) | 28.0247 | + | 4.94151i | 1.82425 | + | 0.321665i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10.3519 | − | 4.82716i | 0.671012 | − | 0.312898i | ||||
\(239\) | 2.31345 | + | 13.1202i | 0.149645 | + | 0.848678i | 0.963520 | + | 0.267638i | \(0.0862431\pi\) |
−0.813875 | + | 0.581040i | \(0.802646\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.5457 | + | 16.4008i | 1.25905 | + | 1.05647i | 0.995783 | + | 0.0917454i | \(0.0292446\pi\) |
0.263267 | + | 0.964723i | \(0.415200\pi\) | |||||||
\(242\) | 2.42956 | − | 2.42956i | 0.156178 | − | 0.156178i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 12.7627i | − | 0.817047i | ||||||
\(245\) | 11.1996 | − | 0.408720i | 0.715519 | − | 0.0261122i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.87528 | + | 4.10632i | −0.182950 | + | 0.261279i | ||||
\(248\) | −0.0739804 | − | 0.158651i | −0.00469776 | − | 0.0100744i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −21.1410 | − | 7.16814i | −1.33707 | − | 0.453353i | ||||
\(251\) | −17.4693 | − | 10.0859i | −1.10265 | − | 0.636617i | −0.165736 | − | 0.986170i | \(-0.553000\pi\) |
−0.936917 | + | 0.349553i | \(0.886333\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.0636 | + | 5.91193i | 1.38713 | + | 0.371680i | ||||
\(254\) | −12.4752 | + | 4.54060i | −0.782764 | + | 0.284903i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.4194 | − | 10.4211i | 0.776213 | − | 0.651320i | ||||
\(257\) | 0.746929 | − | 8.53743i | 0.0465921 | − | 0.532550i | −0.936653 | − | 0.350260i | \(-0.886093\pi\) |
0.983245 | − | 0.182291i | \(-0.0583512\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.40055 | − | 3.84797i | −0.0870257 | − | 0.239101i | ||||
\(260\) | −12.0606 | + | 6.16905i | −0.747964 | + | 0.382588i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 22.7925 | − | 6.10724i | 1.40813 | − | 0.377307i | ||||
\(263\) | 16.5483 | − | 11.5873i | 1.02041 | − | 0.714501i | 0.0614734 | − | 0.998109i | \(-0.480420\pi\) |
0.958941 | + | 0.283607i | \(0.0915312\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.3126 | + | 24.4015i | −0.633499 | + | 1.49897i | ||||
\(266\) | 4.55734 | − | 0.803581i | 0.279428 | − | 0.0492707i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −23.0909 | + | 2.02019i | −1.41050 | + | 0.123403i | ||||
\(269\) | 11.8522 | 0.722639 | 0.361320 | − | 0.932442i | \(-0.382326\pi\) | ||||
0.361320 | + | 0.932442i | \(0.382326\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.7671 | 1.50450 | 0.752249 | − | 0.658879i | \(-0.228969\pi\) | ||||
0.752249 | + | 0.658879i | \(0.228969\pi\) | |||||||
\(272\) | 16.2749 | − | 1.42387i | 0.986808 | − | 0.0863345i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −23.8252 | + | 4.20103i | −1.43934 | + | 0.253794i | ||||
\(275\) | −16.0528 | − | 7.76713i | −0.968021 | − | 0.468375i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.8949 | + | 16.7314i | −1.43571 | + | 1.00529i | −0.441564 | + | 0.897230i | \(0.645576\pi\) |
−0.994144 | + | 0.108064i | \(0.965535\pi\) | |||||||
\(278\) | −25.1202 | + | 6.73095i | −1.50661 | + | 0.403695i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.0803198 | − | 0.0259580i | −0.00480003 | − | 0.00155129i | ||||
\(281\) | 10.0345 | + | 27.5694i | 0.598605 | + | 1.64465i | 0.754055 | + | 0.656811i | \(0.228095\pi\) |
−0.155450 | + | 0.987844i | \(0.549683\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.18317 | − | 13.5237i | 0.0703324 | − | 0.803902i | −0.876338 | − | 0.481697i | \(-0.840020\pi\) |
0.946670 | − | 0.322205i | \(-0.104424\pi\) | |||||||
\(284\) | −1.69780 | + | 1.42462i | −0.100746 | + | 0.0845357i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20.4073 | + | 7.42766i | −1.20671 | + | 0.439207i | ||||
\(287\) | −12.5587 | − | 3.36509i | −0.741315 | − | 0.198635i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.466643 | − | 0.269416i | −0.0274496 | − | 0.0158480i | ||||
\(290\) | −2.76317 | + | 12.0550i | −0.162259 | + | 0.707895i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.12281 | + | 15.2749i | 0.416831 | + | 0.893897i | ||||
\(293\) | −4.73624 | + | 6.76405i | −0.276694 | + | 0.395160i | −0.933314 | − | 0.359062i | \(-0.883097\pi\) |
0.656620 | + | 0.754222i | \(0.271986\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.16815 | − | 32.0094i | −0.0680124 | − | 1.86366i | ||||
\(296\) | − | 0.0777556i | − | 0.00451945i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.07162 | − | 5.07162i | 0.293791 | − | 0.293791i | ||||
\(299\) | −14.9614 | − | 12.5541i | −0.865238 | − | 0.726021i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.39689 | − | 7.92216i | −0.0805155 | − | 0.456626i | ||||
\(302\) | −0.800806 | + | 0.373422i | −0.0460812 | + | 0.0214880i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.51840 | + | 1.14937i | 0.373856 | + | 0.0659209i | ||||
\(305\) | −14.0468 | + | 3.00882i | −0.804317 | + | 0.172284i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.68621 | + | 10.0251i | −0.153310 | + | 0.572161i | 0.845934 | + | 0.533288i | \(0.179044\pi\) |
−0.999244 | + | 0.0388737i | \(0.987623\pi\) | |||||||
\(308\) | 9.05429 | + | 4.22208i | 0.515916 | + | 0.240575i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 23.2857 | − | 17.6045i | 1.32254 | − | 0.999867i | ||||
\(311\) | 12.2675 | + | 14.6199i | 0.695627 | + | 0.829016i | 0.992024 | − | 0.126049i | \(-0.0402297\pi\) |
−0.296397 | + | 0.955065i | \(0.595785\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.95728 | − | 14.9199i | 0.393249 | − | 0.843325i | −0.605619 | − | 0.795755i | \(-0.707075\pi\) |
0.998868 | − | 0.0475700i | \(-0.0151477\pi\) | |||||||
\(314\) | 1.27281 | + | 2.20458i | 0.0718291 | + | 0.124412i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.43220 | + | 9.40884i | −0.305585 | + | 0.529289i | ||||
\(317\) | −4.28594 | − | 6.12095i | −0.240722 | − | 0.343787i | 0.680553 | − | 0.732699i | \(-0.261740\pi\) |
−0.921275 | + | 0.388912i | \(0.872851\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.37917 | + | 9.28420i | −0.189197 | + | 0.519816i | ||||
\(320\) | 13.9238 | + | 10.8433i | 0.778363 | + | 0.606156i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.57139 | + | 17.9611i | 0.0875702 | + | 1.00093i | ||||
\(323\) | 4.71587 | + | 4.71587i | 0.262398 | + | 0.262398i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.63304 | + | 11.8197i | 0.534345 | + | 0.655638i | ||||
\(326\) | 4.59378 | − | 5.47465i | 0.254426 | − | 0.303213i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.202232 | − | 0.141605i | −0.0111664 | − | 0.00781881i | ||||
\(329\) | −10.5531 | − | 3.84101i | −0.581811 | − | 0.211762i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.44127 | − | 8.17383i | 0.0792192 | − | 0.449274i | −0.919236 | − | 0.393707i | \(-0.871192\pi\) |
0.998455 | − | 0.0555668i | \(-0.0176966\pi\) | |||||||
\(332\) | −3.12373 | − | 11.6579i | −0.171437 | − | 0.639812i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −20.8602 | + | 12.0436i | −1.14142 | + | 0.658998i | ||||
\(335\) | 7.66717 | + | 24.9380i | 0.418902 | + | 1.36251i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.6386 | + | 1.36820i | 0.851888 | + | 0.0745305i | 0.504731 | − | 0.863277i | \(-0.331592\pi\) |
0.347157 | + | 0.937807i | \(0.387147\pi\) | |||||||
\(338\) | −7.35946 | − | 0.643869i | −0.400302 | − | 0.0350219i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.29645 | + | 17.2270i | 0.287240 | + | 0.934268i | ||||
\(341\) | 20.1957 | − | 11.6600i | 1.09366 | − | 0.631424i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.38351 | + | 16.3595i | 0.236687 | + | 0.883330i | ||||
\(344\) | 0.0265246 | − | 0.150428i | 0.00143011 | − | 0.00811056i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.9025 | − | 3.96817i | −0.586120 | − | 0.213330i | ||||
\(347\) | −0.751529 | − | 0.526226i | −0.0403442 | − | 0.0282493i | 0.553230 | − | 0.833028i | \(-0.313395\pi\) |
−0.593575 | + | 0.804779i | \(0.702284\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.1000 | + | 27.5295i | −1.23652 | + | 1.47362i | −0.408655 | + | 0.912689i | \(0.634002\pi\) |
−0.827861 | + | 0.560934i | \(0.810442\pi\) | |||||||
\(350\) | 1.42736 | − | 14.0036i | 0.0762953 | − | 0.748522i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 20.1412 | + | 20.1412i | 1.07353 | + | 1.07353i | ||||
\(353\) | 0.420748 | + | 4.80917i | 0.0223942 | + | 0.255966i | 0.999136 | + | 0.0415497i | \(0.0132295\pi\) |
−0.976742 | + | 0.214417i | \(0.931215\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.96822 | + | 1.53277i | 0.104462 | + | 0.0813508i | ||||
\(356\) | 0.100903 | − | 0.277229i | 0.00534786 | − | 0.0146931i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.3753 | + | 31.9552i | 1.18257 | + | 1.68889i | ||||
\(359\) | −1.88801 | + | 3.27013i | −0.0996454 | + | 0.172591i | −0.911538 | − | 0.411216i | \(-0.865104\pi\) |
0.811892 | + | 0.583807i | \(0.198438\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.14897 | − | 14.1144i | −0.428893 | − | 0.742865i | ||||
\(362\) | −8.95055 | + | 19.1945i | −0.470430 | + | 1.00884i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.49072 | − | 6.54359i | −0.287792 | − | 0.342977i | ||||
\(365\) | 15.1326 | − | 11.4406i | 0.792076 | − | 0.598826i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.8495 | − | 10.6549i | −1.19273 | − | 0.556181i | −0.278135 | − | 0.960542i | \(-0.589716\pi\) |
−0.914600 | + | 0.404361i | \(0.867494\pi\) | |||||||
\(368\) | −6.67443 | + | 24.9093i | −0.347929 | + | 1.29849i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12.6788 | − | 2.71579i | 0.659140 | − | 0.141187i | ||||
\(371\) | −16.4505 | − | 2.90067i | −0.854070 | − | 0.150596i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.99084 | − | 4.65880i | 0.517306 | − | 0.241224i | −0.146389 | − | 0.989227i | \(-0.546765\pi\) |
0.663695 | + | 0.748003i | \(0.268987\pi\) | |||||||
\(374\) | 5.01718 | + | 28.4538i | 0.259432 | + | 1.47131i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.163356 | − | 0.137072i | −0.00842442 | − | 0.00706893i | ||||
\(377\) | 5.97348 | − | 5.97348i | 0.307650 | − | 0.307650i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 6.15292i | − | 0.316054i | −0.987435 | − | 0.158027i | \(-0.949487\pi\) | ||
0.987435 | − | 0.158027i | \(-0.0505134\pi\) | |||||||
\(380\) | 0.266301 | + | 7.29712i | 0.0136610 | + | 0.374334i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.47641 | + | 7.82113i | −0.280198 | + | 0.400164i | ||||
\(383\) | −7.45128 | − | 15.9793i | −0.380743 | − | 0.816506i | −0.999521 | − | 0.0309400i | \(-0.990150\pi\) |
0.618778 | − | 0.785566i | \(-0.287628\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.51233 | − | 10.9606i | 0.128040 | − | 0.558606i | ||||
\(386\) | 9.40775 | + | 5.43157i | 0.478842 | + | 0.276460i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 24.7556 | + | 6.63326i | 1.25678 | + | 0.336753i | ||||
\(389\) | 13.1982 | − | 4.80373i | 0.669173 | − | 0.243559i | 0.0149811 | − | 0.999888i | \(-0.495231\pi\) |
0.654192 | + | 0.756329i | \(0.273009\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.9049 | + | 16.7022i | −1.00663 | + | 0.844666i | ||||
\(392\) | −0.0116951 | + | 0.133675i | −0.000590689 | + | 0.00675161i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.48572 | − | 15.0719i | −0.276366 | − | 0.759311i | ||||
\(395\) | 11.6362 | + | 3.76061i | 0.585479 | + | 0.189217i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.2343 | + | 7.83331i | −1.46723 | + | 0.393143i | −0.901980 | − | 0.431778i | \(-0.857886\pi\) |
−0.565248 | + | 0.824921i | \(0.691220\pi\) | |||||||
\(398\) | −19.8890 | + | 13.9264i | −0.996947 | + | 0.698070i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.76890 | − | 18.1232i | 0.438445 | − | 0.906162i | ||||
\(401\) | 16.0405 | − | 2.82837i | 0.801024 | − | 0.141242i | 0.241873 | − | 0.970308i | \(-0.422238\pi\) |
0.559151 | + | 0.829066i | \(0.311127\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.8635 | + | 1.73783i | −0.989472 | + | 0.0865676i | ||||
\(404\) | 10.4918 | 0.521987 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.79855 | −0.387035 | ||||||||
\(407\) | 10.3190 | − | 0.902792i | 0.511492 | − | 0.0447497i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.2731 | − | 3.39837i | 0.952995 | − | 0.168039i | 0.324529 | − | 0.945876i | \(-0.394794\pi\) |
0.628466 | + | 0.777837i | \(0.283683\pi\) | |||||||
\(410\) | 16.0266 | − | 37.9218i | 0.791496 | − | 1.87282i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.25147 | + | 3.67712i | −0.258721 | + | 0.181159i | ||||
\(413\) | 19.5091 | − | 5.22744i | 0.959979 | − | 0.257226i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0945 | + | 6.18639i | −0.593694 | + | 0.303678i | ||||
\(416\) | −8.32980 | − | 22.8859i | −0.408402 | − | 1.12208i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.02024 | + | 11.6614i | −0.0499015 | + | 0.570377i | ||||
\(419\) | 0.141106 | − | 0.118402i | 0.00689349 | − | 0.00578432i | −0.639334 | − | 0.768929i | \(-0.720790\pi\) |
0.646228 | + | 0.763145i | \(0.276346\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.1952 | + | 6.25854i | −0.838043 | + | 0.305023i | −0.725155 | − | 0.688585i | \(-0.758232\pi\) |
−0.112887 | + | 0.993608i | \(0.536010\pi\) | |||||||
\(422\) | −5.75246 | − | 1.54137i | −0.280025 | − | 0.0750325i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.274692 | − | 0.158593i | −0.0133402 | − | 0.00770197i | ||||
\(425\) | 17.7117 | − | 9.89064i | 0.859144 | − | 0.479767i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.82819 | − | 8.20959i | −0.185259 | − | 0.397290i | ||||
\(428\) | −14.7109 | + | 21.0093i | −0.711078 | + | 1.01552i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 25.4552 | − | 0.928965i | 1.22756 | − | 0.0447987i | ||||
\(431\) | 20.4312i | 0.984138i | 0.870556 | + | 0.492069i | \(0.163759\pi\) | ||||
−0.870556 | + | 0.492069i | \(0.836241\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.40075 | + | 1.40075i | −0.0673156 | + | 0.0673156i | −0.739963 | − | 0.672647i | \(-0.765157\pi\) |
0.672647 | + | 0.739963i | \(0.265157\pi\) | |||||||
\(434\) | 14.1006 | + | 11.8318i | 0.676849 | + | 0.567944i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.52621 | − | 14.3269i | −0.120984 | − | 0.686132i | ||||
\(437\) | −9.54109 | + | 4.44908i | −0.456412 | + | 0.212829i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.9335 | + | 2.45686i | 0.665012 | + | 0.117259i | 0.495957 | − | 0.868347i | \(-0.334817\pi\) |
0.169055 | + | 0.985607i | \(0.445929\pi\) | |||||||
\(440\) | 0.116010 | − | 0.179257i | 0.00553058 | − | 0.00854572i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.39395 | − | 23.8625i | 0.304129 | − | 1.13503i | ||||
\(443\) | −14.5440 | − | 6.78197i | −0.691005 | − | 0.322221i | 0.0452014 | − | 0.998978i | \(-0.485607\pi\) |
−0.736207 | + | 0.676757i | \(0.763385\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.328911 | − | 0.0456985i | −0.0155919 | − | 0.00216632i | ||||
\(446\) | −10.3905 | − | 12.3829i | −0.492004 | − | 0.586347i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.70292 | + | 10.0854i | −0.222192 | + | 0.476493i | ||||
\(449\) | 2.86184 | + | 4.95685i | 0.135059 | + | 0.233928i | 0.925620 | − | 0.378455i | \(-0.123544\pi\) |
−0.790561 | + | 0.612383i | \(0.790211\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.4443 | − | 28.4824i | 0.774333 | − | 1.34118i | ||||
\(452\) | 17.3422 | + | 24.7672i | 0.815708 | + | 1.16495i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.26417 | + | 14.4632i | −0.247060 | + | 0.678791i | ||||
\(455\) | −5.90753 | + | 7.58583i | −0.276949 | + | 0.355629i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.72215 | + | 19.6843i | 0.0805589 | + | 0.920793i | 0.923704 | + | 0.383107i | \(0.125146\pi\) |
−0.843145 | + | 0.537686i | \(0.819299\pi\) | |||||||
\(458\) | −6.44862 | − | 6.44862i | −0.301324 | − | 0.301324i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −28.4124 | − | 1.44427i | −1.32474 | − | 0.0673394i | ||||
\(461\) | 11.6371 | − | 13.8685i | 0.541993 | − | 0.645922i | −0.423640 | − | 0.905830i | \(-0.639248\pi\) |
0.965633 | + | 0.259909i | \(0.0836924\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.7175 | + | 7.50444i | 0.498082 | + | 0.348761i | 0.795467 | − | 0.605997i | \(-0.207226\pi\) |
−0.297385 | + | 0.954758i | \(0.596114\pi\) | |||||||
\(464\) | −10.4816 | − | 3.81501i | −0.486598 | − | 0.177107i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.94118 | − | 39.3654i | 0.321544 | − | 1.82357i | ||||
\(467\) | 2.10904 | + | 7.87106i | 0.0975949 | + | 0.364229i | 0.997400 | − | 0.0720628i | \(-0.0229582\pi\) |
−0.899805 | + | 0.436292i | \(0.856292\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.2473 | + | 8.22566i | −0.657877 | + | 0.379826i | ||||
\(470\) | 16.6453 | − | 31.4242i | 0.767790 | − | 1.44949i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.382053 | + | 0.0334253i | 0.0175854 | + | 0.00153852i | ||||
\(473\) | 20.2713 | + | 1.77351i | 0.932077 | + | 0.0815462i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.96853 | − | 2.01340i | 0.365621 | − | 0.0923810i | ||||
\(476\) | −9.84196 | + | 5.68226i | −0.451105 | + | 0.260446i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.88474 | − | 25.6942i | −0.314901 | − | 1.17523i | ||||
\(479\) | 4.41454 | − | 25.0361i | 0.201706 | − | 1.14393i | −0.700835 | − | 0.713324i | \(-0.747189\pi\) |
0.902540 | − | 0.430606i | \(-0.141700\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.32264 | − | 3.02919i | −0.379480 | − | 0.138119i | ||||
\(482\) | −41.7314 | − | 29.2206i | −1.90081 | − | 1.33096i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.19744 | + | 2.61881i | −0.0998838 | + | 0.119037i | ||||
\(485\) | 1.46449 | − | 28.8102i | 0.0664991 | − | 1.30821i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.8770 | − | 20.8770i | −0.946027 | − | 0.946027i | 0.0525891 | − | 0.998616i | \(-0.483253\pi\) |
−0.998616 | + | 0.0525891i | \(0.983253\pi\) | |||||||
\(488\) | −0.0149909 | − | 0.171347i | −0.000678606 | − | 0.00775651i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −22.2055 | + | 2.76191i | −1.00314 | + | 0.124771i | ||||
\(491\) | 4.08765 | − | 11.2307i | 0.184473 | − | 0.506835i | −0.812640 | − | 0.582766i | \(-0.801971\pi\) |
0.997113 | + | 0.0759306i | \(0.0241927\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.44648 | − | 9.20652i | −0.290335 | − | 0.414641i | ||||
\(494\) | 5.00448 | − | 8.66802i | 0.225162 | − | 0.389993i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.1638 | + | 22.8004i | 0.591074 | + | 1.02377i | ||||
\(497\) | −0.664789 | + | 1.42564i | −0.0298199 | + | 0.0639489i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.31792 | + | 3.95415i | 0.148531 | + | 0.177012i | 0.835180 | − | 0.549977i | \(-0.185364\pi\) |
−0.686649 | + | 0.726989i | \(0.740919\pi\) | |||||||
\(500\) | 21.5761 | + | 5.27162i | 0.964912 | + | 0.235754i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 36.5024 | + | 17.0214i | 1.62918 | + | 0.759700i | ||||
\(503\) | 2.60729 | − | 9.73055i | 0.116253 | − | 0.433864i | −0.883124 | − | 0.469139i | \(-0.844564\pi\) |
0.999378 | + | 0.0352755i | \(0.0112309\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.47345 | − | 11.5474i | −0.110067 | − | 0.513854i | ||||
\(506\) | −44.9144 | − | 7.91962i | −1.99669 | − | 0.352070i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.9714 | − | 5.58236i | 0.531145 | − | 0.247677i | ||||
\(509\) | 5.57060 | + | 31.5924i | 0.246912 | + | 1.40031i | 0.816009 | + | 0.578039i | \(0.196182\pi\) |
−0.569097 | + | 0.822270i | \(0.692707\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.16349 | + | 7.68908i | 0.405369 | + | 0.340145i | ||||
\(512\) | −22.5864 | + | 22.5864i | −0.998188 | + | 0.998188i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 17.1113i | 0.754749i | ||||||||
\(515\) | 5.28513 | + | 4.91296i | 0.232891 | + | 0.216491i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.2941 | − | 23.2704i | 0.716615 | − | 1.02343i | ||||
\(518\) | 3.45537 | + | 7.41007i | 0.151820 | + | 0.325580i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.154674 | + | 0.0969895i | −0.00678292 | + | 0.00425327i | ||||
\(521\) | 5.58144 | + | 3.22245i | 0.244528 | + | 0.141178i | 0.617256 | − | 0.786762i | \(-0.288244\pi\) |
−0.372728 | + | 0.927941i | \(0.621578\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.76374 | − | 1.81234i | −0.295758 | − | 0.0792481i | 0.107889 | − | 0.994163i | \(-0.465591\pi\) |
−0.403647 | + | 0.914915i | \(0.632258\pi\) | |||||||
\(524\) | −22.0619 | + | 8.02986i | −0.963777 | + | 0.350786i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −30.8990 | + | 25.9273i | −1.34726 | + | 1.13049i | ||||
\(527\) | −2.31205 | + | 26.4268i | −0.100714 | + | 1.15117i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.16176 | − | 16.9293i | −0.267902 | − | 0.736056i | ||||
\(530\) | 16.2659 | − | 50.3304i | 0.706547 | − | 2.18621i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.44745 | + | 1.19169i | −0.192821 | + | 0.0516663i | ||||
\(533\) | −23.0353 | + | 16.1295i | −0.997770 | + | 0.698646i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.5913 | + | 11.2381i | 1.14964 | + | 0.485863i | ||||
\(536\) | −0.307637 | + | 0.0542447i | −0.0132879 | + | 0.00234301i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −23.5745 | + | 2.06250i | −1.01637 | + | 0.0889208i | ||||
\(539\) | −17.8758 | −0.769966 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.0530 | −1.46405 | −0.732026 | − | 0.681276i | \(-0.761425\pi\) | ||||
−0.732026 | + | 0.681276i | \(0.761425\pi\) | |||||||
\(542\) | −49.2630 | + | 4.30996i | −2.11603 | + | 0.185128i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −31.9097 | + | 5.62655i | −1.36812 | + | 0.241236i | ||||
\(545\) | −15.1728 | + | 6.15796i | −0.649931 | + | 0.263778i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.2173 | − | 14.1563i | 0.864431 | − | 0.605281i | −0.0550200 | − | 0.998485i | \(-0.517522\pi\) |
0.919451 | + | 0.393204i | \(0.128633\pi\) | |||||||
\(548\) | 23.2508 | − | 6.23002i | 0.993224 | − | 0.266133i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 33.2814 | + | 12.6557i | 1.41913 | + | 0.539640i | ||||
\(551\) | −1.55740 | − | 4.27891i | −0.0663474 | − | 0.182288i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.672056 | + | 7.68163i | −0.0285787 | + | 0.326656i | ||||
\(554\) | 44.6166 | − | 37.4378i | 1.89558 | − | 1.59058i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 24.3149 | − | 8.84992i | 1.03118 | − | 0.375320i | ||||
\(557\) | 8.51625 | + | 2.28192i | 0.360845 | + | 0.0966881i | 0.434686 | − | 0.900582i | \(-0.356859\pi\) |
−0.0738415 | + | 0.997270i | \(0.523526\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.0679 | − | 8.69945i | −0.637304 | − | 0.367948i | ||||
\(560\) | 12.3743 | + | 2.83636i | 0.522910 | + | 0.119858i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −24.7566 | − | 53.0907i | −1.04429 | − | 2.23950i | ||||
\(563\) | 13.3979 | − | 19.1342i | 0.564655 | − | 0.806411i | −0.430719 | − | 0.902486i | \(-0.641740\pi\) |
0.995374 | + | 0.0960749i | \(0.0306288\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.1707 | − | 24.9260i | 0.974800 | − | 1.04864i | ||||
\(566\) | 27.1052i | 1.13932i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.0211206 | + | 0.0211206i | −0.000886202 | + | 0.000886202i | ||||
\(569\) | −1.82798 | − | 1.53386i | −0.0766330 | − | 0.0643027i | 0.603667 | − | 0.797237i | \(-0.293706\pi\) |
−0.680300 | + | 0.732934i | \(0.738150\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.32573 | + | 35.8750i | 0.264724 | + | 1.50132i | 0.769821 | + | 0.638260i | \(0.220346\pi\) |
−0.505097 | + | 0.863063i | \(0.668543\pi\) | |||||||
\(572\) | 19.5832 | − | 9.13180i | 0.818815 | − | 0.381820i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 25.5654 | + | 4.50787i | 1.06708 | + | 0.188155i | ||||
\(575\) | 5.10868 | + | 31.6116i | 0.213047 | + | 1.31830i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.50782 | + | 24.2875i | −0.270924 | + | 1.01110i | 0.687600 | + | 0.726090i | \(0.258664\pi\) |
−0.958524 | + | 0.285012i | \(0.908002\pi\) | |||||||
\(578\) | 0.975058 | + | 0.454677i | 0.0405571 | + | 0.0189121i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.69343 | − | 12.1883i | 0.0703157 | − | 0.506091i | ||||
\(581\) | −5.50616 | − | 6.56198i | −0.228434 | − | 0.272237i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.8576 | − | 38.2957i | 0.739586 | − | 1.58605i | ||||
\(584\) | 0.113570 | + | 0.196709i | 0.00469955 | + | 0.00813986i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.24353 | − | 14.2782i | 0.340537 | − | 0.589828i | ||||
\(587\) | −17.4662 | − | 24.9444i | −0.720909 | − | 1.02956i | −0.997643 | − | 0.0686181i | \(-0.978141\pi\) |
0.276734 | − | 0.960947i | \(-0.410748\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.67594 | + | 10.0996i | −0.151465 | + | 0.416145i | ||||
\(590\) | 7.89375 | + | 63.4649i | 0.324980 | + | 2.61281i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.01923 | + | 11.6499i | 0.0418901 | + | 0.478806i | ||||
\(593\) | 26.7405 | + | 26.7405i | 1.09810 | + | 1.09810i | 0.994633 | + | 0.103470i | \(0.0329946\pi\) |
0.103470 | + | 0.994633i | \(0.467005\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.57423 | + | 9.49260i | 0.351509 | + | 0.389159i | ||||
\(596\) | −4.58708 | + | 5.46667i | −0.187894 | + | 0.223924i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 31.9435 | + | 22.3671i | 1.30627 | + | 0.914658i | ||||
\(599\) | 1.09294 | + | 0.397799i | 0.0446564 | + | 0.0162536i | 0.364252 | − | 0.931301i | \(-0.381325\pi\) |
−0.319595 | + | 0.947554i | \(0.603547\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.53128 | − | 14.3556i | 0.103253 | − | 0.585578i | −0.888650 | − | 0.458585i | \(-0.848356\pi\) |
0.991904 | − | 0.126993i | \(-0.0405325\pi\) | |||||||
\(602\) | 4.15709 | + | 15.5145i | 0.169430 | + | 0.632323i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.761360 | − | 0.439571i | 0.0309793 | − | 0.0178859i | ||||
\(605\) | 3.40035 | + | 1.80115i | 0.138244 | + | 0.0732272i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.0709 | − | 2.89333i | −1.34231 | − | 0.117437i | −0.606746 | − | 0.794896i | \(-0.707525\pi\) |
−0.735560 | + | 0.677459i | \(0.763081\pi\) | |||||||
\(608\) | −13.0777 | − | 1.14415i | −0.530372 | − | 0.0464015i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 27.4162 | − | 8.42909i | 1.11005 | − | 0.341284i | ||||
\(611\) | −21.0356 | + | 12.1449i | −0.851008 | + | 0.491330i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.05733 | + | 11.4101i | 0.123484 | + | 0.460849i | 0.999781 | − | 0.0209221i | \(-0.00666018\pi\) |
−0.876297 | + | 0.481772i | \(0.839994\pi\) | |||||||
\(614\) | 3.59845 | − | 20.4078i | 0.145221 | − | 0.823592i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.126518 | + | 0.0460490i | 0.00509757 | + | 0.00185537i | ||||
\(617\) | −37.7549 | − | 26.4363i | −1.51996 | − | 1.06428i | −0.974021 | − | 0.226458i | \(-0.927285\pi\) |
−0.545935 | − | 0.837827i | \(-0.683826\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.15117 | − | 9.71419i | 0.327623 | − | 0.390446i | −0.576939 | − | 0.816787i | \(-0.695753\pi\) |
0.904563 | + | 0.426341i | \(0.140198\pi\) | |||||||
\(620\) | −21.5537 | + | 19.4684i | −0.865617 | + | 0.781871i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −26.9448 | − | 26.9448i | −1.08039 | − | 1.08039i | ||||
\(623\) | −0.0182496 | − | 0.208594i | −0.000731154 | − | 0.00835713i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.715439 | − | 24.9898i | 0.0286176 | − | 0.999590i | ||||
\(626\) | −11.2420 | + | 30.8872i | −0.449321 | + | 1.23450i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.45276 | − | 2.07476i | −0.0579714 | − | 0.0827918i | ||||
\(629\) | −5.89161 | + | 10.2046i | −0.234914 | + | 0.406883i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.7330 | + | 28.9824i | 0.666131 | + | 1.15377i | 0.978977 | + | 0.203969i | \(0.0653841\pi\) |
−0.312847 | + | 0.949804i | \(0.601283\pi\) | |||||||
\(632\) | −0.0618790 | + | 0.132700i | −0.00246142 | + | 0.00527852i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.59010 | + | 11.4290i | 0.380871 | + | 0.453905i | ||||
\(635\) | −8.96630 | − | 11.8599i | −0.355817 | − | 0.470644i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.8524 | + | 6.45949i | 0.548853 | + | 0.255934i | ||||
\(638\) | 5.10571 | − | 19.0548i | 0.202137 | − | 0.754385i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.402066 | + | 0.260207i | 0.0158930 | + | 0.0102856i | ||||
\(641\) | 2.02936 | + | 0.357831i | 0.0801548 | + | 0.0141335i | 0.213582 | − | 0.976925i | \(-0.431487\pi\) |
−0.133427 | + | 0.991059i | \(0.542598\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.5810 | + | 13.7938i | −1.16656 | + | 0.543976i | −0.906744 | − | 0.421682i | \(-0.861440\pi\) |
−0.259816 | + | 0.965658i | \(0.583662\pi\) | |||||||
\(644\) | −3.11506 | − | 17.6664i | −0.122750 | − | 0.696153i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.2007 | − | 8.55944i | −0.401343 | − | 0.336767i | ||||
\(647\) | 10.7867 | − | 10.7867i | 0.424069 | − | 0.424069i | −0.462533 | − | 0.886602i | \(-0.653059\pi\) |
0.886602 | + | 0.462533i | \(0.153059\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 51.0904i | 2.00547i | ||||||||
\(650\) | −21.2174 | − | 21.8336i | −0.832216 | − | 0.856383i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.07851 | + | 5.82472i | −0.159727 | + | 0.228114i | ||||
\(653\) | 7.69299 | + | 16.4977i | 0.301050 | + | 0.645604i | 0.997397 | − | 0.0721010i | \(-0.0229704\pi\) |
−0.696347 | + | 0.717705i | \(0.745193\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.0389 | + | 22.3886i | 0.548545 | + | 0.874794i | ||||
\(656\) | 32.1559 | + | 18.5652i | 1.25548 | + | 0.724851i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 21.6590 | + | 5.80351i | 0.844356 | + | 0.226245i | ||||
\(659\) | 1.94388 | − | 0.707516i | 0.0757229 | − | 0.0275609i | −0.303881 | − | 0.952710i | \(-0.598283\pi\) |
0.379604 | + | 0.925149i | \(0.376060\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.2051 | − | 8.56308i | 0.396932 | − | 0.333065i | −0.422374 | − | 0.906421i | \(-0.638803\pi\) |
0.819306 | + | 0.573356i | \(0.194359\pi\) | |||||||
\(662\) | −1.44434 | + | 16.5089i | −0.0561360 | + | 0.641638i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.0556313 | − | 0.152846i | −0.00215891 | − | 0.00593156i | ||||
\(665\) | 2.36008 | + | 4.61399i | 0.0915201 | + | 0.178923i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.1364 | − | 4.59169i | 0.663525 | − | 0.177791i | ||||
\(668\) | 19.6318 | − | 13.7463i | 0.759576 | − | 0.531861i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −19.5900 | − | 48.2685i | −0.756829 | − | 1.86478i | ||||
\(671\) | 22.5654 | − | 3.97889i | 0.871128 | − | 0.153603i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.3246 | − | 3.35297i | 1.47730 | − | 0.129247i | 0.680172 | − | 0.733052i | \(-0.261905\pi\) |
0.797132 | + | 0.603805i | \(0.206349\pi\) | |||||||
\(674\) | −31.3440 | −1.20732 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.35037 | 0.282707 | ||||||||
\(677\) | −12.9913 | + | 1.13659i | −0.499297 | + | 0.0436829i | −0.334023 | − | 0.942565i | \(-0.608406\pi\) |
−0.165274 | + | 0.986248i | \(0.552851\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.9137 | − | 3.15867i | 0.687465 | − | 0.121219i | ||||
\(680\) | 0.0913427 | + | 0.225062i | 0.00350283 | + | 0.00863075i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −38.1411 | + | 26.7067i | −1.46050 | + | 1.02265i | ||||
\(683\) | −22.2351 | + | 5.95787i | −0.850801 | + | 0.227972i | −0.657768 | − | 0.753221i | \(-0.728499\pi\) |
−0.193033 | + | 0.981192i | \(0.561833\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.3382 | − | 24.1214i | −0.471420 | − | 0.921631i | ||||
\(686\) | −11.5659 | − | 31.7770i | −0.441587 | − | 1.21325i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.00225 | + | 22.8859i | −0.0763352 | + | 0.872515i | ||||
\(689\) | −27.6766 | + | 23.2234i | −1.05439 | + | 0.884741i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.2420 | + | 7.36747i | −0.770040 | + | 0.280272i | −0.697013 | − | 0.717058i | \(-0.745488\pi\) |
−0.0730269 | + | 0.997330i | \(0.523266\pi\) | |||||||
\(692\) | 11.1504 | + | 2.98774i | 0.423874 | + | 0.113577i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.58640 | + | 0.915908i | 0.0602189 | + | 0.0347674i | ||||
\(695\) | −15.4726 | − | 24.6750i | −0.586910 | − | 0.935977i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.8113 | + | 33.9074i | 0.598894 | + | 1.28433i | ||||
\(698\) | 41.1564 | − | 58.7774i | 1.55779 | − | 2.22476i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.200418 | + | 14.0038i | −0.00757510 | + | 0.529294i | ||||
\(701\) | − | 10.6311i | − | 0.401531i | −0.979639 | − | 0.200766i | \(-0.935657\pi\) | ||
0.979639 | − | 0.200766i | \(-0.0643430\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.37571 | + | 3.37571i | −0.127317 | + | 0.127317i | ||||
\(704\) | −21.5635 | − | 18.0939i | −0.812705 | − | 0.681941i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.67378 | − | 9.49245i | −0.0629934 | − | 0.357253i | ||||
\(707\) | 6.74885 | − | 3.14704i | 0.253816 | − | 0.118357i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.87515 | − | 1.21227i | −0.258202 | − | 0.0455279i | 0.0430488 | − | 0.999073i | \(-0.486293\pi\) |
−0.301250 | + | 0.953545i | \(0.597404\pi\) | |||||||
\(710\) | −4.18161 | − | 2.70624i | −0.156933 | − | 0.101563i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.00102906 | − | 0.00384049i | 3.85655e−5 | − | 0.000143929i | ||||
\(713\) | −37.9508 | − | 17.6968i | −1.42127 | − | 0.662749i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.6674 | − | 19.4007i | −0.548528 | − | 0.725546i | ||||
\(716\) | −24.9489 | − | 29.7330i | −0.932386 | − | 1.11117i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.18628 | − | 6.83299i | 0.118911 | − | 0.255005i | ||||
\(719\) | −2.82089 | − | 4.88592i | −0.105201 | − | 0.182214i | 0.808619 | − | 0.588333i | \(-0.200215\pi\) |
−0.913820 | + | 0.406118i | \(0.866882\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.27504 | + | 3.94049i | −0.0847271 | + | 0.146752i | ||||
\(722\) | 18.6649 | + | 26.6562i | 0.694635 | + | 0.992041i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.20710 | − | 19.8013i | 0.267850 | − | 0.735911i | ||||
\(725\) | −13.8138 | + | 1.00959i | −0.513033 | + | 0.0374952i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.05650 | − | 12.0758i | −0.0391832 | − | 0.447867i | −0.990291 | − | 0.139008i | \(-0.955609\pi\) |
0.951108 | − | 0.308858i | \(-0.0999469\pi\) | |||||||
\(728\) | −0.0814023 | − | 0.0814023i | −0.00301697 | − | 0.00301697i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −28.1086 | + | 25.3892i | −1.04034 | + | 0.939695i | ||||
\(731\) | −14.8791 | + | 17.7323i | −0.550325 | + | 0.655852i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.15449 | − | 0.808383i | −0.0426421 | − | 0.0298583i | 0.552061 | − | 0.833804i | \(-0.313842\pi\) |
−0.594703 | + | 0.803945i | \(0.702730\pi\) | |||||||
\(734\) | 47.3029 | + | 17.2169i | 1.74598 | + | 0.635486i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.88151 | − | 50.3696i | 0.327377 | − | 1.85665i | ||||
\(737\) | −10.7707 | − | 40.1967i | −0.396743 | − | 1.48066i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.65920 | − | 4.42204i | 0.281748 | − | 0.162667i | −0.352466 | − | 0.935824i | \(-0.614657\pi\) |
0.634215 | + | 0.773157i | \(0.281324\pi\) | |||||||
\(740\) | −12.3315 | + | 3.79130i | −0.453313 | + | 0.139371i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 33.2257 | + | 2.90687i | 1.21975 | + | 0.106715i | ||||
\(743\) | −20.2590 | − | 1.77243i | −0.743230 | − | 0.0650242i | −0.290751 | − | 0.956799i | \(-0.593905\pi\) |
−0.452480 | + | 0.891775i | \(0.649461\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.09811 | + | 3.75984i | 0.260055 | + | 0.137750i | ||||
\(746\) | −19.0615 | + | 11.0052i | −0.697892 | + | 0.402928i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.44034 | − | 27.7677i | −0.272046 | − | 1.01529i | ||||
\(749\) | −3.16098 | + | 17.9268i | −0.115500 | + | 0.655031i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.99657 | − | 3.27448i | −0.328290 | − | 0.119488i | 0.172617 | − | 0.984989i | \(-0.444778\pi\) |
−0.500906 | + | 0.865501i | \(0.667000\pi\) | |||||||
\(752\) | 26.2718 | + | 18.3957i | 0.958032 | + | 0.670822i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.8420 | + | 12.9210i | −0.394844 | + | 0.470556i | ||||
\(755\) | −0.663290 | − | 0.734334i | −0.0241396 | − | 0.0267252i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.8479 | − | 20.8479i | −0.757730 | − | 0.757730i | 0.218179 | − | 0.975909i | \(-0.429988\pi\) |
−0.975909 | + | 0.218179i | \(0.929988\pi\) | |||||||
\(758\) | 1.07073 | + | 12.2385i | 0.0388905 | + | 0.444521i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.0121464 | + | 0.0976554i | 0.000440595 | + | 0.00354233i | ||||
\(761\) | 9.01441 | − | 24.7669i | 0.326772 | − | 0.897799i | −0.662151 | − | 0.749370i | \(-0.730356\pi\) |
0.988923 | − | 0.148428i | \(-0.0474214\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.92236 | − | 8.45800i | −0.214404 | − | 0.306200i | ||||
\(764\) | 4.74988 | − | 8.22703i | 0.171845 | − | 0.297644i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.6017 | + | 30.4870i | 0.635974 | + | 1.10154i | ||||
\(767\) | 18.4617 | − | 39.5912i | 0.666612 | − | 1.42955i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.0565 | − | 33.4364i | −1.01174 | − | 1.20575i | −0.978489 | − | 0.206301i | \(-0.933857\pi\) |
−0.0332544 | − | 0.999447i | \(-0.510587\pi\) | |||||||
\(770\) | −3.08978 | + | 22.2384i | −0.111348 | + | 0.801417i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.79577 | − | 4.56784i | −0.352558 | − | 0.164400i | ||||
\(773\) | 3.07418 | − | 11.4730i | 0.110571 | − | 0.412655i | −0.888347 | − | 0.459173i | \(-0.848146\pi\) |
0.998917 | + | 0.0465178i | \(0.0148124\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.5086 | + | 19.1326i | 0.952216 | + | 0.687263i | ||||
\(776\) | 0.340151 | + | 0.0599778i | 0.0122107 | + | 0.00215308i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25.4158 | + | 11.8516i | −0.911201 | + | 0.424900i | ||||
\(779\) | 2.63212 | + | 14.9275i | 0.0943053 | + | 0.534832i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.04814 | − | 2.55770i | −0.109071 | − | 0.0915216i | ||||
\(782\) | 36.6853 | − | 36.6853i | 1.31186 | − | 1.31186i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 20.1814i | − | 0.720763i | ||||||
\(785\) | −1.94102 | + | 2.08806i | −0.0692779 | + | 0.0745259i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.0074 | − | 44.2832i | 1.10529 | − | 1.57852i | 0.333385 | − | 0.942791i | \(-0.391809\pi\) |
0.771909 | − | 0.635733i | \(-0.219302\pi\) | |||||||
\(788\) | 6.74431 | + | 14.4632i | 0.240256 | + | 0.515231i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −23.7993 | − | 5.45512i | −0.846741 | − | 0.194085i | ||||
\(791\) | 18.5843 | + | 10.7297i | 0.660783 | + | 0.381503i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.9243 | − | 5.07074i | −0.672020 | − | 0.180067i | ||||
\(794\) | 56.7853 | − | 20.6681i | 2.01523 | − | 0.733485i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.5059 | − | 15.5283i | 0.655925 | − | 0.550386i | ||||
\(797\) | 0.986343 | − | 11.2740i | 0.0349381 | − | 0.399344i | −0.958510 | − | 0.285059i | \(-0.907987\pi\) |
0.993448 | − | 0.114285i | \(-0.0364577\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.0526 | + | 30.3667i | 0.391012 | + | 1.07430i | ||||
\(800\) | −14.1928 | + | 37.3237i | −0.501791 | + | 1.31959i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −31.4131 | + | 8.41712i | −1.10924 | + | 0.297219i | ||||
\(803\) | −24.7866 | + | 17.3558i | −0.874701 | + | 0.612472i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.7095 | + | 7.59334i | −0.659423 | + | 0.267630i | ||||
\(806\) | 39.2070 | − | 6.91326i | 1.38101 | − | 0.243509i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.140859 | − | 0.0123236i | 0.00495540 | − | 0.000433541i | ||||
\(809\) | −3.55739 | −0.125071 | −0.0625355 | − | 0.998043i | \(-0.519919\pi\) | ||||
−0.0625355 | + | 0.998043i | \(0.519919\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.5652 | 1.63512 | 0.817562 | − | 0.575840i | \(-0.195325\pi\) | ||||
0.817562 | + | 0.575840i | \(0.195325\pi\) | |||||||
\(812\) | 7.72975 | − | 0.676266i | 0.271261 | − | 0.0237323i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −20.3678 | + | 3.59139i | −0.713891 | + | 0.125878i | ||||
\(815\) | 7.37228 | + | 3.11569i | 0.258240 | + | 0.109138i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.68231 | + | 5.37921i | −0.268770 | + | 0.188195i | ||||
\(818\) | −37.7438 | + | 10.1134i | −1.31968 | + | 0.353607i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.5967 | + | 38.9770i | −0.439897 | + | 1.36114i | ||||
\(821\) | 14.8508 | + | 40.8021i | 0.518295 | + | 1.42400i | 0.872397 | + | 0.488798i | \(0.162564\pi\) |
−0.354102 | + | 0.935207i | \(0.615213\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.59358 | − | 18.2148i | 0.0555489 | − | 0.634926i | −0.916482 | − | 0.400075i | \(-0.868984\pi\) |
0.972031 | − | 0.234851i | \(-0.0754604\pi\) | |||||||
\(824\) | −0.0661850 | + | 0.0555358i | −0.00230567 | + | 0.00193468i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −37.8948 | + | 13.7926i | −1.31853 | + | 0.479905i | ||||
\(827\) | 38.7367 | + | 10.3795i | 1.34701 | + | 0.360929i | 0.859029 | − | 0.511927i | \(-0.171068\pi\) |
0.487978 | + | 0.872856i | \(0.337735\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.7438 | − | 13.7085i | −0.824656 | − | 0.476115i | 0.0273634 | − | 0.999626i | \(-0.491289\pi\) |
−0.852019 | + | 0.523510i | \(0.824622\pi\) | |||||||
\(830\) | 22.9799 | − | 14.4097i | 0.797644 | − | 0.500168i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 10.1718 | + | 21.8135i | 0.352643 | + | 0.756246i | ||||
\(833\) | 11.6635 | − | 16.6572i | 0.404117 | − | 0.577139i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.7576 | − | 18.3663i | −0.683740 | − | 0.635593i | ||||
\(836\) | − | 11.6470i | − | 0.402819i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.260063 | + | 0.260063i | −0.00898371 | + | 0.00898371i | ||||
\(839\) | 29.8408 | + | 25.0394i | 1.03022 | + | 0.864456i | 0.990877 | − | 0.134770i | \(-0.0430296\pi\) |
0.0393413 | + | 0.999226i | \(0.487474\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.70328 | − | 21.0024i | −0.127699 | − | 0.724219i | ||||
\(842\) | 33.1130 | − | 15.4408i | 1.14115 | − | 0.532126i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.83537 | + | 1.02893i | 0.200862 | + | 0.0354174i | ||||
\(845\) | −1.73286 | − | 8.08993i | −0.0596121 | − | 0.278302i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.627986 | + | 2.34368i | −0.0215779 | + | 0.0805297i | ||||
\(848\) | 43.2350 | + | 20.1608i | 1.48469 | + | 0.692324i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −33.5082 | + | 22.7551i | −1.14932 | + | 0.780495i | ||||
\(851\) | −11.9557 | − | 14.2483i | −0.409838 | − | 0.488425i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.4323 | + | 37.3837i | −0.596871 | + | 1.27999i | 0.343279 | + | 0.939234i | \(0.388462\pi\) |
−0.940150 | + | 0.340761i | \(0.889315\pi\) | |||||||
\(854\) | 9.04308 | + | 15.6631i | 0.309448 | + | 0.535980i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.172825 | + | 0.299342i | −0.00590705 | + | 0.0102313i | ||||
\(857\) | 19.3368 | + | 27.6158i | 0.660532 | + | 0.943338i | 0.999996 | + | 0.00271892i | \(0.000865461\pi\) |
−0.339464 | + | 0.940619i | \(0.610246\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.4264 | − | 28.6463i | 0.355745 | − | 0.977401i | −0.624745 | − | 0.780829i | \(-0.714797\pi\) |
0.980489 | − | 0.196572i | \(-0.0629808\pi\) | |||||||
\(860\) | −25.1501 | + | 3.12817i | −0.857612 | + | 0.106670i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.55542 | − | 40.6387i | −0.121098 | − | 1.38416i | ||||
\(863\) | 32.8323 | + | 32.8323i | 1.11763 | + | 1.11763i | 0.992089 | + | 0.125536i | \(0.0400652\pi\) |
0.125536 | + | 0.992089i | \(0.459935\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.659633 | − | 12.9766i | 0.0224282 | − | 0.441219i | ||||
\(866\) | 2.54240 | − | 3.02991i | 0.0863941 | − | 0.102960i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −15.0022 | − | 10.5047i | −0.509208 | − | 0.356551i | ||||
\(869\) | −18.3291 | − | 6.67124i | −0.621772 | − | 0.226306i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.17875 | + | 35.0414i | −0.209359 | + | 1.18733i | ||||
\(872\) | −0.0507441 | − | 0.189380i | −0.00171841 | − | 0.00641320i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.2035 | − | 10.5098i | 0.615741 | − | 0.355498i | ||||
\(875\) | 15.4600 | − | 3.08083i | 0.522645 | − | 0.104151i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.3879 | + | 2.57111i | 0.992358 | + | 0.0868201i | 0.571755 | − | 0.820425i | \(-0.306263\pi\) |
0.420603 | + | 0.907245i | \(0.361818\pi\) | |||||||
\(878\) | −28.1420 | − | 2.46211i | −0.949747 | − | 0.0830921i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −15.0317 | + | 28.3781i | −0.506720 | + | 0.956624i | ||||
\(881\) | −12.5327 | + | 7.23578i | −0.422239 | + | 0.243780i | −0.696035 | − | 0.718008i | \(-0.745054\pi\) |
0.273796 | + | 0.961788i | \(0.411721\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.19438 | − | 30.5819i | −0.275763 | − | 1.02916i | −0.955328 | − | 0.295547i | \(-0.904498\pi\) |
0.679565 | − | 0.733615i | \(-0.262168\pi\) | |||||||
\(884\) | −4.26826 | + | 24.2065i | −0.143557 | + | 0.814153i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30.1088 | + | 10.9587i | 1.01153 | + | 0.368166i | ||||
\(887\) | −10.4193 | − | 7.29567i | −0.349846 | − | 0.244965i | 0.385423 | − | 0.922740i | \(-0.374055\pi\) |
−0.735269 | + | 0.677775i | \(0.762944\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.02616 | − | 7.18169i | 0.202111 | − | 0.240866i | ||||
\(890\) | 0.662171 | + | 0.0336597i | 0.0221960 | + | 0.00112828i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.3726 | + | 11.3726i | 0.380784 | + | 0.380784i | ||||
\(893\) | 1.14110 | + | 13.0429i | 0.0381856 | + | 0.436463i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.8428 | + | 34.4688i | −0.897257 | + | 1.15216i | ||||
\(896\) | −0.103286 | + | 0.283776i | −0.00345055 | + | 0.00948030i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.55492 | − | 9.36140i | −0.218741 | − | 0.312394i | ||||
\(899\) | 9.05610 | − | 15.6856i | 0.302038 | − | 0.523145i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.0335 | + | 41.6272i | 0.800672 | + | 1.38680i | ||||
\(902\) | −27.7520 | + | 59.5145i | −0.924042 | + | 1.98161i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.261921 | + | 0.312145i | 0.00871135 | + | 0.0103818i | ||||
\(905\) | −23.4927 | − | 3.26405i | −0.780925 | − | 0.108501i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49.0966 | + | 22.8941i | 1.63023 | + | 0.760188i | 0.999870 | − | 0.0161177i | \(-0.00513063\pi\) |
0.630357 | + | 0.776305i | \(0.282908\pi\) | |||||||
\(908\) | 3.96353 | − | 14.7921i | 0.131534 | − | 0.490892i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 10.4303 | − | 16.1166i | 0.345760 | − | 0.534260i | ||||
\(911\) | 11.6520 | + | 2.05456i | 0.386047 | + | 0.0680705i | 0.363303 | − | 0.931671i | \(-0.381649\pi\) |
0.0227434 | + | 0.999741i | \(0.492760\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.6383 | − | 9.15747i | 0.649931 | − | 0.303068i | ||||
\(914\) | −6.85089 | − | 38.8533i | −0.226607 | − | 1.28515i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.95094 | + | 5.83253i | 0.229666 | + | 0.192712i | ||||
\(917\) | −11.7827 | + | 11.7827i | −0.389099 | + | 0.389099i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.2177i | 1.09575i | 0.836560 | + | 0.547875i | \(0.184563\pi\) | ||||
−0.836560 | + | 0.547875i | \(0.815437\pi\) | |||||||
\(920\) | −0.383151 | + | 0.0139827i | −0.0126321 | + | 0.000460997i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20.7333 | + | 29.6102i | −0.682815 | + | 0.975161i | ||||
\(923\) | 1.43785 | + | 3.08348i | 0.0473274 | + | 0.101494i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.07991 | + | 12.6784i | 0.232786 | + | 0.416862i | ||||
\(926\) | −22.6234 | − | 13.0616i | −0.743452 | − | 0.429232i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 21.3691 | + | 5.72583i | 0.701475 | + | 0.187960i | ||||
\(929\) | −29.9496 | + | 10.9008i | −0.982616 | + | 0.357643i | −0.782857 | − | 0.622202i | \(-0.786238\pi\) |
−0.199759 | + | 0.979845i | \(0.564016\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.31115 | − | 5.29569i | 0.206840 | − | 0.173559i | ||||
\(932\) | −3.46630 | + | 39.6200i | −0.113543 | + | 1.29780i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.56470 | − | 15.2889i | −0.182083 | − | 0.500268i | ||||
\(935\) | −28.8075 | + | 14.7352i | −0.942107 | + | 0.481893i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.56398 | − | 2.56266i | 0.312441 | − | 0.0837184i | −0.0991909 | − | 0.995068i | \(-0.531625\pi\) |
0.411632 | + | 0.911350i | \(0.364959\pi\) | |||||||
\(938\) | 26.9070 | − | 18.8405i | 0.878546 | − | 0.615165i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −13.7734 | + | 32.5905i | −0.449240 | + | 1.06298i | ||||
\(941\) | 31.4053 | − | 5.53759i | 1.02378 | − | 0.180520i | 0.363544 | − | 0.931577i | \(-0.381567\pi\) |
0.660238 | + | 0.751057i | \(0.270455\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −58.8312 | + | 5.14706i | −1.91581 | + | 0.167611i | ||||
\(944\) | −57.6798 | −1.87732 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −40.6293 | −1.32097 | ||||||||
\(947\) | 14.1237 | − | 1.23567i | 0.458959 | − | 0.0401537i | 0.144668 | − | 0.989480i | \(-0.453789\pi\) |
0.314291 | + | 0.949327i | \(0.398233\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.4793 | − | 4.49269i | 0.827094 | − | 0.145839i | ||||
\(950\) | −15.4994 | + | 5.39142i | −0.502868 | + | 0.174921i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.125460 | + | 0.0878480i | −0.00406618 | + | 0.00284717i | ||||
\(953\) | −19.5249 | + | 5.23169i | −0.632475 | + | 0.169471i | −0.560792 | − | 0.827956i | \(-0.689503\pi\) |
−0.0716822 | + | 0.997428i | \(0.522837\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.1746 | − | 3.28826i | −0.329242 | − | 0.106405i | ||||
\(956\) | 9.05213 | + | 24.8705i | 0.292767 | + | 0.804370i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.42397 | + | 50.5662i | −0.142932 | + | 1.63372i | ||||
\(959\) | 13.0873 | − | 10.9816i | 0.422612 | − | 0.354613i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.0418 | + | 4.01888i | −0.356186 | + | 0.129641i | ||||
\(962\) | 17.0813 | + | 4.57691i | 0.550722 | + | 0.147565i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 43.8972 | + | 25.3440i | 1.41383 | + | 0.816277i | ||||
\(965\) | −2.71807 | + | 11.8582i | −0.0874979 | + | 0.381730i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.28255 | + | 15.6175i | 0.234191 | + | 0.502224i | 0.987921 | − | 0.154960i | \(-0.0495250\pi\) |
−0.753730 | + | 0.657185i | \(0.771747\pi\) | |||||||
\(968\) | −0.0264260 | + | 0.0377402i | −0.000849363 | + | 0.00121302i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.10059 | + | 57.5597i | 0.0674458 | + | 1.84813i | ||||
\(971\) | − | 4.56855i | − | 0.146612i | −0.997310 | − | 0.0733058i | \(-0.976645\pi\) | ||
0.997310 | − | 0.0733058i | \(-0.0233549\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.9860 | − | 12.9860i | 0.416313 | − | 0.416313i | ||||
\(974\) | 45.1583 | + | 37.8923i | 1.44697 | + | 1.21415i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.49207 | + | 25.4758i | 0.143788 | + | 0.815460i | ||||
\(977\) | 16.0559 | − | 7.48700i | 0.513675 | − | 0.239530i | −0.148456 | − | 0.988919i | \(-0.547430\pi\) |
0.662130 | + | 0.749389i | \(0.269652\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.521620 | + | 0.0919757i | 0.0166711 | + | 0.00293956i | ||||
\(980\) | 21.7701 | − | 4.66314i | 0.695420 | − | 0.148959i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.17616 | + | 23.0498i | −0.197089 | + | 0.735547i | ||||
\(983\) | −39.7929 | − | 18.5557i | −1.26920 | − | 0.591836i | −0.332872 | − | 0.942972i | \(-0.608018\pi\) |
−0.936324 | + | 0.351136i | \(0.885795\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.3285 | − | 10.8326i | 0.456543 | − | 0.345156i | ||||
\(986\) | 14.4245 | + | 17.1904i | 0.459368 | + | 0.547454i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.20867 | + | 9.02553i | −0.133896 | + | 0.287140i | ||||
\(989\) | −18.2695 | − | 31.6436i | −0.580935 | − | 1.00621i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.5103 | − | 23.4004i | 0.429167 | − | 0.743340i | −0.567632 | − | 0.823282i | \(-0.692140\pi\) |
0.996799 | + | 0.0799428i | \(0.0254738\pi\) | |||||||
\(992\) | −29.9504 | − | 42.7736i | −0.950926 | − | 1.35806i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.07421 | − | 2.95136i | 0.0340718 | − | 0.0936115i | ||||
\(995\) | −21.4535 | − | 16.7071i | −0.680121 | − | 0.529650i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.63906 | + | 18.7346i | 0.0519096 | + | 0.593329i | 0.976951 | + | 0.213463i | \(0.0684744\pi\) |
−0.925041 | + | 0.379866i | \(0.875970\pi\) | |||||||
\(998\) | −7.28760 | − | 7.28760i | −0.230685 | − | 0.230685i | ||||
\(999\) | 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 | 405.2.r.a.197.3 | 192 | ||
3.2 | odd | 2 | 135.2.q.a.92.14 | yes | 192 | ||
5.3 | odd | 4 | inner | 405.2.r.a.278.14 | 192 | ||
15.2 | even | 4 | 675.2.ba.b.443.14 | 192 | |||
15.8 | even | 4 | 135.2.q.a.38.3 | yes | 192 | ||
15.14 | odd | 2 | 675.2.ba.b.632.3 | 192 | |||
27.5 | odd | 18 | inner | 405.2.r.a.287.14 | 192 | ||
27.22 | even | 9 | 135.2.q.a.32.3 | ✓ | 192 | ||
135.22 | odd | 36 | 675.2.ba.b.518.3 | 192 | |||
135.49 | even | 18 | 675.2.ba.b.32.14 | 192 | |||
135.103 | odd | 36 | 135.2.q.a.113.14 | yes | 192 | ||
135.113 | even | 36 | inner | 405.2.r.a.368.3 | 192 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.2.q.a.32.3 | ✓ | 192 | 27.22 | even | 9 | ||
135.2.q.a.38.3 | yes | 192 | 15.8 | even | 4 | ||
135.2.q.a.92.14 | yes | 192 | 3.2 | odd | 2 | ||
135.2.q.a.113.14 | yes | 192 | 135.103 | odd | 36 | ||
405.2.r.a.197.3 | 192 | 1.1 | even | 1 | trivial | ||
405.2.r.a.278.14 | 192 | 5.3 | odd | 4 | inner | ||
405.2.r.a.287.14 | 192 | 27.5 | odd | 18 | inner | ||
405.2.r.a.368.3 | 192 | 135.113 | even | 36 | inner | ||
675.2.ba.b.32.14 | 192 | 135.49 | even | 18 | |||
675.2.ba.b.443.14 | 192 | 15.2 | even | 4 | |||
675.2.ba.b.518.3 | 192 | 135.22 | odd | 36 | |||
675.2.ba.b.632.3 | 192 | 15.14 | odd | 2 |