Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(82,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.82");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.bc (of order \(12\), degree \(4\), 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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 82.3 | ||
Character | \(\chi\) | \(=\) | 525.82 |
Dual form | 525.2.bc.e.493.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.49657 | + | 0.401003i | −1.05823 | + | 0.283552i | −0.745649 | − | 0.666338i | \(-0.767861\pi\) |
−0.312582 | + | 0.949891i | \(0.601194\pi\) | |||||||
\(3\) | −0.258819 | + | 0.965926i | −0.149429 | + | 0.557678i | ||||
\(4\) | 0.346853 | − | 0.200256i | 0.173427 | − | 0.100128i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 1.54936i | − | 0.632523i | ||||||
\(7\) | 2.44171 | + | 1.01885i | 0.922880 | + | 0.385088i | ||||
\(8\) | 1.75234 | − | 1.75234i | 0.619545 | − | 0.619545i | ||||
\(9\) | −0.866025 | − | 0.500000i | −0.288675 | − | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.59461 | − | 4.49400i | −0.782306 | − | 1.35499i | −0.930595 | − | 0.366049i | \(-0.880710\pi\) |
0.148290 | − | 0.988944i | \(-0.452623\pi\) | |||||||
\(12\) | 0.103660 | + | 0.386864i | 0.0299241 | + | 0.111678i | ||||
\(13\) | −3.30901 | − | 3.30901i | −0.917755 | − | 0.917755i | 0.0791106 | − | 0.996866i | \(-0.474792\pi\) |
−0.996866 | + | 0.0791106i | \(0.974792\pi\) | |||||||
\(14\) | −4.06274 | − | 0.545636i | −1.08581 | − | 0.145827i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.32031 | + | 4.01889i | −0.580077 | + | 1.00472i | ||||
\(17\) | −0.0194028 | − | 0.00519896i | −0.00470587 | − | 0.00126093i | 0.256465 | − | 0.966553i | \(-0.417442\pi\) |
−0.261171 | + | 0.965292i | \(0.584109\pi\) | |||||||
\(18\) | 1.49657 | + | 0.401003i | 0.352744 | + | 0.0945174i | ||||
\(19\) | −1.24048 | + | 2.14858i | −0.284586 | + | 0.492918i | −0.972509 | − | 0.232866i | \(-0.925190\pi\) |
0.687922 | + | 0.725784i | \(0.258523\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.61609 | + | 2.09481i | −0.352660 | + | 0.457126i | ||||
\(22\) | 5.68512 | + | 5.68512i | 1.21207 | + | 1.21207i | ||||
\(23\) | −0.601811 | − | 2.24599i | −0.125486 | − | 0.468321i | 0.874370 | − | 0.485259i | \(-0.161275\pi\) |
−0.999857 | + | 0.0169383i | \(0.994608\pi\) | |||||||
\(24\) | 1.23909 | + | 2.14617i | 0.252928 | + | 0.438085i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.27908 | + | 3.62523i | 1.23143 | + | 0.710966i | ||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 1.05094 | − | 0.135576i | 0.198610 | − | 0.0256215i | ||||
\(29\) | − | 10.2081i | − | 1.89559i | −0.318874 | − | 0.947797i | \(-0.603305\pi\) | ||
0.318874 | − | 0.947797i | \(-0.396695\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.69268 | − | 3.28667i | 1.02244 | − | 0.590303i | 0.107627 | − | 0.994191i | \(-0.465675\pi\) |
0.914808 | + | 0.403888i | \(0.132342\pi\) | |||||||
\(32\) | 0.578101 | − | 2.15750i | 0.102195 | − | 0.381396i | ||||
\(33\) | 5.01241 | − | 1.34307i | 0.872549 | − | 0.233799i | ||||
\(34\) | 0.0311223 | 0.00533744 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.400511 | −0.0667519 | ||||||||
\(37\) | −2.66573 | + | 0.714279i | −0.438243 | + | 0.117427i | −0.471193 | − | 0.882030i | \(-0.656176\pi\) |
0.0329501 | + | 0.999457i | \(0.489510\pi\) | |||||||
\(38\) | 0.994876 | − | 3.71293i | 0.161390 | − | 0.602316i | ||||
\(39\) | 4.05270 | − | 2.33983i | 0.648951 | − | 0.374672i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.68910i | − | 0.576141i | −0.957609 | − | 0.288070i | \(-0.906986\pi\) | ||
0.957609 | − | 0.288070i | \(-0.0930137\pi\) | |||||||
\(42\) | 1.57856 | − | 3.78308i | 0.243577 | − | 0.583743i | ||||
\(43\) | 2.79725 | − | 2.79725i | 0.426576 | − | 0.426576i | −0.460884 | − | 0.887460i | \(-0.652468\pi\) |
0.887460 | + | 0.460884i | \(0.152468\pi\) | |||||||
\(44\) | −1.79990 | − | 1.03917i | −0.271345 | − | 0.156661i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.80130 | + | 3.11994i | 0.265587 | + | 0.460010i | ||||
\(47\) | −0.303190 | − | 1.13152i | −0.0442248 | − | 0.165049i | 0.940282 | − | 0.340397i | \(-0.110562\pi\) |
−0.984506 | + | 0.175348i | \(0.943895\pi\) | |||||||
\(48\) | −3.28141 | − | 3.28141i | −0.473631 | − | 0.473631i | ||||
\(49\) | 4.92390 | + | 4.97546i | 0.703415 | + | 0.710780i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.0100436 | − | 0.0173961i | 0.00140639 | − | 0.00243594i | ||||
\(52\) | −1.81039 | − | 0.485093i | −0.251056 | − | 0.0672702i | ||||
\(53\) | 4.60942 | + | 1.23509i | 0.633152 | + | 0.169653i | 0.561100 | − | 0.827748i | \(-0.310378\pi\) |
0.0720526 | + | 0.997401i | \(0.477045\pi\) | |||||||
\(54\) | −0.774679 | + | 1.34178i | −0.105420 | + | 0.182594i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.06407 | − | 2.49334i | 0.810345 | − | 0.333187i | ||||
\(57\) | −1.75431 | − | 1.75431i | −0.232364 | − | 0.232364i | ||||
\(58\) | 4.09348 | + | 15.2771i | 0.537500 | + | 2.00598i | ||||
\(59\) | 0.222589 | + | 0.385535i | 0.0289786 | + | 0.0501924i | 0.880151 | − | 0.474694i | \(-0.157441\pi\) |
−0.851172 | + | 0.524886i | \(0.824108\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.18643 | + | 0.684984i | 0.151906 | + | 0.0877032i | 0.574027 | − | 0.818837i | \(-0.305381\pi\) |
−0.422120 | + | 0.906540i | \(0.638714\pi\) | |||||||
\(62\) | −7.20150 | + | 7.20150i | −0.914591 | + | 0.914591i | ||||
\(63\) | −1.60516 | − | 2.10320i | −0.202231 | − | 0.264979i | ||||
\(64\) | − | 5.82056i | − | 0.727570i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.96282 | + | 4.01999i | −0.857064 | + | 0.494826i | ||||
\(67\) | 1.52946 | − | 5.70802i | 0.186853 | − | 0.697346i | −0.807373 | − | 0.590041i | \(-0.799111\pi\) |
0.994226 | − | 0.107304i | \(-0.0342219\pi\) | |||||||
\(68\) | −0.00777104 | + | 0.00208224i | −0.000942377 | + | 0.000252509i | ||||
\(69\) | 2.32522 | 0.279923 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.14741 | −0.254850 | −0.127425 | − | 0.991848i | \(-0.540671\pi\) | ||||
−0.127425 | + | 0.991848i | \(0.540671\pi\) | |||||||
\(72\) | −2.39374 | + | 0.641400i | −0.282105 | + | 0.0755898i | ||||
\(73\) | −1.91752 | + | 7.15629i | −0.224429 | + | 0.837580i | 0.758204 | + | 0.652018i | \(0.226077\pi\) |
−0.982632 | + | 0.185562i | \(0.940589\pi\) | |||||||
\(74\) | 3.70301 | − | 2.13793i | 0.430466 | − | 0.248529i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.993655i | 0.113980i | ||||||||
\(77\) | −1.75660 | − | 13.6166i | −0.200183 | − | 1.55175i | ||||
\(78\) | −5.12685 | + | 5.12685i | −0.580501 | + | 0.580501i | ||||
\(79\) | 3.47085 | + | 2.00389i | 0.390501 | + | 0.225456i | 0.682377 | − | 0.731000i | \(-0.260946\pi\) |
−0.291876 | + | 0.956456i | \(0.594280\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | 1.47934 | + | 5.52098i | 0.163366 | + | 0.609690i | ||||
\(83\) | −3.77525 | − | 3.77525i | −0.414387 | − | 0.414387i | 0.468876 | − | 0.883264i | \(-0.344659\pi\) |
−0.883264 | + | 0.468876i | \(0.844659\pi\) | |||||||
\(84\) | −0.141048 | + | 1.05022i | −0.0153896 | + | 0.114589i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.06456 | + | 5.30797i | −0.330460 | + | 0.572373i | ||||
\(87\) | 9.86025 | + | 2.64205i | 1.05713 | + | 0.283257i | ||||
\(88\) | −12.4217 | − | 3.32837i | −1.32415 | − | 0.354806i | ||||
\(89\) | −1.91942 | + | 3.32453i | −0.203458 | + | 0.352400i | −0.949640 | − | 0.313342i | \(-0.898551\pi\) |
0.746182 | + | 0.665742i | \(0.231885\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.70828 | − | 11.4510i | −0.493561 | − | 1.20039i | ||||
\(92\) | −0.658512 | − | 0.658512i | −0.0686546 | − | 0.0686546i | ||||
\(93\) | 1.70131 | + | 6.34936i | 0.176417 | + | 0.658398i | ||||
\(94\) | 0.907487 | + | 1.57181i | 0.0936001 | + | 0.162120i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.93436 | + | 1.11681i | 0.197425 | + | 0.113983i | ||||
\(97\) | 10.5936 | − | 10.5936i | 1.07561 | − | 1.07561i | 0.0787167 | − | 0.996897i | \(-0.474918\pi\) |
0.996897 | − | 0.0787167i | \(-0.0250822\pi\) | |||||||
\(98\) | −9.36412 | − | 5.47160i | −0.945919 | − | 0.552715i | ||||
\(99\) | 5.18923i | 0.521537i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.87655 | + | 3.39283i | −0.584738 | + | 0.337599i | −0.763014 | − | 0.646382i | \(-0.776281\pi\) |
0.178276 | + | 0.983981i | \(0.442948\pi\) | |||||||
\(102\) | −0.00805505 | + | 0.0300619i | −0.000797569 | + | 0.00297657i | ||||
\(103\) | 9.09265 | − | 2.43637i | 0.895926 | − | 0.240063i | 0.218660 | − | 0.975801i | \(-0.429831\pi\) |
0.677266 | + | 0.735739i | \(0.263165\pi\) | |||||||
\(104\) | −11.5970 | −1.13718 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.39357 | −0.718127 | ||||||||
\(107\) | −12.0162 | + | 3.21974i | −1.16165 | + | 0.311264i | −0.787625 | − | 0.616155i | \(-0.788690\pi\) |
−0.374026 | + | 0.927418i | \(0.622023\pi\) | |||||||
\(108\) | 0.103660 | − | 0.386864i | 0.00997468 | − | 0.0372260i | ||||
\(109\) | −7.55937 | + | 4.36440i | −0.724056 | + | 0.418034i | −0.816244 | − | 0.577708i | \(-0.803947\pi\) |
0.0921875 | + | 0.995742i | \(0.470614\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 2.75976i | − | 0.261945i | ||||||
\(112\) | −9.76015 | + | 7.44893i | −0.922247 | + | 0.703858i | ||||
\(113\) | 2.80125 | − | 2.80125i | 0.263519 | − | 0.263519i | −0.562963 | − | 0.826482i | \(-0.690339\pi\) |
0.826482 | + | 0.562963i | \(0.190339\pi\) | |||||||
\(114\) | 3.32892 | + | 1.92195i | 0.311782 | + | 0.180007i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.04423 | − | 3.54071i | −0.189802 | − | 0.328746i | ||||
\(117\) | 1.21118 | + | 4.52020i | 0.111974 | + | 0.417892i | ||||
\(118\) | −0.487719 | − | 0.487719i | −0.0448982 | − | 0.0448982i | ||||
\(119\) | −0.0420790 | − | 0.0324628i | −0.00385738 | − | 0.00297586i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.96405 | + | 13.7941i | −0.724005 | + | 1.25401i | ||||
\(122\) | −2.05025 | − | 0.549362i | −0.185621 | − | 0.0497369i | ||||
\(123\) | 3.56340 | + | 0.954809i | 0.321301 | + | 0.0860922i | ||||
\(124\) | 1.31635 | − | 2.27998i | 0.118212 | − | 0.204748i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.24562 | + | 2.50391i | 0.289143 | + | 0.223066i | ||||
\(127\) | −2.63342 | − | 2.63342i | −0.233679 | − | 0.233679i | 0.580548 | − | 0.814226i | \(-0.302838\pi\) |
−0.814226 | + | 0.580548i | \(0.802838\pi\) | |||||||
\(128\) | 3.49027 | + | 13.0259i | 0.308499 | + | 1.15133i | ||||
\(129\) | 1.97795 | + | 3.42591i | 0.174149 | + | 0.301635i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.60564 | + | 1.50437i | 0.227656 | + | 0.131437i | 0.609490 | − | 0.792794i | \(-0.291374\pi\) |
−0.381834 | + | 0.924231i | \(0.624707\pi\) | |||||||
\(132\) | 1.46961 | − | 1.46961i | 0.127913 | − | 0.127913i | ||||
\(133\) | −5.21797 | + | 3.98235i | −0.452456 | + | 0.345313i | ||||
\(134\) | 9.15574i | 0.790936i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.0431106 | + | 0.0248899i | −0.00369670 | + | 0.00213429i | ||||
\(137\) | −2.73317 | + | 10.2003i | −0.233510 | + | 0.871472i | 0.745304 | + | 0.666724i | \(0.232304\pi\) |
−0.978815 | + | 0.204748i | \(0.934363\pi\) | |||||||
\(138\) | −3.47984 | + | 0.932421i | −0.296224 | + | 0.0793729i | ||||
\(139\) | 1.76721 | 0.149893 | 0.0749465 | − | 0.997188i | \(-0.476121\pi\) | ||||
0.0749465 | + | 0.997188i | \(0.476121\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.17144 | 0.0986527 | ||||||||
\(142\) | 3.21373 | − | 0.861117i | 0.269691 | − | 0.0722634i | ||||
\(143\) | −6.28511 | + | 23.4563i | −0.525587 | + | 1.96152i | ||||
\(144\) | 4.01889 | − | 2.32031i | 0.334907 | − | 0.193359i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 11.4788i | − | 0.949991i | ||||||
\(147\) | −6.08032 | + | 3.46838i | −0.501497 | + | 0.286067i | ||||
\(148\) | −0.781577 | + | 0.781577i | −0.0642452 | + | 0.0642452i | ||||
\(149\) | −6.38521 | − | 3.68650i | −0.523097 | − | 0.302010i | 0.215104 | − | 0.976591i | \(-0.430991\pi\) |
−0.738201 | + | 0.674581i | \(0.764324\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.17823 | − | 14.1651i | −0.665535 | − | 1.15274i | −0.979140 | − | 0.203187i | \(-0.934870\pi\) |
0.313605 | − | 0.949554i | \(-0.398463\pi\) | |||||||
\(152\) | 1.59129 | + | 5.93879i | 0.129071 | + | 0.481699i | ||||
\(153\) | 0.0142038 | + | 0.0142038i | 0.00114831 | + | 0.00114831i | ||||
\(154\) | 8.08915 | + | 19.6737i | 0.651843 | + | 1.58535i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.937127 | − | 1.62315i | 0.0750302 | − | 0.129956i | ||||
\(157\) | −22.1476 | − | 5.93444i | −1.76757 | − | 0.473620i | −0.779344 | − | 0.626597i | \(-0.784447\pi\) |
−0.988230 | + | 0.152977i | \(0.951114\pi\) | |||||||
\(158\) | −5.99791 | − | 1.60714i | −0.477168 | − | 0.127857i | ||||
\(159\) | −2.38601 | + | 4.13269i | −0.189223 | + | 0.327744i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.818870 | − | 6.09721i | 0.0645360 | − | 0.480527i | ||||
\(162\) | −1.09556 | − | 1.09556i | −0.0860755 | − | 0.0860755i | ||||
\(163\) | −3.95078 | − | 14.7445i | −0.309449 | − | 1.15488i | −0.929048 | − | 0.369960i | \(-0.879372\pi\) |
0.619599 | − | 0.784918i | \(-0.287295\pi\) | |||||||
\(164\) | −0.738763 | − | 1.27958i | −0.0576877 | − | 0.0999180i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.16379 | + | 4.13602i | 0.556018 | + | 0.321017i | ||||
\(167\) | 8.60951 | − | 8.60951i | 0.666224 | − | 0.666224i | −0.290616 | − | 0.956840i | \(-0.593860\pi\) |
0.956840 | + | 0.290616i | \(0.0938603\pi\) | |||||||
\(168\) | 0.838885 | + | 6.50276i | 0.0647214 | + | 0.501699i | ||||
\(169\) | 8.89914i | 0.684550i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.14858 | − | 1.24048i | 0.164306 | − | 0.0948621i | ||||
\(172\) | 0.410069 | − | 1.53040i | 0.0312675 | − | 0.116692i | ||||
\(173\) | −3.49279 | + | 0.935889i | −0.265552 | + | 0.0711543i | −0.389138 | − | 0.921179i | \(-0.627227\pi\) |
0.123586 | + | 0.992334i | \(0.460560\pi\) | |||||||
\(174\) | −15.8160 | −1.19901 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 24.0812 | 1.81519 | ||||||||
\(177\) | −0.430008 | + | 0.115220i | −0.0323214 | + | 0.00866049i | ||||
\(178\) | 1.53939 | − | 5.74507i | 0.115382 | − | 0.430611i | ||||
\(179\) | 12.0294 | − | 6.94520i | 0.899122 | − | 0.519108i | 0.0222069 | − | 0.999753i | \(-0.492931\pi\) |
0.876915 | + | 0.480645i | \(0.159597\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.4270i | 1.14668i | 0.819318 | + | 0.573339i | \(0.194352\pi\) | ||||
−0.819318 | + | 0.573339i | \(0.805648\pi\) | |||||||
\(182\) | 11.6381 | + | 15.2492i | 0.862677 | + | 1.13034i | ||||
\(183\) | −0.968714 | + | 0.968714i | −0.0716094 | + | 0.0716094i | ||||
\(184\) | −4.99031 | − | 2.88116i | −0.367890 | − | 0.212402i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.09223 | − | 8.82000i | −0.373380 | − | 0.646714i | ||||
\(187\) | 0.0269786 | + | 0.100686i | 0.00197287 | + | 0.00736285i | ||||
\(188\) | −0.331756 | − | 0.331756i | −0.0241958 | − | 0.0241958i | ||||
\(189\) | 2.44698 | − | 1.00612i | 0.177992 | − | 0.0731842i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.0283971 | − | 0.0491852i | 0.00205474 | − | 0.00355891i | −0.864996 | − | 0.501778i | \(-0.832679\pi\) |
0.867051 | + | 0.498219i | \(0.166013\pi\) | |||||||
\(192\) | 5.62223 | + | 1.50647i | 0.405750 | + | 0.108720i | ||||
\(193\) | 2.29559 | + | 0.615101i | 0.165240 | + | 0.0442760i | 0.340491 | − | 0.940248i | \(-0.389407\pi\) |
−0.175250 | + | 0.984524i | \(0.556074\pi\) | |||||||
\(194\) | −11.6059 | + | 20.1020i | −0.833256 | + | 1.44324i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.70423 | + | 0.739713i | 0.193160 | + | 0.0528367i | ||||
\(197\) | −0.251120 | − | 0.251120i | −0.0178916 | − | 0.0178916i | 0.698104 | − | 0.715996i | \(-0.254027\pi\) |
−0.715996 | + | 0.698104i | \(0.754027\pi\) | |||||||
\(198\) | −2.08090 | − | 7.76602i | −0.147883 | − | 0.551907i | ||||
\(199\) | −12.5538 | − | 21.7439i | −0.889917 | − | 1.54138i | −0.839972 | − | 0.542629i | \(-0.817429\pi\) |
−0.0499447 | − | 0.998752i | \(-0.515905\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.11767 | + | 2.95469i | 0.360973 | + | 0.208408i | ||||
\(202\) | 7.43410 | − | 7.43410i | 0.523062 | − | 0.523062i | ||||
\(203\) | 10.4005 | − | 24.9252i | 0.729970 | − | 1.74941i | ||||
\(204\) | − | 0.00804517i | − | 0.000563274i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.6308 | + | 7.29237i | −0.880026 | + | 0.508083i | ||||
\(207\) | −0.601811 | + | 2.24599i | −0.0418287 | + | 0.156107i | ||||
\(208\) | 20.9765 | − | 5.62063i | 1.45446 | − | 0.389721i | ||||
\(209\) | 12.8743 | 0.890534 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.2060 | −1.04682 | −0.523411 | − | 0.852080i | \(-0.675341\pi\) | ||||
−0.523411 | + | 0.852080i | \(0.675341\pi\) | |||||||
\(212\) | 1.84612 | − | 0.494668i | 0.126792 | − | 0.0339739i | ||||
\(213\) | 0.555790 | − | 2.07423i | 0.0380821 | − | 0.142124i | ||||
\(214\) | 16.6919 | − | 9.63709i | 1.14104 | − | 0.658778i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 2.47818i | − | 0.168619i | ||||||
\(217\) | 17.2485 | − | 2.22513i | 1.17090 | − | 0.151052i | ||||
\(218\) | 9.56295 | − | 9.56295i | 0.647685 | − | 0.647685i | ||||
\(219\) | −6.41615 | − | 3.70437i | −0.433563 | − | 0.250318i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.0470007 | + | 0.0814075i | 0.00316161 | + | 0.00547606i | ||||
\(222\) | 1.10667 | + | 4.13017i | 0.0742751 | + | 0.277199i | ||||
\(223\) | 3.59679 | + | 3.59679i | 0.240859 | + | 0.240859i | 0.817205 | − | 0.576346i | \(-0.195522\pi\) |
−0.576346 | + | 0.817205i | \(0.695522\pi\) | |||||||
\(224\) | 3.60972 | − | 4.67900i | 0.241185 | − | 0.312629i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.06894 | + | 5.31556i | −0.204143 | + | 0.353586i | ||||
\(227\) | 7.28798 | + | 1.95281i | 0.483720 | + | 0.129612i | 0.492434 | − | 0.870350i | \(-0.336107\pi\) |
−0.00871411 | + | 0.999962i | \(0.502774\pi\) | |||||||
\(228\) | −0.959797 | − | 0.257177i | −0.0635641 | − | 0.0170320i | ||||
\(229\) | 12.8628 | − | 22.2790i | 0.849998 | − | 1.47224i | −0.0312109 | − | 0.999513i | \(-0.509936\pi\) |
0.881209 | − | 0.472727i | \(-0.156730\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.6072 | + | 1.82749i | 0.895291 | + | 0.120240i | ||||
\(232\) | −17.8880 | − | 17.8880i | −1.17441 | − | 1.17441i | ||||
\(233\) | 6.94194 | + | 25.9077i | 0.454782 | + | 1.69727i | 0.688729 | + | 0.725019i | \(0.258169\pi\) |
−0.233947 | + | 0.972249i | \(0.575164\pi\) | |||||||
\(234\) | −3.62523 | − | 6.27908i | −0.236989 | − | 0.410476i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.154411 | + | 0.0891493i | 0.0100513 | + | 0.00580312i | ||||
\(237\) | −2.83393 | + | 2.83393i | −0.184084 | + | 0.184084i | ||||
\(238\) | 0.0759917 | + | 0.0317089i | 0.00492581 | + | 0.00205538i | ||||
\(239\) | − | 19.0811i | − | 1.23425i | −0.786863 | − | 0.617127i | \(-0.788296\pi\) | ||
0.786863 | − | 0.617127i | \(-0.211704\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.6084 | − | 6.12477i | 0.683348 | − | 0.394531i | −0.117767 | − | 0.993041i | \(-0.537574\pi\) |
0.801115 | + | 0.598510i | \(0.204240\pi\) | |||||||
\(242\) | 6.38722 | − | 23.8374i | 0.410586 | − | 1.53233i | ||||
\(243\) | −0.965926 | + | 0.258819i | −0.0619642 | + | 0.0166032i | ||||
\(244\) | 0.548688 | 0.0351261 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.71574 | −0.364422 | ||||||||
\(247\) | 11.2145 | − | 3.00490i | 0.713559 | − | 0.191197i | ||||
\(248\) | 4.21614 | − | 15.7349i | 0.267725 | − | 0.999164i | ||||
\(249\) | 4.62372 | − | 2.66950i | 0.293016 | − | 0.169173i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.6455i | 1.55561i | 0.628505 | + | 0.777806i | \(0.283667\pi\) | ||||
−0.628505 | + | 0.777806i | \(0.716333\pi\) | |||||||
\(252\) | −0.977933 | − | 0.408060i | −0.0616040 | − | 0.0257053i | ||||
\(253\) | −8.53201 | + | 8.53201i | −0.536403 | + | 0.536403i | ||||
\(254\) | 4.99710 | + | 2.88508i | 0.313546 | + | 0.181026i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.62626 | − | 8.01293i | −0.289142 | − | 0.500808i | ||||
\(257\) | 2.19866 | + | 8.20551i | 0.137149 | + | 0.511846i | 0.999980 | + | 0.00635343i | \(0.00202237\pi\) |
−0.862831 | + | 0.505492i | \(0.831311\pi\) | |||||||
\(258\) | −4.33394 | − | 4.33394i | −0.269819 | − | 0.269819i | ||||
\(259\) | −7.23667 | − | 0.971903i | −0.449665 | − | 0.0603911i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.10404 | + | 8.84046i | −0.315932 | + | 0.547211i | ||||
\(262\) | −4.50277 | − | 1.20651i | −0.278182 | − | 0.0745387i | ||||
\(263\) | −23.7671 | − | 6.36838i | −1.46554 | − | 0.392691i | −0.564143 | − | 0.825677i | \(-0.690793\pi\) |
−0.901401 | + | 0.432986i | \(0.857460\pi\) | |||||||
\(264\) | 6.42992 | − | 11.1370i | 0.395735 | − | 0.685432i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.21210 | − | 8.05227i | 0.380888 | − | 0.493716i | ||||
\(267\) | −2.71447 | − | 2.71447i | −0.166123 | − | 0.166123i | ||||
\(268\) | −0.612566 | − | 2.28613i | −0.0374184 | − | 0.139647i | ||||
\(269\) | 9.96695 | + | 17.2633i | 0.607696 | + | 1.05256i | 0.991619 | + | 0.129195i | \(0.0412393\pi\) |
−0.383923 | + | 0.923365i | \(0.625427\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.4726 | + | 14.1293i | 1.48661 | + | 0.858293i | 0.999884 | − | 0.0152637i | \(-0.00485877\pi\) |
0.486723 | + | 0.873556i | \(0.338192\pi\) | |||||||
\(272\) | 0.0659145 | − | 0.0659145i | 0.00399665 | − | 0.00399665i | ||||
\(273\) | 12.2794 | − | 1.58410i | 0.743185 | − | 0.0958741i | ||||
\(274\) | − | 16.3615i | − | 0.988432i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.806509 | − | 0.465638i | 0.0485461 | − | 0.0280281i | ||||
\(277\) | −7.72993 | + | 28.8485i | −0.464447 | + | 1.73334i | 0.194270 | + | 0.980948i | \(0.437766\pi\) |
−0.658717 | + | 0.752391i | \(0.728901\pi\) | |||||||
\(278\) | −2.64475 | + | 0.708658i | −0.158621 | + | 0.0425025i | ||||
\(279\) | −6.57334 | −0.393535 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.9592 | −1.07135 | −0.535677 | − | 0.844423i | \(-0.679944\pi\) | ||||
−0.535677 | + | 0.844423i | \(0.679944\pi\) | |||||||
\(282\) | −1.75313 | + | 0.469750i | −0.104397 | + | 0.0279732i | ||||
\(283\) | 5.89965 | − | 22.0178i | 0.350698 | − | 1.30882i | −0.535116 | − | 0.844779i | \(-0.679732\pi\) |
0.885813 | − | 0.464042i | \(-0.153601\pi\) | |||||||
\(284\) | −0.744834 | + | 0.430030i | −0.0441978 | + | 0.0255176i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 37.6243i | − | 2.22477i | ||||||
\(287\) | 3.75863 | − | 9.00771i | 0.221865 | − | 0.531709i | ||||
\(288\) | −1.57940 | + | 1.57940i | −0.0930671 | + | 0.0930671i | ||||
\(289\) | −14.7221 | − | 8.49980i | −0.866005 | − | 0.499988i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.49078 | + | 12.9744i | 0.439117 | + | 0.760574i | ||||
\(292\) | 0.767989 | + | 2.86617i | 0.0449432 | + | 0.167730i | ||||
\(293\) | 17.3271 | + | 17.3271i | 1.01226 | + | 1.01226i | 0.999924 | + | 0.0123342i | \(0.00392620\pi\) |
0.0123342 | + | 0.999924i | \(0.496074\pi\) | |||||||
\(294\) | 7.70877 | − | 7.62889i | 0.449584 | − | 0.444926i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.41960 | + | 5.92292i | −0.198760 | + | 0.344262i | ||||
\(297\) | −5.01241 | − | 1.34307i | −0.290850 | − | 0.0779329i | ||||
\(298\) | 11.0342 | + | 2.95660i | 0.639193 | + | 0.171271i | ||||
\(299\) | −5.44061 | + | 9.42341i | −0.314638 | + | 0.544970i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.68003 | − | 3.98010i | 0.557948 | − | 0.229409i | ||||
\(302\) | 17.9195 | + | 17.9195i | 1.03115 | + | 1.03115i | ||||
\(303\) | −1.75626 | − | 6.55444i | −0.100894 | − | 0.376543i | ||||
\(304\) | −5.75660 | − | 9.97073i | −0.330164 | − | 0.571860i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.0269527 | − | 0.0155612i | −0.00154079 | − | 0.000889573i | ||||
\(307\) | −7.07730 | + | 7.07730i | −0.403923 | + | 0.403923i | −0.879613 | − | 0.475690i | \(-0.842198\pi\) |
0.475690 | + | 0.879613i | \(0.342198\pi\) | |||||||
\(308\) | −3.33608 | − | 4.37118i | −0.190091 | − | 0.249071i | ||||
\(309\) | 9.41340i | 0.535510i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.32047 | − | 2.49442i | 0.244991 | − | 0.141446i | −0.372477 | − | 0.928041i | \(-0.621492\pi\) |
0.617469 | + | 0.786596i | \(0.288158\pi\) | |||||||
\(312\) | 3.00153 | − | 11.2019i | 0.169928 | − | 0.634181i | ||||
\(313\) | 5.69853 | − | 1.52692i | 0.322100 | − | 0.0863064i | −0.0941462 | − | 0.995558i | \(-0.530012\pi\) |
0.416246 | + | 0.909252i | \(0.363345\pi\) | |||||||
\(314\) | 35.5251 | 2.00480 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.60516 | 0.0902975 | ||||||||
\(317\) | −0.852009 | + | 0.228295i | −0.0478536 | + | 0.0128223i | −0.282666 | − | 0.959218i | \(-0.591219\pi\) |
0.234813 | + | 0.972041i | \(0.424552\pi\) | |||||||
\(318\) | 1.91360 | − | 7.14164i | 0.107309 | − | 0.400483i | ||||
\(319\) | −45.8752 | + | 26.4860i | −2.56852 | + | 1.48293i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 12.4401i | − | 0.694339i | ||||||
\(322\) | 1.21951 | + | 9.45324i | 0.0679605 | + | 0.526808i | ||||
\(323\) | 0.0352392 | − | 0.0352392i | 0.00196076 | − | 0.00196076i | ||||
\(324\) | 0.346853 | + | 0.200256i | 0.0192696 | + | 0.0111253i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.8252 | + | 20.4818i | 0.654937 | + | 1.13438i | ||||
\(327\) | −2.25918 | − | 8.43138i | −0.124933 | − | 0.466257i | ||||
\(328\) | −6.46455 | − | 6.46455i | −0.356945 | − | 0.356945i | ||||
\(329\) | 0.412544 | − | 3.07175i | 0.0227443 | − | 0.169351i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.9792 | − | 20.7485i | 0.658435 | − | 1.14044i | −0.322585 | − | 0.946540i | \(-0.604552\pi\) |
0.981021 | − | 0.193903i | \(-0.0621147\pi\) | |||||||
\(332\) | −2.06547 | − | 0.553441i | −0.113357 | − | 0.0303740i | ||||
\(333\) | 2.66573 | + | 0.714279i | 0.146081 | + | 0.0391423i | ||||
\(334\) | −9.43225 | + | 16.3371i | −0.516110 | + | 0.893928i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.66900 | − | 11.3555i | −0.254715 | − | 0.619494i | ||||
\(337\) | 2.18043 | + | 2.18043i | 0.118776 | + | 0.118776i | 0.763996 | − | 0.645221i | \(-0.223235\pi\) |
−0.645221 | + | 0.763996i | \(0.723235\pi\) | |||||||
\(338\) | −3.56859 | − | 13.3182i | −0.194106 | − | 0.724412i | ||||
\(339\) | 1.98078 | + | 3.43081i | 0.107581 | + | 0.186336i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −29.5406 | − | 17.0553i | −1.59971 | − | 0.923595i | ||||
\(342\) | −2.71805 | + | 2.71805i | −0.146975 | + | 0.146975i | ||||
\(343\) | 6.95352 | + | 17.1653i | 0.375455 | + | 0.926841i | ||||
\(344\) | − | 9.80345i | − | 0.528567i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.85189 | − | 2.80124i | 0.260839 | − | 0.150596i | ||||
\(347\) | 4.03656 | − | 15.0646i | 0.216694 | − | 0.808712i | −0.768870 | − | 0.639406i | \(-0.779180\pi\) |
0.985563 | − | 0.169307i | \(-0.0541529\pi\) | |||||||
\(348\) | 3.94914 | − | 1.05817i | 0.211696 | − | 0.0567239i | ||||
\(349\) | 34.9635 | 1.87155 | 0.935776 | − | 0.352596i | \(-0.114701\pi\) | ||||
0.935776 | + | 0.352596i | \(0.114701\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.67965 | −0.249781 | ||||||||
\(352\) | −11.1958 | + | 2.99990i | −0.596737 | + | 0.159895i | ||||
\(353\) | 0.949422 | − | 3.54329i | 0.0505327 | − | 0.188590i | −0.936046 | − | 0.351878i | \(-0.885543\pi\) |
0.986579 | + | 0.163288i | \(0.0522098\pi\) | |||||||
\(354\) | 0.597332 | − | 0.344870i | 0.0317478 | − | 0.0183296i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.53750i | 0.0814873i | ||||||||
\(357\) | 0.0422475 | − | 0.0322432i | 0.00223598 | − | 0.00170649i | ||||
\(358\) | −15.2178 | + | 15.2178i | −0.804285 | + | 0.804285i | ||||
\(359\) | −13.9528 | − | 8.05567i | −0.736402 | − | 0.425162i | 0.0843575 | − | 0.996436i | \(-0.473116\pi\) |
−0.820760 | + | 0.571274i | \(0.806450\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.42240 | + | 11.1239i | 0.338021 | + | 0.585470i | ||||
\(362\) | −6.18627 | − | 23.0875i | −0.325143 | − | 1.21345i | ||||
\(363\) | −11.2629 | − | 11.2629i | −0.591147 | − | 0.591147i | ||||
\(364\) | −3.92621 | − | 3.02897i | −0.205790 | − | 0.158761i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.06129 | − | 1.83820i | 0.0554743 | − | 0.0960843i | ||||
\(367\) | 28.5321 | + | 7.64516i | 1.48936 | + | 0.399074i | 0.909522 | − | 0.415655i | \(-0.136448\pi\) |
0.579842 | + | 0.814729i | \(0.303114\pi\) | |||||||
\(368\) | 10.4228 | + | 2.79277i | 0.543324 | + | 0.145583i | ||||
\(369\) | −1.84455 | + | 3.19485i | −0.0960234 | + | 0.166317i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.99650 | + | 7.71202i | 0.518992 | + | 0.400388i | ||||
\(372\) | 1.86160 | + | 1.86160i | 0.0965193 | + | 0.0965193i | ||||
\(373\) | −1.96300 | − | 7.32603i | −0.101640 | − | 0.379327i | 0.896302 | − | 0.443444i | \(-0.146244\pi\) |
−0.997942 | + | 0.0641169i | \(0.979577\pi\) | |||||||
\(374\) | −0.0807505 | − | 0.139864i | −0.00417551 | − | 0.00723219i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.51410 | − | 1.45152i | −0.129655 | − | 0.0748562i | ||||
\(377\) | −33.7787 | + | 33.7787i | −1.73969 | + | 1.73969i | ||||
\(378\) | −3.25861 | + | 2.48697i | −0.167605 | + | 0.127916i | ||||
\(379\) | 17.5078i | 0.899317i | 0.893201 | + | 0.449658i | \(0.148454\pi\) | ||||
−0.893201 | + | 0.449658i | \(0.851546\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.22527 | − | 1.86211i | 0.165236 | − | 0.0953989i | ||||
\(382\) | −0.0227746 | + | 0.0849961i | −0.00116525 | + | 0.00434878i | ||||
\(383\) | −11.4817 | + | 3.07651i | −0.586687 | + | 0.157202i | −0.539939 | − | 0.841704i | \(-0.681553\pi\) |
−0.0467483 | + | 0.998907i | \(0.514886\pi\) | |||||||
\(384\) | −13.4854 | −0.688172 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.68216 | −0.187417 | ||||||||
\(387\) | −3.82111 | + | 1.02386i | −0.194238 | + | 0.0520459i | ||||
\(388\) | 1.55299 | − | 5.79583i | 0.0788410 | − | 0.294239i | ||||
\(389\) | −7.50204 | + | 4.33130i | −0.380368 | + | 0.219606i | −0.677979 | − | 0.735082i | \(-0.737144\pi\) |
0.297610 | + | 0.954687i | \(0.403810\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0467072i | 0.00236209i | ||||||||
\(392\) | 17.3470 | + | 0.0903426i | 0.876157 | + | 0.00456299i | ||||
\(393\) | −2.12750 | + | 2.12750i | −0.107318 | + | 0.107318i | ||||
\(394\) | 0.476518 | + | 0.275118i | 0.0240066 | + | 0.0138602i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.03917 | + | 1.79990i | 0.0522204 | + | 0.0904484i | ||||
\(397\) | 0.677958 | + | 2.53017i | 0.0340257 | + | 0.126986i | 0.980850 | − | 0.194766i | \(-0.0623949\pi\) |
−0.946824 | + | 0.321752i | \(0.895728\pi\) | |||||||
\(398\) | 27.5070 | + | 27.5070i | 1.37880 | + | 1.37880i | ||||
\(399\) | −2.49614 | − | 6.07088i | −0.124963 | − | 0.303924i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.98018 | + | 8.62592i | −0.248698 | + | 0.430758i | −0.963165 | − | 0.268912i | \(-0.913336\pi\) |
0.714467 | + | 0.699669i | \(0.246669\pi\) | |||||||
\(402\) | −8.84377 | − | 2.36968i | −0.441087 | − | 0.118189i | ||||
\(403\) | −29.7128 | − | 7.96152i | −1.48010 | − | 0.396591i | ||||
\(404\) | −1.35887 | + | 2.35362i | −0.0676061 | + | 0.117097i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.56990 | + | 41.4728i | −0.276430 | + | 2.05826i | ||||
\(407\) | 10.1265 | + | 10.1265i | 0.501952 | + | 0.501952i | ||||
\(408\) | −0.0128840 | − | 0.0480836i | −0.000637851 | − | 0.00238049i | ||||
\(409\) | 4.03282 | + | 6.98504i | 0.199410 | + | 0.345388i | 0.948337 | − | 0.317264i | \(-0.102764\pi\) |
−0.748927 | + | 0.662652i | \(0.769431\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.14536 | − | 5.28008i | −0.451107 | − | 0.260447i | ||||
\(412\) | 2.66592 | − | 2.66592i | 0.131340 | − | 0.131340i | ||||
\(413\) | 0.150696 | + | 1.16815i | 0.00741527 | + | 0.0574808i | ||||
\(414\) | − | 3.60260i | − | 0.177058i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −9.05215 | + | 5.22626i | −0.443818 | + | 0.256239i | ||||
\(417\) | −0.457388 | + | 1.70700i | −0.0223984 | + | 0.0835919i | ||||
\(418\) | −19.2672 | + | 5.16264i | −0.942391 | + | 0.252513i | ||||
\(419\) | 1.30845 | 0.0639222 | 0.0319611 | − | 0.999489i | \(-0.489825\pi\) | ||||
0.0319611 | + | 0.999489i | \(0.489825\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.88085 | 0.140404 | 0.0702020 | − | 0.997533i | \(-0.477636\pi\) | ||||
0.0702020 | + | 0.997533i | \(0.477636\pi\) | |||||||
\(422\) | 22.7567 | − | 6.09764i | 1.10778 | − | 0.296829i | ||||
\(423\) | −0.303190 | + | 1.13152i | −0.0147416 | + | 0.0550164i | ||||
\(424\) | 10.2416 | − | 5.91297i | 0.497374 | − | 0.287159i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.32710i | 0.161199i | ||||||||
\(427\) | 2.19902 | + | 2.88132i | 0.106418 | + | 0.139437i | ||||
\(428\) | −3.52309 | + | 3.52309i | −0.170295 | + | 0.170295i | ||||
\(429\) | −21.0304 | − | 12.1419i | −1.01536 | − | 0.586216i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.4163 | − | 18.0415i | −0.501734 | − | 0.869028i | −0.999998 | − | 0.00200303i | \(-0.999362\pi\) |
0.498264 | − | 0.867025i | \(-0.333971\pi\) | |||||||
\(432\) | 1.20108 | + | 4.48249i | 0.0577869 | + | 0.215664i | ||||
\(433\) | 5.72121 | + | 5.72121i | 0.274944 | + | 0.274944i | 0.831087 | − | 0.556143i | \(-0.187719\pi\) |
−0.556143 | + | 0.831087i | \(0.687719\pi\) | |||||||
\(434\) | −24.9212 | + | 10.2468i | −1.19626 | + | 0.491860i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.74799 | + | 3.02761i | −0.0837137 | + | 0.144996i | ||||
\(437\) | 5.57222 | + | 1.49307i | 0.266555 | + | 0.0714233i | ||||
\(438\) | 11.0877 | + | 2.97093i | 0.529789 | + | 0.141956i | ||||
\(439\) | −4.31964 | + | 7.48184i | −0.206165 | + | 0.357089i | −0.950503 | − | 0.310714i | \(-0.899432\pi\) |
0.744338 | + | 0.667803i | \(0.232765\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.77650 | − | 6.77082i | −0.0845950 | − | 0.322420i | ||||
\(442\) | −0.102984 | − | 0.102984i | −0.00489846 | − | 0.00489846i | ||||
\(443\) | −8.05575 | − | 30.0644i | −0.382740 | − | 1.42841i | −0.841699 | − | 0.539948i | \(-0.818444\pi\) |
0.458959 | − | 0.888458i | \(-0.348223\pi\) | |||||||
\(444\) | −0.552658 | − | 0.957232i | −0.0262280 | − | 0.0454282i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.82516 | − | 3.94051i | −0.323181 | − | 0.186589i | ||||
\(447\) | 5.21350 | − | 5.21350i | 0.246590 | − | 0.246590i | ||||
\(448\) | 5.93026 | − | 14.2121i | 0.280179 | − | 0.671460i | ||||
\(449\) | 40.3196i | 1.90280i | 0.307962 | + | 0.951399i | \(0.400353\pi\) | ||||
−0.307962 | + | 0.951399i | \(0.599647\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.5788 | + | 9.57179i | −0.780667 | + | 0.450718i | ||||
\(452\) | 0.410655 | − | 1.53259i | 0.0193156 | − | 0.0720868i | ||||
\(453\) | 15.7991 | − | 4.23336i | 0.742308 | − | 0.198901i | ||||
\(454\) | −11.6900 | −0.548640 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.14828 | −0.287920 | ||||||||
\(457\) | −12.9317 | + | 3.46505i | −0.604921 | + | 0.162088i | −0.548264 | − | 0.836305i | \(-0.684711\pi\) |
−0.0566576 | + | 0.998394i | \(0.518044\pi\) | |||||||
\(458\) | −10.3161 | + | 38.5001i | −0.482038 | + | 1.79899i | ||||
\(459\) | −0.0173961 | + | 0.0100436i | −0.000811979 | + | 0.000468796i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.07258i | 0.0965298i | 0.998835 | + | 0.0482649i | \(0.0153692\pi\) | ||||
−0.998835 | + | 0.0482649i | \(0.984631\pi\) | |||||||
\(462\) | −21.0970 | + | 2.72160i | −0.981519 | + | 0.126620i | ||||
\(463\) | −12.9744 | + | 12.9744i | −0.602971 | + | 0.602971i | −0.941100 | − | 0.338129i | \(-0.890206\pi\) |
0.338129 | + | 0.941100i | \(0.390206\pi\) | |||||||
\(464\) | 41.0252 | + | 23.6859i | 1.90455 | + | 1.09959i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.7781 | − | 35.9888i | −0.962529 | − | 1.66715i | ||||
\(467\) | −6.66459 | − | 24.8726i | −0.308400 | − | 1.15097i | −0.929979 | − | 0.367614i | \(-0.880175\pi\) |
0.621578 | − | 0.783352i | \(-0.286492\pi\) | |||||||
\(468\) | 1.32530 | + | 1.32530i | 0.0612619 | + | 0.0612619i | ||||
\(469\) | 9.55010 | − | 12.3791i | 0.440982 | − | 0.571611i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.4645 | − | 19.8570i | 0.528254 | − | 0.914963i | ||||
\(472\) | 1.06564 | + | 0.285537i | 0.0490500 | + | 0.0131429i | ||||
\(473\) | −19.8286 | − | 5.31306i | −0.911721 | − | 0.244295i | ||||
\(474\) | 3.10475 | − | 5.37758i | 0.142606 | − | 0.247001i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.0210961 | − | 0.00283326i | −0.000966939 | − | 0.000129862i | ||||
\(477\) | −3.37433 | − | 3.37433i | −0.154500 | − | 0.154500i | ||||
\(478\) | 7.65159 | + | 28.5561i | 0.349976 | + | 1.30613i | ||||
\(479\) | 12.5000 | + | 21.6506i | 0.571138 | + | 0.989240i | 0.996449 | + | 0.0841932i | \(0.0268313\pi\) |
−0.425311 | + | 0.905047i | \(0.639835\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.1845 | + | 6.45737i | 0.509969 | + | 0.294431i | ||||
\(482\) | −13.4201 | + | 13.4201i | −0.611271 | + | 0.611271i | ||||
\(483\) | 5.67751 | + | 2.36904i | 0.258336 | + | 0.107795i | ||||
\(484\) | 6.37938i | 0.289972i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.34178 | − | 0.774679i | 0.0608645 | − | 0.0351402i | ||||
\(487\) | −7.06031 | + | 26.3494i | −0.319933 | + | 1.19401i | 0.599375 | + | 0.800468i | \(0.295416\pi\) |
−0.919308 | + | 0.393538i | \(0.871251\pi\) | |||||||
\(488\) | 3.27935 | − | 0.878698i | 0.148449 | − | 0.0397768i | ||||
\(489\) | 15.2646 | 0.690290 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.4800 | −1.05964 | −0.529820 | − | 0.848110i | \(-0.677740\pi\) | ||||
−0.529820 | + | 0.848110i | \(0.677740\pi\) | |||||||
\(492\) | 1.42718 | − | 0.382412i | 0.0643423 | − | 0.0172405i | ||||
\(493\) | −0.0530714 | + | 0.198065i | −0.00239022 | + | 0.00892041i | ||||
\(494\) | −15.5782 | + | 8.99407i | −0.700896 | + | 0.404662i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 30.5043i | 1.36968i | ||||||||
\(497\) | −5.24334 | − | 2.18788i | −0.235196 | − | 0.0981397i | ||||
\(498\) | −5.84921 | + | 5.84921i | −0.262109 | + | 0.262109i | ||||
\(499\) | 24.8192 | + | 14.3294i | 1.11106 | + | 0.641470i | 0.939104 | − | 0.343634i | \(-0.111658\pi\) |
0.171956 | + | 0.985105i | \(0.444991\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.08784 | + | 10.5444i | 0.271985 | + | 0.471091i | ||||
\(502\) | −9.88294 | − | 36.8836i | −0.441097 | − | 1.64620i | ||||
\(503\) | 7.43731 | + | 7.43731i | 0.331613 | + | 0.331613i | 0.853199 | − | 0.521586i | \(-0.174659\pi\) |
−0.521586 | + | 0.853199i | \(0.674659\pi\) | |||||||
\(504\) | −6.49831 | − | 0.872739i | −0.289458 | − | 0.0388749i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.34735 | − | 16.1901i | 0.415540 | − | 0.719737i | ||||
\(507\) | −8.59591 | − | 2.30327i | −0.381758 | − | 0.102292i | ||||
\(508\) | −1.44077 | − | 0.386053i | −0.0639238 | − | 0.0171283i | ||||
\(509\) | 5.08320 | − | 8.80437i | 0.225309 | − | 0.390247i | −0.731103 | − | 0.682267i | \(-0.760994\pi\) |
0.956412 | + | 0.292020i | \(0.0943275\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.9732 | + | 15.5199i | −0.529663 | + | 0.686561i | ||||
\(512\) | −8.93446 | − | 8.93446i | −0.394851 | − | 0.394851i | ||||
\(513\) | 0.642121 | + | 2.39643i | 0.0283503 | + | 0.105805i | ||||
\(514\) | −6.58087 | − | 11.3984i | −0.290270 | − | 0.502762i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.37212 | + | 0.792192i | 0.0604041 | + | 0.0348743i | ||||
\(517\) | −4.29840 | + | 4.29840i | −0.189043 | + | 0.189043i | ||||
\(518\) | 11.2199 | − | 1.44741i | 0.492974 | − | 0.0635957i | ||||
\(519\) | − | 3.61600i | − | 0.158725i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.4269 | − | 13.5255i | 1.02635 | − | 0.592565i | 0.110415 | − | 0.993886i | \(-0.464782\pi\) |
0.915938 | + | 0.401321i | \(0.131449\pi\) | |||||||
\(522\) | 4.09348 | − | 15.2771i | 0.179167 | − | 0.668659i | ||||
\(523\) | −5.57429 | + | 1.49363i | −0.243747 | + | 0.0653117i | −0.378624 | − | 0.925551i | \(-0.623603\pi\) |
0.134877 | + | 0.990862i | \(0.456936\pi\) | |||||||
\(524\) | 1.20503 | 0.0526421 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 38.1228 | 1.66223 | ||||||||
\(527\) | −0.127541 | + | 0.0341745i | −0.00555578 | + | 0.00148867i | ||||
\(528\) | −6.23267 | + | 23.2607i | −0.271242 | + | 1.01229i | ||||
\(529\) | 15.2363 | − | 8.79668i | 0.662448 | − | 0.382464i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 0.445177i | − | 0.0193190i | ||||||
\(532\) | −1.01238 | + | 2.42622i | −0.0438923 | + | 0.105190i | ||||
\(533\) | −12.2073 | + | 12.2073i | −0.528756 | + | 0.528756i | ||||
\(534\) | 5.15089 | + | 2.97387i | 0.222901 | + | 0.128692i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.32225 | − | 12.6825i | −0.316273 | − | 0.547801i | ||||
\(537\) | 3.59510 | + | 13.4171i | 0.155140 | + | 0.578990i | ||||
\(538\) | −21.8388 | − | 21.8388i | −0.941539 | − | 0.941539i | ||||
\(539\) | 9.58410 | − | 35.0374i | 0.412816 | − | 1.50917i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.0154 | − | 19.0793i | 0.473590 | − | 0.820283i | −0.525952 | − | 0.850514i | \(-0.676291\pi\) |
0.999543 | + | 0.0302312i | \(0.00962435\pi\) | |||||||
\(542\) | −42.2908 | − | 11.3318i | −1.81654 | − | 0.486742i | ||||
\(543\) | −14.9013 | − | 3.99279i | −0.639476 | − | 0.171347i | ||||
\(544\) | −0.0224335 | + | 0.0388560i | −0.000961830 | + | 0.00166594i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −17.7418 | + | 7.29481i | −0.759277 | + | 0.312189i | ||||
\(547\) | −19.7018 | − | 19.7018i | −0.842388 | − | 0.842388i | 0.146781 | − | 0.989169i | \(-0.453109\pi\) |
−0.989169 | + | 0.146781i | \(0.953109\pi\) | |||||||
\(548\) | 1.09466 | + | 4.08535i | 0.0467618 | + | 0.174517i | ||||
\(549\) | −0.684984 | − | 1.18643i | −0.0292344 | − | 0.0506355i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.9329 | + | 12.6630i | 0.934372 | + | 0.539460i | ||||
\(552\) | 4.07457 | − | 4.07457i | 0.173425 | − | 0.173425i | ||||
\(553\) | 6.43314 | + | 8.42919i | 0.273565 | + | 0.358445i | ||||
\(554\) | − | 46.2734i | − | 1.96597i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.612963 | − | 0.353894i | 0.0259954 | − | 0.0150085i | ||||
\(557\) | 4.14131 | − | 15.4556i | 0.175473 | − | 0.654874i | −0.820998 | − | 0.570932i | \(-0.806582\pi\) |
0.996471 | − | 0.0839424i | \(-0.0267512\pi\) | |||||||
\(558\) | 9.83743 | − | 2.63593i | 0.416452 | − | 0.111588i | ||||
\(559\) | −18.5123 | −0.782985 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.104237 | −0.00440090 | ||||||||
\(562\) | 26.8771 | − | 7.20169i | 1.13374 | − | 0.303785i | ||||
\(563\) | −4.14791 | + | 15.4802i | −0.174813 | + | 0.652413i | 0.821770 | + | 0.569819i | \(0.192987\pi\) |
−0.996583 | + | 0.0825932i | \(0.973680\pi\) | |||||||
\(564\) | 0.406316 | − | 0.234587i | 0.0171090 | − | 0.00987788i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 35.3168i | 1.48448i | ||||||||
\(567\) | 0.338508 | + | 2.62401i | 0.0142160 | + | 0.110198i | ||||
\(568\) | −3.76298 | + | 3.76298i | −0.157891 | + | 0.157891i | ||||
\(569\) | −22.2011 | − | 12.8178i | −0.930717 | − | 0.537350i | −0.0436785 | − | 0.999046i | \(-0.513908\pi\) |
−0.887038 | + | 0.461696i | \(0.847241\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.33247 | + | 14.4323i | 0.348703 | + | 0.603971i | 0.986019 | − | 0.166631i | \(-0.0532888\pi\) |
−0.637316 | + | 0.770602i | \(0.719955\pi\) | |||||||
\(572\) | 2.51726 | + | 9.39453i | 0.105252 | + | 0.392805i | ||||
\(573\) | 0.0401595 | + | 0.0401595i | 0.00167769 | + | 0.00167769i | ||||
\(574\) | −2.01291 | + | 14.9879i | −0.0840171 | + | 0.625581i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.91028 | + | 5.04076i | −0.121262 | + | 0.210031i | ||||
\(577\) | −4.25450 | − | 1.13999i | −0.177117 | − | 0.0474584i | 0.169170 | − | 0.985587i | \(-0.445891\pi\) |
−0.346288 | + | 0.938128i | \(0.612558\pi\) | |||||||
\(578\) | 25.4410 | + | 6.81690i | 1.05821 | + | 0.283546i | ||||
\(579\) | −1.18828 | + | 2.05817i | −0.0493834 | + | 0.0855346i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.37166 | − | 13.0645i | −0.222854 | − | 0.542005i | ||||
\(582\) | −16.4132 | − | 16.4132i | −0.680350 | − | 0.680350i | ||||
\(583\) | −6.40916 | − | 23.9193i | −0.265440 | − | 0.990637i | ||||
\(584\) | 9.18009 | + | 15.9004i | 0.379875 | + | 0.657963i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −32.8793 | − | 18.9829i | −1.35823 | − | 0.784175i | ||||
\(587\) | 25.1535 | − | 25.1535i | 1.03820 | − | 1.03820i | 0.0389571 | − | 0.999241i | \(-0.487596\pi\) |
0.999241 | − | 0.0389571i | \(-0.0124036\pi\) | |||||||
\(588\) | −1.41442 | + | 2.42064i | −0.0583295 | + | 0.0998254i | ||||
\(589\) | 16.3082i | 0.671969i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.307558 | − | 0.177569i | 0.0126512 | − | 0.00730420i | ||||
\(592\) | 3.31469 | − | 12.3706i | 0.136233 | − | 0.508429i | ||||
\(593\) | −41.1024 | + | 11.0134i | −1.68787 | + | 0.452265i | −0.969840 | − | 0.243742i | \(-0.921625\pi\) |
−0.718035 | + | 0.696007i | \(0.754958\pi\) | |||||||
\(594\) | 8.03998 | 0.329884 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.95297 | −0.120959 | ||||||||
\(597\) | 24.2521 | − | 6.49834i | 0.992573 | − | 0.265959i | ||||
\(598\) | 4.36340 | − | 16.2844i | 0.178433 | − | 0.665920i | ||||
\(599\) | 15.9783 | − | 9.22507i | 0.652855 | − | 0.376926i | −0.136694 | − | 0.990613i | \(-0.543648\pi\) |
0.789549 | + | 0.613687i | \(0.210314\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.13978i | 0.168865i | 0.996429 | + | 0.0844326i | \(0.0269078\pi\) | ||||
−0.996429 | + | 0.0844326i | \(0.973092\pi\) | |||||||
\(602\) | −12.8908 | + | 9.83821i | −0.525389 | + | 0.400976i | ||||
\(603\) | −4.17856 | + | 4.17856i | −0.170164 | + | 0.170164i | ||||
\(604\) | −5.67329 | − | 3.27548i | −0.230843 | − | 0.133277i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.25670 | + | 9.10488i | 0.213539 | + | 0.369860i | ||||
\(607\) | 6.39069 | + | 23.8504i | 0.259390 | + | 0.968058i | 0.965595 | + | 0.260050i | \(0.0837391\pi\) |
−0.706205 | + | 0.708008i | \(0.749594\pi\) | |||||||
\(608\) | 3.91844 | + | 3.91844i | 0.158914 | + | 0.158914i | ||||
\(609\) | 21.3840 | + | 16.4972i | 0.866525 | + | 0.668500i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.74096 | + | 4.74748i | −0.110887 | + | 0.192062i | ||||
\(612\) | 0.00777104 | + | 0.00208224i | 0.000314126 | + | 8.41697e-5i | ||||
\(613\) | 46.8375 | + | 12.5501i | 1.89175 | + | 0.506893i | 0.998337 | + | 0.0576548i | \(0.0183623\pi\) |
0.893412 | + | 0.449238i | \(0.148304\pi\) | |||||||
\(614\) | 7.75362 | − | 13.4297i | 0.312910 | − | 0.541977i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −26.9390 | − | 20.7827i | −1.08540 | − | 0.837359i | ||||
\(617\) | 9.77318 | + | 9.77318i | 0.393453 | + | 0.393453i | 0.875916 | − | 0.482463i | \(-0.160258\pi\) |
−0.482463 | + | 0.875916i | \(0.660258\pi\) | |||||||
\(618\) | −3.77481 | − | 14.0878i | −0.151845 | − | 0.566693i | ||||
\(619\) | −13.8899 | − | 24.0580i | −0.558281 | − | 0.966972i | −0.997640 | − | 0.0686600i | \(-0.978128\pi\) |
0.439359 | − | 0.898312i | \(-0.355206\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.01370 | − | 1.16261i | −0.0808069 | − | 0.0466539i | ||||
\(622\) | −5.46559 | + | 5.46559i | −0.219150 | + | 0.219150i | ||||
\(623\) | −8.07386 | + | 6.16195i | −0.323472 | + | 0.246873i | ||||
\(624\) | 21.7165i | 0.869354i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7.91592 | + | 4.57026i | −0.316384 | + | 0.182664i | ||||
\(627\) | −3.33211 | + | 12.4356i | −0.133072 | + | 0.496631i | ||||
\(628\) | −8.87038 | + | 2.37681i | −0.353967 | + | 0.0948451i | ||||
\(629\) | 0.0554360 | 0.00221038 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.9169 | 0.633641 | 0.316821 | − | 0.948486i | \(-0.397385\pi\) | ||||
0.316821 | + | 0.948486i | \(0.397385\pi\) | |||||||
\(632\) | 9.59360 | − | 2.57060i | 0.381613 | − | 0.102253i | ||||
\(633\) | 3.93559 | − | 14.6878i | 0.156426 | − | 0.583789i | ||||
\(634\) | 1.18354 | − | 0.683317i | 0.0470044 | − | 0.0271380i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.91125i | 0.0757859i | ||||||||
\(637\) | 0.170598 | − | 32.7571i | 0.00675932 | − | 1.29788i | ||||
\(638\) | 58.0342 | − | 58.0342i | 2.29760 | − | 2.29760i | ||||
\(639\) | 1.85971 | + | 1.07370i | 0.0735689 | + | 0.0424750i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.7911 | + | 25.6190i | 0.584214 | + | 1.01189i | 0.994973 | + | 0.100144i | \(0.0319304\pi\) |
−0.410759 | + | 0.911744i | \(0.634736\pi\) | |||||||
\(642\) | 4.98852 | + | 18.6174i | 0.196881 | + | 0.734771i | ||||
\(643\) | 23.0451 | + | 23.0451i | 0.908809 | + | 0.908809i | 0.996176 | − | 0.0873668i | \(-0.0278452\pi\) |
−0.0873668 | + | 0.996176i | \(0.527845\pi\) | |||||||
\(644\) | −0.936973 | − | 2.27882i | −0.0369219 | − | 0.0897980i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.0386067 | + | 0.0668688i | −0.00151896 | + | 0.00263092i | ||||
\(647\) | 26.5278 | + | 7.10809i | 1.04291 | + | 0.279448i | 0.739320 | − | 0.673354i | \(-0.235147\pi\) |
0.303593 | + | 0.952802i | \(0.401814\pi\) | |||||||
\(648\) | 2.39374 | + | 0.641400i | 0.0940350 | + | 0.0251966i | ||||
\(649\) | 1.15506 | − | 2.00063i | 0.0453402 | − | 0.0785315i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.31493 | + | 17.2367i | −0.0907291 | + | 0.675558i | ||||
\(652\) | −4.32301 | − | 4.32301i | −0.169302 | − | 0.169302i | ||||
\(653\) | −8.43850 | − | 31.4929i | −0.330224 | − | 1.23241i | −0.908955 | − | 0.416894i | \(-0.863119\pi\) |
0.578731 | − | 0.815518i | \(-0.303548\pi\) | |||||||
\(654\) | 6.76203 | + | 11.7122i | 0.264416 | + | 0.457982i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 14.8261 | + | 8.55984i | 0.578861 | + | 0.334206i | ||||
\(657\) | 5.23877 | − | 5.23877i | 0.204384 | − | 0.204384i | ||||
\(658\) | 0.614384 | + | 4.76250i | 0.0239512 | + | 0.185662i | ||||
\(659\) | 4.16401i | 0.162207i | 0.996706 | + | 0.0811034i | \(0.0258444\pi\) | ||||
−0.996706 | + | 0.0811034i | \(0.974156\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.2035 | + | 5.89099i | −0.396870 | + | 0.229133i | −0.685133 | − | 0.728418i | \(-0.740256\pi\) |
0.288262 | + | 0.957551i | \(0.406922\pi\) | |||||||
\(662\) | −9.60739 | + | 35.8553i | −0.373402 | + | 1.39355i | ||||
\(663\) | −0.0907983 | + | 0.0243293i | −0.00352631 | + | 0.000944873i | ||||
\(664\) | −13.2310 | −0.513463 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.27586 | −0.165686 | ||||||||
\(667\) | −22.9272 | + | 6.14334i | −0.887746 | + | 0.237871i | ||||
\(668\) | 1.26213 | − | 4.71034i | 0.0488333 | − | 0.182248i | ||||
\(669\) | −4.40515 | + | 2.54332i | −0.170313 | + | 0.0983303i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 7.10908i | − | 0.274443i | ||||||
\(672\) | 3.58530 | + | 4.69774i | 0.138306 | + | 0.181219i | ||||
\(673\) | 7.90660 | − | 7.90660i | 0.304777 | − | 0.304777i | −0.538102 | − | 0.842879i | \(-0.680859\pi\) |
0.842879 | + | 0.538102i | \(0.180859\pi\) | |||||||
\(674\) | −4.13752 | − | 2.38880i | −0.159371 | − | 0.0920130i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.78210 | + | 3.08669i | 0.0685425 | + | 0.118719i | ||||
\(677\) | 2.13283 | + | 7.95983i | 0.0819713 | + | 0.305921i | 0.994723 | − | 0.102593i | \(-0.0327139\pi\) |
−0.912752 | + | 0.408514i | \(0.866047\pi\) | |||||||
\(678\) | −4.34013 | − | 4.34013i | −0.166682 | − | 0.166682i | ||||
\(679\) | 36.6596 | − | 15.0732i | 1.40687 | − | 0.578456i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.77254 | + | 6.53422i | −0.144564 | + | 0.250392i | ||||
\(682\) | 51.0487 | + | 13.6785i | 1.95475 | + | 0.523775i | ||||
\(683\) | 20.9907 | + | 5.62443i | 0.803185 | + | 0.215213i | 0.636982 | − | 0.770879i | \(-0.280183\pi\) |
0.166203 | + | 0.986091i | \(0.446849\pi\) | |||||||
\(684\) | 0.496828 | − | 0.860531i | 0.0189967 | − | 0.0329032i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −17.2897 | − | 22.9007i | −0.660126 | − | 0.874351i | ||||
\(687\) | 18.1908 | + | 18.1908i | 0.694020 | + | 0.694020i | ||||
\(688\) | 4.75135 | + | 17.7323i | 0.181144 | + | 0.676038i | ||||
\(689\) | −11.1657 | − | 19.3396i | −0.425379 | − | 0.736779i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.9666 | − | 14.4145i | −0.949775 | − | 0.548353i | −0.0567641 | − | 0.998388i | \(-0.518078\pi\) |
−0.893011 | + | 0.450035i | \(0.851412\pi\) | |||||||
\(692\) | −1.02407 | + | 1.02407i | −0.0389292 | + | 0.0389292i | ||||
\(693\) | −5.28703 | + | 12.6706i | −0.200838 | + | 0.481316i | ||||
\(694\) | 24.1639i | 0.917249i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 21.9083 | − | 12.6487i | 0.830431 | − | 0.479449i | ||||
\(697\) | −0.0191795 | + | 0.0715788i | −0.000726475 | + | 0.00271124i | ||||
\(698\) | −52.3251 | + | 14.0205i | −1.98053 | + | 0.530683i | ||||
\(699\) | −26.8216 | −1.01449 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.9967 | 1.85058 | 0.925290 | − | 0.379259i | \(-0.123821\pi\) | ||||
0.925290 | + | 0.379259i | \(0.123821\pi\) | |||||||
\(702\) | 7.00340 | − | 1.87656i | 0.264326 | − | 0.0708261i | ||||
\(703\) | 1.77210 | − | 6.61358i | 0.0668361 | − | 0.249436i | ||||
\(704\) | −26.1576 | + | 15.1021i | −0.985853 | + | 0.569182i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.68349i | 0.213901i | ||||||||
\(707\) | −17.8056 | + | 2.29700i | −0.669649 | + | 0.0863876i | ||||
\(708\) | −0.126076 | + | 0.126076i | −0.00473823 | + | 0.00473823i | ||||
\(709\) | 18.3623 | + | 10.6015i | 0.689609 | + | 0.398146i | 0.803466 | − | 0.595351i | \(-0.202987\pi\) |
−0.113856 | + | 0.993497i | \(0.536320\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.00389 | − | 3.47085i | −0.0751519 | − | 0.130167i | ||||
\(712\) | 2.46223 | + | 9.18918i | 0.0922761 | + | 0.344379i | ||||
\(713\) | −10.8077 | − | 10.8077i | −0.404753 | − | 0.404753i | ||||
\(714\) | −0.0502965 | + | 0.0651955i | −0.00188230 | + | 0.00243988i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.78163 | − | 4.81793i | 0.103954 | − | 0.180054i | ||||
\(717\) | 18.4309 | + | 4.93856i | 0.688316 | + | 0.184434i | ||||
\(718\) | 24.1117 | + | 6.46070i | 0.899840 | + | 0.241111i | ||||
\(719\) | −7.96647 | + | 13.7983i | −0.297099 | + | 0.514591i | −0.975471 | − | 0.220128i | \(-0.929352\pi\) |
0.678372 | + | 0.734719i | \(0.262686\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.6839 | + | 3.31511i | 0.919277 | + | 0.123461i | ||||
\(722\) | −14.0723 | − | 14.0723i | −0.523716 | − | 0.523716i | ||||
\(723\) | 3.17042 | + | 11.8322i | 0.117909 | + | 0.440043i | ||||
\(724\) | 3.08934 | + | 5.35089i | 0.114814 | + | 0.198864i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 21.3721 | + | 12.3392i | 0.793192 | + | 0.457949i | ||||
\(727\) | 20.1000 | − | 20.1000i | 0.745467 | − | 0.745467i | −0.228157 | − | 0.973624i | \(-0.573270\pi\) |
0.973624 | + | 0.228157i | \(0.0732701\pi\) | |||||||
\(728\) | −28.3166 | − | 11.8156i | −1.04948 | − | 0.437915i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.0688172 | + | 0.0397316i | −0.00254529 | + | 0.00146953i | ||||
\(732\) | −0.142011 | + | 0.529992i | −0.00524887 | + | 0.0195891i | ||||
\(733\) | 14.0293 | − | 3.75914i | 0.518184 | − | 0.138847i | 0.00975769 | − | 0.999952i | \(-0.496894\pi\) |
0.508427 | + | 0.861105i | \(0.330227\pi\) | |||||||
\(734\) | −45.7659 | −1.68925 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.19363 | −0.191440 | ||||||||
\(737\) | −29.6202 | + | 7.93672i | −1.09108 | + | 0.292353i | ||||
\(738\) | 1.47934 | − | 5.52098i | 0.0544553 | − | 0.203230i | ||||
\(739\) | 11.2873 | − | 6.51671i | 0.415209 | − | 0.239721i | −0.277816 | − | 0.960634i | \(-0.589611\pi\) |
0.693025 | + | 0.720913i | \(0.256277\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.6101i | 0.426506i | ||||||||
\(742\) | −18.0530 | − | 7.53292i | −0.662745 | − | 0.276542i | ||||
\(743\) | 18.6181 | − | 18.6181i | 0.683031 | − | 0.683031i | −0.277651 | − | 0.960682i | \(-0.589556\pi\) |
0.960682 | + | 0.277651i | \(0.0895558\pi\) | |||||||
\(744\) | 14.1075 | + | 8.14496i | 0.517206 | + | 0.298609i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.87552 | + | 10.1767i | 0.215118 | + | 0.372596i | ||||
\(747\) | 1.38184 | + | 5.15708i | 0.0505588 | + | 0.188688i | ||||
\(748\) | 0.0295205 | + | 0.0295205i | 0.00107937 | + | 0.00107937i | ||||
\(749\) | −32.6205 | − | 4.38102i | −1.19193 | − | 0.160079i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.7401 | − | 25.5305i | 0.537872 | − | 0.931622i | −0.461146 | − | 0.887324i | \(-0.652562\pi\) |
0.999018 | − | 0.0442977i | \(-0.0141050\pi\) | |||||||
\(752\) | 5.25095 | + | 1.40699i | 0.191482 | + | 0.0513075i | ||||
\(753\) | −23.8057 | − | 6.37873i | −0.867529 | − | 0.232454i | ||||
\(754\) | 37.0067 | − | 64.0974i | 1.34770 | − | 2.33429i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.647263 | − | 0.838997i | 0.0235407 | − | 0.0305140i | ||||
\(757\) | −5.70030 | − | 5.70030i | −0.207181 | − | 0.207181i | 0.595887 | − | 0.803068i | \(-0.296801\pi\) |
−0.803068 | + | 0.595887i | \(0.796801\pi\) | |||||||
\(758\) | −7.02070 | − | 26.2016i | −0.255003 | − | 0.951685i | ||||
\(759\) | −6.03305 | − | 10.4495i | −0.218986 | − | 0.379294i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −47.3925 | − | 27.3621i | −1.71798 | − | 0.991874i | −0.922601 | − | 0.385756i | \(-0.873941\pi\) |
−0.795375 | − | 0.606118i | \(-0.792726\pi\) | |||||||
\(762\) | −4.08012 | + | 4.08012i | −0.147807 | + | 0.147807i | ||||
\(763\) | −22.9045 | + | 2.95477i | −0.829197 | + | 0.106970i | ||||
\(764\) | − | 0.0227467i | − | 0.000822947i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.9494 | − | 9.20839i | 0.576275 | − | 0.332713i | ||||
\(767\) | 0.539191 | − | 2.01229i | 0.0194691 | − | 0.0726595i | ||||
\(768\) | 8.93726 | − | 2.39473i | 0.322495 | − | 0.0864124i | ||||
\(769\) | −42.0339 | −1.51578 | −0.757891 | − | 0.652381i | \(-0.773770\pi\) | ||||
−0.757891 | + | 0.652381i | \(0.773770\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.49497 | −0.305939 | ||||||||
\(772\) | 0.919410 | − | 0.246355i | 0.0330903 | − | 0.00886651i | ||||
\(773\) | 7.39235 | − | 27.5886i | 0.265884 | − | 0.992294i | −0.695822 | − | 0.718214i | \(-0.744960\pi\) |
0.961707 | − | 0.274080i | \(-0.0883734\pi\) | |||||||
\(774\) | 5.30797 | − | 3.06456i | 0.190791 | − | 0.110153i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 37.1270i | − | 1.33278i | ||||||
\(777\) | 2.81178 | − | 6.73854i | 0.100872 | − | 0.241744i | ||||
\(778\) | 9.49042 | − | 9.49042i | 0.340248 | − | 0.340248i | ||||
\(779\) | 7.92632 | + | 4.57627i | 0.283990 | + | 0.163962i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.57169 | + | 9.65045i | 0.199371 | + | 0.345320i | ||||
\(782\) | −0.0187298 | − | 0.0699004i | −0.000669775 | − | 0.00249963i | ||||
\(783\) | −7.21821 | − | 7.21821i | −0.257958 | − | 0.257958i | ||||
\(784\) | −31.4208 | + | 8.24403i | −1.12217 | + | 0.294430i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.33081 | − | 4.03707i | 0.0831371 | − | 0.143998i | ||||
\(787\) | −16.0514 | − | 4.30097i | −0.572172 | − | 0.153313i | −0.0388795 | − | 0.999244i | \(-0.512379\pi\) |
−0.533293 | + | 0.845931i | \(0.679046\pi\) | |||||||
\(788\) | −0.137390 | − | 0.0368135i | −0.00489432 | − | 0.00131143i | ||||
\(789\) | 12.3028 | − | 21.3090i | 0.437990 | − | 0.758621i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.69387 | − | 3.98579i | 0.344674 | − | 0.141718i | ||||
\(792\) | 9.09329 | + | 9.09329i | 0.323116 | + | 0.323116i | ||||
\(793\) | −1.65928 | − | 6.19252i | −0.0589228 | − | 0.219903i | ||||
\(794\) | −2.02922 | − | 3.51471i | −0.0720142 | − | 0.124732i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.70866 | − | 5.02795i | −0.308670 | − | 0.178211i | ||||
\(797\) | −18.2572 | + | 18.2572i | −0.646702 | + | 0.646702i | −0.952194 | − | 0.305492i | \(-0.901179\pi\) |
0.305492 | + | 0.952194i | \(0.401179\pi\) | |||||||
\(798\) | 6.17008 | + | 8.08451i | 0.218419 | + | 0.286189i | ||||
\(799\) | 0.0235309i | 0.000832464i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.32453 | − | 1.91942i | 0.117467 | − | 0.0678193i | ||||
\(802\) | 3.99414 | − | 14.9063i | 0.141038 | − | 0.526361i | ||||
\(803\) | 37.1356 | − | 9.95046i | 1.31049 | − | 0.351144i | ||||
\(804\) | 2.36677 | 0.0834696 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 47.6597 | 1.67874 | ||||||||
\(807\) | −19.2547 | + | 5.15927i | −0.677797 | + | 0.181615i | ||||
\(808\) | −4.35232 | + | 16.2431i | −0.153114 | + | 0.571430i | ||||
\(809\) | −23.6794 | + | 13.6713i | −0.832525 | + | 0.480658i | −0.854716 | − | 0.519095i | \(-0.826269\pi\) |
0.0221916 | + | 0.999754i | \(0.492936\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 23.3175i | − | 0.818788i | −0.912358 | − | 0.409394i | \(-0.865740\pi\) | ||
0.912358 | − | 0.409394i | \(-0.134260\pi\) | |||||||
\(812\) | −1.38398 | − | 10.7281i | −0.0485680 | − | 0.376484i | ||||
\(813\) | −19.9818 | + | 19.9818i | −0.700793 | + | 0.700793i | ||||
\(814\) | −19.2157 | − | 11.0942i | −0.673511 | − | 0.388852i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.0466086 | + | 0.0807284i | 0.00163163 | + | 0.00282606i | ||||
\(817\) | 2.54017 | + | 9.48005i | 0.0888693 | + | 0.331665i | ||||
\(818\) | −8.83640 | − | 8.83640i | −0.308958 | − | 0.308958i | ||||
\(819\) | −1.64803 | + | 12.2710i | −0.0575868 | + | 0.428784i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.20706 | − | 5.55480i | 0.111927 | − | 0.193864i | −0.804620 | − | 0.593790i | \(-0.797631\pi\) |
0.916547 | + | 0.399926i | \(0.130964\pi\) | |||||||
\(822\) | 15.8040 | + | 4.23466i | 0.551226 | + | 0.147701i | ||||
\(823\) | −6.13547 | − | 1.64399i | −0.213869 | − | 0.0573061i | 0.150294 | − | 0.988641i | \(-0.451978\pi\) |
−0.364163 | + | 0.931335i | \(0.618645\pi\) | |||||||
\(824\) | 11.6641 | − | 20.2027i | 0.406337 | − | 0.703796i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.693958 | − | 1.68778i | −0.0241459 | − | 0.0587254i | ||||
\(827\) | 31.0388 | + | 31.0388i | 1.07932 | + | 1.07932i | 0.996570 | + | 0.0827533i | \(0.0263714\pi\) |
0.0827533 | + | 0.996570i | \(0.473629\pi\) | |||||||
\(828\) | 0.241032 | + | 0.899544i | 0.00837644 | + | 0.0312613i | ||||
\(829\) | 25.4622 | + | 44.1019i | 0.884340 | + | 1.53172i | 0.846468 | + | 0.532439i | \(0.178724\pi\) |
0.0378716 | + | 0.999283i | \(0.487942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.8649 | − | 14.9331i | −0.897242 | − | 0.518023i | ||||
\(832\) | −19.2603 | + | 19.2603i | −0.667732 | + | 0.667732i | ||||
\(833\) | −0.0696702 | − | 0.122137i | −0.00241393 | − | 0.00423179i | ||||
\(834\) | − | 2.73804i | − | 0.0948107i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.46549 | − | 2.57815i | 0.154442 | − | 0.0891672i | ||||
\(837\) | 1.70131 | − | 6.34936i | 0.0588057 | − | 0.219466i | ||||
\(838\) | −1.95819 | + | 0.524695i | −0.0676444 | + | 0.0181253i | ||||
\(839\) | 46.0999 | 1.59155 | 0.795773 | − | 0.605596i | \(-0.207065\pi\) | ||||
0.795773 | + | 0.605596i | \(0.207065\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −75.2050 | −2.59328 | ||||||||
\(842\) | −4.31138 | + | 1.15523i | −0.148580 | + | 0.0398119i | ||||
\(843\) | 4.64818 | − | 17.3472i | 0.160092 | − | 0.597471i | ||||
\(844\) | −5.27423 | + | 3.04508i | −0.181547 | + | 0.104816i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 1.81497i | − | 0.0624001i | ||||||
\(847\) | −33.5000 | + | 25.5672i | −1.15107 | + | 0.878498i | ||||
\(848\) | −15.6590 | + | 15.6590i | −0.537731 | + | 0.537731i | ||||
\(849\) | 19.7406 | + | 11.3972i | 0.677496 | + | 0.391152i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.20853 | + | 5.55733i | 0.109987 | + | 0.190503i | ||||
\(852\) | −0.222600 | − | 0.830755i | −0.00762615 | − | 0.0284612i | ||||
\(853\) | −6.59157 | − | 6.59157i | −0.225691 | − | 0.225691i | 0.585199 | − | 0.810890i | \(-0.301017\pi\) |
−0.810890 | + | 0.585199i | \(0.801017\pi\) | |||||||
\(854\) | −4.44639 | − | 3.43027i | −0.152152 | − | 0.117381i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.4144 | + | 26.6985i | −0.526854 | + | 0.912538i | ||||
\(857\) | 10.5425 | + | 2.82487i | 0.360126 | + | 0.0964956i | 0.434345 | − | 0.900746i | \(-0.356980\pi\) |
−0.0742191 | + | 0.997242i | \(0.523646\pi\) | |||||||
\(858\) | 36.3423 | + | 9.73788i | 1.24070 | + | 0.332446i | ||||
\(859\) | −6.71182 | + | 11.6252i | −0.229004 | + | 0.396647i | −0.957513 | − | 0.288389i | \(-0.906880\pi\) |
0.728509 | + | 0.685036i | \(0.240214\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.72798 | + | 5.96192i | 0.263369 | + | 0.203182i | ||||
\(862\) | 22.8233 | + | 22.8233i | 0.777365 | + | 0.777365i | ||||
\(863\) | 14.0677 | + | 52.5015i | 0.478871 | + | 1.78717i | 0.606200 | + | 0.795312i | \(0.292693\pi\) |
−0.127329 | + | 0.991861i | \(0.540640\pi\) | |||||||
\(864\) | −1.11681 | − | 1.93436i | −0.0379945 | − | 0.0658084i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −10.8564 | − | 6.26794i | −0.368915 | − | 0.212993i | ||||
\(867\) | 12.0205 | − | 12.0205i | 0.408239 | − | 0.408239i | ||||
\(868\) | 5.53709 | − | 4.22590i | 0.187941 | − | 0.143436i | ||||
\(869\) | − | 20.7973i | − | 0.705501i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.9489 | + | 13.8269i | −0.811478 | + | 0.468507i | ||||
\(872\) | −5.59866 | + | 20.8945i | −0.189595 | + | 0.707577i | ||||
\(873\) | −14.4711 | + | 3.87751i | −0.489772 | + | 0.131234i | ||||
\(874\) | −8.93792 | −0.302330 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.96728 | −0.100255 | ||||||||
\(877\) | 23.7858 | − | 6.37339i | 0.803191 | − | 0.215214i | 0.166206 | − | 0.986091i | \(-0.446848\pi\) |
0.636984 | + | 0.770877i | \(0.280182\pi\) | |||||||
\(878\) | 3.46438 | − | 12.9292i | 0.116917 | − | 0.436341i | ||||
\(879\) | −21.2212 | + | 12.2521i | −0.715775 | + | 0.413253i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.1540i | 0.544243i | 0.962263 | + | 0.272121i | \(0.0877253\pi\) | ||||
−0.962263 | + | 0.272121i | \(0.912275\pi\) | |||||||
\(882\) | 5.37377 | + | 9.42060i | 0.180944 | + | 0.317208i | ||||
\(883\) | 34.4853 | − | 34.4853i | 1.16052 | − | 1.16052i | 0.176161 | − | 0.984361i | \(-0.443632\pi\) |
0.984361 | − | 0.176161i | \(-0.0563679\pi\) | |||||||
\(884\) | 0.0326046 | + | 0.0188243i | 0.00109661 | + | 0.000633130i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.1119 | + | 41.7630i | 0.810055 | + | 1.40306i | ||||
\(887\) | −4.08925 | − | 15.2613i | −0.137304 | − | 0.512424i | −0.999978 | − | 0.00666382i | \(-0.997879\pi\) |
0.862674 | − | 0.505760i | \(-0.168788\pi\) | |||||||
\(888\) | −4.83604 | − | 4.83604i | −0.162287 | − | 0.162287i | ||||
\(889\) | −3.74700 | − | 9.11311i | −0.125670 | − | 0.305644i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.59461 | − | 4.49400i | 0.0869229 | − | 0.150555i | ||||
\(892\) | 1.96784 | + | 0.527280i | 0.0658880 | + | 0.0176546i | ||||
\(893\) | 2.80726 | + | 0.752204i | 0.0939415 | + | 0.0251715i | ||||
\(894\) | −5.71172 | + | 9.89298i | −0.191028 | + | 0.330871i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.74913 | + | 35.3614i | −0.158657 | + | 1.18134i | ||||
\(897\) | −7.69418 | − | 7.69418i | −0.256901 | − | 0.256901i | ||||
\(898\) | −16.1683 | − | 60.3408i | −0.539542 | − | 2.01360i | ||||
\(899\) | −33.5506 | − | 58.1113i | −1.11898 | − | 1.93812i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.0830144 | − | 0.0479284i | −0.00276561 | − | 0.00159673i | ||||
\(902\) | 20.9730 | − | 20.9730i | 0.698324 | − | 0.698324i | ||||
\(903\) | 1.33911 | + | 10.3803i | 0.0445627 | + | 0.345435i | ||||
\(904\) | − | 9.81746i | − | 0.326524i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −21.9468 | + | 12.6710i | −0.729135 | + | 0.420966i | ||||
\(907\) | 9.51643 | − | 35.5158i | 0.315988 | − | 1.17928i | −0.607078 | − | 0.794642i | \(-0.707659\pi\) |
0.923066 | − | 0.384641i | \(-0.125675\pi\) | |||||||
\(908\) | 2.91892 | − | 0.782122i | 0.0968677 | − | 0.0259556i | ||||
\(909\) | 6.78565 | 0.225066 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.1482 | 0.998856 | 0.499428 | − | 0.866355i | \(-0.333544\pi\) | ||||
0.499428 | + | 0.866355i | \(0.333544\pi\) | |||||||
\(912\) | 11.1209 | − | 2.97984i | 0.368250 | − | 0.0986722i | ||||
\(913\) | −7.17067 | + | 26.7613i | −0.237314 | + | 0.885670i | ||||
\(914\) | 17.9637 | − | 10.3713i | 0.594186 | − | 0.343054i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 10.3034i | − | 0.340434i | ||||||
\(917\) | 4.82950 | + | 6.32798i | 0.159484 | + | 0.208968i | ||||
\(918\) | 0.0220068 | − | 0.0220068i | 0.000726333 | − | 0.000726333i | ||||
\(919\) | −1.03427 | − | 0.597138i | −0.0341175 | − | 0.0196978i | 0.482844 | − | 0.875706i | \(-0.339604\pi\) |
−0.516962 | + | 0.856009i | \(0.672937\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.00440 | − | 8.66788i | −0.164901 | − | 0.285616i | ||||
\(922\) | −0.831113 | − | 3.10176i | −0.0273713 | − | 0.102151i | ||||
\(923\) | 7.10580 | + | 7.10580i | 0.233890 | + | 0.233890i | ||||
\(924\) | 5.08568 | − | 2.09106i | 0.167306 | − | 0.0687908i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 14.2142 | − | 24.6198i | 0.467109 | − | 0.809056i | ||||
\(927\) | −9.09265 | − | 2.43637i | −0.298642 | − | 0.0800208i | ||||
\(928\) | −22.0240 | − | 5.90131i | −0.722972 | − | 0.193720i | ||||
\(929\) | −6.23132 | + | 10.7930i | −0.204443 | + | 0.354105i | −0.949955 | − | 0.312387i | \(-0.898872\pi\) |
0.745512 | + | 0.666492i | \(0.232205\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.7982 | + | 4.40743i | −0.550538 | + | 0.144448i | ||||
\(932\) | 7.59599 | + | 7.59599i | 0.248815 | + | 0.248815i | ||||
\(933\) | 1.29121 | + | 4.81886i | 0.0422723 | + | 0.157762i | ||||
\(934\) | 19.9480 | + | 34.5509i | 0.652718 | + | 1.13054i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 10.0433 | + | 5.79851i | 0.328276 | + | 0.189530i | ||||
\(937\) | 34.0770 | − | 34.0770i | 1.11325 | − | 1.11325i | 0.120539 | − | 0.992709i | \(-0.461538\pi\) |
0.992709 | − | 0.120539i | \(-0.0384623\pi\) | |||||||
\(938\) | −9.32830 | + | 22.3557i | −0.304580 | + | 0.729939i | ||||
\(939\) | 5.89955i | 0.192525i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.3625 | − | 23.3033i | 1.31578 | − | 0.759666i | 0.332734 | − | 0.943021i | \(-0.392029\pi\) |
0.983047 | + | 0.183354i | \(0.0586956\pi\) | |||||||
\(942\) | −9.19457 | + | 34.3146i | −0.299575 | + | 1.11803i | ||||
\(943\) | −8.28567 | + | 2.22014i | −0.269819 | + | 0.0722977i | ||||
\(944\) | −2.06590 | −0.0672392 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 31.8054 | 1.03408 | ||||||||
\(947\) | −11.3990 | + | 3.05436i | −0.370418 | + | 0.0992533i | −0.439226 | − | 0.898377i | \(-0.644747\pi\) |
0.0688075 | + | 0.997630i | \(0.478081\pi\) | |||||||
\(948\) | −0.415447 | + | 1.55047i | −0.0134931 | + | 0.0503569i | ||||
\(949\) | 30.0254 | − | 17.3352i | 0.974665 | − | 0.562723i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 0.882064i | − | 0.0286029i | ||||||
\(952\) | −0.130623 | + | 0.0168509i | −0.00423350 | + | 0.000546140i | ||||
\(953\) | 28.2281 | − | 28.2281i | 0.914399 | − | 0.914399i | −0.0822160 | − | 0.996615i | \(-0.526200\pi\) |
0.996615 | + | 0.0822160i | \(0.0261997\pi\) | |||||||
\(954\) | 6.40302 | + | 3.69679i | 0.207305 | + | 0.119688i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.82110 | − | 6.61834i | −0.123583 | − | 0.214052i | ||||
\(957\) | −13.7102 | − | 51.1671i | −0.443187 | − | 1.65400i | ||||
\(958\) | −27.3890 | − | 27.3890i | −0.884898 | − | 0.884898i | ||||
\(959\) | −17.0662 | + | 22.1216i | −0.551095 | + | 0.714342i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.10438 | − | 10.5731i | 0.196916 | − | 0.341068i | ||||
\(962\) | −19.3277 | − | 5.17885i | −0.623151 | − | 0.166973i | ||||
\(963\) | 12.0162 | + | 3.21974i | 0.387217 | + | 0.103755i | ||||
\(964\) | 2.45304 | − | 4.24879i | 0.0790072 | − | 0.136844i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −9.44676 | − | 1.26872i | −0.303944 | − | 0.0408205i | ||||
\(967\) | 22.3045 | + | 22.3045i | 0.717263 | + | 0.717263i | 0.968044 | − | 0.250781i | \(-0.0806874\pi\) |
−0.250781 | + | 0.968044i | \(0.580687\pi\) | |||||||
\(968\) | 10.2163 | + | 38.1277i | 0.328364 | + | 1.22547i | ||||
\(969\) | 0.0249179 | + | 0.0431590i | 0.000800478 | + | 0.00138647i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.5151 | − | 14.7312i | −0.818819 | − | 0.472745i | 0.0311899 | − | 0.999513i | \(-0.490070\pi\) |
−0.850009 | + | 0.526768i | \(0.823404\pi\) | |||||||
\(972\) | −0.283204 | + | 0.283204i | −0.00908378 | + | 0.00908378i | ||||
\(973\) | 4.31502 | + | 1.80052i | 0.138333 | + | 0.0577220i | ||||
\(974\) | − | 42.2648i | − | 1.35425i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.50575 | + | 3.17875i | −0.176235 | + | 0.101749i | ||||
\(977\) | 1.08082 | − | 4.03368i | 0.0345785 | − | 0.129049i | −0.946479 | − | 0.322765i | \(-0.895388\pi\) |
0.981058 | + | 0.193717i | \(0.0620542\pi\) | |||||||
\(978\) | −22.8445 | + | 6.12117i | −0.730487 | + | 0.195733i | ||||
\(979\) | 19.9206 | 0.636666 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.72881 | 0.278689 | ||||||||
\(982\) | 35.1394 | − | 9.41557i | 1.12134 | − | 0.300463i | ||||
\(983\) | −0.763296 | + | 2.84866i | −0.0243454 | + | 0.0908581i | −0.977030 | − | 0.213104i | \(-0.931643\pi\) |
0.952684 | + | 0.303962i | \(0.0983095\pi\) | |||||||
\(984\) | 7.91743 | − | 4.57113i | 0.252398 | − | 0.145722i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 0.317700i | − | 0.0101176i | ||||||
\(987\) | 2.86031 | + | 1.19351i | 0.0910446 | + | 0.0379900i | ||||
\(988\) | 3.28802 | − | 3.28802i | 0.104606 | − | 0.104606i | ||||
\(989\) | −7.96600 | − | 4.59917i | −0.253304 | − | 0.146245i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.7168 | + | 23.7582i | 0.435729 | + | 0.754706i | 0.997355 | − | 0.0726861i | \(-0.0231571\pi\) |
−0.561625 | + | 0.827392i | \(0.689824\pi\) | |||||||
\(992\) | −3.80005 | − | 14.1820i | −0.120652 | − | 0.450279i | ||||
\(993\) | 16.9411 | + | 16.9411i | 0.537610 | + | 0.537610i | ||||
\(994\) | 8.72435 | + | 1.17170i | 0.276720 | + | 0.0371641i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.06917 | − | 1.85185i | 0.0338778 | − | 0.0586781i | ||||
\(997\) | −20.6315 | − | 5.52820i | −0.653407 | − | 0.175080i | −0.0831381 | − | 0.996538i | \(-0.526494\pi\) |
−0.570269 | + | 0.821458i | \(0.693161\pi\) | |||||||
\(998\) | −42.8897 | − | 11.4922i | −1.35765 | − | 0.363781i | ||||
\(999\) | −1.37988 | + | 2.39003i | −0.0436575 | + | 0.0756170i |
(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 | 525.2.bc.e.82.3 | 32 | ||
5.2 | odd | 4 | 105.2.u.a.103.3 | yes | 32 | ||
5.3 | odd | 4 | inner | 525.2.bc.e.418.6 | 32 | ||
5.4 | even | 2 | 105.2.u.a.82.6 | yes | 32 | ||
7.3 | odd | 6 | inner | 525.2.bc.e.157.6 | 32 | ||
15.2 | even | 4 | 315.2.bz.d.208.6 | 32 | |||
15.14 | odd | 2 | 315.2.bz.d.82.3 | 32 | |||
35.2 | odd | 12 | 735.2.m.c.538.5 | 32 | |||
35.3 | even | 12 | inner | 525.2.bc.e.493.3 | 32 | ||
35.4 | even | 6 | 735.2.v.b.472.3 | 32 | |||
35.9 | even | 6 | 735.2.m.c.97.6 | 32 | |||
35.12 | even | 12 | 735.2.m.c.538.6 | 32 | |||
35.17 | even | 12 | 105.2.u.a.73.6 | yes | 32 | ||
35.19 | odd | 6 | 735.2.m.c.97.5 | 32 | |||
35.24 | odd | 6 | 105.2.u.a.52.3 | ✓ | 32 | ||
35.27 | even | 4 | 735.2.v.b.313.3 | 32 | |||
35.32 | odd | 12 | 735.2.v.b.178.6 | 32 | |||
35.34 | odd | 2 | 735.2.v.b.607.6 | 32 | |||
105.17 | odd | 12 | 315.2.bz.d.73.3 | 32 | |||
105.59 | even | 6 | 315.2.bz.d.262.6 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.u.a.52.3 | ✓ | 32 | 35.24 | odd | 6 | ||
105.2.u.a.73.6 | yes | 32 | 35.17 | even | 12 | ||
105.2.u.a.82.6 | yes | 32 | 5.4 | even | 2 | ||
105.2.u.a.103.3 | yes | 32 | 5.2 | odd | 4 | ||
315.2.bz.d.73.3 | 32 | 105.17 | odd | 12 | |||
315.2.bz.d.82.3 | 32 | 15.14 | odd | 2 | |||
315.2.bz.d.208.6 | 32 | 15.2 | even | 4 | |||
315.2.bz.d.262.6 | 32 | 105.59 | even | 6 | |||
525.2.bc.e.82.3 | 32 | 1.1 | even | 1 | trivial | ||
525.2.bc.e.157.6 | 32 | 7.3 | odd | 6 | inner | ||
525.2.bc.e.418.6 | 32 | 5.3 | odd | 4 | inner | ||
525.2.bc.e.493.3 | 32 | 35.3 | even | 12 | inner | ||
735.2.m.c.97.5 | 32 | 35.19 | odd | 6 | |||
735.2.m.c.97.6 | 32 | 35.9 | even | 6 | |||
735.2.m.c.538.5 | 32 | 35.2 | odd | 12 | |||
735.2.m.c.538.6 | 32 | 35.12 | even | 12 | |||
735.2.v.b.178.6 | 32 | 35.32 | odd | 12 | |||
735.2.v.b.313.3 | 32 | 35.27 | even | 4 | |||
735.2.v.b.472.3 | 32 | 35.4 | even | 6 | |||
735.2.v.b.607.6 | 32 | 35.34 | odd | 2 |