Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(49,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.j (of order \(6\), degree \(2\), 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: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 11x^{14} + 82x^{12} - 337x^{10} + 1006x^{8} - 1596x^{6} + 1765x^{4} - 414x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 349.6 | ||
Root | \(-1.77290 - 1.02359i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.349 |
Dual form | 475.2.j.c.49.6 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.03136 | − | 0.595455i | 0.729280 | − | 0.421050i | −0.0888786 | − | 0.996042i | \(-0.528328\pi\) |
0.818159 | + | 0.574992i | \(0.194995\pi\) | |||||||
\(3\) | 2.63893 | − | 1.52359i | 1.52359 | − | 0.879643i | 0.523975 | − | 0.851734i | \(-0.324448\pi\) |
0.999610 | − | 0.0279089i | \(-0.00888485\pi\) | |||||||
\(4\) | −0.290867 | + | 0.503797i | −0.145434 | + | 0.251898i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.81445 | − | 3.14272i | 0.740747 | − | 1.28301i | ||||
\(7\) | 0.609175i | 0.230247i | 0.993351 | + | 0.115123i | \(0.0367263\pi\) | ||||
−0.993351 | + | 0.115123i | \(0.963274\pi\) | |||||||
\(8\) | 3.07461i | 1.08704i | ||||||||
\(9\) | 3.14263 | − | 5.44319i | 1.04754 | − | 1.81440i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.48517 | 1.35233 | 0.676164 | − | 0.736751i | \(-0.263641\pi\) | ||||
0.676164 | + | 0.736751i | \(0.263641\pi\) | |||||||
\(12\) | 1.77264i | 0.511718i | ||||||||
\(13\) | −3.84342 | − | 2.21900i | −1.06597 | − | 0.615439i | −0.138894 | − | 0.990307i | \(-0.544355\pi\) |
−0.927078 | + | 0.374868i | \(0.877688\pi\) | |||||||
\(14\) | 0.362736 | + | 0.628278i | 0.0969454 | + | 0.167914i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.24906 | + | 2.16343i | 0.312265 | + | 0.540858i | ||||
\(17\) | −2.51445 | + | 1.45172i | −0.609843 | + | 0.352093i | −0.772904 | − | 0.634523i | \(-0.781197\pi\) |
0.163061 | + | 0.986616i | \(0.447863\pi\) | |||||||
\(18\) | − | 7.48517i | − | 1.76427i | ||||||
\(19\) | −3.60532 | − | 2.44983i | −0.827117 | − | 0.562030i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.928131 | + | 1.60757i | 0.202535 | + | 0.350800i | ||||
\(22\) | 4.62581 | − | 2.67071i | 0.986227 | − | 0.569398i | ||||
\(23\) | 2.46580 | + | 1.42363i | 0.514154 | + | 0.296847i | 0.734540 | − | 0.678566i | \(-0.237398\pi\) |
−0.220386 | + | 0.975413i | \(0.570732\pi\) | |||||||
\(24\) | 4.68443 | + | 8.11368i | 0.956206 | + | 1.65620i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.28525 | −1.03652 | ||||||||
\(27\) | − | 10.0107i | − | 1.92656i | ||||||
\(28\) | −0.306901 | − | 0.177189i | −0.0579987 | − | 0.0334856i | ||||
\(29\) | 0.558149 | − | 0.966742i | 0.103646 | − | 0.179519i | −0.809538 | − | 0.587067i | \(-0.800283\pi\) |
0.913184 | + | 0.407547i | \(0.133616\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.22908 | −1.11877 | −0.559387 | − | 0.828906i | \(-0.688964\pi\) | ||||
−0.559387 | + | 0.828906i | \(0.688964\pi\) | |||||||
\(32\) | −2.74893 | − | 1.58710i | −0.485947 | − | 0.280562i | ||||
\(33\) | 11.8360 | − | 6.83354i | 2.06039 | − | 1.18957i | ||||
\(34\) | −1.72886 | + | 2.99448i | −0.296498 | + | 0.513549i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.82817 | + | 3.16649i | 0.304696 | + | 0.527748i | ||||
\(37\) | 3.77264i | 0.620219i | 0.950701 | + | 0.310109i | \(0.100366\pi\) | ||||
−0.950701 | + | 0.310109i | \(0.899634\pi\) | |||||||
\(38\) | −5.17714 | − | 0.379847i | −0.839843 | − | 0.0616193i | ||||
\(39\) | −13.5233 | −2.16547 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.15184 | + | 7.19120i | 0.648409 | + | 1.12308i | 0.983503 | + | 0.180893i | \(0.0578987\pi\) |
−0.335094 | + | 0.942185i | \(0.608768\pi\) | |||||||
\(42\) | 1.91447 | + | 1.10532i | 0.295409 | + | 0.170555i | ||||
\(43\) | −8.65053 | + | 4.99438i | −1.31919 | + | 0.761637i | −0.983599 | − | 0.180370i | \(-0.942270\pi\) |
−0.335594 | + | 0.942007i | \(0.608937\pi\) | |||||||
\(44\) | −1.30459 | + | 2.25961i | −0.196674 | + | 0.340649i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.39082 | 0.499950 | ||||||||
\(47\) | −5.09656 | − | 2.94250i | −0.743409 | − | 0.429208i | 0.0798983 | − | 0.996803i | \(-0.474540\pi\) |
−0.823308 | + | 0.567595i | \(0.807874\pi\) | |||||||
\(48\) | 6.59235 | + | 3.80609i | 0.951524 | + | 0.549362i | ||||
\(49\) | 6.62891 | 0.946986 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.42363 | + | 7.66195i | −0.619432 | + | 1.07289i | ||||
\(52\) | 2.23585 | − | 1.29087i | 0.310056 | − | 0.179011i | ||||
\(53\) | −7.31681 | − | 4.22436i | −1.00504 | − | 0.580261i | −0.0953049 | − | 0.995448i | \(-0.530383\pi\) |
−0.909736 | + | 0.415188i | \(0.863716\pi\) | |||||||
\(54\) | −5.96093 | − | 10.3246i | −0.811180 | − | 1.40501i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.87298 | −0.250287 | ||||||||
\(57\) | −13.2467 | − | 0.971912i | −1.75457 | − | 0.128733i | ||||
\(58\) | − | 1.32941i | − | 0.174560i | ||||||
\(59\) | 5.11793 | + | 8.86451i | 0.666297 | + | 1.15406i | 0.978932 | + | 0.204187i | \(0.0654552\pi\) |
−0.312634 | + | 0.949874i | \(0.601211\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.49099 | − | 4.31453i | 0.318939 | − | 0.552419i | −0.661328 | − | 0.750097i | \(-0.730007\pi\) |
0.980267 | + | 0.197678i | \(0.0633401\pi\) | |||||||
\(62\) | −6.42441 | + | 3.70913i | −0.815900 | + | 0.471060i | ||||
\(63\) | 3.31586 | + | 1.91441i | 0.417759 | + | 0.241193i | ||||
\(64\) | −8.77641 | −1.09705 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8.13812 | − | 14.0956i | 1.00173 | − | 1.73505i | ||||
\(67\) | 7.34057 | + | 4.23808i | 0.896794 | + | 0.517764i | 0.876159 | − | 0.482023i | \(-0.160098\pi\) |
0.0206350 | + | 0.999787i | \(0.493431\pi\) | |||||||
\(68\) | − | 1.68903i | − | 0.204825i | ||||||
\(69\) | 8.67608 | 1.04448 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.80995 | − | 10.0631i | −0.689514 | − | 1.19427i | −0.971995 | − | 0.235001i | \(-0.924491\pi\) |
0.282481 | − | 0.959273i | \(-0.408843\pi\) | |||||||
\(72\) | 16.7357 | + | 9.66236i | 1.97232 | + | 1.13872i | ||||
\(73\) | 3.22443 | − | 1.86162i | 0.377391 | − | 0.217887i | −0.299292 | − | 0.954162i | \(-0.596750\pi\) |
0.676682 | + | 0.736275i | \(0.263417\pi\) | |||||||
\(74\) | 2.24644 | + | 3.89095i | 0.261143 | + | 0.452313i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.28289 | − | 1.10377i | 0.261865 | − | 0.126611i | ||||
\(77\) | 2.73225i | 0.311369i | ||||||||
\(78\) | −13.9474 | + | 8.05253i | −1.57923 | + | 0.911770i | ||||
\(79\) | 4.51908 | + | 7.82728i | 0.508437 | + | 0.880638i | 0.999952 | + | 0.00976923i | \(0.00310969\pi\) |
−0.491516 | + | 0.870869i | \(0.663557\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.82432 | − | 10.0880i | −0.647146 | − | 1.12089i | ||||
\(82\) | 8.56407 | + | 4.94447i | 0.945744 | + | 0.546025i | ||||
\(83\) | − | 2.12178i | − | 0.232896i | −0.993197 | − | 0.116448i | \(-0.962849\pi\) | ||
0.993197 | − | 0.116448i | \(-0.0371508\pi\) | |||||||
\(84\) | −1.07985 | −0.117821 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.94786 | + | 10.3020i | −0.641374 | + | 1.11089i | ||||
\(87\) | − | 3.40155i | − | 0.364684i | ||||||
\(88\) | 13.7901i | 1.47003i | ||||||||
\(89\) | 3.96608 | − | 6.86946i | 0.420404 | − | 0.728161i | −0.575575 | − | 0.817749i | \(-0.695222\pi\) |
0.995979 | + | 0.0895879i | \(0.0285550\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.35176 | − | 2.34131i | 0.141703 | − | 0.245436i | ||||
\(92\) | −1.43444 | + | 0.828173i | −0.149551 | + | 0.0863430i | ||||
\(93\) | −16.4381 | + | 9.49053i | −1.70455 | + | 0.984122i | ||||
\(94\) | −7.00850 | −0.722872 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9.67231 | −0.987176 | ||||||||
\(97\) | 8.37668 | − | 4.83628i | 0.850523 | − | 0.491050i | −0.0103043 | − | 0.999947i | \(-0.503280\pi\) |
0.860827 | + | 0.508897i | \(0.169947\pi\) | |||||||
\(98\) | 6.83677 | − | 3.94721i | 0.690619 | − | 0.398729i | ||||
\(99\) | 14.0952 | − | 24.4136i | 1.41662 | − | 2.45366i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.485632 | − | 0.841140i | 0.0483222 | − | 0.0836965i | −0.840853 | − | 0.541264i | \(-0.817946\pi\) |
0.889175 | + | 0.457568i | \(0.151279\pi\) | |||||||
\(102\) | 10.5363i | 1.04325i | ||||||||
\(103\) | − | 3.34143i | − | 0.329241i | −0.986357 | − | 0.164620i | \(-0.947360\pi\) | ||
0.986357 | − | 0.164620i | \(-0.0526399\pi\) | |||||||
\(104\) | 6.82256 | − | 11.8170i | 0.669007 | − | 1.15875i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.0617 | −0.977275 | ||||||||
\(107\) | − | 9.51655i | − | 0.920000i | −0.887919 | − | 0.460000i | \(-0.847849\pi\) | ||
0.887919 | − | 0.460000i | \(-0.152151\pi\) | |||||||
\(108\) | 5.04337 | + | 2.91179i | 0.485298 | + | 0.280187i | ||||
\(109\) | 2.77178 | + | 4.80087i | 0.265489 | + | 0.459840i | 0.967692 | − | 0.252137i | \(-0.0811333\pi\) |
−0.702203 | + | 0.711977i | \(0.747800\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.74795 | + | 9.95573i | 0.545571 | + | 0.944956i | ||||
\(112\) | −1.31791 | + | 0.760896i | −0.124531 | + | 0.0718979i | ||||
\(113\) | 1.54134i | 0.144997i | 0.997369 | + | 0.0724987i | \(0.0230973\pi\) | ||||
−0.997369 | + | 0.0724987i | \(0.976903\pi\) | |||||||
\(114\) | −14.2408 | + | 6.88542i | −1.33378 | + | 0.644879i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.324694 | + | 0.562387i | 0.0301471 | + | 0.0522163i | ||||
\(117\) | −24.1568 | + | 13.9470i | −2.23330 | + | 1.28940i | ||||
\(118\) | 10.5568 | + | 6.09499i | 0.971835 | + | 0.561089i | ||||
\(119\) | −0.884350 | − | 1.53174i | −0.0810682 | − | 0.140414i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.11672 | 0.828793 | ||||||||
\(122\) | − | 5.93310i | − | 0.537158i | ||||||
\(123\) | 21.9128 | + | 12.6514i | 1.97581 | + | 1.14074i | ||||
\(124\) | 1.81183 | − | 3.13819i | 0.162707 | − | 0.281818i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.55978 | 0.406217 | ||||||||
\(127\) | 1.99661 | + | 1.15274i | 0.177171 | + | 0.102289i | 0.585963 | − | 0.810338i | \(-0.300717\pi\) |
−0.408792 | + | 0.912628i | \(0.634050\pi\) | |||||||
\(128\) | −3.55376 | + | 2.05176i | −0.314111 | + | 0.181352i | ||||
\(129\) | −15.2187 | + | 26.3596i | −1.33994 | + | 2.32084i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.45905 | + | 11.1874i | 0.564330 | + | 0.977448i | 0.997112 | + | 0.0759493i | \(0.0241987\pi\) |
−0.432782 | + | 0.901499i | \(0.642468\pi\) | |||||||
\(132\) | 7.95060i | 0.692011i | ||||||||
\(133\) | 1.49238 | − | 2.19627i | 0.129405 | − | 0.190441i | ||||
\(134\) | 10.0943 | 0.872018 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.46346 | − | 7.73095i | −0.382739 | − | 0.662923i | ||||
\(137\) | −11.0276 | − | 6.36677i | −0.942149 | − | 0.543950i | −0.0515159 | − | 0.998672i | \(-0.516405\pi\) |
−0.890633 | + | 0.454722i | \(0.849739\pi\) | |||||||
\(138\) | 8.94814 | − | 5.16621i | 0.761716 | − | 0.439777i | ||||
\(139\) | 5.30433 | − | 9.18738i | 0.449908 | − | 0.779263i | −0.548472 | − | 0.836169i | \(-0.684790\pi\) |
0.998380 | + | 0.0569059i | \(0.0181235\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.9326 | −1.51020 | ||||||||
\(142\) | −11.9843 | − | 6.91913i | −1.00570 | − | 0.580640i | ||||
\(143\) | −17.2384 | − | 9.95258i | −1.44154 | − | 0.832276i | ||||
\(144\) | 15.7013 | 1.30844 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.21703 | − | 3.84000i | 0.183482 | − | 0.317801i | ||||
\(147\) | 17.4932 | − | 10.0997i | 1.44281 | − | 0.833010i | ||||
\(148\) | −1.90065 | − | 1.09734i | −0.156232 | − | 0.0902006i | ||||
\(149\) | 1.88653 | + | 3.26757i | 0.154551 | + | 0.267690i | 0.932895 | − | 0.360147i | \(-0.117274\pi\) |
−0.778344 | + | 0.627837i | \(0.783940\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.51562 | −0.774370 | −0.387185 | − | 0.922002i | \(-0.626553\pi\) | ||||
−0.387185 | + | 0.922002i | \(0.626553\pi\) | |||||||
\(152\) | 7.53228 | − | 11.0850i | 0.610948 | − | 0.899109i | ||||
\(153\) | 18.2488i | 1.47533i | ||||||||
\(154\) | 1.62693 | + | 2.81793i | 0.131102 | + | 0.227075i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.93349 | − | 6.81301i | 0.314931 | − | 0.545477i | ||||
\(157\) | 2.99336 | − | 1.72822i | 0.238896 | − | 0.137927i | −0.375773 | − | 0.926712i | \(-0.622623\pi\) |
0.614669 | + | 0.788785i | \(0.289290\pi\) | |||||||
\(158\) | 9.32158 | + | 5.38182i | 0.741585 | + | 0.428155i | ||||
\(159\) | −25.7447 | −2.04169 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.867239 | + | 1.50210i | −0.0683480 | + | 0.118382i | ||||
\(162\) | −12.0139 | − | 6.93624i | −0.943902 | − | 0.544962i | ||||
\(163\) | 6.65283i | 0.521090i | 0.965462 | + | 0.260545i | \(0.0839022\pi\) | ||||
−0.965462 | + | 0.260545i | \(0.916098\pi\) | |||||||
\(164\) | −4.83054 | −0.377202 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.26343 | − | 2.18832i | −0.0980609 | − | 0.169846i | ||||
\(167\) | −14.2509 | − | 8.22775i | −1.10277 | − | 0.636682i | −0.165820 | − | 0.986156i | \(-0.553027\pi\) |
−0.936946 | + | 0.349474i | \(0.886360\pi\) | |||||||
\(168\) | −4.94265 | + | 2.85364i | −0.381334 | + | 0.220163i | ||||
\(169\) | 3.34790 | + | 5.79874i | 0.257531 | + | 0.446057i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.6651 | + | 11.9255i | −1.88618 | + | 0.911968i | ||||
\(172\) | − | 5.81081i | − | 0.443070i | ||||||
\(173\) | −19.7302 | + | 11.3912i | −1.50006 | + | 0.866058i | −0.500057 | + | 0.865992i | \(0.666688\pi\) |
−1.00000 | 6.58713e-5i | \(0.999979\pi\) | ||||||||
\(174\) | −2.02547 | − | 3.50822i | −0.153550 | − | 0.265957i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.60224 | + | 9.70336i | 0.422284 | + | 0.731418i | ||||
\(177\) | 27.0117 | + | 15.5952i | 2.03032 | + | 1.17221i | ||||
\(178\) | − | 9.44650i | − | 0.708045i | ||||||
\(179\) | 2.32916 | 0.174090 | 0.0870449 | − | 0.996204i | \(-0.472258\pi\) | ||||
0.0870449 | + | 0.996204i | \(0.472258\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.1696 | − | 19.3463i | 0.830230 | − | 1.43800i | −0.0676258 | − | 0.997711i | \(-0.521542\pi\) |
0.897856 | − | 0.440290i | \(-0.145124\pi\) | |||||||
\(182\) | − | 3.21965i | − | 0.238656i | ||||||
\(183\) | − | 15.1810i | − | 1.12221i | ||||||
\(184\) | −4.37710 | + | 7.58137i | −0.322684 | + | 0.558906i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −11.3024 | + | 19.5763i | −0.828729 | + | 1.43540i | ||||
\(187\) | −11.2777 | + | 6.51119i | −0.824708 | + | 0.476145i | ||||
\(188\) | 2.96484 | − | 1.71175i | 0.216233 | − | 0.124842i | ||||
\(189\) | 6.09829 | 0.443585 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.23766 | 0.161911 | 0.0809556 | − | 0.996718i | \(-0.474203\pi\) | ||||
0.0809556 | + | 0.996718i | \(0.474203\pi\) | |||||||
\(192\) | −23.1603 | + | 13.3716i | −1.67145 | + | 0.965013i | ||||
\(193\) | −3.93441 | + | 2.27153i | −0.283205 | + | 0.163508i | −0.634873 | − | 0.772616i | \(-0.718948\pi\) |
0.351669 | + | 0.936125i | \(0.385614\pi\) | |||||||
\(194\) | 5.75957 | − | 9.97587i | 0.413513 | − | 0.716226i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.92813 | + | 3.33962i | −0.137724 | + | 0.238544i | ||||
\(197\) | 19.2236i | 1.36962i | 0.728720 | + | 0.684812i | \(0.240116\pi\) | ||||
−0.728720 | + | 0.684812i | \(0.759884\pi\) | |||||||
\(198\) | − | 33.5722i | − | 2.38587i | ||||||
\(199\) | −3.07547 | + | 5.32687i | −0.218014 | + | 0.377612i | −0.954201 | − | 0.299167i | \(-0.903291\pi\) |
0.736186 | + | 0.676779i | \(0.236625\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 25.8283 | 1.82179 | ||||||||
\(202\) | − | 1.15669i | − | 0.0813843i | ||||||
\(203\) | 0.588915 | + | 0.340010i | 0.0413338 | + | 0.0238641i | ||||
\(204\) | −2.57338 | − | 4.45722i | −0.180172 | − | 0.312068i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.98967 | − | 3.44621i | −0.138627 | − | 0.240109i | ||||
\(207\) | 15.4981 | − | 8.94786i | 1.07720 | − | 0.621919i | ||||
\(208\) | − | 11.0866i | − | 0.768720i | ||||||
\(209\) | −16.1705 | − | 10.9879i | −1.11853 | − | 0.760049i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.34661 | − | 10.9926i | −0.436919 | − | 0.756765i | 0.560531 | − | 0.828133i | \(-0.310597\pi\) |
−0.997450 | + | 0.0713679i | \(0.977264\pi\) | |||||||
\(212\) | 4.25644 | − | 2.45746i | 0.292333 | − | 0.168779i | ||||
\(213\) | −30.6641 | − | 17.7039i | −2.10107 | − | 1.21305i | ||||
\(214\) | −5.66668 | − | 9.81497i | −0.387366 | − | 0.670938i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 30.7791 | 2.09425 | ||||||||
\(217\) | − | 3.79460i | − | 0.257594i | ||||||
\(218\) | 5.71740 | + | 3.30094i | 0.387231 | + | 0.223568i | ||||
\(219\) | 5.67269 | − | 9.82538i | 0.383325 | − | 0.663938i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.8854 | 0.866767 | ||||||||
\(222\) | 11.8564 | + | 6.84528i | 0.795748 | + | 0.459425i | ||||
\(223\) | 19.5181 | − | 11.2688i | 1.30703 | − | 0.754614i | 0.325430 | − | 0.945566i | \(-0.394491\pi\) |
0.981599 | + | 0.190952i | \(0.0611575\pi\) | |||||||
\(224\) | 0.966820 | − | 1.67458i | 0.0645984 | − | 0.111888i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.917800 | + | 1.58968i | 0.0610512 | + | 0.105744i | ||||
\(227\) | − | 18.1124i | − | 1.20216i | −0.799189 | − | 0.601080i | \(-0.794737\pi\) | ||
0.799189 | − | 0.601080i | \(-0.205263\pi\) | |||||||
\(228\) | 4.34268 | − | 6.39095i | 0.287601 | − | 0.423251i | ||||
\(229\) | 9.41604 | 0.622229 | 0.311115 | − | 0.950372i | \(-0.399298\pi\) | ||||
0.311115 | + | 0.950372i | \(0.399298\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.16282 | + | 7.21022i | 0.273894 | + | 0.474398i | ||||
\(232\) | 2.97236 | + | 1.71609i | 0.195145 | + | 0.112667i | ||||
\(233\) | 13.5966 | − | 7.85000i | 0.890743 | − | 0.514271i | 0.0165573 | − | 0.999863i | \(-0.494729\pi\) |
0.874185 | + | 0.485592i | \(0.161396\pi\) | |||||||
\(234\) | −16.6096 | + | 28.7686i | −1.08580 | + | 1.88066i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.95455 | −0.387608 | ||||||||
\(237\) | 23.8511 | + | 13.7704i | 1.54929 | + | 0.894485i | ||||
\(238\) | −1.82416 | − | 1.05318i | −0.118243 | − | 0.0682676i | ||||
\(239\) | 23.4610 | 1.51757 | 0.758783 | − | 0.651344i | \(-0.225795\pi\) | ||||
0.758783 | + | 0.651344i | \(0.225795\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.58469 | + | 11.4050i | −0.424157 | + | 0.734662i | −0.996341 | − | 0.0854634i | \(-0.972763\pi\) |
0.572184 | + | 0.820125i | \(0.306096\pi\) | |||||||
\(242\) | 9.40260 | − | 5.42860i | 0.604422 | − | 0.348963i | ||||
\(243\) | −4.73128 | − | 2.73161i | −0.303512 | − | 0.175233i | ||||
\(244\) | 1.44910 | + | 2.50991i | 0.0927689 | + | 0.160680i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 30.1333 | 1.92123 | ||||||||
\(247\) | 8.42058 | + | 17.4159i | 0.535789 | + | 1.10815i | ||||
\(248\) | − | 19.1520i | − | 1.21615i | ||||||
\(249\) | −3.23272 | − | 5.59923i | −0.204865 | − | 0.354837i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.66257 | − | 15.0040i | 0.546776 | − | 0.947045i | −0.451716 | − | 0.892162i | \(-0.649188\pi\) |
0.998493 | − | 0.0548830i | \(-0.0174786\pi\) | |||||||
\(252\) | −1.92895 | + | 1.11368i | −0.121512 | + | 0.0701551i | ||||
\(253\) | 11.0595 | + | 6.38521i | 0.695305 | + | 0.401435i | ||||
\(254\) | 2.74563 | 0.172276 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.33295 | − | 10.9690i | 0.395809 | − | 0.685562i | ||||
\(257\) | −4.91867 | − | 2.83980i | −0.306818 | − | 0.177142i | 0.338683 | − | 0.940900i | \(-0.390018\pi\) |
−0.645502 | + | 0.763759i | \(0.723352\pi\) | |||||||
\(258\) | 36.2483i | 2.25672i | ||||||||
\(259\) | −2.29820 | −0.142803 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.50811 | − | 6.07622i | −0.217146 | − | 0.376108i | ||||
\(262\) | 13.3232 | + | 7.69215i | 0.823109 | + | 0.475222i | ||||
\(263\) | 4.89966 | − | 2.82882i | 0.302126 | − | 0.174433i | −0.341272 | − | 0.939965i | \(-0.610858\pi\) |
0.643398 | + | 0.765532i | \(0.277524\pi\) | |||||||
\(264\) | 21.0105 | + | 36.3912i | 1.29311 | + | 2.23972i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.231393 | − | 3.15379i | 0.0141876 | − | 0.193371i | ||||
\(267\) | − | 24.1707i | − | 1.47922i | ||||||
\(268\) | −4.27026 | + | 2.46544i | −0.260848 | + | 0.150601i | ||||
\(269\) | −11.9959 | − | 20.7775i | −0.731402 | − | 1.26683i | −0.956284 | − | 0.292440i | \(-0.905533\pi\) |
0.224881 | − | 0.974386i | \(-0.427801\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.6497 | + | 18.4459i | 0.646926 | + | 1.12051i | 0.983853 | + | 0.178978i | \(0.0572791\pi\) |
−0.336927 | + | 0.941531i | \(0.609388\pi\) | |||||||
\(272\) | −6.28138 | − | 3.62656i | −0.380865 | − | 0.219892i | ||||
\(273\) | − | 8.23808i | − | 0.498591i | ||||||
\(274\) | −15.1645 | −0.916121 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.52359 | + | 4.37098i | −0.151902 | + | 0.263102i | ||||
\(277\) | 0.821109i | 0.0493357i | 0.999696 | + | 0.0246678i | \(0.00785281\pi\) | ||||
−0.999696 | + | 0.0246678i | \(0.992147\pi\) | |||||||
\(278\) | − | 12.6340i | − | 0.757735i | ||||||
\(279\) | −19.5757 | + | 33.9060i | −1.17196 | + | 2.02990i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.293739 | − | 0.508772i | 0.0175230 | − | 0.0303508i | −0.857131 | − | 0.515099i | \(-0.827755\pi\) |
0.874654 | + | 0.484748i | \(0.161089\pi\) | |||||||
\(282\) | −18.4949 | + | 10.6780i | −1.10136 | + | 0.635869i | ||||
\(283\) | 26.7969 | − | 15.4712i | 1.59291 | − | 0.919667i | 0.600105 | − | 0.799921i | \(-0.295125\pi\) |
0.992805 | − | 0.119746i | \(-0.0382080\pi\) | |||||||
\(284\) | 6.75969 | 0.401114 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −23.7052 | −1.40172 | ||||||||
\(287\) | −4.38070 | + | 2.52920i | −0.258585 | + | 0.149294i | ||||
\(288\) | −17.2777 | + | 9.97530i | −1.01810 | + | 0.587800i | ||||
\(289\) | −4.28504 | + | 7.42191i | −0.252061 | + | 0.436583i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.7370 | − | 25.5252i | 0.863896 | − | 1.49631i | ||||
\(292\) | 2.16594i | 0.126752i | ||||||||
\(293\) | 3.76271i | 0.219820i | 0.993942 | + | 0.109910i | \(0.0350562\pi\) | ||||
−0.993942 | + | 0.109910i | \(0.964944\pi\) | |||||||
\(294\) | 12.0278 | − | 20.8328i | 0.701478 | − | 1.21499i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −11.5994 | −0.674202 | ||||||||
\(297\) | − | 44.8998i | − | 2.60535i | ||||||
\(298\) | 3.89138 | + | 2.24669i | 0.225422 | + | 0.130147i | ||||
\(299\) | −6.31806 | − | 10.9432i | −0.365383 | − | 0.632861i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.04246 | − | 5.26969i | −0.175364 | − | 0.303740i | ||||
\(302\) | −9.81401 | + | 5.66612i | −0.564733 | + | 0.326049i | ||||
\(303\) | − | 2.95961i | − | 0.170025i | ||||||
\(304\) | 0.796788 | − | 10.8598i | 0.0456989 | − | 0.622855i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 10.8663 | + | 18.8211i | 0.621187 | + | 1.07593i | ||||
\(307\) | −17.6166 | + | 10.1709i | −1.00543 | + | 0.580485i | −0.909850 | − | 0.414936i | \(-0.863804\pi\) |
−0.0955798 | + | 0.995422i | \(0.530471\pi\) | |||||||
\(308\) | −1.37650 | − | 0.794723i | −0.0784334 | − | 0.0452835i | ||||
\(309\) | −5.09095 | − | 8.81779i | −0.289614 | − | 0.501626i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.67830 | −0.435397 | −0.217698 | − | 0.976016i | \(-0.569855\pi\) | ||||
−0.217698 | + | 0.976016i | \(0.569855\pi\) | |||||||
\(312\) | − | 41.5790i | − | 2.35395i | ||||||
\(313\) | −20.7783 | − | 11.9964i | −1.17446 | − | 0.678074i | −0.219733 | − | 0.975560i | \(-0.570519\pi\) |
−0.954726 | + | 0.297486i | \(0.903852\pi\) | |||||||
\(314\) | 2.05815 | − | 3.56482i | 0.116148 | − | 0.201174i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.25781 | −0.295775 | ||||||||
\(317\) | 0.899831 | + | 0.519518i | 0.0505395 | + | 0.0291790i | 0.525057 | − | 0.851067i | \(-0.324044\pi\) |
−0.474517 | + | 0.880246i | \(0.657377\pi\) | |||||||
\(318\) | −26.5520 | + | 15.3298i | −1.48896 | + | 0.859653i | ||||
\(319\) | 2.50339 | − | 4.33600i | 0.140163 | − | 0.242769i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.4993 | − | 25.1135i | −0.809271 | − | 1.40170i | ||||
\(322\) | 2.06561i | 0.115112i | ||||||||
\(323\) | 12.6218 | + | 0.926066i | 0.702298 | + | 0.0515277i | ||||
\(324\) | 6.77641 | 0.376467 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.96146 | + | 6.86145i | 0.219405 | + | 0.380020i | ||||
\(327\) | 14.6291 | + | 8.44610i | 0.808990 | + | 0.467070i | ||||
\(328\) | −22.1102 | + | 12.7653i | −1.22083 | + | 0.704846i | ||||
\(329\) | 1.79250 | − | 3.10470i | 0.0988236 | − | 0.171167i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.8316 | 1.69466 | 0.847328 | − | 0.531069i | \(-0.178210\pi\) | ||||
0.847328 | + | 0.531069i | \(0.178210\pi\) | |||||||
\(332\) | 1.06895 | + | 0.617157i | 0.0586661 | + | 0.0338709i | ||||
\(333\) | 20.5352 | + | 11.8560i | 1.12532 | + | 0.649705i | ||||
\(334\) | −19.5970 | −1.07230 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.31858 | + | 4.01590i | −0.126489 | + | 0.219085i | ||||
\(337\) | −17.9400 | + | 10.3576i | −0.977252 | + | 0.564217i | −0.901439 | − | 0.432906i | \(-0.857488\pi\) |
−0.0758124 | + | 0.997122i | \(0.524155\pi\) | |||||||
\(338\) | 6.90577 | + | 3.98705i | 0.375625 | + | 0.216867i | ||||
\(339\) | 2.34837 | + | 4.06749i | 0.127546 | + | 0.220916i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −27.9384 | −1.51295 | ||||||||
\(342\) | −18.3374 | + | 26.9864i | −0.991572 | + | 1.45926i | ||||
\(343\) | 8.30239i | 0.448287i | ||||||||
\(344\) | −15.3558 | − | 26.5970i | −0.827929 | − | 1.43402i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.5659 | + | 23.4968i | −0.729308 | + | 1.26320i | ||||
\(347\) | −7.11991 | + | 4.11068i | −0.382217 | + | 0.220673i | −0.678782 | − | 0.734340i | \(-0.737492\pi\) |
0.296566 | + | 0.955013i | \(0.404159\pi\) | |||||||
\(348\) | 1.71369 | + | 0.989399i | 0.0918634 | + | 0.0530373i | ||||
\(349\) | −11.9216 | −0.638150 | −0.319075 | − | 0.947730i | \(-0.603372\pi\) | ||||
−0.319075 | + | 0.947730i | \(0.603372\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −22.2138 | + | 38.4754i | −1.18568 | + | 2.05366i | ||||
\(352\) | −12.3294 | − | 7.11839i | −0.657160 | − | 0.379412i | ||||
\(353\) | − | 11.7983i | − | 0.627959i | −0.949430 | − | 0.313980i | \(-0.898338\pi\) | ||
0.949430 | − | 0.313980i | \(-0.101662\pi\) | |||||||
\(354\) | 37.1450 | 1.97423 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.30721 | + | 3.99620i | 0.122282 | + | 0.211798i | ||||
\(357\) | −4.66747 | − | 2.69477i | −0.247029 | − | 0.142622i | ||||
\(358\) | 2.40220 | − | 1.38691i | 0.126960 | − | 0.0733005i | ||||
\(359\) | 0.0554058 | + | 0.0959656i | 0.00292420 | + | 0.00506487i | 0.867484 | − | 0.497465i | \(-0.165736\pi\) |
−0.864560 | + | 0.502530i | \(0.832403\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.99666 | + | 17.6648i | 0.368245 | + | 0.929729i | ||||
\(362\) | − | 26.6040i | − | 1.39827i | ||||||
\(363\) | 24.0584 | − | 13.8901i | 1.26274 | − | 0.729042i | ||||
\(364\) | 0.786364 | + | 1.36202i | 0.0412167 | + | 0.0713894i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.03958 | − | 15.6570i | −0.472507 | − | 0.818405i | ||||
\(367\) | 10.1669 | + | 5.86986i | 0.530708 | + | 0.306404i | 0.741305 | − | 0.671169i | \(-0.234207\pi\) |
−0.210597 | + | 0.977573i | \(0.567541\pi\) | |||||||
\(368\) | 7.11278i | 0.370779i | ||||||||
\(369\) | 52.1908 | 2.71694 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.57338 | − | 4.45722i | 0.133603 | − | 0.231407i | ||||
\(372\) | − | 11.0419i | − | 0.572498i | ||||||
\(373\) | 14.5190i | 0.751763i | 0.926668 | + | 0.375882i | \(0.122660\pi\) | ||||
−0.926668 | + | 0.375882i | \(0.877340\pi\) | |||||||
\(374\) | −7.75424 | + | 13.4307i | −0.400962 | + | 0.694487i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.04704 | − | 15.6699i | 0.466566 | − | 0.808115i | ||||
\(377\) | −4.29040 | + | 2.47706i | −0.220967 | + | 0.127575i | ||||
\(378\) | 6.28952 | − | 3.63125i | 0.323498 | − | 0.186772i | ||||
\(379\) | 6.59023 | 0.338518 | 0.169259 | − | 0.985572i | \(-0.445863\pi\) | ||||
0.169259 | + | 0.985572i | \(0.445863\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.02522 | 0.359913 | ||||||||
\(382\) | 2.30782 | − | 1.33242i | 0.118079 | − | 0.0681727i | ||||
\(383\) | −2.48481 | + | 1.43461i | −0.126968 | + | 0.0733049i | −0.562139 | − | 0.827043i | \(-0.690021\pi\) |
0.435171 | + | 0.900348i | \(0.356688\pi\) | |||||||
\(384\) | −6.25207 | + | 10.8289i | −0.319050 | + | 0.552610i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.70519 | + | 4.68552i | −0.137690 | + | 0.238487i | ||||
\(387\) | 62.7819i | 3.19138i | ||||||||
\(388\) | 5.62686i | 0.285660i | ||||||||
\(389\) | −3.16575 | + | 5.48323i | −0.160510 | + | 0.278011i | −0.935052 | − | 0.354512i | \(-0.884647\pi\) |
0.774542 | + | 0.632523i | \(0.217980\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.26682 | −0.418071 | ||||||||
\(392\) | 20.3813i | 1.02941i | ||||||||
\(393\) | 34.0899 | + | 19.6818i | 1.71961 | + | 0.992817i | ||||
\(394\) | 11.4468 | + | 19.8264i | 0.576680 | + | 0.998840i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.19966 | + | 14.2022i | 0.412049 | + | 0.713689i | ||||
\(397\) | 26.4569 | − | 15.2749i | 1.32784 | − | 0.766626i | 0.342871 | − | 0.939382i | \(-0.388601\pi\) |
0.984965 | + | 0.172756i | \(0.0552672\pi\) | |||||||
\(398\) | 7.32522i | 0.367180i | ||||||||
\(399\) | 0.592065 | − | 8.06957i | 0.0296403 | − | 0.403984i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.1711 | − | 26.2771i | −0.757609 | − | 1.31222i | −0.944067 | − | 0.329754i | \(-0.893034\pi\) |
0.186458 | − | 0.982463i | \(-0.440299\pi\) | |||||||
\(402\) | 26.6382 | − | 15.3796i | 1.32859 | − | 0.767064i | ||||
\(403\) | 23.9409 | + | 13.8223i | 1.19258 | + | 0.688538i | ||||
\(404\) | 0.282509 | + | 0.489320i | 0.0140553 | + | 0.0243446i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.809843 | 0.0401919 | ||||||||
\(407\) | 16.9209i | 0.838740i | ||||||||
\(408\) | −23.5575 | − | 13.6009i | −1.16627 | − | 0.673347i | ||||
\(409\) | −7.48628 | + | 12.9666i | −0.370173 | + | 0.641158i | −0.989592 | − | 0.143903i | \(-0.954035\pi\) |
0.619419 | + | 0.785060i | \(0.287368\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −38.8013 | −1.91393 | ||||||||
\(412\) | 1.68340 | + | 0.971912i | 0.0829352 | + | 0.0478827i | ||||
\(413\) | −5.40004 | + | 3.11772i | −0.265719 | + | 0.153413i | ||||
\(414\) | 10.6561 | − | 18.4569i | 0.523718 | − | 0.907107i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7.04353 | + | 12.1997i | 0.345337 | + | 0.598142i | ||||
\(417\) | − | 32.3264i | − | 1.58303i | ||||||
\(418\) | −23.2203 | − | 1.70368i | −1.13574 | − | 0.0833296i | ||||
\(419\) | 6.17419 | 0.301629 | 0.150815 | − | 0.988562i | \(-0.451810\pi\) | ||||
0.150815 | + | 0.988562i | \(0.451810\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.7714 | + | 23.8528i | 0.671177 | + | 1.16251i | 0.977571 | + | 0.210608i | \(0.0675443\pi\) |
−0.306394 | + | 0.951905i | \(0.599122\pi\) | |||||||
\(422\) | −13.0913 | − | 7.55824i | −0.637272 | − | 0.367929i | ||||
\(423\) | −32.0331 | + | 18.4943i | −1.55750 | + | 0.899226i | ||||
\(424\) | 12.9883 | − | 22.4963i | 0.630766 | − | 1.09252i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −42.1675 | −2.04302 | ||||||||
\(427\) | 2.62830 | + | 1.51745i | 0.127193 | + | 0.0734347i | ||||
\(428\) | 4.79441 | + | 2.76805i | 0.231746 | + | 0.133799i | ||||
\(429\) | −60.6544 | −2.92842 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.52941 | − | 13.0413i | 0.362679 | − | 0.628179i | −0.625722 | − | 0.780046i | \(-0.715195\pi\) |
0.988401 | + | 0.151868i | \(0.0485288\pi\) | |||||||
\(432\) | 21.6575 | − | 12.5040i | 1.04200 | − | 0.601598i | ||||
\(433\) | 0.840772 | + | 0.485420i | 0.0404049 | + | 0.0233278i | 0.520066 | − | 0.854126i | \(-0.325907\pi\) |
−0.479661 | + | 0.877454i | \(0.659241\pi\) | |||||||
\(434\) | −2.25951 | − | 3.91359i | −0.108460 | − | 0.187858i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.22488 | −0.154444 | ||||||||
\(437\) | −5.40234 | − | 11.1734i | −0.258429 | − | 0.534497i | ||||
\(438\) | − | 13.5113i | − | 0.645596i | ||||||
\(439\) | −13.7187 | − | 23.7616i | −0.654760 | − | 1.13408i | −0.981954 | − | 0.189120i | \(-0.939436\pi\) |
0.327194 | − | 0.944957i | \(-0.393897\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.8322 | − | 36.0824i | 0.992008 | − | 1.71821i | ||||
\(442\) | 13.2895 | − | 7.67269i | 0.632116 | − | 0.364952i | ||||
\(443\) | 7.59109 | + | 4.38272i | 0.360664 | + | 0.208229i | 0.669372 | − | 0.742928i | \(-0.266563\pi\) |
−0.308708 | + | 0.951157i | \(0.599897\pi\) | |||||||
\(444\) | −6.68755 | −0.317377 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 13.4201 | − | 23.2443i | 0.635461 | − | 1.10065i | ||||
\(447\) | 9.95686 | + | 5.74859i | 0.470943 | + | 0.271899i | ||||
\(448\) | − | 5.34637i | − | 0.252592i | ||||||
\(449\) | 9.63397 | 0.454655 | 0.227327 | − | 0.973818i | \(-0.427001\pi\) | ||||
0.227327 | + | 0.973818i | \(0.427001\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.6217 | + | 32.2538i | 0.876862 | + | 1.51877i | ||||
\(452\) | −0.776524 | − | 0.448326i | −0.0365246 | − | 0.0210875i | ||||
\(453\) | −25.1110 | + | 14.4979i | −1.17982 | + | 0.681169i | ||||
\(454\) | −10.7851 | − | 18.6803i | −0.506169 | − | 0.876711i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.98825 | − | 40.7285i | 0.139938 | − | 1.90729i | ||||
\(457\) | 10.6708i | 0.499161i | 0.968354 | + | 0.249580i | \(0.0802927\pi\) | ||||
−0.968354 | + | 0.249580i | \(0.919707\pi\) | |||||||
\(458\) | 9.71131 | − | 5.60683i | 0.453780 | − | 0.261990i | ||||
\(459\) | 14.5327 | + | 25.1714i | 0.678330 | + | 1.17490i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.84340 | − | 4.92491i | −0.132430 | − | 0.229376i | 0.792183 | − | 0.610284i | \(-0.208945\pi\) |
−0.924613 | + | 0.380908i | \(0.875611\pi\) | |||||||
\(462\) | 8.58672 | + | 4.95754i | 0.399490 | + | 0.230646i | ||||
\(463\) | 35.3550i | 1.64309i | 0.570147 | + | 0.821543i | \(0.306886\pi\) | ||||
−0.570147 | + | 0.821543i | \(0.693114\pi\) | |||||||
\(464\) | 2.78864 | 0.129459 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.34864 | − | 16.1923i | 0.433067 | − | 0.750095i | ||||
\(467\) | 32.9071i | 1.52276i | 0.648306 | + | 0.761380i | \(0.275478\pi\) | ||||
−0.648306 | + | 0.761380i | \(0.724522\pi\) | |||||||
\(468\) | − | 16.2269i | − | 0.750086i | ||||||
\(469\) | −2.58173 | + | 4.47169i | −0.119213 | + | 0.206484i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.26617 | − | 9.12127i | 0.242652 | − | 0.420286i | ||||
\(472\) | −27.2549 | + | 15.7356i | −1.25451 | + | 0.724292i | ||||
\(473\) | −38.7991 | + | 22.4006i | −1.78398 | + | 1.02998i | ||||
\(474\) | 32.7986 | 1.50649 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.02891 | 0.0471602 | ||||||||
\(477\) | −45.9880 | + | 26.5512i | −2.10564 | + | 1.21569i | ||||
\(478\) | 24.1967 | − | 13.9700i | 1.10673 | − | 0.638971i | ||||
\(479\) | −4.52861 | + | 7.84378i | −0.206917 | + | 0.358391i | −0.950742 | − | 0.309984i | \(-0.899676\pi\) |
0.743825 | + | 0.668375i | \(0.233010\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.37149 | − | 14.4998i | 0.381707 | − | 0.661136i | ||||
\(482\) | 15.6835i | 0.714366i | ||||||||
\(483\) | 5.28525i | 0.240487i | ||||||||
\(484\) | −2.65175 | + | 4.59297i | −0.120534 | + | 0.208772i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −6.50619 | −0.295127 | ||||||||
\(487\) | 16.5206i | 0.748620i | 0.927304 | + | 0.374310i | \(0.122120\pi\) | ||||
−0.927304 | + | 0.374310i | \(0.877880\pi\) | |||||||
\(488\) | 13.2655 | + | 7.65884i | 0.600501 | + | 0.346700i | ||||
\(489\) | 10.1362 | + | 17.5563i | 0.458373 | + | 0.793925i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.695625 | + | 1.20486i | 0.0313931 | + | 0.0543745i | 0.881295 | − | 0.472566i | \(-0.156672\pi\) |
−0.849902 | + | 0.526941i | \(0.823339\pi\) | |||||||
\(492\) | −12.7474 | + | 7.35974i | −0.574699 | + | 0.331803i | ||||
\(493\) | 3.24109i | 0.145972i | ||||||||
\(494\) | 19.0550 | + | 12.9480i | 0.857326 | + | 0.582557i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.78048 | − | 13.4762i | −0.349354 | − | 0.605099i | ||||
\(497\) | 6.13021 | − | 3.53928i | 0.274977 | − | 0.158758i | ||||
\(498\) | −6.66818 | − | 3.84988i | −0.298808 | − | 0.172517i | ||||
\(499\) | −8.33255 | − | 14.4324i | −0.373016 | − | 0.646083i | 0.617012 | − | 0.786954i | \(-0.288343\pi\) |
−0.990028 | + | 0.140871i | \(0.955010\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −50.1427 | −2.24021 | ||||||||
\(502\) | − | 20.6327i | − | 0.920881i | ||||||
\(503\) | −13.5439 | − | 7.81956i | −0.603892 | − | 0.348657i | 0.166679 | − | 0.986011i | \(-0.446696\pi\) |
−0.770571 | + | 0.637354i | \(0.780029\pi\) | |||||||
\(504\) | −5.88607 | + | 10.1950i | −0.262186 | + | 0.454120i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 15.2084 | 0.676096 | ||||||||
\(507\) | 17.6697 | + | 10.2016i | 0.784741 | + | 0.453070i | ||||
\(508\) | −1.16150 | + | 0.670591i | −0.0515331 | + | 0.0297526i | ||||
\(509\) | −9.57702 | + | 16.5879i | −0.424494 | + | 0.735245i | −0.996373 | − | 0.0850929i | \(-0.972881\pi\) |
0.571879 | + | 0.820338i | \(0.306215\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.13406 | + | 1.96424i | 0.0501677 | + | 0.0868929i | ||||
\(512\) | − | 23.2910i | − | 1.02933i | ||||||
\(513\) | −24.5246 | + | 36.0919i | −1.08279 | + | 1.59349i | ||||
\(514\) | −6.76389 | −0.298342 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −8.85327 | − | 15.3343i | −0.389743 | − | 0.675055i | ||||
\(517\) | −22.8589 | − | 13.1976i | −1.00533 | − | 0.580430i | ||||
\(518\) | −2.37027 | + | 1.36848i | −0.104144 | + | 0.0601273i | ||||
\(519\) | −34.7110 | + | 60.1212i | −1.52364 | + | 2.63903i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.2394 | −0.842892 | −0.421446 | − | 0.906853i | \(-0.638477\pi\) | ||||
−0.421446 | + | 0.906853i | \(0.638477\pi\) | |||||||
\(522\) | −7.23622 | − | 4.17784i | −0.316721 | − | 0.182859i | ||||
\(523\) | −5.74993 | − | 3.31973i | −0.251427 | − | 0.145161i | 0.368990 | − | 0.929433i | \(-0.379704\pi\) |
−0.620418 | + | 0.784272i | \(0.713037\pi\) | |||||||
\(524\) | −7.51490 | −0.328290 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.36887 | − | 5.83505i | 0.146890 | − | 0.254420i | ||||
\(527\) | 15.6627 | − | 9.04285i | 0.682277 | − | 0.393913i | ||||
\(528\) | 29.5678 | + | 17.0710i | 1.28677 | + | 0.742919i | ||||
\(529\) | −7.44657 | − | 12.8978i | −0.323764 | − | 0.560775i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 64.3349 | 2.79190 | ||||||||
\(532\) | 0.672391 | + | 1.39068i | 0.0291519 | + | 0.0602935i | ||||
\(533\) | − | 36.8517i | − | 1.59623i | ||||||
\(534\) | −14.3925 | − | 24.9286i | −0.622826 | − | 1.07877i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13.0305 | + | 22.5694i | −0.562830 | + | 0.974850i | ||||
\(537\) | 6.14649 | − | 3.54868i | 0.265241 | − | 0.153137i | ||||
\(538\) | −24.7441 | − | 14.2860i | −1.06679 | − | 0.615914i | ||||
\(539\) | 29.7317 | 1.28064 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.8756 | + | 36.1575i | −0.897510 | + | 1.55453i | −0.0668435 | + | 0.997763i | \(0.521293\pi\) |
−0.830667 | + | 0.556770i | \(0.812040\pi\) | |||||||
\(542\) | 21.9674 | + | 12.6829i | 0.943581 | + | 0.544777i | ||||
\(543\) | − | 68.0714i | − | 2.92122i | ||||||
\(544\) | 9.21606 | 0.395135 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.90540 | − | 8.49641i | −0.209932 | − | 0.363613i | ||||
\(547\) | 10.5700 | + | 6.10258i | 0.451939 | + | 0.260927i | 0.708649 | − | 0.705561i | \(-0.249305\pi\) |
−0.256710 | + | 0.966489i | \(0.582638\pi\) | |||||||
\(548\) | 6.41512 | − | 3.70377i | 0.274040 | − | 0.158217i | ||||
\(549\) | −15.6565 | − | 27.1179i | −0.668204 | − | 1.15736i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.38066 | + | 2.11804i | −0.186622 | + | 0.0902317i | ||||
\(552\) | 26.6756i | 1.13539i | ||||||||
\(553\) | −4.76819 | + | 2.75291i | −0.202764 | + | 0.117066i | ||||
\(554\) | 0.488934 | + | 0.846858i | 0.0207728 | + | 0.0359795i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.08571 | + | 5.34461i | 0.130863 | + | 0.226662i | ||||
\(557\) | 30.4450 | + | 17.5774i | 1.28999 | + | 0.744779i | 0.978653 | − | 0.205519i | \(-0.0658883\pi\) |
0.311342 | + | 0.950298i | \(0.399222\pi\) | |||||||
\(558\) | 46.6257i | 1.97382i | ||||||||
\(559\) | 44.3301 | 1.87496 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.8407 | + | 34.3651i | −0.837675 | + | 1.45090i | ||||
\(562\) | − | 0.699634i | − | 0.0295123i | ||||||
\(563\) | 17.8406i | 0.751891i | 0.926642 | + | 0.375945i | \(0.122682\pi\) | ||||
−0.926642 | + | 0.375945i | \(0.877318\pi\) | |||||||
\(564\) | 5.21600 | − | 9.03438i | 0.219633 | − | 0.380416i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 18.4248 | − | 31.9127i | 0.774452 | − | 1.34139i | ||||
\(567\) | 6.14537 | − | 3.54803i | 0.258081 | − | 0.149003i | ||||
\(568\) | 30.9402 | − | 17.8633i | 1.29822 | − | 0.749529i | ||||
\(569\) | −31.6042 | −1.32492 | −0.662459 | − | 0.749098i | \(-0.730487\pi\) | ||||
−0.662459 | + | 0.749098i | \(0.730487\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.73053 | −0.197967 | −0.0989833 | − | 0.995089i | \(-0.531559\pi\) | ||||
−0.0989833 | + | 0.995089i | \(0.531559\pi\) | |||||||
\(572\) | 10.0281 | − | 5.78975i | 0.419298 | − | 0.242082i | ||||
\(573\) | 5.90501 | − | 3.40926i | 0.246685 | − | 0.142424i | ||||
\(574\) | −3.01205 | + | 5.21702i | −0.125721 | + | 0.217754i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −27.5810 | + | 47.7717i | −1.14921 | + | 1.99049i | ||||
\(577\) | − | 24.4074i | − | 1.01609i | −0.861330 | − | 0.508047i | \(-0.830368\pi\) | ||
0.861330 | − | 0.508047i | \(-0.169632\pi\) | |||||||
\(578\) | 10.2062i | 0.424522i | ||||||||
\(579\) | −6.92174 | + | 11.9888i | −0.287658 | + | 0.498238i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.29254 | 0.0536235 | ||||||||
\(582\) | − | 35.1008i | − | 1.45497i | ||||||
\(583\) | −32.8171 | − | 18.9470i | −1.35915 | − | 0.784703i | ||||
\(584\) | 5.72377 | + | 9.91386i | 0.236851 | + | 0.410239i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.24052 | + | 3.88070i | 0.0925551 | + | 0.160310i | ||||
\(587\) | 24.7817 | − | 14.3077i | 1.02285 | − | 0.590543i | 0.107922 | − | 0.994159i | \(-0.465580\pi\) |
0.914928 | + | 0.403616i | \(0.132247\pi\) | |||||||
\(588\) | 11.7507i | 0.484590i | ||||||||
\(589\) | 22.4578 | + | 15.2602i | 0.925358 | + | 0.628785i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 29.2888 | + | 50.7297i | 1.20478 | + | 2.08674i | ||||
\(592\) | −8.16186 | + | 4.71225i | −0.335450 | + | 0.193672i | ||||
\(593\) | −3.21738 | − | 1.85756i | −0.132122 | − | 0.0762807i | 0.432482 | − | 0.901642i | \(-0.357638\pi\) |
−0.564604 | + | 0.825362i | \(0.690971\pi\) | |||||||
\(594\) | −26.7358 | − | 46.3077i | −1.09698 | − | 1.90003i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.19492 | −0.0899076 | ||||||||
\(597\) | 18.7430i | 0.767099i | ||||||||
\(598\) | −13.0324 | − | 7.52423i | −0.532933 | − | 0.307689i | ||||
\(599\) | 3.54970 | − | 6.14826i | 0.145037 | − | 0.251211i | −0.784350 | − | 0.620319i | \(-0.787003\pi\) |
0.929387 | + | 0.369108i | \(0.120337\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.0596 | −0.451131 | −0.225566 | − | 0.974228i | \(-0.572423\pi\) | ||||
−0.225566 | + | 0.974228i | \(0.572423\pi\) | |||||||
\(602\) | −6.27572 | − | 3.62329i | −0.255779 | − | 0.147674i | ||||
\(603\) | 46.1373 | − | 26.6374i | 1.87886 | − | 1.08476i | ||||
\(604\) | 2.76778 | − | 4.79394i | 0.112619 | − | 0.195063i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.76231 | − | 3.05242i | −0.0715891 | − | 0.123996i | ||||
\(607\) | − | 27.1193i | − | 1.10074i | −0.834921 | − | 0.550369i | \(-0.814487\pi\) | ||
0.834921 | − | 0.550369i | \(-0.185513\pi\) | |||||||
\(608\) | 6.02266 | + | 12.4564i | 0.244251 | + | 0.505174i | ||||
\(609\) | 2.07214 | 0.0839673 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.0588 | + | 22.6185i | 0.528302 | + | 0.915046i | ||||
\(612\) | −9.19369 | − | 5.30798i | −0.371633 | − | 0.214562i | ||||
\(613\) | 36.2268 | − | 20.9156i | 1.46319 | − | 0.844772i | 0.464031 | − | 0.885819i | \(-0.346403\pi\) |
0.999157 | + | 0.0410468i | \(0.0130693\pi\) | |||||||
\(614\) | −12.1127 | + | 20.9797i | −0.488827 | + | 0.846673i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.40062 | −0.338471 | ||||||||
\(617\) | −15.3332 | − | 8.85262i | −0.617291 | − | 0.356393i | 0.158523 | − | 0.987355i | \(-0.449327\pi\) |
−0.775813 | + | 0.630962i | \(0.782660\pi\) | |||||||
\(618\) | −10.5012 | − | 6.06286i | −0.422420 | − | 0.243884i | ||||
\(619\) | 39.8064 | 1.59995 | 0.799976 | − | 0.600032i | \(-0.204845\pi\) | ||||
0.799976 | + | 0.600032i | \(0.204845\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.2515 | − | 24.6844i | 0.571895 | − | 0.990551i | ||||
\(622\) | −7.91908 | + | 4.57208i | −0.317526 | + | 0.183324i | ||||
\(623\) | 4.18471 | + | 2.41604i | 0.167657 | + | 0.0967966i | ||||
\(624\) | −16.8914 | − | 29.2568i | −0.676198 | − | 1.17121i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −28.5732 | −1.14201 | ||||||||
\(627\) | −59.4137 | − | 4.35919i | −2.37275 | − | 0.174089i | ||||
\(628\) | 2.01072i | 0.0802366i | ||||||||
\(629\) | −5.47681 | − | 9.48611i | −0.218375 | − | 0.378236i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.0990 | + | 40.0087i | −0.919557 | + | 1.59272i | −0.119469 | + | 0.992838i | \(0.538119\pi\) |
−0.800088 | + | 0.599882i | \(0.795214\pi\) | |||||||
\(632\) | −24.0659 | + | 13.8944i | −0.957288 | + | 0.552691i | ||||
\(633\) | −33.4965 | − | 19.3392i | −1.33137 | − | 0.768664i | ||||
\(634\) | 1.23740 | 0.0491433 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7.48829 | − | 12.9701i | 0.296930 | − | 0.514298i | ||||
\(637\) | −25.4776 | − | 14.7095i | −1.00946 | − | 0.582813i | ||||
\(638\) | − | 5.96262i | − | 0.236062i | ||||||
\(639\) | −73.0340 | −2.88918 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.30674 | − | 5.72744i | −0.130608 | − | 0.226220i | 0.793303 | − | 0.608827i | \(-0.208360\pi\) |
−0.923911 | + | 0.382607i | \(0.875026\pi\) | |||||||
\(642\) | −29.9079 | − | 17.2673i | −1.18037 | − | 0.681487i | ||||
\(643\) | −26.5135 | + | 15.3076i | −1.04559 | + | 0.603673i | −0.921412 | − | 0.388587i | \(-0.872963\pi\) |
−0.124180 | + | 0.992260i | \(0.539630\pi\) | |||||||
\(644\) | −0.504503 | − | 0.873824i | −0.0198802 | − | 0.0344335i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.5691 | − | 6.56063i | 0.533868 | − | 0.258125i | ||||
\(647\) | 11.8979i | 0.467753i | 0.972266 | + | 0.233877i | \(0.0751412\pi\) | ||||
−0.972266 | + | 0.233877i | \(0.924859\pi\) | |||||||
\(648\) | 31.0167 | − | 17.9075i | 1.21845 | − | 0.703474i | ||||
\(649\) | 22.9548 | + | 39.7588i | 0.901053 | + | 1.56067i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.78140 | − | 10.0137i | −0.226591 | − | 0.392467i | ||||
\(652\) | −3.35167 | − | 1.93509i | −0.131262 | − | 0.0757839i | ||||
\(653\) | − | 1.42899i | − | 0.0559207i | −0.999609 | − | 0.0279604i | \(-0.991099\pi\) | ||
0.999609 | − | 0.0279604i | \(-0.00890122\pi\) | |||||||
\(654\) | 20.1171 | 0.786640 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −10.3718 | + | 17.9645i | −0.404950 | + | 0.701395i | ||||
\(657\) | − | 23.4015i | − | 0.912981i | ||||||
\(658\) | − | 4.26941i | − | 0.166439i | ||||||
\(659\) | −12.2485 | + | 21.2150i | −0.477134 | + | 0.826420i | −0.999657 | − | 0.0262051i | \(-0.991658\pi\) |
0.522523 | + | 0.852625i | \(0.324991\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.61303 | − | 2.79385i | 0.0627396 | − | 0.108668i | −0.832949 | − | 0.553349i | \(-0.813350\pi\) |
0.895689 | + | 0.444681i | \(0.146683\pi\) | |||||||
\(662\) | 31.7984 | − | 18.3588i | 1.23588 | − | 0.713535i | ||||
\(663\) | 34.0037 | − | 19.6320i | 1.32059 | − | 0.762445i | ||||
\(664\) | 6.52366 | 0.253167 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 28.2389 | 1.09423 | ||||||||
\(667\) | 2.75256 | − | 1.58919i | 0.106580 | − | 0.0615338i | ||||
\(668\) | 8.29023 | − | 4.78636i | 0.320758 | − | 0.185190i | ||||
\(669\) | 34.3379 | − | 59.4750i | 1.32758 | − | 2.29944i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.1725 | − | 19.3514i | 0.431311 | − | 0.747052i | ||||
\(672\) | − | 5.89213i | − | 0.227294i | ||||||
\(673\) | 37.1424i | 1.43173i | 0.698237 | + | 0.715866i | \(0.253968\pi\) | ||||
−0.698237 | + | 0.715866i | \(0.746032\pi\) | |||||||
\(674\) | −12.3350 | + | 21.3649i | −0.475127 | + | 0.822944i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.89518 | −0.149815 | ||||||||
\(677\) | 24.7550i | 0.951412i | 0.879604 | + | 0.475706i | \(0.157807\pi\) | ||||
−0.879604 | + | 0.475706i | \(0.842193\pi\) | |||||||
\(678\) | 4.84402 | + | 2.79669i | 0.186033 | + | 0.107406i | ||||
\(679\) | 2.94614 | + | 5.10287i | 0.113063 | + | 0.195830i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −27.5957 | − | 47.7972i | −1.05747 | − | 1.83159i | ||||
\(682\) | −28.8145 | + | 16.6361i | −1.10337 | + | 0.637028i | ||||
\(683\) | 40.1153i | 1.53497i | 0.641068 | + | 0.767484i | \(0.278492\pi\) | ||||
−0.641068 | + | 0.767484i | \(0.721508\pi\) | |||||||
\(684\) | 1.16621 | − | 15.8949i | 0.0445912 | − | 0.607757i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.94370 | + | 8.56274i | 0.188751 | + | 0.326927i | ||||
\(687\) | 24.8482 | − | 14.3461i | 0.948020 | − | 0.547340i | ||||
\(688\) | −21.6100 | − | 12.4766i | −0.823875 | − | 0.475664i | ||||
\(689\) | 18.7477 | + | 32.4720i | 0.714230 | + | 1.23708i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.4963 | 1.50251 | 0.751254 | − | 0.660013i | \(-0.229449\pi\) | ||||
0.751254 | + | 0.660013i | \(0.229449\pi\) | |||||||
\(692\) | − | 13.2533i | − | 0.503816i | ||||||
\(693\) | 14.8722 | + | 8.58645i | 0.564947 | + | 0.326172i | ||||
\(694\) | −4.89545 | + | 8.47917i | −0.185829 | + | 0.321865i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 10.4584 | 0.396426 | ||||||||
\(697\) | −20.8792 | − | 12.0546i | −0.790855 | − | 0.456600i | ||||
\(698\) | −12.2955 | + | 7.09879i | −0.465390 | + | 0.268693i | ||||
\(699\) | 23.9203 | − | 41.4312i | 0.904748 | − | 1.56707i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.0109776 | − | 0.0190137i | −0.000414618 | − | 0.000718139i | 0.865818 | − | 0.500359i | \(-0.166799\pi\) |
−0.866233 | + | 0.499641i | \(0.833465\pi\) | |||||||
\(702\) | 52.9092i | 1.99693i | ||||||||
\(703\) | 9.24234 | − | 13.6016i | 0.348581 | − | 0.512994i | ||||
\(704\) | −39.3637 | −1.48357 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.02535 | − | 12.1683i | −0.264402 | − | 0.457958i | ||||
\(707\) | 0.512402 | + | 0.295835i | 0.0192708 | + | 0.0111260i | ||||
\(708\) | −15.7136 | + | 9.07226i | −0.590554 | + | 0.340957i | ||||
\(709\) | −8.90087 | + | 15.4168i | −0.334279 | + | 0.578989i | −0.983346 | − | 0.181743i | \(-0.941826\pi\) |
0.649067 | + | 0.760731i | \(0.275160\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 56.8071 | 2.13043 | ||||||||
\(712\) | 21.1209 | + | 12.1942i | 0.791540 | + | 0.456996i | ||||
\(713\) | −15.3596 | − | 8.86789i | −0.575223 | − | 0.332105i | ||||
\(714\) | −6.41844 | −0.240204 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.677477 | + | 1.17342i | −0.0253185 | + | 0.0438529i | ||||
\(717\) | 61.9118 | − | 35.7448i | 2.31214 | − | 1.33491i | ||||
\(718\) | 0.114286 | + | 0.0659833i | 0.00426513 | + | 0.00246247i | ||||
\(719\) | 9.40515 | + | 16.2902i | 0.350753 | + | 0.607522i | 0.986382 | − | 0.164473i | \(-0.0525923\pi\) |
−0.635629 | + | 0.771995i | \(0.719259\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.03552 | 0.0758066 | ||||||||
\(722\) | 17.7347 | + | 14.0526i | 0.660016 | + | 0.522983i | ||||
\(723\) | 40.1294i | 1.49243i | ||||||||
\(724\) | 6.49774 | + | 11.2544i | 0.241487 | + | 0.418267i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 16.5419 | − | 28.6513i | 0.613926 | − | 1.06335i | ||||
\(727\) | −4.33274 | + | 2.50151i | −0.160692 | + | 0.0927758i | −0.578190 | − | 0.815902i | \(-0.696241\pi\) |
0.417497 | + | 0.908678i | \(0.362907\pi\) | |||||||
\(728\) | 7.19864 | + | 4.15613i | 0.266799 | + | 0.154037i | ||||
\(729\) | 18.2986 | 0.677725 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.5009 | − | 25.1162i | 0.536334 | − | 0.928957i | ||||
\(732\) | 7.64812 | + | 4.41565i | 0.282683 | + | 0.163207i | ||||
\(733\) | − | 23.5259i | − | 0.868950i | −0.900684 | − | 0.434475i | \(-0.856934\pi\) | ||
0.900684 | − | 0.434475i | \(-0.143066\pi\) | |||||||
\(734\) | 13.9809 | 0.516046 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.51887 | − | 7.82691i | −0.166568 | − | 0.288504i | ||||
\(737\) | 32.9237 | + | 19.0085i | 1.21276 | + | 0.700187i | ||||
\(738\) | 53.8274 | − | 31.0772i | 1.98141 | − | 1.14397i | ||||
\(739\) | −18.6918 | − | 32.3752i | −0.687590 | − | 1.19094i | −0.972615 | − | 0.232421i | \(-0.925335\pi\) |
0.285026 | − | 0.958520i | \(-0.407998\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 48.7559 | + | 33.1299i | 1.79109 | + | 1.21706i | ||||
\(742\) | − | 6.12932i | − | 0.225014i | ||||||
\(743\) | 8.99679 | − | 5.19430i | 0.330060 | − | 0.190560i | −0.325808 | − | 0.945436i | \(-0.605636\pi\) |
0.655868 | + | 0.754876i | \(0.272303\pi\) | |||||||
\(744\) | −29.1797 | − | 50.5407i | −1.06978 | − | 1.85291i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 8.64539 | + | 14.9742i | 0.316530 | + | 0.548246i | ||||
\(747\) | −11.5493 | − | 6.66797i | −0.422566 | − | 0.243968i | ||||
\(748\) | − | 7.57556i | − | 0.276990i | ||||||
\(749\) | 5.79725 | 0.211827 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.6413 | − | 27.0915i | 0.570758 | − | 0.988581i | −0.425731 | − | 0.904850i | \(-0.639983\pi\) |
0.996488 | − | 0.0837314i | \(-0.0266838\pi\) | |||||||
\(752\) | − | 14.7014i | − | 0.536105i | ||||||
\(753\) | − | 52.7927i | − | 1.92387i | ||||||
\(754\) | −2.94996 | + | 5.10947i | −0.107431 | + | 0.186076i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.77379 | + | 3.07230i | −0.0645122 | + | 0.111738i | ||||
\(757\) | 10.9328 | − | 6.31205i | 0.397359 | − | 0.229415i | −0.287985 | − | 0.957635i | \(-0.592985\pi\) |
0.685344 | + | 0.728220i | \(0.259652\pi\) | |||||||
\(758\) | 6.79689 | − | 3.92419i | 0.246874 | − | 0.142533i | ||||
\(759\) | 38.9137 | 1.41248 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.5495 | 0.418668 | 0.209334 | − | 0.977844i | \(-0.432870\pi\) | ||||
0.209334 | + | 0.977844i | \(0.432870\pi\) | |||||||
\(762\) | 7.24551 | − | 4.18320i | 0.262477 | − | 0.151541i | ||||
\(763\) | −2.92457 | + | 1.68850i | −0.105877 | + | 0.0611279i | ||||
\(764\) | −0.650861 | + | 1.12732i | −0.0235473 | + | 0.0407851i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.70849 | + | 2.95918i | −0.0617301 | + | 0.106920i | ||||
\(767\) | − | 45.4267i | − | 1.64026i | ||||||
\(768\) | − | 38.5951i | − | 1.39268i | ||||||
\(769\) | −13.4603 | + | 23.3140i | −0.485392 | + | 0.840724i | −0.999859 | − | 0.0167864i | \(-0.994656\pi\) |
0.514467 | + | 0.857510i | \(0.327990\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.3067 | −0.623286 | ||||||||
\(772\) | − | 2.64286i | − | 0.0951184i | ||||||
\(773\) | −18.4750 | − | 10.6666i | −0.664500 | − | 0.383649i | 0.129489 | − | 0.991581i | \(-0.458666\pi\) |
−0.793989 | + | 0.607932i | \(0.791999\pi\) | |||||||
\(774\) | 37.3838 | + | 64.7506i | 1.34373 | + | 2.32741i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14.8697 | + | 25.7550i | 0.533790 | + | 0.924552i | ||||
\(777\) | −6.06479 | + | 3.50151i | −0.217573 | + | 0.125616i | ||||
\(778\) | 7.54024i | 0.270331i | ||||||||
\(779\) | 2.64851 | − | 36.0979i | 0.0948926 | − | 1.29334i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.0586 | − | 45.1348i | −0.932450 | − | 1.61505i | ||||
\(782\) | −8.52605 | + | 4.92252i | −0.304891 | + | 0.176029i | ||||
\(783\) | −9.67779 | − | 5.58747i | −0.345856 | − | 0.199680i | ||||
\(784\) | 8.27989 | + | 14.3412i | 0.295710 | + | 0.512185i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 46.8786 | 1.67210 | ||||||||
\(787\) | − | 3.52489i | − | 0.125649i | −0.998025 | − | 0.0628243i | \(-0.979989\pi\) | ||
0.998025 | − | 0.0628243i | \(-0.0200108\pi\) | |||||||
\(788\) | −9.68478 | − | 5.59151i | −0.345006 | − | 0.199189i | ||||
\(789\) | 8.61990 | − | 14.9301i | 0.306877 | − | 0.531526i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.938948 | −0.0333852 | ||||||||
\(792\) | 75.0624 | + | 43.3373i | 2.66723 | + | 1.53992i | ||||
\(793\) | −19.1479 | + | 11.0550i | −0.679961 | + | 0.392575i | ||||
\(794\) | 18.1911 | − | 31.5078i | 0.645576 | − | 1.11817i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.78911 | − | 3.09882i | −0.0634132 | − | 0.109835i | ||||
\(797\) | 39.0084i | 1.38175i | 0.722974 | + | 0.690875i | \(0.242774\pi\) | ||||
−0.722974 | + | 0.690875i | \(0.757226\pi\) | |||||||
\(798\) | −4.19443 | − | 8.67516i | −0.148481 | − | 0.307097i | ||||
\(799\) | 17.0867 | 0.604484 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.9278 | − | 43.1763i | −0.880782 | − | 1.52556i | ||||
\(802\) | −31.2937 | − | 18.0674i | −1.10502 | − | 0.637983i | ||||
\(803\) | 14.4621 | − | 8.34969i | 0.510356 | − | 0.294654i | ||||
\(804\) | −7.51261 | + | 13.0122i | −0.264949 | + | 0.458906i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 32.9222 | 1.15964 | ||||||||
\(807\) | −63.3126 | − | 36.5535i | −2.22871 | − | 1.28675i | ||||
\(808\) | 2.58618 | + | 1.49313i | 0.0909814 | + | 0.0525282i | ||||
\(809\) | −50.7196 | −1.78321 | −0.891604 | − | 0.452816i | \(-0.850419\pi\) | ||||
−0.891604 | + | 0.452816i | \(0.850419\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.5188 | + | 25.1473i | −0.509824 | + | 0.883041i | 0.490111 | + | 0.871660i | \(0.336956\pi\) |
−0.999935 | + | 0.0113812i | \(0.996377\pi\) | |||||||
\(812\) | −0.342592 | + | 0.197796i | −0.0120226 | + | 0.00694127i | ||||
\(813\) | 56.2078 | + | 32.4516i | 1.97129 | + | 1.13813i | ||||
\(814\) | 10.0757 | + | 17.4515i | 0.353151 | + | 0.611676i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −22.1015 | −0.773706 | ||||||||
\(817\) | 43.4233 | + | 3.18597i | 1.51919 | + | 0.111463i | ||||
\(818\) | 17.8310i | 0.623445i | ||||||||
\(819\) | −8.49614 | − | 14.7158i | −0.296879 | − | 0.514210i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.4939 | + | 28.5682i | −0.575640 | + | 0.997038i | 0.420331 | + | 0.907371i | \(0.361914\pi\) |
−0.995972 | + | 0.0896677i | \(0.971420\pi\) | |||||||
\(822\) | −40.0180 | + | 23.1044i | −1.39579 | + | 0.805859i | ||||
\(823\) | 22.9959 | + | 13.2767i | 0.801586 | + | 0.462796i | 0.844025 | − | 0.536303i | \(-0.180180\pi\) |
−0.0424397 | + | 0.999099i | \(0.513513\pi\) | |||||||
\(824\) | 10.2736 | 0.357898 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.71292 | + | 6.43096i | −0.129189 | + | 0.223762i | ||||
\(827\) | −28.3767 | − | 16.3833i | −0.986754 | − | 0.569703i | −0.0824515 | − | 0.996595i | \(-0.526275\pi\) |
−0.904302 | + | 0.426892i | \(0.859608\pi\) | |||||||
\(828\) | 10.4106i | 0.361792i | ||||||||
\(829\) | −32.4548 | −1.12720 | −0.563601 | − | 0.826047i | \(-0.690584\pi\) | ||||
−0.563601 | + | 0.826047i | \(0.690584\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.25103 | + | 2.16685i | 0.0433978 | + | 0.0751671i | ||||
\(832\) | 33.7314 | + | 19.4748i | 1.16943 | + | 0.675168i | ||||
\(833\) | −16.6680 | + | 9.62329i | −0.577513 | + | 0.333427i | ||||
\(834\) | −19.2489 | − | 33.3401i | −0.666536 | − | 1.15447i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 10.2391 | − | 4.95061i | 0.354127 | − | 0.171220i | ||||
\(837\) | 62.3576i | 2.15539i | ||||||||
\(838\) | 6.36780 | − | 3.67645i | 0.219972 | − | 0.127001i | ||||
\(839\) | −17.6049 | − | 30.4926i | −0.607788 | − | 1.05272i | −0.991604 | − | 0.129310i | \(-0.958724\pi\) |
0.383816 | − | 0.923410i | \(-0.374610\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.8769 | + | 24.0356i | 0.478515 | + | 0.828813i | ||||
\(842\) | 28.4065 | + | 16.4005i | 0.978952 | + | 0.565198i | ||||
\(843\) | − | 1.79015i | − | 0.0616560i | ||||||
\(844\) | 7.38408 | 0.254171 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −22.0251 | + | 38.1486i | −0.757238 | + | 1.31158i | ||||
\(847\) | 5.55368i | 0.190827i | ||||||||
\(848\) | − | 21.1059i | − | 0.724779i | ||||||
\(849\) | 47.1434 | − | 81.6547i | 1.61796 | − | 2.80238i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.37084 | + | 9.30257i | −0.184110 | + | 0.318888i | ||||
\(852\) | 17.8383 | − | 10.2990i | 0.611132 | − | 0.352837i | ||||
\(853\) | −1.54867 | + | 0.894126i | −0.0530255 | + | 0.0306143i | −0.526278 | − | 0.850312i | \(-0.676413\pi\) |
0.473253 | + | 0.880927i | \(0.343080\pi\) | |||||||
\(854\) | 3.61430 | 0.123679 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.2597 | 1.00008 | ||||||||
\(857\) | −3.12964 | + | 1.80690i | −0.106906 | + | 0.0617224i | −0.552500 | − | 0.833513i | \(-0.686326\pi\) |
0.445594 | + | 0.895235i | \(0.352993\pi\) | |||||||
\(858\) | −62.5564 | + | 36.1170i | −2.13564 | + | 1.23301i | ||||
\(859\) | −12.6824 | + | 21.9666i | −0.432719 | + | 0.749491i | −0.997106 | − | 0.0760192i | \(-0.975779\pi\) |
0.564388 | + | 0.825510i | \(0.309112\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.70691 | + | 13.3488i | −0.262651 | + | 0.454924i | ||||
\(862\) | − | 17.9337i | − | 0.610824i | ||||||
\(863\) | − | 29.9878i | − | 1.02080i | −0.859939 | − | 0.510398i | \(-0.829498\pi\) | ||
0.859939 | − | 0.510398i | \(-0.170502\pi\) | |||||||
\(864\) | −15.8880 | + | 27.5188i | −0.540520 | + | 0.936209i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.15618 | 0.0392887 | ||||||||
\(867\) | 26.1145i | 0.886895i | ||||||||
\(868\) | 1.91171 | + | 1.10372i | 0.0648875 | + | 0.0374628i | ||||
\(869\) | 20.2688 | + | 35.1067i | 0.687573 | + | 1.19091i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.8086 | − | 32.5774i | −0.637305 | − | 1.10384i | ||||
\(872\) | −14.7608 | + | 8.52216i | −0.499864 | + | 0.288597i | ||||
\(873\) | − | 60.7945i | − | 2.05758i | ||||||
\(874\) | −12.2250 | − | 8.30695i | −0.413517 | − | 0.280987i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.30000 | + | 5.71576i | 0.111497 | + | 0.193118i | ||||
\(877\) | −9.22125 | + | 5.32389i | −0.311380 | + | 0.179775i | −0.647544 | − | 0.762028i | \(-0.724204\pi\) |
0.336164 | + | 0.941803i | \(0.390870\pi\) | |||||||
\(878\) | −28.2979 | − | 16.3378i | −0.955007 | − | 0.551374i | ||||
\(879\) | 5.73281 | + | 9.92951i | 0.193363 | + | 0.334914i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.5797 | −1.06395 | −0.531973 | − | 0.846761i | \(-0.678549\pi\) | ||||
−0.531973 | + | 0.846761i | \(0.678549\pi\) | |||||||
\(882\) | − | 49.6185i | − | 1.67074i | ||||||
\(883\) | −14.7375 | − | 8.50871i | −0.495957 | − | 0.286341i | 0.231085 | − | 0.972933i | \(-0.425772\pi\) |
−0.727042 | + | 0.686593i | \(0.759106\pi\) | |||||||
\(884\) | −3.74795 | + | 6.49163i | −0.126057 | + | 0.218337i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.4388 | 0.350700 | ||||||||
\(887\) | −11.4567 | − | 6.61451i | −0.384677 | − | 0.222093i | 0.295174 | − | 0.955443i | \(-0.404622\pi\) |
−0.679851 | + | 0.733350i | \(0.737956\pi\) | |||||||
\(888\) | −30.6100 | + | 17.6727i | −1.02721 | + | 0.593057i | ||||
\(889\) | −0.702223 | + | 1.21629i | −0.0235518 | + | 0.0407929i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −26.1230 | − | 45.2464i | −0.875155 | − | 1.51581i | ||||
\(892\) | 13.1109i | 0.438985i | ||||||||
\(893\) | 11.1661 | + | 23.0943i | 0.373659 | + | 0.772823i | ||||
\(894\) | 13.6921 | 0.457933 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.24988 | − | 2.16486i | −0.0417557 | − | 0.0723229i | ||||
\(897\) | −33.3458 | − | 19.2522i | −1.11338 | − | 0.642812i | ||||
\(898\) | 9.93607 | − | 5.73659i | 0.331571 | − | 0.191433i | ||||
\(899\) | −3.47675 | + | 6.02191i | −0.115956 | + | 0.200842i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.5303 | 0.817222 | ||||||||
\(902\) | 38.4113 | + | 22.1768i | 1.27896 | + | 0.738406i | ||||
\(903\) | −16.0576 | − | 9.27088i | −0.534365 | − | 0.308516i | ||||
\(904\) | −4.73903 | −0.157618 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −17.2656 | + | 29.9050i | −0.573613 | + | 0.993526i | ||||
\(907\) | 12.8955 | − | 7.44520i | 0.428187 | − | 0.247214i | −0.270387 | − | 0.962752i | \(-0.587152\pi\) |
0.698574 | + | 0.715538i | \(0.253818\pi\) | |||||||
\(908\) | 9.12494 | + | 5.26829i | 0.302822 | + | 0.174834i | ||||
\(909\) | −3.05232 | − | 5.28678i | −0.101239 | − | 0.175351i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.5480 | −1.64160 | −0.820800 | − | 0.571216i | \(-0.806472\pi\) | ||||
−0.820800 | + | 0.571216i | \(0.806472\pi\) | |||||||
\(912\) | −14.4432 | − | 29.8723i | −0.478263 | − | 0.989172i | ||||
\(913\) | − | 9.51655i | − | 0.314952i | ||||||
\(914\) | 6.35400 | + | 11.0055i | 0.210172 | + | 0.364028i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.73882 | + | 4.74377i | −0.0904931 | + | 0.156739i | ||||
\(917\) | −6.81509 | + | 3.93469i | −0.225054 | + | 0.129935i | ||||
\(918\) | 29.9769 | + | 17.3072i | 0.989385 | + | 0.571222i | ||||
\(919\) | −27.3835 | −0.903300 | −0.451650 | − | 0.892195i | \(-0.649164\pi\) | ||||
−0.451650 | + | 0.892195i | \(0.649164\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.9926 | + | 53.6807i | −1.02124 | + | 1.76884i | ||||
\(922\) | −5.86513 | − | 3.38623i | −0.193158 | − | 0.111520i | ||||
\(923\) | 51.5691i | 1.69742i | ||||||||
\(924\) | −4.84331 | −0.159333 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 21.0523 | + | 36.4637i | 0.691821 | + | 1.19827i | ||||
\(927\) | −18.1880 | − | 10.5009i | −0.597373 | − | 0.344893i | ||||
\(928\) | −3.06863 | + | 1.77167i | −0.100733 | + | 0.0581580i | ||||
\(929\) | 26.0947 | + | 45.1973i | 0.856139 | + | 1.48288i | 0.875584 | + | 0.483066i | \(0.160477\pi\) |
−0.0194449 | + | 0.999811i | \(0.506190\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.8993 | − | 16.2397i | −0.783269 | − | 0.532234i | ||||
\(932\) | 9.13323i | 0.299169i | ||||||||
\(933\) | −20.2625 | + | 11.6985i | −0.663364 | + | 0.382993i | ||||
\(934\) | 19.5947 | + | 33.9390i | 0.641158 | + | 1.11052i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −42.8815 | − | 74.2729i | −1.40163 | − | 2.42769i | ||||
\(937\) | 13.4925 | + | 7.78988i | 0.440780 | + | 0.254484i | 0.703928 | − | 0.710271i | \(-0.251428\pi\) |
−0.263149 | + | 0.964755i | \(0.584761\pi\) | |||||||
\(938\) | 6.14922i | 0.200779i | ||||||||
\(939\) | −73.1099 | −2.38585 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.3277 | − | 50.7970i | 0.956055 | − | 1.65594i | 0.224119 | − | 0.974562i | \(-0.428050\pi\) |
0.731936 | − | 0.681373i | \(-0.238617\pi\) | |||||||
\(942\) | − | 12.5431i | − | 0.408675i | ||||||
\(943\) | 23.6427i | 0.769913i | ||||||||
\(944\) | −12.7852 | + | 22.1446i | −0.416122 | + | 0.720745i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −26.6771 | + | 46.2062i | −0.867349 | + | 1.50229i | ||||
\(947\) | −10.6578 | + | 6.15326i | −0.346331 | + | 0.199954i | −0.663068 | − | 0.748559i | \(-0.730746\pi\) |
0.316737 | + | 0.948513i | \(0.397413\pi\) | |||||||
\(948\) | −13.8750 | + | 8.01072i | −0.450638 | + | 0.260176i | ||||
\(949\) | −16.5238 | −0.536384 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.16612 | 0.102668 | ||||||||
\(952\) | 4.70950 | − | 2.71903i | 0.152636 | − | 0.0881244i | ||||
\(953\) | 7.16201 | − | 4.13499i | 0.232000 | − | 0.133945i | −0.379494 | − | 0.925194i | \(-0.623902\pi\) |
0.611494 | + | 0.791249i | \(0.290569\pi\) | |||||||
\(954\) | −31.6200 | + | 54.7675i | −1.02374 | + | 1.77316i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.82403 | + | 11.8196i | −0.220705 | + | 0.382272i | ||||
\(957\) | − | 15.2565i | − | 0.493173i | ||||||
\(958\) | 10.7863i | 0.348490i | ||||||||
\(959\) | 3.87848 | − | 6.71773i | 0.125243 | − | 0.216927i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.80138 | 0.251657 | ||||||||
\(962\) | − | 19.9394i | − | 0.642871i | ||||||
\(963\) | −51.8004 | − | 29.9070i | −1.66924 | − | 0.963738i | ||||
\(964\) | −3.83054 | − | 6.63469i | −0.123373 | − | 0.213689i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.14713 | + | 5.45099i | 0.101257 | + | 0.175383i | ||||
\(967\) | −12.3190 | + | 7.11235i | −0.396151 | + | 0.228718i | −0.684822 | − | 0.728711i | \(-0.740120\pi\) |
0.288671 | + | 0.957428i | \(0.406787\pi\) | |||||||
\(968\) | 28.0304i | 0.900931i | ||||||||
\(969\) | 34.7191 | − | 16.7866i | 1.11534 | − | 0.539264i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.86930 | − | 8.43388i | −0.156263 | − | 0.270656i | 0.777255 | − | 0.629186i | \(-0.216612\pi\) |
−0.933518 | + | 0.358530i | \(0.883278\pi\) | |||||||
\(972\) | 2.75235 | − | 1.58907i | 0.0882816 | − | 0.0509694i | ||||
\(973\) | 5.59672 | + | 3.23127i | 0.179423 | + | 0.103590i | ||||
\(974\) | 9.83727 | + | 17.0387i | 0.315207 | + | 0.545954i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.4456 | 0.398374 | ||||||||
\(977\) | 6.35308i | 0.203253i | 0.994823 | + | 0.101627i | \(0.0324047\pi\) | ||||
−0.994823 | + | 0.101627i | \(0.967595\pi\) | |||||||
\(978\) | 20.9080 | + | 12.0712i | 0.668564 | + | 0.385996i | ||||
\(979\) | 17.7885 | − | 30.8107i | 0.568524 | − | 0.984713i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 34.8427 | 1.11244 | ||||||||
\(982\) | 1.43488 | + | 0.828426i | 0.0457887 | + | 0.0264361i | ||||
\(983\) | 8.55708 | − | 4.94043i | 0.272929 | − | 0.157575i | −0.357289 | − | 0.933994i | \(-0.616299\pi\) |
0.630218 | + | 0.776418i | \(0.282966\pi\) | |||||||
\(984\) | −38.8981 | + | 67.3735i | −1.24003 | + | 2.14779i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.92993 | + | 3.34273i | 0.0614613 | + | 0.106454i | ||||
\(987\) | − | 10.9241i | − | 0.347718i | ||||||
\(988\) | −11.2234 | − | 0.823458i | −0.357062 | − | 0.0261977i | ||||
\(989\) | −28.4406 | −0.904358 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.6675 | − | 32.3331i | −0.592993 | − | 1.02709i | −0.993827 | − | 0.110943i | \(-0.964613\pi\) |
0.400834 | − | 0.916151i | \(-0.368720\pi\) | |||||||
\(992\) | 17.1233 | + | 9.88614i | 0.543665 | + | 0.313885i | ||||
\(993\) | 81.3623 | − | 46.9745i | 2.58195 | − | 1.49069i | ||||
\(994\) | 4.21496 | − | 7.30053i | 0.133690 | − | 0.231559i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.76117 | 0.119177 | ||||||||
\(997\) | −37.8408 | − | 21.8474i | −1.19843 | − | 0.691914i | −0.238225 | − | 0.971210i | \(-0.576566\pi\) |
−0.960205 | + | 0.279296i | \(0.909899\pi\) | |||||||
\(998\) | −17.1877 | − | 9.92332i | −0.544067 | − | 0.314117i | ||||
\(999\) | 37.7669 | 1.19489 |
(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 | 475.2.j.c.349.6 | 16 | ||
5.2 | odd | 4 | 95.2.e.c.26.3 | yes | 8 | ||
5.3 | odd | 4 | 475.2.e.e.26.2 | 8 | |||
5.4 | even | 2 | inner | 475.2.j.c.349.3 | 16 | ||
15.2 | even | 4 | 855.2.k.h.406.2 | 8 | |||
19.11 | even | 3 | inner | 475.2.j.c.49.3 | 16 | ||
20.7 | even | 4 | 1520.2.q.o.881.4 | 8 | |||
95.7 | odd | 12 | 1805.2.a.o.1.2 | 4 | |||
95.12 | even | 12 | 1805.2.a.i.1.3 | 4 | |||
95.49 | even | 6 | inner | 475.2.j.c.49.6 | 16 | ||
95.68 | odd | 12 | 475.2.e.e.201.2 | 8 | |||
95.83 | odd | 12 | 9025.2.a.bg.1.3 | 4 | |||
95.87 | odd | 12 | 95.2.e.c.11.3 | ✓ | 8 | ||
95.88 | even | 12 | 9025.2.a.bp.1.2 | 4 | |||
285.182 | even | 12 | 855.2.k.h.676.2 | 8 | |||
380.87 | even | 12 | 1520.2.q.o.961.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.e.c.11.3 | ✓ | 8 | 95.87 | odd | 12 | ||
95.2.e.c.26.3 | yes | 8 | 5.2 | odd | 4 | ||
475.2.e.e.26.2 | 8 | 5.3 | odd | 4 | |||
475.2.e.e.201.2 | 8 | 95.68 | odd | 12 | |||
475.2.j.c.49.3 | 16 | 19.11 | even | 3 | inner | ||
475.2.j.c.49.6 | 16 | 95.49 | even | 6 | inner | ||
475.2.j.c.349.3 | 16 | 5.4 | even | 2 | inner | ||
475.2.j.c.349.6 | 16 | 1.1 | even | 1 | trivial | ||
855.2.k.h.406.2 | 8 | 15.2 | even | 4 | |||
855.2.k.h.676.2 | 8 | 285.182 | even | 12 | |||
1520.2.q.o.881.4 | 8 | 20.7 | even | 4 | |||
1520.2.q.o.961.4 | 8 | 380.87 | even | 12 | |||
1805.2.a.i.1.3 | 4 | 95.12 | even | 12 | |||
1805.2.a.o.1.2 | 4 | 95.7 | odd | 12 | |||
9025.2.a.bg.1.3 | 4 | 95.83 | odd | 12 | |||
9025.2.a.bp.1.2 | 4 | 95.88 | even | 12 |