Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [625,2,Mod(24,625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(625, base_ring=CyclotomicField(50))
chi = DirichletCharacter(H, H._module([11]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("625.24");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 625 = 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 625.h (of order \(50\), degree \(20\), 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: | \(4.99065012633\) |
Analytic rank: | \(0\) |
Dimension: | \(440\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{50})\) |
Twist minimal: | no (minimal twist has level 125) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{50}]$ |
Embedding invariants
Embedding label | 274.21 | ||
Character | \(\chi\) | \(=\) | 625.274 |
Dual form | 625.2.h.b.349.21 |
$q$-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 \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{21}{50}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.618528 | + | 2.40901i | 0.437365 | + | 1.70342i | 0.679920 | + | 0.733287i | \(0.262015\pi\) |
−0.242555 | + | 0.970138i | \(0.577985\pi\) | |||||||
\(3\) | 3.26064 | − | 0.622000i | 1.88253 | − | 0.359112i | 0.887678 | − | 0.460464i | \(-0.152317\pi\) |
0.994851 | + | 0.101352i | \(0.0323169\pi\) | |||||||
\(4\) | −3.66812 | + | 2.01657i | −1.83406 | + | 1.00828i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.51519 | + | 7.47017i | 1.43507 | + | 3.04968i | ||||
\(7\) | 0.463359 | − | 0.637759i | 0.175133 | − | 0.241050i | −0.712422 | − | 0.701751i | \(-0.752402\pi\) |
0.887555 | + | 0.460701i | \(0.152402\pi\) | |||||||
\(8\) | −3.72162 | − | 3.96312i | −1.31579 | − | 1.40117i | ||||
\(9\) | 7.45553 | − | 2.95185i | 2.48518 | − | 0.983952i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00576 | − | 0.258235i | 0.303247 | − | 0.0778607i | −0.0940002 | − | 0.995572i | \(-0.529965\pi\) |
0.397248 | + | 0.917711i | \(0.369965\pi\) | |||||||
\(12\) | −10.7061 | + | 8.85686i | −3.09059 | + | 2.55675i | ||||
\(13\) | −0.207600 | − | 0.524337i | −0.0575779 | − | 0.145425i | 0.898140 | − | 0.439710i | \(-0.144919\pi\) |
−0.955718 | + | 0.294285i | \(0.904919\pi\) | |||||||
\(14\) | 1.82297 | + | 0.721763i | 0.487208 | + | 0.192899i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.75944 | − | 4.34818i | 0.689860 | − | 1.08705i | ||||
\(17\) | −1.66584 | + | 3.03015i | −0.404025 | + | 0.734919i | −0.997554 | − | 0.0698933i | \(-0.977734\pi\) |
0.593529 | + | 0.804812i | \(0.297734\pi\) | |||||||
\(18\) | 11.7225 | + | 16.1346i | 2.76302 | + | 3.80297i | ||||
\(19\) | −0.598583 | + | 3.13788i | −0.137324 | + | 0.719880i | 0.845303 | + | 0.534288i | \(0.179420\pi\) |
−0.982627 | + | 0.185592i | \(0.940580\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.11416 | − | 2.36771i | 0.243129 | − | 0.516676i | ||||
\(22\) | 1.24418 | + | 2.26315i | 0.265260 | + | 0.482506i | ||||
\(23\) | −3.37563 | − | 0.212377i | −0.703868 | − | 0.0442836i | −0.293177 | − | 0.956058i | \(-0.594713\pi\) |
−0.410691 | + | 0.911775i | \(0.634713\pi\) | |||||||
\(24\) | −14.5999 | − | 10.6075i | −2.98019 | − | 2.16524i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.13473 | − | 0.824427i | 0.222538 | − | 0.161683i | ||||
\(27\) | 14.0657 | − | 8.92634i | 2.70694 | − | 1.71788i | ||||
\(28\) | −0.413573 | + | 3.27377i | −0.0781580 | + | 0.618684i | ||||
\(29\) | −2.01748 | − | 0.254867i | −0.374637 | − | 0.0473276i | −0.0642393 | − | 0.997935i | \(-0.520462\pi\) |
−0.310397 | + | 0.950607i | \(0.600462\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.56625 | − | 3.06007i | −0.999729 | − | 0.549605i | −0.104175 | − | 0.994559i | \(-0.533220\pi\) |
−0.895554 | + | 0.444954i | \(0.853220\pi\) | |||||||
\(32\) | 1.84053 | + | 0.598023i | 0.325362 | + | 0.105717i | ||||
\(33\) | 3.11879 | − | 1.46759i | 0.542911 | − | 0.255475i | ||||
\(34\) | −8.33001 | − | 2.13878i | −1.42859 | − | 0.366798i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −21.3952 | + | 25.8623i | −3.56586 | + | 4.31039i | ||||
\(37\) | −4.67893 | − | 2.96934i | −0.769212 | − | 0.488157i | 0.0924015 | − | 0.995722i | \(-0.470546\pi\) |
−0.861613 | + | 0.507565i | \(0.830546\pi\) | |||||||
\(38\) | −7.92942 | + | 0.498877i | −1.28632 | + | 0.0809285i | ||||
\(39\) | −1.00305 | − | 1.58055i | −0.160616 | − | 0.253090i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.714850 | − | 11.3622i | −0.111641 | − | 1.77448i | −0.512835 | − | 0.858487i | \(-0.671405\pi\) |
0.401195 | − | 0.915993i | \(-0.368595\pi\) | |||||||
\(42\) | 6.39296 | + | 1.21952i | 0.986456 | + | 0.188176i | ||||
\(43\) | 2.69982 | − | 0.877225i | 0.411719 | − | 0.133776i | −0.0958317 | − | 0.995398i | \(-0.530551\pi\) |
0.507551 | + | 0.861622i | \(0.330551\pi\) | |||||||
\(44\) | −3.16849 | + | 2.97541i | −0.477668 | + | 0.448560i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.57631 | − | 8.26328i | −0.232414 | − | 1.21835i | ||||
\(47\) | 1.00997 | − | 1.07551i | 0.147319 | − | 0.156879i | −0.651077 | − | 0.759012i | \(-0.725682\pi\) |
0.798396 | + | 0.602133i | \(0.205682\pi\) | |||||||
\(48\) | 6.29296 | − | 15.8942i | 0.908311 | − | 2.29413i | ||||
\(49\) | 1.97108 | + | 6.06637i | 0.281583 | + | 0.866625i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.54694 | + | 10.9164i | −0.496671 | + | 1.52860i | ||||
\(52\) | 1.81886 | + | 1.50469i | 0.252231 | + | 0.208664i | ||||
\(53\) | 2.80343 | + | 1.31919i | 0.385081 | + | 0.181205i | 0.608568 | − | 0.793502i | \(-0.291744\pi\) |
−0.223487 | + | 0.974707i | \(0.571744\pi\) | |||||||
\(54\) | 30.2036 | + | 28.3631i | 4.11019 | + | 3.85973i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.25196 | + | 0.537148i | −0.568192 | + | 0.0717794i | ||||
\(57\) | 10.6038i | 1.40451i | ||||||||
\(58\) | −0.633891 | − | 5.01776i | −0.0832340 | − | 0.658865i | ||||
\(59\) | −2.27401 | − | 2.74880i | −0.296051 | − | 0.357864i | 0.601424 | − | 0.798930i | \(-0.294600\pi\) |
−0.897474 | + | 0.441066i | \(0.854600\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.470039 | − | 7.47105i | 0.0601823 | − | 0.956570i | −0.845866 | − | 0.533396i | \(-0.820916\pi\) |
0.906048 | − | 0.423174i | \(-0.139084\pi\) | |||||||
\(62\) | 3.92885 | − | 15.3019i | 0.498965 | − | 1.94334i | ||||
\(63\) | 1.57202 | − | 6.12260i | 0.198056 | − | 0.771375i | ||||
\(64\) | 0.344501 | − | 5.47569i | 0.0430626 | − | 0.684461i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.46449 | + | 6.60544i | 0.672632 | + | 0.813073i | ||||
\(67\) | 1.70582 | + | 13.5029i | 0.208398 | + | 1.64964i | 0.655525 | + | 0.755173i | \(0.272447\pi\) |
−0.447127 | + | 0.894471i | \(0.647553\pi\) | |||||||
\(68\) | − | 14.4742i | − | 1.75526i | ||||||
\(69\) | −11.1388 | + | 1.40716i | −1.34096 | + | 0.169402i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.81072 | + | 3.57851i | 0.452249 | + | 0.424690i | 0.876904 | − | 0.480665i | \(-0.159605\pi\) |
−0.424655 | + | 0.905355i | \(0.639605\pi\) | |||||||
\(72\) | −39.4452 | − | 18.5615i | −4.64866 | − | 2.18749i | ||||
\(73\) | 4.81135 | + | 3.98029i | 0.563126 | + | 0.465858i | 0.874904 | − | 0.484297i | \(-0.160924\pi\) |
−0.311778 | + | 0.950155i | \(0.600924\pi\) | |||||||
\(74\) | 4.25911 | − | 13.1082i | 0.495112 | − | 1.52380i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.13207 | − | 12.7172i | −0.473981 | − | 1.45876i | ||||
\(77\) | 0.301335 | − | 0.761087i | 0.0343404 | − | 0.0867339i | ||||
\(78\) | 3.18714 | − | 3.39395i | 0.360872 | − | 0.384290i | ||||
\(79\) | −1.73061 | − | 9.07217i | −0.194709 | − | 1.02070i | −0.936659 | − | 0.350243i | \(-0.886099\pi\) |
0.741950 | − | 0.670455i | \(-0.233901\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 22.7748 | − | 21.3870i | 2.53054 | − | 2.37633i | ||||
\(82\) | 26.9295 | − | 8.74992i | 2.97386 | − | 0.966267i | ||||
\(83\) | −0.187696 | − | 0.0358049i | −0.0206023 | − | 0.00393010i | 0.177070 | − | 0.984198i | \(-0.443338\pi\) |
−0.197672 | + | 0.980268i | \(0.563338\pi\) | |||||||
\(84\) | 0.687772 | + | 10.9318i | 0.0750420 | + | 1.19276i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.78315 | + | 5.96130i | 0.407948 | + | 0.642823i | ||||
\(87\) | −6.73680 | + | 0.423843i | −0.722260 | + | 0.0454408i | ||||
\(88\) | −4.76646 | − | 3.02489i | −0.508107 | − | 0.322454i | ||||
\(89\) | 1.42021 | − | 1.71673i | 0.150542 | − | 0.181973i | −0.689851 | − | 0.723951i | \(-0.742324\pi\) |
0.840393 | + | 0.541977i | \(0.182324\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.430594 | − | 0.110558i | −0.0451385 | − | 0.0115896i | ||||
\(92\) | 12.8105 | − | 6.02816i | 1.33559 | − | 0.628480i | ||||
\(93\) | −20.0529 | − | 6.51558i | −2.07939 | − | 0.675634i | ||||
\(94\) | 3.21559 | + | 1.76779i | 0.331663 | + | 0.182333i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.37326 | + | 0.805130i | 0.650468 | + | 0.0821732i | ||||
\(97\) | −1.51887 | + | 12.0231i | −0.154218 | + | 1.22076i | 0.705020 | + | 0.709187i | \(0.250938\pi\) |
−0.859238 | + | 0.511576i | \(0.829062\pi\) | |||||||
\(98\) | −13.3948 | + | 8.50057i | −1.35307 | + | 0.858687i | ||||
\(99\) | 6.73619 | − | 4.89413i | 0.677013 | − | 0.491879i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.25784 | − | 5.99967i | −0.821686 | − | 0.596990i | 0.0955088 | − | 0.995429i | \(-0.469552\pi\) |
−0.917195 | + | 0.398439i | \(0.869552\pi\) | |||||||
\(102\) | −28.4915 | − | 1.79253i | −2.82108 | − | 0.177487i | ||||
\(103\) | 8.16330 | + | 14.8490i | 0.804353 | + | 1.46311i | 0.884606 | + | 0.466339i | \(0.154427\pi\) |
−0.0802527 | + | 0.996775i | \(0.525573\pi\) | |||||||
\(104\) | −1.30541 | + | 2.77413i | −0.128006 | + | 0.272026i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.44395 | + | 7.56944i | −0.140249 | + | 0.735209i | ||||
\(107\) | −8.29283 | − | 11.4141i | −0.801698 | − | 1.10344i | −0.992552 | − | 0.121824i | \(-0.961126\pi\) |
0.190854 | − | 0.981618i | \(-0.438874\pi\) | |||||||
\(108\) | −33.5940 | + | 61.1072i | −3.23258 | + | 5.88005i | ||||
\(109\) | 0.443460 | − | 0.698780i | 0.0424757 | − | 0.0669310i | −0.822427 | − | 0.568871i | \(-0.807380\pi\) |
0.864902 | + | 0.501940i | \(0.167380\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.1032 | − | 6.77165i | −1.62337 | − | 0.642736i | ||||
\(112\) | −1.49448 | − | 3.77463i | −0.141215 | − | 0.356669i | ||||
\(113\) | −5.01705 | + | 4.15047i | −0.471965 | + | 0.390443i | −0.842775 | − | 0.538265i | \(-0.819080\pi\) |
0.370811 | + | 0.928708i | \(0.379080\pi\) | |||||||
\(114\) | −25.5446 | + | 6.55875i | −2.39248 | + | 0.614283i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.91432 | − | 3.13350i | 0.734826 | − | 0.290938i | ||||
\(117\) | −3.09554 | − | 3.29641i | −0.286182 | − | 0.304753i | ||||
\(118\) | 5.21535 | − | 7.17831i | 0.480111 | − | 0.660817i | ||||
\(119\) | 1.16062 | + | 2.46645i | 0.106394 | + | 0.226099i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.69451 | + | 4.77985i | −0.790410 | + | 0.434532i | ||||
\(122\) | 18.2885 | − | 3.48872i | 1.65577 | − | 0.315854i | ||||
\(123\) | −9.39816 | − | 36.6034i | −0.847403 | − | 3.30042i | ||||
\(124\) | 26.5885 | 2.38772 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 15.7217 | 1.40060 | ||||||||
\(127\) | −2.07182 | − | 8.06920i | −0.183844 | − | 0.716026i | −0.991911 | − | 0.126935i | \(-0.959486\pi\) |
0.808067 | − | 0.589091i | \(-0.200514\pi\) | |||||||
\(128\) | 17.2060 | − | 3.28221i | 1.52081 | − | 0.290110i | ||||
\(129\) | 8.25750 | − | 4.53960i | 0.727032 | − | 0.399689i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.08655 | + | 8.68436i | 0.357043 | + | 0.758756i | 0.999974 | − | 0.00716837i | \(-0.00228178\pi\) |
−0.642931 | + | 0.765924i | \(0.722282\pi\) | |||||||
\(132\) | −8.48060 | + | 11.6725i | −0.738141 | + | 1.01596i | ||||
\(133\) | 1.72385 | + | 1.83572i | 0.149477 | + | 0.159177i | ||||
\(134\) | −31.4735 | + | 12.4612i | −2.71890 | + | 1.07649i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 18.2085 | − | 4.67514i | 1.56136 | − | 0.400890i | ||||
\(137\) | 1.38806 | − | 1.14830i | 0.118590 | − | 0.0981061i | −0.576239 | − | 0.817281i | \(-0.695480\pi\) |
0.694829 | + | 0.719175i | \(0.255480\pi\) | |||||||
\(138\) | −10.2795 | − | 25.9631i | −0.875051 | − | 2.21013i | ||||
\(139\) | −8.38439 | − | 3.31961i | −0.711154 | − | 0.281566i | −0.0154363 | − | 0.999881i | \(-0.504914\pi\) |
−0.695718 | + | 0.718315i | \(0.744914\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.62417 | − | 4.13503i | 0.220995 | − | 0.348232i | ||||
\(142\) | −6.26361 | + | 11.3935i | −0.525630 | + | 0.956118i | ||||
\(143\) | −0.344197 | − | 0.473747i | −0.0287832 | − | 0.0396167i | ||||
\(144\) | 7.73790 | − | 40.5635i | 0.644825 | − | 3.38029i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.61260 | + | 14.0525i | −0.547263 | + | 1.16299i | ||||
\(147\) | 10.2003 | + | 18.5542i | 0.841304 | + | 1.53033i | ||||
\(148\) | 23.1508 | + | 1.45652i | 1.90298 | + | 0.119725i | ||||
\(149\) | 4.91478 | + | 3.57079i | 0.402634 | + | 0.292531i | 0.770613 | − | 0.637303i | \(-0.219950\pi\) |
−0.367979 | + | 0.929834i | \(0.619950\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.84022 | − | 6.42279i | 0.719407 | − | 0.522680i | −0.166788 | − | 0.985993i | \(-0.553340\pi\) |
0.886195 | + | 0.463313i | \(0.153340\pi\) | |||||||
\(152\) | 14.6635 | − | 9.30575i | 1.18937 | − | 0.754796i | ||||
\(153\) | −3.47516 | + | 27.5087i | −0.280950 | + | 2.22395i | ||||
\(154\) | 2.01985 | + | 0.255166i | 0.162764 | + | 0.0205619i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.86657 | + | 3.77493i | 0.549765 | + | 0.302236i | ||||
\(157\) | 14.1931 | + | 4.61162i | 1.13273 | + | 0.368048i | 0.814614 | − | 0.580003i | \(-0.196949\pi\) |
0.318120 | + | 0.948051i | \(0.396949\pi\) | |||||||
\(158\) | 20.7845 | − | 9.78043i | 1.65352 | − | 0.778089i | ||||
\(159\) | 9.96151 | + | 2.55768i | 0.789999 | + | 0.202837i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.69958 | + | 2.05443i | −0.133945 | + | 0.161912i | ||||
\(162\) | 65.6083 | + | 41.6363i | 5.15467 | + | 3.27125i | ||||
\(163\) | 7.83419 | − | 0.492885i | 0.613621 | − | 0.0386057i | 0.247060 | − | 0.969000i | \(-0.420535\pi\) |
0.366560 | + | 0.930394i | \(0.380535\pi\) | |||||||
\(164\) | 25.5348 | + | 40.2364i | 1.99393 | + | 3.14194i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.0298409 | − | 0.474307i | −0.00231610 | − | 0.0368134i | ||||
\(167\) | −9.20316 | − | 1.75560i | −0.712162 | − | 0.135852i | −0.181445 | − | 0.983401i | \(-0.558077\pi\) |
−0.530717 | + | 0.847549i | \(0.678077\pi\) | |||||||
\(168\) | −13.5300 | + | 4.39616i | −1.04386 | + | 0.339171i | ||||
\(169\) | 9.24476 | − | 8.68141i | 0.711135 | − | 0.667801i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.79982 | + | 25.1615i | 0.367051 | + | 1.92415i | ||||
\(172\) | −8.13428 | + | 8.66213i | −0.620233 | + | 0.660481i | ||||
\(173\) | −8.18603 | + | 20.6756i | −0.622372 | + | 1.57193i | 0.185544 | + | 0.982636i | \(0.440595\pi\) |
−0.807916 | + | 0.589297i | \(0.799405\pi\) | |||||||
\(174\) | −5.18794 | − | 15.9668i | −0.393296 | − | 1.21044i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.65248 | − | 5.08580i | 0.124560 | − | 0.383357i | ||||
\(177\) | −9.12446 | − | 7.54841i | −0.685837 | − | 0.567373i | ||||
\(178\) | 5.01406 | + | 2.35944i | 0.375820 | + | 0.176847i | ||||
\(179\) | −4.89894 | − | 4.60041i | −0.366164 | − | 0.343851i | 0.479524 | − | 0.877529i | \(-0.340809\pi\) |
−0.845688 | + | 0.533678i | \(0.820809\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.3240 | − | 2.69385i | 1.58500 | − | 0.200232i | 0.717100 | − | 0.696970i | \(-0.245469\pi\) |
0.867900 | + | 0.496738i | \(0.165469\pi\) | |||||||
\(182\) | − | 1.10569i | − | 0.0819590i | ||||||
\(183\) | −3.11437 | − | 24.6527i | −0.230220 | − | 1.82238i | ||||
\(184\) | 11.7211 | + | 14.1684i | 0.864094 | + | 1.04451i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.29280 | − | 52.3376i | 0.241440 | − | 3.83758i | ||||
\(187\) | −0.892941 | + | 3.47777i | −0.0652983 | + | 0.254320i | ||||
\(188\) | −1.53585 | + | 5.98175i | −0.112013 | + | 0.436264i | ||||
\(189\) | 0.824598 | − | 13.1066i | 0.0599807 | − | 0.953365i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.43755 | − | 7.78166i | −0.465805 | − | 0.563061i | 0.484336 | − | 0.874882i | \(-0.339061\pi\) |
−0.950141 | + | 0.311821i | \(0.899061\pi\) | |||||||
\(192\) | −2.28258 | − | 18.0685i | −0.164731 | − | 1.30398i | ||||
\(193\) | 15.7585i | 1.13433i | 0.823606 | + | 0.567163i | \(0.191959\pi\) | ||||
−0.823606 | + | 0.567163i | \(0.808041\pi\) | |||||||
\(194\) | −29.9032 | + | 3.77766i | −2.14693 | + | 0.271220i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −19.4634 | − | 18.2774i | −1.39024 | − | 1.30553i | ||||
\(197\) | −14.1591 | − | 6.66276i | −1.00879 | − | 0.474702i | −0.150910 | − | 0.988547i | \(-0.548220\pi\) |
−0.857883 | + | 0.513846i | \(0.828220\pi\) | |||||||
\(198\) | 15.9565 | + | 13.2004i | 1.13398 | + | 0.938110i | ||||
\(199\) | 4.36121 | − | 13.4224i | 0.309158 | − | 0.951490i | −0.668935 | − | 0.743321i | \(-0.733250\pi\) |
0.978093 | − | 0.208169i | \(-0.0667505\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.9609 | + | 42.9671i | 0.984723 | + | 3.03066i | ||||
\(202\) | 9.34555 | − | 23.6042i | 0.657550 | − | 1.66078i | ||||
\(203\) | −1.09736 | + | 1.16857i | −0.0770197 | + | 0.0820176i | ||||
\(204\) | −9.00296 | − | 47.1952i | −0.630333 | − | 3.30432i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −30.7221 | + | 28.8499i | −2.14051 | + | 2.01007i | ||||
\(207\) | −25.7941 | + | 8.38100i | −1.79281 | + | 0.582520i | ||||
\(208\) | −2.85277 | − | 0.544196i | −0.197804 | − | 0.0377332i | ||||
\(209\) | 0.208281 | + | 3.31053i | 0.0144071 | + | 0.228994i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.2934 | + | 16.2198i | 0.708625 | + | 1.11661i | 0.987702 | + | 0.156346i | \(0.0499714\pi\) |
−0.279077 | + | 0.960269i | \(0.590029\pi\) | |||||||
\(212\) | −12.9436 | + | 0.814340i | −0.888968 | + | 0.0559291i | ||||
\(213\) | 14.6512 | + | 9.29794i | 1.00388 | + | 0.637084i | ||||
\(214\) | 22.3673 | − | 27.0374i | 1.52900 | − | 1.84824i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −87.7232 | − | 22.5235i | −5.96881 | − | 1.53253i | ||||
\(217\) | −4.53076 | + | 2.13202i | −0.307568 | + | 0.144731i | ||||
\(218\) | 1.95766 | + | 0.636082i | 0.132589 | + | 0.0430809i | ||||
\(219\) | 18.1638 | + | 9.98563i | 1.22740 | + | 0.674767i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.93465 | + | 0.244403i | 0.130139 | + | 0.0164403i | ||||
\(222\) | 5.73412 | − | 45.3902i | 0.384849 | − | 3.04639i | ||||
\(223\) | −3.95744 | + | 2.51147i | −0.265010 | + | 0.168180i | −0.661692 | − | 0.749776i | \(-0.730161\pi\) |
0.396682 | + | 0.917956i | \(0.370161\pi\) | |||||||
\(224\) | 1.23422 | − | 0.896713i | 0.0824647 | − | 0.0599141i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.1017 | − | 9.51893i | −0.871511 | − | 0.633190i | ||||
\(227\) | 7.25785 | + | 0.456625i | 0.481721 | + | 0.0303073i | 0.301795 | − | 0.953373i | \(-0.402414\pi\) |
0.179926 | + | 0.983680i | \(0.442414\pi\) | |||||||
\(228\) | −21.3833 | − | 38.8961i | −1.41614 | − | 2.57595i | ||||
\(229\) | −6.50796 | + | 13.8301i | −0.430058 | + | 0.913920i | 0.565932 | + | 0.824452i | \(0.308517\pi\) |
−0.995990 | + | 0.0894676i | \(0.971483\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.509150 | − | 2.66906i | 0.0334996 | − | 0.175611i | ||||
\(232\) | 6.49822 | + | 8.94404i | 0.426629 | + | 0.587205i | ||||
\(233\) | 7.63001 | − | 13.8789i | 0.499858 | − | 0.909239i | −0.499227 | − | 0.866471i | \(-0.666383\pi\) |
0.999085 | − | 0.0427674i | \(-0.0136175\pi\) | |||||||
\(234\) | 6.02640 | − | 9.49609i | 0.393958 | − | 0.620779i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 13.8845 | + | 5.49725i | 0.903802 | + | 0.357841i | ||||
\(237\) | −11.2858 | − | 28.5046i | −0.733089 | − | 1.85157i | ||||
\(238\) | −5.22382 | + | 4.32152i | −0.338610 | + | 0.280122i | ||||
\(239\) | −7.69706 | + | 1.97627i | −0.497882 | + | 0.127834i | −0.489277 | − | 0.872129i | \(-0.662739\pi\) |
−0.00860512 | + | 0.999963i | \(0.502739\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.3987 | + | 4.51307i | −0.734256 | + | 0.290712i | −0.705340 | − | 0.708869i | \(-0.749206\pi\) |
−0.0289160 | + | 0.999582i | \(0.509206\pi\) | |||||||
\(242\) | −16.8925 | − | 17.9887i | −1.08589 | − | 1.15635i | ||||
\(243\) | 31.5820 | − | 43.4689i | 2.02599 | − | 2.78853i | ||||
\(244\) | 13.3417 | + | 28.3526i | 0.854115 | + | 1.81509i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 82.3648 | − | 45.2804i | 5.25139 | − | 2.88698i | ||||
\(247\) | 1.76958 | − | 0.337565i | 0.112595 | − | 0.0214787i | ||||
\(248\) | 8.58803 | + | 33.4482i | 0.545340 | + | 2.12396i | ||||
\(249\) | −0.634279 | −0.0401958 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.12354 | −0.386514 | −0.193257 | − | 0.981148i | \(-0.561905\pi\) | ||||
−0.193257 | + | 0.981148i | \(0.561905\pi\) | |||||||
\(252\) | 6.58029 | + | 25.6285i | 0.414519 | + | 1.61444i | ||||
\(253\) | −3.44991 | + | 0.658106i | −0.216894 | + | 0.0413748i | ||||
\(254\) | 18.1573 | − | 9.98204i | 1.13929 | − | 0.626329i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.8772 | + | 29.4905i | 0.867322 | + | 1.84315i | ||||
\(257\) | −10.4816 | + | 14.4267i | −0.653823 | + | 0.899910i | −0.999257 | − | 0.0385326i | \(-0.987732\pi\) |
0.345434 | + | 0.938443i | \(0.387732\pi\) | |||||||
\(258\) | 16.0434 | + | 17.0845i | 0.998819 | + | 1.06363i | ||||
\(259\) | −4.06175 | + | 1.60816i | −0.252385 | + | 0.0999262i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.7937 | + | 4.05514i | −0.977607 | + | 0.251007i | ||||
\(262\) | −18.3930 | + | 15.2160i | −1.13632 | + | 0.940050i | ||||
\(263\) | 9.06757 | + | 22.9021i | 0.559131 | + | 1.41220i | 0.884466 | + | 0.466604i | \(0.154523\pi\) |
−0.325336 | + | 0.945599i | \(0.605477\pi\) | |||||||
\(264\) | −17.4232 | − | 6.89833i | −1.07232 | − | 0.424563i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.35600 | + | 5.28822i | −0.205770 | + | 0.324241i | ||||
\(267\) | 3.56297 | − | 6.48101i | 0.218050 | − | 0.396632i | ||||
\(268\) | −33.4867 | − | 46.0904i | −2.04552 | − | 2.81542i | ||||
\(269\) | −1.33637 | + | 7.00550i | −0.0814799 | + | 0.427133i | 0.918050 | + | 0.396465i | \(0.129763\pi\) |
−0.999530 | + | 0.0306674i | \(0.990237\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9628 | − | 23.2971i | 0.665942 | − | 1.41520i | −0.230958 | − | 0.972964i | \(-0.574186\pi\) |
0.896900 | − | 0.442234i | \(-0.145814\pi\) | |||||||
\(272\) | 8.57885 | + | 15.6049i | 0.520169 | + | 0.946185i | ||||
\(273\) | −1.47278 | − | 0.0926593i | −0.0891366 | − | 0.00560800i | ||||
\(274\) | 3.62482 | + | 2.63359i | 0.218983 | + | 0.159101i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 38.0209 | − | 27.6238i | 2.28859 | − | 1.66276i | ||||
\(277\) | −3.21964 | + | 2.04324i | −0.193449 | + | 0.122767i | −0.629024 | − | 0.777386i | \(-0.716545\pi\) |
0.435575 | + | 0.900153i | \(0.356545\pi\) | |||||||
\(278\) | 2.81099 | − | 22.2513i | 0.168592 | − | 1.33455i | ||||
\(279\) | −50.5323 | − | 6.38371i | −3.02529 | − | 0.382183i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.82242 | − | 3.75065i | −0.406991 | − | 0.223745i | 0.265089 | − | 0.964224i | \(-0.414599\pi\) |
−0.672080 | + | 0.740479i | \(0.734599\pi\) | |||||||
\(282\) | 11.5844 | + | 3.76401i | 0.689843 | + | 0.224144i | ||||
\(283\) | 2.16893 | − | 1.02062i | 0.128930 | − | 0.0606697i | −0.360232 | − | 0.932863i | \(-0.617303\pi\) |
0.489162 | + | 0.872193i | \(0.337303\pi\) | |||||||
\(284\) | −21.1945 | − | 5.44182i | −1.25766 | − | 0.322912i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.928364 | − | 1.12220i | 0.0548953 | − | 0.0663570i | ||||
\(287\) | −7.57759 | − | 4.80888i | −0.447291 | − | 0.283859i | ||||
\(288\) | 15.4874 | − | 0.974384i | 0.912603 | − | 0.0574161i | ||||
\(289\) | 2.70227 | + | 4.25810i | 0.158957 | + | 0.250476i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.52588 | + | 40.1478i | 0.148070 | + | 2.35350i | ||||
\(292\) | −25.6751 | − | 4.89779i | −1.50252 | − | 0.286622i | ||||
\(293\) | −10.5387 | + | 3.42423i | −0.615677 | + | 0.200046i | −0.600220 | − | 0.799835i | \(-0.704920\pi\) |
−0.0154571 | + | 0.999881i | \(0.504920\pi\) | |||||||
\(294\) | −38.3881 | + | 36.0488i | −2.23884 | + | 2.10241i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.64535 | + | 29.5939i | 0.328129 | + | 1.72011i | ||||
\(297\) | 11.8416 | − | 12.6100i | 0.687117 | − | 0.731705i | ||||
\(298\) | −5.56214 | + | 14.0484i | −0.322206 | + | 0.813800i | ||||
\(299\) | 0.589424 | + | 1.81406i | 0.0340873 | + | 0.104910i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.691528 | − | 2.12830i | 0.0398590 | − | 0.122673i | ||||
\(302\) | 20.9405 | + | 17.3235i | 1.20499 | + | 0.996853i | ||||
\(303\) | −30.6576 | − | 14.4264i | −1.76123 | − | 0.828774i | ||||
\(304\) | 11.9923 | + | 11.2615i | 0.687807 | + | 0.645894i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −68.4181 | + | 8.64321i | −3.91120 | + | 0.494100i | ||||
\(307\) | − | 9.15311i | − | 0.522396i | −0.965285 | − | 0.261198i | \(-0.915882\pi\) | ||
0.965285 | − | 0.261198i | \(-0.0841175\pi\) | |||||||
\(308\) | 0.429447 | + | 3.39942i | 0.0244700 | + | 0.193700i | ||||
\(309\) | 35.8536 | + | 43.3396i | 2.03964 | + | 2.46550i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.68332 | + | 26.7556i | −0.0954523 | + | 1.51717i | 0.600815 | + | 0.799388i | \(0.294843\pi\) |
−0.696267 | + | 0.717782i | \(0.745157\pi\) | |||||||
\(312\) | −2.53095 | + | 9.85738i | −0.143287 | + | 0.558064i | ||||
\(313\) | 6.52893 | − | 25.4285i | 0.369037 | − | 1.43730i | −0.464860 | − | 0.885384i | \(-0.653895\pi\) |
0.833897 | − | 0.551920i | \(-0.186105\pi\) | |||||||
\(314\) | −2.33059 | + | 37.0437i | −0.131523 | + | 2.09050i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.6427 | + | 29.7879i | 1.38626 | + | 1.67570i | ||||
\(317\) | 1.58301 | + | 12.5308i | 0.0889106 | + | 0.703800i | 0.972064 | + | 0.234716i | \(0.0754160\pi\) |
−0.883153 | + | 0.469084i | \(0.844584\pi\) | |||||||
\(318\) | 25.5793i | 1.43442i | ||||||||
\(319\) | −2.09491 | + | 0.264649i | −0.117293 | + | 0.0148175i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −34.1395 | − | 32.0591i | −1.90548 | − | 1.78936i | ||||
\(322\) | −6.00038 | − | 2.82356i | −0.334388 | − | 0.157351i | ||||
\(323\) | −8.51111 | − | 7.04100i | −0.473571 | − | 0.391772i | ||||
\(324\) | −40.4126 | + | 124.377i | −2.24514 | + | 6.90984i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.03302 | + | 18.5677i | 0.334138 | + | 1.02837i | ||||
\(327\) | 1.01132 | − | 2.55430i | 0.0559261 | − | 0.141253i | ||||
\(328\) | −42.3694 | + | 45.1189i | −2.33946 | + | 2.49127i | ||||
\(329\) | −0.217936 | − | 1.14246i | −0.0120152 | − | 0.0629859i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.72986 | − | 7.25882i | 0.424871 | − | 0.398981i | −0.442399 | − | 0.896818i | \(-0.645872\pi\) |
0.867270 | + | 0.497838i | \(0.165872\pi\) | |||||||
\(332\) | 0.760695 | − | 0.247165i | 0.0417486 | − | 0.0135649i | ||||
\(333\) | −43.6490 | − | 8.32650i | −2.39195 | − | 0.456289i | ||||
\(334\) | −1.46317 | − | 23.2564i | −0.0800609 | − | 1.27253i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.22077 | − | 11.3781i | −0.393925 | − | 0.620727i | ||||
\(337\) | 35.3624 | − | 2.22481i | 1.92631 | − | 0.121193i | 0.946703 | − | 0.322108i | \(-0.104392\pi\) |
0.979609 | + | 0.200915i | \(0.0643915\pi\) | |||||||
\(338\) | 26.6317 | + | 16.9010i | 1.44857 | + | 0.919293i | ||||
\(339\) | −13.7772 | + | 16.6538i | −0.748275 | + | 0.904509i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.38852 | − | 1.64029i | −0.345958 | − | 0.0888269i | ||||
\(342\) | −57.6454 | + | 27.1259i | −3.11711 | + | 1.46680i | ||||
\(343\) | 10.0303 | + | 3.25905i | 0.541586 | + | 0.175972i | ||||
\(344\) | −13.5243 | − | 7.43502i | −0.729179 | − | 0.400869i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −54.8708 | − | 6.93180i | −2.94987 | − | 0.372656i | ||||
\(347\) | −3.75356 | + | 29.7125i | −0.201502 | + | 1.59505i | 0.489372 | + | 0.872075i | \(0.337226\pi\) |
−0.690874 | + | 0.722975i | \(0.742774\pi\) | |||||||
\(348\) | 23.8567 | − | 15.1399i | 1.27885 | − | 0.811584i | ||||
\(349\) | −10.9765 | + | 7.97493i | −0.587561 | + | 0.426888i | −0.841442 | − | 0.540347i | \(-0.818293\pi\) |
0.253881 | + | 0.967235i | \(0.418293\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.60045 | − | 5.52205i | −0.405682 | − | 0.294745i | ||||
\(352\) | 2.00555 | + | 0.126179i | 0.106896 | + | 0.00672535i | ||||
\(353\) | −11.0371 | − | 20.0764i | −0.587445 | − | 1.06856i | −0.988315 | − | 0.152424i | \(-0.951292\pi\) |
0.400870 | − | 0.916135i | \(-0.368708\pi\) | |||||||
\(354\) | 12.5404 | − | 26.6498i | 0.666517 | − | 1.41642i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.74758 | + | 9.16113i | −0.0926215 | + | 0.485539i | ||||
\(357\) | 5.31850 | + | 7.32029i | 0.281485 | + | 0.387431i | ||||
\(358\) | 8.05229 | − | 14.6471i | 0.425577 | − | 0.774122i | ||||
\(359\) | 10.3356 | − | 16.2863i | 0.545493 | − | 0.859559i | −0.454013 | − | 0.890995i | \(-0.650008\pi\) |
0.999506 | + | 0.0314359i | \(0.0100080\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.17775 | + | 3.23780i | 0.430408 | + | 0.170410i | ||||
\(362\) | 19.6790 | + | 49.7034i | 1.03430 | + | 2.61235i | ||||
\(363\) | −25.3766 | + | 20.9933i | −1.33192 | + | 1.10186i | ||||
\(364\) | 1.80242 | − | 0.462782i | 0.0944724 | − | 0.0242564i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 57.4623 | − | 22.7509i | 3.00360 | − | 1.18921i | ||||
\(367\) | 4.39423 | + | 4.67937i | 0.229377 | + | 0.244261i | 0.833353 | − | 0.552741i | \(-0.186418\pi\) |
−0.603977 | + | 0.797002i | \(0.706418\pi\) | |||||||
\(368\) | −10.2383 | + | 14.0918i | −0.533709 | + | 0.734587i | ||||
\(369\) | −38.8692 | − | 82.6012i | −2.02345 | − | 4.30005i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.14032 | − | 1.17665i | 0.111120 | − | 0.0610888i | ||||
\(372\) | 86.6955 | − | 16.5381i | 4.49495 | − | 0.857458i | ||||
\(373\) | −1.32347 | − | 5.15457i | −0.0685267 | − | 0.266894i | 0.925083 | − | 0.379765i | \(-0.123995\pi\) |
−0.993610 | + | 0.112871i | \(0.963995\pi\) | |||||||
\(374\) | −8.93029 | −0.461774 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.02107 | −0.413655 | ||||||||
\(377\) | 0.285192 | + | 1.11075i | 0.0146882 | + | 0.0572066i | ||||
\(378\) | 32.0839 | − | 6.12034i | 1.65022 | − | 0.314796i | ||||
\(379\) | −29.2409 | + | 16.0753i | −1.50201 | + | 0.825735i | −0.999251 | − | 0.0386947i | \(-0.987680\pi\) |
−0.502755 | + | 0.864429i | \(0.667680\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.7745 | − | 25.0221i | −0.603225 | − | 1.28192i | ||||
\(382\) | 14.7643 | − | 20.3213i | 0.755405 | − | 1.03973i | ||||
\(383\) | 10.6083 | + | 11.2967i | 0.542061 | + | 0.577236i | 0.940429 | − | 0.339990i | \(-0.110424\pi\) |
−0.398369 | + | 0.917225i | \(0.630424\pi\) | |||||||
\(384\) | 54.0609 | − | 21.4042i | 2.75878 | − | 1.09228i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −37.9624 | + | 9.74710i | −1.93224 | + | 0.496114i | ||||
\(387\) | 17.5392 | − | 14.5097i | 0.891566 | − | 0.737567i | ||||
\(388\) | −18.6740 | − | 47.1652i | −0.948029 | − | 2.39445i | ||||
\(389\) | 8.97238 | + | 3.55241i | 0.454917 | + | 0.180115i | 0.584398 | − | 0.811467i | \(-0.301331\pi\) |
−0.129480 | + | 0.991582i | \(0.541331\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.26679 | − | 9.87489i | 0.316925 | − | 0.499395i | ||||
\(392\) | 16.7061 | − | 30.3884i | 0.843788 | − | 1.53484i | ||||
\(393\) | 18.7264 | + | 25.7747i | 0.944623 | + | 1.30016i | ||||
\(394\) | 7.29284 | − | 38.2304i | 0.367408 | − | 1.92602i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −14.8398 | + | 31.5362i | −0.745729 | + | 1.58476i | ||||
\(397\) | −4.88630 | − | 8.88815i | −0.245236 | − | 0.446083i | 0.724828 | − | 0.688929i | \(-0.241919\pi\) |
−0.970065 | + | 0.242846i | \(0.921919\pi\) | |||||||
\(398\) | 35.0322 | + | 2.20404i | 1.75601 | + | 0.110479i | ||||
\(399\) | 6.76268 | + | 4.91337i | 0.338557 | + | 0.245976i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.5702 | − | 11.3124i | 0.777537 | − | 0.564914i | −0.126702 | − | 0.991941i | \(-0.540439\pi\) |
0.904239 | + | 0.427027i | \(0.140439\pi\) | |||||||
\(402\) | −94.8728 | + | 60.2081i | −4.73182 | + | 3.00291i | ||||
\(403\) | −0.448958 | + | 3.55387i | −0.0223642 | + | 0.177031i | ||||
\(404\) | 42.3895 | + | 5.35504i | 2.10896 | + | 0.266423i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.49384 | − | 1.92076i | −0.173397 | − | 0.0953255i | ||||
\(407\) | −5.47266 | − | 1.77818i | −0.271270 | − | 0.0881409i | ||||
\(408\) | 56.4632 | − | 26.5696i | 2.79535 | − | 1.31539i | ||||
\(409\) | −24.7135 | − | 6.34535i | −1.22201 | − | 0.313758i | −0.418037 | − | 0.908430i | \(-0.637282\pi\) |
−0.803968 | + | 0.594672i | \(0.797282\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.81171 | − | 4.60757i | 0.188018 | − | 0.227275i | ||||
\(412\) | −59.8879 | − | 38.0060i | −2.95047 | − | 1.87242i | ||||
\(413\) | −2.80676 | + | 0.176586i | −0.138111 | + | 0.00868923i | ||||
\(414\) | −36.1442 | − | 56.9542i | −1.77639 | − | 2.79914i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.0685271 | − | 1.08921i | −0.00335982 | − | 0.0534027i | ||||
\(417\) | −29.4032 | − | 5.60897i | −1.43988 | − | 0.274672i | ||||
\(418\) | −7.84625 | + | 2.54940i | −0.383773 | + | 0.124695i | ||||
\(419\) | 26.8086 | − | 25.1749i | 1.30969 | − | 1.22988i | 0.354084 | − | 0.935213i | \(-0.384793\pi\) |
0.955601 | − | 0.294663i | \(-0.0952074\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.27563 | − | 22.4137i | −0.208382 | − | 1.09237i | −0.920627 | − | 0.390444i | \(-0.872322\pi\) |
0.712245 | − | 0.701931i | \(-0.247678\pi\) | |||||||
\(422\) | −32.7068 | + | 34.8292i | −1.59214 | + | 1.69546i | ||||
\(423\) | 4.35511 | − | 10.9997i | 0.211752 | − | 0.534826i | ||||
\(424\) | −5.20517 | − | 16.0199i | −0.252786 | − | 0.777994i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −13.3366 | + | 41.0459i | −0.646161 | + | 1.98868i | ||||
\(427\) | −4.54693 | − | 3.76155i | −0.220041 | − | 0.182034i | ||||
\(428\) | 53.4364 | + | 25.1452i | 2.58294 | + | 1.21544i | ||||
\(429\) | −1.41697 | − | 1.33063i | −0.0684121 | − | 0.0642432i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.7583 | + | 2.62238i | −0.999891 | + | 0.126316i | −0.608202 | − | 0.793782i | \(-0.708109\pi\) |
−0.391689 | + | 0.920098i | \(0.628109\pi\) | |||||||
\(432\) | − | 85.7917i | − | 4.12766i | ||||||
\(433\) | 1.84693 | + | 14.6200i | 0.0887578 | + | 0.702590i | 0.972217 | + | 0.234082i | \(0.0752084\pi\) |
−0.883459 | + | 0.468508i | \(0.844792\pi\) | |||||||
\(434\) | −7.93844 | − | 9.59592i | −0.381057 | − | 0.460619i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.217526 | + | 3.45748i | −0.0104176 | + | 0.165583i | ||||
\(437\) | 2.68701 | − | 10.4652i | 0.128537 | − | 0.500619i | ||||
\(438\) | −12.8206 | + | 49.9331i | −0.612594 | + | 2.38590i | ||||
\(439\) | 0.861319 | − | 13.6903i | 0.0411085 | − | 0.653401i | −0.922485 | − | 0.386032i | \(-0.873846\pi\) |
0.963594 | − | 0.267370i | \(-0.0861545\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 32.6025 | + | 39.4097i | 1.55250 | + | 1.87665i | ||||
\(442\) | 0.607865 | + | 4.81175i | 0.0289132 | + | 0.228872i | ||||
\(443\) | 5.72633i | 0.272066i | 0.990704 | + | 0.136033i | \(0.0434354\pi\) | ||||
−0.990704 | + | 0.136033i | \(0.956565\pi\) | |||||||
\(444\) | 76.3922 | − | 9.65058i | 3.62541 | − | 0.457996i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.49792 | − | 7.98008i | −0.402388 | − | 0.377868i | ||||
\(447\) | 18.2463 | + | 8.58607i | 0.863022 | + | 0.406107i | ||||
\(448\) | −3.33254 | − | 2.75692i | −0.157448 | − | 0.130252i | ||||
\(449\) | 0.254531 | − | 0.783366i | 0.0120121 | − | 0.0369693i | −0.944871 | − | 0.327443i | \(-0.893813\pi\) |
0.956883 | + | 0.290474i | \(0.0938130\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.65308 | − | 11.2430i | −0.172017 | − | 0.529414i | ||||
\(452\) | 10.0335 | − | 25.3416i | 0.471934 | − | 1.19197i | ||||
\(453\) | 24.8298 | − | 26.4410i | 1.16660 | − | 1.24231i | ||||
\(454\) | 3.38917 | + | 17.7666i | 0.159062 | + | 0.833830i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 42.0242 | − | 39.4633i | 1.96796 | − | 1.84804i | ||||
\(457\) | −8.06467 | + | 2.62037i | −0.377250 | + | 0.122576i | −0.491503 | − | 0.870876i | \(-0.663552\pi\) |
0.114254 | + | 0.993452i | \(0.463552\pi\) | |||||||
\(458\) | −37.3422 | − | 7.12340i | −1.74489 | − | 0.332855i | ||||
\(459\) | 3.61702 | + | 57.4909i | 0.168828 | + | 2.68345i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.7334 | − | 29.5191i | −0.872502 | − | 1.37484i | −0.926497 | − | 0.376303i | \(-0.877195\pi\) |
0.0539945 | − | 0.998541i | \(-0.482805\pi\) | |||||||
\(462\) | 6.74470 | − | 0.424340i | 0.313792 | − | 0.0197421i | ||||
\(463\) | −5.58091 | − | 3.54176i | −0.259367 | − | 0.164599i | 0.399785 | − | 0.916609i | \(-0.369085\pi\) |
−0.659152 | + | 0.752010i | \(0.729085\pi\) | |||||||
\(464\) | −6.67532 | + | 8.06908i | −0.309894 | + | 0.374598i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 38.1538 | + | 9.79623i | 1.76744 | + | 0.453801i | ||||
\(467\) | 13.3371 | − | 6.27598i | 0.617170 | − | 0.290418i | −0.0916681 | − | 0.995790i | \(-0.529220\pi\) |
0.708838 | + | 0.705372i | \(0.249220\pi\) | |||||||
\(468\) | 18.0022 | + | 5.84928i | 0.832153 | + | 0.270383i | ||||
\(469\) | 9.40201 | + | 5.16880i | 0.434145 | + | 0.238673i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 49.1470 | + | 6.20871i | 2.26457 | + | 0.286082i | ||||
\(472\) | −2.43085 | + | 19.2422i | −0.111889 | + | 0.885692i | ||||
\(473\) | 2.48884 | − | 1.57946i | 0.114437 | − | 0.0726238i | ||||
\(474\) | 61.6872 | − | 44.8184i | 2.83339 | − | 2.05858i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −9.23107 | − | 6.70676i | −0.423105 | − | 0.307404i | ||||
\(477\) | 24.7951 | + | 1.55998i | 1.13529 | + | 0.0714265i | ||||
\(478\) | −9.52169 | − | 17.3199i | −0.435512 | − | 0.792194i | ||||
\(479\) | −3.28956 | + | 6.99068i | −0.150304 | + | 0.319412i | −0.965773 | − | 0.259388i | \(-0.916479\pi\) |
0.815469 | + | 0.578801i | \(0.196479\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.585591 | + | 3.06978i | −0.0267006 | + | 0.139970i | ||||
\(482\) | −17.9224 | − | 24.6681i | −0.816344 | − | 1.12360i | ||||
\(483\) | −4.26384 | + | 7.75590i | −0.194011 | + | 0.352906i | ||||
\(484\) | 22.2536 | − | 35.0661i | 1.01153 | − | 1.59391i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 124.251 | + | 49.1945i | 5.63615 | + | 2.23151i | ||||
\(487\) | 10.2387 | + | 25.8600i | 0.463959 | + | 1.17183i | 0.953914 | + | 0.300079i | \(0.0970131\pi\) |
−0.489955 | + | 0.871748i | \(0.662987\pi\) | |||||||
\(488\) | −31.3580 | + | 25.9416i | −1.41951 | + | 1.17432i | ||||
\(489\) | 25.2379 | − | 6.47998i | 1.14130 | − | 0.293035i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.9298 | − | 6.30707i | 0.718904 | − | 0.284634i | 0.0199499 | − | 0.999801i | \(-0.493649\pi\) |
0.698954 | + | 0.715167i | \(0.253649\pi\) | |||||||
\(492\) | 108.287 | + | 115.314i | 4.88194 | + | 5.19874i | ||||
\(493\) | 4.13308 | − | 5.68870i | 0.186145 | − | 0.256206i | ||||
\(494\) | 1.90773 | + | 4.05412i | 0.0858327 | + | 0.182404i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −28.6655 | + | 15.7590i | −1.28712 | + | 0.707599i | ||||
\(497\) | 4.04796 | − | 0.772189i | 0.181576 | − | 0.0346374i | ||||
\(498\) | −0.392319 | − | 1.52798i | −0.0175802 | − | 0.0684705i | ||||
\(499\) | 7.49374 | 0.335466 | 0.167733 | − | 0.985832i | \(-0.446355\pi\) | ||||
0.167733 | + | 0.985832i | \(0.446355\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −31.1001 | −1.38945 | ||||||||
\(502\) | −3.78758 | − | 14.7516i | −0.169048 | − | 0.658398i | ||||
\(503\) | −31.6850 | + | 6.04424i | −1.41276 | + | 0.269499i | −0.836591 | − | 0.547828i | \(-0.815455\pi\) |
−0.576174 | + | 0.817327i | \(0.695455\pi\) | |||||||
\(504\) | −30.1151 | + | 16.5559i | −1.34143 | + | 0.737458i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.71925 | − | 7.90381i | −0.165341 | − | 0.351367i | ||||
\(507\) | 24.7440 | − | 34.0571i | 1.09892 | − | 1.51253i | ||||
\(508\) | 23.8718 | + | 25.4208i | 1.05914 | + | 1.12787i | ||||
\(509\) | −21.8917 | + | 8.66755i | −0.970335 | + | 0.384183i | −0.799200 | − | 0.601065i | \(-0.794743\pi\) |
−0.171134 | + | 0.985248i | \(0.554743\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.76785 | − | 1.22418i | 0.210917 | − | 0.0541544i | ||||
\(512\) | −35.4663 | + | 29.3403i | −1.56740 | + | 1.29667i | ||||
\(513\) | 19.5903 | + | 49.4796i | 0.864935 | + | 2.18458i | ||||
\(514\) | −41.2371 | − | 16.3269i | −1.81889 | − | 0.720149i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −21.1351 | + | 33.3036i | −0.930421 | + | 1.46611i | ||||
\(517\) | 0.738049 | − | 1.34251i | 0.0324594 | − | 0.0590434i | ||||
\(518\) | −6.38637 | − | 8.79009i | −0.280601 | − | 0.386214i | ||||
\(519\) | −13.8315 | + | 72.5072i | −0.607135 | + | 3.18271i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.43758 | + | 13.6806i | −0.282036 | + | 0.599356i | −0.994777 | − | 0.102071i | \(-0.967453\pi\) |
0.712742 | + | 0.701427i | \(0.247453\pi\) | |||||||
\(522\) | −19.5377 | − | 35.5390i | −0.855142 | − | 1.55550i | ||||
\(523\) | 38.1685 | + | 2.40136i | 1.66899 | + | 0.105004i | 0.868937 | − | 0.494922i | \(-0.164803\pi\) |
0.800055 | + | 0.599926i | \(0.204803\pi\) | |||||||
\(524\) | −32.5025 | − | 23.6145i | −1.41988 | − | 1.03160i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −49.5627 | + | 36.0094i | −2.16104 | + | 1.57008i | ||||
\(527\) | 18.5450 | − | 11.7690i | 0.807831 | − | 0.512665i | ||||
\(528\) | 2.22476 | − | 17.6108i | 0.0968202 | − | 0.766411i | ||||
\(529\) | −11.4688 | − | 1.44885i | −0.498645 | − | 0.0629935i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −25.0680 | − | 13.7813i | −1.08786 | − | 0.598055i | ||||
\(532\) | −10.0251 | − | 3.25737i | −0.434645 | − | 0.141225i | ||||
\(533\) | −5.80923 | + | 2.73362i | −0.251626 | + | 0.118406i | ||||
\(534\) | 17.8166 | + | 4.57452i | 0.771000 | + | 0.197959i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 47.1653 | − | 57.0131i | 2.03723 | − | 2.46259i | ||||
\(537\) | −18.8351 | − | 11.9531i | −0.812796 | − | 0.515816i | ||||
\(538\) | −17.7029 | + | 1.11377i | −0.763225 | + | 0.0480180i | ||||
\(539\) | 3.54898 | + | 5.59230i | 0.152865 | + | 0.240877i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.275102 | − | 4.37262i | −0.0118276 | − | 0.187994i | −0.999504 | − | 0.0314854i | \(-0.989976\pi\) |
0.987677 | − | 0.156508i | \(-0.0500238\pi\) | |||||||
\(542\) | 62.9036 | + | 11.9995i | 2.70194 | + | 0.515423i | ||||
\(543\) | 67.8542 | − | 22.0472i | 2.91190 | − | 0.946135i | ||||
\(544\) | −4.87812 | + | 4.58086i | −0.209148 | + | 0.196403i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.687737 | − | 3.60524i | −0.0294324 | − | 0.154290i | ||||
\(547\) | −18.4117 | + | 19.6064i | −0.787226 | + | 0.838311i | −0.990022 | − | 0.140910i | \(-0.954997\pi\) |
0.202796 | + | 0.979221i | \(0.434997\pi\) | |||||||
\(548\) | −2.77594 | + | 7.01122i | −0.118582 | + | 0.299505i | ||||
\(549\) | −18.5491 | − | 57.0882i | −0.791655 | − | 2.43646i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.00737 | − | 6.17806i | 0.0855169 | − | 0.263194i | ||||
\(552\) | 47.0312 | + | 38.9076i | 2.00178 | + | 1.65602i | ||||
\(553\) | −6.58775 | − | 3.09996i | −0.280140 | − | 0.131824i | ||||
\(554\) | −6.91362 | − | 6.49232i | −0.293731 | − | 0.275832i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 37.4492 | − | 4.73093i | 1.58820 | − | 0.200636i | ||||
\(557\) | − | 9.84523i | − | 0.417156i | −0.978006 | − | 0.208578i | \(-0.933117\pi\) | ||
0.978006 | − | 0.208578i | \(-0.0668835\pi\) | |||||||
\(558\) | −15.8772 | − | 125.681i | −0.672136 | − | 5.32050i | ||||
\(559\) | −1.02044 | − | 1.23351i | −0.0431602 | − | 0.0521717i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.748380 | + | 11.8952i | −0.0315966 | + | 0.502214i | ||||
\(562\) | 4.81550 | − | 18.7551i | 0.203129 | − | 0.791137i | ||||
\(563\) | −3.54726 | + | 13.8157i | −0.149499 | + | 0.582260i | 0.849045 | + | 0.528320i | \(0.177178\pi\) |
−0.998544 | + | 0.0539400i | \(0.982822\pi\) | |||||||
\(564\) | −1.28721 | + | 20.4596i | −0.0542013 | + | 0.861505i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.80023 | + | 4.59369i | 0.159736 | + | 0.193087i | ||||
\(567\) | −3.08682 | − | 24.4347i | −0.129634 | − | 1.02616i | ||||
\(568\) | − | 28.4202i | − | 1.19248i | ||||||
\(569\) | 26.4864 | − | 3.34601i | 1.11037 | − | 0.140272i | 0.451311 | − | 0.892367i | \(-0.350956\pi\) |
0.659055 | + | 0.752095i | \(0.270956\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.4283 | + | 15.4272i | 0.687503 | + | 0.645609i | 0.947409 | − | 0.320025i | \(-0.103691\pi\) |
−0.259906 | + | 0.965634i | \(0.583691\pi\) | |||||||
\(572\) | 2.21790 | + | 1.04366i | 0.0927350 | + | 0.0436378i | ||||
\(573\) | −25.8307 | − | 21.3690i | −1.07909 | − | 0.892703i | ||||
\(574\) | 6.89768 | − | 21.2289i | 0.287904 | − | 0.886076i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −13.5950 | − | 41.8411i | −0.566458 | − | 1.74338i | ||||
\(577\) | −6.80093 | + | 17.1772i | −0.283126 | + | 0.715095i | 0.716716 | + | 0.697365i | \(0.245644\pi\) |
−0.999843 | + | 0.0177308i | \(0.994356\pi\) | |||||||
\(578\) | −8.58635 | + | 9.14354i | −0.357145 | + | 0.380321i | ||||
\(579\) | 9.80181 | + | 51.3829i | 0.407349 | + | 2.13540i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.109806 | + | 0.103114i | −0.00455550 | + | 0.00427790i | ||||
\(582\) | −95.1539 | + | 30.9174i | −3.94426 | + | 1.28157i | ||||
\(583\) | 3.16023 | + | 0.602847i | 0.130884 | + | 0.0249674i | ||||
\(584\) | −2.13162 | − | 33.8811i | −0.0882070 | − | 1.40201i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.7675 | − | 23.2698i | −0.610038 | − | 0.961267i | ||||
\(587\) | 28.2931 | − | 1.78005i | 1.16778 | − | 0.0734705i | 0.532966 | − | 0.846136i | \(-0.321077\pi\) |
0.634813 | + | 0.772666i | \(0.281077\pi\) | |||||||
\(588\) | −74.8316 | − | 47.4896i | −3.08600 | − | 1.95844i | ||||
\(589\) | 12.9340 | − | 15.6345i | 0.532937 | − | 0.644210i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −50.3119 | − | 12.9179i | −2.06955 | − | 0.531371i | ||||
\(592\) | −25.8225 | + | 12.1511i | −1.06130 | + | 0.499408i | ||||
\(593\) | −39.4502 | − | 12.8181i | −1.62003 | − | 0.526378i | −0.648078 | − | 0.761574i | \(-0.724427\pi\) |
−0.971948 | + | 0.235196i | \(0.924427\pi\) | |||||||
\(594\) | 37.7019 | + | 20.7268i | 1.54693 | + | 0.850430i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −25.2287 | − | 3.18713i | −1.03341 | − | 0.130550i | ||||
\(597\) | 5.87157 | − | 46.4783i | 0.240308 | − | 1.90223i | ||||
\(598\) | −4.00551 | + | 2.54197i | −0.163797 | + | 0.103949i | ||||
\(599\) | −27.7097 | + | 20.1323i | −1.13219 | + | 0.822583i | −0.986012 | − | 0.166675i | \(-0.946697\pi\) |
−0.146177 | + | 0.989258i | \(0.546697\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.0658 | + | 19.6644i | 1.10404 | + | 0.802130i | 0.981714 | − | 0.190361i | \(-0.0609658\pi\) |
0.122322 | + | 0.992490i | \(0.460966\pi\) | |||||||
\(602\) | 5.55483 | + | 0.349480i | 0.226398 | + | 0.0142437i | ||||
\(603\) | 52.5764 | + | 95.6362i | 2.14108 | + | 3.89461i | ||||
\(604\) | −19.4750 | + | 41.3865i | −0.792426 | + | 1.68399i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 15.7907 | − | 82.7775i | 0.641451 | − | 3.36261i | ||||
\(607\) | 16.7437 | + | 23.0458i | 0.679607 | + | 0.935399i | 0.999929 | − | 0.0119096i | \(-0.00379104\pi\) |
−0.320322 | + | 0.947309i | \(0.603791\pi\) | |||||||
\(608\) | −2.97823 | + | 5.41739i | −0.120783 | + | 0.219704i | ||||
\(609\) | −2.85125 | + | 4.49284i | −0.115538 | + | 0.182059i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.773597 | − | 0.306289i | −0.0312964 | − | 0.0123911i | ||||
\(612\) | −42.7258 | − | 107.913i | −1.72709 | − | 4.36213i | ||||
\(613\) | −3.71313 | + | 3.07177i | −0.149972 | + | 0.124068i | −0.709384 | − | 0.704822i | \(-0.751027\pi\) |
0.559412 | + | 0.828890i | \(0.311027\pi\) | |||||||
\(614\) | 22.0499 | − | 5.66145i | 0.889862 | − | 0.228478i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.13773 | + | 1.63824i | −0.166714 | + | 0.0660068i | ||||
\(617\) | −15.2887 | − | 16.2808i | −0.615498 | − | 0.655439i | 0.343400 | − | 0.939189i | \(-0.388421\pi\) |
−0.958898 | + | 0.283750i | \(0.908421\pi\) | |||||||
\(618\) | −82.2288 | + | 113.178i | −3.30773 | + | 4.55270i | ||||
\(619\) | 8.92369 | + | 18.9638i | 0.358673 | + | 0.762220i | 0.999987 | − | 0.00505895i | \(-0.00161032\pi\) |
−0.641314 | + | 0.767279i | \(0.721610\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −49.3763 | + | 27.1448i | −1.98140 | + | 1.08928i | ||||
\(622\) | −65.4956 | + | 12.4939i | −2.62613 | + | 0.500962i | ||||
\(623\) | −0.436797 | − | 1.70121i | −0.0174999 | − | 0.0681577i | ||||
\(624\) | −9.64034 | −0.385923 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 65.2957 | 2.60974 | ||||||||
\(627\) | 2.73827 | + | 10.6649i | 0.109356 | + | 0.425914i | ||||
\(628\) | −61.3617 | + | 11.7054i | −2.44860 | + | 0.467095i | ||||
\(629\) | 16.7919 | − | 9.23142i | 0.669537 | − | 0.368081i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.6737 | + | 39.6835i | 0.743386 | + | 1.57978i | 0.813042 | + | 0.582205i | \(0.197810\pi\) |
−0.0696553 | + | 0.997571i | \(0.522190\pi\) | |||||||
\(632\) | −29.5134 | + | 40.6218i | −1.17398 | + | 1.61585i | ||||
\(633\) | 43.6516 | + | 46.4843i | 1.73500 | + | 1.84758i | ||||
\(634\) | −29.2077 | + | 11.5641i | −1.15998 | + | 0.459270i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −41.6977 | + | 10.7062i | −1.65342 | + | 0.424527i | ||||
\(637\) | 2.77163 | − | 2.29289i | 0.109816 | − | 0.0908477i | ||||
\(638\) | −1.93330 | − | 4.88296i | −0.0765402 | − | 0.193318i | ||||
\(639\) | 38.9742 | + | 15.4310i | 1.54180 | + | 0.610440i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.4110 | − | 21.1323i | 0.529701 | − | 0.834675i | −0.469124 | − | 0.883132i | \(-0.655430\pi\) |
0.998825 | + | 0.0484569i | \(0.0154304\pi\) | |||||||
\(642\) | 56.1143 | − | 102.072i | 2.21466 | − | 4.02844i | ||||
\(643\) | −4.15494 | − | 5.71879i | −0.163855 | − | 0.225527i | 0.719192 | − | 0.694811i | \(-0.244512\pi\) |
−0.883047 | + | 0.469284i | \(0.844512\pi\) | |||||||
\(644\) | 2.09135 | − | 10.9632i | 0.0824106 | − | 0.432011i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.6975 | − | 24.8584i | 0.460230 | − | 0.978039i | ||||
\(647\) | 4.89054 | + | 8.89586i | 0.192267 | + | 0.349732i | 0.954816 | − | 0.297198i | \(-0.0960523\pi\) |
−0.762549 | + | 0.646931i | \(0.776052\pi\) | |||||||
\(648\) | −169.519 | − | 10.6652i | −6.65932 | − | 0.418969i | ||||
\(649\) | −2.99694 | − | 2.17740i | −0.117640 | − | 0.0854705i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.4471 | + | 9.76986i | −0.527032 | + | 0.382911i | ||||
\(652\) | −27.7428 | + | 17.6061i | −1.08649 | + | 0.689509i | ||||
\(653\) | 1.92930 | − | 15.2720i | 0.0754993 | − | 0.597639i | −0.908294 | − | 0.418332i | \(-0.862615\pi\) |
0.983793 | − | 0.179306i | \(-0.0573853\pi\) | |||||||
\(654\) | 6.77885 | + | 0.856368i | 0.265074 | + | 0.0334867i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −51.3775 | − | 28.2450i | −2.00596 | − | 1.10278i | ||||
\(657\) | 47.6204 | + | 15.4728i | 1.85785 | + | 0.603652i | ||||
\(658\) | 2.61739 | − | 1.23165i | 0.102037 | − | 0.0480148i | ||||
\(659\) | 25.0852 | + | 6.44078i | 0.977180 | + | 0.250897i | 0.703321 | − | 0.710873i | \(-0.251700\pi\) |
0.273859 | + | 0.961770i | \(0.411700\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.1644 | + | 34.0449i | −1.09547 | + | 1.32419i | −0.153628 | + | 0.988129i | \(0.549096\pi\) |
−0.941839 | + | 0.336064i | \(0.890904\pi\) | |||||||
\(662\) | 22.2677 | + | 14.1315i | 0.865457 | + | 0.549236i | ||||
\(663\) | 6.46020 | − | 0.406442i | 0.250893 | − | 0.0157849i | ||||
\(664\) | 0.556634 | + | 0.877115i | 0.0216016 | + | 0.0340387i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.93955 | − | 110.301i | −0.268902 | − | 4.27407i | ||||
\(667\) | 6.75615 | + | 1.28880i | 0.261599 | + | 0.0499027i | ||||
\(668\) | 37.2986 | − | 12.1190i | 1.44313 | − | 0.468900i | ||||
\(669\) | −11.3416 | + | 10.6505i | −0.438493 | + | 0.411772i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.45654 | − | 7.63545i | −0.0562291 | − | 0.294763i | ||||
\(672\) | 3.46658 | − | 3.69154i | 0.133726 | − | 0.142404i | ||||
\(673\) | 6.95425 | − | 17.5644i | 0.268067 | − | 0.677059i | −0.731924 | − | 0.681386i | \(-0.761377\pi\) |
0.999991 | + | 0.00432713i | \(0.00137737\pi\) | |||||||
\(674\) | 27.2322 | + | 83.8121i | 1.04894 | + | 3.22832i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16.4043 | + | 50.4871i | −0.630933 | + | 1.94181i | ||||
\(677\) | −34.8177 | − | 28.8037i | −1.33815 | − | 1.10702i | −0.985206 | − | 0.171371i | \(-0.945180\pi\) |
−0.352945 | − | 0.935644i | \(-0.614820\pi\) | |||||||
\(678\) | −48.6406 | − | 22.8885i | −1.86803 | − | 0.879029i | ||||
\(679\) | 6.96407 | + | 6.53970i | 0.267257 | + | 0.250971i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.9492 | − | 3.02549i | 0.917737 | − | 0.115937i | ||||
\(682\) | − | 16.4045i | − | 0.628163i | ||||||
\(683\) | 1.23898 | + | 9.80757i | 0.0474084 | + | 0.375276i | 0.997913 | + | 0.0645669i | \(0.0205666\pi\) |
−0.950505 | + | 0.310709i | \(0.899433\pi\) | |||||||
\(684\) | −68.3462 | − | 82.6163i | −2.61328 | − | 3.15891i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.64704 | + | 26.1789i | −0.0628842 | + | 0.999515i | ||||
\(687\) | −12.6178 | + | 49.1429i | −0.481397 | + | 1.87492i | ||||
\(688\) | 3.63566 | − | 14.1600i | 0.138608 | − | 0.539843i | ||||
\(689\) | 0.109711 | − | 1.74381i | 0.00417966 | − | 0.0664338i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.3817 | + | 14.9669i | 0.471023 | + | 0.569369i | 0.951504 | − | 0.307636i | \(-0.0995378\pi\) |
−0.480481 | + | 0.877005i | \(0.659538\pi\) | |||||||
\(692\) | −11.6663 | − | 92.3481i | −0.443485 | − | 3.51055i | ||||
\(693\) | − | 6.56381i | − | 0.249338i | ||||||
\(694\) | −73.8993 | + | 9.33565i | −2.80518 | + | 0.354376i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 26.7515 | + | 25.1214i | 1.01401 | + | 0.952223i | ||||
\(697\) | 35.6200 | + | 16.7615i | 1.34920 | + | 0.634888i | ||||
\(698\) | −26.0010 | − | 21.5099i | −0.984151 | − | 0.814160i | ||||
\(699\) | 16.2460 | − | 50.0000i | 0.614479 | − | 1.89117i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.01298 | − | 12.3507i | −0.151568 | − | 0.466479i | 0.846229 | − | 0.532820i | \(-0.178868\pi\) |
−0.997797 | + | 0.0663408i | \(0.978868\pi\) | |||||||
\(702\) | 8.60156 | − | 21.7251i | 0.324645 | − | 0.819959i | ||||
\(703\) | 12.1182 | − | 12.9045i | 0.457046 | − | 0.486704i | ||||
\(704\) | −1.06753 | − | 5.59618i | −0.0402340 | − | 0.210914i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 41.5374 | − | 39.0062i | 1.56328 | − | 1.46802i | ||||
\(707\) | −7.65269 | + | 2.48651i | −0.287809 | + | 0.0935149i | ||||
\(708\) | 48.6915 | + | 9.28840i | 1.82994 | + | 0.349079i | ||||
\(709\) | −2.19608 | − | 34.9057i | −0.0824755 | − | 1.31091i | −0.793857 | − | 0.608104i | \(-0.791930\pi\) |
0.711382 | − | 0.702806i | \(-0.248070\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −39.6823 | − | 62.5293i | −1.48820 | − | 2.34503i | ||||
\(712\) | −12.0891 | + | 0.760581i | −0.453058 | + | 0.0285040i | ||||
\(713\) | 18.1397 | + | 11.5118i | 0.679339 | + | 0.431121i | ||||
\(714\) | −14.3450 | + | 17.3401i | −0.536847 | + | 0.648937i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 27.2470 | + | 6.99583i | 1.01827 | + | 0.261446i | ||||
\(717\) | −23.8681 | + | 11.2315i | −0.891370 | + | 0.419447i | ||||
\(718\) | 45.6267 | + | 14.8250i | 1.70277 | + | 0.553265i | ||||
\(719\) | 27.0272 | + | 14.8583i | 1.00794 | + | 0.554121i | 0.898083 | − | 0.439826i | \(-0.144960\pi\) |
0.109860 | + | 0.993947i | \(0.464960\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.2526 | + | 1.67419i | 0.493553 | + | 0.0623502i | ||||
\(722\) | −2.74172 | + | 21.7029i | −0.102036 | + | 0.807699i | ||||
\(723\) | −34.3599 | + | 21.8055i | −1.27786 | + | 0.810954i | ||||
\(724\) | −72.7867 | + | 52.8826i | −2.70510 | + | 1.96537i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −66.2692 | − | 48.1474i | −2.45948 | − | 1.78692i | ||||
\(727\) | −9.26913 | − | 0.583164i | −0.343773 | − | 0.0216284i | −0.110034 | − | 0.993928i | \(-0.535096\pi\) |
−0.233739 | + | 0.972299i | \(0.575096\pi\) | |||||||
\(728\) | 1.16435 | + | 2.11795i | 0.0431538 | + | 0.0784965i | ||||
\(729\) | 36.0325 | − | 76.5729i | 1.33454 | − | 2.83603i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.83934 | + | 9.64217i | −0.0680306 | + | 0.356629i | ||||
\(732\) | 61.1377 | + | 84.1489i | 2.25972 | + | 3.11023i | ||||
\(733\) | 2.88620 | − | 5.24998i | 0.106604 | − | 0.193913i | −0.817624 | − | 0.575752i | \(-0.804709\pi\) |
0.924229 | + | 0.381840i | \(0.124709\pi\) | |||||||
\(734\) | −8.55469 | + | 13.4800i | −0.315759 | + | 0.497557i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.08594 | − | 2.40959i | −0.224331 | − | 0.0888188i | ||||
\(737\) | 5.20256 | + | 13.1402i | 0.191639 | + | 0.484024i | ||||
\(738\) | 174.945 | − | 144.727i | 6.43982 | − | 5.32748i | ||||
\(739\) | −13.1162 | + | 3.36768i | −0.482489 | + | 0.123882i | −0.482097 | − | 0.876118i | \(-0.660125\pi\) |
−0.000391910 | 1.00000i | \(0.500125\pi\) | ||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.55998 | − | 2.20135i | 0.204251 | − | 0.0808686i | ||||
\(742\) | 4.15841 | + | 4.42826i | 0.152660 | + | 0.162567i | ||||
\(743\) | −13.6581 | + | 18.7987i | −0.501066 | + | 0.689658i | −0.982381 | − | 0.186890i | \(-0.940159\pi\) |
0.481315 | + | 0.876548i | \(0.340159\pi\) | |||||||
\(744\) | 48.8072 | + | 103.721i | 1.78936 | + | 3.80258i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 11.5988 | − | 6.37649i | 0.424662 | − | 0.233460i | ||||
\(747\) | −1.50507 | + | 0.287107i | −0.0550675 | + | 0.0105047i | ||||
\(748\) | −3.73775 | − | 14.5576i | −0.136666 | − | 0.532277i | ||||
\(749\) | −11.1220 | −0.406389 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.1704 | 1.64829 | 0.824146 | − | 0.566377i | \(-0.191655\pi\) | ||||
0.824146 | + | 0.566377i | \(0.191655\pi\) | |||||||
\(752\) | −1.88955 | − | 7.35931i | −0.0689048 | − | 0.268366i | ||||
\(753\) | −19.9666 | + | 3.80884i | −0.727624 | + | 0.138802i | ||||
\(754\) | −2.49941 | + | 1.37406i | −0.0910230 | + | 0.0500403i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 23.4056 | + | 49.7395i | 0.851254 | + | 1.80901i | ||||
\(757\) | 21.7999 | − | 30.0050i | 0.792332 | − | 1.09055i | −0.201482 | − | 0.979492i | \(-0.564576\pi\) |
0.993814 | − | 0.111059i | \(-0.0354242\pi\) | |||||||
\(758\) | −56.8119 | − | 60.4985i | −2.06350 | − | 2.19741i | ||||
\(759\) | −10.8396 | + | 4.29169i | −0.393451 | + | 0.155778i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.23285 | + | 1.60032i | −0.225941 | + | 0.0580117i | −0.359963 | − | 0.932967i | \(-0.617211\pi\) |
0.134022 | + | 0.990978i | \(0.457211\pi\) | |||||||
\(762\) | 52.9954 | − | 43.8416i | 1.91982 | − | 1.58821i | ||||
\(763\) | −0.240173 | − | 0.606607i | −0.00869483 | − | 0.0219606i | ||||
\(764\) | 39.3059 | + | 15.5623i | 1.42204 | + | 0.563025i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.6523 | + | 32.5429i | −0.746199 | + | 1.17582i | ||||
\(767\) | −0.969216 | + | 1.76300i | −0.0349964 | + | 0.0636582i | ||||
\(768\) | 63.5914 | + | 87.5261i | 2.29466 | + | 3.15833i | ||||
\(769\) | −2.99673 | + | 15.7094i | −0.108065 | + | 0.566495i | 0.886531 | + | 0.462669i | \(0.153108\pi\) |
−0.994596 | + | 0.103825i | \(0.966892\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.2033 | + | 53.5596i | −0.907673 | + | 1.92890i | ||||
\(772\) | −31.7782 | − | 57.8042i | −1.14372 | − | 2.08042i | ||||
\(773\) | −8.52249 | − | 0.536189i | −0.306533 | − | 0.0192854i | −0.0912206 | − | 0.995831i | \(-0.529077\pi\) |
−0.215312 | + | 0.976545i | \(0.569077\pi\) | |||||||
\(774\) | 45.8023 | + | 33.2773i | 1.64633 | + | 1.19613i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 53.3018 | − | 38.7260i | 1.91342 | − | 1.39018i | ||||
\(777\) | −12.2436 | + | 7.77003i | −0.439237 | + | 0.278748i | ||||
\(778\) | −3.00813 | + | 23.8118i | −0.107847 | + | 0.853693i | ||||
\(779\) | 36.0812 | + | 4.55811i | 1.29274 | + | 0.163311i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.75676 | + | 2.61505i | 0.170210 | + | 0.0935738i | ||||
\(782\) | 27.6648 | + | 8.98885i | 0.989293 | + | 0.321441i | ||||
\(783\) | −30.6522 | + | 14.4238i | −1.09542 | + | 0.515466i | ||||
\(784\) | 31.8168 | + | 8.16916i | 1.13631 | + | 0.291756i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −50.5086 | + | 61.0544i | −1.80158 | + | 2.17774i | ||||
\(787\) | 6.35500 | + | 4.03301i | 0.226531 | + | 0.143761i | 0.644249 | − | 0.764816i | \(-0.277170\pi\) |
−0.417718 | + | 0.908577i | \(0.637170\pi\) | |||||||
\(788\) | 65.3731 | − | 4.11293i | 2.32882 | − | 0.146517i | ||||
\(789\) | 43.8111 | + | 69.0353i | 1.55972 | + | 2.45772i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.322301 | + | 5.12283i | 0.0114597 | + | 0.182147i | ||||
\(792\) | −44.4656 | − | 8.48226i | −1.58002 | − | 0.301404i | ||||
\(793\) | −4.01493 | + | 1.30453i | −0.142574 | + | 0.0463252i | ||||
\(794\) | 18.3893 | − | 17.2687i | 0.652612 | − | 0.612843i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.0698 | + | 58.0297i | 0.392357 | + | 2.05681i | ||||
\(797\) | 19.3269 | − | 20.5811i | 0.684594 | − | 0.729019i | −0.288994 | − | 0.957331i | \(-0.593321\pi\) |
0.973588 | + | 0.228312i | \(0.0733207\pi\) | |||||||
\(798\) | −7.65344 | + | 19.3304i | −0.270929 | + | 0.684288i | ||||
\(799\) | 1.57650 | + | 4.85197i | 0.0557726 | + | 0.171650i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.52085 | − | 16.9914i | 0.195069 | − | 0.600362i | ||||
\(802\) | 36.8822 | + | 30.5116i | 1.30236 | + | 1.07740i | ||||
\(803\) | 5.86690 | + | 2.76076i | 0.207039 | + | 0.0974249i | ||||
\(804\) | −137.856 | − | 129.455i | −4.86181 | − | 4.56554i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.83898 | + | 1.11662i | −0.311340 | + | 0.0393313i | ||||
\(807\) | 23.6736i | 0.833350i | ||||||||
\(808\) | 6.95511 | + | 55.0553i | 0.244680 | + | 1.93684i | ||||
\(809\) | 7.95125 | + | 9.61141i | 0.279551 | + | 0.337919i | 0.891536 | − | 0.452951i | \(-0.149629\pi\) |
−0.611985 | + | 0.790870i | \(0.709629\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.05459 | − | 32.6568i | 0.0721464 | − | 1.14673i | −0.780816 | − | 0.624761i | \(-0.785196\pi\) |
0.852962 | − | 0.521973i | \(-0.174804\pi\) | |||||||
\(812\) | 1.66875 | − | 6.49936i | 0.0585617 | − | 0.228083i | ||||
\(813\) | 21.2549 | − | 82.7822i | 0.745441 | − | 2.90330i | ||||
\(814\) | 0.898643 | − | 14.2835i | 0.0314974 | − | 0.500637i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 37.6787 | + | 45.5458i | 1.31902 | + | 1.59442i | ||||
\(817\) | 1.13656 | + | 8.99681i | 0.0397633 | + | 0.314759i | ||||
\(818\) | − | 63.4598i | − | 2.21882i | ||||||
\(819\) | −3.53666 | + | 0.446784i | −0.123581 | + | 0.0156119i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.26838 | + | 5.88640i | 0.218768 | + | 0.205437i | 0.786181 | − | 0.617997i | \(-0.212056\pi\) |
−0.567413 | + | 0.823434i | \(0.692056\pi\) | |||||||
\(822\) | 13.4573 | + | 6.33253i | 0.469378 | + | 0.220872i | ||||
\(823\) | −28.4119 | − | 23.5043i | −0.990375 | − | 0.819310i | −0.00683079 | − | 0.999977i | \(-0.502174\pi\) |
−0.983544 | + | 0.180667i | \(0.942174\pi\) | |||||||
\(824\) | 28.4676 | − | 87.6144i | 0.991717 | − | 3.05219i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.16145 | − | 6.65227i | −0.0752065 | − | 0.231462i | ||||
\(827\) | −3.60867 | + | 9.11447i | −0.125486 | + | 0.316941i | −0.978915 | − | 0.204268i | \(-0.934519\pi\) |
0.853429 | + | 0.521209i | \(0.174519\pi\) | |||||||
\(828\) | 77.7149 | − | 82.7579i | 2.70078 | − | 2.87604i | ||||
\(829\) | 3.95671 | + | 20.7418i | 0.137422 | + | 0.720393i | 0.982575 | + | 0.185868i | \(0.0595096\pi\) |
−0.845153 | + | 0.534525i | \(0.820490\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.22716 | + | 8.66488i | −0.320087 | + | 0.300582i | ||||
\(832\) | −2.94263 | + | 0.956117i | −0.102017 | + | 0.0331474i | ||||
\(833\) | −21.6655 | − | 4.13292i | −0.750666 | − | 0.143197i | ||||
\(834\) | −4.67468 | − | 74.3019i | −0.161871 | − | 2.57286i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7.43989 | − | 11.7234i | −0.257314 | − | 0.405462i | ||||
\(837\) | −105.608 | + | 6.64431i | −3.65036 | + | 0.229661i | ||||
\(838\) | 77.2285 | + | 49.0107i | 2.66781 | + | 1.69305i | ||||
\(839\) | 21.3524 | − | 25.8107i | 0.737168 | − | 0.891083i | −0.260052 | − | 0.965595i | \(-0.583740\pi\) |
0.997220 | + | 0.0745113i | \(0.0237397\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.0836 | − | 6.18363i | −0.830470 | − | 0.213229i | ||||
\(842\) | 51.3500 | − | 24.1635i | 1.76964 | − | 0.832729i | ||||
\(843\) | −24.5783 | − | 7.98598i | −0.846522 | − | 0.275052i | ||||
\(844\) | −70.4655 | − | 38.7388i | −2.42552 | − | 1.33344i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 29.1922 | + | 3.68783i | 1.00365 | + | 0.126790i | ||||
\(847\) | −0.980289 | + | 7.75979i | −0.0336831 | + | 0.266629i | ||||
\(848\) | 13.4720 | − | 8.54959i | 0.462630 | − | 0.293594i | ||||
\(849\) | 6.43728 | − | 4.67696i | 0.220927 | − | 0.160513i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.1637 | + | 11.0171i | 0.519807 | + | 0.377662i | ||||
\(852\) | −72.4923 | − | 4.56083i | −2.48354 | − | 0.156251i | ||||
\(853\) | −21.3979 | − | 38.9227i | −0.732652 | − | 1.33269i | −0.935447 | − | 0.353467i | \(-0.885003\pi\) |
0.202795 | − | 0.979221i | \(-0.434997\pi\) | |||||||
\(854\) | 6.24919 | − | 13.2802i | 0.213843 | − | 0.454439i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.3727 | + | 75.3444i | −0.491249 | + | 2.57522i | ||||
\(857\) | −18.8965 | − | 26.0088i | −0.645493 | − | 0.888445i | 0.353401 | − | 0.935472i | \(-0.385025\pi\) |
−0.998894 | + | 0.0470273i | \(0.985025\pi\) | |||||||
\(858\) | 2.32905 | − | 4.23653i | 0.0795124 | − | 0.144633i | ||||
\(859\) | 9.16371 | − | 14.4397i | 0.312662 | − | 0.492676i | −0.651263 | − | 0.758852i | \(-0.725760\pi\) |
0.963924 | + | 0.266176i | \(0.0857604\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.6989 | − | 10.9668i | −0.943975 | − | 0.373746i | ||||
\(862\) | −19.1569 | − | 48.3848i | −0.652487 | − | 1.64799i | ||||
\(863\) | −1.51625 | + | 1.25435i | −0.0516138 | + | 0.0426986i | −0.662873 | − | 0.748732i | \(-0.730663\pi\) |
0.611259 | + | 0.791430i | \(0.290663\pi\) | |||||||
\(864\) | 31.2264 | − | 8.01757i | 1.06234 | − | 0.272763i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −34.0772 | + | 13.4921i | −1.15799 | + | 0.458481i | ||||
\(867\) | 11.4597 | + | 12.2033i | 0.389190 | + | 0.414446i | ||||
\(868\) | 12.3200 | − | 16.9571i | 0.418169 | − | 0.575560i | ||||
\(869\) | −4.08332 | − | 8.67750i | −0.138517 | − | 0.294364i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.72596 | − | 3.69763i | 0.227900 | − | 0.125289i | ||||
\(872\) | −4.41974 | + | 0.843110i | −0.149671 | + | 0.0285513i | ||||
\(873\) | 24.1665 | + | 94.1223i | 0.817912 | + | 3.18556i | ||||
\(874\) | 26.8728 | 0.908985 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −86.7637 | −2.93147 | ||||||||
\(877\) | −6.26965 | − | 24.4187i | −0.211711 | − | 0.824561i | −0.982313 | − | 0.187244i | \(-0.940044\pi\) |
0.770602 | − | 0.637316i | \(-0.219956\pi\) | |||||||
\(878\) | 33.5127 | − | 6.39289i | 1.13100 | − | 0.215750i | ||||
\(879\) | −32.2330 | + | 17.7202i | −1.08719 | + | 0.597689i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.48675 | − | 15.9102i | −0.252235 | − | 0.536027i | 0.738105 | − | 0.674686i | \(-0.235721\pi\) |
−0.990340 | + | 0.138659i | \(0.955721\pi\) | |||||||
\(882\) | −74.7726 | + | 102.916i | −2.51773 | + | 3.46535i | ||||
\(883\) | 12.3227 | + | 13.1224i | 0.414693 | + | 0.441603i | 0.902071 | − | 0.431588i | \(-0.142047\pi\) |
−0.487378 | + | 0.873191i | \(0.662047\pi\) | |||||||
\(884\) | −7.58938 | + | 3.00485i | −0.255258 | + | 0.101064i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.7948 | + | 3.54190i | −0.463444 | + | 0.118992i | ||||
\(887\) | −0.0957476 | + | 0.0792093i | −0.00321489 | + | 0.00265959i | −0.639030 | − | 0.769182i | \(-0.720664\pi\) |
0.635815 | + | 0.771841i | \(0.280664\pi\) | |||||||
\(888\) | 36.8148 | + | 92.9837i | 1.23542 | + | 3.12033i | ||||
\(889\) | −6.10620 | − | 2.41762i | −0.204795 | − | 0.0810842i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17.3831 | − | 27.3914i | 0.582356 | − | 0.917646i | ||||
\(892\) | 9.45182 | − | 17.1928i | 0.316470 | − | 0.575657i | ||||
\(893\) | 2.77026 | + | 3.81294i | 0.0927032 | + | 0.127595i | ||||
\(894\) | −9.39804 | + | 49.2662i | −0.314317 | + | 1.64771i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 5.87928 | − | 12.4941i | 0.196413 | − | 0.417399i | ||||
\(897\) | 3.05024 | + | 5.54837i | 0.101845 | + | 0.185255i | ||||
\(898\) | 2.04457 | + | 0.128633i | 0.0682281 | + | 0.00429255i | ||||
\(899\) | 10.4499 | + | 7.59229i | 0.348523 | + | 0.253217i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.66742 | + | 6.29725i | −0.288754 | + | 0.209792i | ||||
\(902\) | 24.8250 | − | 15.7544i | 0.826583 | − | 0.524565i | ||||
\(903\) | 0.931017 | − | 7.36976i | 0.0309823 | − | 0.245250i | ||||
\(904\) | 35.1204 | + | 4.43673i | 1.16809 | + | 0.147564i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 79.0544 | + | 43.4605i | 2.62641 | + | 1.44388i | ||||
\(907\) | 1.40695 | + | 0.457146i | 0.0467170 | + | 0.0151793i | 0.332282 | − | 0.943180i | \(-0.392181\pi\) |
−0.285565 | + | 0.958359i | \(0.592181\pi\) | |||||||
\(908\) | −27.5435 | + | 12.9610i | −0.914063 | + | 0.430125i | ||||
\(909\) | −79.2768 | − | 20.3548i | −2.62945 | − | 0.675127i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.6996 | − | 41.9446i | 1.14965 | − | 1.38969i | 0.241834 | − | 0.970318i | \(-0.422251\pi\) |
0.907815 | − | 0.419370i | \(-0.137749\pi\) | |||||||
\(912\) | 46.1073 | + | 29.2606i | 1.52676 | + | 0.968914i | ||||
\(913\) | −0.198023 | + | 0.0124585i | −0.00655360 | + | 0.000412318i | ||||
\(914\) | −11.3007 | − | 17.8071i | −0.373794 | − | 0.589006i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.01737 | − | 63.8542i | −0.132738 | − | 2.10980i | ||||
\(917\) | 7.43207 | + | 1.41774i | 0.245428 | + | 0.0468180i | ||||
\(918\) | −136.259 | + | 44.2731i | −4.49721 | + | 1.46123i | ||||
\(919\) | −8.82636 | + | 8.28850i | −0.291155 | + | 0.273412i | −0.816335 | − | 0.577578i | \(-0.803998\pi\) |
0.525181 | + | 0.850991i | \(0.323998\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.69323 | − | 29.8450i | −0.187598 | − | 0.983425i | ||||
\(922\) | 59.5247 | − | 63.3873i | 1.96034 | − | 2.08755i | ||||
\(923\) | 1.08524 | − | 2.74100i | 0.0357211 | − | 0.0902212i | ||||
\(924\) | 3.51471 | + | 10.8172i | 0.115625 | + | 0.355858i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 5.08016 | − | 15.6351i | 0.166944 | − | 0.513802i | ||||
\(927\) | 104.694 | + | 86.6102i | 3.43859 | + | 2.84465i | ||||
\(928\) | −3.56081 | − | 1.67559i | −0.116889 | − | 0.0550039i | ||||
\(929\) | −15.2833 | − | 14.3520i | −0.501430 | − | 0.470874i | 0.392071 | − | 0.919935i | \(-0.371759\pi\) |
−0.893501 | + | 0.449061i | \(0.851759\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.2154 | + | 2.55380i | −0.662534 | + | 0.0836975i | ||||
\(932\) | 66.2960i | 2.17160i | ||||||||
\(933\) | 11.1533 | + | 88.2873i | 0.365142 | + | 2.89040i | ||||
\(934\) | 23.3683 | + | 28.2474i | 0.764633 | + | 0.924283i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.54367 | + | 24.5360i | −0.0504565 | + | 0.801983i | ||||
\(937\) | 5.07137 | − | 19.7517i | 0.165674 | − | 0.645259i | −0.830434 | − | 0.557117i | \(-0.811907\pi\) |
0.996108 | − | 0.0881413i | \(-0.0280927\pi\) | |||||||
\(938\) | −6.63627 | + | 25.8465i | −0.216682 | + | 0.843920i | ||||
\(939\) | 5.47194 | − | 86.9741i | 0.178570 | − | 2.83829i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.3352 | − | 24.5810i | −0.662908 | − | 0.801318i | 0.326698 | − | 0.945129i | \(-0.394064\pi\) |
−0.989605 | + | 0.143811i | \(0.954064\pi\) | |||||||
\(942\) | 15.4420 | + | 122.236i | 0.503126 | + | 3.98265i | ||||
\(943\) | 38.5065i | 1.25394i | ||||||||
\(944\) | −18.2273 | + | 2.30264i | −0.593247 | + | 0.0749445i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.34435 | + | 5.01868i | 0.173760 | + | 0.163171i | ||||
\(947\) | −45.4700 | − | 21.3965i | −1.47758 | − | 0.695294i | −0.492964 | − | 0.870050i | \(-0.664087\pi\) |
−0.984612 | + | 0.174755i | \(0.944087\pi\) | |||||||
\(948\) | 98.8789 | + | 81.7998i | 3.21144 | + | 2.65673i | ||||
\(949\) | 1.08818 | − | 3.34908i | 0.0353239 | − | 0.108716i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.9558 | + | 39.8738i | 0.420120 | + | 1.29300i | ||||
\(952\) | 5.45544 | − | 13.7789i | 0.176812 | − | 0.446576i | ||||
\(953\) | −14.3314 | + | 15.2613i | −0.464238 | + | 0.494363i | −0.917901 | − | 0.396810i | \(-0.870117\pi\) |
0.453663 | + | 0.891174i | \(0.350117\pi\) | |||||||
\(954\) | 11.5785 | + | 60.6965i | 0.374867 | + | 1.96512i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 24.2485 | − | 22.7708i | 0.784252 | − | 0.736461i | ||||
\(957\) | −6.66613 | + | 2.16596i | −0.215486 | + | 0.0700155i | ||||
\(958\) | −18.8753 | − | 3.60065i | −0.609832 | − | 0.116332i | ||||
\(959\) | −0.0891704 | − | 1.41732i | −0.00287946 | − | 0.0457678i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00849 | + | 7.89212i | 0.161564 | + | 0.254584i | ||||
\(962\) | −7.75731 | + | 0.488049i | −0.250106 | + | 0.0157353i | ||||
\(963\) | −95.5202 | − | 60.6190i | −3.07810 | − | 1.95342i | ||||
\(964\) | 32.7109 | − | 39.5407i | 1.05355 | − | 1.27352i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −21.3213 | − | 5.47438i | −0.686002 | − | 0.176135i | ||||
\(967\) | −4.10340 | + | 1.93091i | −0.131956 | + | 0.0620940i | −0.490624 | − | 0.871371i | \(-0.663231\pi\) |
0.358668 | + | 0.933465i | \(0.383231\pi\) | |||||||
\(968\) | 51.3008 | + | 16.6686i | 1.64887 | + | 0.535750i | ||||
\(969\) | −32.1311 | − | 17.6642i | −1.03220 | − | 0.567457i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.5189 | − | 1.96050i | −0.498026 | − | 0.0629153i | −0.127692 | − | 0.991814i | \(-0.540757\pi\) |
−0.370334 | + | 0.928899i | \(0.620757\pi\) | |||||||
\(972\) | −28.1887 | + | 223.136i | −0.904152 | + | 7.15710i | ||||
\(973\) | −6.00210 | + | 3.80905i | −0.192418 | + | 0.122112i | ||||
\(974\) | −55.9639 | + | 40.6601i | −1.79320 | + | 1.30284i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31.1884 | − | 22.6597i | −0.998317 | − | 0.725320i | ||||
\(977\) | 9.15641 | + | 0.576072i | 0.292940 | + | 0.0184302i | 0.208580 | − | 0.978005i | \(-0.433116\pi\) |
0.0843591 | + | 0.996435i | \(0.473116\pi\) | |||||||
\(978\) | 31.2206 | + | 56.7901i | 0.998325 | + | 1.81595i | ||||
\(979\) | 0.985063 | − | 2.09337i | 0.0314828 | − | 0.0669043i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.24353 | − | 6.51881i | 0.0397028 | − | 0.208130i | ||||
\(982\) | 25.0468 | + | 34.4740i | 0.799276 | + | 1.10011i | ||||
\(983\) | 19.5778 | − | 35.6119i | 0.624435 | − | 1.13584i | −0.355149 | − | 0.934810i | \(-0.615570\pi\) |
0.979584 | − | 0.201034i | \(-0.0644302\pi\) | |||||||
\(984\) | −110.087 | + | 173.470i | −3.50946 | + | 5.53002i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 16.2605 | + | 6.43800i | 0.517841 | + | 0.205028i | ||||
\(987\) | −1.42122 | − | 3.58959i | −0.0452379 | − | 0.114258i | ||||
\(988\) | −5.81029 | + | 4.80669i | −0.184850 | + | 0.152921i | ||||
\(989\) | −9.29991 | + | 2.38781i | −0.295720 | + | 0.0759280i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.4956 | + | 13.2619i | −1.06402 | + | 0.421277i | −0.833918 | − | 0.551888i | \(-0.813907\pi\) |
−0.230106 | + | 0.973165i | \(0.573907\pi\) | |||||||
\(992\) | −8.41484 | − | 8.96089i | −0.267171 | − | 0.284509i | ||||
\(993\) | 20.6893 | − | 28.4763i | 0.656554 | − | 0.903669i | ||||
\(994\) | 4.36398 | + | 9.27393i | 0.138417 | + | 0.294151i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.32661 | − | 1.27907i | 0.0737216 | − | 0.0405288i | ||||
\(997\) | 7.53095 | − | 1.43661i | 0.238508 | − | 0.0454977i | −0.0667415 | − | 0.997770i | \(-0.521260\pi\) |
0.305249 | + | 0.952273i | \(0.401260\pi\) | |||||||
\(998\) | 4.63509 | + | 18.0525i | 0.146721 | + | 0.571441i | ||||
\(999\) | −92.3177 | −2.92080 |
(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 | 625.2.h.b.274.21 | 440 | ||
5.2 | odd | 4 | 125.2.g.a.21.2 | yes | 220 | ||
5.3 | odd | 4 | 625.2.g.a.351.10 | 220 | |||
5.4 | even | 2 | inner | 625.2.h.b.274.2 | 440 | ||
125.6 | even | 25 | inner | 625.2.h.b.349.2 | 440 | ||
125.33 | odd | 100 | 625.2.g.a.276.10 | 220 | |||
125.92 | odd | 100 | 125.2.g.a.6.2 | ✓ | 220 | ||
125.119 | even | 50 | inner | 625.2.h.b.349.21 | 440 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
125.2.g.a.6.2 | ✓ | 220 | 125.92 | odd | 100 | ||
125.2.g.a.21.2 | yes | 220 | 5.2 | odd | 4 | ||
625.2.g.a.276.10 | 220 | 125.33 | odd | 100 | |||
625.2.g.a.351.10 | 220 | 5.3 | odd | 4 | |||
625.2.h.b.274.2 | 440 | 5.4 | even | 2 | inner | ||
625.2.h.b.274.21 | 440 | 1.1 | even | 1 | trivial | ||
625.2.h.b.349.2 | 440 | 125.6 | even | 25 | inner | ||
625.2.h.b.349.21 | 440 | 125.119 | even | 50 | inner |