Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(107,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.bm (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 107.10 | ||
Character | \(\chi\) | \(=\) | 504.107 |
Dual form | 504.2.bm.c.179.10 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.576030 | + | 1.29158i | −0.407315 | + | 0.913288i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.33638 | − | 1.48798i | −0.668189 | − | 0.743991i | ||||
\(5\) | −1.88256 | + | 3.26069i | −0.841907 | + | 1.45823i | 0.0463738 | + | 0.998924i | \(0.485233\pi\) |
−0.888281 | + | 0.459301i | \(0.848100\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.23426 | + | 1.41706i | −0.844472 | + | 0.535600i | ||||
\(8\) | 2.69165 | − | 0.868922i | 0.951642 | − | 0.307210i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.12704 | − | 4.30974i | −0.988858 | − | 1.36286i | ||||
\(11\) | −1.47084 | + | 0.849192i | −0.443476 | + | 0.256041i | −0.705071 | − | 0.709137i | \(-0.749085\pi\) |
0.261595 | + | 0.965178i | \(0.415752\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.64222i | − | 1.56487i | −0.622733 | − | 0.782435i | \(-0.713978\pi\) | ||
0.622733 | − | 0.782435i | \(-0.286022\pi\) | |||||||
\(14\) | −0.543254 | − | 3.70201i | −0.145191 | − | 0.989404i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.428185 | + | 3.97702i | −0.107046 | + | 0.994254i | ||||
\(17\) | 2.26012 | − | 1.30488i | 0.548158 | − | 0.316479i | −0.200220 | − | 0.979751i | \(-0.564166\pi\) |
0.748379 | + | 0.663271i | \(0.230833\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.18076 | + | 2.04513i | −0.270885 | + | 0.469186i | −0.969089 | − | 0.246713i | \(-0.920649\pi\) |
0.698204 | + | 0.715899i | \(0.253983\pi\) | |||||||
\(20\) | 7.36767 | − | 1.55630i | 1.64746 | − | 0.347999i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.249553 | − | 2.38888i | −0.0532048 | − | 0.509311i | ||||
\(23\) | 0.653873 | − | 1.13254i | 0.136342 | − | 0.236151i | −0.789767 | − | 0.613406i | \(-0.789799\pi\) |
0.926109 | + | 0.377255i | \(0.123132\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.58807 | − | 7.94677i | −0.917614 | − | 1.58935i | ||||
\(26\) | 7.28740 | + | 3.25009i | 1.42918 | + | 0.637395i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.09439 | + | 1.43081i | 0.962749 | + | 0.270398i | ||||
\(29\) | −6.80944 | −1.26448 | −0.632241 | − | 0.774772i | \(-0.717865\pi\) | ||||
−0.632241 | + | 0.774772i | \(0.717865\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.75107 | − | 2.74303i | 0.853317 | − | 0.492663i | −0.00845183 | − | 0.999964i | \(-0.502690\pi\) |
0.861769 | + | 0.507302i | \(0.169357\pi\) | |||||||
\(32\) | −4.89000 | − | 2.84392i | −0.864439 | − | 0.502739i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.383465 | + | 3.67078i | 0.0657637 | + | 0.629533i | ||||
\(35\) | −0.414472 | − | 9.95295i | −0.0700586 | − | 1.68236i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.20109 | − | 3.00285i | −0.855054 | − | 0.493666i | 0.00729899 | − | 0.999973i | \(-0.497677\pi\) |
−0.862353 | + | 0.506308i | \(0.831010\pi\) | |||||||
\(38\) | −1.96131 | − | 2.70311i | −0.318166 | − | 0.438502i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.23391 | + | 10.4124i | −0.353212 | + | 1.64635i | ||||
\(41\) | − | 6.10456i | − | 0.953373i | −0.879073 | − | 0.476686i | \(-0.841838\pi\) | ||
0.879073 | − | 0.476686i | \(-0.158162\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.49804 | −0.990943 | −0.495471 | − | 0.868624i | \(-0.665005\pi\) | ||||
−0.495471 | + | 0.868624i | \(0.665005\pi\) | |||||||
\(44\) | 3.22919 | + | 1.05375i | 0.486818 | + | 0.158859i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.08612 | + | 1.49691i | 0.160140 | + | 0.220707i | ||||
\(47\) | −3.53360 | + | 6.12038i | −0.515429 | + | 0.892749i | 0.484411 | + | 0.874841i | \(0.339034\pi\) |
−0.999840 | + | 0.0179081i | \(0.994299\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.98386 | − | 6.33219i | 0.426266 | − | 0.904598i | ||||
\(50\) | 12.9068 | − | 1.34830i | 1.82530 | − | 0.190678i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.39552 | + | 7.54014i | −1.16425 | + | 1.04563i | ||||
\(53\) | 0.488913 | + | 0.846821i | 0.0671573 | + | 0.116320i | 0.897649 | − | 0.440711i | \(-0.145274\pi\) |
−0.830492 | + | 0.557031i | \(0.811940\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.39462i | − | 0.862251i | ||||||
\(56\) | −4.78253 | + | 5.75564i | −0.639093 | + | 0.769130i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.92244 | − | 8.79496i | 0.515042 | − | 1.15484i | ||||
\(59\) | −6.67395 | + | 3.85320i | −0.868874 | + | 0.501645i | −0.866974 | − | 0.498354i | \(-0.833938\pi\) |
−0.00190001 | + | 0.999998i | \(0.500605\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.64484 | + | 4.41375i | 0.978822 | + | 0.565123i | 0.901914 | − | 0.431915i | \(-0.142162\pi\) |
0.0769075 | + | 0.997038i | \(0.475495\pi\) | |||||||
\(62\) | 0.806095 | + | 7.71647i | 0.102374 | + | 0.979993i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.48995 | − | 4.67767i | 0.811244 | − | 0.584708i | ||||
\(65\) | 18.3975 | + | 10.6218i | 2.28193 | + | 1.31747i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.69828 | + | 11.6018i | 0.818325 | + | 1.41738i | 0.906916 | + | 0.421312i | \(0.138430\pi\) |
−0.0885910 | + | 0.996068i | \(0.528236\pi\) | |||||||
\(68\) | −4.96201 | − | 1.61920i | −0.601732 | − | 0.196357i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 13.0938 | + | 5.19787i | 1.56501 | + | 0.621265i | ||||
\(71\) | −9.40544 | −1.11622 | −0.558110 | − | 0.829767i | \(-0.688473\pi\) | ||||
−0.558110 | + | 0.829767i | \(0.688473\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.09003 | − | 1.88798i | −0.127578 | − | 0.220971i | 0.795160 | − | 0.606400i | \(-0.207387\pi\) |
−0.922738 | + | 0.385429i | \(0.874054\pi\) | |||||||
\(74\) | 6.87442 | − | 4.98791i | 0.799135 | − | 0.579833i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.62106 | − | 0.976124i | 0.530072 | − | 0.111969i | ||||
\(77\) | 2.08289 | − | 3.98160i | 0.237368 | − | 0.453745i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.0908 | − | 8.71267i | −1.69785 | − | 0.980252i | −0.947800 | − | 0.318865i | \(-0.896698\pi\) |
−0.750045 | − | 0.661386i | \(-0.769968\pi\) | |||||||
\(80\) | −12.1617 | − | 8.88315i | −1.35972 | − | 0.993167i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.88456 | + | 3.51641i | 0.870704 | + | 0.388323i | ||||
\(83\) | 11.8864i | 1.30471i | 0.757915 | + | 0.652353i | \(0.226218\pi\) | ||||
−0.757915 | + | 0.652353i | \(0.773782\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.82605i | 1.06578i | ||||||||
\(86\) | 3.74307 | − | 8.39277i | 0.403626 | − | 0.905016i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.22111 | + | 3.56378i | −0.343372 | + | 0.379900i | ||||
\(89\) | −9.58642 | − | 5.53472i | −1.01616 | − | 0.586679i | −0.103170 | − | 0.994664i | \(-0.532898\pi\) |
−0.912989 | + | 0.407984i | \(0.866232\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.99538 | + | 12.6062i | 0.838144 | + | 1.32149i | ||||
\(92\) | −2.55902 | + | 0.540552i | −0.266797 | + | 0.0563564i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.86952 | − | 8.08946i | −0.605395 | − | 0.834364i | ||||
\(95\) | −4.44570 | − | 7.70018i | −0.456119 | − | 0.790021i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.0631 | 1.52943 | 0.764715 | − | 0.644369i | \(-0.222880\pi\) | ||||
0.764715 | + | 0.644369i | \(0.222880\pi\) | |||||||
\(98\) | 6.45976 | + | 7.50144i | 0.652534 | + | 0.757759i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.69326 | + | 17.4469i | −0.569326 | + | 1.74469i | ||||
\(101\) | −0.777899 | − | 1.34736i | −0.0774039 | − | 0.134067i | 0.824725 | − | 0.565534i | \(-0.191330\pi\) |
−0.902129 | + | 0.431466i | \(0.857996\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.94066 | + | 4.00719i | 0.683883 | + | 0.394840i | 0.801317 | − | 0.598240i | \(-0.204133\pi\) |
−0.117433 | + | 0.993081i | \(0.537467\pi\) | |||||||
\(104\) | −4.90265 | − | 15.1869i | −0.480744 | − | 1.48919i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.37537 | + | 0.143677i | −0.133588 | + | 0.0139551i | ||||
\(107\) | −12.6257 | − | 7.28943i | −1.22057 | − | 0.704696i | −0.255530 | − | 0.966801i | \(-0.582250\pi\) |
−0.965039 | + | 0.262105i | \(0.915583\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.655188 | + | 0.378273i | −0.0627556 | + | 0.0362320i | −0.531050 | − | 0.847341i | \(-0.678202\pi\) |
0.468294 | + | 0.883573i | \(0.344869\pi\) | |||||||
\(110\) | 8.25920 | + | 3.68350i | 0.787483 | + | 0.351208i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.67901 | − | 9.49246i | −0.442125 | − | 0.896954i | ||||
\(113\) | 9.87390i | 0.928859i | 0.885610 | + | 0.464429i | \(0.153741\pi\) | ||||
−0.885610 | + | 0.464429i | \(0.846259\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.46191 | + | 4.26416i | 0.229574 | + | 0.397635i | ||||
\(116\) | 9.09999 | + | 10.1323i | 0.844913 | + | 0.940763i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.13234 | − | 10.8395i | −0.104241 | − | 0.997859i | ||||
\(119\) | −3.20060 | + | 6.11817i | −0.293398 | + | 0.560852i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.05774 | + | 7.02822i | −0.368886 | + | 0.638929i | ||||
\(122\) | −10.1044 | + | 7.33150i | −0.914809 | + | 0.663763i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −10.4308 | − | 3.40378i | −0.936714 | − | 0.305668i | ||||
\(125\) | 15.7237 | 1.40637 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.50847i | 0.400062i | 0.979790 | + | 0.200031i | \(0.0641043\pi\) | ||||
−0.979790 | + | 0.200031i | \(0.935896\pi\) | |||||||
\(128\) | 2.30319 | + | 11.0768i | 0.203575 | + | 0.979059i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −24.3165 | + | 17.6435i | −2.13270 | + | 1.54743i | ||||
\(131\) | −14.0673 | − | 8.12176i | −1.22907 | − | 0.709601i | −0.262231 | − | 0.965005i | \(-0.584458\pi\) |
−0.966835 | + | 0.255404i | \(0.917792\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.259961 | − | 6.24258i | −0.0225414 | − | 0.541300i | ||||
\(134\) | −18.8431 | + | 1.96843i | −1.62779 | + | 0.170046i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.94960 | − | 5.47614i | 0.424425 | − | 0.469575i | ||||
\(137\) | −3.63470 | + | 2.09849i | −0.310533 | + | 0.179286i | −0.647165 | − | 0.762350i | \(-0.724046\pi\) |
0.336632 | + | 0.941636i | \(0.390712\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.70274 | −0.483700 | −0.241850 | − | 0.970314i | \(-0.577754\pi\) | ||||
−0.241850 | + | 0.970314i | \(0.577754\pi\) | |||||||
\(140\) | −14.2559 | + | 13.9176i | −1.20485 | + | 1.17625i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.41782 | − | 12.1479i | 0.454653 | − | 1.01943i | ||||
\(143\) | 4.79133 | + | 8.29882i | 0.400671 | + | 0.693982i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.8192 | − | 22.2035i | 1.06458 | − | 1.84390i | ||||
\(146\) | 3.06637 | − | 0.320326i | 0.253775 | − | 0.0265104i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.48243 | + | 11.7521i | 0.204055 | + | 0.966015i | ||||
\(149\) | −6.74195 | + | 11.6774i | −0.552322 | + | 0.956650i | 0.445784 | + | 0.895140i | \(0.352925\pi\) |
−0.998106 | + | 0.0615095i | \(0.980409\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.4727 | + | 10.6652i | −1.50329 | + | 0.867924i | −0.503295 | + | 0.864115i | \(0.667879\pi\) |
−0.999993 | + | 0.00380878i | \(0.998788\pi\) | |||||||
\(152\) | −1.40113 | + | 6.53077i | −0.113646 | + | 0.529715i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.94276 | + | 4.98375i | 0.317717 | + | 0.401602i | ||||
\(155\) | 20.6557i | 1.65910i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.97251 | + | 4.60293i | −0.636276 | + | 0.367354i | −0.783179 | − | 0.621797i | \(-0.786403\pi\) |
0.146903 | + | 0.989151i | \(0.453070\pi\) | |||||||
\(158\) | 19.9459 | − | 14.4723i | 1.58681 | − | 1.15135i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 18.4789 | − | 10.5909i | 1.46088 | − | 0.837287i | ||||
\(161\) | 0.143959 | + | 3.45697i | 0.0113456 | + | 0.272448i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.0600325 | − | 0.103979i | 0.00470211 | − | 0.00814429i | −0.863665 | − | 0.504067i | \(-0.831837\pi\) |
0.868367 | + | 0.495922i | \(0.165170\pi\) | |||||||
\(164\) | −9.08349 | + | 8.15801i | −0.709301 | + | 0.637033i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.3523 | − | 6.84695i | −1.19157 | − | 0.531426i | ||||
\(167\) | 12.9810 | 1.00450 | 0.502251 | − | 0.864722i | \(-0.332505\pi\) | ||||
0.502251 | + | 0.864722i | \(0.332505\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.8346 | −1.44882 | ||||||||
\(170\) | −12.6912 | − | 5.66010i | −0.973368 | − | 0.434110i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.68385 | + | 9.66898i | 0.662137 | + | 0.737253i | ||||
\(173\) | 3.44458 | − | 5.96618i | 0.261886 | − | 0.453600i | −0.704857 | − | 0.709350i | \(-0.748989\pi\) |
0.966743 | + | 0.255749i | \(0.0823221\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21.5120 | + | 11.2536i | 1.62616 | + | 0.850691i | ||||
\(176\) | −2.74746 | − | 6.21318i | −0.207097 | − | 0.468336i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.6706 | − | 9.19350i | 0.949704 | − | 0.689082i | ||||
\(179\) | 13.6043 | − | 7.85445i | 1.01683 | − | 0.587070i | 0.103649 | − | 0.994614i | \(-0.466948\pi\) |
0.913185 | + | 0.407544i | \(0.133615\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.6714i | − | 1.16485i | −0.812886 | − | 0.582423i | \(-0.802105\pi\) | ||
0.812886 | − | 0.582423i | \(-0.197895\pi\) | |||||||
\(182\) | −20.8875 | + | 3.06516i | −1.54829 | + | 0.227205i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.775906 | − | 3.61657i | 0.0572006 | − | 0.266617i | ||||
\(185\) | 19.5827 | − | 11.3061i | 1.43975 | − | 0.831241i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.21618 | + | 3.83854i | −0.162063 | + | 0.280702i | ||||
\(188\) | 13.8292 | − | 2.92120i | 1.00860 | − | 0.213051i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.5063 | − | 1.30646i | 0.907301 | − | 0.0947805i | ||||
\(191\) | 12.0633 | − | 20.8943i | 0.872873 | − | 1.51186i | 0.0138617 | − | 0.999904i | \(-0.495588\pi\) |
0.859011 | − | 0.511957i | \(-0.171079\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.80306 | − | 8.31914i | −0.345732 | − | 0.598825i | 0.639755 | − | 0.768579i | \(-0.279036\pi\) |
−0.985486 | + | 0.169754i | \(0.945703\pi\) | |||||||
\(194\) | −8.67682 | + | 19.4553i | −0.622959 | + | 1.39681i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −13.4097 | + | 4.02227i | −0.957839 | + | 0.287305i | ||||
\(197\) | −2.05305 | −0.146274 | −0.0731371 | − | 0.997322i | \(-0.523301\pi\) | ||||
−0.0731371 | + | 0.997322i | \(0.523301\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.62103 | − | 4.97735i | 0.611128 | − | 0.352835i | −0.162279 | − | 0.986745i | \(-0.551884\pi\) |
0.773407 | + | 0.633910i | \(0.218551\pi\) | |||||||
\(200\) | −19.2546 | − | 17.4032i | −1.36151 | − | 1.23060i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.18832 | − | 0.228602i | 0.153970 | − | 0.0160844i | ||||
\(203\) | 15.2141 | − | 9.64941i | 1.06782 | − | 0.677256i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.9051 | + | 11.4922i | 1.39023 | + | 0.802651i | ||||
\(206\) | −9.17365 | + | 6.65618i | −0.639159 | + | 0.463758i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 22.4392 | + | 2.41591i | 1.55588 | + | 0.167514i | ||||
\(209\) | − | 4.01076i | − | 0.277430i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.9757 | −0.962128 | −0.481064 | − | 0.876685i | \(-0.659750\pi\) | ||||
−0.481064 | + | 0.876685i | \(0.659750\pi\) | |||||||
\(212\) | 0.606683 | − | 1.85917i | 0.0416672 | − | 0.127688i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 16.6877 | − | 12.1082i | 1.14075 | − | 0.827698i | ||||
\(215\) | 12.2330 | − | 21.1881i | 0.834281 | − | 1.44502i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.72808 | + | 12.8612i | −0.456732 | + | 0.873076i | ||||
\(218\) | −0.111163 | − | 1.06413i | −0.00752893 | − | 0.0720718i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.51509 | + | 8.54564i | −0.641507 | + | 0.576147i | ||||
\(221\) | −7.36241 | − | 12.7521i | −0.495249 | − | 0.857796i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.8817i | 1.06352i | 0.846896 | + | 0.531759i | \(0.178469\pi\) | ||||
−0.846896 | + | 0.531759i | \(0.821531\pi\) | |||||||
\(224\) | 14.9556 | − | 0.575385i | 0.999261 | − | 0.0384446i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.7530 | − | 5.68767i | −0.848315 | − | 0.378338i | ||||
\(227\) | 0.620059 | − | 0.357991i | 0.0411548 | − | 0.0237607i | −0.479281 | − | 0.877661i | \(-0.659103\pi\) |
0.520436 | + | 0.853901i | \(0.325769\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.89913 | + | 2.25117i | 0.257662 | + | 0.148761i | 0.623268 | − | 0.782009i | \(-0.285805\pi\) |
−0.365606 | + | 0.930770i | \(0.619138\pi\) | |||||||
\(230\) | −6.92565 | + | 0.723483i | −0.456664 | + | 0.0477051i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −18.3286 | + | 5.91687i | −1.20333 | + | 0.388462i | ||||
\(233\) | 6.69604 | + | 3.86596i | 0.438672 | + | 0.253267i | 0.703034 | − | 0.711156i | \(-0.251828\pi\) |
−0.264362 | + | 0.964423i | \(0.585161\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.3044 | − | 23.0440i | −0.867886 | − | 1.50322i | ||||
\(236\) | 14.6524 | + | 4.78138i | 0.953791 | + | 0.311241i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.05849 | − | 7.65809i | −0.392713 | − | 0.496400i | ||||
\(239\) | 21.3788 | 1.38288 | 0.691440 | − | 0.722433i | \(-0.256976\pi\) | ||||
0.691440 | + | 0.722433i | \(0.256976\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.25688 | + | 7.37313i | 0.274210 | + | 0.474945i | 0.969935 | − | 0.243362i | \(-0.0782504\pi\) |
−0.695726 | + | 0.718308i | \(0.744917\pi\) | |||||||
\(242\) | −6.74015 | − | 9.28939i | −0.433273 | − | 0.597144i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.64882 | − | 17.2738i | −0.233592 | − | 1.10584i | ||||
\(245\) | 15.0300 | + | 21.6502i | 0.960232 | + | 1.38318i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.5391 | + | 6.66209i | 0.734215 | + | 0.423899i | ||||
\(248\) | 10.4047 | − | 11.5116i | 0.660701 | − | 0.730986i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.05731 | + | 20.3084i | −0.572835 | + | 1.28442i | ||||
\(251\) | 0.778871i | 0.0491619i | 0.999698 | + | 0.0245810i | \(0.00782515\pi\) | ||||
−0.999698 | + | 0.0245810i | \(0.992175\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.22106i | 0.139637i | ||||||||
\(254\) | −5.82307 | − | 2.59702i | −0.365372 | − | 0.162951i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.6333 | − | 3.40580i | −0.977082 | − | 0.212862i | ||||
\(257\) | −10.6901 | − | 6.17195i | −0.666832 | − | 0.384996i | 0.128043 | − | 0.991769i | \(-0.459130\pi\) |
−0.794875 | + | 0.606773i | \(0.792464\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.8758 | − | 0.661120i | 0.986476 | − | 0.0410800i | ||||
\(260\) | −8.78098 | − | 41.5700i | −0.544573 | − | 2.57806i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18.5931 | − | 13.4907i | 1.14869 | − | 0.833460i | ||||
\(263\) | 1.01432 | + | 1.75686i | 0.0625458 | + | 0.108333i | 0.895603 | − | 0.444855i | \(-0.146745\pi\) |
−0.833057 | + | 0.553187i | \(0.813411\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.68163 | −0.226161 | ||||||||
\(266\) | 8.21256 | + | 3.26015i | 0.503544 | + | 0.199893i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.31178 | − | 25.4713i | 0.507723 | − | 1.55590i | ||||
\(269\) | −13.1346 | − | 22.7498i | −0.800833 | − | 1.38708i | −0.919069 | − | 0.394097i | \(-0.871057\pi\) |
0.118236 | − | 0.992986i | \(-0.462276\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.01591 | − | 4.05064i | −0.426186 | − | 0.246059i | 0.271535 | − | 0.962429i | \(-0.412469\pi\) |
−0.697720 | + | 0.716370i | \(0.745802\pi\) | |||||||
\(272\) | 4.22177 | + | 9.54724i | 0.255983 | + | 0.578887i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.616685 | − | 5.90331i | −0.0372553 | − | 0.356632i | ||||
\(275\) | 13.4967 | + | 7.79231i | 0.813880 | + | 0.469894i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.45693 | + | 4.88261i | −0.508127 | + | 0.293368i | −0.732064 | − | 0.681236i | \(-0.761443\pi\) |
0.223936 | + | 0.974604i | \(0.428109\pi\) | |||||||
\(278\) | 3.28495 | − | 7.36557i | 0.197018 | − | 0.441758i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −9.76395 | − | 26.4297i | −0.583508 | − | 1.57948i | ||||
\(281\) | − | 1.88752i | − | 0.112600i | −0.998414 | − | 0.0562999i | \(-0.982070\pi\) | ||
0.998414 | − | 0.0562999i | \(-0.0179303\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.28892 | + | 5.69657i | 0.195506 | + | 0.338626i | 0.947066 | − | 0.321038i | \(-0.104032\pi\) |
−0.751560 | + | 0.659664i | \(0.770698\pi\) | |||||||
\(284\) | 12.5692 | + | 13.9951i | 0.745847 | + | 0.830458i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −13.4786 | + | 1.40803i | −0.797005 | + | 0.0832585i | ||||
\(287\) | 8.65056 | + | 13.6392i | 0.510626 | + | 0.805097i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.09459 | + | 8.82408i | −0.299682 | + | 0.519064i | ||||
\(290\) | 21.2934 | + | 29.3469i | 1.25039 | + | 1.72331i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.35259 | + | 4.14500i | −0.0791546 | + | 0.242567i | ||||
\(293\) | 14.1311 | 0.825545 | 0.412772 | − | 0.910834i | \(-0.364560\pi\) | ||||
0.412772 | + | 0.910834i | \(0.364560\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 29.0156i | − | 1.68935i | ||||||
\(296\) | −16.6088 | − | 3.56328i | −0.965364 | − | 0.207111i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.1988 | − | 15.4343i | −0.648728 | − | 0.894087i | ||||
\(299\) | −6.39004 | − | 3.68929i | −0.369546 | − | 0.213357i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.5183 | − | 9.20814i | 0.836823 | − | 0.530749i | ||||
\(302\) | −3.13419 | − | 30.0025i | −0.180353 | − | 1.72645i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.62795 | − | 5.57159i | −0.437493 | − | 0.319553i | ||||
\(305\) | −28.7838 | + | 16.6183i | −1.64815 | + | 0.951562i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.5973 | −1.00433 | −0.502167 | − | 0.864771i | \(-0.667464\pi\) | ||||
−0.502167 | + | 0.864771i | \(0.667464\pi\) | |||||||
\(308\) | −8.70808 | + | 2.22162i | −0.496189 | + | 0.126588i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −26.6785 | − | 11.8983i | −1.51524 | − | 0.675778i | ||||
\(311\) | 5.44683 | + | 9.43418i | 0.308861 | + | 0.534963i | 0.978114 | − | 0.208072i | \(-0.0667188\pi\) |
−0.669252 | + | 0.743035i | \(0.733385\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.76535 | + | 3.05768i | −0.0997835 | + | 0.172830i | −0.911595 | − | 0.411090i | \(-0.865148\pi\) |
0.811811 | + | 0.583920i | \(0.198482\pi\) | |||||||
\(314\) | −1.35267 | − | 12.9486i | −0.0763354 | − | 0.730732i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.20270 | + | 34.0982i | 0.405183 | + | 1.91818i | ||||
\(317\) | 8.09426 | − | 14.0197i | 0.454619 | − | 0.787423i | −0.544047 | − | 0.839055i | \(-0.683109\pi\) |
0.998666 | + | 0.0516316i | \(0.0164422\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.0156 | − | 5.78252i | 0.560767 | − | 0.323759i | ||||
\(320\) | 3.03470 | + | 29.9677i | 0.169645 | + | 1.67525i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.54790 | − | 1.80539i | −0.253444 | − | 0.100610i | ||||
\(323\) | 6.16298i | 0.342918i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −44.8374 | + | 25.8869i | −2.48713 | + | 1.43595i | ||||
\(326\) | 0.0997175 | + | 0.137432i | 0.00552284 | + | 0.00761167i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.30439 | − | 16.4313i | −0.292886 | − | 0.907269i | ||||
\(329\) | −0.777972 | − | 18.6819i | −0.0428910 | − | 1.02996i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.79835 | − | 10.0430i | 0.318706 | − | 0.552016i | −0.661512 | − | 0.749935i | \(-0.730085\pi\) |
0.980218 | + | 0.197919i | \(0.0634183\pi\) | |||||||
\(332\) | 17.6868 | − | 15.8848i | 0.970690 | − | 0.871791i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.47747 | + | 16.7661i | −0.409149 | + | 0.917400i | ||||
\(335\) | −50.4397 | −2.75581 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.81073 | 0.153110 | 0.0765550 | − | 0.997065i | \(-0.475608\pi\) | ||||
0.0765550 | + | 0.997065i | \(0.475608\pi\) | |||||||
\(338\) | 10.8493 | − | 24.3265i | 0.590124 | − | 1.32319i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 14.6210 | − | 13.1313i | 0.792935 | − | 0.712146i | ||||
\(341\) | −4.65872 | + | 8.06914i | −0.252284 | + | 0.436968i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.30639 | + | 18.3761i | 0.124533 | + | 0.992215i | ||||
\(344\) | −17.4905 | + | 5.64629i | −0.943022 | + | 0.304428i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.72164 | + | 7.88566i | 0.307597 | + | 0.423936i | ||||
\(347\) | −18.7883 | + | 10.8474i | −1.00861 | + | 0.582320i | −0.910784 | − | 0.412884i | \(-0.864522\pi\) |
−0.0978242 | + | 0.995204i | \(0.531188\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 7.44465i | − | 0.398503i | −0.979948 | − | 0.199251i | \(-0.936149\pi\) | ||
0.979948 | − | 0.199251i | \(-0.0638511\pi\) | |||||||
\(350\) | −26.9265 | + | 21.3022i | −1.43928 | + | 1.13865i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.60747 | + | 0.0304086i | 0.512080 | + | 0.00162078i | ||||
\(353\) | 13.0365 | − | 7.52665i | 0.693865 | − | 0.400603i | −0.111193 | − | 0.993799i | \(-0.535467\pi\) |
0.805058 | + | 0.593196i | \(0.202134\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.7063 | − | 30.6682i | 0.939754 | − | 1.62770i | ||||
\(356\) | 4.57551 | + | 21.6609i | 0.242502 | + | 1.14803i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.30819 | + | 22.0955i | 0.121992 | + | 1.16778i | ||||
\(359\) | −9.01876 | + | 15.6210i | −0.475992 | + | 0.824442i | −0.999622 | − | 0.0275035i | \(-0.991244\pi\) |
0.523630 | + | 0.851946i | \(0.324578\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.71162 | + | 11.6249i | 0.353243 | + | 0.611835i | ||||
\(362\) | 20.2409 | + | 9.02720i | 1.06384 | + | 0.474459i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.07294 | − | 28.7436i | 0.423137 | − | 1.50658i | ||||
\(365\) | 8.20816 | 0.429635 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.38897 | + | 1.95662i | −0.176903 | + | 0.102135i | −0.585837 | − | 0.810429i | \(-0.699234\pi\) |
0.408934 | + | 0.912564i | \(0.365901\pi\) | |||||||
\(368\) | 4.22416 | + | 3.08540i | 0.220199 | + | 0.160838i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.32253 | + | 31.8054i | 0.172730 | + | 1.65348i | ||||
\(371\) | −2.29236 | − | 1.19920i | −0.119013 | − | 0.0622594i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.8513 | + | 9.15178i | 0.820752 | + | 0.473861i | 0.850676 | − | 0.525691i | \(-0.176193\pi\) |
−0.0299239 | + | 0.999552i | \(0.509527\pi\) | |||||||
\(374\) | −3.68121 | − | 5.07351i | −0.190351 | − | 0.262345i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.19308 | + | 19.5443i | −0.216242 | + | 1.00792i | ||||
\(377\) | 38.4203i | 1.97875i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.8073 | 1.32563 | 0.662816 | − | 0.748783i | \(-0.269361\pi\) | ||||
0.662816 | + | 0.748783i | \(0.269361\pi\) | |||||||
\(380\) | −5.51659 | + | 16.9055i | −0.282995 | + | 0.867232i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 20.0379 | + | 27.6166i | 1.02523 | + | 1.41299i | ||||
\(383\) | −7.37665 | + | 12.7767i | −0.376929 | + | 0.652860i | −0.990614 | − | 0.136691i | \(-0.956353\pi\) |
0.613685 | + | 0.789551i | \(0.289687\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.06159 | + | 14.2873i | 0.461822 | + | 0.728147i | ||||
\(386\) | 13.5116 | − | 1.41148i | 0.687721 | − | 0.0718423i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −20.1300 | − | 22.4137i | −1.02195 | − | 1.13788i | ||||
\(389\) | 8.70264 | + | 15.0734i | 0.441242 | + | 0.764253i | 0.997782 | − | 0.0665677i | \(-0.0212049\pi\) |
−0.556540 | + | 0.830821i | \(0.687872\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.41290i | − | 0.172598i | ||||||
\(392\) | 2.52933 | − | 19.6368i | 0.127750 | − | 0.991806i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.18262 | − | 2.65169i | 0.0595796 | − | 0.133590i | ||||
\(395\) | 56.8186 | − | 32.8042i | 2.85886 | − | 1.65056i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0273 | + | 5.78926i | 0.503255 | + | 0.290554i | 0.730057 | − | 0.683387i | \(-0.239494\pi\) |
−0.226802 | + | 0.973941i | \(0.572827\pi\) | |||||||
\(398\) | 1.46270 | + | 14.0019i | 0.0733184 | + | 0.701851i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 33.5690 | − | 14.8441i | 1.67845 | − | 0.742207i | ||||
\(401\) | −31.1453 | − | 17.9818i | −1.55532 | − | 0.897967i | −0.997694 | − | 0.0678773i | \(-0.978377\pi\) |
−0.557630 | − | 0.830089i | \(-0.688289\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.4768 | − | 26.8065i | −0.770953 | − | 1.33533i | ||||
\(404\) | −0.965282 | + | 2.95809i | −0.0480246 | + | 0.147170i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.69926 | + | 25.2086i | 0.183591 | + | 1.25108i | ||||
\(407\) | 10.2000 | 0.505595 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.1615 | + | 21.0644i | 0.601349 | + | 1.04157i | 0.992617 | + | 0.121290i | \(0.0387031\pi\) |
−0.391268 | + | 0.920277i | \(0.627964\pi\) | |||||||
\(410\) | −26.3091 | + | 19.0892i | −1.29931 | + | 0.942751i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.31272 | − | 15.6827i | −0.163206 | − | 0.772631i | ||||
\(413\) | 9.45111 | − | 18.0665i | 0.465059 | − | 0.888993i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −38.7580 | − | 22.3769i | −1.90256 | − | 1.09844i | ||||
\(416\) | −16.0460 | + | 27.5905i | −0.786720 | + | 1.35273i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.18024 | + | 2.31032i | 0.253374 | + | 0.113001i | ||||
\(419\) | 6.92954i | 0.338530i | 0.985571 | + | 0.169265i | \(0.0541394\pi\) | ||||
−0.985571 | + | 0.169265i | \(0.945861\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 12.6192i | − | 0.615024i | −0.951544 | − | 0.307512i | \(-0.900504\pi\) | ||
0.951544 | − | 0.307512i | \(-0.0994965\pi\) | |||||||
\(422\) | 8.05043 | − | 18.0508i | 0.391889 | − | 0.878700i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.05180 | + | 1.85452i | 0.0996444 | + | 0.0900634i | ||||
\(425\) | −20.7391 | − | 11.9737i | −1.00600 | − | 0.580812i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.3352 | + | 0.971750i | −1.12927 | + | 0.0470263i | ||||
\(428\) | 6.02612 | + | 28.5282i | 0.291284 | + | 1.37896i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 20.3197 | + | 28.0049i | 0.979902 | + | 1.35052i | ||||
\(431\) | −11.1759 | − | 19.3571i | −0.538322 | − | 0.932401i | −0.998995 | − | 0.0448306i | \(-0.985725\pi\) |
0.460673 | − | 0.887570i | \(-0.347608\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.2813 | −1.55134 | −0.775671 | − | 0.631138i | \(-0.782588\pi\) | ||||
−0.775671 | + | 0.631138i | \(0.782588\pi\) | |||||||
\(434\) | −12.7358 | − | 16.0983i | −0.611336 | − | 0.772745i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.43844 | + | 0.469393i | 0.0688889 | + | 0.0224798i | ||||
\(437\) | 1.54413 | + | 2.67451i | 0.0738658 | + | 0.127939i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.42798 | − | 1.40180i | −0.115881 | − | 0.0669041i | 0.440939 | − | 0.897537i | \(-0.354645\pi\) |
−0.556820 | + | 0.830633i | \(0.687979\pi\) | |||||||
\(440\) | −5.55643 | − | 17.2121i | −0.264892 | − | 0.820554i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.7113 | − | 2.16359i | 0.985137 | − | 0.102912i | ||||
\(443\) | 16.2066 | + | 9.35689i | 0.769999 | + | 0.444559i | 0.832874 | − | 0.553462i | \(-0.186694\pi\) |
−0.0628752 | + | 0.998021i | \(0.520027\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 36.0940 | − | 20.8389i | 1.71102 | − | 0.987859i | ||||
\(446\) | −20.5126 | − | 9.14834i | −0.971298 | − | 0.433187i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.87170 | + | 19.6478i | −0.371903 | + | 0.928272i | ||||
\(449\) | 13.8950i | 0.655747i | 0.944722 | + | 0.327874i | \(0.106332\pi\) | ||||
−0.944722 | + | 0.327874i | \(0.893668\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.18395 | + | 8.97886i | 0.244103 | + | 0.422798i | ||||
\(452\) | 14.6922 | − | 13.1953i | 0.691063 | − | 0.620653i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.105203 | + | 1.00707i | 0.00493742 | + | 0.0472642i | ||||
\(455\) | −56.1567 | + | 2.33854i | −2.63267 | + | 0.109633i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.88922 | − | 5.00428i | 0.135152 | − | 0.234090i | −0.790503 | − | 0.612458i | \(-0.790181\pi\) |
0.925656 | + | 0.378367i | \(0.123514\pi\) | |||||||
\(458\) | −5.15359 | + | 3.73932i | −0.240811 | + | 0.174727i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.05494 | − | 9.36181i | 0.142438 | − | 0.436496i | ||||
\(461\) | −15.4222 | −0.718285 | −0.359142 | − | 0.933283i | \(-0.616931\pi\) | ||||
−0.359142 | + | 0.933283i | \(0.616931\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 11.5902i | − | 0.538644i | −0.963050 | − | 0.269322i | \(-0.913200\pi\) | ||
0.963050 | − | 0.269322i | \(-0.0867996\pi\) | |||||||
\(464\) | 2.91570 | − | 27.0813i | 0.135358 | − | 1.25722i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.85033 | + | 6.42159i | −0.409984 | + | 0.297474i | ||||
\(467\) | −1.98153 | − | 1.14404i | −0.0916943 | − | 0.0529397i | 0.453452 | − | 0.891281i | \(-0.350192\pi\) |
−0.545146 | + | 0.838341i | \(0.683526\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −31.4061 | − | 16.4295i | −1.45020 | − | 0.758643i | ||||
\(470\) | 37.4270 | − | 3.90978i | 1.72638 | − | 0.180345i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −14.6158 | + | 16.1706i | −0.672746 | + | 0.744313i | ||||
\(473\) | 9.55761 | − | 5.51809i | 0.439459 | − | 0.253722i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.6696 | 0.994270 | ||||||||
\(476\) | 13.3809 | − | 3.41376i | 0.613314 | − | 0.156469i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.3148 | + | 27.6125i | −0.563268 | + | 1.26297i | ||||
\(479\) | 9.42948 | + | 16.3323i | 0.430844 | + | 0.746244i | 0.996946 | − | 0.0780912i | \(-0.0248825\pi\) |
−0.566102 | + | 0.824335i | \(0.691549\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.9427 | + | 29.3457i | −0.772522 | + | 1.33805i | ||||
\(482\) | −11.9751 | + | 1.25097i | −0.545451 | + | 0.0569802i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15.8806 | − | 3.35451i | 0.721843 | − | 0.152478i | ||||
\(485\) | −28.3573 | + | 49.1162i | −1.28764 | + | 2.23025i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.9019 | + | 15.5318i | −1.21904 | + | 0.703813i | −0.964713 | − | 0.263305i | \(-0.915187\pi\) |
−0.254327 | + | 0.967118i | \(0.581854\pi\) | |||||||
\(488\) | 24.4124 | + | 5.23750i | 1.10510 | + | 0.237090i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −36.6207 | + | 6.94136i | −1.65436 | + | 0.313579i | ||||
\(491\) | − | 7.52948i | − | 0.339801i | −0.985461 | − | 0.169900i | \(-0.945655\pi\) | ||
0.985461 | − | 0.169900i | \(-0.0543446\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.3901 | + | 8.88549i | −0.693136 | + | 0.400182i | ||||
\(494\) | −15.2515 | + | 11.0661i | −0.686198 | + | 0.497889i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.87474 | + | 20.0696i | 0.398487 | + | 0.901151i | ||||
\(497\) | 21.0142 | − | 13.3281i | 0.942617 | − | 0.597848i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.883277 | + | 1.52988i | −0.0395409 | + | 0.0684869i | −0.885119 | − | 0.465366i | \(-0.845923\pi\) |
0.845578 | + | 0.533852i | \(0.179256\pi\) | |||||||
\(500\) | −21.0128 | − | 23.3966i | −0.939720 | − | 1.04633i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.00598 | − | 0.448653i | −0.0448990 | − | 0.0200244i | ||||
\(503\) | 16.9584 | 0.756136 | 0.378068 | − | 0.925778i | \(-0.376589\pi\) | ||||
0.378068 | + | 0.925778i | \(0.376589\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.85777 | 0.260667 | ||||||||
\(506\) | −2.86868 | − | 1.27940i | −0.127528 | − | 0.0568760i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.70853 | − | 6.02503i | 0.297643 | − | 0.267317i | ||||
\(509\) | 5.13114 | − | 8.88739i | 0.227434 | − | 0.393927i | −0.729613 | − | 0.683860i | \(-0.760300\pi\) |
0.957047 | + | 0.289934i | \(0.0936332\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.11079 | + | 2.67361i | 0.226088 | + | 0.118273i | ||||
\(512\) | 13.4041 | − | 18.2299i | 0.592385 | − | 0.805655i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.1294 | − | 10.2520i | 0.623223 | − | 0.452195i | ||||
\(515\) | −26.1324 | + | 15.0876i | −1.15153 | + | 0.664837i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 12.0028i | − | 0.527884i | ||||||
\(518\) | −8.29107 | + | 20.8858i | −0.364289 | + | 0.917669i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 58.7492 | + | 12.6042i | 2.57632 | + | 0.552730i | ||||
\(521\) | −32.7368 | + | 18.9006i | −1.43423 | + | 0.828051i | −0.997440 | − | 0.0715138i | \(-0.977217\pi\) |
−0.436787 | + | 0.899565i | \(0.643884\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.6691 | − | 34.0679i | 0.860070 | − | 1.48968i | −0.0117911 | − | 0.999930i | \(-0.503753\pi\) |
0.871861 | − | 0.489754i | \(-0.162913\pi\) | |||||||
\(524\) | 6.71420 | + | 31.7856i | 0.293311 | + | 1.38856i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.85341 | + | 0.298080i | −0.124415 | + | 0.0129969i | ||||
\(527\) | 7.15864 | − | 12.3991i | 0.311835 | − | 0.540114i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.6449 | + | 18.4375i | 0.462822 | + | 0.801631i | ||||
\(530\) | 2.12073 | − | 4.75514i | 0.0921186 | − | 0.206550i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.94144 | + | 8.72926i | −0.387661 | + | 0.378461i | ||||
\(533\) | −34.4433 | −1.49190 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 47.5372 | − | 27.4456i | 2.05521 | − | 1.18658i | ||||
\(536\) | 28.1104 | + | 25.4076i | 1.21419 | + | 1.09744i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 36.9493 | − | 3.85988i | 1.59300 | − | 0.166411i | ||||
\(539\) | 0.988451 | + | 11.8475i | 0.0425756 | + | 0.510309i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.8385 | + | 7.41231i | 0.551970 | + | 0.318680i | 0.749916 | − | 0.661533i | \(-0.230094\pi\) |
−0.197946 | + | 0.980213i | \(0.563427\pi\) | |||||||
\(542\) | 9.27311 | − | 6.72834i | 0.398314 | − | 0.289007i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −14.7629 | − | 0.0467261i | −0.632956 | − | 0.00200337i | ||||
\(545\) | − | 2.84849i | − | 0.122016i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.2017 | −0.692736 | −0.346368 | − | 0.938099i | \(-0.612585\pi\) | ||||
−0.346368 | + | 0.938099i | \(0.612585\pi\) | |||||||
\(548\) | 7.97986 | + | 2.60399i | 0.340883 | + | 0.111237i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −17.8389 | + | 12.9435i | −0.760654 | + | 0.551912i | ||||
\(551\) | 8.04030 | − | 13.9262i | 0.342528 | − | 0.593277i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 46.0632 | − | 1.91822i | 1.95881 | − | 0.0815708i | ||||
\(554\) | −1.43485 | − | 13.7354i | −0.0609611 | − | 0.583560i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.62102 | + | 8.48558i | 0.323203 | + | 0.359869i | ||||
\(557\) | −1.17534 | − | 2.03574i | −0.0498006 | − | 0.0862572i | 0.840051 | − | 0.542508i | \(-0.182525\pi\) |
−0.889851 | + | 0.456251i | \(0.849192\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.6634i | 1.55070i | ||||||||
\(560\) | 39.7605 | + | 2.61334i | 1.68019 | + | 0.110434i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.43789 | + | 1.08727i | 0.102836 | + | 0.0458636i | ||||
\(563\) | −6.40537 | + | 3.69814i | −0.269954 | + | 0.155858i | −0.628867 | − | 0.777513i | \(-0.716481\pi\) |
0.358913 | + | 0.933371i | \(0.383148\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.1957 | − | 18.5882i | −1.35449 | − | 0.782012i | ||||
\(566\) | −9.25211 | + | 0.966515i | −0.388895 | + | 0.0406257i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −25.3161 | + | 8.17260i | −1.06224 | + | 0.342914i | ||||
\(569\) | −30.2952 | − | 17.4909i | −1.27004 | − | 0.733258i | −0.295045 | − | 0.955483i | \(-0.595334\pi\) |
−0.974995 | + | 0.222226i | \(0.928668\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.4081 | + | 28.4197i | 0.686659 | + | 1.18933i | 0.972912 | + | 0.231174i | \(0.0742567\pi\) |
−0.286254 | + | 0.958154i | \(0.592410\pi\) | |||||||
\(572\) | 5.94548 | − | 18.2198i | 0.248593 | − | 0.761807i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −22.5992 | + | 3.31633i | −0.943271 | + | 0.138421i | ||||
\(575\) | −12.0001 | −0.500437 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.58139 | + | 7.93520i | 0.190726 | + | 0.330347i | 0.945491 | − | 0.325648i | \(-0.105583\pi\) |
−0.754765 | + | 0.655995i | \(0.772249\pi\) | |||||||
\(578\) | −8.46241 | − | 11.6630i | −0.351990 | − | 0.485118i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −50.1697 | + | 10.5975i | −2.08318 | + | 0.440038i | ||||
\(581\) | −16.8438 | − | 26.5574i | −0.698800 | − | 1.10179i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.43823 | − | 0.830362i | −0.0595653 | − | 0.0343901i | ||||
\(584\) | −4.57447 | − | 4.13463i | −0.189293 | − | 0.171092i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.13991 | + | 18.2514i | −0.336257 | + | 0.753960i | ||||
\(587\) | − | 17.4528i | − | 0.720354i | −0.932884 | − | 0.360177i | \(-0.882716\pi\) | ||
0.932884 | − | 0.360177i | \(-0.117284\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.9554i | 0.533819i | ||||||||
\(590\) | 37.4760 | + | 16.7138i | 1.54286 | + | 0.688098i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 14.1694 | − | 19.3990i | 0.582359 | − | 0.797296i | ||||
\(593\) | −17.0385 | − | 9.83721i | −0.699689 | − | 0.403966i | 0.107542 | − | 0.994200i | \(-0.465702\pi\) |
−0.807232 | + | 0.590235i | \(0.799035\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.9241 | − | 21.9540i | −0.570834 | − | 0.900025i | ||||
\(596\) | 26.3856 | − | 5.57352i | 1.08079 | − | 0.228300i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.44589 | − | 6.12813i | 0.345378 | − | 0.250598i | ||||
\(599\) | −2.68048 | − | 4.64273i | −0.109521 | − | 0.189697i | 0.806055 | − | 0.591841i | \(-0.201598\pi\) |
−0.915576 | + | 0.402144i | \(0.868265\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.4609 | 0.508291 | 0.254145 | − | 0.967166i | \(-0.418206\pi\) | ||||
0.254145 | + | 0.967166i | \(0.418206\pi\) | |||||||
\(602\) | 3.53009 | + | 24.0558i | 0.143876 | + | 0.980442i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 40.5562 | + | 13.2343i | 1.65021 | + | 0.538496i | ||||
\(605\) | −15.2779 | − | 26.4621i | −0.621135 | − | 1.07584i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.6807 | + | 6.16649i | 0.433515 | + | 0.250290i | 0.700843 | − | 0.713315i | \(-0.252807\pi\) |
−0.267328 | + | 0.963606i | \(0.586141\pi\) | |||||||
\(608\) | 11.5901 | − | 6.64273i | 0.470041 | − | 0.269398i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.88363 | − | 46.7493i | −0.197732 | − | 1.89282i | ||||
\(611\) | 34.5325 | + | 19.9373i | 1.39704 | + | 0.806579i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.55744 | − | 2.05389i | 0.143683 | − | 0.0829557i | −0.426435 | − | 0.904518i | \(-0.640231\pi\) |
0.570118 | + | 0.821563i | \(0.306897\pi\) | |||||||
\(614\) | 10.1366 | − | 22.7284i | 0.409080 | − | 0.917245i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.14672 | − | 12.5269i | 0.0864937 | − | 0.504725i | ||||
\(617\) | 36.1255i | 1.45436i | 0.686447 | + | 0.727180i | \(0.259169\pi\) | ||||
−0.686447 | + | 0.727180i | \(0.740831\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.802674 | − | 1.39027i | −0.0322622 | − | 0.0558798i | 0.849443 | − | 0.527680i | \(-0.176938\pi\) |
−0.881706 | + | 0.471800i | \(0.843604\pi\) | |||||||
\(620\) | 30.7353 | − | 27.6038i | 1.23436 | − | 1.10860i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15.3226 | + | 1.60066i | −0.614379 | + | 0.0641807i | ||||
\(623\) | 29.2616 | − | 1.21855i | 1.17234 | − | 0.0488201i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.66043 | + | 11.5362i | −0.266417 | + | 0.461448i | ||||
\(626\) | −2.93235 | − | 4.04141i | −0.117200 | − | 0.161527i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17.5034 | + | 5.71170i | 0.698461 | + | 0.227922i | ||||
\(629\) | −15.6734 | −0.624940 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 8.98270i | − | 0.357596i | −0.983886 | − | 0.178798i | \(-0.942779\pi\) | ||
0.983886 | − | 0.178798i | \(-0.0572208\pi\) | |||||||
\(632\) | −48.1897 | − | 10.3387i | −1.91688 | − | 0.411253i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.4450 | + | 18.5302i | 0.533971 | + | 0.735927i | ||||
\(635\) | −14.7007 | − | 8.48748i | −0.583381 | − | 0.336815i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −35.7276 | − | 16.8356i | −1.41558 | − | 0.667050i | ||||
\(638\) | 1.69931 | + | 16.2669i | 0.0672764 | + | 0.644014i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −40.4539 | − | 13.3427i | −1.59908 | − | 0.527418i | ||||
\(641\) | 34.1214 | − | 19.7000i | 1.34772 | − | 0.778104i | 0.359790 | − | 0.933033i | \(-0.382848\pi\) |
0.987926 | + | 0.154929i | \(0.0495149\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.0002 | 1.57745 | 0.788726 | − | 0.614745i | \(-0.210741\pi\) | ||||
0.788726 | + | 0.614745i | \(0.210741\pi\) | |||||||
\(644\) | 4.95153 | − | 4.83403i | 0.195118 | − | 0.190488i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.96001 | − | 3.55006i | −0.313182 | − | 0.139675i | ||||
\(647\) | 19.8854 | + | 34.4425i | 0.781775 | + | 1.35407i | 0.930907 | + | 0.365257i | \(0.119019\pi\) |
−0.149132 | + | 0.988817i | \(0.547648\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.54422 | − | 11.3349i | 0.256883 | − | 0.444935i | ||||
\(650\) | −7.60739 | − | 72.8229i | −0.298386 | − | 2.85635i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.234946 | + | 0.0496284i | −0.00920118 | + | 0.00194360i | ||||
\(653\) | −1.64003 | + | 2.84061i | −0.0641792 | + | 0.111162i | −0.896330 | − | 0.443388i | \(-0.853776\pi\) |
0.832150 | + | 0.554550i | \(0.187110\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 52.9651 | − | 30.5794i | 2.06952 | − | 1.19484i | ||||
\(656\) | 24.2780 | + | 2.61388i | 0.947895 | + | 0.102055i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 24.5773 | + | 9.75650i | 0.958124 | + | 0.380348i | ||||
\(659\) | 16.7484i | 0.652425i | 0.945297 | + | 0.326212i | \(0.105772\pi\) | ||||
−0.945297 | + | 0.326212i | \(0.894228\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.50164 | − | 2.59902i | 0.175093 | − | 0.101090i | −0.409892 | − | 0.912134i | \(-0.634434\pi\) |
0.584985 | + | 0.811044i | \(0.301100\pi\) | |||||||
\(662\) | 9.63141 | + | 13.2742i | 0.374335 | + | 0.515915i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.3284 | + | 31.9941i | 0.400819 | + | 1.24161i | ||||
\(665\) | 20.8445 | + | 10.9044i | 0.808315 | + | 0.422854i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.45251 | + | 7.71197i | −0.172402 | + | 0.298609i | ||||
\(668\) | −17.3476 | − | 19.3156i | −0.671198 | − | 0.747341i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 29.0548 | − | 65.1471i | 1.12248 | − | 2.51685i | ||||
\(671\) | −14.9925 | −0.578779 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.9571 | −1.15476 | −0.577380 | − | 0.816475i | \(-0.695925\pi\) | ||||
−0.577380 | + | 0.816475i | \(0.695925\pi\) | |||||||
\(674\) | −1.61906 | + | 3.63029i | −0.0623640 | + | 0.139833i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 25.1702 | + | 28.0256i | 0.968083 | + | 1.07791i | ||||
\(677\) | −15.2704 | + | 26.4492i | −0.586891 | + | 1.01652i | 0.407746 | + | 0.913095i | \(0.366315\pi\) |
−0.994637 | + | 0.103429i | \(0.967018\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −33.6550 | + | 21.3454i | −1.29156 | + | 0.819162i | ||||
\(680\) | 8.53807 | + | 26.4483i | 0.327420 | + | 1.01425i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.73841 | − | 10.6652i | −0.296319 | − | 0.408391i | ||||
\(683\) | 11.1942 | − | 6.46296i | 0.428333 | − | 0.247298i | −0.270303 | − | 0.962775i | \(-0.587124\pi\) |
0.698636 | + | 0.715477i | \(0.253791\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 15.8022i | − | 0.603770i | ||||||
\(686\) | −25.0628 | − | 7.60629i | −0.956902 | − | 0.290409i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.78237 | − | 25.8428i | 0.106077 | − | 0.985249i | ||||
\(689\) | 4.77795 | − | 2.75855i | 0.182025 | − | 0.105092i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.33676 | + | 14.4397i | −0.317145 | + | 0.549312i | −0.979891 | − | 0.199533i | \(-0.936058\pi\) |
0.662746 | + | 0.748844i | \(0.269391\pi\) | |||||||
\(692\) | −13.4808 | + | 2.84761i | −0.512464 | + | 0.108250i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.18774 | − | 30.5151i | −0.121005 | − | 1.15834i | ||||
\(695\) | 10.7358 | − | 18.5949i | 0.407231 | − | 0.705344i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.96571 | − | 13.7970i | −0.301723 | − | 0.522599i | ||||
\(698\) | 9.61539 | + | 4.28834i | 0.363948 | + | 0.162316i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −12.0031 | − | 47.0486i | −0.453674 | − | 1.77827i | ||||
\(701\) | −24.5914 | −0.928805 | −0.464403 | − | 0.885624i | \(-0.653731\pi\) | ||||
−0.464403 | + | 0.885624i | \(0.653731\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.2825 | − | 7.09128i | 0.463242 | − | 0.267453i | ||||
\(704\) | −5.57347 | + | 12.3913i | −0.210058 | + | 0.467016i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.21186 | + | 21.1734i | 0.0832444 | + | 0.796870i | ||||
\(707\) | 3.64733 | + | 1.90803i | 0.137172 | + | 0.0717587i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.59843 | − | 2.65490i | −0.172698 | − | 0.0997070i | 0.411160 | − | 0.911563i | \(-0.365124\pi\) |
−0.583857 | + | 0.811856i | \(0.698457\pi\) | |||||||
\(710\) | 29.4112 | + | 40.5350i | 1.10378 | + | 1.52125i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −30.6125 | − | 6.56768i | −1.14725 | − | 0.246134i | ||||
\(713\) | − | 7.17437i | − | 0.268682i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.0799 | −1.34931 | ||||||||
\(716\) | −29.8678 | − | 9.74646i | −1.11621 | − | 0.364242i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14.9807 | − | 20.6466i | −0.559075 | − | 0.770525i | ||||
\(719\) | −5.16456 | + | 8.94528i | −0.192606 | + | 0.333603i | −0.946113 | − | 0.323837i | \(-0.895027\pi\) |
0.753507 | + | 0.657439i | \(0.228360\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.1857 | + | 0.882240i | −0.788997 | + | 0.0328563i | ||||
\(722\) | −18.8806 | + | 1.97235i | −0.702663 | + | 0.0734031i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −23.3188 | + | 20.9429i | −0.866636 | + | 0.778338i | ||||
\(725\) | 31.2422 | + | 54.1131i | 1.16031 | + | 2.00971i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.6727i | 1.06341i | 0.846929 | + | 0.531706i | \(0.178449\pi\) | ||||
−0.846929 | + | 0.531706i | \(0.821551\pi\) | |||||||
\(728\) | 32.4746 | + | 26.9841i | 1.20359 | + | 1.00010i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.72815 | + | 10.6015i | −0.174997 | + | 0.392380i | ||||
\(731\) | −14.6863 | + | 8.47916i | −0.543193 | + | 0.313613i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.6091 | + | 19.4042i | 1.24138 | + | 0.716710i | 0.969375 | − | 0.245586i | \(-0.0789803\pi\) |
0.272004 | + | 0.962296i | \(0.412314\pi\) | |||||||
\(734\) | −0.574993 | − | 5.50421i | −0.0212234 | − | 0.203164i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.41830 | + | 3.67857i | −0.236582 | + | 0.135594i | ||||
\(737\) | −19.7042 | − | 11.3763i | −0.725815 | − | 0.419050i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.59773 | − | 9.69556i | −0.205916 | − | 0.356657i | 0.744508 | − | 0.667613i | \(-0.232684\pi\) |
−0.950424 | + | 0.310956i | \(0.899351\pi\) | |||||||
\(740\) | −42.9932 | − | 14.0295i | −1.58046 | − | 0.515736i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.86934 | − | 2.27000i | 0.105337 | − | 0.0833343i | ||||
\(743\) | −6.68201 | −0.245139 | −0.122570 | − | 0.992460i | \(-0.539113\pi\) | ||||
−0.122570 | + | 0.992460i | \(0.539113\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25.3843 | − | 43.9668i | −0.930007 | − | 1.61082i | ||||
\(746\) | −20.9511 | + | 15.2016i | −0.767076 | + | 0.556572i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.67335 | − | 1.83210i | 0.317129 | − | 0.0669883i | ||||
\(749\) | 38.5387 | − | 1.60487i | 1.40817 | − | 0.0586407i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.2883 | − | 24.9925i | −1.57961 | − | 0.911990i | −0.994913 | − | 0.100741i | \(-0.967879\pi\) |
−0.584701 | − | 0.811249i | \(-0.698788\pi\) | |||||||
\(752\) | −22.8278 | − | 16.6738i | −0.832444 | − | 0.608032i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −49.6231 | − | 22.1313i | −1.80717 | − | 0.805973i | ||||
\(755\) | − | 80.3117i | − | 2.92284i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.8378i | 1.19351i | 0.802424 | + | 0.596755i | \(0.203543\pi\) | ||||
−0.802424 | + | 0.596755i | \(0.796457\pi\) | |||||||
\(758\) | −14.8658 | + | 33.3323i | −0.539949 | + | 1.21068i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −18.6571 | − | 16.8632i | −0.676765 | − | 0.611693i | ||||
\(761\) | 28.7157 | + | 16.5790i | 1.04094 | + | 0.600988i | 0.920100 | − | 0.391683i | \(-0.128107\pi\) |
0.120842 | + | 0.992672i | \(0.461440\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.927825 | − | 1.77360i | 0.0335895 | − | 0.0642088i | ||||
\(764\) | −47.2116 | + | 9.97268i | −1.70806 | + | 0.360799i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.2530 | − | 16.8873i | −0.442721 | − | 0.610165i | ||||
\(767\) | 21.7406 | + | 37.6559i | 0.785008 | + | 1.35967i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.1183 | −1.73519 | −0.867596 | − | 0.497270i | \(-0.834336\pi\) | ||||
−0.867596 | + | 0.497270i | \(0.834336\pi\) | |||||||
\(770\) | −23.6730 | + | 3.47391i | −0.853114 | + | 0.125191i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.96004 | + | 18.2644i | −0.214506 | + | 0.657350i | ||||
\(773\) | 14.2293 | + | 24.6458i | 0.511791 | + | 0.886449i | 0.999907 | + | 0.0136695i | \(0.00435128\pi\) |
−0.488115 | + | 0.872779i | \(0.662315\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −43.5965 | − | 25.1704i | −1.56603 | − | 0.904148i | ||||
\(776\) | 40.5447 | − | 13.0887i | 1.45547 | − | 0.469857i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.4816 | + | 2.55745i | −0.877707 | + | 0.0916890i | ||||
\(779\) | 12.4847 | + | 7.20802i | 0.447309 | + | 0.258254i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8339 | − | 7.98703i | 0.495017 | − | 0.285798i | ||||
\(782\) | 4.40804 | + | 1.96593i | 0.157631 | + | 0.0703016i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 23.9056 | + | 14.5782i | 0.853770 | + | 0.520650i | ||||
\(785\) | − | 34.6612i | − | 1.23711i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.0597 | − | 19.1559i | −0.394234 | − | 0.682834i | 0.598769 | − | 0.800922i | \(-0.295657\pi\) |
−0.993003 | + | 0.118088i | \(0.962323\pi\) | |||||||
\(788\) | 2.74366 | + | 3.05491i | 0.0977388 | + | 0.108827i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 9.64020 | + | 92.2823i | 0.342983 | + | 3.28326i | ||||
\(791\) | −13.9920 | − | 22.0609i | −0.497497 | − | 0.784395i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.9033 | − | 43.1339i | 0.884344 | − | 1.53173i | ||||
\(794\) | −13.2533 | + | 9.61629i | −0.470343 | + | 0.341270i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.9272 | − | 6.17631i | −0.670856 | − | 0.218914i | ||||
\(797\) | 25.7820 | 0.913247 | 0.456623 | − | 0.889660i | \(-0.349059\pi\) | ||||
0.456623 | + | 0.889660i | \(0.349059\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.4437i | 0.652490i | ||||||||
\(800\) | −0.164293 | + | 51.9078i | −0.00580864 | + | 1.83522i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 41.1656 | − | 29.8688i | 1.45361 | − | 1.05470i | ||||
\(803\) | 3.20652 | + | 1.85128i | 0.113156 | + | 0.0653304i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.5431 | − | 6.03856i | −0.406842 | − | 0.212831i | ||||
\(806\) | 43.5380 | − | 4.54816i | 1.53356 | − | 0.160202i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.26458 | − | 2.95069i | −0.114848 | − | 0.103805i | ||||
\(809\) | 2.56573 | − | 1.48132i | 0.0902062 | − | 0.0520806i | −0.454218 | − | 0.890890i | \(-0.650081\pi\) |
0.544425 | + | 0.838810i | \(0.316748\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −51.9174 | −1.82307 | −0.911533 | − | 0.411228i | \(-0.865100\pi\) | ||||
−0.911533 | + | 0.411228i | \(0.865100\pi\) | |||||||
\(812\) | −34.6899 | − | 9.74302i | −1.21738 | − | 0.341913i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.87550 | + | 13.1741i | −0.205936 | + | 0.461754i | ||||
\(815\) | 0.226030 | + | 0.391495i | 0.00791747 | + | 0.0137135i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.67262 | − | 13.2894i | 0.268431 | − | 0.464936i | ||||
\(818\) | −34.2118 | + | 3.57391i | −1.19619 | + | 0.124959i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.50053 | − | 44.9764i | −0.331773 | − | 1.57064i | ||||
\(821\) | 10.7741 | − | 18.6612i | 0.376017 | − | 0.651281i | −0.614462 | − | 0.788947i | \(-0.710627\pi\) |
0.990479 | + | 0.137666i | \(0.0439601\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.0162 | + | 17.3299i | −1.04630 | + | 0.604082i | −0.921611 | − | 0.388114i | \(-0.873127\pi\) |
−0.124689 | + | 0.992196i | \(0.539793\pi\) | |||||||
\(824\) | 22.1638 | + | 4.75506i | 0.772111 | + | 0.165650i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.8903 | + | 22.6137i | 0.622481 | + | 0.786833i | ||||
\(827\) | − | 40.6029i | − | 1.41190i | −0.708260 | − | 0.705951i | \(-0.750520\pi\) | ||
0.708260 | − | 0.705951i | \(-0.249480\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.2837 | − | 16.3296i | 0.982334 | − | 0.567151i | 0.0793604 | − | 0.996846i | \(-0.474712\pi\) |
0.902974 | + | 0.429695i | \(0.141379\pi\) | |||||||
\(830\) | 51.2275 | − | 37.1694i | 1.77813 | − | 1.29017i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −26.3924 | − | 36.6177i | −0.914992 | − | 1.26949i | ||||
\(833\) | −1.51886 | − | 18.2050i | −0.0526256 | − | 0.630767i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.4376 | + | 42.3271i | −0.845697 | + | 1.46479i | ||||
\(836\) | −5.96795 | + | 5.35990i | −0.206406 | + | 0.185376i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.95008 | − | 3.99162i | −0.309175 | − | 0.137888i | ||||
\(839\) | −35.4704 | −1.22458 | −0.612288 | − | 0.790635i | \(-0.709751\pi\) | ||||
−0.612288 | + | 0.790635i | \(0.709751\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.3685 | 0.598913 | ||||||||
\(842\) | 16.2988 | + | 7.26906i | 0.561694 | + | 0.250508i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.6768 | + | 20.7956i | 0.642884 | + | 0.715815i | ||||
\(845\) | 35.4573 | − | 61.4138i | 1.21977 | − | 2.11270i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.893370 | − | 21.4530i | −0.0306965 | − | 0.737133i | ||||
\(848\) | −3.57717 | + | 1.58182i | −0.122840 | + | 0.0543198i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 27.4115 | − | 19.8891i | 0.940205 | − | 0.682190i | ||||
\(851\) | −6.80170 | + | 3.92697i | −0.233159 | + | 0.134615i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 2.87597i | − | 0.0984714i | −0.998787 | − | 0.0492357i | \(-0.984321\pi\) | ||
0.998787 | − | 0.0492357i | \(-0.0156786\pi\) | |||||||
\(854\) | 12.1867 | − | 30.6991i | 0.417019 | − | 1.05050i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −40.3178 | − | 8.64987i | −1.37803 | − | 0.295647i | ||||
\(857\) | 5.76468 | − | 3.32824i | 0.196918 | − | 0.113691i | −0.398299 | − | 0.917256i | \(-0.630399\pi\) |
0.595217 | + | 0.803565i | \(0.297066\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.2685 | − | 17.7855i | 0.350355 | − | 0.606833i | −0.635956 | − | 0.771725i | \(-0.719394\pi\) |
0.986312 | + | 0.164892i | \(0.0527276\pi\) | |||||||
\(860\) | −47.8754 | + | 10.1129i | −1.63254 | + | 0.344847i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 31.4390 | − | 3.28425i | 1.07082 | − | 0.111862i | ||||
\(863\) | 15.7546 | − | 27.2877i | 0.536292 | − | 0.928886i | −0.462807 | − | 0.886459i | \(-0.653158\pi\) |
0.999100 | − | 0.0424266i | \(-0.0135089\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.9692 | + | 22.4634i | 0.440968 | + | 0.763778i | ||||
\(866\) | 18.5950 | − | 41.6940i | 0.631884 | − | 1.41682i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 28.1285 | − | 7.17618i | 0.954744 | − | 0.243575i | ||||
\(869\) | 29.5949 | 1.00394 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 65.4596 | − | 37.7931i | 2.21801 | − | 1.28057i | ||||
\(872\) | −1.43485 | + | 1.58749i | −0.0485900 | + | 0.0537590i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.34383 | + | 0.453775i | −0.146932 | + | 0.0153492i | ||||
\(875\) | −35.1308 | + | 22.2815i | −1.18764 | + | 0.753251i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 48.3067 | + | 27.8899i | 1.63120 | + | 0.941774i | 0.983723 | + | 0.179689i | \(0.0575091\pi\) |
0.647477 | + | 0.762085i | \(0.275824\pi\) | |||||||
\(878\) | 3.20913 | − | 2.32847i | 0.108303 | − | 0.0785819i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 25.4315 | + | 2.73808i | 0.857297 | + | 0.0923008i | ||||
\(881\) | 21.9485i | 0.739464i | 0.929138 | + | 0.369732i | \(0.120550\pi\) | ||||
−0.929138 | + | 0.369732i | \(0.879450\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.4287 | 1.12497 | 0.562483 | − | 0.826809i | \(-0.309846\pi\) | ||||
0.562483 | + | 0.826809i | \(0.309846\pi\) | |||||||
\(884\) | −9.13589 | + | 27.9967i | −0.307273 | + | 0.941631i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21.4207 | + | 15.5423i | −0.719643 | + | 0.522155i | ||||
\(887\) | 6.18309 | − | 10.7094i | 0.207608 | − | 0.359587i | −0.743353 | − | 0.668900i | \(-0.766766\pi\) |
0.950960 | + | 0.309313i | \(0.100099\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.38880 | − | 10.0731i | −0.214273 | − | 0.337841i | ||||
\(890\) | 6.12394 | + | 58.6223i | 0.205275 | + | 1.96502i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 23.6317 | − | 21.2240i | 0.791248 | − | 0.710631i | ||||
\(893\) | −8.34466 | − | 14.4534i | −0.279243 | − | 0.483664i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 59.1460i | 1.97703i | ||||||||
\(896\) | −20.8425 | − | 21.4847i | −0.696298 | − | 0.717753i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.9466 | − | 8.00396i | −0.598886 | − | 0.267096i | ||||
\(899\) | −32.3521 | + | 18.6785i | −1.07900 | + | 0.622963i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.21000 | + | 1.27594i | 0.0736257 | + | 0.0425078i | ||||
\(902\) | −14.5831 | + | 1.52341i | −0.485563 | + | 0.0507240i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.57965 | + | 26.5771i | 0.285355 | + | 0.883941i | ||||
\(905\) | 51.0996 | + | 29.5024i | 1.69861 | + | 0.980692i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.85914 | − | 11.8804i | −0.227754 | − | 0.394481i | 0.729388 | − | 0.684100i | \(-0.239805\pi\) |
−0.957142 | + | 0.289619i | \(0.906471\pi\) | |||||||
\(908\) | −1.36132 | − | 0.444225i | −0.0451769 | − | 0.0147421i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 29.3275 | − | 73.8782i | 0.972198 | − | 2.44904i | ||||
\(911\) | −9.02706 | −0.299080 | −0.149540 | − | 0.988756i | \(-0.547779\pi\) | ||||
−0.149540 | + | 0.988756i | \(0.547779\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.0939 | − | 17.4831i | −0.334058 | − | 0.578606i | ||||
\(914\) | 4.79917 | + | 6.61429i | 0.158742 | + | 0.218781i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.86102 | − | 8.81025i | −0.0614899 | − | 0.291099i | ||||
\(917\) | 42.9391 | − | 1.78812i | 1.41797 | − | 0.0590489i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.8104 | + | 21.8298i | 1.24725 | + | 0.720100i | 0.970560 | − | 0.240860i | \(-0.0774294\pi\) |
0.276689 | + | 0.960959i | \(0.410763\pi\) | |||||||
\(920\) | 10.3318 | + | 9.33840i | 0.340630 | + | 0.307878i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.88367 | − | 19.9191i | 0.292568 | − | 0.656001i | ||||
\(923\) | 53.0675i | 1.74674i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 55.1092i | 1.81198i | ||||||||
\(926\) | 14.9698 | + | 6.67633i | 0.491937 | + | 0.219398i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 33.2982 | + | 19.3655i | 1.09307 | + | 0.635703i | ||||
\(929\) | 43.0944 | + | 24.8806i | 1.41388 | + | 0.816304i | 0.995751 | − | 0.0920830i | \(-0.0293525\pi\) |
0.418129 | + | 0.908387i | \(0.362686\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.42695 | + | 13.5792i | 0.308956 | + | 0.445039i | ||||
\(932\) | −3.19596 | − | 15.1300i | −0.104687 | − | 0.495599i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.61904 | − | 1.90031i | 0.0856977 | − | 0.0621802i | ||||
\(935\) | −8.34421 | − | 14.4526i | −0.272885 | − | 0.472650i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.5415 | 1.32443 | 0.662216 | − | 0.749313i | \(-0.269616\pi\) | ||||
0.662216 | + | 0.749313i | \(0.269616\pi\) | |||||||
\(938\) | 39.3109 | − | 31.0998i | 1.28355 | − | 1.01544i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −16.5093 | + | 50.5922i | −0.538472 | + | 1.65014i | ||||
\(941\) | −27.1914 | − | 47.0968i | −0.886414 | − | 1.53531i | −0.844085 | − | 0.536209i | \(-0.819856\pi\) |
−0.0423286 | − | 0.999104i | \(-0.513478\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.91367 | − | 3.99161i | −0.225140 | − | 0.129985i | ||||
\(944\) | −12.4666 | − | 28.1923i | −0.405752 | − | 0.917581i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.62160 | + | 15.5230i | 0.0527229 | + | 0.504698i | ||||
\(947\) | −12.3501 | − | 7.13032i | −0.401323 | − | 0.231704i | 0.285732 | − | 0.958310i | \(-0.407763\pi\) |
−0.687055 | + | 0.726606i | \(0.741097\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.6524 | + | 6.15016i | −0.345791 | + | 0.199643i | ||||
\(950\) | −12.4823 | + | 27.9881i | −0.404981 | + | 0.908055i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.29867 | + | 19.2490i | −0.106910 | + | 0.623865i | ||||
\(953\) | − | 3.31610i | − | 0.107419i | −0.998557 | − | 0.0537095i | \(-0.982896\pi\) | ||
0.998557 | − | 0.0537095i | \(-0.0171045\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 45.4200 | + | 78.6697i | 1.46976 | + | 2.54569i | ||||
\(956\) | −28.5702 | − | 31.8113i | −0.924026 | − | 1.02885i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26.5263 | + | 2.77105i | −0.857025 | + | 0.0895285i | ||||
\(959\) | 5.14717 | − | 9.83919i | 0.166211 | − | 0.317724i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.451578 | + | 0.782157i | −0.0145670 | + | 0.0252309i | ||||
\(962\) | −28.1429 | − | 38.7870i | −0.907363 | − | 1.25054i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.28229 | − | 16.1875i | 0.170131 | − | 0.521363i | ||||
\(965\) | 36.1682 | 1.16430 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 18.6637i | − | 0.600185i | −0.953910 | − | 0.300092i | \(-0.902982\pi\) | ||
0.953910 | − | 0.300092i | \(-0.0970175\pi\) | |||||||
\(968\) | −4.81505 | + | 22.4434i | −0.154762 | + | 0.721357i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −47.1031 | − | 64.9182i | −1.51239 | − | 2.08440i | ||||
\(971\) | 4.93811 | + | 2.85102i | 0.158472 | + | 0.0914936i | 0.577139 | − | 0.816646i | \(-0.304169\pi\) |
−0.418667 | + | 0.908140i | \(0.637503\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.7414 | − | 8.08115i | 0.408471 | − | 0.259070i | ||||
\(974\) | −4.56434 | − | 43.6928i | −0.146251 | − | 1.40001i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −20.8270 | + | 28.5138i | −0.666655 | + | 0.912703i | ||||
\(977\) | −3.52730 | + | 2.03649i | −0.112848 | + | 0.0651530i | −0.555362 | − | 0.831609i | \(-0.687420\pi\) |
0.442514 | + | 0.896762i | \(0.354087\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.8002 | 0.600856 | ||||||||
\(980\) | 12.1293 | − | 51.2972i | 0.387456 | − | 1.63863i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.72496 | + | 4.33721i | 0.310336 | + | 0.138406i | ||||
\(983\) | 13.6318 | + | 23.6109i | 0.434786 | + | 0.753071i | 0.997278 | − | 0.0737313i | \(-0.0234907\pi\) |
−0.562492 | + | 0.826803i | \(0.690157\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.86500 | − | 6.69438i | 0.123149 | − | 0.213301i | ||||
\(986\) | −2.61118 | − | 24.9959i | −0.0831570 | − | 0.796033i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.50750 | − | 26.0730i | −0.175217 | − | 0.829494i | ||||
\(989\) | −4.24890 | + | 7.35930i | −0.135107 | + | 0.234012i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.91978 | − | 4.57249i | 0.251580 | − | 0.145250i | −0.368907 | − | 0.929466i | \(-0.620268\pi\) |
0.620488 | + | 0.784216i | \(0.286935\pi\) | |||||||
\(992\) | −31.0337 | − | 0.0982246i | −0.985320 | − | 0.00311863i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.10955 | + | 34.8190i | 0.162065 | + | 1.10439i | ||||
\(995\) | 37.4807i | 1.18822i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.5025 | + | 23.3841i | −1.28273 | + | 0.740583i | −0.977346 | − | 0.211647i | \(-0.932117\pi\) |
−0.305381 | + | 0.952230i | \(0.598784\pi\) | |||||||
\(998\) | −1.46718 | − | 2.02208i | −0.0464426 | − | 0.0640080i | ||||
\(999\) | 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 | 504.2.bm.c.107.10 | yes | 48 | |
3.2 | odd | 2 | inner | 504.2.bm.c.107.15 | yes | 48 | |
4.3 | odd | 2 | 2016.2.bu.c.1871.1 | 48 | |||
7.4 | even | 3 | inner | 504.2.bm.c.179.8 | yes | 48 | |
8.3 | odd | 2 | inner | 504.2.bm.c.107.17 | yes | 48 | |
8.5 | even | 2 | 2016.2.bu.c.1871.23 | 48 | |||
12.11 | even | 2 | 2016.2.bu.c.1871.24 | 48 | |||
21.11 | odd | 6 | inner | 504.2.bm.c.179.17 | yes | 48 | |
24.5 | odd | 2 | 2016.2.bu.c.1871.2 | 48 | |||
24.11 | even | 2 | inner | 504.2.bm.c.107.8 | ✓ | 48 | |
28.11 | odd | 6 | 2016.2.bu.c.431.2 | 48 | |||
56.11 | odd | 6 | inner | 504.2.bm.c.179.15 | yes | 48 | |
56.53 | even | 6 | 2016.2.bu.c.431.24 | 48 | |||
84.11 | even | 6 | 2016.2.bu.c.431.23 | 48 | |||
168.11 | even | 6 | inner | 504.2.bm.c.179.10 | yes | 48 | |
168.53 | odd | 6 | 2016.2.bu.c.431.1 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bm.c.107.8 | ✓ | 48 | 24.11 | even | 2 | inner | |
504.2.bm.c.107.10 | yes | 48 | 1.1 | even | 1 | trivial | |
504.2.bm.c.107.15 | yes | 48 | 3.2 | odd | 2 | inner | |
504.2.bm.c.107.17 | yes | 48 | 8.3 | odd | 2 | inner | |
504.2.bm.c.179.8 | yes | 48 | 7.4 | even | 3 | inner | |
504.2.bm.c.179.10 | yes | 48 | 168.11 | even | 6 | inner | |
504.2.bm.c.179.15 | yes | 48 | 56.11 | odd | 6 | inner | |
504.2.bm.c.179.17 | yes | 48 | 21.11 | odd | 6 | inner | |
2016.2.bu.c.431.1 | 48 | 168.53 | odd | 6 | |||
2016.2.bu.c.431.2 | 48 | 28.11 | odd | 6 | |||
2016.2.bu.c.431.23 | 48 | 84.11 | even | 6 | |||
2016.2.bu.c.431.24 | 48 | 56.53 | even | 6 | |||
2016.2.bu.c.1871.1 | 48 | 4.3 | odd | 2 | |||
2016.2.bu.c.1871.2 | 48 | 24.5 | odd | 2 | |||
2016.2.bu.c.1871.23 | 48 | 8.5 | even | 2 | |||
2016.2.bu.c.1871.24 | 48 | 12.11 | even | 2 |