Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(311,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.c (of order \(2\), degree \(1\), 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: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 311.21 | ||
Character | \(\chi\) | \(=\) | 403.311 |
Dual form | 403.2.c.b.311.12 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.01245i | 0.715908i | 0.933739 | + | 0.357954i | \(0.116526\pi\) | ||||
−0.933739 | + | 0.357954i | \(0.883474\pi\) | |||||||
\(3\) | −1.05136 | −0.607006 | −0.303503 | − | 0.952831i | \(-0.598156\pi\) | ||||
−0.303503 | + | 0.952831i | \(0.598156\pi\) | |||||||
\(4\) | 0.974950 | 0.487475 | ||||||||
\(5\) | 3.24438i | 1.45093i | 0.688258 | + | 0.725466i | \(0.258376\pi\) | ||||
−0.688258 | + | 0.725466i | \(0.741624\pi\) | |||||||
\(6\) | − | 1.06445i | − | 0.434561i | ||||||
\(7\) | 1.79572i | 0.678719i | 0.940657 | + | 0.339360i | \(0.110210\pi\) | ||||
−0.940657 | + | 0.339360i | \(0.889790\pi\) | |||||||
\(8\) | 3.01198i | 1.06490i | ||||||||
\(9\) | −1.89463 | −0.631544 | ||||||||
\(10\) | −3.28477 | −1.03873 | ||||||||
\(11\) | − | 6.09683i | − | 1.83826i | −0.393951 | − | 0.919131i | \(-0.628892\pi\) | ||
0.393951 | − | 0.919131i | \(-0.371108\pi\) | |||||||
\(12\) | −1.02503 | −0.295900 | ||||||||
\(13\) | −1.47046 | + | 3.29207i | −0.407832 | + | 0.913057i | ||||
\(14\) | −1.81807 | −0.485901 | ||||||||
\(15\) | − | 3.41103i | − | 0.880724i | ||||||
\(16\) | −1.09957 | −0.274893 | ||||||||
\(17\) | 4.79598 | 1.16320 | 0.581598 | − | 0.813476i | \(-0.302428\pi\) | ||||
0.581598 | + | 0.813476i | \(0.302428\pi\) | |||||||
\(18\) | − | 1.91821i | − | 0.452128i | ||||||
\(19\) | 1.84875i | 0.424133i | 0.977255 | + | 0.212066i | \(0.0680193\pi\) | ||||
−0.977255 | + | 0.212066i | \(0.931981\pi\) | |||||||
\(20\) | 3.16311i | 0.707293i | ||||||||
\(21\) | − | 1.88796i | − | 0.411986i | ||||||
\(22\) | 6.17272 | 1.31603 | ||||||||
\(23\) | −7.94273 | −1.65617 | −0.828086 | − | 0.560600i | \(-0.810570\pi\) | ||||
−0.828086 | + | 0.560600i | \(0.810570\pi\) | |||||||
\(24\) | − | 3.16669i | − | 0.646398i | ||||||
\(25\) | −5.52601 | −1.10520 | ||||||||
\(26\) | −3.33305 | − | 1.48876i | −0.653665 | − | 0.291970i | ||||
\(27\) | 5.14604 | 0.990357 | ||||||||
\(28\) | 1.75074i | 0.330859i | ||||||||
\(29\) | −2.23287 | −0.414633 | −0.207317 | − | 0.978274i | \(-0.566473\pi\) | ||||
−0.207317 | + | 0.978274i | \(0.566473\pi\) | |||||||
\(30\) | 3.45349 | 0.630518 | ||||||||
\(31\) | − | 1.00000i | − | 0.179605i | ||||||
\(32\) | 4.91070i | 0.868098i | ||||||||
\(33\) | 6.40999i | 1.11584i | ||||||||
\(34\) | 4.85568i | 0.832742i | ||||||||
\(35\) | −5.82601 | −0.984775 | ||||||||
\(36\) | −1.84717 | −0.307862 | ||||||||
\(37\) | 8.64644i | 1.42147i | 0.703462 | + | 0.710733i | \(0.251636\pi\) | ||||
−0.703462 | + | 0.710733i | \(0.748364\pi\) | |||||||
\(38\) | −1.87176 | −0.303640 | ||||||||
\(39\) | 1.54599 | − | 3.46117i | 0.247556 | − | 0.554231i | ||||
\(40\) | −9.77201 | −1.54509 | ||||||||
\(41\) | 0.0498113i | 0.00777923i | 0.999992 | + | 0.00388961i | \(0.00123811\pi\) | ||||
−0.999992 | + | 0.00388961i | \(0.998762\pi\) | |||||||
\(42\) | 1.91146 | 0.294945 | ||||||||
\(43\) | 4.76573 | 0.726767 | 0.363384 | − | 0.931640i | \(-0.381621\pi\) | ||||
0.363384 | + | 0.931640i | \(0.381621\pi\) | |||||||
\(44\) | − | 5.94410i | − | 0.896107i | ||||||
\(45\) | − | 6.14691i | − | 0.916327i | ||||||
\(46\) | − | 8.04159i | − | 1.18567i | ||||||
\(47\) | − | 4.00376i | − | 0.584008i | −0.956417 | − | 0.292004i | \(-0.905678\pi\) | ||
0.956417 | − | 0.292004i | \(-0.0943221\pi\) | |||||||
\(48\) | 1.15605 | 0.166862 | ||||||||
\(49\) | 3.77538 | 0.539341 | ||||||||
\(50\) | − | 5.59480i | − | 0.791224i | ||||||
\(51\) | −5.04233 | −0.706067 | ||||||||
\(52\) | −1.43362 | + | 3.20961i | −0.198808 | + | 0.445093i | ||||
\(53\) | 0.588394 | 0.0808221 | 0.0404111 | − | 0.999183i | \(-0.487133\pi\) | ||||
0.0404111 | + | 0.999183i | \(0.487133\pi\) | |||||||
\(54\) | 5.21010i | 0.709005i | ||||||||
\(55\) | 19.7804 | 2.66719 | ||||||||
\(56\) | −5.40868 | −0.722765 | ||||||||
\(57\) | − | 1.94371i | − | 0.257451i | ||||||
\(58\) | − | 2.26066i | − | 0.296840i | ||||||
\(59\) | 3.49014i | 0.454377i | 0.973851 | + | 0.227189i | \(0.0729534\pi\) | ||||
−0.973851 | + | 0.227189i | \(0.927047\pi\) | |||||||
\(60\) | − | 3.32558i | − | 0.429331i | ||||||
\(61\) | 12.1590 | 1.55680 | 0.778400 | − | 0.627769i | \(-0.216032\pi\) | ||||
0.778400 | + | 0.627769i | \(0.216032\pi\) | |||||||
\(62\) | 1.01245 | 0.128581 | ||||||||
\(63\) | − | 3.40223i | − | 0.428641i | ||||||
\(64\) | −7.17097 | −0.896371 | ||||||||
\(65\) | −10.6807 | − | 4.77073i | −1.32478 | − | 0.591736i | ||||
\(66\) | −6.48978 | −0.798836 | ||||||||
\(67\) | − | 1.72095i | − | 0.210247i | −0.994459 | − | 0.105124i | \(-0.966476\pi\) | ||
0.994459 | − | 0.105124i | \(-0.0335238\pi\) | |||||||
\(68\) | 4.67585 | 0.567029 | ||||||||
\(69\) | 8.35070 | 1.00531 | ||||||||
\(70\) | − | 5.89852i | − | 0.705009i | ||||||
\(71\) | 10.3643i | 1.23002i | 0.788519 | + | 0.615011i | \(0.210848\pi\) | ||||
−0.788519 | + | 0.615011i | \(0.789152\pi\) | |||||||
\(72\) | − | 5.70659i | − | 0.672529i | ||||||
\(73\) | 2.28292i | 0.267196i | 0.991036 | + | 0.133598i | \(0.0426531\pi\) | ||||
−0.991036 | + | 0.133598i | \(0.957347\pi\) | |||||||
\(74\) | −8.75406 | −1.01764 | ||||||||
\(75\) | 5.80985 | 0.670864 | ||||||||
\(76\) | 1.80244i | 0.206754i | ||||||||
\(77\) | 10.9482 | 1.24766 | ||||||||
\(78\) | 3.50425 | + | 1.56523i | 0.396779 | + | 0.177228i | ||||
\(79\) | 16.1812 | 1.82053 | 0.910265 | − | 0.414027i | \(-0.135878\pi\) | ||||
0.910265 | + | 0.414027i | \(0.135878\pi\) | |||||||
\(80\) | − | 3.56743i | − | 0.398851i | ||||||
\(81\) | 0.273525 | 0.0303917 | ||||||||
\(82\) | −0.0504314 | −0.00556921 | ||||||||
\(83\) | − | 10.2561i | − | 1.12575i | −0.826541 | − | 0.562877i | \(-0.809694\pi\) | ||
0.826541 | − | 0.562877i | \(-0.190306\pi\) | |||||||
\(84\) | − | 1.84067i | − | 0.200833i | ||||||
\(85\) | 15.5600i | 1.68772i | ||||||||
\(86\) | 4.82505i | 0.520299i | ||||||||
\(87\) | 2.34756 | 0.251685 | ||||||||
\(88\) | 18.3635 | 1.95756 | ||||||||
\(89\) | − | 7.99914i | − | 0.847907i | −0.905684 | − | 0.423953i | \(-0.860642\pi\) | ||
0.905684 | − | 0.423953i | \(-0.139358\pi\) | |||||||
\(90\) | 6.22342 | 0.656006 | ||||||||
\(91\) | −5.91165 | − | 2.64053i | −0.619709 | − | 0.276803i | ||||
\(92\) | −7.74376 | −0.807343 | ||||||||
\(93\) | 1.05136i | 0.109021i | ||||||||
\(94\) | 4.05360 | 0.418097 | ||||||||
\(95\) | −5.99805 | −0.615387 | ||||||||
\(96\) | − | 5.16294i | − | 0.526940i | ||||||
\(97\) | 10.1745i | 1.03307i | 0.856268 | + | 0.516533i | \(0.172777\pi\) | ||||
−0.856268 | + | 0.516533i | \(0.827223\pi\) | |||||||
\(98\) | 3.82238i | 0.386118i | ||||||||
\(99\) | 11.5512i | 1.16094i | ||||||||
\(100\) | −5.38759 | −0.538759 | ||||||||
\(101\) | −10.3806 | −1.03291 | −0.516454 | − | 0.856315i | \(-0.672748\pi\) | ||||
−0.516454 | + | 0.856315i | \(0.672748\pi\) | |||||||
\(102\) | − | 5.10509i | − | 0.505479i | ||||||
\(103\) | 7.56287 | 0.745191 | 0.372596 | − | 0.927994i | \(-0.378468\pi\) | ||||
0.372596 | + | 0.927994i | \(0.378468\pi\) | |||||||
\(104\) | −9.91566 | − | 4.42899i | −0.972311 | − | 0.434299i | ||||
\(105\) | 6.12526 | 0.597764 | ||||||||
\(106\) | 0.595718i | 0.0578612i | ||||||||
\(107\) | 9.88355 | 0.955478 | 0.477739 | − | 0.878502i | \(-0.341456\pi\) | ||||
0.477739 | + | 0.878502i | \(0.341456\pi\) | |||||||
\(108\) | 5.01714 | 0.482774 | ||||||||
\(109\) | − | 5.97227i | − | 0.572040i | −0.958224 | − | 0.286020i | \(-0.907668\pi\) | ||
0.958224 | − | 0.286020i | \(-0.0923323\pi\) | |||||||
\(110\) | 20.0266i | 1.90947i | ||||||||
\(111\) | − | 9.09056i | − | 0.862838i | ||||||
\(112\) | − | 1.97452i | − | 0.186575i | ||||||
\(113\) | 5.83695 | 0.549094 | 0.274547 | − | 0.961574i | \(-0.411472\pi\) | ||||
0.274547 | + | 0.961574i | \(0.411472\pi\) | |||||||
\(114\) | 1.96791 | 0.184311 | ||||||||
\(115\) | − | 25.7692i | − | 2.40299i | ||||||
\(116\) | −2.17694 | −0.202123 | ||||||||
\(117\) | 2.78598 | − | 6.23727i | 0.257564 | − | 0.576636i | ||||
\(118\) | −3.53358 | −0.325292 | ||||||||
\(119\) | 8.61225i | 0.789484i | ||||||||
\(120\) | 10.2740 | 0.937879 | ||||||||
\(121\) | −26.1713 | −2.37921 | ||||||||
\(122\) | 12.3103i | 1.11453i | ||||||||
\(123\) | − | 0.0523699i | − | 0.00472204i | ||||||
\(124\) | − | 0.974950i | − | 0.0875531i | ||||||
\(125\) | − | 1.70658i | − | 0.152641i | ||||||
\(126\) | 3.44458 | 0.306868 | ||||||||
\(127\) | 1.76344 | 0.156480 | 0.0782399 | − | 0.996935i | \(-0.475070\pi\) | ||||
0.0782399 | + | 0.996935i | \(0.475070\pi\) | |||||||
\(128\) | 2.56118i | 0.226378i | ||||||||
\(129\) | −5.01052 | −0.441152 | ||||||||
\(130\) | 4.83011 | − | 10.8137i | 0.423629 | − | 0.948423i | ||||
\(131\) | 15.7996 | 1.38042 | 0.690209 | − | 0.723610i | \(-0.257518\pi\) | ||||
0.690209 | + | 0.723610i | \(0.257518\pi\) | |||||||
\(132\) | 6.24942i | 0.543942i | ||||||||
\(133\) | −3.31984 | −0.287867 | ||||||||
\(134\) | 1.74237 | 0.150518 | ||||||||
\(135\) | 16.6957i | 1.43694i | ||||||||
\(136\) | 14.4454i | 1.23868i | ||||||||
\(137\) | − | 14.0263i | − | 1.19835i | −0.800619 | − | 0.599174i | \(-0.795496\pi\) | ||
0.800619 | − | 0.599174i | \(-0.204504\pi\) | |||||||
\(138\) | 8.45465i | 0.719707i | ||||||||
\(139\) | −8.87486 | −0.752756 | −0.376378 | − | 0.926466i | \(-0.622831\pi\) | ||||
−0.376378 | + | 0.926466i | \(0.622831\pi\) | |||||||
\(140\) | −5.68007 | −0.480053 | ||||||||
\(141\) | 4.20941i | 0.354497i | ||||||||
\(142\) | −10.4934 | −0.880583 | ||||||||
\(143\) | 20.0712 | + | 8.96513i | 1.67844 | + | 0.749702i | ||||
\(144\) | 2.08328 | 0.173607 | ||||||||
\(145\) | − | 7.24428i | − | 0.601605i | ||||||
\(146\) | −2.31134 | −0.191288 | ||||||||
\(147\) | −3.96931 | −0.327383 | ||||||||
\(148\) | 8.42985i | 0.692929i | ||||||||
\(149\) | 0.896489i | 0.0734432i | 0.999326 | + | 0.0367216i | \(0.0116915\pi\) | ||||
−0.999326 | + | 0.0367216i | \(0.988309\pi\) | |||||||
\(150\) | 5.88217i | 0.480277i | ||||||||
\(151\) | 0.221338i | 0.0180122i | 0.999959 | + | 0.00900611i | \(0.00286677\pi\) | ||||
−0.999959 | + | 0.00900611i | \(0.997133\pi\) | |||||||
\(152\) | −5.56840 | −0.451657 | ||||||||
\(153\) | −9.08662 | −0.734610 | ||||||||
\(154\) | 11.0845i | 0.893213i | ||||||||
\(155\) | 3.24438 | 0.260595 | ||||||||
\(156\) | 1.50726 | − | 3.37447i | 0.120678 | − | 0.270174i | ||||
\(157\) | 8.52165 | 0.680102 | 0.340051 | − | 0.940407i | \(-0.389556\pi\) | ||||
0.340051 | + | 0.940407i | \(0.389556\pi\) | |||||||
\(158\) | 16.3826i | 1.30333i | ||||||||
\(159\) | −0.618617 | −0.0490595 | ||||||||
\(160\) | −15.9322 | −1.25955 | ||||||||
\(161\) | − | 14.2629i | − | 1.12408i | ||||||
\(162\) | 0.276930i | 0.0217576i | ||||||||
\(163\) | − | 0.474988i | − | 0.0372039i | −0.999827 | − | 0.0186019i | \(-0.994078\pi\) | ||
0.999827 | − | 0.0186019i | \(-0.00592153\pi\) | |||||||
\(164\) | 0.0485636i | 0.00379218i | ||||||||
\(165\) | −20.7965 | −1.61900 | ||||||||
\(166\) | 10.3838 | 0.805937 | ||||||||
\(167\) | − | 5.99300i | − | 0.463752i | −0.972745 | − | 0.231876i | \(-0.925514\pi\) | ||
0.972745 | − | 0.231876i | \(-0.0744864\pi\) | |||||||
\(168\) | 5.68650 | 0.438723 | ||||||||
\(169\) | −8.67550 | − | 9.68172i | −0.667346 | − | 0.744748i | ||||
\(170\) | −15.7537 | −1.20825 | ||||||||
\(171\) | − | 3.50270i | − | 0.267858i | ||||||
\(172\) | 4.64635 | 0.354281 | ||||||||
\(173\) | 0.0189761 | 0.00144272 | 0.000721362 | − | 1.00000i | \(-0.499770\pi\) | ||||
0.000721362 | 1.00000i | \(0.499770\pi\) | ||||||||
\(174\) | 2.37678i | 0.180183i | ||||||||
\(175\) | − | 9.92318i | − | 0.750122i | ||||||
\(176\) | 6.70390i | 0.505325i | ||||||||
\(177\) | − | 3.66941i | − | 0.275810i | ||||||
\(178\) | 8.09870 | 0.607024 | ||||||||
\(179\) | 5.66716 | 0.423583 | 0.211792 | − | 0.977315i | \(-0.432070\pi\) | ||||
0.211792 | + | 0.977315i | \(0.432070\pi\) | |||||||
\(180\) | − | 5.99293i | − | 0.446687i | ||||||
\(181\) | −15.5416 | −1.15520 | −0.577598 | − | 0.816322i | \(-0.696010\pi\) | ||||
−0.577598 | + | 0.816322i | \(0.696010\pi\) | |||||||
\(182\) | 2.67340 | − | 5.98523i | 0.198166 | − | 0.443655i | ||||
\(183\) | −12.7835 | −0.944986 | ||||||||
\(184\) | − | 23.9233i | − | 1.76365i | ||||||
\(185\) | −28.0523 | −2.06245 | ||||||||
\(186\) | −1.06445 | −0.0780494 | ||||||||
\(187\) | − | 29.2403i | − | 2.13826i | ||||||
\(188\) | − | 3.90347i | − | 0.284690i | ||||||
\(189\) | 9.24086i | 0.672174i | ||||||||
\(190\) | − | 6.07271i | − | 0.440561i | ||||||
\(191\) | −7.38826 | −0.534596 | −0.267298 | − | 0.963614i | \(-0.586131\pi\) | ||||
−0.267298 | + | 0.963614i | \(0.586131\pi\) | |||||||
\(192\) | 7.53931 | 0.544103 | ||||||||
\(193\) | − | 4.22194i | − | 0.303902i | −0.988388 | − | 0.151951i | \(-0.951444\pi\) | ||
0.988388 | − | 0.151951i | \(-0.0485556\pi\) | |||||||
\(194\) | −10.3012 | −0.739580 | ||||||||
\(195\) | 11.2294 | + | 5.01578i | 0.804151 | + | 0.359187i | ||||
\(196\) | 3.68081 | 0.262915 | ||||||||
\(197\) | 7.13939i | 0.508660i | 0.967117 | + | 0.254330i | \(0.0818550\pi\) | ||||
−0.967117 | + | 0.254330i | \(0.918145\pi\) | |||||||
\(198\) | −11.6950 | −0.831129 | ||||||||
\(199\) | −17.5333 | −1.24290 | −0.621452 | − | 0.783453i | \(-0.713457\pi\) | ||||
−0.621452 | + | 0.783453i | \(0.713457\pi\) | |||||||
\(200\) | − | 16.6442i | − | 1.17693i | ||||||
\(201\) | 1.80934i | 0.127621i | ||||||||
\(202\) | − | 10.5098i | − | 0.739467i | ||||||
\(203\) | − | 4.00961i | − | 0.281420i | ||||||
\(204\) | −4.91602 | −0.344190 | ||||||||
\(205\) | −0.161607 | −0.0112871 | ||||||||
\(206\) | 7.65701i | 0.533489i | ||||||||
\(207\) | 15.0485 | 1.04595 | ||||||||
\(208\) | 1.61687 | − | 3.61987i | 0.112110 | − | 0.250993i | ||||
\(209\) | 11.2715 | 0.779667 | ||||||||
\(210\) | 6.20150i | 0.427944i | ||||||||
\(211\) | 12.5199 | 0.861905 | 0.430952 | − | 0.902375i | \(-0.358178\pi\) | ||||
0.430952 | + | 0.902375i | \(0.358178\pi\) | |||||||
\(212\) | 0.573655 | 0.0393988 | ||||||||
\(213\) | − | 10.8967i | − | 0.746630i | ||||||
\(214\) | 10.0066i | 0.684035i | ||||||||
\(215\) | 15.4619i | 1.05449i | ||||||||
\(216\) | 15.4998i | 1.05463i | ||||||||
\(217\) | 1.79572 | 0.121902 | ||||||||
\(218\) | 6.04661 | 0.409528 | ||||||||
\(219\) | − | 2.40019i | − | 0.162190i | ||||||
\(220\) | 19.2849 | 1.30019 | ||||||||
\(221\) | −7.05230 | + | 15.7887i | −0.474389 | + | 1.06206i | ||||
\(222\) | 9.20371 | 0.617713 | ||||||||
\(223\) | 13.4782i | 0.902565i | 0.892381 | + | 0.451282i | \(0.149033\pi\) | ||||
−0.892381 | + | 0.451282i | \(0.850967\pi\) | |||||||
\(224\) | −8.81826 | −0.589195 | ||||||||
\(225\) | 10.4698 | 0.697984 | ||||||||
\(226\) | 5.90961i | 0.393101i | ||||||||
\(227\) | − | 21.7487i | − | 1.44351i | −0.692149 | − | 0.721755i | \(-0.743336\pi\) | ||
0.692149 | − | 0.721755i | \(-0.256664\pi\) | |||||||
\(228\) | − | 1.89502i | − | 0.125501i | ||||||
\(229\) | 4.82129i | 0.318600i | 0.987230 | + | 0.159300i | \(0.0509237\pi\) | ||||
−0.987230 | + | 0.159300i | \(0.949076\pi\) | |||||||
\(230\) | 26.0900 | 1.72032 | ||||||||
\(231\) | −11.5106 | −0.757339 | ||||||||
\(232\) | − | 6.72536i | − | 0.441541i | ||||||
\(233\) | −29.1203 | −1.90774 | −0.953868 | − | 0.300227i | \(-0.902938\pi\) | ||||
−0.953868 | + | 0.300227i | \(0.902938\pi\) | |||||||
\(234\) | 6.31491 | + | 2.82066i | 0.412818 | + | 0.184392i | ||||
\(235\) | 12.9897 | 0.847356 | ||||||||
\(236\) | 3.40271i | 0.221498i | ||||||||
\(237\) | −17.0124 | −1.10507 | ||||||||
\(238\) | −8.71945 | −0.565198 | ||||||||
\(239\) | 27.1826i | 1.75829i | 0.476552 | + | 0.879147i | \(0.341887\pi\) | ||||
−0.476552 | + | 0.879147i | \(0.658113\pi\) | |||||||
\(240\) | 3.75067i | 0.242105i | ||||||||
\(241\) | 21.6242i | 1.39294i | 0.717588 | + | 0.696468i | \(0.245246\pi\) | ||||
−0.717588 | + | 0.696468i | \(0.754754\pi\) | |||||||
\(242\) | − | 26.4971i | − | 1.70330i | ||||||
\(243\) | −15.7257 | −1.00880 | ||||||||
\(244\) | 11.8544 | 0.758901 | ||||||||
\(245\) | 12.2488i | 0.782546i | ||||||||
\(246\) | 0.0530218 | 0.00338054 | ||||||||
\(247\) | −6.08623 | − | 2.71851i | −0.387257 | − | 0.172975i | ||||
\(248\) | 3.01198 | 0.191261 | ||||||||
\(249\) | 10.7829i | 0.683339i | ||||||||
\(250\) | 1.72782 | 0.109277 | ||||||||
\(251\) | 23.7774 | 1.50082 | 0.750410 | − | 0.660973i | \(-0.229856\pi\) | ||||
0.750410 | + | 0.660973i | \(0.229856\pi\) | |||||||
\(252\) | − | 3.31701i | − | 0.208952i | ||||||
\(253\) | 48.4254i | 3.04448i | ||||||||
\(254\) | 1.78539i | 0.112025i | ||||||||
\(255\) | − | 16.3592i | − | 1.02446i | ||||||
\(256\) | −16.9350 | −1.05844 | ||||||||
\(257\) | 3.84862 | 0.240070 | 0.120035 | − | 0.992770i | \(-0.461699\pi\) | ||||
0.120035 | + | 0.992770i | \(0.461699\pi\) | |||||||
\(258\) | − | 5.07289i | − | 0.315824i | ||||||
\(259\) | −15.5266 | −0.964776 | ||||||||
\(260\) | −10.4132 | − | 4.65122i | −0.645799 | − | 0.288457i | ||||
\(261\) | 4.23046 | 0.261859 | ||||||||
\(262\) | 15.9963i | 0.988253i | ||||||||
\(263\) | −27.4393 | −1.69198 | −0.845991 | − | 0.533198i | \(-0.820990\pi\) | ||||
−0.845991 | + | 0.533198i | \(0.820990\pi\) | |||||||
\(264\) | −19.3068 | −1.18825 | ||||||||
\(265\) | 1.90897i | 0.117267i | ||||||||
\(266\) | − | 3.36117i | − | 0.206086i | ||||||
\(267\) | 8.41001i | 0.514684i | ||||||||
\(268\) | − | 1.67784i | − | 0.102490i | ||||||
\(269\) | 4.99431 | 0.304508 | 0.152254 | − | 0.988341i | \(-0.451347\pi\) | ||||
0.152254 | + | 0.988341i | \(0.451347\pi\) | |||||||
\(270\) | −16.9035 | −1.02872 | ||||||||
\(271\) | − | 27.8192i | − | 1.68990i | −0.534848 | − | 0.844948i | \(-0.679631\pi\) | ||
0.534848 | − | 0.844948i | \(-0.320369\pi\) | |||||||
\(272\) | −5.27353 | −0.319754 | ||||||||
\(273\) | 6.21530 | + | 2.77617i | 0.376167 | + | 0.168021i | ||||
\(274\) | 14.2009 | 0.857908 | ||||||||
\(275\) | 33.6911i | 2.03165i | ||||||||
\(276\) | 8.14152 | 0.490062 | ||||||||
\(277\) | 19.5970 | 1.17747 | 0.588734 | − | 0.808327i | \(-0.299627\pi\) | ||||
0.588734 | + | 0.808327i | \(0.299627\pi\) | |||||||
\(278\) | − | 8.98533i | − | 0.538904i | ||||||
\(279\) | 1.89463i | 0.113429i | ||||||||
\(280\) | − | 17.5478i | − | 1.04868i | ||||||
\(281\) | − | 9.44497i | − | 0.563440i | −0.959497 | − | 0.281720i | \(-0.909095\pi\) | ||
0.959497 | − | 0.281720i | \(-0.0909049\pi\) | |||||||
\(282\) | −4.26181 | −0.253787 | ||||||||
\(283\) | 11.1656 | 0.663726 | 0.331863 | − | 0.943328i | \(-0.392323\pi\) | ||||
0.331863 | + | 0.943328i | \(0.392323\pi\) | |||||||
\(284\) | 10.1047i | 0.599605i | ||||||||
\(285\) | 6.30614 | 0.373544 | ||||||||
\(286\) | −9.07673 | + | 20.3210i | −0.536718 | + | 1.20161i | ||||
\(287\) | −0.0894473 | −0.00527991 | ||||||||
\(288\) | − | 9.30397i | − | 0.548242i | ||||||
\(289\) | 6.00145 | 0.353027 | ||||||||
\(290\) | 7.33445 | 0.430694 | ||||||||
\(291\) | − | 10.6971i | − | 0.627077i | ||||||
\(292\) | 2.22574i | 0.130251i | ||||||||
\(293\) | − | 19.3914i | − | 1.13286i | −0.824110 | − | 0.566429i | \(-0.808324\pi\) | ||
0.824110 | − | 0.566429i | \(-0.191676\pi\) | |||||||
\(294\) | − | 4.01871i | − | 0.234376i | ||||||
\(295\) | −11.3233 | −0.659270 | ||||||||
\(296\) | −26.0429 | −1.51371 | ||||||||
\(297\) | − | 31.3745i | − | 1.82054i | ||||||
\(298\) | −0.907647 | −0.0525786 | ||||||||
\(299\) | 11.6795 | − | 26.1480i | 0.675440 | − | 1.51218i | ||||
\(300\) | 5.66432 | 0.327030 | ||||||||
\(301\) | 8.55793i | 0.493271i | ||||||||
\(302\) | −0.224093 | −0.0128951 | ||||||||
\(303\) | 10.9138 | 0.626981 | ||||||||
\(304\) | − | 2.03283i | − | 0.116591i | ||||||
\(305\) | 39.4484i | 2.25881i | ||||||||
\(306\) | − | 9.19973i | − | 0.525913i | ||||||
\(307\) | 2.97843i | 0.169988i | 0.996381 | + | 0.0849939i | \(0.0270871\pi\) | ||||
−0.996381 | + | 0.0849939i | \(0.972913\pi\) | |||||||
\(308\) | 10.6740 | 0.608205 | ||||||||
\(309\) | −7.95133 | −0.452336 | ||||||||
\(310\) | 3.28477i | 0.186562i | ||||||||
\(311\) | −15.2149 | −0.862756 | −0.431378 | − | 0.902171i | \(-0.641972\pi\) | ||||
−0.431378 | + | 0.902171i | \(0.641972\pi\) | |||||||
\(312\) | 10.4250 | + | 4.65649i | 0.590198 | + | 0.263622i | ||||
\(313\) | −6.83949 | −0.386591 | −0.193295 | − | 0.981141i | \(-0.561918\pi\) | ||||
−0.193295 | + | 0.981141i | \(0.561918\pi\) | |||||||
\(314\) | 8.62773i | 0.486891i | ||||||||
\(315\) | 11.0381 | 0.621929 | ||||||||
\(316\) | 15.7759 | 0.887463 | ||||||||
\(317\) | 17.3492i | 0.974431i | 0.873282 | + | 0.487215i | \(0.161987\pi\) | ||||
−0.873282 | + | 0.487215i | \(0.838013\pi\) | |||||||
\(318\) | − | 0.626317i | − | 0.0351221i | ||||||
\(319\) | 13.6134i | 0.762205i | ||||||||
\(320\) | − | 23.2654i | − | 1.30057i | ||||||
\(321\) | −10.3912 | −0.579981 | ||||||||
\(322\) | 14.4405 | 0.804735 | ||||||||
\(323\) | 8.86658i | 0.493350i | ||||||||
\(324\) | 0.266673 | 0.0148152 | ||||||||
\(325\) | 8.12577 | − | 18.1920i | 0.450737 | − | 1.00911i | ||||
\(326\) | 0.480900 | 0.0266346 | ||||||||
\(327\) | 6.27904i | 0.347231i | ||||||||
\(328\) | −0.150031 | −0.00828407 | ||||||||
\(329\) | 7.18964 | 0.396378 | ||||||||
\(330\) | − | 21.0553i | − | 1.15906i | ||||||
\(331\) | 5.82160i | 0.319984i | 0.987118 | + | 0.159992i | \(0.0511469\pi\) | ||||
−0.987118 | + | 0.159992i | \(0.948853\pi\) | |||||||
\(332\) | − | 9.99920i | − | 0.548777i | ||||||
\(333\) | − | 16.3818i | − | 0.897718i | ||||||
\(334\) | 6.06760 | 0.332004 | ||||||||
\(335\) | 5.58341 | 0.305054 | ||||||||
\(336\) | 2.07595i | 0.113252i | ||||||||
\(337\) | −30.6724 | −1.67083 | −0.835415 | − | 0.549620i | \(-0.814773\pi\) | ||||
−0.835415 | + | 0.549620i | \(0.814773\pi\) | |||||||
\(338\) | 9.80223 | − | 8.78349i | 0.533171 | − | 0.477759i | ||||
\(339\) | −6.13677 | −0.333303 | ||||||||
\(340\) | 15.1702i | 0.822721i | ||||||||
\(341\) | −6.09683 | −0.330162 | ||||||||
\(342\) | 3.54630 | 0.191762 | ||||||||
\(343\) | 19.3496i | 1.04478i | ||||||||
\(344\) | 14.3543i | 0.773932i | ||||||||
\(345\) | 27.0929i | 1.45863i | ||||||||
\(346\) | 0.0192123i | 0.00103286i | ||||||||
\(347\) | −24.5555 | −1.31821 | −0.659103 | − | 0.752053i | \(-0.729064\pi\) | ||||
−0.659103 | + | 0.752053i | \(0.729064\pi\) | |||||||
\(348\) | 2.28875 | 0.122690 | ||||||||
\(349\) | − | 27.8390i | − | 1.49019i | −0.666959 | − | 0.745094i | \(-0.732404\pi\) | ||
0.666959 | − | 0.745094i | \(-0.267596\pi\) | |||||||
\(350\) | 10.0467 | 0.537018 | ||||||||
\(351\) | −7.56705 | + | 16.9412i | −0.403899 | + | 0.904252i | ||||
\(352\) | 29.9397 | 1.59579 | ||||||||
\(353\) | − | 7.01905i | − | 0.373586i | −0.982399 | − | 0.186793i | \(-0.940191\pi\) | ||
0.982399 | − | 0.186793i | \(-0.0598094\pi\) | |||||||
\(354\) | 3.71508 | 0.197454 | ||||||||
\(355\) | −33.6259 | −1.78468 | ||||||||
\(356\) | − | 7.79876i | − | 0.413333i | ||||||
\(357\) | − | 9.05462i | − | 0.479221i | ||||||
\(358\) | 5.73770i | 0.303247i | ||||||||
\(359\) | − | 15.7950i | − | 0.833628i | −0.908992 | − | 0.416814i | \(-0.863147\pi\) | ||
0.908992 | − | 0.416814i | \(-0.136853\pi\) | |||||||
\(360\) | 18.5144 | 0.975793 | ||||||||
\(361\) | 15.5821 | 0.820112 | ||||||||
\(362\) | − | 15.7350i | − | 0.827014i | ||||||
\(363\) | 27.5156 | 1.44419 | ||||||||
\(364\) | −5.76356 | − | 2.57439i | −0.302093 | − | 0.134935i | ||||
\(365\) | −7.40667 | −0.387683 | ||||||||
\(366\) | − | 12.9427i | − | 0.676523i | ||||||
\(367\) | 10.2880 | 0.537029 | 0.268515 | − | 0.963276i | \(-0.413467\pi\) | ||||
0.268515 | + | 0.963276i | \(0.413467\pi\) | |||||||
\(368\) | 8.73359 | 0.455270 | ||||||||
\(369\) | − | 0.0943742i | − | 0.00491292i | ||||||
\(370\) | − | 28.4015i | − | 1.47652i | ||||||
\(371\) | 1.05659i | 0.0548555i | ||||||||
\(372\) | 1.02503i | 0.0531453i | ||||||||
\(373\) | 33.4821 | 1.73364 | 0.866820 | − | 0.498622i | \(-0.166160\pi\) | ||||
0.866820 | + | 0.498622i | \(0.166160\pi\) | |||||||
\(374\) | 29.6042 | 1.53080 | ||||||||
\(375\) | 1.79424i | 0.0926541i | ||||||||
\(376\) | 12.0592 | 0.621908 | ||||||||
\(377\) | 3.28334 | − | 7.35077i | 0.169101 | − | 0.378584i | ||||
\(378\) | −9.35589 | −0.481215 | ||||||||
\(379\) | − | 31.2200i | − | 1.60367i | −0.597548 | − | 0.801833i | \(-0.703858\pi\) | ||
0.597548 | − | 0.801833i | \(-0.296142\pi\) | |||||||
\(380\) | −5.84781 | −0.299986 | ||||||||
\(381\) | −1.85402 | −0.0949841 | ||||||||
\(382\) | − | 7.48023i | − | 0.382722i | ||||||
\(383\) | − | 8.55469i | − | 0.437124i | −0.975823 | − | 0.218562i | \(-0.929863\pi\) | ||
0.975823 | − | 0.218562i | \(-0.0701366\pi\) | |||||||
\(384\) | − | 2.69273i | − | 0.137413i | ||||||
\(385\) | 35.5202i | 1.81027i | ||||||||
\(386\) | 4.27450 | 0.217566 | ||||||||
\(387\) | −9.02931 | −0.458985 | ||||||||
\(388\) | 9.91964i | 0.503594i | ||||||||
\(389\) | 38.2805 | 1.94090 | 0.970450 | − | 0.241303i | \(-0.0775749\pi\) | ||||
0.970450 | + | 0.241303i | \(0.0775749\pi\) | |||||||
\(390\) | −5.07821 | + | 11.3691i | −0.257145 | + | 0.575699i | ||||
\(391\) | −38.0932 | −1.92645 | ||||||||
\(392\) | 11.3714i | 0.574342i | ||||||||
\(393\) | −16.6112 | −0.837922 | ||||||||
\(394\) | −7.22825 | −0.364154 | ||||||||
\(395\) | 52.4980i | 2.64146i | ||||||||
\(396\) | 11.2619i | 0.565931i | ||||||||
\(397\) | − | 18.1469i | − | 0.910767i | −0.890295 | − | 0.455383i | \(-0.849502\pi\) | ||
0.890295 | − | 0.455383i | \(-0.150498\pi\) | |||||||
\(398\) | − | 17.7515i | − | 0.889805i | ||||||
\(399\) | 3.49037 | 0.174737 | ||||||||
\(400\) | 6.07624 | 0.303812 | ||||||||
\(401\) | − | 23.7338i | − | 1.18521i | −0.805493 | − | 0.592605i | \(-0.798100\pi\) | ||
0.805493 | − | 0.592605i | \(-0.201900\pi\) | |||||||
\(402\) | −1.83187 | −0.0913651 | ||||||||
\(403\) | 3.29207 | + | 1.47046i | 0.163990 | + | 0.0732488i | ||||
\(404\) | −10.1206 | −0.503517 | ||||||||
\(405\) | 0.887419i | 0.0440962i | ||||||||
\(406\) | 4.05952 | 0.201471 | ||||||||
\(407\) | 52.7158 | 2.61303 | ||||||||
\(408\) | − | 15.1874i | − | 0.751888i | ||||||
\(409\) | − | 29.4641i | − | 1.45691i | −0.685096 | − | 0.728453i | \(-0.740240\pi\) | ||
0.685096 | − | 0.728453i | \(-0.259760\pi\) | |||||||
\(410\) | − | 0.163619i | − | 0.00808055i | ||||||
\(411\) | 14.7468i | 0.727404i | ||||||||
\(412\) | 7.37342 | 0.363262 | ||||||||
\(413\) | −6.26731 | −0.308394 | ||||||||
\(414\) | 15.2359i | 0.748801i | ||||||||
\(415\) | 33.2747 | 1.63339 | ||||||||
\(416\) | −16.1664 | − | 7.22099i | −0.792623 | − | 0.354038i | ||||
\(417\) | 9.33071 | 0.456927 | ||||||||
\(418\) | 11.4118i | 0.558170i | ||||||||
\(419\) | 24.8096 | 1.21203 | 0.606014 | − | 0.795454i | \(-0.292768\pi\) | ||||
0.606014 | + | 0.795454i | \(0.292768\pi\) | |||||||
\(420\) | 5.97182 | 0.291395 | ||||||||
\(421\) | 0.191902i | 0.00935275i | 0.999989 | + | 0.00467637i | \(0.00148854\pi\) | ||||
−0.999989 | + | 0.00467637i | \(0.998511\pi\) | |||||||
\(422\) | 12.6757i | 0.617045i | ||||||||
\(423\) | 7.58565i | 0.368827i | ||||||||
\(424\) | 1.77223i | 0.0860672i | ||||||||
\(425\) | −26.5027 | −1.28557 | ||||||||
\(426\) | 11.0323 | 0.534519 | ||||||||
\(427\) | 21.8342i | 1.05663i | ||||||||
\(428\) | 9.63597 | 0.465772 | ||||||||
\(429\) | −21.1022 | − | 9.42563i | −1.01882 | − | 0.455074i | ||||
\(430\) | −15.6543 | −0.754918 | ||||||||
\(431\) | − | 15.0633i | − | 0.725574i | −0.931872 | − | 0.362787i | \(-0.881825\pi\) | ||
0.931872 | − | 0.362787i | \(-0.118175\pi\) | |||||||
\(432\) | −5.65844 | −0.272242 | ||||||||
\(433\) | 12.8565 | 0.617844 | 0.308922 | − | 0.951087i | \(-0.400032\pi\) | ||||
0.308922 | + | 0.951087i | \(0.400032\pi\) | |||||||
\(434\) | 1.81807i | 0.0872703i | ||||||||
\(435\) | 7.61638i | 0.365178i | ||||||||
\(436\) | − | 5.82267i | − | 0.278855i | ||||||
\(437\) | − | 14.6841i | − | 0.702437i | ||||||
\(438\) | 2.43006 | 0.116113 | ||||||||
\(439\) | −0.561664 | −0.0268068 | −0.0134034 | − | 0.999910i | \(-0.504267\pi\) | ||||
−0.0134034 | + | 0.999910i | \(0.504267\pi\) | |||||||
\(440\) | 59.5783i | 2.84028i | ||||||||
\(441\) | −7.15296 | −0.340617 | ||||||||
\(442\) | −15.9853 | − | 7.14008i | −0.760341 | − | 0.339619i | ||||
\(443\) | −10.0558 | −0.477765 | −0.238883 | − | 0.971048i | \(-0.576781\pi\) | ||||
−0.238883 | + | 0.971048i | \(0.576781\pi\) | |||||||
\(444\) | − | 8.86284i | − | 0.420612i | ||||||
\(445\) | 25.9522 | 1.23025 | ||||||||
\(446\) | −13.6459 | −0.646154 | ||||||||
\(447\) | − | 0.942537i | − | 0.0445805i | ||||||
\(448\) | − | 12.8771i | − | 0.608384i | ||||||
\(449\) | − | 15.4936i | − | 0.731187i | −0.930775 | − | 0.365594i | \(-0.880866\pi\) | ||
0.930775 | − | 0.365594i | \(-0.119134\pi\) | |||||||
\(450\) | 10.6001i | 0.499692i | ||||||||
\(451\) | 0.303691 | 0.0143003 | ||||||||
\(452\) | 5.69074 | 0.267670 | ||||||||
\(453\) | − | 0.232707i | − | 0.0109335i | ||||||
\(454\) | 22.0194 | 1.03342 | ||||||||
\(455\) | 8.56690 | − | 19.1796i | 0.401623 | − | 0.899156i | ||||
\(456\) | 5.85442 | 0.274159 | ||||||||
\(457\) | 22.5213i | 1.05350i | 0.850020 | + | 0.526751i | \(0.176590\pi\) | ||||
−0.850020 | + | 0.526751i | \(0.823410\pi\) | |||||||
\(458\) | −4.88131 | −0.228088 | ||||||||
\(459\) | 24.6803 | 1.15198 | ||||||||
\(460\) | − | 25.1237i | − | 1.17140i | ||||||
\(461\) | 11.9714i | 0.557563i | 0.960354 | + | 0.278782i | \(0.0899306\pi\) | ||||
−0.960354 | + | 0.278782i | \(0.910069\pi\) | |||||||
\(462\) | − | 11.6538i | − | 0.542186i | ||||||
\(463\) | − | 42.4947i | − | 1.97489i | −0.157950 | − | 0.987447i | \(-0.550489\pi\) | ||
0.157950 | − | 0.987447i | \(-0.449511\pi\) | |||||||
\(464\) | 2.45520 | 0.113980 | ||||||||
\(465\) | −3.41103 | −0.158183 | ||||||||
\(466\) | − | 29.4828i | − | 1.36576i | ||||||
\(467\) | 35.2701 | 1.63211 | 0.816053 | − | 0.577977i | \(-0.196158\pi\) | ||||
0.816053 | + | 0.577977i | \(0.196158\pi\) | |||||||
\(468\) | 2.71619 | − | 6.08103i | 0.125556 | − | 0.281096i | ||||
\(469\) | 3.09034 | 0.142699 | ||||||||
\(470\) | 13.1514i | 0.606629i | ||||||||
\(471\) | −8.95937 | −0.412826 | ||||||||
\(472\) | −10.5122 | −0.483864 | ||||||||
\(473\) | − | 29.0558i | − | 1.33599i | ||||||
\(474\) | − | 17.2241i | − | 0.791130i | ||||||
\(475\) | − | 10.2162i | − | 0.468752i | ||||||
\(476\) | 8.39652i | 0.384854i | ||||||||
\(477\) | −1.11479 | −0.0510427 | ||||||||
\(478\) | −27.5209 | −1.25878 | ||||||||
\(479\) | 17.0249i | 0.777888i | 0.921261 | + | 0.388944i | \(0.127160\pi\) | ||||
−0.921261 | + | 0.388944i | \(0.872840\pi\) | |||||||
\(480\) | 16.7506 | 0.764555 | ||||||||
\(481\) | −28.4647 | − | 12.7142i | −1.29788 | − | 0.579719i | ||||
\(482\) | −21.8933 | −0.997214 | ||||||||
\(483\) | 14.9955i | 0.682321i | ||||||||
\(484\) | −25.5157 | −1.15981 | ||||||||
\(485\) | −33.0100 | −1.49891 | ||||||||
\(486\) | − | 15.9215i | − | 0.722212i | ||||||
\(487\) | 3.52549i | 0.159755i | 0.996805 | + | 0.0798776i | \(0.0254529\pi\) | ||||
−0.996805 | + | 0.0798776i | \(0.974547\pi\) | |||||||
\(488\) | 36.6226i | 1.65783i | ||||||||
\(489\) | 0.499385i | 0.0225830i | ||||||||
\(490\) | −12.4012 | −0.560231 | ||||||||
\(491\) | −29.9606 | −1.35210 | −0.676051 | − | 0.736855i | \(-0.736310\pi\) | ||||
−0.676051 | + | 0.736855i | \(0.736310\pi\) | |||||||
\(492\) | − | 0.0510581i | − | 0.00230187i | ||||||
\(493\) | −10.7088 | −0.482300 | ||||||||
\(494\) | 2.75235 | − | 6.16198i | 0.123834 | − | 0.277241i | ||||
\(495\) | −37.4766 | −1.68445 | ||||||||
\(496\) | 1.09957i | 0.0493722i | ||||||||
\(497\) | −18.6115 | −0.834839 | ||||||||
\(498\) | −10.9171 | −0.489208 | ||||||||
\(499\) | − | 9.74284i | − | 0.436149i | −0.975932 | − | 0.218075i | \(-0.930022\pi\) | ||
0.975932 | − | 0.218075i | \(-0.0699776\pi\) | |||||||
\(500\) | − | 1.66383i | − | 0.0744088i | ||||||
\(501\) | 6.30083i | 0.281500i | ||||||||
\(502\) | 24.0734i | 1.07445i | ||||||||
\(503\) | 15.7364 | 0.701651 | 0.350825 | − | 0.936441i | \(-0.385901\pi\) | ||||
0.350825 | + | 0.936441i | \(0.385901\pi\) | |||||||
\(504\) | 10.2475 | 0.456458 | ||||||||
\(505\) | − | 33.6786i | − | 1.49868i | ||||||
\(506\) | −49.0282 | −2.17957 | ||||||||
\(507\) | 9.12112 | + | 10.1790i | 0.405083 | + | 0.452066i | ||||
\(508\) | 1.71926 | 0.0762800 | ||||||||
\(509\) | − | 30.5793i | − | 1.35541i | −0.735336 | − | 0.677703i | \(-0.762976\pi\) | ||
0.735336 | − | 0.677703i | \(-0.237024\pi\) | |||||||
\(510\) | 16.5629 | 0.733416 | ||||||||
\(511\) | −4.09950 | −0.181351 | ||||||||
\(512\) | − | 12.0234i | − | 0.531366i | ||||||
\(513\) | 9.51376i | 0.420043i | ||||||||
\(514\) | 3.89652i | 0.171868i | ||||||||
\(515\) | 24.5368i | 1.08122i | ||||||||
\(516\) | −4.88501 | −0.215051 | ||||||||
\(517\) | −24.4102 | −1.07356 | ||||||||
\(518\) | − | 15.7199i | − | 0.690691i | ||||||
\(519\) | −0.0199508 | −0.000875742 | ||||||||
\(520\) | 14.3693 | − | 32.1702i | 0.630137 | − | 1.41076i | ||||
\(521\) | −36.3668 | −1.59326 | −0.796628 | − | 0.604469i | \(-0.793385\pi\) | ||||
−0.796628 | + | 0.604469i | \(0.793385\pi\) | |||||||
\(522\) | 4.28312i | 0.187467i | ||||||||
\(523\) | −12.1385 | −0.530780 | −0.265390 | − | 0.964141i | \(-0.585501\pi\) | ||||
−0.265390 | + | 0.964141i | \(0.585501\pi\) | |||||||
\(524\) | 15.4038 | 0.672920 | ||||||||
\(525\) | 10.4329i | 0.455328i | ||||||||
\(526\) | − | 27.7809i | − | 1.21130i | ||||||
\(527\) | − | 4.79598i | − | 0.208916i | ||||||
\(528\) | − | 7.04824i | − | 0.306735i | ||||||
\(529\) | 40.0869 | 1.74291 | ||||||||
\(530\) | −1.93274 | −0.0839527 | ||||||||
\(531\) | − | 6.61252i | − | 0.286959i | ||||||
\(532\) | −3.23668 | −0.140328 | ||||||||
\(533\) | −0.163983 | − | 0.0732455i | −0.00710288 | − | 0.00317262i | ||||
\(534\) | −8.51469 | −0.368467 | ||||||||
\(535\) | 32.0660i | 1.38633i | ||||||||
\(536\) | 5.18346 | 0.223891 | ||||||||
\(537\) | −5.95825 | −0.257118 | ||||||||
\(538\) | 5.05648i | 0.218000i | ||||||||
\(539\) | − | 23.0179i | − | 0.991450i | ||||||
\(540\) | 16.2775i | 0.700472i | ||||||||
\(541\) | 36.2301i | 1.55765i | 0.627240 | + | 0.778826i | \(0.284184\pi\) | ||||
−0.627240 | + | 0.778826i | \(0.715816\pi\) | |||||||
\(542\) | 28.1655 | 1.20981 | ||||||||
\(543\) | 16.3399 | 0.701210 | ||||||||
\(544\) | 23.5516i | 1.00977i | ||||||||
\(545\) | 19.3763 | 0.829991 | ||||||||
\(546\) | −2.81072 | + | 6.29266i | −0.120288 | + | 0.269301i | ||||
\(547\) | −4.85710 | −0.207675 | −0.103837 | − | 0.994594i | \(-0.533112\pi\) | ||||
−0.103837 | + | 0.994594i | \(0.533112\pi\) | |||||||
\(548\) | − | 13.6750i | − | 0.584165i | ||||||
\(549\) | −23.0368 | −0.983187 | ||||||||
\(550\) | −34.1105 | −1.45448 | ||||||||
\(551\) | − | 4.12802i | − | 0.175860i | ||||||
\(552\) | 25.1522i | 1.07055i | ||||||||
\(553\) | 29.0570i | 1.23563i | ||||||||
\(554\) | 19.8409i | 0.842959i | ||||||||
\(555\) | 29.4932 | 1.25192 | ||||||||
\(556\) | −8.65254 | −0.366950 | ||||||||
\(557\) | 41.4847i | 1.75776i | 0.477040 | + | 0.878882i | \(0.341710\pi\) | ||||
−0.477040 | + | 0.878882i | \(0.658290\pi\) | |||||||
\(558\) | −1.91821 | −0.0812045 | ||||||||
\(559\) | −7.00781 | + | 15.6891i | −0.296399 | + | 0.663580i | ||||
\(560\) | 6.40611 | 0.270708 | ||||||||
\(561\) | 30.7422i | 1.29794i | ||||||||
\(562\) | 9.56254 | 0.403371 | ||||||||
\(563\) | −5.12904 | −0.216163 | −0.108082 | − | 0.994142i | \(-0.534471\pi\) | ||||
−0.108082 | + | 0.994142i | \(0.534471\pi\) | |||||||
\(564\) | 4.10397i | 0.172808i | ||||||||
\(565\) | 18.9373i | 0.796698i | ||||||||
\(566\) | 11.3046i | 0.475167i | ||||||||
\(567\) | 0.491175i | 0.0206274i | ||||||||
\(568\) | −31.2172 | −1.30984 | ||||||||
\(569\) | −20.7637 | −0.870458 | −0.435229 | − | 0.900320i | \(-0.643333\pi\) | ||||
−0.435229 | + | 0.900320i | \(0.643333\pi\) | |||||||
\(570\) | 6.38464i | 0.267423i | ||||||||
\(571\) | −29.8037 | −1.24725 | −0.623623 | − | 0.781726i | \(-0.714340\pi\) | ||||
−0.623623 | + | 0.781726i | \(0.714340\pi\) | |||||||
\(572\) | 19.5684 | + | 8.74056i | 0.818197 | + | 0.365461i | ||||
\(573\) | 7.76776 | 0.324503 | ||||||||
\(574\) | − | 0.0905607i | − | 0.00377993i | ||||||
\(575\) | 43.8916 | 1.83041 | ||||||||
\(576\) | 13.5863 | 0.566098 | ||||||||
\(577\) | 31.5439i | 1.31319i | 0.754243 | + | 0.656596i | \(0.228004\pi\) | ||||
−0.754243 | + | 0.656596i | \(0.771996\pi\) | |||||||
\(578\) | 6.07615i | 0.252735i | ||||||||
\(579\) | 4.43880i | 0.184470i | ||||||||
\(580\) | − | 7.06281i | − | 0.293267i | ||||||
\(581\) | 18.4171 | 0.764071 | ||||||||
\(582\) | 10.8303 | 0.448929 | ||||||||
\(583\) | − | 3.58734i | − | 0.148572i | ||||||
\(584\) | −6.87612 | −0.284536 | ||||||||
\(585\) | 20.2361 | + | 9.03878i | 0.836659 | + | 0.373707i | ||||
\(586\) | 19.6328 | 0.811023 | ||||||||
\(587\) | − | 32.0469i | − | 1.32272i | −0.750071 | − | 0.661358i | \(-0.769981\pi\) | ||
0.750071 | − | 0.661358i | \(-0.230019\pi\) | |||||||
\(588\) | −3.86988 | −0.159591 | ||||||||
\(589\) | 1.84875 | 0.0761765 | ||||||||
\(590\) | − | 11.4643i | − | 0.471977i | ||||||
\(591\) | − | 7.50610i | − | 0.308760i | ||||||
\(592\) | − | 9.50737i | − | 0.390751i | ||||||
\(593\) | 30.8314i | 1.26609i | 0.774114 | + | 0.633046i | \(0.218196\pi\) | ||||
−0.774114 | + | 0.633046i | \(0.781804\pi\) | |||||||
\(594\) | 31.7651 | 1.30334 | ||||||||
\(595\) | −27.9414 | −1.14549 | ||||||||
\(596\) | 0.874032i | 0.0358017i | ||||||||
\(597\) | 18.4339 | 0.754449 | ||||||||
\(598\) | 26.4735 | + | 11.8248i | 1.08258 | + | 0.483553i | ||||
\(599\) | −29.6376 | −1.21096 | −0.605479 | − | 0.795861i | \(-0.707018\pi\) | ||||
−0.605479 | + | 0.795861i | \(0.707018\pi\) | |||||||
\(600\) | 17.4992i | 0.714401i | ||||||||
\(601\) | 29.7503 | 1.21354 | 0.606769 | − | 0.794878i | \(-0.292465\pi\) | ||||
0.606769 | + | 0.794878i | \(0.292465\pi\) | |||||||
\(602\) | −8.66445 | −0.353137 | ||||||||
\(603\) | 3.26056i | 0.132780i | ||||||||
\(604\) | 0.215793i | 0.00878051i | ||||||||
\(605\) | − | 84.9097i | − | 3.45207i | ||||||
\(606\) | 11.0496i | 0.448861i | ||||||||
\(607\) | −34.1070 | −1.38436 | −0.692181 | − | 0.721724i | \(-0.743350\pi\) | ||||
−0.692181 | + | 0.721724i | \(0.743350\pi\) | |||||||
\(608\) | −9.07867 | −0.368189 | ||||||||
\(609\) | 4.21556i | 0.170823i | ||||||||
\(610\) | −39.9394 | −1.61710 | ||||||||
\(611\) | 13.1807 | + | 5.88736i | 0.533233 | + | 0.238177i | ||||
\(612\) | −8.85900 | −0.358104 | ||||||||
\(613\) | − | 23.4986i | − | 0.949100i | −0.880228 | − | 0.474550i | \(-0.842611\pi\) | ||
0.880228 | − | 0.474550i | \(-0.157389\pi\) | |||||||
\(614\) | −3.01550 | −0.121696 | ||||||||
\(615\) | 0.169908 | 0.00685135 | ||||||||
\(616\) | 32.9758i | 1.32863i | ||||||||
\(617\) | − | 13.5012i | − | 0.543539i | −0.962362 | − | 0.271770i | \(-0.912391\pi\) | ||
0.962362 | − | 0.271770i | \(-0.0876089\pi\) | |||||||
\(618\) | − | 8.05031i | − | 0.323831i | ||||||
\(619\) | − | 15.3528i | − | 0.617080i | −0.951211 | − | 0.308540i | \(-0.900160\pi\) | ||
0.951211 | − | 0.308540i | \(-0.0998404\pi\) | |||||||
\(620\) | 3.16311 | 0.127034 | ||||||||
\(621\) | −40.8736 | −1.64020 | ||||||||
\(622\) | − | 15.4043i | − | 0.617654i | ||||||
\(623\) | 14.3642 | 0.575490 | ||||||||
\(624\) | −1.69992 | + | 3.80580i | −0.0680515 | + | 0.152354i | ||||
\(625\) | −22.0933 | −0.883730 | ||||||||
\(626\) | − | 6.92463i | − | 0.276764i | ||||||
\(627\) | −11.8505 | −0.473263 | ||||||||
\(628\) | 8.30819 | 0.331533 | ||||||||
\(629\) | 41.4682i | 1.65344i | ||||||||
\(630\) | 11.1755i | 0.445244i | ||||||||
\(631\) | − | 12.9193i | − | 0.514310i | −0.966370 | − | 0.257155i | \(-0.917215\pi\) | ||
0.966370 | − | 0.257155i | \(-0.0827850\pi\) | |||||||
\(632\) | 48.7375i | 1.93867i | ||||||||
\(633\) | −13.1630 | −0.523181 | ||||||||
\(634\) | −17.5652 | −0.697603 | ||||||||
\(635\) | 5.72126i | 0.227041i | ||||||||
\(636\) | −0.603121 | −0.0239153 | ||||||||
\(637\) | −5.55155 | + | 12.4288i | −0.219960 | + | 0.492449i | ||||
\(638\) | −13.7829 | −0.545669 | ||||||||
\(639\) | − | 19.6366i | − | 0.776813i | ||||||
\(640\) | −8.30943 | −0.328459 | ||||||||
\(641\) | 37.2265 | 1.47036 | 0.735180 | − | 0.677872i | \(-0.237098\pi\) | ||||
0.735180 | + | 0.677872i | \(0.237098\pi\) | |||||||
\(642\) | − | 10.5206i | − | 0.415213i | ||||||
\(643\) | 24.3497i | 0.960259i | 0.877198 | + | 0.480130i | \(0.159410\pi\) | ||||
−0.877198 | + | 0.480130i | \(0.840590\pi\) | |||||||
\(644\) | − | 13.9056i | − | 0.547959i | ||||||
\(645\) | − | 16.2560i | − | 0.640081i | ||||||
\(646\) | −8.97695 | −0.353193 | ||||||||
\(647\) | 24.9639 | 0.981433 | 0.490717 | − | 0.871319i | \(-0.336735\pi\) | ||||
0.490717 | + | 0.871319i | \(0.336735\pi\) | |||||||
\(648\) | 0.823852i | 0.0323640i | ||||||||
\(649\) | 21.2788 | 0.835264 | ||||||||
\(650\) | 18.4185 | + | 8.22692i | 0.722432 | + | 0.322686i | ||||
\(651\) | −1.88796 | −0.0739949 | ||||||||
\(652\) | − | 0.463089i | − | 0.0181360i | ||||||
\(653\) | −2.17194 | −0.0849947 | −0.0424974 | − | 0.999097i | \(-0.513531\pi\) | ||||
−0.0424974 | + | 0.999097i | \(0.513531\pi\) | |||||||
\(654\) | −6.35719 | −0.248586 | ||||||||
\(655\) | 51.2600i | 2.00289i | ||||||||
\(656\) | − | 0.0547711i | − | 0.00213845i | ||||||
\(657\) | − | 4.32530i | − | 0.168746i | ||||||
\(658\) | 7.27913i | 0.283770i | ||||||||
\(659\) | 3.53137 | 0.137563 | 0.0687814 | − | 0.997632i | \(-0.478089\pi\) | ||||
0.0687814 | + | 0.997632i | \(0.478089\pi\) | |||||||
\(660\) | −20.2755 | −0.789223 | ||||||||
\(661\) | − | 0.781774i | − | 0.0304075i | −0.999884 | − | 0.0152037i | \(-0.995160\pi\) | ||
0.999884 | − | 0.0152037i | \(-0.00483969\pi\) | |||||||
\(662\) | −5.89407 | −0.229079 | ||||||||
\(663\) | 7.41454 | − | 16.5997i | 0.287957 | − | 0.644680i | ||||
\(664\) | 30.8912 | 1.19881 | ||||||||
\(665\) | − | 10.7708i | − | 0.417675i | ||||||
\(666\) | 16.5857 | 0.642684 | ||||||||
\(667\) | 17.7351 | 0.686705 | ||||||||
\(668\) | − | 5.84288i | − | 0.226068i | ||||||
\(669\) | − | 14.1705i | − | 0.547862i | ||||||
\(670\) | 5.65291i | 0.218391i | ||||||||
\(671\) | − | 74.1313i | − | 2.86181i | ||||||
\(672\) | 9.27121 | 0.357645 | ||||||||
\(673\) | −39.4571 | −1.52096 | −0.760479 | − | 0.649362i | \(-0.775036\pi\) | ||||
−0.760479 | + | 0.649362i | \(0.775036\pi\) | |||||||
\(674\) | − | 31.0541i | − | 1.19616i | ||||||
\(675\) | −28.4371 | −1.09454 | ||||||||
\(676\) | −8.45818 | − | 9.43919i | −0.325315 | − | 0.363046i | ||||
\(677\) | 44.1582 | 1.69714 | 0.848569 | − | 0.529085i | \(-0.177465\pi\) | ||||
0.848569 | + | 0.529085i | \(0.177465\pi\) | |||||||
\(678\) | − | 6.21315i | − | 0.238615i | ||||||
\(679\) | −18.2706 | −0.701161 | ||||||||
\(680\) | −46.8664 | −1.79724 | ||||||||
\(681\) | 22.8658i | 0.876219i | ||||||||
\(682\) | − | 6.17272i | − | 0.236366i | ||||||
\(683\) | 49.3853i | 1.88967i | 0.327540 | + | 0.944837i | \(0.393781\pi\) | ||||
−0.327540 | + | 0.944837i | \(0.606219\pi\) | |||||||
\(684\) | − | 3.41496i | − | 0.130574i | ||||||
\(685\) | 45.5067 | 1.73872 | ||||||||
\(686\) | −19.5904 | −0.747967 | ||||||||
\(687\) | − | 5.06894i | − | 0.193392i | ||||||
\(688\) | −5.24026 | −0.199783 | ||||||||
\(689\) | −0.865209 | + | 1.93704i | −0.0329618 | + | 0.0737952i | ||||
\(690\) | −27.4301 | −1.04425 | ||||||||
\(691\) | 12.4149i | 0.472284i | 0.971719 | + | 0.236142i | \(0.0758831\pi\) | ||||
−0.971719 | + | 0.236142i | \(0.924117\pi\) | |||||||
\(692\) | 0.0185007 | 0.000703292 | ||||||||
\(693\) | −20.7428 | −0.787955 | ||||||||
\(694\) | − | 24.8611i | − | 0.943715i | ||||||
\(695\) | − | 28.7934i | − | 1.09220i | ||||||
\(696\) | 7.07081i | 0.268018i | ||||||||
\(697\) | 0.238894i | 0.00904877i | ||||||||
\(698\) | 28.1855 | 1.06684 | ||||||||
\(699\) | 30.6161 | 1.15801 | ||||||||
\(700\) | − | 9.67461i | − | 0.365666i | ||||||
\(701\) | 27.1200 | 1.02431 | 0.512155 | − | 0.858893i | \(-0.328847\pi\) | ||||
0.512155 | + | 0.858893i | \(0.328847\pi\) | |||||||
\(702\) | −17.1520 | − | 7.66124i | −0.647362 | − | 0.289155i | ||||
\(703\) | −15.9851 | −0.602890 | ||||||||
\(704\) | 43.7202i | 1.64777i | ||||||||
\(705\) | −13.6569 | −0.514350 | ||||||||
\(706\) | 7.10642 | 0.267454 | ||||||||
\(707\) | − | 18.6406i | − | 0.701054i | ||||||
\(708\) | − | 3.57749i | − | 0.134450i | ||||||
\(709\) | − | 9.01510i | − | 0.338569i | −0.985567 | − | 0.169285i | \(-0.945854\pi\) | ||
0.985567 | − | 0.169285i | \(-0.0541457\pi\) | |||||||
\(710\) | − | 34.0444i | − | 1.27767i | ||||||
\(711\) | −30.6574 | −1.14974 | ||||||||
\(712\) | 24.0932 | 0.902932 | ||||||||
\(713\) | 7.94273i | 0.297457i | ||||||||
\(714\) | 9.16732 | 0.343078 | ||||||||
\(715\) | −29.0863 | + | 65.1187i | −1.08777 | + | 2.43530i | ||||
\(716\) | 5.52520 | 0.206486 | ||||||||
\(717\) | − | 28.5788i | − | 1.06729i | ||||||
\(718\) | 15.9916 | 0.596801 | ||||||||
\(719\) | 2.03502 | 0.0758934 | 0.0379467 | − | 0.999280i | \(-0.487918\pi\) | ||||
0.0379467 | + | 0.999280i | \(0.487918\pi\) | |||||||
\(720\) | 6.75896i | 0.251892i | ||||||||
\(721\) | 13.5808i | 0.505776i | ||||||||
\(722\) | 15.7761i | 0.587125i | ||||||||
\(723\) | − | 22.7349i | − | 0.845520i | ||||||
\(724\) | −15.1523 | −0.563129 | ||||||||
\(725\) | 12.3389 | 0.458254 | ||||||||
\(726\) | 27.8581i | 1.03391i | ||||||||
\(727\) | 6.51447 | 0.241608 | 0.120804 | − | 0.992676i | \(-0.461453\pi\) | ||||
0.120804 | + | 0.992676i | \(0.461453\pi\) | |||||||
\(728\) | 7.95324 | − | 17.8058i | 0.294767 | − | 0.659926i | ||||
\(729\) | 15.7129 | 0.581959 | ||||||||
\(730\) | − | 7.49887i | − | 0.277546i | ||||||
\(731\) | 22.8564 | 0.845373 | ||||||||
\(732\) | −12.4633 | −0.460657 | ||||||||
\(733\) | − | 3.11568i | − | 0.115080i | −0.998343 | − | 0.0575402i | \(-0.981674\pi\) | ||
0.998343 | − | 0.0575402i | \(-0.0183257\pi\) | |||||||
\(734\) | 10.4161i | 0.384464i | ||||||||
\(735\) | − | 12.8779i | − | 0.475010i | ||||||
\(736\) | − | 39.0044i | − | 1.43772i | ||||||
\(737\) | −10.4923 | −0.386490 | ||||||||
\(738\) | 0.0955489 | 0.00351720 | ||||||||
\(739\) | − | 39.1735i | − | 1.44102i | −0.693444 | − | 0.720510i | \(-0.743908\pi\) | ||
0.693444 | − | 0.720510i | \(-0.256092\pi\) | |||||||
\(740\) | −27.3496 | −1.00539 | ||||||||
\(741\) | 6.39884 | + | 2.85815i | 0.235067 | + | 0.104997i | ||||
\(742\) | −1.06974 | −0.0392715 | ||||||||
\(743\) | − | 30.6791i | − | 1.12551i | −0.826625 | − | 0.562753i | \(-0.809742\pi\) | ||
0.826625 | − | 0.562753i | \(-0.190258\pi\) | |||||||
\(744\) | −3.16669 | −0.116097 | ||||||||
\(745\) | −2.90855 | −0.106561 | ||||||||
\(746\) | 33.8989i | 1.24113i | ||||||||
\(747\) | 19.4315i | 0.710963i | ||||||||
\(748\) | − | 28.5078i | − | 1.04235i | ||||||
\(749\) | 17.7481i | 0.648501i | ||||||||
\(750\) | −1.81657 | −0.0663318 | ||||||||
\(751\) | −25.5019 | −0.930578 | −0.465289 | − | 0.885159i | \(-0.654050\pi\) | ||||
−0.465289 | + | 0.885159i | \(0.654050\pi\) | |||||||
\(752\) | 4.40242i | 0.160540i | ||||||||
\(753\) | −24.9988 | −0.911006 | ||||||||
\(754\) | 7.44227 | + | 3.32421i | 0.271031 | + | 0.121061i | ||||
\(755\) | −0.718105 | −0.0261345 | ||||||||
\(756\) | 9.00938i | 0.327668i | ||||||||
\(757\) | −8.04879 | −0.292538 | −0.146269 | − | 0.989245i | \(-0.546727\pi\) | ||||
−0.146269 | + | 0.989245i | \(0.546727\pi\) | |||||||
\(758\) | 31.6087 | 1.14808 | ||||||||
\(759\) | − | 50.9128i | − | 1.84802i | ||||||
\(760\) | − | 18.0660i | − | 0.655324i | ||||||
\(761\) | 52.1296i | 1.88970i | 0.327508 | + | 0.944848i | \(0.393791\pi\) | ||||
−0.327508 | + | 0.944848i | \(0.606209\pi\) | |||||||
\(762\) | − | 1.87709i | − | 0.0679999i | ||||||
\(763\) | 10.7245 | 0.388254 | ||||||||
\(764\) | −7.20319 | −0.260602 | ||||||||
\(765\) | − | 29.4805i | − | 1.06587i | ||||||
\(766\) | 8.66117 | 0.312941 | ||||||||
\(767\) | −11.4898 | − | 5.13210i | −0.414872 | − | 0.185309i | ||||
\(768\) | 17.8049 | 0.642478 | ||||||||
\(769\) | − | 3.62057i | − | 0.130561i | −0.997867 | − | 0.0652806i | \(-0.979206\pi\) | ||
0.997867 | − | 0.0652806i | \(-0.0207942\pi\) | |||||||
\(770\) | −35.9623 | −1.29599 | ||||||||
\(771\) | −4.04630 | −0.145724 | ||||||||
\(772\) | − | 4.11619i | − | 0.148145i | ||||||
\(773\) | − | 32.4020i | − | 1.16542i | −0.812680 | − | 0.582710i | \(-0.801992\pi\) | ||
0.812680 | − | 0.582710i | \(-0.198008\pi\) | |||||||
\(774\) | − | 9.14170i | − | 0.328592i | ||||||
\(775\) | 5.52601i | 0.198500i | ||||||||
\(776\) | −30.6454 | −1.10011 | ||||||||
\(777\) | 16.3241 | 0.585624 | ||||||||
\(778\) | 38.7570i | 1.38951i | ||||||||
\(779\) | −0.0920888 | −0.00329942 | ||||||||
\(780\) | 10.9481 | + | 4.89013i | 0.392004 | + | 0.175095i | ||||
\(781\) | 63.1896 | 2.26110 | ||||||||
\(782\) | − | 38.5673i | − | 1.37917i | ||||||
\(783\) | −11.4904 | −0.410635 | ||||||||
\(784\) | −4.15130 | −0.148261 | ||||||||
\(785\) | 27.6475i | 0.986781i | ||||||||
\(786\) | − | 16.8179i | − | 0.599876i | ||||||
\(787\) | − | 13.0411i | − | 0.464866i | −0.972612 | − | 0.232433i | \(-0.925331\pi\) | ||
0.972612 | − | 0.232433i | \(-0.0746686\pi\) | |||||||
\(788\) | 6.96055i | 0.247959i | ||||||||
\(789\) | 28.8487 | 1.02704 | ||||||||
\(790\) | −53.1515 | −1.89105 | ||||||||
\(791\) | 10.4815i | 0.372681i | ||||||||
\(792\) | −34.7921 | −1.23628 | ||||||||
\(793\) | −17.8793 | + | 40.0283i | −0.634912 | + | 1.42145i | ||||
\(794\) | 18.3728 | 0.652026 | ||||||||
\(795\) | − | 2.00703i | − | 0.0711820i | ||||||
\(796\) | −17.0941 | −0.605884 | ||||||||
\(797\) | 1.44802 | 0.0512914 | 0.0256457 | − | 0.999671i | \(-0.491836\pi\) | ||||
0.0256457 | + | 0.999671i | \(0.491836\pi\) | |||||||
\(798\) | 3.53381i | 0.125096i | ||||||||
\(799\) | − | 19.2020i | − | 0.679317i | ||||||
\(800\) | − | 27.1366i | − | 0.959424i | ||||||
\(801\) | 15.1554i | 0.535490i | ||||||||
\(802\) | 24.0292 | 0.848501 | ||||||||
\(803\) | 13.9186 | 0.491176 | ||||||||
\(804\) | 1.76402i | 0.0622122i | ||||||||
\(805\) | 46.2744 | 1.63096 | ||||||||
\(806\) | −1.48876 | + | 3.33305i | −0.0524394 | + | 0.117402i | ||||
\(807\) | −5.25084 | −0.184838 | ||||||||
\(808\) | − | 31.2661i | − | 1.09994i | ||||||
\(809\) | −21.8771 | −0.769156 | −0.384578 | − | 0.923092i | \(-0.625653\pi\) | ||||
−0.384578 | + | 0.923092i | \(0.625653\pi\) | |||||||
\(810\) | −0.898465 | −0.0315689 | ||||||||
\(811\) | − | 25.9895i | − | 0.912614i | −0.889822 | − | 0.456307i | \(-0.849172\pi\) | ||
0.889822 | − | 0.456307i | \(-0.150828\pi\) | |||||||
\(812\) | − | 3.90917i | − | 0.137185i | ||||||
\(813\) | 29.2481i | 1.02578i | ||||||||
\(814\) | 53.3720i | 1.87069i | ||||||||
\(815\) | 1.54104 | 0.0539803 | ||||||||
\(816\) | 5.54440 | 0.194093 | ||||||||
\(817\) | 8.81065i | 0.308246i | ||||||||
\(818\) | 29.8309 | 1.04301 | ||||||||
\(819\) | 11.2004 | + | 5.00284i | 0.391374 | + | 0.174813i | ||||
\(820\) | −0.157559 | −0.00550219 | ||||||||
\(821\) | 10.0098i | 0.349345i | 0.984627 | + | 0.174672i | \(0.0558866\pi\) | ||||
−0.984627 | + | 0.174672i | \(0.944113\pi\) | |||||||
\(822\) | −14.9303 | −0.520755 | ||||||||
\(823\) | −27.5363 | −0.959857 | −0.479928 | − | 0.877308i | \(-0.659337\pi\) | ||||
−0.479928 | + | 0.877308i | \(0.659337\pi\) | |||||||
\(824\) | 22.7792i | 0.793551i | ||||||||
\(825\) | − | 35.4217i | − | 1.23322i | ||||||
\(826\) | − | 6.34533i | − | 0.220782i | ||||||
\(827\) | 6.20407i | 0.215737i | 0.994165 | + | 0.107868i | \(0.0344025\pi\) | ||||
−0.994165 | + | 0.107868i | \(0.965598\pi\) | |||||||
\(828\) | 14.6716 | 0.509873 | ||||||||
\(829\) | 47.6602 | 1.65531 | 0.827654 | − | 0.561239i | \(-0.189675\pi\) | ||||
0.827654 | + | 0.561239i | \(0.189675\pi\) | |||||||
\(830\) | 33.6889i | 1.16936i | ||||||||
\(831\) | −20.6036 | −0.714729 | ||||||||
\(832\) | 10.5446 | − | 23.6074i | 0.365569 | − | 0.818438i | ||||
\(833\) | 18.1067 | 0.627359 | ||||||||
\(834\) | 9.44686i | 0.327118i | ||||||||
\(835\) | 19.4436 | 0.672873 | ||||||||
\(836\) | 10.9892 | 0.380068 | ||||||||
\(837\) | − | 5.14604i | − | 0.177873i | ||||||
\(838\) | 25.1184i | 0.867701i | ||||||||
\(839\) | 49.1966i | 1.69846i | 0.528026 | + | 0.849228i | \(0.322932\pi\) | ||||
−0.528026 | + | 0.849228i | \(0.677068\pi\) | |||||||
\(840\) | 18.4492i | 0.636557i | ||||||||
\(841\) | −24.0143 | −0.828079 | ||||||||
\(842\) | −0.194291 | −0.00669571 | ||||||||
\(843\) | 9.93011i | 0.342011i | ||||||||
\(844\) | 12.2063 | 0.420157 | ||||||||
\(845\) | 31.4112 | − | 28.1466i | 1.08058 | − | 0.968274i | ||||
\(846\) | −7.68007 | −0.264046 | ||||||||
\(847\) | − | 46.9964i | − | 1.61481i | ||||||
\(848\) | −0.646981 | −0.0222174 | ||||||||
\(849\) | −11.7391 | −0.402885 | ||||||||
\(850\) | − | 26.8325i | − | 0.920349i | ||||||
\(851\) | − | 68.6763i | − | 2.35419i | ||||||
\(852\) | − | 10.6237i | − | 0.363964i | ||||||
\(853\) | 38.1893i | 1.30758i | 0.756677 | + | 0.653789i | \(0.226821\pi\) | ||||
−0.756677 | + | 0.653789i | \(0.773179\pi\) | |||||||
\(854\) | −22.1059 | −0.756450 | ||||||||
\(855\) | 11.3641 | 0.388644 | ||||||||
\(856\) | 29.7690i | 1.01749i | ||||||||
\(857\) | −18.2224 | −0.622466 | −0.311233 | − | 0.950334i | \(-0.600742\pi\) | ||||
−0.311233 | + | 0.950334i | \(0.600742\pi\) | |||||||
\(858\) | 9.54295 | − | 21.3648i | 0.325791 | − | 0.729383i | ||||
\(859\) | 22.2461 | 0.759028 | 0.379514 | − | 0.925186i | \(-0.376091\pi\) | ||||
0.379514 | + | 0.925186i | \(0.376091\pi\) | |||||||
\(860\) | 15.0745i | 0.514037i | ||||||||
\(861\) | 0.0940418 | 0.00320494 | ||||||||
\(862\) | 15.2508 | 0.519444 | ||||||||
\(863\) | − | 9.63571i | − | 0.328003i | −0.986460 | − | 0.164002i | \(-0.947560\pi\) | ||
0.986460 | − | 0.164002i | \(-0.0524402\pi\) | |||||||
\(864\) | 25.2707i | 0.859727i | ||||||||
\(865\) | 0.0615656i | 0.00209329i | ||||||||
\(866\) | 13.0165i | 0.442319i | ||||||||
\(867\) | −6.30972 | −0.214289 | ||||||||
\(868\) | 1.75074 | 0.0594240 | ||||||||
\(869\) | − | 98.6541i | − | 3.34661i | ||||||
\(870\) | −7.71118 | −0.261434 | ||||||||
\(871\) | 5.66549 | + | 2.53058i | 0.191968 | + | 0.0857455i | ||||
\(872\) | 17.9884 | 0.609163 | ||||||||
\(873\) | − | 19.2770i | − | 0.652426i | ||||||
\(874\) | 14.8669 | 0.502881 | ||||||||
\(875\) | 3.06454 | 0.103600 | ||||||||
\(876\) | − | 2.34006i | − | 0.0790634i | ||||||
\(877\) | 29.0418i | 0.980672i | 0.871534 | + | 0.490336i | \(0.163126\pi\) | ||||
−0.871534 | + | 0.490336i | \(0.836874\pi\) | |||||||
\(878\) | − | 0.568656i | − | 0.0191912i | ||||||
\(879\) | 20.3875i | 0.687652i | ||||||||
\(880\) | −21.7500 | −0.733192 | ||||||||
\(881\) | 24.1421 | 0.813368 | 0.406684 | − | 0.913569i | \(-0.366685\pi\) | ||||
0.406684 | + | 0.913569i | \(0.366685\pi\) | |||||||
\(882\) | − | 7.24200i | − | 0.243851i | ||||||
\(883\) | 6.46930 | 0.217709 | 0.108855 | − | 0.994058i | \(-0.465282\pi\) | ||||
0.108855 | + | 0.994058i | \(0.465282\pi\) | |||||||
\(884\) | −6.87564 | + | 15.3932i | −0.231253 | + | 0.517730i | ||||
\(885\) | 11.9050 | 0.400181 | ||||||||
\(886\) | − | 10.1810i | − | 0.342036i | ||||||
\(887\) | −14.4837 | −0.486315 | −0.243158 | − | 0.969987i | \(-0.578183\pi\) | ||||
−0.243158 | + | 0.969987i | \(0.578183\pi\) | |||||||
\(888\) | 27.3806 | 0.918832 | ||||||||
\(889\) | 3.16664i | 0.106206i | ||||||||
\(890\) | 26.2753i | 0.880750i | ||||||||
\(891\) | − | 1.66763i | − | 0.0558679i | ||||||
\(892\) | 13.1405i | 0.439978i | ||||||||
\(893\) | 7.40196 | 0.247697 | ||||||||
\(894\) | 0.954269 | 0.0319155 | ||||||||
\(895\) | 18.3864i | 0.614590i | ||||||||
\(896\) | −4.59916 | −0.153647 | ||||||||
\(897\) | −12.2794 | + | 27.4911i | −0.409996 | + | 0.917902i | ||||
\(898\) | 15.6864 | 0.523463 | ||||||||
\(899\) | 2.23287i | 0.0744704i | ||||||||
\(900\) | 10.2075 | 0.340250 | ||||||||
\(901\) | 2.82193 | 0.0940120 | ||||||||
\(902\) | 0.307471i | 0.0102377i | ||||||||
\(903\) | − | 8.99751i | − | 0.299418i | ||||||
\(904\) | 17.5808i | 0.584728i | ||||||||
\(905\) | − | 50.4228i | − | 1.67611i | ||||||
\(906\) | 0.235604 | 0.00782740 | ||||||||
\(907\) | 33.0392 | 1.09705 | 0.548525 | − | 0.836134i | \(-0.315190\pi\) | ||||
0.548525 | + | 0.836134i | \(0.315190\pi\) | |||||||
\(908\) | − | 21.2039i | − | 0.703675i | ||||||
\(909\) | 19.6674 | 0.652326 | ||||||||
\(910\) | 19.4184 | + | 8.67354i | 0.643713 | + | 0.287525i | ||||
\(911\) | −42.4959 | −1.40795 | −0.703975 | − | 0.710225i | \(-0.748593\pi\) | ||||
−0.703975 | + | 0.710225i | \(0.748593\pi\) | |||||||
\(912\) | 2.13725i | 0.0707714i | ||||||||
\(913\) | −62.5297 | −2.06943 | ||||||||
\(914\) | −22.8016 | −0.754211 | ||||||||
\(915\) | − | 41.4747i | − | 1.37111i | ||||||
\(916\) | 4.70052i | 0.155310i | ||||||||
\(917\) | 28.3717i | 0.936916i | ||||||||
\(918\) | 24.9875i | 0.824712i | ||||||||
\(919\) | 5.17140 | 0.170589 | 0.0852944 | − | 0.996356i | \(-0.472817\pi\) | ||||
0.0852944 | + | 0.996356i | \(0.472817\pi\) | |||||||
\(920\) | 77.6164 | 2.55894 | ||||||||
\(921\) | − | 3.13141i | − | 0.103184i | ||||||
\(922\) | −12.1204 | −0.399164 | ||||||||
\(923\) | −34.1202 | − | 15.2403i | −1.12308 | − | 0.501642i | ||||
\(924\) | −11.2222 | −0.369184 | ||||||||
\(925\) | − | 47.7803i | − | 1.57101i | ||||||
\(926\) | 43.0236 | 1.41384 | ||||||||
\(927\) | −14.3288 | −0.470621 | ||||||||
\(928\) | − | 10.9650i | − | 0.359942i | ||||||
\(929\) | 4.37621i | 0.143579i | 0.997420 | + | 0.0717894i | \(0.0228709\pi\) | ||||
−0.997420 | + | 0.0717894i | \(0.977129\pi\) | |||||||
\(930\) | − | 3.45349i | − | 0.113244i | ||||||
\(931\) | 6.97975i | 0.228752i | ||||||||
\(932\) | −28.3909 | −0.929974 | ||||||||
\(933\) | 15.9964 | 0.523698 | ||||||||
\(934\) | 35.7091i | 1.16844i | ||||||||
\(935\) | 94.8666 | 3.10247 | ||||||||
\(936\) | 18.7865 | + | 8.39131i | 0.614057 | + | 0.274279i | ||||
\(937\) | 2.77193 | 0.0905550 | 0.0452775 | − | 0.998974i | \(-0.485583\pi\) | ||||
0.0452775 | + | 0.998974i | \(0.485583\pi\) | |||||||
\(938\) | 3.12881i | 0.102159i | ||||||||
\(939\) | 7.19080 | 0.234663 | ||||||||
\(940\) | 12.6643 | 0.413065 | ||||||||
\(941\) | 36.3782i | 1.18589i | 0.805241 | + | 0.592947i | \(0.202036\pi\) | ||||
−0.805241 | + | 0.592947i | \(0.797964\pi\) | |||||||
\(942\) | − | 9.07089i | − | 0.295545i | ||||||
\(943\) | − | 0.395638i | − | 0.0128837i | ||||||
\(944\) | − | 3.83765i | − | 0.124905i | ||||||
\(945\) | −29.9809 | −0.975278 | ||||||||
\(946\) | 29.4175 | 0.956446 | ||||||||
\(947\) | 28.0675i | 0.912071i | 0.889962 | + | 0.456035i | \(0.150731\pi\) | ||||
−0.889962 | + | 0.456035i | \(0.849269\pi\) | |||||||
\(948\) | −16.5862 | −0.538695 | ||||||||
\(949\) | −7.51555 | − | 3.35694i | −0.243965 | − | 0.108971i | ||||
\(950\) | 10.3434 | 0.335584 | ||||||||
\(951\) | − | 18.2404i | − | 0.591485i | ||||||
\(952\) | −25.9399 | −0.840718 | ||||||||
\(953\) | 47.1931 | 1.52874 | 0.764368 | − | 0.644781i | \(-0.223051\pi\) | ||||
0.764368 | + | 0.644781i | \(0.223051\pi\) | |||||||
\(954\) | − | 1.12867i | − | 0.0365419i | ||||||
\(955\) | − | 23.9703i | − | 0.775662i | ||||||
\(956\) | 26.5016i | 0.857124i | ||||||||
\(957\) | − | 14.3127i | − | 0.462663i | ||||||
\(958\) | −17.2368 | −0.556896 | ||||||||
\(959\) | 25.1873 | 0.813342 | ||||||||
\(960\) | 24.4604i | 0.789456i | ||||||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | 12.8725 | − | 28.8190i | 0.415026 | − | 0.929163i | ||||
\(963\) | −18.7257 | −0.603427 | ||||||||
\(964\) | 21.0825i | 0.679022i | ||||||||
\(965\) | 13.6976 | 0.440941 | ||||||||
\(966\) | −15.1822 | −0.488479 | ||||||||
\(967\) | − | 19.0739i | − | 0.613375i | −0.951810 | − | 0.306688i | \(-0.900779\pi\) | ||
0.951810 | − | 0.306688i | \(-0.0992207\pi\) | |||||||
\(968\) | − | 78.8275i | − | 2.53361i | ||||||
\(969\) | − | 9.32201i | − | 0.299466i | ||||||
\(970\) | − | 33.4209i | − | 1.07308i | ||||||
\(971\) | 56.9080 | 1.82626 | 0.913132 | − | 0.407664i | \(-0.133656\pi\) | ||||
0.913132 | + | 0.407664i | \(0.133656\pi\) | |||||||
\(972\) | −15.3318 | −0.491767 | ||||||||
\(973\) | − | 15.9368i | − | 0.510909i | ||||||
\(974\) | −3.56937 | −0.114370 | ||||||||
\(975\) | −8.54315 | + | 19.1265i | −0.273600 | + | 0.612537i | ||||
\(976\) | −13.3697 | −0.427953 | ||||||||
\(977\) | 34.4785i | 1.10307i | 0.834153 | + | 0.551533i | \(0.185957\pi\) | ||||
−0.834153 | + | 0.551533i | \(0.814043\pi\) | |||||||
\(978\) | −0.505601 | −0.0161673 | ||||||||
\(979\) | −48.7694 | −1.55868 | ||||||||
\(980\) | 11.9420i | 0.381472i | ||||||||
\(981\) | 11.3153i | 0.361268i | ||||||||
\(982\) | − | 30.3335i | − | 0.967981i | ||||||
\(983\) | − | 33.5510i | − | 1.07011i | −0.844817 | − | 0.535056i | \(-0.820291\pi\) | ||
0.844817 | − | 0.535056i | \(-0.179709\pi\) | |||||||
\(984\) | 0.157737 | 0.00502848 | ||||||||
\(985\) | −23.1629 | −0.738031 | ||||||||
\(986\) | − | 10.8421i | − | 0.345283i | ||||||
\(987\) | −7.55893 | −0.240604 | ||||||||
\(988\) | −5.93377 | − | 2.65041i | −0.188778 | − | 0.0843209i | ||||
\(989\) | −37.8529 | −1.20365 | ||||||||
\(990\) | − | 37.9431i | − | 1.20591i | ||||||
\(991\) | 0.204273 | 0.00648894 | 0.00324447 | − | 0.999995i | \(-0.498967\pi\) | ||||
0.00324447 | + | 0.999995i | \(0.498967\pi\) | |||||||
\(992\) | 4.91070 | 0.155915 | ||||||||
\(993\) | − | 6.12063i | − | 0.194232i | ||||||
\(994\) | − | 18.8431i | − | 0.597668i | ||||||
\(995\) | − | 56.8847i | − | 1.80337i | ||||||
\(996\) | 10.5128i | 0.333111i | ||||||||
\(997\) | −36.7937 | −1.16527 | −0.582634 | − | 0.812735i | \(-0.697978\pi\) | ||||
−0.582634 | + | 0.812735i | \(0.697978\pi\) | |||||||
\(998\) | 9.86411 | 0.312243 | ||||||||
\(999\) | 44.4949i | 1.40776i |
(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 | 403.2.c.b.311.21 | yes | 32 | |
13.5 | odd | 4 | 5239.2.a.l.1.10 | 16 | |||
13.8 | odd | 4 | 5239.2.a.k.1.7 | 16 | |||
13.12 | even | 2 | inner | 403.2.c.b.311.12 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.c.b.311.12 | ✓ | 32 | 13.12 | even | 2 | inner | |
403.2.c.b.311.21 | yes | 32 | 1.1 | even | 1 | trivial | |
5239.2.a.k.1.7 | 16 | 13.8 | odd | 4 | |||
5239.2.a.l.1.10 | 16 | 13.5 | odd | 4 |