Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(107,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 5, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.w (of order \(8\), 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: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(128\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 107.4 | ||
Character | \(\chi\) | \(=\) | 864.107 |
Dual form | 864.2.w.a.323.4 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(e\left(\frac{5}{8}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36834 | + | 0.357292i | −0.967559 | + | 0.252644i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.74468 | − | 0.977791i | 0.872342 | − | 0.488896i | ||||
\(5\) | 0.202568 | + | 0.0839066i | 0.0905913 | + | 0.0375242i | 0.427519 | − | 0.904006i | \(-0.359388\pi\) |
−0.336928 | + | 0.941531i | \(0.609388\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0119413 | + | 0.0119413i | −0.00451339 | + | 0.00451339i | −0.709360 | − | 0.704846i | \(-0.751016\pi\) |
0.704846 | + | 0.709360i | \(0.251016\pi\) | |||||||
\(8\) | −2.03796 | + | 1.96131i | −0.720527 | + | 0.693427i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.307161 | − | 0.0424363i | −0.0971327 | − | 0.0134195i | ||||
\(11\) | −3.46699 | − | 1.43608i | −1.04534 | − | 0.432993i | −0.207112 | − | 0.978317i | \(-0.566407\pi\) |
−0.838225 | + | 0.545324i | \(0.816407\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.44858 | + | 3.49717i | 0.401763 | + | 0.969941i | 0.987238 | + | 0.159251i | \(0.0509079\pi\) |
−0.585475 | + | 0.810690i | \(0.699092\pi\) | |||||||
\(14\) | 0.0120732 | − | 0.0206062i | 0.00322669 | − | 0.00550725i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.08785 | − | 3.41187i | 0.521962 | − | 0.852969i | ||||
\(17\) | −1.93975 | −0.470458 | −0.235229 | − | 0.971940i | \(-0.575584\pi\) | ||||
−0.235229 | + | 0.971940i | \(0.575584\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.32957 | + | 0.964939i | −0.534440 | + | 0.221372i | −0.633546 | − | 0.773705i | \(-0.718401\pi\) |
0.0991068 | + | 0.995077i | \(0.468401\pi\) | |||||||
\(20\) | 0.435461 | − | 0.0516790i | 0.0973720 | − | 0.0115558i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.25711 | + | 0.726304i | 1.12082 | + | 0.154849i | ||||
\(23\) | −4.79172 | + | 4.79172i | −0.999143 | + | 0.999143i | −1.00000 | 0.000856866i | \(-0.999727\pi\) | |
0.000856866 | 1.00000i | \(0.499727\pi\) | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.50154 | − | 3.50154i | −0.700308 | − | 0.700308i | ||||
\(26\) | −3.23165 | − | 4.26774i | −0.633779 | − | 0.836973i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.00915771 | + | 0.0325099i | −0.00173064 | + | 0.00614380i | ||||
\(29\) | 1.79276 | + | 4.32810i | 0.332906 | + | 0.803707i | 0.998359 | + | 0.0572669i | \(0.0182386\pi\) |
−0.665453 | + | 0.746440i | \(0.731761\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.213195i | − | 0.0382910i | −0.999817 | − | 0.0191455i | \(-0.993905\pi\) | ||
0.999817 | − | 0.0191455i | \(-0.00609458\pi\) | |||||||
\(32\) | −1.63784 | + | 5.41456i | −0.289532 | + | 0.957168i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.65423 | − | 0.693057i | 0.455196 | − | 0.118858i | ||||
\(35\) | −0.00342088 | + | 0.00141698i | −0.000578235 | + | 0.000239513i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.04659 | − | 2.52670i | 0.172059 | − | 0.415386i | −0.814202 | − | 0.580581i | \(-0.802825\pi\) |
0.986261 | + | 0.165195i | \(0.0528253\pi\) | |||||||
\(38\) | 2.84287 | − | 2.15270i | 0.461174 | − | 0.349214i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.577392 | + | 0.226301i | −0.0912937 | + | 0.0357813i | ||||
\(41\) | 2.21601 | + | 2.21601i | 0.346082 | + | 0.346082i | 0.858648 | − | 0.512566i | \(-0.171305\pi\) |
−0.512566 | + | 0.858648i | \(0.671305\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.38417 | + | 3.34169i | −0.211085 | + | 0.509603i | −0.993590 | − | 0.113040i | \(-0.963941\pi\) |
0.782506 | + | 0.622643i | \(0.213941\pi\) | |||||||
\(44\) | −7.45299 | + | 0.884495i | −1.12358 | + | 0.133343i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.84464 | − | 8.26873i | 0.714303 | − | 1.21916i | ||||
\(47\) | − | 2.42072i | − | 0.353099i | −0.984292 | − | 0.176549i | \(-0.943506\pi\) | ||
0.984292 | − | 0.176549i | \(-0.0564935\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.99971i | 0.999959i | ||||||||
\(50\) | 6.04235 | + | 3.54021i | 0.854518 | + | 0.500661i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.94681 | + | 4.68506i | 0.824675 | + | 0.649701i | ||||
\(53\) | −1.24746 | + | 3.01163i | −0.171352 | + | 0.413679i | −0.986104 | − | 0.166130i | \(-0.946873\pi\) |
0.814752 | + | 0.579809i | \(0.196873\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.581807 | − | 0.581807i | −0.0784508 | − | 0.0784508i | ||||
\(56\) | 0.000915288 | − | 0.0477564i | 0.000122310 | − | 0.00638172i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.99949 | − | 5.28175i | −0.525158 | − | 0.693528i | ||||
\(59\) | 1.49224 | − | 3.60257i | 0.194272 | − | 0.469015i | −0.796485 | − | 0.604658i | \(-0.793310\pi\) |
0.990758 | + | 0.135643i | \(0.0433099\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.46424 | + | 1.43494i | −0.443551 | + | 0.183725i | −0.593270 | − | 0.805004i | \(-0.702163\pi\) |
0.149719 | + | 0.988729i | \(0.452163\pi\) | |||||||
\(62\) | 0.0761730 | + | 0.291723i | 0.00967398 | + | 0.0370488i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.306539 | − | 7.99412i | 0.0383174 | − | 0.999266i | ||||
\(65\) | 0.829962i | 0.102944i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.85824 | + | 9.31462i | 0.471359 | + | 1.13796i | 0.963563 | + | 0.267482i | \(0.0861916\pi\) |
−0.492203 | + | 0.870480i | \(0.663808\pi\) | |||||||
\(68\) | −3.38425 | + | 1.89667i | −0.410401 | + | 0.230005i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.00417464 | − | 0.00316115i | 0.000498965 | − | 0.000377830i | ||||
\(71\) | −8.45626 | − | 8.45626i | −1.00357 | − | 1.00357i | −0.999994 | − | 0.00357951i | \(-0.998861\pi\) |
−0.00357951 | − | 0.999994i | \(-0.501139\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.0555 | + | 11.0555i | −1.29394 | + | 1.29394i | −0.361618 | + | 0.932326i | \(0.617776\pi\) |
−0.932326 | + | 0.361618i | \(0.882224\pi\) | |||||||
\(74\) | −0.529321 | + | 3.83131i | −0.0615323 | + | 0.445381i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.12085 | + | 3.96135i | −0.357987 | + | 0.454398i | ||||
\(77\) | 0.0585490 | − | 0.0242518i | 0.00667228 | − | 0.00276375i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.3461 | −1.72658 | −0.863288 | − | 0.504712i | \(-0.831599\pi\) | ||||
−0.863288 | + | 0.504712i | \(0.831599\pi\) | |||||||
\(80\) | 0.709211 | − | 0.515953i | 0.0792922 | − | 0.0576854i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.82400 | − | 2.24048i | −0.422290 | − | 0.247420i | ||||
\(83\) | 1.25116 | + | 3.02056i | 0.137332 | + | 0.331549i | 0.977551 | − | 0.210698i | \(-0.0675736\pi\) |
−0.840219 | + | 0.542247i | \(0.817574\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.392932 | − | 0.162758i | −0.0426194 | − | 0.0176536i | ||||
\(86\) | 0.700054 | − | 5.06711i | 0.0754888 | − | 0.546400i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.88217 | − | 3.87318i | 1.05344 | − | 0.412882i | ||||
\(89\) | −1.44269 | + | 1.44269i | −0.152925 | + | 0.152925i | −0.779423 | − | 0.626498i | \(-0.784488\pi\) |
0.626498 | + | 0.779423i | \(0.284488\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0590587 | − | 0.0244629i | −0.00619103 | − | 0.00256441i | ||||
\(92\) | −3.67474 | + | 13.0453i | −0.383118 | + | 1.36007i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.864905 | + | 3.31236i | 0.0892081 | + | 0.341644i | ||||
\(95\) | −0.552862 | −0.0567224 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.8857 | −1.20681 | −0.603404 | − | 0.797436i | \(-0.706189\pi\) | ||||
−0.603404 | + | 0.797436i | \(0.706189\pi\) | |||||||
\(98\) | −2.50094 | − | 9.57796i | −0.252633 | − | 0.967520i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.53286 | − | 2.68531i | −0.953286 | − | 0.268531i | ||||
\(101\) | 9.63369 | + | 3.99041i | 0.958588 | + | 0.397060i | 0.806452 | − | 0.591299i | \(-0.201385\pi\) |
0.152136 | + | 0.988360i | \(0.451385\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.67304 | − | 1.67304i | 0.164850 | − | 0.164850i | −0.619861 | − | 0.784711i | \(-0.712811\pi\) |
0.784711 | + | 0.619861i | \(0.212811\pi\) | |||||||
\(104\) | −9.81117 | − | 4.28598i | −0.962065 | − | 0.420275i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.630910 | − | 4.56663i | 0.0612794 | − | 0.443550i | ||||
\(107\) | −14.0152 | − | 5.80527i | −1.35490 | − | 0.561217i | −0.417246 | − | 0.908794i | \(-0.637005\pi\) |
−0.937651 | + | 0.347577i | \(0.887005\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.85189 | − | 6.88507i | −0.273161 | − | 0.659470i | 0.726454 | − | 0.687215i | \(-0.241167\pi\) |
−0.999615 | + | 0.0277456i | \(0.991167\pi\) | |||||||
\(110\) | 1.00398 | + | 0.588232i | 0.0957259 | + | 0.0560857i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.0158106 | + | 0.0656739i | 0.00149396 | + | 0.00620560i | ||||
\(113\) | 14.2128 | 1.33703 | 0.668514 | − | 0.743700i | \(-0.266931\pi\) | ||||
0.668514 | + | 0.743700i | \(0.266931\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.37271 | + | 0.568594i | −0.128006 | + | 0.0530217i | ||||
\(116\) | 7.35977 | + | 5.79822i | 0.683337 | + | 0.538351i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.754707 | + | 5.46269i | −0.0694764 | + | 0.502882i | ||||
\(119\) | 0.0231631 | − | 0.0231631i | 0.00212336 | − | 0.00212336i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.17955 | + | 2.17955i | 0.198141 | + | 0.198141i | ||||
\(122\) | 4.22755 | − | 3.20122i | 0.382745 | − | 0.289825i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.208461 | − | 0.371959i | −0.0187203 | − | 0.0334029i | ||||
\(125\) | −0.835032 | − | 2.01595i | −0.0746875 | − | 0.180312i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.594874i | 0.0527865i | 0.999652 | + | 0.0263933i | \(0.00840222\pi\) | ||||
−0.999652 | + | 0.0263933i | \(0.991598\pi\) | |||||||
\(128\) | 2.43679 | + | 11.0482i | 0.215384 | + | 0.976529i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.296539 | − | 1.13567i | −0.0260082 | − | 0.0996045i | ||||
\(131\) | −11.9207 | + | 4.93770i | −1.04151 | + | 0.431409i | −0.836855 | − | 0.547424i | \(-0.815608\pi\) |
−0.204658 | + | 0.978833i | \(0.565608\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0162955 | − | 0.0393407i | 0.00141300 | − | 0.00341127i | ||||
\(134\) | −8.60741 | − | 11.3670i | −0.743567 | − | 0.981960i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.95313 | − | 3.80445i | 0.338978 | − | 0.326229i | ||||
\(137\) | 10.8258 | + | 10.8258i | 0.924915 | + | 0.924915i | 0.997372 | − | 0.0724568i | \(-0.0230840\pi\) |
−0.0724568 | + | 0.997372i | \(0.523084\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.55148 | + | 8.57403i | −0.301232 | + | 0.727239i | 0.698698 | + | 0.715417i | \(0.253763\pi\) |
−0.999930 | + | 0.0118224i | \(0.996237\pi\) | |||||||
\(140\) | −0.00458286 | + | 0.00581709i | −0.000387322 | + | 0.000491634i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14.5924 | + | 8.54964i | 1.22456 | + | 0.717470i | ||||
\(143\) | − | 14.2049i | − | 1.18788i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.02716i | 0.0853009i | ||||||||
\(146\) | 11.1776 | − | 19.0776i | 0.925061 | − | 1.57888i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.644608 | − | 5.43164i | −0.0529865 | − | 0.446478i | ||||
\(149\) | 4.25928 | − | 10.2828i | 0.348933 | − | 0.842400i | −0.647813 | − | 0.761799i | \(-0.724316\pi\) |
0.996746 | − | 0.0806006i | \(-0.0256838\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.71514 | − | 9.71514i | −0.790607 | − | 0.790607i | 0.190986 | − | 0.981593i | \(-0.438831\pi\) |
−0.981593 | + | 0.190986i | \(0.938831\pi\) | |||||||
\(152\) | 2.85502 | − | 6.53551i | 0.231573 | − | 0.530100i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.0714497 | + | 0.0541037i | −0.00575758 | + | 0.00435980i | ||||
\(155\) | 0.0178885 | − | 0.0431866i | 0.00143684 | − | 0.00346883i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.4671 | − | 4.74982i | 0.915172 | − | 0.379077i | 0.125138 | − | 0.992139i | \(-0.460063\pi\) |
0.790034 | + | 0.613063i | \(0.210063\pi\) | |||||||
\(158\) | 20.9987 | − | 5.48305i | 1.67056 | − | 0.436208i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.786092 | + | 0.959393i | −0.0621461 | + | 0.0758467i | ||||
\(161\) | − | 0.114439i | − | 0.00901904i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.79553 | + | 9.16322i | 0.297289 | + | 0.717719i | 0.999981 | + | 0.00622432i | \(0.00198128\pi\) |
−0.702692 | + | 0.711494i | \(0.748019\pi\) | |||||||
\(164\) | 6.03302 | + | 1.69944i | 0.471100 | + | 0.132704i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.79122 | − | 3.68611i | −0.216641 | − | 0.286097i | ||||
\(167\) | 8.08092 | + | 8.08092i | 0.625320 | + | 0.625320i | 0.946887 | − | 0.321567i | \(-0.104209\pi\) |
−0.321567 | + | 0.946887i | \(0.604209\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.939459 | + | 0.939459i | −0.0722661 | + | 0.0722661i | ||||
\(170\) | 0.595815 | + | 0.0823157i | 0.0456969 | + | 0.00631333i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.852529 | + | 7.18363i | 0.0650047 | + | 0.547747i | ||||
\(173\) | −1.73554 | + | 0.718885i | −0.131951 | + | 0.0546558i | −0.447682 | − | 0.894193i | \(-0.647750\pi\) |
0.315731 | + | 0.948849i | \(0.397750\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.0836259 | 0.00632153 | ||||||||
\(176\) | −12.1383 | + | 8.83063i | −0.914956 | + | 0.665634i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.45862 | − | 2.48954i | 0.109328 | − | 0.186599i | ||||
\(179\) | −2.93125 | − | 7.07665i | −0.219092 | − | 0.528934i | 0.775672 | − | 0.631136i | \(-0.217411\pi\) |
−0.994764 | + | 0.102202i | \(0.967411\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.2266 | + | 8.37811i | 1.50343 | + | 0.622740i | 0.974189 | − | 0.225733i | \(-0.0724777\pi\) |
0.529239 | + | 0.848473i | \(0.322478\pi\) | |||||||
\(182\) | 0.0895525 | + | 0.0123723i | 0.00663808 | + | 0.000917094i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.367280 | − | 19.1634i | 0.0270762 | − | 1.41274i | ||||
\(185\) | 0.424013 | − | 0.424013i | 0.0311741 | − | 0.0311741i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.72510 | + | 2.78563i | 0.491788 | + | 0.203705i | ||||
\(188\) | −2.36696 | − | 4.22340i | −0.172628 | − | 0.308023i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.756500 | − | 0.197533i | 0.0548823 | − | 0.0143306i | ||||
\(191\) | 2.52579 | 0.182760 | 0.0913800 | − | 0.995816i | \(-0.470872\pi\) | ||||
0.0913800 | + | 0.995816i | \(0.470872\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.18898 | −0.445492 | −0.222746 | − | 0.974876i | \(-0.571502\pi\) | ||||
−0.222746 | + | 0.974876i | \(0.571502\pi\) | |||||||
\(194\) | 16.2636 | − | 4.24666i | 1.16766 | − | 0.304892i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.84426 | + | 12.2123i | 0.488876 | + | 0.872307i | ||||
\(197\) | 22.6357 | + | 9.37602i | 1.61273 | + | 0.668014i | 0.993142 | − | 0.116915i | \(-0.0373005\pi\) |
0.619586 | + | 0.784929i | \(0.287301\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.71266 | + | 1.71266i | −0.121407 | + | 0.121407i | −0.765200 | − | 0.643793i | \(-0.777360\pi\) |
0.643793 | + | 0.765200i | \(0.277360\pi\) | |||||||
\(200\) | 14.0036 | + | 0.268389i | 0.990203 | + | 0.0189780i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −14.6079 | − | 2.01817i | −1.02781 | − | 0.141998i | ||||
\(203\) | −0.0730909 | − | 0.0302753i | −0.00512998 | − | 0.00212491i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.262955 | + | 0.634830i | 0.0183656 | + | 0.0443385i | ||||
\(206\) | −1.69152 | + | 2.88705i | −0.117854 | + | 0.201150i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 14.9563 | + | 2.35921i | 1.03703 | + | 0.163582i | ||||
\(209\) | 9.46232 | 0.654522 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.84986 | − | 3.66573i | 0.609249 | − | 0.252359i | −0.0566581 | − | 0.998394i | \(-0.518045\pi\) |
0.665908 | + | 0.746034i | \(0.268045\pi\) | |||||||
\(212\) | 0.768324 | + | 6.47410i | 0.0527687 | + | 0.444643i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 21.2516 | + | 2.93605i | 1.45273 | + | 0.200704i | ||||
\(215\) | −0.560780 | + | 0.560780i | −0.0382449 | + | 0.0382449i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.00254583 | + | 0.00254583i | 0.000172822 | + | 0.000172822i | ||||
\(218\) | 6.36232 | + | 8.40213i | 0.430911 | + | 0.569064i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.58395 | − | 0.446184i | −0.106790 | − | 0.0300817i | ||||
\(221\) | −2.80988 | − | 6.78364i | −0.189013 | − | 0.456317i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 25.7423i | − | 1.72383i | −0.507049 | − | 0.861917i | \(-0.669264\pi\) | ||
0.507049 | − | 0.861917i | \(-0.330736\pi\) | |||||||
\(224\) | −0.0450989 | − | 0.0842149i | −0.00301330 | − | 0.00562684i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.4479 | + | 5.07812i | −1.29365 | + | 0.337792i | ||||
\(227\) | 20.1573 | − | 8.34944i | 1.33789 | − | 0.554172i | 0.404994 | − | 0.914319i | \(-0.367274\pi\) |
0.932895 | + | 0.360147i | \(0.117274\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.08085 | − | 5.02362i | 0.137507 | − | 0.331970i | −0.840093 | − | 0.542442i | \(-0.817500\pi\) |
0.977600 | + | 0.210471i | \(0.0674999\pi\) | |||||||
\(230\) | 1.67517 | − | 1.26849i | 0.110457 | − | 0.0836414i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.1423 | − | 5.30433i | −0.797180 | − | 0.348246i | ||||
\(233\) | 11.8444 | + | 11.8444i | 0.775951 | + | 0.775951i | 0.979140 | − | 0.203188i | \(-0.0651304\pi\) |
−0.203188 | + | 0.979140i | \(0.565130\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.203114 | − | 0.490362i | 0.0132497 | − | 0.0319877i | ||||
\(236\) | −0.919085 | − | 7.74445i | −0.0598273 | − | 0.504121i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.0234189 | + | 0.0399709i | −0.00151802 | + | 0.00259093i | ||||
\(239\) | − | 10.0203i | − | 0.648161i | −0.946030 | − | 0.324080i | \(-0.894945\pi\) | ||
0.946030 | − | 0.324080i | \(-0.105055\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.24829i | 0.144825i | 0.997375 | + | 0.0724124i | \(0.0230698\pi\) | ||||
−0.997375 | + | 0.0724124i | \(0.976930\pi\) | |||||||
\(242\) | −3.76109 | − | 2.20362i | −0.241772 | − | 0.141654i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.64094 | + | 5.89081i | −0.297106 | + | 0.377121i | ||||
\(245\) | −0.587322 | + | 1.41792i | −0.0375226 | + | 0.0905876i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.74912 | − | 6.74912i | −0.429436 | − | 0.429436i | ||||
\(248\) | 0.418142 | + | 0.434483i | 0.0265520 | + | 0.0275897i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.86289 | + | 2.46014i | 0.117819 | + | 0.155593i | ||||
\(251\) | 7.33649 | − | 17.7119i | 0.463075 | − | 1.11796i | −0.504053 | − | 0.863673i | \(-0.668158\pi\) |
0.967128 | − | 0.254290i | \(-0.0818418\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.4941 | − | 9.73159i | 1.47706 | − | 0.611820i | ||||
\(254\) | −0.212544 | − | 0.813988i | −0.0133362 | − | 0.0510741i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.28177 | − | 14.2470i | −0.455111 | − | 0.890435i | ||||
\(257\) | − | 26.7917i | − | 1.67122i | −0.549325 | − | 0.835609i | \(-0.685115\pi\) | ||
0.549325 | − | 0.835609i | \(-0.314885\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0176744 | + | 0.0426697i | 0.00109823 | + | 0.00265137i | ||||
\(260\) | 0.811529 | + | 1.44802i | 0.0503289 | + | 0.0898025i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.5473 | − | 11.0156i | 0.898733 | − | 0.680546i | ||||
\(263\) | −17.1686 | − | 17.1686i | −1.05866 | − | 1.05866i | −0.998169 | − | 0.0604905i | \(-0.980734\pi\) |
−0.0604905 | − | 0.998169i | \(-0.519266\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.505391 | + | 0.505391i | −0.0310459 | + | 0.0310459i | ||||
\(266\) | −0.00824153 | + | 0.0596535i | −0.000505321 | + | 0.00365759i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.8392 | + | 12.4785i | 0.967531 | + | 0.762247i | ||||
\(269\) | −20.0795 | + | 8.31721i | −1.22427 | + | 0.507109i | −0.898765 | − | 0.438431i | \(-0.855534\pi\) |
−0.325505 | + | 0.945540i | \(0.605534\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.7852 | 1.68783 | 0.843915 | − | 0.536476i | \(-0.180245\pi\) | ||||
0.843915 | + | 0.536476i | \(0.180245\pi\) | |||||||
\(272\) | −4.04990 | + | 6.61818i | −0.245562 | + | 0.401286i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.6814 | − | 10.9454i | −1.12858 | − | 0.661236i | ||||
\(275\) | 7.11134 | + | 17.1683i | 0.428830 | + | 1.03529i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.1201 | − | 5.84875i | −0.848396 | − | 0.351417i | −0.0842374 | − | 0.996446i | \(-0.526845\pi\) |
−0.764158 | + | 0.645029i | \(0.776845\pi\) | |||||||
\(278\) | 1.79618 | − | 13.0011i | 0.107728 | − | 0.779752i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.00419249 | − | 0.00959715i | 0.000250549 | − | 0.000573539i | ||||
\(281\) | −17.2705 | + | 17.2705i | −1.03027 | + | 1.03027i | −0.0307455 | + | 0.999527i | \(0.509788\pi\) |
−0.999527 | + | 0.0307455i | \(0.990212\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.6752 | + | 11.0492i | 1.58568 | + | 0.656808i | 0.989300 | − | 0.145897i | \(-0.0466067\pi\) |
0.596376 | + | 0.802705i | \(0.296607\pi\) | |||||||
\(284\) | −23.0220 | − | 6.48505i | −1.36610 | − | 0.384817i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.07531 | + | 19.4371i | 0.300109 | + | 1.14934i | ||||
\(287\) | −0.0529240 | −0.00312401 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.2374 | −0.778669 | ||||||||
\(290\) | −0.366996 | − | 1.40550i | −0.0215507 | − | 0.0825337i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.47837 | + | 30.0982i | −0.496159 | + | 1.76137i | ||||
\(293\) | 25.5733 | + | 10.5928i | 1.49401 | + | 0.618838i | 0.972185 | − | 0.234215i | \(-0.0752520\pi\) |
0.521823 | + | 0.853054i | \(0.325252\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.604559 | − | 0.604559i | 0.0351988 | − | 0.0351988i | ||||
\(296\) | 2.82272 | + | 7.20199i | 0.164067 | + | 0.418607i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.15416 | + | 15.5921i | −0.124787 | + | 0.903228i | ||||
\(299\) | −23.6987 | − | 9.81630i | −1.37053 | − | 0.567691i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0233753 | − | 0.0564330i | −0.00134733 | − | 0.00325274i | ||||
\(302\) | 16.7647 | + | 9.82243i | 0.964701 | + | 0.565217i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.57154 | + | 9.96284i | −0.0901339 | + | 0.571408i | ||||
\(305\) | −0.822146 | −0.0470760 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.03022 | + | 0.426730i | −0.0587976 | + | 0.0243548i | −0.411888 | − | 0.911234i | \(-0.635131\pi\) |
0.353091 | + | 0.935589i | \(0.385131\pi\) | |||||||
\(308\) | 0.0784364 | − | 0.0995604i | 0.00446933 | − | 0.00567298i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.00904721 | + | 0.0654852i | −0.000513847 | + | 0.00371931i | ||||
\(311\) | −23.9114 | + | 23.9114i | −1.35589 | + | 1.35589i | −0.476971 | + | 0.878919i | \(0.658265\pi\) |
−0.878919 | + | 0.476971i | \(0.841735\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.43744 | − | 4.43744i | −0.250819 | − | 0.250819i | 0.570487 | − | 0.821306i | \(-0.306754\pi\) |
−0.821306 | + | 0.570487i | \(0.806754\pi\) | |||||||
\(314\) | −13.9937 | + | 10.5964i | −0.789712 | + | 0.597991i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −26.7742 | + | 15.0053i | −1.50616 | + | 0.844115i | ||||
\(317\) | 2.38033 | + | 5.74662i | 0.133693 | + | 0.322763i | 0.976522 | − | 0.215419i | \(-0.0691116\pi\) |
−0.842829 | + | 0.538181i | \(0.819112\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 17.5800i | − | 0.984291i | ||||||
\(320\) | 0.732855 | − | 1.59364i | 0.0409678 | − | 0.0890870i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.0408881 | + | 0.156591i | 0.00227860 | + | 0.00872646i | ||||
\(323\) | 4.51878 | − | 1.87174i | 0.251432 | − | 0.104146i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.17324 | − | 17.3177i | 0.397900 | − | 0.960616i | ||||
\(326\) | −8.46750 | − | 11.1822i | −0.468972 | − | 0.619327i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.86240 | − | 0.169854i | −0.489344 | − | 0.00937864i | ||||
\(329\) | 0.0289066 | + | 0.0289066i | 0.00159367 | + | 0.00159367i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.95616 | + | 16.7937i | −0.382345 | + | 0.923063i | 0.609166 | + | 0.793043i | \(0.291504\pi\) |
−0.991511 | + | 0.130021i | \(0.958496\pi\) | |||||||
\(332\) | 5.13635 | + | 4.04655i | 0.281894 | + | 0.222083i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13.9447 | − | 8.17016i | −0.763018 | − | 0.447051i | ||||
\(335\) | 2.21058i | 0.120777i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 19.6482i | − | 1.07030i | −0.844756 | − | 0.535152i | \(-0.820254\pi\) | ||
0.844756 | − | 0.535152i | \(-0.179746\pi\) | |||||||
\(338\) | 0.949834 | − | 1.62116i | 0.0516641 | − | 0.0881793i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.844685 | + | 0.100244i | −0.0458095 | + | 0.00543651i | ||||
\(341\) | −0.306165 | + | 0.739147i | −0.0165797 | + | 0.0400270i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.167175 | − | 0.167175i | −0.00902659 | − | 0.00902659i | ||||
\(344\) | −3.73320 | − | 9.52501i | −0.201281 | − | 0.513554i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.11795 | − | 1.60377i | 0.113862 | − | 0.0862193i | ||||
\(347\) | −6.02247 | + | 14.5395i | −0.323303 | + | 0.780523i | 0.675755 | + | 0.737126i | \(0.263818\pi\) |
−0.999058 | + | 0.0433963i | \(0.986182\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.4951 | − | 4.34720i | 0.561788 | − | 0.232700i | −0.0836734 | − | 0.996493i | \(-0.526665\pi\) |
0.645461 | + | 0.763793i | \(0.276665\pi\) | |||||||
\(350\) | −0.114428 | + | 0.0298789i | −0.00611645 | + | 0.00159709i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.4541 | − | 16.4202i | 0.717106 | − | 0.875198i | ||||
\(353\) | − | 30.0234i | − | 1.59798i | −0.601342 | − | 0.798992i | \(-0.705367\pi\) | ||
0.601342 | − | 0.798992i | \(-0.294633\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.00343 | − | 2.42251i | −0.0532568 | − | 0.128573i | ||||
\(356\) | −1.10639 | + | 3.92769i | −0.0586385 | + | 0.208167i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.53936 | + | 8.63593i | 0.345616 | + | 0.456423i | ||||
\(359\) | 10.5864 | + | 10.5864i | 0.558730 | + | 0.558730i | 0.928946 | − | 0.370216i | \(-0.120716\pi\) |
−0.370216 | + | 0.928946i | \(0.620716\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.93925 | + | 8.93925i | −0.470487 | + | 0.470487i | ||||
\(362\) | −30.6701 | − | 4.23728i | −1.61199 | − | 0.222707i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.126958 | + | 0.0150670i | −0.00665443 | + | 0.000789725i | ||||
\(365\) | −3.16711 | + | 1.31186i | −0.165774 | + | 0.0686660i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.82385 | −0.199604 | −0.0998018 | − | 0.995007i | \(-0.531821\pi\) | ||||
−0.0998018 | + | 0.995007i | \(0.531821\pi\) | |||||||
\(368\) | 6.34436 | + | 26.3531i | 0.330722 | + | 1.37375i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.428696 | + | 0.731689i | −0.0222868 | + | 0.0380387i | ||||
\(371\) | −0.0210665 | − | 0.0508591i | −0.00109372 | − | 0.00264047i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.5062 | + | 9.73660i | 1.21711 | + | 0.504142i | 0.896489 | − | 0.443067i | \(-0.146110\pi\) |
0.320617 | + | 0.947209i | \(0.396110\pi\) | |||||||
\(374\) | −10.1975 | − | 1.40885i | −0.527299 | − | 0.0728498i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.74778 | + | 4.93333i | 0.244848 | + | 0.254417i | ||||
\(377\) | −12.5392 | + | 12.5392i | −0.645799 | + | 0.645799i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.96668 | − | 1.22884i | −0.152388 | − | 0.0631212i | 0.305186 | − | 0.952293i | \(-0.401281\pi\) |
−0.457574 | + | 0.889172i | \(0.651281\pi\) | |||||||
\(380\) | −0.964569 | + | 0.540583i | −0.0494814 | + | 0.0277313i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.45613 | + | 0.902446i | −0.176831 | + | 0.0461731i | ||||
\(383\) | 4.97811 | 0.254369 | 0.127185 | − | 0.991879i | \(-0.459406\pi\) | ||||
0.127185 | + | 0.991879i | \(0.459406\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0138951 | 0.000708158 | ||||||||
\(386\) | 8.46860 | − | 2.21127i | 0.431040 | − | 0.112551i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −20.7368 | + | 11.6217i | −1.05275 | + | 0.590003i | ||||
\(389\) | −8.47226 | − | 3.50933i | −0.429561 | − | 0.177930i | 0.157418 | − | 0.987532i | \(-0.449683\pi\) |
−0.586979 | + | 0.809602i | \(0.699683\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.29474 | − | 9.29474i | 0.470055 | − | 0.470055i | ||||
\(392\) | −13.7286 | − | 14.2651i | −0.693399 | − | 0.720497i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −34.3232 | − | 4.74198i | −1.72918 | − | 0.238897i | ||||
\(395\) | −3.10864 | − | 1.28764i | −0.156413 | − | 0.0647883i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.22095 | − | 2.94765i | −0.0612780 | − | 0.147938i | 0.890275 | − | 0.455424i | \(-0.150512\pi\) |
−0.951553 | + | 0.307486i | \(0.900512\pi\) | |||||||
\(398\) | 1.73157 | − | 2.95541i | 0.0867958 | − | 0.148141i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −19.2575 | + | 4.63613i | −0.962875 | + | 0.231806i | ||||
\(401\) | −27.8490 | −1.39071 | −0.695356 | − | 0.718665i | \(-0.744753\pi\) | ||||
−0.695356 | + | 0.718665i | \(0.744753\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.745581 | − | 0.308830i | 0.0371400 | − | 0.0153839i | ||||
\(404\) | 20.7095 | − | 2.45774i | 1.03034 | − | 0.122277i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.110830 | + | 0.0153119i | 0.00550040 | + | 0.000759917i | ||||
\(407\) | −7.25705 | + | 7.25705i | −0.359719 | + | 0.359719i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.776560 | − | 0.776560i | −0.0383984 | − | 0.0383984i | 0.687647 | − | 0.726045i | \(-0.258644\pi\) |
−0.726045 | + | 0.687647i | \(0.758644\pi\) | |||||||
\(410\) | −0.586631 | − | 0.774709i | −0.0289716 | − | 0.0382602i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.28305 | − | 4.55482i | 0.0632111 | − | 0.224400i | ||||
\(413\) | 0.0252002 | + | 0.0608387i | 0.00124002 | + | 0.00299368i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.716849i | 0.0351888i | ||||||||
\(416\) | −21.3082 | + | 2.11559i | −1.04472 | + | 0.103725i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −12.9476 | + | 3.38081i | −0.633289 | + | 0.165361i | ||||
\(419\) | −6.17161 | + | 2.55636i | −0.301503 | + | 0.124887i | −0.528306 | − | 0.849054i | \(-0.677173\pi\) |
0.226803 | + | 0.973941i | \(0.427173\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.54054 | − | 10.9618i | 0.221293 | − | 0.534248i | −0.773773 | − | 0.633462i | \(-0.781633\pi\) |
0.995066 | + | 0.0992148i | \(0.0316331\pi\) | |||||||
\(422\) | −10.7998 | + | 8.17794i | −0.525728 | + | 0.398096i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.36447 | − | 8.58423i | −0.163393 | − | 0.416887i | ||||
\(425\) | 6.79211 | + | 6.79211i | 0.329466 | + | 0.329466i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0242326 | − | 0.0585026i | 0.00117270 | − | 0.00283114i | ||||
\(428\) | −30.1284 | + | 3.57553i | −1.45631 | + | 0.172830i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.566973 | − | 0.967697i | 0.0273418 | − | 0.0466665i | ||||
\(431\) | − | 14.2802i | − | 0.687851i | −0.938997 | − | 0.343925i | \(-0.888243\pi\) | ||
0.938997 | − | 0.343925i | \(-0.111757\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.5612i | 1.75702i | 0.477723 | + | 0.878510i | \(0.341462\pi\) | ||||
−0.477723 | + | 0.878510i | \(0.658538\pi\) | |||||||
\(434\) | −0.00439316 | − | 0.00257395i | −0.000210878 | − | 0.000123553i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.7078 | − | 9.22372i | −0.560702 | − | 0.441736i | ||||
\(437\) | 6.53892 | − | 15.7864i | 0.312799 | − | 0.755164i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.9584 | − | 19.9584i | −0.952563 | − | 0.952563i | 0.0463616 | − | 0.998925i | \(-0.485237\pi\) |
−0.998925 | + | 0.0463616i | \(0.985237\pi\) | |||||||
\(440\) | 2.32680 | + | 0.0445948i | 0.110926 | + | 0.00212598i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.26859 | + | 8.27835i | 0.298167 | + | 0.393761i | ||||
\(443\) | 1.86847 | − | 4.51089i | 0.0887737 | − | 0.214319i | −0.873257 | − | 0.487260i | \(-0.837996\pi\) |
0.962031 | + | 0.272941i | \(0.0879965\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.413294 | + | 0.171192i | −0.0195920 | + | 0.00811528i | ||||
\(446\) | 9.19753 | + | 35.2241i | 0.435516 | + | 1.66791i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.0917998 | + | 0.0991208i | 0.00433713 | + | 0.00468302i | ||||
\(449\) | 18.5243i | 0.874217i | 0.899409 | + | 0.437109i | \(0.143997\pi\) | ||||
−0.899409 | + | 0.437109i | \(0.856003\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.50053 | − | 10.8652i | −0.211921 | − | 0.511624i | ||||
\(452\) | 24.7969 | − | 13.8971i | 1.16635 | − | 0.653667i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −24.5988 | + | 18.6269i | −1.15448 | + | 0.874204i | ||||
\(455\) | −0.00991083 | − | 0.00991083i | −0.000464627 | − | 0.000464627i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.31755 | − | 4.31755i | 0.201967 | − | 0.201967i | −0.598876 | − | 0.800842i | \(-0.704386\pi\) |
0.800842 | + | 0.598876i | \(0.204386\pi\) | |||||||
\(458\) | −1.05240 | + | 7.61748i | −0.0491756 | + | 0.355941i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.83898 | + | 2.33424i | −0.0857427 | + | 0.108834i | ||||
\(461\) | −8.85130 | + | 3.66633i | −0.412246 | + | 0.170758i | −0.579161 | − | 0.815213i | \(-0.696620\pi\) |
0.166915 | + | 0.985971i | \(0.446620\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.4291 | −1.41416 | −0.707080 | − | 0.707134i | \(-0.749988\pi\) | ||||
−0.707080 | + | 0.707134i | \(0.749988\pi\) | |||||||
\(464\) | 18.5099 | + | 2.91975i | 0.859301 | + | 0.135546i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.4390 | − | 11.9752i | −0.946818 | − | 0.554740i | ||||
\(467\) | 11.8108 | + | 28.5138i | 0.546539 | + | 1.31946i | 0.920038 | + | 0.391830i | \(0.128158\pi\) |
−0.373499 | + | 0.927631i | \(0.621842\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.157301 | − | 0.0651563i | −0.00726349 | − | 0.00300864i | ||||
\(470\) | −0.102726 | + | 0.743551i | −0.00473842 | + | 0.0342974i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.02465 | + | 10.2686i | 0.185249 | + | 0.472652i | ||||
\(473\) | 9.59784 | − | 9.59784i | 0.441309 | − | 0.441309i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.5359 | + | 4.77831i | 0.529301 | + | 0.219244i | ||||
\(476\) | 0.0177637 | − | 0.0630611i | 0.000814196 | − | 0.00289040i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.58018 | + | 13.7112i | 0.163754 | + | 0.627134i | ||||
\(479\) | 33.1421 | 1.51430 | 0.757151 | − | 0.653240i | \(-0.226591\pi\) | ||||
0.757151 | + | 0.653240i | \(0.226591\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.3524 | 0.472027 | ||||||||
\(482\) | −0.803295 | − | 3.07641i | −0.0365891 | − | 0.140127i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.93377 | + | 1.67148i | 0.269717 | + | 0.0759764i | ||||
\(485\) | −2.40766 | − | 0.997286i | −0.109326 | − | 0.0452844i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.33714 | − | 8.33714i | 0.377792 | − | 0.377792i | −0.492513 | − | 0.870305i | \(-0.663922\pi\) |
0.870305 | + | 0.492513i | \(0.163922\pi\) | |||||||
\(488\) | 4.24562 | − | 9.71878i | 0.192190 | − | 0.439949i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.297042 | − | 2.15004i | 0.0134190 | − | 0.0971288i | ||||
\(491\) | −9.27696 | − | 3.84264i | −0.418664 | − | 0.173416i | 0.163399 | − | 0.986560i | \(-0.447754\pi\) |
−0.582063 | + | 0.813144i | \(0.697754\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.47750 | − | 8.39542i | −0.156619 | − | 0.378111i | ||||
\(494\) | 11.6465 | + | 6.82365i | 0.523999 | + | 0.307011i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.727396 | − | 0.445120i | −0.0326610 | − | 0.0199865i | ||||
\(497\) | 0.201957 | 0.00905903 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.2993 | − | 4.26612i | 0.461061 | − | 0.190978i | −0.140048 | − | 0.990145i | \(-0.544726\pi\) |
0.601109 | + | 0.799167i | \(0.294726\pi\) | |||||||
\(500\) | −3.42804 | − | 2.70070i | −0.153307 | − | 0.120779i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.71048 | + | 26.8570i | −0.165607 | + | 1.19869i | ||||
\(503\) | −17.7557 | + | 17.7557i | −0.791687 | + | 0.791687i | −0.981768 | − | 0.190082i | \(-0.939125\pi\) |
0.190082 | + | 0.981768i | \(0.439125\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.61666 | + | 1.61666i | 0.0719404 | + | 0.0719404i | ||||
\(506\) | −28.6708 | + | 21.7103i | −1.27457 | + | 0.965142i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.581663 | + | 1.03787i | 0.0258071 | + | 0.0460479i | ||||
\(509\) | −16.3316 | − | 39.4279i | −0.723884 | − | 1.74761i | −0.661971 | − | 0.749530i | \(-0.730280\pi\) |
−0.0619134 | − | 0.998082i | \(-0.519720\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 0.264033i | − | 0.0116801i | ||||||
\(512\) | 15.0542 | + | 16.8929i | 0.665309 | + | 0.746568i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.57245 | + | 36.6600i | 0.422223 | + | 1.61700i | ||||
\(515\) | 0.479285 | − | 0.198526i | 0.0211198 | − | 0.00874811i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.47634 | + | 8.39262i | −0.152889 | + | 0.369107i | ||||
\(518\) | −0.0394301 | − | 0.0520716i | −0.00173246 | − | 0.00228790i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.62781 | − | 1.69143i | −0.0713842 | − | 0.0741740i | ||||
\(521\) | 2.59199 | + | 2.59199i | 0.113557 | + | 0.113557i | 0.761602 | − | 0.648045i | \(-0.224413\pi\) |
−0.648045 | + | 0.761602i | \(0.724413\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.55437 | − | 15.8236i | 0.286602 | − | 0.691919i | −0.713358 | − | 0.700800i | \(-0.752827\pi\) |
0.999961 | + | 0.00888020i | \(0.00282669\pi\) | |||||||
\(524\) | −15.9698 | + | 20.2707i | −0.697642 | + | 0.885528i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 29.6266 | + | 17.3582i | 1.29178 | + | 0.756852i | ||||
\(527\) | 0.413546i | 0.0180143i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 22.9212i | − | 0.996573i | ||||||
\(530\) | 0.510973 | − | 0.872117i | 0.0221952 | − | 0.0378823i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.0100366 | − | 0.0845707i | −0.000435140 | − | 0.00366661i | ||||
\(533\) | −4.53970 | + | 10.9598i | −0.196636 | + | 0.474722i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.35193 | − | 2.35193i | −0.101683 | − | 0.101683i | ||||
\(536\) | −26.1318 | − | 11.4156i | −1.12872 | − | 0.493079i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 24.5039 | − | 18.5550i | 1.05644 | − | 0.799962i | ||||
\(539\) | 10.0521 | − | 24.2680i | 0.432975 | − | 1.04529i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.3688 | − | 12.9934i | 1.34865 | − | 0.558628i | 0.412733 | − | 0.910852i | \(-0.364574\pi\) |
0.935916 | + | 0.352224i | \(0.114574\pi\) | |||||||
\(542\) | −38.0195 | + | 9.92743i | −1.63308 | + | 0.426420i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.17700 | − | 10.5029i | 0.136213 | − | 0.450308i | ||||
\(545\) | − | 1.63399i | − | 0.0699924i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.7932 | + | 40.5423i | 0.718024 | + | 1.73346i | 0.678903 | + | 0.734228i | \(0.262456\pi\) |
0.0391202 | + | 0.999235i | \(0.487544\pi\) | |||||||
\(548\) | 29.4731 | + | 8.30228i | 1.25903 | + | 0.354656i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −15.8648 | − | 20.9512i | −0.676477 | − | 0.893360i | ||||
\(551\) | −8.35270 | − | 8.35270i | −0.355837 | − | 0.355837i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.183253 | − | 0.183253i | 0.00779271 | − | 0.00779271i | ||||
\(554\) | 21.4108 | + | 2.95804i | 0.909657 | + | 0.125675i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.18740 | + | 18.4316i | 0.0927663 | + | 0.781673i | ||||
\(557\) | −23.9875 | + | 9.93595i | −1.01638 | + | 0.421000i | −0.827780 | − | 0.561053i | \(-0.810396\pi\) |
−0.188604 | + | 0.982053i | \(0.560396\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.6916 | −0.579091 | ||||||||
\(560\) | −0.00230775 | + | 0.0146301i | −9.75200e−5 | + | 0.000618233i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17.4612 | − | 29.8025i | 0.736558 | − | 1.25714i | ||||
\(563\) | 15.7397 | + | 37.9991i | 0.663350 | + | 1.60147i | 0.792519 | + | 0.609847i | \(0.208769\pi\) |
−0.129169 | + | 0.991623i | \(0.541231\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.87906 | + | 1.19255i | 0.121123 | + | 0.0501708i | ||||
\(566\) | −40.4484 | − | 5.58822i | −1.70017 | − | 0.234890i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 33.8188 | + | 0.648163i | 1.41901 | + | 0.0271963i | ||||
\(569\) | −26.5263 | + | 26.5263i | −1.11204 | + | 1.11204i | −0.119168 | + | 0.992874i | \(0.538023\pi\) |
−0.992874 | + | 0.119168i | \(0.961977\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.44812 | + | 1.84247i | 0.186148 | + | 0.0771050i | 0.473811 | − | 0.880627i | \(-0.342878\pi\) |
−0.287663 | + | 0.957732i | \(0.592878\pi\) | |||||||
\(572\) | −13.8895 | − | 24.7831i | −0.580747 | − | 1.03624i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.0724178 | − | 0.0189093i | 0.00302266 | − | 0.000789260i | ||||
\(575\) | 33.5568 | 1.39942 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.0428 | −1.12581 | −0.562903 | − | 0.826523i | \(-0.690315\pi\) | ||||
−0.562903 | + | 0.826523i | \(0.690315\pi\) | |||||||
\(578\) | 18.1132 | − | 4.72961i | 0.753408 | − | 0.196726i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.00435 | + | 1.79207i | 0.0417032 | + | 0.0744116i | ||||
\(581\) | −0.0510098 | − | 0.0211290i | −0.00211624 | − | 0.000876577i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.64986 | − | 8.64986i | 0.358240 | − | 0.358240i | ||||
\(584\) | 0.847389 | − | 44.2137i | 0.0350652 | − | 1.82958i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −38.7776 | − | 5.35738i | −1.60189 | − | 0.221311i | ||||
\(587\) | −24.7371 | − | 10.2464i | −1.02101 | − | 0.422915i | −0.191549 | − | 0.981483i | \(-0.561351\pi\) |
−0.829459 | + | 0.558568i | \(0.811351\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.205721 | + | 0.496653i | 0.00847657 | + | 0.0204642i | ||||
\(590\) | −0.611236 | + | 1.04324i | −0.0251642 | + | 0.0429497i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.43565 | − | 8.84620i | −0.264503 | − | 0.363577i | ||||
\(593\) | 14.7443 | 0.605477 | 0.302738 | − | 0.953074i | \(-0.402099\pi\) | ||||
0.302738 | + | 0.953074i | \(0.402099\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.00663566 | − | 0.00274858i | 0.000272035 | − | 0.000112681i | ||||
\(596\) | −2.62334 | − | 22.1049i | −0.107456 | − | 0.905453i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 35.9350 | + | 4.96466i | 1.46949 | + | 0.203020i | ||||
\(599\) | −3.57851 | + | 3.57851i | −0.146214 | + | 0.146214i | −0.776424 | − | 0.630210i | \(-0.782969\pi\) |
0.630210 | + | 0.776424i | \(0.282969\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.91144 | − | 2.91144i | −0.118760 | − | 0.118760i | 0.645229 | − | 0.763989i | \(-0.276762\pi\) |
−0.763989 | + | 0.645229i | \(0.776762\pi\) | |||||||
\(602\) | 0.0521483 | + | 0.0688675i | 0.00212541 | + | 0.00280683i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −26.4492 | − | 7.45048i | −1.07620 | − | 0.303156i | ||||
\(605\) | 0.258629 | + | 0.624386i | 0.0105148 | + | 0.0253849i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.29692i | 0.174406i | 0.996191 | + | 0.0872032i | \(0.0277929\pi\) | ||||
−0.996191 | + | 0.0872032i | \(0.972207\pi\) | |||||||
\(608\) | −1.40925 | − | 14.1940i | −0.0571527 | − | 0.575643i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.12497 | − | 0.293746i | 0.0455488 | − | 0.0118934i | ||||
\(611\) | 8.46568 | − | 3.50660i | 0.342485 | − | 0.141862i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.8444 | − | 38.2518i | 0.639949 | − | 1.54497i | −0.186797 | − | 0.982399i | \(-0.559811\pi\) |
0.826746 | − | 0.562575i | \(-0.190189\pi\) | |||||||
\(614\) | 1.25722 | − | 0.951998i | 0.0507371 | − | 0.0384195i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.0717551 | + | 0.164257i | −0.00289110 | + | 0.00661810i | ||||
\(617\) | −16.9817 | − | 16.9817i | −0.683659 | − | 0.683659i | 0.277163 | − | 0.960823i | \(-0.410606\pi\) |
−0.960823 | + | 0.277163i | \(0.910606\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.89007 | − | 14.2199i | 0.236742 | − | 0.571545i | −0.760200 | − | 0.649689i | \(-0.774899\pi\) |
0.996942 | + | 0.0781434i | \(0.0248992\pi\) | |||||||
\(620\) | −0.0110177 | − | 0.0928383i | −0.000442483 | − | 0.00372847i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.1754 | − | 41.2621i | 0.969347 | − | 1.65446i | ||||
\(623\) | − | 0.0344552i | − | 0.00138042i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.2812i | 0.971248i | ||||||||
\(626\) | 7.65737 | + | 4.48645i | 0.306050 | + | 0.179314i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.3621 | − | 19.4993i | 0.613014 | − | 0.778108i | ||||
\(629\) | −2.03013 | + | 4.90116i | −0.0809464 | + | 0.195422i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.5566 | + | 23.5566i | 0.937772 | + | 0.937772i | 0.998174 | − | 0.0604020i | \(-0.0192383\pi\) |
−0.0604020 | + | 0.998174i | \(0.519238\pi\) | |||||||
\(632\) | 31.2748 | − | 30.0985i | 1.24404 | − | 1.19725i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.31031 | − | 7.01284i | −0.210900 | − | 0.278515i | ||||
\(635\) | −0.0499139 | + | 0.120503i | −0.00198077 | + | 0.00478200i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.4792 | + | 10.1396i | −0.969902 | + | 0.401746i | ||||
\(638\) | 6.28120 | + | 24.0553i | 0.248675 | + | 0.952360i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.433398 | + | 2.44247i | −0.0171315 | + | 0.0965472i | ||||
\(641\) | − | 32.1521i | − | 1.26993i | −0.772540 | − | 0.634966i | \(-0.781014\pi\) | ||
0.772540 | − | 0.634966i | \(-0.218986\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.0638 | + | 41.1958i | 0.672932 | + | 1.62460i | 0.776603 | + | 0.629991i | \(0.216941\pi\) |
−0.103670 | + | 0.994612i | \(0.533059\pi\) | |||||||
\(644\) | −0.111897 | − | 0.199660i | −0.00440937 | − | 0.00786769i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.51445 | + | 4.17569i | −0.216963 | + | 0.164290i | ||||
\(647\) | 10.0224 | + | 10.0224i | 0.394023 | + | 0.394023i | 0.876119 | − | 0.482096i | \(-0.160124\pi\) |
−0.482096 | + | 0.876119i | \(0.660124\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.3471 | + | 10.3471i | −0.406161 | + | 0.406161i | ||||
\(650\) | −3.62791 | + | 26.2594i | −0.142298 | + | 1.02998i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.5817 | + | 12.2757i | 0.610227 | + | 0.480753i | ||||
\(653\) | −32.9549 | + | 13.6503i | −1.28962 | + | 0.534179i | −0.918873 | − | 0.394553i | \(-0.870899\pi\) |
−0.370750 | + | 0.928733i | \(0.620899\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.82906 | −0.110540 | ||||||||
\(656\) | 12.1874 | − | 2.93405i | 0.475839 | − | 0.114555i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.0498820 | − | 0.0292258i | −0.00194460 | − | 0.00113934i | ||||
\(659\) | 12.1112 | + | 29.2389i | 0.471784 | + | 1.13899i | 0.963374 | + | 0.268161i | \(0.0864159\pi\) |
−0.491590 | + | 0.870827i | \(0.663584\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.46878 | − | 0.608388i | −0.0571289 | − | 0.0236636i | 0.353936 | − | 0.935270i | \(-0.384843\pi\) |
−0.411065 | + | 0.911606i | \(0.634843\pi\) | |||||||
\(662\) | 3.51812 | − | 25.4648i | 0.136736 | − | 0.989716i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.47405 | − | 3.70186i | −0.328857 | − | 0.143660i | ||||
\(665\) | 0.00660189 | − | 0.00660189i | 0.000256010 | − | 0.000256010i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.3294 | − | 12.1486i | −1.13564 | − | 0.470397i | ||||
\(668\) | 22.0001 | + | 6.19721i | 0.851210 | + | 0.239777i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.789823 | − | 3.02482i | −0.0305135 | − | 0.116859i | ||||
\(671\) | 14.0712 | 0.543212 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.9627 | 0.730957 | 0.365478 | − | 0.930820i | \(-0.380905\pi\) | ||||
0.365478 | + | 0.930820i | \(0.380905\pi\) | |||||||
\(674\) | 7.02014 | + | 26.8853i | 0.270406 | + | 1.03558i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.720465 | + | 2.55765i | −0.0277102 | + | 0.0983713i | ||||
\(677\) | −30.8482 | − | 12.7778i | −1.18559 | − | 0.491089i | −0.299276 | − | 0.954166i | \(-0.596745\pi\) |
−0.886318 | + | 0.463077i | \(0.846745\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.141930 | − | 0.141930i | 0.00544679 | − | 0.00544679i | ||||
\(680\) | 1.12000 | − | 0.438967i | 0.0429499 | − | 0.0168336i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.154845 | − | 1.12079i | 0.00592931 | − | 0.0429173i | ||||
\(683\) | 23.3005 | + | 9.65139i | 0.891570 | + | 0.369300i | 0.780973 | − | 0.624565i | \(-0.214724\pi\) |
0.110597 | + | 0.993865i | \(0.464724\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.28461 | + | 3.10133i | 0.0490826 | + | 0.118496i | ||||
\(686\) | 0.288482 | + | 0.169021i | 0.0110143 | + | 0.00645325i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.51148 | + | 11.6996i | 0.324497 | + | 0.446042i | ||||
\(689\) | −12.3392 | −0.470087 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.6321 | − | 7.30344i | 0.670756 | − | 0.277836i | −0.0212009 | − | 0.999775i | \(-0.506749\pi\) |
0.691957 | + | 0.721939i | \(0.256749\pi\) | |||||||
\(692\) | −2.32506 | + | 2.95123i | −0.0883854 | + | 0.112189i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.04590 | − | 22.0467i | 0.115621 | − | 0.836883i | ||||
\(695\) | −1.43883 | + | 1.43883i | −0.0545781 | + | 0.0545781i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.29850 | − | 4.29850i | −0.162817 | − | 0.162817i | ||||
\(698\) | −12.8075 | + | 9.69823i | −0.484773 | + | 0.367083i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.145901 | − | 0.0817687i | 0.00551453 | − | 0.00309057i | ||||
\(701\) | 3.99504 | + | 9.64488i | 0.150891 | + | 0.364282i | 0.981192 | − | 0.193032i | \(-0.0618321\pi\) |
−0.830302 | + | 0.557314i | \(0.811832\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.89601i | 0.260088i | ||||||||
\(704\) | −12.5429 | + | 27.2754i | −0.472730 | + | 1.02798i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.7271 | + | 41.0821i | 0.403721 | + | 1.54614i | ||||
\(707\) | −0.162689 | + | 0.0673882i | −0.00611857 | + | 0.00253439i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.5796 | + | 32.7841i | −0.509994 | + | 1.23123i | 0.433893 | + | 0.900965i | \(0.357140\pi\) |
−0.943887 | + | 0.330270i | \(0.892860\pi\) | |||||||
\(710\) | 2.23858 | + | 2.95628i | 0.0840123 | + | 0.110947i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.110581 | − | 5.76970i | 0.00414418 | − | 0.216229i | ||||
\(713\) | 1.02157 | + | 1.02157i | 0.0382582 | + | 0.0382582i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.19189 | − | 2.87747i | 0.0445741 | − | 0.107611i | ||||
\(716\) | −12.0336 | − | 9.48038i | −0.449716 | − | 0.354299i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18.2682 | − | 10.7033i | −0.681764 | − | 0.399445i | ||||
\(719\) | − | 33.9773i | − | 1.26714i | −0.773686 | − | 0.633570i | \(-0.781589\pi\) | ||
0.773686 | − | 0.633570i | \(-0.218411\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.0399566i | 0.00148806i | ||||||||
\(722\) | 9.03797 | − | 15.4258i | 0.336358 | − | 0.574089i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 43.4810 | − | 5.16018i | 1.61596 | − | 0.191776i | ||||
\(725\) | 8.87759 | − | 21.4324i | 0.329706 | − | 0.795980i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.66650 | − | 6.66650i | −0.247247 | − | 0.247247i | 0.572593 | − | 0.819840i | \(-0.305938\pi\) |
−0.819840 | + | 0.572593i | \(0.805938\pi\) | |||||||
\(728\) | 0.168338 | − | 0.0659780i | 0.00623904 | − | 0.00244531i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.86496 | − | 2.92665i | 0.143048 | − | 0.108320i | ||||
\(731\) | 2.68495 | − | 6.48204i | 0.0993065 | − | 0.239747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.4629 | + | 8.47602i | −0.755815 | + | 0.313069i | −0.727112 | − | 0.686519i | \(-0.759138\pi\) |
−0.0287034 | + | 0.999588i | \(0.509138\pi\) | |||||||
\(734\) | 5.23232 | − | 1.36623i | 0.193128 | − | 0.0504286i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.0970 | − | 33.7931i | −0.667063 | − | 1.24563i | ||||
\(737\) | − | 37.8345i | − | 1.39365i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.5912 | − | 35.2264i | −0.536748 | − | 1.29582i | −0.926981 | − | 0.375108i | \(-0.877606\pi\) |
0.390234 | − | 0.920716i | \(-0.372394\pi\) | |||||||
\(740\) | 0.325173 | − | 1.15437i | 0.0119536 | − | 0.0424353i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.0469976 | + | 0.0620654i | 0.00172534 | + | 0.00227849i | ||||
\(743\) | 30.0108 | + | 30.0108i | 1.10099 | + | 1.10099i | 0.994292 | + | 0.106696i | \(0.0340272\pi\) |
0.106696 | + | 0.994292i | \(0.465973\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.72559 | − | 1.72559i | 0.0632207 | − | 0.0632207i | ||||
\(746\) | −35.6432 | − | 4.92434i | −1.30499 | − | 0.180293i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 14.4569 | − | 1.71570i | 0.528598 | − | 0.0627322i | ||||
\(749\) | 0.236682 | − | 0.0980368i | 0.00864817 | − | 0.00358219i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.3413 | 1.32611 | 0.663056 | − | 0.748570i | \(-0.269259\pi\) | ||||
0.663056 | + | 0.748570i | \(0.269259\pi\) | |||||||
\(752\) | −8.25920 | − | 5.05410i | −0.301182 | − | 0.184304i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.6776 | − | 21.6379i | 0.461692 | − | 0.788006i | ||||
\(755\) | −1.15282 | − | 2.78314i | −0.0419553 | − | 0.101289i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.0419 | − | 8.30162i | −0.728435 | − | 0.301728i | −0.0125261 | − | 0.999922i | \(-0.503987\pi\) |
−0.715909 | + | 0.698194i | \(0.753987\pi\) | |||||||
\(758\) | 4.49847 | + | 0.621493i | 0.163392 | + | 0.0225736i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.12671 | − | 1.08433i | 0.0408700 | − | 0.0393329i | ||||
\(761\) | 29.5308 | − | 29.5308i | 1.07049 | − | 1.07049i | 0.0731706 | − | 0.997319i | \(-0.476688\pi\) |
0.997319 | − | 0.0731706i | \(-0.0233118\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.116272 | + | 0.0481614i | 0.00420933 | + | 0.00174356i | ||||
\(764\) | 4.40671 | − | 2.46970i | 0.159429 | − | 0.0893505i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.81172 | + | 1.77864i | −0.246118 | + | 0.0642648i | ||||
\(767\) | 14.7604 | 0.532969 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.12972 | −0.148922 | −0.0744608 | − | 0.997224i | \(-0.523724\pi\) | ||||
−0.0744608 | + | 0.997224i | \(0.523724\pi\) | |||||||
\(770\) | −0.0190131 | + | 0.00496460i | −0.000685185 | + | 0.000178912i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.7978 | + | 6.05153i | −0.388622 | + | 0.217799i | ||||
\(773\) | 40.0041 | + | 16.5702i | 1.43885 | + | 0.595990i | 0.959519 | − | 0.281645i | \(-0.0908800\pi\) |
0.479329 | + | 0.877635i | \(0.340880\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.746512 | + | 0.746512i | −0.0268155 | + | 0.0268155i | ||||
\(776\) | 24.2225 | − | 23.3115i | 0.869537 | − | 0.836833i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.8468 | + | 1.77486i | 0.460579 | + | 0.0636319i | ||||
\(779\) | −7.30065 | − | 3.02403i | −0.261573 | − | 0.108347i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.1740 | + | 41.4616i | 0.614532 | + | 1.48361i | ||||
\(782\) | −9.39738 | + | 16.0393i | −0.336050 | + | 0.573563i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 23.8821 | + | 14.6144i | 0.852934 | + | 0.521941i | ||||
\(785\) | 2.72141 | 0.0971311 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.6785 | + | 14.7785i | −1.27180 | + | 0.526797i | −0.913511 | − | 0.406813i | \(-0.866640\pi\) |
−0.358290 | + | 0.933610i | \(0.616640\pi\) | |||||||
\(788\) | 48.6600 | − | 5.77480i | 1.73344 | − | 0.205719i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.71373 | + | 0.651233i | 0.167707 | + | 0.0231698i | ||||
\(791\) | −0.169719 | + | 0.169719i | −0.00603453 | + | 0.00603453i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.0364 | − | 10.0364i | −0.356404 | − | 0.356404i | ||||
\(794\) | 2.72385 | + | 3.59713i | 0.0966657 | + | 0.127657i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.31343 | + | 4.66267i | −0.0465531 | + | 0.165264i | ||||
\(797\) | −18.5765 | − | 44.8475i | −0.658012 | − | 1.58858i | −0.800870 | − | 0.598838i | \(-0.795629\pi\) |
0.142858 | − | 0.989743i | \(-0.454371\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.69559i | 0.166118i | ||||||||
\(800\) | 24.6943 | − | 13.2243i | 0.873075 | − | 0.467551i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 38.1068 | − | 9.95023i | 1.34560 | − | 0.351355i | ||||
\(803\) | 54.2057 | − | 22.4527i | 1.91288 | − | 0.792340i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.00960217 | − | 0.0231817i | 0.000338432 | − | 0.000817047i | ||||
\(806\) | −0.909863 | + | 0.688973i | −0.0320485 | + | 0.0242680i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −27.4595 | + | 10.7624i | −0.966021 | + | 0.378619i | ||||
\(809\) | 21.0608 | + | 21.0608i | 0.740458 | + | 0.740458i | 0.972666 | − | 0.232208i | \(-0.0745951\pi\) |
−0.232208 | + | 0.972666i | \(0.574595\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.0466 | + | 31.4972i | −0.458126 | + | 1.10602i | 0.511029 | + | 0.859564i | \(0.329265\pi\) |
−0.969155 | + | 0.246451i | \(0.920735\pi\) | |||||||
\(812\) | −0.157124 | + | 0.0186469i | −0.00551395 | + | 0.000654377i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.33720 | − | 12.5230i | 0.257169 | − | 0.438930i | ||||
\(815\) | 2.17465i | 0.0761746i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 9.12034i | − | 0.319080i | ||||||
\(818\) | 1.34005 | + | 0.785136i | 0.0468539 | + | 0.0274516i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.07951 | + | 0.850463i | 0.0376980 | + | 0.0296995i | ||||
\(821\) | 19.7064 | − | 47.5755i | 0.687758 | − | 1.66040i | −0.0614909 | − | 0.998108i | \(-0.519586\pi\) |
0.749249 | − | 0.662288i | \(-0.230414\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.83221 | − | 8.83221i | −0.307872 | − | 0.307872i | 0.536212 | − | 0.844083i | \(-0.319855\pi\) |
−0.844083 | + | 0.536212i | \(0.819855\pi\) | |||||||
\(824\) | −0.128237 | + | 6.69094i | −0.00446734 | + | 0.233090i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.0562195 | − | 0.0742439i | −0.00195613 | − | 0.00258328i | ||||
\(827\) | −4.85317 | + | 11.7166i | −0.168761 | + | 0.407426i | −0.985521 | − | 0.169552i | \(-0.945768\pi\) |
0.816760 | + | 0.576977i | \(0.195768\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.5493 | + | 12.2397i | −1.02629 | + | 0.425102i | −0.831371 | − | 0.555717i | \(-0.812444\pi\) |
−0.194917 | + | 0.980820i | \(0.562444\pi\) | |||||||
\(830\) | −0.256125 | − | 0.980891i | −0.00889022 | − | 0.0340472i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 28.4009 | − | 10.5081i | 0.984624 | − | 0.364302i | ||||
\(833\) | − | 13.5777i | − | 0.470439i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.958897 | + | 2.31498i | 0.0331840 | + | 0.0801132i | ||||
\(836\) | 16.5088 | − | 9.25217i | 0.570968 | − | 0.319993i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.53146 | − | 5.70303i | 0.260170 | − | 0.197008i | ||||
\(839\) | 1.90644 | + | 1.90644i | 0.0658177 | + | 0.0658177i | 0.739249 | − | 0.673432i | \(-0.235180\pi\) |
−0.673432 | + | 0.739249i | \(0.735180\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.98766 | − | 4.98766i | 0.171988 | − | 0.171988i | ||||
\(842\) | −2.29641 | + | 16.6218i | −0.0791395 | + | 0.572824i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11.8559 | − | 15.0489i | 0.408097 | − | 0.518003i | ||||
\(845\) | −0.269131 | + | 0.111478i | −0.00925840 | + | 0.00383496i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.0520533 | −0.00178857 | ||||||||
\(848\) | 7.67080 | + | 10.5440i | 0.263416 | + | 0.362083i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −11.7207 | − | 6.86712i | −0.402015 | − | 0.235540i | ||||
\(851\) | 7.09225 | + | 17.1222i | 0.243119 | + | 0.586942i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.4447 | + | 13.8532i | 1.14512 | + | 0.474326i | 0.872896 | − | 0.487907i | \(-0.162239\pi\) |
0.272228 | + | 0.962233i | \(0.412239\pi\) | |||||||
\(854\) | −0.0122558 | + | 0.0887093i | −0.000419384 | + | 0.00303557i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 39.9482 | − | 15.6572i | 1.36540 | − | 0.535151i | ||||
\(857\) | −34.3898 | + | 34.3898i | −1.17473 | + | 1.17473i | −0.193667 | + | 0.981067i | \(0.562038\pi\) |
−0.981067 | + | 0.193667i | \(0.937962\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.8239 | − | 14.4245i | −1.18818 | − | 0.492158i | −0.301015 | − | 0.953619i | \(-0.597325\pi\) |
−0.887160 | + | 0.461461i | \(0.847325\pi\) | |||||||
\(860\) | −0.430058 | + | 1.52671i | −0.0146649 | + | 0.0520603i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.10219 | + | 19.5400i | 0.173781 | + | 0.665537i | ||||
\(863\) | 18.2887 | 0.622556 | 0.311278 | − | 0.950319i | \(-0.399243\pi\) | ||||
0.311278 | + | 0.950319i | \(0.399243\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.411885 | −0.0140045 | ||||||||
\(866\) | −13.0630 | − | 50.0280i | −0.443900 | − | 1.70002i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.00693096 | + | 0.00195238i | 0.000235252 | + | 6.62681e-5i | ||||
\(869\) | 53.2049 | + | 22.0382i | 1.80485 | + | 0.747595i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.9859 | + | 26.9859i | −0.914382 | + | 0.914382i | ||||
\(872\) | 19.3158 | + | 8.43804i | 0.654114 | + | 0.285748i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.30710 | + | 23.9373i | −0.111864 | + | 0.809693i | ||||
\(875\) | 0.0340444 | + | 0.0141016i | 0.00115091 | + | 0.000476723i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.49573 | − | 3.61102i | −0.0505073 | − | 0.121935i | 0.896612 | − | 0.442817i | \(-0.146021\pi\) |
−0.947119 | + | 0.320882i | \(0.896021\pi\) | |||||||
\(878\) | 34.4408 | + | 20.1788i | 1.16232 | + | 0.681002i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.19978 | + | 0.770327i | −0.107864 | + | 0.0259677i | ||||
\(881\) | −38.4824 | −1.29650 | −0.648252 | − | 0.761426i | \(-0.724500\pi\) | ||||
−0.648252 | + | 0.761426i | \(0.724500\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.9974 | + | 19.0528i | −1.54794 | + | 0.641177i | −0.982942 | − | 0.183918i | \(-0.941122\pi\) |
−0.564995 | + | 0.825094i | \(0.691122\pi\) | |||||||
\(884\) | −11.5353 | − | 9.08784i | −0.387975 | − | 0.305657i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.944990 | + | 6.83999i | −0.0317476 | + | 0.229794i | ||||
\(887\) | −22.1513 | + | 22.1513i | −0.743769 | + | 0.743769i | −0.973301 | − | 0.229532i | \(-0.926280\pi\) |
0.229532 | + | 0.973301i | \(0.426280\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.00710357 | − | 0.00710357i | −0.000238246 | − | 0.000238246i | ||||
\(890\) | 0.504360 | − | 0.381915i | 0.0169062 | − | 0.0128018i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −25.1706 | − | 44.9123i | −0.842775 | − | 1.50377i | ||||
\(893\) | 2.33585 | + | 5.63924i | 0.0781662 | + | 0.188710i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.67946i | − | 0.0561381i | ||||||
\(896\) | −0.161028 | − | 0.102831i | −0.00537957 | − | 0.00343535i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.61860 | − | 25.3475i | −0.220865 | − | 0.845857i | ||||
\(899\) | 0.922730 | − | 0.382207i | 0.0307748 | − | 0.0127473i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.41976 | − | 5.84181i | 0.0806138 | − | 0.194619i | ||||
\(902\) | 10.0403 | + | 13.2593i | 0.334305 | + | 0.441486i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −28.9651 | + | 27.8757i | −0.963364 | + | 0.927131i | ||||
\(905\) | 3.39428 | + | 3.39428i | 0.112830 | + | 0.112830i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.313807 | − | 0.757598i | 0.0104198 | − | 0.0251556i | −0.918584 | − | 0.395226i | \(-0.870666\pi\) |
0.929004 | + | 0.370070i | \(0.120666\pi\) | |||||||
\(908\) | 27.0042 | − | 34.2768i | 0.896165 | − | 1.13752i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.0171024 | + | 0.0100203i | 0.000566939 | + | 0.000332169i | ||||
\(911\) | 19.5639i | 0.648182i | 0.946026 | + | 0.324091i | \(0.105058\pi\) | ||||
−0.946026 | + | 0.324091i | \(0.894942\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 12.2690i | − | 0.406045i | ||||||
\(914\) | −4.36523 | + | 7.45049i | −0.144389 | + | 0.246440i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.28162 | − | 10.7993i | −0.0423460 | − | 0.356818i | ||||
\(917\) | 0.0833857 | − | 0.201311i | 0.00275364 | − | 0.00664787i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.8704 | + | 29.8704i | 0.985333 | + | 0.985333i | 0.999894 | − | 0.0145606i | \(-0.00463493\pi\) |
−0.0145606 | + | 0.999894i | \(0.504635\pi\) | |||||||
\(920\) | 1.68233 | − | 3.85107i | 0.0554648 | − | 0.126966i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10.8016 | − | 8.17927i | 0.355732 | − | 0.269370i | ||||
\(923\) | 17.3235 | − | 41.8225i | 0.570209 | − | 1.37661i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.5120 | + | 5.18265i | −0.411393 | + | 0.170404i | ||||
\(926\) | 41.6372 | − | 10.8721i | 1.36828 | − | 0.357278i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −26.3710 | + | 2.61824i | −0.865670 | + | 0.0859481i | ||||
\(929\) | − | 32.3872i | − | 1.06259i | −0.847187 | − | 0.531295i | \(-0.821706\pi\) | ||
0.847187 | − | 0.531295i | \(-0.178294\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.75430 | − | 16.3063i | −0.221363 | − | 0.534418i | ||||
\(932\) | 32.2460 | + | 9.08338i | 1.05625 | + | 0.297536i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −26.3489 | − | 34.7965i | −0.862162 | − | 1.13858i | ||||
\(935\) | 1.12856 | + | 1.12856i | 0.0369078 | + | 0.0369078i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.5697 | + | 25.5697i | −0.835326 | + | 0.835326i | −0.988240 | − | 0.152914i | \(-0.951134\pi\) |
0.152914 | + | 0.988240i | \(0.451134\pi\) | |||||||
\(938\) | 0.238521 | + | 0.0329532i | 0.00778798 | + | 0.00107596i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.125101 | − | 1.05413i | −0.00408033 | − | 0.0343819i | ||||
\(941\) | −36.3130 | + | 15.0413i | −1.18377 | + | 0.490334i | −0.885721 | − | 0.464217i | \(-0.846336\pi\) |
−0.298048 | + | 0.954551i | \(0.596336\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.2370 | −0.691571 | ||||||||
\(944\) | −9.17597 | − | 12.6130i | −0.298652 | − | 0.410517i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.70383 | + | 16.5623i | −0.315499 | + | 0.538487i | ||||
\(947\) | 0.876633 | + | 2.11638i | 0.0284868 | + | 0.0687731i | 0.937483 | − | 0.348032i | \(-0.113150\pi\) |
−0.908996 | + | 0.416805i | \(0.863150\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −54.6776 | − | 22.6482i | −1.77491 | − | 0.735191i | ||||
\(950\) | −17.4922 | − | 2.41666i | −0.567521 | − | 0.0784067i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.00177543 | + | 0.0926355i | −5.75420e−5 | + | 0.00300233i | ||||
\(953\) | −26.6396 | + | 26.6396i | −0.862941 | + | 0.862941i | −0.991679 | − | 0.128738i | \(-0.958907\pi\) |
0.128738 | + | 0.991679i | \(0.458907\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.511646 | + | 0.211931i | 0.0165565 | + | 0.00685791i | ||||
\(956\) | −9.79778 | − | 17.4823i | −0.316883 | − | 0.565418i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −45.3496 | + | 11.8414i | −1.46518 | + | 0.382579i | ||||
\(959\) | −0.258550 | −0.00834900 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.9545 | 0.998534 | ||||||||
\(962\) | −14.1655 | + | 3.69882i | −0.456714 | + | 0.119255i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.19835 | + | 3.92255i | 0.0708042 | + | 0.126337i | ||||
\(965\) | −1.25369 | − | 0.519296i | −0.0403578 | − | 0.0167167i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.6148 | + | 35.6148i | −1.14529 | + | 1.14529i | −0.157828 | + | 0.987467i | \(0.550449\pi\) |
−0.987467 | + | 0.157828i | \(0.949551\pi\) | |||||||
\(968\) | −8.71659 | − | 0.167060i | −0.280162 | − | 0.00536951i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.65081 | + | 0.504384i | 0.117220 | + | 0.0161948i | ||||
\(971\) | −6.57654 | − | 2.72409i | −0.211051 | − | 0.0874203i | 0.274653 | − | 0.961543i | \(-0.411437\pi\) |
−0.485705 | + | 0.874123i | \(0.661437\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.0599758 | − | 0.144794i | −0.00192274 | − | 0.00464189i | ||||
\(974\) | −8.42921 | + | 14.3868i | −0.270089 | + | 0.460983i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.33699 | + | 14.8155i | −0.0748054 | + | 0.474232i | ||||
\(977\) | 11.5407 | 0.369220 | 0.184610 | − | 0.982812i | \(-0.440898\pi\) | ||||
0.184610 | + | 0.982812i | \(0.440898\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.07360 | − | 2.92998i | 0.226073 | − | 0.0936426i | ||||
\(980\) | 0.361738 | + | 3.04810i | 0.0115553 | + | 0.0973681i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 14.0669 | + | 1.94344i | 0.448894 | + | 0.0620177i | ||||
\(983\) | 15.7142 | − | 15.7142i | 0.501204 | − | 0.501204i | −0.410608 | − | 0.911812i | \(-0.634684\pi\) |
0.911812 | + | 0.410608i | \(0.134684\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.79857 | + | 3.79857i | 0.121033 | + | 0.121033i | ||||
\(986\) | 7.75800 | + | 10.2453i | 0.247065 | + | 0.326276i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −18.3743 | − | 5.17586i | −0.584565 | − | 0.164666i | ||||
\(989\) | −9.37988 | − | 22.6450i | −0.298263 | − | 0.720070i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.5998i | 0.972033i | 0.873950 | + | 0.486017i | \(0.161551\pi\) | ||||
−0.873950 | + | 0.486017i | \(0.838449\pi\) | |||||||
\(992\) | 1.15436 | + | 0.349181i | 0.0366509 | + | 0.0110865i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.276346 | + | 0.0721578i | −0.00876515 | + | 0.00228871i | ||||
\(995\) | −0.490633 | + | 0.203227i | −0.0155541 | + | 0.00644273i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.7966 | + | 40.5506i | −0.531954 | + | 1.28425i | 0.398273 | + | 0.917267i | \(0.369610\pi\) |
−0.930227 | + | 0.366984i | \(0.880390\pi\) | |||||||
\(998\) | −12.5687 | + | 9.51735i | −0.397855 | + | 0.301267i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 864.2.w.a.107.4 | ✓ | 128 | |
3.2 | odd | 2 | inner | 864.2.w.a.107.29 | yes | 128 | |
32.3 | odd | 8 | inner | 864.2.w.a.323.29 | yes | 128 | |
96.35 | even | 8 | inner | 864.2.w.a.323.4 | yes | 128 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.2.w.a.107.4 | ✓ | 128 | 1.1 | even | 1 | trivial | |
864.2.w.a.107.29 | yes | 128 | 3.2 | odd | 2 | inner | |
864.2.w.a.323.4 | yes | 128 | 96.35 | even | 8 | inner | |
864.2.w.a.323.29 | yes | 128 | 32.3 | odd | 8 | inner |