Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(49,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.j (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 349.9 | ||
Character | \(\chi\) | \(=\) | 475.349 |
Dual form | 475.2.j.d.49.9 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.28275 | − | 0.740597i | 0.907043 | − | 0.523681i | 0.0275641 | − | 0.999620i | \(-0.491225\pi\) |
0.879478 | + | 0.475939i | \(0.157892\pi\) | |||||||
\(3\) | −0.157277 | + | 0.0908038i | −0.0908038 | + | 0.0524256i | −0.544714 | − | 0.838622i | \(-0.683362\pi\) |
0.453910 | + | 0.891047i | \(0.350029\pi\) | |||||||
\(4\) | 0.0969683 | − | 0.167954i | 0.0484841 | − | 0.0839770i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.134498 | + | 0.232958i | −0.0549086 | + | 0.0951045i | ||||
\(7\) | 1.30422i | 0.492948i | 0.969149 | + | 0.246474i | \(0.0792719\pi\) | ||||
−0.969149 | + | 0.246474i | \(0.920728\pi\) | |||||||
\(8\) | 2.67513i | 0.945802i | ||||||||
\(9\) | −1.48351 | + | 2.56951i | −0.494503 | + | 0.856505i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.98247 | 1.50227 | 0.751136 | − | 0.660147i | \(-0.229506\pi\) | ||||
0.751136 | + | 0.660147i | \(0.229506\pi\) | |||||||
\(12\) | 0.0352204i | 0.0101672i | ||||||||
\(13\) | 0.351723 | + | 0.203067i | 0.0975504 | + | 0.0563207i | 0.547982 | − | 0.836490i | \(-0.315396\pi\) |
−0.450431 | + | 0.892811i | \(0.648730\pi\) | |||||||
\(14\) | 0.965899 | + | 1.67299i | 0.258147 | + | 0.447124i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.17513 | + | 3.76744i | 0.543783 | + | 0.941859i | ||||
\(17\) | 2.38173 | − | 1.37510i | 0.577656 | − | 0.333510i | −0.182546 | − | 0.983197i | \(-0.558434\pi\) |
0.760201 | + | 0.649688i | \(0.225100\pi\) | |||||||
\(18\) | 4.39473i | 1.03585i | ||||||||
\(19\) | 4.35785 | − | 0.0955054i | 0.999760 | − | 0.0219104i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.118428 | − | 0.205123i | −0.0258431 | − | 0.0447615i | ||||
\(22\) | 6.39128 | − | 3.69001i | 1.36262 | − | 0.786712i | ||||
\(23\) | −6.02510 | − | 3.47860i | −1.25632 | − | 0.725337i | −0.283964 | − | 0.958835i | \(-0.591650\pi\) |
−0.972357 | + | 0.233498i | \(0.924983\pi\) | |||||||
\(24\) | −0.242912 | − | 0.420736i | −0.0495842 | − | 0.0858824i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.601564 | 0.117976 | ||||||||
\(27\) | − | 1.08366i | − | 0.208550i | ||||||
\(28\) | 0.219048 | + | 0.126468i | 0.0413963 | + | 0.0239001i | ||||
\(29\) | −2.00728 | + | 3.47672i | −0.372743 | + | 0.645610i | −0.989986 | − | 0.141162i | \(-0.954916\pi\) |
0.617243 | + | 0.786772i | \(0.288249\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.57321 | −0.462163 | −0.231081 | − | 0.972934i | \(-0.574226\pi\) | ||||
−0.231081 | + | 0.972934i | \(0.574226\pi\) | |||||||
\(32\) | 0.946844 | + | 0.546661i | 0.167380 | + | 0.0966369i | ||||
\(33\) | −0.783628 | + | 0.452428i | −0.136412 | + | 0.0787576i | ||||
\(34\) | 2.03678 | − | 3.52781i | 0.349305 | − | 0.605015i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.287707 | + | 0.498323i | 0.0479511 | + | 0.0830538i | ||||
\(37\) | − | 3.71348i | − | 0.610492i | −0.952274 | − | 0.305246i | \(-0.901261\pi\) | ||
0.952274 | − | 0.305246i | \(-0.0987387\pi\) | |||||||
\(38\) | 5.51931 | − | 3.34992i | 0.895351 | − | 0.543429i | ||||
\(39\) | −0.0737572 | −0.0118106 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.607965 | + | 1.05303i | 0.0949482 | + | 0.164455i | 0.909587 | − | 0.415514i | \(-0.136398\pi\) |
−0.814639 | + | 0.579969i | \(0.803065\pi\) | |||||||
\(42\) | −0.303827 | − | 0.175415i | −0.0468816 | − | 0.0270671i | ||||
\(43\) | 2.70426 | − | 1.56130i | 0.412396 | − | 0.238097i | −0.279423 | − | 0.960168i | \(-0.590143\pi\) |
0.691819 | + | 0.722071i | \(0.256810\pi\) | |||||||
\(44\) | 0.483142 | − | 0.836826i | 0.0728364 | − | 0.126156i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.3050 | −1.51938 | ||||||||
\(47\) | −5.63617 | − | 3.25405i | −0.822120 | − | 0.474651i | 0.0290269 | − | 0.999579i | \(-0.490759\pi\) |
−0.851147 | + | 0.524927i | \(0.824093\pi\) | |||||||
\(48\) | −0.684196 | − | 0.395020i | −0.0987551 | − | 0.0570163i | ||||
\(49\) | 5.29902 | 0.757003 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.249728 | + | 0.432541i | −0.0349689 | + | 0.0605679i | ||||
\(52\) | 0.0682119 | − | 0.0393822i | 0.00945929 | − | 0.00546132i | ||||
\(53\) | −5.47490 | − | 3.16094i | −0.752036 | − | 0.434188i | 0.0743934 | − | 0.997229i | \(-0.476298\pi\) |
−0.826429 | + | 0.563041i | \(0.809631\pi\) | |||||||
\(54\) | −0.802553 | − | 1.39006i | −0.109214 | − | 0.189164i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.48895 | −0.466231 | ||||||||
\(57\) | −0.676717 | + | 0.410731i | −0.0896334 | + | 0.0544026i | ||||
\(58\) | 5.94636i | 0.780795i | ||||||||
\(59\) | 5.61636 | + | 9.72783i | 0.731188 | + | 1.26646i | 0.956376 | + | 0.292140i | \(0.0943672\pi\) |
−0.225187 | + | 0.974315i | \(0.572299\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.467072 | + | 0.808992i | −0.0598024 | + | 0.103581i | −0.894377 | − | 0.447315i | \(-0.852380\pi\) |
0.834574 | + | 0.550896i | \(0.185714\pi\) | |||||||
\(62\) | −3.30079 | + | 1.90571i | −0.419201 | + | 0.242026i | ||||
\(63\) | −3.35120 | − | 1.93482i | −0.422212 | − | 0.243764i | ||||
\(64\) | −7.08110 | −0.885138 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.670133 | + | 1.16071i | −0.0824877 | + | 0.142873i | ||||
\(67\) | 4.58585 | + | 2.64764i | 0.560251 | + | 0.323461i | 0.753246 | − | 0.657739i | \(-0.228487\pi\) |
−0.192995 | + | 0.981200i | \(0.561820\pi\) | |||||||
\(68\) | − | 0.533363i | − | 0.0646797i | ||||||
\(69\) | 1.26348 | 0.152105 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.817659 | + | 1.41623i | 0.0970383 | + | 0.168075i | 0.910457 | − | 0.413603i | \(-0.135730\pi\) |
−0.813419 | + | 0.581678i | \(0.802396\pi\) | |||||||
\(72\) | −6.87378 | − | 3.96858i | −0.810083 | − | 0.467702i | ||||
\(73\) | 6.65794 | − | 3.84396i | 0.779252 | − | 0.449902i | −0.0569129 | − | 0.998379i | \(-0.518126\pi\) |
0.836165 | + | 0.548478i | \(0.184792\pi\) | |||||||
\(74\) | −2.75019 | − | 4.76347i | −0.319703 | − | 0.553742i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.406533 | − | 0.741180i | 0.0466325 | − | 0.0850191i | ||||
\(77\) | 6.49822i | 0.740541i | ||||||||
\(78\) | −0.0946121 | + | 0.0546243i | −0.0107127 | + | 0.00618499i | ||||
\(79\) | −7.27699 | − | 12.6041i | −0.818725 | − | 1.41807i | −0.906622 | − | 0.421944i | \(-0.861348\pi\) |
0.0878971 | − | 0.996130i | \(-0.471985\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.35213 | − | 7.53811i | −0.483570 | − | 0.837567i | ||||
\(82\) | 1.55974 | + | 0.900514i | 0.172244 | + | 0.0994452i | ||||
\(83\) | − | 15.2643i | − | 1.67547i | −0.546077 | − | 0.837735i | \(-0.683879\pi\) | ||
0.546077 | − | 0.837735i | \(-0.316121\pi\) | |||||||
\(84\) | −0.0459350 | −0.00501192 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.31260 | − | 4.00553i | 0.249374 | − | 0.431928i | ||||
\(87\) | − | 0.729076i | − | 0.0781652i | ||||||
\(88\) | 13.3288i | 1.42085i | ||||||||
\(89\) | 7.10727 | − | 12.3101i | 0.753369 | − | 1.30487i | −0.192812 | − | 0.981236i | \(-0.561761\pi\) |
0.946181 | − | 0.323638i | \(-0.104906\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.264844 | + | 0.458723i | −0.0277632 | + | 0.0480872i | ||||
\(92\) | −1.16849 | + | 0.674627i | −0.121823 | + | 0.0703347i | ||||
\(93\) | 0.404707 | − | 0.233658i | 0.0419661 | − | 0.0242292i | ||||
\(94\) | −9.63975 | −0.994264 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.198556 | −0.0202650 | ||||||||
\(97\) | −15.8329 | + | 9.14111i | −1.60758 | + | 0.928139i | −0.617676 | + | 0.786433i | \(0.711926\pi\) |
−0.989909 | + | 0.141707i | \(0.954741\pi\) | |||||||
\(98\) | 6.79733 | − | 3.92444i | 0.686634 | − | 0.396428i | ||||
\(99\) | −7.39155 | + | 12.8025i | −0.742878 | + | 1.28670i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.99763 | − | 13.8523i | 0.795794 | − | 1.37836i | −0.126540 | − | 0.991962i | \(-0.540387\pi\) |
0.922334 | − | 0.386394i | \(-0.126280\pi\) | |||||||
\(102\) | 0.739791i | 0.0732502i | ||||||||
\(103\) | 5.30941i | 0.523152i | 0.965183 | + | 0.261576i | \(0.0842422\pi\) | ||||
−0.965183 | + | 0.261576i | \(0.915758\pi\) | |||||||
\(104\) | −0.543232 | + | 0.940905i | −0.0532682 | + | 0.0922633i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.36392 | −0.909504 | ||||||||
\(107\) | 13.0024i | 1.25699i | 0.777814 | + | 0.628494i | \(0.216329\pi\) | ||||
−0.777814 | + | 0.628494i | \(0.783671\pi\) | |||||||
\(108\) | −0.182004 | − | 0.105080i | −0.0175134 | − | 0.0101114i | ||||
\(109\) | −4.09697 | − | 7.09616i | −0.392418 | − | 0.679689i | 0.600350 | − | 0.799738i | \(-0.295028\pi\) |
−0.992768 | + | 0.120049i | \(0.961695\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.337198 | + | 0.584044i | 0.0320054 | + | 0.0554350i | ||||
\(112\) | −4.91355 | + | 2.83684i | −0.464287 | + | 0.268056i | ||||
\(113\) | − | 6.54779i | − | 0.615964i | −0.951392 | − | 0.307982i | \(-0.900346\pi\) | ||
0.951392 | − | 0.307982i | \(-0.0996536\pi\) | |||||||
\(114\) | −0.563874 | + | 1.02804i | −0.0528117 | + | 0.0962848i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.389286 | + | 0.674263i | 0.0361443 | + | 0.0626037i | ||||
\(117\) | −1.04357 | + | 0.602504i | −0.0964779 | + | 0.0557016i | ||||
\(118\) | 14.4088 | + | 8.31892i | 1.32644 | + | 0.765819i | ||||
\(119\) | 1.79342 | + | 3.10630i | 0.164403 | + | 0.284754i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.8250 | 1.25682 | ||||||||
\(122\) | 1.38365i | 0.125270i | ||||||||
\(123\) | −0.191238 | − | 0.110411i | −0.0172433 | − | 0.00995544i | ||||
\(124\) | −0.249520 | + | 0.432181i | −0.0224076 | + | 0.0388110i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.73168 | −0.510619 | ||||||||
\(127\) | 13.0844 | + | 7.55431i | 1.16106 | + | 0.670336i | 0.951557 | − | 0.307472i | \(-0.0994832\pi\) |
0.209500 | + | 0.977809i | \(0.432817\pi\) | |||||||
\(128\) | −10.9770 | + | 6.33757i | −0.970238 | + | 0.560167i | ||||
\(129\) | −0.283545 | + | 0.491114i | −0.0249647 | + | 0.0432402i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.24679 | + | 2.15950i | 0.108933 | + | 0.188677i | 0.915338 | − | 0.402686i | \(-0.131923\pi\) |
−0.806406 | + | 0.591363i | \(0.798590\pi\) | |||||||
\(132\) | 0.175485i | 0.0152740i | ||||||||
\(133\) | 0.124560 | + | 5.68358i | 0.0108007 | + | 0.492829i | ||||
\(134\) | 7.84335 | 0.677562 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.67856 | + | 6.37145i | 0.315434 | + | 0.546348i | ||||
\(137\) | −15.2491 | − | 8.80405i | −1.30282 | − | 0.752181i | −0.321930 | − | 0.946764i | \(-0.604331\pi\) |
−0.980886 | + | 0.194583i | \(0.937665\pi\) | |||||||
\(138\) | 1.62073 | − | 0.935729i | 0.137966 | − | 0.0796546i | ||||
\(139\) | 1.57736 | − | 2.73207i | 0.133790 | − | 0.231731i | −0.791345 | − | 0.611370i | \(-0.790619\pi\) |
0.925135 | + | 0.379639i | \(0.123952\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.18192 | 0.0995356 | ||||||||
\(142\) | 2.09771 | + | 1.21111i | 0.176036 | + | 0.101634i | ||||
\(143\) | 1.75245 | + | 1.01178i | 0.146547 | + | 0.0846091i | ||||
\(144\) | −12.9073 | −1.07561 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.69365 | − | 9.86170i | 0.471210 | − | 0.816160i | ||||
\(147\) | −0.833413 | + | 0.481171i | −0.0687388 | + | 0.0396863i | ||||
\(148\) | −0.623693 | − | 0.360090i | −0.0512673 | − | 0.0295992i | ||||
\(149\) | −3.18694 | − | 5.51994i | −0.261084 | − | 0.452211i | 0.705446 | − | 0.708764i | \(-0.250747\pi\) |
−0.966530 | + | 0.256552i | \(0.917413\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.96340 | 0.403915 | 0.201958 | − | 0.979394i | \(-0.435270\pi\) | ||||
0.201958 | + | 0.979394i | \(0.435270\pi\) | |||||||
\(152\) | 0.255489 | + | 11.6578i | 0.0207229 | + | 0.945575i | ||||
\(153\) | 8.15987i | 0.659686i | ||||||||
\(154\) | 4.81257 | + | 8.33561i | 0.387808 | + | 0.671703i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.00715211 | + | 0.0123878i | −0.000572627 | + | 0.000991819i | ||||
\(157\) | 1.81432 | − | 1.04750i | 0.144798 | − | 0.0835993i | −0.425851 | − | 0.904793i | \(-0.640025\pi\) |
0.570649 | + | 0.821194i | \(0.306692\pi\) | |||||||
\(158\) | −18.6691 | − | 10.7786i | −1.48524 | − | 0.857502i | ||||
\(159\) | 1.14810 | 0.0910503 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.53684 | − | 7.85804i | 0.357553 | − | 0.619300i | ||||
\(162\) | −11.1654 | − | 6.44635i | −0.877237 | − | 0.506473i | ||||
\(163\) | 9.55821i | 0.748656i | 0.927296 | + | 0.374328i | \(0.122127\pi\) | ||||
−0.927296 | + | 0.374328i | \(0.877873\pi\) | |||||||
\(164\) | 0.235813 | 0.0184139 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.3047 | − | 19.5803i | −0.877412 | − | 1.51972i | ||||
\(167\) | 14.4968 | + | 8.36974i | 1.12180 | + | 0.647670i | 0.941859 | − | 0.336008i | \(-0.109077\pi\) |
0.179938 | + | 0.983678i | \(0.442410\pi\) | |||||||
\(168\) | 0.548731 | − | 0.316810i | 0.0423355 | − | 0.0244424i | ||||
\(169\) | −6.41753 | − | 11.1155i | −0.493656 | − | 0.855037i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.21951 | + | 11.3392i | −0.475618 | + | 0.867134i | ||||
\(172\) | − | 0.605588i | − | 0.0461757i | ||||||
\(173\) | 12.1030 | − | 6.98769i | 0.920177 | − | 0.531264i | 0.0364853 | − | 0.999334i | \(-0.488384\pi\) |
0.883691 | + | 0.468070i | \(0.155050\pi\) | |||||||
\(174\) | −0.539952 | − | 0.935224i | −0.0409336 | − | 0.0708992i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.8375 | + | 18.7712i | 0.816910 | + | 1.41493i | ||||
\(177\) | −1.76665 | − | 1.01997i | −0.132789 | − | 0.0766660i | ||||
\(178\) | − | 21.0545i | − | 1.57810i | ||||||
\(179\) | 9.86133 | 0.737071 | 0.368535 | − | 0.929614i | \(-0.379859\pi\) | ||||
0.368535 | + | 0.929614i | \(0.379859\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.38629 | + | 12.7934i | −0.549019 | + | 0.950929i | 0.449323 | + | 0.893369i | \(0.351665\pi\) |
−0.998342 | + | 0.0575593i | \(0.981668\pi\) | |||||||
\(182\) | 0.784570i | 0.0581562i | ||||||||
\(183\) | − | 0.169648i | − | 0.0125407i | ||||||
\(184\) | 9.30570 | − | 16.1179i | 0.686025 | − | 1.18823i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.346092 | − | 0.599450i | 0.0253767 | − | 0.0439538i | ||||
\(187\) | 11.8669 | − | 6.85138i | 0.867796 | − | 0.501022i | ||||
\(188\) | −1.09306 | + | 0.631078i | −0.0797196 | + | 0.0460261i | ||||
\(189\) | 1.41332 | 0.102804 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.6797 | −1.49633 | −0.748166 | − | 0.663512i | \(-0.769065\pi\) | ||||
−0.748166 | + | 0.663512i | \(0.769065\pi\) | |||||||
\(192\) | 1.11369 | − | 0.642991i | 0.0803739 | − | 0.0464039i | ||||
\(193\) | 17.5615 | − | 10.1391i | 1.26410 | − | 0.729831i | 0.290238 | − | 0.956954i | \(-0.406265\pi\) |
0.973866 | + | 0.227123i | \(0.0729320\pi\) | |||||||
\(194\) | −13.5398 | + | 23.4516i | −0.972099 | + | 1.68372i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.513837 | − | 0.889991i | 0.0367026 | − | 0.0635708i | ||||
\(197\) | − | 15.9172i | − | 1.13406i | −0.823698 | − | 0.567028i | \(-0.808093\pi\) | ||
0.823698 | − | 0.567028i | \(-0.191907\pi\) | |||||||
\(198\) | 21.8966i | 1.55613i | ||||||||
\(199\) | −6.61785 | + | 11.4625i | −0.469127 | + | 0.812552i | −0.999377 | − | 0.0352892i | \(-0.988765\pi\) |
0.530250 | + | 0.847841i | \(0.322098\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.961665 | −0.0678306 | ||||||||
\(202\) | − | 23.6921i | − | 1.66697i | ||||||
\(203\) | −4.53439 | − | 2.61793i | −0.318252 | − | 0.183743i | ||||
\(204\) | 0.0484314 | + | 0.0838856i | 0.00339087 | + | 0.00587317i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.93214 | + | 6.81066i | 0.273965 | + | 0.474521i | ||||
\(207\) | 17.8766 | − | 10.3211i | 1.24251 | − | 0.717363i | ||||
\(208\) | 1.76679i | 0.122505i | ||||||||
\(209\) | 21.7129 | − | 0.475853i | 1.50191 | − | 0.0329154i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.88917 | + | 8.46829i | 0.336584 | + | 0.582981i | 0.983788 | − | 0.179336i | \(-0.0573950\pi\) |
−0.647204 | + | 0.762317i | \(0.724062\pi\) | |||||||
\(212\) | −1.06178 | + | 0.613021i | −0.0729236 | + | 0.0421025i | ||||
\(213\) | −0.257198 | − | 0.148493i | −0.0176229 | − | 0.0101746i | ||||
\(214\) | 9.62954 | + | 16.6788i | 0.658262 | + | 1.14014i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.89892 | 0.197247 | ||||||||
\(217\) | − | 3.35603i | − | 0.227822i | ||||||
\(218\) | −10.5108 | − | 6.06841i | −0.711880 | − | 0.411004i | ||||
\(219\) | −0.698093 | + | 1.20913i | −0.0471727 | + | 0.0817056i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.11695 | 0.0751340 | ||||||||
\(222\) | 0.865083 | + | 0.499456i | 0.0580606 | + | 0.0335213i | ||||
\(223\) | −22.3971 | + | 12.9310i | −1.49982 | + | 0.865923i | −1.00000 | 0.000205308i | \(-0.999935\pi\) | |
−0.499822 | + | 0.866128i | \(0.666601\pi\) | |||||||
\(224\) | −0.712964 | + | 1.23489i | −0.0476369 | + | 0.0825095i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.84927 | − | 8.39918i | −0.322569 | − | 0.558705i | ||||
\(227\) | − | 2.28573i | − | 0.151709i | −0.997119 | − | 0.0758545i | \(-0.975832\pi\) | ||
0.997119 | − | 0.0758545i | \(-0.0241684\pi\) | |||||||
\(228\) | 0.00336373 | + | 0.153485i | 0.000222769 | + | 0.0101648i | ||||
\(229\) | 21.8805 | 1.44590 | 0.722952 | − | 0.690898i | \(-0.242785\pi\) | ||||
0.722952 | + | 0.690898i | \(0.242785\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.590064 | − | 1.02202i | −0.0388233 | − | 0.0672440i | ||||
\(232\) | −9.30068 | − | 5.36975i | −0.610619 | − | 0.352541i | ||||
\(233\) | −1.77868 | + | 1.02692i | −0.116525 | + | 0.0672758i | −0.557130 | − | 0.830425i | \(-0.688097\pi\) |
0.440605 | + | 0.897701i | \(0.354764\pi\) | |||||||
\(234\) | −0.892426 | + | 1.54573i | −0.0583397 | + | 0.101047i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.17844 | 0.141804 | ||||||||
\(237\) | 2.28900 | + | 1.32156i | 0.148687 | + | 0.0858443i | ||||
\(238\) | 4.60103 | + | 2.65641i | 0.298241 | + | 0.172189i | ||||
\(239\) | −7.68110 | −0.496849 | −0.248425 | − | 0.968651i | \(-0.579913\pi\) | ||||
−0.248425 | + | 0.968651i | \(0.579913\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.26832 | + | 12.5891i | −0.468194 | + | 0.810935i | −0.999339 | − | 0.0363455i | \(-0.988428\pi\) |
0.531146 | + | 0.847280i | \(0.321762\pi\) | |||||||
\(242\) | 17.7341 | − | 10.2388i | 1.13999 | − | 0.658174i | ||||
\(243\) | 4.18440 | + | 2.41586i | 0.268429 | + | 0.154978i | ||||
\(244\) | 0.0905823 | + | 0.156893i | 0.00579894 | + | 0.0100441i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.327081 | −0.0208539 | ||||||||
\(247\) | 1.55215 | + | 0.851346i | 0.0987610 | + | 0.0541698i | ||||
\(248\) | − | 6.88368i | − | 0.437114i | ||||||
\(249\) | 1.38605 | + | 2.40072i | 0.0878376 | + | 0.152139i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.59365 | + | 6.22439i | −0.226829 | + | 0.392880i | −0.956867 | − | 0.290527i | \(-0.906169\pi\) |
0.730037 | + | 0.683407i | \(0.239503\pi\) | |||||||
\(252\) | −0.649921 | + | 0.375232i | −0.0409412 | + | 0.0236374i | ||||
\(253\) | −30.0199 | − | 17.3320i | −1.88734 | − | 1.08965i | ||||
\(254\) | 22.3788 | 1.40417 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.30606 | + | 3.99422i | −0.144129 | + | 0.249639i | ||||
\(257\) | −7.53951 | − | 4.35294i | −0.470302 | − | 0.271529i | 0.246064 | − | 0.969254i | \(-0.420863\pi\) |
−0.716366 | + | 0.697725i | \(0.754196\pi\) | |||||||
\(258\) | 0.839970i | 0.0522943i | ||||||||
\(259\) | 4.84318 | 0.300940 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.95565 | − | 10.3155i | −0.368645 | − | 0.638513i | ||||
\(262\) | 3.19864 | + | 1.84674i | 0.197613 | + | 0.114092i | ||||
\(263\) | 26.4339 | − | 15.2616i | 1.62998 | − | 0.941072i | 0.645888 | − | 0.763432i | \(-0.276487\pi\) |
0.984096 | − | 0.177639i | \(-0.0568461\pi\) | |||||||
\(264\) | −1.21030 | − | 2.09631i | −0.0744890 | − | 0.129019i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.36903 | + | 7.19838i | 0.267882 | + | 0.441361i | ||||
\(267\) | 2.58147i | 0.157983i | ||||||||
\(268\) | 0.889365 | − | 0.513475i | 0.0543266 | − | 0.0313655i | ||||
\(269\) | −9.20379 | − | 15.9414i | −0.561165 | − | 0.971966i | −0.997395 | − | 0.0721309i | \(-0.977020\pi\) |
0.436230 | − | 0.899835i | \(-0.356313\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.73694 | + | 9.93668i | 0.348494 | + | 0.603610i | 0.985982 | − | 0.166850i | \(-0.0533597\pi\) |
−0.637488 | + | 0.770460i | \(0.720026\pi\) | |||||||
\(272\) | 10.3612 | + | 5.98202i | 0.628238 | + | 0.362714i | ||||
\(273\) | − | 0.0961953i | − | 0.00582201i | ||||||
\(274\) | −26.0810 | −1.57561 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.122517 | − | 0.212206i | 0.00737468 | − | 0.0127733i | ||||
\(277\) | − | 1.79689i | − | 0.107965i | −0.998542 | − | 0.0539823i | \(-0.982809\pi\) | ||
0.998542 | − | 0.0539823i | \(-0.0171914\pi\) | |||||||
\(278\) | − | 4.67276i | − | 0.280253i | ||||||
\(279\) | 3.81739 | − | 6.61191i | 0.228541 | − | 0.395844i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.09550 | − | 12.2898i | 0.423282 | − | 0.733146i | −0.572976 | − | 0.819572i | \(-0.694211\pi\) |
0.996258 | + | 0.0864258i | \(0.0275446\pi\) | |||||||
\(282\) | 1.51611 | − | 0.875326i | 0.0902830 | − | 0.0521249i | ||||
\(283\) | −15.5094 | + | 8.95435i | −0.921938 | + | 0.532281i | −0.884253 | − | 0.467009i | \(-0.845332\pi\) |
−0.0376851 | + | 0.999290i | \(0.511998\pi\) | |||||||
\(284\) | 0.317148 | 0.0188193 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.99728 | 0.177233 | ||||||||
\(287\) | −1.37337 | + | 0.792918i | −0.0810677 | + | 0.0468045i | ||||
\(288\) | −2.80930 | + | 1.62195i | −0.165540 | + | 0.0955744i | ||||
\(289\) | −4.71823 | + | 8.17221i | −0.277543 | + | 0.480718i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.66010 | − | 2.87537i | 0.0973166 | − | 0.168557i | ||||
\(292\) | − | 1.49097i | − | 0.0872524i | ||||||
\(293\) | 33.3088i | 1.94592i | 0.230970 | + | 0.972961i | \(0.425810\pi\) | ||||
−0.230970 | + | 0.972961i | \(0.574190\pi\) | |||||||
\(294\) | −0.712708 | + | 1.23445i | −0.0415660 | + | 0.0719944i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.93404 | 0.577404 | ||||||||
\(297\) | − | 5.39929i | − | 0.313299i | ||||||
\(298\) | −8.17610 | − | 4.72048i | −0.473629 | − | 0.273450i | ||||
\(299\) | −1.41278 | − | 2.44700i | −0.0817031 | − | 0.141514i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.03628 | + | 3.52694i | 0.117369 | + | 0.203289i | ||||
\(302\) | 6.36681 | − | 3.67588i | 0.366369 | − | 0.211523i | ||||
\(303\) | 2.90486i | 0.166880i | ||||||||
\(304\) | 9.83871 | + | 16.2102i | 0.564289 | + | 0.929719i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.04317 | + | 10.4671i | 0.345465 | + | 0.598363i | ||||
\(307\) | 13.4728 | − | 7.77854i | 0.768935 | − | 0.443945i | −0.0635594 | − | 0.997978i | \(-0.520245\pi\) |
0.832495 | + | 0.554033i | \(0.186912\pi\) | |||||||
\(308\) | 1.09140 | + | 0.630122i | 0.0621884 | + | 0.0359045i | ||||
\(309\) | −0.482115 | − | 0.835048i | −0.0274266 | − | 0.0475042i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.1959 | 1.65555 | 0.827773 | − | 0.561063i | \(-0.189608\pi\) | ||||
0.827773 | + | 0.561063i | \(0.189608\pi\) | |||||||
\(312\) | − | 0.197310i | − | 0.0111705i | ||||||
\(313\) | 27.6158 | + | 15.9440i | 1.56094 | + | 0.901207i | 0.997163 | + | 0.0752782i | \(0.0239845\pi\) |
0.563774 | + | 0.825929i | \(0.309349\pi\) | |||||||
\(314\) | 1.55155 | − | 2.68736i | 0.0875588 | − | 0.151656i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.82255 | −0.158781 | ||||||||
\(317\) | 11.7520 | + | 6.78505i | 0.660061 | + | 0.381086i | 0.792300 | − | 0.610131i | \(-0.208883\pi\) |
−0.132239 | + | 0.991218i | \(0.542217\pi\) | |||||||
\(318\) | 1.47273 | − | 0.850280i | 0.0825865 | − | 0.0476813i | ||||
\(319\) | −10.0012 | + | 17.3227i | −0.559962 | + | 0.969882i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.18067 | − | 2.04498i | −0.0658984 | − | 0.114139i | ||||
\(322\) | − | 13.4399i | − | 0.748976i | ||||||
\(323\) | 10.2479 | − | 6.21993i | 0.570210 | − | 0.346086i | ||||
\(324\) | −1.68807 | −0.0937819 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.07878 | + | 12.2608i | 0.392057 | + | 0.679063i | ||||
\(327\) | 1.28872 | + | 0.744041i | 0.0712662 | + | 0.0411456i | ||||
\(328\) | −2.81698 | + | 1.62639i | −0.155542 | + | 0.0898022i | ||||
\(329\) | 4.24398 | − | 7.35079i | 0.233978 | − | 0.405262i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.4274 | −1.61747 | −0.808737 | − | 0.588171i | \(-0.799848\pi\) | ||||
−0.808737 | + | 0.588171i | \(0.799848\pi\) | |||||||
\(332\) | −2.56369 | − | 1.48015i | −0.140701 | − | 0.0812337i | ||||
\(333\) | 9.54183 | + | 5.50898i | 0.522889 | + | 0.301890i | ||||
\(334\) | 24.7944 | 1.35669 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.515192 | − | 0.892339i | 0.0281060 | − | 0.0486811i | ||||
\(337\) | −13.4336 | + | 7.75588i | −0.731773 | + | 0.422489i | −0.819071 | − | 0.573693i | \(-0.805510\pi\) |
0.0872973 | + | 0.996182i | \(0.472177\pi\) | |||||||
\(338\) | −16.4642 | − | 9.50560i | −0.895534 | − | 0.517037i | ||||
\(339\) | 0.594564 | + | 1.02982i | 0.0322923 | + | 0.0559319i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.8210 | −0.694294 | ||||||||
\(342\) | 0.419720 | + | 19.1516i | 0.0226959 | + | 1.03560i | ||||
\(343\) | 16.0406i | 0.866110i | ||||||||
\(344\) | 4.17669 | + | 7.23425i | 0.225192 | + | 0.390044i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.3501 | − | 17.9269i | 0.556426 | − | 0.963759i | ||||
\(347\) | −19.5615 | + | 11.2938i | −1.05012 | + | 0.606285i | −0.922682 | − | 0.385562i | \(-0.874008\pi\) |
−0.127434 | + | 0.991847i | \(0.540674\pi\) | |||||||
\(348\) | −0.122451 | − | 0.0706973i | −0.00656408 | − | 0.00378977i | ||||
\(349\) | −25.4885 | −1.36437 | −0.682184 | − | 0.731181i | \(-0.738970\pi\) | ||||
−0.682184 | + | 0.731181i | \(0.738970\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.220055 | − | 0.381147i | 0.0117457 | − | 0.0203441i | ||||
\(352\) | 4.71762 | + | 2.72372i | 0.251450 | + | 0.145175i | ||||
\(353\) | − | 10.2959i | − | 0.547994i | −0.961730 | − | 0.273997i | \(-0.911654\pi\) | ||
0.961730 | − | 0.273997i | \(-0.0883459\pi\) | |||||||
\(354\) | −3.02156 | −0.160594 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.37836 | − | 2.38739i | −0.0730529 | − | 0.126531i | ||||
\(357\) | −0.564128 | − | 0.325699i | −0.0298568 | − | 0.0172378i | ||||
\(358\) | 12.6496 | − | 7.30328i | 0.668555 | − | 0.385990i | ||||
\(359\) | 0.991256 | + | 1.71691i | 0.0523165 | + | 0.0906148i | 0.890998 | − | 0.454008i | \(-0.150006\pi\) |
−0.838681 | + | 0.544623i | \(0.816673\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9818 | − | 0.832397i | 0.999040 | − | 0.0438103i | ||||
\(362\) | 21.8811i | 1.15004i | ||||||||
\(363\) | −2.17436 | + | 1.25537i | −0.114124 | + | 0.0658897i | ||||
\(364\) | 0.0513629 | + | 0.0889631i | 0.00269215 | + | 0.00466294i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.125641 | − | 0.217616i | −0.00656734 | − | 0.0113750i | ||||
\(367\) | 4.56763 | + | 2.63712i | 0.238428 | + | 0.137657i | 0.614454 | − | 0.788953i | \(-0.289376\pi\) |
−0.376026 | + | 0.926609i | \(0.622710\pi\) | |||||||
\(368\) | − | 30.2656i | − | 1.57770i | ||||||
\(369\) | −3.60769 | −0.187809 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.12255 | − | 7.14046i | 0.214032 | − | 0.370714i | ||||
\(372\) | − | 0.0906295i | − | 0.00469892i | ||||||
\(373\) | 31.7192i | 1.64236i | 0.570670 | + | 0.821179i | \(0.306683\pi\) | ||||
−0.570670 | + | 0.821179i | \(0.693317\pi\) | |||||||
\(374\) | 10.1482 | − | 17.5772i | 0.524752 | − | 0.908897i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.70500 | − | 15.0775i | 0.448926 | − | 0.777563i | ||||
\(377\) | −1.41202 | + | 0.815227i | −0.0727225 | + | 0.0419863i | ||||
\(378\) | 1.81294 | − | 1.04670i | 0.0932477 | − | 0.0538366i | ||||
\(379\) | −35.5119 | −1.82412 | −0.912062 | − | 0.410052i | \(-0.865510\pi\) | ||||
−0.912062 | + | 0.410052i | \(0.865510\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.74384 | −0.140571 | ||||||||
\(382\) | −26.5269 | + | 15.3153i | −1.35724 | + | 0.783601i | ||||
\(383\) | −12.0639 | + | 6.96509i | −0.616436 | + | 0.355899i | −0.775480 | − | 0.631372i | \(-0.782492\pi\) |
0.159044 | + | 0.987271i | \(0.449159\pi\) | |||||||
\(384\) | 1.15095 | − | 1.99350i | 0.0587342 | − | 0.101731i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15.0180 | − | 26.0120i | 0.764398 | − | 1.32398i | ||||
\(387\) | 9.26484i | 0.470958i | ||||||||
\(388\) | 3.54559i | 0.180000i | ||||||||
\(389\) | −0.471434 | + | 0.816548i | −0.0239027 | + | 0.0414006i | −0.877729 | − | 0.479157i | \(-0.840943\pi\) |
0.853827 | + | 0.520557i | \(0.174276\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.1336 | −0.967628 | ||||||||
\(392\) | 14.1756i | 0.715974i | ||||||||
\(393\) | −0.392183 | − | 0.226427i | −0.0197830 | − | 0.0114217i | ||||
\(394\) | −11.7883 | − | 20.4179i | −0.593884 | − | 1.02864i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.43349 | + | 2.48288i | 0.0720356 | + | 0.124769i | ||||
\(397\) | −24.7386 | + | 14.2828i | −1.24159 | + | 0.716834i | −0.969418 | − | 0.245414i | \(-0.921076\pi\) |
−0.272174 | + | 0.962248i | \(0.587743\pi\) | |||||||
\(398\) | 19.6047i | 0.982693i | ||||||||
\(399\) | −0.535682 | − | 0.882586i | −0.0268176 | − | 0.0441846i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.58365 | + | 6.20707i | 0.178959 | + | 0.309966i | 0.941524 | − | 0.336945i | \(-0.109394\pi\) |
−0.762565 | + | 0.646911i | \(0.776060\pi\) | |||||||
\(402\) | −1.23358 | + | 0.712206i | −0.0615252 | + | 0.0355216i | ||||
\(403\) | −0.905058 | − | 0.522535i | −0.0450841 | − | 0.0260293i | ||||
\(404\) | −1.55103 | − | 2.68647i | −0.0771668 | − | 0.133657i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.75534 | −0.384891 | ||||||||
\(407\) | − | 18.5023i | − | 0.917125i | ||||||
\(408\) | −1.15710 | − | 0.668055i | −0.0572852 | − | 0.0330736i | ||||
\(409\) | −5.26624 | + | 9.12140i | −0.260399 | + | 0.451024i | −0.966348 | − | 0.257238i | \(-0.917187\pi\) |
0.705949 | + | 0.708263i | \(0.250521\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.19777 | 0.157734 | ||||||||
\(412\) | 0.891737 | + | 0.514845i | 0.0439327 | + | 0.0253646i | ||||
\(413\) | −12.6872 | + | 7.32495i | −0.624296 | + | 0.360437i | ||||
\(414\) | 15.2875 | − | 26.4787i | 0.751339 | − | 1.30136i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.222018 | + | 0.384546i | 0.0108853 | + | 0.0188539i | ||||
\(417\) | 0.572922i | 0.0280561i | ||||||||
\(418\) | 27.4998 | − | 16.6909i | 1.34506 | − | 0.816379i | ||||
\(419\) | −2.52693 | −0.123448 | −0.0617242 | − | 0.998093i | \(-0.519660\pi\) | ||||
−0.0617242 | + | 0.998093i | \(0.519660\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.43346 | − | 12.8751i | −0.362285 | − | 0.627495i | 0.626052 | − | 0.779781i | \(-0.284670\pi\) |
−0.988336 | + | 0.152286i | \(0.951336\pi\) | |||||||
\(422\) | 12.5432 | + | 7.24181i | 0.610592 | + | 0.352526i | ||||
\(423\) | 16.7226 | − | 9.65481i | 0.813082 | − | 0.469433i | ||||
\(424\) | 8.45592 | − | 14.6461i | 0.410656 | − | 0.711276i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.439895 | −0.0213130 | ||||||||
\(427\) | −1.05510 | − | 0.609163i | −0.0510599 | − | 0.0294794i | ||||
\(428\) | 2.18380 | + | 1.26082i | 0.105558 | + | 0.0609440i | ||||
\(429\) | −0.367493 | −0.0177427 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.09034 | − | 3.62057i | 0.100688 | − | 0.174397i | −0.811280 | − | 0.584657i | \(-0.801229\pi\) |
0.911968 | + | 0.410261i | \(0.134562\pi\) | |||||||
\(432\) | 4.08261 | − | 2.35709i | 0.196425 | − | 0.113406i | ||||
\(433\) | −21.9150 | − | 12.6527i | −1.05317 | − | 0.608048i | −0.129635 | − | 0.991562i | \(-0.541380\pi\) |
−0.923535 | + | 0.383514i | \(0.874714\pi\) | |||||||
\(434\) | −2.48546 | − | 4.30495i | −0.119306 | − | 0.206644i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.58910 | −0.0761043 | ||||||||
\(437\) | −26.5887 | − | 14.5838i | −1.27191 | − | 0.697637i | ||||
\(438\) | 2.06802i | 0.0988139i | ||||||||
\(439\) | 14.4561 | + | 25.0386i | 0.689950 | + | 1.19503i | 0.971854 | + | 0.235585i | \(0.0757008\pi\) |
−0.281904 | + | 0.959443i | \(0.590966\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.86114 | + | 13.6159i | −0.374340 | + | 0.648376i | ||||
\(442\) | 1.43277 | − | 0.827208i | 0.0681498 | − | 0.0393463i | ||||
\(443\) | −3.97388 | − | 2.29432i | −0.188805 | − | 0.109007i | 0.402618 | − | 0.915368i | \(-0.368100\pi\) |
−0.591423 | + | 0.806362i | \(0.701434\pi\) | |||||||
\(444\) | 0.130790 | 0.00620702 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −19.1533 | + | 33.1745i | −0.906935 | + | 1.57086i | ||||
\(447\) | 1.00246 | + | 0.578773i | 0.0474149 | + | 0.0273750i | ||||
\(448\) | − | 9.23529i | − | 0.436327i | ||||||
\(449\) | −29.2171 | −1.37884 | −0.689420 | − | 0.724362i | \(-0.742135\pi\) | ||||
−0.689420 | + | 0.724362i | \(0.742135\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.02917 | + | 5.24668i | 0.142638 | + | 0.247056i | ||||
\(452\) | −1.09973 | − | 0.634928i | −0.0517268 | − | 0.0298645i | ||||
\(453\) | −0.780628 | + | 0.450696i | −0.0366771 | + | 0.0211755i | ||||
\(454\) | −1.69280 | − | 2.93202i | −0.0794471 | − | 0.137606i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.09876 | − | 1.81031i | −0.0514541 | − | 0.0847754i | ||||
\(457\) | − | 23.7113i | − | 1.10917i | −0.832128 | − | 0.554584i | \(-0.812878\pi\) | ||
0.832128 | − | 0.554584i | \(-0.187122\pi\) | |||||||
\(458\) | 28.0673 | − | 16.2046i | 1.31150 | − | 0.757193i | ||||
\(459\) | −1.49013 | − | 2.58098i | −0.0695534 | − | 0.120470i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.5109 | − | 30.3298i | −0.815565 | − | 1.41260i | −0.908922 | − | 0.416967i | \(-0.863093\pi\) |
0.0933568 | − | 0.995633i | \(-0.470240\pi\) | |||||||
\(462\) | −1.51381 | − | 0.873999i | −0.0704289 | − | 0.0406621i | ||||
\(463\) | − | 20.4936i | − | 0.952417i | −0.879332 | − | 0.476209i | \(-0.842011\pi\) | ||
0.879332 | − | 0.476209i | \(-0.157989\pi\) | |||||||
\(464\) | −17.4644 | −0.810765 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.52107 | + | 2.63457i | −0.0704621 | + | 0.122044i | ||||
\(467\) | 9.24346i | 0.427736i | 0.976863 | + | 0.213868i | \(0.0686063\pi\) | ||||
−0.976863 | + | 0.213868i | \(0.931394\pi\) | |||||||
\(468\) | 0.233695i | 0.0108026i | ||||||||
\(469\) | −3.45310 | + | 5.98095i | −0.159449 | + | 0.276174i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.190233 | + | 0.329494i | −0.00876549 | + | 0.0151823i | ||||
\(472\) | −26.0232 | + | 15.0245i | −1.19782 | + | 0.691559i | ||||
\(473\) | 13.4739 | − | 7.77916i | 0.619530 | − | 0.357686i | ||||
\(474\) | 3.91496 | 0.179820 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.695620 | 0.0318837 | ||||||||
\(477\) | 16.2441 | − | 9.37856i | 0.743768 | − | 0.429415i | ||||
\(478\) | −9.85295 | + | 5.68860i | −0.450663 | + | 0.260191i | ||||
\(479\) | 1.88377 | − | 3.26278i | 0.0860715 | − | 0.149080i | −0.819776 | − | 0.572685i | \(-0.805902\pi\) |
0.905847 | + | 0.423604i | \(0.139235\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.754086 | − | 1.30611i | 0.0343834 | − | 0.0595537i | ||||
\(482\) | 21.5316i | 0.980737i | ||||||||
\(483\) | 1.64785i | 0.0749798i | ||||||||
\(484\) | 1.34059 | − | 2.32197i | 0.0609359 | − | 0.105544i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 7.15673 | 0.324636 | ||||||||
\(487\) | 11.7981i | 0.534621i | 0.963610 | + | 0.267311i | \(0.0861349\pi\) | ||||
−0.963610 | + | 0.267311i | \(0.913865\pi\) | |||||||
\(488\) | −2.16416 | − | 1.24948i | −0.0979669 | − | 0.0565612i | ||||
\(489\) | −0.867922 | − | 1.50328i | −0.0392488 | − | 0.0679809i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.91782 | − | 6.78586i | −0.176809 | − | 0.306241i | 0.763977 | − | 0.645243i | \(-0.223244\pi\) |
−0.940786 | + | 0.339002i | \(0.889911\pi\) | |||||||
\(492\) | −0.0370880 | + | 0.0214128i | −0.00167206 | + | 0.000965362i | ||||
\(493\) | 11.0408i | 0.497254i | ||||||||
\(494\) | 2.62153 | − | 0.0574526i | 0.117948 | − | 0.00258491i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.59707 | − | 9.69442i | −0.251316 | − | 0.435292i | ||||
\(497\) | −1.84707 | + | 1.06641i | −0.0828523 | + | 0.0478348i | ||||
\(498\) | 3.55593 | + | 2.05301i | 0.159345 | + | 0.0919978i | ||||
\(499\) | 0.529796 | + | 0.917633i | 0.0237169 | + | 0.0410789i | 0.877640 | − | 0.479320i | \(-0.159117\pi\) |
−0.853923 | + | 0.520399i | \(0.825783\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.04002 | −0.135818 | ||||||||
\(502\) | 10.6458i | 0.475145i | ||||||||
\(503\) | 4.65671 | + | 2.68855i | 0.207633 | + | 0.119877i | 0.600211 | − | 0.799842i | \(-0.295083\pi\) |
−0.392578 | + | 0.919719i | \(0.628417\pi\) | |||||||
\(504\) | 5.17589 | − | 8.96490i | 0.230552 | − | 0.399329i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −51.3441 | −2.28253 | ||||||||
\(507\) | 2.01866 | + | 1.16547i | 0.0896517 | + | 0.0517604i | ||||
\(508\) | 2.53755 | − | 1.46506i | 0.112586 | − | 0.0650014i | ||||
\(509\) | 16.9240 | − | 29.3132i | 0.750142 | − | 1.29928i | −0.197611 | − | 0.980280i | \(-0.563318\pi\) |
0.947753 | − | 0.319004i | \(-0.103348\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.01336 | + | 8.68339i | 0.221778 | + | 0.384131i | ||||
\(512\) | − | 18.5188i | − | 0.818423i | ||||||
\(513\) | −0.103495 | − | 4.72242i | −0.00456942 | − | 0.208500i | ||||
\(514\) | −12.8951 | −0.568778 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.0549897 | + | 0.0952450i | 0.00242079 | + | 0.00419293i | ||||
\(517\) | −28.0821 | − | 16.2132i | −1.23505 | − | 0.713056i | ||||
\(518\) | 6.21260 | − | 3.58684i | 0.272966 | − | 0.157597i | ||||
\(519\) | −1.26902 | + | 2.19800i | −0.0557037 | + | 0.0964817i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.5742 | −1.29567 | −0.647834 | − | 0.761782i | \(-0.724325\pi\) | ||||
−0.647834 | + | 0.761782i | \(0.724325\pi\) | |||||||
\(522\) | −15.2792 | − | 8.82147i | −0.668754 | − | 0.386105i | ||||
\(523\) | −20.8232 | − | 12.0223i | −0.910536 | − | 0.525698i | −0.0299323 | − | 0.999552i | \(-0.509529\pi\) |
−0.880604 | + | 0.473854i | \(0.842863\pi\) | |||||||
\(524\) | 0.483596 | 0.0211260 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.6054 | − | 39.1537i | 0.985643 | − | 1.70718i | ||||
\(527\) | −6.12871 | + | 3.53841i | −0.266971 | + | 0.154136i | ||||
\(528\) | −3.40899 | − | 1.96818i | −0.148357 | − | 0.0856540i | ||||
\(529\) | 12.7013 | + | 21.9992i | 0.552228 | + | 0.956488i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −33.3277 | −1.44630 | ||||||||
\(532\) | 0.966659 | + | 0.530207i | 0.0419100 | + | 0.0229874i | ||||
\(533\) | 0.493831i | 0.0213902i | ||||||||
\(534\) | 1.91183 | + | 3.31138i | 0.0827329 | + | 0.143298i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.08279 | + | 12.2678i | −0.305930 | + | 0.529886i | ||||
\(537\) | −1.55096 | + | 0.895447i | −0.0669289 | + | 0.0386414i | ||||
\(538\) | −23.6124 | − | 13.6326i | −1.01800 | − | 0.587743i | ||||
\(539\) | 26.4022 | 1.13722 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.0959 | − | 22.6827i | 0.563035 | − | 0.975205i | −0.434195 | − | 0.900819i | \(-0.642967\pi\) |
0.997230 | − | 0.0743856i | \(-0.0236996\pi\) | |||||||
\(542\) | 14.7181 | + | 8.49753i | 0.632199 | + | 0.365000i | ||||
\(543\) | − | 2.68282i | − | 0.115131i | ||||||
\(544\) | 3.00684 | 0.128917 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.0712420 | − | 0.123395i | −0.00304888 | − | 0.00528081i | ||||
\(547\) | −12.9284 | − | 7.46421i | −0.552778 | − | 0.319146i | 0.197464 | − | 0.980310i | \(-0.436730\pi\) |
−0.750242 | + | 0.661164i | \(0.770063\pi\) | |||||||
\(548\) | −2.95735 | + | 1.70743i | −0.126332 | + | 0.0729377i | ||||
\(549\) | −1.38581 | − | 2.40029i | −0.0591449 | − | 0.102442i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.41540 | + | 15.3427i | −0.358508 | + | 0.653622i | ||||
\(552\) | 3.37997i | 0.143861i | ||||||||
\(553\) | 16.4385 | − | 9.49077i | 0.699036 | − | 0.403588i | ||||
\(554\) | −1.33077 | − | 2.30496i | −0.0565390 | − | 0.0979284i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.305908 | − | 0.529848i | −0.0129734 | − | 0.0224706i | ||||
\(557\) | −4.56841 | − | 2.63757i | −0.193570 | − | 0.111758i | 0.400083 | − | 0.916479i | \(-0.368981\pi\) |
−0.593653 | + | 0.804721i | \(0.702315\pi\) | |||||||
\(558\) | − | 11.3086i | − | 0.478730i | ||||||
\(559\) | 1.26820 | 0.0536391 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.24426 | + | 2.15513i | −0.0525328 | + | 0.0909895i | ||||
\(562\) | − | 21.0196i | − | 0.886660i | ||||||
\(563\) | 17.8950i | 0.754186i | 0.926175 | + | 0.377093i | \(0.123076\pi\) | ||||
−0.926175 | + | 0.377093i | \(0.876924\pi\) | |||||||
\(564\) | 0.114609 | − | 0.198508i | 0.00482590 | − | 0.00835870i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13.2631 | + | 22.9724i | −0.557491 | + | 0.965603i | ||||
\(567\) | 9.83132 | − | 5.67612i | 0.412877 | − | 0.238375i | ||||
\(568\) | −3.78859 | + | 2.18735i | −0.158966 | + | 0.0917790i | ||||
\(569\) | −6.81848 | −0.285846 | −0.142923 | − | 0.989734i | \(-0.545650\pi\) | ||||
−0.142923 | + | 0.989734i | \(0.545650\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.16915 | 0.216322 | 0.108161 | − | 0.994133i | \(-0.465504\pi\) | ||||
0.108161 | + | 0.994133i | \(0.465504\pi\) | |||||||
\(572\) | 0.339864 | − | 0.196221i | 0.0142104 | − | 0.00820440i | ||||
\(573\) | 3.25244 | − | 1.87780i | 0.135873 | − | 0.0784461i | ||||
\(574\) | −1.17447 | + | 2.03423i | −0.0490213 | + | 0.0849073i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 10.5049 | − | 18.1950i | 0.437703 | − | 0.758125i | ||||
\(577\) | 28.5621i | 1.18905i | 0.804076 | + | 0.594527i | \(0.202661\pi\) | ||||
−0.804076 | + | 0.594527i | \(0.797339\pi\) | |||||||
\(578\) | 13.9772i | 0.581376i | ||||||||
\(579\) | −1.84135 | + | 3.18930i | −0.0765237 | + | 0.132543i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.9079 | 0.825919 | ||||||||
\(582\) | − | 4.91785i | − | 0.203851i | ||||||
\(583\) | −27.2786 | − | 15.7493i | −1.12976 | − | 0.652269i | ||||
\(584\) | 10.2831 | + | 17.8108i | 0.425518 | + | 0.737018i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.6684 | + | 42.7269i | 1.01904 | + | 1.76503i | ||||
\(587\) | 34.9228 | − | 20.1627i | 1.44142 | − | 0.832204i | 0.443476 | − | 0.896286i | \(-0.353745\pi\) |
0.997945 | + | 0.0640822i | \(0.0204120\pi\) | |||||||
\(588\) | 0.186633i | 0.00769663i | ||||||||
\(589\) | −11.2137 | + | 0.245756i | −0.462052 | + | 0.0101262i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.44535 | + | 2.50341i | 0.0594536 | + | 0.102977i | ||||
\(592\) | 13.9903 | − | 8.07730i | 0.574997 | − | 0.331975i | ||||
\(593\) | 23.9806 | + | 13.8452i | 0.984767 | + | 0.568555i | 0.903706 | − | 0.428154i | \(-0.140836\pi\) |
0.0810610 | + | 0.996709i | \(0.474169\pi\) | |||||||
\(594\) | −3.99870 | − | 6.92595i | −0.164069 | − | 0.284175i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.23613 | −0.0506338 | ||||||||
\(597\) | − | 2.40371i | − | 0.0983771i | ||||||
\(598\) | −3.62449 | − | 2.09260i | −0.148216 | − | 0.0855727i | ||||
\(599\) | −1.31466 | + | 2.27706i | −0.0537156 | + | 0.0930382i | −0.891633 | − | 0.452759i | \(-0.850440\pi\) |
0.837917 | + | 0.545797i | \(0.183773\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.7009 | 1.12994 | 0.564972 | − | 0.825110i | \(-0.308887\pi\) | ||||
0.564972 | + | 0.825110i | \(0.308887\pi\) | |||||||
\(602\) | 5.22408 | + | 3.01613i | 0.212918 | + | 0.122928i | ||||
\(603\) | −13.6063 | + | 7.85561i | −0.554092 | + | 0.319905i | ||||
\(604\) | 0.481292 | − | 0.833622i | 0.0195835 | − | 0.0339196i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.15133 | + | 3.72622i | 0.0873919 | + | 0.151367i | ||||
\(607\) | 32.0668i | 1.30155i | 0.759271 | + | 0.650775i | \(0.225556\pi\) | ||||
−0.759271 | + | 0.650775i | \(0.774444\pi\) | |||||||
\(608\) | 4.17842 | + | 2.29184i | 0.169457 | + | 0.0929463i | ||||
\(609\) | 0.950874 | 0.0385313 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.32158 | − | 2.28904i | −0.0534654 | − | 0.0926048i | ||||
\(612\) | 1.37048 | + | 0.791248i | 0.0553985 | + | 0.0319843i | ||||
\(613\) | 10.7909 | − | 6.23014i | 0.435841 | − | 0.251633i | −0.265991 | − | 0.963976i | \(-0.585699\pi\) |
0.701832 | + | 0.712343i | \(0.252366\pi\) | |||||||
\(614\) | 11.5215 | − | 19.9559i | 0.464971 | − | 0.805354i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −17.3836 | −0.700405 | ||||||||
\(617\) | −22.9271 | − | 13.2370i | −0.923009 | − | 0.532900i | −0.0384155 | − | 0.999262i | \(-0.512231\pi\) |
−0.884594 | + | 0.466362i | \(0.845564\pi\) | |||||||
\(618\) | −1.23687 | − | 0.714106i | −0.0497541 | − | 0.0287256i | ||||
\(619\) | −33.3766 | −1.34152 | −0.670760 | − | 0.741674i | \(-0.734032\pi\) | ||||
−0.670760 | + | 0.741674i | \(0.734032\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.76960 | + | 6.52914i | −0.151269 | + | 0.262005i | ||||
\(622\) | 37.4511 | − | 21.6224i | 1.50165 | − | 0.866978i | ||||
\(623\) | 16.0551 | + | 9.26942i | 0.643234 | + | 0.371371i | ||||
\(624\) | −0.160431 | − | 0.277875i | −0.00642240 | − | 0.0111239i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 47.2323 | 1.88778 | ||||||||
\(627\) | −3.37173 | + | 2.04645i | −0.134654 | + | 0.0817275i | ||||
\(628\) | − | 0.406296i | − | 0.0162130i | ||||||
\(629\) | −5.10638 | − | 8.84452i | −0.203605 | − | 0.352654i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.0601 | + | 34.7450i | −0.798578 | + | 1.38318i | 0.121964 | + | 0.992535i | \(0.461081\pi\) |
−0.920542 | + | 0.390643i | \(0.872253\pi\) | |||||||
\(632\) | 33.7176 | − | 19.4669i | 1.34122 | − | 0.774351i | ||||
\(633\) | −1.53791 | − | 0.887911i | −0.0611263 | − | 0.0352913i | ||||
\(634\) | 20.1000 | 0.798271 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.111329 | − | 0.192828i | 0.00441450 | − | 0.00764613i | ||||
\(637\) | 1.86379 | + | 1.07606i | 0.0738459 | + | 0.0426349i | ||||
\(638\) | 29.6276i | 1.17297i | ||||||||
\(639\) | −4.85202 | −0.191943 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.203273 | − | 0.352079i | −0.00802880 | − | 0.0139063i | 0.861983 | − | 0.506937i | \(-0.169222\pi\) |
−0.870012 | + | 0.493031i | \(0.835889\pi\) | |||||||
\(642\) | −3.02901 | − | 1.74880i | −0.119545 | − | 0.0690195i | ||||
\(643\) | −21.7975 | + | 12.5848i | −0.859610 | + | 0.496296i | −0.863882 | − | 0.503695i | \(-0.831974\pi\) |
0.00427137 | + | 0.999991i | \(0.498640\pi\) | |||||||
\(644\) | −0.879860 | − | 1.52396i | −0.0346713 | − | 0.0600525i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.53908 | − | 15.5682i | 0.335965 | − | 0.612523i | ||||
\(647\) | − | 18.3604i | − | 0.721821i | −0.932600 | − | 0.360911i | \(-0.882466\pi\) | ||
0.932600 | − | 0.360911i | \(-0.117534\pi\) | |||||||
\(648\) | 20.1654 | − | 11.6425i | 0.792173 | − | 0.457361i | ||||
\(649\) | 27.9834 | + | 48.4686i | 1.09844 | + | 1.90256i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.304740 | + | 0.527825i | 0.0119437 | + | 0.0206871i | ||||
\(652\) | 1.60534 | + | 0.926843i | 0.0628699 | + | 0.0362980i | ||||
\(653\) | 33.0301i | 1.29257i | 0.763097 | + | 0.646284i | \(0.223678\pi\) | ||||
−0.763097 | + | 0.646284i | \(0.776322\pi\) | |||||||
\(654\) | 2.20414 | 0.0861886 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.64481 | + | 4.58094i | −0.103262 | + | 0.178856i | ||||
\(657\) | 22.8102i | 0.889911i | ||||||||
\(658\) | − | 12.5723i | − | 0.490120i | ||||||
\(659\) | −13.2310 | + | 22.9167i | −0.515406 | + | 0.892709i | 0.484434 | + | 0.874828i | \(0.339025\pi\) |
−0.999840 | + | 0.0178814i | \(0.994308\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.79673 | − | 13.5043i | 0.303258 | − | 0.525258i | −0.673614 | − | 0.739083i | \(-0.735259\pi\) |
0.976872 | + | 0.213825i | \(0.0685924\pi\) | |||||||
\(662\) | −37.7480 | + | 21.7938i | −1.46712 | + | 0.847041i | ||||
\(663\) | −0.175670 | + | 0.101423i | −0.00682246 | + | 0.00393895i | ||||
\(664\) | 40.8339 | 1.58466 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 16.3197 | 0.632377 | ||||||||
\(667\) | 24.1882 | − | 13.9651i | 0.936570 | − | 0.540729i | ||||
\(668\) | 2.81146 | − | 1.62320i | 0.108779 | − | 0.0628034i | ||||
\(669\) | 2.34837 | − | 4.06749i | 0.0907931 | − | 0.157258i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.32717 | + | 4.03078i | −0.0898395 | + | 0.155607i | ||||
\(672\) | − | 0.258959i | − | 0.00998958i | ||||||
\(673\) | − | 6.13645i | − | 0.236543i | −0.992981 | − | 0.118271i | \(-0.962265\pi\) | ||
0.992981 | − | 0.118271i | \(-0.0377353\pi\) | |||||||
\(674\) | −11.4880 | + | 19.8977i | −0.442500 | + | 0.766432i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.48919 | −0.0957379 | ||||||||
\(677\) | − | 22.2754i | − | 0.856112i | −0.903752 | − | 0.428056i | \(-0.859199\pi\) | ||
0.903752 | − | 0.428056i | \(-0.140801\pi\) | |||||||
\(678\) | 1.52536 | + | 0.880665i | 0.0585810 | + | 0.0338217i | ||||
\(679\) | −11.9220 | − | 20.6495i | −0.457524 | − | 0.792455i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.207553 | + | 0.359492i | 0.00795344 | + | 0.0137758i | ||||
\(682\) | −16.4461 | + | 9.49517i | −0.629754 | + | 0.363589i | ||||
\(683\) | 16.7397i | 0.640527i | 0.947328 | + | 0.320264i | \(0.103772\pi\) | ||||
−0.947328 | + | 0.320264i | \(0.896228\pi\) | |||||||
\(684\) | 1.30138 | + | 2.14414i | 0.0497594 | + | 0.0819832i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 11.8796 | + | 20.5761i | 0.453566 | + | 0.785599i | ||||
\(687\) | −3.44130 | + | 1.98683i | −0.131294 | + | 0.0758024i | ||||
\(688\) | 11.7642 | + | 6.79208i | 0.448507 | + | 0.258946i | ||||
\(689\) | −1.28377 | − | 2.22355i | −0.0489076 | − | 0.0847104i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.7557 | 1.39825 | 0.699126 | − | 0.714999i | \(-0.253573\pi\) | ||||
0.699126 | + | 0.714999i | \(0.253573\pi\) | |||||||
\(692\) | − | 2.71034i | − | 0.103032i | ||||||
\(693\) | −16.6973 | − | 9.64018i | −0.634277 | − | 0.366200i | ||||
\(694\) | −16.7284 | + | 28.9744i | −0.635000 | + | 1.09985i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.95037 | 0.0739288 | ||||||||
\(697\) | 2.89602 | + | 1.67202i | 0.109695 | + | 0.0633323i | ||||
\(698\) | −32.6954 | + | 18.8767i | −1.23754 | + | 0.714494i | ||||
\(699\) | 0.186497 | − | 0.323021i | 0.00705395 | − | 0.0122178i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.7053 | − | 30.6665i | −0.668721 | − | 1.15826i | −0.978262 | − | 0.207372i | \(-0.933509\pi\) |
0.309541 | − | 0.950886i | \(-0.399824\pi\) | |||||||
\(702\) | − | 0.651889i | − | 0.0246040i | ||||||
\(703\) | −0.354657 | − | 16.1828i | −0.0133761 | − | 0.610345i | ||||
\(704\) | −35.2814 | −1.32972 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.62510 | − | 13.2071i | −0.286974 | − | 0.497054i | ||||
\(707\) | 18.0664 | + | 10.4306i | 0.679457 | + | 0.392285i | ||||
\(708\) | −0.342618 | + | 0.197810i | −0.0128764 | + | 0.00743417i | ||||
\(709\) | 16.9184 | − | 29.3036i | 0.635386 | − | 1.10052i | −0.351048 | − | 0.936358i | \(-0.614174\pi\) |
0.986433 | − | 0.164163i | \(-0.0524922\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 43.1819 | 1.61945 | ||||||||
\(712\) | 32.9313 | + | 19.0129i | 1.23415 | + | 0.712538i | ||||
\(713\) | 15.5039 | + | 8.95117i | 0.580625 | + | 0.335224i | ||||
\(714\) | −0.964848 | −0.0361085 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.956237 | − | 1.65625i | 0.0357362 | − | 0.0618970i | ||||
\(717\) | 1.20806 | − | 0.697474i | 0.0451158 | − | 0.0260476i | ||||
\(718\) | 2.54307 | + | 1.46824i | 0.0949066 | + | 0.0547943i | ||||
\(719\) | 13.4970 | + | 23.3775i | 0.503353 | + | 0.871833i | 0.999992 | + | 0.00387581i | \(0.00123371\pi\) |
−0.496640 | + | 0.867957i | \(0.665433\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.92463 | −0.257887 | ||||||||
\(722\) | 23.7324 | − | 15.1256i | 0.883229 | − | 0.562916i | ||||
\(723\) | − | 2.63997i | − | 0.0981814i | ||||||
\(724\) | 1.43247 | + | 2.48111i | 0.0532374 | + | 0.0922099i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.85944 | + | 3.22065i | −0.0690104 | + | 0.119529i | ||||
\(727\) | −18.7090 | + | 10.8016i | −0.693878 | + | 0.400610i | −0.805063 | − | 0.593189i | \(-0.797869\pi\) |
0.111185 | + | 0.993800i | \(0.464535\pi\) | |||||||
\(728\) | −1.22714 | − | 0.708492i | −0.0454810 | − | 0.0262584i | ||||
\(729\) | 25.2353 | 0.934640 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.29388 | − | 7.43723i | 0.158815 | − | 0.275076i | ||||
\(732\) | −0.0284930 | − | 0.0164504i | −0.00105313 | − | 0.000608026i | ||||
\(733\) | 17.2551i | 0.637332i | 0.947867 | + | 0.318666i | \(0.103235\pi\) | ||||
−0.947867 | + | 0.318666i | \(0.896765\pi\) | |||||||
\(734\) | 7.81217 | 0.288353 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.80322 | − | 6.58737i | −0.140189 | − | 0.242814i | ||||
\(737\) | 22.8489 | + | 13.1918i | 0.841650 | + | 0.485927i | ||||
\(738\) | −4.62777 | + | 2.67184i | −0.170350 | + | 0.0983519i | ||||
\(739\) | 2.39553 | + | 4.14918i | 0.0881210 | + | 0.152630i | 0.906717 | − | 0.421740i | \(-0.138580\pi\) |
−0.818596 | + | 0.574370i | \(0.805247\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.321423 | + | 0.00704420i | −0.0118078 | + | 0.000258775i | ||||
\(742\) | − | 12.2126i | − | 0.448338i | ||||||
\(743\) | −12.5465 | + | 7.24373i | −0.460287 | + | 0.265747i | −0.712165 | − | 0.702012i | \(-0.752285\pi\) |
0.251878 | + | 0.967759i | \(0.418952\pi\) | |||||||
\(744\) | 0.625065 | + | 1.08264i | 0.0229160 | + | 0.0396917i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 23.4912 | + | 40.6879i | 0.860072 | + | 1.48969i | ||||
\(747\) | 39.2217 | + | 22.6447i | 1.43505 | + | 0.828525i | ||||
\(748\) | − | 2.65746i | − | 0.0971665i | ||||||
\(749\) | −16.9579 | −0.619630 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.22637 | + | 5.58824i | −0.117732 | + | 0.203918i | −0.918869 | − | 0.394564i | \(-0.870896\pi\) |
0.801137 | + | 0.598482i | \(0.204229\pi\) | |||||||
\(752\) | − | 28.3119i | − | 1.03243i | ||||||
\(753\) | − | 1.30527i | − | 0.0475667i | ||||||
\(754\) | −1.20751 | + | 2.09147i | −0.0439749 | + | 0.0761668i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.137047 | − | 0.237373i | 0.00498437 | − | 0.00863318i | ||||
\(757\) | 32.0074 | − | 18.4795i | 1.16333 | − | 0.671649i | 0.211230 | − | 0.977436i | \(-0.432253\pi\) |
0.952100 | + | 0.305788i | \(0.0989197\pi\) | |||||||
\(758\) | −45.5530 | + | 26.3000i | −1.65456 | + | 0.955260i | ||||
\(759\) | 6.29525 | 0.228503 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 48.3893 | 1.75411 | 0.877055 | − | 0.480389i | \(-0.159505\pi\) | ||||
0.877055 | + | 0.480389i | \(0.159505\pi\) | |||||||
\(762\) | −3.51967 | + | 2.03208i | −0.127504 | + | 0.0736145i | ||||
\(763\) | 9.25493 | − | 5.34333i | 0.335051 | − | 0.193442i | ||||
\(764\) | −2.00528 | + | 3.47324i | −0.0725484 | + | 0.125657i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.3167 | + | 17.8690i | −0.372756 | + | 0.645632i | ||||
\(767\) | 4.56200i | 0.164724i | ||||||||
\(768\) | − | 0.837598i | − | 0.0302242i | ||||||
\(769\) | 20.7177 | − | 35.8841i | 0.747098 | − | 1.29401i | −0.202110 | − | 0.979363i | \(-0.564780\pi\) |
0.949208 | − | 0.314649i | \(-0.101887\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.58105 | 0.0569403 | ||||||||
\(772\) | − | 3.93270i | − | 0.141541i | ||||||
\(773\) | −33.6285 | − | 19.4154i | −1.20953 | − | 0.698325i | −0.246877 | − | 0.969047i | \(-0.579404\pi\) |
−0.962658 | + | 0.270722i | \(0.912738\pi\) | |||||||
\(774\) | 6.86151 | + | 11.8845i | 0.246632 | + | 0.427179i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −24.4537 | − | 42.3550i | −0.877836 | − | 1.52046i | ||||
\(777\) | −0.761720 | + | 0.439779i | −0.0273266 | + | 0.0157770i | ||||
\(778\) | 1.39657i | 0.0500695i | ||||||||
\(779\) | 2.74999 | + | 4.53087i | 0.0985287 | + | 0.162335i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.07397 | + | 7.05632i | 0.145778 | + | 0.252495i | ||||
\(782\) | −24.5437 | + | 14.1703i | −0.877680 | + | 0.506729i | ||||
\(783\) | 3.76757 | + | 2.17521i | 0.134642 | + | 0.0777355i | ||||
\(784\) | 11.5261 | + | 19.9637i | 0.411645 | + | 0.712990i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.670764 | −0.0239254 | ||||||||
\(787\) | − | 51.4952i | − | 1.83561i | −0.397037 | − | 0.917803i | \(-0.629962\pi\) | ||
0.397037 | − | 0.917803i | \(-0.370038\pi\) | |||||||
\(788\) | −2.67336 | − | 1.54347i | −0.0952347 | − | 0.0549838i | ||||
\(789\) | −2.77163 | + | 4.80060i | −0.0986725 | + | 0.170906i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.53973 | 0.303638 | ||||||||
\(792\) | −34.2485 | − | 19.7734i | −1.21697 | − | 0.702615i | ||||
\(793\) | −0.328560 | + | 0.189694i | −0.0116675 | + | 0.00673623i | ||||
\(794\) | −21.1556 | + | 36.6426i | −0.750785 | + | 1.30040i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.28344 | + | 2.22299i | 0.0454905 | + | 0.0787918i | ||||
\(797\) | 7.50433i | 0.265817i | 0.991128 | + | 0.132908i | \(0.0424316\pi\) | ||||
−0.991128 | + | 0.132908i | \(0.957568\pi\) | |||||||
\(798\) | −1.34079 | − | 0.735414i | −0.0474634 | − | 0.0260334i | ||||
\(799\) | −17.8985 | −0.633203 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.0874 | + | 36.5244i | 0.745087 | + | 1.29053i | ||||
\(802\) | 9.19387 | + | 5.30809i | 0.324647 | + | 0.187435i | ||||
\(803\) | 33.1730 | − | 19.1524i | 1.17065 | − | 0.675875i | ||||
\(804\) | −0.0932510 | + | 0.161515i | −0.00328871 | + | 0.00569621i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.54795 | −0.0545243 | ||||||||
\(807\) | 2.89509 | + | 1.67148i | 0.101912 | + | 0.0588388i | ||||
\(808\) | 37.0567 | + | 21.3947i | 1.30365 | + | 0.752663i | ||||
\(809\) | 17.9109 | 0.629714 | 0.314857 | − | 0.949139i | \(-0.398043\pi\) | ||||
0.314857 | + | 0.949139i | \(0.398043\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.57516 | + | 4.46030i | −0.0904260 | + | 0.156622i | −0.907690 | − | 0.419640i | \(-0.862156\pi\) |
0.817264 | + | 0.576263i | \(0.195490\pi\) | |||||||
\(812\) | −0.879385 | + | 0.507713i | −0.0308604 | + | 0.0178172i | ||||
\(813\) | −1.80458 | − | 1.04187i | −0.0632893 | − | 0.0365401i | ||||
\(814\) | −13.7028 | − | 23.7339i | −0.480281 | − | 0.831871i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.17276 | −0.0760619 | ||||||||
\(817\) | 11.6356 | − | 7.06221i | 0.407080 | − | 0.247075i | ||||
\(818\) | 15.6007i | 0.545464i | ||||||||
\(819\) | −0.785796 | − | 1.36104i | −0.0274579 | − | 0.0475586i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.690525 | − | 1.19602i | 0.0240995 | − | 0.0417415i | −0.853724 | − | 0.520726i | \(-0.825661\pi\) |
0.877824 | + | 0.478984i | \(0.158995\pi\) | |||||||
\(822\) | 4.10194 | − | 2.36826i | 0.143072 | − | 0.0826025i | ||||
\(823\) | 12.4846 | + | 7.20798i | 0.435185 | + | 0.251254i | 0.701553 | − | 0.712617i | \(-0.252490\pi\) |
−0.266368 | + | 0.963871i | \(0.585824\pi\) | |||||||
\(824\) | −14.2034 | −0.494798 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.8497 | + | 18.7922i | −0.377509 | + | 0.653864i | ||||
\(827\) | −8.20404 | − | 4.73660i | −0.285282 | − | 0.164708i | 0.350530 | − | 0.936552i | \(-0.386001\pi\) |
−0.635812 | + | 0.771844i | \(0.719335\pi\) | |||||||
\(828\) | − | 4.00326i | − | 0.139123i | ||||||
\(829\) | 12.3950 | 0.430497 | 0.215248 | − | 0.976559i | \(-0.430944\pi\) | ||||
0.215248 | + | 0.976559i | \(0.430944\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.163164 | + | 0.282609i | 0.00566011 | + | 0.00980359i | ||||
\(832\) | −2.49059 | − | 1.43794i | −0.0863455 | − | 0.0498516i | ||||
\(833\) | 12.6209 | − | 7.28666i | 0.437287 | − | 0.252468i | ||||
\(834\) | 0.424304 | + | 0.734916i | 0.0146925 | + | 0.0254481i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.02554 | − | 3.69291i | 0.0700548 | − | 0.127722i | ||||
\(837\) | 2.78848i | 0.0963839i | ||||||||
\(838\) | −3.24142 | + | 1.87144i | −0.111973 | + | 0.0646477i | ||||
\(839\) | 6.26491 | + | 10.8511i | 0.216289 | + | 0.374623i | 0.953670 | − | 0.300853i | \(-0.0972714\pi\) |
−0.737382 | + | 0.675476i | \(0.763938\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.44162 | + | 11.1572i | 0.222125 | + | 0.384732i | ||||
\(842\) | −19.0706 | − | 11.0104i | −0.657215 | − | 0.379443i | ||||
\(843\) | 2.57720i | 0.0887633i | ||||||||
\(844\) | 1.89638 | 0.0652760 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 14.3007 | − | 24.7695i | 0.491667 | − | 0.851592i | ||||
\(847\) | 18.0308i | 0.619547i | ||||||||
\(848\) | − | 27.5018i | − | 0.944416i | ||||||
\(849\) | 1.62618 | − | 2.81663i | 0.0558103 | − | 0.0966663i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.9177 | + | 22.3741i | −0.442813 | + | 0.766974i | ||||
\(852\) | −0.0498801 | + | 0.0287983i | −0.00170886 | + | 0.000986613i | ||||
\(853\) | −3.00771 | + | 1.73650i | −0.102982 | + | 0.0594567i | −0.550606 | − | 0.834765i | \(-0.685603\pi\) |
0.447624 | + | 0.894222i | \(0.352270\pi\) | |||||||
\(854\) | −1.80458 | −0.0617513 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −34.7831 | −1.18886 | ||||||||
\(857\) | −14.4295 | + | 8.33085i | −0.492901 | + | 0.284577i | −0.725777 | − | 0.687930i | \(-0.758520\pi\) |
0.232876 | + | 0.972506i | \(0.425186\pi\) | |||||||
\(858\) | −0.471402 | + | 0.272164i | −0.0160934 | + | 0.00929154i | ||||
\(859\) | 20.4042 | − | 35.3412i | 0.696183 | − | 1.20583i | −0.273597 | − | 0.961844i | \(-0.588213\pi\) |
0.969780 | − | 0.243981i | \(-0.0784533\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.144000 | − | 0.249415i | 0.00490751 | − | 0.00850005i | ||||
\(862\) | − | 6.19239i | − | 0.210914i | ||||||
\(863\) | − | 4.07050i | − | 0.138561i | −0.997597 | − | 0.0692806i | \(-0.977930\pi\) | ||
0.997597 | − | 0.0692806i | \(-0.0220704\pi\) | |||||||
\(864\) | 0.592392 | − | 1.02605i | 0.0201536 | − | 0.0349071i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −37.4821 | −1.27369 | ||||||||
\(867\) | − | 1.71373i | − | 0.0582014i | ||||||
\(868\) | −0.563658 | − | 0.325428i | −0.0191318 | − | 0.0110458i | ||||
\(869\) | −36.2574 | − | 62.7996i | −1.22995 | − | 2.13033i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.07530 | + | 1.86247i | 0.0364351 | + | 0.0631075i | ||||
\(872\) | 18.9831 | − | 10.9599i | 0.642851 | − | 0.371150i | ||||
\(873\) | − | 54.2437i | − | 1.83587i | ||||||
\(874\) | −44.9075 | + | 0.984178i | −1.51902 | + | 0.0332903i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.135386 | + | 0.234495i | 0.00457426 | + | 0.00792285i | ||||
\(877\) | −22.9621 | + | 13.2572i | −0.775376 | + | 0.447663i | −0.834789 | − | 0.550570i | \(-0.814410\pi\) |
0.0594132 | + | 0.998233i | \(0.481077\pi\) | |||||||
\(878\) | 37.0871 | + | 21.4122i | 1.25163 | + | 0.722628i | ||||
\(879\) | −3.02457 | − | 5.23871i | −0.102016 | − | 0.176697i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.3730 | −0.753766 | −0.376883 | − | 0.926261i | \(-0.623004\pi\) | ||||
−0.376883 | + | 0.926261i | \(0.623004\pi\) | |||||||
\(882\) | 23.2878i | 0.784140i | ||||||||
\(883\) | 17.0726 | + | 9.85689i | 0.574540 | + | 0.331711i | 0.758961 | − | 0.651137i | \(-0.225708\pi\) |
−0.184421 | + | 0.982847i | \(0.559041\pi\) | |||||||
\(884\) | 0.108308 | − | 0.187596i | 0.00364281 | − | 0.00630953i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.79667 | −0.228339 | ||||||||
\(887\) | −9.89139 | − | 5.71080i | −0.332120 | − | 0.191750i | 0.324662 | − | 0.945830i | \(-0.394750\pi\) |
−0.656782 | + | 0.754080i | \(0.728083\pi\) | |||||||
\(888\) | −1.56239 | + | 0.902049i | −0.0524305 | + | 0.0302708i | ||||
\(889\) | −9.85245 | + | 17.0649i | −0.330441 | + | 0.572340i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.6844 | − | 37.5584i | −0.726453 | − | 1.25825i | ||||
\(892\) | 5.01558i | 0.167934i | ||||||||
\(893\) | −24.8724 | − | 13.6424i | −0.832323 | − | 0.456524i | ||||
\(894\) | 1.71455 | 0.0573431 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.26556 | − | 14.3164i | −0.276133 | − | 0.478276i | ||||
\(897\) | 0.444395 | + | 0.256571i | 0.0148379 | + | 0.00856667i | ||||
\(898\) | −37.4783 | + | 21.6381i | −1.25067 | + | 0.722073i | ||||
\(899\) | 5.16517 | − | 8.94634i | 0.172268 | − | 0.298377i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.3864 | −0.579223 | ||||||||
\(902\) | 7.77135 | + | 4.48679i | 0.258758 | + | 0.149394i | ||||
\(903\) | −0.640519 | − | 0.369804i | −0.0213151 | − | 0.0123063i | ||||
\(904\) | 17.5162 | 0.582580 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.667568 | + | 1.15626i | −0.0221784 | + | 0.0384142i | ||||
\(907\) | −9.29964 | + | 5.36915i | −0.308789 | + | 0.178280i | −0.646385 | − | 0.763012i | \(-0.723720\pi\) |
0.337595 | + | 0.941291i | \(0.390387\pi\) | |||||||
\(908\) | −0.383897 | − | 0.221643i | −0.0127401 | − | 0.00735548i | ||||
\(909\) | 23.7291 | + | 41.1000i | 0.787045 | + | 1.36320i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.5952 | −0.914269 | −0.457134 | − | 0.889398i | \(-0.651124\pi\) | ||||
−0.457134 | + | 0.889398i | \(0.651124\pi\) | |||||||
\(912\) | −3.01935 | − | 1.65610i | −0.0999807 | − | 0.0548388i | ||||
\(913\) | − | 76.0538i | − | 2.51701i | ||||||
\(914\) | −17.5605 | − | 30.4157i | −0.580850 | − | 1.00606i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.12171 | − | 3.67492i | 0.0701034 | − | 0.121423i | ||||
\(917\) | −2.81646 | + | 1.62608i | −0.0930077 | + | 0.0536980i | ||||
\(918\) | −3.82294 | − | 2.20717i | −0.126176 | − | 0.0728476i | ||||
\(919\) | 49.2639 | 1.62507 | 0.812533 | − | 0.582915i | \(-0.198088\pi\) | ||||
0.812533 | + | 0.582915i | \(0.198088\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.41264 | + | 2.44677i | −0.0465482 | + | 0.0806238i | ||||
\(922\) | −44.9243 | − | 25.9371i | −1.47950 | − | 0.854192i | ||||
\(923\) | 0.664160i | 0.0218611i | ||||||||
\(924\) | −0.228870 | −0.00752927 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −15.1775 | − | 26.2882i | −0.498763 | − | 0.863883i | ||||
\(927\) | −13.6426 | − | 7.87657i | −0.448082 | − | 0.258700i | ||||
\(928\) | −3.80117 | + | 2.19461i | −0.124779 | + | 0.0720415i | ||||
\(929\) | 21.5374 | + | 37.3039i | 0.706619 | + | 1.22390i | 0.966104 | + | 0.258153i | \(0.0831138\pi\) |
−0.259485 | + | 0.965747i | \(0.583553\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.0923 | − | 0.506085i | 0.756821 | − | 0.0165863i | ||||
\(932\) | 0.398315i | 0.0130472i | ||||||||
\(933\) | −4.59183 | + | 2.65110i | −0.150330 | + | 0.0867930i | ||||
\(934\) | 6.84568 | + | 11.8571i | 0.223998 | + | 0.387975i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.61178 | − | 2.79168i | −0.0526826 | − | 0.0912490i | ||||
\(937\) | 37.6239 | + | 21.7222i | 1.22912 | + | 0.709633i | 0.966846 | − | 0.255360i | \(-0.0821941\pi\) |
0.262275 | + | 0.964993i | \(0.415527\pi\) | |||||||
\(938\) | 10.2294i | 0.334003i | ||||||||
\(939\) | −5.79110 | −0.188985 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.6471 | + | 25.3694i | −0.477480 | + | 0.827020i | −0.999667 | − | 0.0258111i | \(-0.991783\pi\) |
0.522186 | + | 0.852831i | \(0.325117\pi\) | |||||||
\(942\) | 0.563545i | 0.0183613i | ||||||||
\(943\) | − | 8.45946i | − | 0.275478i | ||||||
\(944\) | −24.4326 | + | 42.3186i | −0.795215 | + | 1.37735i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.5224 | − | 19.9575i | 0.374627 | − | 0.648873i | ||||
\(947\) | 1.73715 | − | 1.00294i | 0.0564498 | − | 0.0325913i | −0.471509 | − | 0.881861i | \(-0.656291\pi\) |
0.527959 | + | 0.849270i | \(0.322957\pi\) | |||||||
\(948\) | 0.443921 | − | 0.256298i | 0.0144179 | − | 0.00832418i | ||||
\(949\) | 3.12233 | 0.101355 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.46443 | −0.0799148 | ||||||||
\(952\) | −8.30975 | + | 4.79764i | −0.269321 | + | 0.155492i | ||||
\(953\) | −16.6614 | + | 9.61946i | −0.539716 | + | 0.311605i | −0.744964 | − | 0.667105i | \(-0.767533\pi\) |
0.205248 | + | 0.978710i | \(0.434200\pi\) | |||||||
\(954\) | 13.8915 | − | 24.0607i | 0.449753 | − | 0.778995i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.744823 | + | 1.29007i | −0.0240893 | + | 0.0417239i | ||||
\(957\) | − | 3.63260i | − | 0.117425i | ||||||
\(958\) | − | 5.58045i | − | 0.180296i | ||||||
\(959\) | 11.4824 | − | 19.8881i | 0.370786 | − | 0.642220i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.3786 | −0.786406 | ||||||||
\(962\) | − | 2.23390i | − | 0.0720237i | ||||||
\(963\) | −33.4098 | − | 19.2892i | −1.07662 | − | 0.621585i | ||||
\(964\) | 1.40959 | + | 2.44149i | 0.0453999 | + | 0.0786350i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.22039 | + | 2.11378i | 0.0392655 | + | 0.0680099i | ||||
\(967\) | −24.6075 | + | 14.2071i | −0.791324 | + | 0.456871i | −0.840428 | − | 0.541923i | \(-0.817697\pi\) |
0.0491047 | + | 0.998794i | \(0.484363\pi\) | |||||||
\(968\) | 36.9838i | 1.18870i | ||||||||
\(969\) | −1.04697 | + | 1.90880i | −0.0336334 | + | 0.0613196i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.98811 | − | 15.5679i | −0.288442 | − | 0.499597i | 0.684996 | − | 0.728547i | \(-0.259804\pi\) |
−0.973438 | + | 0.228950i | \(0.926471\pi\) | |||||||
\(972\) | 0.811508 | − | 0.468524i | 0.0260291 | − | 0.0150279i | ||||
\(973\) | 3.56321 | + | 2.05722i | 0.114231 | + | 0.0659515i | ||||
\(974\) | 8.73761 | + | 15.1340i | 0.279971 | + | 0.484924i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.06377 | −0.130078 | ||||||||
\(977\) | − | 13.2288i | − | 0.423226i | −0.977354 | − | 0.211613i | \(-0.932128\pi\) | ||
0.977354 | − | 0.211613i | \(-0.0678716\pi\) | |||||||
\(978\) | −2.22666 | − | 1.28556i | −0.0712006 | − | 0.0411077i | ||||
\(979\) | 35.4118 | − | 61.3350i | 1.13177 | − | 1.96027i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.3116 | 0.776208 | ||||||||
\(982\) | −10.0512 | − | 5.80305i | −0.320746 | − | 0.185183i | ||||
\(983\) | 42.0225 | − | 24.2617i | 1.34031 | − | 0.773828i | 0.353457 | − | 0.935451i | \(-0.385006\pi\) |
0.986853 | + | 0.161623i | \(0.0516727\pi\) | |||||||
\(984\) | 0.295364 | − | 0.511586i | 0.00941587 | − | 0.0163088i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8.17680 | + | 14.1626i | 0.260403 | + | 0.451030i | ||||
\(987\) | 1.54148i | 0.0490658i | ||||||||
\(988\) | 0.293496 | − | 0.178136i | 0.00933736 | − | 0.00566727i | ||||
\(989\) | −21.7246 | −0.690802 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.1402 | − | 34.8838i | −0.639773 | − | 1.10812i | −0.985482 | − | 0.169778i | \(-0.945695\pi\) |
0.345709 | − | 0.938342i | \(-0.387638\pi\) | |||||||
\(992\) | −2.43643 | − | 1.40667i | −0.0773568 | − | 0.0446619i | ||||
\(993\) | 4.62824 | − | 2.67212i | 0.146873 | − | 0.0847971i | ||||
\(994\) | −1.57955 | + | 2.73587i | −0.0501004 | + | 0.0867764i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.537613 | 0.0170349 | ||||||||
\(997\) | 23.8668 | + | 13.7795i | 0.755869 | + | 0.436401i | 0.827811 | − | 0.561008i | \(-0.189586\pi\) |
−0.0719414 | + | 0.997409i | \(0.522919\pi\) | |||||||
\(998\) | 1.35919 | + | 0.784730i | 0.0430245 | + | 0.0248402i | ||||
\(999\) | −4.02413 | −0.127318 |
(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 | 475.2.j.d.349.9 | 24 | ||
5.2 | odd | 4 | 475.2.e.f.26.6 | ✓ | 12 | ||
5.3 | odd | 4 | 475.2.e.h.26.1 | yes | 12 | ||
5.4 | even | 2 | inner | 475.2.j.d.349.4 | 24 | ||
19.11 | even | 3 | inner | 475.2.j.d.49.4 | 24 | ||
95.7 | odd | 12 | 9025.2.a.bz.1.1 | 6 | |||
95.12 | even | 12 | 9025.2.a.bs.1.6 | 6 | |||
95.49 | even | 6 | inner | 475.2.j.d.49.9 | 24 | ||
95.68 | odd | 12 | 475.2.e.h.201.1 | yes | 12 | ||
95.83 | odd | 12 | 9025.2.a.br.1.6 | 6 | |||
95.87 | odd | 12 | 475.2.e.f.201.6 | yes | 12 | ||
95.88 | even | 12 | 9025.2.a.by.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.2.e.f.26.6 | ✓ | 12 | 5.2 | odd | 4 | ||
475.2.e.f.201.6 | yes | 12 | 95.87 | odd | 12 | ||
475.2.e.h.26.1 | yes | 12 | 5.3 | odd | 4 | ||
475.2.e.h.201.1 | yes | 12 | 95.68 | odd | 12 | ||
475.2.j.d.49.4 | 24 | 19.11 | even | 3 | inner | ||
475.2.j.d.49.9 | 24 | 95.49 | even | 6 | inner | ||
475.2.j.d.349.4 | 24 | 5.4 | even | 2 | inner | ||
475.2.j.d.349.9 | 24 | 1.1 | even | 1 | trivial | ||
9025.2.a.br.1.6 | 6 | 95.83 | odd | 12 | |||
9025.2.a.bs.1.6 | 6 | 95.12 | even | 12 | |||
9025.2.a.by.1.1 | 6 | 95.88 | even | 12 | |||
9025.2.a.bz.1.1 | 6 | 95.7 | odd | 12 |