Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1890,2,Mod(1369,1890)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1890, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1890.1369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1890.ba (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.0917259820\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(48\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1369.7 | ||
Character | \(\chi\) | \(=\) | 1890.1369 |
Dual form | 1890.2.ba.a.1549.7 |
$q$-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 \(\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(1081\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.60072 | + | 1.56131i | −0.715864 | + | 0.698240i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.585831 | − | 2.58008i | 0.221423 | − | 0.975178i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.56131 | − | 1.60072i | −0.493730 | − | 0.506192i | ||||
\(11\) | 2.05292 | + | 3.55576i | 0.618979 | + | 1.07210i | 0.989672 | + | 0.143348i | \(0.0457867\pi\) |
−0.370694 | + | 0.928755i | \(0.620880\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.36239 | + | 1.94128i | −0.932560 | + | 0.538414i | −0.887620 | − | 0.460576i | \(-0.847643\pi\) |
−0.0449397 | + | 0.998990i | \(0.514310\pi\) | |||||||
\(14\) | 2.58008 | + | 0.585831i | 0.689555 | + | 0.156570i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.40480 | + | 1.38841i | 0.583249 | + | 0.336739i | 0.762424 | − | 0.647078i | \(-0.224009\pi\) |
−0.179175 | + | 0.983817i | \(0.557343\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.40977 | − | 2.44179i | −0.323424 | − | 0.560186i | 0.657768 | − | 0.753220i | \(-0.271501\pi\) |
−0.981192 | + | 0.193034i | \(0.938167\pi\) | |||||||
\(20\) | 1.60072 | − | 1.56131i | 0.357932 | − | 0.349120i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.55576 | + | 2.05292i | −0.758091 | + | 0.437684i | ||||
\(23\) | −5.13166 | − | 2.96277i | −1.07003 | − | 0.617780i | −0.141837 | − | 0.989890i | \(-0.545301\pi\) |
−0.928188 | + | 0.372111i | \(0.878634\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.124606 | − | 4.99845i | 0.0249212 | − | 0.999689i | ||||
\(26\) | −1.94128 | − | 3.36239i | −0.380716 | − | 0.659420i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.585831 | + | 2.58008i | −0.110712 | + | 0.487589i | ||||
\(29\) | −2.36090 | + | 4.08921i | −0.438409 | + | 0.759346i | −0.997567 | − | 0.0697147i | \(-0.977791\pi\) |
0.559158 | + | 0.829061i | \(0.311124\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.89489 | −0.699542 | −0.349771 | − | 0.936835i | \(-0.613741\pi\) | ||||
−0.349771 | + | 0.936835i | \(0.613741\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.38841 | + | 2.40480i | −0.238110 | + | 0.412419i | ||||
\(35\) | 3.09056 | + | 5.04465i | 0.522400 | + | 0.852701i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.356887 | − | 0.206049i | 0.0586718 | − | 0.0338742i | −0.470377 | − | 0.882465i | \(-0.655882\pi\) |
0.529049 | + | 0.848591i | \(0.322549\pi\) | |||||||
\(38\) | 2.44179 | − | 1.40977i | 0.396111 | − | 0.228695i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.56131 | + | 1.60072i | 0.246865 | + | 0.253096i | ||||
\(41\) | 3.43052 | + | 5.94183i | 0.535757 | + | 0.927958i | 0.999126 | + | 0.0417929i | \(0.0133070\pi\) |
−0.463369 | + | 0.886165i | \(0.653360\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.08691 | + | 0.627530i | 0.165753 | + | 0.0956975i | 0.580582 | − | 0.814202i | \(-0.302825\pi\) |
−0.414829 | + | 0.909899i | \(0.636159\pi\) | |||||||
\(44\) | −2.05292 | − | 3.55576i | −0.309489 | − | 0.536051i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.96277 | − | 5.13166i | 0.436836 | − | 0.756622i | ||||
\(47\) | − | 5.10612i | − | 0.744804i | −0.928072 | − | 0.372402i | \(-0.878534\pi\) | ||
0.928072 | − | 0.372402i | \(-0.121466\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.31361 | − | 3.02298i | −0.901944 | − | 0.431854i | ||||
\(50\) | 4.99845 | + | 0.124606i | 0.706887 | + | 0.0176219i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.36239 | − | 1.94128i | 0.466280 | − | 0.269207i | ||||
\(53\) | 4.20182 | + | 2.42592i | 0.577164 | + | 0.333226i | 0.760006 | − | 0.649917i | \(-0.225196\pi\) |
−0.182842 | + | 0.983142i | \(0.558530\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.83781 | − | 2.48653i | −1.19169 | − | 0.335283i | ||||
\(56\) | −2.58008 | − | 0.585831i | −0.344777 | − | 0.0782849i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.08921 | − | 2.36090i | −0.536939 | − | 0.310002i | ||||
\(59\) | −12.4810 | −1.62489 | −0.812445 | − | 0.583038i | \(-0.801864\pi\) | ||||
−0.812445 | + | 0.583038i | \(0.801864\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.08850 | −0.139369 | −0.0696843 | − | 0.997569i | \(-0.522199\pi\) | ||||
−0.0696843 | + | 0.997569i | \(0.522199\pi\) | |||||||
\(62\) | − | 3.89489i | − | 0.494651i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.35131 | − | 8.35719i | 0.291644 | − | 1.03658i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.5268i | − | 1.53039i | −0.643799 | − | 0.765195i | \(-0.722643\pi\) | ||
0.643799 | − | 0.765195i | \(-0.277357\pi\) | |||||||
\(68\) | −2.40480 | − | 1.38841i | −0.291625 | − | 0.168369i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.04465 | + | 3.09056i | −0.602951 | + | 0.369392i | ||||
\(71\) | −16.3189 | −1.93669 | −0.968346 | − | 0.249611i | \(-0.919697\pi\) | ||||
−0.968346 | + | 0.249611i | \(0.919697\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.1123 | − | 6.41567i | −1.30059 | − | 0.750897i | −0.320086 | − | 0.947389i | \(-0.603712\pi\) |
−0.980505 | + | 0.196492i | \(0.937045\pi\) | |||||||
\(74\) | 0.206049 | + | 0.356887i | 0.0239527 | + | 0.0414872i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.40977 | + | 2.44179i | 0.161712 | + | 0.280093i | ||||
\(77\) | 10.3768 | − | 3.21362i | 1.18255 | − | 0.366226i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.02746 | 0.678142 | 0.339071 | − | 0.940761i | \(-0.389887\pi\) | ||||
0.339071 | + | 0.940761i | \(0.389887\pi\) | |||||||
\(80\) | −1.60072 | + | 1.56131i | −0.178966 | + | 0.174560i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.94183 | + | 3.43052i | −0.656165 | + | 0.378837i | ||||
\(83\) | −13.4228 | − | 7.74967i | −1.47335 | − | 0.850637i | −0.473796 | − | 0.880635i | \(-0.657116\pi\) |
−0.999550 | + | 0.0299982i | \(0.990450\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.01715 | + | 1.53218i | −0.652651 | + | 0.166189i | ||||
\(86\) | −0.627530 | + | 1.08691i | −0.0676683 | + | 0.117205i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.55576 | − | 2.05292i | 0.379046 | − | 0.218842i | ||||
\(89\) | −3.68803 | − | 6.38786i | −0.390931 | − | 0.677112i | 0.601642 | − | 0.798766i | \(-0.294513\pi\) |
−0.992573 | + | 0.121654i | \(0.961180\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.03886 | + | 9.81250i | 0.318559 | + | 1.02863i | ||||
\(92\) | 5.13166 | + | 2.96277i | 0.535013 | + | 0.308890i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.10612 | 0.526656 | ||||||||
\(95\) | 6.06905 | + | 1.70754i | 0.622672 | + | 0.175189i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.62553 | + | 2.09320i | 0.368117 | + | 0.212532i | 0.672635 | − | 0.739974i | \(-0.265162\pi\) |
−0.304519 | + | 0.952506i | \(0.598496\pi\) | |||||||
\(98\) | 3.02298 | − | 6.31361i | 0.305367 | − | 0.637770i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.124606 | + | 4.99845i | −0.0124606 | + | 0.499845i | ||||
\(101\) | −6.33196 | − | 10.9673i | −0.630053 | − | 1.09128i | −0.987540 | − | 0.157366i | \(-0.949700\pi\) |
0.357487 | − | 0.933918i | \(-0.383634\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.79293 | − | 2.18985i | −0.373729 | − | 0.215772i | 0.301357 | − | 0.953511i | \(-0.402560\pi\) |
−0.675086 | + | 0.737739i | \(0.735894\pi\) | |||||||
\(104\) | 1.94128 | + | 3.36239i | 0.190358 | + | 0.329710i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.42592 | + | 4.20182i | −0.235626 | + | 0.408117i | ||||
\(107\) | 2.83265 | − | 1.63543i | 0.273843 | − | 0.158103i | −0.356790 | − | 0.934185i | \(-0.616129\pi\) |
0.630633 | + | 0.776081i | \(0.282795\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.65955 | + | 2.87443i | −0.158956 | + | 0.275321i | −0.934493 | − | 0.355983i | \(-0.884146\pi\) |
0.775536 | + | 0.631303i | \(0.217480\pi\) | |||||||
\(110\) | 2.48653 | − | 8.83781i | 0.237081 | − | 0.842652i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.585831 | − | 2.58008i | 0.0553558 | − | 0.243794i | ||||
\(113\) | 6.85140 | − | 3.95566i | 0.644526 | − | 0.372117i | −0.141830 | − | 0.989891i | \(-0.545299\pi\) |
0.786356 | + | 0.617774i | \(0.211965\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.8402 | − | 3.26957i | 1.19735 | − | 0.304889i | ||||
\(116\) | 2.36090 | − | 4.08921i | 0.219204 | − | 0.379673i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 12.4810i | − | 1.14897i | ||||||
\(119\) | 4.99101 | − | 5.39119i | 0.457525 | − | 0.494210i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.92897 | + | 5.07312i | −0.266270 | + | 0.461193i | ||||
\(122\) | − | 1.08850i | − | 0.0985485i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.89489 | 0.349771 | ||||||||
\(125\) | 7.60468 | + | 8.19566i | 0.680183 | + | 0.733042i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.37701i | 0.654604i | 0.944920 | + | 0.327302i | \(0.106139\pi\) | ||||
−0.944920 | + | 0.327302i | \(0.893861\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.35719 | + | 2.35131i | 0.732974 | + | 0.206223i | ||||
\(131\) | 5.96168 | − | 10.3259i | 0.520874 | − | 0.902181i | −0.478831 | − | 0.877907i | \(-0.658939\pi\) |
0.999705 | − | 0.0242736i | \(-0.00772729\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.12591 | + | 2.20684i | −0.617894 | + | 0.191357i | ||||
\(134\) | 12.5268 | 1.08215 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.38841 | − | 2.40480i | 0.119055 | − | 0.206210i | ||||
\(137\) | 17.1599 | − | 9.90727i | 1.46607 | − | 0.846435i | 0.466788 | − | 0.884369i | \(-0.345411\pi\) |
0.999280 | + | 0.0379338i | \(0.0120776\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.84915 | + | 4.93488i | 0.241662 | + | 0.418571i | 0.961188 | − | 0.275895i | \(-0.0889741\pi\) |
−0.719526 | + | 0.694466i | \(0.755641\pi\) | |||||||
\(140\) | −3.09056 | − | 5.04465i | −0.261200 | − | 0.426350i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 16.3189i | − | 1.36945i | ||||||
\(143\) | −13.8055 | − | 7.97058i | −1.15447 | − | 0.666534i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.60538 | − | 10.2318i | −0.216365 | − | 0.849703i | ||||
\(146\) | 6.41567 | − | 11.1123i | 0.530964 | − | 0.919657i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.356887 | + | 0.206049i | −0.0293359 | + | 0.0169371i | ||||
\(149\) | −10.4021 | + | 18.0169i | −0.852169 | + | 1.47600i | 0.0270774 | + | 0.999633i | \(0.491380\pi\) |
−0.879247 | + | 0.476367i | \(0.841953\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.13217 | − | 14.0853i | −0.661786 | − | 1.14625i | −0.980146 | − | 0.198278i | \(-0.936465\pi\) |
0.318359 | − | 0.947970i | \(-0.396868\pi\) | |||||||
\(152\) | −2.44179 | + | 1.40977i | −0.198056 | + | 0.114347i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.21362 | + | 10.3768i | 0.258961 | + | 0.836187i | ||||
\(155\) | 6.23462 | − | 6.08113i | 0.500777 | − | 0.488448i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.2586i | 1.61681i | 0.588625 | + | 0.808406i | \(0.299669\pi\) | ||||
−0.588625 | + | 0.808406i | \(0.700331\pi\) | |||||||
\(158\) | 6.02746i | 0.479519i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.56131 | − | 1.60072i | −0.123433 | − | 0.126548i | ||||
\(161\) | −10.6505 | + | 11.5044i | −0.839373 | + | 0.906674i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.81431 | − | 3.93424i | 0.533738 | − | 0.308154i | −0.208799 | − | 0.977958i | \(-0.566956\pi\) |
0.742537 | + | 0.669805i | \(0.233622\pi\) | |||||||
\(164\) | −3.43052 | − | 5.94183i | −0.267878 | − | 0.463979i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.74967 | − | 13.4228i | 0.601491 | − | 1.04181i | ||||
\(167\) | −18.3747 | + | 10.6086i | −1.42187 | + | 0.820919i | −0.996459 | − | 0.0840795i | \(-0.973205\pi\) |
−0.425415 | + | 0.904999i | \(0.639872\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.03712 | − | 1.79635i | 0.0797788 | − | 0.138181i | ||||
\(170\) | −1.53218 | − | 6.01715i | −0.117513 | − | 0.461494i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.08691 | − | 0.627530i | −0.0828764 | − | 0.0478487i | ||||
\(173\) | 4.93214i | 0.374984i | 0.982266 | + | 0.187492i | \(0.0600358\pi\) | ||||
−0.982266 | + | 0.187492i | \(0.939964\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.8234 | − | 3.24974i | −0.969357 | − | 0.245657i | ||||
\(176\) | 2.05292 | + | 3.55576i | 0.154745 | + | 0.268026i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.38786 | − | 3.68803i | 0.478790 | − | 0.276430i | ||||
\(179\) | 2.63272 | − | 4.56000i | 0.196779 | − | 0.340831i | −0.750703 | − | 0.660639i | \(-0.770285\pi\) |
0.947482 | + | 0.319809i | \(0.103619\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.1029 | 1.49423 | 0.747117 | − | 0.664692i | \(-0.231437\pi\) | ||||
0.747117 | + | 0.664692i | \(0.231437\pi\) | |||||||
\(182\) | −9.81250 | + | 3.03886i | −0.727351 | + | 0.225255i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.96277 | + | 5.13166i | −0.218418 | + | 0.378311i | ||||
\(185\) | −0.249569 | + | 0.887037i | −0.0183487 | + | 0.0652163i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.4012i | 0.833737i | ||||||||
\(188\) | 5.10612i | 0.372402i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.70754 | + | 6.06905i | −0.123878 | + | 0.440295i | ||||
\(191\) | 2.99287 | 0.216557 | 0.108278 | − | 0.994121i | \(-0.465466\pi\) | ||||
0.108278 | + | 0.994121i | \(0.465466\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 21.4412i | − | 1.54337i | −0.636003 | − | 0.771687i | \(-0.719413\pi\) | ||
0.636003 | − | 0.771687i | \(-0.280587\pi\) | |||||||
\(194\) | −2.09320 | + | 3.62553i | −0.150283 | + | 0.260298i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.31361 | + | 3.02298i | 0.450972 | + | 0.215927i | ||||
\(197\) | 3.13660i | 0.223474i | 0.993738 | + | 0.111737i | \(0.0356414\pi\) | ||||
−0.993738 | + | 0.111737i | \(0.964359\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.45046 | + | 12.9046i | −0.528149 | + | 0.914781i | 0.471313 | + | 0.881966i | \(0.343780\pi\) |
−0.999461 | + | 0.0328145i | \(0.989553\pi\) | |||||||
\(200\) | −4.99845 | − | 0.124606i | −0.353444 | − | 0.00881097i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.9673 | − | 6.33196i | 0.771655 | − | 0.445515i | ||||
\(203\) | 9.16738 | + | 8.48690i | 0.643424 | + | 0.595663i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.7684 | − | 4.15509i | −1.03147 | − | 0.290204i | ||||
\(206\) | 2.18985 | − | 3.79293i | 0.152574 | − | 0.264266i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.36239 | + | 1.94128i | −0.233140 | + | 0.134603i | ||||
\(209\) | 5.78829 | − | 10.0256i | 0.400385 | − | 0.693487i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.20990 | + | 12.4879i | 0.496350 | + | 0.859704i | 0.999991 | − | 0.00420922i | \(-0.00133984\pi\) |
−0.503641 | + | 0.863913i | \(0.668007\pi\) | |||||||
\(212\) | −4.20182 | − | 2.42592i | −0.288582 | − | 0.166613i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.63543 | + | 2.83265i | 0.111796 | + | 0.193636i | ||||
\(215\) | −2.71962 | + | 0.692513i | −0.185476 | + | 0.0472290i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.28174 | + | 10.0491i | −0.154895 | + | 0.682178i | ||||
\(218\) | −2.87443 | − | 1.65955i | −0.194681 | − | 0.112399i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8.83781 | + | 2.48653i | 0.595845 | + | 0.167642i | ||||
\(221\) | −10.7812 | −0.725220 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.8455 | − | 9.14843i | −1.06110 | − | 0.612624i | −0.135361 | − | 0.990796i | \(-0.543219\pi\) |
−0.925735 | + | 0.378172i | \(0.876553\pi\) | |||||||
\(224\) | 2.58008 | + | 0.585831i | 0.172389 | + | 0.0391425i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.95566 | + | 6.85140i | 0.263126 | + | 0.455748i | ||||
\(227\) | 7.81588 | − | 4.51250i | 0.518758 | − | 0.299505i | −0.217668 | − | 0.976023i | \(-0.569845\pi\) |
0.736426 | + | 0.676518i | \(0.236512\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.59266 | + | 14.8829i | −0.567819 | + | 0.983492i | 0.428962 | + | 0.903322i | \(0.358879\pi\) |
−0.996781 | + | 0.0801691i | \(0.974454\pi\) | |||||||
\(230\) | 3.26957 | + | 12.8402i | 0.215589 | + | 0.846655i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.08921 | + | 2.36090i | 0.268469 | + | 0.155001i | ||||
\(233\) | −4.18657 | + | 2.41712i | −0.274272 | + | 0.158351i | −0.630827 | − | 0.775923i | \(-0.717284\pi\) |
0.356556 | + | 0.934274i | \(0.383951\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.97225 | + | 8.17346i | 0.520052 | + | 0.533178i | ||||
\(236\) | 12.4810 | 0.812445 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.39119 | + | 4.99101i | 0.349459 | + | 0.323519i | ||||
\(239\) | 8.08215 | + | 13.9987i | 0.522791 | + | 0.905500i | 0.999648 | + | 0.0265194i | \(0.00844237\pi\) |
−0.476858 | + | 0.878981i | \(0.658224\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.83873 | + | 8.38092i | 0.311690 | + | 0.539862i | 0.978728 | − | 0.205161i | \(-0.0657717\pi\) |
−0.667039 | + | 0.745023i | \(0.732438\pi\) | |||||||
\(242\) | −5.07312 | − | 2.92897i | −0.326113 | − | 0.188281i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.08850 | 0.0696843 | ||||||||
\(245\) | 14.8261 | − | 5.01857i | 0.947206 | − | 0.320625i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.48041 | + | 5.47352i | 0.603224 | + | 0.348271i | ||||
\(248\) | 3.89489i | 0.247325i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.19566 | + | 7.60468i | −0.518339 | + | 0.480962i | ||||
\(251\) | −17.3945 | −1.09793 | −0.548967 | − | 0.835844i | \(-0.684979\pi\) | ||||
−0.548967 | + | 0.835844i | \(0.684979\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 24.3293i | − | 1.52957i | ||||||
\(254\) | −7.37701 | −0.462875 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.02404 | − | 2.32328i | −0.251013 | − | 0.144922i | 0.369215 | − | 0.929344i | \(-0.379627\pi\) |
−0.620228 | + | 0.784422i | \(0.712960\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.322546 | − | 1.04150i | −0.0200421 | − | 0.0647160i | ||||
\(260\) | −2.35131 | + | 8.35719i | −0.145822 | + | 0.518291i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.3259 | + | 5.96168i | 0.637938 | + | 0.368314i | ||||
\(263\) | −24.3416 | + | 14.0537i | −1.50097 | + | 0.866586i | −0.500971 | + | 0.865464i | \(0.667024\pi\) |
−0.999999 | + | 0.00112136i | \(0.999643\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.5136 | + | 2.67713i | −0.645842 | + | 0.164455i | ||||
\(266\) | −2.20684 | − | 7.12591i | −0.135310 | − | 0.436917i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.5268i | 0.765195i | ||||||||
\(269\) | −14.0809 | + | 24.3889i | −0.858529 | + | 1.48702i | 0.0148033 | + | 0.999890i | \(0.495288\pi\) |
−0.873332 | + | 0.487125i | \(0.838046\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.1408 | − | 17.5644i | −0.616009 | − | 1.06696i | −0.990207 | − | 0.139610i | \(-0.955415\pi\) |
0.374197 | − | 0.927349i | \(-0.377918\pi\) | |||||||
\(272\) | 2.40480 | + | 1.38841i | 0.145812 | + | 0.0841847i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.90727 | + | 17.1599i | 0.598520 | + | 1.03667i | ||||
\(275\) | 18.0291 | − | 9.81835i | 1.08720 | − | 0.592069i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.86564 | + | 5.11858i | −0.532685 | + | 0.307546i | −0.742109 | − | 0.670279i | \(-0.766174\pi\) |
0.209424 | + | 0.977825i | \(0.432841\pi\) | |||||||
\(278\) | −4.93488 | + | 2.84915i | −0.295974 | + | 0.170881i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.04465 | − | 3.09056i | 0.301475 | − | 0.184696i | ||||
\(281\) | −10.5038 | + | 18.1931i | −0.626604 | + | 1.08531i | 0.361625 | + | 0.932324i | \(0.382222\pi\) |
−0.988228 | + | 0.152986i | \(0.951111\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 4.88129i | − | 0.290162i | −0.989420 | − | 0.145081i | \(-0.953656\pi\) | ||
0.989420 | − | 0.145081i | \(-0.0463443\pi\) | |||||||
\(284\) | 16.3189 | 0.968346 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.97058 | − | 13.8055i | 0.471310 | − | 0.816334i | ||||
\(287\) | 17.3401 | − | 5.37010i | 1.02355 | − | 0.316987i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.64463 | − | 8.04474i | −0.273214 | − | 0.473220i | ||||
\(290\) | 10.2318 | − | 2.60538i | 0.600831 | − | 0.152993i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.1123 | + | 6.41567i | 0.650296 | + | 0.375448i | ||||
\(293\) | −3.55724 | + | 2.05377i | −0.207816 | + | 0.119983i | −0.600296 | − | 0.799778i | \(-0.704951\pi\) |
0.392480 | + | 0.919761i | \(0.371617\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.9786 | − | 19.4868i | 1.16320 | − | 1.13456i | ||||
\(296\) | −0.206049 | − | 0.356887i | −0.0119763 | − | 0.0207436i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.0169 | − | 10.4021i | −1.04369 | − | 0.602575i | ||||
\(299\) | 23.0062 | 1.33048 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.25582 | − | 2.43670i | 0.130024 | − | 0.140449i | ||||
\(302\) | 14.0853 | − | 8.13217i | 0.810520 | − | 0.467954i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.40977 | − | 2.44179i | −0.0808559 | − | 0.140047i | ||||
\(305\) | 1.74239 | − | 1.69949i | 0.0997689 | − | 0.0973127i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.22215i | 0.412190i | 0.978532 | + | 0.206095i | \(0.0660755\pi\) | ||||
−0.978532 | + | 0.206095i | \(0.933924\pi\) | |||||||
\(308\) | −10.3768 | + | 3.21362i | −0.591274 | + | 0.183113i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.08113 | + | 6.23462i | 0.345385 | + | 0.354103i | ||||
\(311\) | 23.2889 | 1.32059 | 0.660296 | − | 0.751005i | \(-0.270431\pi\) | ||||
0.660296 | + | 0.751005i | \(0.270431\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.1702i | 1.02704i | 0.858078 | + | 0.513520i | \(0.171659\pi\) | ||||
−0.858078 | + | 0.513520i | \(0.828341\pi\) | |||||||
\(314\) | −20.2586 | −1.14326 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.02746 | −0.339071 | ||||||||
\(317\) | − | 0.679752i | − | 0.0381787i | −0.999818 | − | 0.0190893i | \(-0.993923\pi\) | ||
0.999818 | − | 0.0190893i | \(-0.00607670\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.3870 | −1.08546 | ||||||||
\(320\) | 1.60072 | − | 1.56131i | 0.0894829 | − | 0.0872800i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11.5044 | − | 10.6505i | −0.641116 | − | 0.593527i | ||||
\(323\) | − | 7.82936i | − | 0.435637i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.28440 | + | 17.0486i | 0.515006 | + | 0.945688i | ||||
\(326\) | 3.93424 | + | 6.81431i | 0.217898 | + | 0.377410i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.94183 | − | 3.43052i | 0.328083 | − | 0.189419i | ||||
\(329\) | −13.1742 | − | 2.99132i | −0.726316 | − | 0.164917i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.7220 | 0.699262 | 0.349631 | − | 0.936888i | \(-0.386307\pi\) | ||||
0.349631 | + | 0.936888i | \(0.386307\pi\) | |||||||
\(332\) | 13.4228 | + | 7.74967i | 0.736673 | + | 0.425318i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.6086 | − | 18.3747i | −0.580477 | − | 1.00542i | ||||
\(335\) | 19.5582 | + | 20.0519i | 1.06858 | + | 1.09555i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.7645 | + | 8.52431i | −0.804276 | + | 0.464349i | −0.844964 | − | 0.534823i | \(-0.820378\pi\) |
0.0406882 | + | 0.999172i | \(0.487045\pi\) | |||||||
\(338\) | 1.79635 | + | 1.03712i | 0.0977087 | + | 0.0564122i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.01715 | − | 1.53218i | 0.326326 | − | 0.0830944i | ||||
\(341\) | −7.99589 | − | 13.8493i | −0.433002 | − | 0.749981i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.4982 | + | 14.5186i | −0.620846 | + | 0.783933i | ||||
\(344\) | 0.627530 | − | 1.08691i | 0.0338342 | − | 0.0586025i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.93214 | −0.265154 | ||||||||
\(347\) | − | 25.1265i | − | 1.34886i | −0.738337 | − | 0.674431i | \(-0.764389\pi\) | ||
0.738337 | − | 0.674431i | \(-0.235611\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.80323 | − | 8.31944i | 0.257111 | − | 0.445329i | −0.708356 | − | 0.705856i | \(-0.750563\pi\) |
0.965467 | + | 0.260526i | \(0.0838961\pi\) | |||||||
\(350\) | 3.24974 | − | 12.8234i | 0.173706 | − | 0.685439i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.55576 | + | 2.05292i | −0.189523 | + | 0.109421i | ||||
\(353\) | −23.4317 | + | 13.5283i | −1.24715 | + | 0.720040i | −0.970539 | − | 0.240944i | \(-0.922543\pi\) |
−0.276606 | + | 0.960983i | \(0.589210\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.1219 | − | 25.4788i | 1.38641 | − | 1.35228i | ||||
\(356\) | 3.68803 | + | 6.38786i | 0.195465 | + | 0.338556i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.56000 | + | 2.63272i | 0.241004 | + | 0.139144i | ||||
\(359\) | 4.43043 | + | 7.67373i | 0.233829 | + | 0.405004i | 0.958932 | − | 0.283637i | \(-0.0915410\pi\) |
−0.725103 | + | 0.688641i | \(0.758208\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.52509 | − | 9.56974i | 0.290794 | − | 0.503671i | ||||
\(362\) | 20.1029i | 1.05658i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.03886 | − | 9.81250i | −0.159279 | − | 0.514315i | ||||
\(365\) | 27.8045 | − | 7.08003i | 1.45535 | − | 0.370586i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.32611 | + | 5.38443i | −0.486819 | + | 0.281065i | −0.723254 | − | 0.690582i | \(-0.757354\pi\) |
0.236435 | + | 0.971647i | \(0.424021\pi\) | |||||||
\(368\) | −5.13166 | − | 2.96277i | −0.267506 | − | 0.154445i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.887037 | − | 0.249569i | −0.0461149 | − | 0.0129745i | ||||
\(371\) | 8.72062 | − | 9.41984i | 0.452752 | − | 0.489054i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.25812 | + | 2.45843i | 0.220477 | + | 0.127293i | 0.606171 | − | 0.795334i | \(-0.292705\pi\) |
−0.385694 | + | 0.922627i | \(0.626038\pi\) | |||||||
\(374\) | −11.4012 | −0.589541 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.10612 | −0.263328 | ||||||||
\(377\) | − | 18.3327i | − | 0.944181i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.3873 | 1.86909 | 0.934544 | − | 0.355848i | \(-0.115808\pi\) | ||||
0.934544 | + | 0.355848i | \(0.115808\pi\) | |||||||
\(380\) | −6.06905 | − | 1.70754i | −0.311336 | − | 0.0875947i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.99287i | 0.153129i | ||||||||
\(383\) | 8.10908 | + | 4.68178i | 0.414355 | + | 0.239228i | 0.692659 | − | 0.721265i | \(-0.256439\pi\) |
−0.278304 | + | 0.960493i | \(0.589772\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.5929 | + | 21.3455i | −0.590829 | + | 1.08787i | ||||
\(386\) | 21.4412 | 1.09133 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.62553 | − | 2.09320i | −0.184058 | − | 0.106266i | ||||
\(389\) | −1.02428 | − | 1.77411i | −0.0519332 | − | 0.0899509i | 0.838890 | − | 0.544301i | \(-0.183205\pi\) |
−0.890823 | + | 0.454350i | \(0.849872\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.22707 | − | 14.2497i | −0.416061 | − | 0.720639i | ||||
\(392\) | −3.02298 | + | 6.31361i | −0.152683 | + | 0.318885i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.13660 | −0.158020 | ||||||||
\(395\) | −9.64827 | + | 9.41074i | −0.485457 | + | 0.473506i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.1640 | − | 14.5284i | 1.26294 | − | 0.729161i | 0.289302 | − | 0.957238i | \(-0.406577\pi\) |
0.973643 | + | 0.228077i | \(0.0732436\pi\) | |||||||
\(398\) | −12.9046 | − | 7.45046i | −0.646848 | − | 0.373458i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.124606 | − | 4.99845i | 0.00623030 | − | 0.249922i | ||||
\(401\) | −10.0005 | + | 17.3213i | −0.499399 | + | 0.864985i | −1.00000 | 0.000693636i | \(-0.999779\pi\) | |
0.500601 | + | 0.865678i | \(0.333113\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.0961 | − | 7.56106i | 0.652365 | − | 0.376643i | ||||
\(404\) | 6.33196 | + | 10.9673i | 0.315027 | + | 0.545642i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.48690 | + | 9.16738i | −0.421198 | + | 0.454969i | ||||
\(407\) | 1.46532 | + | 0.846003i | 0.0726332 | + | 0.0419348i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.0715 | −1.04192 | −0.520959 | − | 0.853582i | \(-0.674426\pi\) | ||||
−0.520959 | + | 0.853582i | \(0.674426\pi\) | |||||||
\(410\) | 4.15509 | − | 14.7684i | 0.205205 | − | 0.729357i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.79293 | + | 2.18985i | 0.186864 | + | 0.107886i | ||||
\(413\) | −7.31176 | + | 32.2020i | −0.359788 | + | 1.58456i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 33.5858 | − | 8.55217i | 1.64866 | − | 0.419810i | ||||
\(416\) | −1.94128 | − | 3.36239i | −0.0951790 | − | 0.164855i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.0256 | + | 5.78829i | 0.490369 | + | 0.283115i | ||||
\(419\) | 10.8551 | + | 18.8016i | 0.530306 | + | 0.918517i | 0.999375 | + | 0.0353551i | \(0.0112562\pi\) |
−0.469069 | + | 0.883162i | \(0.655410\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.3520 | + | 17.9301i | −0.504524 | + | 0.873861i | 0.495463 | + | 0.868629i | \(0.334999\pi\) |
−0.999986 | + | 0.00523148i | \(0.998335\pi\) | |||||||
\(422\) | −12.4879 | + | 7.20990i | −0.607902 | + | 0.350973i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.42592 | − | 4.20182i | 0.117813 | − | 0.204058i | ||||
\(425\) | 7.23955 | − | 11.8472i | 0.351170 | − | 0.574676i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.637678 | + | 2.80842i | −0.0308594 | + | 0.135909i | ||||
\(428\) | −2.83265 | + | 1.63543i | −0.136921 | + | 0.0790516i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.692513 | − | 2.71962i | −0.0333959 | − | 0.131152i | ||||
\(431\) | 1.15807 | − | 2.00583i | 0.0557821 | − | 0.0966174i | −0.836786 | − | 0.547530i | \(-0.815568\pi\) |
0.892568 | + | 0.450913i | \(0.148901\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 22.2752i | − | 1.07048i | −0.844701 | − | 0.535238i | \(-0.820222\pi\) | ||
0.844701 | − | 0.535238i | \(-0.179778\pi\) | |||||||
\(434\) | −10.0491 | − | 2.28174i | −0.482373 | − | 0.109527i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.65955 | − | 2.87443i | 0.0794782 | − | 0.137660i | ||||
\(437\) | 16.7073i | 0.799218i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.7548 | 0.990575 | 0.495287 | − | 0.868729i | \(-0.335063\pi\) | ||||
0.495287 | + | 0.868729i | \(0.335063\pi\) | |||||||
\(440\) | −2.48653 | + | 8.83781i | −0.118541 | + | 0.421326i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 10.7812i | − | 0.512808i | ||||||
\(443\) | 18.7632i | 0.891467i | 0.895166 | + | 0.445733i | \(0.147057\pi\) | ||||
−0.895166 | + | 0.445733i | \(0.852943\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.8770 | + | 4.46700i | 0.752640 | + | 0.211756i | ||||
\(446\) | 9.14843 | − | 15.8455i | 0.433191 | − | 0.750308i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.585831 | + | 2.58008i | −0.0276779 | + | 0.121897i | ||||
\(449\) | −4.33662 | −0.204658 | −0.102329 | − | 0.994751i | \(-0.532629\pi\) | ||||
−0.102329 | + | 0.994751i | \(0.532629\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.0852 | + | 24.3962i | −0.663244 | + | 1.14877i | ||||
\(452\) | −6.85140 | + | 3.95566i | −0.322263 | + | 0.186059i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.51250 | + | 7.81588i | 0.211782 | + | 0.366817i | ||||
\(455\) | −20.1847 | − | 10.9624i | −0.946275 | − | 0.513928i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.7169i | 1.06265i | 0.847168 | + | 0.531325i | \(0.178306\pi\) | ||||
−0.847168 | + | 0.531325i | \(0.821694\pi\) | |||||||
\(458\) | −14.8829 | − | 8.59266i | −0.695434 | − | 0.401509i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.8402 | + | 3.26957i | −0.598675 | + | 0.152445i | ||||
\(461\) | −8.41648 | + | 14.5778i | −0.391995 | + | 0.678955i | −0.992713 | − | 0.120506i | \(-0.961548\pi\) |
0.600718 | + | 0.799461i | \(0.294882\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.0438 | − | 13.8817i | 1.11741 | − | 0.645138i | 0.176673 | − | 0.984270i | \(-0.443467\pi\) |
0.940739 | + | 0.339132i | \(0.110133\pi\) | |||||||
\(464\) | −2.36090 | + | 4.08921i | −0.109602 | + | 0.189837i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.41712 | − | 4.18657i | −0.111971 | − | 0.193939i | ||||
\(467\) | −29.8191 | + | 17.2161i | −1.37986 | + | 0.796665i | −0.992143 | − | 0.125112i | \(-0.960071\pi\) |
−0.387721 | + | 0.921777i | \(0.626738\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.3201 | − | 7.33857i | −1.49240 | − | 0.338864i | ||||
\(470\) | −8.17346 | + | 7.97225i | −0.377014 | + | 0.367732i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.4810i | 0.574486i | ||||||||
\(473\) | 5.15308i | 0.236939i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.3808 | + | 6.74240i | −0.568072 | + | 0.309363i | ||||
\(476\) | −4.99101 | + | 5.39119i | −0.228763 | + | 0.247105i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13.9987 | + | 8.08215i | −0.640285 | + | 0.369669i | ||||
\(479\) | −5.64351 | − | 9.77485i | −0.257859 | − | 0.446624i | 0.707809 | − | 0.706403i | \(-0.249684\pi\) |
−0.965668 | + | 0.259779i | \(0.916350\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.799995 | + | 1.38563i | −0.0364766 | + | 0.0631794i | ||||
\(482\) | −8.38092 | + | 4.83873i | −0.381740 | + | 0.220398i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.92897 | − | 5.07312i | 0.133135 | − | 0.230596i | ||||
\(485\) | −9.07159 | + | 2.30996i | −0.411920 | + | 0.104890i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.2703 | + | 12.2804i | 0.963848 | + | 0.556478i | 0.897355 | − | 0.441309i | \(-0.145486\pi\) |
0.0664931 | + | 0.997787i | \(0.478819\pi\) | |||||||
\(488\) | 1.08850i | 0.0492742i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.01857 | + | 14.8261i | 0.226716 | + | 0.669776i | ||||
\(491\) | 9.08350 | + | 15.7331i | 0.409933 | + | 0.710024i | 0.994882 | − | 0.101046i | \(-0.0322188\pi\) |
−0.584949 | + | 0.811070i | \(0.698885\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.3550 | + | 6.55581i | −0.511403 | + | 0.295259i | ||||
\(494\) | −5.47352 | + | 9.48041i | −0.246265 | + | 0.426544i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.89489 | −0.174886 | ||||||||
\(497\) | −9.56009 | + | 42.1039i | −0.428829 | + | 1.88862i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.69190 | − | 9.85866i | 0.254805 | − | 0.441334i | −0.710038 | − | 0.704164i | \(-0.751322\pi\) |
0.964842 | + | 0.262829i | \(0.0846555\pi\) | |||||||
\(500\) | −7.60468 | − | 8.19566i | −0.340092 | − | 0.366521i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 17.3945i | − | 0.776357i | ||||||
\(503\) | − | 7.11598i | − | 0.317286i | −0.987336 | − | 0.158643i | \(-0.949288\pi\) | ||
0.987336 | − | 0.158643i | \(-0.0507118\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.2590 | + | 7.66936i | 1.21301 | + | 0.341282i | ||||
\(506\) | 24.3293 | 1.08157 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 7.37701i | − | 0.327302i | ||||||
\(509\) | 12.2001 | − | 21.1313i | 0.540762 | − | 0.936627i | −0.458099 | − | 0.888901i | \(-0.651469\pi\) |
0.998860 | − | 0.0477257i | \(-0.0151973\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.0628 | + | 24.9120i | −1.02024 | + | 1.10204i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.32328 | − | 4.02404i | 0.102476 | − | 0.177493i | ||||
\(515\) | 9.49047 | − | 2.41662i | 0.418200 | − | 0.106489i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.1561 | − | 10.4825i | 0.798506 | − | 0.461018i | ||||
\(518\) | 1.04150 | − | 0.322546i | 0.0457611 | − | 0.0141719i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.35719 | − | 2.35131i | −0.366487 | − | 0.103112i | ||||
\(521\) | 10.6836 | − | 18.5046i | 0.468058 | − | 0.810701i | −0.531275 | − | 0.847199i | \(-0.678287\pi\) |
0.999334 | + | 0.0364984i | \(0.0116204\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.4124 | + | 12.9398i | −0.980028 | + | 0.565819i | −0.902278 | − | 0.431154i | \(-0.858107\pi\) |
−0.0777491 | + | 0.996973i | \(0.524773\pi\) | |||||||
\(524\) | −5.96168 | + | 10.3259i | −0.260437 | + | 0.451090i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.0537 | − | 24.3416i | −0.612769 | − | 1.06135i | ||||
\(527\) | −9.36641 | − | 5.40770i | −0.408007 | − | 0.235563i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.05597 | + | 10.4892i | 0.263303 | + | 0.456054i | ||||
\(530\) | −2.67713 | − | 10.5136i | −0.116287 | − | 0.456679i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.12591 | − | 2.20684i | 0.308947 | − | 0.0956787i | ||||
\(533\) | −23.0695 | − | 13.3192i | −0.999251 | − | 0.576918i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.98086 | + | 7.04052i | −0.0856400 | + | 0.304388i | ||||
\(536\) | −12.5268 | −0.541075 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −24.3889 | − | 14.0809i | −1.05148 | − | 0.607072i | ||||
\(539\) | −2.21234 | − | 28.6556i | −0.0952922 | − | 1.23428i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0736 | − | 31.3045i | −0.777047 | − | 1.34588i | −0.933637 | − | 0.358221i | \(-0.883384\pi\) |
0.156590 | − | 0.987664i | \(-0.449950\pi\) | |||||||
\(542\) | 17.5644 | − | 10.1408i | 0.754454 | − | 0.435584i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.38841 | + | 2.40480i | −0.0595276 | + | 0.103105i | ||||
\(545\) | −1.83141 | − | 7.19224i | −0.0784488 | − | 0.308082i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.13044 | − | 4.69411i | −0.347633 | − | 0.200706i | 0.316010 | − | 0.948756i | \(-0.397657\pi\) |
−0.663642 | + | 0.748050i | \(0.730990\pi\) | |||||||
\(548\) | −17.1599 | + | 9.90727i | −0.733034 | + | 0.423218i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.81835 | + | 18.0291i | 0.418656 | + | 0.768763i | ||||
\(551\) | 13.3133 | 0.567167 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.53107 | − | 15.5513i | 0.150156 | − | 0.661309i | ||||
\(554\) | −5.11858 | − | 8.86564i | −0.217468 | − | 0.376665i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.84915 | − | 4.93488i | −0.120831 | − | 0.209285i | ||||
\(557\) | 18.3702 | + | 10.6060i | 0.778370 | + | 0.449392i | 0.835852 | − | 0.548955i | \(-0.184974\pi\) |
−0.0574826 | + | 0.998347i | \(0.518307\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.87284 | −0.206099 | ||||||||
\(560\) | 3.09056 | + | 5.04465i | 0.130600 | + | 0.213175i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.1931 | − | 10.5038i | −0.767429 | − | 0.443076i | ||||
\(563\) | 22.5552i | 0.950588i | 0.879827 | + | 0.475294i | \(0.157658\pi\) | ||||
−0.879827 | + | 0.475294i | \(0.842342\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.79115 | + | 17.0291i | −0.201565 | + | 0.716419i | ||||
\(566\) | 4.88129 | 0.205176 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.3189i | 0.684724i | ||||||||
\(569\) | −9.13134 | −0.382806 | −0.191403 | − | 0.981512i | \(-0.561304\pi\) | ||||
−0.191403 | + | 0.981512i | \(0.561304\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.9976 | 1.84124 | 0.920621 | − | 0.390457i | \(-0.127683\pi\) | ||||
0.920621 | + | 0.390457i | \(0.127683\pi\) | |||||||
\(572\) | 13.8055 | + | 7.97058i | 0.577235 | + | 0.333267i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.37010 | + | 17.3401i | 0.224144 | + | 0.723761i | ||||
\(575\) | −15.4487 | + | 25.2812i | −0.644254 | + | 1.05430i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.2964 | − | 9.40875i | −0.678429 | − | 0.391691i | 0.120834 | − | 0.992673i | \(-0.461443\pi\) |
−0.799263 | + | 0.600981i | \(0.794777\pi\) | |||||||
\(578\) | 8.04474 | − | 4.64463i | 0.334617 | − | 0.193191i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.60538 | + | 10.2318i | 0.108183 | + | 0.424852i | ||||
\(581\) | −27.8582 | + | 30.0919i | −1.15575 | + | 1.24842i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.9209i | 0.825039i | ||||||||
\(584\) | −6.41567 | + | 11.1123i | −0.265482 | + | 0.459828i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.05377 | − | 3.55724i | −0.0848405 | − | 0.146948i | ||||
\(587\) | 13.2631 | + | 7.65744i | 0.547426 | + | 0.316056i | 0.748083 | − | 0.663605i | \(-0.230974\pi\) |
−0.200657 | + | 0.979661i | \(0.564308\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.49090 | + | 9.51051i | 0.226248 | + | 0.391874i | ||||
\(590\) | 19.4868 | + | 19.9786i | 0.802258 | + | 0.822506i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.356887 | − | 0.206049i | 0.0146679 | − | 0.00846854i | ||||
\(593\) | 18.6589 | − | 10.7727i | 0.766231 | − | 0.442384i | −0.0652975 | − | 0.997866i | \(-0.520800\pi\) |
0.831528 | + | 0.555482i | \(0.187466\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.428126 | + | 16.4223i | 0.0175515 | + | 0.673249i | ||||
\(596\) | 10.4021 | − | 18.0169i | 0.426085 | − | 0.738000i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 23.0062i | 0.940794i | ||||||||
\(599\) | 37.8675 | 1.54722 | 0.773612 | − | 0.633659i | \(-0.218448\pi\) | ||||
0.773612 | + | 0.633659i | \(0.218448\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.2700 | + | 28.1804i | −0.663666 | + | 1.14950i | 0.315979 | + | 0.948766i | \(0.397667\pi\) |
−0.979645 | + | 0.200737i | \(0.935666\pi\) | |||||||
\(602\) | 2.43670 | + | 2.25582i | 0.0993124 | + | 0.0919405i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.13217 | + | 14.0853i | 0.330893 | + | 0.573124i | ||||
\(605\) | −3.23227 | − | 12.6937i | −0.131411 | − | 0.516071i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.9715 | − | 16.7267i | −1.17592 | − | 0.678916i | −0.220851 | − | 0.975308i | \(-0.570883\pi\) |
−0.955067 | + | 0.296391i | \(0.904217\pi\) | |||||||
\(608\) | 2.44179 | − | 1.40977i | 0.0990278 | − | 0.0571737i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.69949 | + | 1.74239i | 0.0688105 | + | 0.0705472i | ||||
\(611\) | 9.91240 | + | 17.1688i | 0.401013 | + | 0.694574i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.1077 | + | 8.14510i | 0.569806 | + | 0.328978i | 0.757072 | − | 0.653332i | \(-0.226629\pi\) |
−0.187266 | + | 0.982309i | \(0.559963\pi\) | |||||||
\(614\) | −7.22215 | −0.291462 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.21362 | − | 10.3768i | −0.129480 | − | 0.418094i | ||||
\(617\) | 3.39147 | − | 1.95807i | 0.136536 | − | 0.0788289i | −0.430176 | − | 0.902745i | \(-0.641549\pi\) |
0.566712 | + | 0.823916i | \(0.308215\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.5743 | + | 20.0474i | 0.465212 | + | 0.805771i | 0.999211 | − | 0.0397140i | \(-0.0126447\pi\) |
−0.533999 | + | 0.845485i | \(0.679311\pi\) | |||||||
\(620\) | −6.23462 | + | 6.08113i | −0.250388 | + | 0.244224i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 23.2889i | 0.933800i | ||||||||
\(623\) | −18.6417 | + | 5.77321i | −0.746866 | + | 0.231299i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.9689 | − | 1.24567i | −0.998758 | − | 0.0498269i | ||||
\(626\) | −18.1702 | −0.726227 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 20.2586i | − | 0.808406i | ||||||
\(629\) | 1.14432 | 0.0456270 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.9516 | 1.19235 | 0.596177 | − | 0.802853i | \(-0.296686\pi\) | ||||
0.596177 | + | 0.802853i | \(0.296686\pi\) | |||||||
\(632\) | − | 6.02746i | − | 0.239759i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.679752 | 0.0269964 | ||||||||
\(635\) | −11.5178 | − | 11.8085i | −0.457071 | − | 0.468607i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.0973 | − | 2.09203i | 1.07363 | − | 0.0828892i | ||||
\(638\) | − | 19.3870i | − | 0.767538i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.56131 | + | 1.60072i | 0.0617163 | + | 0.0632740i | ||||
\(641\) | −7.38355 | − | 12.7887i | −0.291633 | − | 0.505123i | 0.682563 | − | 0.730827i | \(-0.260865\pi\) |
−0.974196 | + | 0.225704i | \(0.927532\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.76719 | + | 3.90704i | −0.266872 | + | 0.154078i | −0.627465 | − | 0.778645i | \(-0.715908\pi\) |
0.360593 | + | 0.932723i | \(0.382574\pi\) | |||||||
\(644\) | 10.6505 | − | 11.5044i | 0.419687 | − | 0.453337i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.82936 | 0.308042 | ||||||||
\(647\) | −21.1027 | − | 12.1837i | −0.829634 | − | 0.478989i | 0.0240933 | − | 0.999710i | \(-0.492330\pi\) |
−0.853727 | + | 0.520720i | \(0.825663\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.6225 | − | 44.3795i | −1.00577 | − | 1.74205i | ||||
\(650\) | −17.0486 | + | 9.28440i | −0.668703 | + | 0.364164i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.81431 | + | 3.93424i | −0.266869 | + | 0.154077i | ||||
\(653\) | −17.7518 | − | 10.2490i | −0.694680 | − | 0.401074i | 0.110683 | − | 0.993856i | \(-0.464696\pi\) |
−0.805363 | + | 0.592782i | \(0.798030\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.57903 | + | 25.8370i | 0.257064 | + | 1.00953i | ||||
\(656\) | 3.43052 | + | 5.94183i | 0.133939 | + | 0.231990i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.99132 | − | 13.1742i | 0.116614 | − | 0.513583i | ||||
\(659\) | 5.19823 | − | 9.00360i | 0.202494 | − | 0.350731i | −0.746837 | − | 0.665007i | \(-0.768429\pi\) |
0.949332 | + | 0.314276i | \(0.101762\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.7189 | −1.00035 | −0.500174 | − | 0.865925i | \(-0.666731\pi\) | ||||
−0.500174 | + | 0.865925i | \(0.666731\pi\) | |||||||
\(662\) | 12.7220i | 0.494453i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.74967 | + | 13.4228i | −0.300745 | + | 0.520906i | ||||
\(665\) | 7.96101 | − | 14.6583i | 0.308715 | − | 0.568425i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.2307 | − | 13.9896i | 0.938217 | − | 0.541680i | ||||
\(668\) | 18.3747 | − | 10.6086i | 0.710937 | − | 0.410460i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −20.0519 | + | 19.5582i | −0.774671 | + | 0.755600i | ||||
\(671\) | −2.23461 | − | 3.87046i | −0.0862662 | − | 0.149417i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.4068 | − | 7.16309i | −0.478248 | − | 0.276117i | 0.241438 | − | 0.970416i | \(-0.422381\pi\) |
−0.719686 | + | 0.694300i | \(0.755714\pi\) | |||||||
\(674\) | −8.52431 | − | 14.7645i | −0.328344 | − | 0.568709i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.03712 | + | 1.79635i | −0.0398894 | + | 0.0690905i | ||||
\(677\) | − | 0.895442i | − | 0.0344146i | −0.999852 | − | 0.0172073i | \(-0.994522\pi\) | ||
0.999852 | − | 0.0172073i | \(-0.00547753\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.52456 | − | 8.12789i | 0.288766 | − | 0.311920i | ||||
\(680\) | 1.53218 | + | 6.01715i | 0.0587566 | + | 0.230747i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 13.8493 | − | 7.99589i | 0.530317 | − | 0.306179i | ||||
\(683\) | −17.0207 | − | 9.82692i | −0.651280 | − | 0.376016i | 0.137667 | − | 0.990479i | \(-0.456040\pi\) |
−0.788946 | + | 0.614462i | \(0.789373\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.9998 | + | 42.6507i | −0.458490 | + | 1.62960i | ||||
\(686\) | −14.5186 | − | 11.4982i | −0.554324 | − | 0.439004i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.08691 | + | 0.627530i | 0.0414382 | + | 0.0239244i | ||||
\(689\) | −18.8375 | −0.717653 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.3254 | 0.735171 | 0.367586 | − | 0.929990i | \(-0.380184\pi\) | ||||
0.367586 | + | 0.929990i | \(0.380184\pi\) | |||||||
\(692\) | − | 4.93214i | − | 0.187492i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.1265 | 0.953790 | ||||||||
\(695\) | −12.2656 | − | 3.45094i | −0.465260 | − | 0.130901i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.0519i | 0.721641i | ||||||||
\(698\) | 8.31944 | + | 4.80323i | 0.314895 | + | 0.181805i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 12.8234 | + | 3.24974i | 0.484678 | + | 0.122828i | ||||
\(701\) | 37.8106 | 1.42809 | 0.714044 | − | 0.700101i | \(-0.246862\pi\) | ||||
0.714044 | + | 0.700101i | \(0.246862\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.00626 | − | 0.580962i | −0.0379517 | − | 0.0219114i | ||||
\(704\) | −2.05292 | − | 3.55576i | −0.0773724 | − | 0.134013i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.5283 | − | 23.4317i | −0.509145 | − | 0.881865i | ||||
\(707\) | −32.0059 | + | 9.91198i | −1.20370 | + | 0.372778i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 43.4760 | 1.63277 | 0.816387 | − | 0.577505i | \(-0.195974\pi\) | ||||
0.816387 | + | 0.577505i | \(0.195974\pi\) | |||||||
\(710\) | 25.4788 | + | 26.1219i | 0.956204 | + | 0.980338i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.38786 | + | 3.68803i | −0.239395 | + | 0.138215i | ||||
\(713\) | 19.9872 | + | 11.5396i | 0.748528 | + | 0.432163i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 34.5432 | − | 8.79596i | 1.29184 | − | 0.328950i | ||||
\(716\) | −2.63272 | + | 4.56000i | −0.0983894 | + | 0.170415i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.67373 | + | 4.43043i | −0.286381 | + | 0.165342i | ||||
\(719\) | −14.5195 | − | 25.1485i | −0.541486 | − | 0.937881i | −0.998819 | − | 0.0485854i | \(-0.984529\pi\) |
0.457333 | − | 0.889295i | \(-0.348805\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.87200 | + | 8.50318i | −0.293169 | + | 0.316675i | ||||
\(722\) | 9.56974 | + | 5.52509i | 0.356149 | + | 0.205623i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −20.1029 | −0.747117 | ||||||||
\(725\) | 20.1455 | + | 12.3104i | 0.748185 | + | 0.457196i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.94247 | − | 1.12149i | −0.0720423 | − | 0.0415936i | 0.463546 | − | 0.886073i | \(-0.346577\pi\) |
−0.535588 | + | 0.844479i | \(0.679910\pi\) | |||||||
\(728\) | 9.81250 | − | 3.03886i | 0.363675 | − | 0.112628i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.08003 | + | 27.8045i | 0.262044 | + | 1.02909i | ||||
\(731\) | 1.74254 | + | 3.01817i | 0.0644501 | + | 0.111631i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.753946 | + | 0.435291i | 0.0278476 | + | 0.0160778i | 0.513859 | − | 0.857875i | \(-0.328215\pi\) |
−0.486012 | + | 0.873952i | \(0.661549\pi\) | |||||||
\(734\) | −5.38443 | − | 9.32611i | −0.198743 | − | 0.344233i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.96277 | − | 5.13166i | 0.109209 | − | 0.189156i | ||||
\(737\) | 44.5423 | − | 25.7165i | 1.64074 | − | 0.947279i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.25114 | − | 16.0234i | 0.340309 | − | 0.589432i | −0.644181 | − | 0.764873i | \(-0.722802\pi\) |
0.984490 | + | 0.175441i | \(0.0561351\pi\) | |||||||
\(740\) | 0.249569 | − | 0.887037i | 0.00917434 | − | 0.0326081i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.41984 | + | 8.72062i | 0.345813 | + | 0.320144i | ||||
\(743\) | 7.22866 | − | 4.17347i | 0.265194 | − | 0.153110i | −0.361508 | − | 0.932369i | \(-0.617738\pi\) |
0.626701 | + | 0.779259i | \(0.284405\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.4792 | − | 45.0808i | −0.420566 | − | 1.65163i | ||||
\(746\) | −2.45843 | + | 4.25812i | −0.0900095 | + | 0.155901i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 11.4012i | − | 0.416869i | ||||||
\(749\) | −2.56009 | − | 8.26655i | −0.0935436 | − | 0.302053i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.5031 | + | 33.7804i | −0.711678 | + | 1.23266i | 0.252548 | + | 0.967584i | \(0.418731\pi\) |
−0.964227 | + | 0.265079i | \(0.914602\pi\) | |||||||
\(752\) | − | 5.10612i | − | 0.186201i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 18.3327 | 0.667637 | ||||||||
\(755\) | 35.0089 | + | 9.84980i | 1.27410 | + | 0.358471i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 37.6562i | − | 1.36864i | −0.729182 | − | 0.684320i | \(-0.760099\pi\) | ||
0.729182 | − | 0.684320i | \(-0.239901\pi\) | |||||||
\(758\) | 36.3873i | 1.32164i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.70754 | − | 6.06905i | 0.0619388 | − | 0.220148i | ||||
\(761\) | 18.1162 | − | 31.3783i | 0.656714 | − | 1.13746i | −0.324748 | − | 0.945801i | \(-0.605279\pi\) |
0.981461 | − | 0.191661i | \(-0.0613873\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.44404 | + | 5.96571i | 0.233290 | + | 0.215973i | ||||
\(764\) | −2.99287 | −0.108278 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.68178 | + | 8.10908i | −0.169160 | + | 0.292993i | ||||
\(767\) | 41.9661 | − | 24.2291i | 1.51531 | − | 0.874863i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.17687 | + | 10.6986i | 0.222744 | + | 0.385803i | 0.955640 | − | 0.294537i | \(-0.0951654\pi\) |
−0.732897 | + | 0.680340i | \(0.761832\pi\) | |||||||
\(770\) | −21.3455 | − | 11.5929i | −0.769240 | − | 0.417779i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 21.4412i | 0.771687i | ||||||||
\(773\) | −37.1712 | − | 21.4608i | −1.33695 | − | 0.771891i | −0.350600 | − | 0.936525i | \(-0.614022\pi\) |
−0.986355 | + | 0.164634i | \(0.947356\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.485326 | + | 19.4684i | −0.0174334 | + | 0.699325i | ||||
\(776\) | 2.09320 | − | 3.62553i | 0.0751415 | − | 0.130149i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.77411 | − | 1.02428i | 0.0636049 | − | 0.0367223i | ||||
\(779\) | 9.67249 | − | 16.7532i | 0.346553 | − | 0.600247i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.5013 | − | 58.0260i | −1.19877 | − | 2.07633i | ||||
\(782\) | 14.2497 | − | 8.22707i | 0.509568 | − | 0.294199i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.31361 | − | 3.02298i | −0.225486 | − | 0.107963i | ||||
\(785\) | −31.6300 | − | 32.4283i | −1.12892 | − | 1.15742i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 32.1303i | − | 1.14532i | −0.819792 | − | 0.572662i | \(-0.805911\pi\) | ||
0.819792 | − | 0.572662i | \(-0.194089\pi\) | |||||||
\(788\) | − | 3.13660i | − | 0.111737i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.41074 | − | 9.64827i | −0.334819 | − | 0.343270i | ||||
\(791\) | −6.19215 | − | 19.9945i | −0.220167 | − | 0.710922i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.65998 | − | 2.11309i | 0.129970 | − | 0.0750380i | ||||
\(794\) | 14.5284 | + | 25.1640i | 0.515595 | + | 0.893037i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.45046 | − | 12.9046i | 0.264074 | − | 0.457390i | ||||
\(797\) | −31.8223 | + | 18.3726i | −1.12720 | + | 0.650791i | −0.943230 | − | 0.332140i | \(-0.892229\pi\) |
−0.183973 | + | 0.982931i | \(0.558896\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.08939 | − | 12.2792i | 0.250805 | − | 0.434406i | ||||
\(800\) | 4.99845 | + | 0.124606i | 0.176722 | + | 0.00440548i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17.3213 | − | 10.0005i | −0.611637 | − | 0.353129i | ||||
\(803\) | − | 52.6834i | − | 1.85916i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.913591 | − | 35.0440i | −0.0321998 | − | 1.23514i | ||||
\(806\) | 7.56106 | + | 13.0961i | 0.266327 | + | 0.461292i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.9673 | + | 6.33196i | −0.385827 | + | 0.222757i | ||||
\(809\) | −1.13309 | + | 1.96256i | −0.0398372 | + | 0.0690001i | −0.885257 | − | 0.465103i | \(-0.846017\pi\) |
0.845419 | + | 0.534103i | \(0.179351\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.0434 | 0.949622 | 0.474811 | − | 0.880088i | \(-0.342516\pi\) | ||||
0.474811 | + | 0.880088i | \(0.342516\pi\) | |||||||
\(812\) | −9.16738 | − | 8.48690i | −0.321712 | − | 0.297832i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.846003 | + | 1.46532i | −0.0296524 | + | 0.0513594i | ||||
\(815\) | −4.76521 | + | 16.9369i | −0.166918 | + | 0.593273i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 3.53869i | − | 0.123803i | ||||||
\(818\) | − | 21.0715i | − | 0.736747i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14.7684 | + | 4.15509i | 0.515733 | + | 0.145102i | ||||
\(821\) | −10.1500 | −0.354238 | −0.177119 | − | 0.984189i | \(-0.556678\pi\) | ||||
−0.177119 | + | 0.984189i | \(0.556678\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.13372i | 0.283524i | 0.989901 | + | 0.141762i | \(0.0452767\pi\) | ||||
−0.989901 | + | 0.141762i | \(0.954723\pi\) | |||||||
\(824\) | −2.18985 | + | 3.79293i | −0.0762871 | + | 0.132133i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −32.2020 | − | 7.31176i | −1.12045 | − | 0.254409i | ||||
\(827\) | 2.64164i | 0.0918589i | 0.998945 | + | 0.0459294i | \(0.0146249\pi\) | ||||
−0.998945 | + | 0.0459294i | \(0.985375\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.6215 | − | 25.3252i | 0.507827 | − | 0.879582i | −0.492132 | − | 0.870521i | \(-0.663782\pi\) |
0.999959 | − | 0.00906143i | \(-0.00288438\pi\) | |||||||
\(830\) | 8.55217 | + | 33.5858i | 0.296850 | + | 1.16578i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.36239 | − | 1.94128i | 0.116570 | − | 0.0673017i | ||||
\(833\) | −10.9858 | − | 16.0355i | −0.380636 | − | 0.555598i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.8493 | − | 45.6700i | 0.444669 | − | 1.58048i | ||||
\(836\) | −5.78829 | + | 10.0256i | −0.200192 | + | 0.346743i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −18.8016 | + | 10.8551i | −0.649489 | + | 0.374983i | ||||
\(839\) | 3.93007 | − | 6.80707i | 0.135681 | − | 0.235006i | −0.790176 | − | 0.612879i | \(-0.790011\pi\) |
0.925857 | + | 0.377873i | \(0.123344\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.35227 | + | 5.80630i | 0.115595 | + | 0.200217i | ||||
\(842\) | −17.9301 | − | 10.3520i | −0.617913 | − | 0.356752i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.20990 | − | 12.4879i | −0.248175 | − | 0.429852i | ||||
\(845\) | 1.14452 | + | 4.49473i | 0.0393728 | + | 0.154624i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.3732 | + | 10.5290i | 0.390787 | + | 0.361779i | ||||
\(848\) | 4.20182 | + | 2.42592i | 0.144291 | + | 0.0833064i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 11.8472 | + | 7.23955i | 0.406357 | + | 0.248314i | ||||
\(851\) | −2.44189 | −0.0837071 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.09946 | + | 3.52152i | 0.208841 | + | 0.120575i | 0.600773 | − | 0.799420i | \(-0.294860\pi\) |
−0.391931 | + | 0.919994i | \(0.628193\pi\) | |||||||
\(854\) | −2.80842 | − | 0.637678i | −0.0961023 | − | 0.0218209i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.63543 | − | 2.83265i | −0.0558979 | − | 0.0968180i | ||||
\(857\) | 2.71486 | − | 1.56742i | 0.0927377 | − | 0.0535422i | −0.452914 | − | 0.891554i | \(-0.649616\pi\) |
0.545652 | + | 0.838012i | \(0.316282\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.3632 | + | 26.6099i | −0.524187 | + | 0.907918i | 0.475417 | + | 0.879761i | \(0.342297\pi\) |
−0.999604 | + | 0.0281573i | \(0.991036\pi\) | |||||||
\(860\) | 2.71962 | − | 0.692513i | 0.0927381 | − | 0.0236145i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.00583 | + | 1.15807i | 0.0683188 | + | 0.0394439i | ||||
\(863\) | 26.0574 | − | 15.0443i | 0.887004 | − | 0.512112i | 0.0140430 | − | 0.999901i | \(-0.495530\pi\) |
0.872962 | + | 0.487789i | \(0.162196\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.70061 | − | 7.89497i | −0.261829 | − | 0.268437i | ||||
\(866\) | 22.2752 | 0.756941 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.28174 | − | 10.0491i | 0.0774474 | − | 0.341089i | ||||
\(869\) | 12.3739 | + | 21.4322i | 0.419756 | + | 0.727038i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.3180 | + | 42.1200i | 0.823983 | + | 1.42718i | ||||
\(872\) | 2.87443 | + | 1.65955i | 0.0973405 | + | 0.0561996i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −16.7073 | −0.565132 | ||||||||
\(875\) | 25.6005 | − | 14.8194i | 0.865455 | − | 0.500987i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.2261 | − | 8.21347i | −0.480383 | − | 0.277349i | 0.240193 | − | 0.970725i | \(-0.422789\pi\) |
−0.720576 | + | 0.693376i | \(0.756123\pi\) | |||||||
\(878\) | 20.7548i | 0.700442i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.83781 | − | 2.48653i | −0.297922 | − | 0.0838209i | ||||
\(881\) | 33.4780 | 1.12790 | 0.563951 | − | 0.825808i | \(-0.309281\pi\) | ||||
0.563951 | + | 0.825808i | \(0.309281\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 44.7104i | − | 1.50462i | −0.658807 | − | 0.752312i | \(-0.728939\pi\) | ||
0.658807 | − | 0.752312i | \(-0.271061\pi\) | |||||||
\(884\) | 10.7812 | 0.362610 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18.7632 | −0.630362 | ||||||||
\(887\) | 20.4666 | + | 11.8164i | 0.687201 | + | 0.396755i | 0.802562 | − | 0.596568i | \(-0.203469\pi\) |
−0.115362 | + | 0.993324i | \(0.536803\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.0333 | + | 4.32168i | 0.638355 | + | 0.144944i | ||||
\(890\) | −4.46700 | + | 15.8770i | −0.149734 | + | 0.532197i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 15.8455 | + | 9.14843i | 0.530548 | + | 0.306312i | ||||
\(893\) | −12.4681 | + | 7.19846i | −0.417229 | + | 0.240887i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.90535 | + | 11.4098i | 0.0971150 | + | 0.381387i | ||||
\(896\) | −2.58008 | − | 0.585831i | −0.0861944 | − | 0.0195712i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 4.33662i | − | 0.144715i | ||||||
\(899\) | 9.19545 | − | 15.9270i | 0.306685 | − | 0.531195i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.73635 | + | 11.6677i | 0.224420 | + | 0.388707i | ||||
\(902\) | −24.3962 | − | 14.0852i | −0.812305 | − | 0.468985i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.95566 | − | 6.85140i | −0.131563 | − | 0.227874i | ||||
\(905\) | −32.1791 | + | 31.3869i | −1.06967 | + | 1.04333i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.1604 | + | 25.4960i | −1.46632 | + | 0.846582i | −0.999291 | − | 0.0376579i | \(-0.988010\pi\) |
−0.467033 | + | 0.884240i | \(0.654677\pi\) | |||||||
\(908\) | −7.81588 | + | 4.51250i | −0.259379 | + | 0.149753i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 10.9624 | − | 20.1847i | 0.363402 | − | 0.669117i | ||||
\(911\) | −23.6679 | + | 40.9939i | −0.784151 | + | 1.35819i | 0.145354 | + | 0.989380i | \(0.453568\pi\) |
−0.929505 | + | 0.368810i | \(0.879765\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 63.6378i | − | 2.10610i | ||||||
\(914\) | −22.7169 | −0.751407 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.59266 | − | 14.8829i | 0.283910 | − | 0.491746i | ||||
\(917\) | −23.1492 | − | 21.4308i | −0.764453 | − | 0.707709i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.2990 | − | 43.8191i | −0.834536 | − | 1.44546i | −0.894408 | − | 0.447253i | \(-0.852402\pi\) |
0.0598717 | − | 0.998206i | \(-0.480931\pi\) | |||||||
\(920\) | −3.26957 | − | 12.8402i | −0.107795 | − | 0.423327i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −14.5778 | − | 8.41648i | −0.480093 | − | 0.277182i | ||||
\(923\) | 54.8704 | − | 31.6795i | 1.80608 | − | 1.04274i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.985453 | − | 1.80955i | −0.0324015 | − | 0.0594978i | ||||
\(926\) | 13.8817 | + | 24.0438i | 0.456181 | + | 0.790129i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.08921 | − | 2.36090i | −0.134235 | − | 0.0775005i | ||||
\(929\) | 1.06340 | 0.0348891 | 0.0174446 | − | 0.999848i | \(-0.494447\pi\) | ||||
0.0174446 | + | 0.999848i | \(0.494447\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.51925 | + | 19.6782i | 0.0497913 | + | 0.644928i | ||||
\(932\) | 4.18657 | − | 2.41712i | 0.137136 | − | 0.0791754i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17.2161 | − | 29.8191i | −0.563327 | − | 0.975711i | ||||
\(935\) | −17.8008 | − | 18.2501i | −0.582149 | − | 0.596842i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.6086i | 1.29396i | 0.762508 | + | 0.646978i | \(0.223968\pi\) | ||||
−0.762508 | + | 0.646978i | \(0.776032\pi\) | |||||||
\(938\) | 7.33857 | − | 32.3201i | 0.239613 | − | 1.05529i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.97225 | − | 8.17346i | −0.260026 | − | 0.266589i | ||||
\(941\) | 2.41836 | 0.0788363 | 0.0394182 | − | 0.999223i | \(-0.487450\pi\) | ||||
0.0394182 | + | 0.999223i | \(0.487450\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 40.6553i | − | 1.32392i | ||||||
\(944\) | −12.4810 | −0.406223 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.15308 | −0.167541 | ||||||||
\(947\) | − | 35.4602i | − | 1.15230i | −0.817343 | − | 0.576151i | \(-0.804554\pi\) | ||
0.817343 | − | 0.576151i | \(-0.195446\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 49.8184 | 1.61717 | ||||||||
\(950\) | −6.74240 | − | 12.3808i | −0.218752 | − | 0.401688i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.39119 | − | 4.99101i | −0.174730 | − | 0.161760i | ||||
\(953\) | 50.6918i | 1.64207i | 0.570878 | + | 0.821035i | \(0.306603\pi\) | ||||
−0.570878 | + | 0.821035i | \(0.693397\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.79075 | + | 4.67281i | −0.155025 | + | 0.151208i | ||||
\(956\) | −8.08215 | − | 13.9987i | −0.261395 | − | 0.452750i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.77485 | − | 5.64351i | 0.315811 | − | 0.182334i | ||||
\(959\) | −15.5087 | − | 50.0778i | −0.500803 | − | 1.61710i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.8299 | −0.510641 | ||||||||
\(962\) | −1.38563 | − | 0.799995i | −0.0446746 | − | 0.0257929i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.83873 | − | 8.38092i | −0.155845 | − | 0.269931i | ||||
\(965\) | 33.4765 | + | 34.3214i | 1.07765 | + | 1.10484i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.4021 | − | 10.6245i | 0.591772 | − | 0.341659i | −0.174026 | − | 0.984741i | \(-0.555678\pi\) |
0.765798 | + | 0.643082i | \(0.222344\pi\) | |||||||
\(968\) | 5.07312 | + | 2.92897i | 0.163056 | + | 0.0941406i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.30996 | − | 9.07159i | −0.0741683 | − | 0.291271i | ||||
\(971\) | 3.26795 | + | 5.66026i | 0.104874 | + | 0.181646i | 0.913687 | − | 0.406420i | \(-0.133223\pi\) |
−0.808813 | + | 0.588066i | \(0.799890\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.4015 | − | 4.46003i | 0.461691 | − | 0.142982i | ||||
\(974\) | −12.2804 | + | 21.2703i | −0.393489 | + | 0.681544i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.08850 | −0.0348421 | ||||||||
\(977\) | − | 33.2788i | − | 1.06468i | −0.846529 | − | 0.532342i | \(-0.821312\pi\) | ||
0.846529 | − | 0.532342i | \(-0.178688\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.1425 | − | 26.2275i | 0.483956 | − | 0.838236i | ||||
\(980\) | −14.8261 | + | 5.01857i | −0.473603 | + | 0.160312i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15.7331 | + | 9.08350i | −0.502063 | + | 0.289866i | ||||
\(983\) | 20.3932 | − | 11.7740i | 0.650441 | − | 0.375532i | −0.138184 | − | 0.990407i | \(-0.544127\pi\) |
0.788625 | + | 0.614874i | \(0.210793\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.89722 | − | 5.02082i | −0.156038 | − | 0.159977i | ||||
\(986\) | −6.55581 | − | 11.3550i | −0.208779 | − | 0.361617i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.48041 | − | 5.47352i | −0.301612 | − | 0.174136i | ||||
\(989\) | −3.71845 | − | 6.44055i | −0.118240 | − | 0.204797i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.3486 | + | 30.0487i | −0.551097 | + | 0.954527i | 0.447099 | + | 0.894484i | \(0.352457\pi\) |
−0.998196 | + | 0.0600429i | \(0.980876\pi\) | |||||||
\(992\) | − | 3.89489i | − | 0.123663i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −42.1039 | − | 9.56009i | −1.33546 | − | 0.303228i | ||||
\(995\) | −8.22198 | − | 32.2891i | −0.260654 | − | 1.02363i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.7308 | − | 24.6707i | 1.35330 | − | 0.781328i | 0.364589 | − | 0.931168i | \(-0.381209\pi\) |
0.988710 | + | 0.149841i | \(0.0478761\pi\) | |||||||
\(998\) | 9.85866 | + | 5.69190i | 0.312071 | + | 0.180174i | ||||
\(999\) | 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 | 1890.2.ba.a.1369.7 | 96 | ||
3.2 | odd | 2 | 630.2.ba.a.529.10 | yes | 96 | ||
5.4 | even | 2 | inner | 1890.2.ba.a.1369.46 | 96 | ||
7.2 | even | 3 | 1890.2.bq.a.289.47 | 96 | |||
9.4 | even | 3 | 1890.2.bq.a.739.18 | 96 | |||
9.5 | odd | 6 | 630.2.bq.a.319.43 | yes | 96 | ||
15.14 | odd | 2 | 630.2.ba.a.529.39 | yes | 96 | ||
21.2 | odd | 6 | 630.2.bq.a.79.6 | yes | 96 | ||
35.9 | even | 6 | 1890.2.bq.a.289.18 | 96 | |||
45.4 | even | 6 | 1890.2.bq.a.739.47 | 96 | |||
45.14 | odd | 6 | 630.2.bq.a.319.6 | yes | 96 | ||
63.23 | odd | 6 | 630.2.ba.a.499.15 | ✓ | 96 | ||
63.58 | even | 3 | inner | 1890.2.ba.a.1549.46 | 96 | ||
105.44 | odd | 6 | 630.2.bq.a.79.43 | yes | 96 | ||
315.149 | odd | 6 | 630.2.ba.a.499.34 | yes | 96 | ||
315.184 | even | 6 | inner | 1890.2.ba.a.1549.7 | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.ba.a.499.15 | ✓ | 96 | 63.23 | odd | 6 | ||
630.2.ba.a.499.34 | yes | 96 | 315.149 | odd | 6 | ||
630.2.ba.a.529.10 | yes | 96 | 3.2 | odd | 2 | ||
630.2.ba.a.529.39 | yes | 96 | 15.14 | odd | 2 | ||
630.2.bq.a.79.6 | yes | 96 | 21.2 | odd | 6 | ||
630.2.bq.a.79.43 | yes | 96 | 105.44 | odd | 6 | ||
630.2.bq.a.319.6 | yes | 96 | 45.14 | odd | 6 | ||
630.2.bq.a.319.43 | yes | 96 | 9.5 | odd | 6 | ||
1890.2.ba.a.1369.7 | 96 | 1.1 | even | 1 | trivial | ||
1890.2.ba.a.1369.46 | 96 | 5.4 | even | 2 | inner | ||
1890.2.ba.a.1549.7 | 96 | 315.184 | even | 6 | inner | ||
1890.2.ba.a.1549.46 | 96 | 63.58 | even | 3 | inner | ||
1890.2.bq.a.289.18 | 96 | 35.9 | even | 6 | |||
1890.2.bq.a.289.47 | 96 | 7.2 | even | 3 | |||
1890.2.bq.a.739.18 | 96 | 9.4 | even | 3 | |||
1890.2.bq.a.739.47 | 96 | 45.4 | even | 6 |