Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [693,2,Mod(64,693)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(693, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("693.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 693 = 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 693.m (of order \(5\), degree \(4\), 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: | \(5.53363286007\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 7x^{14} + 25x^{12} + 52x^{10} + 309x^{8} + 218x^{6} + 60x^{4} - 2x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 64.1 | ||
Root | \(-0.698216 + 2.14889i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 693.64 |
Dual form | 693.2.m.h.379.1 |
$q$-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 \(\left(\mathbb{Z}/693\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(442\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.698216 | + | 2.14889i | −0.493713 | + | 1.51949i | 0.325240 | + | 0.945632i | \(0.394555\pi\) |
−0.818953 | + | 0.573861i | \(0.805445\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.51217 | − | 1.82520i | −1.25609 | − | 0.912601i | ||||
\(5\) | −0.476925 | − | 1.46782i | −0.213287 | − | 0.656431i | −0.999271 | − | 0.0381834i | \(-0.987843\pi\) |
0.785983 | − | 0.618248i | \(-0.212157\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.809017 | + | 0.587785i | 0.305780 | + | 0.222162i | ||||
\(8\) | 2.02029 | − | 1.46782i | 0.714279 | − | 0.518954i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.48718 | 1.10274 | ||||||||
\(11\) | −2.83882 | − | 1.71497i | −0.855936 | − | 0.517081i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.784027 | − | 2.41299i | 0.217450 | − | 0.669242i | −0.781521 | − | 0.623879i | \(-0.785556\pi\) |
0.998971 | − | 0.0453628i | \(-0.0144444\pi\) | |||||||
\(14\) | −1.82795 | + | 1.32808i | −0.488541 | + | 0.354946i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.175538 | − | 0.540251i | −0.0438846 | − | 0.135063i | ||||
\(17\) | 2.03818 | + | 6.27288i | 0.494332 | + | 1.52140i | 0.817995 | + | 0.575225i | \(0.195085\pi\) |
−0.323663 | + | 0.946172i | \(0.604915\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.11739 | − | 4.44455i | 1.40343 | − | 1.01965i | 0.409189 | − | 0.912450i | \(-0.365812\pi\) |
0.994238 | − | 0.107199i | \(-0.0341882\pi\) | |||||||
\(20\) | −1.48096 | + | 4.55792i | −0.331152 | + | 1.01918i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.66737 | − | 4.90289i | 1.20829 | − | 1.04530i | ||||
\(23\) | 5.61973 | 1.17179 | 0.585897 | − | 0.810385i | \(-0.300742\pi\) | ||||
0.585897 | + | 0.810385i | \(0.300742\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.11803 | − | 1.53884i | 0.423607 | − | 0.307768i | ||||
\(26\) | 4.63782 | + | 3.36957i | 0.909550 | + | 0.660827i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.959565 | − | 2.95324i | −0.181341 | − | 0.558110i | ||||
\(29\) | −4.40969 | − | 3.20383i | −0.818859 | − | 0.594936i | 0.0975266 | − | 0.995233i | \(-0.468907\pi\) |
−0.916385 | + | 0.400297i | \(0.868907\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.64565 | + | 5.06480i | −0.295568 | + | 0.909665i | 0.687462 | + | 0.726220i | \(0.258725\pi\) |
−0.983030 | + | 0.183445i | \(0.941275\pi\) | |||||||
\(32\) | 6.27793 | 1.10979 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −14.9028 | −2.55581 | ||||||||
\(35\) | 0.476925 | − | 1.46782i | 0.0806150 | − | 0.248108i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00465 | + | 3.63609i | 0.822759 | + | 0.597770i | 0.917502 | − | 0.397732i | \(-0.130203\pi\) |
−0.0947421 | + | 0.995502i | \(0.530203\pi\) | |||||||
\(38\) | 5.27957 | + | 16.2488i | 0.856459 | + | 2.63591i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.11803 | − | 2.26538i | −0.493004 | − | 0.358189i | ||||
\(41\) | 7.91777 | − | 5.75260i | 1.23655 | − | 0.898405i | 0.239184 | − | 0.970974i | \(-0.423120\pi\) |
0.997363 | + | 0.0725696i | \(0.0231200\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.61149 | 1.46574 | 0.732870 | − | 0.680369i | \(-0.238181\pi\) | ||||
0.732870 | + | 0.680369i | \(0.238181\pi\) | |||||||
\(44\) | 4.00145 | + | 9.48971i | 0.603242 | + | 1.43063i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.92378 | + | 12.0762i | −0.578530 | + | 1.78053i | ||||
\(47\) | −3.11001 | + | 2.25955i | −0.453641 | + | 0.329590i | −0.791032 | − | 0.611775i | \(-0.790456\pi\) |
0.337390 | + | 0.941365i | \(0.390456\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.309017 | + | 0.951057i | 0.0441453 | + | 0.135865i | ||||
\(50\) | 1.82795 | + | 5.62586i | 0.258511 | + | 0.795617i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.37380 | + | 4.63084i | −0.883887 | + | 0.642182i | ||||
\(53\) | 0.164274 | − | 0.505582i | 0.0225647 | − | 0.0694470i | −0.939140 | − | 0.343534i | \(-0.888376\pi\) |
0.961705 | + | 0.274087i | \(0.0883758\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.16336 | + | 4.98480i | −0.156868 | + | 0.672150i | ||||
\(56\) | 2.49721 | 0.333704 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.96358 | − | 7.23896i | 1.30828 | − | 0.950522i | ||||
\(59\) | 1.42449 | + | 1.03495i | 0.185453 | + | 0.134740i | 0.676638 | − | 0.736316i | \(-0.263436\pi\) |
−0.491185 | + | 0.871055i | \(0.663436\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.46709 | − | 4.51524i | −0.187842 | − | 0.578117i | 0.812144 | − | 0.583457i | \(-0.198300\pi\) |
−0.999986 | + | 0.00533985i | \(0.998300\pi\) | |||||||
\(62\) | −9.73466 | − | 7.07265i | −1.23630 | − | 0.898227i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.03227 | + | 12.4101i | −0.504034 | + | 1.55126i | ||||
\(65\) | −3.91576 | −0.485691 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.60824 | −1.17383 | −0.586917 | − | 0.809647i | \(-0.699658\pi\) | ||||
−0.586917 | + | 0.809647i | \(0.699658\pi\) | |||||||
\(68\) | 6.32900 | − | 19.4787i | 0.767504 | − | 2.36214i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.82119 | + | 2.04972i | 0.337197 | + | 0.244988i | ||||
\(71\) | −3.07233 | − | 9.45567i | −0.364619 | − | 1.12218i | −0.950219 | − | 0.311582i | \(-0.899141\pi\) |
0.585600 | − | 0.810600i | \(-0.300859\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.85836 | − | 5.70943i | −0.919751 | − | 0.668238i | 0.0237110 | − | 0.999719i | \(-0.492452\pi\) |
−0.943462 | + | 0.331481i | \(0.892452\pi\) | |||||||
\(74\) | −11.3079 | + | 8.21565i | −1.31451 | + | 0.955050i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −23.4802 | −2.69336 | ||||||||
\(77\) | −1.28862 | − | 3.05605i | −0.146852 | − | 0.348269i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.639754 | − | 1.96896i | 0.0719780 | − | 0.221525i | −0.908596 | − | 0.417677i | \(-0.862844\pi\) |
0.980574 | + | 0.196151i | \(0.0628444\pi\) | |||||||
\(80\) | −0.709276 | + | 0.515319i | −0.0792994 | + | 0.0576144i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.83337 | + | 21.0309i | 0.754619 | + | 2.32248i | ||||
\(83\) | −0.0136710 | − | 0.0420751i | −0.00150059 | − | 0.00461834i | 0.950303 | − | 0.311325i | \(-0.100773\pi\) |
−0.951804 | + | 0.306707i | \(0.900773\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.23543 | − | 5.98339i | 0.893258 | − | 0.648990i | ||||
\(86\) | −6.71090 | + | 20.6540i | −0.723654 | + | 2.22718i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.25250 | + | 0.702166i | −0.879719 | + | 0.0748512i | ||||
\(89\) | 6.38297 | 0.676594 | 0.338297 | − | 0.941039i | \(-0.390149\pi\) | ||||
0.338297 | + | 0.941039i | \(0.390149\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.05261 | − | 1.49131i | 0.215172 | − | 0.156332i | ||||
\(92\) | −14.1177 | − | 10.2571i | −1.47188 | − | 1.06938i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.68407 | − | 8.26071i | −0.276840 | − | 0.852027i | ||||
\(95\) | −9.44135 | − | 6.85954i | −0.968662 | − | 0.703774i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.09442 | + | 12.6013i | −0.415726 | + | 1.27947i | 0.495874 | + | 0.868394i | \(0.334848\pi\) |
−0.911600 | + | 0.411078i | \(0.865152\pi\) | |||||||
\(98\) | −2.25947 | −0.228241 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.12957 | −0.812957 | ||||||||
\(101\) | 1.70908 | − | 5.26002i | 0.170060 | − | 0.523391i | −0.829313 | − | 0.558784i | \(-0.811268\pi\) |
0.999373 | + | 0.0353926i | \(0.0112682\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.42112 | − | 3.93867i | −0.534159 | − | 0.388089i | 0.287752 | − | 0.957705i | \(-0.407092\pi\) |
−0.821911 | + | 0.569616i | \(0.807092\pi\) | |||||||
\(104\) | −1.95788 | − | 6.02574i | −0.191986 | − | 0.590872i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.971740 | + | 0.706011i | 0.0943837 | + | 0.0685738i | ||||
\(107\) | 4.65571 | − | 3.38257i | 0.450085 | − | 0.327006i | −0.339545 | − | 0.940590i | \(-0.610273\pi\) |
0.789629 | + | 0.613584i | \(0.210273\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.7061 | 1.31281 | 0.656405 | − | 0.754409i | \(-0.272076\pi\) | ||||
0.656405 | + | 0.754409i | \(0.272076\pi\) | |||||||
\(110\) | −9.89949 | − | 5.98040i | −0.943879 | − | 0.570209i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.175538 | − | 0.540251i | 0.0165868 | − | 0.0510490i | ||||
\(113\) | 11.8152 | − | 8.58425i | 1.11148 | − | 0.807538i | 0.128584 | − | 0.991699i | \(-0.458957\pi\) |
0.982896 | + | 0.184161i | \(0.0589567\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.68019 | − | 8.24877i | −0.249929 | − | 0.769202i | ||||
\(116\) | 5.23028 | + | 16.0971i | 0.485619 | + | 1.49458i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.21860 | + | 2.33845i | −0.296296 | + | 0.215272i | ||||
\(119\) | −2.03818 | + | 6.27288i | −0.186840 | + | 0.575034i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.11779 | + | 9.73695i | 0.465254 | + | 0.885177i | ||||
\(122\) | 10.7271 | 0.971184 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 13.3785 | − | 9.72001i | 1.20142 | − | 0.872883i | ||||
\(125\) | −9.51192 | − | 6.91082i | −0.850772 | − | 0.618122i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.17367 | + | 12.8452i | 0.370353 | + | 1.13983i | 0.946560 | + | 0.322526i | \(0.104532\pi\) |
−0.576207 | + | 0.817304i | \(0.695468\pi\) | |||||||
\(128\) | −13.6945 | − | 9.94964i | −1.21043 | − | 0.879432i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.73405 | − | 8.41453i | 0.239792 | − | 0.738003i | ||||
\(131\) | −4.30276 | −0.375934 | −0.187967 | − | 0.982175i | \(-0.560190\pi\) | ||||
−0.187967 | + | 0.982175i | \(0.560190\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.56151 | 0.655666 | ||||||||
\(134\) | 6.70863 | − | 20.6470i | 0.579537 | − | 1.78363i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.3252 | + | 9.68133i | 1.14263 | + | 0.830167i | ||||
\(137\) | 3.87152 | + | 11.9153i | 0.330767 | + | 1.01799i | 0.968770 | + | 0.247961i | \(0.0797606\pi\) |
−0.638003 | + | 0.770034i | \(0.720239\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.08225 | − | 6.59864i | −0.770346 | − | 0.559689i | 0.131720 | − | 0.991287i | \(-0.457950\pi\) |
−0.902066 | + | 0.431598i | \(0.857950\pi\) | |||||||
\(140\) | −3.87719 | + | 2.81695i | −0.327683 | + | 0.238075i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 22.4643 | 1.88516 | ||||||||
\(143\) | −6.36390 | + | 5.50546i | −0.532176 | + | 0.460389i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.59956 | + | 8.00064i | −0.215882 | + | 0.664417i | ||||
\(146\) | 17.7557 | − | 12.9003i | 1.46948 | − | 1.06764i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.93596 | − | 18.2690i | −0.487933 | − | 1.50170i | ||||
\(149\) | −3.74376 | − | 11.5221i | −0.306701 | − | 0.943928i | −0.979037 | − | 0.203682i | \(-0.934709\pi\) |
0.672336 | − | 0.740246i | \(-0.265291\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.72751 | + | 6.34091i | −0.710234 | + | 0.516016i | −0.883249 | − | 0.468904i | \(-0.844649\pi\) |
0.173015 | + | 0.984919i | \(0.444649\pi\) | |||||||
\(152\) | 5.83508 | − | 17.9585i | 0.473287 | − | 1.45663i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.46685 | − | 0.635319i | 0.601696 | − | 0.0511955i | ||||
\(155\) | 8.21909 | 0.660173 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.99575 | − | 2.17654i | 0.239087 | − | 0.173707i | −0.461790 | − | 0.886989i | \(-0.652793\pi\) |
0.700876 | + | 0.713283i | \(0.252793\pi\) | |||||||
\(158\) | 3.78439 | + | 2.74952i | 0.301070 | + | 0.218740i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.99410 | − | 9.21489i | −0.236704 | − | 0.728501i | ||||
\(161\) | 4.54645 | + | 3.30319i | 0.358311 | + | 0.260328i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.96669 | − | 21.4413i | 0.545674 | − | 1.67941i | −0.173709 | − | 0.984797i | \(-0.555575\pi\) |
0.719383 | − | 0.694614i | \(-0.244425\pi\) | |||||||
\(164\) | −30.3905 | −2.37310 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.0999599 | 0.00775839 | ||||||||
\(167\) | −4.39351 | + | 13.5218i | −0.339980 | + | 1.04635i | 0.624237 | + | 0.781235i | \(0.285410\pi\) |
−0.964217 | + | 0.265116i | \(0.914590\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.30941 | + | 3.85751i | 0.408416 | + | 0.296732i | ||||
\(170\) | 7.10752 | + | 21.8747i | 0.545122 | + | 1.67771i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −24.1458 | − | 17.5429i | −1.84110 | − | 1.33763i | ||||
\(173\) | 15.2734 | − | 11.0968i | 1.16121 | − | 0.843671i | 0.171283 | − | 0.985222i | \(-0.445209\pi\) |
0.989931 | + | 0.141551i | \(0.0452088\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.61803 | 0.197905 | ||||||||
\(176\) | −0.428191 | + | 1.83472i | −0.0322761 | + | 0.138297i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.45669 | + | 13.7163i | −0.334043 | + | 1.02808i | ||||
\(179\) | −3.55826 | + | 2.58523i | −0.265957 | + | 0.193229i | −0.712769 | − | 0.701399i | \(-0.752559\pi\) |
0.446812 | + | 0.894628i | \(0.352559\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.50777 | + | 4.64044i | 0.112072 | + | 0.344921i | 0.991325 | − | 0.131433i | \(-0.0419580\pi\) |
−0.879253 | + | 0.476354i | \(0.841958\pi\) | |||||||
\(182\) | 1.77149 | + | 5.45208i | 0.131311 | + | 0.404135i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 11.3535 | − | 8.24877i | 0.836988 | − | 0.608108i | ||||
\(185\) | 2.95030 | − | 9.08009i | 0.216910 | − | 0.667582i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.97174 | − | 21.3030i | 0.363570 | − | 1.55783i | ||||
\(188\) | 11.9370 | 0.870597 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 21.3325 | − | 15.4990i | 1.54762 | − | 1.12441i | ||||
\(191\) | 12.8089 | + | 9.30619i | 0.926818 | + | 0.673373i | 0.945212 | − | 0.326458i | \(-0.105855\pi\) |
−0.0183938 | + | 0.999831i | \(0.505855\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.57558 | − | 7.92682i | −0.185394 | − | 0.570585i | 0.814561 | − | 0.580078i | \(-0.196978\pi\) |
−0.999955 | + | 0.00949361i | \(0.996978\pi\) | |||||||
\(194\) | −24.2201 | − | 17.5969i | −1.73890 | − | 1.26338i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.959565 | − | 2.95324i | 0.0685404 | − | 0.210946i | ||||
\(197\) | 3.63957 | 0.259309 | 0.129654 | − | 0.991559i | \(-0.458613\pi\) | ||||
0.129654 | + | 0.991559i | \(0.458613\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.58189 | −0.324801 | −0.162401 | − | 0.986725i | \(-0.551924\pi\) | ||||
−0.162401 | + | 0.986725i | \(0.551924\pi\) | |||||||
\(200\) | 2.02029 | − | 6.21780i | 0.142856 | − | 0.439665i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.1099 | + | 7.34525i | 0.711328 | + | 0.516810i | ||||
\(203\) | −1.68435 | − | 5.18390i | −0.118218 | − | 0.363839i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.2200 | − | 8.87834i | −0.853481 | − | 0.620090i | ||||
\(206\) | 12.2489 | − | 8.89933i | 0.853419 | − | 0.620046i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.44125 | −0.0999325 | ||||||||
\(209\) | −24.9884 | + | 2.12615i | −1.72848 | + | 0.147069i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.361382 | − | 1.11222i | 0.0248785 | − | 0.0765683i | −0.937846 | − | 0.347051i | \(-0.887183\pi\) |
0.962725 | + | 0.270482i | \(0.0871832\pi\) | |||||||
\(212\) | −1.33547 | + | 0.970278i | −0.0917207 | + | 0.0666390i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.01807 | + | 12.3664i | 0.274670 | + | 0.845347i | ||||
\(215\) | −4.58396 | − | 14.1080i | −0.312624 | − | 0.962157i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.30838 | + | 3.13022i | −0.292472 | + | 0.212493i | ||||
\(218\) | −9.56983 | + | 29.4529i | −0.648151 | + | 1.99480i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 12.0208 | − | 10.3993i | 0.810445 | − | 0.701121i | ||||
\(221\) | 16.7344 | 1.12568 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.18187 | − | 2.31176i | 0.213073 | − | 0.154807i | −0.476130 | − | 0.879375i | \(-0.657961\pi\) |
0.689203 | + | 0.724568i | \(0.257961\pi\) | |||||||
\(224\) | 5.07895 | + | 3.69007i | 0.339352 | + | 0.246553i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.1970 | + | 31.3832i | 0.678295 | + | 2.08758i | ||||
\(227\) | −19.7069 | − | 14.3179i | −1.30799 | − | 0.950313i | −0.307994 | − | 0.951388i | \(-0.599658\pi\) |
−0.999999 | + | 0.00107543i | \(0.999658\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.48670 | + | 23.0417i | −0.494735 | + | 1.52264i | 0.322635 | + | 0.946523i | \(0.395431\pi\) |
−0.817370 | + | 0.576114i | \(0.804569\pi\) | |||||||
\(230\) | 19.5970 | 1.29219 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.6115 | −0.893638 | ||||||||
\(233\) | 8.71308 | − | 26.8161i | 0.570813 | − | 1.75678i | −0.0792020 | − | 0.996859i | \(-0.525237\pi\) |
0.650015 | − | 0.759922i | \(-0.274763\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.79987 | + | 3.48731i | 0.313109 | + | 0.227487i | ||||
\(236\) | −1.68957 | − | 5.19997i | −0.109982 | − | 0.338489i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.0566 | − | 8.75965i | −0.781515 | − | 0.567804i | ||||
\(239\) | −15.0794 | + | 10.9558i | −0.975406 | + | 0.708674i | −0.956677 | − | 0.291151i | \(-0.905962\pi\) |
−0.0187288 | + | 0.999825i | \(0.505962\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.4814 | −1.12608 | −0.563039 | − | 0.826430i | \(-0.690368\pi\) | ||||
−0.563039 | + | 0.826430i | \(0.690368\pi\) | |||||||
\(242\) | −24.4969 | + | 4.19906i | −1.57472 | + | 0.269926i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.55563 | + | 14.0208i | −0.291645 | + | 0.897590i | ||||
\(245\) | 1.24861 | − | 0.907165i | 0.0797705 | − | 0.0579567i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.92843 | − | 18.2458i | −0.377217 | − | 1.16095i | ||||
\(248\) | 4.10955 | + | 12.6479i | 0.260956 | + | 0.803141i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 21.4919 | − | 15.6148i | 1.35927 | − | 0.987567i | ||||
\(251\) | −1.24878 | + | 3.84335i | −0.0788224 | + | 0.242590i | −0.982701 | − | 0.185198i | \(-0.940707\pi\) |
0.903879 | + | 0.427789i | \(0.140707\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.9534 | − | 9.63764i | −1.00298 | − | 0.605913i | ||||
\(254\) | −30.5171 | −1.91481 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.82911 | − | 7.14127i | 0.614319 | − | 0.446329i | ||||
\(257\) | −7.83513 | − | 5.69255i | −0.488742 | − | 0.355092i | 0.315958 | − | 0.948773i | \(-0.397674\pi\) |
−0.804700 | + | 0.593681i | \(0.797674\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.91161 | + | 5.88332i | 0.118781 | + | 0.365572i | ||||
\(260\) | 9.83708 | + | 7.14706i | 0.610070 | + | 0.443242i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.00425 | − | 9.24614i | 0.185603 | − | 0.571229i | ||||
\(263\) | 5.08831 | 0.313759 | 0.156879 | − | 0.987618i | \(-0.449857\pi\) | ||||
0.156879 | + | 0.987618i | \(0.449857\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.820452 | −0.0504000 | ||||||||
\(266\) | −5.27957 | + | 16.2488i | −0.323711 | + | 0.996280i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 24.1376 | + | 17.5370i | 1.47444 | + | 1.07124i | ||||
\(269\) | −0.0694072 | − | 0.213613i | −0.00423183 | − | 0.0130242i | 0.948918 | − | 0.315522i | \(-0.102180\pi\) |
−0.953150 | + | 0.302498i | \(0.902180\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.7069 | + | 14.3179i | 1.19711 | + | 0.869749i | 0.993997 | − | 0.109407i | \(-0.0348951\pi\) |
0.203110 | + | 0.979156i | \(0.434895\pi\) | |||||||
\(272\) | 3.03115 | − | 2.20226i | 0.183791 | − | 0.133532i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −28.3078 | −1.71014 | ||||||||
\(275\) | −8.65178 | + | 0.736139i | −0.521722 | + | 0.0443909i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.40772 | + | 16.6432i | −0.324918 | + | 0.999995i | 0.646559 | + | 0.762864i | \(0.276207\pi\) |
−0.971478 | + | 0.237132i | \(0.923793\pi\) | |||||||
\(278\) | 20.5211 | − | 14.9095i | 1.23077 | − | 0.894209i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.19098 | − | 3.66547i | −0.0711748 | − | 0.219054i | ||||
\(281\) | −4.43593 | − | 13.6524i | −0.264625 | − | 0.814433i | −0.991780 | − | 0.127959i | \(-0.959158\pi\) |
0.727154 | − | 0.686474i | \(-0.240842\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.6569 | + | 16.4612i | −1.34681 | + | 0.978516i | −0.347649 | + | 0.937625i | \(0.613020\pi\) |
−0.999164 | + | 0.0408916i | \(0.986980\pi\) | |||||||
\(284\) | −9.54027 | + | 29.3619i | −0.566111 | + | 1.74231i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.38722 | − | 17.5193i | −0.436816 | − | 1.03594i | ||||
\(287\) | 9.78690 | 0.577702 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −21.4416 | + | 15.5782i | −1.26127 | + | 0.916365i | ||||
\(290\) | −15.3774 | − | 11.1723i | −0.902992 | − | 0.656062i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.32070 | + | 28.6862i | 0.545453 | + | 1.67873i | ||||
\(293\) | 10.8074 | + | 7.85202i | 0.631374 | + | 0.458720i | 0.856876 | − | 0.515523i | \(-0.172402\pi\) |
−0.225502 | + | 0.974243i | \(0.572402\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.839755 | − | 2.58450i | 0.0488924 | − | 0.150475i | ||||
\(296\) | 15.4480 | 0.897895 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 27.3737 | 1.58571 | ||||||||
\(299\) | 4.40602 | − | 13.5603i | 0.254807 | − | 0.784214i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.77586 | + | 5.64949i | 0.448193 | + | 0.325631i | ||||
\(302\) | −7.53220 | − | 23.1817i | −0.433430 | − | 1.33396i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.47501 | − | 2.52474i | −0.199305 | − | 0.144804i | ||||
\(305\) | −5.92788 | + | 4.30686i | −0.339430 | + | 0.246610i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.14669 | −0.179591 | −0.0897955 | − | 0.995960i | \(-0.528621\pi\) | ||||
−0.0897955 | + | 0.995960i | \(0.528621\pi\) | |||||||
\(308\) | −2.34067 | + | 10.0293i | −0.133372 | + | 0.571474i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.73870 | + | 17.6619i | −0.325936 | + | 1.00313i | ||||
\(311\) | −19.8693 | + | 14.4359i | −1.12668 | + | 0.818584i | −0.985209 | − | 0.171357i | \(-0.945185\pi\) |
−0.141476 | + | 0.989942i | \(0.545185\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.65760 | − | 20.4900i | −0.376310 | − | 1.15816i | −0.942591 | − | 0.333951i | \(-0.891618\pi\) |
0.566281 | − | 0.824213i | \(-0.308382\pi\) | |||||||
\(314\) | 2.58545 | + | 7.95721i | 0.145906 | + | 0.449051i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.20092 | + | 3.77869i | −0.292575 | + | 0.212568i | ||||
\(317\) | −2.28231 | + | 7.02424i | −0.128187 | + | 0.394520i | −0.994468 | − | 0.105037i | \(-0.966504\pi\) |
0.866281 | + | 0.499557i | \(0.166504\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.02386 | + | 16.6575i | 0.393261 | + | 0.932644i | ||||
\(320\) | 20.1389 | 1.12580 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.2726 | + | 7.46348i | −0.572469 | + | 0.415923i | ||||
\(323\) | 40.3485 | + | 29.3149i | 2.24505 | + | 1.63112i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.05261 | − | 6.31728i | −0.113858 | − | 0.350420i | ||||
\(326\) | 41.2106 | + | 29.9413i | 2.28245 | + | 1.65829i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.55236 | − | 23.2438i | 0.417010 | − | 1.28342i | ||||
\(329\) | −3.84418 | −0.211937 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.0897 | −1.15919 | −0.579597 | − | 0.814903i | \(-0.696790\pi\) | ||||
−0.579597 | + | 0.814903i | \(0.696790\pi\) | |||||||
\(332\) | −0.0424515 | + | 0.130652i | −0.00232983 | + | 0.00717048i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −25.9893 | − | 18.8823i | −1.42207 | − | 1.03319i | ||||
\(335\) | 4.58241 | + | 14.1032i | 0.250364 | + | 0.770541i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.4208 | + | 11.9304i | 0.894499 | + | 0.649892i | 0.937047 | − | 0.349203i | \(-0.113548\pi\) |
−0.0425480 | + | 0.999094i | \(0.513548\pi\) | |||||||
\(338\) | −11.9965 | + | 8.71595i | −0.652522 | + | 0.474085i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −31.6097 | −1.71428 | ||||||||
\(341\) | 13.3577 | − | 11.5558i | 0.723358 | − | 0.625782i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.309017 | + | 0.951057i | −0.0166853 | + | 0.0513522i | ||||
\(344\) | 19.4180 | − | 14.1080i | 1.04695 | − | 0.760652i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.1816 | + | 40.5687i | 0.708646 | + | 2.18099i | ||||
\(347\) | 5.07345 | + | 15.6145i | 0.272357 | + | 0.838229i | 0.989907 | + | 0.141722i | \(0.0452638\pi\) |
−0.717549 | + | 0.696508i | \(0.754736\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.9742 | − | 16.6918i | 1.22978 | − | 0.893489i | 0.232908 | − | 0.972499i | \(-0.425176\pi\) |
0.996874 | + | 0.0790098i | \(0.0251758\pi\) | |||||||
\(350\) | −1.82795 | + | 5.62586i | −0.0977082 | + | 0.300715i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −17.8219 | − | 10.7664i | −0.949910 | − | 0.573852i | ||||
\(353\) | 6.54122 | 0.348154 | 0.174077 | − | 0.984732i | \(-0.444306\pi\) | ||||
0.174077 | + | 0.984732i | \(0.444306\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.4140 | + | 9.01929i | −0.658866 | + | 0.478694i | ||||
\(356\) | −16.0351 | − | 11.6502i | −0.849861 | − | 0.617460i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.07093 | − | 9.45134i | −0.162304 | − | 0.499519i | ||||
\(359\) | −2.88567 | − | 2.09656i | −0.152300 | − | 0.110652i | 0.509026 | − | 0.860751i | \(-0.330006\pi\) |
−0.661326 | + | 0.750099i | \(0.730006\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.7972 | − | 36.3080i | 0.620905 | − | 1.91095i | ||||
\(362\) | −11.0245 | −0.579436 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.87845 | −0.412943 | ||||||||
\(365\) | −4.63259 | + | 14.2577i | −0.242481 | + | 0.746280i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.16169 | − | 3.75018i | −0.269438 | − | 0.195758i | 0.444860 | − | 0.895600i | \(-0.353254\pi\) |
−0.714297 | + | 0.699842i | \(0.753254\pi\) | |||||||
\(368\) | −0.986478 | − | 3.03607i | −0.0514237 | − | 0.158266i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 17.4521 | + | 12.6797i | 0.907294 | + | 0.659187i | ||||
\(371\) | 0.430074 | − | 0.312467i | 0.0223283 | − | 0.0162225i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.6135 | −1.27444 | −0.637218 | − | 0.770683i | \(-0.719915\pi\) | ||||
−0.637218 | + | 0.770683i | \(0.719915\pi\) | |||||||
\(374\) | 42.3064 | + | 25.5578i | 2.18761 | + | 1.32156i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.96648 | + | 9.12989i | −0.152985 | + | 0.470838i | ||||
\(377\) | −11.1881 | + | 8.12864i | −0.576217 | + | 0.418646i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.76327 | + | 30.0483i | 0.501506 | + | 1.54348i | 0.806567 | + | 0.591143i | \(0.201323\pi\) |
−0.305061 | + | 0.952333i | \(0.598677\pi\) | |||||||
\(380\) | 11.1983 | + | 34.4647i | 0.574459 | + | 1.76800i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −28.9413 | + | 21.0271i | −1.48077 | + | 1.07584i | ||||
\(383\) | −5.25906 | + | 16.1857i | −0.268725 | + | 0.827052i | 0.722086 | + | 0.691803i | \(0.243183\pi\) |
−0.990812 | + | 0.135249i | \(0.956817\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.87117 | + | 3.34898i | −0.197293 | + | 0.170680i | ||||
\(386\) | 18.8321 | 0.958531 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 33.2859 | − | 24.1836i | 1.68984 | − | 1.22774i | ||||
\(389\) | −2.19079 | − | 1.59170i | −0.111077 | − | 0.0807023i | 0.530860 | − | 0.847460i | \(-0.321869\pi\) |
−0.641937 | + | 0.766757i | \(0.721869\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.4540 | + | 35.2519i | 0.579255 | + | 1.78276i | ||||
\(392\) | 2.02029 | + | 1.46782i | 0.102040 | + | 0.0741363i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.54121 | + | 7.82103i | −0.128024 | + | 0.394018i | ||||
\(395\) | −3.19520 | −0.160768 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.9423 | −1.05106 | −0.525531 | − | 0.850774i | \(-0.676133\pi\) | ||||
−0.525531 | + | 0.850774i | \(0.676133\pi\) | |||||||
\(398\) | 3.19914 | − | 9.84595i | 0.160359 | − | 0.493533i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.20316 | − | 0.874145i | −0.0601579 | − | 0.0437073i | ||||
\(401\) | 3.93349 | + | 12.1060i | 0.196429 | + | 0.604547i | 0.999957 | + | 0.00927969i | \(0.00295386\pi\) |
−0.803528 | + | 0.595267i | \(0.797046\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.9311 | + | 7.94188i | 0.544515 | + | 0.395613i | ||||
\(404\) | −13.8941 | + | 10.0947i | −0.691258 | + | 0.502228i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.3157 | 0.611216 | ||||||||
\(407\) | −7.97153 | − | 18.9050i | −0.395134 | − | 0.937086i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.54958 | − | 7.84681i | 0.126069 | − | 0.388000i | −0.868025 | − | 0.496520i | \(-0.834611\pi\) |
0.994094 | + | 0.108520i | \(0.0346111\pi\) | |||||||
\(410\) | 27.6107 | − | 20.0604i | 1.36360 | − | 0.990711i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.42993 | + | 19.7893i | 0.316780 | + | 0.974948i | ||||
\(413\) | 0.544108 | + | 1.67459i | 0.0267738 | + | 0.0824013i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.0552388 | + | 0.0401333i | −0.00271157 | + | 0.00197007i | ||||
\(416\) | 4.92206 | − | 15.1486i | 0.241324 | − | 0.742719i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 12.8785 | − | 55.1818i | 0.629906 | − | 2.69903i | ||||
\(419\) | 5.81767 | 0.284212 | 0.142106 | − | 0.989851i | \(-0.454613\pi\) | ||||
0.142106 | + | 0.989851i | \(0.454613\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.15254 | + | 4.47008i | −0.299856 | + | 0.217858i | −0.727532 | − | 0.686074i | \(-0.759333\pi\) |
0.427675 | + | 0.903932i | \(0.359333\pi\) | |||||||
\(422\) | 2.13771 | + | 1.55314i | 0.104062 | + | 0.0756055i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.410226 | − | 1.26255i | −0.0199223 | − | 0.0613146i | ||||
\(425\) | 13.9699 | + | 10.1497i | 0.677640 | + | 0.492334i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.46709 | − | 4.51524i | 0.0709974 | − | 0.218508i | ||||
\(428\) | −17.8698 | −0.863771 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 33.5171 | 1.61634 | ||||||||
\(431\) | −7.21400 | + | 22.2024i | −0.347486 | + | 1.06945i | 0.612753 | + | 0.790274i | \(0.290062\pi\) |
−0.960239 | + | 0.279178i | \(0.909938\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.9955 | + | 7.98872i | 0.528412 | + | 0.383913i | 0.819763 | − | 0.572703i | \(-0.194105\pi\) |
−0.291352 | + | 0.956616i | \(0.594105\pi\) | |||||||
\(434\) | −3.71831 | − | 11.4438i | −0.178485 | − | 0.549319i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −34.4322 | − | 25.0165i | −1.64900 | − | 1.19807i | ||||
\(437\) | 34.3781 | − | 24.9771i | 1.64453 | − | 1.19482i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −37.4203 | −1.78597 | −0.892986 | − | 0.450084i | \(-0.851394\pi\) | ||||
−0.892986 | + | 0.450084i | \(0.851394\pi\) | |||||||
\(440\) | 4.96648 | + | 11.7783i | 0.236768 | + | 0.561510i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.6842 | + | 35.9603i | −0.555761 | + | 1.71046i | ||||
\(443\) | −23.6890 | + | 17.2111i | −1.12550 | + | 0.817723i | −0.985034 | − | 0.172363i | \(-0.944860\pi\) |
−0.140466 | + | 0.990086i | \(0.544860\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.04420 | − | 9.36908i | −0.144309 | − | 0.444137i | ||||
\(446\) | 2.74608 | + | 8.45158i | 0.130031 | + | 0.400194i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −10.5566 | + | 7.66983i | −0.498753 | + | 0.362366i | ||||
\(449\) | 1.51530 | − | 4.66362i | 0.0715115 | − | 0.220090i | −0.908913 | − | 0.416986i | \(-0.863086\pi\) |
0.980424 | + | 0.196897i | \(0.0630863\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.3426 | + | 2.75188i | −1.52295 | + | 0.129581i | ||||
\(452\) | −45.3498 | −2.13308 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 44.5272 | − | 32.3509i | 2.08977 | − | 1.51830i | ||||
\(455\) | −3.16792 | − | 2.30163i | −0.148514 | − | 0.107902i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.481305 | + | 1.48131i | 0.0225145 | + | 0.0692925i | 0.961682 | − | 0.274166i | \(-0.0884016\pi\) |
−0.939168 | + | 0.343458i | \(0.888402\pi\) | |||||||
\(458\) | −44.2866 | − | 32.1761i | −2.06938 | − | 1.50349i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.32257 | + | 25.6142i | −0.388042 | + | 1.19427i | ||||
\(461\) | 17.6580 | 0.822414 | 0.411207 | − | 0.911542i | \(-0.365107\pi\) | ||||
0.411207 | + | 0.911542i | \(0.365107\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.54726 | −0.211329 | −0.105664 | − | 0.994402i | \(-0.533697\pi\) | ||||
−0.105664 | + | 0.994402i | \(0.533697\pi\) | |||||||
\(464\) | −0.956803 | + | 2.94474i | −0.0444184 | + | 0.136706i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 51.5411 | + | 37.4468i | 2.38760 | + | 1.73469i | ||||
\(467\) | 0.631244 | + | 1.94277i | 0.0292105 | + | 0.0899007i | 0.964599 | − | 0.263721i | \(-0.0849499\pi\) |
−0.935388 | + | 0.353622i | \(0.884950\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.77323 | − | 5.64758i | −0.358935 | − | 0.260781i | ||||
\(470\) | −10.8452 | + | 7.87948i | −0.500250 | + | 0.363453i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.39701 | 0.202389 | ||||||||
\(473\) | −27.2853 | − | 16.4834i | −1.25458 | − | 0.757906i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.11739 | − | 18.8274i | 0.280685 | − | 0.863860i | ||||
\(476\) | 16.5695 | − | 12.0385i | 0.759464 | − | 0.551783i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13.0142 | − | 40.0535i | −0.595254 | − | 1.83200i | ||||
\(479\) | 2.51277 | + | 7.73350i | 0.114811 | + | 0.353353i | 0.991908 | − | 0.126962i | \(-0.0405226\pi\) |
−0.877096 | + | 0.480314i | \(0.840523\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.6976 | − | 9.22536i | 0.578962 | − | 0.420640i | ||||
\(482\) | 12.2058 | − | 37.5656i | 0.555959 | − | 1.71107i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.91512 | − | 33.8019i | 0.223415 | − | 1.53645i | ||||
\(485\) | 20.4493 | 0.928555 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.2813 | − | 16.9149i | 1.05498 | − | 0.766485i | 0.0818241 | − | 0.996647i | \(-0.473925\pi\) |
0.973152 | + | 0.230161i | \(0.0739254\pi\) | |||||||
\(488\) | −9.59152 | − | 6.96865i | −0.434188 | − | 0.315456i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.07760 | + | 3.31651i | 0.0486810 | + | 0.149825i | ||||
\(491\) | −4.28191 | − | 3.11099i | −0.193240 | − | 0.140397i | 0.486958 | − | 0.873425i | \(-0.338106\pi\) |
−0.680198 | + | 0.733028i | \(0.738106\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.1095 | − | 34.1914i | 0.500346 | − | 1.53991i | ||||
\(494\) | 43.3476 | 1.95030 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.02514 | 0.135833 | ||||||||
\(497\) | 3.07233 | − | 9.45567i | 0.137813 | − | 0.424145i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.6031 | + | 14.9690i | 0.922319 | + | 0.670104i | 0.944100 | − | 0.329659i | \(-0.106934\pi\) |
−0.0217809 | + | 0.999763i | \(0.506934\pi\) | |||||||
\(500\) | 11.2820 | + | 34.7224i | 0.504545 | + | 1.55283i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.38701 | − | 5.36698i | −0.329698 | − | 0.239540i | ||||
\(503\) | −33.9895 | + | 24.6948i | −1.51552 | + | 1.10109i | −0.551861 | + | 0.833936i | \(0.686082\pi\) |
−0.963655 | + | 0.267150i | \(0.913918\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.53588 | −0.379842 | ||||||||
\(506\) | 31.8491 | − | 27.5529i | 1.41586 | − | 1.22487i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.9602 | − | 39.8873i | 0.575014 | − | 1.76971i | ||||
\(509\) | −25.8755 | + | 18.7996i | −1.14691 | + | 0.833279i | −0.988067 | − | 0.154025i | \(-0.950776\pi\) |
−0.158843 | + | 0.987304i | \(0.550776\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.00163 | − | 9.23805i | −0.132784 | − | 0.408667i | ||||
\(512\) | −1.97873 | − | 6.08990i | −0.0874483 | − | 0.269138i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 17.7033 | − | 12.8622i | 0.780857 | − | 0.567326i | ||||
\(515\) | −3.19581 | + | 9.83570i | −0.140824 | + | 0.433413i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.7038 | − | 1.08091i | 0.558713 | − | 0.0475383i | ||||
\(518\) | −13.9773 | −0.614127 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.91097 | + | 5.74765i | −0.346919 | + | 0.252051i | ||||
\(521\) | 27.4604 | + | 19.9512i | 1.20306 | + | 0.874076i | 0.994582 | − | 0.103951i | \(-0.0331485\pi\) |
0.208480 | + | 0.978027i | \(0.433148\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.31280 | + | 16.3511i | 0.232313 | + | 0.714985i | 0.997467 | + | 0.0711373i | \(0.0226628\pi\) |
−0.765154 | + | 0.643847i | \(0.777337\pi\) | |||||||
\(524\) | 10.8093 | + | 7.85341i | 0.472206 | + | 0.343078i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.55274 | + | 10.9342i | −0.154907 | + | 0.476754i | ||||
\(527\) | −35.1250 | −1.53007 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.58133 | 0.373101 | ||||||||
\(530\) | 0.572852 | − | 1.76306i | 0.0248831 | − | 0.0765823i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −18.9958 | − | 13.8013i | −0.823574 | − | 0.598362i | ||||
\(533\) | −7.67319 | − | 23.6157i | −0.332363 | − | 1.02291i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.18545 | − | 5.22053i | −0.310654 | − | 0.225703i | ||||
\(536\) | −19.4114 | + | 14.1032i | −0.838445 | + | 0.609166i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.507492 | 0.0218796 | ||||||||
\(539\) | 0.753785 | − | 3.22983i | 0.0324678 | − | 0.139119i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.36527 | − | 7.27956i | 0.101691 | − | 0.312973i | −0.887249 | − | 0.461292i | \(-0.847386\pi\) |
0.988940 | + | 0.148319i | \(0.0473862\pi\) | |||||||
\(542\) | −44.5271 | + | 32.3509i | −1.91260 | + | 1.38959i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 12.7956 | + | 39.3807i | 0.548605 | + | 1.68843i | ||||
\(545\) | −6.53680 | − | 20.1182i | −0.280006 | − | 0.861769i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.2902 | − | 23.4602i | 1.38063 | − | 1.00308i | 0.383806 | − | 0.923414i | \(-0.374613\pi\) |
0.996821 | − | 0.0796709i | \(-0.0253869\pi\) | |||||||
\(548\) | 12.0219 | − | 36.9997i | 0.513551 | − | 1.58055i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.45892 | − | 19.1057i | 0.190129 | − | 0.814668i | ||||
\(551\) | −41.2154 | −1.75583 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.67490 | − | 1.21688i | 0.0712239 | − | 0.0517472i | ||||
\(554\) | −31.9887 | − | 23.2411i | −1.35907 | − | 0.987421i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.7723 | + | 33.1539i | 0.456849 | + | 1.40604i | ||||
\(557\) | 14.0186 | + | 10.1851i | 0.593989 | + | 0.431558i | 0.843740 | − | 0.536752i | \(-0.180349\pi\) |
−0.249751 | + | 0.968310i | \(0.580349\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.53567 | − | 23.1924i | 0.318725 | − | 0.980934i | ||||
\(560\) | −0.876713 | −0.0370479 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 32.4346 | 1.36817 | ||||||||
\(563\) | −11.3506 | + | 34.9334i | −0.478369 | + | 1.47227i | 0.362991 | + | 0.931793i | \(0.381756\pi\) |
−0.841360 | + | 0.540476i | \(0.818244\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.2351 | − | 13.2486i | −0.767158 | − | 0.557373i | ||||
\(566\) | −19.5538 | − | 60.1806i | −0.821909 | − | 2.52958i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −20.0863 | − | 14.5935i | −0.842801 | − | 0.612331i | ||||
\(569\) | 25.0590 | − | 18.2064i | 1.05053 | − | 0.763252i | 0.0782135 | − | 0.996937i | \(-0.475078\pi\) |
0.972312 | + | 0.233685i | \(0.0750784\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.7450 | 1.11925 | 0.559623 | − | 0.828748i | \(-0.310946\pi\) | ||||
0.559623 | + | 0.828748i | \(0.310946\pi\) | |||||||
\(572\) | 26.0358 | − | 2.21526i | 1.08861 | − | 0.0926249i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.83337 | + | 21.0309i | −0.285219 | + | 0.877814i | ||||
\(575\) | 11.9028 | − | 8.64787i | 0.496380 | − | 0.360641i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.47227 | − | 29.1526i | −0.394336 | − | 1.21364i | −0.929478 | − | 0.368878i | \(-0.879742\pi\) |
0.535142 | − | 0.844762i | \(-0.320258\pi\) | |||||||
\(578\) | −18.5050 | − | 56.9524i | −0.769705 | − | 2.36891i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 21.1333 | − | 15.3543i | 0.877514 | − | 0.637551i | ||||
\(581\) | 0.0136710 | − | 0.0420751i | 0.000567170 | − | 0.00174557i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.33340 | + | 1.15353i | −0.0552237 | + | 0.0477744i | ||||
\(584\) | −24.2566 | −1.00374 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24.4190 | + | 17.7414i | −1.00874 | + | 0.732892i | ||||
\(587\) | −13.4594 | − | 9.77880i | −0.555528 | − | 0.403614i | 0.274292 | − | 0.961647i | \(-0.411557\pi\) |
−0.829819 | + | 0.558032i | \(0.811557\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.4436 | + | 38.2976i | 0.512731 | + | 1.57802i | ||||
\(590\) | 4.96747 | + | 3.60908i | 0.204507 | + | 0.148583i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.08590 | − | 3.34204i | 0.0446300 | − | 0.137357i | ||||
\(593\) | 37.7740 | 1.55119 | 0.775596 | − | 0.631230i | \(-0.217450\pi\) | ||||
0.775596 | + | 0.631230i | \(0.217450\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.1795 | 0.417321 | ||||||||
\(596\) | −11.6252 | + | 35.7787i | −0.476186 | + | 1.46555i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 26.0633 | + | 18.9361i | 1.06581 | + | 0.774353i | ||||
\(599\) | −7.74200 | − | 23.8274i | −0.316330 | − | 0.973562i | −0.975204 | − | 0.221309i | \(-0.928967\pi\) |
0.658874 | − | 0.752253i | \(-0.271033\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.7268 | + | 25.2305i | 1.41654 | + | 1.02917i | 0.992331 | + | 0.123607i | \(0.0394463\pi\) |
0.424205 | + | 0.905566i | \(0.360554\pi\) | |||||||
\(602\) | −17.5694 | + | 12.7649i | −0.716073 | + | 0.520258i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 33.4985 | 1.36303 | ||||||||
\(605\) | 11.8513 | − | 12.1558i | 0.481825 | − | 0.494204i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.69740 | − | 8.30174i | 0.109484 | − | 0.336957i | −0.881273 | − | 0.472608i | \(-0.843313\pi\) |
0.990757 | + | 0.135651i | \(0.0433126\pi\) | |||||||
\(608\) | 38.4045 | − | 27.9025i | 1.55751 | − | 1.13160i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.11601 | − | 15.7455i | −0.207141 | − | 0.637515i | ||||
\(611\) | 3.01394 | + | 9.27596i | 0.121931 | + | 0.375265i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.11370 | + | 5.16840i | −0.287319 | + | 0.208750i | −0.722104 | − | 0.691785i | \(-0.756825\pi\) |
0.434784 | + | 0.900535i | \(0.356825\pi\) | |||||||
\(614\) | 2.19707 | − | 6.76188i | 0.0886664 | − | 0.272887i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.08913 | − | 4.28263i | −0.285629 | − | 0.172552i | ||||
\(617\) | −8.31423 | −0.334718 | −0.167359 | − | 0.985896i | \(-0.553524\pi\) | ||||
−0.167359 | + | 0.985896i | \(0.553524\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.90794 | + | 1.38620i | −0.0766866 | + | 0.0557161i | −0.625468 | − | 0.780250i | \(-0.715092\pi\) |
0.548781 | + | 0.835966i | \(0.315092\pi\) | |||||||
\(620\) | −20.6478 | − | 15.0015i | −0.829235 | − | 0.602475i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −17.1480 | − | 52.7762i | −0.687574 | − | 2.11613i | ||||
\(623\) | 5.16393 | + | 3.75182i | 0.206889 | + | 0.150313i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.56231 | + | 4.80828i | −0.0624922 | + | 0.192331i | ||||
\(626\) | 48.6791 | 1.94561 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.4985 | −0.458838 | ||||||||
\(629\) | −12.6084 | + | 38.8046i | −0.502729 | + | 1.54724i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.6274 | − | 23.7052i | −1.29888 | − | 0.943689i | −0.298932 | − | 0.954274i | \(-0.596631\pi\) |
−0.999944 | + | 0.0105854i | \(0.996631\pi\) | |||||||
\(632\) | −1.59760 | − | 4.91691i | −0.0635492 | − | 0.195584i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.5007 | − | 9.80886i | −0.536183 | − | 0.389560i | ||||
\(635\) | 16.8640 | − | 12.2524i | 0.669228 | − | 0.486223i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.53716 | 0.100526 | ||||||||
\(638\) | −40.6994 | + | 3.46292i | −1.61130 | + | 0.137098i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.07307 | + | 24.8463i | −0.319116 | + | 0.982138i | ||||
\(641\) | −10.2731 | + | 7.46384i | −0.405763 | + | 0.294804i | −0.771884 | − | 0.635763i | \(-0.780686\pi\) |
0.366121 | + | 0.930567i | \(0.380686\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.55209 | + | 14.0099i | 0.179517 | + | 0.552497i | 0.999811 | − | 0.0194456i | \(-0.00619011\pi\) |
−0.820294 | + | 0.571942i | \(0.806190\pi\) | |||||||
\(644\) | −5.39250 | − | 16.5964i | −0.212494 | − | 0.653990i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −91.1663 | + | 66.2362i | −3.58689 | + | 2.60603i | ||||
\(647\) | −1.43416 | + | 4.41390i | −0.0563828 | + | 0.173528i | −0.975282 | − | 0.220964i | \(-0.929080\pi\) |
0.918899 | + | 0.394493i | \(0.129080\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.26897 | − | 5.38100i | −0.0890647 | − | 0.211223i | ||||
\(650\) | 15.0083 | 0.588673 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −56.6362 | + | 41.1486i | −2.21805 | + | 1.61150i | ||||
\(653\) | 18.5028 | + | 13.4431i | 0.724071 | + | 0.526068i | 0.887682 | − | 0.460457i | \(-0.152314\pi\) |
−0.163611 | + | 0.986525i | \(0.552314\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.05209 | + | 6.31570i | 0.0801820 | + | 0.246775i | ||||
\(656\) | −4.49772 | − | 3.26779i | −0.175606 | − | 0.127586i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.68407 | − | 8.26071i | 0.104636 | − | 0.322036i | ||||
\(659\) | 17.8597 | 0.695717 | 0.347858 | − | 0.937547i | \(-0.386909\pi\) | ||||
0.347858 | + | 0.937547i | \(0.386909\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.7110 | −0.727774 | −0.363887 | − | 0.931443i | \(-0.618551\pi\) | ||||
−0.363887 | + | 0.931443i | \(0.618551\pi\) | |||||||
\(662\) | 14.7251 | − | 45.3193i | 0.572309 | − | 1.76139i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.0893782 | − | 0.0649371i | −0.00346855 | − | 0.00252005i | ||||
\(665\) | −3.60628 | − | 11.0990i | −0.139845 | − | 0.430400i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.7813 | − | 18.0046i | −0.959534 | − | 0.697142i | ||||
\(668\) | 35.7173 | − | 25.9502i | 1.38195 | − | 1.00404i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −33.5057 | −1.29444 | ||||||||
\(671\) | −3.57867 | + | 15.3340i | −0.138153 | + | 0.591961i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.21223 | − | 6.80855i | 0.0852753 | − | 0.262450i | −0.899322 | − | 0.437287i | \(-0.855940\pi\) |
0.984598 | + | 0.174836i | \(0.0559395\pi\) | |||||||
\(674\) | −37.1024 | + | 26.9565i | −1.42913 | + | 1.03832i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.29743 | − | 19.3815i | −0.242209 | − | 0.745442i | ||||
\(677\) | −7.10903 | − | 21.8793i | −0.273222 | − | 0.840892i | −0.989684 | − | 0.143265i | \(-0.954240\pi\) |
0.716462 | − | 0.697626i | \(-0.245760\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.7193 | + | 7.78806i | −0.411371 | + | 0.298878i | ||||
\(680\) | 7.85536 | − | 24.1763i | 0.301239 | − | 0.927120i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 15.5056 | + | 36.7726i | 0.593740 | + | 1.40809i | ||||
\(683\) | −18.0889 | −0.692152 | −0.346076 | − | 0.938206i | \(-0.612486\pi\) | ||||
−0.346076 | + | 0.938206i | \(0.612486\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.6432 | − | 11.3654i | 0.597695 | − | 0.434251i | ||||
\(686\) | −1.82795 | − | 1.32808i | −0.0697915 | − | 0.0507065i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.68719 | − | 5.19262i | −0.0643234 | − | 0.197967i | ||||
\(689\) | −1.09117 | − | 0.792780i | −0.0415702 | − | 0.0302025i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.24611 | + | 25.3789i | −0.313697 | + | 0.965459i | 0.662591 | + | 0.748982i | \(0.269457\pi\) |
−0.976288 | + | 0.216478i | \(0.930543\pi\) | |||||||
\(692\) | −58.6232 | −2.22852 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −37.0961 | −1.40815 | ||||||||
\(695\) | −5.35409 | + | 16.4782i | −0.203092 | + | 0.625054i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 52.2232 | + | 37.9424i | 1.97810 | + | 1.43717i | ||||
\(698\) | 19.8277 | + | 61.0234i | 0.750490 | + | 2.30977i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.57696 | − | 4.77844i | −0.248586 | − | 0.180608i | ||||
\(701\) | 11.5341 | − | 8.38001i | 0.435637 | − | 0.316509i | −0.348262 | − | 0.937397i | \(-0.613228\pi\) |
0.783899 | + | 0.620889i | \(0.213228\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 46.7762 | 1.76420 | ||||||||
\(704\) | 32.7297 | − | 28.3147i | 1.23355 | − | 1.06715i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.56718 | + | 14.0563i | −0.171888 | + | 0.529017i | ||||
\(707\) | 4.47444 | − | 3.25087i | 0.168279 | − | 0.122261i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.96231 | + | 15.2724i | 0.186364 | + | 0.573568i | 0.999969 | − | 0.00784897i | \(-0.00249843\pi\) |
−0.813606 | + | 0.581417i | \(0.802498\pi\) | |||||||
\(710\) | −10.7138 | − | 32.9737i | −0.402082 | − | 1.23748i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.8954 | − | 9.36908i | 0.483277 | − | 0.351121i | ||||
\(713\) | −9.24812 | + | 28.4628i | −0.346345 | + | 1.06594i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.1161 | + | 6.71540i | 0.415720 | + | 0.251142i | ||||
\(716\) | 13.6575 | 0.510406 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.52009 | − | 4.73713i | 0.243328 | − | 0.176788i | ||||
\(719\) | 29.9838 | + | 21.7845i | 1.11821 | + | 0.812426i | 0.983937 | − | 0.178519i | \(-0.0571305\pi\) |
0.134272 | + | 0.990945i | \(0.457131\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.07068 | − | 6.37291i | −0.0771163 | − | 0.237340i | ||||
\(722\) | 69.7848 | + | 50.7016i | 2.59712 | + | 1.88692i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.68195 | − | 14.4096i | 0.174003 | − | 0.535527i | ||||
\(725\) | −14.2701 | −0.529977 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.6597 | 0.543698 | 0.271849 | − | 0.962340i | \(-0.412365\pi\) | ||||
0.271849 | + | 0.962340i | \(0.412365\pi\) | |||||||
\(728\) | 1.95788 | − | 6.02574i | 0.0725639 | − | 0.223329i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −27.4035 | − | 19.9098i | −1.01425 | − | 0.736896i | ||||
\(731\) | 19.5900 | + | 60.2918i | 0.724562 | + | 2.22997i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.4255 | + | 17.0196i | 0.865240 | + | 0.628633i | 0.929305 | − | 0.369312i | \(-0.120407\pi\) |
−0.0640657 | + | 0.997946i | \(0.520407\pi\) | |||||||
\(734\) | 11.6627 | − | 8.47344i | 0.430478 | − | 0.312760i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 35.2802 | 1.30045 | ||||||||
\(737\) | 27.2761 | + | 16.4778i | 1.00473 | + | 0.606968i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.60786 | − | 8.02617i | 0.0959317 | − | 0.295247i | −0.891564 | − | 0.452895i | \(-0.850391\pi\) |
0.987495 | + | 0.157648i | \(0.0503911\pi\) | |||||||
\(740\) | −23.9847 | + | 17.4259i | −0.881694 | + | 0.640588i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.371172 | + | 1.14235i | 0.0136261 | + | 0.0419370i | ||||
\(743\) | −14.7531 | − | 45.4054i | −0.541239 | − | 1.66576i | −0.729768 | − | 0.683694i | \(-0.760372\pi\) |
0.188530 | − | 0.982067i | \(-0.439628\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.1269 | + | 10.9904i | −0.554208 | + | 0.402656i | ||||
\(746\) | 17.1855 | − | 52.8915i | 0.629206 | − | 1.93650i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −51.3721 | + | 44.4424i | −1.87835 | + | 1.62497i | ||||
\(749\) | 5.75478 | 0.210275 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.753694 | − | 0.547591i | 0.0275027 | − | 0.0199819i | −0.573949 | − | 0.818891i | \(-0.694589\pi\) |
0.601452 | + | 0.798909i | \(0.294589\pi\) | |||||||
\(752\) | 1.76665 | + | 1.28355i | 0.0644232 | + | 0.0468062i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.65581 | − | 29.7175i | −0.351644 | − | 1.08225i | ||||
\(755\) | 13.4697 | + | 9.78631i | 0.490213 | + | 0.356160i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.91728 | + | 15.1338i | −0.178722 | + | 0.550049i | −0.999784 | − | 0.0207901i | \(-0.993382\pi\) |
0.821062 | + | 0.570839i | \(0.193382\pi\) | |||||||
\(758\) | −71.3872 | −2.59290 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −29.1428 | −1.05712 | ||||||||
\(761\) | −0.0685939 | + | 0.211110i | −0.00248653 | + | 0.00765274i | −0.952292 | − | 0.305188i | \(-0.901281\pi\) |
0.949806 | + | 0.312841i | \(0.101281\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.0885 | + | 8.05626i | 0.401430 | + | 0.291656i | ||||
\(764\) | −15.1925 | − | 46.7576i | −0.549644 | − | 1.69163i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −31.1093 | − | 22.6022i | −1.12403 | − | 0.816652i | ||||
\(767\) | 3.61417 | − | 2.62585i | 0.130500 | − | 0.0948139i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.0307 | −1.58779 | −0.793894 | − | 0.608056i | \(-0.791949\pi\) | ||||
−0.793894 | + | 0.608056i | \(0.791949\pi\) | |||||||
\(770\) | −4.49366 | − | 10.6570i | −0.161940 | − | 0.384052i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.99773 | + | 24.6145i | −0.287845 | + | 0.885895i | ||||
\(773\) | −35.9008 | + | 26.0835i | −1.29126 | + | 0.938158i | −0.999830 | − | 0.0184332i | \(-0.994132\pi\) |
−0.291433 | + | 0.956591i | \(0.594132\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.30838 | + | 13.2598i | 0.154761 | + | 0.476307i | ||||
\(776\) | 10.2246 | + | 31.4682i | 0.367043 | + | 1.12964i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.95002 | − | 3.59640i | 0.177467 | − | 0.128937i | ||||
\(779\) | 22.8684 | − | 70.3818i | 0.819346 | − | 2.52169i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.49435 | + | 32.1119i | −0.268169 | + | 1.14905i | ||||
\(782\) | −83.7497 | −2.99488 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.459565 | − | 0.333894i | 0.0164130 | − | 0.0119248i | ||||
\(785\) | −4.62352 | − | 3.35918i | −0.165020 | − | 0.119894i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.32459 | − | 16.3874i | −0.189801 | − | 0.584148i | 0.810197 | − | 0.586158i | \(-0.199360\pi\) |
−0.999998 | + | 0.00200988i | \(0.999360\pi\) | |||||||
\(788\) | −9.14324 | − | 6.64296i | −0.325715 | − | 0.236645i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.23094 | − | 6.86613i | 0.0793733 | − | 0.244286i | ||||
\(791\) | 14.6044 | 0.519272 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.0454 | −0.427746 | ||||||||
\(794\) | 14.6222 | − | 45.0025i | 0.518923 | − | 1.59708i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.5105 | + | 8.36287i | 0.407979 | + | 0.296414i | ||||
\(797\) | −10.1146 | − | 31.1294i | −0.358276 | − | 1.10266i | −0.954085 | − | 0.299535i | \(-0.903168\pi\) |
0.595809 | − | 0.803126i | \(-0.296832\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.5127 | − | 14.9033i | −0.725686 | − | 0.527242i | ||||
\(800\) | 13.2969 | − | 9.66074i | 0.470115 | − | 0.341559i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −28.7609 | −1.01558 | ||||||||
\(803\) | 12.5170 | + | 29.6848i | 0.441715 | + | 1.04756i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.68019 | − | 8.24877i | 0.0944642 | − | 0.290731i | ||||
\(806\) | −24.6984 | + | 17.9445i | −0.869965 | + | 0.632067i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.26794 | − | 13.1354i | −0.150146 | − | 0.462101i | ||||
\(809\) | −11.4251 | − | 35.1629i | −0.401686 | − | 1.23626i | −0.923631 | − | 0.383283i | \(-0.874793\pi\) |
0.521945 | − | 0.852979i | \(-0.325207\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.3164 | − | 9.67497i | 0.467604 | − | 0.339734i | −0.328903 | − | 0.944364i | \(-0.606679\pi\) |
0.796507 | + | 0.604630i | \(0.206679\pi\) | |||||||
\(812\) | −5.23028 | + | 16.0971i | −0.183547 | + | 0.564899i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 46.1906 | − | 3.93014i | 1.61898 | − | 0.137751i | ||||
\(815\) | −34.7946 | −1.21880 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 58.7973 | − | 42.7187i | 2.05706 | − | 1.49454i | ||||
\(818\) | 15.0818 | + | 10.9575i | 0.527321 | + | 0.383121i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14.4940 | + | 44.6079i | 0.506152 | + | 1.55777i | ||||
\(821\) | −6.05473 | − | 4.39902i | −0.211312 | − | 0.153527i | 0.477095 | − | 0.878852i | \(-0.341690\pi\) |
−0.688407 | + | 0.725325i | \(0.741690\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.7159 | + | 45.2909i | −0.512965 | + | 1.57874i | 0.273990 | + | 0.961733i | \(0.411656\pi\) |
−0.786955 | + | 0.617011i | \(0.788344\pi\) | |||||||
\(824\) | −16.7335 | −0.582939 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.97841 | −0.138427 | ||||||||
\(827\) | −11.6888 | + | 35.9745i | −0.406460 | + | 1.25095i | 0.513210 | + | 0.858263i | \(0.328456\pi\) |
−0.919670 | + | 0.392692i | \(0.871544\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.07270 | + | 3.68554i | 0.176182 | + | 0.128004i | 0.672382 | − | 0.740205i | \(-0.265271\pi\) |
−0.496199 | + | 0.868209i | \(0.665271\pi\) | |||||||
\(830\) | −0.0476734 | − | 0.146724i | −0.00165477 | − | 0.00509285i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 26.7839 | + | 19.4596i | 0.928564 | + | 0.674641i | ||||
\(833\) | −5.33603 | + | 3.87685i | −0.184883 | + | 0.134325i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.9431 | 0.759371 | ||||||||
\(836\) | 66.6559 | + | 40.2676i | 2.30534 | + | 1.39269i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.06199 | + | 12.5015i | −0.140319 | + | 0.431858i | ||||
\(839\) | −11.2286 | + | 8.15804i | −0.387654 | + | 0.281647i | −0.764493 | − | 0.644632i | \(-0.777011\pi\) |
0.376840 | + | 0.926279i | \(0.377011\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.219362 | + | 0.675127i | 0.00756421 | + | 0.0232802i | ||||
\(842\) | −5.30990 | − | 16.3422i | −0.182991 | − | 0.563189i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.93788 | + | 2.13449i | −0.101126 | + | 0.0734723i | ||||
\(845\) | 3.12996 | − | 9.63303i | 0.107674 | − | 0.331386i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.58286 | + | 10.8855i | −0.0543877 | + | 0.374031i | ||||
\(848\) | −0.301978 | −0.0103700 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −31.5646 | + | 22.9331i | −1.08266 | + | 0.786597i | ||||
\(851\) | 28.1248 | + | 20.4338i | 0.964105 | + | 0.700463i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.86783 | − | 24.2147i | −0.269389 | − | 0.829095i | −0.990650 | − | 0.136431i | \(-0.956437\pi\) |
0.721260 | − | 0.692664i | \(-0.243563\pi\) | |||||||
\(854\) | 8.67839 | + | 6.30522i | 0.296968 | + | 0.215760i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.44085 | − | 13.6675i | 0.151785 | − | 0.467147i | ||||
\(857\) | −50.8757 | −1.73788 | −0.868941 | − | 0.494916i | \(-0.835199\pi\) | ||||
−0.868941 | + | 0.494916i | \(0.835199\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.2976 | −1.27258 | −0.636288 | − | 0.771452i | \(-0.719531\pi\) | ||||
−0.636288 | + | 0.771452i | \(0.719531\pi\) | |||||||
\(860\) | −14.2342 | + | 43.8084i | −0.485382 | + | 1.49385i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −42.6735 | − | 31.0041i | −1.45347 | − | 1.05600i | ||||
\(863\) | −3.97930 | − | 12.2470i | −0.135457 | − | 0.416893i | 0.860204 | − | 0.509950i | \(-0.170336\pi\) |
−0.995661 | + | 0.0930569i | \(0.970336\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.5724 | − | 17.1263i | −0.801484 | − | 0.582312i | ||||
\(866\) | −24.8441 | + | 18.0503i | −0.844237 | + | 0.613374i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.5367 | 0.561291 | ||||||||
\(869\) | −5.19284 | + | 4.49237i | −0.176155 | + | 0.152393i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.53312 | + | 23.1846i | −0.255250 | + | 0.785579i | ||||
\(872\) | 27.6903 | − | 20.1182i | 0.937713 | − | 0.681288i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 29.6697 | + | 91.3140i | 1.00359 | + | 3.08874i | ||||
\(875\) | −3.63323 | − | 11.1819i | −0.122826 | − | 0.378018i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.74591 | − | 6.35428i | 0.295328 | − | 0.214569i | −0.430247 | − | 0.902711i | \(-0.641574\pi\) |
0.725576 | + | 0.688142i | \(0.241574\pi\) | |||||||
\(878\) | 26.1274 | − | 80.4119i | 0.881758 | − | 2.71377i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.89726 | − | 0.246514i | 0.0976666 | − | 0.00831000i | ||||
\(881\) | −19.9303 | −0.671467 | −0.335734 | − | 0.941957i | \(-0.608984\pi\) | ||||
−0.335734 | + | 0.941957i | \(0.608984\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.9722 | − | 15.9637i | 0.739422 | − | 0.537221i | −0.153108 | − | 0.988209i | \(-0.548928\pi\) |
0.892530 | + | 0.450988i | \(0.148928\pi\) | |||||||
\(884\) | −42.0397 | − | 30.5436i | −1.41395 | − | 1.02729i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.4446 | − | 62.9221i | −0.686850 | − | 2.11391i | ||||
\(887\) | 5.15401 | + | 3.74461i | 0.173055 | + | 0.125732i | 0.670941 | − | 0.741511i | \(-0.265890\pi\) |
−0.497886 | + | 0.867242i | \(0.665890\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.17367 | + | 12.8452i | −0.139980 | + | 0.430815i | ||||
\(890\) | 22.2586 | 0.746110 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.2128 | −0.408916 | ||||||||
\(893\) | −8.98245 | + | 27.6451i | −0.300586 | + | 0.925110i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.49168 | + | 3.98994i | 0.183567 | + | 0.133369i | ||||
\(896\) | −5.23083 | − | 16.0988i | −0.174750 | − | 0.537825i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.96358 | + | 6.51242i | 0.299118 | + | 0.217322i | ||||
\(899\) | 23.4836 | − | 17.0618i | 0.783221 | − | 0.569043i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.50628 | 0.116811 | ||||||||
\(902\) | 16.6686 | − | 71.4220i | 0.555005 | − | 2.37809i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.2699 | − | 34.6853i | 0.374832 | − | 1.15362i | ||||
\(905\) | 6.09225 | − | 4.42628i | 0.202513 | − | 0.147135i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.47376 | − | 10.6911i | −0.115344 | − | 0.354993i | 0.876674 | − | 0.481084i | \(-0.159757\pi\) |
−0.992019 | + | 0.126091i | \(0.959757\pi\) | |||||||
\(908\) | 23.3741 | + | 71.9382i | 0.775698 | + | 2.38735i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.15783 | − | 5.20047i | 0.237280 | − | 0.172394i | ||||
\(911\) | −9.99054 | + | 30.7477i | −0.331001 | + | 1.01872i | 0.637657 | + | 0.770321i | \(0.279904\pi\) |
−0.968658 | + | 0.248397i | \(0.920096\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.0333477 | + | 0.142889i | −0.00110365 | + | 0.00472893i | ||||
\(914\) | −3.51921 | −0.116405 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 60.8636 | − | 44.2200i | 2.01099 | − | 1.46107i | ||||
\(917\) | −3.48101 | − | 2.52910i | −0.114953 | − | 0.0835182i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.24659 | − | 16.1473i | −0.173069 | − | 0.532651i | 0.826471 | − | 0.562979i | \(-0.190345\pi\) |
−0.999540 | + | 0.0303279i | \(0.990345\pi\) | |||||||
\(920\) | −17.5225 | − | 12.7308i | −0.577700 | − | 0.419723i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.3291 | + | 37.9450i | −0.406037 | + | 1.24965i | ||||
\(923\) | −25.2252 | −0.830298 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.1954 | 0.532501 | ||||||||
\(926\) | 3.17497 | − | 9.77154i | 0.104336 | − | 0.321113i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −27.6837 | − | 20.1134i | −0.908762 | − | 0.660254i | ||||
\(929\) | 2.19807 | + | 6.76495i | 0.0721162 | + | 0.221951i | 0.980618 | − | 0.195931i | \(-0.0627727\pi\) |
−0.908502 | + | 0.417881i | \(0.862773\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.11739 | + | 4.44455i | 0.200489 | + | 0.145664i | ||||
\(932\) | −70.8335 | + | 51.4636i | −2.32023 | + | 1.68575i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.61554 | −0.151025 | ||||||||
\(935\) | −33.6402 | + | 2.86229i | −1.10015 | + | 0.0936068i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.83045 | − | 14.8666i | 0.157804 | − | 0.485671i | −0.840630 | − | 0.541610i | \(-0.817815\pi\) |
0.998434 | + | 0.0559386i | \(0.0178151\pi\) | |||||||
\(938\) | 17.5634 | − | 12.7606i | 0.573466 | − | 0.416647i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.69307 | − | 17.5215i | −0.185687 | − | 0.571487i | ||||
\(941\) | −1.56074 | − | 4.80345i | −0.0508785 | − | 0.156588i | 0.922389 | − | 0.386262i | \(-0.126234\pi\) |
−0.973268 | + | 0.229674i | \(0.926234\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44.4957 | − | 32.3280i | 1.44898 | − | 1.05275i | ||||
\(944\) | 0.309083 | − | 0.951258i | 0.0100598 | − | 0.0309608i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 54.4719 | − | 47.1241i | 1.77104 | − | 1.53214i | ||||
\(947\) | 20.3081 | 0.659925 | 0.329963 | − | 0.943994i | \(-0.392964\pi\) | ||||
0.329963 | + | 0.943994i | \(0.392964\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.9379 | + | 14.4858i | −0.647213 | + | 0.470228i | ||||
\(950\) | 36.1867 | + | 26.2912i | 1.17405 | + | 0.852998i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.08977 | + | 15.6647i | 0.164961 | + | 0.507696i | ||||
\(953\) | 23.7390 | + | 17.2474i | 0.768983 | + | 0.558699i | 0.901652 | − | 0.432462i | \(-0.142355\pi\) |
−0.132670 | + | 0.991160i | \(0.542355\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.55098 | − | 23.2395i | 0.244344 | − | 0.752014i | ||||
\(956\) | 57.8787 | 1.87193 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −18.3729 | −0.593600 | ||||||||
\(959\) | −3.87152 | + | 11.9153i | −0.125018 | + | 0.384766i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.13550 | + | 1.55153i | 0.0688871 | + | 0.0500494i | ||||
\(962\) | 10.9586 | + | 33.7270i | 0.353319 | + | 1.08740i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 43.9164 | + | 31.9071i | 1.41445 | + | 1.02766i | ||||
\(965\) | −10.4068 | + | 7.56099i | −0.335007 | + | 0.243397i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.2155 | 1.13245 | 0.566227 | − | 0.824249i | \(-0.308402\pi\) | ||||
0.566227 | + | 0.824249i | \(0.308402\pi\) | |||||||
\(968\) | 24.6315 | + | 12.1594i | 0.791688 | + | 0.390819i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.2780 | + | 43.9432i | −0.458439 | + | 1.41093i | ||||
\(971\) | 3.99064 | − | 2.89937i | 0.128066 | − | 0.0930452i | −0.521908 | − | 0.853002i | \(-0.674780\pi\) |
0.649974 | + | 0.759956i | \(0.274780\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.46911 | − | 10.6768i | −0.111215 | − | 0.342283i | ||||
\(974\) | 20.0927 | + | 61.8391i | 0.643813 | + | 1.98145i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.18183 | + | 1.58519i | −0.0698388 | + | 0.0507409i | ||||
\(977\) | −9.37271 | + | 28.8462i | −0.299860 | + | 0.922873i | 0.681686 | + | 0.731645i | \(0.261247\pi\) |
−0.981546 | + | 0.191228i | \(0.938753\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.1201 | − | 10.9466i | −0.579121 | − | 0.349854i | ||||
\(980\) | −4.79248 | −0.153090 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.67487 | − | 7.02920i | 0.308737 | − | 0.224311i | ||||
\(983\) | −32.9851 | − | 23.9650i | −1.05206 | − | 0.764366i | −0.0794567 | − | 0.996838i | \(-0.525319\pi\) |
−0.972603 | + | 0.232472i | \(0.925319\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.73580 | − | 5.34225i | −0.0553073 | − | 0.170218i | ||||
\(986\) | 65.7167 | + | 47.7460i | 2.09285 | + | 1.52054i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −18.4091 | + | 56.6573i | −0.585671 | + | 1.80251i | ||||
\(989\) | 54.0140 | 1.71754 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.0927 | 0.352370 | 0.176185 | − | 0.984357i | \(-0.443624\pi\) | ||||
0.176185 | + | 0.984357i | \(0.443624\pi\) | |||||||
\(992\) | −10.3313 | + | 31.7964i | −0.328019 | + | 1.00954i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 18.1740 | + | 13.2042i | 0.576445 | + | 0.418812i | ||||
\(995\) | 2.18522 | + | 6.72540i | 0.0692760 | + | 0.213210i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.2921 | + | 15.4696i | 0.674328 | + | 0.489928i | 0.871471 | − | 0.490447i | \(-0.163166\pi\) |
−0.197143 | + | 0.980375i | \(0.563166\pi\) | |||||||
\(998\) | −46.5520 | + | 33.8220i | −1.47358 | + | 1.07062i | ||||
\(999\) | 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 | 693.2.m.h.64.1 | ✓ | 16 | |
3.2 | odd | 2 | inner | 693.2.m.h.64.4 | yes | 16 | |
11.4 | even | 5 | 7623.2.a.cu.1.1 | 8 | |||
11.5 | even | 5 | inner | 693.2.m.h.379.1 | yes | 16 | |
11.7 | odd | 10 | 7623.2.a.cv.1.8 | 8 | |||
33.5 | odd | 10 | inner | 693.2.m.h.379.4 | yes | 16 | |
33.26 | odd | 10 | 7623.2.a.cu.1.8 | 8 | |||
33.29 | even | 10 | 7623.2.a.cv.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
693.2.m.h.64.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
693.2.m.h.64.4 | yes | 16 | 3.2 | odd | 2 | inner | |
693.2.m.h.379.1 | yes | 16 | 11.5 | even | 5 | inner | |
693.2.m.h.379.4 | yes | 16 | 33.5 | odd | 10 | inner | |
7623.2.a.cu.1.1 | 8 | 11.4 | even | 5 | |||
7623.2.a.cu.1.8 | 8 | 33.26 | odd | 10 | |||
7623.2.a.cv.1.1 | 8 | 33.29 | even | 10 | |||
7623.2.a.cv.1.8 | 8 | 11.7 | odd | 10 |