Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(311,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.c (of order \(2\), degree \(1\), 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: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 311.27 | ||
Character | \(\chi\) | \(=\) | 403.311 |
Dual form | 403.2.c.b.311.6 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.99449i | 1.41032i | 0.709050 | + | 0.705158i | \(0.249124\pi\) | ||||
−0.709050 | + | 0.705158i | \(0.750876\pi\) | |||||||
\(3\) | −1.58843 | −0.917080 | −0.458540 | − | 0.888674i | \(-0.651627\pi\) | ||||
−0.458540 | + | 0.888674i | \(0.651627\pi\) | |||||||
\(4\) | −1.97798 | −0.988990 | ||||||||
\(5\) | 2.66789i | 1.19311i | 0.802570 | + | 0.596557i | \(0.203465\pi\) | ||||
−0.802570 | + | 0.596557i | \(0.796535\pi\) | |||||||
\(6\) | − | 3.16810i | − | 1.29337i | ||||||
\(7\) | − | 1.73927i | − | 0.657383i | −0.944437 | − | 0.328692i | \(-0.893392\pi\) | ||
0.944437 | − | 0.328692i | \(-0.106608\pi\) | |||||||
\(8\) | 0.0439183i | 0.0155275i | ||||||||
\(9\) | −0.476895 | −0.158965 | ||||||||
\(10\) | −5.32107 | −1.68267 | ||||||||
\(11\) | 2.93947i | 0.886283i | 0.896452 | + | 0.443142i | \(0.146136\pi\) | ||||
−0.896452 | + | 0.443142i | \(0.853864\pi\) | |||||||
\(12\) | 3.14188 | 0.906983 | ||||||||
\(13\) | −3.42506 | − | 1.12648i | −0.949941 | − | 0.312430i | ||||
\(14\) | 3.46896 | 0.927118 | ||||||||
\(15\) | − | 4.23775i | − | 1.09418i | ||||||
\(16\) | −4.04355 | −1.01089 | ||||||||
\(17\) | −1.90448 | −0.461905 | −0.230952 | − | 0.972965i | \(-0.574184\pi\) | ||||
−0.230952 | + | 0.972965i | \(0.574184\pi\) | |||||||
\(18\) | − | 0.951161i | − | 0.224191i | ||||||
\(19\) | − | 4.24721i | − | 0.974376i | −0.873297 | − | 0.487188i | \(-0.838023\pi\) | ||
0.873297 | − | 0.487188i | \(-0.161977\pi\) | |||||||
\(20\) | − | 5.27703i | − | 1.17998i | ||||||
\(21\) | 2.76271i | 0.602873i | ||||||||
\(22\) | −5.86273 | −1.24994 | ||||||||
\(23\) | 3.75923 | 0.783853 | 0.391927 | − | 0.919996i | \(-0.371809\pi\) | ||||
0.391927 | + | 0.919996i | \(0.371809\pi\) | |||||||
\(24\) | − | 0.0697611i | − | 0.0142399i | ||||||
\(25\) | −2.11762 | −0.423523 | ||||||||
\(26\) | 2.24675 | − | 6.83124i | 0.440624 | − | 1.33972i | ||||
\(27\) | 5.52280 | 1.06286 | ||||||||
\(28\) | 3.44025i | 0.650146i | ||||||||
\(29\) | −4.27051 | −0.793014 | −0.396507 | − | 0.918032i | \(-0.629778\pi\) | ||||
−0.396507 | + | 0.918032i | \(0.629778\pi\) | |||||||
\(30\) | 8.45213 | 1.54314 | ||||||||
\(31\) | 1.00000i | 0.179605i | ||||||||
\(32\) | − | 7.97698i | − | 1.41014i | ||||||
\(33\) | − | 4.66914i | − | 0.812792i | ||||||
\(34\) | − | 3.79847i | − | 0.651432i | ||||||
\(35\) | 4.64018 | 0.784334 | ||||||||
\(36\) | 0.943288 | 0.157215 | ||||||||
\(37\) | 3.05862i | 0.502835i | 0.967879 | + | 0.251417i | \(0.0808967\pi\) | ||||
−0.967879 | + | 0.251417i | \(0.919103\pi\) | |||||||
\(38\) | 8.47100 | 1.37418 | ||||||||
\(39\) | 5.44046 | + | 1.78933i | 0.871171 | + | 0.286523i | ||||
\(40\) | −0.117169 | −0.0185260 | ||||||||
\(41\) | − | 5.80663i | − | 0.906843i | −0.891296 | − | 0.453421i | \(-0.850203\pi\) | ||
0.891296 | − | 0.453421i | \(-0.149797\pi\) | |||||||
\(42\) | −5.51019 | −0.850241 | ||||||||
\(43\) | −11.6866 | −1.78218 | −0.891092 | − | 0.453822i | \(-0.850060\pi\) | ||||
−0.891092 | + | 0.453822i | \(0.850060\pi\) | |||||||
\(44\) | − | 5.81421i | − | 0.876525i | ||||||
\(45\) | − | 1.27230i | − | 0.189663i | ||||||
\(46\) | 7.49773i | 1.10548i | ||||||||
\(47\) | 10.5119i | 1.53332i | 0.642054 | + | 0.766659i | \(0.278083\pi\) | ||||
−0.642054 | + | 0.766659i | \(0.721917\pi\) | |||||||
\(48\) | 6.42290 | 0.927065 | ||||||||
\(49\) | 3.97493 | 0.567847 | ||||||||
\(50\) | − | 4.22356i | − | 0.597301i | ||||||
\(51\) | 3.02514 | 0.423604 | ||||||||
\(52\) | 6.77470 | + | 2.22816i | 0.939482 | + | 0.308990i | ||||
\(53\) | −13.8094 | −1.89687 | −0.948433 | − | 0.316979i | \(-0.897332\pi\) | ||||
−0.948433 | + | 0.316979i | \(0.897332\pi\) | |||||||
\(54\) | 11.0152i | 1.49897i | ||||||||
\(55\) | −7.84217 | −1.05744 | ||||||||
\(56\) | 0.0763859 | 0.0102075 | ||||||||
\(57\) | 6.74639i | 0.893581i | ||||||||
\(58\) | − | 8.51748i | − | 1.11840i | ||||||
\(59\) | 13.7930i | 1.79569i | 0.440308 | + | 0.897847i | \(0.354869\pi\) | ||||
−0.440308 | + | 0.897847i | \(0.645131\pi\) | |||||||
\(60\) | 8.38218i | 1.08213i | ||||||||
\(61\) | 5.05405 | 0.647104 | 0.323552 | − | 0.946210i | \(-0.395123\pi\) | ||||
0.323552 | + | 0.946210i | \(0.395123\pi\) | |||||||
\(62\) | −1.99449 | −0.253300 | ||||||||
\(63\) | 0.829450i | 0.104501i | ||||||||
\(64\) | 7.82288 | 0.977860 | ||||||||
\(65\) | 3.00532 | − | 9.13767i | 0.372764 | − | 1.13339i | ||||
\(66\) | 9.31253 | 1.14629 | ||||||||
\(67\) | 12.7046i | 1.55211i | 0.630664 | + | 0.776056i | \(0.282782\pi\) | ||||
−0.630664 | + | 0.776056i | \(0.717218\pi\) | |||||||
\(68\) | 3.76703 | 0.456819 | ||||||||
\(69\) | −5.97127 | −0.718856 | ||||||||
\(70\) | 9.25478i | 1.10616i | ||||||||
\(71\) | 5.83066i | 0.691971i | 0.938240 | + | 0.345986i | \(0.112455\pi\) | ||||
−0.938240 | + | 0.345986i | \(0.887545\pi\) | |||||||
\(72\) | − | 0.0209444i | − | 0.00246832i | ||||||
\(73\) | − | 4.92019i | − | 0.575865i | −0.957651 | − | 0.287932i | \(-0.907032\pi\) | ||
0.957651 | − | 0.287932i | \(-0.0929678\pi\) | |||||||
\(74\) | −6.10039 | −0.709156 | ||||||||
\(75\) | 3.36368 | 0.388405 | ||||||||
\(76\) | 8.40089i | 0.963648i | ||||||||
\(77\) | 5.11254 | 0.582628 | ||||||||
\(78\) | −3.56881 | + | 10.8509i | −0.404088 | + | 1.22863i | ||||
\(79\) | 0.743732 | 0.0836764 | 0.0418382 | − | 0.999124i | \(-0.486679\pi\) | ||||
0.0418382 | + | 0.999124i | \(0.486679\pi\) | |||||||
\(80\) | − | 10.7877i | − | 1.20611i | ||||||
\(81\) | −7.34189 | −0.815765 | ||||||||
\(82\) | 11.5812 | 1.27893 | ||||||||
\(83\) | − | 0.165627i | − | 0.0181799i | −0.999959 | − | 0.00908994i | \(-0.997107\pi\) | ||
0.999959 | − | 0.00908994i | \(-0.00289346\pi\) | |||||||
\(84\) | − | 5.46459i | − | 0.596235i | ||||||
\(85\) | − | 5.08094i | − | 0.551106i | ||||||
\(86\) | − | 23.3087i | − | 2.51344i | ||||||
\(87\) | 6.78340 | 0.727257 | ||||||||
\(88\) | −0.129096 | −0.0137617 | ||||||||
\(89\) | 1.85214i | 0.196326i | 0.995170 | + | 0.0981631i | \(0.0312967\pi\) | ||||
−0.995170 | + | 0.0981631i | \(0.968703\pi\) | |||||||
\(90\) | 2.53759 | 0.267485 | ||||||||
\(91\) | −1.95926 | + | 5.95712i | −0.205386 | + | 0.624475i | ||||
\(92\) | −7.43568 | −0.775223 | ||||||||
\(93\) | − | 1.58843i | − | 0.164712i | ||||||
\(94\) | −20.9659 | −2.16246 | ||||||||
\(95\) | 11.3311 | 1.16254 | ||||||||
\(96\) | 12.6709i | 1.29321i | ||||||||
\(97\) | 6.35644i | 0.645399i | 0.946501 | + | 0.322699i | \(0.104590\pi\) | ||||
−0.946501 | + | 0.322699i | \(0.895410\pi\) | |||||||
\(98\) | 7.92795i | 0.800844i | ||||||||
\(99\) | − | 1.40182i | − | 0.140888i | ||||||
\(100\) | 4.18860 | 0.418860 | ||||||||
\(101\) | 3.11790 | 0.310243 | 0.155122 | − | 0.987895i | \(-0.450423\pi\) | ||||
0.155122 | + | 0.987895i | \(0.450423\pi\) | |||||||
\(102\) | 6.03359i | 0.597415i | ||||||||
\(103\) | 2.88258 | 0.284029 | 0.142015 | − | 0.989865i | \(-0.454642\pi\) | ||||
0.142015 | + | 0.989865i | \(0.454642\pi\) | |||||||
\(104\) | 0.0494731 | − | 0.150423i | 0.00485124 | − | 0.0147502i | ||||
\(105\) | −7.37060 | −0.719297 | ||||||||
\(106\) | − | 27.5427i | − | 2.67518i | ||||||
\(107\) | −7.35117 | −0.710664 | −0.355332 | − | 0.934740i | \(-0.615632\pi\) | ||||
−0.355332 | + | 0.934740i | \(0.615632\pi\) | |||||||
\(108\) | −10.9240 | −1.05116 | ||||||||
\(109\) | 12.9872i | 1.24395i | 0.783038 | + | 0.621974i | \(0.213669\pi\) | ||||
−0.783038 | + | 0.621974i | \(0.786331\pi\) | |||||||
\(110\) | − | 15.6411i | − | 1.49132i | ||||||
\(111\) | − | 4.85841i | − | 0.461140i | ||||||
\(112\) | 7.03285i | 0.664541i | ||||||||
\(113\) | −7.63258 | −0.718013 | −0.359006 | − | 0.933335i | \(-0.616884\pi\) | ||||
−0.359006 | + | 0.933335i | \(0.616884\pi\) | |||||||
\(114\) | −13.4556 | −1.26023 | ||||||||
\(115\) | 10.0292i | 0.935227i | ||||||||
\(116\) | 8.44698 | 0.784282 | ||||||||
\(117\) | 1.63339 | + | 0.537213i | 0.151007 | + | 0.0496653i | ||||
\(118\) | −27.5099 | −2.53249 | ||||||||
\(119\) | 3.31242i | 0.303649i | ||||||||
\(120\) | 0.186115 | 0.0169899 | ||||||||
\(121\) | 2.35952 | 0.214502 | ||||||||
\(122\) | 10.0802i | 0.912621i | ||||||||
\(123\) | 9.22341i | 0.831647i | ||||||||
\(124\) | − | 1.97798i | − | 0.177628i | ||||||
\(125\) | 7.68987i | 0.687803i | ||||||||
\(126\) | −1.65433 | −0.147379 | ||||||||
\(127\) | −0.0992933 | −0.00881085 | −0.00440543 | − | 0.999990i | \(-0.501402\pi\) | ||||
−0.00440543 | + | 0.999990i | \(0.501402\pi\) | |||||||
\(128\) | − | 0.351325i | − | 0.0310530i | ||||||
\(129\) | 18.5633 | 1.63440 | ||||||||
\(130\) | 18.2250 | + | 5.99408i | 1.59844 | + | 0.525715i | ||||
\(131\) | 1.56404 | 0.136651 | 0.0683256 | − | 0.997663i | \(-0.478234\pi\) | ||||
0.0683256 | + | 0.997663i | \(0.478234\pi\) | |||||||
\(132\) | 9.23546i | 0.803843i | ||||||||
\(133\) | −7.38705 | −0.640539 | ||||||||
\(134\) | −25.3391 | −2.18897 | ||||||||
\(135\) | 14.7342i | 1.26812i | ||||||||
\(136\) | − | 0.0836416i | − | 0.00717221i | ||||||
\(137\) | 7.31021i | 0.624553i | 0.949991 | + | 0.312277i | \(0.101092\pi\) | ||||
−0.949991 | + | 0.312277i | \(0.898908\pi\) | |||||||
\(138\) | − | 11.9096i | − | 1.01381i | ||||||
\(139\) | 8.35831 | 0.708943 | 0.354471 | − | 0.935067i | \(-0.384661\pi\) | ||||
0.354471 | + | 0.935067i | \(0.384661\pi\) | |||||||
\(140\) | −9.17819 | −0.775698 | ||||||||
\(141\) | − | 16.6974i | − | 1.40618i | ||||||
\(142\) | −11.6292 | −0.975898 | ||||||||
\(143\) | 3.31126 | − | 10.0679i | 0.276901 | − | 0.841917i | ||||
\(144\) | 1.92835 | 0.160696 | ||||||||
\(145\) | − | 11.3932i | − | 0.946156i | ||||||
\(146\) | 9.81326 | 0.812151 | ||||||||
\(147\) | −6.31389 | −0.520761 | ||||||||
\(148\) | − | 6.04990i | − | 0.497299i | ||||||
\(149\) | − | 14.9219i | − | 1.22245i | −0.791456 | − | 0.611226i | \(-0.790677\pi\) | ||
0.791456 | − | 0.611226i | \(-0.209323\pi\) | |||||||
\(150\) | 6.70882i | 0.547773i | ||||||||
\(151\) | − | 13.0134i | − | 1.05902i | −0.848304 | − | 0.529509i | \(-0.822376\pi\) | ||
0.848304 | − | 0.529509i | \(-0.177624\pi\) | |||||||
\(152\) | 0.186530 | 0.0151296 | ||||||||
\(153\) | 0.908238 | 0.0734267 | ||||||||
\(154\) | 10.1969i | 0.821689i | ||||||||
\(155\) | −2.66789 | −0.214290 | ||||||||
\(156\) | −10.7611 | − | 3.53927i | −0.861580 | − | 0.283368i | ||||
\(157\) | −18.1118 | −1.44548 | −0.722738 | − | 0.691122i | \(-0.757117\pi\) | ||||
−0.722738 | + | 0.691122i | \(0.757117\pi\) | |||||||
\(158\) | 1.48336i | 0.118010i | ||||||||
\(159\) | 21.9352 | 1.73958 | ||||||||
\(160\) | 21.2817 | 1.68246 | ||||||||
\(161\) | − | 6.53832i | − | 0.515292i | ||||||
\(162\) | − | 14.6433i | − | 1.15049i | ||||||
\(163\) | − | 3.67145i | − | 0.287570i | −0.989609 | − | 0.143785i | \(-0.954073\pi\) | ||
0.989609 | − | 0.143785i | \(-0.0459274\pi\) | |||||||
\(164\) | 11.4854i | 0.896858i | ||||||||
\(165\) | 12.4567 | 0.969755 | ||||||||
\(166\) | 0.330340 | 0.0256394 | ||||||||
\(167\) | − | 3.59433i | − | 0.278138i | −0.990283 | − | 0.139069i | \(-0.955589\pi\) | ||
0.990283 | − | 0.139069i | \(-0.0444110\pi\) | |||||||
\(168\) | −0.121334 | −0.00936108 | ||||||||
\(169\) | 10.4621 | + | 7.71653i | 0.804776 | + | 0.593579i | ||||
\(170\) | 10.1339 | 0.777233 | ||||||||
\(171\) | 2.02547i | 0.154892i | ||||||||
\(172\) | 23.1158 | 1.76256 | ||||||||
\(173\) | 13.7740 | 1.04721 | 0.523607 | − | 0.851960i | \(-0.324586\pi\) | ||||
0.523607 | + | 0.851960i | \(0.324586\pi\) | |||||||
\(174\) | 13.5294i | 1.02566i | ||||||||
\(175\) | 3.68311i | 0.278417i | ||||||||
\(176\) | − | 11.8859i | − | 0.895934i | ||||||
\(177\) | − | 21.9092i | − | 1.64679i | ||||||
\(178\) | −3.69407 | −0.276882 | ||||||||
\(179\) | 13.7364 | 1.02671 | 0.513353 | − | 0.858178i | \(-0.328403\pi\) | ||||
0.513353 | + | 0.858178i | \(0.328403\pi\) | |||||||
\(180\) | 2.51659i | 0.187575i | ||||||||
\(181\) | −8.36084 | −0.621457 | −0.310728 | − | 0.950499i | \(-0.600573\pi\) | ||||
−0.310728 | + | 0.950499i | \(0.600573\pi\) | |||||||
\(182\) | −11.8814 | − | 3.90771i | −0.880707 | − | 0.289659i | ||||
\(183\) | −8.02799 | −0.593446 | ||||||||
\(184\) | 0.165099i | 0.0121712i | ||||||||
\(185\) | −8.16006 | −0.599940 | ||||||||
\(186\) | 3.16810 | 0.232296 | ||||||||
\(187\) | − | 5.59817i | − | 0.409379i | ||||||
\(188\) | − | 20.7923i | − | 1.51644i | ||||||
\(189\) | − | 9.60565i | − | 0.698709i | ||||||
\(190\) | 22.5997i | 1.63955i | ||||||||
\(191\) | 25.1884 | 1.82257 | 0.911286 | − | 0.411774i | \(-0.135091\pi\) | ||||
0.911286 | + | 0.411774i | \(0.135091\pi\) | |||||||
\(192\) | −12.4261 | −0.896776 | ||||||||
\(193\) | 8.03820i | 0.578603i | 0.957238 | + | 0.289301i | \(0.0934229\pi\) | ||||
−0.957238 | + | 0.289301i | \(0.906577\pi\) | |||||||
\(194\) | −12.6778 | −0.910216 | ||||||||
\(195\) | −4.77374 | + | 14.5145i | −0.341855 | + | 1.03941i | ||||
\(196\) | −7.86233 | −0.561595 | ||||||||
\(197\) | 2.79581i | 0.199193i | 0.995028 | + | 0.0995964i | \(0.0317552\pi\) | ||||
−0.995028 | + | 0.0995964i | \(0.968245\pi\) | |||||||
\(198\) | 2.79591 | 0.198696 | ||||||||
\(199\) | 16.3408 | 1.15837 | 0.579183 | − | 0.815197i | \(-0.303372\pi\) | ||||
0.579183 | + | 0.815197i | \(0.303372\pi\) | |||||||
\(200\) | − | 0.0930021i | − | 0.00657624i | ||||||
\(201\) | − | 20.1803i | − | 1.42341i | ||||||
\(202\) | 6.21862i | 0.437541i | ||||||||
\(203\) | 7.42758i | 0.521314i | ||||||||
\(204\) | −5.98366 | −0.418940 | ||||||||
\(205\) | 15.4914 | 1.08197 | ||||||||
\(206\) | 5.74927i | 0.400571i | ||||||||
\(207\) | −1.79276 | −0.124605 | ||||||||
\(208\) | 13.8494 | + | 4.55499i | 0.960285 | + | 0.315832i | ||||
\(209\) | 12.4845 | 0.863573 | ||||||||
\(210\) | − | 14.7006i | − | 1.01444i | ||||||
\(211\) | 16.1104 | 1.10909 | 0.554544 | − | 0.832155i | \(-0.312893\pi\) | ||||
0.554544 | + | 0.832155i | \(0.312893\pi\) | |||||||
\(212\) | 27.3147 | 1.87598 | ||||||||
\(213\) | − | 9.26158i | − | 0.634593i | ||||||
\(214\) | − | 14.6618i | − | 1.00226i | ||||||
\(215\) | − | 31.1784i | − | 2.12635i | ||||||
\(216\) | 0.242552i | 0.0165036i | ||||||||
\(217\) | 1.73927 | 0.118070 | ||||||||
\(218\) | −25.9028 | −1.75436 | ||||||||
\(219\) | 7.81537i | 0.528114i | ||||||||
\(220\) | 15.5117 | 1.04580 | ||||||||
\(221\) | 6.52297 | + | 2.14536i | 0.438782 | + | 0.144313i | ||||
\(222\) | 9.69003 | 0.650352 | ||||||||
\(223\) | 10.5250i | 0.704805i | 0.935849 | + | 0.352403i | \(0.114635\pi\) | ||||
−0.935849 | + | 0.352403i | \(0.885365\pi\) | |||||||
\(224\) | −13.8741 | −0.927006 | ||||||||
\(225\) | 1.00988 | 0.0673253 | ||||||||
\(226\) | − | 15.2231i | − | 1.01262i | ||||||
\(227\) | 1.53439i | 0.101841i | 0.998703 | + | 0.0509204i | \(0.0162155\pi\) | ||||
−0.998703 | + | 0.0509204i | \(0.983785\pi\) | |||||||
\(228\) | − | 13.3442i | − | 0.883742i | ||||||
\(229\) | 1.33677i | 0.0883364i | 0.999024 | + | 0.0441682i | \(0.0140637\pi\) | ||||
−0.999024 | + | 0.0441682i | \(0.985936\pi\) | |||||||
\(230\) | −20.0031 | −1.31897 | ||||||||
\(231\) | −8.12090 | −0.534316 | ||||||||
\(232\) | − | 0.187553i | − | 0.0123135i | ||||||
\(233\) | −23.1697 | −1.51790 | −0.758948 | − | 0.651151i | \(-0.774287\pi\) | ||||
−0.758948 | + | 0.651151i | \(0.774287\pi\) | |||||||
\(234\) | −1.07146 | + | 3.25778i | −0.0700438 | + | 0.212968i | ||||
\(235\) | −28.0446 | −1.82943 | ||||||||
\(236\) | − | 27.2822i | − | 1.77592i | ||||||
\(237\) | −1.18137 | −0.0767379 | ||||||||
\(238\) | −6.60657 | −0.428240 | ||||||||
\(239\) | − | 5.95278i | − | 0.385053i | −0.981292 | − | 0.192527i | \(-0.938332\pi\) | ||
0.981292 | − | 0.192527i | \(-0.0616682\pi\) | |||||||
\(240\) | 17.1356i | 1.10610i | ||||||||
\(241\) | − | 27.2642i | − | 1.75624i | −0.478439 | − | 0.878121i | \(-0.658797\pi\) | ||
0.478439 | − | 0.878121i | \(-0.341203\pi\) | |||||||
\(242\) | 4.70604i | 0.302516i | ||||||||
\(243\) | −4.90633 | −0.314741 | ||||||||
\(244\) | −9.99680 | −0.639980 | ||||||||
\(245\) | 10.6047i | 0.677507i | ||||||||
\(246\) | −18.3960 | −1.17288 | ||||||||
\(247\) | −4.78440 | + | 14.5469i | −0.304424 | + | 0.925600i | ||||
\(248\) | −0.0439183 | −0.00278881 | ||||||||
\(249\) | 0.263086i | 0.0166724i | ||||||||
\(250\) | −15.3374 | −0.970019 | ||||||||
\(251\) | −26.2008 | −1.65378 | −0.826888 | − | 0.562366i | \(-0.809891\pi\) | ||||
−0.826888 | + | 0.562366i | \(0.809891\pi\) | |||||||
\(252\) | − | 1.64064i | − | 0.103350i | ||||||
\(253\) | 11.0501i | 0.694716i | ||||||||
\(254\) | − | 0.198039i | − | 0.0124261i | ||||||
\(255\) | 8.07072i | 0.505408i | ||||||||
\(256\) | 16.3465 | 1.02165 | ||||||||
\(257\) | 19.4518 | 1.21337 | 0.606684 | − | 0.794943i | \(-0.292499\pi\) | ||||
0.606684 | + | 0.794943i | \(0.292499\pi\) | |||||||
\(258\) | 37.0242i | 2.30503i | ||||||||
\(259\) | 5.31978 | 0.330555 | ||||||||
\(260\) | −5.94447 | + | 18.0741i | −0.368660 | + | 1.12091i | ||||
\(261\) | 2.03658 | 0.126061 | ||||||||
\(262\) | 3.11947i | 0.192721i | ||||||||
\(263\) | −29.8002 | −1.83756 | −0.918781 | − | 0.394768i | \(-0.870825\pi\) | ||||
−0.918781 | + | 0.394768i | \(0.870825\pi\) | |||||||
\(264\) | 0.205060 | 0.0126206 | ||||||||
\(265\) | − | 36.8419i | − | 2.26318i | ||||||
\(266\) | − | 14.7334i | − | 0.903362i | ||||||
\(267\) | − | 2.94199i | − | 0.180047i | ||||||
\(268\) | − | 25.1294i | − | 1.53502i | ||||||
\(269\) | 7.60454 | 0.463657 | 0.231829 | − | 0.972757i | \(-0.425529\pi\) | ||||
0.231829 | + | 0.972757i | \(0.425529\pi\) | |||||||
\(270\) | −29.3872 | −1.78845 | ||||||||
\(271\) | 22.1272i | 1.34413i | 0.740493 | + | 0.672065i | \(0.234592\pi\) | ||||
−0.740493 | + | 0.672065i | \(0.765408\pi\) | |||||||
\(272\) | 7.70088 | 0.466935 | ||||||||
\(273\) | 3.11214 | − | 9.46245i | 0.188355 | − | 0.572694i | ||||
\(274\) | −14.5801 | −0.880817 | ||||||||
\(275\) | − | 6.22467i | − | 0.375362i | ||||||
\(276\) | 11.8110 | 0.710941 | ||||||||
\(277\) | −9.45363 | −0.568013 | −0.284007 | − | 0.958822i | \(-0.591664\pi\) | ||||
−0.284007 | + | 0.958822i | \(0.591664\pi\) | |||||||
\(278\) | 16.6705i | 0.999833i | ||||||||
\(279\) | − | 0.476895i | − | 0.0285509i | ||||||
\(280\) | 0.203789i | 0.0121787i | ||||||||
\(281\) | − | 12.6507i | − | 0.754676i | −0.926076 | − | 0.377338i | \(-0.876840\pi\) | ||
0.926076 | − | 0.377338i | \(-0.123160\pi\) | |||||||
\(282\) | 33.3028 | 1.98315 | ||||||||
\(283\) | 17.2687 | 1.02652 | 0.513258 | − | 0.858234i | \(-0.328438\pi\) | ||||
0.513258 | + | 0.858234i | \(0.328438\pi\) | |||||||
\(284\) | − | 11.5329i | − | 0.684353i | ||||||
\(285\) | −17.9986 | −1.06614 | ||||||||
\(286\) | 20.0802 | + | 6.60426i | 1.18737 | + | 0.390518i | ||||
\(287\) | −10.0993 | −0.596143 | ||||||||
\(288\) | 3.80418i | 0.224164i | ||||||||
\(289\) | −13.3729 | −0.786644 | ||||||||
\(290\) | 22.7237 | 1.33438 | ||||||||
\(291\) | − | 10.0968i | − | 0.591882i | ||||||
\(292\) | 9.73204i | 0.569525i | ||||||||
\(293\) | 6.27750i | 0.366736i | 0.983044 | + | 0.183368i | \(0.0586999\pi\) | ||||
−0.983044 | + | 0.183368i | \(0.941300\pi\) | |||||||
\(294\) | − | 12.5930i | − | 0.734437i | ||||||
\(295\) | −36.7981 | −2.14247 | ||||||||
\(296\) | −0.134330 | −0.00780775 | ||||||||
\(297\) | 16.2341i | 0.941998i | ||||||||
\(298\) | 29.7616 | 1.72404 | ||||||||
\(299\) | −12.8756 | − | 4.23470i | −0.744614 | − | 0.244899i | ||||
\(300\) | −6.65330 | −0.384128 | ||||||||
\(301\) | 20.3261i | 1.17158i | ||||||||
\(302\) | 25.9551 | 1.49355 | ||||||||
\(303\) | −4.95257 | −0.284518 | ||||||||
\(304\) | 17.1738i | 0.984986i | ||||||||
\(305\) | 13.4836i | 0.772070i | ||||||||
\(306\) | 1.81147i | 0.103555i | ||||||||
\(307\) | 17.0517i | 0.973191i | 0.873627 | + | 0.486595i | \(0.161761\pi\) | ||||
−0.873627 | + | 0.486595i | \(0.838239\pi\) | |||||||
\(308\) | −10.1125 | −0.576213 | ||||||||
\(309\) | −4.57877 | −0.260477 | ||||||||
\(310\) | − | 5.32107i | − | 0.302216i | ||||||
\(311\) | 4.01012 | 0.227393 | 0.113697 | − | 0.993516i | \(-0.463731\pi\) | ||||
0.113697 | + | 0.993516i | \(0.463731\pi\) | |||||||
\(312\) | −0.0785845 | + | 0.238936i | −0.00444897 | + | 0.0135271i | ||||
\(313\) | −6.03967 | −0.341382 | −0.170691 | − | 0.985325i | \(-0.554600\pi\) | ||||
−0.170691 | + | 0.985325i | \(0.554600\pi\) | |||||||
\(314\) | − | 36.1237i | − | 2.03858i | ||||||
\(315\) | −2.21288 | −0.124682 | ||||||||
\(316\) | −1.47109 | −0.0827551 | ||||||||
\(317\) | − | 14.0309i | − | 0.788056i | −0.919098 | − | 0.394028i | \(-0.871081\pi\) | ||
0.919098 | − | 0.394028i | \(-0.128919\pi\) | |||||||
\(318\) | 43.7495i | 2.45335i | ||||||||
\(319\) | − | 12.5530i | − | 0.702834i | ||||||
\(320\) | 20.8706i | 1.16670i | ||||||||
\(321\) | 11.6768 | 0.651736 | ||||||||
\(322\) | 13.0406 | 0.726724 | ||||||||
\(323\) | 8.08873i | 0.450069i | ||||||||
\(324\) | 14.5221 | 0.806784 | ||||||||
\(325\) | 7.25296 | + | 2.38545i | 0.402322 | + | 0.132321i | ||||
\(326\) | 7.32265 | 0.405564 | ||||||||
\(327\) | − | 20.6292i | − | 1.14080i | ||||||
\(328\) | 0.255017 | 0.0140810 | ||||||||
\(329\) | 18.2831 | 1.00798 | ||||||||
\(330\) | 24.8448i | 1.36766i | ||||||||
\(331\) | 11.1671i | 0.613802i | 0.951741 | + | 0.306901i | \(0.0992920\pi\) | ||||
−0.951741 | + | 0.306901i | \(0.900708\pi\) | |||||||
\(332\) | 0.327606i | 0.0179797i | ||||||||
\(333\) | − | 1.45864i | − | 0.0799331i | ||||||
\(334\) | 7.16885 | 0.392262 | ||||||||
\(335\) | −33.8944 | −1.85185 | ||||||||
\(336\) | − | 11.1712i | − | 0.609437i | ||||||
\(337\) | −5.01505 | −0.273187 | −0.136594 | − | 0.990627i | \(-0.543615\pi\) | ||||
−0.136594 | + | 0.990627i | \(0.543615\pi\) | |||||||
\(338\) | −15.3905 | + | 20.8665i | −0.837134 | + | 1.13499i | ||||
\(339\) | 12.1238 | 0.658475 | ||||||||
\(340\) | 10.0500i | 0.545038i | ||||||||
\(341\) | −2.93947 | −0.159181 | ||||||||
\(342\) | −4.03978 | −0.218446 | ||||||||
\(343\) | − | 19.0884i | − | 1.03068i | ||||||
\(344\) | − | 0.513254i | − | 0.0276728i | ||||||
\(345\) | − | 15.9307i | − | 0.857678i | ||||||
\(346\) | 27.4720i | 1.47690i | ||||||||
\(347\) | −0.923189 | −0.0495594 | −0.0247797 | − | 0.999693i | \(-0.507888\pi\) | ||||
−0.0247797 | + | 0.999693i | \(0.507888\pi\) | |||||||
\(348\) | −13.4174 | −0.719250 | ||||||||
\(349\) | 13.5903i | 0.727473i | 0.931502 | + | 0.363736i | \(0.118499\pi\) | ||||
−0.931502 | + | 0.363736i | \(0.881501\pi\) | |||||||
\(350\) | −7.34592 | −0.392656 | ||||||||
\(351\) | −18.9159 | − | 6.22133i | −1.00966 | − | 0.332070i | ||||
\(352\) | 23.4481 | 1.24979 | ||||||||
\(353\) | − | 23.8408i | − | 1.26892i | −0.772957 | − | 0.634459i | \(-0.781223\pi\) | ||
0.772957 | − | 0.634459i | \(-0.218777\pi\) | |||||||
\(354\) | 43.6976 | 2.32250 | ||||||||
\(355\) | −15.5555 | −0.825602 | ||||||||
\(356\) | − | 3.66349i | − | 0.194165i | ||||||
\(357\) | − | 5.26154i | − | 0.278470i | ||||||
\(358\) | 27.3970i | 1.44798i | ||||||||
\(359\) | 5.95185i | 0.314127i | 0.987589 | + | 0.157063i | \(0.0502027\pi\) | ||||
−0.987589 | + | 0.157063i | \(0.949797\pi\) | |||||||
\(360\) | 0.0558773 | 0.00294499 | ||||||||
\(361\) | 0.961228 | 0.0505910 | ||||||||
\(362\) | − | 16.6756i | − | 0.876450i | ||||||
\(363\) | −3.74794 | −0.196716 | ||||||||
\(364\) | 3.87537 | − | 11.7831i | 0.203125 | − | 0.617600i | ||||
\(365\) | 13.1265 | 0.687073 | ||||||||
\(366\) | − | 16.0117i | − | 0.836947i | ||||||
\(367\) | 28.6410 | 1.49505 | 0.747523 | − | 0.664236i | \(-0.231243\pi\) | ||||
0.747523 | + | 0.664236i | \(0.231243\pi\) | |||||||
\(368\) | −15.2006 | −0.792388 | ||||||||
\(369\) | 2.76915i | 0.144156i | ||||||||
\(370\) | − | 16.2751i | − | 0.846104i | ||||||
\(371\) | 24.0183i | 1.24697i | ||||||||
\(372\) | 3.14188i | 0.162899i | ||||||||
\(373\) | −32.6896 | −1.69260 | −0.846302 | − | 0.532704i | \(-0.821176\pi\) | ||||
−0.846302 | + | 0.532704i | \(0.821176\pi\) | |||||||
\(374\) | 11.1655 | 0.577353 | ||||||||
\(375\) | − | 12.2148i | − | 0.630770i | ||||||
\(376\) | −0.461665 | −0.0238085 | ||||||||
\(377\) | 14.6268 | + | 4.81065i | 0.753316 | + | 0.247761i | ||||
\(378\) | 19.1584 | 0.985400 | ||||||||
\(379\) | − | 13.9594i | − | 0.717044i | −0.933521 | − | 0.358522i | \(-0.883281\pi\) | ||
0.933521 | − | 0.358522i | \(-0.116719\pi\) | |||||||
\(380\) | −22.4126 | −1.14974 | ||||||||
\(381\) | 0.157720 | 0.00808025 | ||||||||
\(382\) | 50.2380i | 2.57040i | ||||||||
\(383\) | − | 4.62452i | − | 0.236302i | −0.992996 | − | 0.118151i | \(-0.962303\pi\) | ||
0.992996 | − | 0.118151i | \(-0.0376967\pi\) | |||||||
\(384\) | 0.558055i | 0.0284781i | ||||||||
\(385\) | 13.6397i | 0.695142i | ||||||||
\(386\) | −16.0321 | −0.816012 | ||||||||
\(387\) | 5.57326 | 0.283305 | ||||||||
\(388\) | − | 12.5729i | − | 0.638293i | ||||||
\(389\) | −28.4539 | −1.44267 | −0.721336 | − | 0.692585i | \(-0.756472\pi\) | ||||
−0.721336 | + | 0.692585i | \(0.756472\pi\) | |||||||
\(390\) | −28.9491 | − | 9.52117i | −1.46589 | − | 0.482123i | ||||
\(391\) | −7.15939 | −0.362066 | ||||||||
\(392\) | 0.174572i | 0.00881722i | ||||||||
\(393\) | −2.48437 | −0.125320 | ||||||||
\(394\) | −5.57620 | −0.280925 | ||||||||
\(395\) | 1.98419i | 0.0998356i | ||||||||
\(396\) | 2.77277i | 0.139337i | ||||||||
\(397\) | − | 4.82894i | − | 0.242358i | −0.992631 | − | 0.121179i | \(-0.961333\pi\) | ||
0.992631 | − | 0.121179i | \(-0.0386674\pi\) | |||||||
\(398\) | 32.5915i | 1.63366i | ||||||||
\(399\) | 11.7338 | 0.587425 | ||||||||
\(400\) | 8.56270 | 0.428135 | ||||||||
\(401\) | 33.7317i | 1.68448i | 0.539101 | + | 0.842241i | \(0.318764\pi\) | ||||
−0.539101 | + | 0.842241i | \(0.681236\pi\) | |||||||
\(402\) | 40.2494 | 2.00746 | ||||||||
\(403\) | 1.12648 | − | 3.42506i | 0.0561140 | − | 0.170614i | ||||
\(404\) | −6.16715 | −0.306827 | ||||||||
\(405\) | − | 19.5873i | − | 0.973302i | ||||||
\(406\) | −14.8142 | −0.735217 | ||||||||
\(407\) | −8.99073 | −0.445654 | ||||||||
\(408\) | 0.132859i | 0.00657749i | ||||||||
\(409\) | − | 34.0260i | − | 1.68248i | −0.540664 | − | 0.841239i | \(-0.681827\pi\) | ||
0.540664 | − | 0.841239i | \(-0.318173\pi\) | |||||||
\(410\) | 30.8974i | 1.52592i | ||||||||
\(411\) | − | 11.6117i | − | 0.572765i | ||||||
\(412\) | −5.70169 | −0.280902 | ||||||||
\(413\) | 23.9898 | 1.18046 | ||||||||
\(414\) | − | 3.57563i | − | 0.175733i | ||||||
\(415\) | 0.441873 | 0.0216907 | ||||||||
\(416\) | −8.98592 | + | 27.3216i | −0.440571 | + | 1.33955i | ||||
\(417\) | −13.2766 | −0.650157 | ||||||||
\(418\) | 24.9002i | 1.21791i | ||||||||
\(419\) | 19.7565 | 0.965166 | 0.482583 | − | 0.875850i | \(-0.339699\pi\) | ||||
0.482583 | + | 0.875850i | \(0.339699\pi\) | |||||||
\(420\) | 14.5789 | 0.711377 | ||||||||
\(421\) | − | 24.0860i | − | 1.17388i | −0.809631 | − | 0.586940i | \(-0.800333\pi\) | ||
0.809631 | − | 0.586940i | \(-0.199667\pi\) | |||||||
\(422\) | 32.1320i | 1.56416i | ||||||||
\(423\) | − | 5.01307i | − | 0.243744i | ||||||
\(424\) | − | 0.606485i | − | 0.0294535i | ||||||
\(425\) | 4.03296 | 0.195628 | ||||||||
\(426\) | 18.4721 | 0.894976 | ||||||||
\(427\) | − | 8.79037i | − | 0.425396i | ||||||
\(428\) | 14.5405 | 0.702840 | ||||||||
\(429\) | −5.25969 | + | 15.9921i | −0.253940 | + | 0.772105i | ||||
\(430\) | 62.1850 | 2.99883 | ||||||||
\(431\) | 34.5870i | 1.66600i | 0.553276 | + | 0.832998i | \(0.313377\pi\) | ||||
−0.553276 | + | 0.832998i | \(0.686623\pi\) | |||||||
\(432\) | −22.3317 | −1.07444 | ||||||||
\(433\) | 19.9707 | 0.959731 | 0.479865 | − | 0.877342i | \(-0.340686\pi\) | ||||
0.479865 | + | 0.877342i | \(0.340686\pi\) | |||||||
\(434\) | 3.46896i | 0.166515i | ||||||||
\(435\) | 18.0973i | 0.867701i | ||||||||
\(436\) | − | 25.6884i | − | 1.23025i | ||||||
\(437\) | − | 15.9662i | − | 0.763768i | ||||||
\(438\) | −15.5877 | −0.744807 | ||||||||
\(439\) | −16.2325 | −0.774733 | −0.387366 | − | 0.921926i | \(-0.626615\pi\) | ||||
−0.387366 | + | 0.921926i | \(0.626615\pi\) | |||||||
\(440\) | − | 0.344415i | − | 0.0164193i | ||||||
\(441\) | −1.89562 | −0.0902678 | ||||||||
\(442\) | −4.27890 | + | 13.0100i | −0.203527 | + | 0.618822i | ||||
\(443\) | 38.9490 | 1.85052 | 0.925261 | − | 0.379330i | \(-0.123846\pi\) | ||||
0.925261 | + | 0.379330i | \(0.123846\pi\) | |||||||
\(444\) | 9.60983i | 0.456062i | ||||||||
\(445\) | −4.94129 | −0.234240 | ||||||||
\(446\) | −20.9919 | −0.993997 | ||||||||
\(447\) | 23.7024i | 1.12109i | ||||||||
\(448\) | − | 13.6061i | − | 0.642829i | ||||||
\(449\) | 20.3615i | 0.960919i | 0.877017 | + | 0.480459i | \(0.159530\pi\) | ||||
−0.877017 | + | 0.480459i | \(0.840470\pi\) | |||||||
\(450\) | 2.01419i | 0.0949500i | ||||||||
\(451\) | 17.0684 | 0.803719 | ||||||||
\(452\) | 15.0971 | 0.710108 | ||||||||
\(453\) | 20.6709i | 0.971204i | ||||||||
\(454\) | −3.06032 | −0.143628 | ||||||||
\(455\) | −15.8929 | − | 5.22708i | −0.745071 | − | 0.245049i | ||||
\(456\) | −0.296290 | −0.0138750 | ||||||||
\(457\) | 14.9242i | 0.698123i | 0.937100 | + | 0.349061i | \(0.113500\pi\) | ||||
−0.937100 | + | 0.349061i | \(0.886500\pi\) | |||||||
\(458\) | −2.66617 | −0.124582 | ||||||||
\(459\) | −10.5181 | −0.490942 | ||||||||
\(460\) | − | 19.8375i | − | 0.924930i | ||||||
\(461\) | 17.9790i | 0.837367i | 0.908132 | + | 0.418683i | \(0.137508\pi\) | ||||
−0.908132 | + | 0.418683i | \(0.862492\pi\) | |||||||
\(462\) | − | 16.1970i | − | 0.753554i | ||||||
\(463\) | − | 40.4466i | − | 1.87971i | −0.341571 | − | 0.939856i | \(-0.610959\pi\) | ||
0.341571 | − | 0.939856i | \(-0.389041\pi\) | |||||||
\(464\) | 17.2680 | 0.801648 | ||||||||
\(465\) | 4.23775 | 0.196521 | ||||||||
\(466\) | − | 46.2117i | − | 2.14071i | ||||||
\(467\) | 37.4781 | 1.73428 | 0.867139 | − | 0.498066i | \(-0.165956\pi\) | ||||
0.867139 | + | 0.498066i | \(0.165956\pi\) | |||||||
\(468\) | −3.23082 | − | 1.06260i | −0.149345 | − | 0.0491185i | ||||
\(469\) | 22.0967 | 1.02033 | ||||||||
\(470\) | − | 55.9345i | − | 2.58007i | ||||||
\(471\) | 28.7692 | 1.32562 | ||||||||
\(472\) | −0.605764 | −0.0278826 | ||||||||
\(473\) | − | 34.3523i | − | 1.57952i | ||||||
\(474\) | − | 2.35622i | − | 0.108225i | ||||||
\(475\) | 8.99396i | 0.412671i | ||||||||
\(476\) | − | 6.55189i | − | 0.300306i | ||||||
\(477\) | 6.58562 | 0.301535 | ||||||||
\(478\) | 11.8727 | 0.543047 | ||||||||
\(479\) | 4.59305i | 0.209862i | 0.994480 | + | 0.104931i | \(0.0334622\pi\) | ||||
−0.994480 | + | 0.104931i | \(0.966538\pi\) | |||||||
\(480\) | −33.8044 | −1.54295 | ||||||||
\(481\) | 3.44548 | − | 10.4760i | 0.157100 | − | 0.477663i | ||||
\(482\) | 54.3781 | 2.47685 | ||||||||
\(483\) | 10.3857i | 0.472564i | ||||||||
\(484\) | −4.66709 | −0.212141 | ||||||||
\(485\) | −16.9583 | −0.770035 | ||||||||
\(486\) | − | 9.78562i | − | 0.443885i | ||||||
\(487\) | 29.6112i | 1.34181i | 0.741542 | + | 0.670906i | \(0.234095\pi\) | ||||
−0.741542 | + | 0.670906i | \(0.765905\pi\) | |||||||
\(488\) | 0.221965i | 0.0100479i | ||||||||
\(489\) | 5.83183i | 0.263725i | ||||||||
\(490\) | −21.1509 | −0.955499 | ||||||||
\(491\) | 35.0863 | 1.58342 | 0.791712 | − | 0.610894i | \(-0.209190\pi\) | ||||
0.791712 | + | 0.610894i | \(0.209190\pi\) | |||||||
\(492\) | − | 18.2437i | − | 0.822491i | ||||||
\(493\) | 8.13311 | 0.366297 | ||||||||
\(494\) | −29.0137 | − | 9.54242i | −1.30539 | − | 0.429334i | ||||
\(495\) | 3.73989 | 0.168095 | ||||||||
\(496\) | − | 4.04355i | − | 0.181561i | ||||||
\(497\) | 10.1411 | 0.454891 | ||||||||
\(498\) | −0.524722 | −0.0235133 | ||||||||
\(499\) | − | 3.07949i | − | 0.137857i | −0.997622 | − | 0.0689284i | \(-0.978042\pi\) | ||
0.997622 | − | 0.0689284i | \(-0.0219580\pi\) | |||||||
\(500\) | − | 15.2104i | − | 0.680230i | ||||||
\(501\) | 5.70934i | 0.255075i | ||||||||
\(502\) | − | 52.2571i | − | 2.33235i | ||||||
\(503\) | 10.3434 | 0.461189 | 0.230594 | − | 0.973050i | \(-0.425933\pi\) | ||||
0.230594 | + | 0.973050i | \(0.425933\pi\) | |||||||
\(504\) | −0.0364280 | −0.00162263 | ||||||||
\(505\) | 8.31821i | 0.370156i | ||||||||
\(506\) | −22.0394 | −0.979769 | ||||||||
\(507\) | −16.6183 | − | 12.2572i | −0.738043 | − | 0.544359i | ||||
\(508\) | 0.196400 | 0.00871385 | ||||||||
\(509\) | 4.96830i | 0.220216i | 0.993920 | + | 0.110108i | \(0.0351197\pi\) | ||||
−0.993920 | + | 0.110108i | \(0.964880\pi\) | |||||||
\(510\) | −16.0969 | −0.712785 | ||||||||
\(511\) | −8.55755 | −0.378564 | ||||||||
\(512\) | 31.9002i | 1.40980i | ||||||||
\(513\) | − | 23.4565i | − | 1.03563i | ||||||
\(514\) | 38.7963i | 1.71123i | ||||||||
\(515\) | 7.69039i | 0.338879i | ||||||||
\(516\) | −36.7178 | −1.61641 | ||||||||
\(517\) | −30.8994 | −1.35895 | ||||||||
\(518\) | 10.6102i | 0.466187i | ||||||||
\(519\) | −21.8789 | −0.960379 | ||||||||
\(520\) | 0.401311 | + | 0.131989i | 0.0175986 | + | 0.00578808i | ||||
\(521\) | −6.67995 | −0.292654 | −0.146327 | − | 0.989236i | \(-0.546745\pi\) | ||||
−0.146327 | + | 0.989236i | \(0.546745\pi\) | |||||||
\(522\) | 4.06194i | 0.177786i | ||||||||
\(523\) | 11.6369 | 0.508846 | 0.254423 | − | 0.967093i | \(-0.418114\pi\) | ||||
0.254423 | + | 0.967093i | \(0.418114\pi\) | |||||||
\(524\) | −3.09365 | −0.135147 | ||||||||
\(525\) | − | 5.85036i | − | 0.255331i | ||||||
\(526\) | − | 59.4362i | − | 2.59154i | ||||||
\(527\) | − | 1.90448i | − | 0.0829606i | ||||||
\(528\) | 18.8799i | 0.821642i | ||||||||
\(529\) | −8.86820 | −0.385574 | ||||||||
\(530\) | 73.4807 | 3.19180 | ||||||||
\(531\) | − | 6.57780i | − | 0.285452i | ||||||
\(532\) | 14.6114 | 0.633486 | ||||||||
\(533\) | −6.54105 | + | 19.8880i | −0.283324 | + | 0.861447i | ||||
\(534\) | 5.86776 | 0.253923 | ||||||||
\(535\) | − | 19.6121i | − | 0.847904i | ||||||
\(536\) | −0.557963 | −0.0241003 | ||||||||
\(537\) | −21.8193 | −0.941571 | ||||||||
\(538\) | 15.1672i | 0.653903i | ||||||||
\(539\) | 11.6842i | 0.503273i | ||||||||
\(540\) | − | 29.1440i | − | 1.25416i | ||||||
\(541\) | 8.27417i | 0.355734i | 0.984054 | + | 0.177867i | \(0.0569198\pi\) | ||||
−0.984054 | + | 0.177867i | \(0.943080\pi\) | |||||||
\(542\) | −44.1323 | −1.89565 | ||||||||
\(543\) | 13.2806 | 0.569925 | ||||||||
\(544\) | 15.1920i | 0.651353i | ||||||||
\(545\) | −34.6483 | −1.48417 | ||||||||
\(546\) | 18.8727 | + | 6.20713i | 0.807679 | + | 0.265640i | ||||
\(547\) | −9.31963 | −0.398479 | −0.199239 | − | 0.979951i | \(-0.563847\pi\) | ||||
−0.199239 | + | 0.979951i | \(0.563847\pi\) | |||||||
\(548\) | − | 14.4595i | − | 0.617677i | ||||||
\(549\) | −2.41025 | −0.102867 | ||||||||
\(550\) | 12.4150 | 0.529378 | ||||||||
\(551\) | 18.1377i | 0.772694i | ||||||||
\(552\) | − | 0.262248i | − | 0.0111620i | ||||||
\(553\) | − | 1.29355i | − | 0.0550075i | ||||||
\(554\) | − | 18.8551i | − | 0.801078i | ||||||
\(555\) | 12.9617 | 0.550192 | ||||||||
\(556\) | −16.5326 | −0.701137 | ||||||||
\(557\) | 22.3462i | 0.946839i | 0.880837 | + | 0.473419i | \(0.156980\pi\) | ||||
−0.880837 | + | 0.473419i | \(0.843020\pi\) | |||||||
\(558\) | 0.951161 | 0.0402658 | ||||||||
\(559\) | 40.0272 | + | 13.1647i | 1.69297 | + | 0.556807i | ||||
\(560\) | −18.7628 | −0.792874 | ||||||||
\(561\) | 8.89229i | 0.375433i | ||||||||
\(562\) | 25.2316 | 1.06433 | ||||||||
\(563\) | −19.9509 | −0.840832 | −0.420416 | − | 0.907332i | \(-0.638116\pi\) | ||||
−0.420416 | + | 0.907332i | \(0.638116\pi\) | |||||||
\(564\) | 33.0271i | 1.39069i | ||||||||
\(565\) | − | 20.3629i | − | 0.856672i | ||||||
\(566\) | 34.4422i | 1.44771i | ||||||||
\(567\) | 12.7695i | 0.536270i | ||||||||
\(568\) | −0.256072 | −0.0107446 | ||||||||
\(569\) | −30.1940 | −1.26580 | −0.632898 | − | 0.774235i | \(-0.718135\pi\) | ||||
−0.632898 | + | 0.774235i | \(0.718135\pi\) | |||||||
\(570\) | − | 35.8980i | − | 1.50360i | ||||||
\(571\) | −35.6144 | −1.49042 | −0.745208 | − | 0.666832i | \(-0.767650\pi\) | ||||
−0.745208 | + | 0.666832i | \(0.767650\pi\) | |||||||
\(572\) | −6.54960 | + | 19.9140i | −0.273852 | + | 0.832647i | ||||
\(573\) | −40.0100 | −1.67144 | ||||||||
\(574\) | − | 20.1429i | − | 0.840750i | ||||||
\(575\) | −7.96060 | −0.331980 | ||||||||
\(576\) | −3.73069 | −0.155445 | ||||||||
\(577\) | 30.0336i | 1.25032i | 0.780498 | + | 0.625158i | \(0.214965\pi\) | ||||
−0.780498 | + | 0.625158i | \(0.785035\pi\) | |||||||
\(578\) | − | 26.6722i | − | 1.10942i | ||||||
\(579\) | − | 12.7681i | − | 0.530625i | ||||||
\(580\) | 22.5356i | 0.935739i | ||||||||
\(581\) | −0.288070 | −0.0119511 | ||||||||
\(582\) | 20.1378 | 0.834741 | ||||||||
\(583\) | − | 40.5923i | − | 1.68116i | ||||||
\(584\) | 0.216086 | 0.00894172 | ||||||||
\(585\) | −1.43322 | + | 4.35771i | −0.0592565 | + | 0.180169i | ||||
\(586\) | −12.5204 | −0.517213 | ||||||||
\(587\) | − | 16.0884i | − | 0.664039i | −0.943272 | − | 0.332020i | \(-0.892270\pi\) | ||
0.943272 | − | 0.332020i | \(-0.107730\pi\) | |||||||
\(588\) | 12.4888 | 0.515027 | ||||||||
\(589\) | 4.24721 | 0.175003 | ||||||||
\(590\) | − | 73.3934i | − | 3.02156i | ||||||
\(591\) | − | 4.44094i | − | 0.182676i | ||||||
\(592\) | − | 12.3677i | − | 0.508310i | ||||||
\(593\) | − | 7.42015i | − | 0.304709i | −0.988326 | − | 0.152355i | \(-0.951314\pi\) | ||
0.988326 | − | 0.152355i | \(-0.0486856\pi\) | |||||||
\(594\) | −32.3787 | −1.32851 | ||||||||
\(595\) | −8.83715 | −0.362288 | ||||||||
\(596\) | 29.5153i | 1.20899i | ||||||||
\(597\) | −25.9561 | −1.06231 | ||||||||
\(598\) | 8.44605 | − | 25.6802i | 0.345385 | − | 1.05014i | ||||
\(599\) | 30.1928 | 1.23364 | 0.616822 | − | 0.787102i | \(-0.288420\pi\) | ||||
0.616822 | + | 0.787102i | \(0.288420\pi\) | |||||||
\(600\) | 0.147727i | 0.00603094i | ||||||||
\(601\) | 30.9392 | 1.26204 | 0.631019 | − | 0.775767i | \(-0.282637\pi\) | ||||
0.631019 | + | 0.775767i | \(0.282637\pi\) | |||||||
\(602\) | −40.5402 | −1.65230 | ||||||||
\(603\) | − | 6.05875i | − | 0.246731i | ||||||
\(604\) | 25.7403i | 1.04736i | ||||||||
\(605\) | 6.29494i | 0.255926i | ||||||||
\(606\) | − | 9.87783i | − | 0.401260i | ||||||
\(607\) | −0.0358681 | −0.00145584 | −0.000727920 | − | 1.00000i | \(-0.500232\pi\) | ||||
−0.000727920 | 1.00000i | \(0.500232\pi\) | ||||||||
\(608\) | −33.8799 | −1.37401 | ||||||||
\(609\) | − | 11.7982i | − | 0.478086i | ||||||
\(610\) | −26.8929 | −1.08886 | ||||||||
\(611\) | 11.8415 | − | 36.0039i | 0.479054 | − | 1.45656i | ||||
\(612\) | −1.79648 | −0.0726183 | ||||||||
\(613\) | 38.0409i | 1.53646i | 0.640176 | + | 0.768228i | \(0.278861\pi\) | ||||
−0.640176 | + | 0.768228i | \(0.721139\pi\) | |||||||
\(614\) | −34.0094 | −1.37251 | ||||||||
\(615\) | −24.6070 | −0.992250 | ||||||||
\(616\) | 0.224534i | 0.00904673i | ||||||||
\(617\) | − | 29.8852i | − | 1.20313i | −0.798822 | − | 0.601567i | \(-0.794543\pi\) | ||
0.798822 | − | 0.601567i | \(-0.205457\pi\) | |||||||
\(618\) | − | 9.13230i | − | 0.367355i | ||||||
\(619\) | − | 10.9872i | − | 0.441612i | −0.975318 | − | 0.220806i | \(-0.929131\pi\) | ||
0.975318 | − | 0.220806i | \(-0.0708687\pi\) | |||||||
\(620\) | 5.27703 | 0.211930 | ||||||||
\(621\) | 20.7615 | 0.833129 | ||||||||
\(622\) | 7.99814i | 0.320696i | ||||||||
\(623\) | 3.22137 | 0.129062 | ||||||||
\(624\) | −21.9988 | − | 7.23527i | −0.880657 | − | 0.289643i | ||||
\(625\) | −31.1038 | −1.24415 | ||||||||
\(626\) | − | 12.0460i | − | 0.481457i | ||||||
\(627\) | −19.8308 | −0.791965 | ||||||||
\(628\) | 35.8247 | 1.42956 | ||||||||
\(629\) | − | 5.82510i | − | 0.232262i | ||||||
\(630\) | − | 4.41356i | − | 0.175840i | ||||||
\(631\) | − | 7.51654i | − | 0.299229i | −0.988744 | − | 0.149614i | \(-0.952197\pi\) | ||
0.988744 | − | 0.149614i | \(-0.0478032\pi\) | |||||||
\(632\) | 0.0326634i | 0.00129928i | ||||||||
\(633\) | −25.5903 | −1.01712 | ||||||||
\(634\) | 27.9845 | 1.11141 | ||||||||
\(635\) | − | 0.264903i | − | 0.0105124i | ||||||
\(636\) | −43.3874 | −1.72042 | ||||||||
\(637\) | −13.6144 | − | 4.47768i | −0.539421 | − | 0.177412i | ||||
\(638\) | 25.0369 | 0.991218 | ||||||||
\(639\) | − | 2.78061i | − | 0.109999i | ||||||
\(640\) | 0.937295 | 0.0370498 | ||||||||
\(641\) | −19.8746 | −0.785001 | −0.392501 | − | 0.919752i | \(-0.628390\pi\) | ||||
−0.392501 | + | 0.919752i | \(0.628390\pi\) | |||||||
\(642\) | 23.2892i | 0.919153i | ||||||||
\(643\) | − | 33.0105i | − | 1.30181i | −0.759160 | − | 0.650904i | \(-0.774390\pi\) | ||
0.759160 | − | 0.650904i | \(-0.225610\pi\) | |||||||
\(644\) | 12.9327i | 0.509619i | ||||||||
\(645\) | 49.5247i | 1.95003i | ||||||||
\(646\) | −16.1329 | −0.634740 | ||||||||
\(647\) | −11.6044 | −0.456215 | −0.228107 | − | 0.973636i | \(-0.573254\pi\) | ||||
−0.228107 | + | 0.973636i | \(0.573254\pi\) | |||||||
\(648\) | − | 0.322443i | − | 0.0126668i | ||||||
\(649\) | −40.5440 | −1.59149 | ||||||||
\(650\) | −4.75776 | + | 14.4659i | −0.186615 | + | 0.567401i | ||||
\(651\) | −2.76271 | −0.108279 | ||||||||
\(652\) | 7.26205i | 0.284404i | ||||||||
\(653\) | 43.0663 | 1.68531 | 0.842656 | − | 0.538452i | \(-0.180991\pi\) | ||||
0.842656 | + | 0.538452i | \(0.180991\pi\) | |||||||
\(654\) | 41.1447 | 1.60889 | ||||||||
\(655\) | 4.17269i | 0.163041i | ||||||||
\(656\) | 23.4794i | 0.916717i | ||||||||
\(657\) | 2.34641i | 0.0915423i | ||||||||
\(658\) | 36.4654i | 1.42157i | ||||||||
\(659\) | 22.3540 | 0.870787 | 0.435393 | − | 0.900240i | \(-0.356609\pi\) | ||||
0.435393 | + | 0.900240i | \(0.356609\pi\) | |||||||
\(660\) | −24.6391 | −0.959078 | ||||||||
\(661\) | − | 39.9481i | − | 1.55380i | −0.629624 | − | 0.776900i | \(-0.716791\pi\) | ||
0.629624 | − | 0.776900i | \(-0.283209\pi\) | |||||||
\(662\) | −22.2727 | −0.865654 | ||||||||
\(663\) | −10.3613 | − | 3.40776i | −0.402398 | − | 0.132346i | ||||
\(664\) | 0.00727403 | 0.000282287 | ||||||||
\(665\) | − | 19.7078i | − | 0.764236i | ||||||
\(666\) | 2.90924 | 0.112731 | ||||||||
\(667\) | −16.0538 | −0.621606 | ||||||||
\(668\) | 7.10952i | 0.275076i | ||||||||
\(669\) | − | 16.7182i | − | 0.646362i | ||||||
\(670\) | − | 67.6019i | − | 2.61169i | ||||||
\(671\) | 14.8562i | 0.573518i | ||||||||
\(672\) | 22.0381 | 0.850138 | ||||||||
\(673\) | −4.24478 | −0.163624 | −0.0818121 | − | 0.996648i | \(-0.526071\pi\) | ||||
−0.0818121 | + | 0.996648i | \(0.526071\pi\) | |||||||
\(674\) | − | 10.0025i | − | 0.385280i | ||||||
\(675\) | −11.6952 | −0.450147 | ||||||||
\(676\) | −20.6938 | − | 15.2631i | −0.795915 | − | 0.587044i | ||||
\(677\) | 49.0530 | 1.88526 | 0.942629 | − | 0.333842i | \(-0.108345\pi\) | ||||
0.942629 | + | 0.333842i | \(0.108345\pi\) | |||||||
\(678\) | 24.1808i | 0.928658i | ||||||||
\(679\) | 11.0556 | 0.424274 | ||||||||
\(680\) | 0.223146 | 0.00855727 | ||||||||
\(681\) | − | 2.43726i | − | 0.0933962i | ||||||
\(682\) | − | 5.86273i | − | 0.224496i | ||||||
\(683\) | 45.4851i | 1.74044i | 0.492666 | + | 0.870219i | \(0.336023\pi\) | ||||
−0.492666 | + | 0.870219i | \(0.663977\pi\) | |||||||
\(684\) | − | 4.00634i | − | 0.153186i | ||||||
\(685\) | −19.5028 | −0.745164 | ||||||||
\(686\) | 38.0716 | 1.45358 | ||||||||
\(687\) | − | 2.12337i | − | 0.0810115i | ||||||
\(688\) | 47.2553 | 1.80159 | ||||||||
\(689\) | 47.2980 | + | 15.5560i | 1.80191 | + | 0.592637i | ||||
\(690\) | 31.7735 | 1.20960 | ||||||||
\(691\) | − | 1.63712i | − | 0.0622791i | −0.999515 | − | 0.0311395i | \(-0.990086\pi\) | ||
0.999515 | − | 0.0311395i | \(-0.00991363\pi\) | |||||||
\(692\) | −27.2446 | −1.03568 | ||||||||
\(693\) | −2.43814 | −0.0926174 | ||||||||
\(694\) | − | 1.84129i | − | 0.0698944i | ||||||
\(695\) | 22.2990i | 0.845850i | ||||||||
\(696\) | 0.297915i | 0.0112924i | ||||||||
\(697\) | 11.0586i | 0.418875i | ||||||||
\(698\) | −27.1057 | −1.02597 | ||||||||
\(699\) | 36.8034 | 1.39203 | ||||||||
\(700\) | − | 7.28512i | − | 0.275352i | ||||||
\(701\) | −1.61823 | −0.0611197 | −0.0305599 | − | 0.999533i | \(-0.509729\pi\) | ||||
−0.0305599 | + | 0.999533i | \(0.509729\pi\) | |||||||
\(702\) | 12.4084 | − | 37.7276i | 0.468323 | − | 1.42394i | ||||
\(703\) | 12.9906 | 0.489950 | ||||||||
\(704\) | 22.9951i | 0.866661i | ||||||||
\(705\) | 44.5468 | 1.67773 | ||||||||
\(706\) | 47.5502 | 1.78957 | ||||||||
\(707\) | − | 5.42289i | − | 0.203949i | ||||||
\(708\) | 43.3359i | 1.62866i | ||||||||
\(709\) | 21.6641i | 0.813614i | 0.913514 | + | 0.406807i | \(0.133358\pi\) | ||||
−0.913514 | + | 0.406807i | \(0.866642\pi\) | |||||||
\(710\) | − | 31.0253i | − | 1.16436i | ||||||
\(711\) | −0.354682 | −0.0133016 | ||||||||
\(712\) | −0.0813427 | −0.00304845 | ||||||||
\(713\) | 3.75923i | 0.140784i | ||||||||
\(714\) | 10.4941 | 0.392731 | ||||||||
\(715\) | 26.8599 | + | 8.83405i | 1.00450 | + | 0.330375i | ||||
\(716\) | −27.1703 | −1.01540 | ||||||||
\(717\) | 9.45556i | 0.353125i | ||||||||
\(718\) | −11.8709 | −0.443018 | ||||||||
\(719\) | −11.6958 | −0.436178 | −0.218089 | − | 0.975929i | \(-0.569982\pi\) | ||||
−0.218089 | + | 0.975929i | \(0.569982\pi\) | |||||||
\(720\) | 5.14462i | 0.191729i | ||||||||
\(721\) | − | 5.01359i | − | 0.186716i | ||||||
\(722\) | 1.91716i | 0.0713492i | ||||||||
\(723\) | 43.3072i | 1.61061i | ||||||||
\(724\) | 16.5376 | 0.614614 | ||||||||
\(725\) | 9.04330 | 0.335860 | ||||||||
\(726\) | − | 7.47521i | − | 0.277431i | ||||||
\(727\) | −10.7050 | −0.397026 | −0.198513 | − | 0.980098i | \(-0.563611\pi\) | ||||
−0.198513 | + | 0.980098i | \(0.563611\pi\) | |||||||
\(728\) | −0.261626 | − | 0.0860472i | −0.00969652 | − | 0.00318912i | ||||
\(729\) | 29.8190 | 1.10441 | ||||||||
\(730\) | 26.1807i | 0.968990i | ||||||||
\(731\) | 22.2569 | 0.823200 | ||||||||
\(732\) | 15.8792 | 0.586912 | ||||||||
\(733\) | 37.8613i | 1.39844i | 0.714907 | + | 0.699220i | \(0.246469\pi\) | ||||
−0.714907 | + | 0.699220i | \(0.753531\pi\) | |||||||
\(734\) | 57.1240i | 2.10849i | ||||||||
\(735\) | − | 16.8447i | − | 0.621328i | ||||||
\(736\) | − | 29.9873i | − | 1.10535i | ||||||
\(737\) | −37.3447 | −1.37561 | ||||||||
\(738\) | −5.52303 | −0.203306 | ||||||||
\(739\) | − | 8.15442i | − | 0.299965i | −0.988689 | − | 0.149983i | \(-0.952078\pi\) | ||
0.988689 | − | 0.149983i | \(-0.0479218\pi\) | |||||||
\(740\) | 16.1404 | 0.593334 | ||||||||
\(741\) | 7.59967 | − | 23.1068i | 0.279181 | − | 0.848849i | ||||
\(742\) | −47.9042 | −1.75862 | ||||||||
\(743\) | 32.4382i | 1.19004i | 0.803711 | + | 0.595020i | \(0.202856\pi\) | ||||
−0.803711 | + | 0.595020i | \(0.797144\pi\) | |||||||
\(744\) | 0.0697611 | 0.00255756 | ||||||||
\(745\) | 39.8100 | 1.45853 | ||||||||
\(746\) | − | 65.1990i | − | 2.38711i | ||||||
\(747\) | 0.0789864i | 0.00288996i | ||||||||
\(748\) | 11.0731i | 0.404871i | ||||||||
\(749\) | 12.7857i | 0.467179i | ||||||||
\(750\) | 24.3623 | 0.889585 | ||||||||
\(751\) | −18.4928 | −0.674811 | −0.337405 | − | 0.941359i | \(-0.609549\pi\) | ||||
−0.337405 | + | 0.941359i | \(0.609549\pi\) | |||||||
\(752\) | − | 42.5055i | − | 1.55001i | ||||||
\(753\) | 41.6180 | 1.51665 | ||||||||
\(754\) | −9.59477 | + | 29.1729i | −0.349421 | + | 1.06241i | ||||
\(755\) | 34.7184 | 1.26353 | ||||||||
\(756\) | 18.9998i | 0.691016i | ||||||||
\(757\) | 36.0911 | 1.31175 | 0.655877 | − | 0.754868i | \(-0.272299\pi\) | ||||
0.655877 | + | 0.754868i | \(0.272299\pi\) | |||||||
\(758\) | 27.8417 | 1.01126 | ||||||||
\(759\) | − | 17.5523i | − | 0.637110i | ||||||
\(760\) | 0.497641i | 0.0180513i | ||||||||
\(761\) | − | 6.79105i | − | 0.246175i | −0.992396 | − | 0.123088i | \(-0.960720\pi\) | ||
0.992396 | − | 0.123088i | \(-0.0392797\pi\) | |||||||
\(762\) | 0.314571i | 0.0113957i | ||||||||
\(763\) | 22.5883 | 0.817750 | ||||||||
\(764\) | −49.8222 | −1.80251 | ||||||||
\(765\) | 2.42308i | 0.0876065i | ||||||||
\(766\) | 9.22356 | 0.333261 | ||||||||
\(767\) | 15.5375 | − | 47.2418i | 0.561028 | − | 1.70580i | ||||
\(768\) | −25.9652 | −0.936939 | ||||||||
\(769\) | − | 8.83997i | − | 0.318777i | −0.987216 | − | 0.159389i | \(-0.949048\pi\) | ||
0.987216 | − | 0.159389i | \(-0.0509523\pi\) | |||||||
\(770\) | −27.2041 | −0.980369 | ||||||||
\(771\) | −30.8978 | −1.11276 | ||||||||
\(772\) | − | 15.8994i | − | 0.572232i | ||||||
\(773\) | 40.7935i | 1.46724i | 0.679559 | + | 0.733620i | \(0.262171\pi\) | ||||
−0.679559 | + | 0.733620i | \(0.737829\pi\) | |||||||
\(774\) | 11.1158i | 0.399549i | ||||||||
\(775\) | − | 2.11762i | − | 0.0760670i | ||||||
\(776\) | −0.279164 | −0.0100214 | ||||||||
\(777\) | −8.45009 | −0.303145 | ||||||||
\(778\) | − | 56.7510i | − | 2.03462i | ||||||
\(779\) | −24.6619 | −0.883606 | ||||||||
\(780\) | 9.44236 | − | 28.7095i | 0.338091 | − | 1.02796i | ||||
\(781\) | −17.1390 | −0.613283 | ||||||||
\(782\) | − | 14.2793i | − | 0.510627i | ||||||
\(783\) | −23.5852 | −0.842865 | ||||||||
\(784\) | −16.0728 | −0.574030 | ||||||||
\(785\) | − | 48.3201i | − | 1.72462i | ||||||
\(786\) | − | 4.95505i | − | 0.176741i | ||||||
\(787\) | − | 42.3875i | − | 1.51095i | −0.655176 | − | 0.755476i | \(-0.727406\pi\) | ||
0.655176 | − | 0.755476i | \(-0.272594\pi\) | |||||||
\(788\) | − | 5.53005i | − | 0.197000i | ||||||
\(789\) | 47.3356 | 1.68519 | ||||||||
\(790\) | −3.95745 | −0.140800 | ||||||||
\(791\) | 13.2751i | 0.472010i | ||||||||
\(792\) | 0.0615654 | 0.00218763 | ||||||||
\(793\) | −17.3104 | − | 5.69329i | −0.614711 | − | 0.202175i | ||||
\(794\) | 9.63126 | 0.341801 | ||||||||
\(795\) | 58.5207i | 2.07551i | ||||||||
\(796\) | −32.3217 | −1.14561 | ||||||||
\(797\) | 40.5744 | 1.43722 | 0.718610 | − | 0.695413i | \(-0.244779\pi\) | ||||
0.718610 | + | 0.695413i | \(0.244779\pi\) | |||||||
\(798\) | 23.4029i | 0.828455i | ||||||||
\(799\) | − | 20.0197i | − | 0.708248i | ||||||
\(800\) | 16.8922i | 0.597229i | ||||||||
\(801\) | − | 0.883275i | − | 0.0312090i | ||||||
\(802\) | −67.2775 | −2.37565 | ||||||||
\(803\) | 14.4627 | 0.510379 | ||||||||
\(804\) | 39.9163i | 1.40774i | ||||||||
\(805\) | 17.4435 | 0.614803 | ||||||||
\(806\) | 6.83124 | + | 2.24675i | 0.240620 | + | 0.0791385i | ||||
\(807\) | −12.0793 | −0.425211 | ||||||||
\(808\) | 0.136933i | 0.00481729i | ||||||||
\(809\) | −32.9403 | −1.15812 | −0.579060 | − | 0.815285i | \(-0.696580\pi\) | ||||
−0.579060 | + | 0.815285i | \(0.696580\pi\) | |||||||
\(810\) | 39.0667 | 1.37266 | ||||||||
\(811\) | 4.85286i | 0.170407i | 0.996364 | + | 0.0852034i | \(0.0271540\pi\) | ||||
−0.996364 | + | 0.0852034i | \(0.972846\pi\) | |||||||
\(812\) | − | 14.6916i | − | 0.515574i | ||||||
\(813\) | − | 35.1474i | − | 1.23267i | ||||||
\(814\) | − | 17.9319i | − | 0.628513i | ||||||
\(815\) | 9.79500 | 0.343104 | ||||||||
\(816\) | −12.2323 | −0.428216 | ||||||||
\(817\) | 49.6353i | 1.73652i | ||||||||
\(818\) | 67.8644 | 2.37282 | ||||||||
\(819\) | 0.934360 | − | 2.84092i | 0.0326492 | − | 0.0992697i | ||||
\(820\) | −30.6417 | −1.07006 | ||||||||
\(821\) | − | 19.3648i | − | 0.675836i | −0.941176 | − | 0.337918i | \(-0.890277\pi\) | ||
0.941176 | − | 0.337918i | \(-0.109723\pi\) | |||||||
\(822\) | 23.1595 | 0.807780 | ||||||||
\(823\) | 16.5691 | 0.577562 | 0.288781 | − | 0.957395i | \(-0.406750\pi\) | ||||
0.288781 | + | 0.957395i | \(0.406750\pi\) | |||||||
\(824\) | 0.126598i | 0.00441025i | ||||||||
\(825\) | 9.88744i | 0.344236i | ||||||||
\(826\) | 47.8473i | 1.66482i | ||||||||
\(827\) | 26.9392i | 0.936769i | 0.883525 | + | 0.468385i | \(0.155164\pi\) | ||||
−0.883525 | + | 0.468385i | \(0.844836\pi\) | |||||||
\(828\) | 3.54604 | 0.123233 | ||||||||
\(829\) | −8.76091 | −0.304279 | −0.152140 | − | 0.988359i | \(-0.548616\pi\) | ||||
−0.152140 | + | 0.988359i | \(0.548616\pi\) | |||||||
\(830\) | 0.881310i | 0.0305907i | ||||||||
\(831\) | 15.0164 | 0.520914 | ||||||||
\(832\) | −26.7938 | − | 8.81233i | −0.928909 | − | 0.305512i | ||||
\(833\) | −7.57019 | −0.262291 | ||||||||
\(834\) | − | 26.4800i | − | 0.916927i | ||||||
\(835\) | 9.58927 | 0.331850 | ||||||||
\(836\) | −24.6942 | −0.854065 | ||||||||
\(837\) | 5.52280i | 0.190896i | ||||||||
\(838\) | 39.4040i | 1.36119i | ||||||||
\(839\) | 41.9803i | 1.44932i | 0.689107 | + | 0.724660i | \(0.258003\pi\) | ||||
−0.689107 | + | 0.724660i | \(0.741997\pi\) | |||||||
\(840\) | − | 0.323704i | − | 0.0111689i | ||||||
\(841\) | −10.7628 | −0.371130 | ||||||||
\(842\) | 48.0392 | 1.65554 | ||||||||
\(843\) | 20.0947i | 0.692098i | ||||||||
\(844\) | −31.8661 | −1.09688 | ||||||||
\(845\) | −20.5868 | + | 27.9116i | −0.708208 | + | 0.960190i | ||||
\(846\) | 9.99851 | 0.343756 | ||||||||
\(847\) | − | 4.10386i | − | 0.141010i | ||||||
\(848\) | 55.8390 | 1.91752 | ||||||||
\(849\) | −27.4301 | −0.941398 | ||||||||
\(850\) | 8.04370i | 0.275897i | ||||||||
\(851\) | 11.4981i | 0.394149i | ||||||||
\(852\) | 18.3192i | 0.627606i | ||||||||
\(853\) | − | 6.25658i | − | 0.214221i | −0.994247 | − | 0.107111i | \(-0.965840\pi\) | ||
0.994247 | − | 0.107111i | \(-0.0341599\pi\) | |||||||
\(854\) | 17.5323 | 0.599942 | ||||||||
\(855\) | −5.40373 | −0.184804 | ||||||||
\(856\) | − | 0.322851i | − | 0.0110348i | ||||||
\(857\) | −43.5856 | −1.48886 | −0.744429 | − | 0.667702i | \(-0.767278\pi\) | ||||
−0.744429 | + | 0.667702i | \(0.767278\pi\) | |||||||
\(858\) | −31.8960 | − | 10.4904i | −1.08891 | − | 0.358136i | ||||
\(859\) | −1.98766 | −0.0678180 | −0.0339090 | − | 0.999425i | \(-0.510796\pi\) | ||||
−0.0339090 | + | 0.999425i | \(0.510796\pi\) | |||||||
\(860\) | 61.6703i | 2.10294i | ||||||||
\(861\) | 16.0420 | 0.546711 | ||||||||
\(862\) | −68.9833 | −2.34958 | ||||||||
\(863\) | − | 44.2665i | − | 1.50685i | −0.657535 | − | 0.753424i | \(-0.728401\pi\) | ||
0.657535 | − | 0.753424i | \(-0.271599\pi\) | |||||||
\(864\) | − | 44.0553i | − | 1.49879i | ||||||
\(865\) | 36.7473i | 1.24945i | ||||||||
\(866\) | 39.8313i | 1.35352i | ||||||||
\(867\) | 21.2420 | 0.721415 | ||||||||
\(868\) | −3.44025 | −0.116770 | ||||||||
\(869\) | 2.18618i | 0.0741610i | ||||||||
\(870\) | −36.0949 | −1.22373 | ||||||||
\(871\) | 14.3115 | − | 43.5140i | 0.484925 | − | 1.47441i | ||||
\(872\) | −0.570375 | −0.0193153 | ||||||||
\(873\) | − | 3.03135i | − | 0.102596i | ||||||
\(874\) | 31.8444 | 1.07715 | ||||||||
\(875\) | 13.3748 | 0.452150 | ||||||||
\(876\) | − | 15.4586i | − | 0.522299i | ||||||
\(877\) | − | 14.4318i | − | 0.487327i | −0.969860 | − | 0.243664i | \(-0.921651\pi\) | ||
0.969860 | − | 0.243664i | \(-0.0783493\pi\) | |||||||
\(878\) | − | 32.3754i | − | 1.09262i | ||||||
\(879\) | − | 9.97137i | − | 0.336326i | ||||||
\(880\) | 31.7102 | 1.06895 | ||||||||
\(881\) | −12.7791 | −0.430539 | −0.215269 | − | 0.976555i | \(-0.569063\pi\) | ||||
−0.215269 | + | 0.976555i | \(0.569063\pi\) | |||||||
\(882\) | − | 3.78080i | − | 0.127306i | ||||||
\(883\) | 40.3665 | 1.35844 | 0.679221 | − | 0.733934i | \(-0.262318\pi\) | ||||
0.679221 | + | 0.733934i | \(0.262318\pi\) | |||||||
\(884\) | −12.9023 | − | 4.24349i | −0.433951 | − | 0.142724i | ||||
\(885\) | 58.4512 | 1.96481 | ||||||||
\(886\) | 77.6833i | 2.60982i | ||||||||
\(887\) | −26.7184 | −0.897115 | −0.448558 | − | 0.893754i | \(-0.648062\pi\) | ||||
−0.448558 | + | 0.893754i | \(0.648062\pi\) | |||||||
\(888\) | 0.213373 | 0.00716033 | ||||||||
\(889\) | 0.172698i | 0.00579211i | ||||||||
\(890\) | − | 9.85535i | − | 0.330352i | ||||||
\(891\) | − | 21.5812i | − | 0.722999i | ||||||
\(892\) | − | 20.8182i | − | 0.697045i | ||||||
\(893\) | 44.6462 | 1.49403 | ||||||||
\(894\) | −47.2742 | −1.58109 | ||||||||
\(895\) | 36.6471i | 1.22498i | ||||||||
\(896\) | −0.611050 | −0.0204137 | ||||||||
\(897\) | 20.4519 | + | 6.72652i | 0.682871 | + | 0.224592i | ||||
\(898\) | −40.6108 | −1.35520 | ||||||||
\(899\) | − | 4.27051i | − | 0.142429i | ||||||
\(900\) | −1.99752 | −0.0665841 | ||||||||
\(901\) | 26.2997 | 0.876172 | ||||||||
\(902\) | 34.0427i | 1.13350i | ||||||||
\(903\) | − | 32.2866i | − | 1.07443i | ||||||
\(904\) | − | 0.335210i | − | 0.0111489i | ||||||
\(905\) | − | 22.3058i | − | 0.741469i | ||||||
\(906\) | −41.2279 | −1.36970 | ||||||||
\(907\) | −43.7286 | −1.45199 | −0.725993 | − | 0.687702i | \(-0.758619\pi\) | ||||
−0.725993 | + | 0.687702i | \(0.758619\pi\) | |||||||
\(908\) | − | 3.03499i | − | 0.100720i | ||||||
\(909\) | −1.48691 | −0.0493178 | ||||||||
\(910\) | 10.4253 | − | 31.6982i | 0.345597 | − | 1.05079i | ||||
\(911\) | −24.8683 | −0.823925 | −0.411962 | − | 0.911201i | \(-0.635157\pi\) | ||||
−0.411962 | + | 0.911201i | \(0.635157\pi\) | |||||||
\(912\) | − | 27.2794i | − | 0.903311i | ||||||
\(913\) | 0.486854 | 0.0161125 | ||||||||
\(914\) | −29.7661 | −0.984574 | ||||||||
\(915\) | − | 21.4178i | − | 0.708050i | ||||||
\(916\) | − | 2.64411i | − | 0.0873638i | ||||||
\(917\) | − | 2.72030i | − | 0.0898322i | ||||||
\(918\) | − | 20.9782i | − | 0.692383i | ||||||
\(919\) | −9.82945 | −0.324244 | −0.162122 | − | 0.986771i | \(-0.551834\pi\) | ||||
−0.162122 | + | 0.986771i | \(0.551834\pi\) | |||||||
\(920\) | −0.440465 | −0.0145217 | ||||||||
\(921\) | − | 27.0854i | − | 0.892493i | ||||||
\(922\) | −35.8589 | −1.18095 | ||||||||
\(923\) | 6.56812 | − | 19.9703i | 0.216192 | − | 0.657332i | ||||
\(924\) | 16.0630 | 0.528433 | ||||||||
\(925\) | − | 6.47699i | − | 0.212962i | ||||||
\(926\) | 80.6702 | 2.65099 | ||||||||
\(927\) | −1.37469 | −0.0451507 | ||||||||
\(928\) | 34.0658i | 1.11826i | ||||||||
\(929\) | − | 36.8412i | − | 1.20872i | −0.796711 | − | 0.604360i | \(-0.793429\pi\) | ||
0.796711 | − | 0.604360i | \(-0.206571\pi\) | |||||||
\(930\) | 8.45213i | 0.277156i | ||||||||
\(931\) | − | 16.8824i | − | 0.553297i | ||||||
\(932\) | 45.8292 | 1.50119 | ||||||||
\(933\) | −6.36980 | −0.208538 | ||||||||
\(934\) | 74.7495i | 2.44588i | ||||||||
\(935\) | 14.9353 | 0.488436 | ||||||||
\(936\) | −0.0235935 | + | 0.0717358i | −0.000771177 | + | 0.00234476i | ||||
\(937\) | −27.3075 | −0.892099 | −0.446049 | − | 0.895008i | \(-0.647169\pi\) | ||||
−0.446049 | + | 0.895008i | \(0.647169\pi\) | |||||||
\(938\) | 44.0716i | 1.43899i | ||||||||
\(939\) | 9.59358 | 0.313075 | ||||||||
\(940\) | 55.4716 | 1.80928 | ||||||||
\(941\) | 55.6611i | 1.81450i | 0.420593 | + | 0.907249i | \(0.361822\pi\) | ||||
−0.420593 | + | 0.907249i | \(0.638178\pi\) | |||||||
\(942\) | 57.3799i | 1.86954i | ||||||||
\(943\) | − | 21.8284i | − | 0.710832i | ||||||
\(944\) | − | 55.7727i | − | 1.81525i | ||||||
\(945\) | 25.6268 | 0.833640 | ||||||||
\(946\) | 68.5152 | 2.22762 | ||||||||
\(947\) | − | 30.9641i | − | 1.00620i | −0.864228 | − | 0.503100i | \(-0.832193\pi\) | ||
0.864228 | − | 0.503100i | \(-0.167807\pi\) | |||||||
\(948\) | 2.33672 | 0.0758930 | ||||||||
\(949\) | −5.54250 | + | 16.8520i | −0.179917 | + | 0.547038i | ||||
\(950\) | −17.9383 | −0.581996 | ||||||||
\(951\) | 22.2871i | 0.722710i | ||||||||
\(952\) | −0.145476 | −0.00471489 | ||||||||
\(953\) | 16.9362 | 0.548618 | 0.274309 | − | 0.961642i | \(-0.411551\pi\) | ||||
0.274309 | + | 0.961642i | \(0.411551\pi\) | |||||||
\(954\) | 13.1349i | 0.425260i | ||||||||
\(955\) | 67.1999i | 2.17454i | ||||||||
\(956\) | 11.7745i | 0.380814i | ||||||||
\(957\) | 19.9396i | 0.644555i | ||||||||
\(958\) | −9.16079 | −0.295972 | ||||||||
\(959\) | 12.7145 | 0.410571 | ||||||||
\(960\) | − | 33.1514i | − | 1.06996i | ||||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | 20.8942 | + | 6.87197i | 0.673656 | + | 0.221561i | ||||
\(963\) | 3.50573 | 0.112971 | ||||||||
\(964\) | 53.9280i | 1.73691i | ||||||||
\(965\) | −21.4450 | −0.690339 | ||||||||
\(966\) | −20.7141 | −0.666464 | ||||||||
\(967\) | 10.2460i | 0.329488i | 0.986336 | + | 0.164744i | \(0.0526797\pi\) | ||||
−0.986336 | + | 0.164744i | \(0.947320\pi\) | |||||||
\(968\) | 0.103626i | 0.00333068i | ||||||||
\(969\) | − | 12.8484i | − | 0.412749i | ||||||
\(970\) | − | 33.8230i | − | 1.08599i | ||||||
\(971\) | −41.0649 | −1.31784 | −0.658918 | − | 0.752214i | \(-0.728986\pi\) | ||||
−0.658918 | + | 0.752214i | \(0.728986\pi\) | |||||||
\(972\) | 9.70463 | 0.311276 | ||||||||
\(973\) | − | 14.5374i | − | 0.466047i | ||||||
\(974\) | −59.0592 | −1.89238 | ||||||||
\(975\) | −11.5208 | − | 3.78912i | −0.368961 | − | 0.121349i | ||||
\(976\) | −20.4363 | −0.654151 | ||||||||
\(977\) | − | 15.4726i | − | 0.495013i | −0.968886 | − | 0.247507i | \(-0.920389\pi\) | ||
0.968886 | − | 0.247507i | \(-0.0796112\pi\) | |||||||
\(978\) | −11.6315 | −0.371935 | ||||||||
\(979\) | −5.44430 | −0.174001 | ||||||||
\(980\) | − | 20.9758i | − | 0.670048i | ||||||
\(981\) | − | 6.19352i | − | 0.197744i | ||||||
\(982\) | 69.9793i | 2.23313i | ||||||||
\(983\) | 14.4229i | 0.460020i | 0.973188 | + | 0.230010i | \(0.0738759\pi\) | ||||
−0.973188 | + | 0.230010i | \(0.926124\pi\) | |||||||
\(984\) | −0.405076 | −0.0129134 | ||||||||
\(985\) | −7.45889 | −0.237660 | ||||||||
\(986\) | 16.2214i | 0.516594i | ||||||||
\(987\) | −29.0414 | −0.924396 | ||||||||
\(988\) | 9.46344 | − | 28.7736i | 0.301072 | − | 0.915409i | ||||
\(989\) | −43.9325 | −1.39697 | ||||||||
\(990\) | 7.45916i | 0.237068i | ||||||||
\(991\) | −55.8859 | −1.77527 | −0.887637 | − | 0.460543i | \(-0.847655\pi\) | ||||
−0.887637 | + | 0.460543i | \(0.847655\pi\) | |||||||
\(992\) | 7.97698 | 0.253269 | ||||||||
\(993\) | − | 17.7382i | − | 0.562905i | ||||||
\(994\) | 20.2263i | 0.641539i | ||||||||
\(995\) | 43.5953i | 1.38206i | ||||||||
\(996\) | − | 0.520379i | − | 0.0164888i | ||||||
\(997\) | −21.4634 | −0.679753 | −0.339877 | − | 0.940470i | \(-0.610385\pi\) | ||||
−0.339877 | + | 0.940470i | \(0.610385\pi\) | |||||||
\(998\) | 6.14200 | 0.194421 | ||||||||
\(999\) | 16.8922i | 0.534445i |
(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 | 403.2.c.b.311.27 | yes | 32 | |
13.5 | odd | 4 | 5239.2.a.k.1.14 | 16 | |||
13.8 | odd | 4 | 5239.2.a.l.1.3 | 16 | |||
13.12 | even | 2 | inner | 403.2.c.b.311.6 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.c.b.311.6 | ✓ | 32 | 13.12 | even | 2 | inner | |
403.2.c.b.311.27 | yes | 32 | 1.1 | even | 1 | trivial | |
5239.2.a.k.1.14 | 16 | 13.5 | odd | 4 | |||
5239.2.a.l.1.3 | 16 | 13.8 | odd | 4 |