Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(46,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([20, 18]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.46");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.r (of order \(15\), degree \(8\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(224\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{15})\) |
Twist minimal: | no (minimal twist has level 225) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{15}]$ |
Embedding invariants
Embedding label | 46.19 | ||
Character | \(\chi\) | \(=\) | 675.46 |
Dual form | 675.2.r.a.631.19 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.727367 | + | 0.807823i | 0.514326 | + | 0.571217i | 0.943233 | − | 0.332131i | \(-0.107768\pi\) |
−0.428907 | + | 0.903349i | \(0.641101\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.0855417 | − | 0.813875i | 0.0427709 | − | 0.406938i | ||||
\(5\) | −0.934297 | + | 2.03152i | −0.417830 | + | 0.908525i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73969 | − | 3.01324i | 0.657542 | − | 1.13890i | −0.323708 | − | 0.946157i | \(-0.604930\pi\) |
0.981250 | − | 0.192739i | \(-0.0617370\pi\) | |||||||
\(8\) | 2.47854 | − | 1.80077i | 0.876298 | − | 0.636668i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.32069 | + | 0.722917i | −0.733866 | + | 0.228607i | ||||
\(11\) | −2.35402 | − | 2.61440i | −0.709764 | − | 0.788272i | 0.275135 | − | 0.961406i | \(-0.411278\pi\) |
−0.984898 | + | 0.173133i | \(0.944611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.45133 | − | 1.61187i | 0.402527 | − | 0.447052i | −0.507468 | − | 0.861671i | \(-0.669418\pi\) |
0.909995 | + | 0.414619i | \(0.136085\pi\) | |||||||
\(14\) | 3.69956 | − | 0.786365i | 0.988748 | − | 0.210165i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.65656 | + | 0.352114i | 0.414141 | + | 0.0880284i | ||||
\(17\) | 1.54674 | − | 1.12377i | 0.375140 | − | 0.272555i | −0.384199 | − | 0.923250i | \(-0.625522\pi\) |
0.759339 | + | 0.650695i | \(0.225522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.970198 | + | 0.704890i | −0.222579 | + | 0.161713i | −0.693487 | − | 0.720469i | \(-0.743926\pi\) |
0.470908 | + | 0.882182i | \(0.343926\pi\) | |||||||
\(20\) | 1.57349 | + | 0.934181i | 0.351842 | + | 0.208889i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.399739 | − | 3.80326i | 0.0852247 | − | 0.810859i | ||||
\(23\) | 1.96627 | − | 0.417944i | 0.409996 | − | 0.0871474i | 0.00170377 | − | 0.999999i | \(-0.499458\pi\) |
0.408293 | + | 0.912851i | \(0.366124\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.25418 | − | 3.79609i | −0.650836 | − | 0.759219i | ||||
\(26\) | 2.35776 | 0.462394 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.30358 | − | 1.67365i | −0.435336 | − | 0.316290i | ||||
\(29\) | 3.26898 | − | 1.45544i | 0.607035 | − | 0.270269i | −0.0801144 | − | 0.996786i | \(-0.525529\pi\) |
0.687149 | + | 0.726516i | \(0.258862\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.79773 | + | 2.58132i | 1.04130 | + | 0.463618i | 0.854866 | − | 0.518849i | \(-0.173639\pi\) |
0.186437 | + | 0.982467i | \(0.440306\pi\) | |||||||
\(32\) | −2.14316 | − | 3.71207i | −0.378862 | − | 0.656207i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.03286 | + | 0.432098i | 0.348633 | + | 0.0741042i | ||||
\(35\) | 4.49607 | + | 6.34948i | 0.759975 | + | 1.07326i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.46324 | + | 7.58107i | 0.404954 | + | 1.24632i | 0.920934 | + | 0.389719i | \(0.127428\pi\) |
−0.515980 | + | 0.856601i | \(0.672572\pi\) | |||||||
\(38\) | −1.27512 | − | 0.271034i | −0.206851 | − | 0.0439676i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.34261 | + | 6.71767i | 0.212285 | + | 1.06216i | ||||
\(41\) | −1.73464 | + | 1.92652i | −0.270906 | + | 0.300871i | −0.863212 | − | 0.504842i | \(-0.831551\pi\) |
0.592306 | + | 0.805713i | \(0.298218\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.34941 | − | 9.26545i | 0.815778 | − | 1.41297i | −0.0929908 | − | 0.995667i | \(-0.529643\pi\) |
0.908768 | − | 0.417301i | \(-0.137024\pi\) | |||||||
\(44\) | −2.32917 | + | 1.69224i | −0.351135 | + | 0.255114i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.76783 | + | 1.28440i | 0.260652 | + | 0.189375i | ||||
\(47\) | −11.9942 | + | 5.34016i | −1.74953 | + | 0.778942i | −0.757518 | + | 0.652814i | \(0.773588\pi\) |
−0.992014 | + | 0.126128i | \(0.959745\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.55306 | − | 4.42203i | −0.364723 | − | 0.631718i | ||||
\(50\) | 0.699589 | − | 5.38996i | 0.0989369 | − | 0.762255i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.18771 | − | 1.31909i | −0.164706 | − | 0.182924i | ||||
\(53\) | 11.2674 | + | 8.18624i | 1.54770 | + | 1.12447i | 0.945269 | + | 0.326293i | \(0.105800\pi\) |
0.602427 | + | 0.798174i | \(0.294200\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.51058 | − | 2.33962i | 1.01273 | − | 0.315474i | ||||
\(56\) | −1.11423 | − | 10.6012i | −0.148896 | − | 1.41665i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.55349 | + | 1.58212i | 0.466597 | + | 0.207742i | ||||
\(59\) | 3.64544 | − | 4.04867i | 0.474596 | − | 0.527092i | −0.457545 | − | 0.889186i | \(-0.651271\pi\) |
0.932142 | + | 0.362094i | \(0.117938\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.353232 | + | 0.392304i | 0.0452268 | + | 0.0502294i | 0.765334 | − | 0.643634i | \(-0.222574\pi\) |
−0.720107 | + | 0.693863i | \(0.755907\pi\) | |||||||
\(62\) | 2.13183 | + | 6.56111i | 0.270743 | + | 0.833262i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.48651 | − | 7.65270i | 0.310814 | − | 0.956588i | ||||
\(65\) | 1.91857 | + | 4.45438i | 0.237970 | + | 0.552498i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.83507 | − | 4.37885i | −1.20154 | − | 0.534962i | −0.294360 | − | 0.955695i | \(-0.595106\pi\) |
−0.907185 | + | 0.420732i | \(0.861773\pi\) | |||||||
\(68\) | −0.782301 | − | 1.35499i | −0.0948680 | − | 0.164316i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.85897 | + | 8.25044i | −0.222189 | + | 0.986116i | ||||
\(71\) | −6.38098 | − | 4.63605i | −0.757283 | − | 0.550198i | 0.140793 | − | 0.990039i | \(-0.455035\pi\) |
−0.898076 | + | 0.439841i | \(0.855035\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.75054 | + | 8.46529i | −0.321926 | + | 0.990787i | 0.650883 | + | 0.759178i | \(0.274399\pi\) |
−0.972809 | + | 0.231609i | \(0.925601\pi\) | |||||||
\(74\) | −4.33248 | + | 7.50408i | −0.503641 | + | 0.872332i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.490700 | + | 0.849917i | 0.0562871 | + | 0.0974922i | ||||
\(77\) | −11.9731 | + | 2.54496i | −1.36446 | + | 0.290025i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.17366 | − | 2.74869i | 0.694591 | − | 0.309252i | −0.0289032 | − | 0.999582i | \(-0.509201\pi\) |
0.723494 | + | 0.690330i | \(0.242535\pi\) | |||||||
\(80\) | −2.26305 | + | 3.03637i | −0.253017 | + | 0.339477i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.81801 | −0.311197 | ||||||||
\(83\) | −0.372037 | − | 3.53969i | −0.0408363 | − | 0.388532i | −0.995782 | − | 0.0917511i | \(-0.970754\pi\) |
0.954946 | − | 0.296781i | \(-0.0959131\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.837858 | + | 4.19218i | 0.0908784 | + | 0.454706i | ||||
\(86\) | 11.3758 | − | 2.41801i | 1.22669 | − | 0.260741i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.5425 | − | 2.24087i | −1.12383 | − | 0.238878i | ||||
\(89\) | −2.71707 | + | 8.36227i | −0.288008 | + | 0.886399i | 0.697472 | + | 0.716612i | \(0.254308\pi\) |
−0.985481 | + | 0.169787i | \(0.945692\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.33207 | − | 7.17736i | −0.244467 | − | 0.752392i | ||||
\(92\) | −0.171956 | − | 1.63605i | −0.0179277 | − | 0.170570i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −13.0381 | − | 5.80493i | −1.34478 | − | 0.598733i | ||||
\(95\) | −0.525548 | − | 2.62956i | −0.0539201 | − | 0.269787i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.6914 | + | 6.98627i | −1.59322 | + | 0.709348i | −0.995712 | − | 0.0925124i | \(-0.970510\pi\) |
−0.597511 | + | 0.801861i | \(0.703844\pi\) | |||||||
\(98\) | 1.71520 | − | 5.27886i | 0.173262 | − | 0.533245i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.36791 | + | 2.32377i | −0.336791 | + | 0.232377i | ||||
\(101\) | −4.67773 | + | 8.10206i | −0.465451 | + | 0.806185i | −0.999222 | − | 0.0394441i | \(-0.987441\pi\) |
0.533770 | + | 0.845629i | \(0.320775\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.837734 | + | 7.97051i | −0.0825444 | + | 0.785358i | 0.872444 | + | 0.488714i | \(0.162534\pi\) |
−0.954988 | + | 0.296643i | \(0.904133\pi\) | |||||||
\(104\) | 0.694592 | − | 6.60860i | 0.0681104 | − | 0.648027i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.58250 | + | 15.0565i | 0.153706 | + | 1.46241i | ||||
\(107\) | −5.04642 | −0.487855 | −0.243928 | − | 0.969793i | \(-0.578436\pi\) | ||||
−0.243928 | + | 0.969793i | \(0.578436\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.49707 | − | 4.60752i | −0.143394 | − | 0.441320i | 0.853407 | − | 0.521245i | \(-0.174532\pi\) |
−0.996801 | + | 0.0799245i | \(0.974532\pi\) | |||||||
\(110\) | 7.35295 | + | 4.36546i | 0.701076 | + | 0.416230i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.94291 | − | 4.37905i | 0.372570 | − | 0.413781i | ||||
\(113\) | −1.47427 | + | 1.63734i | −0.138688 | + | 0.154028i | −0.808487 | − | 0.588514i | \(-0.799713\pi\) |
0.669800 | + | 0.742542i | \(0.266380\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.988019 | + | 4.38501i | −0.0921333 | + | 0.408905i | ||||
\(116\) | −0.904916 | − | 2.78505i | −0.0840193 | − | 0.258585i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.92219 | 0.545182 | ||||||||
\(119\) | −0.695340 | − | 6.61572i | −0.0637418 | − | 0.606462i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.143885 | + | 1.36898i | −0.0130805 | + | 0.124453i | ||||
\(122\) | −0.0599828 | + | 0.570699i | −0.00543059 | + | 0.0516686i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.59682 | − | 4.49782i | 0.233201 | − | 0.403916i | ||||
\(125\) | 10.7522 | − | 3.06426i | 0.961708 | − | 0.274076i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.91345 | + | 18.1997i | −0.524734 | + | 1.61497i | 0.240106 | + | 0.970747i | \(0.422818\pi\) |
−0.764841 | + | 0.644219i | \(0.777182\pi\) | |||||||
\(128\) | 0.159129 | − | 0.0708488i | 0.0140652 | − | 0.00626221i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.20285 | + | 4.78984i | −0.193202 | + | 0.420097i | ||||
\(131\) | 7.04977 | + | 3.13876i | 0.615941 | + | 0.274235i | 0.690898 | − | 0.722952i | \(-0.257215\pi\) |
−0.0749569 | + | 0.997187i | \(0.523882\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.436154 | + | 4.14972i | 0.0378193 | + | 0.359827i | ||||
\(134\) | −3.61637 | − | 11.1300i | −0.312407 | − | 0.961488i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.81001 | − | 5.57065i | 0.155207 | − | 0.477679i | ||||
\(137\) | 6.13544 | + | 1.30413i | 0.524186 | + | 0.111419i | 0.462402 | − | 0.886670i | \(-0.346988\pi\) |
0.0617840 | + | 0.998090i | \(0.480321\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.9459 | − | 4.23963i | 1.69179 | − | 0.359601i | 0.741496 | − | 0.670958i | \(-0.234117\pi\) |
0.950293 | + | 0.311357i | \(0.100783\pi\) | |||||||
\(140\) | 5.55229 | − | 3.11609i | 0.469254 | − | 0.263358i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.896205 | − | 8.52682i | −0.0752078 | − | 0.715555i | ||||
\(143\) | −7.63054 | −0.638098 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.0974297 | + | 8.00083i | −0.00809110 | + | 0.664433i | ||||
\(146\) | −8.83911 | + | 3.93543i | −0.731530 | + | 0.325698i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.38075 | − | 1.35627i | 0.524495 | − | 0.111485i | ||||
\(149\) | 3.52387 | + | 6.10353i | 0.288687 | + | 0.500021i | 0.973497 | − | 0.228701i | \(-0.0734480\pi\) |
−0.684810 | + | 0.728722i | \(0.740115\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.0155849 | − | 0.0269939i | 0.00126828 | − | 0.00219673i | −0.865391 | − | 0.501098i | \(-0.832930\pi\) |
0.866659 | + | 0.498901i | \(0.166263\pi\) | |||||||
\(152\) | −1.13533 | + | 3.49420i | −0.0920878 | + | 0.283417i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.7647 | − | 7.82102i | −0.867445 | − | 0.630236i | ||||
\(155\) | −10.6608 | + | 9.36651i | −0.856297 | + | 0.752337i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.694083 | − | 1.20219i | −0.0553938 | − | 0.0959450i | 0.836999 | − | 0.547205i | \(-0.184308\pi\) |
−0.892393 | + | 0.451260i | \(0.850975\pi\) | |||||||
\(158\) | 6.71098 | + | 2.98792i | 0.533897 | + | 0.237706i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9.54351 | − | 0.885714i | 0.754481 | − | 0.0700219i | ||||
\(161\) | 2.16135 | − | 6.65194i | 0.170338 | − | 0.524246i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.385069 | + | 1.18512i | 0.0301609 | + | 0.0928258i | 0.965004 | − | 0.262236i | \(-0.0844598\pi\) |
−0.934843 | + | 0.355062i | \(0.884460\pi\) | |||||||
\(164\) | 1.41956 | + | 1.57658i | 0.110849 | + | 0.123110i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.58884 | − | 2.87520i | 0.200933 | − | 0.223159i | ||||
\(167\) | −0.203316 | − | 0.0905220i | −0.0157330 | − | 0.00700480i | 0.398855 | − | 0.917014i | \(-0.369408\pi\) |
−0.414588 | + | 0.910009i | \(0.636074\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.867117 | + | 8.25007i | 0.0667013 | + | 0.634621i | ||||
\(170\) | −2.77711 | + | 3.72610i | −0.212995 | + | 0.285779i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.08332 | − | 5.14634i | −0.540098 | − | 0.392404i | ||||
\(173\) | −12.7920 | − | 14.2070i | −0.972561 | − | 1.08014i | −0.996760 | − | 0.0804313i | \(-0.974370\pi\) |
0.0241991 | − | 0.999707i | \(-0.492296\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.0998 | + | 3.20157i | −1.29262 | + | 0.242016i | ||||
\(176\) | −2.97902 | − | 5.15981i | −0.224552 | − | 0.388935i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.73154 | + | 3.88753i | −0.654457 | + | 0.291383i | ||||
\(179\) | −15.4208 | − | 11.2038i | −1.15260 | − | 0.837415i | −0.163778 | − | 0.986497i | \(-0.552368\pi\) |
−0.988825 | + | 0.149082i | \(0.952368\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.13951 | − | 6.64024i | 0.679335 | − | 0.493565i | −0.193802 | − | 0.981041i | \(-0.562082\pi\) |
0.873137 | + | 0.487475i | \(0.162082\pi\) | |||||||
\(182\) | 4.10177 | − | 7.10448i | 0.304044 | − | 0.526619i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.12088 | − | 4.57670i | 0.303795 | − | 0.337398i | ||||
\(185\) | −17.7025 | − | 2.07884i | −1.30152 | − | 0.152840i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.57906 | − | 1.39842i | −0.481109 | − | 0.102263i | ||||
\(188\) | 3.32022 | + | 10.2186i | 0.242152 | + | 0.745266i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.74195 | − | 2.33720i | 0.126374 | − | 0.169559i | ||||
\(191\) | −2.20315 | − | 0.468294i | −0.159414 | − | 0.0338845i | 0.127513 | − | 0.991837i | \(-0.459301\pi\) |
−0.286927 | + | 0.957952i | \(0.592634\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.89562 | + | 13.6756i | 0.568339 | + | 0.984393i | 0.996730 | + | 0.0807992i | \(0.0257472\pi\) |
−0.428391 | + | 0.903593i | \(0.640919\pi\) | |||||||
\(194\) | −17.0571 | − | 7.59431i | −1.22463 | − | 0.545240i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.81737 | + | 1.69960i | −0.272669 | + | 0.121400i | ||||
\(197\) | −17.3982 | − | 12.6405i | −1.23957 | − | 0.900601i | −0.242001 | − | 0.970276i | \(-0.577804\pi\) |
−0.997570 | + | 0.0696750i | \(0.977804\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.1687 | −1.21706 | −0.608530 | − | 0.793531i | \(-0.708240\pi\) | ||||
−0.608530 | + | 0.793531i | \(0.708240\pi\) | |||||||
\(200\) | −14.9015 | − | 3.54877i | −1.05370 | − | 0.250936i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.94746 | + | 2.11440i | −0.699901 | + | 0.148769i | ||||
\(203\) | 1.30143 | − | 12.3822i | 0.0913422 | − | 0.869063i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.29309 | − | 5.32391i | −0.160157 | − | 0.371838i | ||||
\(206\) | −7.04810 | + | 5.12075i | −0.491065 | + | 0.356779i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.97179 | − | 2.15913i | 0.206056 | − | 0.149709i | ||||
\(209\) | 4.12673 | + | 0.877164i | 0.285452 | + | 0.0606747i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.3645 | − | 2.84072i | 0.920053 | − | 0.195563i | 0.276544 | − | 0.961001i | \(-0.410811\pi\) |
0.643510 | + | 0.765438i | \(0.277478\pi\) | |||||||
\(212\) | 7.62641 | − | 8.46999i | 0.523784 | − | 0.581721i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.67060 | − | 4.07661i | −0.250917 | − | 0.278672i | ||||
\(215\) | 13.8250 | + | 19.5241i | 0.942860 | + | 1.33154i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.8644 | − | 12.9792i | 1.21271 | − | 0.881088i | ||||
\(218\) | 2.63314 | − | 4.56073i | 0.178339 | − | 0.308892i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.26169 | − | 6.31281i | −0.0850631 | − | 0.425609i | ||||
\(221\) | 0.433462 | − | 4.12412i | 0.0291578 | − | 0.277418i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.6520 | + | 16.2727i | 0.981169 | + | 1.08970i | 0.995959 | + | 0.0898080i | \(0.0286253\pi\) |
−0.0147900 | + | 0.999891i | \(0.504708\pi\) | |||||||
\(224\) | −14.9138 | −0.996469 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.39502 | −0.159314 | ||||||||
\(227\) | 17.3202 | + | 19.2360i | 1.14958 | + | 1.27674i | 0.955248 | + | 0.295806i | \(0.0955880\pi\) |
0.194334 | + | 0.980935i | \(0.437745\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.40196 | + | 22.8532i | −0.158726 | + | 1.51018i | 0.567872 | + | 0.823117i | \(0.307767\pi\) |
−0.726598 | + | 0.687063i | \(0.758900\pi\) | |||||||
\(230\) | −4.26097 | + | 2.39137i | −0.280960 | + | 0.157682i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.48140 | − | 9.49406i | 0.359872 | − | 0.623316i | ||||
\(233\) | 7.19284 | − | 5.22590i | 0.471219 | − | 0.342360i | −0.326697 | − | 0.945129i | \(-0.605936\pi\) |
0.797916 | + | 0.602769i | \(0.205936\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.357478 | − | 29.3558i | 0.0233193 | − | 1.91496i | ||||
\(236\) | −2.98328 | − | 3.31327i | −0.194195 | − | 0.215675i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.83857 | − | 5.37377i | 0.313638 | − | 0.348330i | ||||
\(239\) | −5.06749 | + | 1.07713i | −0.327788 | + | 0.0696736i | −0.368867 | − | 0.929482i | \(-0.620254\pi\) |
0.0410781 | + | 0.999156i | \(0.486921\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.41203 | + | 1.36292i | 0.413035 | + | 0.0877933i | 0.409742 | − | 0.912201i | \(-0.365619\pi\) |
0.00329255 | + | 0.999995i | \(0.498952\pi\) | |||||||
\(242\) | −1.21055 | + | 0.879516i | −0.0778171 | + | 0.0565374i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.349503 | − | 0.253929i | 0.0223746 | − | 0.0162561i | ||||
\(245\) | 11.3688 | − | 1.05511i | 0.726324 | − | 0.0674087i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.271890 | + | 2.58686i | −0.0173000 | + | 0.164598i | ||||
\(248\) | 19.0183 | − | 4.04246i | 1.20766 | − | 0.256697i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.2962 | + | 6.45705i | 0.651189 | + | 0.408380i | ||||
\(251\) | 7.14839 | 0.451202 | 0.225601 | − | 0.974220i | \(-0.427565\pi\) | ||||
0.225601 | + | 0.974220i | \(0.427565\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.72132 | − | 4.15678i | −0.359696 | − | 0.261335i | ||||
\(254\) | −19.0034 | + | 8.46087i | −1.19238 | + | 0.530882i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.5288 | − | 6.46862i | −0.908048 | − | 0.404289i | ||||
\(257\) | −2.06283 | − | 3.57292i | −0.128676 | − | 0.222873i | 0.794488 | − | 0.607280i | \(-0.207739\pi\) |
−0.923164 | + | 0.384407i | \(0.874406\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 27.1288 | + | 5.76641i | 1.68570 | + | 0.358307i | ||||
\(260\) | 3.78943 | − | 1.18044i | 0.235010 | − | 0.0732080i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.59221 | + | 7.97800i | 0.160147 | + | 0.492883i | ||||
\(263\) | 17.2609 | + | 3.66892i | 1.06435 | + | 0.226235i | 0.706623 | − | 0.707590i | \(-0.250218\pi\) |
0.357730 | + | 0.933825i | \(0.383551\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −27.1576 | + | 15.2416i | −1.66828 | + | 0.936284i | ||||
\(266\) | −3.03500 | + | 3.37071i | −0.186088 | + | 0.206671i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.40515 | + | 7.62994i | −0.269087 | + | 0.466073i | ||||
\(269\) | 21.6298 | − | 15.7150i | 1.31879 | − | 0.958158i | 0.318845 | − | 0.947807i | \(-0.396705\pi\) |
0.999946 | − | 0.0103508i | \(-0.00329481\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.6749 | + | 12.8416i | 1.07367 | + | 0.780069i | 0.976569 | − | 0.215205i | \(-0.0690419\pi\) |
0.0971044 | + | 0.995274i | \(0.469042\pi\) | |||||||
\(272\) | 2.95798 | − | 1.31698i | 0.179354 | − | 0.0798534i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.40921 | + | 5.90493i | 0.205958 | + | 0.356730i | ||||
\(275\) | −2.26412 | + | 17.4438i | −0.136532 | + | 1.05190i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.51723 | − | 10.5700i | −0.571835 | − | 0.635087i | 0.385968 | − | 0.922512i | \(-0.373867\pi\) |
−0.957803 | + | 0.287425i | \(0.907201\pi\) | |||||||
\(278\) | 17.9329 | + | 13.0290i | 1.07554 | + | 0.781427i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 22.5777 | + | 7.64110i | 1.34927 | + | 0.456643i | ||||
\(281\) | −0.750893 | − | 7.14427i | −0.0447945 | − | 0.426192i | −0.993821 | − | 0.110995i | \(-0.964596\pi\) |
0.949026 | − | 0.315197i | \(-0.102070\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.3369 | + | 5.49275i | 0.733353 | + | 0.326510i | 0.739212 | − | 0.673473i | \(-0.235198\pi\) |
−0.00585864 | + | 0.999983i | \(0.501865\pi\) | |||||||
\(284\) | −4.31901 | + | 4.79675i | −0.256286 | + | 0.284635i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.55021 | − | 6.16413i | −0.328191 | − | 0.364493i | ||||
\(287\) | 2.78730 | + | 8.57843i | 0.164529 | + | 0.506369i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.12374 | + | 12.6916i | −0.242573 | + | 0.746564i | ||||
\(290\) | −6.53413 | + | 5.74084i | −0.383697 | + | 0.337114i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.65441 | + | 2.96273i | 0.389420 | + | 0.173381i | ||||
\(293\) | 0.157560 | + | 0.272902i | 0.00920475 | + | 0.0159431i | 0.870591 | − | 0.492007i | \(-0.163737\pi\) |
−0.861386 | + | 0.507950i | \(0.830403\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.81905 | + | 11.1885i | 0.280576 | + | 0.651418i | ||||
\(296\) | 19.7570 | + | 14.3543i | 1.14835 | + | 0.834327i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.36742 | + | 7.28617i | −0.137141 | + | 0.422077i | ||||
\(299\) | 2.18005 | − | 3.77595i | 0.126075 | − | 0.218369i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.6127 | − | 32.2381i | −1.07282 | − | 1.85817i | ||||
\(302\) | 0.0331423 | − | 0.00704461i | 0.00190712 | − | 0.000405372i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.85540 | + | 0.826076i | −0.106414 | + | 0.0473787i | ||||
\(305\) | −1.12700 | + | 0.351071i | −0.0645318 | + | 0.0201023i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.35636 | −0.476923 | −0.238461 | − | 0.971152i | \(-0.576643\pi\) | ||||
−0.238461 | + | 0.971152i | \(0.576643\pi\) | |||||||
\(308\) | 1.04708 | + | 9.96230i | 0.0596629 | + | 0.567655i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.3208 | − | 1.79915i | −0.870164 | − | 0.102185i | ||||
\(311\) | 19.9820 | − | 4.24731i | 1.13308 | − | 0.240843i | 0.397050 | − | 0.917797i | \(-0.370034\pi\) |
0.736025 | + | 0.676954i | \(0.236701\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.4110 | − | 3.27572i | −0.871083 | − | 0.185154i | −0.249378 | − | 0.968406i | \(-0.580226\pi\) |
−0.621705 | + | 0.783252i | \(0.713560\pi\) | |||||||
\(314\) | 0.466301 | − | 1.43513i | 0.0263149 | − | 0.0809889i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.70899 | − | 5.25972i | −0.0961380 | − | 0.295882i | ||||
\(317\) | 1.33731 | + | 12.7236i | 0.0751108 | + | 0.714631i | 0.965671 | + | 0.259767i | \(0.0836456\pi\) |
−0.890561 | + | 0.454865i | \(0.849688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.5004 | − | 5.12029i | −0.643897 | − | 0.286681i | ||||
\(320\) | 13.2235 | + | 12.2013i | 0.739217 | + | 0.682074i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.94568 | − | 3.09242i | 0.387068 | − | 0.172334i | ||||
\(323\) | −0.708509 | + | 2.18057i | −0.0394225 | + | 0.121330i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.8417 | − | 0.264088i | −0.601389 | − | 0.0146489i | ||||
\(326\) | −0.677282 | + | 1.17309i | −0.0375112 | + | 0.0649712i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.830181 | + | 7.89865i | −0.0458391 | + | 0.436130i | ||||
\(329\) | −4.77505 | + | 45.4315i | −0.263257 | + | 2.50472i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.62711 | − | 24.9953i | −0.144399 | − | 1.37386i | −0.791364 | − | 0.611345i | \(-0.790629\pi\) |
0.646965 | − | 0.762519i | \(-0.276038\pi\) | |||||||
\(332\) | −2.91269 | −0.159855 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.0747594 | − | 0.230086i | −0.00409065 | − | 0.0125897i | ||||
\(335\) | 18.0846 | − | 15.8890i | 0.988068 | − | 0.868110i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.6373 | − | 14.0351i | 0.688396 | − | 0.764541i | −0.293088 | − | 0.956085i | \(-0.594683\pi\) |
0.981484 | + | 0.191545i | \(0.0613497\pi\) | |||||||
\(338\) | −6.03388 | + | 6.70131i | −0.328200 | + | 0.364503i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.48359 | − | 0.323305i | 0.188924 | − | 0.0175337i | ||||
\(341\) | −6.89937 | − | 21.2341i | −0.373622 | − | 1.14989i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.58955 | 0.355802 | ||||||||
\(344\) | −3.42618 | − | 32.5979i | −0.184727 | − | 1.75756i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.17223 | − | 20.6674i | 0.116780 | − | 1.11109i | ||||
\(347\) | −2.94999 | + | 28.0672i | −0.158364 | + | 1.50673i | 0.570061 | + | 0.821603i | \(0.306920\pi\) |
−0.728424 | + | 0.685126i | \(0.759747\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.1548 | − | 17.5887i | 0.543575 | − | 0.941500i | −0.455120 | − | 0.890430i | \(-0.650404\pi\) |
0.998695 | − | 0.0510695i | \(-0.0162630\pi\) | |||||||
\(350\) | −15.0241 | − | 11.4849i | −0.803074 | − | 0.613893i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.65980 | + | 14.3414i | −0.248368 | + | 0.764398i | ||||
\(353\) | −8.23808 | + | 3.66783i | −0.438469 | + | 0.195219i | −0.614085 | − | 0.789240i | \(-0.710475\pi\) |
0.175616 | + | 0.984459i | \(0.443808\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.3800 | − | 8.63166i | 0.816285 | − | 0.458121i | ||||
\(356\) | 6.57342 | + | 2.92668i | 0.348391 | + | 0.155113i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.16584 | − | 20.6066i | −0.114468 | − | 1.08909i | ||||
\(359\) | −2.84427 | − | 8.75376i | −0.150115 | − | 0.462006i | 0.847518 | − | 0.530766i | \(-0.178096\pi\) |
−0.997633 | + | 0.0687601i | \(0.978096\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.42691 | + | 16.7023i | −0.285627 | + | 0.879069i | ||||
\(362\) | 12.0119 | + | 2.55321i | 0.631333 | + | 0.134194i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.04097 | + | 1.28405i | −0.316633 | + | 0.0673024i | ||||
\(365\) | −14.6276 | − | 13.4969i | −0.765645 | − | 0.706459i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.99047 | + | 18.9381i | 0.103902 | + | 0.988558i | 0.914947 | + | 0.403575i | \(0.132232\pi\) |
−0.811045 | + | 0.584984i | \(0.801101\pi\) | |||||||
\(368\) | 3.40442 | 0.177468 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11.1969 | − | 15.8126i | −0.582099 | − | 0.822057i | ||||
\(371\) | 44.2689 | − | 19.7098i | 2.29833 | − | 1.02328i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.19359 | + | 0.891374i | −0.217136 | + | 0.0461536i | −0.315195 | − | 0.949027i | \(-0.602070\pi\) |
0.0980592 | + | 0.995181i | \(0.468737\pi\) | |||||||
\(374\) | −3.65572 | − | 6.33189i | −0.189033 | − | 0.327414i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −20.1117 | + | 34.8346i | −1.03718 | + | 1.79646i | ||||
\(377\) | 2.39840 | − | 7.38151i | 0.123524 | − | 0.380167i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.81297 | − | 5.67645i | −0.401325 | − | 0.291580i | 0.368755 | − | 0.929526i | \(-0.379784\pi\) |
−0.770081 | + | 0.637947i | \(0.779784\pi\) | |||||||
\(380\) | −2.18509 | + | 0.202794i | −0.112093 | + | 0.0104031i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.22420 | − | 2.12038i | −0.0626355 | − | 0.108488i | ||||
\(383\) | −8.53168 | − | 3.79855i | −0.435948 | − | 0.194097i | 0.177015 | − | 0.984208i | \(-0.443356\pi\) |
−0.612963 | + | 0.790111i | \(0.710023\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.01627 | − | 26.7014i | 0.306618 | − | 1.36083i | ||||
\(386\) | −5.30447 | + | 16.3255i | −0.269990 | + | 0.830944i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.34368 | + | 13.3685i | 0.220517 | + | 0.678682i | ||||
\(389\) | 17.3886 | + | 19.3120i | 0.881638 | + | 0.979158i | 0.999904 | − | 0.0138240i | \(-0.00440046\pi\) |
−0.118267 | + | 0.992982i | \(0.537734\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.57164 | − | 2.85610i | 0.130054 | − | 0.144439i | ||||
\(392\) | −14.2909 | − | 6.36272i | −0.721800 | − | 0.321366i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.44357 | − | 23.2490i | −0.123105 | − | 1.17127i | ||||
\(395\) | −0.184002 | + | 15.1100i | −0.00925812 | + | 0.760268i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.9374 | + | 7.94651i | 0.548934 | + | 0.398824i | 0.827392 | − | 0.561624i | \(-0.189823\pi\) |
−0.278458 | + | 0.960448i | \(0.589823\pi\) | |||||||
\(398\) | −12.4880 | − | 13.8693i | −0.625966 | − | 0.695205i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.05410 | − | 7.43431i | −0.202705 | − | 0.371716i | ||||
\(401\) | −3.70665 | − | 6.42010i | −0.185101 | − | 0.320604i | 0.758509 | − | 0.651662i | \(-0.225928\pi\) |
−0.943611 | + | 0.331057i | \(0.892595\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.5752 | − | 5.59883i | 0.626415 | − | 0.278898i | ||||
\(404\) | 6.19393 | + | 4.50015i | 0.308159 | + | 0.223891i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.9493 | − | 7.95511i | 0.543403 | − | 0.394806i | ||||
\(407\) | 14.0215 | − | 24.2859i | 0.695018 | − | 1.20381i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.17339 | − | 7.96686i | 0.354701 | − | 0.393936i | −0.539216 | − | 0.842167i | \(-0.681279\pi\) |
0.893917 | + | 0.448232i | \(0.147946\pi\) | |||||||
\(410\) | 2.63286 | − | 5.72485i | 0.130027 | − | 0.282730i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.41534 | + | 1.36362i | 0.316061 | + | 0.0671809i | ||||
\(413\) | −5.85766 | − | 18.0280i | −0.288237 | − | 0.887101i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.53857 | + | 2.55132i | 0.370054 | + | 0.125240i | ||||
\(416\) | −9.09382 | − | 1.93295i | −0.445861 | − | 0.0947707i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.29306 | + | 3.97169i | 0.112157 | + | 0.194262i | ||||
\(419\) | 10.9245 | + | 4.86390i | 0.533697 | + | 0.237617i | 0.655846 | − | 0.754895i | \(-0.272312\pi\) |
−0.122149 | + | 0.992512i | \(0.538979\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.07815 | + | 3.59663i | −0.393705 | + | 0.175289i | −0.594034 | − | 0.804440i | \(-0.702466\pi\) |
0.200329 | + | 0.979729i | \(0.435799\pi\) | |||||||
\(422\) | 12.0157 | + | 8.72994i | 0.584917 | + | 0.424967i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 42.6683 | 2.07215 | ||||||||
\(425\) | −9.29933 | − | 2.21462i | −0.451084 | − | 0.107425i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.79662 | − | 0.381884i | 0.0869446 | − | 0.0184806i | ||||
\(428\) | −0.431679 | + | 4.10715i | −0.0208660 | + | 0.198527i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.71617 | + | 25.3694i | −0.275658 | + | 1.22342i | ||||
\(431\) | 2.85794 | − | 2.07642i | 0.137662 | − | 0.100017i | −0.516823 | − | 0.856092i | \(-0.672885\pi\) |
0.654485 | + | 0.756075i | \(0.272885\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.00164 | + | 1.45427i | −0.0961924 | + | 0.0698879i | −0.634842 | − | 0.772642i | \(-0.718935\pi\) |
0.538649 | + | 0.842530i | \(0.318935\pi\) | |||||||
\(434\) | 23.4789 | + | 4.99059i | 1.12702 | + | 0.239556i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.87801 | + | 0.824296i | −0.185723 | + | 0.0394766i | ||||
\(437\) | −1.61307 | + | 1.79149i | −0.0771635 | + | 0.0856988i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.56157 | − | 6.17675i | −0.265439 | − | 0.294800i | 0.595660 | − | 0.803236i | \(-0.296890\pi\) |
−0.861100 | + | 0.508436i | \(0.830224\pi\) | |||||||
\(440\) | 14.4022 | − | 19.3237i | 0.686598 | − | 0.921219i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.64685 | − | 2.64959i | 0.173463 | − | 0.126028i | ||||
\(443\) | −11.6123 | + | 20.1132i | −0.551719 | + | 0.955606i | 0.446432 | + | 0.894818i | \(0.352695\pi\) |
−0.998151 | + | 0.0607879i | \(0.980639\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.4496 | − | 13.3326i | −0.684977 | − | 0.632027i | ||||
\(446\) | −2.48807 | + | 23.6724i | −0.117814 | + | 1.12092i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −18.7336 | − | 20.8058i | −0.885081 | − | 0.982982i | ||||
\(449\) | −18.8212 | −0.888227 | −0.444114 | − | 0.895970i | \(-0.646481\pi\) | ||||
−0.444114 | + | 0.895970i | \(0.646481\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.12008 | 0.429448 | ||||||||
\(452\) | 1.20648 | + | 1.33993i | 0.0567481 | + | 0.0630251i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.94117 | + | 27.9833i | −0.138036 | + | 1.31332i | ||||
\(455\) | 16.7598 | + | 1.96814i | 0.785713 | + | 0.0922678i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.31514 | + | 2.27788i | −0.0615194 | + | 0.106555i | −0.895145 | − | 0.445776i | \(-0.852928\pi\) |
0.833625 | + | 0.552330i | \(0.186261\pi\) | |||||||
\(458\) | −20.2084 | + | 14.6823i | −0.944278 | + | 0.686058i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.48434 | + | 1.17923i | 0.162458 | + | 0.0549817i | ||||
\(461\) | 13.0570 | + | 14.5013i | 0.608126 | + | 0.675392i | 0.966049 | − | 0.258359i | \(-0.0831816\pi\) |
−0.357923 | + | 0.933751i | \(0.616515\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.02652 | − | 1.14007i | 0.0477065 | − | 0.0529834i | −0.718819 | − | 0.695197i | \(-0.755317\pi\) |
0.766526 | + | 0.642214i | \(0.221984\pi\) | |||||||
\(464\) | 5.92776 | − | 1.25998i | 0.275189 | − | 0.0584933i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.45344 | + | 2.00939i | 0.437922 | + | 0.0930833i | ||||
\(467\) | 5.25538 | − | 3.81826i | 0.243190 | − | 0.176688i | −0.459513 | − | 0.888171i | \(-0.651976\pi\) |
0.702703 | + | 0.711483i | \(0.251976\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.3045 | + | 22.0175i | −1.39933 | + | 1.01667i | ||||
\(470\) | 23.9743 | − | 21.0637i | 1.10585 | − | 0.971594i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.74467 | − | 16.5994i | 0.0803049 | − | 0.764050i | ||||
\(473\) | −36.8163 | + | 7.82554i | −1.69281 | + | 0.359819i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.83302 | + | 1.38912i | 0.267637 | + | 0.0637373i | ||||
\(476\) | −5.44385 | −0.249519 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.55605 | − | 3.31017i | −0.208389 | − | 0.151403i | ||||
\(479\) | −5.00312 | + | 2.22753i | −0.228598 | + | 0.101779i | −0.517840 | − | 0.855478i | \(-0.673264\pi\) |
0.289241 | + | 0.957256i | \(0.406597\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.7947 | + | 7.03224i | 0.720175 | + | 0.320643i | ||||
\(482\) | 3.56290 | + | 6.17113i | 0.162286 | + | 0.281087i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.10187 | + | 0.234209i | 0.0500850 | + | 0.0106459i | ||||
\(485\) | 0.467672 | − | 38.4047i | 0.0212359 | − | 1.74387i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.8960 | − | 33.5344i | −0.493744 | − | 1.51959i | −0.818905 | − | 0.573929i | \(-0.805419\pi\) |
0.325162 | − | 0.945658i | \(-0.394581\pi\) | |||||||
\(488\) | 1.58195 | + | 0.336254i | 0.0716116 | + | 0.0152215i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.12161 | + | 8.41650i | 0.412072 | + | 0.380219i | ||||
\(491\) | −1.91440 | + | 2.12616i | −0.0863958 | + | 0.0959523i | −0.784792 | − | 0.619759i | \(-0.787231\pi\) |
0.698397 | + | 0.715711i | \(0.253897\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.42068 | − | 5.92480i | 0.154060 | − | 0.266839i | ||||
\(494\) | −2.28749 | + | 1.66196i | −0.102919 | + | 0.0747751i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.69540 | + | 6.31758i | 0.390435 | + | 0.283668i | ||||
\(497\) | −25.0705 | + | 11.1621i | −1.12456 | + | 0.500688i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.3438 | + | 31.7725i | 0.821183 | + | 1.42233i | 0.904802 | + | 0.425833i | \(0.140019\pi\) |
−0.0836188 | + | 0.996498i | \(0.526648\pi\) | |||||||
\(500\) | −1.57416 | − | 9.01309i | −0.0703987 | − | 0.403078i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.19950 | + | 5.77463i | 0.232065 | + | 0.257734i | ||||
\(503\) | −14.2611 | − | 10.3613i | −0.635873 | − | 0.461989i | 0.222557 | − | 0.974920i | \(-0.428560\pi\) |
−0.858430 | + | 0.512931i | \(0.828560\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0891 | − | 17.0726i | −0.537960 | − | 0.759723i | ||||
\(506\) | −0.803556 | − | 7.64533i | −0.0357224 | − | 0.339876i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.3065 | + | 6.36965i | 0.634747 | + | 0.282608i | ||||
\(509\) | 10.0917 | − | 11.2080i | 0.447306 | − | 0.496784i | −0.476751 | − | 0.879038i | \(-0.658186\pi\) |
0.924057 | + | 0.382255i | \(0.124852\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.7228 | + | 23.0150i | 0.916724 | + | 1.01812i | ||||
\(512\) | −5.44990 | − | 16.7731i | −0.240854 | − | 0.741272i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.38585 | − | 4.26522i | 0.0611274 | − | 0.188131i | ||||
\(515\) | −15.4096 | − | 9.14870i | −0.679028 | − | 0.403140i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 42.1959 | + | 18.7868i | 1.85577 | + | 0.826243i | ||||
\(518\) | 15.0744 | + | 26.1096i | 0.662330 | + | 1.14719i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.7766 | + | 7.58548i | 0.560290 | + | 0.332645i | ||||
\(521\) | −29.3467 | − | 21.3216i | −1.28570 | − | 0.934118i | −0.285994 | − | 0.958231i | \(-0.592324\pi\) |
−0.999709 | + | 0.0241133i | \(0.992324\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.83321 | + | 8.71972i | −0.123888 | + | 0.381287i | −0.993697 | − | 0.112102i | \(-0.964242\pi\) |
0.869809 | + | 0.493388i | \(0.164242\pi\) | |||||||
\(524\) | 3.15761 | − | 5.46914i | 0.137941 | − | 0.238920i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.59118 | + | 16.6124i | 0.418195 | + | 0.724336i | ||||
\(527\) | 11.8684 | − | 2.52271i | 0.516996 | − | 0.109891i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.3200 | + | 7.71136i | −0.753043 | + | 0.335276i | ||||
\(530\) | −32.0661 | − | 10.8523i | −1.39286 | − | 0.471395i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.41467 | 0.148045 | ||||||||
\(533\) | 0.587747 | + | 5.59204i | 0.0254581 | + | 0.242218i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.71485 | − | 10.2519i | 0.203841 | − | 0.443229i | ||||
\(536\) | −32.2620 | + | 6.85749i | −1.39350 | + | 0.296198i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 28.4277 | + | 6.04249i | 1.22561 | + | 0.260510i | ||||
\(539\) | −5.55101 | + | 17.0843i | −0.239099 | + | 0.735871i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.66886 | − | 14.3693i | −0.200730 | − | 0.617784i | −0.999862 | − | 0.0166277i | \(-0.994707\pi\) |
0.799132 | − | 0.601156i | \(-0.205293\pi\) | |||||||
\(542\) | 2.48243 | + | 23.6187i | 0.106629 | + | 1.01451i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.48645 | − | 3.33318i | −0.320979 | − | 0.142909i | ||||
\(545\) | 10.7590 | + | 1.26345i | 0.460865 | + | 0.0541202i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.3098 | + | 15.7209i | −1.50974 | + | 0.672178i | −0.983951 | − | 0.178439i | \(-0.942895\pi\) |
−0.525785 | + | 0.850617i | \(0.676229\pi\) | |||||||
\(548\) | 1.58623 | − | 4.88193i | 0.0677606 | − | 0.208546i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −15.7384 | + | 10.8591i | −0.671086 | + | 0.463032i | ||||
\(551\) | −2.14563 | + | 3.71634i | −0.0914069 | + | 0.158321i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.45782 | − | 23.3846i | 0.104517 | − | 0.994413i | ||||
\(554\) | 1.61613 | − | 15.3765i | 0.0686629 | − | 0.653284i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.74432 | − | 16.5961i | −0.0739758 | − | 0.703833i | ||||
\(557\) | 16.9105 | 0.716522 | 0.358261 | − | 0.933621i | \(-0.383370\pi\) | ||||
0.358261 | + | 0.933621i | \(0.383370\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.17092 | − | 22.0698i | −0.303297 | − | 0.933453i | ||||
\(560\) | 5.21229 | + | 12.1015i | 0.220259 | + | 0.511380i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.22514 | − | 5.80310i | 0.220409 | − | 0.244789i | ||||
\(563\) | 15.1527 | − | 16.8287i | 0.638609 | − | 0.709247i | −0.333770 | − | 0.942654i | \(-0.608321\pi\) |
0.972379 | + | 0.233408i | \(0.0749877\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.94889 | − | 4.52478i | −0.0819906 | − | 0.190359i | ||||
\(566\) | 4.53630 | + | 13.9613i | 0.190675 | + | 0.586837i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −24.1640 | −1.01390 | ||||||||
\(569\) | −1.87892 | − | 17.8767i | −0.0787683 | − | 0.749431i | −0.960613 | − | 0.277890i | \(-0.910365\pi\) |
0.881844 | − | 0.471540i | \(-0.156302\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.55774 | − | 14.8209i | 0.0651893 | − | 0.620235i | −0.912340 | − | 0.409434i | \(-0.865726\pi\) |
0.977529 | − | 0.210801i | \(-0.0676071\pi\) | |||||||
\(572\) | −0.652730 | + | 6.21031i | −0.0272920 | + | 0.259666i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.90247 | + | 8.49132i | −0.204625 | + | 0.354421i | ||||
\(575\) | −7.98516 | − | 6.10409i | −0.333004 | − | 0.254558i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.48625 | + | 23.0403i | −0.311657 | + | 0.959181i | 0.665452 | + | 0.746441i | \(0.268239\pi\) |
−0.977109 | + | 0.212740i | \(0.931761\pi\) | |||||||
\(578\) | −13.2520 | + | 5.90018i | −0.551212 | + | 0.245415i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.50335 | + | 0.763701i | 0.270037 | + | 0.0317109i | ||||
\(581\) | −11.3132 | − | 5.03694i | −0.469349 | − | 0.208968i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.12153 | − | 48.7281i | −0.212112 | − | 2.01811i | ||||
\(584\) | 8.42669 | + | 25.9347i | 0.348699 | + | 1.07319i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.105852 | + | 0.325780i | −0.00437272 | + | 0.0134579i | ||||
\(587\) | −9.91962 | − | 2.10848i | −0.409426 | − | 0.0870263i | −0.00140582 | − | 0.999999i | \(-0.500447\pi\) |
−0.408021 | + | 0.912973i | \(0.633781\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.44449 | + | 1.58238i | −0.306745 | + | 0.0652006i | ||||
\(590\) | −5.53308 | + | 12.0311i | −0.227793 | + | 0.495311i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.41112 | + | 13.4259i | 0.0579965 | + | 0.551800i | ||||
\(593\) | −28.7337 | −1.17995 | −0.589975 | − | 0.807422i | \(-0.700862\pi\) | ||||
−0.589975 | + | 0.807422i | \(0.700862\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.0897 | + | 4.76845i | 0.577619 | + | 0.195487i | ||||
\(596\) | 5.26895 | − | 2.34589i | 0.215825 | − | 0.0960913i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.63600 | − | 0.985411i | 0.189580 | − | 0.0402965i | ||||
\(599\) | 0.738992 | + | 1.27997i | 0.0301944 | + | 0.0522982i | 0.880728 | − | 0.473623i | \(-0.157054\pi\) |
−0.850533 | + | 0.525921i | \(0.823721\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.97465 | + | 17.2766i | −0.406874 | + | 0.704727i | −0.994538 | − | 0.104378i | \(-0.966715\pi\) |
0.587663 | + | 0.809106i | \(0.300048\pi\) | |||||||
\(602\) | 12.5044 | − | 38.4847i | 0.509642 | − | 1.56852i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.0206365 | − | 0.0149933i | −0.000839688 | − | 0.000610069i | ||||
\(605\) | −2.64668 | − | 1.57134i | −0.107603 | − | 0.0638840i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.5351 | − | 19.9793i | −0.468194 | − | 0.810935i | 0.531146 | − | 0.847281i | \(-0.321762\pi\) |
−0.999339 | + | 0.0363452i | \(0.988428\pi\) | |||||||
\(608\) | 4.69589 | + | 2.09075i | 0.190444 | + | 0.0847910i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.10335 | − | 0.655059i | −0.0446732 | − | 0.0265225i | ||||
\(611\) | −8.79993 | + | 27.0834i | −0.356007 | + | 1.09568i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.36834 | − | 22.6774i | −0.297605 | − | 0.915932i | −0.982334 | − | 0.187135i | \(-0.940080\pi\) |
0.684730 | − | 0.728797i | \(-0.259920\pi\) | |||||||
\(614\) | −6.07815 | − | 6.75047i | −0.245294 | − | 0.272427i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −25.0929 | + | 27.8685i | −1.01102 | + | 1.12286i | ||||
\(617\) | −0.814192 | − | 0.362502i | −0.0327782 | − | 0.0145938i | 0.390282 | − | 0.920695i | \(-0.372377\pi\) |
−0.423060 | + | 0.906102i | \(0.639044\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.0314900 | + | 0.299608i | 0.00126569 | + | 0.0120422i | 0.995137 | − | 0.0985054i | \(-0.0314062\pi\) |
−0.993871 | + | 0.110548i | \(0.964740\pi\) | |||||||
\(620\) | 6.71123 | + | 9.47780i | 0.269529 | + | 0.380638i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.9653 | + | 13.0526i | 0.720344 | + | 0.523361i | ||||
\(623\) | 20.4706 | + | 22.7349i | 0.820138 | + | 0.910856i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.82065 | + | 24.7063i | −0.152826 | + | 0.988253i | ||||
\(626\) | −8.56328 | − | 14.8320i | −0.342258 | − | 0.592808i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.03780 | + | 0.462060i | −0.0414129 | + | 0.0184382i | ||||
\(629\) | 12.3294 | + | 8.95784i | 0.491606 | + | 0.357173i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.5670 | + | 8.40394i | −0.460476 | + | 0.334556i | −0.793718 | − | 0.608286i | \(-0.791857\pi\) |
0.333242 | + | 0.942841i | \(0.391857\pi\) | |||||||
\(632\) | 10.3519 | − | 17.9301i | 0.411778 | − | 0.713221i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.30574 | + | 10.3351i | −0.369578 | + | 0.410458i | ||||
\(635\) | −31.4483 | − | 29.0173i | −1.24799 | − | 1.15152i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.8331 | − | 2.30264i | −0.429222 | − | 0.0912339i | ||||
\(638\) | −4.22870 | − | 13.0146i | −0.167416 | − | 0.515253i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.00474273 | + | 0.389468i | −0.000187473 | + | 0.0153951i | ||||
\(641\) | 1.18274 | + | 0.251398i | 0.0467152 | + | 0.00992963i | 0.231210 | − | 0.972904i | \(-0.425732\pi\) |
−0.184495 | + | 0.982833i | \(0.559065\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.3127 | − | 21.3262i | −0.485566 | − | 0.841025i | 0.514297 | − | 0.857612i | \(-0.328053\pi\) |
−0.999862 | + | 0.0165876i | \(0.994720\pi\) | |||||||
\(644\) | −5.22896 | − | 2.32808i | −0.206050 | − | 0.0917394i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.27686 | + | 1.01372i | −0.0895818 | + | 0.0398844i | ||||
\(647\) | −5.45922 | − | 3.96635i | −0.214624 | − | 0.155933i | 0.475279 | − | 0.879835i | \(-0.342347\pi\) |
−0.689903 | + | 0.723901i | \(0.742347\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.1663 | −0.752344 | ||||||||
\(650\) | −7.67256 | − | 8.95027i | −0.300943 | − | 0.351058i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.997480 | − | 0.212021i | 0.0390643 | − | 0.00830338i | ||||
\(653\) | −0.182163 | + | 1.73317i | −0.00712860 | + | 0.0678241i | −0.997508 | − | 0.0705556i | \(-0.977523\pi\) |
0.990379 | + | 0.138380i | \(0.0441894\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.9630 | + | 11.3892i | −0.506508 | + | 0.445015i | ||||
\(656\) | −3.55190 | + | 2.58061i | −0.138678 | + | 0.100756i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −40.1739 | + | 29.1880i | −1.56614 | + | 1.13787i | ||||
\(659\) | 32.0109 | + | 6.80414i | 1.24697 | + | 0.265051i | 0.783685 | − | 0.621158i | \(-0.213338\pi\) |
0.463284 | + | 0.886210i | \(0.346671\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −43.1830 | + | 9.17882i | −1.67962 | + | 0.357015i | −0.946406 | − | 0.322980i | \(-0.895315\pi\) |
−0.733217 | + | 0.679995i | \(0.761982\pi\) | |||||||
\(662\) | 18.2809 | − | 20.3030i | 0.710507 | − | 0.789098i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.29628 | − | 8.10334i | −0.283150 | − | 0.314470i | ||||
\(665\) | −8.83776 | − | 2.99102i | −0.342714 | − | 0.115987i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.81942 | − | 4.22805i | 0.225329 | − | 0.163711i | ||||
\(668\) | −0.0910656 | + | 0.157730i | −0.00352343 | + | 0.00610276i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 25.9897 | + | 3.05202i | 1.00407 | + | 0.117910i | ||||
\(671\) | 0.194126 | − | 1.84698i | 0.00749415 | − | 0.0713020i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.23131 | + | 4.69934i | 0.163105 | + | 0.181146i | 0.819157 | − | 0.573569i | \(-0.194442\pi\) |
−0.656052 | + | 0.754715i | \(0.727775\pi\) | |||||||
\(674\) | 20.5298 | 0.790779 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.78870 | 0.261104 | ||||||||
\(677\) | −33.5415 | − | 37.2516i | −1.28911 | − | 1.43170i | −0.844116 | − | 0.536161i | \(-0.819874\pi\) |
−0.444989 | − | 0.895536i | \(-0.646793\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.24697 | + | 59.4359i | −0.239737 | + | 2.28094i | ||||
\(680\) | 9.62582 | + | 8.88173i | 0.369133 | + | 0.340599i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.1350 | − | 21.0185i | 0.464674 | − | 0.804838i | ||||
\(683\) | −15.2867 | + | 11.1065i | −0.584931 | + | 0.424977i | −0.840498 | − | 0.541814i | \(-0.817738\pi\) |
0.255568 | + | 0.966791i | \(0.417738\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.38169 | + | 11.2459i | −0.320248 | + | 0.429682i | ||||
\(686\) | 4.79302 | + | 5.32319i | 0.182999 | + | 0.203240i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 12.1241 | − | 13.4652i | 0.462228 | − | 0.513357i | ||||
\(689\) | 29.5479 | − | 6.28060i | 1.12569 | − | 0.239272i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.3183 | − | 5.80669i | −1.03924 | − | 0.220897i | −0.343470 | − | 0.939163i | \(-0.611603\pi\) |
−0.695768 | + | 0.718266i | \(0.744936\pi\) | |||||||
\(692\) | −12.6570 | + | 9.19584i | −0.481146 | + | 0.349573i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −24.8191 | + | 18.0321i | −0.942120 | + | 0.684490i | ||||
\(695\) | −10.0225 | + | 44.4816i | −0.380174 | + | 1.68728i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.518077 | + | 4.92917i | −0.0196236 | + | 0.186706i | ||||
\(698\) | 21.5948 | − | 4.59012i | 0.817376 | − | 0.173739i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.14293 | + | 14.1910i | 0.0431988 | + | 0.536368i | ||||
\(701\) | 14.8415 | 0.560556 | 0.280278 | − | 0.959919i | \(-0.409573\pi\) | ||||
0.280278 | + | 0.959919i | \(0.409573\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.73365 | − | 5.61882i | −0.291680 | − | 0.211918i | ||||
\(704\) | −25.8606 | + | 11.5139i | −0.974657 | + | 0.433945i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.95506 | − | 3.98705i | −0.337028 | − | 0.150055i | ||||
\(707\) | 16.2756 | + | 28.1902i | 0.612107 | + | 1.06020i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.56454 | − | 0.332554i | −0.0587577 | − | 0.0124893i | 0.178439 | − | 0.983951i | \(-0.442895\pi\) |
−0.237197 | + | 0.971462i | \(0.576229\pi\) | |||||||
\(710\) | 18.1598 | + | 6.14592i | 0.681524 | + | 0.230652i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.32414 | + | 25.6191i | 0.311960 | + | 0.960115i | ||||
\(713\) | 12.4788 | + | 2.65244i | 0.467334 | + | 0.0993348i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.12919 | − | 15.5016i | 0.266617 | − | 0.579728i | ||||
\(716\) | −10.4377 | + | 11.5922i | −0.390073 | + | 0.433220i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.00266 | − | 8.66487i | 0.186698 | − | 0.323370i | ||||
\(719\) | 19.6770 | − | 14.2962i | 0.733830 | − | 0.533159i | −0.156943 | − | 0.987608i | \(-0.550164\pi\) |
0.890773 | + | 0.454449i | \(0.150164\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.5596 | + | 16.3905i | 0.840164 | + | 0.610415i | ||||
\(722\) | −17.4399 | + | 7.76473i | −0.649045 | + | 0.288973i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.62252 | − | 8.00644i | −0.171795 | − | 0.297557i | ||||
\(725\) | −16.1629 | − | 7.67309i | −0.600273 | − | 0.284971i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.01143 | − | 8.89759i | −0.297127 | − | 0.329993i | 0.576033 | − | 0.817426i | \(-0.304600\pi\) |
−0.873160 | + | 0.487433i | \(0.837933\pi\) | |||||||
\(728\) | −18.7049 | − | 13.5899i | −0.693250 | − | 0.503675i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.263443 | − | 21.6337i | 0.00975048 | − | 0.800700i | ||||
\(731\) | −2.13811 | − | 20.3428i | −0.0790810 | − | 0.752406i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.53117 | − | 4.24355i | −0.352042 | − | 0.156739i | 0.223094 | − | 0.974797i | \(-0.428384\pi\) |
−0.575136 | + | 0.818058i | \(0.695051\pi\) | |||||||
\(734\) | −13.8508 | + | 15.3829i | −0.511242 | + | 0.567792i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.76548 | − | 6.40322i | −0.212519 | − | 0.236026i | ||||
\(737\) | 11.7039 | + | 36.0208i | 0.431117 | + | 1.32684i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.63830 | − | 29.6636i | 0.354551 | − | 1.09119i | −0.601719 | − | 0.798708i | \(-0.705517\pi\) |
0.956270 | − | 0.292487i | \(-0.0944827\pi\) | |||||||
\(740\) | −3.20622 | + | 14.2298i | −0.117863 | + | 0.523098i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 48.1217 | + | 21.4252i | 1.76660 | + | 0.786543i | ||||
\(743\) | −17.4838 | − | 30.2828i | −0.641418 | − | 1.11097i | −0.985116 | − | 0.171889i | \(-0.945013\pi\) |
0.343698 | − | 0.939080i | \(-0.388320\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.6918 | + | 1.45633i | −0.574903 | + | 0.0533556i | ||||
\(746\) | −3.77035 | − | 2.73932i | −0.138042 | − | 0.100294i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.70093 | + | 5.23491i | −0.0621920 | + | 0.191407i | ||||
\(749\) | −8.77921 | + | 15.2060i | −0.320785 | + | 0.555617i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.7941 | − | 23.8921i | −0.503354 | − | 0.871835i | −0.999992 | − | 0.00387741i | \(-0.998766\pi\) |
0.496638 | − | 0.867958i | \(-0.334568\pi\) | |||||||
\(752\) | −21.7495 | + | 4.62300i | −0.793122 | + | 0.168583i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.70747 | − | 3.43159i | 0.280689 | − | 0.124971i | ||||
\(755\) | 0.0402778 | + | 0.0568815i | 0.00146586 | + | 0.00207013i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.2879 | 1.13718 | 0.568589 | − | 0.822622i | \(-0.307489\pi\) | ||||
0.568589 | + | 0.822622i | \(0.307489\pi\) | |||||||
\(758\) | −1.09733 | − | 10.4404i | −0.0398567 | − | 0.379211i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.03781 | − | 5.57108i | −0.219015 | − | 0.202084i | ||||
\(761\) | −18.3181 | + | 3.89364i | −0.664032 | + | 0.141144i | −0.527584 | − | 0.849503i | \(-0.676902\pi\) |
−0.136448 | + | 0.990647i | \(0.543569\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.4880 | − | 3.50463i | −0.596905 | − | 0.126876i | ||||
\(764\) | −0.569594 | + | 1.75303i | −0.0206072 | + | 0.0634224i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.13711 | − | 9.65503i | −0.113348 | − | 0.348850i | ||||
\(767\) | −1.23518 | − | 11.7520i | −0.0445998 | − | 0.424338i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.3024 | − | 9.48442i | −0.768183 | − | 0.342017i | −0.0150511 | − | 0.999887i | \(-0.504791\pi\) |
−0.753132 | + | 0.657870i | \(0.771458\pi\) | |||||||
\(770\) | 25.9460 | − | 14.5616i | 0.935030 | − | 0.524764i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.8057 | − | 5.25622i | 0.424895 | − | 0.189175i | ||||
\(773\) | 0.276069 | − | 0.849654i | 0.00992952 | − | 0.0305599i | −0.945969 | − | 0.324257i | \(-0.894886\pi\) |
0.955899 | + | 0.293697i | \(0.0948857\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.06794 | − | 30.4088i | −0.325730 | − | 1.09232i | ||||
\(776\) | −26.3112 | + | 45.5724i | −0.944518 | + | 1.63595i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.95278 | + | 28.0939i | −0.105862 | + | 1.00721i | ||||
\(779\) | 0.324965 | − | 3.09183i | 0.0116431 | − | 0.110776i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.90044 | + | 27.5958i | 0.103786 | + | 0.987456i | ||||
\(782\) | 4.17775 | 0.149396 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.67225 | − | 8.22434i | −0.0954375 | − | 0.293726i | ||||
\(785\) | 3.09075 | − | 0.286846i | 0.110314 | − | 0.0102380i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.1943 | − | 23.5387i | 0.755496 | − | 0.839063i | −0.235651 | − | 0.971838i | \(-0.575722\pi\) |
0.991146 | + | 0.132775i | \(0.0423887\pi\) | |||||||
\(788\) | −11.7761 | + | 13.0787i | −0.419506 | + | 0.465909i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.3401 | + | 10.8419i | −0.439040 | + | 0.385738i | ||||
\(791\) | 2.36892 | + | 7.29079i | 0.0842292 | + | 0.259231i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.14500 | 0.0406602 | ||||||||
\(794\) | 1.53616 | + | 14.6156i | 0.0545161 | + | 0.518686i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.46864 | + | 13.9732i | −0.0520547 | + | 0.495267i | ||||
\(797\) | 3.55475 | − | 33.8212i | 0.125916 | − | 1.19801i | −0.730936 | − | 0.682446i | \(-0.760916\pi\) |
0.856852 | − | 0.515562i | \(-0.172417\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.5508 | + | 21.7386i | −0.444015 | + | 0.769057i | ||||
\(800\) | −7.11712 | + | 20.2154i | −0.251628 | + | 0.714722i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.49021 | − | 7.66409i | 0.0879325 | − | 0.270628i | ||||
\(803\) | 28.6065 | − | 12.7364i | 1.00950 | − | 0.449459i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.4942 | + | 10.6057i | 0.405118 | + | 0.373802i | ||||
\(806\) | 13.6696 | + | 6.08612i | 0.481493 | + | 0.214374i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.99598 | + | 28.5048i | 0.105398 | + | 1.00280i | ||||
\(809\) | 9.52295 | + | 29.3086i | 0.334809 | + | 1.03044i | 0.966816 | + | 0.255474i | \(0.0822315\pi\) |
−0.632007 | + | 0.774963i | \(0.717769\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.77389 | + | 8.53714i | −0.0974043 | + | 0.299780i | −0.987873 | − | 0.155265i | \(-0.950377\pi\) |
0.890469 | + | 0.455045i | \(0.150377\pi\) | |||||||
\(812\) | −9.96627 | − | 2.11840i | −0.349748 | − | 0.0743411i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 29.8175 | − | 6.33790i | 1.04510 | − | 0.222143i | ||||
\(815\) | −2.76737 | − | 0.324978i | −0.0969368 | − | 0.0113835i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.34114 | + | 12.7601i | 0.0469204 | + | 0.446418i | ||||
\(818\) | 11.6535 | 0.407455 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.52915 | + | 1.41087i | −0.158165 | + | 0.0492699i | ||||
\(821\) | −6.37522 | + | 2.83843i | −0.222497 | + | 0.0990619i | −0.514958 | − | 0.857215i | \(-0.672192\pi\) |
0.292461 | + | 0.956277i | \(0.405526\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.3991 | + | 6.24896i | −1.02479 | + | 0.217825i | −0.689496 | − | 0.724290i | \(-0.742168\pi\) |
−0.335291 | + | 0.942115i | \(0.608835\pi\) | |||||||
\(824\) | 12.2767 | + | 21.2638i | 0.427678 | + | 0.740761i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.3028 | − | 17.8449i | 0.358480 | − | 0.620905i | ||||
\(827\) | 2.38874 | − | 7.35179i | 0.0830647 | − | 0.255647i | −0.900895 | − | 0.434037i | \(-0.857089\pi\) |
0.983960 | + | 0.178390i | \(0.0570888\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.9296 | + | 29.7371i | 1.42155 | + | 1.03281i | 0.991514 | + | 0.129999i | \(0.0414973\pi\) |
0.430031 | + | 0.902814i | \(0.358503\pi\) | |||||||
\(830\) | 3.42229 | + | 7.94558i | 0.118789 | + | 0.275795i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.72639 | − | 15.1146i | −0.302533 | − | 0.524003i | ||||
\(833\) | −8.91829 | − | 3.97068i | −0.309000 | − | 0.137576i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.373855 | − | 0.328466i | 0.0129378 | − | 0.0113670i | ||||
\(836\) | 1.06691 | − | 3.28361i | 0.0368998 | − | 0.113566i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.01695 | + | 12.3629i | 0.138763 | + | 0.427070i | ||||
\(839\) | −2.23739 | − | 2.48488i | −0.0772434 | − | 0.0857875i | 0.703284 | − | 0.710909i | \(-0.251716\pi\) |
−0.780528 | + | 0.625121i | \(0.785049\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.8369 | + | 12.0356i | −0.373685 | + | 0.415019i | ||||
\(842\) | −8.78122 | − | 3.90965i | −0.302621 | − | 0.134736i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.16877 | − | 11.1201i | −0.0402306 | − | 0.382769i | ||||
\(845\) | −17.5704 | − | 5.94644i | −0.604438 | − | 0.204564i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.87474 | + | 2.81516i | 0.133138 | + | 0.0967301i | ||||
\(848\) | 15.7827 | + | 17.5284i | 0.541979 | + | 0.601929i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.97501 | − | 9.12306i | −0.170641 | − | 0.312918i | ||||
\(851\) | 8.01186 | + | 13.8770i | 0.274643 | + | 0.475696i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.2076 | − | 20.5729i | 1.58212 | − | 0.704404i | 0.587617 | − | 0.809139i | \(-0.300066\pi\) |
0.994500 | + | 0.104735i | \(0.0333994\pi\) | |||||||
\(854\) | 1.61530 | + | 1.17358i | 0.0552743 | + | 0.0401592i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.5078 | + | 9.08743i | −0.427507 | + | 0.310602i | ||||
\(857\) | 24.3694 | − | 42.2090i | 0.832443 | − | 1.44183i | −0.0636526 | − | 0.997972i | \(-0.520275\pi\) |
0.896096 | − | 0.443861i | \(-0.146392\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.2741 | − | 38.0652i | 1.16942 | − | 1.29877i | 0.223371 | − | 0.974734i | \(-0.428294\pi\) |
0.946045 | − | 0.324034i | \(-0.105039\pi\) | |||||||
\(860\) | 17.0728 | − | 9.58173i | 0.582179 | − | 0.326734i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.75615 | + | 0.798395i | 0.127935 | + | 0.0271934i | ||||
\(863\) | 3.13109 | + | 9.63651i | 0.106584 | + | 0.328031i | 0.990099 | − | 0.140372i | \(-0.0448298\pi\) |
−0.883515 | + | 0.468402i | \(0.844830\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40.8134 | − | 12.7138i | 1.38770 | − | 0.432281i | ||||
\(866\) | −2.63072 | − | 0.559177i | −0.0893955 | − | 0.0190016i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9.03533 | − | 15.6496i | −0.306679 | − | 0.531184i | ||||
\(869\) | −21.7191 | − | 9.66997i | −0.736770 | − | 0.328031i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.3321 | + | 9.49766i | −0.722811 | + | 0.321816i | ||||
\(872\) | −12.0076 | − | 8.72406i | −0.406630 | − | 0.295434i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.62050 | −0.0886399 | ||||||||
\(875\) | 9.47221 | − | 37.7299i | 0.320219 | − | 1.27550i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.6196 | + | 5.65817i | −0.898880 | + | 0.191063i | −0.634104 | − | 0.773247i | \(-0.718631\pi\) |
−0.264775 | + | 0.964310i | \(0.585298\pi\) | |||||||
\(878\) | 0.944418 | − | 8.98553i | 0.0318726 | − | 0.303247i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 13.2656 | − | 1.23115i | 0.447182 | − | 0.0415021i | ||||
\(881\) | −26.5743 | + | 19.3074i | −0.895312 | + | 0.650482i | −0.937257 | − | 0.348638i | \(-0.886644\pi\) |
0.0419459 | + | 0.999120i | \(0.486644\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.3821 | + | 20.6208i | −0.955134 | + | 0.693946i | −0.952016 | − | 0.306050i | \(-0.900993\pi\) |
−0.00311854 | + | 0.999995i | \(0.500993\pi\) | |||||||
\(884\) | −3.31944 | − | 0.705568i | −0.111645 | − | 0.0237308i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.6943 | + | 5.24894i | −0.829622 | + | 0.176342i | ||||
\(887\) | 9.87336 | − | 10.9655i | 0.331515 | − | 0.368185i | −0.554225 | − | 0.832367i | \(-0.686985\pi\) |
0.885740 | + | 0.464182i | \(0.153652\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 44.5525 | + | 49.4806i | 1.49424 | + | 1.65953i | ||||
\(890\) | 0.260237 | − | 21.3704i | 0.00872317 | − | 0.716339i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.4973 | − | 10.5329i | 0.485405 | − | 0.352667i | ||||
\(893\) | 7.87251 | − | 13.6356i | 0.263444 | − | 0.456298i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37.1685 | − | 20.8599i | 1.24240 | − | 0.697271i | ||||
\(896\) | 0.0633514 | − | 0.602749i | 0.00211642 | − | 0.0201364i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.6899 | − | 15.2042i | −0.456839 | − | 0.507371i | ||||
\(899\) | 22.7096 | 0.757409 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.6273 | 0.887083 | ||||||||
\(902\) | 6.63365 | + | 7.36741i | 0.220876 | + | 0.245308i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.705569 | + | 6.71304i | −0.0234669 | + | 0.223272i | ||||
\(905\) | 4.95080 | + | 24.7711i | 0.164570 | + | 0.823419i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.4907 | + | 49.3473i | −0.946018 | + | 1.63855i | −0.192318 | + | 0.981333i | \(0.561601\pi\) |
−0.753700 | + | 0.657219i | \(0.771733\pi\) | |||||||
\(908\) | 17.1373 | − | 12.4510i | 0.568723 | − | 0.413201i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 10.6006 | + | 14.9705i | 0.351408 | + | 0.496269i | ||||
\(911\) | 16.7345 | + | 18.5855i | 0.554438 | + | 0.615765i | 0.953586 | − | 0.301121i | \(-0.0973608\pi\) |
−0.399148 | + | 0.916886i | \(0.630694\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.37841 | + | 9.30516i | −0.277285 | + | 0.307956i | ||||
\(914\) | −2.79671 | + | 0.594459i | −0.0925070 | + | 0.0196630i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.3942 | + | 3.90980i | 0.607760 | + | 0.129183i | ||||
\(917\) | 21.7223 | − | 15.7821i | 0.717332 | − | 0.521172i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.0477 | − | 30.5494i | 1.38703 | − | 1.00773i | 0.390841 | − | 0.920458i | \(-0.372184\pi\) |
0.996184 | − | 0.0872745i | \(-0.0278157\pi\) | |||||||
\(920\) | 5.44754 | + | 12.6476i | 0.179600 | + | 0.416981i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.21723 | + | 21.0955i | −0.0730206 | + | 0.694744i | ||||
\(923\) | −16.7336 | + | 3.55685i | −0.550795 | + | 0.117075i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.7626 | − | 34.0208i | 0.682671 | − | 1.11860i | ||||
\(926\) | 1.66763 | 0.0548017 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −12.4087 | − | 9.01543i | −0.407335 | − | 0.295946i | ||||
\(929\) | −4.34150 | + | 1.93296i | −0.142440 | + | 0.0634184i | −0.476719 | − | 0.879056i | \(-0.658174\pi\) |
0.334279 | + | 0.942474i | \(0.391507\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.59401 | + | 2.49061i | 0.183336 | + | 0.0816266i | ||||
\(932\) | −3.63795 | − | 6.30111i | −0.119165 | − | 0.206400i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.90707 | + | 1.46814i | 0.226006 | + | 0.0480391i | ||||
\(935\) | 8.98773 | − | 12.0590i | 0.293930 | − | 0.394371i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.81033 | − | 5.57164i | −0.0591410 | − | 0.182017i | 0.917122 | − | 0.398608i | \(-0.130506\pi\) |
−0.976263 | + | 0.216590i | \(0.930506\pi\) | |||||||
\(938\) | −39.8288 | − | 8.46587i | −1.30046 | − | 0.276420i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −23.8614 | − | 2.80209i | −0.778272 | − | 0.0913940i | ||||
\(941\) | 23.6391 | − | 26.2539i | 0.770613 | − | 0.855852i | −0.222266 | − | 0.974986i | \(-0.571345\pi\) |
0.992878 | + | 0.119134i | \(0.0380119\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.60561 | + | 4.51304i | −0.0848502 | + | 0.146965i | ||||
\(944\) | 7.46450 | − | 5.42328i | 0.242949 | − | 0.176513i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −33.1006 | − | 24.0490i | −1.07619 | − | 0.781900i | ||||
\(947\) | −34.3051 | + | 15.2736i | −1.11476 | + | 0.496325i | −0.879640 | − | 0.475640i | \(-0.842217\pi\) |
−0.235125 | + | 0.971965i | \(0.575550\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.65299 | + | 16.7195i | 0.313349 | + | 0.542737i | ||||
\(950\) | 3.12058 | + | 5.72245i | 0.101245 | + | 0.185661i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −13.6368 | − | 15.1452i | −0.441972 | − | 0.490859i | ||||
\(953\) | −1.17391 | − | 0.852898i | −0.0380268 | − | 0.0276281i | 0.568609 | − | 0.822608i | \(-0.307482\pi\) |
−0.606636 | + | 0.794979i | \(0.707482\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.00974 | − | 4.03822i | 0.0973930 | − | 0.130674i | ||||
\(956\) | 0.443166 | + | 4.21644i | 0.0143330 | + | 0.136369i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.43856 | − | 2.42140i | −0.175712 | − | 0.0782320i | ||||
\(959\) | 14.6034 | − | 16.2187i | 0.471569 | − | 0.523731i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.20745 | + | 6.89408i | 0.200240 | + | 0.222390i | ||||
\(962\) | 5.80772 | + | 17.8743i | 0.187248 | + | 0.576291i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.65774 | − | 5.10200i | 0.0533922 | − | 0.164324i | ||||
\(965\) | −35.1592 | + | 3.26306i | −1.13181 | + | 0.105041i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.5396 | − | 19.3851i | −1.40014 | − | 0.623383i | −0.438760 | − | 0.898604i | \(-0.644582\pi\) |
−0.961381 | + | 0.275222i | \(0.911249\pi\) | |||||||
\(968\) | 2.10859 | + | 3.65218i | 0.0677725 | + | 0.117385i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 31.3644 | − | 27.5566i | 1.00705 | − | 0.884788i | ||||
\(971\) | 14.0919 | + | 10.2383i | 0.452229 | + | 0.328564i | 0.790475 | − | 0.612494i | \(-0.209834\pi\) |
−0.338246 | + | 0.941058i | \(0.609834\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.9247 | − | 67.4773i | 0.702874 | − | 2.16322i | ||||
\(974\) | 19.1645 | − | 33.1938i | 0.614069 | − | 1.06360i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.447017 | + | 0.774255i | 0.0143086 | + | 0.0247833i | ||||
\(977\) | −2.03039 | + | 0.431574i | −0.0649581 | + | 0.0138073i | −0.240276 | − | 0.970705i | \(-0.577238\pi\) |
0.175318 | + | 0.984512i | \(0.443905\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.2584 | − | 12.5814i | 0.903141 | − | 0.402104i | ||||
\(980\) | 0.113774 | − | 9.34301i | 0.00363438 | − | 0.298452i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.11004 | −0.0992453 | ||||||||
\(983\) | −3.12635 | − | 29.7452i | −0.0997150 | − | 0.948724i | −0.923959 | − | 0.382490i | \(-0.875067\pi\) |
0.824245 | − | 0.566234i | \(-0.191600\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.9346 | − | 23.5349i | 1.33615 | − | 0.749883i | ||||
\(986\) | 7.27428 | − | 1.54620i | 0.231660 | − | 0.0492409i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.08212 | + | 0.442569i | 0.0662412 | + | 0.0140800i | ||||
\(989\) | 6.64596 | − | 20.4542i | 0.211329 | − | 0.650405i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.05364 | + | 9.39812i | 0.0970019 | + | 0.298541i | 0.987770 | − | 0.155916i | \(-0.0498331\pi\) |
−0.890768 | + | 0.454458i | \(0.849833\pi\) | |||||||
\(992\) | −2.84347 | − | 27.0538i | −0.0902801 | − | 0.858958i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −27.2524 | − | 12.1336i | −0.864395 | − | 0.384853i | ||||
\(995\) | 16.0407 | − | 34.8787i | 0.508524 | − | 1.10573i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.1343 | + | 6.29299i | −0.447638 | + | 0.199301i | −0.618159 | − | 0.786053i | \(-0.712121\pi\) |
0.170522 | + | 0.985354i | \(0.445455\pi\) | |||||||
\(998\) | −12.3238 | + | 37.9288i | −0.390104 | + | 1.20062i | ||||
\(999\) | 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 | 675.2.r.a.46.19 | 224 | ||
3.2 | odd | 2 | 225.2.q.a.196.10 | yes | 224 | ||
9.4 | even | 3 | inner | 675.2.r.a.496.10 | 224 | ||
9.5 | odd | 6 | 225.2.q.a.121.19 | yes | 224 | ||
25.6 | even | 5 | inner | 675.2.r.a.181.10 | 224 | ||
75.56 | odd | 10 | 225.2.q.a.106.19 | yes | 224 | ||
225.31 | even | 15 | inner | 675.2.r.a.631.19 | 224 | ||
225.131 | odd | 30 | 225.2.q.a.31.10 | ✓ | 224 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.2.q.a.31.10 | ✓ | 224 | 225.131 | odd | 30 | ||
225.2.q.a.106.19 | yes | 224 | 75.56 | odd | 10 | ||
225.2.q.a.121.19 | yes | 224 | 9.5 | odd | 6 | ||
225.2.q.a.196.10 | yes | 224 | 3.2 | odd | 2 | ||
675.2.r.a.46.19 | 224 | 1.1 | even | 1 | trivial | ||
675.2.r.a.181.10 | 224 | 25.6 | even | 5 | inner | ||
675.2.r.a.496.10 | 224 | 9.4 | even | 3 | inner | ||
675.2.r.a.631.19 | 224 | 225.31 | even | 15 | inner |