Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [156,3,Mod(103,156)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(156, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("156.103");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 156 = 2^{2} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 156.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.25069212402\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 103.8 | ||
Character | \(\chi\) | \(=\) | 156.103 |
Dual form | 156.3.e.c.103.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/156\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(79\) | \(145\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.31729 | + | 1.50490i | −0.658647 | + | 0.752452i | ||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | −0.529474 | − | 3.96480i | −0.132368 | − | 0.991201i | ||||
\(5\) | 7.41736i | 1.48347i | 0.670692 | + | 0.741736i | \(0.265997\pi\) | ||||
−0.670692 | + | 0.741736i | \(0.734003\pi\) | |||||||
\(6\) | −2.60657 | − | 2.28162i | −0.434428 | − | 0.380270i | ||||
\(7\) | 13.3843 | 1.91204 | 0.956020 | − | 0.293303i | \(-0.0947544\pi\) | ||||
0.956020 | + | 0.293303i | \(0.0947544\pi\) | |||||||
\(8\) | 6.66412 | + | 4.42600i | 0.833015 | + | 0.553250i | ||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | −11.1624 | − | 9.77084i | −1.11624 | − | 0.977084i | ||||
\(11\) | −14.6051 | −1.32773 | −0.663867 | − | 0.747851i | \(-0.731086\pi\) | ||||
−0.663867 | + | 0.747851i | \(0.731086\pi\) | |||||||
\(12\) | 6.86724 | − | 0.917075i | 0.572270 | − | 0.0764229i | ||||
\(13\) | 9.82465 | + | 8.51330i | 0.755742 | + | 0.654869i | ||||
\(14\) | −17.6310 | + | 20.1421i | −1.25936 | + | 1.43872i | ||||
\(15\) | −12.8472 | −0.856483 | ||||||||
\(16\) | −15.4393 | + | 4.19852i | −0.964957 | + | 0.262407i | ||||
\(17\) | −3.85621 | −0.226836 | −0.113418 | − | 0.993547i | \(-0.536180\pi\) | ||||
−0.113418 | + | 0.993547i | \(0.536180\pi\) | |||||||
\(18\) | 3.95188 | − | 4.51471i | 0.219549 | − | 0.250817i | ||||
\(19\) | −19.0947 | −1.00499 | −0.502493 | − | 0.864581i | \(-0.667584\pi\) | ||||
−0.502493 | + | 0.864581i | \(0.667584\pi\) | |||||||
\(20\) | 29.4084 | − | 3.92730i | 1.47042 | − | 0.196365i | ||||
\(21\) | 23.1822i | 1.10392i | ||||||||
\(22\) | 19.2392 | − | 21.9792i | 0.874508 | − | 0.999056i | ||||
\(23\) | − | 2.41298i | − | 0.104912i | −0.998623 | − | 0.0524561i | \(-0.983295\pi\) | ||
0.998623 | − | 0.0524561i | \(-0.0167050\pi\) | |||||||
\(24\) | −7.66606 | + | 11.5426i | −0.319419 | + | 0.480941i | ||||
\(25\) | −30.0172 | −1.20069 | ||||||||
\(26\) | −25.7537 | + | 3.57064i | −0.990525 | + | 0.137332i | ||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | −7.08662 | − | 53.0660i | −0.253094 | − | 1.89521i | ||||
\(29\) | 18.9541 | 0.653589 | 0.326795 | − | 0.945095i | \(-0.394031\pi\) | ||||
0.326795 | + | 0.945095i | \(0.394031\pi\) | |||||||
\(30\) | 16.9236 | − | 19.3339i | 0.564120 | − | 0.644462i | ||||
\(31\) | −11.2035 | −0.361403 | −0.180702 | − | 0.983538i | \(-0.557837\pi\) | ||||
−0.180702 | + | 0.983538i | \(0.557837\pi\) | |||||||
\(32\) | 14.0198 | − | 28.7654i | 0.438117 | − | 0.898918i | ||||
\(33\) | − | 25.2967i | − | 0.766567i | ||||||
\(34\) | 5.07976 | − | 5.80322i | 0.149405 | − | 0.170683i | ||||
\(35\) | 99.2760i | 2.83646i | ||||||||
\(36\) | 1.58842 | + | 11.8944i | 0.0441228 | + | 0.330400i | ||||
\(37\) | 38.0750i | 1.02906i | 0.857474 | + | 0.514528i | \(0.172033\pi\) | ||||
−0.857474 | + | 0.514528i | \(0.827967\pi\) | |||||||
\(38\) | 25.1534 | − | 28.7358i | 0.661931 | − | 0.756204i | ||||
\(39\) | −14.7455 | + | 17.0168i | −0.378089 | + | 0.436328i | ||||
\(40\) | −32.8293 | + | 49.4302i | −0.820731 | + | 1.23575i | ||||
\(41\) | − | 35.5289i | − | 0.866558i | −0.901260 | − | 0.433279i | \(-0.857356\pi\) | ||
0.901260 | − | 0.433279i | \(-0.142644\pi\) | |||||||
\(42\) | −34.8871 | − | 30.5378i | −0.830644 | − | 0.727091i | ||||
\(43\) | − | 10.1670i | − | 0.236443i | −0.992987 | − | 0.118221i | \(-0.962281\pi\) | ||
0.992987 | − | 0.118221i | \(-0.0377192\pi\) | |||||||
\(44\) | 7.73300 | + | 57.9062i | 0.175750 | + | 1.31605i | ||||
\(45\) | − | 22.2521i | − | 0.494491i | ||||||
\(46\) | 3.63130 | + | 3.17860i | 0.0789414 | + | 0.0691001i | ||||
\(47\) | 52.7193 | 1.12169 | 0.560843 | − | 0.827922i | \(-0.310477\pi\) | ||||
0.560843 | + | 0.827922i | \(0.310477\pi\) | |||||||
\(48\) | −7.27204 | − | 26.7417i | −0.151501 | − | 0.557118i | ||||
\(49\) | 130.139 | 2.65589 | ||||||||
\(50\) | 39.5415 | − | 45.1730i | 0.790830 | − | 0.903461i | ||||
\(51\) | − | 6.67915i | − | 0.130964i | ||||||
\(52\) | 28.5517 | − | 43.4604i | 0.549070 | − | 0.835776i | ||||
\(53\) | 56.1801 | 1.06000 | 0.530001 | − | 0.847997i | \(-0.322191\pi\) | ||||
0.530001 | + | 0.847997i | \(0.322191\pi\) | |||||||
\(54\) | 7.81971 | + | 6.84486i | 0.144809 | + | 0.126757i | ||||
\(55\) | − | 108.331i | − | 1.96966i | ||||||
\(56\) | 89.1944 | + | 59.2388i | 1.59276 | + | 1.05784i | ||||
\(57\) | − | 33.0731i | − | 0.580229i | ||||||
\(58\) | −24.9681 | + | 28.5241i | −0.430485 | + | 0.491795i | ||||
\(59\) | −22.9260 | −0.388576 | −0.194288 | − | 0.980945i | \(-0.562240\pi\) | ||||
−0.194288 | + | 0.980945i | \(0.562240\pi\) | |||||||
\(60\) | 6.80228 | + | 50.9368i | 0.113371 | + | 0.848946i | ||||
\(61\) | −2.26008 | −0.0370505 | −0.0185252 | − | 0.999828i | \(-0.505897\pi\) | ||||
−0.0185252 | + | 0.999828i | \(0.505897\pi\) | |||||||
\(62\) | 14.7583 | − | 16.8602i | 0.238037 | − | 0.271939i | ||||
\(63\) | −40.1528 | −0.637346 | ||||||||
\(64\) | 24.8210 | + | 58.9908i | 0.387828 | + | 0.921732i | ||||
\(65\) | −63.1462 | + | 72.8729i | −0.971480 | + | 1.12112i | ||||
\(66\) | 38.0691 | + | 33.3232i | 0.576805 | + | 0.504897i | ||||
\(67\) | 27.1686 | 0.405501 | 0.202750 | − | 0.979230i | \(-0.435012\pi\) | ||||
0.202750 | + | 0.979230i | \(0.435012\pi\) | |||||||
\(68\) | 2.04176 | + | 15.2891i | 0.0300259 | + | 0.224840i | ||||
\(69\) | 4.17941 | 0.0605711 | ||||||||
\(70\) | −149.401 | − | 130.776i | −2.13430 | − | 1.86822i | ||||
\(71\) | 25.9461 | 0.365439 | 0.182719 | − | 0.983165i | \(-0.441510\pi\) | ||||
0.182719 | + | 0.983165i | \(0.441510\pi\) | |||||||
\(72\) | −19.9924 | − | 13.2780i | −0.277672 | − | 0.184417i | ||||
\(73\) | 20.2720i | 0.277699i | 0.990314 | + | 0.138849i | \(0.0443404\pi\) | ||||
−0.990314 | + | 0.138849i | \(0.955660\pi\) | |||||||
\(74\) | −57.2993 | − | 50.1560i | −0.774315 | − | 0.677784i | ||||
\(75\) | − | 51.9913i | − | 0.693218i | ||||||
\(76\) | 10.1102 | + | 75.7069i | 0.133028 | + | 0.996143i | ||||
\(77\) | −195.478 | −2.53868 | ||||||||
\(78\) | −6.18453 | − | 44.6066i | −0.0792888 | − | 0.571880i | ||||
\(79\) | 14.9255i | 0.188931i | 0.995528 | + | 0.0944654i | \(0.0301142\pi\) | ||||
−0.995528 | + | 0.0944654i | \(0.969886\pi\) | |||||||
\(80\) | −31.1419 | − | 114.519i | −0.389274 | − | 1.43149i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 53.4676 | + | 46.8020i | 0.652044 | + | 0.570756i | ||||
\(83\) | −3.46387 | −0.0417334 | −0.0208667 | − | 0.999782i | \(-0.506643\pi\) | ||||
−0.0208667 | + | 0.999782i | \(0.506643\pi\) | |||||||
\(84\) | 91.9130 | − | 12.2744i | 1.09420 | − | 0.146124i | ||||
\(85\) | − | 28.6029i | − | 0.336504i | ||||||
\(86\) | 15.3004 | + | 13.3930i | 0.177912 | + | 0.155732i | ||||
\(87\) | 32.8295i | 0.377350i | ||||||||
\(88\) | −97.3299 | − | 64.6421i | −1.10602 | − | 0.734569i | ||||
\(89\) | − | 147.408i | − | 1.65627i | −0.560525 | − | 0.828137i | \(-0.689401\pi\) | ||
0.560525 | − | 0.828137i | \(-0.310599\pi\) | |||||||
\(90\) | 33.4872 | + | 29.3125i | 0.372080 | + | 0.325695i | ||||
\(91\) | 131.496 | + | 113.944i | 1.44501 | + | 1.25214i | ||||
\(92\) | −9.56699 | + | 1.27761i | −0.103989 | + | 0.0138871i | ||||
\(93\) | − | 19.4050i | − | 0.208656i | ||||||
\(94\) | −69.4468 | + | 79.3375i | −0.738795 | + | 0.844015i | ||||
\(95\) | − | 141.633i | − | 1.49087i | ||||||
\(96\) | 49.8231 | + | 24.2829i | 0.518990 | + | 0.252947i | ||||
\(97\) | 163.142i | 1.68187i | 0.541135 | + | 0.840936i | \(0.317995\pi\) | ||||
−0.541135 | + | 0.840936i | \(0.682005\pi\) | |||||||
\(98\) | −171.431 | + | 195.846i | −1.74930 | + | 1.99843i | ||||
\(99\) | 43.8152 | 0.442578 | ||||||||
\(100\) | 15.8933 | + | 119.012i | 0.158933 | + | 1.19012i | ||||
\(101\) | −45.3731 | −0.449238 | −0.224619 | − | 0.974447i | \(-0.572114\pi\) | ||||
−0.224619 | + | 0.974447i | \(0.572114\pi\) | |||||||
\(102\) | 10.0515 | + | 8.79840i | 0.0985439 | + | 0.0862588i | ||||
\(103\) | − | 106.266i | − | 1.03171i | −0.856677 | − | 0.515853i | \(-0.827475\pi\) | ||
0.856677 | − | 0.515853i | \(-0.172525\pi\) | |||||||
\(104\) | 27.7928 | + | 100.218i | 0.267238 | + | 0.963631i | ||||
\(105\) | −171.951 | −1.63763 | ||||||||
\(106\) | −74.0057 | + | 84.5457i | −0.698167 | + | 0.797601i | ||||
\(107\) | 76.2855i | 0.712949i | 0.934305 | + | 0.356474i | \(0.116021\pi\) | ||||
−0.934305 | + | 0.356474i | \(0.883979\pi\) | |||||||
\(108\) | −20.6017 | + | 2.75123i | −0.190757 | + | 0.0254743i | ||||
\(109\) | − | 137.421i | − | 1.26075i | −0.776293 | − | 0.630373i | \(-0.782902\pi\) | ||
0.776293 | − | 0.630373i | \(-0.217098\pi\) | |||||||
\(110\) | 163.028 | + | 142.704i | 1.48207 | + | 1.29731i | ||||
\(111\) | −65.9479 | −0.594125 | ||||||||
\(112\) | −206.644 | + | 56.1941i | −1.84504 | + | 0.501733i | ||||
\(113\) | 168.559 | 1.49167 | 0.745837 | − | 0.666129i | \(-0.232050\pi\) | ||||
0.745837 | + | 0.666129i | \(0.232050\pi\) | |||||||
\(114\) | 49.7718 | + | 43.5669i | 0.436595 | + | 0.382166i | ||||
\(115\) | 17.8979 | 0.155634 | ||||||||
\(116\) | −10.0357 | − | 75.1492i | −0.0865146 | − | 0.647838i | ||||
\(117\) | −29.4739 | − | 25.5399i | −0.251914 | − | 0.218290i | ||||
\(118\) | 30.2002 | − | 34.5014i | 0.255934 | − | 0.292385i | ||||
\(119\) | −51.6125 | −0.433719 | ||||||||
\(120\) | −85.6156 | − | 56.8619i | −0.713463 | − | 0.473849i | ||||
\(121\) | 92.3080 | 0.762876 | ||||||||
\(122\) | 2.97719 | − | 3.40120i | 0.0244032 | − | 0.0278787i | ||||
\(123\) | 61.5378 | 0.500308 | ||||||||
\(124\) | 5.93196 | + | 44.4197i | 0.0478383 | + | 0.358223i | ||||
\(125\) | − | 37.2145i | − | 0.297716i | ||||||
\(126\) | 52.8931 | − | 60.4262i | 0.419786 | − | 0.479573i | ||||
\(127\) | 124.858i | 0.983131i | 0.870841 | + | 0.491565i | \(0.163575\pi\) | ||||
−0.870841 | + | 0.491565i | \(0.836425\pi\) | |||||||
\(128\) | −121.472 | − | 40.3550i | −0.949001 | − | 0.315274i | ||||
\(129\) | 17.6098 | 0.136510 | ||||||||
\(130\) | −26.4847 | − | 191.024i | −0.203729 | − | 1.46942i | ||||
\(131\) | − | 98.6905i | − | 0.753363i | −0.926343 | − | 0.376681i | \(-0.877065\pi\) | ||
0.926343 | − | 0.376681i | \(-0.122935\pi\) | |||||||
\(132\) | −100.297 | + | 13.3939i | −0.759822 | + | 0.101469i | ||||
\(133\) | −255.569 | −1.92157 | ||||||||
\(134\) | −35.7890 | + | 40.8861i | −0.267082 | + | 0.305120i | ||||
\(135\) | 38.5417 | 0.285494 | ||||||||
\(136\) | −25.6982 | − | 17.0676i | −0.188958 | − | 0.125497i | ||||
\(137\) | − | 96.5730i | − | 0.704912i | −0.935828 | − | 0.352456i | \(-0.885347\pi\) | ||
0.935828 | − | 0.352456i | \(-0.114653\pi\) | |||||||
\(138\) | −5.50550 | + | 6.28960i | −0.0398950 | + | 0.0455768i | ||||
\(139\) | − | 253.423i | − | 1.82318i | −0.411096 | − | 0.911592i | \(-0.634854\pi\) | ||
0.411096 | − | 0.911592i | \(-0.365146\pi\) | |||||||
\(140\) | 393.610 | − | 52.5640i | 2.81150 | − | 0.375457i | ||||
\(141\) | 91.3125i | 0.647606i | ||||||||
\(142\) | −34.1787 | + | 39.0465i | −0.240695 | + | 0.274975i | ||||
\(143\) | −143.490 | − | 124.337i | −1.00342 | − | 0.869492i | ||||
\(144\) | 46.3179 | − | 12.5955i | 0.321652 | − | 0.0874691i | ||||
\(145\) | 140.589i | 0.969582i | ||||||||
\(146\) | −30.5074 | − | 26.7042i | −0.208955 | − | 0.182905i | ||||
\(147\) | 225.407i | 1.53338i | ||||||||
\(148\) | 150.960 | − | 20.1597i | 1.02000 | − | 0.136214i | ||||
\(149\) | 86.7895i | 0.582480i | 0.956650 | + | 0.291240i | \(0.0940677\pi\) | ||||
−0.956650 | + | 0.291240i | \(0.905932\pi\) | |||||||
\(150\) | 78.2420 | + | 68.4879i | 0.521613 | + | 0.456586i | ||||
\(151\) | 196.093 | 1.29863 | 0.649314 | − | 0.760520i | \(-0.275056\pi\) | ||||
0.649314 | + | 0.760520i | \(0.275056\pi\) | |||||||
\(152\) | −127.250 | − | 84.5134i | −0.837169 | − | 0.556009i | ||||
\(153\) | 11.5686 | 0.0756119 | ||||||||
\(154\) | 257.502 | − | 294.176i | 1.67209 | − | 1.91023i | ||||
\(155\) | − | 83.1004i | − | 0.536131i | ||||||
\(156\) | 75.2756 | + | 49.4529i | 0.482536 | + | 0.317006i | ||||
\(157\) | −92.4509 | −0.588859 | −0.294430 | − | 0.955673i | \(-0.595130\pi\) | ||||
−0.294430 | + | 0.955673i | \(0.595130\pi\) | |||||||
\(158\) | −22.4615 | − | 19.6613i | −0.142161 | − | 0.124439i | ||||
\(159\) | 97.3068i | 0.611993i | ||||||||
\(160\) | 213.363 | + | 103.990i | 1.33352 | + | 0.649935i | ||||
\(161\) | − | 32.2960i | − | 0.200596i | ||||||
\(162\) | −11.8556 | + | 13.5441i | −0.0731830 | + | 0.0836058i | ||||
\(163\) | 227.182 | 1.39375 | 0.696877 | − | 0.717190i | \(-0.254572\pi\) | ||||
0.696877 | + | 0.717190i | \(0.254572\pi\) | |||||||
\(164\) | −140.865 | + | 18.8116i | −0.858933 | + | 0.114705i | ||||
\(165\) | 187.635 | 1.13718 | ||||||||
\(166\) | 4.56293 | − | 5.21279i | 0.0274875 | − | 0.0314024i | ||||
\(167\) | −209.783 | −1.25618 | −0.628092 | − | 0.778139i | \(-0.716164\pi\) | ||||
−0.628092 | + | 0.778139i | \(0.716164\pi\) | |||||||
\(168\) | −102.605 | + | 154.489i | −0.610742 | + | 0.919579i | ||||
\(169\) | 24.0475 | + | 167.280i | 0.142293 | + | 0.989825i | ||||
\(170\) | 43.0446 | + | 37.6784i | 0.253203 | + | 0.221638i | ||||
\(171\) | 57.2842 | 0.334995 | ||||||||
\(172\) | −40.3103 | + | 5.38318i | −0.234362 | + | 0.0312975i | ||||
\(173\) | 307.527 | 1.77761 | 0.888807 | − | 0.458282i | \(-0.151535\pi\) | ||||
0.888807 | + | 0.458282i | \(0.151535\pi\) | |||||||
\(174\) | −49.4052 | − | 43.2460i | −0.283938 | − | 0.248540i | ||||
\(175\) | −401.759 | −2.29576 | ||||||||
\(176\) | 225.492 | − | 61.3196i | 1.28121 | − | 0.348407i | ||||
\(177\) | − | 39.7089i | − | 0.224344i | ||||||
\(178\) | 221.836 | + | 194.180i | 1.24627 | + | 1.09090i | ||||
\(179\) | 319.597i | 1.78546i | 0.450595 | + | 0.892729i | \(0.351212\pi\) | ||||
−0.450595 | + | 0.892729i | \(0.648788\pi\) | |||||||
\(180\) | −88.2251 | + | 11.7819i | −0.490139 | + | 0.0654549i | ||||
\(181\) | 237.850 | 1.31409 | 0.657044 | − | 0.753852i | \(-0.271806\pi\) | ||||
0.657044 | + | 0.753852i | \(0.271806\pi\) | |||||||
\(182\) | −344.694 | + | 47.7904i | −1.89392 | + | 0.262585i | ||||
\(183\) | − | 3.91457i | − | 0.0213911i | ||||||
\(184\) | 10.6799 | − | 16.0804i | 0.0580427 | − | 0.0873934i | ||||
\(185\) | −282.416 | −1.52657 | ||||||||
\(186\) | 29.2027 | + | 25.5621i | 0.157004 | + | 0.137431i | ||||
\(187\) | 56.3202 | 0.301177 | ||||||||
\(188\) | −27.9135 | − | 209.021i | −0.148476 | − | 1.11182i | ||||
\(189\) | − | 69.5467i | − | 0.367972i | ||||||
\(190\) | 213.143 | + | 186.572i | 1.12181 | + | 0.981956i | ||||
\(191\) | − | 4.29489i | − | 0.0224864i | −0.999937 | − | 0.0112432i | \(-0.996421\pi\) | ||
0.999937 | − | 0.0112432i | \(-0.00357889\pi\) | |||||||
\(192\) | −102.175 | + | 42.9912i | −0.532162 | + | 0.223913i | ||||
\(193\) | − | 375.756i | − | 1.94692i | −0.228848 | − | 0.973462i | \(-0.573496\pi\) | ||
0.228848 | − | 0.973462i | \(-0.426504\pi\) | |||||||
\(194\) | −245.512 | − | 214.905i | −1.26553 | − | 1.10776i | ||||
\(195\) | −126.220 | − | 109.372i | −0.647280 | − | 0.560884i | ||||
\(196\) | −68.9051 | − | 515.975i | −0.351556 | − | 2.63252i | ||||
\(197\) | 54.1267i | 0.274755i | 0.990519 | + | 0.137377i | \(0.0438673\pi\) | ||||
−0.990519 | + | 0.137377i | \(0.956133\pi\) | |||||||
\(198\) | −57.7175 | + | 65.9377i | −0.291503 | + | 0.333019i | ||||
\(199\) | 141.950i | 0.713317i | 0.934235 | + | 0.356658i | \(0.116084\pi\) | ||||
−0.934235 | + | 0.356658i | \(0.883916\pi\) | |||||||
\(200\) | −200.038 | − | 132.856i | −1.00019 | − | 0.664281i | ||||
\(201\) | 47.0573i | 0.234116i | ||||||||
\(202\) | 59.7697 | − | 68.2821i | 0.295889 | − | 0.338030i | ||||
\(203\) | 253.687 | 1.24969 | ||||||||
\(204\) | −26.4815 | + | 3.53643i | −0.129811 | + | 0.0173355i | ||||
\(205\) | 263.531 | 1.28551 | ||||||||
\(206\) | 159.920 | + | 139.983i | 0.776309 | + | 0.679530i | ||||
\(207\) | 7.23894i | 0.0349707i | ||||||||
\(208\) | −187.429 | − | 90.1906i | −0.901101 | − | 0.433609i | ||||
\(209\) | 278.880 | 1.33435 | ||||||||
\(210\) | 226.510 | − | 258.770i | 1.07862 | − | 1.23224i | ||||
\(211\) | 80.1749i | 0.379976i | 0.981786 | + | 0.189988i | \(0.0608449\pi\) | ||||
−0.981786 | + | 0.189988i | \(0.939155\pi\) | |||||||
\(212\) | −29.7459 | − | 222.743i | −0.140311 | − | 1.05067i | ||||
\(213\) | 44.9400i | 0.210986i | ||||||||
\(214\) | −114.802 | − | 100.490i | −0.536460 | − | 0.469582i | ||||
\(215\) | 75.4125 | 0.350756 | ||||||||
\(216\) | 22.9982 | − | 34.6278i | 0.106473 | − | 0.160314i | ||||
\(217\) | −149.951 | −0.691017 | ||||||||
\(218\) | 206.806 | + | 181.024i | 0.948650 | + | 0.830386i | ||||
\(219\) | −35.1121 | −0.160329 | ||||||||
\(220\) | −429.511 | + | 57.3584i | −1.95232 | + | 0.260720i | ||||
\(221\) | −37.8859 | − | 32.8291i | −0.171429 | − | 0.148548i | ||||
\(222\) | 86.8728 | − | 99.2453i | 0.391319 | − | 0.447051i | ||||
\(223\) | −274.866 | −1.23258 | −0.616291 | − | 0.787519i | \(-0.711365\pi\) | ||||
−0.616291 | + | 0.787519i | \(0.711365\pi\) | |||||||
\(224\) | 187.644 | − | 385.004i | 0.837697 | − | 1.71877i | ||||
\(225\) | 90.0516 | 0.400230 | ||||||||
\(226\) | −222.042 | + | 253.665i | −0.982486 | + | 1.12241i | ||||
\(227\) | −265.324 | −1.16883 | −0.584414 | − | 0.811456i | \(-0.698675\pi\) | ||||
−0.584414 | + | 0.811456i | \(0.698675\pi\) | |||||||
\(228\) | −131.128 | + | 17.5113i | −0.575123 | + | 0.0768040i | ||||
\(229\) | − | 239.829i | − | 1.04729i | −0.851937 | − | 0.523644i | \(-0.824572\pi\) | ||
0.851937 | − | 0.523644i | \(-0.175428\pi\) | |||||||
\(230\) | −23.5769 | + | 26.9347i | −0.102508 | + | 0.117107i | ||||
\(231\) | − | 338.578i | − | 1.46571i | ||||||
\(232\) | 126.312 | + | 83.8909i | 0.544450 | + | 0.361599i | ||||
\(233\) | −28.7181 | −0.123254 | −0.0616268 | − | 0.998099i | \(-0.519629\pi\) | ||||
−0.0616268 | + | 0.998099i | \(0.519629\pi\) | |||||||
\(234\) | 77.2610 | − | 10.7119i | 0.330175 | − | 0.0457774i | ||||
\(235\) | 391.038i | 1.66399i | ||||||||
\(236\) | 12.1387 | + | 90.8969i | 0.0514351 | + | 0.385157i | ||||
\(237\) | −25.8518 | −0.109079 | ||||||||
\(238\) | 67.9889 | − | 77.6719i | 0.285668 | − | 0.326353i | ||||
\(239\) | 53.5722 | 0.224151 | 0.112076 | − | 0.993700i | \(-0.464250\pi\) | ||||
0.112076 | + | 0.993700i | \(0.464250\pi\) | |||||||
\(240\) | 198.353 | − | 53.9394i | 0.826469 | − | 0.224747i | ||||
\(241\) | − | 56.8926i | − | 0.236069i | −0.993009 | − | 0.118034i | \(-0.962341\pi\) | ||
0.993009 | − | 0.118034i | \(-0.0376593\pi\) | |||||||
\(242\) | −121.597 | + | 138.915i | −0.502466 | + | 0.574028i | ||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 1.19665 | + | 8.96077i | 0.00490431 | + | 0.0367245i | ||||
\(245\) | 965.286i | 3.93994i | ||||||||
\(246\) | −81.0634 | + | 92.6086i | −0.329526 | + | 0.376458i | ||||
\(247\) | −187.599 | − | 162.559i | −0.759511 | − | 0.658135i | ||||
\(248\) | −74.6615 | − | 49.5867i | −0.301054 | − | 0.199946i | ||||
\(249\) | − | 5.99960i | − | 0.0240948i | ||||||
\(250\) | 56.0042 | + | 49.0224i | 0.224017 | + | 0.196090i | ||||
\(251\) | 0.708529i | 0.00282283i | 0.999999 | + | 0.00141141i | \(0.000449267\pi\) | ||||
−0.999999 | + | 0.00141141i | \(0.999551\pi\) | |||||||
\(252\) | 21.2599 | + | 159.198i | 0.0843645 | + | 0.631738i | ||||
\(253\) | 35.2418i | 0.139295i | ||||||||
\(254\) | −187.899 | − | 164.474i | −0.739759 | − | 0.647536i | ||||
\(255\) | 49.5416 | 0.194281 | ||||||||
\(256\) | 220.745 | − | 129.644i | 0.862285 | − | 0.506424i | ||||
\(257\) | −151.217 | −0.588395 | −0.294197 | − | 0.955745i | \(-0.595052\pi\) | ||||
−0.294197 | + | 0.955745i | \(0.595052\pi\) | |||||||
\(258\) | −23.1973 | + | 26.5011i | −0.0899120 | + | 0.102717i | ||||
\(259\) | 509.607i | 1.96759i | ||||||||
\(260\) | 322.361 | + | 211.778i | 1.23985 | + | 0.814530i | ||||
\(261\) | −56.8623 | −0.217863 | ||||||||
\(262\) | 148.520 | + | 130.004i | 0.566869 | + | 0.496200i | ||||
\(263\) | 215.466i | 0.819262i | 0.912251 | + | 0.409631i | \(0.134342\pi\) | ||||
−0.912251 | + | 0.409631i | \(0.865658\pi\) | |||||||
\(264\) | 111.963 | − | 168.580i | 0.424104 | − | 0.638562i | ||||
\(265\) | 416.708i | 1.57248i | ||||||||
\(266\) | 336.660 | − | 384.607i | 1.26564 | − | 1.44589i | ||||
\(267\) | 255.319 | 0.956251 | ||||||||
\(268\) | −14.3850 | − | 107.718i | −0.0536755 | − | 0.401933i | ||||
\(269\) | −296.034 | −1.10050 | −0.550249 | − | 0.835000i | \(-0.685467\pi\) | ||||
−0.550249 | + | 0.835000i | \(0.685467\pi\) | |||||||
\(270\) | −50.7708 | + | 58.0016i | −0.188040 | + | 0.214821i | ||||
\(271\) | −226.738 | −0.836673 | −0.418336 | − | 0.908292i | \(-0.637387\pi\) | ||||
−0.418336 | + | 0.908292i | \(0.637387\pi\) | |||||||
\(272\) | 59.5372 | − | 16.1904i | 0.218887 | − | 0.0595233i | ||||
\(273\) | −197.357 | + | 227.757i | −0.722921 | + | 0.834276i | ||||
\(274\) | 145.333 | + | 127.215i | 0.530413 | + | 0.464288i | ||||
\(275\) | 438.403 | 1.59419 | ||||||||
\(276\) | −2.21288 | − | 16.5705i | −0.00801770 | − | 0.0600381i | ||||
\(277\) | −57.2551 | −0.206697 | −0.103349 | − | 0.994645i | \(-0.532956\pi\) | ||||
−0.103349 | + | 0.994645i | \(0.532956\pi\) | |||||||
\(278\) | 381.377 | + | 333.832i | 1.37186 | + | 1.20083i | ||||
\(279\) | 33.6105 | 0.120468 | ||||||||
\(280\) | −439.396 | + | 661.587i | −1.56927 | + | 2.36281i | ||||
\(281\) | − | 169.616i | − | 0.603615i | −0.953369 | − | 0.301808i | \(-0.902410\pi\) | ||
0.953369 | − | 0.301808i | \(-0.0975901\pi\) | |||||||
\(282\) | −137.417 | − | 120.285i | −0.487293 | − | 0.426544i | ||||
\(283\) | − | 355.164i | − | 1.25500i | −0.778618 | − | 0.627498i | \(-0.784079\pi\) | ||
0.778618 | − | 0.627498i | \(-0.215921\pi\) | |||||||
\(284\) | −13.7378 | − | 102.871i | −0.0483725 | − | 0.362223i | ||||
\(285\) | 245.315 | 0.860753 | ||||||||
\(286\) | 376.134 | − | 52.1494i | 1.31515 | − | 0.182341i | ||||
\(287\) | − | 475.528i | − | 1.65689i | ||||||
\(288\) | −42.0593 | + | 86.2961i | −0.146039 | + | 0.299639i | ||||
\(289\) | −274.130 | −0.948546 | ||||||||
\(290\) | −211.573 | − | 185.197i | −0.729564 | − | 0.638612i | ||||
\(291\) | −282.569 | −0.971029 | ||||||||
\(292\) | 80.3745 | − | 10.7335i | 0.275255 | − | 0.0367585i | ||||
\(293\) | − | 484.480i | − | 1.65351i | −0.562559 | − | 0.826757i | \(-0.690183\pi\) | ||
0.562559 | − | 0.826757i | \(-0.309817\pi\) | |||||||
\(294\) | −339.216 | − | 296.927i | −1.15380 | − | 1.00996i | ||||
\(295\) | − | 170.050i | − | 0.576441i | ||||||
\(296\) | −168.520 | + | 253.737i | −0.569325 | + | 0.857218i | ||||
\(297\) | 75.8902i | 0.255522i | ||||||||
\(298\) | −130.610 | − | 114.327i | −0.438288 | − | 0.383648i | ||||
\(299\) | 20.5424 | − | 23.7067i | 0.0687038 | − | 0.0792866i | ||||
\(300\) | −206.135 | + | 27.5280i | −0.687118 | + | 0.0917601i | ||||
\(301\) | − | 136.078i | − | 0.452088i | ||||||
\(302\) | −258.312 | + | 295.101i | −0.855338 | + | 0.977156i | ||||
\(303\) | − | 78.5885i | − | 0.259368i | ||||||
\(304\) | 294.810 | − | 80.1696i | 0.969769 | − | 0.263716i | ||||
\(305\) | − | 16.7638i | − | 0.0549633i | ||||||
\(306\) | −15.2393 | + | 17.4097i | −0.0498016 | + | 0.0568944i | ||||
\(307\) | −179.917 | −0.586047 | −0.293024 | − | 0.956105i | \(-0.594661\pi\) | ||||
−0.293024 | + | 0.956105i | \(0.594661\pi\) | |||||||
\(308\) | 103.501 | + | 775.033i | 0.336041 | + | 2.51634i | ||||
\(309\) | 184.058 | 0.595656 | ||||||||
\(310\) | 125.058 | + | 109.468i | 0.403413 | + | 0.353121i | ||||
\(311\) | − | 9.50603i | − | 0.0305660i | −0.999883 | − | 0.0152830i | \(-0.995135\pi\) | ||
0.999883 | − | 0.0152830i | \(-0.00486492\pi\) | |||||||
\(312\) | −173.582 | + | 48.1385i | −0.556352 | + | 0.154290i | ||||
\(313\) | −67.4047 | −0.215350 | −0.107675 | − | 0.994186i | \(-0.534341\pi\) | ||||
−0.107675 | + | 0.994186i | \(0.534341\pi\) | |||||||
\(314\) | 121.785 | − | 139.130i | 0.387850 | − | 0.443088i | ||||
\(315\) | − | 297.828i | − | 0.945485i | ||||||
\(316\) | 59.1768 | − | 7.90267i | 0.187268 | − | 0.0250085i | ||||
\(317\) | − | 355.562i | − | 1.12165i | −0.827936 | − | 0.560823i | \(-0.810485\pi\) | ||
0.827936 | − | 0.560823i | \(-0.189515\pi\) | |||||||
\(318\) | −146.437 | − | 128.182i | −0.460495 | − | 0.403087i | ||||
\(319\) | −276.826 | −0.867793 | ||||||||
\(320\) | −437.556 | + | 184.106i | −1.36736 | + | 0.575332i | ||||
\(321\) | −132.130 | −0.411621 | ||||||||
\(322\) | 48.6024 | + | 42.5433i | 0.150939 | + | 0.132122i | ||||
\(323\) | 73.6333 | 0.227967 | ||||||||
\(324\) | −4.76526 | − | 35.6832i | −0.0147076 | − | 0.110133i | ||||
\(325\) | −294.909 | − | 255.546i | −0.907411 | − | 0.786294i | ||||
\(326\) | −299.266 | + | 341.887i | −0.917992 | + | 1.04873i | ||||
\(327\) | 238.021 | 0.727891 | ||||||||
\(328\) | 157.251 | − | 236.769i | 0.479424 | − | 0.721856i | ||||
\(329\) | 705.609 | 2.14471 | ||||||||
\(330\) | −247.170 | + | 282.373i | −0.749001 | + | 0.855674i | ||||
\(331\) | −332.355 | −1.00409 | −0.502047 | − | 0.864840i | \(-0.667420\pi\) | ||||
−0.502047 | + | 0.864840i | \(0.667420\pi\) | |||||||
\(332\) | 1.83403 | + | 13.7336i | 0.00552418 | + | 0.0413661i | ||||
\(333\) | − | 114.225i | − | 0.343018i | ||||||
\(334\) | 276.345 | − | 315.703i | 0.827381 | − | 0.945218i | ||||
\(335\) | 201.519i | 0.601549i | ||||||||
\(336\) | −97.3310 | − | 357.918i | −0.289676 | − | 1.06523i | ||||
\(337\) | −419.712 | −1.24544 | −0.622718 | − | 0.782446i | \(-0.713972\pi\) | ||||
−0.622718 | + | 0.782446i | \(0.713972\pi\) | |||||||
\(338\) | −283.419 | − | 184.168i | −0.838516 | − | 0.544877i | ||||
\(339\) | 291.953i | 0.861218i | ||||||||
\(340\) | −113.405 | + | 15.1445i | −0.333543 | + | 0.0445426i | ||||
\(341\) | 163.628 | 0.479847 | ||||||||
\(342\) | −75.4601 | + | 86.2073i | −0.220644 | + | 0.252068i | ||||
\(343\) | 1085.98 | 3.16613 | ||||||||
\(344\) | 44.9993 | − | 67.7543i | 0.130812 | − | 0.196960i | ||||
\(345\) | 31.0001i | 0.0898555i | ||||||||
\(346\) | −405.104 | + | 462.799i | −1.17082 | + | 1.33757i | ||||
\(347\) | 338.651i | 0.975938i | 0.872861 | + | 0.487969i | \(0.162262\pi\) | ||||
−0.872861 | + | 0.487969i | \(0.837738\pi\) | |||||||
\(348\) | 130.162 | − | 17.3823i | 0.374030 | − | 0.0499492i | ||||
\(349\) | 201.723i | 0.578004i | 0.957329 | + | 0.289002i | \(0.0933234\pi\) | ||||
−0.957329 | + | 0.289002i | \(0.906677\pi\) | |||||||
\(350\) | 529.234 | − | 604.608i | 1.51210 | − | 1.72745i | ||||
\(351\) | 44.2364 | − | 51.0504i | 0.126030 | − | 0.145443i | ||||
\(352\) | −204.759 | + | 420.120i | −0.581703 | + | 1.19352i | ||||
\(353\) | 214.052i | 0.606378i | 0.952930 | + | 0.303189i | \(0.0980514\pi\) | ||||
−0.952930 | + | 0.303189i | \(0.901949\pi\) | |||||||
\(354\) | 59.7582 | + | 52.3083i | 0.168808 | + | 0.147764i | ||||
\(355\) | 192.452i | 0.542118i | ||||||||
\(356\) | −584.445 | + | 78.0489i | −1.64170 | + | 0.219238i | ||||
\(357\) | − | 89.3956i | − | 0.250408i | ||||||
\(358\) | −480.963 | − | 421.003i | −1.34347 | − | 1.17599i | ||||
\(359\) | −44.1415 | −0.122957 | −0.0614784 | − | 0.998108i | \(-0.519582\pi\) | ||||
−0.0614784 | + | 0.998108i | \(0.519582\pi\) | |||||||
\(360\) | 98.4878 | − | 148.291i | 0.273577 | − | 0.411918i | ||||
\(361\) | 3.60902 | 0.00999730 | ||||||||
\(362\) | −313.318 | + | 357.942i | −0.865521 | + | 0.988789i | ||||
\(363\) | 159.882i | 0.440447i | ||||||||
\(364\) | 382.143 | − | 581.685i | 1.04984 | − | 1.59804i | ||||
\(365\) | −150.365 | −0.411958 | ||||||||
\(366\) | 5.89106 | + | 5.15664i | 0.0160958 | + | 0.0140892i | ||||
\(367\) | − | 520.972i | − | 1.41954i | −0.704432 | − | 0.709772i | \(-0.748798\pi\) | ||
0.704432 | − | 0.709772i | \(-0.251202\pi\) | |||||||
\(368\) | 10.1309 | + | 37.2548i | 0.0275297 | + | 0.101236i | ||||
\(369\) | 106.587i | 0.288853i | ||||||||
\(370\) | 372.025 | − | 425.009i | 1.00547 | − | 1.14867i | ||||
\(371\) | 751.930 | 2.02677 | ||||||||
\(372\) | −76.9371 | + | 10.2744i | −0.206820 | + | 0.0276195i | ||||
\(373\) | 42.1017 | 0.112873 | 0.0564367 | − | 0.998406i | \(-0.482026\pi\) | ||||
0.0564367 | + | 0.998406i | \(0.482026\pi\) | |||||||
\(374\) | −74.1902 | + | 84.7565i | −0.198370 | + | 0.226622i | ||||
\(375\) | 64.4574 | 0.171886 | ||||||||
\(376\) | 351.328 | + | 233.336i | 0.934382 | + | 0.620574i | ||||
\(377\) | 186.217 | + | 161.362i | 0.493945 | + | 0.428016i | ||||
\(378\) | 104.661 | + | 91.6135i | 0.276881 | + | 0.242364i | ||||
\(379\) | −306.632 | −0.809056 | −0.404528 | − | 0.914526i | \(-0.632564\pi\) | ||||
−0.404528 | + | 0.914526i | \(0.632564\pi\) | |||||||
\(380\) | −561.545 | + | 74.9907i | −1.47775 | + | 0.197344i | ||||
\(381\) | −216.260 | −0.567611 | ||||||||
\(382\) | 6.46340 | + | 5.65764i | 0.0169199 | + | 0.0148106i | ||||
\(383\) | 362.077 | 0.945372 | 0.472686 | − | 0.881231i | \(-0.343285\pi\) | ||||
0.472686 | + | 0.881231i | \(0.343285\pi\) | |||||||
\(384\) | 69.8970 | − | 210.396i | 0.182023 | − | 0.547906i | ||||
\(385\) | − | 1449.93i | − | 3.76606i | ||||||
\(386\) | 565.477 | + | 494.982i | 1.46497 | + | 1.28234i | ||||
\(387\) | 30.5011i | 0.0788142i | ||||||||
\(388\) | 646.824 | − | 86.3791i | 1.66707 | − | 0.222627i | ||||
\(389\) | −216.745 | −0.557184 | −0.278592 | − | 0.960409i | \(-0.589868\pi\) | ||||
−0.278592 | + | 0.960409i | \(0.589868\pi\) | |||||||
\(390\) | 330.863 | − | 45.8729i | 0.848368 | − | 0.117623i | ||||
\(391\) | 9.30496i | 0.0237978i | ||||||||
\(392\) | 867.261 | + | 575.995i | 2.21240 | + | 1.46937i | ||||
\(393\) | 170.937 | 0.434954 | ||||||||
\(394\) | −81.4555 | − | 71.3008i | −0.206740 | − | 0.180966i | ||||
\(395\) | −110.708 | −0.280273 | ||||||||
\(396\) | −23.1990 | − | 173.719i | −0.0585833 | − | 0.438683i | ||||
\(397\) | 187.791i | 0.473025i | 0.971628 | + | 0.236513i | \(0.0760045\pi\) | ||||
−0.971628 | + | 0.236513i | \(0.923996\pi\) | |||||||
\(398\) | −213.621 | − | 186.990i | −0.536737 | − | 0.469824i | ||||
\(399\) | − | 442.659i | − | 1.10942i | ||||||
\(400\) | 463.445 | − | 126.028i | 1.15861 | − | 0.315069i | ||||
\(401\) | − | 261.183i | − | 0.651329i | −0.945485 | − | 0.325665i | \(-0.894412\pi\) | ||
0.945485 | − | 0.325665i | \(-0.105588\pi\) | |||||||
\(402\) | −70.8168 | − | 61.9883i | −0.176161 | − | 0.154200i | ||||
\(403\) | −110.070 | − | 95.3787i | −0.273128 | − | 0.236672i | ||||
\(404\) | 24.0238 | + | 179.895i | 0.0594650 | + | 0.445285i | ||||
\(405\) | 66.7562i | 0.164830i | ||||||||
\(406\) | −334.180 | + | 381.774i | −0.823104 | + | 0.940331i | ||||
\(407\) | − | 556.089i | − | 1.36631i | ||||||
\(408\) | 29.5619 | − | 44.5106i | 0.0724557 | − | 0.109095i | ||||
\(409\) | 461.162i | 1.12754i | 0.825933 | + | 0.563768i | \(0.190649\pi\) | ||||
−0.825933 | + | 0.563768i | \(0.809351\pi\) | |||||||
\(410\) | −347.147 | + | 396.588i | −0.846700 | + | 0.967288i | ||||
\(411\) | 167.269 | 0.406981 | ||||||||
\(412\) | −421.322 | + | 56.2649i | −1.02263 | + | 0.136565i | ||||
\(413\) | −306.847 | −0.742972 | ||||||||
\(414\) | −10.8939 | − | 9.53581i | −0.0263138 | − | 0.0230334i | ||||
\(415\) | − | 25.6928i | − | 0.0619103i | ||||||
\(416\) | 382.627 | − | 163.255i | 0.919777 | − | 0.392441i | ||||
\(417\) | 438.941 | 1.05262 | ||||||||
\(418\) | −367.367 | + | 419.688i | −0.878868 | + | 1.00404i | ||||
\(419\) | − | 303.528i | − | 0.724411i | −0.932098 | − | 0.362205i | \(-0.882024\pi\) | ||
0.932098 | − | 0.362205i | \(-0.117976\pi\) | |||||||
\(420\) | 91.0435 | + | 681.752i | 0.216770 | + | 1.62322i | ||||
\(421\) | − | 463.284i | − | 1.10044i | −0.835021 | − | 0.550219i | \(-0.814544\pi\) | ||
0.835021 | − | 0.550219i | \(-0.185456\pi\) | |||||||
\(422\) | −120.656 | − | 105.614i | −0.285914 | − | 0.250270i | ||||
\(423\) | −158.158 | −0.373896 | ||||||||
\(424\) | 374.391 | + | 248.653i | 0.882998 | + | 0.586447i | ||||
\(425\) | 115.753 | 0.272359 | ||||||||
\(426\) | −67.6304 | − | 59.1992i | −0.158757 | − | 0.138965i | ||||
\(427\) | −30.2495 | −0.0708420 | ||||||||
\(428\) | 302.457 | − | 40.3912i | 0.706675 | − | 0.0943719i | ||||
\(429\) | 215.359 | − | 248.531i | 0.502001 | − | 0.579327i | ||||
\(430\) | −99.3405 | + | 113.489i | −0.231024 | + | 0.263927i | ||||
\(431\) | −435.301 | −1.00998 | −0.504990 | − | 0.863125i | \(-0.668504\pi\) | ||||
−0.504990 | + | 0.863125i | \(0.668504\pi\) | |||||||
\(432\) | 21.8161 | + | 80.2250i | 0.0505003 | + | 0.185706i | ||||
\(433\) | −262.026 | −0.605142 | −0.302571 | − | 0.953127i | \(-0.597845\pi\) | ||||
−0.302571 | + | 0.953127i | \(0.597845\pi\) | |||||||
\(434\) | 197.529 | − | 225.661i | 0.455136 | − | 0.519957i | ||||
\(435\) | −243.508 | −0.559788 | ||||||||
\(436\) | −544.848 | + | 72.7609i | −1.24965 | + | 0.166883i | ||||
\(437\) | 46.0752i | 0.105435i | ||||||||
\(438\) | 46.2530 | − | 52.8404i | 0.105600 | − | 0.120640i | ||||
\(439\) | − | 108.928i | − | 0.248127i | −0.992274 | − | 0.124063i | \(-0.960407\pi\) | ||
0.992274 | − | 0.124063i | \(-0.0395926\pi\) | |||||||
\(440\) | 479.474 | − | 721.931i | 1.08971 | − | 1.64075i | ||||
\(441\) | −390.416 | −0.885298 | ||||||||
\(442\) | 99.3114 | − | 13.7691i | 0.224687 | − | 0.0311519i | ||||
\(443\) | − | 156.345i | − | 0.352923i | −0.984308 | − | 0.176462i | \(-0.943535\pi\) | ||
0.984308 | − | 0.176462i | \(-0.0564652\pi\) | |||||||
\(444\) | 34.9177 | + | 261.470i | 0.0786434 | + | 0.588897i | ||||
\(445\) | 1093.38 | 2.45704 | ||||||||
\(446\) | 362.079 | − | 413.647i | 0.811836 | − | 0.927459i | ||||
\(447\) | −150.324 | −0.336295 | ||||||||
\(448\) | 332.211 | + | 789.549i | 0.741542 | + | 1.76239i | ||||
\(449\) | 6.51043i | 0.0144998i | 0.999974 | + | 0.00724992i | \(0.00230774\pi\) | ||||
−0.999974 | + | 0.00724992i | \(0.997692\pi\) | |||||||
\(450\) | −118.624 | + | 135.519i | −0.263610 | + | 0.301154i | ||||
\(451\) | 518.902i | 1.15056i | ||||||||
\(452\) | −89.2476 | − | 668.303i | −0.197450 | − | 1.47855i | ||||
\(453\) | 339.643i | 0.749764i | ||||||||
\(454\) | 349.509 | − | 399.287i | 0.769844 | − | 0.879487i | ||||
\(455\) | −845.166 | + | 975.352i | −1.85751 | + | 2.14363i | ||||
\(456\) | 146.381 | − | 220.403i | 0.321012 | − | 0.483340i | ||||
\(457\) | 114.069i | 0.249603i | 0.992182 | + | 0.124802i | \(0.0398294\pi\) | ||||
−0.992182 | + | 0.124802i | \(0.960171\pi\) | |||||||
\(458\) | 360.920 | + | 315.925i | 0.788034 | + | 0.689793i | ||||
\(459\) | 20.0374i | 0.0436546i | ||||||||
\(460\) | −9.47649 | − | 70.9618i | −0.0206011 | − | 0.154265i | ||||
\(461\) | 346.907i | 0.752510i | 0.926516 | + | 0.376255i | \(0.122788\pi\) | ||||
−0.926516 | + | 0.376255i | \(0.877212\pi\) | |||||||
\(462\) | 509.528 | + | 446.007i | 1.10287 | + | 0.965383i | ||||
\(463\) | 558.360 | 1.20596 | 0.602980 | − | 0.797756i | \(-0.293980\pi\) | ||||
0.602980 | + | 0.797756i | \(0.293980\pi\) | |||||||
\(464\) | −292.638 | + | 79.5791i | −0.630686 | + | 0.171507i | ||||
\(465\) | 143.934 | 0.309536 | ||||||||
\(466\) | 37.8301 | − | 43.2179i | 0.0811806 | − | 0.0927424i | ||||
\(467\) | − | 470.970i | − | 1.00850i | −0.863558 | − | 0.504250i | \(-0.831769\pi\) | ||
0.863558 | − | 0.504250i | \(-0.168231\pi\) | |||||||
\(468\) | −85.6550 | + | 130.381i | −0.183023 | + | 0.278592i | ||||
\(469\) | 363.631 | 0.775334 | ||||||||
\(470\) | −588.474 | − | 515.112i | −1.25207 | − | 1.09598i | ||||
\(471\) | − | 160.130i | − | 0.339978i | ||||||
\(472\) | −152.781 | − | 101.470i | −0.323689 | − | 0.214980i | ||||
\(473\) | 148.490i | 0.313933i | ||||||||
\(474\) | 34.0544 | − | 38.9044i | 0.0718447 | − | 0.0820769i | ||||
\(475\) | 573.171 | 1.20668 | ||||||||
\(476\) | 27.3275 | + | 204.634i | 0.0574107 | + | 0.429902i | ||||
\(477\) | −168.540 | −0.353334 | ||||||||
\(478\) | −70.5703 | + | 80.6210i | −0.147637 | + | 0.168663i | ||||
\(479\) | 198.543 | 0.414495 | 0.207248 | − | 0.978289i | \(-0.433549\pi\) | ||||
0.207248 | + | 0.978289i | \(0.433549\pi\) | |||||||
\(480\) | −180.115 | + | 369.556i | −0.375240 | + | 0.769908i | ||||
\(481\) | −324.144 | + | 374.074i | −0.673897 | + | 0.777700i | ||||
\(482\) | 85.6180 | + | 74.9443i | 0.177631 | + | 0.155486i | ||||
\(483\) | 55.9383 | 0.115814 | ||||||||
\(484\) | −48.8747 | − | 365.983i | −0.100981 | − | 0.756164i | ||||
\(485\) | −1210.08 | −2.49501 | ||||||||
\(486\) | −23.4591 | − | 20.5346i | −0.0482698 | − | 0.0422522i | ||||
\(487\) | 42.2257 | 0.0867057 | 0.0433528 | − | 0.999060i | \(-0.486196\pi\) | ||||
0.0433528 | + | 0.999060i | \(0.486196\pi\) | |||||||
\(488\) | −15.0614 | − | 10.0031i | −0.0308636 | − | 0.0204982i | ||||
\(489\) | 393.491i | 0.804685i | ||||||||
\(490\) | −1452.66 | − | 1271.57i | −2.96462 | − | 2.59503i | ||||
\(491\) | − | 159.084i | − | 0.324000i | −0.986791 | − | 0.162000i | \(-0.948206\pi\) | ||
0.986791 | − | 0.162000i | \(-0.0517944\pi\) | |||||||
\(492\) | −32.5827 | − | 243.985i | −0.0662249 | − | 0.495905i | ||||
\(493\) | −73.0909 | −0.148257 | ||||||||
\(494\) | 491.759 | − | 68.1804i | 0.995464 | − | 0.138017i | ||||
\(495\) | 324.993i | 0.656552i | ||||||||
\(496\) | 172.974 | − | 47.0381i | 0.348739 | − | 0.0948348i | ||||
\(497\) | 347.270 | 0.698733 | ||||||||
\(498\) | 9.02882 | + | 7.90323i | 0.0181302 | + | 0.0158699i | ||||
\(499\) | −47.8199 | −0.0958315 | −0.0479158 | − | 0.998851i | \(-0.515258\pi\) | ||||
−0.0479158 | + | 0.998851i | \(0.515258\pi\) | |||||||
\(500\) | −147.548 | + | 19.7041i | −0.295096 | + | 0.0394082i | ||||
\(501\) | − | 363.354i | − | 0.725258i | ||||||
\(502\) | −1.06627 | − | 0.933342i | −0.00212404 | − | 0.00185925i | ||||
\(503\) | 656.485i | 1.30514i | 0.757729 | + | 0.652569i | \(0.226309\pi\) | ||||
−0.757729 | + | 0.652569i | \(0.773691\pi\) | |||||||
\(504\) | −267.583 | − | 177.717i | −0.530919 | − | 0.352612i | ||||
\(505\) | − | 336.548i | − | 0.666432i | ||||||
\(506\) | −53.0355 | − | 46.4237i | −0.104813 | − | 0.0917465i | ||||
\(507\) | −289.738 | + | 41.6514i | −0.571476 | + | 0.0821527i | ||||
\(508\) | 495.036 | − | 66.1088i | 0.974480 | − | 0.130135i | ||||
\(509\) | 287.339i | 0.564517i | 0.959338 | + | 0.282258i | \(0.0910835\pi\) | ||||
−0.959338 | + | 0.282258i | \(0.908916\pi\) | |||||||
\(510\) | −65.2609 | + | 74.5554i | −0.127963 | + | 0.146187i | ||||
\(511\) | 271.326i | 0.530971i | ||||||||
\(512\) | −95.6835 | + | 502.980i | −0.186882 | + | 0.982382i | ||||
\(513\) | 99.2192i | 0.193410i | ||||||||
\(514\) | 199.198 | − | 227.568i | 0.387544 | − | 0.442739i | ||||
\(515\) | 788.211 | 1.53051 | ||||||||
\(516\) | −9.32393 | − | 69.8195i | −0.0180696 | − | 0.135309i | ||||
\(517\) | −769.969 | −1.48930 | ||||||||
\(518\) | −766.909 | − | 671.302i | −1.48052 | − | 1.29595i | ||||
\(519\) | 532.653i | 1.02631i | ||||||||
\(520\) | −743.350 | + | 206.149i | −1.42952 | + | 0.396440i | ||||
\(521\) | −574.903 | −1.10346 | −0.551730 | − | 0.834023i | \(-0.686032\pi\) | ||||
−0.551730 | + | 0.834023i | \(0.686032\pi\) | |||||||
\(522\) | 74.9043 | − | 85.5723i | 0.143495 | − | 0.163932i | ||||
\(523\) | 468.034i | 0.894903i | 0.894308 | + | 0.447452i | \(0.147668\pi\) | ||||
−0.894308 | + | 0.447452i | \(0.852332\pi\) | |||||||
\(524\) | −391.288 | + | 52.2540i | −0.746733 | + | 0.0997214i | ||||
\(525\) | − | 695.866i | − | 1.32546i | ||||||
\(526\) | −324.255 | − | 283.832i | −0.616455 | − | 0.539604i | ||||
\(527\) | 43.2030 | 0.0819792 | ||||||||
\(528\) | 106.209 | + | 390.564i | 0.201153 | + | 0.739705i | ||||
\(529\) | 523.178 | 0.988993 | ||||||||
\(530\) | −627.106 | − | 548.927i | −1.18322 | − | 1.03571i | ||||
\(531\) | 68.7779 | 0.129525 | ||||||||
\(532\) | 135.317 | + | 1013.28i | 0.254356 | + | 1.90466i | ||||
\(533\) | 302.468 | − | 349.059i | 0.567482 | − | 0.654895i | ||||
\(534\) | −336.330 | + | 384.231i | −0.629832 | + | 0.719533i | ||||
\(535\) | −565.837 | −1.05764 | ||||||||
\(536\) | 181.055 | + | 120.248i | 0.337788 | + | 0.224344i | ||||
\(537\) | −553.558 | −1.03083 | ||||||||
\(538\) | 389.964 | − | 445.503i | 0.724840 | − | 0.828072i | ||||
\(539\) | −1900.69 | −3.52632 | ||||||||
\(540\) | −20.4068 | − | 152.810i | −0.0377904 | − | 0.282982i | ||||
\(541\) | 670.174i | 1.23877i | 0.785088 | + | 0.619384i | \(0.212618\pi\) | ||||
−0.785088 | + | 0.619384i | \(0.787382\pi\) | |||||||
\(542\) | 298.681 | − | 341.219i | 0.551072 | − | 0.629556i | ||||
\(543\) | 411.968i | 0.758690i | ||||||||
\(544\) | −54.0631 | + | 110.925i | −0.0993807 | + | 0.203907i | ||||
\(545\) | 1019.30 | 1.87028 | ||||||||
\(546\) | −82.7754 | − | 597.027i | −0.151603 | − | 1.09346i | ||||
\(547\) | − | 453.519i | − | 0.829102i | −0.910026 | − | 0.414551i | \(-0.863939\pi\) | ||
0.910026 | − | 0.414551i | \(-0.136061\pi\) | |||||||
\(548\) | −382.893 | + | 51.1328i | −0.698709 | + | 0.0933081i | ||||
\(549\) | 6.78024 | 0.0123502 | ||||||||
\(550\) | −577.506 | + | 659.755i | −1.05001 | + | 1.19955i | ||||
\(551\) | −361.923 | −0.656848 | ||||||||
\(552\) | 27.8521 | + | 18.4981i | 0.0504566 | + | 0.0335110i | ||||
\(553\) | 199.767i | 0.361243i | ||||||||
\(554\) | 75.4218 | − | 86.1635i | 0.136141 | − | 0.155530i | ||||
\(555\) | − | 489.159i | − | 0.881368i | ||||||
\(556\) | −1004.77 | + | 134.181i | −1.80714 | + | 0.241332i | ||||
\(557\) | 146.356i | 0.262758i | 0.991332 | + | 0.131379i | \(0.0419404\pi\) | ||||
−0.991332 | + | 0.131379i | \(0.958060\pi\) | |||||||
\(558\) | −44.2749 | + | 50.5806i | −0.0793457 | + | 0.0906462i | ||||
\(559\) | 86.5550 | − | 99.8875i | 0.154839 | − | 0.178690i | ||||
\(560\) | −416.812 | − | 1532.75i | −0.744307 | − | 2.73706i | ||||
\(561\) | 97.5494i | 0.173885i | ||||||||
\(562\) | 255.256 | + | 223.434i | 0.454192 | + | 0.397570i | ||||
\(563\) | − | 273.083i | − | 0.485050i | −0.970145 | − | 0.242525i | \(-0.922024\pi\) | ||
0.970145 | − | 0.242525i | \(-0.0779757\pi\) | |||||||
\(564\) | 362.036 | − | 48.3475i | 0.641908 | − | 0.0857226i | ||||
\(565\) | 1250.26i | 2.21285i | ||||||||
\(566\) | 534.487 | + | 467.855i | 0.944324 | + | 0.826599i | ||||
\(567\) | 120.458 | 0.212449 | ||||||||
\(568\) | 172.908 | + | 114.838i | 0.304416 | + | 0.202179i | ||||
\(569\) | 787.692 | 1.38435 | 0.692173 | − | 0.721732i | \(-0.256654\pi\) | ||||
0.692173 | + | 0.721732i | \(0.256654\pi\) | |||||||
\(570\) | −323.152 | + | 369.175i | −0.566933 | + | 0.647676i | ||||
\(571\) | − | 552.730i | − | 0.968004i | −0.875067 | − | 0.484002i | \(-0.839183\pi\) | ||
0.875067 | − | 0.484002i | \(-0.160817\pi\) | |||||||
\(572\) | −416.999 | + | 634.742i | −0.729019 | + | 1.10969i | ||||
\(573\) | 7.43897 | 0.0129825 | ||||||||
\(574\) | 715.625 | + | 626.411i | 1.24673 | + | 1.09131i | ||||
\(575\) | 72.4310i | 0.125967i | ||||||||
\(576\) | −74.4630 | − | 176.972i | −0.129276 | − | 0.307244i | ||||
\(577\) | 961.217i | 1.66589i | 0.553357 | + | 0.832944i | \(0.313346\pi\) | ||||
−0.553357 | + | 0.832944i | \(0.686654\pi\) | |||||||
\(578\) | 361.109 | − | 412.539i | 0.624757 | − | 0.713735i | ||||
\(579\) | 650.829 | 1.12406 | ||||||||
\(580\) | 557.409 | − | 74.4383i | 0.961050 | − | 0.128342i | ||||
\(581\) | −46.3614 | −0.0797958 | ||||||||
\(582\) | 372.227 | − | 425.240i | 0.639565 | − | 0.730653i | ||||
\(583\) | −820.515 | −1.40740 | ||||||||
\(584\) | −89.7240 | + | 135.095i | −0.153637 | + | 0.231327i | ||||
\(585\) | 189.439 | − | 218.619i | 0.323827 | − | 0.373707i | ||||
\(586\) | 729.095 | + | 638.202i | 1.24419 | + | 1.08908i | ||||
\(587\) | 416.312 | 0.709220 | 0.354610 | − | 0.935014i | \(-0.384614\pi\) | ||||
0.354610 | + | 0.935014i | \(0.384614\pi\) | |||||||
\(588\) | 893.694 | − | 119.347i | 1.51989 | − | 0.202971i | ||||
\(589\) | 213.928 | 0.363205 | ||||||||
\(590\) | 255.909 | + | 224.006i | 0.433744 | + | 0.379671i | ||||
\(591\) | −93.7502 | −0.158630 | ||||||||
\(592\) | −159.859 | − | 587.853i | −0.270032 | − | 0.992994i | ||||
\(593\) | − | 956.542i | − | 1.61306i | −0.591196 | − | 0.806528i | \(-0.701344\pi\) | ||
0.591196 | − | 0.806528i | \(-0.298656\pi\) | |||||||
\(594\) | −114.207 | − | 99.9697i | −0.192268 | − | 0.168299i | ||||
\(595\) | − | 382.829i | − | 0.643410i | ||||||
\(596\) | 344.103 | − | 45.9527i | 0.577354 | − | 0.0771019i | ||||
\(597\) | −245.865 | −0.411834 | ||||||||
\(598\) | 8.61588 | + | 62.1431i | 0.0144078 | + | 0.103918i | ||||
\(599\) | 80.3454i | 0.134132i | 0.997749 | + | 0.0670662i | \(0.0213639\pi\) | ||||
−0.997749 | + | 0.0670662i | \(0.978636\pi\) | |||||||
\(600\) | 230.114 | − | 346.477i | 0.383523 | − | 0.577461i | ||||
\(601\) | 337.707 | 0.561908 | 0.280954 | − | 0.959721i | \(-0.409349\pi\) | ||||
0.280954 | + | 0.959721i | \(0.409349\pi\) | |||||||
\(602\) | 204.785 | + | 179.255i | 0.340174 | + | 0.297766i | ||||
\(603\) | −81.5057 | −0.135167 | ||||||||
\(604\) | −103.826 | − | 777.470i | −0.171897 | − | 1.28720i | ||||
\(605\) | 684.682i | 1.13171i | ||||||||
\(606\) | 118.268 | + | 103.524i | 0.195162 | + | 0.170832i | ||||
\(607\) | 519.206i | 0.855365i | 0.903929 | + | 0.427682i | \(0.140670\pi\) | ||||
−0.903929 | + | 0.427682i | \(0.859330\pi\) | |||||||
\(608\) | −267.703 | + | 549.267i | −0.440302 | + | 0.903400i | ||||
\(609\) | 439.398i | 0.721508i | ||||||||
\(610\) | 25.2279 | + | 22.0829i | 0.0413573 | + | 0.0362014i | ||||
\(611\) | 517.948 | + | 448.815i | 0.847706 | + | 0.734558i | ||||
\(612\) | −6.12528 | − | 45.8673i | −0.0100086 | − | 0.0749466i | ||||
\(613\) | − | 538.029i | − | 0.877698i | −0.898561 | − | 0.438849i | \(-0.855386\pi\) | ||
0.898561 | − | 0.438849i | \(-0.144614\pi\) | |||||||
\(614\) | 237.003 | − | 270.757i | 0.385998 | − | 0.440973i | ||||
\(615\) | 456.448i | 0.742192i | ||||||||
\(616\) | −1302.69 | − | 865.187i | −2.11476 | − | 1.40452i | ||||
\(617\) | 136.853i | 0.221803i | 0.993831 | + | 0.110902i | \(0.0353739\pi\) | ||||
−0.993831 | + | 0.110902i | \(0.964626\pi\) | |||||||
\(618\) | −242.458 | + | 276.989i | −0.392327 | + | 0.448202i | ||||
\(619\) | −734.349 | −1.18635 | −0.593174 | − | 0.805074i | \(-0.702125\pi\) | ||||
−0.593174 | + | 0.805074i | \(0.702125\pi\) | |||||||
\(620\) | −329.476 | + | 43.9994i | −0.531414 | + | 0.0709668i | ||||
\(621\) | −12.5382 | −0.0201904 | ||||||||
\(622\) | 14.3057 | + | 12.5222i | 0.0229995 | + | 0.0201322i | ||||
\(623\) | − | 1972.96i | − | 3.16686i | ||||||
\(624\) | 156.215 | − | 324.637i | 0.250344 | − | 0.520251i | ||||
\(625\) | −474.397 | −0.759036 | ||||||||
\(626\) | 88.7918 | − | 101.438i | 0.141840 | − | 0.162041i | ||||
\(627\) | 483.034i | 0.770390i | ||||||||
\(628\) | 48.9503 | + | 366.549i | 0.0779463 | + | 0.583677i | ||||
\(629\) | − | 146.825i | − | 0.233427i | ||||||
\(630\) | 448.202 | + | 392.327i | 0.711433 | + | 0.622741i | ||||
\(631\) | 535.698 | 0.848967 | 0.424484 | − | 0.905436i | \(-0.360456\pi\) | ||||
0.424484 | + | 0.905436i | \(0.360456\pi\) | |||||||
\(632\) | −66.0604 | + | 99.4655i | −0.104526 | + | 0.157382i | ||||
\(633\) | −138.867 | −0.219379 | ||||||||
\(634\) | 535.086 | + | 468.379i | 0.843985 | + | 0.738768i | ||||
\(635\) | −926.114 | −1.45845 | ||||||||
\(636\) | 385.802 | − | 51.5214i | 0.606607 | − | 0.0810085i | ||||
\(637\) | 1278.57 | + | 1107.91i | 2.00717 | + | 1.73926i | ||||
\(638\) | 364.661 | − | 416.596i | 0.571569 | − | 0.652972i | ||||
\(639\) | −77.8384 | −0.121813 | ||||||||
\(640\) | 299.328 | − | 901.002i | 0.467700 | − | 1.40782i | ||||
\(641\) | −635.460 | −0.991358 | −0.495679 | − | 0.868506i | \(-0.665081\pi\) | ||||
−0.495679 | + | 0.868506i | \(0.665081\pi\) | |||||||
\(642\) | 174.055 | − | 198.844i | 0.271113 | − | 0.309725i | ||||
\(643\) | 690.793 | 1.07433 | 0.537164 | − | 0.843478i | \(-0.319495\pi\) | ||||
0.537164 | + | 0.843478i | \(0.319495\pi\) | |||||||
\(644\) | −128.047 | + | 17.0999i | −0.198831 | + | 0.0265526i | ||||
\(645\) | 130.618i | 0.202509i | ||||||||
\(646\) | −96.9967 | + | 110.811i | −0.150150 | + | 0.171534i | ||||
\(647\) | 1203.66i | 1.86036i | 0.367099 | + | 0.930182i | \(0.380351\pi\) | ||||
−0.367099 | + | 0.930182i | \(0.619649\pi\) | |||||||
\(648\) | 59.9771 | + | 39.8340i | 0.0925572 | + | 0.0614723i | ||||
\(649\) | 334.835 | 0.515925 | ||||||||
\(650\) | 773.053 | − | 107.181i | 1.18931 | − | 0.164893i | ||||
\(651\) | − | 259.722i | − | 0.398959i | ||||||
\(652\) | −120.287 | − | 900.732i | −0.184489 | − | 1.38149i | ||||
\(653\) | −1145.08 | −1.75357 | −0.876784 | − | 0.480884i | \(-0.840316\pi\) | ||||
−0.876784 | + | 0.480884i | \(0.840316\pi\) | |||||||
\(654\) | −313.543 | + | 358.198i | −0.479424 | + | 0.547703i | ||||
\(655\) | 732.023 | 1.11759 | ||||||||
\(656\) | 149.169 | + | 548.542i | 0.227391 | + | 0.836192i | ||||
\(657\) | − | 60.8160i | − | 0.0925662i | ||||||
\(658\) | −929.495 | + | 1061.87i | −1.41261 | + | 1.61379i | ||||
\(659\) | − | 462.567i | − | 0.701922i | −0.936390 | − | 0.350961i | \(-0.885855\pi\) | ||
0.936390 | − | 0.350961i | \(-0.114145\pi\) | |||||||
\(660\) | −99.3477 | − | 743.935i | −0.150527 | − | 1.12717i | ||||
\(661\) | − | 225.809i | − | 0.341617i | −0.985304 | − | 0.170808i | \(-0.945362\pi\) | ||
0.985304 | − | 0.170808i | \(-0.0546379\pi\) | |||||||
\(662\) | 437.809 | − | 500.162i | 0.661343 | − | 0.755532i | ||||
\(663\) | 56.8616 | − | 65.6203i | 0.0857641 | − | 0.0989748i | ||||
\(664\) | −23.0836 | − | 15.3311i | −0.0347645 | − | 0.0230890i | ||||
\(665\) | − | 1895.65i | − | 2.85060i | ||||||
\(666\) | 171.898 | + | 150.468i | 0.258105 | + | 0.225928i | ||||
\(667\) | − | 45.7359i | − | 0.0685695i | ||||||
\(668\) | 111.074 | + | 831.746i | 0.166279 | + | 1.24513i | ||||
\(669\) | − | 476.081i | − | 0.711632i | ||||||
\(670\) | −303.267 | − | 265.460i | −0.452637 | − | 0.396209i | ||||
\(671\) | 33.0086 | 0.0491932 | ||||||||
\(672\) | 666.846 | + | 325.009i | 0.992330 | + | 0.483645i | ||||
\(673\) | −320.086 | −0.475611 | −0.237805 | − | 0.971313i | \(-0.576428\pi\) | ||||
−0.237805 | + | 0.971313i | \(0.576428\pi\) | |||||||
\(674\) | 552.884 | − | 631.626i | 0.820303 | − | 0.937131i | ||||
\(675\) | 155.974i | 0.231073i | ||||||||
\(676\) | 650.501 | − | 183.914i | 0.962280 | − | 0.272062i | ||||
\(677\) | 401.560 | 0.593146 | 0.296573 | − | 0.955010i | \(-0.404156\pi\) | ||||
0.296573 | + | 0.955010i | \(0.404156\pi\) | |||||||
\(678\) | −439.361 | − | 384.588i | −0.648025 | − | 0.567239i | ||||
\(679\) | 2183.53i | 3.21580i | ||||||||
\(680\) | 126.596 | − | 190.613i | 0.186171 | − | 0.280313i | ||||
\(681\) | − | 459.554i | − | 0.674823i | ||||||
\(682\) | −215.546 | + | 246.244i | −0.316050 | + | 0.361062i | ||||
\(683\) | −1349.93 | −1.97647 | −0.988233 | − | 0.152954i | \(-0.951121\pi\) | ||||
−0.988233 | + | 0.152954i | \(0.951121\pi\) | |||||||
\(684\) | −30.3305 | − | 227.121i | −0.0443428 | − | 0.332048i | ||||
\(685\) | 716.316 | 1.04572 | ||||||||
\(686\) | −1430.56 | + | 1634.30i | −2.08536 | + | 2.38236i | ||||
\(687\) | 415.396 | 0.604652 | ||||||||
\(688\) | 42.6865 | + | 156.972i | 0.0620443 | + | 0.228157i | ||||
\(689\) | 551.950 | + | 478.278i | 0.801089 | + | 0.694163i | ||||
\(690\) | −46.6523 | − | 40.8363i | −0.0676120 | − | 0.0591831i | ||||
\(691\) | 357.059 | 0.516728 | 0.258364 | − | 0.966048i | \(-0.416817\pi\) | ||||
0.258364 | + | 0.966048i | \(0.416817\pi\) | |||||||
\(692\) | −162.827 | − | 1219.28i | −0.235300 | − | 1.76197i | ||||
\(693\) | 586.435 | 0.846226 | ||||||||
\(694\) | −509.637 | − | 446.102i | −0.734347 | − | 0.642799i | ||||
\(695\) | 1879.73 | 2.70464 | ||||||||
\(696\) | −145.303 | + | 218.779i | −0.208769 | + | 0.314338i | ||||
\(697\) | 137.007i | 0.196566i | ||||||||
\(698\) | −303.574 | − | 265.729i | −0.434920 | − | 0.380700i | ||||
\(699\) | − | 49.7412i | − | 0.0711605i | ||||||
\(700\) | 212.721 | + | 1592.89i | 0.303887 | + | 2.27556i | ||||
\(701\) | 878.148 | 1.25271 | 0.626354 | − | 0.779539i | \(-0.284546\pi\) | ||||
0.626354 | + | 0.779539i | \(0.284546\pi\) | |||||||
\(702\) | 18.5536 | + | 133.820i | 0.0264296 | + | 0.190627i | ||||
\(703\) | − | 727.033i | − | 1.03419i | ||||||
\(704\) | −362.512 | − | 861.565i | −0.514932 | − | 1.22381i | ||||
\(705\) | −677.297 | −0.960705 | ||||||||
\(706\) | −322.127 | − | 281.969i | −0.456271 | − | 0.399389i | ||||
\(707\) | −607.286 | −0.858961 | ||||||||
\(708\) | −157.438 | + | 21.0248i | −0.222370 | + | 0.0296961i | ||||
\(709\) | − | 939.736i | − | 1.32544i | −0.748868 | − | 0.662719i | \(-0.769402\pi\) | ||
0.748868 | − | 0.662719i | \(-0.230598\pi\) | |||||||
\(710\) | −289.622 | − | 253.516i | −0.407918 | − | 0.357064i | ||||
\(711\) | − | 44.7766i | − | 0.0629769i | ||||||
\(712\) | 652.430 | − | 982.348i | 0.916335 | − | 1.37970i | ||||
\(713\) | 27.0338i | 0.0379156i | ||||||||
\(714\) | 134.532 | + | 117.760i | 0.188420 | + | 0.164930i | ||||
\(715\) | 922.255 | − | 1064.31i | 1.28987 | − | 1.48855i | ||||
\(716\) | 1267.14 | − | 169.218i | 1.76975 | − | 0.236338i | ||||
\(717\) | 92.7897i | 0.129414i | ||||||||
\(718\) | 58.1473 | − | 66.4287i | 0.0809851 | − | 0.0925191i | ||||
\(719\) | − | 570.999i | − | 0.794157i | −0.917785 | − | 0.397078i | \(-0.870024\pi\) | ||
0.917785 | − | 0.397078i | \(-0.129976\pi\) | |||||||
\(720\) | 93.4257 | + | 343.557i | 0.129758 | + | 0.477162i | ||||
\(721\) | − | 1422.29i | − | 1.97266i | ||||||
\(722\) | −4.75415 | + | 5.43124i | −0.00658469 | + | 0.00752249i | ||||
\(723\) | 98.5409 | 0.136294 | ||||||||
\(724\) | −125.935 | − | 943.029i | −0.173944 | − | 1.30253i | ||||
\(725\) | −568.949 | −0.784757 | ||||||||
\(726\) | −240.607 | − | 210.612i | −0.331415 | − | 0.290099i | ||||
\(727\) | 754.407i | 1.03770i | 0.854866 | + | 0.518849i | \(0.173639\pi\) | ||||
−0.854866 | + | 0.518849i | \(0.826361\pi\) | |||||||
\(728\) | 371.986 | + | 1341.34i | 0.510970 | + | 1.84250i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 198.075 | − | 226.285i | 0.271335 | − | 0.309979i | ||||
\(731\) | 39.2062i | 0.0536337i | ||||||||
\(732\) | −15.5205 | + | 2.07266i | −0.0212029 | + | 0.00283151i | ||||
\(733\) | − | 360.331i | − | 0.491584i | −0.969323 | − | 0.245792i | \(-0.920952\pi\) | ||
0.969323 | − | 0.245792i | \(-0.0790480\pi\) | |||||||
\(734\) | 784.014 | + | 686.274i | 1.06814 | + | 0.934978i | ||||
\(735\) | −1671.92 | −2.27473 | ||||||||
\(736\) | −69.4103 | − | 33.8294i | −0.0943075 | − | 0.0459638i | ||||
\(737\) | −396.799 | −0.538397 | ||||||||
\(738\) | −160.403 | − | 140.406i | −0.217348 | − | 0.190252i | ||||
\(739\) | −112.666 | −0.152458 | −0.0762290 | − | 0.997090i | \(-0.524288\pi\) | ||||
−0.0762290 | + | 0.997090i | \(0.524288\pi\) | |||||||
\(740\) | 149.532 | + | 1119.72i | 0.202070 | + | 1.51314i | ||||
\(741\) | 281.561 | − | 324.931i | 0.379974 | − | 0.438504i | ||||
\(742\) | −990.513 | + | 1131.58i | −1.33492 | + | 1.52504i | ||||
\(743\) | −553.113 | −0.744431 | −0.372216 | − | 0.928146i | \(-0.621402\pi\) | ||||
−0.372216 | + | 0.928146i | \(0.621402\pi\) | |||||||
\(744\) | 85.8867 | − | 129.317i | 0.115439 | − | 0.173814i | ||||
\(745\) | −643.749 | −0.864092 | ||||||||
\(746\) | −55.4604 | + | 63.3591i | −0.0743437 | + | 0.0849318i | ||||
\(747\) | 10.3916 | 0.0139111 | ||||||||
\(748\) | −29.8200 | − | 223.298i | −0.0398664 | − | 0.298527i | ||||
\(749\) | 1021.03i | 1.36319i | ||||||||
\(750\) | −84.9093 | + | 97.0021i | −0.113212 | + | 0.129336i | ||||
\(751\) | − | 871.208i | − | 1.16006i | −0.814594 | − | 0.580032i | \(-0.803040\pi\) | ||
0.814594 | − | 0.580032i | \(-0.196960\pi\) | |||||||
\(752\) | −813.949 | + | 221.343i | −1.08238 | + | 0.294339i | ||||
\(753\) | −1.22721 | −0.00162976 | ||||||||
\(754\) | −488.137 | + | 67.6782i | −0.647397 | + | 0.0897589i | ||||
\(755\) | 1454.49i | 1.92648i | ||||||||
\(756\) | −275.739 | + | 36.8232i | −0.364734 | + | 0.0487079i | ||||
\(757\) | 360.627 | 0.476390 | 0.238195 | − | 0.971217i | \(-0.423444\pi\) | ||||
0.238195 | + | 0.971217i | \(0.423444\pi\) | |||||||
\(758\) | 403.925 | − | 461.452i | 0.532882 | − | 0.608776i | ||||
\(759\) | −61.0405 | −0.0804223 | ||||||||
\(760\) | 626.866 | − | 943.856i | 0.824824 | − | 1.24192i | ||||
\(761\) | − | 925.537i | − | 1.21621i | −0.793856 | − | 0.608106i | \(-0.791930\pi\) | ||
0.793856 | − | 0.608106i | \(-0.208070\pi\) | |||||||
\(762\) | 284.878 | − | 325.450i | 0.373855 | − | 0.427100i | ||||
\(763\) | − | 1839.28i | − | 2.41059i | ||||||
\(764\) | −17.0284 | + | 2.27403i | −0.0222885 | + | 0.00297648i | ||||
\(765\) | 85.8086i | 0.112168i | ||||||||
\(766\) | −476.962 | + | 544.892i | −0.622666 | + | 0.711347i | ||||
\(767\) | −225.240 | − | 195.176i | −0.293663 | − | 0.254466i | ||||
\(768\) | 224.551 | + | 382.341i | 0.292384 | + | 0.497840i | ||||
\(769\) | 106.770i | 0.138842i | 0.997587 | + | 0.0694211i | \(0.0221152\pi\) | ||||
−0.997587 | + | 0.0694211i | \(0.977885\pi\) | |||||||
\(770\) | 2182.01 | + | 1909.99i | 2.83378 | + | 2.48050i | ||||
\(771\) | − | 261.916i | − | 0.339710i | ||||||
\(772\) | −1489.80 | + | 198.953i | −1.92979 | + | 0.257711i | ||||
\(773\) | − | 118.583i | − | 0.153406i | −0.997054 | − | 0.0767032i | \(-0.975561\pi\) | ||
0.997054 | − | 0.0767032i | \(-0.0244394\pi\) | |||||||
\(774\) | −45.9012 | − | 40.1789i | −0.0593039 | − | 0.0519107i | ||||
\(775\) | 336.298 | 0.433933 | ||||||||
\(776\) | −722.065 | + | 1087.19i | −0.930496 | + | 1.40102i | ||||
\(777\) | −882.665 | −1.13599 | ||||||||
\(778\) | 285.516 | − | 326.180i | 0.366988 | − | 0.419255i | ||||
\(779\) | 678.415i | 0.870879i | ||||||||
\(780\) | −366.810 | + | 558.346i | −0.470269 | + | 0.715828i | ||||
\(781\) | −378.945 | −0.485205 | ||||||||
\(782\) | −14.0031 | − | 12.2574i | −0.0179067 | − | 0.0156744i | ||||
\(783\) | − | 98.4884i | − | 0.125783i | ||||||
\(784\) | −2009.25 | + | 546.390i | −2.56282 | + | 0.696926i | ||||
\(785\) | − | 685.741i | − | 0.873556i | ||||||
\(786\) | −225.174 | + | 257.244i | −0.286481 | + | 0.327282i | ||||
\(787\) | 1328.64 | 1.68823 | 0.844117 | − | 0.536160i | \(-0.180126\pi\) | ||||
0.844117 | + | 0.536160i | \(0.180126\pi\) | |||||||
\(788\) | 214.602 | − | 28.6587i | 0.272337 | − | 0.0363689i | ||||
\(789\) | −373.198 | −0.473001 | ||||||||
\(790\) | 145.835 | − | 166.605i | 0.184601 | − | 0.210892i | ||||
\(791\) | 2256.04 | 2.85214 | ||||||||
\(792\) | 291.990 | + | 193.926i | 0.368674 | + | 0.244856i | ||||
\(793\) | −22.2045 | − | 19.2407i | −0.0280006 | − | 0.0242632i | ||||
\(794\) | −282.608 | − | 247.376i | −0.355929 | − | 0.311557i | ||||
\(795\) | −721.760 | −0.907874 | ||||||||
\(796\) | 562.804 | − | 75.1588i | 0.707040 | − | 0.0944206i | ||||
\(797\) | −1194.46 | −1.49869 | −0.749347 | − | 0.662178i | \(-0.769632\pi\) | ||||
−0.749347 | + | 0.662178i | \(0.769632\pi\) | |||||||
\(798\) | 666.159 | + | 583.112i | 0.834786 | + | 0.730717i | ||||
\(799\) | −203.296 | −0.254439 | ||||||||
\(800\) | −420.834 | + | 863.456i | −0.526042 | + | 1.07932i | ||||
\(801\) | 442.225i | 0.552092i | ||||||||
\(802\) | 393.056 | + | 344.055i | 0.490094 | + | 0.428996i | ||||
\(803\) | − | 296.074i | − | 0.368710i | ||||||
\(804\) | 186.573 | − | 24.9156i | 0.232056 | − | 0.0309896i | ||||
\(805\) | 239.551 | 0.297579 | ||||||||
\(806\) | 288.531 | − | 40.0036i | 0.357979 | − | 0.0496323i | ||||
\(807\) | − | 512.746i | − | 0.635373i | ||||||
\(808\) | −302.372 | − | 200.821i | −0.374222 | − | 0.248541i | ||||
\(809\) | 466.988 | 0.577241 | 0.288621 | − | 0.957444i | \(-0.406803\pi\) | ||||
0.288621 | + | 0.957444i | \(0.406803\pi\) | |||||||
\(810\) | −100.462 | − | 87.9376i | −0.124027 | − | 0.108565i | ||||
\(811\) | −1484.79 | −1.83081 | −0.915407 | − | 0.402530i | \(-0.868131\pi\) | ||||
−0.915407 | + | 0.402530i | \(0.868131\pi\) | |||||||
\(812\) | −134.320 | − | 1005.82i | −0.165419 | − | 1.23869i | ||||
\(813\) | − | 392.722i | − | 0.483053i | ||||||
\(814\) | 836.860 | + | 732.532i | 1.02808 | + | 0.899917i | ||||
\(815\) | 1685.09i | 2.06760i | ||||||||
\(816\) | 28.0425 | + | 103.121i | 0.0343658 | + | 0.126374i | ||||
\(817\) | 194.137i | 0.237622i | ||||||||
\(818\) | −694.005 | − | 607.486i | −0.848416 | − | 0.742648i | ||||
\(819\) | −394.487 | − | 341.833i | −0.481670 | − | 0.417379i | ||||
\(820\) | −139.532 | − | 1044.85i | −0.170162 | − | 1.27420i | ||||
\(821\) | 1560.92i | 1.90124i | 0.310357 | + | 0.950620i | \(0.399551\pi\) | ||||
−0.310357 | + | 0.950620i | \(0.600449\pi\) | |||||||
\(822\) | −220.343 | + | 251.724i | −0.268057 | + | 0.306234i | ||||
\(823\) | − | 800.989i | − | 0.973255i | −0.873610 | − | 0.486627i | \(-0.838227\pi\) | ||
0.873610 | − | 0.486627i | \(-0.161773\pi\) | |||||||
\(824\) | 470.332 | − | 708.167i | 0.570792 | − | 0.859426i | ||||
\(825\) | 759.337i | 0.920409i | ||||||||
\(826\) | 404.208 | − | 461.776i | 0.489356 | − | 0.559051i | ||||
\(827\) | 324.850 | 0.392805 | 0.196402 | − | 0.980523i | \(-0.437074\pi\) | ||||
0.196402 | + | 0.980523i | \(0.437074\pi\) | |||||||
\(828\) | 28.7010 | − | 3.83283i | 0.0346630 | − | 0.00462902i | ||||
\(829\) | −1114.31 | −1.34416 | −0.672078 | − | 0.740480i | \(-0.734598\pi\) | ||||
−0.672078 | + | 0.740480i | \(0.734598\pi\) | |||||||
\(830\) | 38.6651 | + | 33.8449i | 0.0465845 | + | 0.0407770i | ||||
\(831\) | − | 99.1688i | − | 0.119337i | ||||||
\(832\) | −258.349 | + | 790.873i | −0.310516 | + | 0.950568i | ||||
\(833\) | −501.842 | −0.602452 | ||||||||
\(834\) | −578.214 | + | 660.564i | −0.693302 | + | 0.792043i | ||||
\(835\) | − | 1556.03i | − | 1.86351i | ||||||
\(836\) | −147.660 | − | 1105.70i | −0.176626 | − | 1.32261i | ||||
\(837\) | 58.2151i | 0.0695521i | ||||||||
\(838\) | 456.781 | + | 399.836i | 0.545085 | + | 0.477131i | ||||
\(839\) | 362.224 | 0.431733 | 0.215867 | − | 0.976423i | \(-0.430742\pi\) | ||||
0.215867 | + | 0.976423i | \(0.430742\pi\) | |||||||
\(840\) | −1145.90 | − | 761.056i | −1.36417 | − | 0.906019i | ||||
\(841\) | −481.742 | −0.572821 | ||||||||
\(842\) | 697.198 | + | 610.281i | 0.828026 | + | 0.724800i | ||||
\(843\) | 293.783 | 0.348498 | ||||||||
\(844\) | 317.878 | − | 42.4505i | 0.376632 | − | 0.0502968i | ||||
\(845\) | −1240.78 | + | 178.369i | −1.46838 | + | 0.211087i | ||||
\(846\) | 208.340 | − | 238.012i | 0.246265 | − | 0.281338i | ||||
\(847\) | 1235.48 | 1.45865 | ||||||||
\(848\) | −867.383 | + | 235.873i | −1.02286 | + | 0.278152i | ||||
\(849\) | 615.161 | 0.724572 | ||||||||
\(850\) | −152.480 | + | 174.197i | −0.179388 | + | 0.204937i | ||||
\(851\) | 91.8743 | 0.107960 | ||||||||
\(852\) | 178.178 | − | 23.7946i | 0.209129 | − | 0.0279279i | ||||
\(853\) | − | 433.461i | − | 0.508160i | −0.967183 | − | 0.254080i | \(-0.918227\pi\) | ||
0.967183 | − | 0.254080i | \(-0.0817727\pi\) | |||||||
\(854\) | 39.8475 | − | 45.5226i | 0.0466599 | − | 0.0533052i | ||||
\(855\) | 424.898i | 0.496956i | ||||||||
\(856\) | −337.640 | + | 508.376i | −0.394439 | + | 0.593897i | ||||
\(857\) | 287.654 | 0.335653 | 0.167826 | − | 0.985817i | \(-0.446325\pi\) | ||||
0.167826 | + | 0.985817i | \(0.446325\pi\) | |||||||
\(858\) | 90.3255 | + | 651.483i | 0.105274 | + | 0.759304i | ||||
\(859\) | − | 385.620i | − | 0.448917i | −0.974484 | − | 0.224459i | \(-0.927939\pi\) | ||
0.974484 | − | 0.224459i | \(-0.0720614\pi\) | |||||||
\(860\) | −39.9289 | − | 298.996i | −0.0464290 | − | 0.347670i | ||||
\(861\) | 823.639 | 0.956608 | ||||||||
\(862\) | 573.420 | − | 655.087i | 0.665220 | − | 0.759961i | ||||
\(863\) | 1384.23 | 1.60397 | 0.801985 | − | 0.597344i | \(-0.203777\pi\) | ||||
0.801985 | + | 0.597344i | \(0.203777\pi\) | |||||||
\(864\) | −149.469 | − | 72.8488i | −0.172997 | − | 0.0843157i | ||||
\(865\) | 2281.04i | 2.63704i | ||||||||
\(866\) | 345.166 | − | 394.325i | 0.398575 | − | 0.455340i | ||||
\(867\) | − | 474.806i | − | 0.547643i | ||||||
\(868\) | 79.3949 | + | 594.525i | 0.0914688 | + | 0.684936i | ||||
\(869\) | − | 217.988i | − | 0.250850i | ||||||
\(870\) | 320.771 | − | 366.456i | 0.368703 | − | 0.421214i | ||||
\(871\) | 266.922 | + | 231.294i | 0.306454 | + | 0.265550i | ||||
\(872\) | 608.227 | − | 915.791i | 0.697508 | − | 1.05022i | ||||
\(873\) | − | 489.425i | − | 0.560624i | ||||||
\(874\) | −69.3388 | − | 60.6946i | −0.0793350 | − | 0.0694447i | ||||
\(875\) | − | 498.089i | − | 0.569244i | ||||||
\(876\) | 18.5910 | + | 139.213i | 0.0212225 | + | 0.158919i | ||||
\(877\) | − | 983.819i | − | 1.12180i | −0.827883 | − | 0.560900i | \(-0.810455\pi\) | ||
0.827883 | − | 0.560900i | \(-0.189545\pi\) | |||||||
\(878\) | 163.926 | + | 143.490i | 0.186704 | + | 0.163428i | ||||
\(879\) | 839.143 | 0.954657 | ||||||||
\(880\) | 454.830 | + | 1672.56i | 0.516852 | + | 1.90063i | ||||
\(881\) | 762.632 | 0.865644 | 0.432822 | − | 0.901479i | \(-0.357518\pi\) | ||||
0.432822 | + | 0.901479i | \(0.357518\pi\) | |||||||
\(882\) | 514.293 | − | 587.539i | 0.583099 | − | 0.666144i | ||||
\(883\) | 1129.18i | 1.27879i | 0.768877 | + | 0.639397i | \(0.220816\pi\) | ||||
−0.768877 | + | 0.639397i | \(0.779184\pi\) | |||||||
\(884\) | −110.101 | + | 167.592i | −0.124549 | + | 0.189584i | ||||
\(885\) | 294.535 | 0.332808 | ||||||||
\(886\) | 235.284 | + | 205.952i | 0.265558 | + | 0.232452i | ||||
\(887\) | − | 1424.54i | − | 1.60602i | −0.595963 | − | 0.803012i | \(-0.703229\pi\) | ||
0.595963 | − | 0.803012i | \(-0.296771\pi\) | |||||||
\(888\) | −439.485 | − | 291.886i | −0.494915 | − | 0.328700i | ||||
\(889\) | 1671.13i | 1.87978i | ||||||||
\(890\) | −1440.30 | + | 1645.43i | −1.61832 | + | 1.84880i | ||||
\(891\) | −131.446 | −0.147526 | ||||||||
\(892\) | 145.534 | + | 1089.79i | 0.163155 | + | 1.22174i | ||||
\(893\) | −1006.66 | −1.12728 | ||||||||
\(894\) | 198.021 | − | 226.223i | 0.221500 | − | 0.253046i | ||||
\(895\) | −2370.56 | −2.64868 | ||||||||
\(896\) | −1625.82 | − | 540.123i | −1.81453 | − | 0.602816i | ||||
\(897\) | 41.0612 | + | 35.5805i | 0.0457761 | + | 0.0396661i | ||||
\(898\) | −9.79757 | − | 8.57615i | −0.0109104 | − | 0.00955028i | ||||
\(899\) | −212.352 | −0.236209 | ||||||||
\(900\) | −47.6800 | − | 357.037i | −0.0529777 | − | 0.396708i | ||||
\(901\) | −216.642 | −0.240446 | ||||||||
\(902\) | −780.898 | − | 683.546i | −0.865740 | − | 0.757812i | ||||
\(903\) | 235.695 | 0.261013 | ||||||||
\(904\) | 1123.30 | + | 746.043i | 1.24259 | + | 0.825269i | ||||
\(905\) | 1764.22i | 1.94941i | ||||||||
\(906\) | −511.130 | − | 447.410i | −0.564161 | − | 0.493830i | ||||
\(907\) | 844.091i | 0.930641i | 0.885142 | + | 0.465320i | \(0.154061\pi\) | ||||
−0.885142 | + | 0.465320i | \(0.845939\pi\) | |||||||
\(908\) | 140.482 | + | 1051.96i | 0.154716 | + | 1.15854i | ||||
\(909\) | 136.119 | 0.149746 | ||||||||
\(910\) | −354.479 | − | 2556.72i | −0.389537 | − | 2.80958i | ||||
\(911\) | 1205.50i | 1.32327i | 0.749826 | + | 0.661635i | \(0.230137\pi\) | ||||
−0.749826 | + | 0.661635i | \(0.769863\pi\) | |||||||
\(912\) | 138.858 | + | 510.625i | 0.152256 | + | 0.559896i | ||||
\(913\) | 50.5900 | 0.0554108 | ||||||||
\(914\) | −171.662 | − | 150.262i | −0.187814 | − | 0.164400i | ||||
\(915\) | 29.0358 | 0.0317331 | ||||||||
\(916\) | −950.874 | + | 126.983i | −1.03807 | + | 0.138628i | ||||
\(917\) | − | 1320.90i | − | 1.44046i | ||||||
\(918\) | −30.1544 | − | 26.3952i | −0.0328480 | − | 0.0287529i | ||||
\(919\) | − | 38.0600i | − | 0.0414146i | −0.999786 | − | 0.0207073i | \(-0.993408\pi\) | ||
0.999786 | − | 0.0207073i | \(-0.00659181\pi\) | |||||||
\(920\) | 119.274 | + | 79.2164i | 0.129646 | + | 0.0861047i | ||||
\(921\) | − | 311.625i | − | 0.338355i | ||||||
\(922\) | −522.062 | − | 456.979i | −0.566228 | − | 0.495638i | ||||
\(923\) | 254.912 | + | 220.887i | 0.276177 | + | 0.239314i | ||||
\(924\) | −1342.40 | + | 179.268i | −1.45281 | + | 0.194013i | ||||
\(925\) | − | 1142.91i | − | 1.23557i | ||||||
\(926\) | −735.524 | + | 840.278i | −0.794302 | + | 0.907428i | ||||
\(927\) | 318.797i | 0.343902i | ||||||||
\(928\) | 265.732 | − | 545.222i | 0.286349 | − | 0.587523i | ||||
\(929\) | 160.346i | 0.172601i | 0.996269 | + | 0.0863005i | \(0.0275045\pi\) | ||||
−0.996269 | + | 0.0863005i | \(0.972495\pi\) | |||||||
\(930\) | −189.603 | + | 216.607i | −0.203875 | + | 0.232911i | ||||
\(931\) | −2484.97 | −2.66914 | ||||||||
\(932\) | 15.2055 | + | 113.861i | 0.0163149 | + | 0.122169i | ||||
\(933\) | 16.4649 | 0.0176473 | ||||||||
\(934\) | 708.764 | + | 620.405i | 0.758848 | + | 0.664246i | ||||
\(935\) | 417.747i | 0.446788i | ||||||||
\(936\) | −83.3783 | − | 300.653i | −0.0890793 | − | 0.321210i | ||||
\(937\) | 1656.50 | 1.76787 | 0.883937 | − | 0.467605i | \(-0.154883\pi\) | ||||
0.883937 | + | 0.467605i | \(0.154883\pi\) | |||||||
\(938\) | −479.010 | + | 547.231i | −0.510671 | + | 0.583401i | ||||
\(939\) | − | 116.748i | − | 0.124333i | ||||||
\(940\) | 1550.39 | − | 207.044i | 1.64935 | − | 0.220260i | ||||
\(941\) | − | 561.474i | − | 0.596678i | −0.954460 | − | 0.298339i | \(-0.903567\pi\) | ||
0.954460 | − | 0.298339i | \(-0.0964326\pi\) | |||||||
\(942\) | 240.980 | + | 210.938i | 0.255817 | + | 0.223925i | ||||
\(943\) | −85.7305 | −0.0909125 | ||||||||
\(944\) | 353.961 | − | 96.2550i | 0.374959 | − | 0.101965i | ||||
\(945\) | 515.853 | 0.545876 | ||||||||
\(946\) | −223.464 | − | 195.605i | −0.236219 | − | 0.206771i | ||||
\(947\) | −221.394 | −0.233785 | −0.116892 | − | 0.993145i | \(-0.537293\pi\) | ||||
−0.116892 | + | 0.993145i | \(0.537293\pi\) | |||||||
\(948\) | 13.6878 | + | 102.497i | 0.0144386 | + | 0.108119i | ||||
\(949\) | −172.582 | + | 199.165i | −0.181856 | + | 0.209869i | ||||
\(950\) | −755.034 | + | 862.567i | −0.794773 | + | 0.907965i | ||||
\(951\) | 615.851 | 0.647582 | ||||||||
\(952\) | −343.952 | − | 228.437i | −0.361294 | − | 0.239955i | ||||
\(953\) | 1070.55 | 1.12335 | 0.561673 | − | 0.827360i | \(-0.310158\pi\) | ||||
0.561673 | + | 0.827360i | \(0.310158\pi\) | |||||||
\(954\) | 222.017 | − | 253.637i | 0.232722 | − | 0.265867i | ||||
\(955\) | 31.8568 | 0.0333579 | ||||||||
\(956\) | −28.3651 | − | 212.403i | −0.0296706 | − | 0.222179i | ||||
\(957\) | − | 479.476i | − | 0.501020i | ||||||
\(958\) | −261.540 | + | 298.789i | −0.273006 | + | 0.311888i | ||||
\(959\) | − | 1292.56i | − | 1.34782i | ||||||
\(960\) | −318.881 | − | 757.870i | −0.332168 | − | 0.789447i | ||||
\(961\) | −835.482 | −0.869388 | ||||||||
\(962\) | −135.952 | − | 980.571i | −0.141322 | − | 1.01930i | ||||
\(963\) | − | 228.857i | − | 0.237650i | ||||||
\(964\) | −225.568 | + | 30.1231i | −0.233992 | + | 0.0312481i | ||||
\(965\) | 2787.12 | 2.88821 | ||||||||
\(966\) | −73.6872 | + | 84.1818i | −0.0762807 | + | 0.0871447i | ||||
\(967\) | 856.229 | 0.885449 | 0.442724 | − | 0.896658i | \(-0.354012\pi\) | ||||
0.442724 | + | 0.896658i | \(0.354012\pi\) | |||||||
\(968\) | 615.152 | + | 408.556i | 0.635488 | + | 0.422062i | ||||
\(969\) | 127.537i | 0.131617i | ||||||||
\(970\) | 1594.03 | − | 1821.05i | 1.64333 | − | 1.87738i | ||||
\(971\) | − | 505.753i | − | 0.520858i | −0.965493 | − | 0.260429i | \(-0.916136\pi\) | ||
0.965493 | − | 0.260429i | \(-0.0838640\pi\) | |||||||
\(972\) | 61.8052 | − | 8.25368i | 0.0635855 | − | 0.00849144i | ||||
\(973\) | − | 3391.88i | − | 3.48600i | ||||||
\(974\) | −55.6236 | + | 63.5456i | −0.0571084 | + | 0.0652419i | ||||
\(975\) | 442.618 | − | 510.797i | 0.453967 | − | 0.523894i | ||||
\(976\) | 34.8941 | − | 9.48898i | 0.0357521 | − | 0.00972232i | ||||
\(977\) | 1308.46i | 1.33927i | 0.742693 | + | 0.669633i | \(0.233548\pi\) | ||||
−0.742693 | + | 0.669633i | \(0.766452\pi\) | |||||||
\(978\) | −592.166 | − | 518.343i | −0.605487 | − | 0.530003i | ||||
\(979\) | 2152.91i | 2.19909i | ||||||||
\(980\) | 3827.17 | − | 511.094i | 3.90527 | − | 0.521524i | ||||
\(981\) | 412.264i | 0.420248i | ||||||||
\(982\) | 239.406 | + | 209.560i | 0.243794 | + | 0.213401i | ||||
\(983\) | 99.6372 | 0.101360 | 0.0506802 | − | 0.998715i | \(-0.483861\pi\) | ||||
0.0506802 | + | 0.998715i | \(0.483861\pi\) | |||||||
\(984\) | 410.096 | + | 272.367i | 0.416764 | + | 0.276795i | ||||
\(985\) | −401.477 | −0.407591 | ||||||||
\(986\) | 96.2822 | − | 109.995i | 0.0976493 | − | 0.111557i | ||||
\(987\) | 1222.15i | 1.23825i | ||||||||
\(988\) | −545.186 | + | 829.864i | −0.551808 | + | 0.839944i | ||||
\(989\) | −24.5329 | −0.0248057 | ||||||||
\(990\) | −489.084 | − | 428.111i | −0.494024 | − | 0.432436i | ||||
\(991\) | − | 1381.79i | − | 1.39434i | −0.716906 | − | 0.697170i | \(-0.754442\pi\) | ||
0.716906 | − | 0.697170i | \(-0.245558\pi\) | |||||||
\(992\) | −157.070 | + | 322.273i | −0.158337 | + | 0.324872i | ||||
\(993\) | − | 575.656i | − | 0.579714i | ||||||
\(994\) | −457.457 | + | 522.608i | −0.460218 | + | 0.525763i | ||||
\(995\) | −1052.89 | −1.05819 | ||||||||
\(996\) | −23.7872 | + | 3.17663i | −0.0238827 | + | 0.00318938i | ||||
\(997\) | −1498.53 | −1.50304 | −0.751518 | − | 0.659713i | \(-0.770678\pi\) | ||||
−0.751518 | + | 0.659713i | \(0.770678\pi\) | |||||||
\(998\) | 62.9929 | − | 71.9644i | 0.0631191 | − | 0.0721086i | ||||
\(999\) | 197.844 | 0.198042 |
(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 | 156.3.e.c.103.8 | yes | 24 | |
3.2 | odd | 2 | 468.3.e.m.415.17 | 24 | |||
4.3 | odd | 2 | inner | 156.3.e.c.103.18 | yes | 24 | |
12.11 | even | 2 | 468.3.e.m.415.7 | 24 | |||
13.12 | even | 2 | inner | 156.3.e.c.103.17 | yes | 24 | |
39.38 | odd | 2 | 468.3.e.m.415.8 | 24 | |||
52.51 | odd | 2 | inner | 156.3.e.c.103.7 | ✓ | 24 | |
156.155 | even | 2 | 468.3.e.m.415.18 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
156.3.e.c.103.7 | ✓ | 24 | 52.51 | odd | 2 | inner | |
156.3.e.c.103.8 | yes | 24 | 1.1 | even | 1 | trivial | |
156.3.e.c.103.17 | yes | 24 | 13.12 | even | 2 | inner | |
156.3.e.c.103.18 | yes | 24 | 4.3 | odd | 2 | inner | |
468.3.e.m.415.7 | 24 | 12.11 | even | 2 | |||
468.3.e.m.415.8 | 24 | 39.38 | odd | 2 | |||
468.3.e.m.415.17 | 24 | 3.2 | odd | 2 | |||
468.3.e.m.415.18 | 24 | 156.155 | even | 2 |