Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(143,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([7, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.ba (of order \(18\), degree \(6\), 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: | \(4.52751779461\) |
Analytic rank: | \(0\) |
Dimension: | \(132\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 189) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 341.7 | ||
Character | \(\chi\) | \(=\) | 567.341 |
Dual form | 567.2.ba.a.143.7 |
$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.905074 | − | 1.07862i | −0.639984 | − | 0.762703i | 0.344384 | − | 0.938829i | \(-0.388088\pi\) |
−0.984368 | + | 0.176126i | \(0.943643\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.00302336 | − | 0.0171463i | 0.00151168 | − | 0.00857316i | ||||
\(5\) | −1.61655 | − | 1.35644i | −0.722942 | − | 0.606620i | 0.205256 | − | 0.978708i | \(-0.434197\pi\) |
−0.928197 | + | 0.372088i | \(0.878642\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.08812 | + | 2.41164i | 0.411273 | + | 0.911512i | ||||
\(8\) | −2.46004 | + | 1.42030i | −0.869754 | + | 0.502153i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.97133i | 0.939616i | ||||||||
\(11\) | 2.38051 | + | 2.83698i | 0.717751 | + | 0.855382i | 0.994410 | − | 0.105586i | \(-0.0336717\pi\) |
−0.276659 | + | 0.960968i | \(0.589227\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.27684 | + | 6.25557i | 0.631482 | + | 1.73498i | 0.676963 | + | 0.736017i | \(0.263296\pi\) |
−0.0454806 | + | 0.998965i | \(0.514482\pi\) | |||||||
\(14\) | 1.61642 | − | 3.35639i | 0.432005 | − | 0.897032i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.72576 | + | 1.35607i | 0.931441 | + | 0.339017i | ||||
\(17\) | 3.23775 | 0.785270 | 0.392635 | − | 0.919694i | \(-0.371564\pi\) | ||||
0.392635 | + | 0.919694i | \(0.371564\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.32762i | − | 1.22224i | −0.791538 | − | 0.611120i | \(-0.790719\pi\) | ||
0.791538 | − | 0.611120i | \(-0.209281\pi\) | |||||||
\(20\) | −0.0281454 | + | 0.0236168i | −0.00629351 | + | 0.00528088i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.905502 | − | 5.13536i | 0.193054 | − | 1.09486i | ||||
\(23\) | 0.239559 | + | 0.658182i | 0.0499514 | + | 0.137240i | 0.962160 | − | 0.272487i | \(-0.0878461\pi\) |
−0.912208 | + | 0.409727i | \(0.865624\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.0949575 | − | 0.538530i | −0.0189915 | − | 0.107706i | ||||
\(26\) | 4.68670 | − | 8.11761i | 0.919138 | − | 1.59199i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.0446405 | − | 0.0113661i | 0.00843625 | − | 0.00214799i | ||||
\(29\) | −1.50083 | + | 4.12351i | −0.278698 | + | 0.765716i | 0.718813 | + | 0.695204i | \(0.244686\pi\) |
−0.997511 | + | 0.0705128i | \(0.977536\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.47986 | − | 0.260940i | −0.265791 | − | 0.0468662i | 0.0391641 | − | 0.999233i | \(-0.487530\pi\) |
−0.304955 | + | 0.952367i | \(0.598642\pi\) | |||||||
\(32\) | 0.0336848 | + | 0.0925482i | 0.00595468 | + | 0.0163604i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.93040 | − | 3.49232i | −0.502560 | − | 0.598927i | ||||
\(35\) | 1.51224 | − | 5.37450i | 0.255616 | − | 0.908456i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.24831 | − | 5.62624i | −0.534019 | − | 0.924947i | −0.999210 | − | 0.0397374i | \(-0.987348\pi\) |
0.465191 | − | 0.885210i | \(-0.345985\pi\) | |||||||
\(38\) | −5.74650 | + | 4.82189i | −0.932206 | + | 0.782213i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.90332 | + | 1.04091i | 0.933397 | + | 0.164583i | ||||
\(41\) | 10.4849 | − | 3.81619i | 1.63746 | − | 0.595988i | 0.650871 | − | 0.759188i | \(-0.274404\pi\) |
0.986593 | + | 0.163200i | \(0.0521817\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.29121 | + | 7.32280i | 0.196907 | + | 1.11672i | 0.909676 | + | 0.415318i | \(0.136330\pi\) |
−0.712769 | + | 0.701399i | \(0.752559\pi\) | |||||||
\(44\) | 0.0558409 | − | 0.0322398i | 0.00841834 | − | 0.00486033i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.493113 | − | 0.854097i | 0.0727056 | − | 0.125930i | ||||
\(47\) | 1.04114 | + | 5.90462i | 0.151866 | + | 0.861278i | 0.961595 | + | 0.274473i | \(0.0885033\pi\) |
−0.809728 | + | 0.586805i | \(0.800386\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.63197 | + | 5.24832i | −0.661710 | + | 0.749760i | ||||
\(50\) | −0.494929 | + | 0.589833i | −0.0699935 | + | 0.0834150i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.114144 | − | 0.0201266i | 0.0158289 | − | 0.00279106i | ||||
\(53\) | 0.766350 | − | 0.442452i | 0.105266 | − | 0.0607755i | −0.446443 | − | 0.894812i | \(-0.647309\pi\) |
0.551709 | + | 0.834037i | \(0.313976\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 7.81514i | − | 1.05379i | ||||||
\(56\) | −6.10208 | − | 4.38724i | −0.815424 | − | 0.586270i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.80608 | − | 2.11324i | 0.762376 | − | 0.277482i | ||||
\(59\) | −5.85868 | + | 2.13238i | −0.762735 | + | 0.277613i | −0.693954 | − | 0.720019i | \(-0.744133\pi\) |
−0.0687807 | + | 0.997632i | \(0.521911\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.32422 | − | 1.29146i | 0.937771 | − | 0.165354i | 0.316183 | − | 0.948698i | \(-0.397599\pi\) |
0.621588 | + | 0.783344i | \(0.286488\pi\) | |||||||
\(62\) | 1.05793 | + | 1.83239i | 0.134357 | + | 0.232713i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.03421 | − | 6.98746i | 0.504277 | − | 0.873433i | ||||
\(65\) | 4.80471 | − | 13.2008i | 0.595951 | − | 1.63736i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.05809 | + | 6.76154i | 0.984453 | + | 0.826054i | 0.984755 | − | 0.173946i | \(-0.0556518\pi\) |
−0.000302478 | 1.00000i | \(0.500096\pi\) | ||||||||
\(68\) | 0.00978888 | − | 0.0555155i | 0.00118708 | − | 0.00673224i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.16576 | + | 3.23318i | −0.856472 | + | 0.386438i | ||||
\(71\) | 3.83248 | + | 2.21268i | 0.454832 | + | 0.262597i | 0.709869 | − | 0.704334i | \(-0.248754\pi\) |
−0.255037 | + | 0.966931i | \(0.582088\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.65123 | − | 1.53069i | −0.310303 | − | 0.179154i | 0.336759 | − | 0.941591i | \(-0.390669\pi\) |
−0.647062 | + | 0.762437i | \(0.724003\pi\) | |||||||
\(74\) | −3.12864 | + | 8.59586i | −0.363697 | + | 0.999249i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.0913491 | − | 0.0161073i | −0.0104785 | − | 0.00184763i | ||||
\(77\) | −4.25147 | + | 8.82791i | −0.484500 | + | 1.00603i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.29250 | + | 6.11913i | −0.820470 | + | 0.688456i | −0.953082 | − | 0.302712i | \(-0.902108\pi\) |
0.132612 | + | 0.991168i | \(0.457664\pi\) | |||||||
\(80\) | −4.18344 | − | 7.24593i | −0.467723 | − | 0.810120i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −13.6058 | − | 7.85533i | −1.50251 | − | 0.867476i | ||||
\(83\) | 11.4377 | + | 4.16299i | 1.25545 | + | 0.456947i | 0.882241 | − | 0.470799i | \(-0.156034\pi\) |
0.373212 | + | 0.927746i | \(0.378256\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.23397 | − | 4.39182i | −0.567704 | − | 0.476360i | ||||
\(86\) | 6.72991 | − | 8.02040i | 0.725705 | − | 0.864862i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.88551 | − | 3.59803i | −1.05380 | − | 0.383552i | ||||
\(89\) | 4.35832 | 0.461982 | 0.230991 | − | 0.972956i | \(-0.425803\pi\) | ||||
0.230991 | + | 0.972956i | \(0.425803\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.6087 | + | 12.2977i | −1.32175 | + | 1.28915i | ||||
\(92\) | 0.0120097 | − | 0.00211763i | 0.00125210 | − | 0.000220778i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.42656 | − | 6.46712i | 0.559707 | − | 0.667033i | ||||
\(95\) | −7.22662 | + | 8.61234i | −0.741435 | + | 0.883608i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.85869 | − | 1.20937i | 0.696394 | − | 0.122793i | 0.185765 | − | 0.982594i | \(-0.440524\pi\) |
0.510629 | + | 0.859801i | \(0.329413\pi\) | |||||||
\(98\) | 9.85324 | + | 0.246039i | 0.995328 | + | 0.0248537i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.00952091 | −0.000952091 | ||||||||
\(101\) | −3.49388 | − | 1.27167i | −0.347654 | − | 0.126536i | 0.162290 | − | 0.986743i | \(-0.448112\pi\) |
−0.509945 | + | 0.860207i | \(0.670334\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.98929 | − | 4.75425i | 0.393076 | − | 0.468450i | −0.532820 | − | 0.846229i | \(-0.678868\pi\) |
0.925896 | + | 0.377779i | \(0.123312\pi\) | |||||||
\(104\) | −14.4859 | − | 12.1551i | −1.42046 | − | 1.19191i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.17084 | − | 0.426152i | −0.113722 | − | 0.0413915i | ||||
\(107\) | 2.47461 | + | 1.42872i | 0.239230 | + | 0.138119i | 0.614823 | − | 0.788665i | \(-0.289228\pi\) |
−0.375593 | + | 0.926785i | \(0.622561\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.81692 | + | 4.87905i | 0.269812 | + | 0.467328i | 0.968813 | − | 0.247792i | \(-0.0797051\pi\) |
−0.699001 | + | 0.715121i | \(0.746372\pi\) | |||||||
\(110\) | −8.42961 | + | 7.07328i | −0.803731 | + | 0.674411i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.783757 | + | 10.4608i | 0.0740581 | + | 0.988448i | ||||
\(113\) | −9.04367 | − | 1.59464i | −0.850757 | − | 0.150011i | −0.268765 | − | 0.963206i | \(-0.586615\pi\) |
−0.581992 | + | 0.813194i | \(0.697727\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.505529 | − | 1.38893i | 0.0471408 | − | 0.129518i | ||||
\(116\) | 0.0661654 | + | 0.0382006i | 0.00614331 | + | 0.00354684i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.60258 | + | 4.38935i | 0.699874 | + | 0.404073i | ||||
\(119\) | 3.52308 | + | 7.80827i | 0.322960 | + | 0.715783i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.471507 | + | 2.67405i | −0.0428643 | + | 0.243095i | ||||
\(122\) | −8.02196 | − | 6.73122i | −0.726274 | − | 0.609416i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.00894832 | + | 0.0245853i | −0.000803582 | + | 0.00220782i | ||||
\(125\) | −5.85261 | + | 10.1370i | −0.523474 | + | 0.906683i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.958294 | − | 1.65981i | −0.0850349 | − | 0.147285i | 0.820371 | − | 0.571831i | \(-0.193767\pi\) |
−0.905406 | + | 0.424547i | \(0.860433\pi\) | |||||||
\(128\) | −10.9941 | + | 1.93856i | −0.971752 | + | 0.171346i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −18.5873 | + | 6.76524i | −1.63022 | + | 0.593351i | ||||
\(131\) | 8.18242 | − | 2.97816i | 0.714901 | − | 0.260203i | 0.0411416 | − | 0.999153i | \(-0.486901\pi\) |
0.673760 | + | 0.738951i | \(0.264678\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.8483 | − | 5.79712i | 1.11409 | − | 0.502674i | ||||
\(134\) | − | 14.8114i | − | 1.27951i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.96498 | + | 4.59858i | −0.682991 | + | 0.394325i | ||||
\(137\) | −6.87107 | + | 1.21155i | −0.587035 | + | 0.103510i | −0.459274 | − | 0.888295i | \(-0.651890\pi\) |
−0.127761 | + | 0.991805i | \(0.540779\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.76177 | − | 8.05836i | 0.573526 | − | 0.683501i | −0.398825 | − | 0.917027i | \(-0.630582\pi\) |
0.972351 | + | 0.233526i | \(0.0750263\pi\) | |||||||
\(140\) | −0.0875808 | − | 0.0421784i | −0.00740193 | − | 0.00356473i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.08202 | − | 6.13645i | −0.0908012 | − | 0.514959i | ||||
\(143\) | −12.3269 | + | 21.3508i | −1.03083 | + | 1.78544i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.01948 | − | 4.63005i | 0.665981 | − | 0.384504i | ||||
\(146\) | 0.748521 | + | 4.24507i | 0.0619480 | + | 0.351325i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.106290 | + | 0.0386864i | −0.00873699 | + | 0.00318000i | ||||
\(149\) | −10.9584 | − | 1.93227i | −0.897750 | − | 0.158298i | −0.294314 | − | 0.955709i | \(-0.595091\pi\) |
−0.603436 | + | 0.797411i | \(0.706202\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.4692 | + | 12.9802i | −1.25887 | + | 1.05632i | −0.263066 | + | 0.964778i | \(0.584734\pi\) |
−0.995802 | + | 0.0915375i | \(0.970822\pi\) | |||||||
\(152\) | 7.56683 | + | 13.1061i | 0.613751 | + | 1.06305i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 13.3699 | − | 3.40417i | 1.07738 | − | 0.274316i | ||||
\(155\) | 2.03832 | + | 2.42917i | 0.163722 | + | 0.195116i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.67332 | + | 4.59740i | 0.133545 | + | 0.366912i | 0.988383 | − | 0.151983i | \(-0.0485658\pi\) |
−0.854838 | + | 0.518895i | \(0.826344\pi\) | |||||||
\(158\) | 13.2005 | + | 2.32760i | 1.05017 | + | 0.185174i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.0710834 | − | 0.195300i | 0.00561963 | − | 0.0154398i | ||||
\(161\) | −1.32663 | + | 1.29391i | −0.104553 | + | 0.101975i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.68621 | + | 8.11676i | −0.367053 | + | 0.635754i | −0.989103 | − | 0.147223i | \(-0.952966\pi\) |
0.622051 | + | 0.782977i | \(0.286300\pi\) | |||||||
\(164\) | −0.0337340 | − | 0.191315i | −0.00263418 | − | 0.0149392i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.86167 | − | 16.1048i | −0.454954 | − | 1.24998i | ||||
\(167\) | 1.49566 | − | 8.48231i | 0.115738 | − | 0.656381i | −0.870645 | − | 0.491912i | \(-0.836298\pi\) |
0.986382 | − | 0.164468i | \(-0.0525908\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.9896 | + | 20.1296i | −1.84535 | + | 1.54843i | ||||
\(170\) | 9.62042i | 0.737852i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.129463 | 0.00987145 | ||||||||
\(173\) | −7.96256 | − | 2.89813i | −0.605382 | − | 0.220341i | 0.0210995 | − | 0.999777i | \(-0.493283\pi\) |
−0.626481 | + | 0.779436i | \(0.715506\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.19541 | − | 0.814991i | 0.0903648 | − | 0.0616075i | ||||
\(176\) | 5.02208 | + | 13.7981i | 0.378554 | + | 1.04007i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.94460 | − | 4.70100i | −0.295661 | − | 0.352355i | ||||
\(179\) | 4.83578i | 0.361443i | 0.983534 | + | 0.180722i | \(0.0578433\pi\) | ||||
−0.983534 | + | 0.180722i | \(0.942157\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.95269 | + | 2.28209i | −0.293801 | + | 0.169626i | −0.639655 | − | 0.768662i | \(-0.720923\pi\) |
0.345854 | + | 0.938288i | \(0.387589\pi\) | |||||||
\(182\) | 24.6764 | + | 2.46965i | 1.82914 | + | 0.183062i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.52414 | − | 1.27891i | −0.112361 | − | 0.0942822i | ||||
\(185\) | −2.38063 | + | 13.5012i | −0.175027 | + | 0.992629i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.70750 | + | 9.18544i | 0.563628 | + | 0.671706i | ||||
\(188\) | 0.104390 | 0.00761344 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 15.8301 | 1.14844 | ||||||||
\(191\) | −6.64760 | − | 7.92230i | −0.481003 | − | 0.573237i | 0.469902 | − | 0.882718i | \(-0.344289\pi\) |
−0.950906 | + | 0.309481i | \(0.899845\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.80685 | − | 10.2471i | 0.130060 | − | 0.737605i | −0.848114 | − | 0.529814i | \(-0.822262\pi\) |
0.978173 | − | 0.207791i | \(-0.0666273\pi\) | |||||||
\(194\) | −7.51207 | − | 6.30338i | −0.539335 | − | 0.452556i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.0759853 | + | 0.0952888i | 0.00542752 | + | 0.00680634i | ||||
\(197\) | −12.2795 | + | 7.08959i | −0.874880 | + | 0.505112i | −0.868967 | − | 0.494870i | \(-0.835216\pi\) |
−0.00591309 | + | 0.999983i | \(0.501882\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 20.1176i | − | 1.42610i | −0.701113 | − | 0.713050i | \(-0.747313\pi\) | ||
0.701113 | − | 0.713050i | \(-0.252687\pi\) | |||||||
\(200\) | 0.998475 | + | 1.18994i | 0.0706028 | + | 0.0841412i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.79057 | + | 4.91954i | 0.125984 | + | 0.346138i | ||||
\(203\) | −11.5775 | + | 0.867427i | −0.812581 | + | 0.0608815i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −22.1257 | − | 8.05311i | −1.54533 | − | 0.562454i | ||||
\(206\) | −8.73865 | −0.608851 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 26.3943i | 1.83012i | ||||||||
\(209\) | 15.1144 | − | 12.6825i | 1.04548 | − | 0.877264i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.582787 | − | 3.30515i | 0.0401207 | − | 0.227536i | −0.958154 | − | 0.286254i | \(-0.907590\pi\) |
0.998275 | + | 0.0587176i | \(0.0187011\pi\) | |||||||
\(212\) | −0.00526948 | − | 0.0144778i | −0.000361909 | − | 0.000994338i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.698655 | − | 3.96227i | −0.0477591 | − | 0.270855i | ||||
\(215\) | 7.84567 | − | 13.5891i | 0.535070 | − | 0.926768i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.980985 | − | 3.85283i | −0.0665936 | − | 0.261547i | ||||
\(218\) | 2.71314 | − | 7.45430i | 0.183757 | − | 0.504869i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.134001 | − | 0.0236280i | −0.00903434 | − | 0.00159300i | ||||
\(221\) | 7.37184 | + | 20.2540i | 0.495884 | + | 1.36243i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.45098 | + | 7.68798i | 0.431990 | + | 0.514825i | 0.937495 | − | 0.347998i | \(-0.113138\pi\) |
−0.505506 | + | 0.862823i | \(0.668694\pi\) | |||||||
\(224\) | −0.186539 | + | 0.181939i | −0.0124637 | + | 0.0121563i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.46517 | + | 11.1980i | 0.430056 | + | 0.744880i | ||||
\(227\) | 13.5964 | − | 11.4088i | 0.902427 | − | 0.757226i | −0.0682365 | − | 0.997669i | \(-0.521737\pi\) |
0.970663 | + | 0.240443i | \(0.0772928\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.8653 | − | 2.26849i | −0.850160 | − | 0.149906i | −0.268441 | − | 0.963296i | \(-0.586509\pi\) |
−0.581719 | + | 0.813390i | \(0.697620\pi\) | |||||||
\(230\) | −1.95568 | + | 0.711808i | −0.128953 | + | 0.0469352i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.16452 | − | 12.2756i | −0.142108 | − | 0.805934i | ||||
\(233\) | 16.4302 | − | 9.48596i | 1.07638 | − | 0.621446i | 0.146460 | − | 0.989217i | \(-0.453212\pi\) |
0.929917 | + | 0.367771i | \(0.119879\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.32623 | − | 10.9573i | 0.412678 | − | 0.714779i | ||||
\(236\) | 0.0188497 | + | 0.106902i | 0.00122701 | + | 0.00695871i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.23355 | − | 10.8671i | 0.339241 | − | 0.704412i | ||||
\(239\) | 13.6545 | − | 16.2728i | 0.883236 | − | 1.05260i | −0.115008 | − | 0.993365i | \(-0.536689\pi\) |
0.998244 | − | 0.0592349i | \(-0.0188661\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.6046 | + | 2.04621i | −0.747519 | + | 0.131808i | −0.534415 | − | 0.845222i | \(-0.679468\pi\) |
−0.213103 | + | 0.977030i | \(0.568357\pi\) | |||||||
\(242\) | 3.31104 | − | 1.91163i | 0.212842 | − | 0.122884i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 0.129488i | − | 0.00828962i | ||||||
\(245\) | 14.6068 | − | 2.20115i | 0.933197 | − | 0.140626i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 33.3273 | − | 12.1301i | 2.12056 | − | 0.771822i | ||||
\(248\) | 4.01113 | − | 1.45993i | 0.254707 | − | 0.0927058i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 16.2311 | − | 2.86198i | 1.02654 | − | 0.181007i | ||||
\(251\) | −13.6923 | − | 23.7157i | −0.864248 | − | 1.49692i | −0.867792 | − | 0.496927i | \(-0.834462\pi\) |
0.00354445 | − | 0.999994i | \(-0.498872\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.29698 | + | 2.24643i | −0.0815404 | + | 0.141232i | ||||
\(254\) | −0.922990 | + | 2.53589i | −0.0579135 | + | 0.159116i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.320075 | − | 0.268575i | −0.0200047 | − | 0.0167859i | ||||
\(257\) | 2.77342 | − | 15.7288i | 0.173001 | − | 0.981138i | −0.767425 | − | 0.641139i | \(-0.778462\pi\) |
0.940426 | − | 0.339999i | \(-0.110427\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.0339 | − | 13.9558i | 0.623474 | − | 0.867170i | ||||
\(260\) | −0.211819 | − | 0.122294i | −0.0131365 | − | 0.00758434i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.6180 | − | 6.13031i | −0.655983 | − | 0.378732i | ||||
\(263\) | 9.86756 | − | 27.1109i | 0.608460 | − | 1.67173i | −0.125132 | − | 0.992140i | \(-0.539935\pi\) |
0.733592 | − | 0.679590i | \(-0.237842\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.83900 | − | 0.324266i | −0.112969 | − | 0.0199195i | ||||
\(266\) | −17.8815 | − | 8.61165i | −1.09639 | − | 0.528014i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.140298 | − | 0.117724i | 0.00857007 | − | 0.00719114i | ||||
\(269\) | −4.08105 | − | 7.06859i | −0.248826 | − | 0.430979i | 0.714374 | − | 0.699764i | \(-0.246711\pi\) |
−0.963200 | + | 0.268784i | \(0.913378\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.1461 | + | 5.85783i | 0.616329 | + | 0.355838i | 0.775438 | − | 0.631423i | \(-0.217529\pi\) |
−0.159109 | + | 0.987261i | \(0.550862\pi\) | |||||||
\(272\) | 12.0631 | + | 4.39061i | 0.731432 | + | 0.266220i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.52564 | + | 6.31476i | 0.454640 | + | 0.381488i | ||||
\(275\) | 1.30175 | − | 1.55137i | 0.0784987 | − | 0.0935511i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.94325 | + | 3.25508i | 0.537348 | + | 0.195579i | 0.596416 | − | 0.802675i | \(-0.296591\pi\) |
−0.0590684 | + | 0.998254i | \(0.518813\pi\) | |||||||
\(278\) | −14.8118 | −0.888356 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.91324 | + | 15.3693i | 0.233861 | + | 0.918491i | ||||
\(281\) | −20.5328 | + | 3.62048i | −1.22488 | + | 0.215980i | −0.748426 | − | 0.663218i | \(-0.769190\pi\) |
−0.476457 | + | 0.879198i | \(0.658079\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.946510 | − | 1.12801i | 0.0562642 | − | 0.0670531i | −0.737178 | − | 0.675698i | \(-0.763842\pi\) |
0.793443 | + | 0.608645i | \(0.208287\pi\) | |||||||
\(284\) | 0.0495263 | − | 0.0590232i | 0.00293885 | − | 0.00350238i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 34.1863 | − | 6.02796i | 2.02148 | − | 0.356441i | ||||
\(287\) | 20.6121 | + | 21.1332i | 1.21669 | + | 1.24746i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.51698 | −0.383352 | ||||||||
\(290\) | −12.2523 | − | 4.45947i | −0.719480 | − | 0.261869i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.0342613 | + | 0.0408310i | −0.00200499 | + | 0.00238946i | ||||
\(293\) | 4.11874 | + | 3.45603i | 0.240619 | + | 0.201904i | 0.755120 | − | 0.655586i | \(-0.227578\pi\) |
−0.514501 | + | 0.857490i | \(0.672023\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.3633 | + | 4.49987i | 0.719818 | + | 0.261992i | ||||
\(296\) | 15.9819 | + | 9.22716i | 0.928930 | + | 0.536318i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.83400 | + | 13.5689i | 0.453811 | + | 0.786024i | ||||
\(299\) | −3.57187 | + | 2.99715i | −0.206566 | + | 0.173330i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.2549 | + | 11.0820i | −0.936918 | + | 0.638758i | ||||
\(302\) | 28.0016 | + | 4.93743i | 1.61131 | + | 0.284117i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.22461 | − | 19.8495i | 0.414360 | − | 1.13844i | ||||
\(305\) | −13.5917 | − | 7.84719i | −0.778261 | − | 0.449329i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.76941 | + | 3.90832i | 0.386351 | + | 0.223060i | 0.680578 | − | 0.732676i | \(-0.261729\pi\) |
−0.294227 | + | 0.955736i | \(0.595062\pi\) | |||||||
\(308\) | 0.138513 | + | 0.0995871i | 0.00789248 | + | 0.00567450i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.775338 | − | 4.39716i | 0.0440362 | − | 0.249742i | ||||
\(311\) | 9.50108 | + | 7.97235i | 0.538757 | + | 0.452071i | 0.871113 | − | 0.491083i | \(-0.163399\pi\) |
−0.332356 | + | 0.943154i | \(0.607843\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.42423 | − | 6.66051i | 0.137026 | − | 0.376474i | −0.852133 | − | 0.523325i | \(-0.824691\pi\) |
0.989159 | + | 0.146850i | \(0.0469136\pi\) | |||||||
\(314\) | 3.44439 | − | 5.96587i | 0.194378 | − | 0.336673i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.0828727 | + | 0.143540i | 0.00466196 | + | 0.00807475i | ||||
\(317\) | −16.6689 | + | 2.93919i | −0.936221 | + | 0.165081i | −0.620887 | − | 0.783900i | \(-0.713228\pi\) |
−0.315334 | + | 0.948981i | \(0.602117\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.2711 | + | 5.55822i | −0.855016 | + | 0.311200i | ||||
\(320\) | −15.9996 | + | 5.82337i | −0.894404 | + | 0.325537i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.59634 | + | 0.259845i | 0.144688 | + | 0.0144806i | ||||
\(323\) | − | 17.2495i | − | 0.959788i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.15261 | − | 1.82016i | 0.174875 | − | 0.100964i | ||||
\(326\) | 12.9963 | − | 2.29160i | 0.719799 | − | 0.126920i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −20.3730 | + | 24.2797i | −1.12491 | + | 1.34062i | ||||
\(329\) | −13.1069 | + | 8.93583i | −0.722607 | + | 0.492648i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.51122 | + | 14.2418i | 0.138029 | + | 0.782801i | 0.972702 | + | 0.232056i | \(0.0745452\pi\) |
−0.834674 | + | 0.550745i | \(0.814344\pi\) | |||||||
\(332\) | 0.105960 | − | 0.183529i | 0.00581532 | − | 0.0100724i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.5029 | + | 6.06386i | −0.574694 | + | 0.331799i | ||||
\(335\) | −3.85463 | − | 21.8607i | −0.210601 | − | 1.19438i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.9144 | + | 5.42839i | −0.812438 | + | 0.295703i | −0.714630 | − | 0.699502i | \(-0.753405\pi\) |
−0.0978073 | + | 0.995205i | \(0.531183\pi\) | |||||||
\(338\) | 43.4246 | + | 7.65693i | 2.36199 | + | 0.416482i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.0911278 | + | 0.0764653i | −0.00494210 | + | 0.00414691i | ||||
\(341\) | −2.78255 | − | 4.81952i | −0.150683 | − | 0.260991i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.6972 | − | 5.45979i | −0.955559 | − | 0.294801i | ||||
\(344\) | −13.5770 | − | 16.1804i | −0.732023 | − | 0.872391i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.08070 | + | 11.2116i | 0.219380 | + | 0.602741i | ||||
\(347\) | 5.06257 | + | 0.892668i | 0.271773 | + | 0.0479209i | 0.307874 | − | 0.951427i | \(-0.400383\pi\) |
−0.0361006 | + | 0.999348i | \(0.511494\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.81124 | − | 10.4713i | 0.204011 | − | 0.560516i | −0.794921 | − | 0.606713i | \(-0.792488\pi\) |
0.998932 | + | 0.0461967i | \(0.0147101\pi\) | |||||||
\(350\) | −1.96101 | − | 0.551775i | −0.104820 | − | 0.0294936i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.182371 | + | 0.315875i | −0.00972038 | + | 0.0168362i | ||||
\(353\) | 0.534901 | + | 3.03357i | 0.0284699 | + | 0.161461i | 0.995728 | − | 0.0923333i | \(-0.0294325\pi\) |
−0.967258 | + | 0.253794i | \(0.918321\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.19400 | − | 8.77545i | −0.169520 | − | 0.465752i | ||||
\(356\) | 0.0131768 | − | 0.0747292i | 0.000698368 | − | 0.00396064i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.21599 | − | 4.37674i | 0.275674 | − | 0.231318i | ||||
\(359\) | 21.9068i | 1.15620i | 0.815967 | + | 0.578099i | \(0.196205\pi\) | ||||
−0.815967 | + | 0.578099i | \(0.803795\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.38353 | −0.493870 | ||||||||
\(362\) | 6.03899 | + | 2.19801i | 0.317402 | + | 0.115525i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.172741 | + | 0.253373i | 0.00905407 | + | 0.0132803i | ||||
\(365\) | 2.20955 | + | 6.07068i | 0.115653 | + | 0.317754i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.25108 | − | 5.06624i | −0.221905 | − | 0.264456i | 0.643594 | − | 0.765367i | \(-0.277443\pi\) |
−0.865499 | + | 0.500912i | \(0.832998\pi\) | |||||||
\(368\) | 2.77709i | 0.144766i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 16.7174 | − | 9.65179i | 0.869096 | − | 0.501773i | ||||
\(371\) | 1.90092 | + | 1.36671i | 0.0986908 | + | 0.0709562i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.8688 | + | 15.8328i | 0.976988 | + | 0.819790i | 0.983632 | − | 0.180188i | \(-0.0576705\pi\) |
−0.00664425 | + | 0.999978i | \(0.502115\pi\) | |||||||
\(374\) | 2.93179 | − | 16.6270i | 0.151599 | − | 0.859761i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.9476 | − | 13.0468i | −0.564579 | − | 0.672839i | ||||
\(377\) | −29.2121 | −1.50450 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.06704 | 0.106176 | 0.0530882 | − | 0.998590i | \(-0.483094\pi\) | ||||
0.0530882 | + | 0.998590i | \(0.483094\pi\) | |||||||
\(380\) | 0.125821 | + | 0.149948i | 0.00645450 | + | 0.00769217i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.52862 | + | 14.3405i | −0.129376 | + | 0.733725i | ||||
\(383\) | −5.29740 | − | 4.44505i | −0.270685 | − | 0.227131i | 0.497334 | − | 0.867559i | \(-0.334313\pi\) |
−0.768018 | + | 0.640428i | \(0.778757\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.8473 | − | 8.50385i | 0.960546 | − | 0.433396i | ||||
\(386\) | −12.6881 | + | 7.32550i | −0.645810 | + | 0.372858i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 0.121258i | − | 0.00615592i | ||||||
\(389\) | 8.68514 | + | 10.3505i | 0.440354 | + | 0.524794i | 0.939880 | − | 0.341505i | \(-0.110937\pi\) |
−0.499526 | + | 0.866299i | \(0.666492\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.775631 | + | 2.13103i | 0.0392254 | + | 0.107771i | ||||
\(392\) | 3.94061 | − | 19.4898i | 0.199031 | − | 0.984386i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.7609 | + | 6.82840i | 0.945159 | + | 0.344010i | ||||
\(395\) | 20.0889 | 1.01078 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.5333i | 1.08072i | 0.841433 | + | 0.540362i | \(0.181713\pi\) | ||||
−0.841433 | + | 0.540362i | \(0.818287\pi\) | |||||||
\(398\) | −21.6994 | + | 18.2079i | −1.08769 | + | 0.912681i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.376494 | − | 2.13521i | 0.0188247 | − | 0.106760i | ||||
\(401\) | 9.04869 | + | 24.8611i | 0.451870 | + | 1.24150i | 0.931407 | + | 0.363981i | \(0.118583\pi\) |
−0.479537 | + | 0.877522i | \(0.659195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.73709 | − | 9.85151i | −0.0865304 | − | 0.490738i | ||||
\(404\) | −0.0323677 | + | 0.0560625i | −0.00161035 | + | 0.00278921i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.4141 | + | 11.7027i | 0.566473 | + | 0.580794i | ||||
\(407\) | 8.22890 | − | 22.6087i | 0.407891 | − | 1.12067i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.6998 | − | 4.35525i | −1.22133 | − | 0.215353i | −0.474431 | − | 0.880293i | \(-0.657346\pi\) |
−0.746897 | + | 0.664939i | \(0.768457\pi\) | |||||||
\(410\) | 11.3391 | + | 31.1540i | 0.560000 | + | 1.53859i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.0694568 | − | 0.0827754i | −0.00342189 | − | 0.00407805i | ||||
\(413\) | −11.5175 | − | 11.8087i | −0.566740 | − | 0.581068i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.8427 | − | 22.2443i | −0.630426 | − | 1.09193i | ||||
\(416\) | −0.502247 | + | 0.421435i | −0.0246247 | + | 0.0206625i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −27.3592 | − | 4.82417i | −1.33818 | − | 0.235958i | ||||
\(419\) | −22.3814 | + | 8.14616i | −1.09340 | + | 0.397966i | −0.824880 | − | 0.565307i | \(-0.808758\pi\) |
−0.268522 | + | 0.963273i | \(0.586535\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.34235 | − | 7.61285i | −0.0654222 | − | 0.371027i | −0.999888 | − | 0.0149744i | \(-0.995233\pi\) |
0.934466 | − | 0.356053i | \(-0.115878\pi\) | |||||||
\(422\) | −4.09248 | + | 2.36280i | −0.199219 | + | 0.115019i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.25683 | + | 2.17690i | −0.0610372 | + | 0.105719i | ||||
\(425\) | −0.307448 | − | 1.74363i | −0.0149134 | − | 0.0845783i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.0842 | + | 16.2581i | 0.536402 | + | 0.786784i | ||||
\(428\) | 0.0319789 | − | 0.0381110i | 0.00154576 | − | 0.00184216i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −21.7584 | + | 3.83660i | −1.04928 | + | 0.185017i | ||||
\(431\) | −4.73254 | + | 2.73233i | −0.227959 | + | 0.131612i | −0.609630 | − | 0.792686i | \(-0.708682\pi\) |
0.381671 | + | 0.924298i | \(0.375349\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 35.5423i | − | 1.70805i | −0.520229 | − | 0.854027i | \(-0.674154\pi\) | ||
0.520229 | − | 0.854027i | \(-0.325846\pi\) | |||||||
\(434\) | −3.26789 | + | 4.54521i | −0.156864 | + | 0.218177i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.0921743 | − | 0.0335487i | 0.00441435 | − | 0.00160669i | ||||
\(437\) | 3.50654 | − | 1.27628i | 0.167741 | − | 0.0610526i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.99689 | + | 0.704759i | −0.190761 | + | 0.0336363i | −0.268212 | − | 0.963360i | \(-0.586433\pi\) |
0.0774513 | + | 0.996996i | \(0.475322\pi\) | |||||||
\(440\) | 11.0999 | + | 19.2255i | 0.529165 | + | 0.916541i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.1744 | − | 26.2828i | 0.721771 | − | 1.25014i | ||||
\(443\) | −2.83479 | + | 7.78852i | −0.134685 | + | 0.370044i | −0.988640 | − | 0.150303i | \(-0.951975\pi\) |
0.853955 | + | 0.520347i | \(0.174197\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.04544 | − | 5.91182i | −0.333986 | − | 0.280247i | ||||
\(446\) | 2.45383 | − | 13.9164i | 0.116192 | − | 0.658960i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 21.2409 | + | 2.12582i | 1.00354 | + | 0.100435i | ||||
\(449\) | −25.1276 | − | 14.5074i | −1.18585 | − | 0.684648i | −0.228486 | − | 0.973547i | \(-0.573377\pi\) |
−0.957359 | + | 0.288899i | \(0.906711\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 35.7858 | + | 20.6610i | 1.68509 | + | 0.972887i | ||||
\(452\) | −0.0546845 | + | 0.150244i | −0.00257214 | + | 0.00706691i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −24.6115 | − | 4.33968i | −1.15508 | − | 0.203671i | ||||
\(455\) | 37.0637 | − | 2.77695i | 1.73757 | − | 0.130185i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.02502 | + | 4.21649i | −0.235061 | + | 0.197239i | −0.752708 | − | 0.658355i | \(-0.771253\pi\) |
0.517647 | + | 0.855594i | \(0.326808\pi\) | |||||||
\(458\) | 9.19715 | + | 15.9299i | 0.429755 | + | 0.744357i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.0222866 | − | 0.0128672i | −0.00103912 | − | 0.000599936i | ||||
\(461\) | 20.7893 | + | 7.56669i | 0.968255 | + | 0.352416i | 0.777263 | − | 0.629176i | \(-0.216607\pi\) |
0.190992 | + | 0.981592i | \(0.438830\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.6417 | + | 10.6077i | 0.587511 | + | 0.492980i | 0.887404 | − | 0.460993i | \(-0.152507\pi\) |
−0.299893 | + | 0.953973i | \(0.596951\pi\) | |||||||
\(464\) | −11.1835 | + | 13.3280i | −0.519181 | + | 0.618736i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −25.1023 | − | 9.13649i | −1.16284 | − | 0.423240i | ||||
\(467\) | −1.42626 | −0.0659994 | −0.0329997 | − | 0.999455i | \(-0.510506\pi\) | ||||
−0.0329997 | + | 0.999455i | \(0.510506\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.53816 | + | 26.7906i | −0.348080 | + | 1.23707i | ||||
\(470\) | −17.5446 | + | 3.09358i | −0.809271 | + | 0.142696i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.3839 | − | 13.5668i | 0.523988 | − | 0.624464i | ||||
\(473\) | −17.7009 | + | 21.0951i | −0.813889 | + | 0.969955i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.86909 | + | 0.505897i | −0.131643 | + | 0.0232122i | ||||
\(476\) | 0.144535 | − | 0.0368006i | 0.00662473 | − | 0.00168675i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −29.9106 | −1.36808 | ||||||||
\(479\) | −22.5859 | − | 8.22061i | −1.03198 | − | 0.375609i | −0.230144 | − | 0.973157i | \(-0.573920\pi\) |
−0.801834 | + | 0.597547i | \(0.796142\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.7994 | − | 33.1301i | 1.26754 | − | 1.51060i | ||||
\(482\) | 12.7101 | + | 10.6651i | 0.578930 | + | 0.485780i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.0444246 | + | 0.0161692i | 0.00201930 | + | 0.000734965i | ||||
\(485\) | −12.7278 | − | 7.34842i | −0.577941 | − | 0.333674i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.7620 | + | 30.7647i | 0.804874 | + | 1.39408i | 0.916376 | + | 0.400319i | \(0.131101\pi\) |
−0.111501 | + | 0.993764i | \(0.535566\pi\) | |||||||
\(488\) | −16.1836 | + | 13.5796i | −0.732597 | + | 0.614722i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −15.5945 | − | 13.7631i | −0.704487 | − | 0.621753i | ||||
\(491\) | 30.5498 | + | 5.38675i | 1.37869 | + | 0.243101i | 0.813360 | − | 0.581761i | \(-0.197636\pi\) |
0.565334 | + | 0.824862i | \(0.308747\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.85933 | + | 13.3509i | −0.218853 | + | 0.601294i | ||||
\(494\) | −43.2475 | − | 24.9690i | −1.94580 | − | 1.12341i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.15977 | − | 2.97899i | −0.231681 | − | 0.133761i | ||||
\(497\) | −1.16597 | + | 11.6502i | −0.0523008 | + | 0.522584i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.32386 | − | 35.8644i | 0.283095 | − | 1.60551i | −0.428917 | − | 0.903344i | \(-0.641105\pi\) |
0.712012 | − | 0.702167i | \(-0.247784\pi\) | |||||||
\(500\) | 0.156118 | + | 0.130999i | 0.00698181 | + | 0.00585844i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.1878 | + | 36.2332i | −0.588601 | + | 1.61717i | ||||
\(503\) | 9.30116 | − | 16.1101i | 0.414718 | − | 0.718313i | −0.580681 | − | 0.814131i | \(-0.697213\pi\) |
0.995399 | + | 0.0958185i | \(0.0305468\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.92308 | + | 6.79497i | 0.174575 | + | 0.302372i | ||||
\(506\) | 3.59692 | − | 0.634234i | 0.159903 | − | 0.0281951i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.0313570 | + | 0.0114130i | −0.00139124 | + | 0.000506370i | ||||
\(509\) | −4.20101 | + | 1.52904i | −0.186207 | + | 0.0677737i | −0.433441 | − | 0.901182i | \(-0.642701\pi\) |
0.247234 | + | 0.968956i | \(0.420478\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.806593 | − | 8.05939i | 0.0356816 | − | 0.356526i | ||||
\(512\) | 22.9158i | 1.01274i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.4757 | + | 11.2443i | −0.859034 | + | 0.495964i | ||||
\(515\) | −12.8977 | + | 2.27422i | −0.568343 | + | 0.100214i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.2729 | + | 17.0097i | −0.627719 | + | 0.748087i | ||||
\(518\) | −24.1344 | + | 1.80824i | −1.06041 | + | 0.0794494i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.92941 | + | 39.2986i | 0.303875 | + | 1.72336i | ||||
\(521\) | 17.3340 | − | 30.0233i | 0.759415 | − | 1.31535i | −0.183735 | − | 0.982976i | \(-0.558819\pi\) |
0.943149 | − | 0.332369i | \(-0.107848\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.2749 | + | 12.8604i | −0.974015 | + | 0.562348i | −0.900458 | − | 0.434943i | \(-0.856768\pi\) |
−0.0735572 | + | 0.997291i | \(0.523435\pi\) | |||||||
\(524\) | −0.0263260 | − | 0.149302i | −0.00115006 | − | 0.00652231i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −38.1734 | + | 13.8940i | −1.66444 | + | 0.605806i | ||||
\(527\) | −4.79143 | − | 0.844858i | −0.208718 | − | 0.0368026i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.2432 | − | 14.4688i | 0.749705 | − | 0.629077i | ||||
\(530\) | 1.31467 | + | 2.27708i | 0.0571057 | + | 0.0989099i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.0605542 | − | 0.237827i | −0.00262536 | − | 0.0103111i | ||||
\(533\) | 47.7448 | + | 56.9001i | 2.06806 | + | 2.46462i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.06235 | − | 5.66626i | −0.0891632 | − | 0.244974i | ||||
\(536\) | −29.4266 | − | 5.18871i | −1.27104 | − | 0.224118i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.93070 | + | 10.7995i | −0.169465 | + | 0.465600i | ||||
\(539\) | −25.9158 | − | 0.647128i | −1.11627 | − | 0.0278738i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.1658 | − | 22.8039i | 0.566044 | − | 0.980416i | −0.430908 | − | 0.902396i | \(-0.641807\pi\) |
0.996952 | − | 0.0780204i | \(-0.0248599\pi\) | |||||||
\(542\) | −2.86453 | − | 16.2455i | −0.123042 | − | 0.697806i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.109063 | + | 0.299648i | 0.00467603 | + | 0.0128473i | ||||
\(545\) | 2.06447 | − | 11.7082i | 0.0884323 | − | 0.501524i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.7395 | − | 11.5288i | 0.587459 | − | 0.492937i | −0.299928 | − | 0.953962i | \(-0.596963\pi\) |
0.887387 | + | 0.461025i | \(0.152518\pi\) | |||||||
\(548\) | 0.121477i | 0.00518922i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.85153 | −0.121590 | ||||||||
\(551\) | 21.9685 | + | 7.99587i | 0.935889 | + | 0.340636i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.6923 | − | 10.9285i | −0.964973 | − | 0.464726i | ||||
\(554\) | −4.58329 | − | 12.5925i | −0.194725 | − | 0.535004i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.117728 | − | 0.140303i | −0.00499278 | − | 0.00595016i | ||||
\(557\) | − | 1.14693i | − | 0.0485968i | −0.999705 | − | 0.0242984i | \(-0.992265\pi\) | ||
0.999705 | − | 0.0242984i | \(-0.00773518\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −42.8684 | + | 24.7501i | −1.81314 | + | 1.04682i | ||||
\(560\) | 12.9224 | − | 17.9734i | 0.546073 | − | 0.759516i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 22.4888 | + | 18.8704i | 0.948634 | + | 0.795998i | ||||
\(563\) | 1.56861 | − | 8.89601i | 0.0661089 | − | 0.374922i | −0.933747 | − | 0.357934i | \(-0.883481\pi\) |
0.999856 | − | 0.0169880i | \(-0.00540771\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.4565 | + | 14.8450i | 0.524048 | + | 0.624536i | ||||
\(566\) | −2.07336 | −0.0871497 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.5707 | −0.527455 | ||||||||
\(569\) | −27.5657 | − | 32.8516i | −1.15562 | − | 1.37721i | −0.913438 | − | 0.406978i | \(-0.866583\pi\) |
−0.242178 | − | 0.970232i | \(-0.577862\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.74972 | + | 32.6083i | −0.240618 | + | 1.36461i | 0.589834 | + | 0.807524i | \(0.299193\pi\) |
−0.830453 | + | 0.557089i | \(0.811918\pi\) | |||||||
\(572\) | 0.328819 | + | 0.275912i | 0.0137486 | + | 0.0115365i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.13934 | − | 41.3599i | 0.172773 | − | 1.72633i | ||||
\(575\) | 0.331703 | − | 0.191509i | 0.0138330 | − | 0.00798648i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 41.8339i | − | 1.74157i | −0.491665 | − | 0.870784i | \(-0.663612\pi\) | ||
0.491665 | − | 0.870784i | \(-0.336388\pi\) | |||||||
\(578\) | 5.89835 | + | 7.02938i | 0.245339 | + | 0.292383i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.0551425 | − | 0.151503i | −0.00228967 | − | 0.00629081i | ||||
\(581\) | 2.40606 | + | 32.1135i | 0.0998200 | + | 1.33229i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.07953 | + | 1.12086i | 0.127541 | + | 0.0464212i | ||||
\(584\) | 8.69617 | 0.359850 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 7.57054i | − | 0.312736i | ||||||
\(587\) | −10.1800 | + | 8.54200i | −0.420172 | + | 0.352566i | −0.828228 | − | 0.560391i | \(-0.810651\pi\) |
0.408057 | + | 0.912957i | \(0.366207\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.39019 | + | 7.88415i | −0.0572817 | + | 0.324861i | ||||
\(590\) | −6.33602 | − | 17.4081i | −0.260850 | − | 0.716678i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.47288 | − | 25.3670i | −0.183834 | − | 1.04258i | ||||
\(593\) | −6.07625 | + | 10.5244i | −0.249522 | + | 0.432184i | −0.963393 | − | 0.268093i | \(-0.913607\pi\) |
0.713872 | + | 0.700277i | \(0.246940\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.89626 | − | 17.4013i | 0.200727 | − | 0.713383i | ||||
\(596\) | −0.0662626 | + | 0.182055i | −0.00271422 | + | 0.00745726i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.46560 | + | 1.14006i | 0.264398 | + | 0.0466205i | ||||
\(599\) | −10.4793 | − | 28.7916i | −0.428172 | − | 1.17639i | −0.946921 | − | 0.321466i | \(-0.895824\pi\) |
0.518749 | − | 0.854927i | \(-0.326398\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.739101 | + | 0.880827i | 0.0301486 | + | 0.0359297i | 0.780908 | − | 0.624646i | \(-0.214757\pi\) |
−0.750759 | + | 0.660576i | \(0.770312\pi\) | |||||||
\(602\) | 26.6653 | + | 7.50290i | 1.08679 | + | 0.305795i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.175794 | + | 0.304484i | 0.00715296 | + | 0.0123893i | ||||
\(605\) | 4.38941 | − | 3.68315i | 0.178455 | − | 0.149741i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.97007 | + | 0.523704i | 0.120552 | + | 0.0212565i | 0.233598 | − | 0.972333i | \(-0.424950\pi\) |
−0.113047 | + | 0.993590i | \(0.536061\pi\) | |||||||
\(608\) | 0.493061 | − | 0.179460i | 0.0199963 | − | 0.00727805i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.83735 | + | 21.7627i | 0.155370 | + | 0.881145i | ||||
\(611\) | −34.5662 | + | 19.9568i | −1.39840 | + | 0.807367i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.0456 | − | 34.7199i | 0.809633 | − | 1.40232i | −0.103486 | − | 0.994631i | \(-0.533000\pi\) |
0.913119 | − | 0.407694i | \(-0.133667\pi\) | |||||||
\(614\) | −1.91120 | − | 10.8390i | −0.0771299 | − | 0.437425i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.07953 | − | 27.7554i | −0.0837867 | − | 1.11830i | ||||
\(617\) | −6.57249 | + | 7.83278i | −0.264598 | + | 0.315336i | −0.881942 | − | 0.471357i | \(-0.843764\pi\) |
0.617344 | + | 0.786693i | \(0.288209\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.3209 | − | 6.75702i | 1.54025 | − | 0.271587i | 0.661894 | − | 0.749597i | \(-0.269753\pi\) |
0.878354 | + | 0.478010i | \(0.158642\pi\) | |||||||
\(620\) | 0.0478139 | − | 0.0276054i | 0.00192025 | − | 0.00110866i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 17.4637i | − | 0.700229i | ||||||
\(623\) | 4.74240 | + | 10.5107i | 0.190000 | + | 0.421102i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.6420 | − | 7.51308i | 0.825681 | − | 0.300523i | ||||
\(626\) | −9.37830 | + | 3.41342i | −0.374832 | + | 0.136428i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.0838875 | − | 0.0147916i | 0.00334748 | − | 0.000590250i | ||||
\(629\) | −10.5172 | − | 18.2163i | −0.419349 | − | 0.726333i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.94429 | − | 10.2958i | 0.236639 | − | 0.409870i | −0.723109 | − | 0.690734i | \(-0.757288\pi\) |
0.959748 | + | 0.280864i | \(0.0906210\pi\) | |||||||
\(632\) | 9.24879 | − | 25.4108i | 0.367897 | − | 1.01079i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18.2569 | + | 15.3194i | 0.725074 | + | 0.608409i | ||||
\(635\) | −0.702317 | + | 3.98304i | −0.0278706 | + | 0.158062i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −43.3775 | − | 17.0260i | −1.71868 | − | 0.674595i | ||||
\(638\) | 19.8167 | + | 11.4412i | 0.784550 | + | 0.452960i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 20.4021 | + | 11.7791i | 0.806462 | + | 0.465611i | ||||
\(641\) | 17.0872 | − | 46.9468i | 0.674906 | − | 1.85429i | 0.184396 | − | 0.982852i | \(-0.440967\pi\) |
0.490509 | − | 0.871436i | \(-0.336811\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.32572 | − | 1.29172i | −0.288898 | − | 0.0509406i | 0.0273209 | − | 0.999627i | \(-0.491302\pi\) |
−0.316219 | + | 0.948686i | \(0.602414\pi\) | |||||||
\(644\) | 0.0181750 | + | 0.0266587i | 0.000716194 | + | 0.00105050i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.6057 | + | 15.6121i | −0.732033 | + | 0.614248i | ||||
\(647\) | 9.06934 | + | 15.7086i | 0.356553 | + | 0.617567i | 0.987382 | − | 0.158354i | \(-0.0506187\pi\) |
−0.630830 | + | 0.775921i | \(0.717285\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.9962 | − | 11.5448i | −0.784919 | − | 0.453173i | ||||
\(650\) | −4.81662 | − | 1.75310i | −0.188923 | − | 0.0687624i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.125004 | + | 0.104891i | 0.00489555 | + | 0.00410786i | ||||
\(653\) | 14.2828 | − | 17.0215i | 0.558928 | − | 0.666104i | −0.410392 | − | 0.911909i | \(-0.634608\pi\) |
0.969319 | + | 0.245805i | \(0.0790524\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.2670 | − | 6.28466i | −0.674676 | − | 0.245562i | ||||
\(656\) | 44.2392 | 1.72725 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 21.5011 | + | 6.04984i | 0.838200 | + | 0.235847i | ||||
\(659\) | −21.2896 | + | 3.75393i | −0.829324 | + | 0.146232i | −0.572167 | − | 0.820137i | \(-0.693897\pi\) |
−0.257157 | + | 0.966370i | \(0.582786\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.08248 | − | 3.67356i | 0.119895 | − | 0.142885i | −0.702758 | − | 0.711428i | \(-0.748049\pi\) |
0.822653 | + | 0.568544i | \(0.192493\pi\) | |||||||
\(662\) | 13.0887 | − | 15.5986i | 0.508708 | − | 0.606255i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −34.0499 | + | 6.00391i | −1.32139 | + | 0.232997i | ||||
\(665\) | −28.6333 | − | 8.05665i | −1.11035 | − | 0.312424i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.07356 | −0.119009 | ||||||||
\(668\) | −0.140918 | − | 0.0512901i | −0.00545230 | − | 0.00198447i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −20.0908 | + | 23.9432i | −0.776174 | + | 0.925008i | ||||
\(671\) | 21.0992 | + | 17.7044i | 0.814527 | + | 0.683469i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −41.8330 | − | 15.2260i | −1.61255 | − | 0.586918i | −0.630604 | − | 0.776105i | \(-0.717193\pi\) |
−0.981941 | + | 0.189186i | \(0.939415\pi\) | |||||||
\(674\) | 19.3538 | + | 11.1739i | 0.745480 | + | 0.430403i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.272620 | + | 0.472192i | 0.0104854 | + | 0.0181612i | ||||
\(677\) | −30.7338 | + | 25.7887i | −1.18120 | + | 0.991142i | −0.181227 | + | 0.983441i | \(0.558007\pi\) |
−0.999970 | + | 0.00770076i | \(0.997549\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.3797 | + | 15.2247i | 0.398335 | + | 0.584270i | ||||
\(680\) | 19.1135 | + | 3.37022i | 0.732968 | + | 0.129242i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.68004 | + | 7.36334i | −0.102624 | + | 0.281957i | ||||
\(683\) | 28.5877 | + | 16.5051i | 1.09388 | + | 0.631550i | 0.934606 | − | 0.355685i | \(-0.115752\pi\) |
0.159271 | + | 0.987235i | \(0.449086\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.7508 | + | 7.36168i | 0.487183 | + | 0.281275i | ||||
\(686\) | 10.1282 | + | 24.0301i | 0.386696 | + | 0.917475i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.11947 | + | 29.0340i | −0.195178 | + | 1.10691i | ||||
\(689\) | 4.51265 | + | 3.78656i | 0.171918 | + | 0.144257i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.00124 | − | 2.75087i | 0.0380888 | − | 0.104648i | −0.919190 | − | 0.393814i | \(-0.871156\pi\) |
0.957279 | + | 0.289165i | \(0.0933778\pi\) | |||||||
\(692\) | −0.0737660 | + | 0.127766i | −0.00280416 | + | 0.00485695i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.61915 | − | 6.26854i | −0.137381 | − | 0.237951i | ||||
\(695\) | −21.8614 | + | 3.85476i | −0.829251 | + | 0.146219i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.9474 | − | 12.3559i | 1.28585 | − | 0.468011i | ||||
\(698\) | −14.7441 | + | 5.36640i | −0.558071 | + | 0.203121i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.0103599 | − | 0.0229609i | −0.000391569 | − | 0.000867842i | ||||
\(701\) | − | 6.39386i | − | 0.241493i | −0.992683 | − | 0.120746i | \(-0.961471\pi\) | ||
0.992683 | − | 0.120746i | \(-0.0385288\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.9744 | + | 17.3058i | −1.13051 | + | 0.652699i | ||||
\(704\) | 29.4268 | − | 5.18874i | 1.10906 | − | 0.195558i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.78796 | − | 3.32257i | 0.104926 | − | 0.125046i | ||||
\(707\) | −0.734978 | − | 9.80970i | −0.0276417 | − | 0.368932i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.22575 | − | 35.3080i | −0.233813 | − | 1.32602i | −0.845099 | − | 0.534609i | \(-0.820459\pi\) |
0.611287 | − | 0.791409i | \(-0.290652\pi\) | |||||||
\(710\) | −6.57461 | + | 11.3876i | −0.246741 | + | 0.427367i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10.7216 | + | 6.19014i | −0.401810 | + | 0.231985i | ||||
\(713\) | −0.182768 | − | 1.03653i | −0.00684472 | − | 0.0388184i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 48.8882 | − | 17.7938i | 1.82831 | − | 0.665452i | ||||
\(716\) | 0.0829158 | + | 0.0146203i | 0.00309871 | + | 0.000546386i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 23.6292 | − | 19.8273i | 0.881836 | − | 0.739948i | ||||
\(719\) | 17.8398 | + | 30.8994i | 0.665311 | + | 1.15235i | 0.979201 | + | 0.202893i | \(0.0650344\pi\) |
−0.313890 | + | 0.949459i | \(0.601632\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.8064 | + | 4.44749i | 0.588660 | + | 0.165633i | ||||
\(722\) | 8.49278 | + | 10.1213i | 0.316069 | + | 0.376676i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.0271790 | + | 0.0746736i | 0.00101010 | + | 0.00277522i | ||||
\(725\) | 2.36315 | + | 0.416687i | 0.0877652 | + | 0.0154754i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.773622 | + | 2.12551i | −0.0286921 | + | 0.0788308i | −0.953212 | − | 0.302304i | \(-0.902244\pi\) |
0.924520 | + | 0.381135i | \(0.124467\pi\) | |||||||
\(728\) | 13.5512 | − | 48.1610i | 0.502242 | − | 1.78497i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.54818 | − | 7.87768i | 0.168336 | − | 0.291566i | ||||
\(731\) | 4.18060 | + | 23.7094i | 0.154625 | + | 0.876923i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.51496 | + | 15.1522i | 0.203700 | + | 0.559661i | 0.998910 | − | 0.0466729i | \(-0.0148618\pi\) |
−0.795210 | + | 0.606334i | \(0.792640\pi\) | |||||||
\(734\) | −1.61703 | + | 9.17065i | −0.0596858 | + | 0.338495i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.0528441 | + | 0.0443414i | −0.00194786 | + | 0.00163445i | ||||
\(737\) | 38.9566i | 1.43498i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.5989 | 0.904884 | 0.452442 | − | 0.891794i | \(-0.350553\pi\) | ||||
0.452442 | + | 0.891794i | \(0.350553\pi\) | |||||||
\(740\) | 0.224299 | + | 0.0816381i | 0.00824538 | + | 0.00300107i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.246300 | − | 3.28735i | −0.00904197 | − | 0.120683i | ||||
\(743\) | −8.41237 | − | 23.1128i | −0.308620 | − | 0.847926i | −0.992926 | − | 0.118732i | \(-0.962117\pi\) |
0.684307 | − | 0.729194i | \(-0.260105\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.0938 | + | 17.9881i | 0.552994 | + | 0.659033i | ||||
\(746\) | − | 34.6822i | − | 1.26980i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.180799 | − | 0.104384i | 0.00661066 | − | 0.00381667i | ||||
\(749\) | −0.752859 | + | 7.52248i | −0.0275089 | + | 0.274866i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.0407 | − | 23.5290i | −1.02322 | − | 0.858584i | −0.0331922 | − | 0.999449i | \(-0.510567\pi\) |
−0.990029 | + | 0.140865i | \(0.955012\pi\) | |||||||
\(752\) | −4.12801 | + | 23.4111i | −0.150533 | + | 0.853715i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 26.4391 | + | 31.5088i | 0.962854 | + | 1.14748i | ||||
\(755\) | 42.6137 | 1.55087 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.6682 | −1.40542 | −0.702709 | − | 0.711477i | \(-0.748027\pi\) | ||||
−0.702709 | + | 0.711477i | \(0.748027\pi\) | |||||||
\(758\) | −1.87082 | − | 2.22956i | −0.0679512 | − | 0.0809811i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.54560 | − | 31.4506i | 0.201160 | − | 1.14083i | ||||
\(761\) | −36.9741 | − | 31.0250i | −1.34031 | − | 1.12465i | −0.981546 | − | 0.191226i | \(-0.938754\pi\) |
−0.358765 | − | 0.933428i | \(-0.616802\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.70132 | + | 12.1024i | −0.315009 | + | 0.438136i | ||||
\(764\) | −0.155936 | + | 0.0900299i | −0.00564158 | + | 0.00325717i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.73700i | 0.351812i | ||||||||
\(767\) | −26.6786 | − | 31.7943i | −0.963307 | − | 1.14802i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.2750 | − | 44.7151i | −0.586891 | − | 1.61247i | −0.776155 | − | 0.630543i | \(-0.782832\pi\) |
0.189264 | − | 0.981926i | \(-0.439390\pi\) | |||||||
\(770\) | −26.2306 | − | 12.6325i | −0.945286 | − | 0.455244i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.170238 | − | 0.0619615i | −0.00612700 | − | 0.00223004i | ||||
\(773\) | −3.58933 | −0.129099 | −0.0645496 | − | 0.997914i | \(-0.520561\pi\) | ||||
−0.0645496 | + | 0.997914i | \(0.520561\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.821730i | 0.0295174i | ||||||||
\(776\) | −15.1549 | + | 12.7165i | −0.544031 | + | 0.456496i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.30367 | − | 18.7360i | 0.118442 | − | 0.671719i | ||||
\(779\) | −20.3312 | − | 55.8595i | −0.728440 | − | 2.00137i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.84592 | + | 16.1400i | 0.101835 | + | 0.577534i | ||||
\(782\) | 1.59658 | − | 2.76535i | 0.0570935 | − | 0.0988888i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −24.3747 | + | 13.2727i | −0.870525 | + | 0.474027i | ||||
\(785\) | 3.53112 | − | 9.70167i | 0.126031 | − | 0.346267i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.5240 | + | 5.38221i | 1.08806 | + | 0.191855i | 0.688779 | − | 0.724971i | \(-0.258147\pi\) |
0.399286 | + | 0.916827i | \(0.369258\pi\) | |||||||
\(788\) | 0.0844349 | + | 0.231983i | 0.00300787 | + | 0.00826405i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −18.1819 | − | 21.6684i | −0.646885 | − | 0.770927i | ||||
\(791\) | −5.99495 | − | 23.5452i | −0.213156 | − | 0.837171i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.7549 | + | 42.8767i | 0.879072 | + | 1.52260i | ||||
\(794\) | 23.2263 | − | 19.4892i | 0.824271 | − | 0.691645i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.344943 | − | 0.0608228i | −0.0122262 | − | 0.00215581i | ||||
\(797\) | −18.1049 | + | 6.58966i | −0.641310 | + | 0.233418i | −0.642147 | − | 0.766582i | \(-0.721956\pi\) |
0.000836476 | 1.00000i | \(0.499734\pi\) | ||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.37096 | + | 19.1177i | 0.119256 | + | 0.676335i | ||||
\(800\) | 0.0466414 | − | 0.0269284i | 0.00164902 | − | 0.000952063i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.6260 | − | 32.2612i | 0.657708 | − | 1.13918i | ||||
\(803\) | −1.96875 | − | 11.1653i | −0.0694756 | − | 0.394016i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.89967 | − | 0.292177i | 0.137445 | − | 0.0102979i | ||||
\(806\) | −9.05389 | + | 10.7900i | −0.318910 | + | 0.380062i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.4012 | − | 1.83402i | 0.365914 | − | 0.0645205i | ||||
\(809\) | 10.9220 | − | 6.30585i | 0.383999 | − | 0.221702i | −0.295558 | − | 0.955325i | \(-0.595506\pi\) |
0.679557 | + | 0.733623i | \(0.262172\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.6085i | 1.53130i | 0.643256 | + | 0.765652i | \(0.277583\pi\) | ||||
−0.643256 | + | 0.765652i | \(0.722417\pi\) | |||||||
\(812\) | −0.0201297 | + | 0.201134i | −0.000706415 | + | 0.00705842i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −31.8341 | + | 11.5867i | −1.11578 | + | 0.406112i | ||||
\(815\) | 18.5854 | − | 6.76454i | 0.651019 | − | 0.236951i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 39.0131 | − | 6.87906i | 1.36489 | − | 0.240668i | ||||
\(818\) | 17.6575 | + | 30.5837i | 0.617380 | + | 1.06933i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.204975 | + | 0.355028i | −0.00715805 | + | 0.0123981i | ||||
\(821\) | −9.39965 | + | 25.8253i | −0.328050 | + | 0.901310i | 0.660555 | + | 0.750778i | \(0.270321\pi\) |
−0.988605 | + | 0.150532i | \(0.951901\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.92941 | − | 3.29717i | −0.136971 | − | 0.114932i | 0.571728 | − | 0.820443i | \(-0.306273\pi\) |
−0.708699 | + | 0.705511i | \(0.750718\pi\) | |||||||
\(824\) | −3.06132 | + | 17.3616i | −0.106646 | + | 0.604821i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.31296 | + | 23.1108i | −0.0804781 | + | 0.804128i | ||||
\(827\) | −22.7209 | − | 13.1179i | −0.790082 | − | 0.456154i | 0.0499094 | − | 0.998754i | \(-0.484107\pi\) |
−0.839991 | + | 0.542600i | \(0.817440\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.7370 | + | 7.93108i | 0.477107 | + | 0.275458i | 0.719210 | − | 0.694793i | \(-0.244504\pi\) |
−0.242103 | + | 0.970251i | \(0.577837\pi\) | |||||||
\(830\) | −12.3696 | + | 33.9852i | −0.429355 | + | 1.17964i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 52.8958 | + | 9.32696i | 1.83383 | + | 0.323354i | ||||
\(833\) | −14.9972 | + | 16.9927i | −0.519621 | + | 0.588764i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.9236 | + | 11.6833i | −0.481845 | + | 0.404316i | ||||
\(836\) | −0.171761 | − | 0.297499i | −0.00594049 | − | 0.0102892i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 29.0435 | + | 16.7682i | 1.00329 | + | 0.579249i | ||||
\(839\) | 43.7933 | + | 15.9395i | 1.51191 | + | 0.550291i | 0.959113 | − | 0.283023i | \(-0.0913373\pi\) |
0.552800 | + | 0.833314i | \(0.313560\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.46447 | + | 6.26343i | 0.257395 | + | 0.215980i | ||||
\(842\) | −6.99648 | + | 8.33808i | −0.241115 | + | 0.287349i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.0549092 | − | 0.0199853i | −0.00189005 | − | 0.000687923i | ||||
\(845\) | 66.0849 | 2.27339 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.96189 | + | 1.77260i | −0.239213 | + | 0.0609071i | ||||
\(848\) | 3.45523 | − | 0.609251i | 0.118653 | − | 0.0209218i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.60246 | + | 1.90973i | −0.0549638 | + | 0.0655033i | ||||
\(851\) | 2.92493 | − | 3.48579i | 0.100265 | − | 0.119491i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.3113 | + | 5.87368i | −1.14056 | + | 0.201111i | −0.711850 | − | 0.702332i | \(-0.752142\pi\) |
−0.428708 | + | 0.903443i | \(0.641031\pi\) | |||||||
\(854\) | 7.50436 | − | 26.6705i | 0.256794 | − | 0.912644i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.11684 | −0.277428 | ||||||||
\(857\) | 41.3614 | + | 15.0543i | 1.41288 | + | 0.514246i | 0.931973 | − | 0.362527i | \(-0.118086\pi\) |
0.480905 | + | 0.876773i | \(0.340308\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.8856 | − | 35.6162i | 1.01968 | − | 1.21521i | 0.0433218 | − | 0.999061i | \(-0.486206\pi\) |
0.976360 | − | 0.216149i | \(-0.0693496\pi\) | |||||||
\(860\) | −0.209283 | − | 0.175609i | −0.00713648 | − | 0.00598822i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.23046 | + | 2.63167i | 0.246271 | + | 0.0896351i | ||||
\(863\) | 6.24515 | + | 3.60564i | 0.212587 | + | 0.122737i | 0.602513 | − | 0.798109i | \(-0.294166\pi\) |
−0.389926 | + | 0.920846i | \(0.627499\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.94069 | + | 15.4857i | 0.303992 | + | 0.526530i | ||||
\(866\) | −38.3368 | + | 32.1684i | −1.30274 | + | 1.09313i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.0690276 | + | 0.00517180i | −0.00234295 | + | 0.000175542i | ||||
\(869\) | −34.7197 | − | 6.12203i | −1.17779 | − | 0.207676i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.9503 | + | 65.8029i | −0.811525 | + | 2.22965i | ||||
\(872\) | −13.8594 | − | 8.00176i | −0.469340 | − | 0.270974i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.55031 | − | 2.62712i | −0.153916 | − | 0.0888637i | ||||
\(875\) | −30.8152 | − | 3.08402i | −1.04174 | − | 0.104259i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.82720 | + | 44.3903i | −0.264306 | + | 1.49895i | 0.506699 | + | 0.862123i | \(0.330866\pi\) |
−0.771005 | + | 0.636829i | \(0.780246\pi\) | |||||||
\(878\) | 4.37765 | + | 3.67328i | 0.147739 | + | 0.123967i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.5979 | − | 29.1174i | 0.357254 | − | 0.981547i | ||||
\(881\) | −17.2527 | + | 29.8826i | −0.581259 | + | 1.00677i | 0.414071 | + | 0.910245i | \(0.364106\pi\) |
−0.995330 | + | 0.0965261i | \(0.969227\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.2076 | − | 33.2686i | −0.646388 | − | 1.11958i | −0.983979 | − | 0.178284i | \(-0.942945\pi\) |
0.337591 | − | 0.941293i | \(-0.390388\pi\) | |||||||
\(884\) | 0.369569 | − | 0.0651649i | 0.0124299 | − | 0.00219173i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.9666 | − | 3.99151i | 0.368429 | − | 0.134097i | ||||
\(887\) | 25.3610 | − | 9.23065i | 0.851539 | − | 0.309935i | 0.120871 | − | 0.992668i | \(-0.461431\pi\) |
0.730668 | + | 0.682733i | \(0.239209\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.96012 | − | 4.11714i | 0.0992793 | − | 0.138084i | ||||
\(890\) | 12.9500i | 0.434085i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.151324 | − | 0.0873671i | 0.00506671 | − | 0.00292527i | ||||
\(893\) | 31.4576 | − | 5.54682i | 1.05269 | − | 0.185617i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.55946 | − | 7.81726i | 0.219259 | − | 0.261302i | ||||
\(896\) | −16.6381 | − | 24.4044i | −0.555839 | − | 0.815294i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.09426 | + | 40.2335i | 0.236739 | + | 1.34261i | ||||
\(899\) | 3.29702 | − | 5.71060i | 0.109962 | − | 0.190459i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.48125 | − | 1.43255i | 0.0826624 | − | 0.0477252i | ||||
\(902\) | −10.1034 | − | 57.2992i | −0.336406 | − | 1.90785i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 24.5126 | − | 8.92187i | 0.815278 | − | 0.296737i | ||||
\(905\) | 9.48522 | + | 1.67250i | 0.315299 | + | 0.0555958i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.8874 | + | 23.4003i | −0.925987 | + | 0.776996i | −0.975093 | − | 0.221798i | \(-0.928807\pi\) |
0.0491052 | + | 0.998794i | \(0.484363\pi\) | |||||||
\(908\) | −0.154511 | − | 0.267621i | −0.00512764 | − | 0.00888133i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −36.5406 | − | 37.4645i | −1.21131 | − | 1.24194i | ||||
\(911\) | −17.9098 | − | 21.3441i | −0.593378 | − | 0.707160i | 0.382873 | − | 0.923801i | \(-0.374935\pi\) |
−0.976251 | + | 0.216640i | \(0.930490\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.4173 | + | 42.3586i | 0.510238 | + | 1.40187i | ||||
\(914\) | 9.09603 | + | 1.60388i | 0.300870 | + | 0.0530515i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.0777926 | + | 0.213733i | −0.00257034 | + | 0.00706195i | ||||
\(917\) | 16.0857 | + | 16.4924i | 0.531197 | + | 0.544627i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.7371 | − | 42.8459i | 0.816001 | − | 1.41336i | −0.0926055 | − | 0.995703i | \(-0.529520\pi\) |
0.908607 | − | 0.417653i | \(-0.137147\pi\) | |||||||
\(920\) | 0.729081 | + | 4.13482i | 0.0240371 | + | 0.136321i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.6542 | − | 29.2723i | −0.350879 | − | 0.964031i | ||||
\(923\) | −5.11565 | + | 29.0123i | −0.168384 | + | 0.954950i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.72145 | + | 2.28357i | −0.0894807 | + | 0.0750832i | ||||
\(926\) | − | 23.2364i | − | 0.763595i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.432178 | −0.0141870 | ||||||||
\(929\) | 29.3067 | + | 10.6668i | 0.961522 | + | 0.349966i | 0.774630 | − | 0.632415i | \(-0.217936\pi\) |
0.186892 | + | 0.982380i | \(0.440158\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.9611 | + | 24.6774i | 0.916387 | + | 0.808768i | ||||
\(932\) | −0.112975 | − | 0.310396i | −0.00370062 | − | 0.0101674i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.29087 | + | 1.53840i | 0.0422386 | + | 0.0503380i | ||||
\(935\) | − | 25.3035i | − | 0.827512i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.9634 | − | 9.21646i | 0.521501 | − | 0.301089i | −0.216048 | − | 0.976383i | \(-0.569317\pi\) |
0.737548 | + | 0.675294i | \(0.235983\pi\) | |||||||
\(938\) | 35.7196 | − | 16.1166i | 1.16629 | − | 0.526226i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.168752 | − | 0.141600i | −0.00550407 | − | 0.00461847i | ||||
\(941\) | 3.99360 | − | 22.6488i | 0.130188 | − | 0.738331i | −0.847903 | − | 0.530152i | \(-0.822135\pi\) |
0.978091 | − | 0.208180i | \(-0.0667539\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.02349 | + | 5.98676i | 0.163587 | + | 0.194956i | ||||
\(944\) | −24.7197 | −0.804558 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 38.7744 | 1.26066 | ||||||||
\(947\) | 11.7046 | + | 13.9490i | 0.380349 | + | 0.453282i | 0.921924 | − | 0.387370i | \(-0.126616\pi\) |
−0.541575 | + | 0.840652i | \(0.682172\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.53890 | − | 20.0701i | 0.114878 | − | 0.651503i | ||||
\(950\) | 3.14241 | + | 2.63679i | 0.101953 | + | 0.0855488i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −19.7570 | − | 14.2048i | −0.640328 | − | 0.460380i | ||||
\(953\) | 20.4233 | − | 11.7914i | 0.661576 | − | 0.381961i | −0.131301 | − | 0.991343i | \(-0.541915\pi\) |
0.792877 | + | 0.609381i | \(0.208582\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.8239i | 0.706203i | ||||||||
\(956\) | −0.237736 | − | 0.283323i | −0.00768893 | − | 0.00916331i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.5750 | + | 31.8020i | 0.373971 | + | 1.02748i | ||||
\(959\) | −10.3984 | − | 15.2522i | −0.335782 | − | 0.492519i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0086 | − | 9.83031i | −0.871244 | − | 0.317107i | ||||
\(962\) | −60.8954 | −1.96335 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.205163i | 0.00660785i | ||||||||
\(965\) | −16.8205 | + | 14.1141i | −0.541472 | + | 0.454349i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.40078 | + | 36.3006i | −0.205835 | + | 1.16735i | 0.690285 | + | 0.723537i | \(0.257485\pi\) |
−0.896120 | + | 0.443811i | \(0.853626\pi\) | |||||||
\(968\) | −2.63803 | − | 7.24794i | −0.0847896 | − | 0.232958i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.59344 | + | 20.3794i | 0.115378 | + | 0.654343i | ||||
\(971\) | 6.28287 | − | 10.8822i | 0.201627 | − | 0.349228i | −0.747426 | − | 0.664345i | \(-0.768711\pi\) |
0.949053 | + | 0.315117i | \(0.102044\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.7915 | + | 7.53842i | 0.858895 | + | 0.241671i | ||||
\(974\) | 17.1077 | − | 47.0029i | 0.548165 | − | 1.50607i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 29.0396 | + | 5.12047i | 0.929536 | + | 0.163902i | ||||
\(977\) | −5.53944 | − | 15.2195i | −0.177222 | − | 0.486914i | 0.818996 | − | 0.573799i | \(-0.194531\pi\) |
−0.996218 | + | 0.0868850i | \(0.972309\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.3750 | + | 12.3645i | 0.331588 | + | 0.395171i | ||||
\(980\) | 0.00642009 | − | 0.257108i | 0.000205082 | − | 0.00821303i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21.8395 | − | 37.8272i | −0.696927 | − | 1.20711i | ||||
\(983\) | 0.923122 | − | 0.774591i | 0.0294430 | − | 0.0247056i | −0.627947 | − | 0.778256i | \(-0.716105\pi\) |
0.657390 | + | 0.753550i | \(0.271660\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.4670 | + | 5.19584i | 0.938898 | + | 0.165553i | ||||
\(986\) | 18.7986 | − | 6.84215i | 0.598671 | − | 0.217898i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.107227 | − | 0.608114i | −0.00341134 | − | 0.0193467i | ||||
\(989\) | −4.51042 | + | 2.60409i | −0.143423 | + | 0.0828052i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.7781 | − | 46.3810i | 0.850635 | − | 1.47334i | −0.0300019 | − | 0.999550i | \(-0.509551\pi\) |
0.880636 | − | 0.473793i | \(-0.157115\pi\) | |||||||
\(992\) | −0.0256994 | − | 0.145748i | −0.000815956 | − | 0.00462752i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 13.6215 | − | 9.28666i | 0.432048 | − | 0.294555i | ||||
\(995\) | −27.2884 | + | 32.5211i | −0.865101 | + | 1.03099i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.68170 | + | 0.472857i | −0.0849304 | + | 0.0149755i | −0.215952 | − | 0.976404i | \(-0.569285\pi\) |
0.131021 | + | 0.991380i | \(0.458174\pi\) | |||||||
\(998\) | −44.4078 | + | 25.6388i | −1.40570 | + | 0.811584i | ||||
\(999\) | 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 | 567.2.ba.a.341.7 | 132 | ||
3.2 | odd | 2 | 189.2.ba.a.131.16 | yes | 132 | ||
7.3 | odd | 6 | 567.2.bd.a.17.16 | 132 | |||
21.17 | even | 6 | 189.2.bd.a.185.7 | yes | 132 | ||
27.7 | even | 9 | 189.2.bd.a.47.7 | yes | 132 | ||
27.20 | odd | 18 | 567.2.bd.a.467.16 | 132 | |||
189.101 | even | 18 | inner | 567.2.ba.a.143.7 | 132 | ||
189.115 | odd | 18 | 189.2.ba.a.101.16 | ✓ | 132 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.ba.a.101.16 | ✓ | 132 | 189.115 | odd | 18 | ||
189.2.ba.a.131.16 | yes | 132 | 3.2 | odd | 2 | ||
189.2.bd.a.47.7 | yes | 132 | 27.7 | even | 9 | ||
189.2.bd.a.185.7 | yes | 132 | 21.17 | even | 6 | ||
567.2.ba.a.143.7 | 132 | 189.101 | even | 18 | inner | ||
567.2.ba.a.341.7 | 132 | 1.1 | even | 1 | trivial | ||
567.2.bd.a.17.16 | 132 | 7.3 | odd | 6 | |||
567.2.bd.a.467.16 | 132 | 27.20 | odd | 18 |