Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [688,2,Mod(17,688)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(688, base_ring=CyclotomicField(42))
chi = DirichletCharacter(H, H._module([0, 0, 38]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("688.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 688 = 2^{4} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 688.bg (of order \(21\), degree \(12\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.49370765906\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{21})\) |
Twist minimal: | no (minimal twist has level 43) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{21}]$ |
Embedding invariants
Embedding label | 401.1 | ||
Character | \(\chi\) | \(=\) | 688.401 |
Dual form | 688.2.bg.c.513.1 |
$q$-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 \(\left(\mathbb{Z}/688\mathbb{Z}\right)^\times\).
\(n\) | \(431\) | \(433\) | \(517\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{10}{21}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.109070 | − | 1.45544i | −0.0629716 | − | 0.840298i | −0.935859 | − | 0.352375i | \(-0.885374\pi\) |
0.872887 | − | 0.487922i | \(-0.162245\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.29085 | − | 0.398175i | 0.577286 | − | 0.178069i | 0.00765630 | − | 0.999971i | \(-0.497563\pi\) |
0.569629 | + | 0.821902i | \(0.307087\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.108163 | − | 0.187343i | 0.0408816 | − | 0.0708091i | −0.844861 | − | 0.534987i | \(-0.820317\pi\) |
0.885742 | + | 0.464177i | \(0.153650\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.860089 | − | 0.129637i | 0.286696 | − | 0.0432125i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.76031 | + | 4.71528i | 1.13378 | + | 1.42171i | 0.892380 | + | 0.451285i | \(0.149034\pi\) |
0.241397 | + | 0.970426i | \(0.422394\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.10767 | + | 1.95563i | 0.584562 | + | 0.542395i | 0.916050 | − | 0.401065i | \(-0.131360\pi\) |
−0.331487 | + | 0.943460i | \(0.607550\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.720312 | − | 1.83532i | −0.185984 | − | 0.473879i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.270054 | + | 0.0833006i | 0.0654977 | + | 0.0202034i | 0.327331 | − | 0.944910i | \(-0.393851\pi\) |
−0.261833 | + | 0.965113i | \(0.584327\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.12457 | − | 0.169502i | −0.257994 | − | 0.0388863i | 0.0187716 | − | 0.999824i | \(-0.494024\pi\) |
−0.276766 | + | 0.960937i | \(0.589263\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.284464 | − | 0.136990i | −0.0620751 | − | 0.0298938i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.44040 | − | 3.67008i | 0.300344 | − | 0.765265i | −0.698426 | − | 0.715682i | \(-0.746116\pi\) |
0.998770 | − | 0.0495821i | \(-0.0157890\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.62344 | + | 1.78863i | −0.524688 | + | 0.357727i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.25681 | − | 5.50644i | −0.241873 | − | 1.05972i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.515946 | − | 6.88482i | 0.0958088 | − | 1.27848i | −0.717463 | − | 0.696596i | \(-0.754697\pi\) |
0.813272 | − | 0.581883i | \(-0.197684\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.17225 | + | 5.57174i | 1.46778 | + | 1.00071i | 0.992679 | + | 0.120783i | \(0.0385405\pi\) |
0.475100 | + | 0.879932i | \(0.342412\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.45267 | − | 5.98720i | 1.12326 | − | 1.04224i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0650265 | − | 0.284900i | 0.0109915 | − | 0.0481568i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.77129 | − | 6.53207i | −0.619996 | − | 1.07387i | −0.989486 | − | 0.144630i | \(-0.953801\pi\) |
0.369489 | − | 0.929235i | \(-0.379533\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.61642 | − | 3.28088i | 0.418962 | − | 0.525362i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.62195 | + | 2.22581i | −0.721827 | + | 0.347613i | −0.758464 | − | 0.651715i | \(-0.774050\pi\) |
0.0366371 | + | 0.999329i | \(0.488335\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.90092 | − | 2.85993i | −0.899881 | − | 0.436135i | ||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.05863 | − | 0.509808i | 0.157811 | − | 0.0759977i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.288239 | + | 0.361440i | −0.0420439 | + | 0.0527214i | −0.802409 | − | 0.596775i | \(-0.796449\pi\) |
0.760365 | + | 0.649496i | \(0.225020\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.47660 | + | 6.02165i | 0.496657 | + | 0.860236i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.0917841 | − | 0.402132i | 0.0128523 | − | 0.0563098i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.12346 | + | 5.68174i | −0.841123 | + | 0.780448i | −0.977661 | − | 0.210187i | \(-0.932593\pi\) |
0.136539 | + | 0.990635i | \(0.456402\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.73151 | + | 4.58946i | 0.907676 | + | 0.618843i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.124042 | + | 1.65523i | −0.0164298 | + | 0.219240i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.85926 | − | 8.14595i | −0.242055 | − | 1.06051i | −0.939143 | − | 0.343527i | \(-0.888378\pi\) |
0.697088 | − | 0.716986i | \(-0.254479\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.0987 | − | 7.56700i | 1.42105 | − | 0.968855i | 0.423019 | − | 0.906121i | \(-0.360971\pi\) |
0.998030 | − | 0.0627337i | \(-0.0199819\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0687427 | − | 0.175154i | 0.00866077 | − | 0.0220673i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.49937 | + | 1.68521i | 0.434043 | + | 0.209024i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.22328 | − | 0.938008i | −0.760294 | − | 0.114596i | −0.242559 | − | 0.970137i | \(-0.577987\pi\) |
−0.517736 | + | 0.855541i | \(0.673225\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.49868 | − | 1.69612i | −0.661963 | − | 0.204189i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.540324 | + | 1.37672i | 0.0641247 | + | 0.163387i | 0.959344 | − | 0.282238i | \(-0.0910768\pi\) |
−0.895220 | + | 0.445625i | \(0.852982\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.601198 | + | 0.557830i | 0.0703649 | + | 0.0652891i | 0.714571 | − | 0.699563i | \(-0.246622\pi\) |
−0.644206 | + | 0.764852i | \(0.722812\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.88938 | + | 3.62317i | 0.333637 | + | 0.418368i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.29010 | − | 0.194451i | 0.147021 | − | 0.0221598i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.07798 | − | 5.33121i | 0.346299 | − | 0.599808i | −0.639290 | − | 0.768966i | \(-0.720772\pi\) |
0.985589 | + | 0.169158i | \(0.0541048\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.38373 | + | 1.66066i | −0.598192 | + | 0.184518i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.538458 | + | 7.18523i | 0.0591035 | + | 0.788681i | 0.945473 | + | 0.325702i | \(0.105601\pi\) |
−0.886369 | + | 0.462979i | \(0.846780\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.381767 | 0.0414085 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.0767 | −1.08034 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.331353 | + | 4.42159i | 0.0351233 | + | 0.468688i | 0.986839 | + | 0.161707i | \(0.0516999\pi\) |
−0.951716 | + | 0.306981i | \(0.900681\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.594345 | − | 0.183331i | 0.0623043 | − | 0.0192183i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.21798 | − | 12.5019i | 0.748470 | − | 1.29639i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.51914 | + | 0.228974i | −0.155861 | + | 0.0234922i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.78649 | − | 3.49415i | −0.282925 | − | 0.354777i | 0.619979 | − | 0.784618i | \(-0.287141\pi\) |
−0.902905 | + | 0.429841i | \(0.858570\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.84548 | + | 3.56808i | 0.386485 | + | 0.358606i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.09407 | − | 2.78765i | −0.108864 | − | 0.277382i | 0.866052 | − | 0.499954i | \(-0.166650\pi\) |
−0.974916 | + | 0.222572i | \(0.928555\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.07350 | − | 2.49034i | −0.795505 | − | 0.245381i | −0.129746 | − | 0.991547i | \(-0.541416\pi\) |
−0.665760 | + | 0.746166i | \(0.731892\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.421746 | − | 0.0635680i | −0.0411582 | − | 0.00620360i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.64595 | + | 2.71894i | 0.545814 | + | 0.262850i | 0.686407 | − | 0.727217i | \(-0.259187\pi\) |
−0.140593 | + | 0.990067i | \(0.544901\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.0776988 | − | 0.197973i | 0.00744219 | − | 0.0189624i | −0.927104 | − | 0.374803i | \(-0.877710\pi\) |
0.934547 | + | 0.355841i | \(0.115805\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.09569 | + | 6.20133i | −0.863324 | + | 0.588605i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.46387 | + | 10.7949i | 0.231781 | + | 1.01550i | 0.948161 | + | 0.317789i | \(0.102940\pi\) |
−0.716380 | + | 0.697710i | \(0.754202\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.398009 | − | 5.31105i | 0.0371145 | − | 0.495258i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.06631 | + | 1.40878i | 0.191030 | + | 0.130242i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0448155 | − | 0.0415827i | 0.00410823 | − | 0.00381188i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.64621 | + | 24.7377i | −0.513292 | + | 2.24888i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.74365 | + | 6.48419i | 0.337553 | + | 0.584659i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.88554 | + | 8.63419i | −0.615861 | + | 0.772265i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.04038 | − | 3.39047i | 0.624733 | − | 0.300855i | −0.0946062 | − | 0.995515i | \(-0.530159\pi\) |
0.719339 | + | 0.694659i | \(0.244445\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.51883 | + | 8.90035i | −0.309816 | + | 0.783632i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.1797 | + | 7.79174i | −1.41363 | + | 0.680768i | −0.975876 | − | 0.218327i | \(-0.929940\pi\) |
−0.437753 | + | 0.899095i | \(0.644226\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.153391 | + | 0.192347i | −0.0133007 | + | 0.0166786i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.81488 | − | 6.60757i | −0.328333 | − | 0.568689i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.23563 | + | 9.79494i | −0.191003 | + | 0.836839i | 0.785072 | + | 0.619404i | \(0.212626\pi\) |
−0.976075 | + | 0.217434i | \(0.930231\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.10473 | + | 8.44795i | −0.772253 | + | 0.716546i | −0.964292 | − | 0.264841i | \(-0.914680\pi\) |
0.192039 | + | 0.981387i | \(0.438490\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.557491 | + | 0.380091i | 0.0469492 | + | 0.0320095i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.29586 | + | 17.2920i | −0.108365 | + | 1.44603i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.07535 | − | 9.09271i | −0.172349 | − | 0.755109i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.38495 | − | 5.71676i | 0.691579 | − | 0.471510i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.35074 | + | 3.44162i | −0.110657 | + | 0.281948i | −0.975465 | − | 0.220153i | \(-0.929344\pi\) |
0.864809 | + | 0.502101i | \(0.167440\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.3773 | − | 4.99744i | −0.844492 | − | 0.406686i | −0.0389621 | − | 0.999241i | \(-0.512405\pi\) |
−0.805530 | + | 0.592555i | \(0.798119\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.243069 | + | 0.0366368i | 0.0196510 | + | 0.00296191i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.7677 | + | 3.93831i | 1.02552 | + | 0.316332i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.52520 | − | 19.1739i | −0.600577 | − | 1.53024i | −0.830490 | − | 0.557033i | \(-0.811940\pi\) |
0.229914 | − | 0.973211i | \(-0.426156\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.93731 | + | 8.29262i | 0.708775 | + | 0.657647i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.531767 | − | 0.666815i | −0.0419091 | − | 0.0525524i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.83812 | − | 1.03068i | 0.535603 | − | 0.0807292i | 0.124329 | − | 0.992241i | \(-0.460322\pi\) |
0.411274 | + | 0.911512i | \(0.365084\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.94547 | − | 10.2979i | 0.462855 | − | 0.801688i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.39723 | + | 1.04791i | −0.262886 | + | 0.0810895i | −0.423396 | − | 0.905945i | \(-0.639162\pi\) |
0.160510 | + | 0.987034i | \(0.448686\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.353715 | − | 4.72000i | −0.0272089 | − | 0.363077i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.989203 | −0.0756463 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.0563 | −1.82897 | −0.914483 | − | 0.404623i | \(-0.867403\pi\) | ||||
−0.914483 | + | 0.404623i | \(0.867403\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.0513297 | + | 0.684947i | 0.00388016 | + | 0.0517771i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.6531 | + | 3.59452i | −0.875904 | + | 0.270181i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.60094 | + | 4.50496i | −0.194403 | + | 0.336717i | −0.946705 | − | 0.322103i | \(-0.895610\pi\) |
0.752301 | + | 0.658819i | \(0.228944\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.74306 | − | 0.413450i | 0.203890 | − | 0.0307315i | −0.0463029 | − | 0.998927i | \(-0.514744\pi\) |
0.250193 | + | 0.968196i | \(0.419506\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.2238 | − | 15.3282i | −0.903612 | − | 1.13309i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.46908 | − | 6.93029i | −0.549137 | − | 0.509525i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.622701 | + | 1.58662i | 0.0455364 | + | 0.116025i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.16753 | − | 0.360137i | −0.0849256 | − | 0.0261961i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.41700 | − | 0.515030i | −0.247245 | − | 0.0372662i | 0.0242502 | − | 0.999706i | \(-0.492280\pi\) |
−0.271496 | + | 0.962440i | \(0.587518\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.4497 | + | 7.92174i | 1.18407 | + | 0.570219i | 0.919095 | − | 0.394035i | \(-0.128921\pi\) |
0.264977 | + | 0.964255i | \(0.414636\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.07104 | − | 5.27692i | 0.148310 | − | 0.377888i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.41116 | − | 5.73463i | 0.599270 | − | 0.408575i | −0.225337 | − | 0.974281i | \(-0.572348\pi\) |
0.824607 | + | 0.565705i | \(0.191396\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.04642 | + | 8.96595i | 0.145067 | + | 0.635579i | 0.994214 | + | 0.107422i | \(0.0342596\pi\) |
−0.849147 | + | 0.528157i | \(0.822883\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.686440 | + | 9.15990i | −0.0484177 | + | 0.646090i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.23402 | − | 0.841340i | −0.0866111 | − | 0.0590505i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.07998 | + | 4.71353i | −0.354801 | + | 0.329207i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.763092 | − | 3.34332i | 0.0530385 | − | 0.232377i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.42949 | − | 5.94004i | −0.237222 | − | 0.410881i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.8825 | − | 14.9002i | 0.818025 | − | 1.02577i | −0.181080 | − | 0.983468i | \(-0.557959\pi\) |
0.999105 | − | 0.0423025i | \(-0.0134693\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.94480 | − | 0.936567i | 0.133256 | − | 0.0641725i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.75595 | − | 1.34214i | −0.597151 | − | 0.0915334i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.92776 | − | 0.928360i | 0.130865 | − | 0.0630212i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.746315 | − | 0.935849i | 0.0504313 | − | 0.0632388i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.406279 | + | 0.703696i | 0.0273293 | + | 0.0473357i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.62391 | + | 7.11481i | −0.108745 | + | 0.476443i | 0.891003 | + | 0.453997i | \(0.150002\pi\) |
−0.999748 | + | 0.0224455i | \(0.992855\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.02452 | + | 1.87848i | −0.134968 | + | 0.125232i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.9206 | − | 8.80914i | −0.857573 | − | 0.584683i | 0.0527382 | − | 0.998608i | \(-0.483205\pi\) |
−0.910311 | + | 0.413925i | \(0.864158\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.0803517 | + | 1.07222i | −0.00530979 | + | 0.0708542i | −0.999229 | − | 0.0392558i | \(-0.987501\pi\) |
0.993919 | + | 0.110110i | \(0.0351203\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.423723 | − | 1.85645i | −0.0278790 | − | 0.122146i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.10140 | + | 0.750923i | −0.0721552 | + | 0.0491946i | −0.598860 | − | 0.800853i | \(-0.704380\pi\) |
0.526705 | + | 0.850048i | \(0.323427\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.228157 | + | 0.581334i | −0.0148833 | + | 0.0379220i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.09496 | − | 3.89833i | −0.525824 | − | 0.253224i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.7110 | + | 2.21733i | 0.951579 | + | 0.143427i | 0.606444 | − | 0.795126i | \(-0.292595\pi\) |
0.345134 | + | 0.938553i | \(0.387833\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.8421 | + | 7.04584i | 1.47139 | + | 0.453862i | 0.923796 | − | 0.382885i | \(-0.125069\pi\) |
0.547590 | + | 0.836747i | \(0.315545\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.18621 | − | 8.11832i | −0.204395 | − | 0.520790i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.88544 | + | 6.38876i | 0.439895 | + | 0.408163i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.03874 | − | 2.55650i | −0.129722 | − | 0.162666i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.3989 | − | 1.56739i | 0.659005 | − | 0.0993290i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.2680 | + | 17.7846i | −0.648108 | + | 1.12256i | 0.335466 | + | 0.942052i | \(0.391106\pi\) |
−0.983574 | + | 0.180504i | \(0.942227\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.7218 | − | 7.00875i | 1.42851 | − | 0.440637i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.0416394 | − | 0.555639i | −0.00260756 | − | 0.0347954i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.8388 | −1.42464 | −0.712322 | − | 0.701853i | \(-0.752356\pi\) | ||||
−0.712322 | + | 0.701853i | \(0.752356\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.63165 | −0.101386 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.448772 | − | 5.98844i | −0.0277783 | − | 0.370675i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.88459 | + | 1.81516i | −0.362860 | + | 0.111927i | −0.470823 | − | 0.882227i | \(-0.656043\pi\) |
0.107964 | + | 0.994155i | \(0.465567\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.64215 | + | 9.77249i | −0.346594 | + | 0.600319i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.39922 | − | 0.964527i | 0.391626 | − | 0.0590281i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.36364 | + | 11.7416i | 0.570911 | + | 0.715900i | 0.980533 | − | 0.196355i | \(-0.0629106\pi\) |
−0.409621 | + | 0.912256i | \(0.634339\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.26842 | + | 2.10479i | 0.137797 | + | 0.127857i | 0.746060 | − | 0.665878i | \(-0.231943\pi\) |
−0.608263 | + | 0.793735i | \(0.708134\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.331652 | − | 0.845037i | −0.0200725 | − | 0.0511440i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.2989 | − | 5.64446i | −1.10346 | − | 0.340373i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.9446 | − | 2.25253i | −0.897932 | − | 0.135341i | −0.316172 | − | 0.948702i | \(-0.602398\pi\) |
−0.581760 | + | 0.813360i | \(0.697636\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.75116 | + | 3.73276i | 0.464050 | + | 0.223475i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.07782 | − | 10.3901i | 0.243262 | − | 0.619822i | −0.756139 | − | 0.654411i | \(-0.772917\pi\) |
0.999402 | + | 0.0345883i | \(0.0110120\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.2949 | − | 9.06431i | 0.790300 | − | 0.538818i | −0.0995704 | − | 0.995031i | \(-0.531747\pi\) |
0.889871 | + | 0.456213i | \(0.150794\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.498950 | + | 2.18604i | 0.0295553 | + | 0.129490i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.0829312 | + | 1.10664i | −0.00489527 | + | 0.0653229i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.9801 | − | 9.53145i | −0.822357 | − | 0.560674i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.78160 | + | 4.43667i | −0.280302 | + | 0.260082i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.26781 | − | 14.3172i | 0.190908 | − | 0.836421i | −0.785219 | − | 0.619218i | \(-0.787450\pi\) |
0.976127 | − | 0.217203i | \(-0.0696933\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.64354 | − | 9.77490i | −0.328580 | − | 0.569116i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 21.2384 | − | 26.6322i | 1.23238 | − | 1.54536i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.2132 | − | 4.91842i | 0.590645 | − | 0.284440i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.17405 | + | 0.796159i | −0.0676709 | + | 0.0458898i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.93792 | + | 1.89640i | −0.226228 | + | 0.108946i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.3138 | − | 14.1871i | 0.647828 | − | 0.812351i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.0141820 | + | 0.0245640i | 0.000809410 | + | 0.00140194i | 0.866430 | − | 0.499299i | \(-0.166409\pi\) |
−0.865620 | + | 0.500701i | \(0.833076\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.74397 | + | 12.0221i | −0.156099 | + | 0.683913i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.53405 | + | 6.99057i | −0.427217 | + | 0.396399i | −0.864263 | − | 0.503040i | \(-0.832215\pi\) |
0.437047 | + | 0.899439i | \(0.356024\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.8130 | + | 10.0994i | 0.837283 | + | 0.570850i | 0.904298 | − | 0.426902i | \(-0.140395\pi\) |
−0.0670152 | + | 0.997752i | \(0.521348\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0189949 | − | 0.253469i | 0.00107024 | − | 0.0142813i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.83536 | + | 21.1851i | 0.271581 | + | 1.18987i | 0.908147 | + | 0.418652i | \(0.137497\pi\) |
−0.636566 | + | 0.771222i | \(0.719646\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 34.4040 | − | 23.4563i | 1.92625 | − | 1.31330i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.34145 | − | 8.51388i | 0.186502 | − | 0.475199i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.289575 | − | 0.139452i | −0.0161124 | − | 0.00775931i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.02726 | − | 1.36064i | −0.500742 | − | 0.0754747i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.296612 | − | 0.0914928i | −0.0164027 | − | 0.00505956i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.0365366 | + | 0.0930938i | 0.00201433 | + | 0.00513243i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.69617 | + | 8.99673i | 0.532950 | + | 0.494505i | 0.900116 | − | 0.435650i | \(-0.143482\pi\) |
−0.367166 | + | 0.930155i | \(0.619672\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.09044 | − | 5.12926i | −0.224155 | − | 0.281081i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.40681 | + | 1.26712i | −0.459313 | + | 0.0692303i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.71536 | − | 8.16725i | 0.256862 | − | 0.444898i | −0.708537 | − | 0.705673i | \(-0.750645\pi\) |
0.965400 | + | 0.260775i | \(0.0839780\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.4426 | − | 4.76341i | 0.838726 | − | 0.258713i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.45786 | + | 59.4860i | 0.241406 | + | 3.22135i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.01843 | 0.162980 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.77332 | −0.418502 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.30647 | + | 17.4336i | 0.0701351 | + | 0.935887i | 0.915661 | + | 0.401952i | \(0.131668\pi\) |
−0.845526 | + | 0.533935i | \(0.820713\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.91802 | − | 2.75084i | 0.477370 | − | 0.147249i | −0.0467268 | − | 0.998908i | \(-0.514879\pi\) |
0.524097 | + | 0.851658i | \(0.324403\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.11964 | − | 14.0636i | 0.433394 | − | 0.750661i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.2719 | + | 1.54824i | −0.546718 | + | 0.0824045i | −0.416593 | − | 0.909093i | \(-0.636776\pi\) |
−0.130125 | + | 0.991498i | \(0.541538\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.24565 | + | 1.56200i | 0.0661124 | + | 0.0829024i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.0654091 | − | 0.0606908i | −0.00346182 | − | 0.00321210i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.94742 | − | 10.0579i | −0.208337 | − | 0.530834i | 0.788065 | − | 0.615593i | \(-0.211083\pi\) |
−0.996402 | + | 0.0847587i | \(0.972988\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.9200 | − | 5.21912i | −0.890524 | − | 0.274690i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 36.6200 | + | 5.51957i | 1.92205 | + | 0.289703i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.998170 | + | 0.480694i | 0.0522466 | + | 0.0251606i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.07784 | + | 18.0340i | −0.369460 | + | 0.941369i | 0.618377 | + | 0.785881i | \(0.287790\pi\) |
−0.987838 | + | 0.155488i | \(0.950305\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.68673 | + | 2.51357i | −0.191924 | + | 0.130851i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.402106 | + | 1.76174i | 0.0208763 | + | 0.0914651i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.56665 | − | 34.2496i | 0.132896 | − | 1.77338i | −0.389841 | − | 0.920882i | \(-0.627470\pi\) |
0.522737 | − | 0.852494i | \(-0.324911\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13.3175 | + | 9.07974i | 0.687715 | + | 0.468876i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.5516 | − | 13.5019i | 0.749447 | − | 0.695385i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.574248 | − | 2.51594i | 0.0294971 | − | 0.129235i | −0.958036 | − | 0.286649i | \(-0.907459\pi\) |
0.987533 | + | 0.157414i | \(0.0503157\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.70251 | − | 9.87704i | −0.292148 | − | 0.506016i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.92040 | + | 11.1858i | −0.455811 | + | 0.571569i | −0.955633 | − | 0.294559i | \(-0.904827\pi\) |
0.499822 | + | 0.866128i | \(0.333399\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.58790 | − | 0.764693i | 0.0809270 | − | 0.0389724i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.44606 | − | 1.69481i | −0.276839 | − | 0.0861521i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.2240 | − | 6.84991i | 0.721185 | − | 0.347304i | −0.0370254 | − | 0.999314i | \(-0.511788\pi\) |
0.758210 | + | 0.652010i | \(0.226074\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.694706 | − | 0.871133i | 0.0351328 | − | 0.0440551i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.1051 | + | 22.6987i | 0.661066 | + | 1.14500i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.85045 | − | 8.10736i | 0.0931064 | − | 0.407926i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.3361 | − | 19.7970i | 1.07083 | − | 0.993585i | 0.0708372 | − | 0.997488i | \(-0.477433\pi\) |
0.999992 | + | 0.00390325i | \(0.00124245\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.296679 | + | 0.202272i | 0.0148525 | + | 0.0101263i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.06942 | − | 14.2704i | 0.0534043 | − | 0.712631i | −0.904670 | − | 0.426112i | \(-0.859883\pi\) |
0.958075 | − | 0.286519i | \(-0.0924980\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.32812 | + | 27.7253i | 0.315226 | + | 1.38110i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.28835 | + | 4.28733i | −0.312471 | + | 0.213039i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.6193 | − | 42.3453i | 0.823789 | − | 2.09898i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.4363 | − | 13.2126i | −1.35664 | − | 0.653322i | −0.392754 | − | 0.919644i | \(-0.628478\pi\) |
−0.963884 | + | 0.266321i | \(0.914192\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.4998 | + | 2.18549i | 0.715221 | + | 0.107802i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.72719 | − | 0.532768i | −0.0849895 | − | 0.0262158i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.55604 | + | 9.06065i | 0.174559 | + | 0.444770i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.2885 | + | 12.3300i | 0.650742 | + | 0.603800i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.1749 | − | 27.8065i | −1.08332 | − | 1.35844i | −0.928858 | − | 0.370437i | \(-0.879208\pi\) |
−0.154459 | − | 0.987999i | \(-0.549363\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.3130 | + | 2.45879i | −0.795047 | + | 0.119834i | −0.533992 | − | 0.845490i | \(-0.679309\pi\) |
−0.261056 | + | 0.965324i | \(0.584071\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.201055 | + | 0.348237i | −0.00977561 | + | 0.0169318i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.857465 | + | 0.264493i | −0.0415932 | + | 0.0128298i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.217156 | − | 2.89774i | −0.0105089 | − | 0.140231i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 25.3088 | 1.22192 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.05750 | 0.436285 | 0.218142 | − | 0.975917i | \(-0.430000\pi\) | ||||
0.218142 | + | 0.975917i | \(0.430000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.29146 | + | 17.2334i | 0.0620638 | + | 0.828184i | 0.938194 | + | 0.346110i | \(0.112497\pi\) |
−0.876130 | + | 0.482074i | \(0.839884\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13.0075 | + | 4.01229i | −0.623663 | + | 0.192375i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.24191 | + | 3.88311i | −0.107245 | + | 0.185754i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.2692 | − | 2.75364i | 0.871943 | − | 0.131424i | 0.302197 | − | 0.953245i | \(-0.402280\pi\) |
0.569745 | + | 0.821821i | \(0.307042\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.77082 | + | 4.72845i | 0.179563 | + | 0.225165i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.55737 | − | 6.08435i | −0.311550 | − | 0.289076i | 0.508863 | − | 0.860848i | \(-0.330066\pi\) |
−0.820413 | + | 0.571771i | \(0.806256\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.18829 | + | 5.57568i | 0.103735 | + | 0.264313i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.15639 | + | 1.59054i | 0.243889 | + | 0.0752297i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.0461 | + | 3.02146i | 0.946032 | + | 0.142591i | 0.603900 | − | 0.797060i | \(-0.293613\pi\) |
0.342132 | + | 0.939652i | \(0.388851\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.8753 | − | 13.4240i | −1.31260 | − | 0.632113i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.14162 | + | 15.6486i | −0.288558 | + | 0.735235i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.694213 | − | 0.473306i | 0.0325452 | − | 0.0221889i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.39474 | + | 10.4921i | 0.112021 | + | 0.490797i | 0.999549 | + | 0.0300423i | \(0.00956421\pi\) |
−0.887527 | + | 0.460755i | \(0.847579\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.119284 | − | 1.59173i | 0.00556768 | − | 0.0742956i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.03749 | − | 4.79808i | −0.327769 | − | 0.223469i | 0.388243 | − | 0.921557i | \(-0.373082\pi\) |
−0.716012 | + | 0.698088i | \(0.754034\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.66719 | + | 1.54693i | −0.0774811 | + | 0.0718919i | −0.717963 | − | 0.696082i | \(-0.754925\pi\) |
0.640482 | + | 0.767973i | \(0.278735\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.33939 | − | 19.0121i | 0.201234 | − | 0.881666i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.1256 | − | 26.1983i | −0.699930 | − | 1.21231i | −0.968490 | − | 0.249052i | \(-0.919881\pi\) |
0.268560 | − | 0.963263i | \(-0.413452\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.848855 | + | 1.06443i | −0.0391965 | + | 0.0491509i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −27.0857 | + | 13.0438i | −1.24804 | + | 0.601025i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.70393 | − | 38.5787i | −0.400207 | − | 1.77385i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.25342 | − | 1.56676i | 0.149277 | − | 0.0718881i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.53015 | + | 5.68063i | −0.207422 | + | 0.260098i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.78977 | + | 11.7602i | 0.310233 | + | 0.537338i | 0.978413 | − | 0.206661i | \(-0.0662598\pi\) |
−0.668180 | + | 0.744000i | \(0.732926\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.82568 | − | 21.1427i | 0.220032 | − | 0.964024i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.912508 | + | 0.846683i | −0.0415205 | + | 0.0385254i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.98822 | − | 3.40091i | −0.226504 | − | 0.154428i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.78410 | − | 37.1512i | 0.126159 | − | 1.68348i | −0.471605 | − | 0.881810i | \(-0.656325\pi\) |
0.597765 | − | 0.801672i | \(-0.296056\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.24593 | − | 9.84005i | −0.101564 | − | 0.444982i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.9652 | + | 11.5667i | −0.765629 | + | 0.521997i | −0.882023 | − | 0.471206i | \(-0.843819\pi\) |
0.116394 | + | 0.993203i | \(0.462866\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.712843 | − | 1.81629i | 0.0321048 | − | 0.0818018i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.38466 | + | 3.07469i | 0.286969 | + | 0.138197i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.316363 | + | 0.0476840i | 0.0141908 | + | 0.00213892i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.66084 | − | 2.05460i | −0.298180 | − | 0.0919763i | 0.142056 | − | 0.989859i | \(-0.454629\pi\) |
−0.440235 | + | 0.897882i | \(0.645105\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.89570 | + | 4.83017i | 0.0846937 | + | 0.215796i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.51112 | + | 8.82503i | 0.424080 | + | 0.393488i | 0.863136 | − | 0.504971i | \(-0.168497\pi\) |
−0.439057 | + | 0.898459i | \(0.644687\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.52226 | − | 3.16281i | −0.112239 | − | 0.140743i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.83109 | + | 1.02962i | −0.303379 | + | 0.0457271i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.9031 | + | 25.8129i | −0.660568 | + | 1.14414i | 0.319898 | + | 0.947452i | \(0.396351\pi\) |
−0.980467 | + | 0.196686i | \(0.936982\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.169533 | − | 0.0522939i | 0.00749969 | − | 0.00231335i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.480019 | + | 6.40541i | 0.0211934 | + | 0.282806i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.4133 | −0.502929 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.78816 | −0.122623 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.62382 | + | 35.0125i | 0.115173 | + | 1.53688i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.7906 | + | 9.18917i | −1.30515 | + | 0.402585i | −0.867892 | − | 0.496752i | \(-0.834526\pi\) |
−0.437256 | + | 0.899337i | \(0.644050\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.95091 | − | 12.0393i | 0.303942 | − | 0.526443i | −0.673083 | − | 0.739567i | \(-0.735030\pi\) |
0.977025 | + | 0.213124i | \(0.0683637\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.991300 | − | 0.149414i | 0.0432639 | − | 0.00652098i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.74282 | + | 2.18542i | 0.0759183 | + | 0.0951986i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.46546 | + | 5.07120i | 0.237629 | + | 0.220487i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.65515 | − | 6.76521i | −0.115224 | − | 0.293585i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.0944 | − | 4.34755i | −0.610496 | − | 0.188313i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.37069 | + | 1.26168i | 0.361896 | + | 0.0545471i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.84038 | + | 3.29415i | 0.295184 | + | 0.142153i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.3207 | + | 39.0365i | −0.659908 | + | 1.68142i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.1344 | + | 11.6820i | −0.736664 | + | 0.502249i | −0.872580 | − | 0.488472i | \(-0.837555\pi\) |
0.135916 | + | 0.990720i | \(0.456602\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.900937 | − | 3.94726i | −0.0386629 | − | 0.169393i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.0214696 | − | 0.286491i | 0.000919655 | − | 0.0122719i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.9135 | − | 11.5314i | −0.723169 | − | 0.493049i | 0.144928 | − | 0.989442i | \(-0.453705\pi\) |
−0.868098 | + | 0.496394i | \(0.834657\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.56494 | − | 7.94710i | 0.365543 | − | 0.339174i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.74721 | + | 7.65501i | −0.0744335 | + | 0.326114i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.665844 | − | 1.15328i | −0.0283146 | − | 0.0490423i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.27195 | + | 11.6267i | −0.393573 | + | 0.493524i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.3932 | − | 7.41296i | 0.652229 | − | 0.314097i | −0.0783489 | − | 0.996926i | \(-0.524965\pi\) |
0.730578 | + | 0.682829i | \(0.239251\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.84422 | − | 17.5678i | −0.289480 | − | 0.743039i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.24130 | − | 1.07936i | 0.0946280 | − | 0.0455704i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.02348 | − | 8.80717i | 0.296004 | − | 0.371178i | −0.611483 | − | 0.791258i | \(-0.709427\pi\) |
0.907487 | + | 0.420080i | \(0.137998\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.47874 | + | 12.9536i | 0.314633 | + | 0.544960i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.271205 | + | 1.18823i | −0.0113895 | + | 0.0499008i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.89078 | − | 5.46585i | 0.246955 | − | 0.229140i | −0.546977 | − | 0.837148i | \(-0.684221\pi\) |
0.793931 | + | 0.608007i | \(0.208031\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.0538 | + | 16.3996i | 1.00662 | + | 0.686302i | 0.950050 | − | 0.312096i | \(-0.101031\pi\) |
0.0565700 | + | 0.998399i | \(0.481984\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.376902 | + | 5.02941i | −0.0157453 | + | 0.210106i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.78562 | + | 12.2046i | 0.116168 | + | 0.508967i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.93710 | + | 4.04784i | −0.247165 | + | 0.168514i | −0.680565 | − | 0.732687i | \(-0.738266\pi\) |
0.433401 | + | 0.901201i | \(0.357313\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.73544 | − | 24.8055i | 0.404591 | − | 1.03088i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.40434 | + | 0.676297i | 0.0582620 | + | 0.0280575i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −49.8172 | − | 7.50873i | −2.06322 | − | 0.310980i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.22823 | + | 0.995778i | 0.133471 | + | 0.0411703i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.8541 | + | 27.6558i | 0.447997 | + | 1.14148i | 0.959378 | + | 0.282123i | \(0.0910387\pi\) |
−0.511381 | + | 0.859354i | \(0.670866\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.24584 | − | 7.65102i | −0.339764 | − | 0.315255i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.26380 | − | 11.6164i | −0.381062 | − | 0.477837i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −31.8484 | + | 4.80037i | −1.30786 | + | 0.197127i | −0.765726 | − | 0.643167i | \(-0.777620\pi\) |
−0.542130 | + | 0.840295i | \(0.682382\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.0412930 | − | 0.0715215i | 0.00169285 | − | 0.00293210i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.8262 | − | 3.95635i | 0.524940 | − | 0.161923i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.13778 | + | 15.1826i | 0.0464885 | + | 0.620346i | 0.970983 | + | 0.239150i | \(0.0768687\pi\) |
−0.924494 | + | 0.381196i | \(0.875512\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.8489 | −0.605699 | −0.302849 | − | 0.953038i | \(-0.597938\pi\) | ||||
−0.302849 | + | 0.953038i | \(0.597938\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.47417 | −0.222925 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.56150 | + | 34.1808i | 0.104140 | + | 1.38965i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.93135 | − | 2.75496i | 0.362512 | − | 0.111820i | −0.108148 | − | 0.994135i | \(-0.534492\pi\) |
0.470660 | + | 0.882315i | \(0.344016\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.08992 | + | 1.88780i | −0.0441659 | + | 0.0764976i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.31435 | + | 0.198107i | −0.0531731 | + | 0.00801455i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.2070 | + | 24.0849i | 0.775765 | + | 0.972779i | 0.999998 | − | 0.00175653i | \(-0.000559122\pi\) |
−0.224233 | + | 0.974536i | \(0.571988\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.41433 | + | 6.87949i | 0.298974 | + | 0.277408i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.40309 | − | 3.57502i | −0.0564864 | − | 0.143925i | 0.899845 | − | 0.436210i | \(-0.143680\pi\) |
−0.956331 | + | 0.292285i | \(0.905584\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.6404 | − | 10.0682i | −1.31193 | − | 0.404676i | −0.441629 | − | 0.897198i | \(-0.645599\pi\) |
−0.870300 | + | 0.492521i | \(0.836075\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22.0194 | − | 3.31889i | −0.883608 | − | 0.133182i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.864195 | + | 0.416175i | 0.0346233 | + | 0.0166737i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.349803 | − | 0.891285i | 0.0139921 | − | 0.0356514i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.27131 | + | 5.63928i | −0.330324 | + | 0.225211i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.474327 | − | 2.07816i | −0.0189126 | − | 0.0828617i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.687936 | − | 9.17986i | 0.0273863 | − | 0.365445i | −0.966627 | − | 0.256187i | \(-0.917534\pi\) |
0.994013 | − | 0.109257i | \(-0.0348473\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.9823 | − | 15.6691i | −0.913465 | − | 0.622790i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.73808 | − | 7.17989i | 0.307076 | − | 0.284925i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.44860 | + | 19.4906i | −0.176260 | + | 0.772246i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.643201 | + | 1.11406i | 0.0254447 | + | 0.0440714i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.10948 | − | 2.64521i | 0.0833196 | − | 0.104479i | −0.738424 | − | 0.674336i | \(-0.764430\pi\) |
0.821744 | + | 0.569857i | \(0.193001\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.1874 | − | 4.90598i | 0.401751 | − | 0.193473i | −0.222087 | − | 0.975027i | \(-0.571287\pi\) |
0.623838 | + | 0.781554i | \(0.285573\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.998394 | + | 12.8901i | −0.0393117 | + | 0.507548i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.4890 | + | 9.86700i | −0.805507 | + | 0.387912i | −0.790873 | − | 0.611981i | \(-0.790373\pi\) |
−0.0146350 | + | 0.999893i | \(0.504659\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.4191 | − | 39.3983i | 1.23331 | − | 1.54652i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.56143 | − | 2.70448i | −0.0611973 | − | 0.105997i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.74350 | + | 25.1639i | −0.224760 | + | 0.984739i | 0.729081 | + | 0.684428i | \(0.239948\pi\) |
−0.953841 | + | 0.300312i | \(0.902909\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.7831 | + | 16.5003i | −0.694844 | + | 0.644721i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.589399 | + | 0.401846i | 0.0229947 | + | 0.0156775i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.761704 | + | 10.1642i | −0.0296718 | + | 0.395942i | 0.962519 | + | 0.271214i | \(0.0874251\pi\) |
−0.992191 | + | 0.124729i | \(0.960194\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.96298 | + | 12.9817i | 0.115247 | + | 0.504928i | 0.999295 | + | 0.0375336i | \(0.0119501\pi\) |
−0.884049 | + | 0.467395i | \(0.845193\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.979873 | − | 0.668066i | 0.0380551 | − | 0.0259455i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.121418 | + | 0.309367i | −0.00470838 | + | 0.0119967i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.5247 | − | 11.8105i | −0.949600 | − | 0.457303i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.5323 | + | 1.58749i | 0.407201 | + | 0.0613757i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 77.4153 | + | 23.8795i | 2.98858 | + | 0.921856i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.30694 | − | 5.87798i | −0.0889259 | − | 0.226579i | 0.879491 | − | 0.475915i | \(-0.157883\pi\) |
−0.968417 | + | 0.249336i | \(0.919788\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.1462 | + | 12.1979i | 0.505997 | + | 0.469496i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.2431 | − | 20.3682i | −0.624273 | − | 0.782814i | 0.364666 | − | 0.931139i | \(-0.381183\pi\) |
−0.988939 | + | 0.148325i | \(0.952612\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.955999 | + | 0.144094i | −0.0366879 | + | 0.00552981i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.4119 | + | 19.7660i | −0.437305 | + | 0.757435i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 47.0692 | − | 14.5189i | 1.80105 | − | 0.555551i | 0.801930 | − | 0.597418i | \(-0.203807\pi\) |
0.999123 | + | 0.0418665i | \(0.0133304\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.01423 | + | 13.5340i | 0.0387518 | + | 0.517107i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.56931 | 0.0598730 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24.0176 | −0.914999 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.68891 | + | 49.2251i | 0.140333 | + | 1.87261i | 0.413311 | + | 0.910590i | \(0.364372\pi\) |
−0.272978 | + | 0.962020i | \(0.588009\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.08439 | − | 0.334491i | 0.0411927 | − | 0.0127063i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.38908 | + | 14.5303i | −0.318216 | + | 0.551166i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.43359 | + | 0.216078i | −0.0543009 | + | 0.00818455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.21305 | + | 1.52112i | 0.0458818 | + | 0.0575340i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.8277 | + | 11.9024i | 0.484495 | + | 0.449546i | 0.884207 | − | 0.467095i | \(-0.154699\pi\) |
−0.399712 | + | 0.916641i | \(0.630890\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.13388 | + | 7.98500i | 0.118197 | + | 0.301160i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.870981 | + | 0.268662i | 0.0328030 | + | 0.0101184i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.640585 | − | 0.0965527i | −0.0240917 | − | 0.00363124i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.7314 | − | 13.8363i | −1.07903 | − | 0.519634i | −0.192025 | − | 0.981390i | \(-0.561505\pi\) |
−0.887007 | + | 0.461756i | \(0.847220\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.95621 | − | 4.98433i | 0.0733635 | − | 0.186927i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 32.2201 | − | 21.9673i | 1.20665 | − | 0.822680i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.21249 | + | 22.8374i | 0.194936 | + | 0.854071i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.62266 | − | 21.6529i | 0.0605993 | − | 0.808641i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.7184 | − | 24.3524i | −1.33207 | − | 0.908190i | −0.332677 | − | 0.943041i | \(-0.607952\pi\) |
−0.999393 | + | 0.0348509i | \(0.988904\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.33980 | + | 1.24315i | −0.0498968 | + | 0.0462974i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.76340 | − | 34.0137i | 0.288724 | − | 1.26498i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.9609 | + | 18.9848i | 0.407076 | + | 0.705077i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.61281 | − | 3.27636i | 0.0969039 | − | 0.121514i | −0.731015 | − | 0.682361i | \(-0.760953\pi\) |
0.827919 | + | 0.560848i | \(0.189525\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.6965 | + | 12.8563i | −0.988757 | + | 0.476161i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.35533 | − | 1.26388i | −0.0501288 | − | 0.0467464i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −44.3364 | + | 21.3513i | −1.63760 | + | 0.788629i | −0.637773 | + | 0.770224i | \(0.720144\pi\) |
−0.999831 | + | 0.0184045i | \(0.994141\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.54744 | − | 10.7182i | 0.315277 | − | 0.395345i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.9785 | − | 32.8717i | −0.699082 | − | 1.21085i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.558133 | + | 2.44534i | −0.0205313 | + | 0.0899533i | −0.984156 | − | 0.177307i | \(-0.943261\pi\) |
0.963624 | + | 0.267261i | \(0.0861185\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.49846 | + | 3.24609i | −0.128519 | + | 0.119248i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.7210 | − | 10.0366i | −0.540059 | − | 0.368206i | 0.262357 | − | 0.964971i | \(-0.415500\pi\) |
−0.802416 | + | 0.596765i | \(0.796453\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.373233 | + | 4.98044i | −0.0136742 | + | 0.182469i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.39460 | + | 6.11013i | 0.0510256 | + | 0.223558i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.12006 | − | 0.763641i | 0.0409260 | − | 0.0279028i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.1468 | + | 36.0454i | −0.516223 | + | 1.31532i | 0.400684 | + | 0.916216i | \(0.368772\pi\) |
−0.916908 | + | 0.399099i | \(0.869323\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 27.0044 | + | 13.0046i | 0.984094 | + | 0.473915i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.3854 | − | 2.31897i | −0.559932 | − | 0.0843961i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.5522 | + | 9.11563i | 1.07409 | + | 0.331313i | 0.780846 | − | 0.624724i | \(-0.214788\pi\) |
0.293246 | + | 0.956037i | \(0.405265\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.6791 | − | 32.3058i | −0.460221 | − | 1.17262i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.4994 | + | 29.2271i | 1.14185 | + | 1.05948i | 0.997551 | + | 0.0699487i | \(0.0222836\pi\) |
0.144300 | + | 0.989534i | \(0.453907\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.0286848 | − | 0.0359696i | −0.00103846 | − | 0.00130219i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.328354 | − | 0.0494914i | 0.0118717 | − | 0.00178936i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.0118 | − | 20.8050i | 0.433720 | − | 0.751225i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.0134 | − | 3.39717i | 0.397152 | − | 0.122505i | −0.0897448 | − | 0.995965i | \(-0.528605\pi\) |
0.486896 | + | 0.873460i | \(0.338129\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.49103 | + | 33.2404i | 0.0897121 | + | 1.19712i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.2393 | −0.871828 | −0.435914 | − | 0.899988i | \(-0.643575\pi\) | ||||
−0.435914 | + | 0.899988i | \(0.643575\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31.4052 | −1.12811 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.177964 | + | 2.37477i | 0.00638443 | + | 0.0851943i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.57498 | − | 1.71965i | 0.199744 | − | 0.0616130i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.45985 | + | 7.72469i | −0.159586 | + | 0.276411i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −38.5593 | + | 5.81189i | −1.37800 | + | 0.207700i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.3485 | − | 21.7543i | −0.619194 | − | 0.776444i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.37365 | + | 6.84175i | 0.262842 | + | 0.243882i | 0.800574 | − | 0.599234i | \(-0.204528\pi\) |
−0.537732 | + | 0.843116i | \(0.680719\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.28368 | + | 8.36668i | 0.116902 | + | 0.297862i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.28885 | + | 0.706017i | 0.0813821 | + | 0.0251031i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 38.1907 | + | 5.75633i | 1.35619 | + | 0.204413i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14.8386 | + | 7.14591i | 0.526272 | + | 0.253439i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.9088 | + | 37.9869i | −0.528096 | + | 1.34557i | 0.379294 | + | 0.925276i | \(0.376167\pi\) |
−0.907390 | + | 0.420290i | \(0.861928\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.107948 | + | 0.0735978i | −0.00381893 | + | 0.00260370i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.858197 | + | 3.76001i | 0.0303229 | + | 0.132853i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.369635 | + | 4.93243i | −0.0130441 | + | 0.174062i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.951940 | − | 0.649022i | −0.0335515 | − | 0.0228750i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.0679 | − | 14.9089i | 0.565618 | − | 0.524817i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.4359 | − | 45.7228i | 0.366908 | − | 1.60753i | −0.368313 | − | 0.929702i | \(-0.620065\pi\) |
0.735221 | − | 0.677827i | \(-0.237078\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.1357 | + | 29.6798i | 0.601714 | + | 1.04220i | 0.992562 | + | 0.121744i | \(0.0388487\pi\) |
−0.390847 | + | 0.920456i | \(0.627818\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.81598 | − | 3.53112i | 0.0987606 | − | 0.123842i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.41660 | − | 4.05322i | 0.294821 | − | 0.141978i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.15123 | + | 4.21640i | 0.215204 | + | 0.147513i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.487423 | − | 0.234730i | 0.0170319 | − | 0.00820215i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.5042 | + | 14.4258i | −0.401500 | + | 0.503465i | −0.940947 | − | 0.338555i | \(-0.890062\pi\) |
0.539447 | + | 0.842020i | \(0.318633\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.59427 | + | 7.95750i | 0.160146 | + | 0.277381i | 0.934921 | − | 0.354856i | \(-0.115470\pi\) |
−0.774775 | + | 0.632237i | \(0.782137\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.21930 | + | 27.2485i | −0.216528 | + | 0.948672i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.9067 | − | 24.9658i | 0.935637 | − | 0.868145i | −0.0558380 | − | 0.998440i | \(-0.517783\pi\) |
0.991475 | + | 0.130295i | \(0.0415925\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.75599 | + | 2.56079i | 0.130451 | + | 0.0889400i | 0.626788 | − | 0.779190i | \(-0.284369\pi\) |
−0.496336 | + | 0.868130i | \(0.665322\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.64842 | + | 21.9966i | −0.0571829 | + | 0.763053i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.437263 | + | 1.91577i | 0.0151503 | + | 0.0663776i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.96807 | + | 2.70538i | −0.137321 | + | 0.0936236i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.4095 | − | 52.0026i | 0.705457 | − | 1.79747i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.6424 | − | 10.4224i | −0.747177 | − | 0.359822i | 0.0212370 | − | 0.999774i | \(-0.493240\pi\) |
−0.768414 | + | 0.639953i | \(0.778954\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.4585 | − | 2.78217i | −0.636500 | − | 0.0959369i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.5669 | − | 4.80176i | −0.536154 | − | 0.165382i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.33598 | − | 5.95197i | −0.0803601 | − | 0.204754i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.02372 | + | 3.73347i | 0.138257 | + | 0.128284i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.6426 | − | 18.3613i | −0.502534 | − | 0.630157i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −29.4054 | + | 4.43215i | −1.00800 | + | 0.151932i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.8630 | − | 43.0639i | 0.851292 | − | 1.47448i | −0.0287512 | − | 0.999587i | \(-0.509153\pi\) |
0.880043 | − | 0.474894i | \(-0.157514\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.27691 | + | 0.393876i | −0.0436695 | + | 0.0134703i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.63975 | − | 35.2251i | −0.0901723 | − | 1.20327i | −0.840356 | − | 0.542036i | \(-0.817654\pi\) |
0.750183 | − | 0.661230i | \(-0.229965\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.58814 | −0.293024 | −0.146512 | − | 0.989209i | \(-0.546805\pi\) | ||||
−0.146512 | + | 0.989209i | \(0.546805\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.61969 | 0.0551989 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.53059 | − | 33.7684i | −0.0861424 | − | 1.14949i | −0.857984 | − | 0.513676i | \(-0.828283\pi\) |
0.771842 | − | 0.635814i | \(-0.219336\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31.0531 | + | 9.57861i | −1.05584 | + | 0.325682i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.3476 | + | 21.3867i | −0.419347 | + | 0.726331i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36.7123 | − | 5.53349i | 1.24538 | − | 0.187711i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.2822 | − | 14.1474i | −0.382283 | − | 0.479368i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.84960 | − | 2.64404i | −0.0964444 | − | 0.0894873i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.872799 | + | 2.22386i | 0.0295060 | + | 0.0751800i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.2010 | − | 5.30581i | −0.580837 | − | 0.179164i | −0.00960602 | − | 0.999954i | \(-0.503058\pi\) |
−0.571231 | + | 0.820789i | \(0.693534\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.1943 | − | 3.19452i | −0.714864 | − | 0.107748i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.6192 | + | 11.3744i | 0.795750 | + | 0.383213i | 0.787159 | − | 0.616750i | \(-0.211551\pi\) |
0.00859074 | + | 0.999963i | \(0.497265\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.1802 | − | 46.3225i | 0.611814 | − | 1.55888i | −0.203016 | − | 0.979176i | \(-0.565074\pi\) |
0.814829 | − | 0.579701i | \(-0.196831\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.6112 | + | 9.27997i | −0.457536 | + | 0.311943i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.90844 | − | 8.36143i | −0.0640792 | − | 0.280749i | 0.932730 | − | 0.360577i | \(-0.117420\pi\) |
−0.996809 | + | 0.0798277i | \(0.974563\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.126325 | − | 1.68569i | 0.00423680 | − | 0.0565362i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28.0750 | − | 19.1412i | −0.940547 | − | 0.641254i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.385409 | − | 0.357607i | 0.0128972 | − | 0.0119669i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.56366 | + | 6.85086i | −0.0522675 | + | 0.228999i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.27242 | − | 14.3282i | −0.276208 | − | 0.478406i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 42.5769 | − | 53.3898i | 1.42002 | − | 1.78065i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.12696 | + | 1.02429i | −0.0708592 | + | 0.0341240i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.28681 | + | 1.62191i | 0.0428225 | + | 0.0539739i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.37626 | − | 1.62592i | 0.112231 | − | 0.0540474i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.5664 | − | 22.0275i | 0.583282 | − | 0.731412i | −0.399387 | − | 0.916782i | \(-0.630777\pi\) |
0.982669 | + | 0.185370i | \(0.0593485\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.30238 | − | 2.25579i | −0.0431973 | − | 0.0748200i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.43767 | + | 23.8240i | −0.180158 | + | 0.789324i | 0.801395 | + | 0.598135i | \(0.204091\pi\) |
−0.981553 | + | 0.191189i | \(0.938766\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.8556 | + | 29.5577i | −1.05427 | + | 0.978217i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −21.8824 | − | 14.9192i | −0.723411 | − | 0.493213i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.290311 | + | 3.87394i | −0.00958692 | + | 0.127929i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.55017 | − | 15.5543i | −0.117109 | − | 0.513089i | −0.999123 | − | 0.0418659i | \(-0.986670\pi\) |
0.882014 | − | 0.471223i | \(-0.156187\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.0342045 | − | 0.0233202i | 0.00112708 | − | 0.000768427i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.55354 | + | 3.95835i | −0.0511353 | + | 0.130291i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.5772 | + | 10.3910i | 0.709455 | + | 0.341656i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.26677 | − | 1.09529i | −0.238672 | − | 0.0359740i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.97357 | − | 1.84260i | −0.195987 | − | 0.0604539i | 0.195208 | − | 0.980762i | \(-0.437462\pi\) |
−0.391195 | + | 0.920308i | \(0.627938\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.88900 | − | 7.36105i | −0.0946832 | − | 0.241249i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.9961 | + | 10.2029i | 0.359996 | + | 0.334027i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.43556 | + | 1.80014i | 0.0469480 | + | 0.0588709i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 53.4604 | − | 8.05785i | 1.74647 | − | 0.263239i | 0.803309 | − | 0.595563i | \(-0.203071\pi\) |
0.943165 | + | 0.332324i | \(0.107833\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.0833 | − | 22.6610i | 0.426959 | − | 0.739514i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.8574 | − | 9.20978i | 0.973322 | − | 0.300230i | 0.232996 | − | 0.972478i | \(-0.425147\pi\) |
0.740326 | + | 0.672248i | \(0.234671\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.51146 | + | 20.1690i | 0.0492198 | + | 0.656792i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.65051 | −0.0536911 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.7946 | 1.26066 | 0.630328 | − | 0.776329i | \(-0.282920\pi\) | ||||
0.630328 | + | 0.776329i | \(0.282920\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.176216 | + | 2.35144i | 0.00572022 | + | 0.0763311i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.3062 | − | 9.34823i | 0.982747 | − | 0.303137i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.6148 | − | 25.3136i | 0.473420 | − | 0.819987i | −0.526118 | − | 0.850412i | \(-0.676353\pi\) |
0.999537 | + | 0.0304252i | \(0.00968613\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.61591 | + | 0.695736i | −0.149367 | + | 0.0225135i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −37.8916 | − | 47.5145i | −1.22486 | − | 1.53593i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.59320 | + | 1.47828i | 0.0514472 | + | 0.0477361i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.4157 | + | 62.2103i | 0.787604 | + | 2.00678i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.20849 | + | 1.60661i | 0.167841 | + | 0.0517722i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.3883 | + | 3.67594i | 0.785087 | + | 0.118333i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.9889 | + | 11.0709i | 0.739274 | + | 0.356015i | 0.765324 | − | 0.643645i | \(-0.222579\pi\) |
−0.0260504 | + | 0.999661i | \(0.508293\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.171380 | + | 0.436668i | −0.00550551 | + | 0.0140278i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.1865 | + | 11.7176i | −0.551542 | + | 0.376035i | −0.806788 | − | 0.590841i | \(-0.798796\pi\) |
0.255246 | + | 0.966876i | \(0.417844\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.597875 | + | 2.61946i | 0.0191670 | + | 0.0839761i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.995724 | + | 13.2870i | −0.0318887 | + | 0.425525i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.5522 | − | 10.6033i | −0.497559 | − | 0.339230i | 0.288398 | − | 0.957510i | \(-0.406877\pi\) |
−0.785958 | + | 0.618280i | \(0.787830\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.6031 | + | 18.1890i | −0.626517 | + | 0.581323i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.0411631 | − | 0.180347i | 0.00131424 | − | 0.00575804i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.1156 | − | 19.2529i | −0.354534 | − | 0.614071i | 0.632504 | − | 0.774557i | \(-0.282027\pi\) |
−0.987038 | + | 0.160486i | \(0.948694\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.57416 | − | 10.7517i | 0.273195 | − | 0.342576i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.131507 | − | 0.0633305i | 0.00418592 | − | 0.00201583i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.9958 | + | 17.5374i | −0.604033 | + | 0.557657i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.8081 | − | 6.64964i | 0.438630 | − | 0.211233i | −0.201518 | − | 0.979485i | \(-0.564587\pi\) |
0.640148 | + | 0.768252i | \(0.278873\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.0366 | − | 15.0934i | 0.381971 | − | 0.478976i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.21163 | + | 10.7589i | 0.196922 | + | 0.341079i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.57862 | + | 6.91637i | −0.0499953 | + | 0.219044i | −0.993754 | − | 0.111591i | \(-0.964405\pi\) |
0.943759 | + | 0.330634i | \(0.107263\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −31.2287 | + | 28.9760i | −0.988031 | + | 0.916759i |
(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 | 688.2.bg.c.401.1 | 36 | ||
4.3 | odd | 2 | 43.2.g.a.14.2 | ✓ | 36 | ||
12.11 | even | 2 | 387.2.y.c.100.2 | 36 | |||
43.40 | even | 21 | inner | 688.2.bg.c.513.1 | 36 | ||
172.83 | odd | 42 | 43.2.g.a.40.2 | yes | 36 | ||
172.99 | odd | 42 | 1849.2.a.n.1.13 | 18 | |||
172.159 | even | 42 | 1849.2.a.o.1.6 | 18 | |||
516.83 | even | 42 | 387.2.y.c.298.2 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.2.g.a.14.2 | ✓ | 36 | 4.3 | odd | 2 | ||
43.2.g.a.40.2 | yes | 36 | 172.83 | odd | 42 | ||
387.2.y.c.100.2 | 36 | 12.11 | even | 2 | |||
387.2.y.c.298.2 | 36 | 516.83 | even | 42 | |||
688.2.bg.c.401.1 | 36 | 1.1 | even | 1 | trivial | ||
688.2.bg.c.513.1 | 36 | 43.40 | even | 21 | inner | ||
1849.2.a.n.1.13 | 18 | 172.99 | odd | 42 | |||
1849.2.a.o.1.6 | 18 | 172.159 | even | 42 |