Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [369,2,Mod(46,369)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(369, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([0, 11]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("369.46");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 369 = 3^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 369.u (of order \(20\), degree \(8\), 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: | \(2.94647983459\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{20})\) |
Twist minimal: | no (minimal twist has level 41) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 244.1 | ||
Character | \(\chi\) | \(=\) | 369.244 |
Dual form | 369.2.u.a.307.1 |
$q$-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 \(\left(\mathbb{Z}/369\mathbb{Z}\right)^\times\).
\(n\) | \(83\) | \(334\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{20}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.14785 | + | 0.372958i | −0.811651 | + | 0.263721i | −0.685297 | − | 0.728264i | \(-0.740327\pi\) |
−0.126354 | + | 0.991985i | \(0.540327\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.439578 | + | 0.319372i | −0.219789 | + | 0.159686i | ||||
\(5\) | −1.49595 | − | 2.05900i | −0.669008 | − | 0.920811i | 0.330729 | − | 0.943726i | \(-0.392705\pi\) |
−0.999737 | + | 0.0229146i | \(0.992705\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.01547 | + | 0.517405i | −0.383810 | + | 0.195561i | −0.635240 | − | 0.772314i | \(-0.719099\pi\) |
0.251431 | + | 0.967875i | \(0.419099\pi\) | |||||||
\(8\) | 1.80427 | − | 2.48337i | 0.637907 | − | 0.878004i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.48504 | + | 1.80549i | 0.785839 | + | 0.570945i | ||||
\(11\) | 0.807883 | + | 5.10077i | 0.243586 | + | 1.53794i | 0.741642 | + | 0.670795i | \(0.234047\pi\) |
−0.498057 | + | 0.867144i | \(0.665953\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.17315 | − | 2.30243i | 0.325373 | − | 0.638580i | −0.669147 | − | 0.743130i | \(-0.733340\pi\) |
0.994520 | + | 0.104550i | \(0.0333403\pi\) | |||||||
\(14\) | 0.972629 | − | 0.972629i | 0.259946 | − | 0.259946i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.809030 | + | 2.48994i | −0.202257 | + | 0.622484i | ||||
\(17\) | 3.05576 | − | 0.483986i | 0.741132 | − | 0.117384i | 0.225559 | − | 0.974230i | \(-0.427579\pi\) |
0.515573 | + | 0.856846i | \(0.327579\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.74044 | + | 7.34102i | 0.858115 | + | 1.68415i | 0.720273 | + | 0.693691i | \(0.244017\pi\) |
0.137842 | + | 0.990454i | \(0.455983\pi\) | |||||||
\(20\) | 1.31517 | + | 0.427326i | 0.294082 | + | 0.0955529i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.82970 | − | 5.55360i | −0.603294 | − | 1.18403i | ||||
\(23\) | 1.17869 | + | 3.62763i | 0.245773 | + | 0.756413i | 0.995508 | + | 0.0946746i | \(0.0301811\pi\) |
−0.749735 | + | 0.661738i | \(0.769819\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.456519 | + | 1.40502i | −0.0913038 | + | 0.281004i | ||||
\(26\) | −0.487884 | + | 3.08038i | −0.0956819 | + | 0.604112i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.281132 | − | 0.551752i | 0.0531289 | − | 0.104271i | ||||
\(29\) | −5.72573 | − | 0.906866i | −1.06324 | − | 0.168401i | −0.399780 | − | 0.916611i | \(-0.630913\pi\) |
−0.663461 | + | 0.748211i | \(0.730913\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.65641 | + | 2.65654i | 0.656711 | + | 0.477129i | 0.865551 | − | 0.500821i | \(-0.166969\pi\) |
−0.208840 | + | 0.977950i | \(0.566969\pi\) | |||||||
\(32\) | 2.97943i | 0.526693i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.32705 | + | 1.69521i | −0.570584 | + | 0.290727i | ||||
\(35\) | 2.58442 | + | 1.31683i | 0.436847 | + | 0.222584i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.584132 | − | 0.424397i | 0.0960308 | − | 0.0697704i | −0.538734 | − | 0.842476i | \(-0.681097\pi\) |
0.634765 | + | 0.772706i | \(0.281097\pi\) | |||||||
\(38\) | −7.03134 | − | 7.03134i | −1.14063 | − | 1.14063i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.81235 | −1.23524 | ||||||||
\(41\) | 5.78336 | + | 2.74822i | 0.903210 | + | 0.429200i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.75698 | − | 0.570876i | 0.267936 | − | 0.0870578i | −0.171968 | − | 0.985103i | \(-0.555012\pi\) |
0.439904 | + | 0.898045i | \(0.355012\pi\) | |||||||
\(44\) | −1.98417 | − | 1.98417i | −0.299125 | − | 0.299125i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.70591 | − | 3.72436i | −0.398964 | − | 0.549127i | ||||
\(47\) | 3.15704 | + | 1.60859i | 0.460502 | + | 0.234638i | 0.668821 | − | 0.743423i | \(-0.266799\pi\) |
−0.208319 | + | 0.978061i | \(0.566799\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.35104 | + | 4.61230i | −0.478719 | + | 0.658901i | ||||
\(50\) | − | 1.78301i | − | 0.252156i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.219643 | + | 1.38677i | 0.0304590 | + | 0.192310i | ||||
\(53\) | 5.52741 | + | 0.875456i | 0.759249 | + | 0.120253i | 0.524042 | − | 0.851692i | \(-0.324423\pi\) |
0.235206 | + | 0.971945i | \(0.424423\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.29392 | − | 9.29392i | 1.25319 | − | 1.25319i | ||||
\(56\) | −0.547268 | + | 3.45532i | −0.0731318 | + | 0.461736i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.91048 | − | 1.09451i | 0.907391 | − | 0.143717i | ||||
\(59\) | −0.242763 | − | 0.747149i | −0.0316051 | − | 0.0972705i | 0.934010 | − | 0.357248i | \(-0.116285\pi\) |
−0.965615 | + | 0.259977i | \(0.916285\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.70623 | + | 2.17898i | 0.858644 | + | 0.278990i | 0.705062 | − | 0.709145i | \(-0.250919\pi\) |
0.153582 | + | 0.988136i | \(0.450919\pi\) | |||||||
\(62\) | −5.18778 | − | 1.68561i | −0.658849 | − | 0.214073i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.72926 | − | 8.39980i | −0.341158 | − | 1.04997i | ||||
\(65\) | −6.49567 | + | 1.02881i | −0.805689 | + | 0.127609i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.835907 | + | 5.27771i | −0.102122 | + | 0.644774i | 0.882531 | + | 0.470254i | \(0.155838\pi\) |
−0.984654 | + | 0.174521i | \(0.944162\pi\) | |||||||
\(68\) | −1.18868 | + | 1.18868i | −0.144148 | + | 0.144148i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.45764 | − | 0.547637i | −0.413267 | − | 0.0654551i | ||||
\(71\) | −0.708805 | − | 4.47522i | −0.0841197 | − | 0.531111i | −0.993379 | − | 0.114881i | \(-0.963351\pi\) |
0.909260 | − | 0.416230i | \(-0.136649\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.149836i | 0.0175369i | 0.999962 | + | 0.00876846i | \(0.00279112\pi\) | ||||
−0.999962 | + | 0.00876846i | \(0.997209\pi\) | |||||||
\(74\) | −0.512213 | + | 0.705000i | −0.0595435 | + | 0.0819546i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.98873 | − | 2.03236i | −0.457539 | − | 0.233128i | ||||
\(77\) | −3.45954 | − | 4.76165i | −0.394251 | − | 0.542641i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.4389 | − | 11.4389i | −1.28698 | − | 1.28698i | −0.936613 | − | 0.350367i | \(-0.886057\pi\) |
−0.350367 | − | 0.936613i | \(-0.613943\pi\) | |||||||
\(80\) | 6.33704 | − | 2.05903i | 0.708502 | − | 0.230206i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.66339 | − | 0.997584i | −0.846280 | − | 0.110165i | ||||
\(83\) | −4.27258 | −0.468977 | −0.234488 | − | 0.972119i | \(-0.575341\pi\) | ||||
−0.234488 | + | 0.972119i | \(0.575341\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.56779 | − | 5.56779i | −0.603912 | − | 0.603912i | ||||
\(86\) | −1.80383 | + | 1.31056i | −0.194512 | + | 0.141321i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 14.1247 | + | 7.19691i | 1.50570 | + | 0.767193i | ||||
\(89\) | 1.51781 | − | 0.773362i | 0.160887 | − | 0.0819762i | −0.371693 | − | 0.928356i | \(-0.621223\pi\) |
0.532580 | + | 0.846380i | \(0.321223\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.94503i | 0.308723i | ||||||||
\(92\) | −1.67669 | − | 1.21819i | −0.174807 | − | 0.127005i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.22374 | − | 0.668975i | −0.435646 | − | 0.0689995i | ||||
\(95\) | 9.51963 | − | 18.6833i | 0.976694 | − | 1.91687i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.687542 | − | 4.34097i | 0.0698093 | − | 0.440758i | −0.927884 | − | 0.372870i | \(-0.878374\pi\) |
0.997693 | − | 0.0678885i | \(-0.0216262\pi\) | |||||||
\(98\) | 2.12628 | − | 6.54402i | 0.214787 | − | 0.661046i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.248049 | − | 0.763417i | −0.0248049 | − | 0.0763417i | ||||
\(101\) | −1.40554 | − | 2.75854i | −0.139857 | − | 0.274485i | 0.810445 | − | 0.585815i | \(-0.199225\pi\) |
−0.950302 | + | 0.311330i | \(0.899225\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.80356 | + | 0.910931i | 0.276243 | + | 0.0897567i | 0.443862 | − | 0.896095i | \(-0.353608\pi\) |
−0.167619 | + | 0.985852i | \(0.553608\pi\) | |||||||
\(104\) | −3.60111 | − | 7.06758i | −0.353118 | − | 0.693033i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.67114 | + | 1.05660i | −0.647958 | + | 0.102626i | ||||
\(107\) | 1.04654 | − | 3.22093i | 0.101173 | − | 0.311379i | −0.887640 | − | 0.460538i | \(-0.847656\pi\) |
0.988813 | + | 0.149159i | \(0.0476565\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.65686 | − | 9.65686i | 0.924960 | − | 0.924960i | −0.0724148 | − | 0.997375i | \(-0.523071\pi\) |
0.997375 | + | 0.0724148i | \(0.0230705\pi\) | |||||||
\(110\) | −7.20175 | + | 14.1342i | −0.686660 | + | 1.34765i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.466765 | − | 2.94704i | −0.0441052 | − | 0.278469i | ||||
\(113\) | 10.7162 | + | 7.78581i | 1.00810 | + | 0.732427i | 0.963810 | − | 0.266592i | \(-0.0858975\pi\) |
0.0442897 | + | 0.999019i | \(0.485898\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.70602 | − | 7.85366i | 0.532089 | − | 0.732358i | ||||
\(116\) | 2.80653 | − | 1.43000i | 0.260580 | − | 0.132772i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.557310 | + | 0.767072i | 0.0513046 | + | 0.0706147i | ||||
\(119\) | −2.85261 | + | 2.07254i | −0.261498 | + | 0.189989i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.9036 | + | 4.84246i | −1.35487 | + | 0.440223i | ||||
\(122\) | −8.51039 | −0.770495 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.45570 | −0.220529 | ||||||||
\(125\) | −8.52661 | + | 2.77046i | −0.762643 | + | 0.247798i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.9310 | + | 7.94181i | −0.969966 | + | 0.704721i | −0.955444 | − | 0.295173i | \(-0.904623\pi\) |
−0.0145221 | + | 0.999895i | \(0.504623\pi\) | |||||||
\(128\) | 2.76302 | + | 3.80298i | 0.244219 | + | 0.336139i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.07233 | − | 3.60353i | 0.620285 | − | 0.316051i | ||||
\(131\) | −6.01522 | + | 8.27923i | −0.525552 | + | 0.723360i | −0.986444 | − | 0.164096i | \(-0.947529\pi\) |
0.460893 | + | 0.887456i | \(0.347529\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.59657 | − | 5.51923i | −0.658706 | − | 0.478578i | ||||
\(134\) | −1.00887 | − | 6.36976i | −0.0871532 | − | 0.550263i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.31152 | − | 8.46184i | 0.369710 | − | 0.725596i | ||||
\(137\) | −4.05839 | + | 4.05839i | −0.346731 | + | 0.346731i | −0.858891 | − | 0.512159i | \(-0.828846\pi\) |
0.512159 | + | 0.858891i | \(0.328846\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.98324 | + | 15.3368i | −0.422673 | + | 1.30085i | 0.482532 | + | 0.875878i | \(0.339717\pi\) |
−0.905205 | + | 0.424975i | \(0.860283\pi\) | |||||||
\(140\) | −1.55661 | + | 0.246543i | −0.131558 | + | 0.0208367i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.48267 | + | 4.87251i | 0.208341 | + | 0.408892i | ||||
\(143\) | 12.6919 | + | 4.12386i | 1.06135 | + | 0.344855i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.69816 | + | 13.1459i | 0.556252 | + | 1.09171i | ||||
\(146\) | −0.0558824 | − | 0.171988i | −0.00462486 | − | 0.0142339i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.121231 | + | 0.373111i | −0.00996515 | + | 0.0306696i | ||||
\(149\) | −0.849406 | + | 5.36294i | −0.0695860 | + | 0.439349i | 0.928156 | + | 0.372191i | \(0.121393\pi\) |
−0.997742 | + | 0.0671583i | \(0.978607\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.53796 | − | 3.01842i | 0.125158 | − | 0.245636i | −0.819922 | − | 0.572475i | \(-0.805983\pi\) |
0.945080 | + | 0.326839i | \(0.105983\pi\) | |||||||
\(152\) | 24.9792 | + | 3.95632i | 2.02608 | + | 0.320900i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.74692 | + | 4.17538i | 0.463100 | + | 0.336462i | ||||
\(155\) | − | 11.5026i | − | 0.923910i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.01316 | + | 4.59244i | −0.719329 | + | 0.366516i | −0.775024 | − | 0.631931i | \(-0.782262\pi\) |
0.0556954 | + | 0.998448i | \(0.482262\pi\) | |||||||
\(158\) | 17.3964 | + | 8.86390i | 1.38398 | + | 0.705174i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.13463 | − | 4.45707i | 0.484985 | − | 0.352362i | ||||
\(161\) | −3.07387 | − | 3.07387i | −0.242255 | − | 0.242255i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.7430 | 1.46807 | 0.734033 | − | 0.679113i | \(-0.237635\pi\) | ||||
0.734033 | + | 0.679113i | \(0.237635\pi\) | |||||||
\(164\) | −3.41995 | + | 0.638988i | −0.267053 | + | 0.0498966i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.90427 | − | 1.59349i | 0.380645 | − | 0.123679i | ||||
\(167\) | −2.16228 | − | 2.16228i | −0.167322 | − | 0.167322i | 0.618479 | − | 0.785801i | \(-0.287749\pi\) |
−0.785801 | + | 0.618479i | \(0.787749\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.71629 | + | 5.11503i | 0.285868 | + | 0.393464i | ||||
\(170\) | 8.46753 | + | 4.31442i | 0.649430 | + | 0.330901i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.590006 | + | 0.812074i | −0.0449876 | + | 0.0619201i | ||||
\(173\) | 10.5897i | 0.805117i | 0.915394 | + | 0.402558i | \(0.131879\pi\) | ||||
−0.915394 | + | 0.402558i | \(0.868121\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.263386 | − | 1.66296i | −0.0199101 | − | 0.125708i | ||||
\(176\) | −13.3542 | − | 2.11510i | −1.00661 | − | 0.159431i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.45378 | + | 1.45378i | −0.108965 | + | 0.108965i | ||||
\(179\) | 0.298749 | − | 1.88623i | 0.0223295 | − | 0.140983i | −0.974005 | − | 0.226527i | \(-0.927263\pi\) |
0.996334 | + | 0.0855440i | \(0.0272628\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.82173 | + | 0.922071i | −0.432726 | + | 0.0685370i | −0.368998 | − | 0.929430i | \(-0.620299\pi\) |
−0.0637279 | + | 0.997967i | \(0.520299\pi\) | |||||||
\(182\) | −1.09837 | − | 3.38045i | −0.0814169 | − | 0.250576i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 11.1354 | + | 3.61812i | 0.820914 | + | 0.266731i | ||||
\(185\) | −1.74766 | − | 0.567850i | −0.128491 | − | 0.0417492i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.93740 | + | 15.1957i | 0.361058 | + | 1.11122i | ||||
\(188\) | −1.90151 | + | 0.301169i | −0.138682 | + | 0.0219650i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.95898 | + | 24.9960i | −0.287215 | + | 1.81340i | ||||
\(191\) | 2.23597 | − | 2.23597i | 0.161789 | − | 0.161789i | −0.621570 | − | 0.783359i | \(-0.713505\pi\) |
0.783359 | + | 0.621570i | \(0.213505\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.5972 | + | 2.47036i | 1.12271 | + | 0.177820i | 0.690068 | − | 0.723744i | \(-0.257580\pi\) |
0.432645 | + | 0.901565i | \(0.357580\pi\) | |||||||
\(194\) | 0.829806 | + | 5.23919i | 0.0595766 | + | 0.376152i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | − | 3.09770i | − | 0.221264i | ||||||
\(197\) | −2.67161 | + | 3.67715i | −0.190344 | + | 0.261986i | −0.893514 | − | 0.449036i | \(-0.851767\pi\) |
0.703170 | + | 0.711022i | \(0.251767\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00456 | + | 4.07852i | 0.567428 | + | 0.289119i | 0.714074 | − | 0.700070i | \(-0.246848\pi\) |
−0.146646 | + | 0.989189i | \(0.546848\pi\) | |||||||
\(200\) | 2.66550 | + | 3.66875i | 0.188479 | + | 0.259420i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.64217 | + | 2.64217i | 0.185902 | + | 0.185902i | ||||
\(203\) | 6.28350 | − | 2.04163i | 0.441015 | − | 0.143294i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.99304 | − | 16.0191i | −0.209043 | − | 1.11882i | ||||
\(206\) | −3.55779 | −0.247883 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.78380 | + | 4.78380i | 0.331697 | + | 0.331697i | ||||
\(209\) | −34.4230 | + | 25.0098i | −2.38109 | + | 1.72996i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.75578 | + | 2.93272i | 0.396245 | + | 0.201897i | 0.640747 | − | 0.767752i | \(-0.278625\pi\) |
−0.244503 | + | 0.969649i | \(0.578625\pi\) | |||||||
\(212\) | −2.70933 | + | 1.38047i | −0.186077 | + | 0.0948112i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.08746i | 0.279413i | ||||||||
\(215\) | −3.80378 | − | 2.76361i | −0.259415 | − | 0.188476i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.08747 | − | 0.805776i | −0.345360 | − | 0.0546996i | ||||
\(218\) | −7.48300 | + | 14.6862i | −0.506813 | + | 0.994676i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.11718 | + | 7.05362i | −0.0753205 | + | 0.475555i | ||||
\(221\) | 2.47052 | − | 7.60348i | 0.166185 | − | 0.511465i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.26478 | − | 3.89258i | −0.0846956 | − | 0.260666i | 0.899736 | − | 0.436435i | \(-0.143759\pi\) |
−0.984432 | + | 0.175768i | \(0.943759\pi\) | |||||||
\(224\) | −1.54157 | − | 3.02550i | −0.103001 | − | 0.202150i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.2044 | − | 4.94021i | −1.01138 | − | 0.328618i | ||||
\(227\) | 0.260675 | + | 0.511604i | 0.0173016 | + | 0.0339564i | 0.899496 | − | 0.436930i | \(-0.143934\pi\) |
−0.882194 | + | 0.470886i | \(0.843934\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.7418 | + | 3.76033i | −1.56890 | + | 0.248490i | −0.879504 | − | 0.475892i | \(-0.842125\pi\) |
−0.689399 | + | 0.724382i | \(0.742125\pi\) | |||||||
\(230\) | −3.62055 | + | 11.1429i | −0.238732 | + | 0.734742i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.5829 | + | 12.5829i | −0.826105 | + | 0.826105i | ||||
\(233\) | 5.63580 | − | 11.0609i | 0.369213 | − | 0.724622i | −0.629410 | − | 0.777073i | \(-0.716703\pi\) |
0.998623 | + | 0.0524514i | \(0.0167035\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.41069 | − | 8.90672i | −0.0920230 | − | 0.581010i | ||||
\(236\) | 0.345332 | + | 0.250898i | 0.0224792 | + | 0.0163321i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.50139 | − | 3.44286i | 0.162141 | − | 0.223168i | ||||
\(239\) | 6.04489 | − | 3.08002i | 0.391011 | − | 0.199230i | −0.247421 | − | 0.968908i | \(-0.579583\pi\) |
0.638433 | + | 0.769678i | \(0.279583\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.2730 | − | 15.5159i | −0.726155 | − | 0.999467i | −0.999297 | − | 0.0374932i | \(-0.988063\pi\) |
0.273142 | − | 0.961974i | \(-0.411937\pi\) | |||||||
\(242\) | 15.3010 | − | 11.1168i | 0.983584 | − | 0.714615i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.64382 | + | 1.18395i | −0.233272 | + | 0.0757945i | ||||
\(245\) | 14.5097 | 0.926990 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.2903 | 1.35467 | ||||||||
\(248\) | 13.1943 | − | 4.28710i | 0.837841 | − | 0.272231i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.75398 | − | 6.36014i | 0.553650 | − | 0.402251i | ||||
\(251\) | −1.10805 | − | 1.52510i | −0.0699397 | − | 0.0962637i | 0.772614 | − | 0.634876i | \(-0.218949\pi\) |
−0.842554 | + | 0.538612i | \(0.818949\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.5515 | + | 8.94292i | −1.10345 | + | 0.562236i | ||||
\(254\) | 9.58511 | − | 13.1928i | 0.601423 | − | 0.827788i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.70071 | + | 7.04798i | 0.606294 | + | 0.440499i | ||||
\(257\) | −4.37877 | − | 27.6464i | −0.273140 | − | 1.72454i | −0.618256 | − | 0.785977i | \(-0.712160\pi\) |
0.345116 | − | 0.938560i | \(-0.387840\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.373581 | + | 0.733194i | −0.0232132 | + | 0.0455584i | ||||
\(260\) | 2.52678 | − | 2.52678i | 0.156704 | − | 0.156704i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.81674 | − | 11.7467i | 0.235799 | − | 0.725715i | ||||
\(263\) | −4.08854 | + | 0.647561i | −0.252110 | + | 0.0399303i | −0.281210 | − | 0.959646i | \(-0.590736\pi\) |
0.0291002 | + | 0.999576i | \(0.490736\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.46616 | − | 12.6906i | −0.397213 | − | 0.779575i | ||||
\(266\) | 10.7781 | + | 3.50203i | 0.660850 | + | 0.214723i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.31811 | − | 2.58693i | −0.0805162 | − | 0.158022i | ||||
\(269\) | 9.19596 | + | 28.3022i | 0.560687 | + | 1.72562i | 0.680430 | + | 0.732813i | \(0.261793\pi\) |
−0.119742 | + | 0.992805i | \(0.538207\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.16633 | − | 22.0557i | 0.435324 | − | 1.33979i | −0.457431 | − | 0.889245i | \(-0.651230\pi\) |
0.892754 | − | 0.450544i | \(-0.148770\pi\) | |||||||
\(272\) | −1.26711 | + | 8.00022i | −0.0768299 | + | 0.485085i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.14480 | − | 6.17202i | 0.189984 | − | 0.372865i | ||||
\(275\) | −7.53551 | − | 1.19351i | −0.454408 | − | 0.0719712i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.0368 | + | 14.5576i | 1.20389 | + | 0.874680i | 0.994662 | − | 0.103187i | \(-0.0329039\pi\) |
0.209231 | + | 0.977866i | \(0.432904\pi\) | |||||||
\(278\) | − | 19.4629i | − | 1.16731i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.93317 | − | 4.04215i | 0.474098 | − | 0.241565i | ||||
\(281\) | 0.189482 | + | 0.0965459i | 0.0113035 | + | 0.00575945i | 0.459633 | − | 0.888109i | \(-0.347981\pi\) |
−0.448330 | + | 0.893868i | \(0.647981\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.92649 | − | 6.48547i | 0.530625 | − | 0.385521i | −0.289967 | − | 0.957037i | \(-0.593644\pi\) |
0.820591 | + | 0.571515i | \(0.193644\pi\) | |||||||
\(284\) | 1.74084 | + | 1.74084i | 0.103300 | + | 0.103300i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −16.1064 | −0.952394 | ||||||||
\(287\) | −7.29475 | + | 0.201622i | −0.430595 | + | 0.0119014i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.06450 | + | 2.29540i | −0.415559 | + | 0.135023i | ||||
\(290\) | −12.5913 | − | 12.5913i | −0.739388 | − | 0.739388i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.0478533 | − | 0.0658645i | −0.00280040 | − | 0.00385443i | ||||
\(293\) | −6.77986 | − | 3.45451i | −0.396083 | − | 0.201815i | 0.244593 | − | 0.969626i | \(-0.421346\pi\) |
−0.640676 | + | 0.767811i | \(0.721346\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.17521 | + | 1.61754i | −0.0684237 | + | 0.0941771i | ||||
\(296\) | − | 2.21635i | − | 0.128822i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.02516 | − | 6.47263i | −0.0593861 | − | 0.374949i | ||||
\(299\) | 9.73515 | + | 1.54190i | 0.562998 | + | 0.0891702i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.48877 | + | 1.48877i | −0.0858115 | + | 0.0858115i | ||||
\(302\) | −0.639602 | + | 4.03829i | −0.0368049 | + | 0.232377i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −21.3048 | + | 3.37435i | −1.22191 | + | 0.193532i | ||||
\(305\) | −5.54565 | − | 17.0677i | −0.317543 | − | 0.977296i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.8761 | − | 9.70732i | −1.70512 | − | 0.554026i | −0.715608 | − | 0.698502i | \(-0.753850\pi\) |
−0.989508 | + | 0.144476i | \(0.953850\pi\) | |||||||
\(308\) | 3.04148 | + | 0.988237i | 0.173304 | + | 0.0563100i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.28998 | + | 13.2032i | 0.243655 | + | 0.749892i | ||||
\(311\) | −14.5714 | + | 2.30789i | −0.826270 | + | 0.130868i | −0.555227 | − | 0.831699i | \(-0.687369\pi\) |
−0.271043 | + | 0.962567i | \(0.587369\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.59799 | + | 16.4031i | −0.146847 | + | 0.927155i | 0.798714 | + | 0.601711i | \(0.205514\pi\) |
−0.945561 | + | 0.325445i | \(0.894486\pi\) | |||||||
\(314\) | 8.63295 | − | 8.63295i | 0.487186 | − | 0.487186i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.68158 | + | 1.37503i | 0.488377 | + | 0.0773513i | ||||
\(317\) | −5.09527 | − | 32.1703i | −0.286179 | − | 1.80686i | −0.542264 | − | 0.840208i | \(-0.682433\pi\) |
0.256085 | − | 0.966654i | \(-0.417567\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 29.9383i | − | 1.67622i | ||||||
\(320\) | −13.2123 | + | 18.1852i | −0.738591 | + | 1.01658i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.67476 | + | 2.38191i | 0.260514 | + | 0.132739i | ||||
\(323\) | 14.9828 | + | 20.6221i | 0.833667 | + | 1.14744i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.69940 | + | 2.69940i | 0.149736 | + | 0.149736i | ||||
\(326\) | −21.5141 | + | 6.99036i | −1.19156 | + | 0.387160i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 17.2596 | − | 9.40369i | 0.953003 | − | 0.519232i | ||||
\(329\) | −4.03816 | −0.222631 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.33145 | − | 1.33145i | −0.0731829 | − | 0.0731829i | 0.669568 | − | 0.742751i | \(-0.266479\pi\) |
−0.742751 | + | 0.669568i | \(0.766479\pi\) | |||||||
\(332\) | 1.87813 | − | 1.36454i | 0.103076 | − | 0.0748891i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.28840 | + | 1.67553i | 0.179934 | + | 0.0916807i | ||||
\(335\) | 12.1173 | − | 6.17405i | 0.662036 | − | 0.337324i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 29.3757i | − | 1.60020i | −0.599870 | − | 0.800098i | \(-0.704781\pi\) | ||
0.599870 | − | 0.800098i | \(-0.295219\pi\) | |||||||
\(338\) | −6.17342 | − | 4.48526i | −0.335790 | − | 0.243966i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.22568 | + | 0.669282i | 0.229170 | + | 0.0362969i | ||||
\(341\) | −10.5964 | + | 20.7967i | −0.573830 | + | 1.12620i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.26443 | − | 14.2970i | 0.122268 | − | 0.771968i | ||||
\(344\) | 1.75237 | − | 5.39324i | 0.0944814 | − | 0.290784i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.94950 | − | 12.1553i | −0.212326 | − | 0.653473i | ||||
\(347\) | 12.7217 | + | 24.9677i | 0.682936 | + | 1.34034i | 0.928636 | + | 0.370992i | \(0.120982\pi\) |
−0.245700 | + | 0.969346i | \(0.579018\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.4391 | + | 6.31615i | 1.04055 | + | 0.338096i | 0.778954 | − | 0.627081i | \(-0.215751\pi\) |
0.261598 | + | 0.965177i | \(0.415751\pi\) | |||||||
\(350\) | 0.922541 | + | 1.81059i | 0.0493119 | + | 0.0967800i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −15.1974 | + | 2.40703i | −0.810022 | + | 0.128295i | ||||
\(353\) | 8.94631 | − | 27.5339i | 0.476164 | − | 1.46548i | −0.368217 | − | 0.929740i | \(-0.620032\pi\) |
0.844381 | − | 0.535743i | \(-0.179968\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.15412 | + | 8.15412i | −0.432776 | + | 0.432776i | ||||
\(356\) | −0.420205 | + | 0.824699i | −0.0222708 | + | 0.0437090i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.360565 | + | 2.27652i | 0.0190565 | + | 0.120318i | ||||
\(359\) | −17.5745 | − | 12.7687i | −0.927549 | − | 0.673904i | 0.0178425 | − | 0.999841i | \(-0.494320\pi\) |
−0.945391 | + | 0.325937i | \(0.894320\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −28.7318 | + | 39.5459i | −1.51220 | + | 2.08136i | ||||
\(362\) | 6.33856 | − | 3.22966i | 0.333147 | − | 0.169747i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.940562 | − | 1.29457i | −0.0492989 | − | 0.0678541i | ||||
\(365\) | 0.308511 | − | 0.224146i | 0.0161482 | − | 0.0117324i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.4047 | − | 5.33020i | 0.856316 | − | 0.278234i | 0.152227 | − | 0.988346i | \(-0.451355\pi\) |
0.704089 | + | 0.710112i | \(0.251355\pi\) | |||||||
\(368\) | −9.98616 | −0.520565 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.21784 | 0.115300 | ||||||||
\(371\) | −6.06586 | + | 1.97092i | −0.314924 | + | 0.102325i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.7898 | + | 10.0189i | −0.714007 | + | 0.518756i | −0.884464 | − | 0.466609i | \(-0.845476\pi\) |
0.170457 | + | 0.985365i | \(0.445476\pi\) | |||||||
\(374\) | −11.3348 | − | 15.6010i | −0.586106 | − | 0.806706i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.69091 | − | 4.93776i | 0.499770 | − | 0.254646i | ||||
\(377\) | −8.80513 | + | 12.1192i | −0.453487 | + | 0.624171i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.9726 | − | 21.7764i | −1.53959 | − | 1.11858i | −0.950593 | − | 0.310439i | \(-0.899524\pi\) |
−0.588995 | − | 0.808137i | \(-0.700476\pi\) | |||||||
\(380\) | 1.78231 | + | 11.2531i | 0.0914308 | + | 0.577271i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.73263 | + | 3.40048i | −0.0886491 | + | 0.173984i | ||||
\(383\) | 23.8870 | − | 23.8870i | 1.22057 | − | 1.22057i | 0.253137 | − | 0.967430i | \(-0.418538\pi\) |
0.967430 | − | 0.253137i | \(-0.0814624\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.62893 | + | 14.2464i | −0.235912 | + | 0.726062i | ||||
\(386\) | −18.8246 | + | 2.98152i | −0.958146 | + | 0.151755i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.08416 | + | 2.12778i | 0.0550397 | + | 0.108021i | ||||
\(389\) | 8.46056 | + | 2.74900i | 0.428967 | + | 0.139380i | 0.515540 | − | 0.856866i | \(-0.327591\pi\) |
−0.0865726 | + | 0.996246i | \(0.527591\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.35751 | + | 10.5147i | 0.270941 | + | 0.531752i | ||||
\(392\) | 5.40787 | + | 16.6437i | 0.273139 | + | 0.840635i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.69517 | − | 5.21721i | 0.0854016 | − | 0.262839i | ||||
\(395\) | −6.44066 | + | 40.6647i | −0.324065 | + | 2.04606i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.80671 | − | 7.47109i | 0.191053 | − | 0.374963i | −0.775532 | − | 0.631308i | \(-0.782518\pi\) |
0.966585 | + | 0.256345i | \(0.0825183\pi\) | |||||||
\(398\) | −10.7091 | − | 1.69616i | −0.536800 | − | 0.0850208i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.12908 | − | 2.27341i | −0.156454 | − | 0.113670i | ||||
\(401\) | − | 24.8940i | − | 1.24315i | −0.783356 | − | 0.621573i | \(-0.786494\pi\) | ||
0.783356 | − | 0.621573i | \(-0.213506\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.4060 | − | 5.30213i | 0.518361 | − | 0.264118i | ||||
\(404\) | 1.49885 | + | 0.763701i | 0.0745705 | + | 0.0379955i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.45105 | + | 4.68696i | −0.320160 | + | 0.232610i | ||||
\(407\) | 2.63666 | + | 2.63666i | 0.130694 | + | 0.130694i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.75194 | −0.432756 | −0.216378 | − | 0.976310i | \(-0.569424\pi\) | ||||
−0.216378 | + | 0.976310i | \(0.569424\pi\) | |||||||
\(410\) | 9.41001 | + | 17.2712i | 0.464727 | + | 0.852965i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.52331 | + | 0.494953i | −0.0750480 | + | 0.0243846i | ||||
\(413\) | 0.633096 | + | 0.633096i | 0.0311526 | + | 0.0311526i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.39156 | + | 8.79722i | 0.313749 | + | 0.431839i | ||||
\(416\) | 6.85993 | + | 3.49531i | 0.336336 | + | 0.171372i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 30.1848 | − | 41.5458i | 1.47638 | − | 2.03207i | ||||
\(419\) | − | 24.9286i | − | 1.21784i | −0.793232 | − | 0.608920i | \(-0.791603\pi\) | ||
0.793232 | − | 0.608920i | \(-0.208397\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.70359 | − | 10.7560i | −0.0830279 | − | 0.524217i | −0.993789 | − | 0.111283i | \(-0.964504\pi\) |
0.910761 | − | 0.412934i | \(-0.135496\pi\) | |||||||
\(422\) | −7.70054 | − | 1.21965i | −0.374857 | − | 0.0593714i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.1470 | − | 12.1470i | 0.589913 | − | 0.589913i | ||||
\(425\) | −0.715005 | + | 4.51436i | −0.0346828 | + | 0.218979i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.93736 | + | 1.25715i | −0.384116 | + | 0.0608380i | ||||
\(428\) | 0.568639 | + | 1.75009i | 0.0274862 | + | 0.0845938i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.39686 | + | 1.75355i | 0.260260 | + | 0.0845636i | ||||
\(431\) | 18.5078 | + | 6.01355i | 0.891490 | + | 0.289663i | 0.718720 | − | 0.695300i | \(-0.244728\pi\) |
0.172770 | + | 0.984962i | \(0.444728\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.43880 | − | 4.42816i | −0.0691441 | − | 0.212804i | 0.910514 | − | 0.413479i | \(-0.135686\pi\) |
−0.979658 | + | 0.200675i | \(0.935686\pi\) | |||||||
\(434\) | 6.14016 | − | 0.972505i | 0.294737 | − | 0.0466818i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.16081 | + | 7.32908i | −0.0555928 | + | 0.350999i | ||||
\(437\) | −22.2217 | + | 22.2217i | −1.06301 | + | 1.06301i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.3177 | + | 1.95093i | 0.587891 | + | 0.0931127i | 0.443291 | − | 0.896378i | \(-0.353811\pi\) |
0.144599 | + | 0.989490i | \(0.453811\pi\) | |||||||
\(440\) | −6.31146 | − | 39.8490i | −0.300887 | − | 1.89973i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.64904i | 0.458958i | ||||||||
\(443\) | −8.10317 | + | 11.1531i | −0.384993 | + | 0.529897i | −0.956899 | − | 0.290422i | \(-0.906204\pi\) |
0.571906 | + | 0.820319i | \(0.306204\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.86291 | − | 1.96825i | −0.183120 | − | 0.0933041i | ||||
\(446\) | 2.90354 | + | 3.99638i | 0.137487 | + | 0.189234i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.11757 | + | 7.11757i | 0.336274 | + | 0.336274i | ||||
\(449\) | 5.07254 | − | 1.64817i | 0.239388 | − | 0.0777819i | −0.186866 | − | 0.982385i | \(-0.559833\pi\) |
0.426254 | + | 0.904604i | \(0.359833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.34576 | + | 31.7198i | −0.440075 | + | 1.49363i | ||||
\(452\) | −7.19720 | −0.338528 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.490022 | − | 0.490022i | −0.0229979 | − | 0.0229979i | ||||
\(455\) | 6.06381 | − | 4.40562i | 0.284276 | − | 0.206539i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.05273 | − | 4.61259i | −0.423469 | − | 0.215768i | 0.229251 | − | 0.973367i | \(-0.426372\pi\) |
−0.652720 | + | 0.757599i | \(0.726372\pi\) | |||||||
\(458\) | 25.8495 | − | 13.1710i | 1.20787 | − | 0.615440i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.27464i | 0.245932i | ||||||||
\(461\) | 24.0238 | + | 17.4543i | 1.11890 | + | 0.812927i | 0.984042 | − | 0.177938i | \(-0.0569428\pi\) |
0.134856 | + | 0.990865i | \(0.456943\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.9429 | + | 6.00956i | 1.76336 | + | 0.279288i | 0.952185 | − | 0.305521i | \(-0.0988307\pi\) |
0.811171 | + | 0.584809i | \(0.198831\pi\) | |||||||
\(464\) | 6.89032 | − | 13.5230i | 0.319875 | − | 0.627790i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.34379 | + | 14.7981i | −0.108574 | + | 0.685509i | ||||
\(467\) | −0.851187 | + | 2.61968i | −0.0393882 | + | 0.121224i | −0.968817 | − | 0.247777i | \(-0.920300\pi\) |
0.929429 | + | 0.369001i | \(0.120300\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.88188 | − | 5.79183i | −0.0868971 | − | 0.267442i | ||||
\(470\) | 4.94108 | + | 9.69742i | 0.227915 | + | 0.447309i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.29346 | − | 0.745190i | −0.105565 | − | 0.0343001i | ||||
\(473\) | 4.33134 | + | 8.50073i | 0.199155 | + | 0.390864i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.0219 | + | 1.90408i | −0.551601 | + | 0.0873651i | ||||
\(476\) | 0.592032 | − | 1.82209i | 0.0271357 | − | 0.0835152i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.78989 | + | 5.78989i | −0.264823 | + | 0.264823i | ||||
\(479\) | −16.3580 | + | 32.1043i | −0.747415 | + | 1.46688i | 0.132213 | + | 0.991221i | \(0.457792\pi\) |
−0.879628 | + | 0.475663i | \(0.842208\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.291872 | − | 1.84281i | −0.0133082 | − | 0.0840247i | ||||
\(482\) | 18.7264 | + | 13.6055i | 0.852965 | + | 0.619715i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.00473 | − | 6.88842i | 0.227488 | − | 0.313110i | ||||
\(485\) | −9.96656 | + | 5.07822i | −0.452558 | + | 0.230590i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.99982 | − | 12.3872i | −0.407821 | − | 0.561317i | 0.554865 | − | 0.831941i | \(-0.312770\pi\) |
−0.962685 | + | 0.270624i | \(0.912770\pi\) | |||||||
\(488\) | 17.5111 | − | 12.7226i | 0.792690 | − | 0.575923i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −16.6549 | + | 5.41151i | −0.752392 | + | 0.244467i | ||||
\(491\) | −8.39830 | −0.379010 | −0.189505 | − | 0.981880i | \(-0.560688\pi\) | ||||
−0.189505 | + | 0.981880i | \(0.560688\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.9354 | −0.807769 | ||||||||
\(494\) | −24.4380 | + | 7.94039i | −1.09952 | + | 0.357255i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.57276 | + | 6.95502i | −0.429830 | + | 0.312290i | ||||
\(497\) | 3.03527 | + | 4.17769i | 0.136150 | + | 0.187395i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.86475 | − | 3.49776i | 0.307308 | − | 0.156581i | −0.293535 | − | 0.955948i | \(-0.594832\pi\) |
0.600843 | + | 0.799367i | \(0.294832\pi\) | |||||||
\(500\) | 2.86330 | − | 3.94100i | 0.128051 | − | 0.176247i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.84068 | + | 1.33733i | 0.0821534 | + | 0.0596879i | ||||
\(503\) | −2.90709 | − | 18.3546i | −0.129621 | − | 0.818392i | −0.963747 | − | 0.266818i | \(-0.914028\pi\) |
0.834126 | − | 0.551574i | \(-0.185972\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.57720 | + | 7.02064i | −0.159183 | + | 0.312414i | ||||
\(506\) | 16.8111 | − | 16.8111i | 0.747343 | − | 0.747343i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.26862 | − | 6.98209i | 0.100654 | − | 0.309780i | ||||
\(509\) | 17.4808 | − | 2.76869i | 0.774823 | − | 0.122720i | 0.243513 | − | 0.969898i | \(-0.421700\pi\) |
0.531310 | + | 0.847178i | \(0.321700\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0775257 | − | 0.152153i | −0.00342954 | − | 0.00673085i | ||||
\(512\) | −22.7049 | − | 7.37726i | −1.00342 | − | 0.326032i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.3371 | + | 30.1008i | 0.676491 | + | 1.32769i | ||||
\(515\) | −2.31837 | − | 7.13522i | −0.102160 | − | 0.314415i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.65455 | + | 17.4029i | −0.248687 | + | 0.765379i | ||||
\(518\) | 0.155363 | − | 0.980925i | 0.00682627 | − | 0.0430994i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.16504 | + | 17.9874i | −0.401914 | + | 0.788800i | ||||
\(521\) | 25.2617 | + | 4.00106i | 1.10673 | + | 0.175289i | 0.682944 | − | 0.730471i | \(-0.260699\pi\) |
0.423790 | + | 0.905760i | \(0.360699\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.3827 | + | 15.5354i | 0.934998 | + | 0.679316i | 0.947211 | − | 0.320609i | \(-0.103888\pi\) |
−0.0122132 | + | 0.999925i | \(0.503888\pi\) | |||||||
\(524\) | − | 5.56046i | − | 0.242910i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.45150 | − | 2.26815i | 0.194095 | − | 0.0988962i | ||||
\(527\) | 12.4589 | + | 6.34811i | 0.542717 | + | 0.276528i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.83700 | − | 4.96737i | 0.297261 | − | 0.215973i | ||||
\(530\) | 12.1552 | + | 12.1552i | 0.527989 | + | 0.527989i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.10197 | 0.221199 | ||||||||
\(533\) | 13.1123 | − | 10.0917i | 0.567958 | − | 0.437122i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.19747 | + | 2.66352i | −0.354407 | + | 0.115154i | ||||
\(536\) | 11.5983 | + | 11.5983i | 0.500970 | + | 0.500970i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −21.1111 | − | 29.0569i | −0.910165 | − | 1.25273i | ||||
\(539\) | −26.2335 | − | 13.3667i | −1.12996 | − | 0.575743i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.1474 | − | 15.3431i | 0.479266 | − | 0.659653i | −0.499098 | − | 0.866546i | \(-0.666335\pi\) |
0.978364 | + | 0.206893i | \(0.0663351\pi\) | |||||||
\(542\) | 27.9893i | 1.20224i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.44200 | + | 9.10442i | 0.0618252 | + | 0.390349i | ||||
\(545\) | −34.3296 | − | 5.43728i | −1.47052 | − | 0.232907i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.0744 | − | 11.0744i | 0.473506 | − | 0.473506i | −0.429541 | − | 0.903047i | \(-0.641325\pi\) |
0.903047 | + | 0.429541i | \(0.141325\pi\) | |||||||
\(548\) | 0.487842 | − | 3.08011i | 0.0208396 | − | 0.131576i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.09474 | − | 1.44047i | 0.387801 | − | 0.0614216i | ||||
\(551\) | −14.7594 | − | 45.4247i | −0.628771 | − | 1.93516i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.5344 | + | 5.69727i | 0.745638 | + | 0.242273i | ||||
\(554\) | −28.4285 | − | 9.23699i | −1.20781 | − | 0.392442i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.70764 | − | 8.33325i | −0.114829 | − | 0.353408i | ||||
\(557\) | −30.3636 | + | 4.80913i | −1.28655 | + | 0.203769i | −0.761981 | − | 0.647600i | \(-0.775773\pi\) |
−0.524567 | + | 0.851369i | \(0.675773\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.746789 | − | 4.71504i | 0.0315858 | − | 0.199425i | ||||
\(560\) | −5.36969 | + | 5.36969i | −0.226911 | + | 0.226911i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.253504 | − | 0.0401511i | −0.0106934 | − | 0.00169367i | ||||
\(563\) | 3.47564 | + | 21.9443i | 0.146481 | + | 0.924844i | 0.945991 | + | 0.324192i | \(0.105092\pi\) |
−0.799510 | + | 0.600652i | \(0.794908\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 33.7119i | − | 1.41827i | ||||||
\(566\) | −7.82744 | + | 10.7735i | −0.329012 | + | 0.452846i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.3925 | − | 6.31429i | −0.519978 | − | 0.264942i | ||||
\(569\) | −2.76582 | − | 3.80682i | −0.115949 | − | 0.159590i | 0.747098 | − | 0.664714i | \(-0.231447\pi\) |
−0.863047 | + | 0.505124i | \(0.831447\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.49358 | + | 9.49358i | 0.397294 | + | 0.397294i | 0.877278 | − | 0.479983i | \(-0.159357\pi\) |
−0.479983 | + | 0.877278i | \(0.659357\pi\) | |||||||
\(572\) | −6.89615 | + | 2.24070i | −0.288343 | + | 0.0936882i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.29806 | − | 2.95207i | 0.346354 | − | 0.123217i | ||||
\(575\) | −5.63499 | −0.234995 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.7501 | − | 11.7501i | −0.489162 | − | 0.489162i | 0.418880 | − | 0.908042i | \(-0.362423\pi\) |
−0.908042 | + | 0.418880i | \(0.862423\pi\) | |||||||
\(578\) | 7.25289 | − | 5.26953i | 0.301680 | − | 0.219184i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.14279 | − | 3.63944i | −0.296588 | − | 0.151119i | ||||
\(581\) | 4.33866 | − | 2.21066i | 0.179998 | − | 0.0917135i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.9013i | 1.19697i | ||||||||
\(584\) | 0.372097 | + | 0.270344i | 0.0153975 | + | 0.0111869i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.07063 | + | 1.43665i | 0.374704 | + | 0.0593473i | ||||
\(587\) | 11.9109 | − | 23.3764i | 0.491615 | − | 0.964849i | −0.503298 | − | 0.864113i | \(-0.667880\pi\) |
0.994913 | − | 0.100736i | \(-0.0321197\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.82513 | + | 36.7784i | −0.240020 | + | 1.51543i | ||||
\(590\) | 0.745691 | − | 2.29500i | 0.0306996 | − | 0.0944837i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.584142 | + | 1.79780i | 0.0240081 | + | 0.0738892i | ||||
\(593\) | −1.10491 | − | 2.16850i | −0.0453730 | − | 0.0890496i | 0.867207 | − | 0.497948i | \(-0.165913\pi\) |
−0.912580 | + | 0.408898i | \(0.865913\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.53470 | + | 2.77309i | 0.349889 | + | 0.113686i | ||||
\(596\) | −1.33939 | − | 2.62871i | −0.0548637 | − | 0.107676i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.7495 | + | 1.86094i | −0.480474 | + | 0.0760996i | ||||
\(599\) | −5.18017 | + | 15.9429i | −0.211656 | + | 0.651410i | 0.787718 | + | 0.616036i | \(0.211262\pi\) |
−0.999374 | + | 0.0353745i | \(0.988738\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.61367 | + | 8.61367i | −0.351359 | + | 0.351359i | −0.860615 | − | 0.509256i | \(-0.829921\pi\) |
0.509256 | + | 0.860615i | \(0.329921\pi\) | |||||||
\(602\) | 1.15363 | − | 2.26413i | 0.0470186 | − | 0.0922793i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.287946 | + | 1.81802i | 0.0117163 | + | 0.0739740i | ||||
\(605\) | 32.2656 | + | 23.4423i | 1.31178 | + | 0.953065i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.60922 | − | 3.59129i | 0.105905 | − | 0.145766i | −0.752775 | − | 0.658278i | \(-0.771285\pi\) |
0.858680 | + | 0.512512i | \(0.171285\pi\) | |||||||
\(608\) | −21.8720 | + | 11.1443i | −0.887027 | + | 0.451963i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.7311 | + | 17.5229i | 0.515468 | + | 0.709480i | ||||
\(611\) | 7.40736 | − | 5.38176i | 0.299670 | − | 0.217723i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 45.1753 | − | 14.6783i | 1.82461 | − | 0.592852i | 0.824996 | − | 0.565139i | \(-0.191177\pi\) |
0.999616 | − | 0.0277136i | \(-0.00882263\pi\) | |||||||
\(614\) | 37.9136 | 1.53007 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −18.0669 | −0.727936 | ||||||||
\(617\) | 35.6237 | − | 11.5748i | 1.43416 | − | 0.465985i | 0.514086 | − | 0.857739i | \(-0.328131\pi\) |
0.920070 | + | 0.391753i | \(0.128131\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.2778 | + | 8.92032i | −0.493485 | + | 0.358538i | −0.806523 | − | 0.591203i | \(-0.798653\pi\) |
0.313038 | + | 0.949741i | \(0.398653\pi\) | |||||||
\(620\) | 3.67361 | + | 5.05629i | 0.147536 | + | 0.203065i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.8650 | − | 8.08364i | 0.636130 | − | 0.324125i | ||||
\(623\) | −1.14114 | + | 1.57064i | −0.0457188 | + | 0.0629265i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.4357 | + | 17.7535i | 0.977427 | + | 0.710142i | ||||
\(626\) | −3.13556 | − | 19.7971i | −0.125322 | − | 0.791253i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.49529 | − | 4.89729i | 0.0995731 | − | 0.195423i | ||||
\(629\) | 1.57957 | − | 1.57957i | 0.0629816 | − | 0.0629816i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.82817 | + | 5.62652i | −0.0727782 | + | 0.223988i | −0.980829 | − | 0.194873i | \(-0.937571\pi\) |
0.908050 | + | 0.418861i | \(0.137571\pi\) | |||||||
\(632\) | −49.0460 | + | 7.76813i | −1.95095 | + | 0.308999i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17.8468 | + | 35.0262i | 0.708785 | + | 1.39107i | ||||
\(635\) | 32.7043 | + | 10.6263i | 1.29783 | + | 0.421691i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.68826 | + | 13.1264i | 0.264999 | + | 0.520089i | ||||
\(638\) | 11.1657 | + | 34.3646i | 0.442055 | + | 1.36051i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.69697 | − | 11.3781i | 0.146136 | − | 0.449759i | ||||
\(641\) | 5.46005 | − | 34.4734i | 0.215659 | − | 1.36162i | −0.607732 | − | 0.794143i | \(-0.707920\pi\) |
0.823391 | − | 0.567475i | \(-0.192080\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.6680 | + | 28.7876i | −0.578451 | + | 1.13527i | 0.397565 | + | 0.917574i | \(0.369855\pi\) |
−0.976016 | + | 0.217700i | \(0.930145\pi\) | |||||||
\(644\) | 2.33292 | + | 0.369498i | 0.0919298 | + | 0.0145603i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −24.8892 | − | 18.0831i | −0.979252 | − | 0.711468i | ||||
\(647\) | − | 0.686839i | − | 0.0270024i | −0.999909 | − | 0.0135012i | \(-0.995702\pi\) | ||
0.999909 | − | 0.0135012i | \(-0.00429770\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.61491 | − | 1.84189i | 0.141898 | − | 0.0723004i | ||||
\(650\) | −4.10527 | − | 2.09174i | −0.161022 | − | 0.0820447i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.23903 | + | 5.98600i | −0.322665 | + | 0.234430i | ||||
\(653\) | −33.7065 | − | 33.7065i | −1.31904 | − | 1.31904i | −0.914538 | − | 0.404500i | \(-0.867446\pi\) |
−0.404500 | − | 0.914538i | \(-0.632554\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.0454 | 1.01768 | ||||||||
\(656\) | −11.5218 | + | 12.1768i | −0.449851 | + | 0.475425i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.63520 | − | 1.50607i | 0.180699 | − | 0.0587126i | ||||
\(659\) | −31.4326 | − | 31.4326i | −1.22444 | − | 1.22444i | −0.966037 | − | 0.258404i | \(-0.916803\pi\) |
−0.258404 | − | 0.966037i | \(-0.583197\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.1153 | − | 19.4280i | −0.549020 | − | 0.755662i | 0.440859 | − | 0.897577i | \(-0.354674\pi\) |
−0.989879 | + | 0.141915i | \(0.954674\pi\) | |||||||
\(662\) | 2.02487 | + | 1.03172i | 0.0786989 | + | 0.0400991i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.70890 | + | 10.6104i | −0.299163 | + | 0.411763i | ||||
\(665\) | 23.8978i | 0.926716i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.45907 | − | 21.8397i | −0.133936 | − | 0.845638i | ||||
\(668\) | 1.64106 | + | 0.259919i | 0.0634946 | + | 0.0100566i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11.6061 | + | 11.6061i | −0.448382 | + | 0.448382i | ||||
\(671\) | −5.69666 | + | 35.9673i | −0.219917 | + | 1.38850i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.1756 | − | 2.40357i | 0.584975 | − | 0.0926510i | 0.143070 | − | 0.989713i | \(-0.454303\pi\) |
0.441906 | + | 0.897062i | \(0.354303\pi\) | |||||||
\(674\) | 10.9559 | + | 33.7188i | 0.422006 | + | 1.29880i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.26720 | − | 1.06158i | −0.125662 | − | 0.0408299i | ||||
\(677\) | 30.7055 | + | 9.97682i | 1.18011 | + | 0.383440i | 0.832407 | − | 0.554165i | \(-0.186962\pi\) |
0.347701 | + | 0.937605i | \(0.386962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.54787 | + | 4.76384i | 0.0594016 | + | 0.182819i | ||||
\(680\) | −23.8727 | + | 3.78106i | −0.915476 | + | 0.144997i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.40680 | − | 27.8235i | 0.168745 | − | 1.06542i | ||||
\(683\) | −11.8785 | + | 11.8785i | −0.454518 | + | 0.454518i | −0.896851 | − | 0.442333i | \(-0.854151\pi\) |
0.442333 | + | 0.896851i | \(0.354151\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.4273 | + | 2.28507i | 0.551240 | + | 0.0873079i | ||||
\(686\) | 2.73298 | + | 17.2554i | 0.104346 | + | 0.658813i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.83661i | 0.184394i | ||||||||
\(689\) | 8.50015 | − | 11.6995i | 0.323830 | − | 0.445714i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.1214 | − | 11.7810i | −0.879581 | − | 0.448169i | −0.0449572 | − | 0.998989i | \(-0.514315\pi\) |
−0.834624 | + | 0.550820i | \(0.814315\pi\) | |||||||
\(692\) | −3.38204 | − | 4.65498i | −0.128566 | − | 0.176956i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −23.9145 | − | 23.9145i | −0.907781 | − | 0.907781i | ||||
\(695\) | 39.0332 | − | 12.6826i | 1.48061 | − | 0.481080i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.0027 | + | 5.59885i | 0.719778 | + | 0.212072i | ||||
\(698\) | −24.6688 | −0.933727 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.646881 | + | 0.646881i | 0.0244498 | + | 0.0244498i | ||||
\(701\) | −22.0790 | + | 16.0413i | −0.833911 | + | 0.605872i | −0.920663 | − | 0.390358i | \(-0.872351\pi\) |
0.0867523 | + | 0.996230i | \(0.472351\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.30042 | + | 2.70070i | 0.199909 | + | 0.101859i | ||||
\(704\) | 40.6405 | − | 20.7074i | 1.53170 | − | 0.780439i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 34.9413i | 1.31503i | ||||||||
\(707\) | 2.85456 | + | 2.07396i | 0.107357 | + | 0.0779994i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −44.8571 | − | 7.10466i | −1.68464 | − | 0.266821i | −0.760631 | − | 0.649185i | \(-0.775110\pi\) |
−0.924012 | + | 0.382364i | \(0.875110\pi\) | |||||||
\(710\) | 6.31854 | − | 12.4008i | 0.237131 | − | 0.465395i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.817998 | − | 5.16463i | 0.0306558 | − | 0.193553i | ||||
\(713\) | −5.32717 | + | 16.3953i | −0.199504 | + | 0.614010i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.4955 | − | 32.3018i | −0.392509 | − | 1.20802i | ||||
\(716\) | 0.471085 | + | 0.924556i | 0.0176053 | + | 0.0345523i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24.9351 | + | 8.10189i | 0.930569 | + | 0.302360i | ||||
\(719\) | 12.6131 | + | 24.7546i | 0.470390 | + | 0.923192i | 0.997312 | + | 0.0732784i | \(0.0233462\pi\) |
−0.526922 | + | 0.849914i | \(0.676654\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.31824 | + | 0.525557i | −0.123578 | + | 0.0195728i | ||||
\(722\) | 18.2307 | − | 56.1084i | 0.678477 | − | 2.08814i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.26462 | − | 2.26462i | 0.0841640 | − | 0.0841640i | ||||
\(725\) | 3.88807 | − | 7.63077i | 0.144399 | − | 0.283400i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.75993 | − | 17.4255i | −0.102360 | − | 0.646276i | −0.984513 | − | 0.175313i | \(-0.943906\pi\) |
0.882153 | − | 0.470963i | \(-0.156094\pi\) | |||||||
\(728\) | 7.31361 | + | 5.31365i | 0.271060 | + | 0.196937i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.270526 | + | 0.372347i | −0.0100126 | + | 0.0137812i | ||||
\(731\) | 5.09261 | − | 2.59481i | 0.188357 | − | 0.0959726i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.53747 | − | 7.62168i | −0.204531 | − | 0.281513i | 0.694413 | − | 0.719577i | \(-0.255664\pi\) |
−0.898944 | + | 0.438064i | \(0.855664\pi\) | |||||||
\(734\) | −16.8421 | + | 12.2365i | −0.621653 | + | 0.451658i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −10.8083 | + | 3.51181i | −0.398397 | + | 0.129447i | ||||
\(737\) | −27.5957 | −1.01650 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.347492 | 0.0127827 | 0.00639135 | − | 0.999980i | \(-0.497966\pi\) | ||||
0.00639135 | + | 0.999980i | \(0.497966\pi\) | |||||||
\(740\) | 0.949591 | − | 0.308541i | 0.0349077 | − | 0.0113422i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.22761 | − | 4.52463i | 0.228623 | − | 0.166104i | ||||
\(743\) | −4.23794 | − | 5.83302i | −0.155475 | − | 0.213993i | 0.724173 | − | 0.689618i | \(-0.242222\pi\) |
−0.879648 | + | 0.475626i | \(0.842222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.3129 | − | 6.27375i | 0.451111 | − | 0.229853i | ||||
\(746\) | 12.0919 | − | 16.6431i | 0.442717 | − | 0.609348i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.02347 | − | 5.10285i | −0.256804 | − | 0.186579i | ||||
\(749\) | 0.603799 | + | 3.81223i | 0.0220623 | + | 0.139296i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.85526 | − | 17.3794i | 0.323133 | − | 0.634184i | −0.671107 | − | 0.741361i | \(-0.734181\pi\) |
0.994240 | + | 0.107176i | \(0.0341809\pi\) | |||||||
\(752\) | −6.55944 | + | 6.55944i | −0.239198 | + | 0.239198i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.58698 | − | 17.1950i | 0.203466 | − | 0.626203i | ||||
\(755\) | −8.51564 | + | 1.34874i | −0.309916 | + | 0.0490858i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.98828 | − | 15.6779i | −0.290339 | − | 0.569823i | 0.699057 | − | 0.715066i | \(-0.253603\pi\) |
−0.989396 | + | 0.145244i | \(0.953603\pi\) | |||||||
\(758\) | 42.5256 | + | 13.8174i | 1.54460 | + | 0.501871i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −29.2216 | − | 57.3506i | −1.05998 | − | 2.08032i | ||||
\(761\) | −7.86010 | − | 24.1909i | −0.284928 | − | 0.876919i | −0.986420 | − | 0.164242i | \(-0.947482\pi\) |
0.701492 | − | 0.712678i | \(-0.252518\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.80970 | + | 14.8027i | −0.174123 | + | 0.535895i | ||||
\(764\) | −0.268777 | + | 1.69699i | −0.00972402 | + | 0.0613950i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.5098 | + | 36.3274i | −0.668785 | + | 1.31256i | ||||
\(767\) | −2.00506 | − | 0.317570i | −0.0723984 | − | 0.0114668i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.8491 | − | 7.88236i | −0.391230 | − | 0.284245i | 0.374729 | − | 0.927134i | \(-0.377736\pi\) |
−0.765959 | + | 0.642889i | \(0.777736\pi\) | |||||||
\(770\) | − | 18.0791i | − | 0.651524i | ||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.64517 | + | 3.89541i | −0.275156 | + | 0.140199i | ||||
\(773\) | −33.8688 | − | 17.2570i | −1.21817 | − | 0.620691i | −0.277737 | − | 0.960657i | \(-0.589584\pi\) |
−0.940438 | + | 0.339966i | \(0.889584\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.40172 | + | 3.92458i | −0.194035 | + | 0.140975i | ||||
\(776\) | −9.53971 | − | 9.53971i | −0.342456 | − | 0.342456i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.7367 | −0.384929 | ||||||||
\(779\) | 1.45757 | + | 52.7353i | 0.0522228 | + | 1.88944i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.2544 | − | 7.23090i | 0.796326 | − | 0.258742i | ||||
\(782\) | −10.0712 | − | 10.0712i | −0.360144 | − | 0.360144i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.77326 | − | 12.0754i | −0.313331 | − | 0.431263i | ||||
\(785\) | 22.9390 | + | 11.6880i | 0.818729 | + | 0.417163i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.9010 | + | 39.7788i | −1.03021 | + | 1.41796i | −0.125417 | + | 0.992104i | \(0.540027\pi\) |
−0.904791 | + | 0.425856i | \(0.859973\pi\) | |||||||
\(788\) | − | 2.46963i | − | 0.0879771i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.77335 | − | 49.0790i | −0.276563 | − | 1.74615i | ||||
\(791\) | −14.9104 | − | 2.36157i | −0.530152 | − | 0.0839679i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.8844 | − | 12.8844i | 0.457537 | − | 0.457537i | ||||
\(794\) | −1.58312 | + | 9.99541i | −0.0561827 | + | 0.354724i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.82120 | + | 0.763603i | −0.170883 | + | 0.0270652i | ||||
\(797\) | −1.66232 | − | 5.11611i | −0.0588825 | − | 0.181222i | 0.917289 | − | 0.398222i | \(-0.130373\pi\) |
−0.976172 | + | 0.217000i | \(0.930373\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.4257 | + | 3.38752i | 0.368836 | + | 0.119842i | ||||
\(800\) | −4.18616 | − | 1.36016i | −0.148003 | − | 0.0480891i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.28442 | + | 28.5745i | 0.327844 | + | 1.00900i | ||||
\(803\) | −0.764277 | + | 0.121050i | −0.0269707 | + | 0.00427175i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.73074 | + | 10.9274i | −0.0610005 | + | 0.385142i | ||||
\(806\) | −9.96704 | + | 9.96704i | −0.351074 | + | 0.351074i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.38645 | − | 1.48667i | −0.330214 | − | 0.0523008i | ||||
\(809\) | 4.90251 | + | 30.9532i | 0.172363 | + | 1.08826i | 0.910470 | + | 0.413574i | \(0.135720\pi\) |
−0.738107 | + | 0.674683i | \(0.764280\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.8699i | 0.662610i | 0.943524 | + | 0.331305i | \(0.107489\pi\) | ||||
−0.943524 | + | 0.331305i | \(0.892511\pi\) | |||||||
\(812\) | −2.11005 | + | 2.90423i | −0.0740482 | + | 0.101919i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.00985 | − | 2.04312i | −0.140545 | − | 0.0716113i | ||||
\(815\) | −28.0386 | − | 38.5918i | −0.982149 | − | 1.35181i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.7627 | + | 10.7627i | 0.376538 | + | 0.376538i | ||||
\(818\) | 10.0459 | − | 3.26411i | 0.351246 | − | 0.114127i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.43174 | + | 6.08576i | 0.224606 | + | 0.212524i | ||||
\(821\) | −1.59911 | −0.0558094 | −0.0279047 | − | 0.999611i | \(-0.508883\pi\) | ||||
−0.0279047 | + | 0.999611i | \(0.508883\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.3789 | − | 18.3789i | −0.640647 | − | 0.640647i | 0.310068 | − | 0.950715i | \(-0.399648\pi\) |
−0.950715 | + | 0.310068i | \(0.899648\pi\) | |||||||
\(824\) | 7.32056 | − | 5.31870i | 0.255024 | − | 0.185286i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.962817 | − | 0.490580i | −0.0335007 | − | 0.0170694i | ||||
\(827\) | −7.57401 | + | 3.85915i | −0.263374 | + | 0.134196i | −0.580692 | − | 0.814124i | \(-0.697218\pi\) |
0.317318 | + | 0.948319i | \(0.397218\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.285264i | 0.00990764i | 0.999988 | + | 0.00495382i | \(0.00157686\pi\) | ||||
−0.999988 | + | 0.00495382i | \(0.998423\pi\) | |||||||
\(830\) | −10.6175 | − | 7.71409i | −0.368540 | − | 0.267760i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −22.5418 | − | 3.57027i | −0.781496 | − | 0.123777i | ||||
\(833\) | −8.00769 | + | 15.7160i | −0.277450 | + | 0.544526i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.21747 | + | 7.68678i | −0.0421322 | + | 0.266012i | ||||
\(836\) | 7.14418 | − | 21.9875i | 0.247087 | − | 0.760454i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9.29731 | + | 28.6142i | 0.321170 | + | 0.988460i | ||||
\(839\) | 5.30778 | + | 10.4171i | 0.183245 | + | 0.359638i | 0.964295 | − | 0.264830i | \(-0.0853157\pi\) |
−0.781050 | + | 0.624468i | \(0.785316\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.38091 | + | 1.42344i | 0.151066 | + | 0.0490843i | ||||
\(842\) | 5.96702 | + | 11.7109i | 0.205637 | + | 0.403585i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.46675 | + | 0.549079i | −0.119330 | + | 0.0189001i | ||||
\(845\) | 4.97246 | − | 15.3036i | 0.171058 | − | 0.526461i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.6285 | − | 12.6285i | 0.433921 | − | 0.433921i | ||||
\(848\) | −6.65167 | + | 13.0546i | −0.228419 | + | 0.448298i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.862953 | − | 5.44847i | −0.0295990 | − | 0.186881i | ||||
\(851\) | 2.22807 | + | 1.61878i | 0.0763771 | + | 0.0554912i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.3175 | + | 19.7064i | −0.490223 | + | 0.674734i | −0.980429 | − | 0.196873i | \(-0.936921\pi\) |
0.490206 | + | 0.871607i | \(0.336921\pi\) | |||||||
\(854\) | 8.64201 | − | 4.40332i | 0.295723 | − | 0.150679i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.11052 | − | 8.41040i | −0.208853 | − | 0.287462i | ||||
\(857\) | 4.13061 | − | 3.00106i | 0.141099 | − | 0.102514i | −0.514997 | − | 0.857192i | \(-0.672207\pi\) |
0.656096 | + | 0.754678i | \(0.272207\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.384709 | − | 0.125000i | 0.0131261 | − | 0.00426493i | −0.302447 | − | 0.953166i | \(-0.597803\pi\) |
0.315573 | + | 0.948901i | \(0.397803\pi\) | |||||||
\(860\) | 2.55468 | 0.0871137 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.4869 | −0.799969 | ||||||||
\(863\) | −36.1033 | + | 11.7307i | −1.22897 | + | 0.399316i | −0.850341 | − | 0.526232i | \(-0.823604\pi\) |
−0.378629 | + | 0.925549i | \(0.623604\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.8041 | − | 15.8416i | 0.741360 | − | 0.538630i | ||||
\(866\) | 3.30304 | + | 4.54624i | 0.112242 | + | 0.154488i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.49368 | − | 1.27060i | 0.0846411 | − | 0.0431268i | ||||
\(869\) | 49.1060 | − | 67.5886i | 1.66581 | − | 2.29279i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.1709 | + | 8.11615i | 0.378512 | + | 0.275005i | ||||
\(872\) | −6.55794 | − | 41.4052i | −0.222080 | − | 1.40216i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 17.2193 | − | 33.7949i | 0.582453 | − | 1.14313i | ||||
\(875\) | 7.22503 | − | 7.22503i | 0.244250 | − | 0.244250i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.4052 | − | 35.1015i | 0.385125 | − | 1.18529i | −0.551264 | − | 0.834331i | \(-0.685854\pi\) |
0.936389 | − | 0.350963i | \(-0.114146\pi\) | |||||||
\(878\) | −14.8664 | + | 2.35461i | −0.501718 | + | 0.0794643i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 15.6222 | + | 30.6603i | 0.526625 | + | 1.03356i | ||||
\(881\) | 10.6200 | + | 3.45065i | 0.357798 | + | 0.116255i | 0.482399 | − | 0.875951i | \(-0.339765\pi\) |
−0.124602 | + | 0.992207i | \(0.539765\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.6504 | − | 20.9026i | −0.358415 | − | 0.703429i | 0.639444 | − | 0.768838i | \(-0.279165\pi\) |
−0.997859 | + | 0.0654092i | \(0.979165\pi\) | |||||||
\(884\) | 1.34235 | + | 4.13134i | 0.0451483 | + | 0.138952i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.14158 | − | 15.8241i | 0.172735 | − | 0.531622i | ||||
\(887\) | −4.35893 | + | 27.5212i | −0.146358 | + | 0.924071i | 0.799776 | + | 0.600298i | \(0.204951\pi\) |
−0.946135 | + | 0.323773i | \(0.895049\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.99088 | − | 13.7204i | 0.234467 | − | 0.460166i | ||||
\(890\) | 5.16811 | + | 0.818548i | 0.173235 | + | 0.0274378i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.79915 | + | 1.30716i | 0.0602400 | + | 0.0437669i | ||||
\(893\) | 29.1928i | 0.976899i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.33064 | + | 2.20657i | −0.144757 | + | 0.0737576i | ||||
\(896\) | −4.77344 | − | 2.43219i | −0.159469 | − | 0.0812537i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.20780 | + | 3.78369i | −0.173787 | + | 0.126263i | ||||
\(899\) | −18.5265 | − | 18.5265i | −0.617893 | − | 0.617893i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.3142 | 0.576819 | ||||||||
\(902\) | −1.10267 | − | 39.8951i | −0.0367150 | − | 1.32836i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 38.6701 | − | 12.5647i | 1.28615 | − | 0.417895i | ||||
\(905\) | 10.6075 | + | 10.6075i | 0.352607 | + | 0.352607i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.2821 | + | 30.6687i | 0.739865 | + | 1.01834i | 0.998626 | + | 0.0523958i | \(0.0166857\pi\) |
−0.258761 | + | 0.965941i | \(0.583314\pi\) | |||||||
\(908\) | −0.277979 | − | 0.141638i | −0.00922507 | − | 0.00470041i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.31722 | + | 7.31853i | −0.176264 | + | 0.242607i | ||||
\(911\) | − | 23.3777i | − | 0.774537i | −0.921967 | − | 0.387269i | \(-0.873419\pi\) | ||
0.921967 | − | 0.387269i | \(-0.126581\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.45174 | − | 21.7934i | −0.114236 | − | 0.721258i | ||||
\(914\) | 12.1115 | + | 1.91827i | 0.400611 | + | 0.0634506i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.23544 | − | 9.23544i | 0.305147 | − | 0.305147i | ||||
\(917\) | 1.82452 | − | 11.5196i | 0.0602510 | − | 0.380410i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.4344 | − | 3.07810i | 0.641080 | − | 0.101537i | 0.172573 | − | 0.984997i | \(-0.444792\pi\) |
0.468507 | + | 0.883460i | \(0.344792\pi\) | |||||||
\(920\) | −9.20832 | − | 28.3403i | −0.303589 | − | 0.934352i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −34.0853 | − | 11.0750i | −1.12254 | − | 0.364735i | ||||
\(923\) | −11.1354 | − | 3.61812i | −0.366527 | − | 0.119092i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.329619 | + | 1.01446i | 0.0108378 | + | 0.0333554i | ||||
\(926\) | −45.7940 | + | 7.25305i | −1.50488 | + | 0.238350i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.70194 | − | 17.0594i | 0.0886955 | − | 0.560001i | ||||
\(929\) | −5.06327 | + | 5.06327i | −0.166120 | + | 0.166120i | −0.785272 | − | 0.619151i | \(-0.787477\pi\) |
0.619151 | + | 0.785272i | \(0.287477\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −46.3933 | − | 7.34798i | −1.52048 | − | 0.240820i | ||||
\(932\) | 1.05516 | + | 6.66204i | 0.0345630 | + | 0.218222i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 3.32445i | − | 0.108779i | ||||||
\(935\) | 23.9019 | − | 32.8981i | 0.781676 | − | 1.07588i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.9861 | + | 19.8644i | 1.27362 | + | 0.648942i | 0.954341 | − | 0.298718i | \(-0.0965590\pi\) |
0.319280 | + | 0.947660i | \(0.396559\pi\) | |||||||
\(938\) | 4.32022 | + | 5.94627i | 0.141060 | + | 0.194153i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.46467 | + | 3.46467i | 0.113005 | + | 0.113005i | ||||
\(941\) | 24.9275 | − | 8.09943i | 0.812613 | − | 0.264034i | 0.126909 | − | 0.991914i | \(-0.459494\pi\) |
0.685704 | + | 0.727881i | \(0.259494\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.15274 | + | 24.2192i | −0.102667 | + | 0.788685i | ||||
\(944\) | 2.05676 | 0.0669417 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.14213 | − | 8.14213i | −0.264723 | − | 0.264723i | ||||
\(947\) | −26.7046 | + | 19.4020i | −0.867781 | + | 0.630480i | −0.929991 | − | 0.367583i | \(-0.880185\pi\) |
0.0622093 | + | 0.998063i | \(0.480185\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.344986 | + | 0.175779i | 0.0111987 | + | 0.00570604i | ||||
\(950\) | 13.0891 | − | 6.66925i | 0.424667 | − | 0.216379i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.8235i | 0.350792i | ||||||||
\(953\) | 2.15205 | + | 1.56356i | 0.0697119 | + | 0.0506486i | 0.622095 | − | 0.782941i | \(-0.286282\pi\) |
−0.552384 | + | 0.833590i | \(0.686282\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.94876 | − | 1.25896i | −0.257216 | − | 0.0407390i | ||||
\(956\) | −1.67353 | + | 3.28448i | −0.0541257 | + | 0.106228i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.80288 | − | 42.9517i | 0.219791 | − | 1.38771i | ||||
\(959\) | 2.02132 | − | 6.22098i | 0.0652718 | − | 0.200886i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.26738 | − | 10.0559i | −0.105399 | − | 0.324385i | ||||
\(962\) | 1.02231 | + | 2.00640i | 0.0329607 | + | 0.0646891i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.91070 | + | 3.22018i | 0.319202 | + | 0.103715i | ||||
\(965\) | −18.2462 | − | 35.8102i | −0.587366 | − | 1.15277i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.8463 | − | 2.03466i | 0.413110 | − | 0.0654303i | 0.0535799 | − | 0.998564i | \(-0.482937\pi\) |
0.359531 | + | 0.933133i | \(0.382937\pi\) | |||||||
\(968\) | −14.8645 | + | 45.7482i | −0.477762 | + | 1.47040i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.54613 | − | 9.54613i | 0.306508 | − | 0.306508i | ||||
\(971\) | 3.29747 | − | 6.47166i | 0.105821 | − | 0.207685i | −0.832024 | − | 0.554739i | \(-0.812818\pi\) |
0.937845 | + | 0.347054i | \(0.112818\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.87505 | − | 18.1524i | −0.0921700 | − | 0.581939i | ||||
\(974\) | 14.9503 | + | 10.8620i | 0.479039 | + | 0.348042i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.8511 | + | 14.9352i | −0.347334 | + | 0.478065i | ||||
\(977\) | −26.7289 | + | 13.6190i | −0.855132 | + | 0.435711i | −0.825870 | − | 0.563860i | \(-0.809316\pi\) |
−0.0292617 | + | 0.999572i | \(0.509316\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.17095 | + | 7.11720i | 0.165264 | + | 0.227467i | ||||
\(980\) | −6.37815 | + | 4.63399i | −0.203742 | + | 0.148028i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.63997 | − | 3.13222i | 0.307624 | − | 0.0999530i | ||||
\(983\) | 47.8093 | 1.52488 | 0.762439 | − | 0.647060i | \(-0.224002\pi\) | ||||
0.762439 | + | 0.647060i | \(0.224002\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.5678 | 0.368582 | ||||||||
\(986\) | 20.5871 | − | 6.68915i | 0.655626 | − | 0.213026i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.35875 | + | 6.79953i | −0.297741 | + | 0.216322i | ||||
\(989\) | 4.14185 | + | 5.70077i | 0.131703 | + | 0.181274i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.8416 | + | 19.2812i | −1.20208 | + | 0.612489i | −0.936183 | − | 0.351513i | \(-0.885667\pi\) |
−0.265894 | + | 0.964002i | \(0.585667\pi\) | |||||||
\(992\) | −7.91496 | + | 10.8940i | −0.251300 | + | 0.345885i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.04213 | − | 3.66332i | −0.159927 | − | 0.116193i | ||||
\(995\) | −3.57673 | − | 22.5826i | −0.113390 | − | 0.715917i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.2309 | + | 37.7427i | −0.609048 | + | 1.19532i | 0.356303 | + | 0.934370i | \(0.384037\pi\) |
−0.965351 | + | 0.260954i | \(0.915963\pi\) | |||||||
\(998\) | −6.57516 | + | 6.57516i | −0.208133 | + | 0.208133i | ||||
\(999\) | 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 | 369.2.u.a.244.1 | 24 | ||
3.2 | odd | 2 | 41.2.g.a.39.3 | yes | 24 | ||
12.11 | even | 2 | 656.2.bs.d.449.2 | 24 | |||
41.20 | even | 20 | inner | 369.2.u.a.307.1 | 24 | ||
123.20 | odd | 20 | 41.2.g.a.20.3 | ✓ | 24 | ||
123.26 | even | 40 | 1681.2.a.m.1.16 | 24 | |||
123.56 | even | 40 | 1681.2.a.m.1.15 | 24 | |||
492.143 | even | 20 | 656.2.bs.d.225.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
41.2.g.a.20.3 | ✓ | 24 | 123.20 | odd | 20 | ||
41.2.g.a.39.3 | yes | 24 | 3.2 | odd | 2 | ||
369.2.u.a.244.1 | 24 | 1.1 | even | 1 | trivial | ||
369.2.u.a.307.1 | 24 | 41.20 | even | 20 | inner | ||
656.2.bs.d.225.2 | 24 | 492.143 | even | 20 | |||
656.2.bs.d.449.2 | 24 | 12.11 | even | 2 | |||
1681.2.a.m.1.15 | 24 | 123.56 | even | 40 | |||
1681.2.a.m.1.16 | 24 | 123.26 | even | 40 |