Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,2,Mod(8,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(36))
chi = DirichletCharacter(H, H._module([2, 27]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.r (of order \(36\), degree \(12\), 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: | \(3.23394128186\) |
Analytic rank: | \(0\) |
Dimension: | \(192\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{36})\) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{36}]$ |
Embedding invariants
Embedding label | 368.12 | ||
Character | \(\chi\) | \(=\) | 405.368 |
Dual form | 405.2.r.a.197.12 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{5}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36666 | + | 0.119567i | 0.966373 | + | 0.0845467i | 0.559404 | − | 0.828895i | \(-0.311030\pi\) |
0.406969 | + | 0.913442i | \(0.366586\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.116159 | − | 0.0204819i | −0.0580794 | − | 0.0102410i | ||||
\(5\) | 0.119339 | − | 2.23288i | 0.0533699 | − | 0.998575i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.68447 | − | 1.87969i | −1.01463 | − | 0.710455i | −0.0569801 | − | 0.998375i | \(-0.518147\pi\) |
−0.957654 | + | 0.287921i | \(0.907036\pi\) | |||||||
\(8\) | −2.80657 | − | 0.752017i | −0.992271 | − | 0.265878i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.430074 | − | 3.03731i | 0.136001 | − | 0.960483i | ||||
\(11\) | 1.85785 | − | 5.10439i | 0.560161 | − | 1.53903i | −0.259241 | − | 0.965813i | \(-0.583473\pi\) |
0.819403 | − | 0.573218i | \(-0.194305\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.215209 | + | 2.45985i | 0.0596882 | + | 0.682239i | 0.965815 | + | 0.259233i | \(0.0834697\pi\) |
−0.906127 | + | 0.423006i | \(0.860975\pi\) | |||||||
\(14\) | −3.44400 | − | 2.88986i | −0.920449 | − | 0.772348i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.52402 | − | 1.28264i | −0.881006 | − | 0.320660i | ||||
\(17\) | 3.45292 | − | 0.925208i | 0.837457 | − | 0.224396i | 0.185493 | − | 0.982646i | \(-0.440612\pi\) |
0.651964 | + | 0.758250i | \(0.273945\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.417150 | − | 0.240842i | 0.0957007 | − | 0.0552529i | −0.451386 | − | 0.892329i | \(-0.649070\pi\) |
0.547087 | + | 0.837076i | \(0.315737\pi\) | |||||||
\(20\) | −0.0595960 | + | 0.256925i | −0.0133261 | + | 0.0574501i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.14935 | − | 6.75381i | 0.671445 | − | 1.43992i | ||||
\(23\) | 4.01261 | + | 5.73060i | 0.836687 | + | 1.19491i | 0.978750 | + | 0.205055i | \(0.0657375\pi\) |
−0.142063 | + | 0.989858i | \(0.545374\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.97152 | − | 0.532938i | −0.994303 | − | 0.106588i | ||||
\(26\) | 3.38750i | 0.664344i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.273325 | + | 0.273325i | 0.0516536 | + | 0.0516536i | ||||
\(29\) | −0.0993465 | + | 0.0833616i | −0.0184482 | + | 0.0154799i | −0.651965 | − | 0.758249i | \(-0.726055\pi\) |
0.633517 | + | 0.773729i | \(0.281611\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.509526 | − | 2.88966i | 0.0915135 | − | 0.518999i | −0.904247 | − | 0.427011i | \(-0.859567\pi\) |
0.995760 | − | 0.0919882i | \(-0.0293222\pi\) | |||||||
\(32\) | 0.603911 | + | 0.281608i | 0.106757 | + | 0.0497818i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.82959 | − | 0.851587i | 0.828268 | − | 0.146046i | ||||
\(35\) | −4.51748 | + | 5.76978i | −0.763593 | + | 0.975271i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.67943 | + | 6.26774i | 0.276097 | + | 1.03041i | 0.955102 | + | 0.296276i | \(0.0957448\pi\) |
−0.679005 | + | 0.734134i | \(0.737589\pi\) | |||||||
\(38\) | 0.598898 | − | 0.279271i | 0.0971540 | − | 0.0453037i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.01410 | + | 6.17698i | −0.318457 | + | 0.976667i | ||||
\(41\) | −0.215101 | + | 0.256347i | −0.0335931 | + | 0.0400346i | −0.782579 | − | 0.622551i | \(-0.786096\pi\) |
0.748986 | + | 0.662585i | \(0.230541\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.45933 | − | 5.27405i | −0.375044 | − | 0.804285i | −0.999726 | − | 0.0234058i | \(-0.992549\pi\) |
0.624682 | − | 0.780880i | \(-0.285229\pi\) | |||||||
\(44\) | −0.320353 | + | 0.554867i | −0.0482950 | + | 0.0836494i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.79867 | + | 8.31155i | 0.707526 | + | 1.22547i | ||||
\(47\) | 6.80358 | − | 9.71652i | 0.992405 | − | 1.41730i | 0.0853195 | − | 0.996354i | \(-0.472809\pi\) |
0.907085 | − | 0.420947i | \(-0.138302\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.27902 | + | 3.51408i | 0.182717 | + | 0.502011i | ||||
\(50\) | −6.73064 | − | 1.32277i | −0.951856 | − | 0.187068i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.0253840 | − | 0.290141i | 0.00352013 | − | 0.0402353i | ||||
\(53\) | 0.167838 | − | 0.167838i | 0.0230543 | − | 0.0230543i | −0.695486 | − | 0.718540i | \(-0.744811\pi\) |
0.718540 | + | 0.695486i | \(0.244811\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.1758 | − | 4.75750i | −1.50694 | − | 0.641501i | ||||
\(56\) | 6.12058 | + | 7.29423i | 0.817898 | + | 0.974732i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.145740 | + | 0.102048i | −0.0191366 | + | 0.0133996i | ||||
\(59\) | 3.62976 | − | 1.32113i | 0.472555 | − | 0.171996i | −0.0947544 | − | 0.995501i | \(-0.530207\pi\) |
0.567309 | + | 0.823505i | \(0.307984\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.855508 | − | 4.85182i | −0.109537 | − | 0.621212i | −0.989311 | − | 0.145821i | \(-0.953418\pi\) |
0.879774 | − | 0.475391i | \(-0.157694\pi\) | |||||||
\(62\) | 1.04186 | − | 3.88826i | 0.132316 | − | 0.493809i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.28718 | + | 4.20726i | 0.910898 | + | 0.525907i | ||||
\(65\) | 5.51823 | − | 0.186981i | 0.684452 | − | 0.0231921i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.25953 | − | 0.372661i | 0.520385 | − | 0.0455277i | 0.176062 | − | 0.984379i | \(-0.443664\pi\) |
0.344323 | + | 0.938851i | \(0.388109\pi\) | |||||||
\(68\) | −0.420038 | + | 0.0367485i | −0.0509370 | + | 0.00445641i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.86372 | + | 7.34518i | −0.820372 | + | 0.877917i | ||||
\(71\) | −7.10207 | − | 4.10038i | −0.842861 | − | 0.486626i | 0.0153747 | − | 0.999882i | \(-0.495106\pi\) |
−0.858236 | + | 0.513256i | \(0.828439\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.51625 | + | 13.1228i | −0.411546 | + | 1.53591i | 0.380108 | + | 0.924942i | \(0.375887\pi\) |
−0.791654 | + | 0.610969i | \(0.790780\pi\) | |||||||
\(74\) | 1.54580 | + | 8.76665i | 0.179695 | + | 1.01910i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.0533886 | + | 0.0194318i | −0.00612409 | + | 0.00222899i | ||||
\(77\) | −14.5820 | + | 10.2104i | −1.66177 | + | 1.16358i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.44655 | + | 7.68270i | 0.725293 | + | 0.864371i | 0.995134 | − | 0.0985341i | \(-0.0314153\pi\) |
−0.269840 | + | 0.962905i | \(0.586971\pi\) | |||||||
\(80\) | −3.28453 | + | 7.71565i | −0.367222 | + | 0.862636i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.324619 | + | 0.324619i | −0.0358482 | + | 0.0358482i | ||||
\(83\) | −0.00128626 | + | 0.0147020i | −0.000141185 | + | 0.00161375i | −0.996265 | − | 0.0863488i | \(-0.972480\pi\) |
0.996124 | + | 0.0879626i | \(0.0280356\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.65381 | − | 7.82038i | −0.179381 | − | 0.848239i | ||||
\(86\) | −2.73046 | − | 7.50188i | −0.294433 | − | 0.808948i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.05275 | + | 12.9287i | −0.965026 | + | 1.37820i | ||||
\(89\) | 2.55837 | + | 4.43123i | 0.271187 | + | 0.469709i | 0.969166 | − | 0.246409i | \(-0.0792506\pi\) |
−0.697979 | + | 0.716118i | \(0.745917\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.04602 | − | 7.00791i | 0.424138 | − | 0.734629i | ||||
\(92\) | −0.348726 | − | 0.747846i | −0.0363572 | − | 0.0779683i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.4599 | − | 12.4657i | 1.07886 | − | 1.28574i | ||||
\(95\) | −0.487989 | − | 0.960188i | −0.0500666 | − | 0.0985132i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.77015 | − | 1.75805i | 0.382800 | − | 0.178503i | −0.221686 | − | 0.975118i | \(-0.571156\pi\) |
0.604487 | + | 0.796615i | \(0.293378\pi\) | |||||||
\(98\) | 1.32781 | + | 4.95547i | 0.134129 | + | 0.500578i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.566570 | + | 0.163732i | 0.0566570 | + | 0.0163732i | ||||
\(101\) | −7.79700 | + | 1.37482i | −0.775831 | + | 0.136800i | −0.547525 | − | 0.836789i | \(-0.684430\pi\) |
−0.228306 | + | 0.973589i | \(0.573319\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.88597 | + | 2.27837i | 0.481429 | + | 0.224494i | 0.648154 | − | 0.761509i | \(-0.275541\pi\) |
−0.166725 | + | 0.986004i | \(0.553319\pi\) | |||||||
\(104\) | 1.24585 | − | 7.06556i | 0.122166 | − | 0.692836i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.249444 | − | 0.209309i | 0.0242282 | − | 0.0203299i | ||||
\(107\) | 6.45665 | + | 6.45665i | 0.624188 | + | 0.624188i | 0.946600 | − | 0.322412i | \(-0.104494\pi\) |
−0.322412 | + | 0.946600i | \(0.604494\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.2697i | − | 0.983654i | −0.870693 | − | 0.491827i | \(-0.836329\pi\) | ||
0.870693 | − | 0.491827i | \(-0.163671\pi\) | |||||||
\(110\) | −14.7046 | − | 7.83813i | −1.40203 | − | 0.747336i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.04917 | + | 10.0673i | 0.666084 | + | 0.951267i | ||||
\(113\) | 4.39670 | − | 9.42875i | 0.413607 | − | 0.886982i | −0.583582 | − | 0.812054i | \(-0.698349\pi\) |
0.997189 | − | 0.0749283i | \(-0.0238728\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.2746 | − | 8.27580i | 1.23786 | − | 0.771722i | ||||
\(116\) | 0.0132474 | − | 0.00764838i | 0.00122999 | − | 0.000710134i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.11861 | − | 1.37153i | 0.471206 | − | 0.126259i | ||||
\(119\) | −11.0084 | − | 4.00672i | −1.00914 | − | 0.367295i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.1767 | − | 11.8957i | −1.28879 | − | 1.08142i | ||||
\(122\) | −0.589068 | − | 6.73307i | −0.0533317 | − | 0.609584i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.118372 | + | 0.325224i | −0.0106301 | + | 0.0292060i | ||||
\(125\) | −1.78328 | + | 11.0372i | −0.159502 | + | 0.987198i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.6633 | + | 3.39311i | 1.12368 | + | 0.301090i | 0.772373 | − | 0.635169i | \(-0.219069\pi\) |
0.351311 | + | 0.936259i | \(0.385736\pi\) | |||||||
\(128\) | 8.36436 | + | 5.85679i | 0.739312 | + | 0.517672i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.56389 | + | 0.404260i | 0.663397 | + | 0.0354559i | ||||
\(131\) | 3.19816 | + | 0.563922i | 0.279425 | + | 0.0492701i | 0.311604 | − | 0.950212i | \(-0.399134\pi\) |
−0.0321796 | + | 0.999482i | \(0.510245\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.57253 | − | 0.137579i | −0.136356 | − | 0.0119296i | ||||
\(134\) | 5.86588 | 0.506735 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10.3866 | −0.890646 | ||||||||
\(137\) | 4.68732 | + | 0.410087i | 0.400465 | + | 0.0350361i | 0.285609 | − | 0.958346i | \(-0.407804\pi\) |
0.114855 | + | 0.993382i | \(0.463360\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.3538 | − | 2.00197i | −0.963013 | − | 0.169805i | −0.330030 | − | 0.943971i | \(-0.607059\pi\) |
−0.632983 | + | 0.774165i | \(0.718170\pi\) | |||||||
\(140\) | 0.642921 | − | 0.577685i | 0.0543368 | − | 0.0488233i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.21583 | − | 6.45299i | −0.773375 | − | 0.541523i | ||||
\(143\) | 12.9558 | + | 3.47151i | 1.08342 | + | 0.290302i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.174281 | + | 0.231777i | 0.0144732 | + | 0.0192480i | ||||
\(146\) | −6.37457 | + | 17.5140i | −0.527563 | + | 1.44947i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.0667058 | − | 0.762451i | −0.00548319 | − | 0.0626731i | ||||
\(149\) | −8.56384 | − | 7.18592i | −0.701577 | − | 0.588693i | 0.220645 | − | 0.975354i | \(-0.429184\pi\) |
−0.922222 | + | 0.386661i | \(0.873628\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.0074 | + | 4.00638i | 0.895773 | + | 0.326035i | 0.748558 | − | 0.663070i | \(-0.230747\pi\) |
0.147215 | + | 0.989104i | \(0.452969\pi\) | |||||||
\(152\) | −1.35188 | + | 0.362234i | −0.109652 | + | 0.0293810i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −21.1494 | + | 12.2106i | −1.70427 | + | 0.983959i | ||||
\(155\) | −6.39147 | − | 1.48256i | −0.513375 | − | 0.119082i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.59634 | + | 18.4349i | −0.686062 | + | 1.47127i | 0.186344 | + | 0.982485i | \(0.440336\pi\) |
−0.872407 | + | 0.488781i | \(0.837442\pi\) | |||||||
\(158\) | 7.89163 | + | 11.2704i | 0.627824 | + | 0.896626i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.700868 | − | 1.31486i | 0.0554085 | − | 0.103948i | ||||
\(161\) | − | 22.9261i | − | 1.80683i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.89303 | − | 6.89303i | −0.539904 | − | 0.539904i | 0.383597 | − | 0.923501i | \(-0.374685\pi\) |
−0.923501 | + | 0.383597i | \(0.874685\pi\) | |||||||
\(164\) | 0.0302363 | − | 0.0253713i | 0.00236106 | − | 0.00198116i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.00351574 | + | 0.0199388i | −0.000272875 | + | 0.00154755i | ||||
\(167\) | 7.25712 | + | 3.38405i | 0.561573 | + | 0.261866i | 0.682611 | − | 0.730782i | \(-0.260844\pi\) |
−0.121038 | + | 0.992648i | \(0.538622\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.79796 | − | 1.19866i | 0.522920 | − | 0.0922049i | ||||
\(170\) | −1.32514 | − | 10.8855i | −0.101633 | − | 0.834882i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.177650 | + | 0.663000i | 0.0135457 | + | 0.0505532i | ||||
\(173\) | −13.8817 | + | 6.47315i | −1.05541 | + | 0.492145i | −0.871295 | − | 0.490760i | \(-0.836719\pi\) |
−0.184113 | + | 0.982905i | \(0.558941\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.3441 | + | 10.7755i | 0.933129 | + | 0.814555i | ||||
\(176\) | −13.0942 | + | 15.6050i | −0.987011 | + | 1.17627i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.96659 | + | 6.36186i | 0.222355 | + | 0.476842i | ||||
\(179\) | 10.5577 | − | 18.2866i | 0.789123 | − | 1.36680i | −0.137382 | − | 0.990518i | \(-0.543869\pi\) |
0.926505 | − | 0.376283i | \(-0.122798\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.12182 | + | 8.87125i | 0.380702 | + | 0.659395i | 0.991163 | − | 0.132651i | \(-0.0423491\pi\) |
−0.610461 | + | 0.792046i | \(0.709016\pi\) | |||||||
\(182\) | 6.36744 | − | 9.09365i | 0.471986 | − | 0.674066i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.95214 | − | 19.1009i | −0.512519 | − | 1.40813i | ||||
\(185\) | 14.1955 | − | 3.00200i | 1.04368 | − | 0.220711i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.69238 | − | 19.3440i | 0.123759 | − | 1.41457i | ||||
\(188\) | −0.989310 | + | 0.989310i | −0.0721528 | + | 0.0721528i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.552106 | − | 1.37060i | −0.0400540 | − | 0.0994334i | ||||
\(191\) | 3.94811 | + | 4.70518i | 0.285676 | + | 0.340455i | 0.889729 | − | 0.456489i | \(-0.150893\pi\) |
−0.604054 | + | 0.796944i | \(0.706449\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.19711 | − | 3.63906i | 0.374096 | − | 0.261945i | −0.371375 | − | 0.928483i | \(-0.621113\pi\) |
0.745471 | + | 0.666538i | \(0.232225\pi\) | |||||||
\(194\) | 5.36270 | − | 1.95186i | 0.385020 | − | 0.140136i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.0765943 | − | 0.434388i | −0.00547102 | − | 0.0310277i | ||||
\(197\) | 0.0881812 | − | 0.329097i | 0.00628265 | − | 0.0234472i | −0.962713 | − | 0.270524i | \(-0.912803\pi\) |
0.968996 | + | 0.247076i | \(0.0794699\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.6952 | − | 10.2163i | −1.25438 | − | 0.724216i | −0.282404 | − | 0.959296i | \(-0.591132\pi\) |
−0.971976 | + | 0.235079i | \(0.924465\pi\) | |||||||
\(200\) | 13.5521 | + | 5.23439i | 0.958279 | + | 0.370127i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.8202 | + | 0.946646i | −0.761308 | + | 0.0666058i | ||||
\(203\) | 0.423386 | − | 0.0370415i | 0.0297159 | − | 0.00259980i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.546722 | + | 0.510886i | 0.0381847 | + | 0.0356818i | ||||
\(206\) | 6.40504 | + | 3.69795i | 0.446260 | + | 0.257648i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.39670 | − | 8.94459i | 0.166181 | − | 0.620196i | ||||
\(209\) | −0.454349 | − | 2.57674i | −0.0314280 | − | 0.178237i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.48650 | + | 1.99692i | −0.377706 | + | 0.137474i | −0.523895 | − | 0.851783i | \(-0.675522\pi\) |
0.146189 | + | 0.989257i | \(0.453299\pi\) | |||||||
\(212\) | −0.0229335 | + | 0.0160582i | −0.00157508 | + | 0.00110288i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.05203 | + | 9.59603i | 0.550425 | + | 0.655971i | ||||
\(215\) | −12.0698 | + | 4.86199i | −0.823155 | + | 0.331585i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.79947 | + | 6.79947i | −0.461578 | + | 0.461578i | ||||
\(218\) | 1.22791 | − | 14.0351i | 0.0831647 | − | 0.950577i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.20072 | + | 0.781527i | 0.0809527 | + | 0.0526905i | ||||
\(221\) | 3.01897 | + | 8.29455i | 0.203078 | + | 0.557952i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.2233 | + | 16.0285i | −0.751567 | + | 1.07335i | 0.243079 | + | 0.970006i | \(0.421843\pi\) |
−0.994646 | + | 0.103342i | \(0.967046\pi\) | |||||||
\(224\) | −1.09185 | − | 1.89113i | −0.0729521 | − | 0.126357i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.13615 | − | 12.3602i | 0.474690 | − | 0.822187i | ||||
\(227\) | −4.22532 | − | 9.06123i | −0.280444 | − | 0.601415i | 0.714745 | − | 0.699385i | \(-0.246543\pi\) |
−0.995189 | + | 0.0979701i | \(0.968765\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.12582 | + | 9.68397i | −0.536969 | + | 0.639935i | −0.964505 | − | 0.264063i | \(-0.914937\pi\) |
0.427536 | + | 0.903998i | \(0.359382\pi\) | |||||||
\(230\) | 19.1314 | − | 9.72298i | 1.26148 | − | 0.641114i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.341512 | − | 0.159249i | 0.0224213 | − | 0.0104552i | ||||
\(233\) | −0.393034 | − | 1.46682i | −0.0257485 | − | 0.0960947i | 0.951856 | − | 0.306546i | \(-0.0991733\pi\) |
−0.977604 | + | 0.210451i | \(0.932507\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.8839 | − | 16.3512i | −1.36232 | − | 1.06663i | ||||
\(236\) | −0.448688 | + | 0.0791159i | −0.0292071 | + | 0.00515000i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −14.5656 | − | 6.79205i | −0.944148 | − | 0.440263i | ||||
\(239\) | 3.47433 | − | 19.7039i | 0.224735 | − | 1.27454i | −0.638455 | − | 0.769659i | \(-0.720426\pi\) |
0.863190 | − | 0.504879i | \(-0.168463\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.08193 | + | 6.78155i | −0.520603 | + | 0.436838i | −0.864842 | − | 0.502044i | \(-0.832581\pi\) |
0.344239 | + | 0.938882i | \(0.388137\pi\) | |||||||
\(242\) | −17.9524 | − | 17.9524i | −1.15402 | − | 1.15402i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.581105i | 0.0372014i | ||||||||
\(245\) | 7.99915 | − | 2.43653i | 0.511047 | − | 0.155664i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.682208 | + | 0.974294i | 0.0434079 | + | 0.0619929i | ||||
\(248\) | −3.60309 | + | 7.72686i | −0.228797 | + | 0.490656i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.75682 | + | 14.8709i | −0.237602 | + | 0.940516i | ||||
\(251\) | 8.94339 | − | 5.16347i | 0.564502 | − | 0.325915i | −0.190449 | − | 0.981697i | \(-0.560994\pi\) |
0.754950 | + | 0.655782i | \(0.227661\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 36.7060 | − | 9.83535i | 2.30769 | − | 0.618343i | ||||
\(254\) | 16.9007 | + | 6.15134i | 1.06044 | + | 0.385969i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.16084 | − | 1.81316i | −0.135053 | − | 0.113323i | ||||
\(257\) | 1.34587 | + | 15.3834i | 0.0839533 | + | 0.959591i | 0.915017 | + | 0.403414i | \(0.132177\pi\) |
−0.831064 | + | 0.556177i | \(0.812268\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.27299 | − | 19.9824i | 0.451921 | − | 1.24164i | ||||
\(260\) | −0.644821 | − | 0.0913046i | −0.0399901 | − | 0.00566247i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.30336 | + | 1.15308i | 0.265863 | + | 0.0712377i | ||||
\(263\) | −11.1530 | − | 7.80938i | −0.687721 | − | 0.481547i | 0.176734 | − | 0.984259i | \(-0.443447\pi\) |
−0.864454 | + | 0.502712i | \(0.832336\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.354732 | − | 0.394791i | −0.0217910 | − | 0.0242518i | ||||
\(266\) | −2.13266 | − | 0.376046i | −0.130762 | − | 0.0230569i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.502415 | − | 0.0439556i | −0.0306899 | − | 0.00268502i | ||||
\(269\) | 11.6016 | 0.707363 | 0.353681 | − | 0.935366i | \(-0.384930\pi\) | ||||
0.353681 | + | 0.935366i | \(0.384930\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.5393 | 0.640216 | 0.320108 | − | 0.947381i | \(-0.396281\pi\) | ||||
0.320108 | + | 0.947381i | \(0.396281\pi\) | |||||||
\(272\) | −13.3549 | − | 1.16840i | −0.809759 | − | 0.0708447i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.35693 | + | 1.12090i | 0.384036 | + | 0.0677159i | ||||
\(275\) | −11.9566 | + | 24.3864i | −0.721012 | + | 1.47056i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.5767 | + | 9.50648i | 0.815743 | + | 0.571189i | 0.905290 | − | 0.424793i | \(-0.139653\pi\) |
−0.0895477 | + | 0.995983i | \(0.528542\pi\) | |||||||
\(278\) | −15.2773 | − | 4.09355i | −0.916273 | − | 0.245515i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 17.0176 | − | 12.7961i | 1.01699 | − | 0.764711i | ||||
\(281\) | 4.02535 | − | 11.0596i | 0.240132 | − | 0.659758i | −0.759821 | − | 0.650132i | \(-0.774714\pi\) |
0.999954 | − | 0.00962623i | \(-0.00306417\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.637926 | + | 7.29153i | 0.0379208 | + | 0.433437i | 0.991296 | + | 0.131650i | \(0.0420275\pi\) |
−0.953375 | + | 0.301787i | \(0.902417\pi\) | |||||||
\(284\) | 0.740985 | + | 0.621760i | 0.0439694 | + | 0.0368947i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 17.2911 | + | 6.29345i | 1.02245 | + | 0.372140i | ||||
\(287\) | 1.05928 | − | 0.283834i | 0.0625275 | − | 0.0167542i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.65576 | + | 2.11066i | −0.215045 | + | 0.124156i | ||||
\(290\) | 0.210469 | + | 0.337598i | 0.0123592 | + | 0.0198244i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.677225 | − | 1.45231i | 0.0396316 | − | 0.0849902i | ||||
\(293\) | 4.56171 | + | 6.51480i | 0.266498 | + | 0.380599i | 0.929990 | − | 0.367585i | \(-0.119815\pi\) |
−0.663492 | + | 0.748183i | \(0.730926\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.51675 | − | 8.26249i | −0.146531 | − | 0.481061i | ||||
\(296\) | − | 18.8538i | − | 1.09585i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.8446 | − | 10.8446i | −0.628213 | − | 0.628213i | ||||
\(299\) | −13.2329 | + | 11.1037i | −0.765276 | + | 0.642143i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.31156 | + | 18.7808i | −0.190875 | + | 1.08251i | ||||
\(302\) | 14.5644 | + | 6.79148i | 0.838086 | + | 0.390806i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.77896 | + | 0.313678i | −0.102030 | + | 0.0179907i | ||||
\(305\) | −10.9356 | + | 1.33124i | −0.626173 | + | 0.0762264i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.43216 | − | 9.07696i | −0.138811 | − | 0.518049i | −0.999953 | − | 0.00968516i | \(-0.996917\pi\) |
0.861142 | − | 0.508364i | \(-0.169750\pi\) | |||||||
\(308\) | 1.90295 | − | 0.887362i | 0.108431 | − | 0.0505622i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.55768 | − | 2.79036i | −0.486044 | − | 0.158482i | ||||
\(311\) | 3.85633 | − | 4.59579i | 0.218672 | − | 0.260603i | −0.645545 | − | 0.763722i | \(-0.723370\pi\) |
0.864217 | + | 0.503119i | \(0.167814\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.90239 | − | 8.36871i | −0.220576 | − | 0.473027i | 0.764615 | − | 0.644488i | \(-0.222929\pi\) |
−0.985191 | + | 0.171460i | \(0.945151\pi\) | |||||||
\(314\) | −13.9525 | + | 24.1664i | −0.787383 | + | 1.36379i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.591467 | − | 1.02445i | −0.0332726 | − | 0.0576299i | ||||
\(317\) | −18.3856 | + | 26.2573i | −1.03264 | + | 1.47476i | −0.159551 | + | 0.987190i | \(0.551005\pi\) |
−0.873085 | + | 0.487568i | \(0.837884\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.240939 | + | 0.661976i | 0.0134900 | + | 0.0370635i | ||||
\(320\) | 10.2639 | − | 15.7693i | 0.573772 | − | 0.881532i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.74120 | − | 31.3321i | 0.152761 | − | 1.74607i | ||||
\(323\) | 1.21756 | − | 1.21756i | 0.0677467 | − | 0.0677467i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.241032 | − | 12.3439i | 0.0133701 | − | 0.684715i | ||||
\(326\) | −8.59623 | − | 10.2446i | −0.476101 | − | 0.567396i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.796471 | − | 0.557695i | 0.0439777 | − | 0.0307935i | ||||
\(329\) | −36.5280 | + | 13.2951i | −2.01386 | + | 0.732984i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.34763 | − | 30.3279i | −0.293932 | − | 1.66697i | −0.671511 | − | 0.740995i | \(-0.734354\pi\) |
0.377579 | − | 0.925977i | \(-0.376757\pi\) | |||||||
\(332\) | 0.000450535 | − | 0.00168142i | 2.47263e−5 | − | 9.22799e-5i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.51338 | + | 5.49255i | 0.520549 | + | 0.300539i | ||||
\(335\) | −0.323780 | − | 9.55550i | −0.0176900 | − | 0.522073i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.15374 | − | 0.275916i | 0.171795 | − | 0.0150301i | −0.000933572 | − | 1.00000i | \(-0.500297\pi\) |
0.172729 | + | 0.984969i | \(0.444742\pi\) | |||||||
\(338\) | 9.43381 | − | 0.825351i | 0.513132 | − | 0.0448932i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.0319284 | + | 0.942280i | 0.00173156 | + | 0.0511023i | ||||
\(341\) | −13.8033 | − | 7.96936i | −0.747493 | − | 0.431565i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.76542 | + | 10.3207i | −0.149319 | + | 0.557265i | ||||
\(344\) | 2.93610 | + | 16.6514i | 0.158304 | + | 0.897785i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.7455 | + | 7.18679i | −1.06153 | + | 0.386364i | ||||
\(347\) | −23.8760 | + | 16.7182i | −1.28173 | + | 0.897479i | −0.998110 | − | 0.0614562i | \(-0.980426\pi\) |
−0.283624 | + | 0.958936i | \(0.591537\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.9918 | + | 16.6748i | 0.748963 | + | 0.892579i | 0.997097 | − | 0.0761464i | \(-0.0242616\pi\) |
−0.248134 | + | 0.968726i | \(0.579817\pi\) | |||||||
\(350\) | 15.5818 | + | 16.2024i | 0.832882 | + | 0.866057i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.55941 | − | 2.55941i | 0.136417 | − | 0.136417i | ||||
\(353\) | 0.350221 | − | 4.00305i | 0.0186404 | − | 0.213061i | −0.981162 | − | 0.193186i | \(-0.938118\pi\) |
0.999802 | − | 0.0198744i | \(-0.00632664\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.0032 | + | 15.3687i | −0.530916 | + | 0.815689i | ||||
\(356\) | −0.206417 | − | 0.567126i | −0.0109401 | − | 0.0300576i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.6153 | − | 23.7291i | 0.878146 | − | 1.25412i | ||||
\(359\) | 4.90370 | + | 8.49346i | 0.258807 | + | 0.448268i | 0.965923 | − | 0.258831i | \(-0.0833372\pi\) |
−0.707115 | + | 0.707098i | \(0.750004\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.38399 | + | 16.2535i | −0.493894 | + | 0.855450i | ||||
\(362\) | 5.93907 | + | 12.7364i | 0.312150 | + | 0.669409i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.613517 | + | 0.731161i | −0.0321570 | + | 0.0383232i | ||||
\(365\) | 28.8821 | + | 9.41743i | 1.51176 | + | 0.492931i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.4836 | + | 15.6137i | −1.74783 | + | 0.815027i | −0.761938 | + | 0.647650i | \(0.775752\pi\) |
−0.985893 | + | 0.167377i | \(0.946470\pi\) | |||||||
\(368\) | −6.79023 | − | 25.3415i | −0.353965 | − | 1.32102i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 19.7594 | − | 2.40538i | 1.02724 | − | 0.125050i | ||||
\(371\) | −0.766037 | + | 0.135073i | −0.0397707 | + | 0.00701264i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.6061 | + | 11.0077i | 1.22228 | + | 0.569958i | 0.923218 | − | 0.384276i | \(-0.125549\pi\) |
0.299061 | + | 0.954234i | \(0.403327\pi\) | |||||||
\(374\) | 4.62580 | − | 26.2342i | 0.239194 | − | 1.35654i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −26.4017 | + | 22.1537i | −1.36156 | + | 1.14249i | ||||
\(377\) | −0.226437 | − | 0.226437i | −0.0116621 | − | 0.0116621i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.9056i | 1.33068i | 0.746541 | + | 0.665340i | \(0.231713\pi\) | ||||
−0.746541 | + | 0.665340i | \(0.768287\pi\) | |||||||
\(380\) | 0.0370177 | + | 0.121529i | 0.00189897 | + | 0.00623432i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.83314 | + | 6.90243i | 0.247285 | + | 0.353159i | ||||
\(383\) | −4.13501 | + | 8.86756i | −0.211289 | + | 0.453111i | −0.983179 | − | 0.182645i | \(-0.941534\pi\) |
0.771890 | + | 0.635757i | \(0.219312\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 21.0584 | + | 33.7783i | 1.07324 | + | 1.72150i | ||||
\(386\) | 7.53778 | − | 4.35194i | 0.383663 | − | 0.221508i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.473944 | + | 0.126993i | −0.0240609 | + | 0.00644709i | ||||
\(389\) | −11.3841 | − | 4.14348i | −0.577198 | − | 0.210083i | 0.0368917 | − | 0.999319i | \(-0.488254\pi\) |
−0.614089 | + | 0.789236i | \(0.710477\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.1572 | + | 16.0748i | 0.968823 | + | 0.812939i | ||||
\(392\) | −0.947006 | − | 10.8243i | −0.0478310 | − | 0.546711i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.159863 | − | 0.439219i | 0.00805376 | − | 0.0221275i | ||||
\(395\) | 17.9239 | − | 13.4775i | 0.901848 | − | 0.678128i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.4729 | − | 3.07416i | −0.575810 | − | 0.154288i | −0.0408499 | − | 0.999165i | \(-0.513007\pi\) |
−0.534960 | + | 0.844878i | \(0.679673\pi\) | |||||||
\(398\) | −22.9617 | − | 16.0780i | −1.15097 | − | 0.805917i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.8362 | + | 8.25475i | 0.841808 | + | 0.412737i | ||||
\(401\) | 31.8998 | + | 5.62479i | 1.59300 | + | 0.280889i | 0.898622 | − | 0.438723i | \(-0.144569\pi\) |
0.694377 | + | 0.719612i | \(0.255680\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.21779 | + | 0.631475i | 0.359544 | + | 0.0314560i | ||||
\(404\) | 0.933850 | 0.0464608 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.583053 | 0.0289364 | ||||||||
\(407\) | 35.1131 | + | 3.07200i | 1.74049 | + | 0.152273i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.62791 | + | 0.816026i | 0.228836 | + | 0.0403499i | 0.286890 | − | 0.957964i | \(-0.407379\pi\) |
−0.0580544 | + | 0.998313i | \(0.518490\pi\) | |||||||
\(410\) | 0.686097 | + | 0.763576i | 0.0338839 | + | 0.0377103i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.520884 | − | 0.364727i | −0.0256621 | − | 0.0179688i | ||||
\(413\) | −12.2273 | − | 3.27629i | −0.601666 | − | 0.161216i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.0326743 | + | 0.00462657i | 0.00160392 | + | 0.000227109i | ||||
\(416\) | −0.562747 | + | 1.54613i | −0.0275909 | + | 0.0758055i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.312846 | − | 3.57585i | −0.0153018 | − | 0.174900i | ||||
\(419\) | 16.7939 | + | 14.0917i | 0.820435 | + | 0.688427i | 0.953074 | − | 0.302737i | \(-0.0979005\pi\) |
−0.132639 | + | 0.991164i | \(0.542345\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.6703 | + | 9.70721i | 1.29983 | + | 0.473101i | 0.896942 | − | 0.442148i | \(-0.145783\pi\) |
0.402891 | + | 0.915248i | \(0.368005\pi\) | |||||||
\(422\) | −7.73694 | + | 2.07311i | −0.376628 | + | 0.100917i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.597264 | + | 0.344831i | −0.0290057 | + | 0.0167465i | ||||
\(425\) | −17.6593 | + | 2.75949i | −0.856604 | + | 0.133855i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.82332 | + | 14.6327i | −0.330204 | + | 0.708124i | ||||
\(428\) | −0.617752 | − | 0.882242i | −0.0298602 | − | 0.0426448i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17.0767 | + | 5.20153i | −0.823509 | + | 0.250840i | ||||
\(431\) | 34.6874i | 1.67083i | 0.549617 | + | 0.835417i | \(0.314774\pi\) | ||||
−0.549617 | + | 0.835417i | \(0.685226\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.65895 | − | 3.65895i | −0.175838 | − | 0.175838i | 0.613701 | − | 0.789539i | \(-0.289680\pi\) |
−0.789539 | + | 0.613701i | \(0.789680\pi\) | |||||||
\(434\) | −10.1055 | + | 8.47955i | −0.485081 | + | 0.407031i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.210342 | + | 1.19291i | −0.0100736 | + | 0.0571301i | ||||
\(437\) | 3.05403 | + | 1.42412i | 0.146094 | + | 0.0681247i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.7144 | + | 5.41577i | −1.46592 | + | 0.258481i | −0.848935 | − | 0.528496i | \(-0.822756\pi\) |
−0.616982 | + | 0.786977i | \(0.711645\pi\) | |||||||
\(440\) | 27.7878 | + | 21.7566i | 1.32473 | + | 1.03721i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.13414 | + | 11.6968i | 0.149076 | + | 0.556359i | ||||
\(443\) | 28.1594 | − | 13.1309i | 1.33789 | − | 0.623869i | 0.383809 | − | 0.923413i | \(-0.374612\pi\) |
0.954083 | + | 0.299544i | \(0.0968344\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.1997 | − | 5.18372i | 0.483513 | − | 0.245732i | ||||
\(446\) | −17.2549 | + | 20.5636i | −0.817042 | + | 0.973712i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −11.6539 | − | 24.9919i | −0.550595 | − | 1.18075i | ||||
\(449\) | −5.46364 | + | 9.46330i | −0.257845 | + | 0.446601i | −0.965664 | − | 0.259793i | \(-0.916346\pi\) |
0.707819 | + | 0.706394i | \(0.249679\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.908870 | + | 1.57421i | 0.0427970 | + | 0.0741266i | ||||
\(452\) | −0.703835 | + | 1.00518i | −0.0331056 | + | 0.0472797i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.69114 | − | 12.8888i | −0.220166 | − | 0.604902i | ||||
\(455\) | −15.1650 | − | 9.87060i | −0.710946 | − | 0.462741i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.25825 | + | 25.8119i | −0.105637 | + | 1.20743i | 0.739603 | + | 0.673044i | \(0.235013\pi\) |
−0.845239 | + | 0.534388i | \(0.820542\pi\) | |||||||
\(458\) | −12.2631 | + | 12.2631i | −0.573017 | + | 0.573017i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.71147 | + | 0.689418i | −0.0797976 | + | 0.0321443i | ||||
\(461\) | 10.5103 | + | 12.5256i | 0.489512 | + | 0.583377i | 0.953093 | − | 0.302677i | \(-0.0978804\pi\) |
−0.463582 | + | 0.886054i | \(0.653436\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.973401 | − | 0.681583i | 0.0452378 | − | 0.0316758i | −0.550739 | − | 0.834678i | \(-0.685654\pi\) |
0.595977 | + | 0.803002i | \(0.296765\pi\) | |||||||
\(464\) | 0.457022 | − | 0.166342i | 0.0212167 | − | 0.00772225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.361759 | − | 2.05164i | −0.0167582 | − | 0.0950403i | ||||
\(467\) | 4.13206 | − | 15.4210i | 0.191209 | − | 0.713601i | −0.802007 | − | 0.597315i | \(-0.796234\pi\) |
0.993216 | − | 0.116286i | \(-0.0370989\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.1351 | − | 7.00619i | −0.560345 | − | 0.323516i | ||||
\(470\) | −26.5861 | − | 24.8435i | −1.22633 | − | 1.14594i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11.1807 | + | 0.978183i | −0.514632 | + | 0.0450245i | ||||
\(473\) | −31.4899 | + | 2.75501i | −1.44791 | + | 0.126675i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.20222 | + | 0.975033i | −0.101045 | + | 0.0447376i | ||||
\(476\) | 1.19665 | + | 0.690889i | 0.0548486 | + | 0.0316668i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.10415 | − | 26.5130i | 0.324936 | − | 1.21268i | ||||
\(479\) | 1.29177 | + | 7.32601i | 0.0590226 | + | 0.334734i | 0.999993 | − | 0.00375516i | \(-0.00119531\pi\) |
−0.940970 | + | 0.338489i | \(0.890084\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.0563 | + | 5.48003i | −0.686506 | + | 0.249868i | ||||
\(482\) | −11.8561 | + | 8.30172i | −0.540030 | + | 0.378133i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.40310 | + | 1.67215i | 0.0637774 | + | 0.0760069i | ||||
\(485\) | −3.47559 | − | 8.62809i | −0.157818 | − | 0.391782i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.2649 | − | 13.2649i | 0.601090 | − | 0.601090i | −0.339512 | − | 0.940602i | \(-0.610262\pi\) |
0.940602 | + | 0.339512i | \(0.110262\pi\) | |||||||
\(488\) | −1.24762 | + | 14.2603i | −0.0564769 | + | 0.645534i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 11.2234 | − | 2.37347i | 0.507023 | − | 0.107222i | ||||
\(491\) | −12.3391 | − | 33.9013i | −0.556855 | − | 1.52995i | −0.824173 | − | 0.566337i | \(-0.808360\pi\) |
0.267319 | − | 0.963608i | \(-0.413862\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.265909 | + | 0.379757i | −0.0119759 | + | 0.0171034i | ||||
\(494\) | 0.815851 | + | 1.41310i | 0.0367069 | + | 0.0635782i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.50198 | + | 9.52970i | −0.247046 | + | 0.427896i | ||||
\(497\) | 11.3579 | + | 24.3570i | 0.509470 | + | 1.09256i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.6192 | − | 24.5730i | 0.923042 | − | 1.10004i | −0.0716800 | − | 0.997428i | \(-0.522836\pi\) |
0.994722 | − | 0.102610i | \(-0.0327195\pi\) | |||||||
\(500\) | 0.433207 | − | 1.24554i | 0.0193736 | − | 0.0557024i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.8399 | − | 5.98736i | 0.573074 | − | 0.267229i | ||||
\(503\) | 9.15328 | + | 34.1605i | 0.408124 | + | 1.52314i | 0.798220 | + | 0.602367i | \(0.205775\pi\) |
−0.390095 | + | 0.920775i | \(0.627558\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.13933 | + | 17.5739i | 0.0951990 | + | 0.782026i | ||||
\(506\) | 51.3405 | − | 9.05272i | 2.28237 | − | 0.402443i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.40145 | − | 0.653509i | −0.0621795 | − | 0.0289948i | ||||
\(509\) | −3.11515 | + | 17.6669i | −0.138077 | + | 0.783072i | 0.834591 | + | 0.550870i | \(0.185704\pi\) |
−0.972668 | + | 0.232202i | \(0.925407\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.1061 | − | 28.6184i | 1.50876 | − | 1.26600i | ||||
\(512\) | −17.1769 | − | 17.1769i | −0.759118 | − | 0.759118i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.1848i | 0.934420i | ||||||||
\(515\) | 5.67041 | − | 10.6379i | 0.249868 | − | 0.468762i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −36.9569 | − | 52.7799i | −1.62536 | − | 2.32126i | ||||
\(518\) | 12.3289 | − | 26.4394i | 0.541701 | − | 1.16168i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −15.6279 | − | 3.62503i | −0.685328 | − | 0.158968i | ||||
\(521\) | −5.38399 | + | 3.10845i | −0.235877 | + | 0.136184i | −0.613280 | − | 0.789865i | \(-0.710150\pi\) |
0.377403 | + | 0.926049i | \(0.376817\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −41.3195 | + | 11.0715i | −1.80677 | + | 0.484124i | −0.995002 | − | 0.0998516i | \(-0.968163\pi\) |
−0.811771 | + | 0.583975i | \(0.801497\pi\) | |||||||
\(524\) | −0.359944 | − | 0.131009i | −0.0157242 | − | 0.00572316i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.3085 | − | 12.0063i | −0.623881 | − | 0.523499i | ||||
\(527\) | −0.914187 | − | 10.4492i | −0.0398226 | − | 0.455174i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.87229 | + | 24.3764i | −0.385752 | + | 1.05984i | ||||
\(530\) | −0.437593 | − | 0.581958i | −0.0190078 | − | 0.0252787i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.179846 | + | 0.0481895i | 0.00779730 | + | 0.00208928i | ||||
\(533\) | −0.676866 | − | 0.473947i | −0.0293183 | − | 0.0205289i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.1875 | − | 13.6464i | 0.656611 | − | 0.589986i | ||||
\(536\) | −12.2349 | − | 2.15734i | −0.528467 | − | 0.0931830i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.8554 | + | 1.38717i | 0.683576 | + | 0.0598052i | ||||
\(539\) | 20.3134 | 0.874961 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.3822 | 0.704326 | 0.352163 | − | 0.935939i | \(-0.385446\pi\) | ||||
0.352163 | + | 0.935939i | \(0.385446\pi\) | |||||||
\(542\) | 14.4036 | + | 1.26015i | 0.618687 | + | 0.0541281i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.34581 | + | 0.413629i | 0.100576 | + | 0.0177342i | ||||
\(545\) | −22.9309 | − | 1.22557i | −0.982252 | − | 0.0524975i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.4002 | + | 12.1838i | 0.743980 | + | 0.520940i | 0.883014 | − | 0.469347i | \(-0.155511\pi\) |
−0.139034 | + | 0.990288i | \(0.544400\pi\) | |||||||
\(548\) | −0.536074 | − | 0.143641i | −0.0228999 | − | 0.00613602i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −19.2564 | + | 31.8983i | −0.821097 | + | 1.36015i | ||||
\(551\) | −0.0213654 | + | 0.0587010i | −0.000910198 | + | 0.00250075i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.86451 | − | 32.7415i | −0.121811 | − | 1.39231i | ||||
\(554\) | 17.4180 | + | 14.6154i | 0.740019 | + | 0.620950i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.27783 | + | 0.465094i | 0.0541923 | + | 0.0197244i | ||||
\(557\) | −16.5180 | + | 4.42599i | −0.699891 | + | 0.187535i | −0.591182 | − | 0.806538i | \(-0.701338\pi\) |
−0.108709 | + | 0.994074i | \(0.534672\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.4441 | − | 7.18460i | 0.526329 | − | 0.303876i | ||||
\(560\) | 23.3202 | − | 14.5386i | 0.985460 | − | 0.614366i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.82364 | − | 14.6333i | 0.287838 | − | 0.617270i | ||||
\(563\) | −25.1939 | − | 35.9806i | −1.06180 | − | 1.51640i | −0.840966 | − | 0.541088i | \(-0.818013\pi\) |
−0.220829 | − | 0.975313i | \(-0.570876\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.5286 | − | 10.9425i | −0.863644 | − | 0.460355i | ||||
\(566\) | 10.0413i | 0.422067i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.8489 | + | 16.8489i | 0.706963 | + | 0.706963i | ||||
\(569\) | −31.1911 | + | 26.1725i | −1.30760 | + | 1.09721i | −0.318823 | + | 0.947814i | \(0.603288\pi\) |
−0.988778 | + | 0.149393i | \(0.952268\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.97321 | − | 39.5470i | 0.291820 | − | 1.65499i | −0.388035 | − | 0.921645i | \(-0.626846\pi\) |
0.679855 | − | 0.733347i | \(-0.262043\pi\) | |||||||
\(572\) | −1.43383 | − | 0.668607i | −0.0599515 | − | 0.0279559i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.48161 | − | 0.261248i | 0.0618414 | − | 0.0109043i | ||||
\(575\) | −16.8947 | − | 30.6283i | −0.704558 | − | 1.27729i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.00476 | − | 11.2139i | −0.125090 | − | 0.466841i | 0.874753 | − | 0.484569i | \(-0.161024\pi\) |
−0.999843 | + | 0.0177276i | \(0.994357\pi\) | |||||||
\(578\) | −5.24854 | + | 2.44743i | −0.218311 | + | 0.101800i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.0154970 | − | 0.0304926i | −0.000643477 | − | 0.00126613i | ||||
\(581\) | 0.0310880 | − | 0.0370492i | 0.00128975 | − | 0.00153706i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.544892 | − | 1.16852i | −0.0225671 | − | 0.0483953i | ||||
\(584\) | 19.7372 | − | 34.1858i | 0.816730 | − | 1.41462i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.45534 | + | 9.44893i | 0.225358 | + | 0.390332i | ||||
\(587\) | 24.1649 | − | 34.5111i | 0.997393 | − | 1.42442i | 0.0940196 | − | 0.995570i | \(-0.470028\pi\) |
0.903374 | − | 0.428855i | \(-0.141083\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.483403 | − | 1.32814i | −0.0199183 | − | 0.0547250i | ||||
\(590\) | −2.45161 | − | 11.5929i | −0.100931 | − | 0.477273i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.12088 | − | 24.2418i | 0.0871676 | − | 0.996330i | ||||
\(593\) | 10.2163 | − | 10.2163i | 0.419534 | − | 0.419534i | −0.465509 | − | 0.885043i | \(-0.654129\pi\) |
0.885043 | + | 0.465509i | \(0.154129\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.2603 | + | 24.1022i | −0.420629 | + | 0.988095i | ||||
\(596\) | 0.847584 | + | 1.01011i | 0.0347184 | + | 0.0413758i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −19.4124 | + | 13.5927i | −0.793833 | + | 0.555848i | ||||
\(599\) | 4.58046 | − | 1.66715i | 0.187153 | − | 0.0681180i | −0.246744 | − | 0.969081i | \(-0.579361\pi\) |
0.433896 | + | 0.900963i | \(0.357138\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.94695 | − | 39.3981i | −0.283372 | − | 1.60708i | −0.711043 | − | 0.703149i | \(-0.751777\pi\) |
0.427671 | − | 0.903935i | \(-0.359334\pi\) | |||||||
\(602\) | −6.77134 | + | 25.2710i | −0.275979 | + | 1.02997i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.19655 | − | 0.690830i | −0.0486871 | − | 0.0281095i | ||||
\(605\) | −28.2534 | + | 30.2353i | −1.14866 | + | 1.22924i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.47967 | + | 0.829363i | −0.384768 | + | 0.0336628i | −0.277899 | − | 0.960610i | \(-0.589638\pi\) |
−0.106869 | + | 0.994273i | \(0.534083\pi\) | |||||||
\(608\) | 0.319745 | − | 0.0279740i | 0.0129674 | − | 0.00113450i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15.1045 | + | 0.511802i | −0.611561 | + | 0.0207223i | ||||
\(611\) | 25.3654 | + | 14.6447i | 1.02617 | + | 0.592461i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.22613 | − | 19.5042i | 0.211081 | − | 0.787766i | −0.776428 | − | 0.630206i | \(-0.782971\pi\) |
0.987509 | − | 0.157560i | \(-0.0503628\pi\) | |||||||
\(614\) | −2.23863 | − | 12.6959i | −0.0903437 | − | 0.512365i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 48.6037 | − | 17.6903i | 1.95830 | − | 0.712762i | ||||
\(617\) | 24.4398 | − | 17.1129i | 0.983908 | − | 0.688940i | 0.0333358 | − | 0.999444i | \(-0.489387\pi\) |
0.950572 | + | 0.310505i | \(0.100498\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.44832 | + | 1.72604i | 0.0582129 | + | 0.0693754i | 0.794365 | − | 0.607441i | \(-0.207804\pi\) |
−0.736152 | + | 0.676816i | \(0.763359\pi\) | |||||||
\(620\) | 0.712060 | + | 0.303122i | 0.0285970 | + | 0.0121737i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.81978 | − | 5.81978i | 0.233352 | − | 0.233352i | ||||
\(623\) | 1.46145 | − | 16.7044i | 0.0585517 | − | 0.669249i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.4320 | + | 5.29902i | 0.977278 | + | 0.211961i | ||||
\(626\) | −4.33261 | − | 11.9038i | −0.173166 | − | 0.475770i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.37612 | − | 1.96531i | 0.0549133 | − | 0.0784243i | ||||
\(629\) | 11.5979 | + | 20.0882i | 0.462439 | + | 0.800968i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.8829 | + | 18.8498i | −0.433243 | + | 0.750399i | −0.997150 | − | 0.0754390i | \(-0.975964\pi\) |
0.563907 | + | 0.825838i | \(0.309298\pi\) | |||||||
\(632\) | −12.3151 | − | 26.4099i | −0.489870 | − | 1.05053i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −28.2663 | + | 33.6864i | −1.12260 | + | 1.33786i | ||||
\(635\) | 9.08764 | − | 27.8707i | 0.360632 | − | 1.10601i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.36884 | + | 3.90245i | −0.331585 | + | 0.154621i | ||||
\(638\) | 0.250131 | + | 0.933502i | 0.00990279 | + | 0.0369577i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 14.0757 | − | 17.9777i | 0.556391 | − | 0.710630i | ||||
\(641\) | 15.8779 | − | 2.79971i | 0.627141 | − | 0.110582i | 0.148960 | − | 0.988843i | \(-0.452407\pi\) |
0.478181 | + | 0.878261i | \(0.341296\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.8423 | + | 6.92110i | 0.585325 | + | 0.272941i | 0.692640 | − | 0.721284i | \(-0.256448\pi\) |
−0.107315 | + | 0.994225i | \(0.534225\pi\) | |||||||
\(644\) | −0.469571 | + | 2.66307i | −0.0185037 | + | 0.104940i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.80956 | − | 1.51841i | 0.0711964 | − | 0.0597408i | ||||
\(647\) | 11.6159 | + | 11.6159i | 0.456669 | + | 0.456669i | 0.897560 | − | 0.440892i | \(-0.145338\pi\) |
−0.440892 | + | 0.897560i | \(0.645338\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 20.9822i | − | 0.823622i | ||||||
\(650\) | 1.80533 | − | 16.8410i | 0.0708108 | − | 0.660559i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.659504 | + | 0.941869i | 0.0258282 | + | 0.0368864i | ||||
\(653\) | 18.8657 | − | 40.4576i | 0.738271 | − | 1.58323i | −0.0721611 | − | 0.997393i | \(-0.522990\pi\) |
0.810432 | − | 0.585833i | \(-0.199233\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.64083 | − | 7.07381i | 0.0641127 | − | 0.276397i | ||||
\(656\) | 1.08682 | − | 0.627476i | 0.0424332 | − | 0.0244988i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −51.5110 | + | 13.8023i | −2.00811 | + | 0.538071i | ||||
\(659\) | 0.617551 | + | 0.224770i | 0.0240564 | + | 0.00875580i | 0.354020 | − | 0.935238i | \(-0.384814\pi\) |
−0.329964 | + | 0.943994i | \(0.607037\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.7997 | + | 25.0049i | 1.15907 | + | 0.972578i | 0.999892 | − | 0.0146714i | \(-0.00467022\pi\) |
0.159181 | + | 0.987249i | \(0.449115\pi\) | |||||||
\(662\) | −3.68216 | − | 42.0873i | −0.143111 | − | 1.63577i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.0146661 | − | 0.0402948i | 0.000569155 | − | 0.00156374i | ||||
\(665\) | −0.494861 | + | 3.49486i | −0.0191899 | + | 0.135525i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.876351 | − | 0.234817i | −0.0339324 | − | 0.00909217i | ||||
\(668\) | −0.773667 | − | 0.541728i | −0.0299341 | − | 0.0209601i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.700026 | − | 13.0978i | 0.0270444 | − | 0.506013i | ||||
\(671\) | −26.3550 | − | 4.64710i | −1.01742 | − | 0.179399i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.00299 | − | 0.350216i | −0.154304 | − | 0.0134998i | 0.00974205 | − | 0.999953i | \(-0.496899\pi\) |
−0.164046 | + | 0.986453i | \(0.552455\pi\) | |||||||
\(674\) | 4.34307 | 0.167289 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.814194 | −0.0313152 | ||||||||
\(677\) | −29.2823 | − | 2.56187i | −1.12541 | − | 0.0984607i | −0.490786 | − | 0.871280i | \(-0.663290\pi\) |
−0.634626 | + | 0.772820i | \(0.718846\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.4254 | − | 2.36727i | −0.515221 | − | 0.0908473i | ||||
\(680\) | −1.23953 | + | 23.1921i | −0.0475337 | + | 0.889377i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −17.9116 | − | 12.5418i | −0.685869 | − | 0.480251i | ||||
\(683\) | −7.44976 | − | 1.99616i | −0.285057 | − | 0.0763808i | 0.113457 | − | 0.993543i | \(-0.463807\pi\) |
−0.398515 | + | 0.917162i | \(0.630474\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.47505 | − | 10.4173i | 0.0563589 | − | 0.398024i | ||||
\(686\) | −5.01340 | + | 13.7742i | −0.191412 | + | 0.525901i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.90203 | + | 21.7403i | 0.0725142 | + | 0.828841i | ||||
\(689\) | 0.448975 | + | 0.376735i | 0.0171046 | + | 0.0143525i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.4494 | − | 11.8106i | −1.23443 | − | 0.449297i | −0.359320 | − | 0.933215i | \(-0.616991\pi\) |
−0.875114 | + | 0.483918i | \(0.839213\pi\) | |||||||
\(692\) | 1.74507 | − | 0.467589i | 0.0663375 | − | 0.0177751i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −34.6293 | + | 19.9933i | −1.31451 | + | 0.758933i | ||||
\(695\) | −5.82511 | + | 25.1127i | −0.220959 | + | 0.952578i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.505551 | + | 1.08416i | −0.0191491 | + | 0.0410654i | ||||
\(698\) | 17.1282 | + | 24.4616i | 0.648313 | + | 0.925887i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.21318 | − | 1.50451i | −0.0458537 | − | 0.0568650i | ||||
\(701\) | 2.02183i | 0.0763636i | 0.999271 | + | 0.0381818i | \(0.0121566\pi\) | ||||
−0.999271 | + | 0.0381818i | \(0.987843\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.21011 | + | 2.21011i | 0.0833558 | + | 0.0833558i | ||||
\(704\) | 35.0139 | − | 29.3802i | 1.31964 | − | 1.10731i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.957265 | − | 5.42892i | 0.0360272 | − | 0.204320i | ||||
\(707\) | 23.5151 | + | 10.9653i | 0.884375 | + | 0.412391i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.162501 | − | 0.0286532i | 0.00610284 | − | 0.00107609i | −0.170596 | − | 0.985341i | \(-0.554569\pi\) |
0.176699 | + | 0.984265i | \(0.443458\pi\) | |||||||
\(710\) | −15.5086 | + | 19.8078i | −0.582026 | + | 0.743372i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.84787 | − | 14.3605i | −0.144205 | − | 0.538181i | ||||
\(713\) | 18.6040 | − | 8.67521i | 0.696727 | − | 0.324889i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.29760 | − | 28.5146i | 0.347710 | − | 1.06638i | ||||
\(716\) | −1.60092 | + | 1.90790i | −0.0598292 | + | 0.0713017i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.68614 | + | 12.1940i | 0.212205 | + | 0.455075i | ||||
\(719\) | −0.704484 | + | 1.22020i | −0.0262728 | + | 0.0455059i | −0.878863 | − | 0.477074i | \(-0.841697\pi\) |
0.852590 | + | 0.522580i | \(0.175031\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.83364 | − | 15.3003i | −0.328982 | − | 0.569813i | ||||
\(722\) | −14.7681 | + | 21.0910i | −0.549611 | + | 0.784926i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.413244 | − | 1.13538i | −0.0153581 | − | 0.0421960i | ||||
\(725\) | 0.538329 | − | 0.361488i | 0.0199930 | − | 0.0134253i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.88007 | + | 32.9194i | −0.106816 | + | 1.22091i | 0.733832 | + | 0.679330i | \(0.237730\pi\) |
−0.840648 | + | 0.541581i | \(0.817826\pi\) | |||||||
\(728\) | −16.6255 | + | 16.6255i | −0.616182 | + | 0.616182i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 38.3459 | + | 16.3238i | 1.41925 | + | 0.604169i | ||||
\(731\) | −13.3715 | − | 15.9355i | −0.494562 | − | 0.589396i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.1269 | − | 8.49132i | 0.447916 | − | 0.313634i | −0.327765 | − | 0.944759i | \(-0.606295\pi\) |
0.775681 | + | 0.631125i | \(0.217407\pi\) | |||||||
\(734\) | −47.6275 | + | 17.3350i | −1.75796 | + | 0.639847i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.809475 | + | 4.59076i | 0.0298376 | + | 0.169218i | ||||
\(737\) | 6.01134 | − | 22.4346i | 0.221431 | − | 0.826391i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.7323 | + | 6.19632i | 0.394796 | + | 0.227935i | 0.684236 | − | 0.729261i | \(-0.260136\pi\) |
−0.289440 | + | 0.957196i | \(0.593469\pi\) | |||||||
\(740\) | −1.71042 | + | 0.0579563i | −0.0628764 | + | 0.00213052i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.06306 | + | 0.0930058i | −0.0390262 | + | 0.00341435i | ||||
\(743\) | −3.75974 | + | 0.328934i | −0.137931 | + | 0.0120674i | −0.155912 | − | 0.987771i | \(-0.549832\pi\) |
0.0179809 | + | 0.999838i | \(0.494276\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.0673 | + | 18.2645i | −0.625297 | + | 0.669159i | ||||
\(746\) | 30.9454 | + | 17.8663i | 1.13299 | + | 0.654132i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.592786 | + | 2.21231i | −0.0216744 | + | 0.0808900i | ||||
\(749\) | −5.19621 | − | 29.4692i | −0.189865 | − | 1.07678i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.6339 | + | 4.23440i | −0.424528 | + | 0.154516i | −0.545444 | − | 0.838147i | \(-0.683639\pi\) |
0.120916 | + | 0.992663i | \(0.461417\pi\) | |||||||
\(752\) | −36.4388 | + | 25.5147i | −1.32879 | + | 0.930426i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.282387 | − | 0.336536i | −0.0102839 | − | 0.0122559i | ||||
\(755\) | 10.2594 | − | 24.1002i | 0.373377 | − | 0.877096i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.6821 | − | 14.6821i | 0.533632 | − | 0.533632i | −0.388019 | − | 0.921651i | \(-0.626841\pi\) |
0.921651 | + | 0.388019i | \(0.126841\pi\) | |||||||
\(758\) | −3.09745 | + | 35.4040i | −0.112505 | + | 1.28593i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.647494 | + | 3.06181i | 0.0234871 | + | 0.111063i | ||||
\(761\) | 0.142795 | + | 0.392327i | 0.00517632 | + | 0.0142218i | 0.942254 | − | 0.334899i | \(-0.108702\pi\) |
−0.937078 | + | 0.349121i | \(0.886480\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.3037 | + | 27.5686i | −0.698842 | + | 0.998050i | ||||
\(764\) | −0.362237 | − | 0.627413i | −0.0131053 | − | 0.0226990i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.71141 | + | 11.6245i | −0.242493 | + | 0.420010i | ||||
\(767\) | 4.03093 | + | 8.64435i | 0.145548 | + | 0.312129i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.9703 | − | 14.2656i | 0.431660 | − | 0.514432i | −0.505741 | − | 0.862685i | \(-0.668781\pi\) |
0.937400 | + | 0.348254i | \(0.113225\pi\) | |||||||
\(770\) | 24.7409 | + | 48.6813i | 0.891600 | + | 1.75435i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.678225 | + | 0.316262i | −0.0244099 | + | 0.0113825i | ||||
\(773\) | −4.48345 | − | 16.7325i | −0.161259 | − | 0.601825i | −0.998488 | − | 0.0549731i | \(-0.982493\pi\) |
0.837229 | − | 0.546852i | \(-0.184174\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.07313 | + | 14.0945i | −0.146311 | + | 0.506288i | ||||
\(776\) | −11.9032 | + | 2.09886i | −0.427302 | + | 0.0753448i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.0628 | − | 7.02388i | −0.540026 | − | 0.251818i | ||||
\(779\) | −0.0279902 | + | 0.158740i | −0.00100285 | + | 0.00568746i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34.1245 | + | 28.6339i | −1.22107 | + | 1.02460i | ||||
\(782\) | 24.2594 | + | 24.2594i | 0.867513 | + | 0.867513i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 14.0242i | − | 0.500864i | ||||||
\(785\) | 40.1371 | + | 21.3946i | 1.43255 | + | 0.763606i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.6926 | + | 28.1240i | 0.701966 | + | 1.00251i | 0.998866 | + | 0.0476032i | \(0.0151583\pi\) |
−0.296900 | + | 0.954909i | \(0.595953\pi\) | |||||||
\(788\) | −0.0169836 | + | 0.0364214i | −0.000605014 | + | 0.00129746i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 26.1073 | − | 16.2761i | 0.928855 | − | 0.579077i | ||||
\(791\) | −29.5259 | + | 17.0468i | −1.04982 | + | 0.606114i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.7506 | − | 3.14857i | 0.417277 | − | 0.111809i | ||||
\(794\) | −15.3120 | − | 5.57311i | −0.543402 | − | 0.197782i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.84620 | + | 1.54915i | 0.0654370 | + | 0.0549081i | ||||
\(797\) | −3.24062 | − | 37.0405i | −0.114789 | − | 1.31204i | −0.807088 | − | 0.590431i | \(-0.798958\pi\) |
0.692300 | − | 0.721610i | \(-0.256598\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.5024 | − | 39.8451i | 0.513060 | − | 1.40962i | ||||
\(800\) | −2.85228 | − | 1.72187i | −0.100843 | − | 0.0608772i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 42.9235 | + | 11.5013i | 1.51568 | + | 0.406126i | ||||
\(803\) | 60.4514 | + | 42.3285i | 2.13328 | + | 1.49374i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −51.1912 | − | 2.73597i | −1.80425 | − | 0.0964302i | ||||
\(806\) | 9.78874 | + | 1.72602i | 0.344794 | + | 0.0607964i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 22.9167 | + | 2.00495i | 0.806206 | + | 0.0705339i | ||||
\(809\) | −38.7711 | −1.36312 | −0.681560 | − | 0.731763i | \(-0.738698\pi\) | ||||
−0.681560 | + | 0.731763i | \(0.738698\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.0813 | −0.529577 | −0.264789 | − | 0.964307i | \(-0.585302\pi\) | ||||
−0.264789 | + | 0.964307i | \(0.585302\pi\) | |||||||
\(812\) | −0.0499387 | − | 0.00436907i | −0.00175251 | − | 0.000153324i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 47.6203 | + | 8.39674i | 1.66909 | + | 0.294305i | ||||
\(815\) | −16.2139 | + | 14.5687i | −0.567949 | + | 0.510320i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.29612 | − | 1.60776i | −0.0803311 | − | 0.0562484i | ||||
\(818\) | 6.22720 | + | 1.66857i | 0.217729 | + | 0.0583403i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.0530427 | − | 0.0705419i | −0.00185233 | − | 0.00246343i | ||||
\(821\) | 5.23862 | − | 14.3930i | 0.182829 | − | 0.502318i | −0.814092 | − | 0.580736i | \(-0.802765\pi\) |
0.996921 | + | 0.0784180i | \(0.0249869\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.01659 | + | 34.4798i | 0.105152 | + | 1.20189i | 0.847100 | + | 0.531434i | \(0.178347\pi\) |
−0.741948 | + | 0.670458i | \(0.766098\pi\) | |||||||
\(824\) | −11.9994 | − | 10.0687i | −0.418020 | − | 0.350761i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.3188 | − | 5.93955i | −0.567803 | − | 0.206664i | ||||
\(827\) | 8.57712 | − | 2.29823i | 0.298256 | − | 0.0799174i | −0.106588 | − | 0.994303i | \(-0.533993\pi\) |
0.404844 | + | 0.914386i | \(0.367326\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.2184 | − | 26.1068i | 1.57050 | − | 0.906728i | 0.574391 | − | 0.818581i | \(-0.305239\pi\) |
0.996108 | − | 0.0881465i | \(-0.0280944\pi\) | |||||||
\(830\) | 0.0441013 | + | 0.0102297i | 0.00153078 | + | 0.000355078i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.78095 | + | 18.8308i | −0.304425 | + | 0.652840i | ||||
\(833\) | 7.66760 | + | 10.9505i | 0.265667 | + | 0.379411i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.42224 | − | 15.8004i | 0.291464 | − | 0.546797i | ||||
\(836\) | 0.308617i | 0.0106737i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 21.2666 | + | 21.2666i | 0.734642 | + | 0.734642i | ||||
\(839\) | 11.8964 | − | 9.98230i | 0.410711 | − | 0.344627i | −0.413905 | − | 0.910320i | \(-0.635836\pi\) |
0.824616 | + | 0.565693i | \(0.191391\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.03288 | + | 28.5429i | −0.173547 | + | 0.984237i | ||||
\(842\) | 35.2886 | + | 16.4553i | 1.21612 | + | 0.567088i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.678207 | − | 0.119586i | 0.0233448 | − | 0.00411632i | ||||
\(845\) | −1.86522 | − | 15.3221i | −0.0641654 | − | 0.527096i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.6968 | + | 58.5813i | 0.539349 | + | 2.01288i | ||||
\(848\) | −0.806739 | + | 0.376188i | −0.0277035 | + | 0.0129184i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −24.4642 | + | 1.65981i | −0.839116 | + | 0.0569309i | ||||
\(851\) | −29.1790 | + | 34.7742i | −1.00024 | + | 1.19204i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.3970 | − | 24.4409i | −0.390225 | − | 0.836841i | −0.999052 | − | 0.0435376i | \(-0.986137\pi\) |
0.608826 | − | 0.793303i | \(-0.291641\pi\) | |||||||
\(854\) | −11.0747 | + | 19.1820i | −0.378969 | + | 0.656394i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.2655 | − | 22.9765i | −0.453405 | − | 0.785321i | ||||
\(857\) | −13.4716 | + | 19.2394i | −0.460181 | + | 0.657206i | −0.980444 | − | 0.196800i | \(-0.936945\pi\) |
0.520263 | + | 0.854006i | \(0.325834\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.36480 | − | 3.74977i | −0.0465665 | − | 0.127940i | 0.914229 | − | 0.405197i | \(-0.132797\pi\) |
−0.960796 | + | 0.277257i | \(0.910575\pi\) | |||||||
\(860\) | 1.50160 | − | 0.317550i | 0.0512041 | − | 0.0108284i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.14747 | + | 47.4058i | −0.141263 | + | 1.61465i | ||||
\(863\) | −20.0386 | + | 20.0386i | −0.682123 | + | 0.682123i | −0.960478 | − | 0.278355i | \(-0.910211\pi\) |
0.278355 | + | 0.960478i | \(0.410211\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.7972 | + | 31.7687i | 0.435116 | + | 1.08017i | ||||
\(866\) | −4.56305 | − | 5.43803i | −0.155059 | − | 0.184792i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.929084 | − | 0.650552i | 0.0315352 | − | 0.0220812i | ||||
\(869\) | 51.1922 | − | 18.6324i | 1.73657 | − | 0.632062i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.83338 | + | 10.3976i | 0.0621216 | + | 0.352309i | ||||
\(872\) | −7.72295 | + | 28.8225i | −0.261532 | + | 0.976051i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.00353 | + | 2.31144i | 0.135421 | + | 0.0781856i | ||||
\(875\) | 25.5337 | − | 26.2770i | 0.863195 | − | 0.888326i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.35740 | − | 0.731178i | 0.282209 | − | 0.0246901i | 0.0548277 | − | 0.998496i | \(-0.482539\pi\) |
0.227382 | + | 0.973806i | \(0.426984\pi\) | |||||||
\(878\) | −42.6236 | + | 3.72908i | −1.43848 | + | 0.125850i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 33.2815 | + | 31.1000i | 1.12192 | + | 1.04838i | ||||
\(881\) | −35.8317 | − | 20.6875i | −1.20720 | − | 0.696978i | −0.245055 | − | 0.969509i | \(-0.578806\pi\) |
−0.962147 | + | 0.272531i | \(0.912139\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.7078 | − | 47.4262i | 0.427652 | − | 1.59602i | −0.330411 | − | 0.943837i | \(-0.607187\pi\) |
0.758063 | − | 0.652181i | \(-0.226146\pi\) | |||||||
\(884\) | −0.180792 | − | 1.02532i | −0.00608068 | − | 0.0344852i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 40.0542 | − | 14.5785i | 1.34565 | − | 0.489776i | ||||
\(887\) | −29.4925 | + | 20.6509i | −0.990261 | + | 0.693389i | −0.952069 | − | 0.305882i | \(-0.901049\pi\) |
−0.0381920 | + | 0.999270i | \(0.512160\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.6162 | − | 32.9117i | −0.926218 | − | 1.10382i | ||||
\(890\) | 14.5593 | − | 5.86482i | 0.488029 | − | 0.196589i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.63198 | − | 1.63198i | 0.0546427 | − | 0.0546427i | ||||
\(893\) | 0.497971 | − | 5.69183i | 0.0166640 | − | 0.190470i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −39.5718 | − | 25.7565i | −1.32274 | − | 0.860945i | ||||
\(896\) | −11.4450 | − | 31.4448i | −0.382349 | − | 1.05050i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.59842 | + | 12.2798i | −0.286933 | + | 0.409783i | ||||
\(899\) | 0.190267 | + | 0.329553i | 0.00634577 | + | 0.0109912i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.424246 | − | 0.734815i | 0.0141337 | − | 0.0244802i | ||||
\(902\) | 1.05389 | + | 2.26008i | 0.0350907 | + | 0.0752523i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.4302 | + | 23.1560i | −0.646239 | + | 0.770158i | ||||
\(905\) | 20.4197 | − | 10.3777i | 0.678773 | − | 0.344968i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.5638 | − | 12.3869i | 0.882035 | − | 0.411300i | 0.0718100 | − | 0.997418i | \(-0.477122\pi\) |
0.810225 | + | 0.586118i | \(0.199345\pi\) | |||||||
\(908\) | 0.305217 | + | 1.13909i | 0.0101290 | + | 0.0378019i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −19.5452 | − | 15.3030i | −0.647916 | − | 0.507288i | ||||
\(911\) | −6.24634 | + | 1.10140i | −0.206950 | + | 0.0364909i | −0.276162 | − | 0.961111i | \(-0.589063\pi\) |
0.0692118 | + | 0.997602i | \(0.477952\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.0726549 | + | 0.0338795i | 0.00240453 | + | 0.00112125i | ||||
\(914\) | −6.17252 | + | 35.0061i | −0.204169 | + | 1.15790i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.14223 | − | 0.958446i | 0.0377404 | − | 0.0316680i | ||||
\(917\) | −7.52537 | − | 7.52537i | −0.248510 | − | 0.248510i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.7220i | 1.07940i | 0.841858 | + | 0.539699i | \(0.181462\pi\) | ||||
−0.841858 | + | 0.539699i | \(0.818538\pi\) | |||||||
\(920\) | −43.4796 | + | 13.2438i | −1.43348 | + | 0.436636i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.8663 | + | 18.3749i | 0.423728 | + | 0.605146i | ||||
\(923\) | 8.55789 | − | 18.3525i | 0.281686 | − | 0.604079i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.00902 | − | 32.0552i | −0.164696 | − | 1.05397i | ||||
\(926\) | 1.41180 | − | 0.815104i | 0.0463947 | − | 0.0267860i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.0834718 | + | 0.0223662i | −0.00274010 | + | 0.000734206i | ||||
\(929\) | 43.8241 | + | 15.9507i | 1.43782 | + | 0.523324i | 0.939162 | − | 0.343474i | \(-0.111604\pi\) |
0.498659 | + | 0.866798i | \(0.333826\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.37988 | + | 1.15786i | 0.0452237 | + | 0.0379472i | ||||
\(932\) | 0.0156110 | + | 0.178434i | 0.000511355 | + | 0.00584481i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.49095 | − | 20.5812i | 0.245111 | − | 0.673438i | ||||
\(935\) | −42.9908 | − | 6.08736i | −1.40595 | − | 0.199078i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.0118 | − | 9.38138i | −1.14379 | − | 0.306476i | −0.363313 | − | 0.931667i | \(-0.618355\pi\) |
−0.780472 | + | 0.625191i | \(0.785021\pi\) | |||||||
\(938\) | −15.7468 | − | 11.0260i | −0.514150 | − | 0.360012i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.09095 | + | 2.32707i | 0.0681992 | + | 0.0759008i | ||||
\(941\) | 57.6114 | + | 10.1585i | 1.87808 | + | 0.331156i | 0.991362 | − | 0.131155i | \(-0.0418687\pi\) |
0.886718 | + | 0.462312i | \(0.152980\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.33214 | − | 0.204035i | −0.0759448 | − | 0.00664431i | ||||
\(944\) | −14.4859 | −0.471476 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −43.3653 | −1.40993 | ||||||||
\(947\) | −35.5094 | − | 3.10667i | −1.15390 | − | 0.100953i | −0.505900 | − | 0.862592i | \(-0.668839\pi\) |
−0.648001 | + | 0.761639i | \(0.724395\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33.0369 | − | 5.82530i | −1.07242 | − | 0.189097i | ||||
\(950\) | −3.12626 | + | 1.06922i | −0.101429 | + | 0.0346902i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 27.8826 | + | 19.5236i | 0.903680 | + | 0.632763i | ||||
\(953\) | 31.6489 | + | 8.48031i | 1.02521 | + | 0.274704i | 0.731971 | − | 0.681335i | \(-0.238600\pi\) |
0.293238 | + | 0.956039i | \(0.405267\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.9773 | − | 8.25416i | 0.355216 | − | 0.267098i | ||||
\(956\) | −0.807147 | + | 2.21762i | −0.0261050 | + | 0.0717229i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.889462 | + | 10.1666i | 0.0287372 | + | 0.328468i | ||||
\(959\) | −11.8121 | − | 9.91155i | −0.381434 | − | 0.320061i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.0399 | + | 7.65791i | 0.678708 | + | 0.247029i | ||||
\(962\) | −21.2320 | + | 5.68909i | −0.684546 | + | 0.183424i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.07769 | − | 0.622203i | 0.0347100 | − | 0.0200398i | ||||
\(965\) | −7.50536 | − | 12.0388i | −0.241606 | − | 0.387543i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.66112 | − | 20.7183i | 0.310681 | − | 0.666257i | −0.687523 | − | 0.726162i | \(-0.741302\pi\) |
0.998204 | + | 0.0599053i | \(0.0190799\pi\) | |||||||
\(968\) | 30.8421 | + | 44.0471i | 0.991302 | + | 1.41573i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.71830 | − | 12.2072i | −0.119388 | − | 0.391950i | ||||
\(971\) | 15.4621i | 0.496202i | 0.968734 | + | 0.248101i | \(0.0798065\pi\) | ||||
−0.968734 | + | 0.248101i | \(0.920193\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.7157 | + | 26.7157i | 0.856467 | + | 0.856467i | ||||
\(974\) | 19.7146 | − | 16.5425i | 0.631697 | − | 0.530057i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.20831 | + | 18.1952i | −0.102696 | + | 0.582416i | ||||
\(977\) | 27.0270 | + | 12.6029i | 0.864672 | + | 0.403203i | 0.803770 | − | 0.594941i | \(-0.202824\pi\) |
0.0609021 | + | 0.998144i | \(0.480602\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.3717 | − | 4.82638i | 0.874805 | − | 0.154252i | ||||
\(980\) | −0.979077 | + | 0.119187i | −0.0312755 | + | 0.00380728i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.8098 | − | 47.8069i | −0.408777 | − | 1.52558i | ||||
\(983\) | −18.4209 | + | 8.58979i | −0.587535 | + | 0.273972i | −0.693569 | − | 0.720391i | \(-0.743963\pi\) |
0.106034 | + | 0.994363i | \(0.466185\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.724310 | − | 0.236172i | −0.0230784 | − | 0.00752507i | ||||
\(986\) | −0.408813 | + | 0.487204i | −0.0130193 | + | 0.0155157i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.0592891 | − | 0.127146i | −0.00188624 | − | 0.00404505i | ||||
\(989\) | 20.3552 | − | 35.2562i | 0.647256 | − | 1.12108i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.3395 | − | 23.1047i | −0.423743 | − | 0.733944i | 0.572559 | − | 0.819863i | \(-0.305951\pi\) |
−0.996302 | + | 0.0859191i | \(0.972617\pi\) | |||||||
\(992\) | 1.12146 | − | 1.60161i | 0.0356065 | − | 0.0508513i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12.6100 | + | 34.6457i | 0.399965 | + | 1.09890i | ||||
\(995\) | −24.9236 | + | 38.2921i | −0.790130 | + | 1.21394i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.716120 | + | 8.18529i | −0.0226798 | + | 0.259231i | 0.976387 | + | 0.216030i | \(0.0693110\pi\) |
−0.999066 | + | 0.0432005i | \(0.986245\pi\) | |||||||
\(998\) | 31.1175 | − | 31.1175i | 0.985007 | − | 0.985007i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 405.2.r.a.368.12 | 192 | ||
3.2 | odd | 2 | 135.2.q.a.113.5 | yes | 192 | ||
5.2 | odd | 4 | inner | 405.2.r.a.287.5 | 192 | ||
15.2 | even | 4 | 135.2.q.a.32.12 | ✓ | 192 | ||
15.8 | even | 4 | 675.2.ba.b.32.5 | 192 | |||
15.14 | odd | 2 | 675.2.ba.b.518.12 | 192 | |||
27.11 | odd | 18 | inner | 405.2.r.a.278.5 | 192 | ||
27.16 | even | 9 | 135.2.q.a.38.12 | yes | 192 | ||
135.43 | odd | 36 | 675.2.ba.b.632.12 | 192 | |||
135.92 | even | 36 | inner | 405.2.r.a.197.12 | 192 | ||
135.97 | odd | 36 | 135.2.q.a.92.5 | yes | 192 | ||
135.124 | even | 18 | 675.2.ba.b.443.5 | 192 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.2.q.a.32.12 | ✓ | 192 | 15.2 | even | 4 | ||
135.2.q.a.38.12 | yes | 192 | 27.16 | even | 9 | ||
135.2.q.a.92.5 | yes | 192 | 135.97 | odd | 36 | ||
135.2.q.a.113.5 | yes | 192 | 3.2 | odd | 2 | ||
405.2.r.a.197.12 | 192 | 135.92 | even | 36 | inner | ||
405.2.r.a.278.5 | 192 | 27.11 | odd | 18 | inner | ||
405.2.r.a.287.5 | 192 | 5.2 | odd | 4 | inner | ||
405.2.r.a.368.12 | 192 | 1.1 | even | 1 | trivial | ||
675.2.ba.b.32.5 | 192 | 15.8 | even | 4 | |||
675.2.ba.b.443.5 | 192 | 135.124 | even | 18 | |||
675.2.ba.b.518.12 | 192 | 15.14 | odd | 2 | |||
675.2.ba.b.632.12 | 192 | 135.43 | odd | 36 |