Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [195,2,Mod(16,195)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(195, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("195.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 195 = 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 195.i (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: | \(1.55708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.1714608.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 30x^{2} - 21x + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 16.3 | ||
Root | \(0.500000 - 2.23871i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 195.16 |
Dual form | 195.2.i.d.61.3 |
$q$-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 \(\left(\mathbb{Z}/195\mathbb{Z}\right)^\times\).
\(n\) | \(106\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.13090 | + | 1.95878i | 0.799668 | + | 1.38507i | 0.919832 | + | 0.392311i | \(0.128324\pi\) |
−0.120165 | + | 0.992754i | \(0.538342\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −1.55787 | + | 2.69832i | −0.778937 | + | 1.34916i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.13090 | + | 1.95878i | −0.461688 | + | 0.799668i | ||||
\(7\) | 0.630901 | − | 1.09275i | 0.238458 | − | 0.413022i | −0.721814 | − | 0.692087i | \(-0.756691\pi\) |
0.960272 | + | 0.279066i | \(0.0900247\pi\) | |||||||
\(8\) | −2.52360 | −0.892229 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.13090 | + | 1.95878i | 0.357622 | + | 0.619420i | ||||
\(11\) | −2.26180 | − | 3.91756i | −0.681959 | − | 1.18119i | −0.974382 | − | 0.224899i | \(-0.927795\pi\) |
0.292423 | − | 0.956289i | \(-0.405538\pi\) | |||||||
\(12\) | −3.11575 | −0.899439 | ||||||||
\(13\) | −3.45058 | − | 1.04571i | −0.957018 | − | 0.290028i | ||||
\(14\) | 2.85395 | 0.762749 | ||||||||
\(15\) | 0.500000 | + | 0.866025i | 0.129099 | + | 0.223607i | ||||
\(16\) | 0.261802 | + | 0.453455i | 0.0654506 | + | 0.113364i | ||||
\(17\) | 2.24665 | − | 3.89131i | 0.544893 | − | 0.943782i | −0.453721 | − | 0.891144i | \(-0.649904\pi\) |
0.998614 | − | 0.0526381i | \(-0.0167630\pi\) | |||||||
\(18\) | −2.26180 | −0.533112 | ||||||||
\(19\) | −2.55787 | + | 4.43037i | −0.586817 | + | 1.01640i | 0.407830 | + | 0.913058i | \(0.366286\pi\) |
−0.994646 | + | 0.103338i | \(0.967048\pi\) | |||||||
\(20\) | −1.55787 | + | 2.69832i | −0.348351 | + | 0.603362i | ||||
\(21\) | 1.26180 | 0.275348 | ||||||||
\(22\) | 5.11575 | − | 8.86074i | 1.09068 | − | 1.88912i | ||||
\(23\) | −1.11575 | − | 1.93253i | −0.232650 | − | 0.402961i | 0.725937 | − | 0.687761i | \(-0.241406\pi\) |
−0.958587 | + | 0.284800i | \(0.908073\pi\) | |||||||
\(24\) | −1.26180 | − | 2.18551i | −0.257564 | − | 0.446114i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.85395 | − | 7.94151i | −0.363589 | − | 1.55746i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.96573 | + | 3.40474i | 0.371488 | + | 0.643436i | ||||
\(29\) | 0.688776 | + | 1.19299i | 0.127902 | + | 0.221534i | 0.922864 | − | 0.385127i | \(-0.125842\pi\) |
−0.794961 | + | 0.606660i | \(0.792509\pi\) | |||||||
\(30\) | −1.13090 | + | 1.95878i | −0.206473 | + | 0.357622i | ||||
\(31\) | 8.87085 | 1.59325 | 0.796626 | − | 0.604472i | \(-0.206616\pi\) | ||||
0.796626 | + | 0.604472i | \(0.206616\pi\) | |||||||
\(32\) | −3.11575 | + | 5.39664i | −0.550792 | + | 0.954000i | ||||
\(33\) | 2.26180 | − | 3.91756i | 0.393729 | − | 0.681959i | ||||
\(34\) | 10.1630 | 1.74293 | ||||||||
\(35\) | 0.630901 | − | 1.09275i | 0.106642 | − | 0.184709i | ||||
\(36\) | −1.55787 | − | 2.69832i | −0.259646 | − | 0.449720i | ||||
\(37\) | 0.115749 | + | 0.200484i | 0.0190291 | + | 0.0329593i | 0.875383 | − | 0.483430i | \(-0.160609\pi\) |
−0.856354 | + | 0.516389i | \(0.827276\pi\) | |||||||
\(38\) | −11.5708 | −1.87703 | ||||||||
\(39\) | −0.819677 | − | 3.51114i | −0.131253 | − | 0.562233i | ||||
\(40\) | −2.52360 | −0.399017 | ||||||||
\(41\) | −0.573026 | − | 0.992511i | −0.0894917 | − | 0.155004i | 0.817805 | − | 0.575496i | \(-0.195191\pi\) |
−0.907296 | + | 0.420492i | \(0.861858\pi\) | |||||||
\(42\) | 1.42697 | + | 2.47159i | 0.220187 | + | 0.381375i | ||||
\(43\) | −3.18878 | + | 5.52312i | −0.486284 | + | 0.842268i | −0.999876 | − | 0.0157664i | \(-0.994981\pi\) |
0.513592 | + | 0.858035i | \(0.328315\pi\) | |||||||
\(44\) | 14.0944 | 2.12481 | ||||||||
\(45\) | −0.500000 | + | 0.866025i | −0.0745356 | + | 0.129099i | ||||
\(46\) | 2.52360 | − | 4.37101i | 0.372085 | − | 0.644470i | ||||
\(47\) | −10.7854 | −1.57321 | −0.786607 | − | 0.617454i | \(-0.788164\pi\) | ||||
−0.786607 | + | 0.617454i | \(0.788164\pi\) | |||||||
\(48\) | −0.261802 | + | 0.453455i | −0.0377879 | + | 0.0654506i | ||||
\(49\) | 2.70393 | + | 4.68334i | 0.386275 | + | 0.669049i | ||||
\(50\) | 1.13090 | + | 1.95878i | 0.159934 | + | 0.277013i | ||||
\(51\) | 4.49330 | 0.629188 | ||||||||
\(52\) | 8.19723 | − | 7.68167i | 1.13675 | − | 1.06526i | ||||
\(53\) | 4.52360 | 0.621365 | 0.310682 | − | 0.950514i | \(-0.399442\pi\) | ||||
0.310682 | + | 0.950514i | \(0.399442\pi\) | |||||||
\(54\) | −1.13090 | − | 1.95878i | −0.153896 | − | 0.266556i | ||||
\(55\) | −2.26180 | − | 3.91756i | −0.304981 | − | 0.528243i | ||||
\(56\) | −1.59214 | + | 2.75768i | −0.212759 | + | 0.368510i | ||||
\(57\) | −5.11575 | −0.677598 | ||||||||
\(58\) | −1.55787 | + | 2.69832i | −0.204559 | + | 0.354307i | ||||
\(59\) | 0.426974 | − | 0.739540i | 0.0555872 | − | 0.0962799i | −0.836893 | − | 0.547367i | \(-0.815630\pi\) |
0.892480 | + | 0.451087i | \(0.148964\pi\) | |||||||
\(60\) | −3.11575 | −0.402242 | ||||||||
\(61\) | −2.31968 | + | 4.01780i | −0.297004 | + | 0.514426i | −0.975449 | − | 0.220225i | \(-0.929321\pi\) |
0.678445 | + | 0.734651i | \(0.262654\pi\) | |||||||
\(62\) | 10.0321 | + | 17.3760i | 1.27407 | + | 2.20676i | ||||
\(63\) | 0.630901 | + | 1.09275i | 0.0794861 | + | 0.137674i | ||||
\(64\) | −13.0472 | −1.63090 | ||||||||
\(65\) | −3.45058 | − | 1.04571i | −0.427992 | − | 0.129704i | ||||
\(66\) | 10.2315 | 1.25941 | ||||||||
\(67\) | −6.56633 | − | 11.3732i | −0.802205 | − | 1.38946i | −0.918162 | − | 0.396205i | \(-0.870327\pi\) |
0.115958 | − | 0.993254i | \(-0.463006\pi\) | |||||||
\(68\) | 7.00000 | + | 12.1244i | 0.848875 | + | 1.47029i | ||||
\(69\) | 1.11575 | − | 1.93253i | 0.134320 | − | 0.232650i | ||||
\(70\) | 2.85395 | 0.341112 | ||||||||
\(71\) | 4.80453 | − | 8.32168i | 0.570192 | − | 0.987602i | −0.426354 | − | 0.904557i | \(-0.640202\pi\) |
0.996546 | − | 0.0830453i | \(-0.0264646\pi\) | |||||||
\(72\) | 1.26180 | − | 2.18551i | 0.148705 | − | 0.257564i | ||||
\(73\) | 13.7854 | 1.61346 | 0.806730 | − | 0.590920i | \(-0.201235\pi\) | ||||
0.806730 | + | 0.590920i | \(0.201235\pi\) | |||||||
\(74\) | −0.261802 | + | 0.453455i | −0.0304339 | + | 0.0527130i | ||||
\(75\) | 0.500000 | + | 0.866025i | 0.0577350 | + | 0.100000i | ||||
\(76\) | −7.96970 | − | 13.8039i | −0.914187 | − | 1.58342i | ||||
\(77\) | −5.70789 | −0.650475 | ||||||||
\(78\) | 5.95058 | − | 5.57632i | 0.673770 | − | 0.631394i | ||||
\(79\) | −8.87085 | −0.998049 | −0.499024 | − | 0.866588i | \(-0.666308\pi\) | ||||
−0.499024 | + | 0.866588i | \(0.666308\pi\) | |||||||
\(80\) | 0.261802 | + | 0.453455i | 0.0292704 | + | 0.0506978i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 1.29607 | − | 2.24486i | 0.143127 | − | 0.247904i | ||||
\(83\) | −8.23150 | −0.903524 | −0.451762 | − | 0.892138i | \(-0.649204\pi\) | ||||
−0.451762 | + | 0.892138i | \(0.649204\pi\) | |||||||
\(84\) | −1.96573 | + | 3.40474i | −0.214479 | + | 0.371488i | ||||
\(85\) | 2.24665 | − | 3.89131i | 0.243683 | − | 0.422072i | ||||
\(86\) | −14.4248 | −1.55546 | ||||||||
\(87\) | −0.688776 | + | 1.19299i | −0.0738445 | + | 0.127902i | ||||
\(88\) | 5.70789 | + | 9.88636i | 0.608464 | + | 1.05389i | ||||
\(89\) | −3.31122 | − | 5.73521i | −0.350989 | − | 0.607931i | 0.635434 | − | 0.772155i | \(-0.280821\pi\) |
−0.986423 | + | 0.164224i | \(0.947488\pi\) | |||||||
\(90\) | −2.26180 | −0.238415 | ||||||||
\(91\) | −3.31968 | + | 3.11089i | −0.347997 | + | 0.326110i | ||||
\(92\) | 6.95279 | 0.724879 | ||||||||
\(93\) | 4.43543 | + | 7.68238i | 0.459932 | + | 0.796626i | ||||
\(94\) | −12.1972 | − | 21.1262i | −1.25805 | − | 2.17900i | ||||
\(95\) | −2.55787 | + | 4.43037i | −0.262432 | + | 0.454546i | ||||
\(96\) | −6.23150 | −0.636000 | ||||||||
\(97\) | −5.33483 | + | 9.24019i | −0.541670 | + | 0.938200i | 0.457139 | + | 0.889395i | \(0.348874\pi\) |
−0.998808 | + | 0.0488041i | \(0.984459\pi\) | |||||||
\(98\) | −6.11575 | + | 10.5928i | −0.617784 | + | 1.07003i | ||||
\(99\) | 4.52360 | 0.454639 | ||||||||
\(100\) | −1.55787 | + | 2.69832i | −0.155787 | + | 0.269832i | ||||
\(101\) | 8.52360 | + | 14.7633i | 0.848130 | + | 1.46900i | 0.882875 | + | 0.469609i | \(0.155605\pi\) |
−0.0347444 | + | 0.999396i | \(0.511062\pi\) | |||||||
\(102\) | 5.08148 | + | 8.80138i | 0.503141 | + | 0.871466i | ||||
\(103\) | −13.9484 | −1.37437 | −0.687187 | − | 0.726481i | \(-0.741155\pi\) | ||||
−0.687187 | + | 0.726481i | \(0.741155\pi\) | |||||||
\(104\) | 8.70789 | + | 2.63896i | 0.853879 | + | 0.258771i | ||||
\(105\) | 1.26180 | 0.123139 | ||||||||
\(106\) | 5.11575 | + | 8.86074i | 0.496886 | + | 0.860631i | ||||
\(107\) | −6.24665 | − | 10.8195i | −0.603886 | − | 1.04596i | −0.992226 | − | 0.124446i | \(-0.960285\pi\) |
0.388340 | − | 0.921516i | \(-0.373049\pi\) | |||||||
\(108\) | 1.55787 | − | 2.69832i | 0.149907 | − | 0.259646i | ||||
\(109\) | −2.27871 | −0.218261 | −0.109130 | − | 0.994027i | \(-0.534807\pi\) | ||||
−0.109130 | + | 0.994027i | \(0.534807\pi\) | |||||||
\(110\) | 5.11575 | − | 8.86074i | 0.487768 | − | 0.844838i | ||||
\(111\) | −0.115749 | + | 0.200484i | −0.0109864 | + | 0.0190291i | ||||
\(112\) | 0.660685 | 0.0624289 | ||||||||
\(113\) | 0.738198 | − | 1.27860i | 0.0694438 | − | 0.120280i | −0.829213 | − | 0.558933i | \(-0.811211\pi\) |
0.898657 | + | 0.438653i | \(0.144544\pi\) | |||||||
\(114\) | −5.78541 | − | 10.0206i | −0.541853 | − | 0.938517i | ||||
\(115\) | −1.11575 | − | 1.93253i | −0.104044 | − | 0.180210i | ||||
\(116\) | −4.29211 | −0.398512 | ||||||||
\(117\) | 2.63090 | − | 2.46543i | 0.243227 | − | 0.227929i | ||||
\(118\) | 1.93146 | 0.177805 | ||||||||
\(119\) | −2.83483 | − | 4.91007i | −0.259868 | − | 0.450105i | ||||
\(120\) | −1.26180 | − | 2.18551i | −0.115186 | − | 0.199508i | ||||
\(121\) | −4.73150 | + | 8.19520i | −0.430136 | + | 0.745018i | ||||
\(122\) | −10.4933 | −0.950019 | ||||||||
\(123\) | 0.573026 | − | 0.992511i | 0.0516681 | − | 0.0894917i | ||||
\(124\) | −13.8197 | + | 23.9364i | −1.24104 | + | 2.14955i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.42697 | + | 2.47159i | −0.127125 | + | 0.220187i | ||||
\(127\) | 8.89270 | + | 15.4026i | 0.789100 | + | 1.36676i | 0.926519 | + | 0.376248i | \(0.122786\pi\) |
−0.137419 | + | 0.990513i | \(0.543881\pi\) | |||||||
\(128\) | −8.52360 | − | 14.7633i | −0.753387 | − | 1.30491i | ||||
\(129\) | −6.37755 | −0.561512 | ||||||||
\(130\) | −1.85395 | − | 7.94151i | −0.162602 | − | 0.696517i | ||||
\(131\) | 11.6697 | 1.01958 | 0.509791 | − | 0.860298i | \(-0.329723\pi\) | ||||
0.509791 | + | 0.860298i | \(0.329723\pi\) | |||||||
\(132\) | 7.04721 | + | 12.2061i | 0.613381 | + | 1.06241i | ||||
\(133\) | 3.22753 | + | 5.59025i | 0.279863 | + | 0.484736i | ||||
\(134\) | 14.8517 | − | 25.7240i | 1.28299 | − | 2.22221i | ||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −5.66966 | + | 9.82013i | −0.486169 | + | 0.842070i | ||||
\(137\) | 10.0321 | − | 17.3760i | 0.857096 | − | 1.48453i | −0.0175898 | − | 0.999845i | \(-0.505599\pi\) |
0.874686 | − | 0.484689i | \(-0.161067\pi\) | |||||||
\(138\) | 5.04721 | 0.429647 | ||||||||
\(139\) | −8.16966 | + | 14.1503i | −0.692941 | + | 1.20021i | 0.277928 | + | 0.960602i | \(0.410352\pi\) |
−0.970870 | + | 0.239608i | \(0.922981\pi\) | |||||||
\(140\) | 1.96573 | + | 3.40474i | 0.166134 | + | 0.287753i | ||||
\(141\) | −5.39270 | − | 9.34044i | −0.454148 | − | 0.786607i | ||||
\(142\) | 21.7338 | 1.82386 | ||||||||
\(143\) | 3.70789 | + | 15.8830i | 0.310070 | + | 1.32821i | ||||
\(144\) | −0.523604 | −0.0436337 | ||||||||
\(145\) | 0.688776 | + | 1.19299i | 0.0571997 | + | 0.0990728i | ||||
\(146\) | 15.5899 | + | 27.0026i | 1.29023 | + | 2.23475i | ||||
\(147\) | −2.70393 | + | 4.68334i | −0.223016 | + | 0.386275i | ||||
\(148\) | −0.721292 | −0.0592899 | ||||||||
\(149\) | 1.62245 | − | 2.81016i | 0.132916 | − | 0.230218i | −0.791883 | − | 0.610672i | \(-0.790899\pi\) |
0.924799 | + | 0.380455i | \(0.124233\pi\) | |||||||
\(150\) | −1.13090 | + | 1.95878i | −0.0923377 | + | 0.159934i | ||||
\(151\) | 5.69996 | 0.463856 | 0.231928 | − | 0.972733i | \(-0.425497\pi\) | ||||
0.231928 | + | 0.972733i | \(0.425497\pi\) | |||||||
\(152\) | 6.45506 | − | 11.1805i | 0.523575 | − | 0.906858i | ||||
\(153\) | 2.24665 | + | 3.89131i | 0.181631 | + | 0.314594i | ||||
\(154\) | −6.45506 | − | 11.1805i | −0.520164 | − | 0.900950i | ||||
\(155\) | 8.87085 | 0.712524 | ||||||||
\(156\) | 10.7511 | + | 3.25817i | 0.860780 | + | 0.260863i | ||||
\(157\) | −3.85395 | −0.307578 | −0.153789 | − | 0.988104i | \(-0.549148\pi\) | ||||
−0.153789 | + | 0.988104i | \(0.549148\pi\) | |||||||
\(158\) | −10.0321 | − | 17.3760i | −0.798108 | − | 1.38236i | ||||
\(159\) | 2.26180 | + | 3.91756i | 0.179373 | + | 0.310682i | ||||
\(160\) | −3.11575 | + | 5.39664i | −0.246322 | + | 0.426642i | ||||
\(161\) | −2.81571 | −0.221909 | ||||||||
\(162\) | 1.13090 | − | 1.95878i | 0.0888520 | − | 0.153896i | ||||
\(163\) | 4.86240 | − | 8.42192i | 0.380853 | − | 0.659656i | −0.610332 | − | 0.792146i | \(-0.708964\pi\) |
0.991184 | + | 0.132490i | \(0.0422972\pi\) | |||||||
\(164\) | 3.57081 | 0.278834 | ||||||||
\(165\) | 2.26180 | − | 3.91756i | 0.176081 | − | 0.304981i | ||||
\(166\) | −9.30901 | − | 16.1237i | −0.722519 | − | 1.25144i | ||||
\(167\) | 9.63935 | + | 16.6959i | 0.745916 | + | 1.29196i | 0.949766 | + | 0.312962i | \(0.101321\pi\) |
−0.203850 | + | 0.979002i | \(0.565346\pi\) | |||||||
\(168\) | −3.18429 | −0.245673 | ||||||||
\(169\) | 10.8130 | + | 7.21661i | 0.831768 | + | 0.555124i | ||||
\(170\) | 10.1630 | 0.779463 | ||||||||
\(171\) | −2.55787 | − | 4.43037i | −0.195606 | − | 0.338799i | ||||
\(172\) | −9.93543 | − | 17.2087i | −0.757569 | − | 1.31215i | ||||
\(173\) | 1.50845 | − | 2.61272i | 0.114686 | − | 0.198641i | −0.802968 | − | 0.596022i | \(-0.796747\pi\) |
0.917654 | + | 0.397380i | \(0.130081\pi\) | |||||||
\(174\) | −3.11575 | −0.236204 | ||||||||
\(175\) | 0.630901 | − | 1.09275i | 0.0476916 | − | 0.0826043i | ||||
\(176\) | 1.18429 | − | 2.05125i | 0.0892692 | − | 0.154619i | ||||
\(177\) | 0.853947 | 0.0641866 | ||||||||
\(178\) | 7.48933 | − | 12.9719i | 0.561349 | − | 0.972286i | ||||
\(179\) | 2.65847 | + | 4.60461i | 0.198704 | + | 0.344165i | 0.948108 | − | 0.317947i | \(-0.102994\pi\) |
−0.749405 | + | 0.662112i | \(0.769660\pi\) | |||||||
\(180\) | −1.55787 | − | 2.69832i | −0.116117 | − | 0.201121i | ||||
\(181\) | 25.8709 | 1.92297 | 0.961483 | − | 0.274866i | \(-0.0886333\pi\) | ||||
0.961483 | + | 0.274866i | \(0.0886333\pi\) | |||||||
\(182\) | −9.84777 | − | 2.98440i | −0.729965 | − | 0.221219i | ||||
\(183\) | −4.63935 | −0.342951 | ||||||||
\(184\) | 2.81571 | + | 4.87695i | 0.207577 | + | 0.359534i | ||||
\(185\) | 0.115749 | + | 0.200484i | 0.00851006 | + | 0.0147399i | ||||
\(186\) | −10.0321 | + | 17.3760i | −0.735586 | + | 1.27407i | ||||
\(187\) | −20.3259 | −1.48638 | ||||||||
\(188\) | 16.8023 | − | 29.1025i | 1.22543 | − | 2.12251i | ||||
\(189\) | −0.630901 | + | 1.09275i | −0.0458913 | + | 0.0794861i | ||||
\(190\) | −11.5708 | −0.839435 | ||||||||
\(191\) | −5.32813 | + | 9.22859i | −0.385530 | + | 0.667757i | −0.991843 | − | 0.127469i | \(-0.959315\pi\) |
0.606313 | + | 0.795226i | \(0.292648\pi\) | |||||||
\(192\) | −6.52360 | − | 11.2992i | −0.470801 | − | 0.815451i | ||||
\(193\) | −3.99155 | − | 6.91356i | −0.287318 | − | 0.497649i | 0.685851 | − | 0.727742i | \(-0.259430\pi\) |
−0.973169 | + | 0.230093i | \(0.926097\pi\) | |||||||
\(194\) | −24.1327 | −1.73262 | ||||||||
\(195\) | −0.819677 | − | 3.51114i | −0.0586983 | − | 0.251438i | ||||
\(196\) | −16.8495 | −1.20354 | ||||||||
\(197\) | −8.66966 | − | 15.0163i | −0.617688 | − | 1.06987i | −0.989907 | − | 0.141721i | \(-0.954736\pi\) |
0.372219 | − | 0.928145i | \(-0.378597\pi\) | |||||||
\(198\) | 5.11575 | + | 8.86074i | 0.363560 | + | 0.629705i | ||||
\(199\) | 0.615749 | − | 1.06651i | 0.0436493 | − | 0.0756028i | −0.843375 | − | 0.537325i | \(-0.819435\pi\) |
0.887025 | + | 0.461722i | \(0.152768\pi\) | |||||||
\(200\) | −2.52360 | −0.178446 | ||||||||
\(201\) | 6.56633 | − | 11.3732i | 0.463153 | − | 0.802205i | ||||
\(202\) | −19.2787 | + | 33.3917i | −1.35645 | + | 2.34943i | ||||
\(203\) | 1.73820 | 0.121998 | ||||||||
\(204\) | −7.00000 | + | 12.1244i | −0.490098 | + | 0.848875i | ||||
\(205\) | −0.573026 | − | 0.992511i | −0.0400219 | − | 0.0693200i | ||||
\(206\) | −15.7742 | − | 27.3218i | −1.09904 | − | 1.90360i | ||||
\(207\) | 2.23150 | 0.155100 | ||||||||
\(208\) | −0.429187 | − | 1.83845i | −0.0297587 | − | 0.127474i | ||||
\(209\) | 23.1416 | 1.60074 | ||||||||
\(210\) | 1.42697 | + | 2.47159i | 0.0984705 | + | 0.170556i | ||||
\(211\) | −5.16966 | − | 8.95411i | −0.355894 | − | 0.616426i | 0.631377 | − | 0.775476i | \(-0.282490\pi\) |
−0.987271 | + | 0.159050i | \(0.949157\pi\) | |||||||
\(212\) | −7.04721 | + | 12.2061i | −0.484004 | + | 0.838320i | ||||
\(213\) | 9.60905 | 0.658401 | ||||||||
\(214\) | 14.1287 | − | 24.4716i | 0.965817 | − | 1.67284i | ||||
\(215\) | −3.18878 | + | 5.52312i | −0.217473 | + | 0.376674i | ||||
\(216\) | 2.52360 | 0.171710 | ||||||||
\(217\) | 5.59663 | − | 9.69365i | 0.379924 | − | 0.658048i | ||||
\(218\) | −2.57699 | − | 4.46348i | −0.174536 | − | 0.302305i | ||||
\(219\) | 6.89270 | + | 11.9385i | 0.465766 | + | 0.806730i | ||||
\(220\) | 14.0944 | 0.950245 | ||||||||
\(221\) | −11.8214 | + | 11.0779i | −0.795195 | + | 0.745182i | ||||
\(222\) | −0.523604 | −0.0351420 | ||||||||
\(223\) | −10.7854 | − | 18.6809i | −0.722244 | − | 1.25096i | −0.960098 | − | 0.279663i | \(-0.909777\pi\) |
0.237854 | − | 0.971301i | \(-0.423556\pi\) | |||||||
\(224\) | 3.93146 | + | 6.80949i | 0.262682 | + | 0.454978i | ||||
\(225\) | −0.500000 | + | 0.866025i | −0.0333333 | + | 0.0577350i | ||||
\(226\) | 3.33931 | 0.222128 | ||||||||
\(227\) | −2.72305 | + | 4.71645i | −0.180735 | + | 0.313042i | −0.942131 | − | 0.335245i | \(-0.891181\pi\) |
0.761396 | + | 0.648287i | \(0.224514\pi\) | |||||||
\(228\) | 7.96970 | − | 13.8039i | 0.527806 | − | 0.914187i | ||||
\(229\) | 21.9315 | 1.44927 | 0.724636 | − | 0.689132i | \(-0.242008\pi\) | ||||
0.724636 | + | 0.689132i | \(0.242008\pi\) | |||||||
\(230\) | 2.52360 | − | 4.37101i | 0.166402 | − | 0.288216i | ||||
\(231\) | −2.85395 | − | 4.94318i | −0.187776 | − | 0.325237i | ||||
\(232\) | −1.73820 | − | 3.01065i | −0.114118 | − | 0.197659i | ||||
\(233\) | 25.3125 | 1.65828 | 0.829139 | − | 0.559042i | \(-0.188831\pi\) | ||||
0.829139 | + | 0.559042i | \(0.188831\pi\) | |||||||
\(234\) | 7.80453 | + | 2.36519i | 0.510198 | + | 0.154617i | ||||
\(235\) | −10.7854 | −0.703562 | ||||||||
\(236\) | 1.33034 | + | 2.30422i | 0.0865979 | + | 0.149992i | ||||
\(237\) | −4.43543 | − | 7.68238i | −0.288112 | − | 0.499024i | ||||
\(238\) | 6.41182 | − | 11.1056i | 0.415617 | − | 0.719869i | ||||
\(239\) | 22.5236 | 1.45693 | 0.728465 | − | 0.685083i | \(-0.240234\pi\) | ||||
0.728465 | + | 0.685083i | \(0.240234\pi\) | |||||||
\(240\) | −0.261802 | + | 0.453455i | −0.0168993 | + | 0.0292704i | ||||
\(241\) | −5.55787 | + | 9.62652i | −0.358014 | + | 0.620099i | −0.987629 | − | 0.156809i | \(-0.949879\pi\) |
0.629615 | + | 0.776907i | \(0.283213\pi\) | |||||||
\(242\) | −21.4034 | −1.37586 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −7.22753 | − | 12.5185i | −0.462695 | − | 0.801412i | ||||
\(245\) | 2.70393 | + | 4.68334i | 0.172748 | + | 0.299208i | ||||
\(246\) | 2.59214 | 0.165269 | ||||||||
\(247\) | 13.4590 | − | 12.6125i | 0.856378 | − | 0.802516i | ||||
\(248\) | −22.3865 | −1.42155 | ||||||||
\(249\) | −4.11575 | − | 7.12869i | −0.260825 | − | 0.451762i | ||||
\(250\) | 1.13090 | + | 1.95878i | 0.0715245 | + | 0.123884i | ||||
\(251\) | −5.52360 | + | 9.56716i | −0.348647 | + | 0.603874i | −0.986009 | − | 0.166690i | \(-0.946692\pi\) |
0.637363 | + | 0.770564i | \(0.280025\pi\) | |||||||
\(252\) | −3.93146 | −0.247659 | ||||||||
\(253\) | −5.04721 | + | 8.74202i | −0.317315 | + | 0.549606i | ||||
\(254\) | −20.1135 | + | 34.8377i | −1.26204 | + | 2.18591i | ||||
\(255\) | 4.49330 | 0.281381 | ||||||||
\(256\) | 6.23150 | − | 10.7933i | 0.389469 | − | 0.674580i | ||||
\(257\) | 1.01515 | + | 1.75829i | 0.0633234 | + | 0.109679i | 0.895949 | − | 0.444157i | \(-0.146497\pi\) |
−0.832626 | + | 0.553836i | \(0.813163\pi\) | |||||||
\(258\) | −7.21238 | − | 12.4922i | −0.449023 | − | 0.777731i | ||||
\(259\) | 0.292106 | 0.0181506 | ||||||||
\(260\) | 8.19723 | − | 7.68167i | 0.508371 | − | 0.476397i | ||||
\(261\) | −1.37755 | −0.0852683 | ||||||||
\(262\) | 13.1972 | + | 22.8583i | 0.815328 | + | 1.41219i | ||||
\(263\) | −1.62420 | − | 2.81320i | −0.100153 | − | 0.173469i | 0.811595 | − | 0.584221i | \(-0.198600\pi\) |
−0.911747 | + | 0.410751i | \(0.865266\pi\) | |||||||
\(264\) | −5.70789 | + | 9.88636i | −0.351297 | + | 0.608464i | ||||
\(265\) | 4.52360 | 0.277883 | ||||||||
\(266\) | −7.30004 | + | 12.6440i | −0.447594 | + | 0.775256i | ||||
\(267\) | 3.31122 | − | 5.73521i | 0.202644 | − | 0.350989i | ||||
\(268\) | 40.9181 | 2.49947 | ||||||||
\(269\) | −13.4742 | + | 23.3380i | −0.821535 | + | 1.42294i | 0.0830032 | + | 0.996549i | \(0.473549\pi\) |
−0.904539 | + | 0.426392i | \(0.859784\pi\) | |||||||
\(270\) | −1.13090 | − | 1.95878i | −0.0688245 | − | 0.119207i | ||||
\(271\) | 9.92476 | + | 17.1902i | 0.602886 | + | 1.04423i | 0.992382 | + | 0.123201i | \(0.0393161\pi\) |
−0.389495 | + | 0.921028i | \(0.627351\pi\) | |||||||
\(272\) | 2.35271 | 0.142654 | ||||||||
\(273\) | −4.35395 | − | 1.31948i | −0.263513 | − | 0.0798586i | ||||
\(274\) | 45.3811 | 2.74157 | ||||||||
\(275\) | −2.26180 | − | 3.91756i | −0.136392 | − | 0.236238i | ||||
\(276\) | 3.47640 | + | 6.02129i | 0.209254 | + | 0.362439i | ||||
\(277\) | −8.04721 | + | 13.9382i | −0.483510 | + | 0.837464i | −0.999821 | − | 0.0189376i | \(-0.993972\pi\) |
0.516311 | + | 0.856401i | \(0.327305\pi\) | |||||||
\(278\) | −36.9563 | −2.21649 | ||||||||
\(279\) | −4.43543 | + | 7.68238i | −0.265542 | + | 0.459932i | ||||
\(280\) | −1.59214 | + | 2.75768i | −0.0951489 | + | 0.164803i | ||||
\(281\) | −5.37755 | −0.320798 | −0.160399 | − | 0.987052i | \(-0.551278\pi\) | ||||
−0.160399 | + | 0.987052i | \(0.551278\pi\) | |||||||
\(282\) | 12.1972 | − | 21.1262i | 0.726334 | − | 1.25805i | ||||
\(283\) | −13.4332 | − | 23.2670i | −0.798522 | − | 1.38308i | −0.920579 | − | 0.390557i | \(-0.872282\pi\) |
0.122057 | − | 0.992523i | \(-0.461051\pi\) | |||||||
\(284\) | 14.9697 | + | 25.9283i | 0.888288 | + | 1.53856i | ||||
\(285\) | −5.11575 | −0.303031 | ||||||||
\(286\) | −26.9181 | + | 25.2251i | −1.59170 | + | 1.49159i | ||||
\(287\) | −1.44609 | −0.0853601 | ||||||||
\(288\) | −3.11575 | − | 5.39664i | −0.183597 | − | 0.318000i | ||||
\(289\) | −1.59488 | − | 2.76241i | −0.0938163 | − | 0.162495i | ||||
\(290\) | −1.55787 | + | 2.69832i | −0.0914816 | + | 0.158451i | ||||
\(291\) | −10.6697 | −0.625466 | ||||||||
\(292\) | −21.4759 | + | 37.1974i | −1.25678 | + | 2.17681i | ||||
\(293\) | −10.7096 | + | 18.5497i | −0.625664 | + | 1.08368i | 0.362748 | + | 0.931887i | \(0.381839\pi\) |
−0.988412 | + | 0.151795i | \(0.951495\pi\) | |||||||
\(294\) | −12.2315 | −0.713355 | ||||||||
\(295\) | 0.426974 | − | 0.739540i | 0.0248594 | − | 0.0430577i | ||||
\(296\) | −0.292106 | − | 0.505942i | −0.0169783 | − | 0.0294073i | ||||
\(297\) | 2.26180 | + | 3.91756i | 0.131243 | + | 0.227320i | ||||
\(298\) | 7.33931 | 0.425155 | ||||||||
\(299\) | 1.82911 | + | 7.83511i | 0.105780 | + | 0.453116i | ||||
\(300\) | −3.11575 | −0.179888 | ||||||||
\(301\) | 4.02360 | + | 6.96909i | 0.231917 | + | 0.401692i | ||||
\(302\) | 6.44609 | + | 11.1650i | 0.370931 | + | 0.642471i | ||||
\(303\) | −8.52360 | + | 14.7633i | −0.489668 | + | 0.848130i | ||||
\(304\) | −2.67863 | −0.153630 | ||||||||
\(305\) | −2.31968 | + | 4.01780i | −0.132824 | + | 0.230058i | ||||
\(306\) | −5.08148 | + | 8.80138i | −0.290489 | + | 0.503141i | ||||
\(307\) | −7.85395 | −0.448248 | −0.224124 | − | 0.974561i | \(-0.571952\pi\) | ||||
−0.224124 | + | 0.974561i | \(0.571952\pi\) | |||||||
\(308\) | 8.89218 | − | 15.4017i | 0.506679 | − | 0.877594i | ||||
\(309\) | −6.97418 | − | 12.0796i | −0.396747 | − | 0.687187i | ||||
\(310\) | 10.0321 | + | 17.3760i | 0.569783 | + | 0.986892i | ||||
\(311\) | −27.8744 | −1.58061 | −0.790305 | − | 0.612714i | \(-0.790078\pi\) | ||||
−0.790305 | + | 0.612714i | \(0.790078\pi\) | |||||||
\(312\) | 2.06854 | + | 8.86074i | 0.117108 | + | 0.501641i | ||||
\(313\) | 7.88776 | 0.445842 | 0.222921 | − | 0.974836i | \(-0.428441\pi\) | ||||
0.222921 | + | 0.974836i | \(0.428441\pi\) | |||||||
\(314\) | −4.35843 | − | 7.54903i | −0.245961 | − | 0.426016i | ||||
\(315\) | 0.630901 | + | 1.09275i | 0.0355473 | + | 0.0615696i | ||||
\(316\) | 13.8197 | − | 23.9364i | 0.777418 | − | 1.34653i | ||||
\(317\) | 13.2181 | 0.742403 | 0.371201 | − | 0.928552i | \(-0.378946\pi\) | ||||
0.371201 | + | 0.928552i | \(0.378946\pi\) | |||||||
\(318\) | −5.11575 | + | 8.86074i | −0.286877 | + | 0.496886i | ||||
\(319\) | 3.11575 | − | 5.39664i | 0.174448 | − | 0.302154i | ||||
\(320\) | −13.0472 | −0.729361 | ||||||||
\(321\) | 6.24665 | − | 10.8195i | 0.348654 | − | 0.603886i | ||||
\(322\) | −3.18429 | − | 5.51535i | −0.177454 | − | 0.307359i | ||||
\(323\) | 11.4933 | + | 19.9070i | 0.639504 | + | 1.10765i | ||||
\(324\) | 3.11575 | 0.173097 | ||||||||
\(325\) | −3.45058 | − | 1.04571i | −0.191404 | − | 0.0580056i | ||||
\(326\) | 21.9956 | 1.21822 | ||||||||
\(327\) | −1.13935 | − | 1.97342i | −0.0630064 | − | 0.109130i | ||||
\(328\) | 1.44609 | + | 2.50470i | 0.0798471 | + | 0.138299i | ||||
\(329\) | −6.80453 | + | 11.7858i | −0.375146 | + | 0.649771i | ||||
\(330\) | 10.2315 | 0.563225 | ||||||||
\(331\) | 11.9248 | − | 20.6543i | 0.655444 | − | 1.13526i | −0.326338 | − | 0.945253i | \(-0.605815\pi\) |
0.981782 | − | 0.190009i | \(-0.0608519\pi\) | |||||||
\(332\) | 12.8236 | − | 22.2112i | 0.703789 | − | 1.21900i | ||||
\(333\) | −0.231499 | −0.0126861 | ||||||||
\(334\) | −21.8023 | + | 37.7627i | −1.19297 | + | 2.06628i | ||||
\(335\) | −6.56633 | − | 11.3732i | −0.358757 | − | 0.621385i | ||||
\(336\) | 0.330343 | + | 0.572170i | 0.0180217 | + | 0.0312144i | ||||
\(337\) | 5.68306 | 0.309576 | 0.154788 | − | 0.987948i | \(-0.450531\pi\) | ||||
0.154788 | + | 0.987948i | \(0.450531\pi\) | |||||||
\(338\) | −1.90734 | + | 29.3415i | −0.103745 | + | 1.59597i | ||||
\(339\) | 1.47640 | 0.0801868 | ||||||||
\(340\) | 7.00000 | + | 12.1244i | 0.379628 | + | 0.657536i | ||||
\(341\) | −20.0641 | − | 34.7521i | −1.08653 | − | 1.88193i | ||||
\(342\) | 5.78541 | − | 10.0206i | 0.312839 | − | 0.541853i | ||||
\(343\) | 15.6563 | 0.845359 | ||||||||
\(344\) | 8.04721 | − | 13.9382i | 0.433876 | − | 0.751496i | ||||
\(345\) | 1.11575 | − | 1.93253i | 0.0600699 | − | 0.104044i | ||||
\(346\) | 6.82364 | 0.366841 | ||||||||
\(347\) | 10.7248 | − | 18.5759i | 0.575737 | − | 0.997206i | −0.420224 | − | 0.907421i | \(-0.638048\pi\) |
0.995961 | − | 0.0897859i | \(-0.0286183\pi\) | |||||||
\(348\) | −2.14605 | − | 3.71707i | −0.115041 | − | 0.199256i | ||||
\(349\) | −3.43543 | − | 5.95033i | −0.183894 | − | 0.318514i | 0.759309 | − | 0.650730i | \(-0.225537\pi\) |
−0.943203 | + | 0.332216i | \(0.892204\pi\) | |||||||
\(350\) | 2.85395 | 0.152550 | ||||||||
\(351\) | 3.45058 | + | 1.04571i | 0.184178 | + | 0.0558159i | ||||
\(352\) | 28.1888 | 1.50247 | ||||||||
\(353\) | −17.2484 | − | 29.8751i | −0.918040 | − | 1.59009i | −0.802389 | − | 0.596802i | \(-0.796438\pi\) |
−0.115651 | − | 0.993290i | \(-0.536896\pi\) | |||||||
\(354\) | 0.965730 | + | 1.67269i | 0.0513280 | + | 0.0889026i | ||||
\(355\) | 4.80453 | − | 8.32168i | 0.254998 | − | 0.441669i | ||||
\(356\) | 20.6339 | 1.09359 | ||||||||
\(357\) | 2.83483 | − | 4.91007i | 0.150035 | − | 0.259868i | ||||
\(358\) | −6.01294 | + | 10.4147i | −0.317794 | + | 0.550435i | ||||
\(359\) | −8.15945 | −0.430639 | −0.215320 | − | 0.976544i | \(-0.569079\pi\) | ||||
−0.215320 | + | 0.976544i | \(0.569079\pi\) | |||||||
\(360\) | 1.26180 | − | 2.18551i | 0.0665028 | − | 0.115186i | ||||
\(361\) | −3.58545 | − | 6.21017i | −0.188708 | − | 0.326851i | ||||
\(362\) | 29.2574 | + | 50.6753i | 1.53773 | + | 2.66343i | ||||
\(363\) | −9.46300 | −0.496679 | ||||||||
\(364\) | −3.22253 | − | 13.8039i | −0.168906 | − | 0.723522i | ||||
\(365\) | 13.7854 | 0.721561 | ||||||||
\(366\) | −5.24665 | − | 9.08747i | −0.274247 | − | 0.475009i | ||||
\(367\) | 3.42027 | + | 5.92409i | 0.178537 | + | 0.309235i | 0.941380 | − | 0.337349i | \(-0.109530\pi\) |
−0.762843 | + | 0.646584i | \(0.776197\pi\) | |||||||
\(368\) | 0.584211 | − | 1.01188i | 0.0304541 | − | 0.0527481i | ||||
\(369\) | 1.14605 | 0.0596611 | ||||||||
\(370\) | −0.261802 | + | 0.453455i | −0.0136105 | + | 0.0235740i | ||||
\(371\) | 2.85395 | − | 4.94318i | 0.148170 | − | 0.256637i | ||||
\(372\) | −27.6394 | −1.43303 | ||||||||
\(373\) | −6.90961 | + | 11.9678i | −0.357766 | + | 0.619669i | −0.987587 | − | 0.157071i | \(-0.949795\pi\) |
0.629821 | + | 0.776740i | \(0.283128\pi\) | |||||||
\(374\) | −22.9866 | − | 39.8140i | −1.18861 | − | 2.05873i | ||||
\(375\) | 0.500000 | + | 0.866025i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | 27.2181 | 1.40367 | ||||||||
\(377\) | −1.12915 | − | 4.83678i | −0.0581540 | − | 0.249107i | ||||
\(378\) | −2.85395 | −0.146791 | ||||||||
\(379\) | −5.75784 | − | 9.97286i | −0.295760 | − | 0.512272i | 0.679401 | − | 0.733767i | \(-0.262240\pi\) |
−0.975161 | + | 0.221495i | \(0.928906\pi\) | |||||||
\(380\) | −7.96970 | − | 13.8039i | −0.408837 | − | 0.708126i | ||||
\(381\) | −8.89270 | + | 15.4026i | −0.455587 | + | 0.789100i | ||||
\(382\) | −24.1024 | −1.23318 | ||||||||
\(383\) | −11.4399 | + | 19.8145i | −0.584552 | + | 1.01247i | 0.410379 | + | 0.911915i | \(0.365396\pi\) |
−0.994931 | + | 0.100559i | \(0.967937\pi\) | |||||||
\(384\) | 8.52360 | − | 14.7633i | 0.434968 | − | 0.753387i | ||||
\(385\) | −5.70789 | −0.290901 | ||||||||
\(386\) | 9.02809 | − | 15.6371i | 0.459518 | − | 0.795908i | ||||
\(387\) | −3.18878 | − | 5.52312i | −0.162095 | − | 0.280756i | ||||
\(388\) | −16.6220 | − | 28.7901i | −0.843854 | − | 1.46160i | ||||
\(389\) | −4.35271 | −0.220691 | −0.110346 | − | 0.993893i | \(-0.535196\pi\) | ||||
−0.110346 | + | 0.993893i | \(0.535196\pi\) | |||||||
\(390\) | 5.95058 | − | 5.57632i | 0.301319 | − | 0.282368i | ||||
\(391\) | −10.0268 | −0.507077 | ||||||||
\(392\) | −6.82364 | − | 11.8189i | −0.344646 | − | 0.596944i | ||||
\(393\) | 5.83483 | + | 10.1062i | 0.294328 | + | 0.509791i | ||||
\(394\) | 19.6091 | − | 33.9639i | 0.987890 | − | 1.71108i | ||||
\(395\) | −8.87085 | −0.446341 | ||||||||
\(396\) | −7.04721 | + | 12.2061i | −0.354136 | + | 0.613381i | ||||
\(397\) | −3.81122 | + | 6.60123i | −0.191280 | + | 0.331306i | −0.945675 | − | 0.325115i | \(-0.894597\pi\) |
0.754395 | + | 0.656421i | \(0.227930\pi\) | |||||||
\(398\) | 2.78541 | 0.139620 | ||||||||
\(399\) | −3.22753 | + | 5.59025i | −0.161579 | + | 0.279863i | ||||
\(400\) | 0.261802 | + | 0.453455i | 0.0130901 | + | 0.0226727i | ||||
\(401\) | −10.4248 | − | 18.0562i | −0.520588 | − | 0.901684i | −0.999713 | − | 0.0239381i | \(-0.992380\pi\) |
0.479126 | − | 0.877746i | \(-0.340954\pi\) | |||||||
\(402\) | 29.7035 | 1.48147 | ||||||||
\(403\) | −30.6096 | − | 9.27635i | −1.52477 | − | 0.462088i | ||||
\(404\) | −53.1148 | −2.64256 | ||||||||
\(405\) | −0.500000 | − | 0.866025i | −0.0248452 | − | 0.0430331i | ||||
\(406\) | 1.96573 | + | 3.40474i | 0.0975575 | + | 0.168975i | ||||
\(407\) | 0.523604 | − | 0.906910i | 0.0259541 | − | 0.0449538i | ||||
\(408\) | −11.3393 | −0.561380 | ||||||||
\(409\) | 8.48264 | − | 14.6924i | 0.419439 | − | 0.726490i | −0.576444 | − | 0.817137i | \(-0.695560\pi\) |
0.995883 | + | 0.0906466i | \(0.0288934\pi\) | |||||||
\(410\) | 1.29607 | − | 2.24486i | 0.0640085 | − | 0.110866i | ||||
\(411\) | 20.0641 | 0.989690 | ||||||||
\(412\) | 21.7298 | − | 37.6371i | 1.07055 | − | 1.85425i | ||||
\(413\) | −0.538756 | − | 0.933153i | −0.0265105 | − | 0.0459175i | ||||
\(414\) | 2.52360 | + | 4.37101i | 0.124028 | + | 0.214823i | ||||
\(415\) | −8.23150 | −0.404068 | ||||||||
\(416\) | 16.3945 | − | 15.3633i | 0.803804 | − | 0.753250i | ||||
\(417\) | −16.3393 | −0.800140 | ||||||||
\(418\) | 26.1709 | + | 45.3293i | 1.28006 | + | 2.21713i | ||||
\(419\) | −1.04942 | − | 1.81765i | −0.0512676 | − | 0.0887981i | 0.839253 | − | 0.543742i | \(-0.182993\pi\) |
−0.890520 | + | 0.454943i | \(0.849659\pi\) | |||||||
\(420\) | −1.96573 | + | 3.40474i | −0.0959178 | + | 0.166134i | ||||
\(421\) | −39.6598 | −1.93290 | −0.966449 | − | 0.256857i | \(-0.917313\pi\) | ||||
−0.966449 | + | 0.256857i | \(0.917313\pi\) | |||||||
\(422\) | 11.6927 | − | 20.2524i | 0.569194 | − | 0.985873i | ||||
\(423\) | 5.39270 | − | 9.34044i | 0.262202 | − | 0.454148i | ||||
\(424\) | −11.4158 | −0.554400 | ||||||||
\(425\) | 2.24665 | − | 3.89131i | 0.108979 | − | 0.188756i | ||||
\(426\) | 10.8669 | + | 18.8220i | 0.526502 | + | 0.911929i | ||||
\(427\) | 2.92697 | + | 5.06967i | 0.141646 | + | 0.245338i | ||||
\(428\) | 38.9260 | 1.88156 | ||||||||
\(429\) | −11.9012 | + | 11.1526i | −0.574593 | + | 0.538455i | ||||
\(430\) | −14.4248 | −0.695624 | ||||||||
\(431\) | 11.0641 | + | 19.1636i | 0.532940 | + | 0.923079i | 0.999260 | + | 0.0384626i | \(0.0122461\pi\) |
−0.466320 | + | 0.884616i | \(0.654421\pi\) | |||||||
\(432\) | −0.261802 | − | 0.453455i | −0.0125960 | − | 0.0218169i | ||||
\(433\) | 15.6781 | − | 27.1553i | 0.753442 | − | 1.30500i | −0.192703 | − | 0.981257i | \(-0.561725\pi\) |
0.946145 | − | 0.323743i | \(-0.104941\pi\) | |||||||
\(434\) | 25.3169 | 1.21525 | ||||||||
\(435\) | −0.688776 | + | 1.19299i | −0.0330243 | + | 0.0571997i | ||||
\(436\) | 3.54994 | − | 6.14868i | 0.170011 | − | 0.294468i | ||||
\(437\) | 11.4158 | 0.546091 | ||||||||
\(438\) | −15.5899 | + | 27.0026i | −0.744916 | + | 1.29023i | ||||
\(439\) | −2.15672 | − | 3.73555i | −0.102935 | − | 0.178288i | 0.809958 | − | 0.586488i | \(-0.199490\pi\) |
−0.912892 | + | 0.408200i | \(0.866157\pi\) | |||||||
\(440\) | 5.70789 | + | 9.88636i | 0.272113 | + | 0.471314i | ||||
\(441\) | −5.40786 | −0.257517 | ||||||||
\(442\) | −35.0681 | − | 10.6275i | −1.66802 | − | 0.505499i | ||||
\(443\) | 0.493301 | 0.0234374 | 0.0117187 | − | 0.999931i | \(-0.496270\pi\) | ||||
0.0117187 | + | 0.999931i | \(0.496270\pi\) | |||||||
\(444\) | −0.360646 | − | 0.624657i | −0.0171155 | − | 0.0296449i | ||||
\(445\) | −3.31122 | − | 5.73521i | −0.156967 | − | 0.271875i | ||||
\(446\) | 24.3945 | − | 42.2524i | 1.15511 | − | 2.00071i | ||||
\(447\) | 3.24490 | 0.153478 | ||||||||
\(448\) | −8.23150 | + | 14.2574i | −0.388902 | + | 0.673598i | ||||
\(449\) | 11.6563 | − | 20.1892i | 0.550093 | − | 0.952789i | −0.448174 | − | 0.893946i | \(-0.647926\pi\) |
0.998267 | − | 0.0588427i | \(-0.0187410\pi\) | |||||||
\(450\) | −2.26180 | −0.106622 | ||||||||
\(451\) | −2.59214 | + | 4.48973i | −0.122059 | + | 0.211413i | ||||
\(452\) | 2.30004 | + | 3.98378i | 0.108185 | + | 0.187381i | ||||
\(453\) | 2.84998 | + | 4.93631i | 0.133904 | + | 0.231928i | ||||
\(454\) | −12.3180 | −0.578112 | ||||||||
\(455\) | −3.31968 | + | 3.11089i | −0.155629 | + | 0.145841i | ||||
\(456\) | 12.9101 | 0.604572 | ||||||||
\(457\) | −3.33483 | − | 5.77609i | −0.155997 | − | 0.270194i | 0.777425 | − | 0.628976i | \(-0.216526\pi\) |
−0.933422 | + | 0.358782i | \(0.883192\pi\) | |||||||
\(458\) | 24.8023 | + | 42.9589i | 1.15894 | + | 2.00734i | ||||
\(459\) | −2.24665 | + | 3.89131i | −0.104865 | + | 0.181631i | ||||
\(460\) | 6.95279 | 0.324176 | ||||||||
\(461\) | −14.5596 | + | 25.2180i | −0.678110 | + | 1.17452i | 0.297440 | + | 0.954740i | \(0.403867\pi\) |
−0.975550 | + | 0.219780i | \(0.929466\pi\) | |||||||
\(462\) | 6.45506 | − | 11.1805i | 0.300317 | − | 0.520164i | ||||
\(463\) | −1.79334 | −0.0833436 | −0.0416718 | − | 0.999131i | \(-0.513268\pi\) | ||||
−0.0416718 | + | 0.999131i | \(0.513268\pi\) | |||||||
\(464\) | −0.360646 | + | 0.624657i | −0.0167426 | + | 0.0289990i | ||||
\(465\) | 4.43543 | + | 7.68238i | 0.205688 | + | 0.356262i | ||||
\(466\) | 28.6260 | + | 49.5816i | 1.32607 | + | 2.29682i | ||||
\(467\) | 16.8192 | 0.778301 | 0.389150 | − | 0.921174i | \(-0.372769\pi\) | ||||
0.389150 | + | 0.921174i | \(0.372769\pi\) | |||||||
\(468\) | 2.55391 | + | 10.9398i | 0.118054 | + | 0.505694i | ||||
\(469\) | −16.5708 | −0.765169 | ||||||||
\(470\) | −12.1972 | − | 21.1262i | −0.562616 | − | 0.974480i | ||||
\(471\) | −1.92697 | − | 3.33762i | −0.0887903 | − | 0.153789i | ||||
\(472\) | −1.07751 | + | 1.86631i | −0.0495965 | + | 0.0859037i | ||||
\(473\) | 28.8495 | 1.32650 | ||||||||
\(474\) | 10.0321 | − | 17.3760i | 0.460788 | − | 0.798108i | ||||
\(475\) | −2.55787 | + | 4.43037i | −0.117363 | + | 0.203279i | ||||
\(476\) | 17.6652 | 0.809685 | ||||||||
\(477\) | −2.26180 | + | 3.91756i | −0.103561 | + | 0.179373i | ||||
\(478\) | 25.4720 | + | 44.1187i | 1.16506 | + | 2.01794i | ||||
\(479\) | −17.5765 | − | 30.4434i | −0.803092 | − | 1.39100i | −0.917571 | − | 0.397571i | \(-0.869853\pi\) |
0.114479 | − | 0.993426i | \(-0.463480\pi\) | |||||||
\(480\) | −6.23150 | −0.284428 | ||||||||
\(481\) | −0.189754 | − | 0.812826i | −0.00865205 | − | 0.0370617i | ||||
\(482\) | −25.1416 | −1.14517 | ||||||||
\(483\) | −1.40786 | − | 2.43848i | −0.0640596 | − | 0.110955i | ||||
\(484\) | −14.7422 | − | 25.5342i | −0.670098 | − | 1.16064i | ||||
\(485\) | −5.33483 | + | 9.24019i | −0.242242 | + | 0.419576i | ||||
\(486\) | 2.26180 | 0.102597 | ||||||||
\(487\) | 4.31298 | − | 7.47030i | 0.195440 | − | 0.338511i | −0.751605 | − | 0.659614i | \(-0.770720\pi\) |
0.947045 | + | 0.321102i | \(0.104053\pi\) | |||||||
\(488\) | 5.85395 | − | 10.1393i | 0.264996 | − | 0.458986i | ||||
\(489\) | 9.72480 | 0.439771 | ||||||||
\(490\) | −6.11575 | + | 10.5928i | −0.276281 | + | 0.478533i | ||||
\(491\) | 11.6068 | + | 20.1036i | 0.523809 | + | 0.907264i | 0.999616 | + | 0.0277143i | \(0.00882287\pi\) |
−0.475807 | + | 0.879550i | \(0.657844\pi\) | |||||||
\(492\) | 1.78541 | + | 3.09242i | 0.0804924 | + | 0.139417i | ||||
\(493\) | 6.18975 | 0.278773 | ||||||||
\(494\) | 39.9260 | + | 12.0997i | 1.79636 | + | 0.544392i | ||||
\(495\) | 4.52360 | 0.203321 | ||||||||
\(496\) | 2.32241 | + | 4.02253i | 0.104279 | + | 0.180617i | ||||
\(497\) | −6.06236 | − | 10.5003i | −0.271934 | − | 0.471004i | ||||
\(498\) | 9.30901 | − | 16.1237i | 0.417147 | − | 0.722519i | ||||
\(499\) | 29.0393 | 1.29998 | 0.649988 | − | 0.759944i | \(-0.274774\pi\) | ||||
0.649988 | + | 0.759944i | \(0.274774\pi\) | |||||||
\(500\) | −1.55787 | + | 2.69832i | −0.0696703 | + | 0.120672i | ||||
\(501\) | −9.63935 | + | 16.6959i | −0.430655 | + | 0.745916i | ||||
\(502\) | −24.9866 | −1.11521 | ||||||||
\(503\) | 8.69996 | − | 15.0688i | 0.387912 | − | 0.671883i | −0.604256 | − | 0.796790i | \(-0.706530\pi\) |
0.992169 | + | 0.124906i | \(0.0398631\pi\) | |||||||
\(504\) | −1.59214 | − | 2.75768i | −0.0709198 | − | 0.122837i | ||||
\(505\) | 8.52360 | + | 14.7633i | 0.379295 | + | 0.656959i | ||||
\(506\) | −22.8316 | −1.01499 | ||||||||
\(507\) | −0.843281 | + | 12.9726i | −0.0374514 | + | 0.576134i | ||||
\(508\) | −55.4149 | −2.45864 | ||||||||
\(509\) | 11.4382 | + | 19.8115i | 0.506987 | + | 0.878128i | 0.999967 | + | 0.00808731i | \(0.00257430\pi\) |
−0.492980 | + | 0.870041i | \(0.664092\pi\) | |||||||
\(510\) | 5.08148 | + | 8.80138i | 0.225012 | + | 0.389732i | ||||
\(511\) | 8.69723 | − | 15.0640i | 0.384743 | − | 0.666394i | ||||
\(512\) | −5.90558 | −0.260992 | ||||||||
\(513\) | 2.55787 | − | 4.43037i | 0.112933 | − | 0.195606i | ||||
\(514\) | −2.29607 | + | 3.97691i | −0.101275 | + | 0.175414i | ||||
\(515\) | −13.9484 | −0.614638 | ||||||||
\(516\) | 9.93543 | − | 17.2087i | 0.437383 | − | 0.757569i | ||||
\(517\) | 24.3945 | + | 42.2524i | 1.07287 | + | 1.85826i | ||||
\(518\) | 0.330343 | + | 0.572170i | 0.0145144 | + | 0.0251397i | ||||
\(519\) | 3.01691 | 0.132427 | ||||||||
\(520\) | 8.70789 | + | 2.63896i | 0.381866 | + | 0.115726i | ||||
\(521\) | −26.3642 | −1.15503 | −0.577517 | − | 0.816378i | \(-0.695978\pi\) | ||||
−0.577517 | + | 0.816378i | \(0.695978\pi\) | |||||||
\(522\) | −1.55787 | − | 2.69832i | −0.0681863 | − | 0.118102i | ||||
\(523\) | 13.1461 | + | 22.7696i | 0.574837 | + | 0.995646i | 0.996059 | + | 0.0886892i | \(0.0282678\pi\) |
−0.421223 | + | 0.906957i | \(0.638399\pi\) | |||||||
\(524\) | −18.1799 | + | 31.4884i | −0.794191 | + | 1.37558i | ||||
\(525\) | 1.26180 | 0.0550696 | ||||||||
\(526\) | 3.67362 | − | 6.36290i | 0.160178 | − | 0.277436i | ||||
\(527\) | 19.9297 | − | 34.5193i | 0.868152 | − | 1.50368i | ||||
\(528\) | 2.36858 | 0.103079 | ||||||||
\(529\) | 9.01021 | − | 15.6061i | 0.391748 | − | 0.678528i | ||||
\(530\) | 5.11575 | + | 8.86074i | 0.222214 | + | 0.384886i | ||||
\(531\) | 0.426974 | + | 0.739540i | 0.0185291 | + | 0.0320933i | ||||
\(532\) | −20.1124 | −0.871981 | ||||||||
\(533\) | 0.939393 | + | 4.02396i | 0.0406896 | + | 0.174297i | ||||
\(534\) | 14.9787 | 0.648190 | ||||||||
\(535\) | −6.24665 | − | 10.8195i | −0.270066 | − | 0.467768i | ||||
\(536\) | 16.5708 | + | 28.7015i | 0.715750 | + | 1.23972i | ||||
\(537\) | −2.65847 | + | 4.60461i | −0.114722 | + | 0.198704i | ||||
\(538\) | −60.9519 | −2.62782 | ||||||||
\(539\) | 12.2315 | − | 21.1856i | 0.526848 | − | 0.912527i | ||||
\(540\) | 1.55787 | − | 2.69832i | 0.0670403 | − | 0.116117i | ||||
\(541\) | −0.107816 | −0.00463537 | −0.00231768 | − | 0.999997i | \(-0.500738\pi\) | ||||
−0.00231768 | + | 0.999997i | \(0.500738\pi\) | |||||||
\(542\) | −22.4478 | + | 38.8808i | −0.964218 | + | 1.67007i | ||||
\(543\) | 12.9354 | + | 22.4048i | 0.555112 | + | 0.961483i | ||||
\(544\) | 14.0000 | + | 24.2487i | 0.600245 | + | 1.03965i | ||||
\(545\) | −2.27871 | −0.0976091 | ||||||||
\(546\) | −2.33931 | − | 10.0206i | −0.100113 | − | 0.428843i | ||||
\(547\) | 12.1193 | 0.518182 | 0.259091 | − | 0.965853i | \(-0.416577\pi\) | ||||
0.259091 | + | 0.965853i | \(0.416577\pi\) | |||||||
\(548\) | 31.2574 | + | 54.1394i | 1.33525 | + | 2.31272i | ||||
\(549\) | −2.31968 | − | 4.01780i | −0.0990014 | − | 0.171475i | ||||
\(550\) | 5.11575 | − | 8.86074i | 0.218136 | − | 0.377823i | ||||
\(551\) | −7.04721 | −0.300221 | ||||||||
\(552\) | −2.81571 | + | 4.87695i | −0.119845 | + | 0.207577i | ||||
\(553\) | −5.59663 | + | 9.69365i | −0.237993 | + | 0.412216i | ||||
\(554\) | −36.4024 | −1.54659 | ||||||||
\(555\) | −0.115749 | + | 0.200484i | −0.00491329 | + | 0.00851006i | ||||
\(556\) | −25.4546 | − | 44.0887i | −1.07952 | − | 1.86978i | ||||
\(557\) | −19.0035 | − | 32.9150i | −0.805204 | − | 1.39466i | −0.916153 | − | 0.400829i | \(-0.868722\pi\) |
0.110948 | − | 0.993826i | \(-0.464611\pi\) | |||||||
\(558\) | −20.0641 | −0.849382 | ||||||||
\(559\) | 16.7787 | − | 15.7234i | 0.709664 | − | 0.665030i | ||||
\(560\) | 0.660685 | 0.0279191 | ||||||||
\(561\) | −10.1630 | − | 17.6028i | −0.429080 | − | 0.743189i | ||||
\(562\) | −6.08148 | − | 10.5334i | −0.256532 | − | 0.444326i | ||||
\(563\) | −7.75510 | + | 13.4322i | −0.326839 | + | 0.566101i | −0.981883 | − | 0.189490i | \(-0.939317\pi\) |
0.655044 | + | 0.755591i | \(0.272650\pi\) | |||||||
\(564\) | 33.6046 | 1.41501 | ||||||||
\(565\) | 0.738198 | − | 1.27860i | 0.0310562 | − | 0.0537909i | ||||
\(566\) | 30.3833 | − | 52.6254i | 1.27710 | − | 2.21201i | ||||
\(567\) | −1.26180 | −0.0529907 | ||||||||
\(568\) | −12.1247 | + | 21.0006i | −0.508742 | + | 0.881167i | ||||
\(569\) | −9.62024 | − | 16.6627i | −0.403301 | − | 0.698538i | 0.590821 | − | 0.806803i | \(-0.298804\pi\) |
−0.994122 | + | 0.108265i | \(0.965471\pi\) | |||||||
\(570\) | −5.78541 | − | 10.0206i | −0.242324 | − | 0.419718i | ||||
\(571\) | 27.7338 | 1.16062 | 0.580311 | − | 0.814395i | \(-0.302931\pi\) | ||||
0.580311 | + | 0.814395i | \(0.302931\pi\) | |||||||
\(572\) | −48.6339 | − | 14.7387i | −2.03349 | − | 0.616255i | ||||
\(573\) | −10.6563 | −0.445172 | ||||||||
\(574\) | −1.63539 | − | 2.83257i | −0.0682597 | − | 0.118229i | ||||
\(575\) | −1.11575 | − | 1.93253i | −0.0465300 | − | 0.0805923i | ||||
\(576\) | 6.52360 | − | 11.2992i | 0.271817 | − | 0.470801i | ||||
\(577\) | 26.9866 | 1.12347 | 0.561733 | − | 0.827318i | \(-0.310135\pi\) | ||||
0.561733 | + | 0.827318i | \(0.310135\pi\) | |||||||
\(578\) | 3.60730 | − | 6.24802i | 0.150044 | − | 0.259883i | ||||
\(579\) | 3.99155 | − | 6.91356i | 0.165883 | − | 0.287318i | ||||
\(580\) | −4.29211 | −0.178220 | ||||||||
\(581\) | −5.19326 | + | 8.99499i | −0.215453 | + | 0.373175i | ||||
\(582\) | −12.0663 | − | 20.8995i | −0.500165 | − | 0.866312i | ||||
\(583\) | −10.2315 | − | 17.7215i | −0.423745 | − | 0.733949i | ||||
\(584\) | −34.7889 | −1.43958 | ||||||||
\(585\) | 2.63090 | − | 2.46543i | 0.108774 | − | 0.101933i | ||||
\(586\) | −48.4462 | −2.00129 | ||||||||
\(587\) | 15.4265 | + | 26.7195i | 0.636720 | + | 1.10283i | 0.986148 | + | 0.165869i | \(0.0530428\pi\) |
−0.349427 | + | 0.936963i | \(0.613624\pi\) | |||||||
\(588\) | −8.42476 | − | 14.5921i | −0.347431 | − | 0.601769i | ||||
\(589\) | −22.6905 | + | 39.3012i | −0.934947 | + | 1.61938i | ||||
\(590\) | 1.93146 | 0.0795169 | ||||||||
\(591\) | 8.66966 | − | 15.0163i | 0.356622 | − | 0.617688i | ||||
\(592\) | −0.0606069 | + | 0.104974i | −0.00249093 | + | 0.00431441i | ||||
\(593\) | 4.29211 | 0.176256 | 0.0881278 | − | 0.996109i | \(-0.471912\pi\) | ||||
0.0881278 | + | 0.996109i | \(0.471912\pi\) | |||||||
\(594\) | −5.11575 | + | 8.86074i | −0.209902 | + | 0.363560i | ||||
\(595\) | −2.83483 | − | 4.91007i | −0.116217 | − | 0.201293i | ||||
\(596\) | 5.05514 | + | 8.75576i | 0.207067 | + | 0.358650i | ||||
\(597\) | 1.23150 | 0.0504019 | ||||||||
\(598\) | −13.2787 | + | 12.4436i | −0.543007 | + | 0.508855i | ||||
\(599\) | −24.0224 | −0.981527 | −0.490764 | − | 0.871293i | \(-0.663282\pi\) | ||||
−0.490764 | + | 0.871293i | \(0.663282\pi\) | |||||||
\(600\) | −1.26180 | − | 2.18551i | −0.0515129 | − | 0.0892229i | ||||
\(601\) | −1.26577 | − | 2.19238i | −0.0516318 | − | 0.0894289i | 0.839054 | − | 0.544048i | \(-0.183109\pi\) |
−0.890686 | + | 0.454619i | \(0.849776\pi\) | |||||||
\(602\) | −9.10060 | + | 15.7627i | −0.370913 | + | 0.642440i | ||||
\(603\) | 13.1327 | 0.534803 | ||||||||
\(604\) | −8.87982 | + | 15.3803i | −0.361315 | + | 0.625816i | ||||
\(605\) | −4.73150 | + | 8.19520i | −0.192363 | + | 0.333182i | ||||
\(606\) | −38.5574 | −1.56629 | ||||||||
\(607\) | −5.72083 | + | 9.90877i | −0.232201 | + | 0.402185i | −0.958456 | − | 0.285242i | \(-0.907926\pi\) |
0.726254 | + | 0.687426i | \(0.241260\pi\) | |||||||
\(608\) | −15.9394 | − | 27.6078i | −0.646428 | − | 1.11965i | ||||
\(609\) | 0.869099 | + | 1.50532i | 0.0352177 | + | 0.0609988i | ||||
\(610\) | −10.4933 | −0.424861 | ||||||||
\(611\) | 37.2159 | + | 11.2784i | 1.50559 | + | 0.456276i | ||||
\(612\) | −14.0000 | −0.565916 | ||||||||
\(613\) | 3.59663 | + | 6.22955i | 0.145267 | + | 0.251609i | 0.929472 | − | 0.368892i | \(-0.120263\pi\) |
−0.784206 | + | 0.620501i | \(0.786929\pi\) | |||||||
\(614\) | −8.88204 | − | 15.3841i | −0.358450 | − | 0.620853i | ||||
\(615\) | 0.573026 | − | 0.992511i | 0.0231067 | − | 0.0400219i | ||||
\(616\) | 14.4045 | 0.580373 | ||||||||
\(617\) | −12.7854 | + | 22.1450i | −0.514721 | + | 0.891523i | 0.485133 | + | 0.874440i | \(0.338771\pi\) |
−0.999854 | + | 0.0170827i | \(0.994562\pi\) | |||||||
\(618\) | 15.7742 | − | 27.3218i | 0.634532 | − | 1.09904i | ||||
\(619\) | 5.98660 | 0.240622 | 0.120311 | − | 0.992736i | \(-0.461611\pi\) | ||||
0.120311 | + | 0.992736i | \(0.461611\pi\) | |||||||
\(620\) | −13.8197 | + | 23.9364i | −0.555012 | + | 0.961308i | ||||
\(621\) | 1.11575 | + | 1.93253i | 0.0447735 | + | 0.0775499i | ||||
\(622\) | −31.5231 | − | 54.5997i | −1.26396 | − | 2.18925i | ||||
\(623\) | −8.35622 | −0.334785 | ||||||||
\(624\) | 1.37755 | − | 1.29091i | 0.0551462 | − | 0.0516778i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 8.92027 | + | 15.4504i | 0.356526 | + | 0.617521i | ||||
\(627\) | 11.5708 | + | 20.0412i | 0.462094 | + | 0.800370i | ||||
\(628\) | 6.00397 | − | 10.3992i | 0.239584 | − | 0.414972i | ||||
\(629\) | 1.04019 | 0.0414752 | ||||||||
\(630\) | −1.42697 | + | 2.47159i | −0.0568520 | + | 0.0984705i | ||||
\(631\) | 21.5129 | − | 37.2615i | 0.856417 | − | 1.48336i | −0.0189080 | − | 0.999821i | \(-0.506019\pi\) |
0.875325 | − | 0.483536i | \(-0.160648\pi\) | |||||||
\(632\) | 22.3865 | 0.890488 | ||||||||
\(633\) | 5.16966 | − | 8.95411i | 0.205475 | − | 0.355894i | ||||
\(634\) | 14.9484 | + | 25.8913i | 0.593675 | + | 1.02828i | ||||
\(635\) | 8.89270 | + | 15.4026i | 0.352896 | + | 0.611234i | ||||
\(636\) | −14.0944 | −0.558880 | ||||||||
\(637\) | −4.43269 | − | 18.9878i | −0.175630 | − | 0.752322i | ||||
\(638\) | 14.0944 | 0.558003 | ||||||||
\(639\) | 4.80453 | + | 8.32168i | 0.190064 | + | 0.329201i | ||||
\(640\) | −8.52360 | − | 14.7633i | −0.336925 | − | 0.583571i | ||||
\(641\) | 3.34725 | − | 5.79760i | 0.132208 | − | 0.228992i | −0.792319 | − | 0.610107i | \(-0.791127\pi\) |
0.924528 | + | 0.381115i | \(0.124460\pi\) | |||||||
\(642\) | 28.2574 | 1.11523 | ||||||||
\(643\) | −4.09039 | + | 7.08477i | −0.161309 | + | 0.279396i | −0.935338 | − | 0.353754i | \(-0.884905\pi\) |
0.774029 | + | 0.633150i | \(0.218238\pi\) | |||||||
\(644\) | 4.38652 | − | 7.59768i | 0.172853 | − | 0.299391i | ||||
\(645\) | −6.37755 | −0.251116 | ||||||||
\(646\) | −25.9956 | + | 45.0257i | −1.02278 | + | 1.77151i | ||||
\(647\) | 5.63935 | + | 9.76765i | 0.221706 | + | 0.384006i | 0.955326 | − | 0.295554i | \(-0.0955042\pi\) |
−0.733620 | + | 0.679560i | \(0.762171\pi\) | |||||||
\(648\) | 1.26180 | + | 2.18551i | 0.0495683 | + | 0.0858548i | ||||
\(649\) | −3.86292 | −0.151633 | ||||||||
\(650\) | −1.85395 | − | 7.94151i | −0.0727178 | − | 0.311492i | ||||
\(651\) | 11.1933 | 0.438699 | ||||||||
\(652\) | 15.1500 | + | 26.2406i | 0.593321 | + | 1.02766i | ||||
\(653\) | −13.6242 | − | 23.5978i | −0.533156 | − | 0.923454i | −0.999250 | − | 0.0387184i | \(-0.987672\pi\) |
0.466094 | − | 0.884735i | \(-0.345661\pi\) | |||||||
\(654\) | 2.57699 | − | 4.46348i | 0.100768 | − | 0.174536i | ||||
\(655\) | 11.6697 | 0.455971 | ||||||||
\(656\) | 0.300039 | − | 0.519683i | 0.0117146 | − | 0.0202902i | ||||
\(657\) | −6.89270 | + | 11.9385i | −0.268910 | + | 0.465766i | ||||
\(658\) | −30.7810 | −1.19997 | ||||||||
\(659\) | −3.37755 | + | 5.85009i | −0.131571 | + | 0.227887i | −0.924282 | − | 0.381710i | \(-0.875335\pi\) |
0.792711 | + | 0.609597i | \(0.208669\pi\) | |||||||
\(660\) | 7.04721 | + | 12.2061i | 0.274312 | + | 0.475123i | ||||
\(661\) | 13.2551 | + | 22.9585i | 0.515564 | + | 0.892983i | 0.999837 | + | 0.0180657i | \(0.00575081\pi\) |
−0.484273 | + | 0.874917i | \(0.660916\pi\) | |||||||
\(662\) | 53.9429 | 2.09655 | ||||||||
\(663\) | −15.5045 | − | 4.69869i | −0.602144 | − | 0.182482i | ||||
\(664\) | 20.7730 | 0.806151 | ||||||||
\(665\) | 3.22753 | + | 5.59025i | 0.125158 | + | 0.216781i | ||||
\(666\) | −0.261802 | − | 0.453455i | −0.0101446 | − | 0.0175710i | ||||
\(667\) | 1.53700 | − | 2.66217i | 0.0595130 | − | 0.103079i | ||||
\(668\) | −60.0676 | −2.32409 | ||||||||
\(669\) | 10.7854 | − | 18.6809i | 0.416988 | − | 0.722244i | ||||
\(670\) | 14.8517 | − | 25.7240i | 0.573773 | − | 0.993803i | ||||
\(671\) | 20.9866 | 0.810179 | ||||||||
\(672\) | −3.93146 | + | 6.80949i | −0.151659 | + | 0.262682i | ||||
\(673\) | 0.338795 | + | 0.586811i | 0.0130596 | + | 0.0226199i | 0.872481 | − | 0.488647i | \(-0.162510\pi\) |
−0.859422 | + | 0.511267i | \(0.829176\pi\) | |||||||
\(674\) | 6.42697 | + | 11.1318i | 0.247558 | + | 0.428783i | ||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −36.3180 | + | 17.9343i | −1.39685 | + | 0.689780i | ||||
\(677\) | −10.4630 | −0.402126 | −0.201063 | − | 0.979578i | \(-0.564440\pi\) | ||||
−0.201063 | + | 0.979578i | \(0.564440\pi\) | |||||||
\(678\) | 1.66966 | + | 2.89193i | 0.0641228 | + | 0.111064i | ||||
\(679\) | 6.73150 | + | 11.6593i | 0.258331 | + | 0.447443i | ||||
\(680\) | −5.66966 | + | 9.82013i | −0.217421 | + | 0.376585i | ||||
\(681\) | −5.44609 | −0.208695 | ||||||||
\(682\) | 45.3811 | − | 78.6023i | 1.73773 | − | 3.00984i | ||||
\(683\) | 9.37580 | − | 16.2394i | 0.358755 | − | 0.621382i | −0.628998 | − | 0.777407i | \(-0.716535\pi\) |
0.987753 | + | 0.156025i | \(0.0498680\pi\) | |||||||
\(684\) | 15.9394 | 0.609458 | ||||||||
\(685\) | 10.0321 | − | 17.3760i | 0.383305 | − | 0.663904i | ||||
\(686\) | 17.7057 | + | 30.6671i | 0.676006 | + | 1.17088i | ||||
\(687\) | 10.9657 | + | 18.9932i | 0.418369 | + | 0.724636i | ||||
\(688\) | −3.33931 | −0.127310 | ||||||||
\(689\) | −15.6091 | − | 4.73038i | −0.594657 | − | 0.180213i | ||||
\(690\) | 5.04721 | 0.192144 | ||||||||
\(691\) | −21.7827 | − | 37.7287i | −0.828652 | − | 1.43527i | −0.899096 | − | 0.437752i | \(-0.855775\pi\) |
0.0704440 | − | 0.997516i | \(-0.477558\pi\) | |||||||
\(692\) | 4.69996 | + | 8.14057i | 0.178666 | + | 0.309458i | ||||
\(693\) | 2.85395 | − | 4.94318i | 0.108412 | − | 0.187776i | ||||
\(694\) | 48.5148 | 1.84159 | ||||||||
\(695\) | −8.16966 | + | 14.1503i | −0.309893 | + | 0.536750i | ||||
\(696\) | 1.73820 | − | 3.01065i | 0.0658862 | − | 0.114118i | ||||
\(697\) | −5.14956 | −0.195054 | ||||||||
\(698\) | 7.77026 | − | 13.4585i | 0.294108 | − | 0.509411i | ||||
\(699\) | 12.6563 | + | 21.9213i | 0.478704 | + | 0.829139i | ||||
\(700\) | 1.96573 | + | 3.40474i | 0.0742976 | + | 0.128687i | ||||
\(701\) | −19.0810 | −0.720680 | −0.360340 | − | 0.932821i | \(-0.617339\pi\) | ||||
−0.360340 | + | 0.932821i | \(0.617339\pi\) | |||||||
\(702\) | 1.85395 | + | 7.94151i | 0.0699727 | + | 0.299733i | ||||
\(703\) | −1.18429 | −0.0446663 | ||||||||
\(704\) | 29.5102 | + | 51.1132i | 1.11221 | + | 1.92640i | ||||
\(705\) | −5.39270 | − | 9.34044i | −0.203101 | − | 0.351781i | ||||
\(706\) | 39.0125 | − | 67.5716i | 1.46825 | − | 2.54309i | ||||
\(707\) | 21.5102 | 0.808975 | ||||||||
\(708\) | −1.33034 | + | 2.30422i | −0.0499973 | + | 0.0865979i | ||||
\(709\) | −22.3023 | + | 38.6287i | −0.837581 | + | 1.45073i | 0.0543307 | + | 0.998523i | \(0.482697\pi\) |
−0.891912 | + | 0.452210i | \(0.850636\pi\) | |||||||
\(710\) | 21.7338 | 0.815654 | ||||||||
\(711\) | 4.43543 | − | 7.68238i | 0.166341 | − | 0.288112i | ||||
\(712\) | 8.35622 | + | 14.4734i | 0.313163 | + | 0.542414i | ||||
\(713\) | −9.89765 | − | 17.1432i | −0.370670 | − | 0.642019i | ||||
\(714\) | 12.8236 | 0.479913 | ||||||||
\(715\) | 3.70789 | + | 15.8830i | 0.138667 | + | 0.593991i | ||||
\(716\) | −16.5663 | −0.619110 | ||||||||
\(717\) | 11.2618 | + | 19.5060i | 0.420580 | + | 0.728465i | ||||
\(718\) | −9.22753 | − | 15.9826i | −0.344368 | − | 0.596464i | ||||
\(719\) | 6.49109 | − | 11.2429i | 0.242077 | − | 0.419289i | −0.719229 | − | 0.694773i | \(-0.755505\pi\) |
0.961306 | + | 0.275484i | \(0.0888381\pi\) | |||||||
\(720\) | −0.523604 | −0.0195136 | ||||||||
\(721\) | −8.80004 | + | 15.2421i | −0.327731 | + | 0.567646i | ||||
\(722\) | 8.10957 | − | 14.0462i | 0.301807 | − | 0.522745i | ||||
\(723\) | −11.1157 | −0.413399 | ||||||||
\(724\) | −40.3035 | + | 69.8078i | −1.49787 | + | 2.59439i | ||||
\(725\) | 0.688776 | + | 1.19299i | 0.0255805 | + | 0.0443067i | ||||
\(726\) | −10.7017 | − | 18.5359i | −0.397178 | − | 0.687932i | ||||
\(727\) | 17.3980 | 0.645255 | 0.322627 | − | 0.946526i | \(-0.395434\pi\) | ||||
0.322627 | + | 0.946526i | \(0.395434\pi\) | |||||||
\(728\) | 8.37755 | − | 7.85065i | 0.310493 | − | 0.290965i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 15.5899 | + | 27.0026i | 0.577009 | + | 0.999409i | ||||
\(731\) | 14.3281 | + | 24.8170i | 0.529945 | + | 0.917892i | ||||
\(732\) | 7.22753 | − | 12.5185i | 0.267137 | − | 0.462695i | ||||
\(733\) | 45.8272 | 1.69266 | 0.846332 | − | 0.532655i | \(-0.178806\pi\) | ||||
0.846332 | + | 0.532655i | \(0.178806\pi\) | |||||||
\(734\) | −7.73598 | + | 13.3991i | −0.285540 | + | 0.494570i | ||||
\(735\) | −2.70393 | + | 4.68334i | −0.0997359 | + | 0.172748i | ||||
\(736\) | 13.9056 | 0.512567 | ||||||||
\(737\) | −29.7035 | + | 51.4479i | −1.09414 | + | 1.89511i | ||||
\(738\) | 1.29607 | + | 2.24486i | 0.0477091 | + | 0.0826346i | ||||
\(739\) | −8.78541 | − | 15.2168i | −0.323176 | − | 0.559758i | 0.657965 | − | 0.753048i | \(-0.271417\pi\) |
−0.981142 | + | 0.193290i | \(0.938084\pi\) | |||||||
\(740\) | −0.721292 | −0.0265152 | ||||||||
\(741\) | 17.6523 | + | 5.34959i | 0.648473 | + | 0.196522i | ||||
\(742\) | 12.9101 | 0.473946 | ||||||||
\(743\) | 15.1781 | + | 26.2893i | 0.556831 | + | 0.964459i | 0.997759 | + | 0.0669167i | \(0.0213162\pi\) |
−0.440928 | + | 0.897543i | \(0.645350\pi\) | |||||||
\(744\) | −11.1933 | − | 19.3873i | −0.410365 | − | 0.710773i | ||||
\(745\) | 1.62245 | − | 2.81016i | 0.0594419 | − | 0.102956i | ||||
\(746\) | −31.2563 | −1.14438 | ||||||||
\(747\) | 4.11575 | − | 7.12869i | 0.150587 | − | 0.260825i | ||||
\(748\) | 31.6652 | − | 54.8458i | 1.15780 | − | 2.00536i | ||||
\(749\) | −15.7641 | −0.576007 | ||||||||
\(750\) | −1.13090 | + | 1.95878i | −0.0412947 | + | 0.0715245i | ||||
\(751\) | −1.90162 | − | 3.29369i | −0.0693909 | − | 0.120189i | 0.829242 | − | 0.558889i | \(-0.188772\pi\) |
−0.898633 | + | 0.438700i | \(0.855439\pi\) | |||||||
\(752\) | −2.82364 | − | 4.89069i | −0.102968 | − | 0.178345i | ||||
\(753\) | −11.0472 | −0.402583 | ||||||||
\(754\) | 8.19723 | − | 7.68167i | 0.298525 | − | 0.279750i | ||||
\(755\) | 5.69996 | 0.207443 | ||||||||
\(756\) | −1.96573 | − | 3.40474i | −0.0714929 | − | 0.123829i | ||||
\(757\) | 1.70393 | + | 2.95129i | 0.0619303 | + | 0.107266i | 0.895328 | − | 0.445407i | \(-0.146941\pi\) |
−0.833398 | + | 0.552673i | \(0.813608\pi\) | |||||||
\(758\) | 13.0231 | − | 22.5566i | 0.473020 | − | 0.819294i | ||||
\(759\) | −10.0944 | −0.366404 | ||||||||
\(760\) | 6.45506 | − | 11.1805i | 0.234150 | − | 0.405559i | ||||
\(761\) | −3.62245 | + | 6.27426i | −0.131314 | + | 0.227442i | −0.924183 | − | 0.381949i | \(-0.875253\pi\) |
0.792870 | + | 0.609391i | \(0.208586\pi\) | |||||||
\(762\) | −40.2271 | −1.45727 | ||||||||
\(763\) | −1.43764 | + | 2.49006i | −0.0520460 | + | 0.0901464i | ||||
\(764\) | −16.6011 | − | 28.7540i | −0.600607 | − | 1.04028i | ||||
\(765\) | 2.24665 | + | 3.89131i | 0.0812278 | + | 0.140691i | ||||
\(766\) | −51.7496 | −1.86979 | ||||||||
\(767\) | −2.24665 | + | 2.10535i | −0.0811218 | + | 0.0760198i | ||||
\(768\) | 12.4630 | 0.449720 | ||||||||
\(769\) | −15.5882 | − | 26.9995i | −0.562124 | − | 0.973627i | −0.997311 | − | 0.0732873i | \(-0.976651\pi\) |
0.435187 | − | 0.900340i | \(-0.356682\pi\) | |||||||
\(770\) | −6.45506 | − | 11.1805i | −0.232624 | − | 0.402917i | ||||
\(771\) | −1.01515 | + | 1.75829i | −0.0365598 | + | 0.0633234i | ||||
\(772\) | 24.8733 | 0.895210 | ||||||||
\(773\) | −9.73026 | + | 16.8533i | −0.349973 | + | 0.606172i | −0.986244 | − | 0.165294i | \(-0.947143\pi\) |
0.636271 | + | 0.771466i | \(0.280476\pi\) | |||||||
\(774\) | 7.21238 | − | 12.4922i | 0.259244 | − | 0.449023i | ||||
\(775\) | 8.87085 | 0.318650 | ||||||||
\(776\) | 13.4630 | − | 23.3186i | 0.483293 | − | 0.837089i | ||||
\(777\) | 0.146053 | + | 0.252971i | 0.00523962 | + | 0.00907528i | ||||
\(778\) | −4.92249 | − | 8.52600i | −0.176480 | − | 0.305672i | ||||
\(779\) | 5.86292 | 0.210061 | ||||||||
\(780\) | 10.7511 | + | 3.25817i | 0.384952 | + | 0.116661i | ||||
\(781\) | −43.4675 | −1.55539 | ||||||||
\(782\) | −11.3393 | − | 19.6403i | −0.405493 | − | 0.702335i | ||||
\(783\) | −0.688776 | − | 1.19299i | −0.0246148 | − | 0.0426342i | ||||
\(784\) | −1.41579 | + | 2.45222i | −0.0505639 | + | 0.0875792i | ||||
\(785\) | −3.85395 | −0.137553 | ||||||||
\(786\) | −13.1972 | + | 22.8583i | −0.470730 | + | 0.815328i | ||||
\(787\) | −7.20171 | + | 12.4737i | −0.256713 | + | 0.444641i | −0.965359 | − | 0.260923i | \(-0.915973\pi\) |
0.708646 | + | 0.705564i | \(0.249306\pi\) | |||||||
\(788\) | 54.0250 | 1.92456 | ||||||||
\(789\) | 1.62420 | − | 2.81320i | 0.0578231 | − | 0.100153i | ||||
\(790\) | −10.0321 | − | 17.3760i | −0.356925 | − | 0.618212i | ||||
\(791\) | −0.931460 | − | 1.61334i | −0.0331189 | − | 0.0573636i | ||||
\(792\) | −11.4158 | −0.405642 | ||||||||
\(793\) | 12.2057 | − | 11.4380i | 0.433436 | − | 0.406176i | ||||
\(794\) | −17.2405 | −0.611841 | ||||||||
\(795\) | 2.26180 | + | 3.91756i | 0.0802179 | + | 0.138941i | ||||
\(796\) | 1.91852 | + | 3.32298i | 0.0680002 | + | 0.117780i | ||||
\(797\) | 11.8006 | − | 20.4392i | 0.417997 | − | 0.723992i | −0.577741 | − | 0.816220i | \(-0.696066\pi\) |
0.995738 | + | 0.0922279i | \(0.0293988\pi\) | |||||||
\(798\) | −14.6001 | −0.516837 | ||||||||
\(799\) | −24.2310 | + | 41.9694i | −0.857233 | + | 1.48477i | ||||
\(800\) | −3.11575 | + | 5.39664i | −0.110158 | + | 0.190800i | ||||
\(801\) | 6.62245 | 0.233993 | ||||||||
\(802\) | 23.5787 | − | 40.8396i | 0.832595 | − | 1.44210i | ||||
\(803\) | −31.1799 | − | 54.0051i | −1.10031 | − | 1.90580i | ||||
\(804\) | 20.4590 | + | 35.4361i | 0.721534 | + | 1.24973i | ||||
\(805\) | −2.81571 | −0.0992407 | ||||||||
\(806\) | −16.4461 | − | 70.4480i | −0.579289 | − | 2.48142i | ||||
\(807\) | −26.9484 | −0.948627 | ||||||||
\(808\) | −21.5102 | − | 37.2568i | −0.756726 | − | 1.31069i | ||||
\(809\) | −13.3776 | − | 23.1706i | −0.470330 | − | 0.814635i | 0.529095 | − | 0.848563i | \(-0.322532\pi\) |
−0.999424 | + | 0.0339280i | \(0.989198\pi\) | |||||||
\(810\) | 1.13090 | − | 1.95878i | 0.0397358 | − | 0.0688245i | ||||
\(811\) | −3.58421 | −0.125859 | −0.0629293 | − | 0.998018i | \(-0.520044\pi\) | ||||
−0.0629293 | + | 0.998018i | \(0.520044\pi\) | |||||||
\(812\) | −2.70789 | + | 4.69021i | −0.0950285 | + | 0.164594i | ||||
\(813\) | −9.92476 | + | 17.1902i | −0.348077 | + | 0.602886i | ||||
\(814\) | 2.36858 | 0.0830187 | ||||||||
\(815\) | 4.86240 | − | 8.42192i | 0.170322 | − | 0.295007i | ||||
\(816\) | 1.17636 | + | 2.03751i | 0.0411807 | + | 0.0713271i | ||||
\(817\) | −16.3130 | − | 28.2549i | −0.570719 | − | 0.988514i | ||||
\(818\) | 38.3721 | 1.34165 | ||||||||
\(819\) | −1.03427 | − | 4.43037i | −0.0361403 | − | 0.154810i | ||||
\(820\) | 3.57081 | 0.124698 | ||||||||
\(821\) | −7.91806 | − | 13.7145i | −0.276342 | − | 0.478639i | 0.694131 | − | 0.719849i | \(-0.255789\pi\) |
−0.970473 | + | 0.241210i | \(0.922456\pi\) | |||||||
\(822\) | 22.6905 | + | 39.3012i | 0.791423 | + | 1.37079i | ||||
\(823\) | −3.70789 | + | 6.42226i | −0.129249 | + | 0.223866i | −0.923386 | − | 0.383873i | \(-0.874590\pi\) |
0.794137 | + | 0.607739i | \(0.207923\pi\) | |||||||
\(824\) | 35.2002 | 1.22626 | ||||||||
\(825\) | 2.26180 | − | 3.91756i | 0.0787458 | − | 0.136392i | ||||
\(826\) | 1.21856 | − | 2.11061i | 0.0423991 | − | 0.0734374i | ||||
\(827\) | −16.6036 | −0.577363 | −0.288682 | − | 0.957425i | \(-0.593217\pi\) | ||||
−0.288682 | + | 0.957425i | \(0.593217\pi\) | |||||||
\(828\) | −3.47640 | + | 6.02129i | −0.120813 | + | 0.209254i | ||||
\(829\) | 14.6421 | + | 25.3608i | 0.508541 | + | 0.880818i | 0.999951 | + | 0.00989015i | \(0.00314819\pi\) |
−0.491410 | + | 0.870928i | \(0.663518\pi\) | |||||||
\(830\) | −9.30901 | − | 16.1237i | −0.323120 | − | 0.559661i | ||||
\(831\) | −16.0944 | −0.558309 | ||||||||
\(832\) | 45.0204 | + | 13.6436i | 1.56080 | + | 0.473007i | ||||
\(833\) | 24.2991 | 0.841915 | ||||||||
\(834\) | −18.4781 | − | 32.0051i | −0.639846 | − | 1.10825i | ||||
\(835\) | 9.63935 | + | 16.6959i | 0.333584 | + | 0.577784i | ||||
\(836\) | −36.0518 | + | 62.4435i | −1.24688 | + | 2.15965i | ||||
\(837\) | −8.87085 | −0.306622 | ||||||||
\(838\) | 2.37358 | − | 4.11117i | 0.0819941 | − | 0.142018i | ||||
\(839\) | 15.0810 | − | 26.1211i | 0.520655 | − | 0.901800i | −0.479057 | − | 0.877784i | \(-0.659021\pi\) |
0.999712 | − | 0.0240164i | \(-0.00764541\pi\) | |||||||
\(840\) | −3.18429 | −0.109868 | ||||||||
\(841\) | 13.5512 | − | 23.4713i | 0.467282 | − | 0.809356i | ||||
\(842\) | −44.8513 | − | 77.6847i | −1.54568 | − | 2.67719i | ||||
\(843\) | −2.68878 | − | 4.65710i | −0.0926064 | − | 0.160399i | ||||
\(844\) | 32.2147 | 1.10888 | ||||||||
\(845\) | 10.8130 | + | 7.21661i | 0.371978 | + | 0.248259i | ||||
\(846\) | 24.3945 | 0.838699 | ||||||||
\(847\) | 5.97022 | + | 10.3407i | 0.205139 | + | 0.355311i | ||||
\(848\) | 1.18429 | + | 2.05125i | 0.0406687 | + | 0.0704402i | ||||
\(849\) | 13.4332 | − | 23.2670i | 0.461027 | − | 0.798522i | ||||
\(850\) | 10.1630 | 0.348587 | ||||||||
\(851\) | 0.258295 | − | 0.447379i | 0.00885423 | − | 0.0153360i | ||||
\(852\) | −14.9697 | + | 25.9283i | −0.512853 | + | 0.888288i | ||||
\(853\) | −2.50670 | −0.0858277 | −0.0429139 | − | 0.999079i | \(-0.513664\pi\) | ||||
−0.0429139 | + | 0.999079i | \(0.513664\pi\) | |||||||
\(854\) | −6.62024 | + | 11.4666i | −0.226540 | + | 0.392378i | ||||
\(855\) | −2.55787 | − | 4.43037i | −0.0874775 | − | 0.151515i | ||||
\(856\) | 15.7641 | + | 27.3042i | 0.538805 | + | 0.933238i | ||||
\(857\) | −24.4327 | −0.834605 | −0.417302 | − | 0.908768i | \(-0.637024\pi\) | ||||
−0.417302 | + | 0.908768i | \(0.637024\pi\) | |||||||
\(858\) | −35.3046 | − | 10.6992i | −1.20528 | − | 0.365264i | ||||
\(859\) | −7.10235 | −0.242329 | −0.121165 | − | 0.992632i | \(-0.538663\pi\) | ||||
−0.121165 | + | 0.992632i | \(0.538663\pi\) | |||||||
\(860\) | −9.93543 | − | 17.2087i | −0.338795 | − | 0.586811i | ||||
\(861\) | −0.723046 | − | 1.25235i | −0.0246413 | − | 0.0426801i | ||||
\(862\) | −25.0248 | + | 43.3443i | −0.852349 | + | 1.47631i | ||||
\(863\) | −3.24490 | −0.110458 | −0.0552288 | − | 0.998474i | \(-0.517589\pi\) | ||||
−0.0552288 | + | 0.998474i | \(0.517589\pi\) | |||||||
\(864\) | 3.11575 | − | 5.39664i | 0.106000 | − | 0.183597i | ||||
\(865\) | 1.50845 | − | 2.61272i | 0.0512889 | − | 0.0888350i | ||||
\(866\) | 70.9216 | 2.41001 | ||||||||
\(867\) | 1.59488 | − | 2.76241i | 0.0541649 | − | 0.0938163i | ||||
\(868\) | 17.4377 | + | 30.2030i | 0.591874 | + | 1.02516i | ||||
\(869\) | 20.0641 | + | 34.7521i | 0.680628 | + | 1.17888i | ||||
\(870\) | −3.11575 | −0.105634 | ||||||||
\(871\) | 10.7645 | + | 46.1106i | 0.364742 | + | 1.56240i | ||||
\(872\) | 5.75056 | 0.194738 | ||||||||
\(873\) | −5.33483 | − | 9.24019i | −0.180557 | − | 0.312733i | ||||
\(874\) | 12.9101 | + | 22.3610i | 0.436692 | + | 0.756372i | ||||
\(875\) | 0.630901 | − | 1.09275i | 0.0213284 | − | 0.0369418i | ||||
\(876\) | −42.9519 | −1.45121 | ||||||||
\(877\) | −9.49330 | + | 16.4429i | −0.320566 | + | 0.555237i | −0.980605 | − | 0.195995i | \(-0.937206\pi\) |
0.660039 | + | 0.751231i | \(0.270540\pi\) | |||||||
\(878\) | 4.87807 | − | 8.44907i | 0.164627 | − | 0.285142i | ||||
\(879\) | −21.4193 | −0.722455 | ||||||||
\(880\) | 1.18429 | − | 2.05125i | 0.0399224 | − | 0.0691476i | ||||
\(881\) | 9.73820 | + | 16.8671i | 0.328088 | + | 0.568265i | 0.982132 | − | 0.188191i | \(-0.0602623\pi\) |
−0.654044 | + | 0.756456i | \(0.726929\pi\) | |||||||
\(882\) | −6.11575 | − | 10.5928i | −0.205928 | − | 0.356678i | ||||
\(883\) | −50.5664 | −1.70169 | −0.850847 | − | 0.525413i | \(-0.823911\pi\) | ||||
−0.850847 | + | 0.525413i | \(0.823911\pi\) | |||||||
\(884\) | −11.4755 | − | 49.1560i | −0.385962 | − | 1.65330i | ||||
\(885\) | 0.853947 | 0.0287051 | ||||||||
\(886\) | 0.557875 | + | 0.966267i | 0.0187422 | + | 0.0324624i | ||||
\(887\) | 6.26356 | + | 10.8488i | 0.210310 | + | 0.364267i | 0.951811 | − | 0.306684i | \(-0.0992195\pi\) |
−0.741502 | + | 0.670951i | \(0.765886\pi\) | |||||||
\(888\) | 0.292106 | − | 0.505942i | 0.00980243 | − | 0.0169783i | ||||
\(889\) | 22.4417 | 0.752669 | ||||||||
\(890\) | 7.48933 | − | 12.9719i | 0.251043 | − | 0.434819i | ||||
\(891\) | −2.26180 | + | 3.91756i | −0.0757732 | + | 0.131243i | ||||
\(892\) | 67.2092 | 2.25033 | ||||||||
\(893\) | 27.5877 | − | 47.7833i | 0.923188 | − | 1.59901i | ||||
\(894\) | 3.66966 | + | 6.35603i | 0.122732 | + | 0.212578i | ||||
\(895\) | 2.65847 | + | 4.60461i | 0.0888629 | + | 0.153915i | ||||
\(896\) | −21.5102 | −0.718606 | ||||||||
\(897\) | −5.87085 | + | 5.50161i | −0.196022 | + | 0.183693i | ||||
\(898\) | 52.7283 | 1.75957 | ||||||||
\(899\) | 6.11003 | + | 10.5829i | 0.203781 | + | 0.352959i | ||||
\(900\) | −1.55787 | − | 2.69832i | −0.0519292 | − | 0.0899439i | ||||
\(901\) | 10.1630 | − | 17.6028i | 0.338577 | − | 0.586433i | ||||
\(902\) | −11.7258 | −0.390428 | ||||||||
\(903\) | −4.02360 | + | 6.96909i | −0.133897 | + | 0.231917i | ||||
\(904\) | −1.86292 | + | 3.22667i | −0.0619598 | + | 0.107317i | ||||
\(905\) | 25.8709 | 0.859976 | ||||||||
\(906\) | −6.44609 | + | 11.1650i | −0.214157 | + | 0.370931i | ||||
\(907\) | −14.0209 | − | 24.2849i | −0.465555 | − | 0.806366i | 0.533671 | − | 0.845692i | \(-0.320812\pi\) |
−0.999226 | + | 0.0393265i | \(0.987479\pi\) | |||||||
\(908\) | −8.48433 | − | 14.6953i | −0.281562 | − | 0.487680i | ||||
\(909\) | −17.0472 | −0.565420 | ||||||||
\(910\) | −9.84777 | − | 2.98440i | −0.326450 | − | 0.0989320i | ||||
\(911\) | 16.1977 | 0.536653 | 0.268327 | − | 0.963328i | \(-0.413529\pi\) | ||||
0.268327 | + | 0.963328i | \(0.413529\pi\) | |||||||
\(912\) | −1.33931 | − | 2.31976i | −0.0443491 | − | 0.0768150i | ||||
\(913\) | 18.6180 | + | 32.2474i | 0.616167 | + | 1.06723i | ||||
\(914\) | 7.54272 | − | 13.0644i | 0.249491 | − | 0.432131i | ||||
\(915\) | −4.63935 | −0.153372 | ||||||||
\(916\) | −34.1665 | + | 59.1781i | −1.12889 | + | 1.95530i | ||||
\(917\) | 7.36240 | − | 12.7521i | 0.243128 | − | 0.421110i | ||||
\(918\) | −10.1630 | −0.335428 | ||||||||
\(919\) | 21.6389 | − | 37.4797i | 0.713801 | − | 1.23634i | −0.249619 | − | 0.968344i | \(-0.580305\pi\) |
0.963420 | − | 0.267996i | \(-0.0863614\pi\) | |||||||
\(920\) | 2.81571 | + | 4.87695i | 0.0928312 | + | 0.160788i | ||||
\(921\) | −3.92697 | − | 6.80172i | −0.129398 | − | 0.224124i | ||||
\(922\) | −65.8620 | −2.16905 | ||||||||
\(923\) | −25.2805 | + | 23.6905i | −0.832117 | + | 0.779781i | ||||
\(924\) | 17.7844 | 0.585063 | ||||||||
\(925\) | 0.115749 | + | 0.200484i | 0.00380582 | + | 0.00659187i | ||||
\(926\) | −2.02809 | − | 3.51276i | −0.0666472 | − | 0.115436i | ||||
\(927\) | 6.97418 | − | 12.0796i | 0.229062 | − | 0.396747i | ||||
\(928\) | −8.58421 | −0.281791 | ||||||||
\(929\) | −6.88425 | + | 11.9239i | −0.225865 | + | 0.391210i | −0.956579 | − | 0.291475i | \(-0.905854\pi\) |
0.730714 | + | 0.682684i | \(0.239187\pi\) | |||||||
\(930\) | −10.0321 | + | 17.3760i | −0.328964 | + | 0.569783i | ||||
\(931\) | −27.6652 | −0.906691 | ||||||||
\(932\) | −39.4337 | + | 68.3012i | −1.29169 | + | 2.23728i | ||||
\(933\) | −13.9372 | − | 24.1399i | −0.456283 | − | 0.790305i | ||||
\(934\) | 19.0209 | + | 32.9451i | 0.622382 | + | 1.07800i | ||||
\(935\) | −20.3259 | −0.664729 | ||||||||
\(936\) | −6.63935 | + | 6.22178i | −0.217014 | + | 0.203365i | ||||
\(937\) | −38.1888 | −1.24757 | −0.623787 | − | 0.781594i | \(-0.714407\pi\) | ||||
−0.623787 | + | 0.781594i | \(0.714407\pi\) | |||||||
\(938\) | −18.7400 | − | 32.4585i | −0.611881 | − | 1.05981i | ||||
\(939\) | 3.94388 | + | 6.83100i | 0.128704 | + | 0.222921i | ||||
\(940\) | 16.8023 | − | 29.1025i | 0.548031 | − | 0.949218i | ||||
\(941\) | −13.9618 | −0.455140 | −0.227570 | − | 0.973762i | \(-0.573078\pi\) | ||||
−0.227570 | + | 0.973762i | \(0.573078\pi\) | |||||||
\(942\) | 4.35843 | − | 7.54903i | 0.142005 | − | 0.245961i | ||||
\(943\) | −1.27871 | + | 2.21479i | −0.0416405 | + | 0.0721234i | ||||
\(944\) | 0.447131 | 0.0145529 | ||||||||
\(945\) | −0.630901 | + | 1.09275i | −0.0205232 | + | 0.0355473i | ||||
\(946\) | 32.6260 | + | 56.5098i | 1.06076 | + | 1.83729i | ||||
\(947\) | −3.68481 | − | 6.38228i | −0.119740 | − | 0.207396i | 0.799924 | − | 0.600101i | \(-0.204873\pi\) |
−0.919665 | + | 0.392705i | \(0.871539\pi\) | |||||||
\(948\) | 27.6394 | 0.897684 | ||||||||
\(949\) | −47.5676 | − | 14.4155i | −1.54411 | − | 0.467948i | ||||
\(950\) | −11.5708 | −0.375407 | ||||||||
\(951\) | 6.60905 | + | 11.4472i | 0.214313 | + | 0.371201i | ||||
\(952\) | 7.15399 | + | 12.3911i | 0.231862 | + | 0.401597i | ||||
\(953\) | −11.6091 | + | 20.1075i | −0.376054 | + | 0.651345i | −0.990484 | − | 0.137627i | \(-0.956053\pi\) |
0.614430 | + | 0.788971i | \(0.289386\pi\) | |||||||
\(954\) | −10.2315 | −0.331257 | ||||||||
\(955\) | −5.32813 | + | 9.22859i | −0.172414 | + | 0.298630i | ||||
\(956\) | −35.0890 | + | 60.7759i | −1.13486 | + | 1.96563i | ||||
\(957\) | 6.23150 | 0.201436 | ||||||||
\(958\) | 39.7546 | − | 68.8571i | 1.28441 | − | 2.22467i | ||||
\(959\) | −12.6585 | − | 21.9251i | −0.408763 | − | 0.707999i | ||||
\(960\) | −6.52360 | − | 11.2992i | −0.210548 | − | 0.364681i | ||||
\(961\) | 47.6920 | 1.53845 | ||||||||
\(962\) | 1.37755 | − | 1.29091i | 0.0444140 | − | 0.0416207i | ||||
\(963\) | 12.4933 | 0.402591 | ||||||||
\(964\) | −17.3169 | − | 29.9938i | −0.557741 | − | 0.966036i | ||||
\(965\) | −3.99155 | − | 6.91356i | −0.128492 | − | 0.222555i | ||||
\(966\) | 3.18429 | − | 5.51535i | 0.102453 | − | 0.177454i | ||||
\(967\) | −7.54402 | −0.242599 | −0.121300 | − | 0.992616i | \(-0.538706\pi\) | ||||
−0.121300 | + | 0.992616i | \(0.538706\pi\) | |||||||
\(968\) | 11.9404 | − | 20.6814i | 0.383780 | − | 0.664726i | ||||
\(969\) | −11.4933 | + | 19.9070i | −0.369218 | + | 0.639504i | ||||
\(970\) | −24.1327 | −0.774853 | ||||||||
\(971\) | 15.2921 | − | 26.4867i | 0.490747 | − | 0.849999i | −0.509196 | − | 0.860650i | \(-0.670057\pi\) |
0.999943 | + | 0.0106517i | \(0.00339059\pi\) | |||||||
\(972\) | 1.55787 | + | 2.69832i | 0.0499689 | + | 0.0865486i | ||||
\(973\) | 10.3085 | + | 17.8548i | 0.330475 | + | 0.572400i | ||||
\(974\) | 19.5102 | 0.625147 | ||||||||
\(975\) | −0.819677 | − | 3.51114i | −0.0262507 | − | 0.112447i | ||||
\(976\) | −2.42919 | −0.0777564 | ||||||||
\(977\) | 17.8405 | + | 30.9007i | 0.570770 | + | 0.988602i | 0.996487 | + | 0.0837460i | \(0.0266884\pi\) |
−0.425717 | + | 0.904856i | \(0.639978\pi\) | |||||||
\(978\) | 10.9978 | + | 19.0487i | 0.351670 | + | 0.609111i | ||||
\(979\) | −14.9787 | + | 25.9438i | −0.478720 | + | 0.829168i | ||||
\(980\) | −16.8495 | −0.538238 | ||||||||
\(981\) | 1.13935 | − | 1.97342i | 0.0363768 | − | 0.0630064i | ||||
\(982\) | −26.2524 | + | 45.4704i | −0.837747 | + | 1.45102i | ||||
\(983\) | 12.9866 | 0.414208 | 0.207104 | − | 0.978319i | \(-0.433596\pi\) | ||||
0.207104 | + | 0.978319i | \(0.433596\pi\) | |||||||
\(984\) | −1.44609 | + | 2.50470i | −0.0460997 | + | 0.0798471i | ||||
\(985\) | −8.66966 | − | 15.0163i | −0.276238 | − | 0.478459i | ||||
\(986\) | 7.00000 | + | 12.1244i | 0.222925 | + | 0.386118i | ||||
\(987\) | −13.6091 | −0.433181 | ||||||||
\(988\) | 13.0652 | + | 55.9655i | 0.415658 | + | 1.78050i | ||||
\(989\) | 14.2315 | 0.452535 | ||||||||
\(990\) | 5.11575 | + | 8.86074i | 0.162589 | + | 0.281613i | ||||
\(991\) | 11.3736 | + | 19.6996i | 0.361294 | + | 0.625779i | 0.988174 | − | 0.153336i | \(-0.0490018\pi\) |
−0.626880 | + | 0.779116i | \(0.715668\pi\) | |||||||
\(992\) | −27.6394 | + | 47.8728i | −0.877550 | + | 1.51996i | ||||
\(993\) | 23.8495 | 0.756842 | ||||||||
\(994\) | 13.7119 | − | 23.7496i | 0.434914 | − | 0.753293i | ||||
\(995\) | 0.615749 | − | 1.06651i | 0.0195206 | − | 0.0338106i | ||||
\(996\) | 25.6473 | 0.812665 | ||||||||
\(997\) | 6.92301 | − | 11.9910i | 0.219254 | − | 0.379759i | −0.735326 | − | 0.677713i | \(-0.762971\pi\) |
0.954580 | + | 0.297955i | \(0.0963044\pi\) | |||||||
\(998\) | 32.8405 | + | 56.8815i | 1.03955 | + | 1.80055i | ||||
\(999\) | −0.115749 | − | 0.200484i | −0.00366215 | − | 0.00634303i |
(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 | 195.2.i.d.16.3 | ✓ | 6 | |
3.2 | odd | 2 | 585.2.j.f.406.1 | 6 | |||
5.2 | odd | 4 | 975.2.bb.k.874.2 | 12 | |||
5.3 | odd | 4 | 975.2.bb.k.874.5 | 12 | |||
5.4 | even | 2 | 975.2.i.l.601.1 | 6 | |||
13.3 | even | 3 | 2535.2.a.bb.1.1 | 3 | |||
13.9 | even | 3 | inner | 195.2.i.d.61.3 | yes | 6 | |
13.10 | even | 6 | 2535.2.a.ba.1.3 | 3 | |||
39.23 | odd | 6 | 7605.2.a.bw.1.1 | 3 | |||
39.29 | odd | 6 | 7605.2.a.bv.1.3 | 3 | |||
39.35 | odd | 6 | 585.2.j.f.451.1 | 6 | |||
65.9 | even | 6 | 975.2.i.l.451.1 | 6 | |||
65.22 | odd | 12 | 975.2.bb.k.724.5 | 12 | |||
65.48 | odd | 12 | 975.2.bb.k.724.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.i.d.16.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
195.2.i.d.61.3 | yes | 6 | 13.9 | even | 3 | inner | |
585.2.j.f.406.1 | 6 | 3.2 | odd | 2 | |||
585.2.j.f.451.1 | 6 | 39.35 | odd | 6 | |||
975.2.i.l.451.1 | 6 | 65.9 | even | 6 | |||
975.2.i.l.601.1 | 6 | 5.4 | even | 2 | |||
975.2.bb.k.724.2 | 12 | 65.48 | odd | 12 | |||
975.2.bb.k.724.5 | 12 | 65.22 | odd | 12 | |||
975.2.bb.k.874.2 | 12 | 5.2 | odd | 4 | |||
975.2.bb.k.874.5 | 12 | 5.3 | odd | 4 | |||
2535.2.a.ba.1.3 | 3 | 13.10 | even | 6 | |||
2535.2.a.bb.1.1 | 3 | 13.3 | even | 3 | |||
7605.2.a.bv.1.3 | 3 | 39.29 | odd | 6 | |||
7605.2.a.bw.1.1 | 3 | 39.23 | odd | 6 |