Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,4,Mod(55,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.55");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.g (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.90322347067\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 52 x^{14} + 1899 x^{12} + 33440 x^{10} + 424113 x^{8} + 2869882 x^{6} + 13705540 x^{4} + \cdots + 24920064 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 55.5 | ||
Root | \(0.643348 + 1.11431i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.55 |
Dual form | 117.4.g.f.100.5 |
$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.643348 | + | 1.11431i | 0.227458 | + | 0.393969i | 0.957054 | − | 0.289910i | \(-0.0936253\pi\) |
−0.729596 | + | 0.683878i | \(0.760292\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.17221 | − | 5.49442i | 0.396526 | − | 0.686803i | ||||
\(5\) | −12.4484 | −1.11342 | −0.556710 | − | 0.830707i | \(-0.687937\pi\) | ||||
−0.556710 | + | 0.830707i | \(0.687937\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.50137 | − | 7.79659i | 0.243051 | − | 0.420977i | −0.718531 | − | 0.695495i | \(-0.755185\pi\) |
0.961582 | + | 0.274519i | \(0.0885185\pi\) | |||||||
\(8\) | 18.4569 | 0.815687 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.00866 | − | 13.8714i | −0.253256 | − | 0.438653i | ||||
\(11\) | −25.5387 | − | 44.2343i | −0.700019 | − | 1.21247i | −0.968459 | − | 0.249172i | \(-0.919841\pi\) |
0.268440 | − | 0.963296i | \(-0.413492\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.33646 | − | 46.8139i | 0.0498475 | − | 0.998757i | ||||
\(14\) | 11.5838 | 0.221135 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −13.5034 | − | 23.3886i | −0.210991 | − | 0.365448i | ||||
\(17\) | −3.43100 | + | 5.94266i | −0.0489493 | + | 0.0847827i | −0.889462 | − | 0.457009i | \(-0.848921\pi\) |
0.840513 | + | 0.541792i | \(0.182254\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 41.5585 | − | 71.9815i | 0.501799 | − | 0.869141i | −0.498199 | − | 0.867063i | \(-0.666005\pi\) |
0.999998 | − | 0.00207845i | \(-0.000661591\pi\) | |||||||
\(20\) | −39.4890 | + | 68.3969i | −0.441500 | + | 0.764700i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 32.8606 | − | 56.9162i | 0.318450 | − | 0.551571i | ||||
\(23\) | 93.7893 | + | 162.448i | 0.850279 | + | 1.47273i | 0.880957 | + | 0.473197i | \(0.156900\pi\) |
−0.0306776 | + | 0.999529i | \(0.509767\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 29.9631 | 0.239705 | ||||||||
\(26\) | 53.6684 | − | 27.5141i | 0.404817 | − | 0.207537i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −28.5585 | − | 49.4648i | −0.192752 | − | 0.333856i | ||||
\(29\) | −111.807 | − | 193.656i | −0.715933 | − | 1.24003i | −0.962599 | − | 0.270932i | \(-0.912668\pi\) |
0.246665 | − | 0.969101i | \(-0.420665\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 57.3882 | 0.332491 | 0.166246 | − | 0.986084i | \(-0.446836\pi\) | ||||
0.166246 | + | 0.986084i | \(0.446836\pi\) | |||||||
\(32\) | 91.2024 | − | 157.967i | 0.503827 | − | 0.872654i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.82930 | −0.0445357 | ||||||||
\(35\) | −56.0349 | + | 97.0553i | −0.270618 | + | 0.468724i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 78.1293 | + | 135.324i | 0.347146 | + | 0.601274i | 0.985741 | − | 0.168269i | \(-0.0538177\pi\) |
−0.638596 | + | 0.769542i | \(0.720484\pi\) | |||||||
\(38\) | 106.946 | 0.456552 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −229.759 | −0.908203 | ||||||||
\(41\) | 111.141 | + | 192.501i | 0.423348 | + | 0.733260i | 0.996265 | − | 0.0863539i | \(-0.0275216\pi\) |
−0.572917 | + | 0.819613i | \(0.694188\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −173.987 | + | 301.354i | −0.617041 | + | 1.06875i | 0.372982 | + | 0.927839i | \(0.378335\pi\) |
−0.990023 | + | 0.140908i | \(0.954998\pi\) | |||||||
\(44\) | −324.056 | −1.11030 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −120.678 | + | 209.021i | −0.386805 | + | 0.669966i | ||||
\(47\) | 45.0185 | 0.139715 | 0.0698577 | − | 0.997557i | \(-0.477745\pi\) | ||||
0.0698577 | + | 0.997557i | \(0.477745\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 130.975 | + | 226.856i | 0.381853 | + | 0.661388i | ||||
\(50\) | 19.2767 | + | 33.3882i | 0.0545227 | + | 0.0944361i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −249.804 | − | 161.341i | −0.666183 | − | 0.430268i | ||||
\(53\) | −473.516 | −1.22722 | −0.613608 | − | 0.789611i | \(-0.710282\pi\) | ||||
−0.613608 | + | 0.789611i | \(0.710282\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 317.917 | + | 550.648i | 0.779416 | + | 1.34999i | ||||
\(56\) | 83.0813 | − | 143.901i | 0.198254 | − | 0.343385i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 143.862 | − | 249.176i | 0.325689 | − | 0.564110i | ||||
\(59\) | 307.747 | − | 533.034i | 0.679072 | − | 1.17619i | −0.296188 | − | 0.955130i | \(-0.595716\pi\) |
0.975261 | − | 0.221058i | \(-0.0709511\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −97.6626 | + | 169.157i | −0.204990 | + | 0.355054i | −0.950130 | − | 0.311855i | \(-0.899050\pi\) |
0.745139 | + | 0.666909i | \(0.232383\pi\) | |||||||
\(62\) | 36.9206 | + | 63.9483i | 0.0756277 | + | 0.130991i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 18.6446 | 0.0364151 | ||||||||
\(65\) | −29.0852 | + | 582.759i | −0.0555012 | + | 1.11204i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 177.548 | + | 307.523i | 0.323746 | + | 0.560745i | 0.981258 | − | 0.192700i | \(-0.0617243\pi\) |
−0.657512 | + | 0.753444i | \(0.728391\pi\) | |||||||
\(68\) | 21.7677 | + | 37.7027i | 0.0388194 | + | 0.0672371i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −144.200 | −0.246217 | ||||||||
\(71\) | 381.710 | − | 661.141i | 0.638038 | − | 1.10511i | −0.347825 | − | 0.937559i | \(-0.613080\pi\) |
0.985863 | − | 0.167554i | \(-0.0535869\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 331.595 | 0.531647 | 0.265824 | − | 0.964022i | \(-0.414356\pi\) | ||||
0.265824 | + | 0.964022i | \(0.414356\pi\) | |||||||
\(74\) | −100.529 | + | 174.121i | −0.157922 | + | 0.273529i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −263.664 | − | 456.680i | −0.397952 | − | 0.689274i | ||||
\(77\) | −459.836 | −0.680561 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −207.777 | −0.295908 | −0.147954 | − | 0.988994i | \(-0.547269\pi\) | ||||
−0.147954 | + | 0.988994i | \(0.547269\pi\) | |||||||
\(80\) | 168.096 | + | 291.152i | 0.234922 | + | 0.406897i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −143.004 | + | 247.691i | −0.192587 | + | 0.333571i | ||||
\(83\) | 251.185 | 0.332183 | 0.166091 | − | 0.986110i | \(-0.446885\pi\) | ||||
0.166091 | + | 0.986110i | \(0.446885\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 42.7105 | − | 73.9767i | 0.0545012 | − | 0.0943988i | ||||
\(86\) | −447.737 | −0.561403 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −471.365 | − | 816.429i | −0.570997 | − | 0.988996i | ||||
\(89\) | 359.683 | + | 622.989i | 0.428385 | + | 0.741985i | 0.996730 | − | 0.0808054i | \(-0.0257492\pi\) |
−0.568345 | + | 0.822791i | \(0.692416\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −354.472 | − | 228.943i | −0.408338 | − | 0.263733i | ||||
\(92\) | 1190.08 | 1.34863 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 28.9626 | + | 50.1647i | 0.0317794 | + | 0.0550435i | ||||
\(95\) | −517.338 | + | 896.055i | −0.558713 | + | 0.967719i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 778.080 | − | 1347.67i | 0.814454 | − | 1.41068i | −0.0952647 | − | 0.995452i | \(-0.530370\pi\) |
0.909719 | − | 0.415224i | \(-0.136297\pi\) | |||||||
\(98\) | −168.526 | + | 291.895i | −0.173711 | + | 0.300876i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 95.0491 | − | 164.630i | 0.0950491 | − | 0.164630i | ||||
\(101\) | −391.693 | − | 678.431i | −0.385890 | − | 0.668381i | 0.606002 | − | 0.795463i | \(-0.292772\pi\) |
−0.991892 | + | 0.127082i | \(0.959439\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1033.54 | 0.988720 | 0.494360 | − | 0.869257i | \(-0.335402\pi\) | ||||
0.494360 | + | 0.869257i | \(0.335402\pi\) | |||||||
\(104\) | 43.1238 | − | 864.039i | 0.0406599 | − | 0.814673i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −304.635 | − | 527.644i | −0.279140 | − | 0.483484i | ||||
\(107\) | −120.679 | − | 209.022i | −0.109033 | − | 0.188850i | 0.806346 | − | 0.591444i | \(-0.201442\pi\) |
−0.915379 | + | 0.402594i | \(0.868109\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1763.93 | 1.55003 | 0.775016 | − | 0.631941i | \(-0.217742\pi\) | ||||
0.775016 | + | 0.631941i | \(0.217742\pi\) | |||||||
\(110\) | −409.062 | + | 708.516i | −0.354568 | + | 0.614131i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −243.136 | −0.205126 | ||||||||
\(113\) | 933.917 | − | 1617.59i | 0.777482 | − | 1.34664i | −0.155907 | − | 0.987772i | \(-0.549830\pi\) |
0.933389 | − | 0.358867i | \(-0.116837\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1167.53 | − | 2022.22i | −0.946718 | − | 1.63976i | ||||
\(116\) | −1418.70 | −1.13554 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 791.954 | 0.617841 | ||||||||
\(119\) | 30.8883 | + | 53.5002i | 0.0237944 | + | 0.0412130i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −638.952 | + | 1106.70i | −0.480054 | + | 0.831478i | ||||
\(122\) | −251.324 | −0.186507 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 182.047 | − | 315.315i | 0.131841 | − | 0.228356i | ||||
\(125\) | 1183.06 | 0.846528 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −119.442 | − | 206.880i | −0.0834551 | − | 0.144548i | 0.821277 | − | 0.570530i | \(-0.193262\pi\) |
−0.904732 | + | 0.425982i | \(0.859929\pi\) | |||||||
\(128\) | −717.624 | − | 1242.96i | −0.495544 | − | 0.858308i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −668.087 | + | 342.507i | −0.450732 | + | 0.231076i | ||||
\(131\) | 1158.72 | 0.772807 | 0.386403 | − | 0.922330i | \(-0.373717\pi\) | ||||
0.386403 | + | 0.922330i | \(0.373717\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −374.140 | − | 648.030i | −0.243925 | − | 0.422491i | ||||
\(134\) | −228.451 | + | 395.688i | −0.147277 | + | 0.255092i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −63.3256 | + | 109.683i | −0.0399274 | + | 0.0691562i | ||||
\(137\) | −456.260 | + | 790.265i | −0.284532 | + | 0.492824i | −0.972496 | − | 0.232921i | \(-0.925172\pi\) |
0.687963 | + | 0.725745i | \(0.258505\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1157.52 | + | 2004.88i | −0.706326 | + | 1.22339i | 0.259884 | + | 0.965640i | \(0.416316\pi\) |
−0.966211 | + | 0.257753i | \(0.917018\pi\) | |||||||
\(140\) | 355.508 | + | 615.759i | 0.214614 | + | 0.371722i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 982.290 | 0.580507 | ||||||||
\(143\) | −2130.45 | + | 1092.21i | −1.24586 | + | 0.638711i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1391.82 | + | 2410.71i | 0.797134 | + | 1.38068i | ||||
\(146\) | 213.331 | + | 369.500i | 0.120927 | + | 0.209452i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 991.370 | 0.550609 | ||||||||
\(149\) | −462.704 | + | 801.427i | −0.254404 | + | 0.440641i | −0.964733 | − | 0.263229i | \(-0.915213\pi\) |
0.710329 | + | 0.703869i | \(0.248546\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3523.78 | −1.89908 | −0.949541 | − | 0.313644i | \(-0.898450\pi\) | ||||
−0.949541 | + | 0.313644i | \(0.898450\pi\) | |||||||
\(152\) | 767.042 | − | 1328.55i | 0.409311 | − | 0.708948i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −295.835 | − | 512.401i | −0.154799 | − | 0.268120i | ||||
\(155\) | −714.392 | −0.370202 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1615.83 | 0.821384 | 0.410692 | − | 0.911774i | \(-0.365287\pi\) | ||||
0.410692 | + | 0.911774i | \(0.365287\pi\) | |||||||
\(158\) | −133.673 | − | 231.528i | −0.0673067 | − | 0.116579i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1135.33 | + | 1966.44i | −0.560971 | + | 0.971631i | ||||
\(161\) | 1688.72 | 0.826644 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −504.003 | + | 872.959i | −0.242188 | + | 0.419481i | −0.961337 | − | 0.275374i | \(-0.911198\pi\) |
0.719150 | + | 0.694855i | \(0.244532\pi\) | |||||||
\(164\) | 1410.24 | 0.671473 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 161.600 | + | 279.899i | 0.0755576 | + | 0.130870i | ||||
\(167\) | 1177.02 | + | 2038.66i | 0.545392 | + | 0.944647i | 0.998582 | + | 0.0532328i | \(0.0169525\pi\) |
−0.453190 | + | 0.891414i | \(0.649714\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2186.08 | − | 218.757i | −0.995030 | − | 0.0995710i | ||||
\(170\) | 109.911 | 0.0495869 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1103.84 | + | 1911.92i | 0.489345 | + | 0.847571i | ||||
\(173\) | 1566.16 | − | 2712.67i | 0.688284 | − | 1.19214i | −0.284109 | − | 0.958792i | \(-0.591698\pi\) |
0.972393 | − | 0.233350i | \(-0.0749688\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 134.875 | − | 233.610i | 0.0582604 | − | 0.100910i | ||||
\(176\) | −689.721 | + | 1194.63i | −0.295396 | + | 0.511641i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −462.802 | + | 801.597i | −0.194879 | + | 0.337541i | ||||
\(179\) | −1590.41 | − | 2754.67i | −0.664093 | − | 1.15024i | −0.979530 | − | 0.201297i | \(-0.935484\pi\) |
0.315437 | − | 0.948947i | \(-0.397849\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4230.52 | 1.73731 | 0.868653 | − | 0.495421i | \(-0.164986\pi\) | ||||
0.868653 | + | 0.495421i | \(0.164986\pi\) | |||||||
\(182\) | 27.0650 | − | 542.282i | 0.0110230 | − | 0.220860i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1731.06 | + | 2998.28i | 0.693562 | + | 1.20128i | ||||
\(185\) | −972.587 | − | 1684.57i | −0.386519 | − | 0.669470i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 350.493 | 0.137062 | ||||||||
\(188\) | 142.808 | − | 247.351i | 0.0554008 | − | 0.0959570i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1331.31 | −0.508335 | ||||||||
\(191\) | −1976.40 | + | 3423.22i | −0.748729 | + | 1.29684i | 0.199703 | + | 0.979856i | \(0.436002\pi\) |
−0.948432 | + | 0.316980i | \(0.897331\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2521.22 | − | 4366.89i | −0.940319 | − | 1.62868i | −0.764863 | − | 0.644193i | \(-0.777193\pi\) |
−0.175456 | − | 0.984487i | \(-0.556140\pi\) | |||||||
\(194\) | 2002.31 | 0.741016 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1661.92 | 0.605658 | ||||||||
\(197\) | 1786.06 | + | 3093.55i | 0.645947 | + | 1.11881i | 0.984082 | + | 0.177715i | \(0.0568706\pi\) |
−0.338135 | + | 0.941098i | \(0.609796\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2503.42 | + | 4336.05i | −0.891773 | + | 1.54460i | −0.0540255 | + | 0.998540i | \(0.517205\pi\) |
−0.837748 | + | 0.546057i | \(0.816128\pi\) | |||||||
\(200\) | 553.026 | 0.195524 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 503.989 | − | 872.935i | 0.175547 | − | 0.304057i | ||||
\(203\) | −2013.14 | −0.696033 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1383.52 | − | 2396.34i | −0.471364 | − | 0.816426i | ||||
\(206\) | 664.929 | + | 1151.69i | 0.224892 | + | 0.389525i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1126.46 | + | 577.502i | −0.375511 | + | 0.192512i | ||||
\(209\) | −4245.40 | −1.40508 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −879.615 | − | 1523.54i | −0.286992 | − | 0.497084i | 0.686099 | − | 0.727509i | \(-0.259322\pi\) |
−0.973090 | + | 0.230425i | \(0.925989\pi\) | |||||||
\(212\) | −1502.09 | + | 2601.70i | −0.486622 | + | 0.842855i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 155.277 | − | 268.948i | 0.0496007 | − | 0.0859109i | ||||
\(215\) | 2165.86 | − | 3751.38i | 0.687026 | − | 1.18996i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 258.325 | − | 447.433i | 0.0808123 | − | 0.139971i | ||||
\(218\) | 1134.82 | + | 1965.56i | 0.352567 | + | 0.610664i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4033.99 | 1.23623 | ||||||||
\(221\) | 270.183 | + | 174.503i | 0.0822373 | + | 0.0531147i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −856.260 | − | 1483.09i | −0.257127 | − | 0.445358i | 0.708344 | − | 0.705868i | \(-0.249443\pi\) |
−0.965471 | + | 0.260510i | \(0.916109\pi\) | |||||||
\(224\) | −821.071 | − | 1422.14i | −0.244911 | − | 0.424199i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2403.33 | 0.707378 | ||||||||
\(227\) | 1288.33 | − | 2231.45i | 0.376693 | − | 0.652451i | −0.613886 | − | 0.789394i | \(-0.710395\pi\) |
0.990579 | + | 0.136944i | \(0.0437280\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1963.10 | −0.566486 | −0.283243 | − | 0.959048i | \(-0.591410\pi\) | ||||
−0.283243 | + | 0.959048i | \(0.591410\pi\) | |||||||
\(230\) | 1502.25 | − | 2601.98i | 0.430677 | − | 0.745954i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2063.61 | − | 3574.28i | −0.583978 | − | 1.01148i | ||||
\(233\) | 1078.11 | 0.303131 | 0.151565 | − | 0.988447i | \(-0.451569\pi\) | ||||
0.151565 | + | 0.988447i | \(0.451569\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −560.409 | −0.155562 | ||||||||
\(236\) | −1952.48 | − | 3381.79i | −0.538539 | − | 0.932778i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −39.7439 | + | 68.8385i | −0.0108244 | + | 0.0187485i | ||||
\(239\) | −3998.43 | −1.08216 | −0.541081 | − | 0.840970i | \(-0.681985\pi\) | ||||
−0.541081 | + | 0.840970i | \(0.681985\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1787.36 | − | 3095.80i | 0.477735 | − | 0.827461i | −0.521939 | − | 0.852983i | \(-0.674791\pi\) |
0.999674 | + | 0.0255213i | \(0.00812457\pi\) | |||||||
\(242\) | −1644.27 | −0.436768 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 619.612 | + | 1073.20i | 0.162568 | + | 0.281576i | ||||
\(245\) | −1630.44 | − | 2824.00i | −0.425162 | − | 0.736403i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3272.63 | − | 2113.70i | −0.843047 | − | 0.544500i | ||||
\(248\) | 1059.21 | 0.271209 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 761.119 | + | 1318.30i | 0.192550 | + | 0.333506i | ||||
\(251\) | 1075.35 | − | 1862.55i | 0.270419 | − | 0.468380i | −0.698550 | − | 0.715561i | \(-0.746171\pi\) |
0.968969 | + | 0.247181i | \(0.0795043\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4790.52 | − | 8297.42i | 1.19042 | − | 2.06187i | ||||
\(254\) | 153.686 | − | 266.192i | 0.0379650 | − | 0.0657574i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 997.943 | − | 1728.49i | 0.243638 | − | 0.421994i | ||||
\(257\) | 2137.40 | + | 3702.09i | 0.518784 | + | 0.898560i | 0.999762 | + | 0.0218271i | \(0.00694834\pi\) |
−0.480978 | + | 0.876733i | \(0.659718\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1406.75 | 0.337496 | ||||||||
\(260\) | 3109.66 | + | 2008.44i | 0.741742 | + | 0.479069i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 745.459 | + | 1291.17i | 0.175781 | + | 0.304462i | ||||
\(263\) | 4185.82 | + | 7250.06i | 0.981403 | + | 1.69984i | 0.656944 | + | 0.753940i | \(0.271849\pi\) |
0.324459 | + | 0.945900i | \(0.394818\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5894.52 | 1.36641 | ||||||||
\(266\) | 481.405 | − | 833.818i | 0.110965 | − | 0.192198i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2252.88 | 0.513495 | ||||||||
\(269\) | −2539.82 | + | 4399.10i | −0.575672 | + | 0.997092i | 0.420297 | + | 0.907387i | \(0.361926\pi\) |
−0.995968 | + | 0.0897057i | \(0.971407\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2465.97 | − | 4271.18i | −0.552756 | − | 0.957401i | −0.998074 | − | 0.0620290i | \(-0.980243\pi\) |
0.445318 | − | 0.895372i | \(-0.353090\pi\) | |||||||
\(272\) | 185.321 | 0.0413115 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1174.14 | −0.258876 | ||||||||
\(275\) | −765.219 | − | 1325.40i | −0.167798 | − | 0.290635i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2586.26 | + | 4479.54i | −0.560987 | + | 0.971658i | 0.436424 | + | 0.899741i | \(0.356245\pi\) |
−0.997411 | + | 0.0719165i | \(0.977088\pi\) | |||||||
\(278\) | −2978.75 | −0.642638 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1034.23 | + | 1791.34i | −0.220740 | + | 0.382332i | ||||
\(281\) | 217.515 | 0.0461773 | 0.0230887 | − | 0.999733i | \(-0.492650\pi\) | ||||
0.0230887 | + | 0.999733i | \(0.492650\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2461.49 | − | 4263.42i | −0.517033 | − | 0.895527i | −0.999804 | − | 0.0197808i | \(-0.993703\pi\) |
0.482771 | − | 0.875746i | \(-0.339630\pi\) | |||||||
\(284\) | −2421.73 | − | 4194.55i | −0.505997 | − | 0.876412i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2587.69 | − | 1671.31i | −0.535012 | − | 0.345548i | ||||
\(287\) | 2001.14 | 0.411580 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2432.96 | + | 4214.00i | 0.495208 | + | 0.857725i | ||||
\(290\) | −1790.85 | + | 3101.85i | −0.362629 | + | 0.628092i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1051.89 | − | 1821.92i | 0.210812 | − | 0.365137i | ||||
\(293\) | −1321.13 | + | 2288.26i | −0.263416 | + | 0.456250i | −0.967147 | − | 0.254216i | \(-0.918183\pi\) |
0.703731 | + | 0.710466i | \(0.251516\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3830.97 | + | 6635.43i | −0.756093 | + | 1.30959i | ||||
\(296\) | 1442.03 | + | 2497.66i | 0.283162 | + | 0.490451i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1190.72 | −0.231465 | ||||||||
\(299\) | 7823.95 | − | 4011.09i | 1.51328 | − | 0.775810i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1566.36 | + | 2713.01i | 0.299945 | + | 0.519519i | ||||
\(302\) | −2267.02 | − | 3926.59i | −0.431961 | − | 0.748178i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2244.73 | −0.423501 | ||||||||
\(305\) | 1215.74 | − | 2105.73i | 0.228240 | − | 0.395324i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3386.22 | −0.629517 | −0.314759 | − | 0.949172i | \(-0.601924\pi\) | ||||
−0.314759 | + | 0.949172i | \(0.601924\pi\) | |||||||
\(308\) | −1458.70 | + | 2526.54i | −0.269860 | + | 0.467411i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −459.603 | − | 796.056i | −0.0842055 | − | 0.145848i | ||||
\(311\) | 3.29813 | 0.000601349 | 0.000300675 | − | 1.00000i | \(-0.499904\pi\) | ||||
0.000300675 | 1.00000i | \(0.499904\pi\) | ||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2882.62 | 0.520560 | 0.260280 | − | 0.965533i | \(-0.416185\pi\) | ||||
0.260280 | + | 0.965533i | \(0.416185\pi\) | |||||||
\(314\) | 1039.54 | + | 1800.54i | 0.186830 | + | 0.323599i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −659.112 | + | 1141.62i | −0.117335 | + | 0.203231i | ||||
\(317\) | 1442.70 | 0.255616 | 0.127808 | − | 0.991799i | \(-0.459206\pi\) | ||||
0.127808 | + | 0.991799i | \(0.459206\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5710.82 | + | 9891.43i | −1.00233 | + | 1.73609i | ||||
\(320\) | −232.095 | −0.0405454 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1086.43 | + | 1881.76i | 0.188027 | + | 0.325672i | ||||
\(323\) | 285.174 | + | 493.936i | 0.0491255 | + | 0.0850878i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 70.0075 | − | 1402.69i | 0.0119487 | − | 0.239407i | ||||
\(326\) | −1297.00 | −0.220350 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2051.31 | + | 3552.98i | 0.345319 | + | 0.598111i | ||||
\(329\) | 202.645 | − | 350.991i | 0.0339580 | − | 0.0588169i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1912.49 | − | 3312.53i | 0.317583 | − | 0.550070i | −0.662400 | − | 0.749150i | \(-0.730462\pi\) |
0.979983 | + | 0.199080i | \(0.0637954\pi\) | |||||||
\(332\) | 796.812 | − | 1380.12i | 0.131719 | − | 0.228144i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1514.47 | + | 2623.13i | −0.248107 | + | 0.429735i | ||||
\(335\) | −2210.20 | − | 3828.17i | −0.360465 | − | 0.624344i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2290.22 | 0.370197 | 0.185098 | − | 0.982720i | \(-0.440740\pi\) | ||||
0.185098 | + | 0.982720i | \(0.440740\pi\) | |||||||
\(338\) | −1162.65 | − | 2576.71i | −0.187100 | − | 0.414659i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −270.973 | − | 469.339i | −0.0432223 | − | 0.0748631i | ||||
\(341\) | −1465.62 | − | 2538.53i | −0.232750 | − | 0.403135i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5446.21 | 0.857340 | ||||||||
\(344\) | −3211.26 | + | 5562.06i | −0.503313 | + | 0.871763i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4030.35 | 0.626222 | ||||||||
\(347\) | −167.496 | + | 290.112i | −0.0259126 | + | 0.0448820i | −0.878691 | − | 0.477391i | \(-0.841582\pi\) |
0.852778 | + | 0.522273i | \(0.174916\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4487.64 | + | 7772.81i | 0.688303 | + | 1.19218i | 0.972387 | + | 0.233376i | \(0.0749773\pi\) |
−0.284084 | + | 0.958799i | \(0.591689\pi\) | |||||||
\(350\) | 347.086 | 0.0530072 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9316.77 | −1.41075 | ||||||||
\(353\) | −4962.94 | − | 8596.06i | −0.748302 | − | 1.29610i | −0.948636 | − | 0.316369i | \(-0.897536\pi\) |
0.200334 | − | 0.979728i | \(-0.435797\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4751.69 | + | 8230.16i | −0.710404 | + | 1.23046i | ||||
\(356\) | 4563.95 | 0.679463 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2046.37 | − | 3544.42i | 0.302107 | − | 0.523264i | ||||
\(359\) | −215.661 | −0.0317052 | −0.0158526 | − | 0.999874i | \(-0.505046\pi\) | ||||
−0.0158526 | + | 0.999874i | \(0.505046\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −24.7218 | − | 42.8195i | −0.00360429 | − | 0.00624282i | ||||
\(362\) | 2721.70 | + | 4714.12i | 0.395164 | + | 0.684444i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2382.37 | + | 1221.36i | −0.343049 | + | 0.175870i | ||||
\(365\) | −4127.83 | −0.591947 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1430.76 | + | 2478.15i | 0.203502 | + | 0.352475i | 0.949654 | − | 0.313300i | \(-0.101434\pi\) |
−0.746153 | + | 0.665775i | \(0.768101\pi\) | |||||||
\(368\) | 2532.96 | − | 4387.21i | 0.358803 | − | 0.621465i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1251.42 | − | 2167.53i | 0.175834 | − | 0.304553i | ||||
\(371\) | −2131.47 | + | 3691.81i | −0.298276 | + | 0.516629i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.50723 | − | 14.7350i | 0.00118093 | − | 0.00204544i | −0.865434 | − | 0.501022i | \(-0.832957\pi\) |
0.866615 | + | 0.498977i | \(0.166291\pi\) | |||||||
\(374\) | 225.489 | + | 390.558i | 0.0311758 | + | 0.0539981i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 830.902 | 0.113964 | ||||||||
\(377\) | −9327.01 | + | 4781.66i | −1.27418 | + | 0.653231i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 950.983 | + | 1647.15i | 0.128888 | + | 0.223241i | 0.923246 | − | 0.384209i | \(-0.125526\pi\) |
−0.794358 | + | 0.607450i | \(0.792192\pi\) | |||||||
\(380\) | 3282.20 | + | 5684.95i | 0.443088 | + | 0.767451i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5086.05 | −0.681217 | ||||||||
\(383\) | −3864.89 | + | 6694.18i | −0.515631 | + | 0.893099i | 0.484205 | + | 0.874955i | \(0.339109\pi\) |
−0.999835 | + | 0.0181440i | \(0.994224\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5724.23 | 0.757751 | ||||||||
\(386\) | 3244.05 | − | 5618.85i | 0.427766 | − | 0.740912i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4936.46 | − | 8550.20i | −0.645904 | − | 1.11874i | ||||
\(389\) | 14445.5 | 1.88282 | 0.941408 | − | 0.337271i | \(-0.109504\pi\) | ||||
0.941408 | + | 0.337271i | \(0.109504\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1287.16 | −0.166482 | ||||||||
\(392\) | 2417.40 | + | 4187.06i | 0.311472 | + | 0.539486i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2298.12 | + | 3980.46i | −0.293851 | + | 0.508966i | ||||
\(395\) | 2586.50 | 0.329470 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −516.534 | + | 894.664i | −0.0653000 | + | 0.113103i | −0.896827 | − | 0.442381i | \(-0.854134\pi\) |
0.831527 | + | 0.555484i | \(0.187467\pi\) | |||||||
\(398\) | −6442.29 | −0.811364 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −404.605 | − | 700.796i | −0.0505756 | − | 0.0875995i | ||||
\(401\) | −2305.86 | − | 3993.87i | −0.287155 | − | 0.497368i | 0.685974 | − | 0.727626i | \(-0.259376\pi\) |
−0.973130 | + | 0.230258i | \(0.926043\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 134.085 | − | 2686.57i | 0.0165738 | − | 0.332078i | ||||
\(404\) | −4970.12 | −0.612061 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1295.15 | − | 2243.26i | −0.158318 | − | 0.274215i | ||||
\(407\) | 3990.65 | − | 6912.00i | 0.486017 | − | 0.841806i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1334.28 | + | 2311.04i | −0.161311 | + | 0.279398i | −0.935339 | − | 0.353753i | \(-0.884905\pi\) |
0.774028 | + | 0.633151i | \(0.218239\pi\) | |||||||
\(410\) | 1780.18 | − | 3083.36i | 0.214431 | − | 0.371405i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3278.62 | − | 5678.73i | 0.392053 | − | 0.679056i | ||||
\(413\) | −2770.57 | − | 4798.76i | −0.330098 | − | 0.571747i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3126.86 | −0.369859 | ||||||||
\(416\) | −7181.97 | − | 4638.62i | −0.846455 | − | 0.546700i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2731.27 | − | 4730.70i | −0.319596 | − | 0.553556i | ||||
\(419\) | 3094.91 | + | 5360.55i | 0.360851 | + | 0.625012i | 0.988101 | − | 0.153806i | \(-0.0491531\pi\) |
−0.627250 | + | 0.778818i | \(0.715820\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8991.13 | 1.04086 | 0.520429 | − | 0.853905i | \(-0.325772\pi\) | ||||
0.520429 | + | 0.853905i | \(0.325772\pi\) | |||||||
\(422\) | 1131.80 | − | 1960.33i | 0.130557 | − | 0.226131i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8739.63 | −1.00102 | ||||||||
\(425\) | −102.803 | + | 178.060i | −0.0117334 | + | 0.0203228i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 879.230 | + | 1522.87i | 0.0996462 | + | 0.172592i | ||||
\(428\) | −1531.28 | −0.172937 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5573.61 | 0.625078 | ||||||||
\(431\) | 1034.51 | + | 1791.82i | 0.115616 | + | 0.200253i | 0.918026 | − | 0.396521i | \(-0.129783\pi\) |
−0.802410 | + | 0.596773i | \(0.796449\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7467.33 | − | 12933.8i | 0.828769 | − | 1.43547i | −0.0702363 | − | 0.997530i | \(-0.522375\pi\) |
0.899005 | − | 0.437939i | \(-0.144291\pi\) | |||||||
\(434\) | 664.772 | 0.0735256 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5595.54 | − | 9691.76i | 0.614628 | − | 1.06457i | ||||
\(437\) | 15591.0 | 1.70668 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3000.12 | + | 5196.36i | 0.326168 | + | 0.564940i | 0.981748 | − | 0.190186i | \(-0.0609091\pi\) |
−0.655580 | + | 0.755126i | \(0.727576\pi\) | |||||||
\(440\) | 5867.75 | + | 10163.2i | 0.635760 | + | 1.10117i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −20.6293 | + | 413.334i | −0.00221999 | + | 0.0444803i | ||||
\(443\) | 5392.60 | 0.578352 | 0.289176 | − | 0.957276i | \(-0.406619\pi\) | ||||
0.289176 | + | 0.957276i | \(0.406619\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4477.48 | − | 7755.23i | −0.476973 | − | 0.826141i | ||||
\(446\) | 1101.75 | − | 1908.28i | 0.116971 | − | 0.202600i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 83.9259 | − | 145.364i | 0.00885073 | − | 0.0153299i | ||||
\(449\) | −3023.30 | + | 5236.51i | −0.317769 | + | 0.550392i | −0.980022 | − | 0.198888i | \(-0.936267\pi\) |
0.662253 | + | 0.749280i | \(0.269600\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5676.78 | − | 9832.47i | 0.592703 | − | 1.02659i | ||||
\(452\) | −5925.15 | − | 10262.7i | −0.616584 | − | 1.06795i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3315.37 | 0.342727 | ||||||||
\(455\) | 4412.61 | + | 2849.98i | 0.454651 | + | 0.293646i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −507.286 | − | 878.646i | −0.0519253 | − | 0.0899372i | 0.838894 | − | 0.544294i | \(-0.183202\pi\) |
−0.890820 | + | 0.454357i | \(0.849869\pi\) | |||||||
\(458\) | −1262.96 | − | 2187.51i | −0.128852 | − | 0.223178i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14814.6 | −1.50159 | ||||||||
\(461\) | −7989.45 | + | 13838.1i | −0.807171 | + | 1.39806i | 0.107644 | + | 0.994189i | \(0.465669\pi\) |
−0.914816 | + | 0.403872i | \(0.867664\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −128.805 | −0.0129289 | −0.00646445 | − | 0.999979i | \(-0.502058\pi\) | ||||
−0.00646445 | + | 0.999979i | \(0.502058\pi\) | |||||||
\(464\) | −3019.56 | + | 5230.03i | −0.302111 | + | 0.523272i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 693.601 | + | 1201.35i | 0.0689494 | + | 0.119424i | ||||
\(467\) | −18832.4 | −1.86608 | −0.933039 | − | 0.359776i | \(-0.882853\pi\) | ||||
−0.933039 | + | 0.359776i | \(0.882853\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3196.84 | 0.314747 | ||||||||
\(470\) | −360.538 | − | 624.471i | −0.0353838 | − | 0.0612865i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5680.06 | − | 9838.15i | 0.553911 | − | 0.959402i | ||||
\(473\) | 17773.6 | 1.72776 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1245.22 | − | 2156.79i | 0.120284 | − | 0.208337i | ||||
\(476\) | 391.937 | 0.0377403 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2572.38 | − | 4455.49i | −0.246146 | − | 0.426338i | ||||
\(479\) | −4615.79 | − | 7994.79i | −0.440294 | − | 0.762612i | 0.557417 | − | 0.830233i | \(-0.311793\pi\) |
−0.997711 | + | 0.0676205i | \(0.978459\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6517.59 | − | 3341.36i | 0.617831 | − | 0.316742i | ||||
\(482\) | 4599.58 | 0.434658 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4053.77 | + | 7021.34i | 0.380708 | + | 0.659405i | ||||
\(485\) | −9685.87 | + | 16776.4i | −0.906830 | + | 1.57068i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3616.50 | + | 6263.97i | −0.336508 | + | 0.582849i | −0.983773 | − | 0.179416i | \(-0.942579\pi\) |
0.647265 | + | 0.762265i | \(0.275913\pi\) | |||||||
\(488\) | −1802.55 | + | 3122.11i | −0.167208 | + | 0.289613i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2097.88 | − | 3633.63i | 0.193413 | − | 0.335001i | ||||
\(491\) | −327.565 | − | 567.360i | −0.0301076 | − | 0.0521479i | 0.850579 | − | 0.525847i | \(-0.176252\pi\) |
−0.880687 | + | 0.473699i | \(0.842918\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1534.44 | 0.140178 | ||||||||
\(494\) | 249.876 | − | 5006.58i | 0.0227580 | − | 0.455985i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −774.938 | − | 1342.23i | −0.0701527 | − | 0.121508i | ||||
\(497\) | −3436.43 | − | 5952.08i | −0.310151 | − | 0.537198i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4560.07 | −0.409092 | −0.204546 | − | 0.978857i | \(-0.565572\pi\) | ||||
−0.204546 | + | 0.978857i | \(0.565572\pi\) | |||||||
\(500\) | 3752.91 | − | 6500.23i | 0.335670 | − | 0.581398i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2767.29 | 0.246036 | ||||||||
\(503\) | 4534.34 | − | 7853.70i | 0.401941 | − | 0.696181i | −0.592020 | − | 0.805924i | \(-0.701669\pi\) |
0.993960 | + | 0.109742i | \(0.0350025\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4875.95 | + | 8445.40i | 0.429657 | + | 0.744189i | ||||
\(506\) | 12327.9 | 1.08308 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1515.58 | −0.132368 | ||||||||
\(509\) | −7940.44 | − | 13753.2i | −0.691461 | − | 1.19765i | −0.971359 | − | 0.237616i | \(-0.923634\pi\) |
0.279898 | − | 0.960030i | \(-0.409699\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1492.63 | − | 2585.31i | 0.129217 | − | 0.223811i | ||||
\(512\) | −8913.89 | −0.769418 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2750.19 | + | 4763.46i | −0.236003 | + | 0.408769i | ||||
\(515\) | −12866.0 | −1.10086 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1149.72 | − | 1991.36i | −0.0978035 | − | 0.169401i | ||||
\(518\) | 905.033 | + | 1567.56i | 0.0767662 | + | 0.132963i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −536.823 | + | 10755.9i | −0.0452716 | + | 0.907074i | ||||
\(521\) | 10998.0 | 0.924821 | 0.462410 | − | 0.886666i | \(-0.346985\pi\) | ||||
0.462410 | + | 0.886666i | \(0.346985\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9315.88 | − | 16135.6i | −0.778882 | − | 1.34906i | −0.932587 | − | 0.360946i | \(-0.882454\pi\) |
0.153705 | − | 0.988117i | \(-0.450879\pi\) | |||||||
\(524\) | 3675.69 | − | 6366.49i | 0.306438 | − | 0.530766i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5385.88 | + | 9328.62i | −0.446456 | + | 0.773284i | ||||
\(527\) | −196.899 | + | 341.039i | −0.0162752 | + | 0.0281895i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11509.4 | + | 19934.8i | −0.945949 | + | 1.63843i | ||||
\(530\) | 3792.23 | + | 6568.33i | 0.310800 | + | 0.538321i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4747.40 | −0.386891 | ||||||||
\(533\) | 9271.41 | − | 4753.16i | 0.753451 | − | 0.386270i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1502.26 | + | 2602.00i | 0.121399 | + | 0.210270i | ||||
\(536\) | 3276.99 | + | 5675.92i | 0.264076 | + | 0.457392i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6535.96 | −0.523764 | ||||||||
\(539\) | 6689.89 | − | 11587.2i | 0.534608 | − | 0.925969i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14270.1 | −1.13405 | −0.567023 | − | 0.823702i | \(-0.691905\pi\) | ||||
−0.567023 | + | 0.823702i | \(0.691905\pi\) | |||||||
\(542\) | 3172.95 | − | 5495.71i | 0.251457 | − | 0.435537i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 625.830 | + | 1083.97i | 0.0493240 | + | 0.0854317i | ||||
\(545\) | −21958.1 | −1.72584 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14379.7 | 1.12400 | 0.562002 | − | 0.827136i | \(-0.310031\pi\) | ||||
0.562002 | + | 0.827136i | \(0.310031\pi\) | |||||||
\(548\) | 2894.70 | + | 5013.77i | 0.225649 | + | 0.390835i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 984.604 | − | 1705.38i | 0.0763339 | − | 0.132214i | ||||
\(551\) | −18586.2 | −1.43702 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −935.281 | + | 1619.95i | −0.0719208 | + | 0.124570i | ||||
\(554\) | −6655.46 | −0.510404 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7343.77 | + | 12719.8i | 0.560153 | + | 0.970214i | ||||
\(557\) | −4517.55 | − | 7824.62i | −0.343653 | − | 0.595224i | 0.641455 | − | 0.767160i | \(-0.278331\pi\) |
−0.985108 | + | 0.171936i | \(0.944998\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13701.1 | + | 8849.11i | 1.03666 | + | 0.669548i | ||||
\(560\) | 3026.65 | 0.228392 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 139.938 | + | 242.379i | 0.0105034 | + | 0.0181924i | ||||
\(563\) | −3646.73 | + | 6316.33i | −0.272987 | + | 0.472827i | −0.969625 | − | 0.244595i | \(-0.921345\pi\) |
0.696638 | + | 0.717422i | \(0.254678\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11625.8 | + | 20136.4i | −0.865664 | + | 1.49937i | ||||
\(566\) | 3167.19 | − | 5485.73i | 0.235206 | − | 0.407389i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7045.19 | − | 12202.6i | 0.520439 | − | 0.901427i | ||||
\(569\) | 13207.9 | + | 22876.7i | 0.973117 | + | 1.68549i | 0.686013 | + | 0.727589i | \(0.259359\pi\) |
0.287104 | + | 0.957899i | \(0.407307\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23940.9 | −1.75463 | −0.877317 | − | 0.479912i | \(-0.840669\pi\) | ||||
−0.877317 | + | 0.479912i | \(0.840669\pi\) | |||||||
\(572\) | −757.144 | + | 15170.3i | −0.0553458 | + | 1.10892i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1287.43 | + | 2229.89i | 0.0936171 | + | 0.162150i | ||||
\(575\) | 2810.22 | + | 4867.44i | 0.203816 | + | 0.353019i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10182.8 | 0.734691 | 0.367346 | − | 0.930085i | \(-0.380267\pi\) | ||||
0.367346 | + | 0.930085i | \(0.380267\pi\) | |||||||
\(578\) | −3130.48 | + | 5422.14i | −0.225278 | + | 0.390193i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 17660.6 | 1.26434 | ||||||||
\(581\) | 1130.68 | − | 1958.39i | 0.0807373 | − | 0.139841i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12093.0 | + | 20945.7i | 0.859074 | + | 1.48796i | ||||
\(584\) | 6120.22 | 0.433658 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3399.77 | −0.239664 | ||||||||
\(587\) | 9553.74 | + | 16547.6i | 0.671763 | + | 1.16353i | 0.977404 | + | 0.211381i | \(0.0677960\pi\) |
−0.305641 | + | 0.952147i | \(0.598871\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2384.97 | − | 4130.89i | 0.166844 | − | 0.288982i | ||||
\(590\) | −9858.58 | −0.687917 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2110.03 | − | 3654.68i | 0.146489 | − | 0.253727i | ||||
\(593\) | 13597.5 | 0.941621 | 0.470810 | − | 0.882234i | \(-0.343962\pi\) | ||||
0.470810 | + | 0.882234i | \(0.343962\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −384.511 | − | 665.992i | −0.0264931 | − | 0.0458874i | ||||
\(596\) | 2935.59 | + | 5084.58i | 0.201755 | + | 0.349451i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9503.13 | + | 6137.79i | 0.649852 | + | 0.419721i | ||||
\(599\) | −4150.37 | −0.283104 | −0.141552 | − | 0.989931i | \(-0.545209\pi\) | ||||
−0.141552 | + | 0.989931i | \(0.545209\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9588.73 | − | 16608.2i | −0.650803 | − | 1.12722i | −0.982928 | − | 0.183988i | \(-0.941099\pi\) |
0.332126 | − | 0.943235i | \(-0.392234\pi\) | |||||||
\(602\) | −2015.43 | + | 3490.82i | −0.136450 | + | 0.236338i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11178.2 | + | 19361.1i | −0.753035 | + | 1.30429i | ||||
\(605\) | 7953.94 | − | 13776.6i | 0.534502 | − | 0.925784i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3997.18 | + | 6923.32i | −0.267282 | + | 0.462947i | −0.968159 | − | 0.250336i | \(-0.919459\pi\) |
0.700877 | + | 0.713282i | \(0.252792\pi\) | |||||||
\(608\) | −7580.48 | − | 13129.8i | −0.505640 | − | 0.875794i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3128.59 | 0.207660 | ||||||||
\(611\) | 105.184 | − | 2107.49i | 0.00696446 | − | 0.139542i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7806.69 | − | 13521.6i | −0.514371 | − | 0.890916i | −0.999861 | − | 0.0166742i | \(-0.994692\pi\) |
0.485490 | − | 0.874242i | \(-0.338641\pi\) | |||||||
\(614\) | −2178.52 | − | 3773.30i | −0.143189 | − | 0.248010i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8487.15 | −0.555125 | ||||||||
\(617\) | 10818.1 | − | 18737.5i | 0.705868 | − | 1.22260i | −0.260509 | − | 0.965471i | \(-0.583890\pi\) |
0.966377 | − | 0.257128i | \(-0.0827762\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10394.0 | 0.674911 | 0.337456 | − | 0.941341i | \(-0.390434\pi\) | ||||
0.337456 | + | 0.941341i | \(0.390434\pi\) | |||||||
\(620\) | −2266.20 | + | 3925.17i | −0.146795 | + | 0.254256i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.12184 | + | 3.67514i | 0.000136782 | + | 0.000236913i | ||||
\(623\) | 6476.25 | 0.416478 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18472.6 | −1.18225 | ||||||||
\(626\) | 1854.53 | + | 3212.14i | 0.118405 | + | 0.205084i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5125.74 | − | 8878.05i | 0.325700 | − | 0.564129i | ||||
\(629\) | −1072.25 | −0.0679702 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2322.07 | + | 4021.95i | −0.146498 | + | 0.253742i | −0.929931 | − | 0.367735i | \(-0.880134\pi\) |
0.783433 | + | 0.621476i | \(0.213467\pi\) | |||||||
\(632\) | −3834.92 | −0.241369 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 928.160 | + | 1607.62i | 0.0581419 | + | 0.100705i | ||||
\(635\) | 1486.87 | + | 2575.33i | 0.0929206 | + | 0.160943i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10926.0 | − | 5601.43i | 0.679600 | − | 0.348409i | ||||
\(638\) | −14696.2 | −0.911955 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8933.29 | + | 15472.9i | 0.551749 | + | 0.955657i | ||||
\(641\) | 76.9612 | − | 133.301i | 0.00474225 | − | 0.00821383i | −0.863645 | − | 0.504101i | \(-0.831824\pi\) |
0.868387 | + | 0.495887i | \(0.165157\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4219.02 | − | 7307.56i | 0.258759 | − | 0.448184i | −0.707151 | − | 0.707063i | \(-0.750020\pi\) |
0.965910 | + | 0.258879i | \(0.0833531\pi\) | |||||||
\(644\) | 5356.97 | − | 9278.54i | 0.327786 | − | 0.567742i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −366.933 | + | 635.546i | −0.0223479 | + | 0.0387078i | ||||
\(647\) | 332.618 | + | 576.111i | 0.0202111 | + | 0.0350066i | 0.875954 | − | 0.482395i | \(-0.160233\pi\) |
−0.855743 | + | 0.517401i | \(0.826900\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31437.9 | −1.90145 | ||||||||
\(650\) | 1608.07 | − | 824.407i | 0.0970366 | − | 0.0497475i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3197.60 | + | 5538.41i | 0.192067 | + | 0.332670i | ||||
\(653\) | −11207.4 | − | 19411.7i | −0.671636 | − | 1.16331i | −0.977440 | − | 0.211213i | \(-0.932259\pi\) |
0.305805 | − | 0.952094i | \(-0.401075\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14424.2 | −0.860458 | ||||||||
\(656\) | 3001.56 | − | 5198.86i | 0.178645 | − | 0.309423i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 521.485 | 0.0308960 | ||||||||
\(659\) | −12792.8 | + | 22157.8i | −0.756202 | + | 1.30978i | 0.188572 | + | 0.982059i | \(0.439614\pi\) |
−0.944775 | + | 0.327721i | \(0.893719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6658.75 | + | 11533.3i | 0.391824 | + | 0.678658i | 0.992690 | − | 0.120691i | \(-0.0385110\pi\) |
−0.600866 | + | 0.799349i | \(0.705178\pi\) | |||||||
\(662\) | 4921.59 | 0.288947 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4636.10 | 0.270957 | ||||||||
\(665\) | 4657.45 | + | 8066.95i | 0.271591 | + | 0.470410i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20972.6 | − | 36325.6i | 1.21749 | − | 2.10875i | ||||
\(668\) | 14935.0 | 0.865048 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2843.85 | − | 4925.69i | 0.163981 | − | 0.284024i | ||||
\(671\) | 9976.71 | 0.573989 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4889.14 | − | 8468.24i | −0.280034 | − | 0.485032i | 0.691359 | − | 0.722511i | \(-0.257012\pi\) |
−0.971393 | + | 0.237479i | \(0.923679\pi\) | |||||||
\(674\) | 1473.41 | + | 2552.02i | 0.0842042 | + | 0.145846i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8136.65 | + | 11317.3i | −0.462941 | + | 0.643907i | ||||
\(677\) | −12392.8 | −0.703537 | −0.351769 | − | 0.936087i | \(-0.614420\pi\) | ||||
−0.351769 | + | 0.936087i | \(0.614420\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7004.85 | − | 12132.8i | −0.395908 | − | 0.685732i | ||||
\(680\) | 788.303 | − | 1365.38i | 0.0444559 | − | 0.0769999i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1885.81 | − | 3266.32i | 0.105882 | − | 0.183393i | ||||
\(683\) | −9470.84 | + | 16404.0i | −0.530588 | + | 0.919006i | 0.468775 | + | 0.883318i | \(0.344696\pi\) |
−0.999363 | + | 0.0356881i | \(0.988638\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5679.71 | − | 9837.55i | 0.316804 | − | 0.548721i | ||||
\(686\) | 3503.81 | + | 6068.77i | 0.195009 | + | 0.337765i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9397.69 | 0.520761 | ||||||||
\(689\) | −1106.35 | + | 22167.1i | −0.0611735 | + | 1.22569i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16188.8 | − | 28039.8i | −0.891247 | − | 1.54368i | −0.838382 | − | 0.545083i | \(-0.816498\pi\) |
−0.0528645 | − | 0.998602i | \(-0.516835\pi\) | |||||||
\(692\) | −9936.38 | − | 17210.3i | −0.545844 | − | 0.945430i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −431.034 | −0.0235761 | ||||||||
\(695\) | 14409.3 | − | 24957.6i | 0.786438 | − | 1.36215i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1525.29 | −0.0828903 | ||||||||
\(698\) | −5774.22 | + | 10001.2i | −0.313120 | + | 0.542339i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −855.702 | − | 1482.12i | −0.0462035 | − | 0.0800269i | ||||
\(701\) | −6072.34 | −0.327174 | −0.163587 | − | 0.986529i | \(-0.552306\pi\) | ||||
−0.163587 | + | 0.986529i | \(0.552306\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12987.8 | 0.696789 | ||||||||
\(704\) | −476.158 | − | 824.730i | −0.0254913 | − | 0.0441522i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6385.79 | − | 11060.5i | 0.340414 | − | 0.589615i | ||||
\(707\) | −7052.61 | −0.375163 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1699.26 | − | 2943.21i | 0.0900100 | − | 0.155902i | −0.817505 | − | 0.575921i | \(-0.804643\pi\) |
0.907515 | + | 0.420019i | \(0.137977\pi\) | |||||||
\(710\) | −12228.0 | −0.646348 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6638.63 | + | 11498.4i | 0.349429 | + | 0.605228i | ||||
\(713\) | 5382.40 | + | 9322.59i | 0.282710 | + | 0.489669i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 26520.8 | − | 13596.3i | 1.38716 | − | 0.711153i | ||||
\(716\) | −20180.4 | −1.05332 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −138.745 | − | 240.314i | −0.00721160 | − | 0.0124909i | ||||
\(719\) | 14416.8 | − | 24970.6i | 0.747782 | − | 1.29520i | −0.201102 | − | 0.979570i | \(-0.564452\pi\) |
0.948884 | − | 0.315626i | \(-0.102214\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4652.36 | − | 8058.13i | 0.240309 | − | 0.416228i | ||||
\(722\) | 31.8095 | − | 55.0957i | 0.00163965 | − | 0.00283996i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13420.1 | − | 23244.3i | 0.688886 | − | 1.19319i | ||||
\(725\) | −3350.09 | − | 5802.52i | −0.171613 | − | 0.297242i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12894.7 | −0.657822 | −0.328911 | − | 0.944361i | \(-0.606682\pi\) | ||||
−0.328911 | + | 0.944361i | \(0.606682\pi\) | |||||||
\(728\) | −6542.45 | − | 4225.58i | −0.333076 | − | 0.215124i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2655.63 | − | 4599.69i | −0.134643 | − | 0.233209i | ||||
\(731\) | −1193.90 | − | 2067.89i | −0.0604075 | − | 0.104629i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23754.7 | −1.19700 | −0.598499 | − | 0.801124i | \(-0.704236\pi\) | ||||
−0.598499 | + | 0.801124i | \(0.704236\pi\) | |||||||
\(734\) | −1840.95 | + | 3188.63i | −0.0925761 | + | 0.160347i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 34215.2 | 1.71357 | ||||||||
\(737\) | 9068.71 | − | 15707.5i | 0.453257 | − | 0.785064i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13023.6 | + | 22557.5i | 0.648282 | + | 1.12286i | 0.983533 | + | 0.180728i | \(0.0578455\pi\) |
−0.335251 | + | 0.942129i | \(0.608821\pi\) | |||||||
\(740\) | −12341.0 | −0.613059 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5485.10 | −0.271381 | ||||||||
\(743\) | 7959.65 | + | 13786.5i | 0.393016 | + | 0.680725i | 0.992846 | − | 0.119403i | \(-0.0380982\pi\) |
−0.599829 | + | 0.800128i | \(0.704765\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5759.93 | − | 9976.50i | 0.283259 | − | 0.490618i | ||||
\(746\) | 21.8924 | 0.00107445 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1111.84 | − | 1925.76i | 0.0543486 | − | 0.0941345i | ||||
\(749\) | −2172.88 | −0.106002 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1118.79 | − | 1937.81i | −0.0543613 | − | 0.0941566i | 0.837564 | − | 0.546339i | \(-0.183979\pi\) |
−0.891926 | + | 0.452182i | \(0.850646\pi\) | |||||||
\(752\) | −607.905 | − | 1052.92i | −0.0294787 | − | 0.0510587i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11328.8 | − | 7316.92i | −0.547174 | − | 0.353404i | ||||
\(755\) | 43865.5 | 2.11448 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1631.95 | − | 2826.63i | −0.0783545 | − | 0.135714i | 0.824186 | − | 0.566320i | \(-0.191633\pi\) |
−0.902540 | + | 0.430606i | \(0.858300\pi\) | |||||||
\(758\) | −1223.63 | + | 2119.38i | −0.0586334 | + | 0.101556i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9548.45 | + | 16538.4i | −0.455735 | + | 0.789357i | ||||
\(761\) | −952.456 | + | 1649.70i | −0.0453699 | + | 0.0785830i | −0.887819 | − | 0.460194i | \(-0.847780\pi\) |
0.842449 | + | 0.538777i | \(0.181113\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7940.08 | − | 13752.6i | 0.376737 | − | 0.652527i | ||||
\(764\) | 12539.1 | + | 21718.3i | 0.593781 | + | 1.02846i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9945.88 | −0.469137 | ||||||||
\(767\) | −24234.3 | − | 15652.3i | −1.14088 | − | 0.736858i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1714.94 | − | 2970.36i | −0.0804190 | − | 0.139290i | 0.823011 | − | 0.568025i | \(-0.192292\pi\) |
−0.903430 | + | 0.428736i | \(0.858959\pi\) | |||||||
\(770\) | 3682.68 | + | 6378.58i | 0.172356 | + | 0.298530i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −31991.4 | −1.49144 | ||||||||
\(773\) | −14121.8 | + | 24459.6i | −0.657082 | + | 1.13810i | 0.324285 | + | 0.945959i | \(0.394876\pi\) |
−0.981367 | + | 0.192141i | \(0.938457\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1719.53 | 0.0796997 | ||||||||
\(776\) | 14360.9 | − | 24873.9i | 0.664340 | − | 1.15067i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9293.48 | + | 16096.8i | 0.428261 | + | 0.741770i | ||||
\(779\) | 18475.4 | 0.849741 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −38993.5 | −1.78655 | ||||||||
\(782\) | −828.094 | − | 1434.30i | −0.0378677 | − | 0.0655888i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3537.24 | − | 6126.68i | 0.161135 | − | 0.279094i | ||||
\(785\) | −20114.5 | −0.914545 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3313.36 | + | 5738.91i | −0.150074 | + | 0.259937i | −0.931255 | − | 0.364369i | \(-0.881285\pi\) |
0.781180 | + | 0.624306i | \(0.214618\pi\) | |||||||
\(788\) | 22663.0 | 1.02454 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1664.02 | + | 2882.16i | 0.0749406 | + | 0.129801i | ||||
\(791\) | −8407.80 | − | 14562.7i | −0.377936 | − | 0.654603i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7690.69 | + | 4967.19i | 0.344394 | + | 0.222434i | ||||
\(794\) | −1329.25 | −0.0594120 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15882.7 | + | 27509.7i | 0.707222 | + | 1.22495i | ||||
\(797\) | −10375.4 | + | 17970.8i | −0.461125 | + | 0.798691i | −0.999017 | − | 0.0443221i | \(-0.985887\pi\) |
0.537893 | + | 0.843013i | \(0.319221\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −154.458 | + | 267.530i | −0.00683898 | + | 0.0118455i | ||||
\(800\) | 2732.71 | − | 4733.19i | 0.120770 | − | 0.209179i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2966.94 | − | 5138.90i | 0.130631 | − | 0.226260i | ||||
\(803\) | −8468.51 | − | 14667.9i | −0.372163 | − | 0.644606i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21021.9 | −0.920403 | ||||||||
\(806\) | 3079.93 | − | 1578.98i | 0.134598 | − | 0.0690041i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7229.43 | − | 12521.7i | −0.314765 | − | 0.545190i | ||||
\(809\) | 5002.66 | + | 8664.86i | 0.217409 | + | 0.376564i | 0.954015 | − | 0.299758i | \(-0.0969061\pi\) |
−0.736606 | + | 0.676322i | \(0.763573\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32773.5 | 1.41903 | 0.709515 | − | 0.704690i | \(-0.248914\pi\) | ||||
0.709515 | + | 0.704690i | \(0.248914\pi\) | |||||||
\(812\) | −6386.09 | + | 11061.0i | −0.275995 | + | 0.478037i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10269.5 | 0.442194 | ||||||||
\(815\) | 6274.04 | − | 10867.0i | 0.269657 | − | 0.467059i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14461.3 | + | 25047.7i | 0.619261 | + | 1.07259i | ||||
\(818\) | −3433.63 | −0.146765 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −17555.3 | −0.747632 | ||||||||
\(821\) | −1515.87 | − | 2625.57i | −0.0644388 | − | 0.111611i | 0.832006 | − | 0.554766i | \(-0.187192\pi\) |
−0.896445 | + | 0.443155i | \(0.853859\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15528.5 | + | 26896.2i | −0.657704 | + | 1.13918i | 0.323505 | + | 0.946226i | \(0.395139\pi\) |
−0.981209 | + | 0.192950i | \(0.938195\pi\) | |||||||
\(824\) | 19076.0 | 0.806486 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3564.88 | − | 6174.55i | 0.150167 | − | 0.260097i | ||||
\(827\) | 8770.13 | 0.368764 | 0.184382 | − | 0.982855i | \(-0.440972\pi\) | ||||
0.184382 | + | 0.982855i | \(0.440972\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19349.4 | + | 33514.2i | 0.810656 | + | 1.40410i | 0.912406 | + | 0.409287i | \(0.134223\pi\) |
−0.101750 | + | 0.994810i | \(0.532444\pi\) | |||||||
\(830\) | −2011.66 | − | 3484.30i | −0.0841274 | − | 0.145713i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 43.5622 | − | 872.824i | 0.00181520 | − | 0.0363699i | ||||
\(833\) | −1797.50 | −0.0747657 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14652.0 | − | 25378.1i | −0.607251 | − | 1.05179i | ||||
\(836\) | −13467.3 | + | 23326.0i | −0.557149 | + | 0.965010i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3982.21 | + | 6897.40i | −0.164157 | + | 0.284328i | ||||
\(839\) | −11271.9 | + | 19523.4i | −0.463824 | + | 0.803366i | −0.999148 | − | 0.0412806i | \(-0.986856\pi\) |
0.535324 | + | 0.844647i | \(0.320190\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12807.2 | + | 22182.7i | −0.525121 | + | 0.909535i | ||||
\(842\) | 5784.43 | + | 10018.9i | 0.236751 | + | 0.410065i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11161.3 | −0.455198 | ||||||||
\(845\) | 27213.3 | + | 2723.18i | 1.10789 | + | 0.110864i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5752.31 | + | 9963.29i | 0.233355 | + | 0.404183i | ||||
\(848\) | 6394.09 | + | 11074.9i | 0.258932 | + | 0.448483i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −264.553 | −0.0106754 | ||||||||
\(851\) | −14655.4 | + | 25383.9i | −0.590341 | + | 1.02250i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7751.80 | −0.311156 | −0.155578 | − | 0.987824i | \(-0.549724\pi\) | ||||
−0.155578 | + | 0.987824i | \(0.549724\pi\) | |||||||
\(854\) | −1131.30 | + | 1959.47i | −0.0453306 | + | 0.0785150i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2227.36 | − | 3857.91i | −0.0889366 | − | 0.154043i | ||||
\(857\) | −30235.6 | −1.20517 | −0.602583 | − | 0.798056i | \(-0.705862\pi\) | ||||
−0.602583 | + | 0.798056i | \(0.705862\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3568.09 | 0.141725 | 0.0708624 | − | 0.997486i | \(-0.477425\pi\) | ||||
0.0708624 | + | 0.997486i | \(0.477425\pi\) | |||||||
\(860\) | −13741.1 | − | 23800.3i | −0.544847 | − | 0.943703i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1331.10 | + | 2305.53i | −0.0525955 | + | 0.0910980i | ||||
\(863\) | 406.509 | 0.0160345 | 0.00801723 | − | 0.999968i | \(-0.497448\pi\) | ||||
0.00801723 | + | 0.999968i | \(0.497448\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19496.2 | + | 33768.5i | −0.766349 | + | 1.32736i | ||||
\(866\) | 19216.4 | 0.754040 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1638.92 | − | 2838.70i | −0.0640883 | − | 0.111004i | ||||
\(869\) | 5306.36 | + | 9190.89i | 0.207141 | + | 0.358780i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14811.2 | − | 7593.22i | 0.576185 | − | 0.295392i | ||||
\(872\) | 32556.6 | 1.26434 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 10030.4 | + | 17373.2i | 0.388197 | + | 0.672377i | ||||
\(875\) | 5325.38 | − | 9223.83i | 0.205749 | − | 0.356368i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9480.97 | + | 16421.5i | −0.365051 | + | 0.632287i | −0.988784 | − | 0.149350i | \(-0.952282\pi\) |
0.623733 | + | 0.781637i | \(0.285615\pi\) | |||||||
\(878\) | −3860.24 | + | 6686.13i | −0.148379 | + | 0.257000i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8585.94 | − | 14871.3i | 0.328900 | − | 0.569671i | ||||
\(881\) | −15514.5 | − | 26871.8i | −0.593298 | − | 1.02762i | −0.993785 | − | 0.111320i | \(-0.964492\pi\) |
0.400487 | − | 0.916303i | \(-0.368841\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33896.2 | 1.29184 | 0.645922 | − | 0.763404i | \(-0.276473\pi\) | ||||
0.645922 | + | 0.763404i | \(0.276473\pi\) | |||||||
\(884\) | 1815.87 | − | 930.938i | 0.0690886 | − | 0.0354195i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3469.32 | + | 6009.03i | 0.131551 | + | 0.227853i | ||||
\(887\) | −886.675 | − | 1535.77i | −0.0335644 | − | 0.0581353i | 0.848755 | − | 0.528786i | \(-0.177353\pi\) |
−0.882320 | + | 0.470651i | \(0.844019\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2150.62 | −0.0811354 | ||||||||
\(890\) | 5761.16 | − | 9978.62i | 0.216983 | − | 0.375825i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10864.9 | −0.407831 | ||||||||
\(893\) | 1870.90 | − | 3240.50i | 0.0701091 | − | 0.121432i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19798.1 | + | 34291.3i | 0.739415 | + | 1.28070i | ||||
\(896\) | −12921.2 | −0.481770 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7780.14 | −0.289116 | ||||||||
\(899\) | −6416.41 | − | 11113.5i | −0.238041 | − | 0.412300i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1624.63 | − | 2813.94i | 0.0600714 | − | 0.104047i | ||||
\(902\) | 14608.6 | 0.539260 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17237.2 | − | 29855.7i | 0.634182 | − | 1.09844i | ||||
\(905\) | −52663.3 | −1.93435 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7200.82 | − | 12472.2i | −0.263615 | − | 0.456595i | 0.703584 | − | 0.710612i | \(-0.251582\pi\) |
−0.967200 | + | 0.254016i | \(0.918248\pi\) | |||||||
\(908\) | −8173.67 | − | 14157.2i | −0.298737 | − | 0.517427i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −336.917 | + | 6750.55i | −0.0122733 | + | 0.245911i | ||||
\(911\) | 19324.5 | 0.702799 | 0.351400 | − | 0.936226i | \(-0.385706\pi\) | ||||
0.351400 | + | 0.936226i | \(0.385706\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6414.95 | − | 11111.0i | −0.232534 | − | 0.402761i | ||||
\(914\) | 652.723 | − | 1130.55i | 0.0236216 | − | 0.0409139i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6227.36 | + | 10786.1i | −0.224626 | + | 0.389064i | ||||
\(917\) | 5215.81 | − | 9034.05i | 0.187831 | − | 0.325333i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9324.57 | + | 16150.6i | −0.334700 | + | 0.579717i | −0.983427 | − | 0.181304i | \(-0.941968\pi\) |
0.648727 | + | 0.761021i | \(0.275302\pi\) | |||||||
\(920\) | −21548.9 | − | 37323.9i | −0.772226 | − | 1.33753i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20560.0 | −0.734390 | ||||||||
\(923\) | −30058.8 | − | 19414.1i | −1.07194 | − | 0.692331i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2341.00 | + | 4054.72i | 0.0832124 | + | 0.144128i | ||||
\(926\) | −82.8666 | − | 143.529i | −0.00294078 | − | 0.00509358i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −40788.3 | −1.44283 | ||||||||
\(929\) | 13663.2 | − | 23665.4i | 0.482535 | − | 0.835775i | −0.517264 | − | 0.855826i | \(-0.673049\pi\) |
0.999799 | + | 0.0200506i | \(0.00638272\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21772.6 | 0.766453 | ||||||||
\(932\) | 3419.99 | − | 5923.60i | 0.120199 | − | 0.208191i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12115.8 | − | 20985.1i | −0.424454 | − | 0.735176i | ||||
\(935\) | −4363.08 | −0.152608 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28699.1 | 1.00060 | 0.500298 | − | 0.865853i | \(-0.333224\pi\) | ||||
0.500298 | + | 0.865853i | \(0.333224\pi\) | |||||||
\(938\) | 2056.68 | + | 3562.28i | 0.0715917 | + | 0.124000i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1777.73 | + | 3079.13i | −0.0616844 | + | 0.106840i | ||||
\(941\) | 55401.1 | 1.91926 | 0.959630 | − | 0.281264i | \(-0.0907538\pi\) | ||||
0.959630 | + | 0.281264i | \(0.0907538\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20847.6 | + | 36109.1i | −0.719927 | + | 1.24695i | ||||
\(944\) | −16622.6 | −0.573113 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11434.6 | + | 19805.3i | 0.392993 | + | 0.680684i | ||||
\(947\) | 16629.2 | + | 28802.6i | 0.570619 | + | 0.988341i | 0.996502 | + | 0.0835631i | \(0.0266300\pi\) |
−0.425883 | + | 0.904778i | \(0.640037\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 774.758 | − | 15523.3i | 0.0265013 | − | 0.530986i | ||||
\(950\) | 3204.44 | 0.109438 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 570.103 | + | 987.447i | 0.0194088 | + | 0.0336170i | ||||
\(953\) | 2205.95 | − | 3820.81i | 0.0749817 | − | 0.129872i | −0.826097 | − | 0.563529i | \(-0.809443\pi\) |
0.901078 | + | 0.433656i | \(0.142777\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24603.0 | − | 42613.7i | 0.833650 | − | 1.44392i | ||||
\(956\) | −12683.8 | + | 21969.1i | −0.429105 | + | 0.743232i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5939.13 | − | 10286.9i | 0.200297 | − | 0.346924i | ||||
\(959\) | 4107.59 | + | 7114.55i | 0.138312 | + | 0.239563i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26497.6 | −0.889450 | ||||||||
\(962\) | 7916.39 | + | 5112.97i | 0.265317 | + | 0.171360i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11339.8 | − | 19641.1i | −0.378869 | − | 0.656220i | ||||
\(965\) | 31385.2 | + | 54360.8i | 1.04697 | + | 1.81341i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26014.3 | 0.865114 | 0.432557 | − | 0.901607i | \(-0.357611\pi\) | ||||
0.432557 | + | 0.901607i | \(0.357611\pi\) | |||||||
\(968\) | −11793.1 | + | 20426.2i | −0.391574 | + | 0.678226i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −24925.5 | −0.825063 | ||||||||
\(971\) | −18102.5 | + | 31354.4i | −0.598286 | + | 1.03626i | 0.394788 | + | 0.918772i | \(0.370818\pi\) |
−0.993074 | + | 0.117490i | \(0.962515\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10420.8 | + | 18049.4i | 0.343347 | + | 0.594694i | ||||
\(974\) | −9306.69 | −0.306166 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5275.12 | 0.173005 | ||||||||
\(977\) | −6958.19 | − | 12051.9i | −0.227853 | − | 0.394653i | 0.729319 | − | 0.684174i | \(-0.239837\pi\) |
−0.957172 | + | 0.289522i | \(0.906504\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18371.7 | − | 31820.7i | 0.599756 | − | 1.03881i | ||||
\(980\) | −20688.3 | −0.674351 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 421.477 | − | 730.020i | 0.0136964 | − | 0.0237229i | ||||
\(983\) | 13585.3 | 0.440796 | 0.220398 | − | 0.975410i | \(-0.429264\pi\) | ||||
0.220398 | + | 0.975410i | \(0.429264\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22233.6 | − | 38509.8i | −0.719210 | − | 1.24571i | ||||
\(986\) | 987.178 | + | 1709.84i | 0.0318846 | + | 0.0552257i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21995.0 | + | 11276.1i | −0.708254 | + | 0.363099i | ||||
\(989\) | −65272.4 | −2.09863 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 512.246 | + | 887.237i | 0.0164198 | + | 0.0284400i | 0.874119 | − | 0.485713i | \(-0.161440\pi\) |
−0.857699 | + | 0.514153i | \(0.828107\pi\) | |||||||
\(992\) | 5233.94 | − | 9065.46i | 0.167518 | − | 0.290150i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4421.65 | − | 7658.52i | 0.141093 | − | 0.244380i | ||||
\(995\) | 31163.6 | − | 53977.0i | 0.992919 | − | 1.71979i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9257.43 | + | 16034.3i | −0.294068 | + | 0.509341i | −0.974768 | − | 0.223222i | \(-0.928343\pi\) |
0.680700 | + | 0.732563i | \(0.261676\pi\) | |||||||
\(998\) | −2933.71 | − | 5081.34i | −0.0930512 | − | 0.161169i | ||||
\(999\) | 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 | 117.4.g.f.55.5 | yes | 16 | |
3.2 | odd | 2 | inner | 117.4.g.f.55.4 | ✓ | 16 | |
13.3 | even | 3 | 1521.4.a.bc.1.4 | 8 | |||
13.9 | even | 3 | inner | 117.4.g.f.100.5 | yes | 16 | |
13.10 | even | 6 | 1521.4.a.bd.1.5 | 8 | |||
39.23 | odd | 6 | 1521.4.a.bd.1.4 | 8 | |||
39.29 | odd | 6 | 1521.4.a.bc.1.5 | 8 | |||
39.35 | odd | 6 | inner | 117.4.g.f.100.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.4.g.f.55.4 | ✓ | 16 | 3.2 | odd | 2 | inner | |
117.4.g.f.55.5 | yes | 16 | 1.1 | even | 1 | trivial | |
117.4.g.f.100.4 | yes | 16 | 39.35 | odd | 6 | inner | |
117.4.g.f.100.5 | yes | 16 | 13.9 | even | 3 | inner | |
1521.4.a.bc.1.4 | 8 | 13.3 | even | 3 | |||
1521.4.a.bc.1.5 | 8 | 39.29 | odd | 6 | |||
1521.4.a.bd.1.4 | 8 | 39.23 | odd | 6 | |||
1521.4.a.bd.1.5 | 8 | 13.10 | even | 6 |