Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(17,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(42))
chi = DirichletCharacter(H, H._module([21, 25]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.bg (of order \(42\), degree \(12\), 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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(216\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{42})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{42}]$ |
Embedding invariants
Embedding label | 395.10 | ||
Character | \(\chi\) | \(=\) | 441.395 |
Dual form | 441.2.bg.a.278.10 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{42}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.132489 | + | 0.0519980i | 0.0936836 | + | 0.0367681i | 0.411720 | − | 0.911310i | \(-0.364928\pi\) |
−0.318036 | + | 0.948079i | \(0.603023\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.45125 | − | 1.34657i | −0.725627 | − | 0.673284i | ||||
\(5\) | 1.27700 | + | 0.870646i | 0.571093 | + | 0.389365i | 0.814156 | − | 0.580646i | \(-0.197200\pi\) |
−0.243063 | + | 0.970010i | \(0.578152\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.61234 | − | 2.09770i | −0.609408 | − | 0.792857i | ||||
\(8\) | −0.245763 | − | 0.510332i | −0.0868903 | − | 0.180430i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.123917 | + | 0.181752i | 0.0391859 | + | 0.0574751i | ||||
\(11\) | −0.796043 | − | 5.28140i | −0.240016 | − | 1.59240i | −0.706396 | − | 0.707817i | \(-0.749680\pi\) |
0.466380 | − | 0.884584i | \(-0.345558\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.42567 | + | 3.52936i | −1.22746 | + | 0.978868i | −0.227474 | + | 0.973784i | \(0.573047\pi\) |
−0.999987 | + | 0.00508348i | \(0.998382\pi\) | |||||||
\(14\) | −0.104541 | − | 0.361760i | −0.0279398 | − | 0.0966845i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.289868 | + | 3.86802i | 0.0724670 | + | 0.967006i | ||||
\(17\) | −2.27068 | − | 0.700411i | −0.550720 | − | 0.169875i | 0.00689217 | − | 0.999976i | \(-0.497806\pi\) |
−0.557612 | + | 0.830102i | \(0.688282\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.04813 | − | 1.18249i | 0.469872 | − | 0.271281i | −0.246314 | − | 0.969190i | \(-0.579219\pi\) |
0.716186 | + | 0.697909i | \(0.245886\pi\) | |||||||
\(20\) | −0.680873 | − | 2.98310i | −0.152248 | − | 0.667041i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.169155 | − | 0.741118i | 0.0360640 | − | 0.158007i | ||||
\(23\) | −1.72793 | − | 5.60180i | −0.360298 | − | 1.16806i | −0.936476 | − | 0.350732i | \(-0.885933\pi\) |
0.576178 | − | 0.817324i | \(-0.304543\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.953993 | − | 2.43073i | −0.190799 | − | 0.486147i | ||||
\(26\) | −0.769871 | + | 0.237474i | −0.150984 | + | 0.0465724i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.484776 | + | 5.21543i | −0.0916140 | + | 0.985623i | ||||
\(29\) | 9.35903 | − | 2.13614i | 1.73793 | − | 0.396671i | 0.768076 | − | 0.640359i | \(-0.221215\pi\) |
0.969854 | + | 0.243688i | \(0.0783574\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.48566 | − | 3.74450i | −1.16486 | − | 0.672532i | −0.212396 | − | 0.977184i | \(-0.568127\pi\) |
−0.952464 | + | 0.304652i | \(0.901460\pi\) | |||||||
\(32\) | −0.496639 | + | 1.61006i | −0.0877942 | + | 0.284622i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.264419 | − | 0.210867i | −0.0453475 | − | 0.0361634i | ||||
\(35\) | −0.232612 | − | 4.08255i | −0.0393186 | − | 0.690077i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.55935 | − | 1.44686i | 0.256355 | − | 0.237863i | −0.541517 | − | 0.840690i | \(-0.682150\pi\) |
0.797872 | + | 0.602827i | \(0.205959\pi\) | |||||||
\(38\) | 0.332840 | − | 0.0501676i | 0.0539938 | − | 0.00813826i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.130478 | − | 0.865668i | 0.0206305 | − | 0.136874i | ||||
\(41\) | −0.180363 | + | 0.0868585i | −0.0281680 | + | 0.0135650i | −0.447915 | − | 0.894076i | \(-0.647833\pi\) |
0.419747 | + | 0.907641i | \(0.362119\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.56553 | − | 2.68022i | −0.848735 | − | 0.408729i | −0.0416270 | − | 0.999133i | \(-0.513254\pi\) |
−0.807108 | + | 0.590404i | \(0.798968\pi\) | |||||||
\(44\) | −5.95650 | + | 8.73658i | −0.897976 | + | 1.31709i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.0623516 | − | 0.832024i | 0.00919323 | − | 0.122675i | ||||
\(47\) | −4.15730 | + | 10.5926i | −0.606405 | + | 1.54509i | 0.216121 | + | 0.976367i | \(0.430660\pi\) |
−0.822526 | + | 0.568728i | \(0.807436\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.80070 | + | 6.76443i | −0.257243 | + | 0.966347i | ||||
\(50\) | − | 0.371651i | − | 0.0525593i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 11.1753 | + | 0.837473i | 1.54973 | + | 0.116137i | ||||
\(53\) | 2.89757 | − | 3.12284i | 0.398012 | − | 0.428955i | −0.501968 | − | 0.864886i | \(-0.667390\pi\) |
0.899980 | + | 0.435931i | \(0.143581\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.58168 | − | 7.43743i | 0.482953 | − | 1.00286i | ||||
\(56\) | −0.674270 | + | 1.33837i | −0.0901031 | + | 0.178847i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.35104 | + | 0.203637i | 0.177400 | + | 0.0267388i | ||||
\(59\) | 10.3645 | − | 7.06637i | 1.34934 | − | 0.919962i | 0.349481 | − | 0.936943i | \(-0.386358\pi\) |
0.999856 | + | 0.0169808i | \(0.00540543\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.33764 | + | 3.59712i | 0.427341 | + | 0.460564i | 0.909612 | − | 0.415458i | \(-0.136379\pi\) |
−0.482272 | + | 0.876022i | \(0.660188\pi\) | |||||||
\(62\) | −0.664571 | − | 0.833345i | −0.0844005 | − | 0.105835i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.68735 | − | 5.87775i | 0.585919 | − | 0.734719i | ||||
\(65\) | −8.72442 | + | 0.653805i | −1.08213 | + | 0.0810945i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.48870 | + | 7.77466i | −0.548383 | + | 0.949826i | 0.450003 | + | 0.893027i | \(0.351423\pi\) |
−0.998386 | + | 0.0567994i | \(0.981910\pi\) | |||||||
\(68\) | 2.35218 | + | 4.07409i | 0.285244 | + | 0.494056i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.181466 | − | 0.552987i | 0.0216893 | − | 0.0660946i | ||||
\(71\) | 12.2266 | + | 2.79063i | 1.45103 | + | 0.331187i | 0.874154 | − | 0.485648i | \(-0.161416\pi\) |
0.576871 | + | 0.816835i | \(0.304273\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.02779 | − | 1.97326i | 0.588458 | − | 0.230953i | −0.0523820 | − | 0.998627i | \(-0.516681\pi\) |
0.640840 | + | 0.767674i | \(0.278586\pi\) | |||||||
\(74\) | 0.281830 | − | 0.110610i | 0.0327621 | − | 0.0128582i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.56465 | − | 1.04185i | −0.523601 | − | 0.119509i | ||||
\(77\) | −9.79530 | + | 10.1853i | −1.11628 | + | 1.16072i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.88456 | + | 3.26415i | 0.212029 | + | 0.367245i | 0.952349 | − | 0.305009i | \(-0.0986595\pi\) |
−0.740320 | + | 0.672254i | \(0.765326\pi\) | |||||||
\(80\) | −2.99751 | + | 5.19185i | −0.335132 | + | 0.580466i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.0284126 | + | 0.00212923i | −0.00313765 | + | 0.000235134i | ||||
\(83\) | 5.58349 | − | 7.00147i | 0.612867 | − | 0.768511i | −0.374454 | − | 0.927245i | \(-0.622170\pi\) |
0.987321 | + | 0.158734i | \(0.0507413\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.28985 | − | 2.87138i | −0.248369 | − | 0.311445i | ||||
\(86\) | −0.598003 | − | 0.644494i | −0.0644844 | − | 0.0694976i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.49963 | + | 1.70422i | −0.266461 | + | 0.181670i | ||||
\(89\) | 1.95325 | + | 0.294405i | 0.207044 | + | 0.0312068i | 0.251745 | − | 0.967794i | \(-0.418996\pi\) |
−0.0447013 | + | 0.999000i | \(0.514234\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.5392 | + | 3.59321i | 1.52413 | + | 0.376670i | ||||
\(92\) | −5.03554 | + | 10.4564i | −0.524991 | + | 1.09016i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.10159 | + | 1.18723i | −0.113620 | + | 0.122454i | ||||
\(95\) | 3.64499 | + | 0.273154i | 0.373968 | + | 0.0280250i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.13308i | 0.825789i | 0.910779 | + | 0.412894i | \(0.135482\pi\) | ||||
−0.910779 | + | 0.412894i | \(0.864518\pi\) | |||||||
\(98\) | −0.590309 | + | 0.802577i | −0.0596302 | + | 0.0810726i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.88866 | + | 4.81223i | −0.188866 | + | 0.481223i | ||||
\(101\) | −1.30963 | + | 17.4759i | −0.130313 | + | 1.73891i | 0.423168 | + | 0.906051i | \(0.360918\pi\) |
−0.553482 | + | 0.832861i | \(0.686701\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.00447 | − | 13.2071i | 0.887236 | − | 1.30134i | −0.0655981 | − | 0.997846i | \(-0.520896\pi\) |
0.952834 | − | 0.303491i | \(-0.0981521\pi\) | |||||||
\(104\) | 2.88881 | + | 1.39118i | 0.283271 | + | 0.136416i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.546277 | − | 0.263073i | 0.0530591 | − | 0.0255519i | ||||
\(107\) | 0.349737 | − | 2.32035i | 0.0338104 | − | 0.224317i | −0.965544 | − | 0.260239i | \(-0.916199\pi\) |
0.999355 | + | 0.0359219i | \(0.0114367\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.53500 | + | 0.231364i | −0.147027 | + | 0.0221607i | −0.222143 | − | 0.975014i | \(-0.571305\pi\) |
0.0751165 | + | 0.997175i | \(0.476067\pi\) | |||||||
\(110\) | 0.861263 | − | 0.799135i | 0.0821182 | − | 0.0761946i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.64659 | − | 6.84463i | 0.722535 | − | 0.646757i | ||||
\(113\) | −5.99228 | − | 4.77868i | −0.563706 | − | 0.449541i | 0.299712 | − | 0.954030i | \(-0.403109\pi\) |
−0.863418 | + | 0.504489i | \(0.831681\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.67062 | − | 8.65792i | 0.249036 | − | 0.807356i | ||||
\(116\) | −16.4588 | − | 9.50249i | −1.52816 | − | 0.882284i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.74061 | − | 0.397283i | 0.160236 | − | 0.0365728i | ||||
\(119\) | 2.19186 | + | 5.89250i | 0.200927 | + | 0.540165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.7482 | + | 5.16613i | −1.52256 | + | 0.469648i | ||||
\(122\) | 0.255156 | + | 0.650128i | 0.0231008 | + | 0.0588598i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.37013 | + | 14.1676i | 0.392449 | + | 1.27229i | ||||
\(125\) | 2.61766 | − | 11.4687i | 0.234130 | − | 1.02579i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.921236 | + | 4.03620i | 0.0817465 | + | 0.358155i | 0.999213 | − | 0.0396575i | \(-0.0126267\pi\) |
−0.917467 | + | 0.397812i | \(0.869770\pi\) | |||||||
\(128\) | 3.84502 | − | 2.21992i | 0.339855 | − | 0.196215i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.18988 | − | 0.367030i | −0.104360 | − | 0.0321907i | ||||
\(131\) | 0.577413 | + | 7.70505i | 0.0504488 | + | 0.673193i | 0.963903 | + | 0.266252i | \(0.0857854\pi\) |
−0.913455 | + | 0.406941i | \(0.866596\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.78278 | − | 2.38978i | −0.501431 | − | 0.207220i | ||||
\(134\) | −0.998969 | + | 0.796651i | −0.0862978 | + | 0.0688202i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.200606 | + | 1.33093i | 0.0172018 | + | 0.114127i | ||||
\(137\) | −7.70966 | − | 11.3080i | −0.658681 | − | 0.966107i | −0.999661 | − | 0.0260369i | \(-0.991711\pi\) |
0.340980 | − | 0.940071i | \(-0.389241\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.53176 | − | 17.7164i | −0.723654 | − | 1.50268i | −0.859050 | − | 0.511892i | \(-0.828945\pi\) |
0.135396 | − | 0.990792i | \(-0.456769\pi\) | |||||||
\(140\) | −5.15985 | + | 6.23805i | −0.436087 | + | 0.527211i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.47477 | + | 1.00548i | 0.123760 | + | 0.0843783i | ||||
\(143\) | 22.1630 | + | 20.5642i | 1.85336 | + | 1.71967i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.8113 | + | 5.42055i | 1.14697 | + | 0.450152i | ||||
\(146\) | 0.768731 | 0.0636206 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.21131 | −0.346167 | ||||||||
\(149\) | −7.28530 | − | 2.85927i | −0.596835 | − | 0.234241i | 0.0476415 | − | 0.998864i | \(-0.484829\pi\) |
−0.644477 | + | 0.764624i | \(0.722925\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.0863492 | + | 0.0801204i | 0.00702700 | + | 0.00652010i | 0.683678 | − | 0.729783i | \(-0.260379\pi\) |
−0.676651 | + | 0.736304i | \(0.736570\pi\) | |||||||
\(152\) | −1.10681 | − | 0.754613i | −0.0897745 | − | 0.0612072i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.82738 | + | 0.840099i | −0.147255 | + | 0.0676971i | ||||
\(155\) | −5.02208 | − | 10.4285i | −0.403383 | − | 0.837633i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.14063 | − | 6.07318i | −0.330458 | − | 0.484693i | 0.624669 | − | 0.780890i | \(-0.285234\pi\) |
−0.955127 | + | 0.296197i | \(0.904282\pi\) | |||||||
\(158\) | 0.0799534 | + | 0.530456i | 0.00636075 | + | 0.0422008i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.03600 | + | 1.62366i | −0.160960 | + | 0.128362i | ||||
\(161\) | −8.96489 | + | 12.6567i | −0.706532 | + | 0.997487i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.233664 | − | 3.11803i | −0.0183020 | − | 0.244223i | −0.998850 | − | 0.0479437i | \(-0.984733\pi\) |
0.980548 | − | 0.196279i | \(-0.0628858\pi\) | |||||||
\(164\) | 0.378714 | + | 0.116818i | 0.0295726 | + | 0.00912194i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.10381 | − | 0.637286i | 0.0856724 | − | 0.0494630i | ||||
\(167\) | 1.10358 | + | 4.83508i | 0.0853972 | + | 0.374150i | 0.999510 | − | 0.0313111i | \(-0.00996826\pi\) |
−0.914112 | + | 0.405461i | \(0.867111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.23746 | − | 18.5655i | 0.325958 | − | 1.42812i | ||||
\(170\) | −0.154073 | − | 0.499493i | −0.0118169 | − | 0.0383094i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.46790 | + | 11.3840i | 0.340674 | + | 0.868024i | ||||
\(173\) | 7.47647 | − | 2.30619i | 0.568426 | − | 0.175336i | 0.00279697 | − | 0.999996i | \(-0.499110\pi\) |
0.565629 | + | 0.824660i | \(0.308634\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.56079 | + | 5.92037i | −0.269170 | + | 0.447538i | ||||
\(176\) | 20.1978 | − | 4.61002i | 1.52247 | − | 0.347493i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.243475 | + | 0.140570i | 0.0182492 | + | 0.0105362i | ||||
\(179\) | −1.84791 | + | 5.99077i | −0.138119 | + | 0.447771i | −0.998035 | − | 0.0626651i | \(-0.980040\pi\) |
0.859915 | + | 0.510437i | \(0.170516\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.27095 | + | 1.81102i | 0.168798 | + | 0.134612i | 0.704246 | − | 0.709957i | \(-0.251285\pi\) |
−0.535447 | + | 0.844569i | \(0.679857\pi\) | |||||||
\(182\) | 1.73945 | + | 1.23207i | 0.128936 | + | 0.0913271i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.43412 | + | 2.25853i | −0.179445 | + | 0.166501i | ||||
\(185\) | 3.25100 | − | 0.490009i | 0.239018 | − | 0.0360262i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.89159 | + | 12.5499i | −0.138327 | + | 0.917740i | ||||
\(188\) | 20.2970 | − | 9.77452i | 1.48031 | − | 0.712880i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.468716 | + | 0.225722i | 0.0340043 | + | 0.0163756i | ||||
\(191\) | 7.16605 | − | 10.5107i | 0.518518 | − | 0.760526i | −0.474274 | − | 0.880377i | \(-0.657289\pi\) |
0.992792 | + | 0.119852i | \(0.0382419\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.140668 | − | 1.87709i | 0.0101255 | − | 0.135116i | −0.989850 | − | 0.142116i | \(-0.954609\pi\) |
0.999975 | + | 0.00700057i | \(0.00222837\pi\) | |||||||
\(194\) | −0.422904 | + | 1.07754i | −0.0303627 | + | 0.0773629i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.7220 | − | 7.39214i | 0.837288 | − | 0.528010i | ||||
\(197\) | − | 12.8075i | − | 0.912499i | −0.889852 | − | 0.456250i | \(-0.849192\pi\) | ||
0.889852 | − | 0.456250i | \(-0.150808\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.90734 | + | 0.667513i | 0.631425 | + | 0.0473187i | 0.386598 | − | 0.922248i | \(-0.373650\pi\) |
0.244826 | + | 0.969567i | \(0.421269\pi\) | |||||||
\(200\) | −1.00603 | + | 1.08424i | −0.0711367 | + | 0.0766672i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.08222 | + | 2.24725i | −0.0761448 | + | 0.158116i | ||||
\(203\) | −19.5710 | − | 16.1883i | −1.37361 | − | 1.13619i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.305948 | − | 0.0461142i | −0.0213683 | − | 0.00322075i | ||||
\(206\) | 1.87973 | − | 1.28158i | 0.130967 | − | 0.0892920i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −14.9345 | − | 16.0956i | −1.03552 | − | 1.11603i | ||||
\(209\) | −7.87557 | − | 9.87566i | −0.544765 | − | 0.683114i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.93423 | + | 4.93337i | −0.270844 | + | 0.339627i | −0.898589 | − | 0.438792i | \(-0.855407\pi\) |
0.627745 | + | 0.778419i | \(0.283978\pi\) | |||||||
\(212\) | −8.41023 | + | 0.630260i | −0.577617 | + | 0.0432864i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.166990 | − | 0.289235i | 0.0114152 | − | 0.0197717i | ||||
\(215\) | −4.77367 | − | 8.26825i | −0.325562 | − | 0.563890i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.60227 | + | 19.6424i | 0.176654 | + | 1.33341i | ||||
\(218\) | −0.215401 | − | 0.0491639i | −0.0145888 | − | 0.00332980i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −15.2129 | + | 5.97063i | −1.02566 | + | 0.402540i | ||||
\(221\) | 12.5213 | − | 4.91424i | 0.842272 | − | 0.330567i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.5223 | − | 3.77110i | −1.10641 | − | 0.252531i | −0.369978 | − | 0.929041i | \(-0.620635\pi\) |
−0.736434 | + | 0.676509i | \(0.763492\pi\) | |||||||
\(224\) | 4.17819 | − | 1.55418i | 0.279167 | − | 0.103843i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.545427 | − | 0.944708i | −0.0362813 | − | 0.0628410i | ||||
\(227\) | 7.18229 | − | 12.4401i | 0.476705 | − | 0.825678i | −0.522938 | − | 0.852370i | \(-0.675164\pi\) |
0.999644 | + | 0.0266927i | \(0.00849757\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.9655 | + | 0.896691i | −0.790704 | + | 0.0592550i | −0.463958 | − | 0.885857i | \(-0.653571\pi\) |
−0.326746 | + | 0.945112i | \(0.605952\pi\) | |||||||
\(230\) | 0.804021 | − | 1.00821i | 0.0530156 | − | 0.0664794i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.39024 | − | 4.25123i | −0.222580 | − | 0.279107i | ||||
\(233\) | −10.9139 | − | 11.7624i | −0.714995 | − | 0.770582i | 0.266134 | − | 0.963936i | \(-0.414254\pi\) |
−0.981129 | + | 0.193355i | \(0.938063\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.5313 | + | 9.90729i | −0.947919 | + | 0.646280i | ||||
\(236\) | −24.5568 | − | 3.70134i | −1.59851 | − | 0.240937i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.0160021 | + | 0.894662i | −0.00103726 | + | 0.0579923i | ||||
\(239\) | −0.383320 | + | 0.795973i | −0.0247949 | + | 0.0514872i | −0.912998 | − | 0.407963i | \(-0.866239\pi\) |
0.888204 | + | 0.459450i | \(0.151954\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.5585 | − | 17.8458i | 1.06663 | − | 1.14955i | 0.0783436 | − | 0.996926i | \(-0.475037\pi\) |
0.988284 | − | 0.152625i | \(-0.0487726\pi\) | |||||||
\(242\) | −2.48757 | − | 0.186418i | −0.159907 | − | 0.0119834i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 9.71469i | − | 0.621919i | ||||||
\(245\) | −8.18892 | + | 7.07042i | −0.523171 | + | 0.451713i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.89092 | + | 12.4619i | −0.311202 | + | 0.792930i | ||||
\(248\) | −0.317002 | + | 4.23010i | −0.0201297 | + | 0.268612i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.943159 | − | 1.38336i | 0.0596506 | − | 0.0874914i | ||||
\(251\) | 4.29738 | + | 2.06951i | 0.271248 | + | 0.130626i | 0.564564 | − | 0.825389i | \(-0.309044\pi\) |
−0.293316 | + | 0.956016i | \(0.594759\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −28.2098 | + | 13.5851i | −1.77354 | + | 0.854090i | ||||
\(254\) | −0.0878208 | + | 0.582653i | −0.00551037 | + | 0.0365589i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.2431 | + | 2.14680i | −0.890191 | + | 0.134175i | ||||
\(257\) | −2.64481 | + | 2.45402i | −0.164979 | + | 0.153078i | −0.758342 | − | 0.651857i | \(-0.773990\pi\) |
0.593363 | + | 0.804935i | \(0.297800\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.54929 | − | 0.938205i | −0.344816 | − | 0.0582973i | ||||
\(260\) | 13.5417 | + | 10.7992i | 0.839823 | + | 0.669737i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.324146 | + | 1.05086i | −0.0200258 | + | 0.0649221i | ||||
\(263\) | 2.04056 | + | 1.17812i | 0.125826 | + | 0.0726459i | 0.561592 | − | 0.827414i | \(-0.310189\pi\) |
−0.435766 | + | 0.900060i | \(0.643522\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.41910 | − | 1.46512i | 0.394322 | − | 0.0900015i | ||||
\(266\) | −0.641890 | − | 0.617312i | −0.0393568 | − | 0.0378498i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 16.9834 | − | 5.23867i | 1.03742 | − | 0.320003i | ||||
\(269\) | −11.2079 | − | 28.5573i | −0.683358 | − | 1.74117i | −0.671239 | − | 0.741241i | \(-0.734237\pi\) |
−0.0121194 | − | 0.999927i | \(-0.503858\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.90974 | − | 6.19121i | −0.116008 | − | 0.376089i | 0.878884 | − | 0.477036i | \(-0.158289\pi\) |
−0.994892 | + | 0.100947i | \(0.967813\pi\) | |||||||
\(272\) | 2.05101 | − | 8.98605i | 0.124361 | − | 0.544860i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.433450 | − | 1.89907i | −0.0261857 | − | 0.114727i | ||||
\(275\) | −12.0783 | + | 6.97338i | −0.728346 | + | 0.420511i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.8269 | + | 5.49888i | 1.07112 | + | 0.330395i | 0.779669 | − | 0.626192i | \(-0.215387\pi\) |
0.291446 | + | 0.956587i | \(0.405863\pi\) | |||||||
\(278\) | −0.209146 | − | 2.79085i | −0.0125437 | − | 0.167384i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.02629 | + | 1.12205i | −0.121094 | + | 0.0670552i | ||||
\(281\) | −2.93272 | + | 2.33877i | −0.174952 | + | 0.139519i | −0.707051 | − | 0.707163i | \(-0.749975\pi\) |
0.532099 | + | 0.846682i | \(0.321403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.700508 | − | 4.64757i | −0.0416409 | − | 0.276269i | 0.958314 | − | 0.285716i | \(-0.0922312\pi\) |
−0.999955 | + | 0.00944618i | \(0.996993\pi\) | |||||||
\(284\) | −13.9861 | − | 20.5138i | −0.829921 | − | 1.21727i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.86704 | + | 3.87696i | 0.110401 | + | 0.229249i | ||||
\(287\) | 0.473011 | + | 0.238303i | 0.0279210 | + | 0.0140666i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.38066 | − | 6.39563i | −0.551804 | − | 0.376213i | ||||
\(290\) | 1.54799 | + | 1.43632i | 0.0909010 | + | 0.0843438i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.95373 | − | 3.90655i | −0.582498 | − | 0.228614i | ||||
\(293\) | −0.798413 | −0.0466438 | −0.0233219 | − | 0.999728i | \(-0.507424\pi\) | ||||
−0.0233219 | + | 0.999728i | \(0.507424\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.3877 | 1.12880 | ||||||||
\(296\) | −1.12161 | − | 0.440200i | −0.0651923 | − | 0.0255861i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.816544 | − | 0.757642i | −0.0473011 | − | 0.0438890i | ||||
\(299\) | 27.4180 | + | 18.6933i | 1.58562 | + | 1.08106i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.35124 | + | 15.9962i | 0.193163 | + | 0.922008i | ||||
\(302\) | 0.00727420 | + | 0.0151050i | 0.000418583 | + | 0.000869196i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.16757 | + | 7.57943i | 0.296380 | + | 0.434710i | ||||
\(305\) | 1.13036 | + | 7.49943i | 0.0647241 | + | 0.429416i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.36091 | − | 5.87013i | 0.420109 | − | 0.335026i | −0.390511 | − | 0.920598i | \(-0.627702\pi\) |
0.810620 | + | 0.585572i | \(0.199130\pi\) | |||||||
\(308\) | 27.9306 | − | 1.59141i | 1.59150 | − | 0.0906788i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.123110 | − | 1.64279i | −0.00699218 | − | 0.0933042i | ||||
\(311\) | 15.9258 | + | 4.91246i | 0.903069 | + | 0.278560i | 0.711307 | − | 0.702881i | \(-0.248104\pi\) |
0.191762 | + | 0.981441i | \(0.438580\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.15020 | − | 4.70552i | 0.460677 | − | 0.265972i | −0.251652 | − | 0.967818i | \(-0.580974\pi\) |
0.712329 | + | 0.701846i | \(0.247641\pi\) | |||||||
\(314\) | −0.232793 | − | 1.01993i | −0.0131373 | − | 0.0575581i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.66042 | − | 7.27479i | 0.0934061 | − | 0.409239i | ||||
\(317\) | 4.32032 | + | 14.0061i | 0.242653 | + | 0.786663i | 0.992194 | + | 0.124705i | \(0.0397983\pi\) |
−0.749540 | + | 0.661959i | \(0.769725\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.7320 | − | 47.7283i | −1.04879 | − | 2.67227i | ||||
\(320\) | 11.1032 | − | 3.42488i | 0.620688 | − | 0.191457i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.84587 | + | 1.21071i | −0.102866 | + | 0.0674704i | ||||
\(323\) | −5.47886 | + | 1.25051i | −0.304852 | + | 0.0695804i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.8010 | + | 7.39066i | 0.710071 | + | 0.409960i | ||||
\(326\) | 0.131173 | − | 0.425253i | 0.00726502 | − | 0.0235526i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.0886533 | + | 0.0706987i | 0.00489506 | + | 0.00390368i | ||||
\(329\) | 28.9232 | − | 8.35818i | 1.59459 | − | 0.460802i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.16291 | − | 2.93475i | 0.173849 | − | 0.161309i | −0.588449 | − | 0.808534i | \(-0.700261\pi\) |
0.762299 | + | 0.647226i | \(0.224071\pi\) | |||||||
\(332\) | −17.5310 | + | 2.64237i | −0.962139 | + | 0.145019i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.105203 | + | 0.697977i | −0.00575646 | + | 0.0381916i | ||||
\(335\) | −12.5011 | + | 6.02020i | −0.683006 | + | 0.328918i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.3676 | + | 10.2901i | 1.16397 | + | 0.560537i | 0.913201 | − | 0.407510i | \(-0.133603\pi\) |
0.250767 | + | 0.968047i | \(0.419317\pi\) | |||||||
\(338\) | 1.52678 | − | 2.23938i | 0.0830461 | − | 0.121806i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.543353 | + | 7.25054i | −0.0294675 | + | 0.393216i | ||||
\(341\) | −14.6133 | + | 37.2341i | −0.791356 | + | 2.01634i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0931 | − | 7.12925i | 0.922940 | − | 0.384943i | ||||
\(344\) | 3.49896i | 0.188652i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.11047 | + | 0.0832179i | 0.0596990 | + | 0.00447382i | ||||
\(347\) | −11.0072 | + | 11.8629i | −0.590895 | + | 0.636833i | −0.955732 | − | 0.294238i | \(-0.904934\pi\) |
0.364837 | + | 0.931071i | \(0.381125\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.81027 | + | 12.0651i | −0.311016 | + | 0.645832i | −0.996621 | − | 0.0821423i | \(-0.973824\pi\) |
0.685604 | + | 0.727974i | \(0.259538\pi\) | |||||||
\(350\) | −0.779612 | + | 0.599228i | −0.0416720 | + | 0.0320301i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.89873 | + | 1.34127i | 0.474304 | + | 0.0714898i | ||||
\(353\) | −21.6850 | + | 14.7846i | −1.15417 | + | 0.786903i | −0.980232 | − | 0.197853i | \(-0.936603\pi\) |
−0.173943 | + | 0.984756i | \(0.555651\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.1837 | + | 14.2086i | 0.699718 | + | 0.754117i | ||||
\(356\) | −2.43822 | − | 3.05744i | −0.129226 | − | 0.162044i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.556335 | + | 0.697622i | −0.0294032 | + | 0.0368705i | ||||
\(359\) | 24.8015 | − | 1.85861i | 1.30897 | − | 0.0980938i | 0.598103 | − | 0.801419i | \(-0.295921\pi\) |
0.710868 | + | 0.703325i | \(0.248302\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.70345 | + | 11.6107i | −0.352813 | + | 0.611091i | ||||
\(362\) | 0.206706 | + | 0.358025i | 0.0108642 | + | 0.0188174i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −16.2616 | − | 24.7927i | −0.852342 | − | 1.29949i | ||||
\(365\) | 8.13851 | + | 1.85756i | 0.425989 | + | 0.0972293i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.0028 | + | 12.1677i | −1.61833 | + | 0.635149i | −0.989778 | − | 0.142616i | \(-0.954449\pi\) |
−0.628555 | + | 0.777765i | \(0.716353\pi\) | |||||||
\(368\) | 21.1670 | − | 8.30744i | 1.10341 | − | 0.433055i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.456200 | + | 0.104125i | 0.0237167 | + | 0.00541318i | ||||
\(371\) | −11.2227 | − | 1.04315i | −0.582652 | − | 0.0541577i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.1986 | + | 17.6645i | 0.528063 | + | 0.914631i | 0.999465 | + | 0.0327130i | \(0.0104147\pi\) |
−0.471402 | + | 0.881918i | \(0.656252\pi\) | |||||||
\(374\) | −0.903184 | + | 1.56436i | −0.0467025 | + | 0.0808912i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.42747 | − | 0.481672i | 0.331472 | − | 0.0248404i | ||||
\(377\) | −33.8808 | + | 42.4852i | −1.74495 | + | 2.18810i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.66886 | + | 8.36249i | 0.342556 | + | 0.429552i | 0.923031 | − | 0.384726i | \(-0.125704\pi\) |
−0.580474 | + | 0.814279i | \(0.697133\pi\) | |||||||
\(380\) | −4.92199 | − | 5.30464i | −0.252493 | − | 0.272122i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.49595 | − | 1.01992i | 0.0765397 | − | 0.0521839i | ||||
\(383\) | −11.7815 | − | 1.77578i | −0.602008 | − | 0.0907382i | −0.159035 | − | 0.987273i | \(-0.550838\pi\) |
−0.442973 | + | 0.896535i | \(0.646076\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.3764 | + | 4.47840i | −1.08944 | + | 0.228240i | ||||
\(386\) | 0.116242 | − | 0.241378i | 0.00591654 | − | 0.0122858i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.9517 | − | 11.8032i | 0.555990 | − | 0.599215i | ||||
\(389\) | 13.0029 | + | 0.974431i | 0.659272 | + | 0.0494056i | 0.400165 | − | 0.916443i | \(-0.368953\pi\) |
0.259107 | + | 0.965849i | \(0.416572\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.9301i | 0.704477i | ||||||||
\(392\) | 3.89465 | − | 0.743491i | 0.196709 | − | 0.0375520i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.665966 | − | 1.69685i | 0.0335509 | − | 0.0854863i | ||||
\(395\) | −0.435333 | + | 5.80911i | −0.0219040 | + | 0.292288i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.4223 | − | 18.2202i | 0.623458 | − | 0.914445i | −0.376470 | − | 0.926429i | \(-0.622862\pi\) |
0.999928 | + | 0.0119840i | \(0.00381471\pi\) | |||||||
\(398\) | 1.14541 | + | 0.551602i | 0.0574143 | + | 0.0276493i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.12560 | − | 4.39466i | 0.456280 | − | 0.219733i | ||||
\(401\) | 1.08944 | − | 7.22798i | 0.0544042 | − | 0.360948i | −0.945020 | − | 0.327013i | \(-0.893958\pi\) |
0.999424 | − | 0.0339353i | \(-0.0108040\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 41.9191 | − | 6.31829i | 2.08814 | − | 0.314736i | ||||
\(404\) | 25.4330 | − | 23.5984i | 1.26534 | − | 1.17406i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.75117 | − | 3.16241i | −0.0869092 | − | 0.156948i | ||||
\(407\) | −8.88277 | − | 7.08377i | −0.440302 | − | 0.351129i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.43550 | + | 14.3795i | −0.219321 | + | 0.711022i | 0.777318 | + | 0.629108i | \(0.216580\pi\) |
−0.996639 | + | 0.0819142i | \(0.973897\pi\) | |||||||
\(410\) | −0.0381368 | − | 0.0220183i | −0.00188344 | − | 0.00108740i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −30.8521 | + | 7.04178i | −1.51997 | + | 0.346924i | ||||
\(413\) | −31.5342 | − | 10.3481i | −1.55170 | − | 0.509198i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.2259 | − | 4.07966i | 0.649235 | − | 0.200263i | ||||
\(416\) | −3.48453 | − | 8.87843i | −0.170843 | − | 0.435301i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.529910 | − | 1.71793i | −0.0259188 | − | 0.0840266i | ||||
\(419\) | 0.364788 | − | 1.59824i | 0.0178210 | − | 0.0780791i | −0.965235 | − | 0.261382i | \(-0.915822\pi\) |
0.983056 | + | 0.183303i | \(0.0586789\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.33211 | − | 27.7428i | −0.308608 | − | 1.35210i | −0.856757 | − | 0.515720i | \(-0.827524\pi\) |
0.548149 | − | 0.836381i | \(-0.315333\pi\) | |||||||
\(422\) | −0.777766 | + | 0.449043i | −0.0378611 | + | 0.0218591i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.30580 | − | 0.711246i | −0.111980 | − | 0.0345412i | ||||
\(425\) | 0.463696 | + | 6.18760i | 0.0224926 | + | 0.300143i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.16426 | − | 12.8012i | 0.104736 | − | 0.619492i | ||||
\(428\) | −3.63207 | + | 2.89648i | −0.175563 | + | 0.140007i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.202526 | − | 1.34367i | −0.00976666 | − | 0.0647975i | ||||
\(431\) | 3.73526 | + | 5.47862i | 0.179921 | + | 0.263896i | 0.905595 | − | 0.424143i | \(-0.139424\pi\) |
−0.725674 | + | 0.688038i | \(0.758472\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.9812 | + | 29.0322i | 0.671891 | + | 1.39520i | 0.906122 | + | 0.423016i | \(0.139029\pi\) |
−0.234231 | + | 0.972181i | \(0.575257\pi\) | |||||||
\(434\) | −0.676593 | + | 2.73771i | −0.0324775 | + | 0.131414i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.53923 | + | 1.73122i | 0.121607 | + | 0.0829102i | ||||
\(437\) | −10.1631 | − | 9.42994i | −0.486165 | − | 0.451095i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.5264 | + | 5.70118i | 0.693305 | + | 0.272102i | 0.685716 | − | 0.727869i | \(-0.259489\pi\) |
0.00758904 | + | 0.999971i | \(0.497584\pi\) | |||||||
\(440\) | −4.67580 | −0.222910 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.91446 | 0.0910615 | ||||||||
\(443\) | 10.3309 | + | 4.05457i | 0.490834 | + | 0.192638i | 0.597833 | − | 0.801621i | \(-0.296029\pi\) |
−0.106998 | + | 0.994259i | \(0.534124\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.23798 | + | 2.07654i | 0.106090 | + | 0.0984376i | ||||
\(446\) | −1.99292 | − | 1.35875i | −0.0943676 | − | 0.0643388i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −19.8874 | − | 0.355709i | −0.939590 | − | 0.0168057i | ||||
\(449\) | 1.22019 | + | 2.53375i | 0.0575843 | + | 0.119575i | 0.927775 | − | 0.373140i | \(-0.121719\pi\) |
−0.870191 | + | 0.492715i | \(0.836005\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.602311 | + | 0.883428i | 0.0283617 | + | 0.0415990i | ||||
\(452\) | 2.26150 | + | 15.0041i | 0.106372 | + | 0.705733i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.59843 | − | 1.27471i | 0.0750181 | − | 0.0598249i | ||||
\(455\) | 15.4382 | + | 17.2471i | 0.723756 | + | 0.808555i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.164588 | − | 2.19628i | −0.00769911 | − | 0.102737i | 0.992030 | − | 0.126000i | \(-0.0402138\pi\) |
−0.999729 | + | 0.0232621i | \(0.992595\pi\) | |||||||
\(458\) | −1.63192 | − | 0.503381i | −0.0762547 | − | 0.0235215i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −15.5342 | + | 8.96869i | −0.724287 | + | 0.418167i | ||||
\(461\) | 5.01510 | + | 21.9726i | 0.233577 | + | 1.02337i | 0.946647 | + | 0.322273i | \(0.104447\pi\) |
−0.713070 | + | 0.701093i | \(0.752696\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.0445324 | − | 0.195109i | 0.00206960 | − | 0.00906749i | −0.973883 | − | 0.227052i | \(-0.927091\pi\) |
0.975952 | + | 0.217985i | \(0.0699483\pi\) | |||||||
\(464\) | 10.9755 | + | 35.5818i | 0.509526 | + | 1.65184i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.834350 | − | 2.12589i | −0.0386505 | − | 0.0984799i | ||||
\(467\) | −14.6853 | + | 4.52982i | −0.679556 | + | 0.209615i | −0.615270 | − | 0.788316i | \(-0.710953\pi\) |
−0.0642857 | + | 0.997932i | \(0.520477\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.5463 | − | 3.11946i | 1.08726 | − | 0.144044i | ||||
\(470\) | −2.44039 | + | 0.557004i | −0.112567 | + | 0.0256927i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.15339 | − | 3.55266i | −0.283233 | − | 0.163525i | ||||
\(473\) | −9.72489 | + | 31.5273i | −0.447151 | + | 1.44963i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.82821 | − | 3.85037i | −0.221533 | − | 0.176667i | ||||
\(476\) | 4.75371 | − | 11.5030i | 0.217886 | − | 0.527239i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.0921746 | + | 0.0855255i | −0.00421597 | + | 0.00391185i | ||||
\(479\) | 15.8422 | − | 2.38783i | 0.723850 | − | 0.109103i | 0.223225 | − | 0.974767i | \(-0.428342\pi\) |
0.500625 | + | 0.865664i | \(0.333104\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.79467 | + | 11.9068i | −0.0818298 | + | 0.542905i | ||||
\(482\) | 3.12176 | − | 1.50336i | 0.142192 | − | 0.0684763i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 31.2624 | + | 15.0552i | 1.42102 | + | 0.684326i | ||||
\(485\) | −7.08103 | + | 10.3860i | −0.321533 | + | 0.471602i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.60891 | − | 21.4694i | 0.0729065 | − | 0.972870i | −0.834062 | − | 0.551671i | \(-0.813990\pi\) |
0.906968 | − | 0.421199i | \(-0.138391\pi\) | |||||||
\(488\) | 1.01546 | − | 2.58734i | 0.0459676 | − | 0.117124i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.45259 | + | 0.510944i | −0.0656212 | + | 0.0230821i | ||||
\(491\) | 9.31223i | 0.420255i | 0.977674 | + | 0.210127i | \(0.0673879\pi\) | ||||
−0.977674 | + | 0.210127i | \(0.932612\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.7475 | − | 1.70469i | −1.02450 | − | 0.0767754i | ||||
\(494\) | −1.29598 | + | 1.39674i | −0.0583091 | + | 0.0628422i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.6038 | − | 26.1721i | 0.565928 | − | 1.17516i | ||||
\(497\) | −13.8595 | − | 30.1471i | −0.621683 | − | 1.35228i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.2189 | − | 1.99243i | −0.591761 | − | 0.0891936i | −0.153667 | − | 0.988123i | \(-0.549108\pi\) |
−0.438094 | + | 0.898929i | \(0.644346\pi\) | |||||||
\(500\) | −19.2423 | + | 13.1192i | −0.860540 | + | 0.586706i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.461743 | + | 0.497641i | 0.0206086 | + | 0.0222108i | ||||
\(503\) | 5.59198 | + | 7.01212i | 0.249334 | + | 0.312655i | 0.890710 | − | 0.454572i | \(-0.150208\pi\) |
−0.641376 | + | 0.767227i | \(0.721636\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.8877 | + | 21.1765i | −0.751492 | + | 0.942341i | ||||
\(506\) | −4.44388 | + | 0.333023i | −0.197555 | + | 0.0148047i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.09807 | − | 7.09806i | 0.181822 | − | 0.314925i | ||||
\(509\) | −13.5956 | − | 23.5483i | −0.602614 | − | 1.04376i | −0.992424 | − | 0.122862i | \(-0.960793\pi\) |
0.389810 | − | 0.920895i | \(-0.372541\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.2458 | − | 7.36522i | −0.541724 | − | 0.325818i | ||||
\(512\) | −10.6557 | − | 2.43210i | −0.470921 | − | 0.107485i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.478011 | + | 0.187606i | −0.0210842 | + | 0.00827493i | ||||
\(515\) | 22.9975 | − | 9.02584i | 1.01339 | − | 0.397726i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 59.2533 | + | 13.5242i | 2.60596 | + | 0.594793i | ||||
\(518\) | −0.686433 | − | 0.412853i | −0.0301601 | − | 0.0181397i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.47780 | + | 4.29167i | 0.108659 | + | 0.188202i | ||||
\(521\) | 16.8688 | − | 29.2177i | 0.739037 | − | 1.28005i | −0.213892 | − | 0.976857i | \(-0.568614\pi\) |
0.952929 | − | 0.303192i | \(-0.0980525\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.0598 | + | 2.40255i | −1.40188 | + | 0.105056i | −0.754092 | − | 0.656769i | \(-0.771923\pi\) |
−0.647783 | + | 0.761825i | \(0.724304\pi\) | |||||||
\(524\) | 9.53739 | − | 11.9595i | 0.416643 | − | 0.522453i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.209091 | + | 0.262192i | 0.00911682 | + | 0.0114321i | ||||
\(527\) | 12.1042 | + | 13.0452i | 0.527265 | + | 0.568257i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.39093 | + | 6.40263i | −0.408301 | + | 0.278375i | ||||
\(530\) | 0.926641 | + | 0.139669i | 0.0402507 | + | 0.00606682i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.17429 | + | 11.2551i | 0.224334 | + | 0.487970i | ||||
\(533\) | 0.491675 | − | 1.02097i | 0.0212968 | − | 0.0442233i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.46682 | − | 2.65860i | 0.106650 | − | 0.114941i | ||||
\(536\) | 5.07082 | + | 0.380005i | 0.219026 | + | 0.0164137i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 4.36630i | − | 0.188245i | ||||||
\(539\) | 37.1591 | + | 4.12544i | 1.60055 | + | 0.177695i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.62785 | − | 21.9834i | 0.370940 | − | 0.945140i | −0.616530 | − | 0.787332i | \(-0.711462\pi\) |
0.987470 | − | 0.157808i | \(-0.0504429\pi\) | |||||||
\(542\) | 0.0689121 | − | 0.919568i | 0.00296003 | − | 0.0394988i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.25541 | − | 3.30808i | 0.0967000 | − | 0.141833i | ||||
\(545\) | −2.16164 | − | 1.04099i | −0.0925944 | − | 0.0445911i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.6334 | + | 8.01025i | −0.711195 | + | 0.342493i | −0.754257 | − | 0.656579i | \(-0.772003\pi\) |
0.0430624 | + | 0.999072i | \(0.486289\pi\) | |||||||
\(548\) | −4.03830 | + | 26.7924i | −0.172508 | + | 1.14451i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.96283 | + | 0.295850i | −0.0836955 | + | 0.0126151i | ||||
\(551\) | 16.6425 | − | 15.4420i | 0.708996 | − | 0.657852i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.80866 | − | 9.21617i | 0.161961 | − | 0.391911i | ||||
\(554\) | 2.07593 | + | 1.65550i | 0.0881980 | + | 0.0703356i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.4745 | + | 37.1996i | −0.486629 | + | 1.57761i | ||||
\(557\) | −2.68708 | − | 1.55139i | −0.113855 | − | 0.0657344i | 0.441991 | − | 0.897020i | \(-0.354272\pi\) |
−0.555846 | + | 0.831285i | \(0.687606\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.0906 | − | 7.78097i | 1.44188 | − | 0.329100i | ||||
\(560\) | 15.7240 | − | 2.08315i | 0.664459 | − | 0.0880291i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.510164 | + | 0.157365i | −0.0215200 | + | 0.00663803i | ||||
\(563\) | −10.2429 | − | 26.0984i | −0.431685 | − | 1.09992i | −0.966890 | − | 0.255193i | \(-0.917861\pi\) |
0.535205 | − | 0.844722i | \(-0.320234\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.49162 | − | 11.3195i | −0.146893 | − | 0.476217i | ||||
\(566\) | 0.148855 | − | 0.652175i | 0.00625683 | − | 0.0274130i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.58069 | − | 6.92544i | −0.0663241 | − | 0.290585i | ||||
\(569\) | 12.7564 | − | 7.36489i | 0.534775 | − | 0.308752i | −0.208184 | − | 0.978090i | \(-0.566755\pi\) |
0.742959 | + | 0.669337i | \(0.233422\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.3341 | + | 10.5907i | 1.43684 | + | 0.443205i | 0.912771 | − | 0.408472i | \(-0.133938\pi\) |
0.524066 | + | 0.851678i | \(0.324415\pi\) | |||||||
\(572\) | −4.47299 | − | 59.6878i | −0.187025 | − | 2.49567i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.0502773 | + | 0.0561681i | 0.00209853 | + | 0.00234441i | ||||
\(575\) | −11.9681 | + | 9.54421i | −0.499102 | + | 0.398021i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.23881 | + | 14.8535i | 0.0932029 | + | 0.618361i | 0.985853 | + | 0.167611i | \(0.0536053\pi\) |
−0.892650 | + | 0.450750i | \(0.851157\pi\) | |||||||
\(578\) | −0.910272 | − | 1.33512i | −0.0378623 | − | 0.0555338i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −12.7446 | − | 26.4645i | −0.529192 | − | 1.09888i | ||||
\(581\) | −23.6895 | − | 0.423714i | −0.982806 | − | 0.0175786i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.7996 | − | 12.8173i | −0.778598 | − | 0.530839i | ||||
\(584\) | −2.24266 | − | 2.08089i | −0.0928021 | − | 0.0861077i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.105781 | − | 0.0415158i | −0.00436976 | − | 0.00171500i | ||||
\(587\) | −23.0393 | −0.950936 | −0.475468 | − | 0.879733i | \(-0.657721\pi\) | ||||
−0.475468 | + | 0.879733i | \(0.657721\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.7113 | −0.729780 | ||||||||
\(590\) | 2.56866 | + | 1.00812i | 0.105750 | + | 0.0415038i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.04850 | + | 5.61219i | 0.248592 | + | 0.230660i | ||||
\(593\) | 23.1902 | + | 15.8108i | 0.952308 | + | 0.649272i | 0.936524 | − | 0.350603i | \(-0.114023\pi\) |
0.0157835 | + | 0.999875i | \(0.494976\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.33128 | + | 9.43307i | −0.0955730 | + | 0.386718i | ||||
\(596\) | 6.72263 | + | 13.9597i | 0.275369 | + | 0.571811i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.66056 | + | 3.90233i | 0.108798 | + | 0.159578i | ||||
\(599\) | 4.00751 | + | 26.5881i | 0.163742 | + | 1.08636i | 0.908153 | + | 0.418638i | \(0.137492\pi\) |
−0.744411 | + | 0.667722i | \(0.767269\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.6496 | + | 10.8852i | −0.556780 | + | 0.444017i | −0.861015 | − | 0.508580i | \(-0.830171\pi\) |
0.304235 | + | 0.952597i | \(0.401599\pi\) | |||||||
\(602\) | −0.387770 | + | 2.29358i | −0.0158043 | + | 0.0934793i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.0174272 | − | 0.232550i | −0.000709103 | − | 0.00946233i | ||||
\(605\) | −25.8853 | − | 7.98457i | −1.05239 | − | 0.324619i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.2456 | + | 9.37939i | −0.659388 | + | 0.380698i | −0.792044 | − | 0.610464i | \(-0.790983\pi\) |
0.132656 | + | 0.991162i | \(0.457649\pi\) | |||||||
\(608\) | 0.886699 | + | 3.88488i | 0.0359604 | + | 0.157553i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.240196 | + | 1.05237i | −0.00972524 | + | 0.0426091i | ||||
\(611\) | −18.9863 | − | 61.5522i | −0.768105 | − | 2.49013i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.60979 | + | 14.2935i | 0.226577 | + | 0.577310i | 0.998277 | − | 0.0586776i | \(-0.0186884\pi\) |
−0.771700 | + | 0.635987i | \(0.780593\pi\) | |||||||
\(614\) | 1.28047 | − | 0.394973i | 0.0516757 | − | 0.0159398i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.60520 | + | 2.49569i | 0.306422 | + | 0.100554i | ||||
\(617\) | −36.9315 | + | 8.42938i | −1.48681 | + | 0.339354i | −0.887367 | − | 0.461065i | \(-0.847468\pi\) |
−0.599441 | + | 0.800419i | \(0.704611\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.93774 | − | 5.73756i | −0.399431 | − | 0.230612i | 0.286807 | − | 0.957988i | \(-0.407406\pi\) |
−0.686239 | + | 0.727376i | \(0.740739\pi\) | |||||||
\(620\) | −6.75430 | + | 21.8969i | −0.271259 | + | 0.879401i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.85455 | + | 1.47895i | 0.0743607 | + | 0.0593007i | ||||
\(623\) | −2.53173 | − | 4.57201i | −0.101432 | − | 0.183174i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.75706 | − | 3.48604i | 0.150282 | − | 0.139442i | ||||
\(626\) | 1.32449 | − | 0.199634i | 0.0529371 | − | 0.00797899i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.16885 | + | 14.3894i | −0.0865464 | + | 0.574198i | ||||
\(629\) | −4.55417 | + | 2.19317i | −0.181587 | + | 0.0874476i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.9021 | − | 18.2527i | −1.50886 | − | 0.726628i | −0.517242 | − | 0.855839i | \(-0.673041\pi\) |
−0.991617 | + | 0.129211i | \(0.958756\pi\) | |||||||
\(632\) | 1.20265 | − | 1.76396i | 0.0478387 | − | 0.0701664i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.155897 | + | 2.08030i | −0.00619147 | + | 0.0826194i | ||||
\(635\) | −2.33768 | + | 5.95631i | −0.0927679 | + | 0.236369i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.9048 | − | 36.2925i | −0.630170 | − | 1.43796i | ||||
\(638\) | − | 7.29749i | − | 0.288910i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.84287 | + | 0.512802i | 0.270488 | + | 0.0202703i | ||||
\(641\) | 21.6891 | − | 23.3753i | 0.856669 | − | 0.923269i | −0.141103 | − | 0.989995i | \(-0.545065\pi\) |
0.997771 | + | 0.0667258i | \(0.0212553\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.0844 | + | 20.9404i | −0.397689 | + | 0.825810i | 0.601939 | + | 0.798542i | \(0.294395\pi\) |
−0.999628 | + | 0.0272678i | \(0.991319\pi\) | |||||||
\(644\) | 30.0534 | − | 6.29625i | 1.18427 | − | 0.248107i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.790911 | − | 0.119211i | −0.0311180 | − | 0.00469028i | ||||
\(647\) | −3.53050 | + | 2.40705i | −0.138798 | + | 0.0946310i | −0.630729 | − | 0.776004i | \(-0.717244\pi\) |
0.491930 | + | 0.870635i | \(0.336291\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −45.5708 | − | 49.1137i | −1.78881 | − | 1.92788i | ||||
\(650\) | 1.31169 | + | 1.64480i | 0.0514486 | + | 0.0645145i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.85953 | + | 4.83969i | −0.151151 | + | 0.189537i | ||||
\(653\) | 30.8531 | − | 2.31212i | 1.20737 | − | 0.0904801i | 0.544206 | − | 0.838951i | \(-0.316831\pi\) |
0.663167 | + | 0.748471i | \(0.269212\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.97101 | + | 10.3421i | −0.233307 | + | 0.404099i | ||||
\(656\) | −0.388252 | − | 0.672472i | −0.0151587 | − | 0.0262556i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.26660 | + | 0.396582i | 0.166330 | + | 0.0154604i | ||||
\(659\) | −31.3870 | − | 7.16389i | −1.22267 | − | 0.279065i | −0.437994 | − | 0.898978i | \(-0.644311\pi\) |
−0.784671 | + | 0.619912i | \(0.787168\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.246290 | + | 0.0966616i | −0.00957956 | + | 0.00375970i | −0.370126 | − | 0.928982i | \(-0.620685\pi\) |
0.360546 | + | 0.932741i | \(0.382590\pi\) | |||||||
\(662\) | 0.571651 | − | 0.224357i | 0.0222179 | − | 0.00871986i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.94529 | − | 1.12873i | −0.191914 | − | 0.0438032i | ||||
\(665\) | −5.30398 | − | 8.08652i | −0.205679 | − | 0.313582i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.1379 | − | 48.7363i | −1.08951 | − | 1.88708i | ||||
\(668\) | 4.90919 | − | 8.50297i | 0.189942 | − | 0.328990i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.96929 | + | 0.147578i | −0.0760802 | + | 0.00570142i | ||||
\(671\) | 16.3409 | − | 20.4909i | 0.630834 | − | 0.791041i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.2674 | + | 20.3986i | 0.627060 | + | 0.786309i | 0.989319 | − | 0.145769i | \(-0.0465656\pi\) |
−0.362258 | + | 0.932078i | \(0.617994\pi\) | |||||||
\(674\) | 2.29590 | + | 2.47439i | 0.0884348 | + | 0.0953101i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −31.1493 | + | 21.2373i | −1.19805 | + | 0.816817i | ||||
\(677\) | −28.9323 | − | 4.36084i | −1.11196 | − | 0.167601i | −0.432727 | − | 0.901525i | \(-0.642448\pi\) |
−0.679231 | + | 0.733925i | \(0.737687\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.0608 | − | 13.1133i | 0.654732 | − | 0.503243i | ||||
\(680\) | −0.902598 | + | 1.87426i | −0.0346130 | + | 0.0718747i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.87220 | + | 4.17324i | −0.148274 | + | 0.159802i | ||||
\(683\) | 32.5940 | + | 2.44258i | 1.24717 | + | 0.0934627i | 0.681903 | − | 0.731443i | \(-0.261153\pi\) |
0.565270 | + | 0.824906i | \(0.308772\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 21.1527i | − | 0.808204i | ||||||
\(686\) | 2.63535 | − | 0.0557382i | 0.100618 | − | 0.00212810i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.75387 | − | 22.3045i | 0.333738 | − | 0.850351i | ||||
\(689\) | −1.80209 | + | 24.0473i | −0.0686543 | + | 0.916128i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.21280 | + | 12.0460i | −0.312430 | + | 0.458250i | −0.950049 | − | 0.312102i | \(-0.898967\pi\) |
0.637619 | + | 0.770352i | \(0.279919\pi\) | |||||||
\(692\) | −13.9557 | − | 6.72071i | −0.530516 | − | 0.255483i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.07517 | + | 0.999349i | −0.0787723 | + | 0.0379348i | ||||
\(695\) | 4.52961 | − | 30.0520i | 0.171818 | − | 1.13994i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.470384 | − | 0.0708989i | 0.0178171 | − | 0.00268549i | ||||
\(698\) | −1.39716 | + | 1.29637i | −0.0528832 | + | 0.0490684i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 13.1398 | − | 3.79712i | 0.496637 | − | 0.143518i | ||||
\(701\) | −29.6568 | − | 23.6505i | −1.12012 | − | 0.893268i | −0.125024 | − | 0.992154i | \(-0.539901\pi\) |
−0.995099 | + | 0.0988857i | \(0.968472\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.48284 | − | 4.80726i | 0.0559265 | − | 0.181309i | ||||
\(704\) | −34.7741 | − | 20.0768i | −1.31060 | − | 0.756674i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.64178 | + | 0.831213i | −0.137060 | + | 0.0312831i | ||||
\(707\) | 38.7707 | − | 25.4299i | 1.45812 | − | 0.956388i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.37503 | + | 1.65798i | −0.201863 | + | 0.0622666i | −0.394038 | − | 0.919094i | \(-0.628922\pi\) |
0.192175 | + | 0.981361i | \(0.438446\pi\) | |||||||
\(710\) | 1.00787 | + | 2.56801i | 0.0378247 | + | 0.0963757i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.329792 | − | 1.06916i | −0.0123595 | − | 0.0400684i | ||||
\(713\) | −9.76918 | + | 42.8016i | −0.365859 | + | 1.60293i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.3980 | + | 45.5567i | 0.388864 | + | 1.70372i | ||||
\(716\) | 10.7488 | − | 6.20580i | 0.401700 | − | 0.231922i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.38256 | + | 1.04338i | 0.126236 | + | 0.0389386i | ||||
\(719\) | −3.85528 | − | 51.4451i | −0.143778 | − | 1.91858i | −0.344247 | − | 0.938879i | \(-0.611866\pi\) |
0.200470 | − | 0.979700i | \(-0.435753\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −42.2229 | + | 2.40574i | −1.57246 | + | 0.0895944i | ||||
\(722\) | −1.49187 | + | 1.18972i | −0.0555215 | + | 0.0442769i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.857063 | − | 5.68624i | −0.0318525 | − | 0.211328i | ||||
\(725\) | −14.1208 | − | 20.7115i | −0.524435 | − | 0.769205i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.0750 | + | 27.1505i | 0.484925 | + | 1.00696i | 0.989627 | + | 0.143663i | \(0.0458882\pi\) |
−0.504702 | + | 0.863294i | \(0.668397\pi\) | |||||||
\(728\) | −1.73948 | − | 8.30292i | −0.0644694 | − | 0.307727i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.981671 | + | 0.669292i | 0.0363333 | + | 0.0247716i | ||||
\(731\) | 10.7603 | + | 9.98406i | 0.397982 | + | 0.369274i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 47.3364 | + | 18.5782i | 1.74841 | + | 0.686200i | 0.999729 | + | 0.0232679i | \(0.00740708\pi\) |
0.748680 | + | 0.662932i | \(0.230688\pi\) | |||||||
\(734\) | −4.74022 | −0.174965 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.87741 | 0.364086 | ||||||||
\(737\) | 44.6343 | + | 17.5177i | 1.64413 | + | 0.645272i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.5359 | + | 19.0545i | 0.755424 | + | 0.700931i | 0.960643 | − | 0.277785i | \(-0.0896003\pi\) |
−0.205219 | + | 0.978716i | \(0.565791\pi\) | |||||||
\(740\) | −5.37785 | − | 3.66656i | −0.197694 | − | 0.134785i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.43264 | − | 0.721762i | −0.0525937 | − | 0.0264967i | ||||
\(743\) | −8.02702 | − | 16.6683i | −0.294483 | − | 0.611500i | 0.700262 | − | 0.713886i | \(-0.253067\pi\) |
−0.994745 | + | 0.102386i | \(0.967352\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.81394 | − | 9.99421i | −0.249643 | − | 0.366160i | ||||
\(746\) | 0.432681 | + | 2.87065i | 0.0158416 | + | 0.105102i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 19.6445 | − | 15.6659i | 0.718273 | − | 0.572804i | ||||
\(749\) | −5.43131 | + | 3.00756i | −0.198456 | + | 0.109894i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.447222 | + | 5.96776i | 0.0163194 | + | 0.217767i | 0.999401 | + | 0.0346001i | \(0.0110157\pi\) |
−0.983082 | + | 0.183167i | \(0.941365\pi\) | |||||||
\(752\) | −42.1776 | − | 13.0101i | −1.53806 | − | 0.474429i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.69797 | + | 3.86708i | −0.243926 | + | 0.140831i | ||||
\(755\) | 0.0405117 | + | 0.177493i | 0.00147437 | + | 0.00645965i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.6835 | + | 51.1888i | −0.424645 | + | 1.86049i | 0.0794461 | + | 0.996839i | \(0.474685\pi\) |
−0.504091 | + | 0.863651i | \(0.668172\pi\) | |||||||
\(758\) | 0.448716 | + | 1.45470i | 0.0162981 | + | 0.0528372i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.756404 | − | 1.92729i | −0.0274377 | − | 0.0699100i | ||||
\(761\) | 26.2357 | − | 8.09263i | 0.951042 | − | 0.293358i | 0.219853 | − | 0.975533i | \(-0.429442\pi\) |
0.731189 | + | 0.682175i | \(0.238966\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.96028 | + | 2.84694i | 0.107169 | + | 0.103066i | ||||
\(764\) | −24.5531 | + | 5.60408i | −0.888300 | + | 0.202749i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.46858 | − | 0.847887i | −0.0530621 | − | 0.0306354i | ||||
\(767\) | −20.9300 | + | 67.8533i | −0.755737 | + | 2.45004i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.181697 | + | 0.144899i | 0.00655217 | + | 0.00522518i | 0.626760 | − | 0.779212i | \(-0.284380\pi\) |
−0.620208 | + | 0.784437i | \(0.712952\pi\) | |||||||
\(770\) | −3.06500 | − | 0.518192i | −0.110455 | − | 0.0186744i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.73177 | + | 2.53471i | −0.0983185 | + | 0.0912262i | ||||
\(773\) | 42.5241 | − | 6.40948i | 1.52949 | − | 0.230533i | 0.670259 | − | 0.742127i | \(-0.266183\pi\) |
0.859227 | + | 0.511594i | \(0.170945\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.91461 | + | 19.3371i | −0.104696 | + | 0.694611i | ||||
\(776\) | 4.15057 | − | 1.99881i | 0.148997 | − | 0.0717531i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.67207 | + | 0.805224i | 0.0599464 | + | 0.0288687i | ||||
\(779\) | −0.266698 | + | 0.391174i | −0.00955545 | + | 0.0140153i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.00558 | − | 66.7948i | 0.179114 | − | 2.39011i | ||||
\(782\) | −0.724339 | + | 1.84558i | −0.0259023 | + | 0.0659980i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −26.6869 | − | 5.00436i | −0.953104 | − | 0.178727i | ||||
\(785\) | − | 11.3605i | − | 0.405473i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.2189 | + | 1.88990i | 0.898957 | + | 0.0673675i | 0.516187 | − | 0.856476i | \(-0.327351\pi\) |
0.382770 | + | 0.923844i | \(0.374970\pi\) | |||||||
\(788\) | −17.2462 | + | 18.5870i | −0.614371 | + | 0.662134i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.359739 | + | 0.747005i | −0.0127989 | + | 0.0265772i | ||||
\(791\) | −0.362640 | + | 20.2749i | −0.0128940 | + | 0.720892i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.4668 | − | 4.13996i | −0.975375 | − | 0.147014i | ||||
\(794\) | 2.59323 | − | 1.76803i | 0.0920302 | − | 0.0627451i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.0280 | − | 12.9631i | −0.426320 | − | 0.459464i | ||||
\(797\) | −2.63783 | − | 3.30773i | −0.0934366 | − | 0.117166i | 0.732915 | − | 0.680320i | \(-0.238159\pi\) |
−0.826352 | + | 0.563154i | \(0.809588\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.8591 | − | 21.1406i | 0.596432 | − | 0.747902i | ||||
\(800\) | 4.38743 | − | 0.328792i | 0.155119 | − | 0.0116246i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.520179 | − | 0.900977i | 0.0183682 | − | 0.0318146i | ||||
\(803\) | −14.4239 | − | 24.9830i | −0.509009 | − | 0.881629i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.4677 | + | 8.35739i | −0.791882 | + | 0.294559i | ||||
\(806\) | 5.88235 | + | 1.34261i | 0.207197 | + | 0.0472913i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.24035 | − | 3.62657i | 0.325074 | − | 0.127582i | ||||
\(809\) | 17.1208 | − | 6.71942i | 0.601935 | − | 0.236242i | −0.0447511 | − | 0.998998i | \(-0.514249\pi\) |
0.646686 | + | 0.762756i | \(0.276154\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.0745 | − | 6.17958i | −0.950714 | − | 0.216994i | −0.281079 | − | 0.959685i | \(-0.590692\pi\) |
−0.669635 | + | 0.742690i | \(0.733550\pi\) | |||||||
\(812\) | 6.60384 | + | 49.8469i | 0.231749 | + | 1.74928i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.808524 | − | 1.40041i | −0.0283388 | − | 0.0490842i | ||||
\(815\) | 2.41631 | − | 4.18517i | 0.0846396 | − | 0.146600i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.5682 | + | 1.09174i | −0.509677 | + | 0.0381950i | ||||
\(818\) | −1.33536 | + | 1.67449i | −0.0466898 | + | 0.0585471i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.381912 | + | 0.478902i | 0.0133369 | + | 0.0167240i | ||||
\(821\) | 34.0627 | + | 36.7108i | 1.18880 | + | 1.28122i | 0.950749 | + | 0.309963i | \(0.100317\pi\) |
0.238046 | + | 0.971254i | \(0.423493\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.5671 | − | 28.3400i | 1.44894 | − | 0.987869i | 0.453621 | − | 0.891195i | \(-0.350132\pi\) |
0.995316 | − | 0.0966740i | \(-0.0308204\pi\) | |||||||
\(824\) | −8.95298 | − | 1.34944i | −0.311892 | − | 0.0470101i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.63984 | − | 3.01072i | −0.126646 | − | 0.104756i | ||||
\(827\) | −3.46487 | + | 7.19487i | −0.120485 | + | 0.250190i | −0.952485 | − | 0.304586i | \(-0.901482\pi\) |
0.832000 | + | 0.554776i | \(0.187196\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.9734 | + | 22.6039i | −0.728435 | + | 0.785066i | −0.983316 | − | 0.181906i | \(-0.941773\pi\) |
0.254881 | + | 0.966972i | \(0.417964\pi\) | |||||||
\(830\) | 1.96442 | + | 0.147213i | 0.0681860 | + | 0.00510983i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 42.5563i | 1.47538i | ||||||||
\(833\) | 8.82669 | − | 14.0986i | 0.305827 | − | 0.488487i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.80037 | + | 7.13523i | −0.0969109 | + | 0.246925i | ||||
\(836\) | −1.86878 | + | 24.9371i | −0.0646330 | + | 0.862467i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.131435 | − | 0.192780i | 0.00454036 | − | 0.00665948i | ||||
\(839\) | 38.1667 | + | 18.3801i | 1.31766 | + | 0.634552i | 0.954788 | − | 0.297287i | \(-0.0960819\pi\) |
0.362872 | + | 0.931839i | \(0.381796\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 56.9003 | − | 27.4018i | 1.96208 | − | 0.944888i | ||||
\(842\) | 0.603636 | − | 4.00486i | 0.0208027 | − | 0.138017i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.3527 | − | 1.86187i | 0.425197 | − | 0.0640881i | ||||
\(845\) | 21.5752 | − | 20.0189i | 0.742210 | − | 0.688671i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.8408 | + | 26.8031i | 1.30023 | + | 0.920965i | ||||
\(848\) | 12.9191 | + | 10.3027i | 0.443645 | + | 0.353795i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.260308 | + | 0.843898i | −0.00892849 | + | 0.0289455i | ||||
\(851\) | −10.7995 | − | 6.23508i | −0.370201 | − | 0.213736i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.91444 | − | 0.436959i | 0.0655492 | − | 0.0149612i | −0.189621 | − | 0.981857i | \(-0.560726\pi\) |
0.255170 | + | 0.966896i | \(0.417869\pi\) | |||||||
\(854\) | 0.952375 | − | 1.58347i | 0.0325896 | − | 0.0541853i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.27010 | + | 0.391775i | −0.0434112 | + | 0.0133906i | ||||
\(857\) | 2.53923 | + | 6.46986i | 0.0867385 | + | 0.221006i | 0.967661 | − | 0.252255i | \(-0.0811721\pi\) |
−0.880922 | + | 0.473261i | \(0.843077\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.28966 | − | 17.1486i | −0.180481 | − | 0.585104i | −0.999929 | − | 0.0119505i | \(-0.996196\pi\) |
0.819448 | − | 0.573154i | \(-0.194280\pi\) | |||||||
\(860\) | −4.20593 | + | 18.4274i | −0.143421 | + | 0.628369i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.210002 | + | 0.920080i | 0.00715271 | + | 0.0313381i | ||||
\(863\) | 12.2134 | − | 7.05140i | 0.415748 | − | 0.240032i | −0.277508 | − | 0.960723i | \(-0.589509\pi\) |
0.693257 | + | 0.720691i | \(0.256175\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.5554 | + | 3.56435i | 0.392894 | + | 0.121192i | ||||
\(866\) | 0.342731 | + | 4.57343i | 0.0116465 | + | 0.155411i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 22.6732 | − | 32.0103i | 0.769580 | − | 1.08650i | ||||
\(869\) | 15.7391 | − | 12.5515i | 0.533912 | − | 0.425780i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.57402 | − | 50.2504i | −0.256636 | − | 1.70267i | ||||
\(872\) | 0.495319 | + | 0.726500i | 0.0167736 | + | 0.0246024i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.856153 | − | 1.77782i | −0.0289598 | − | 0.0601356i | ||||
\(875\) | −28.2785 | + | 13.0004i | −0.955987 | + | 0.439494i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.4767 | + | 32.3691i | 1.60317 | + | 1.09303i | 0.938164 | + | 0.346192i | \(0.112525\pi\) |
0.665011 | + | 0.746834i | \(0.268427\pi\) | |||||||
\(878\) | 1.62813 | + | 1.51068i | 0.0549467 | + | 0.0509831i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 29.8064 | + | 11.6981i | 1.00477 | + | 0.394344i | ||||
\(881\) | 36.5243 | 1.23054 | 0.615268 | − | 0.788318i | \(-0.289048\pi\) | ||||
0.615268 | + | 0.788318i | \(0.289048\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.1524 | −1.21663 | −0.608313 | − | 0.793697i | \(-0.708153\pi\) | ||||
−0.608313 | + | 0.793697i | \(0.708153\pi\) | |||||||
\(884\) | −24.7889 | − | 9.72893i | −0.833741 | − | 0.327219i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.15789 | + | 1.07437i | 0.0389002 | + | 0.0360941i | ||||
\(887\) | 40.6621 | + | 27.7229i | 1.36530 | + | 0.930845i | 1.00000 | 4.55407e-5i | \(-1.44961e-5\pi\) | |
0.365299 | + | 0.930890i | \(0.380967\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.98139 | − | 8.44022i | 0.234148 | − | 0.283076i | ||||
\(890\) | 0.188531 | + | 0.391489i | 0.00631958 | + | 0.0131227i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 18.9000 | + | 27.7212i | 0.632818 | + | 0.928173i | ||||
\(893\) | 4.01096 | + | 26.6110i | 0.134222 | + | 0.890503i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.57563 | + | 6.04136i | −0.253225 | + | 0.201940i | ||||
\(896\) | −10.8562 | − | 4.48642i | −0.362681 | − | 0.149881i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.0299115 | + | 0.399141i | 0.000998158 | + | 0.0133195i | ||||
\(899\) | −68.6983 | − | 21.1906i | −2.29122 | − | 0.706747i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.76673 | + | 5.06147i | −0.292062 | + | 0.168622i | ||||
\(902\) | 0.0338629 | + | 0.148363i | 0.00112751 | + | 0.00493995i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.966035 | + | 4.23247i | −0.0321298 | + | 0.140770i | ||||
\(905\) | 1.32325 | + | 4.28988i | 0.0439864 | + | 0.142600i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.1318 | − | 41.1031i | −0.535647 | − | 1.36481i | −0.900953 | − | 0.433918i | \(-0.857131\pi\) |
0.365306 | − | 0.930887i | \(-0.380964\pi\) | |||||||
\(908\) | −27.1747 | + | 8.38230i | −0.901826 | + | 0.278176i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.14858 | + | 3.08780i | 0.0380751 | + | 0.102360i | ||||
\(911\) | −1.11899 | + | 0.255402i | −0.0370737 | + | 0.00846184i | −0.241018 | − | 0.970521i | \(-0.577481\pi\) |
0.203944 | + | 0.978983i | \(0.434624\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −41.4222 | − | 23.9151i | −1.37088 | − | 0.791476i | ||||
\(914\) | 0.0923959 | − | 0.299540i | 0.00305618 | − | 0.00990790i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.5725 | + | 14.8110i | 0.613651 | + | 0.489371i | ||||
\(917\) | 15.2319 | − | 13.6344i | 0.503001 | − | 0.450248i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.6413 | − | 21.9359i | 0.779854 | − | 0.723599i | −0.186039 | − | 0.982542i | \(-0.559565\pi\) |
0.965892 | + | 0.258944i | \(0.0833745\pi\) | |||||||
\(920\) | −5.07475 | + | 0.764896i | −0.167310 | + | 0.0252179i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.478086 | + | 3.17190i | −0.0157449 | + | 0.104461i | ||||
\(923\) | −63.9599 | + | 30.8015i | −2.10527 | + | 1.01384i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.00455 | − | 2.41006i | −0.164548 | − | 0.0792424i | ||||
\(926\) | 0.0160453 | − | 0.0235342i | 0.000527282 | − | 0.000773380i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.20874 | + | 16.1295i | −0.0396789 | + | 0.529478i | ||||
\(929\) | 4.10673 | − | 10.4638i | 0.134737 | − | 0.343305i | −0.847542 | − | 0.530729i | \(-0.821918\pi\) |
0.982279 | + | 0.187423i | \(0.0600136\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.31078 | + | 15.9837i | 0.141280 | + | 0.523845i | ||||
\(932\) | 31.7666i | 1.04055i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.18118 | − | 0.163457i | −0.0713704 | − | 0.00534848i | ||||
\(935\) | −13.3421 | + | 14.3794i | −0.436333 | + | 0.470255i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.3161 | − | 25.5745i | 0.402348 | − | 0.835484i | −0.597097 | − | 0.802169i | \(-0.703679\pi\) |
0.999445 | − | 0.0333149i | \(-0.0106064\pi\) | |||||||
\(938\) | 3.28182 | + | 0.811064i | 0.107155 | + | 0.0264822i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 34.4295 | + | 5.18941i | 1.12297 | + | 0.169260i | ||||
\(941\) | −2.19043 | + | 1.49341i | −0.0714061 | + | 0.0486839i | −0.598497 | − | 0.801125i | \(-0.704235\pi\) |
0.527091 | + | 0.849809i | \(0.323283\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.798218 | + | 0.860275i | 0.0259936 | + | 0.0280144i | ||||
\(944\) | 30.3372 | + | 38.0416i | 0.987391 | + | 1.23815i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.92780 | + | 3.67134i | −0.0951908 | + | 0.119366i | ||||
\(947\) | −35.5917 | + | 2.66723i | −1.15657 | + | 0.0866732i | −0.639168 | − | 0.769067i | \(-0.720721\pi\) |
−0.517406 | + | 0.855740i | \(0.673102\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.2870 | + | 26.4779i | −0.496237 | + | 0.859508i | ||||
\(950\) | −0.439472 | − | 0.761187i | −0.0142583 | − | 0.0246962i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.46846 | − | 2.56673i | 0.0800031 | − | 0.0831883i | ||||
\(953\) | 4.37063 | + | 0.997568i | 0.141579 | + | 0.0323144i | 0.292723 | − | 0.956197i | \(-0.405439\pi\) |
−0.151144 | + | 0.988512i | \(0.548296\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.3021 | − | 7.18306i | 0.592243 | − | 0.232438i | ||||
\(956\) | 1.62813 | − | 0.638992i | 0.0526574 | − | 0.0206665i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.22308 | + | 0.507403i | 0.0718244 | + | 0.0163934i | ||||
\(959\) | −11.2902 | + | 34.4049i | −0.364579 | + | 1.11099i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.5425 | + | 21.7243i | 0.404598 | + | 0.700785i | ||||
\(962\) | −0.856905 | + | 1.48420i | −0.0276277 | + | 0.0478526i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −48.0612 | + | 3.60169i | −1.54795 | + | 0.116003i | ||||
\(965\) | 1.81391 | − | 2.27457i | 0.0583919 | − | 0.0732211i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.75970 | − | 4.71451i | −0.120904 | − | 0.151608i | 0.717696 | − | 0.696356i | \(-0.245197\pi\) |
−0.838600 | + | 0.544748i | \(0.816625\pi\) | |||||||
\(968\) | 6.75252 | + | 7.27749i | 0.217034 | + | 0.233907i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.47821 | + | 1.00782i | −0.0474623 | + | 0.0323593i | ||||
\(971\) | −49.6592 | − | 7.48492i | −1.59364 | − | 0.240202i | −0.708562 | − | 0.705648i | \(-0.750656\pi\) |
−0.885076 | + | 0.465446i | \(0.845894\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.4075 | + | 46.4620i | −0.750412 | + | 1.48950i | ||||
\(974\) | 1.32953 | − | 2.76079i | 0.0426008 | − | 0.0884614i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.9463 | + | 13.9528i | −0.414400 | + | 0.446617i | ||||
\(977\) | 23.9644 | + | 1.79588i | 0.766689 | + | 0.0574554i | 0.452332 | − | 0.891849i | \(-0.350592\pi\) |
0.314357 | + | 0.949305i | \(0.398211\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 10.5502i | − | 0.337187i | ||||||
\(980\) | 21.4050 | + | 0.765951i | 0.683758 | + | 0.0244674i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.484217 | + | 1.23376i | −0.0154520 | + | 0.0393710i | ||||
\(983\) | 3.12311 | − | 41.6749i | 0.0996116 | − | 1.32922i | −0.693636 | − | 0.720325i | \(-0.743992\pi\) |
0.793248 | − | 0.608899i | \(-0.208388\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.1508 | − | 16.3553i | 0.355295 | − | 0.521122i | ||||
\(986\) | −2.92515 | − | 1.40868i | −0.0931557 | − | 0.0448614i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 23.8787 | − | 11.4994i | 0.759683 | − | 0.365844i | ||||
\(989\) | −5.39721 | + | 35.8082i | −0.171621 | + | 1.13863i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.55181 | + | 0.384623i | −0.0810608 | + | 0.0122180i | −0.189447 | − | 0.981891i | \(-0.560670\pi\) |
0.108387 | + | 0.994109i | \(0.465432\pi\) | |||||||
\(992\) | 9.24992 | − | 8.58267i | 0.293685 | − | 0.272500i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.268637 | − | 4.71482i | −0.00852064 | − | 0.149545i | ||||
\(995\) | 10.7935 | + | 8.60755i | 0.342178 | + | 0.272878i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.75188 | + | 21.8891i | −0.213834 | + | 0.693233i | 0.783575 | + | 0.621297i | \(0.213394\pi\) |
−0.997409 | + | 0.0719362i | \(0.977082\pi\) | |||||||
\(998\) | −1.64776 | − | 0.951333i | −0.0521588 | − | 0.0301139i | ||||
\(999\) | 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 | 441.2.bg.a.395.10 | yes | 216 | |
3.2 | odd | 2 | inner | 441.2.bg.a.395.9 | yes | 216 | |
49.33 | odd | 42 | inner | 441.2.bg.a.278.9 | ✓ | 216 | |
147.131 | even | 42 | inner | 441.2.bg.a.278.10 | yes | 216 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.bg.a.278.9 | ✓ | 216 | 49.33 | odd | 42 | inner | |
441.2.bg.a.278.10 | yes | 216 | 147.131 | even | 42 | inner | |
441.2.bg.a.395.9 | yes | 216 | 3.2 | odd | 2 | inner | |
441.2.bg.a.395.10 | yes | 216 | 1.1 | even | 1 | trivial |