Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(47,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.be (of order \(18\), degree \(6\), 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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 47.2 | ||
Character | \(\chi\) | \(=\) | 432.47 |
Dual form | 432.2.be.c.239.2 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{18}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.36628 | + | 1.06456i | −0.788821 | + | 0.614623i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.83017 | − | 0.322709i | 0.818477 | − | 0.144320i | 0.251294 | − | 0.967911i | \(-0.419144\pi\) |
0.567184 | + | 0.823591i | \(0.308033\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.441545 | − | 0.526213i | 0.166888 | − | 0.198890i | −0.676118 | − | 0.736793i | \(-0.736339\pi\) |
0.843006 | + | 0.537903i | \(0.180784\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.733433 | − | 2.90896i | 0.244478 | − | 0.969655i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0632128 | − | 0.358498i | 0.0190594 | − | 0.108091i | −0.973794 | − | 0.227432i | \(-0.926967\pi\) |
0.992853 | + | 0.119341i | \(0.0380782\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.50997 | + | 0.913554i | 0.696140 | + | 0.253374i | 0.665762 | − | 0.746164i | \(-0.268107\pi\) |
0.0303782 | + | 0.999538i | \(0.490329\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.15698 | + | 2.38923i | −0.556930 | + | 0.616897i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.50099 | − | 1.44395i | 0.606580 | − | 0.350209i | −0.165046 | − | 0.986286i | \(-0.552777\pi\) |
0.771626 | + | 0.636077i | \(0.219444\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.50751 | + | 1.44771i | 0.575262 | + | 0.332128i | 0.759248 | − | 0.650801i | \(-0.225567\pi\) |
−0.183986 | + | 0.982929i | \(0.558900\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0430893 | + | 1.18900i | −0.00940286 | + | 0.259462i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.39029 | − | 1.16659i | 0.289896 | − | 0.243252i | −0.486228 | − | 0.873832i | \(-0.661628\pi\) |
0.776124 | + | 0.630580i | \(0.217183\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.45308 | + | 0.528877i | −0.290616 | + | 0.105775i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.09469 | + | 4.75524i | 0.403123 | + | 0.915146i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.03639 | + | 5.59492i | 0.378147 | + | 1.03895i | 0.972124 | + | 0.234469i | \(0.0753350\pi\) |
−0.593976 | + | 0.804482i | \(0.702443\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.94453 | + | 3.50915i | 0.528853 | + | 0.630262i | 0.962650 | − | 0.270748i | \(-0.0872710\pi\) |
−0.433797 | + | 0.901011i | \(0.642827\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.295275 | + | 0.557101i | 0.0514008 | + | 0.0969788i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.638290 | − | 1.10555i | 0.107891 | − | 0.186872i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.77265 | + | 3.07032i | 0.291422 | + | 0.504757i | 0.974146 | − | 0.225919i | \(-0.0725384\pi\) |
−0.682725 | + | 0.730676i | \(0.739205\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.40185 | + | 1.42384i | −0.704860 | + | 0.227997i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.29740 | − | 9.05952i | 0.514967 | − | 1.41486i | −0.361035 | − | 0.932552i | \(-0.617577\pi\) |
0.876002 | − | 0.482308i | \(-0.160201\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.8245 | + | 2.08497i | 1.80322 | + | 0.317956i | 0.971463 | − | 0.237190i | \(-0.0762264\pi\) |
0.831753 | + | 0.555146i | \(0.187338\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.403559 | − | 5.56059i | 0.0601591 | − | 0.828923i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.61569 | − | 6.39032i | −1.11086 | − | 0.932124i | −0.112755 | − | 0.993623i | \(-0.535967\pi\) |
−0.998107 | + | 0.0614989i | \(0.980412\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.13360 | + | 6.42896i | 0.161943 | + | 0.918423i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.87989 | + | 4.63529i | −0.263237 | + | 0.649070i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.01980i | 0.140081i | 0.997544 | + | 0.0700403i | \(0.0223128\pi\) | ||||
−0.997544 | + | 0.0700403i | \(0.977687\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.676511i | − | 0.0912207i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.96713 | + | 0.691413i | −0.657913 | + | 0.0915799i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.864840 | − | 4.90475i | −0.112593 | − | 0.638544i | −0.987914 | − | 0.155003i | \(-0.950461\pi\) |
0.875321 | − | 0.483541i | \(-0.160650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.61210 | − | 8.06551i | −1.23070 | − | 1.03268i | −0.998193 | − | 0.0600881i | \(-0.980862\pi\) |
−0.232510 | − | 0.972594i | \(-0.574694\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.20689 | − | 1.67038i | −0.152054 | − | 0.210448i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.88848 | + | 0.861972i | 0.606342 | + | 0.106914i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.71306 | + | 4.70659i | −0.209283 | + | 0.575001i | −0.999273 | − | 0.0381187i | \(-0.987863\pi\) |
0.789990 | + | 0.613120i | \(0.210086\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.657619 | + | 3.07394i | −0.0791681 | + | 0.370059i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.29859 | − | 14.3736i | −0.984862 | − | 1.70583i | −0.642549 | − | 0.766244i | \(-0.722123\pi\) |
−0.342312 | − | 0.939586i | \(-0.611210\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.84801 | + | 11.8611i | −0.801499 | + | 1.38824i | 0.117131 | + | 0.993117i | \(0.462630\pi\) |
−0.918629 | + | 0.395120i | \(0.870703\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.42229 | − | 2.26948i | 0.164232 | − | 0.262057i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.160735 | − | 0.191556i | −0.0183174 | − | 0.0218299i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.52383 | − | 6.93417i | −0.283953 | − | 0.780155i | −0.996881 | − | 0.0789179i | \(-0.974854\pi\) |
0.712928 | − | 0.701237i | \(-0.247369\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.92415 | − | 4.26706i | −0.880461 | − | 0.474118i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.65593 | + | 1.33065i | −0.401291 | + | 0.146058i | −0.534778 | − | 0.844993i | \(-0.679605\pi\) |
0.133487 | + | 0.991051i | \(0.457383\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.11127 | − | 3.44977i | 0.445930 | − | 0.374180i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.73839 | − | 5.47637i | −0.936854 | − | 0.587129i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.1121 | − | 6.99291i | −1.28388 | − | 0.741247i | −0.306323 | − | 0.951928i | \(-0.599099\pi\) |
−0.977555 | + | 0.210680i | \(0.932432\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.58899 | − | 0.917403i | 0.166571 | − | 0.0961700i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.75874 | − | 1.65986i | −0.804544 | − | 0.172119i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.05636 | + | 1.84037i | 0.518772 | + | 0.188818i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.204961 | + | 1.16239i | −0.0208106 | + | 0.118023i | −0.993443 | − | 0.114325i | \(-0.963530\pi\) |
0.972633 | + | 0.232348i | \(0.0746407\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.996494 | − | 0.446818i | −0.100151 | − | 0.0449069i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.52719 | + | 5.39529i | −0.450472 | + | 0.536851i | −0.942712 | − | 0.333608i | \(-0.891734\pi\) |
0.492240 | + | 0.870460i | \(0.336178\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.09521 | − | 1.60373i | 0.896178 | − | 0.158020i | 0.293457 | − | 0.955972i | \(-0.405194\pi\) |
0.602721 | + | 0.797952i | \(0.294083\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.304841 | + | 2.18999i | 0.0297494 | + | 0.213721i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.7246 | 1.13346 | 0.566730 | − | 0.823904i | \(-0.308208\pi\) | ||||
0.566730 | + | 0.823904i | \(0.308208\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.7988 | −1.22590 | −0.612951 | − | 0.790121i | \(-0.710018\pi\) | ||||
−0.612951 | + | 0.790121i | \(0.710018\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.69046 | − | 2.30782i | −0.540115 | − | 0.219049i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.2080 | − | 1.97627i | 1.05436 | − | 0.185912i | 0.380506 | − | 0.924779i | \(-0.375750\pi\) |
0.673851 | + | 0.738867i | \(0.264639\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.16800 | − | 2.58372i | 0.202167 | − | 0.240934i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.49839 | − | 6.63138i | 0.415876 | − | 0.613071i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.344477 | − | 1.95362i | 0.0315781 | − | 0.179088i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.2121 | + | 3.71690i | 0.928372 | + | 0.337900i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.13923 | + | 15.8881i | 0.463388 | + | 1.43258i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.5358 | + | 6.08287i | −0.942354 | + | 0.544068i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.3478 | − | 5.97431i | −0.918220 | − | 0.530135i | −0.0351532 | − | 0.999382i | \(-0.511192\pi\) |
−0.883067 | + | 0.469247i | \(0.844525\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.3751 | + | 9.73919i | −1.61784 | + | 0.857488i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.871001 | + | 0.730857i | −0.0760998 | + | 0.0638553i | −0.680044 | − | 0.733171i | \(-0.738039\pi\) |
0.603944 | + | 0.797027i | \(0.293595\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.86898 | − | 0.680255i | 0.162062 | − | 0.0589856i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.36819 | + | 8.02692i | 0.462021 | + | 0.690848i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.75201 | + | 7.56110i | 0.235120 | + | 0.645988i | 0.999998 | + | 0.00181278i | \(0.000577027\pi\) |
−0.764878 | + | 0.644175i | \(0.777201\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.48845 | + | 4.15737i | 0.295886 | + | 0.352623i | 0.893422 | − | 0.449219i | \(-0.148298\pi\) |
−0.597535 | + | 0.801843i | \(0.703853\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.2080 | + | 0.623615i | 1.44918 | + | 0.0525179i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.486169 | − | 0.842069i | 0.0406555 | − | 0.0704174i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.53246 | + | 9.58251i | 0.459446 | + | 0.795784i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.39281 | − | 7.57697i | −0.692228 | − | 0.624938i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.679944 | − | 1.86813i | 0.0557032 | − | 0.153043i | −0.908720 | − | 0.417406i | \(-0.862939\pi\) |
0.964423 | + | 0.264363i | \(0.0851616\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.82458 | + | 0.498049i | 0.229861 | + | 0.0405307i | 0.287392 | − | 0.957813i | \(-0.407212\pi\) |
−0.0575312 | + | 0.998344i | \(0.518323\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.36609 | − | 8.33434i | −0.191287 | − | 0.673792i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.52142 | + | 5.47212i | 0.523813 | + | 0.439532i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.10204 | − | 11.9213i | −0.167761 | − | 0.951421i | −0.946172 | − | 0.323665i | \(-0.895085\pi\) |
0.778411 | − | 0.627756i | \(-0.216026\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.08564 | − | 1.39333i | −0.0860968 | − | 0.110499i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.24669i | − | 0.0982532i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3.69079i | − | 0.289085i | −0.989499 | − | 0.144543i | \(-0.953829\pi\) | ||
0.989499 | − | 0.144543i | \(-0.0461710\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.720185 | + | 0.924302i | 0.0560663 | + | 0.0719568i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.60391 | + | 20.4388i | 0.278879 | + | 1.58160i | 0.726365 | + | 0.687309i | \(0.241208\pi\) |
−0.447487 | + | 0.894291i | \(0.647681\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.49321 | − | 3.77025i | −0.345632 | − | 0.290020i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.05043 | − | 6.23246i | 0.462688 | − | 0.476608i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.14247 | + | 1.08308i | 0.467003 | + | 0.0823452i | 0.402198 | − | 0.915553i | \(-0.368246\pi\) |
0.0648051 | + | 0.997898i | \(0.479357\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.363298 | + | 0.998152i | −0.0274627 | + | 0.0754532i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.40300 | + | 5.78058i | 0.481279 | + | 0.434495i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.76734 | − | 11.7214i | −0.505815 | − | 0.876097i | −0.999977 | − | 0.00672715i | \(-0.997859\pi\) |
0.494163 | − | 0.869369i | \(-0.335475\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.39270 | + | 5.87633i | −0.252177 | + | 0.436784i | −0.964125 | − | 0.265449i | \(-0.914480\pi\) |
0.711948 | + | 0.702232i | \(0.247813\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.7190 | + | 0.787093i | 1.60551 | + | 0.0581836i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.23507 | + | 5.04715i | 0.311368 | + | 0.371074i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.359557 | − | 0.987876i | −0.0262934 | − | 0.0722406i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.42717 | + | 0.997400i | 0.249290 | + | 0.0725502i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.3682 | + | 5.59358i | −1.11201 | + | 0.404737i | −0.831729 | − | 0.555181i | \(-0.812649\pi\) |
−0.280278 | + | 0.959919i | \(0.590427\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.5207 | − | 12.1843i | 1.04522 | − | 0.877046i | 0.0526393 | − | 0.998614i | \(-0.483237\pi\) |
0.992583 | + | 0.121568i | \(0.0387922\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.59665 | + | 4.02638i | −0.544007 | + | 0.288335i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.4041 | − | 11.7803i | −1.45373 | − | 0.839312i | −0.455040 | − | 0.890471i | \(-0.650375\pi\) |
−0.998691 | + | 0.0511593i | \(0.983708\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.8690 | + | 6.27522i | −0.770482 | + | 0.444838i | −0.833047 | − | 0.553203i | \(-0.813406\pi\) |
0.0625642 | + | 0.998041i | \(0.480072\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.66992 | − | 8.25416i | −0.188322 | − | 0.582203i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.84328 | + | 1.39884i | 0.269745 | + | 0.0981792i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.11121 | − | 17.6446i | 0.217297 | − | 1.23235i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.37389 | − | 4.89993i | −0.164997 | − | 0.340569i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.677508 | − | 0.807423i | 0.0468642 | − | 0.0558506i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.5778 | + | 3.45209i | −1.34779 | + | 0.237652i | −0.800520 | − | 0.599305i | \(-0.795444\pi\) |
−0.547269 | + | 0.836957i | \(0.684332\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 26.6397 | + | 10.8040i | 1.82532 | + | 0.740277i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 22.3137 | 1.52178 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.14670 | 0.213612 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.27054 | − | 23.4957i | −0.221003 | − | 1.58769i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.59654 | − | 1.33948i | 0.510999 | − | 0.0901029i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.80196 | + | 6.91450i | −0.388528 | + | 0.463029i | −0.924486 | − | 0.381215i | \(-0.875506\pi\) |
0.535959 | + | 0.844244i | \(0.319950\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.472750 | + | 4.61485i | 0.0315167 | + | 0.307657i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.31547 | + | 13.1317i | −0.153683 | + | 0.871579i | 0.806297 | + | 0.591511i | \(0.201468\pi\) |
−0.959980 | + | 0.280068i | \(0.909643\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.54248 | + | 3.10921i | 0.564503 | + | 0.205462i | 0.608479 | − | 0.793570i | \(-0.291780\pi\) |
−0.0439755 | + | 0.999033i | \(0.514002\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.423531 | + | 0.0906077i | 0.0278663 | + | 0.00596155i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.17144 | − | 3.56308i | 0.404304 | − | 0.233425i | −0.284035 | − | 0.958814i | \(-0.591673\pi\) |
0.688340 | + | 0.725389i | \(0.258340\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.0002 | − | 9.23773i | −1.04374 | − | 0.602603i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.8301 | + | 6.78724i | 0.703490 | + | 0.440879i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.43186 | + | 5.39697i | −0.416042 | + | 0.349101i | −0.826655 | − | 0.562709i | \(-0.809759\pi\) |
0.410613 | + | 0.911810i | \(0.365315\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.89267 | − | 2.87270i | 0.508412 | − | 0.185047i | −0.0750618 | − | 0.997179i | \(-0.523915\pi\) |
0.583474 | + | 0.812132i | \(0.301693\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.3691 | − | 2.60573i | 0.985930 | − | 0.167158i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.14936 | + | 11.4003i | 0.265093 | + | 0.728337i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.97121 | + | 5.92446i | 0.316311 | + | 0.376964i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.57847 | − | 5.70999i | 0.226776 | − | 0.361856i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.6479 | + | 27.1030i | −0.987688 | + | 1.71073i | −0.358366 | + | 0.933581i | \(0.616666\pi\) |
−0.629322 | + | 0.777145i | \(0.716667\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.330337 | − | 0.572160i | −0.0207681 | − | 0.0359714i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.94466 | + | 9.09003i | −0.121780 | + | 0.569240i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.17068 | − | 19.7013i | 0.447295 | − | 1.22893i | −0.487305 | − | 0.873232i | \(-0.662020\pi\) |
0.934600 | − | 0.355700i | \(-0.115758\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.39834 | + | 0.422893i | 0.149026 | + | 0.0262773i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.7690 | − | 1.82027i | 1.09987 | − | 0.112672i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.60982 | + | 4.70720i | 0.345916 | + | 0.290258i | 0.799148 | − | 0.601135i | \(-0.205284\pi\) |
−0.453231 | + | 0.891393i | \(0.649729\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.329099 | + | 1.86641i | 0.0202164 | + | 0.114653i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 23.9928 | − | 3.33975i | 1.46834 | − | 0.204389i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.3626i | 1.11959i | 0.828632 | + | 0.559793i | \(0.189120\pi\) | ||||
−0.828632 | + | 0.559793i | \(0.810880\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.08071i | 0.0656483i | 0.999461 | + | 0.0328241i | \(0.0104501\pi\) | ||||
−0.999461 | + | 0.0328241i | \(0.989550\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.19437 | + | 2.94500i | −0.0722867 | + | 0.178239i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.0977481 | + | 0.554357i | 0.00589443 | + | 0.0334290i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.6528 | − | 8.93879i | −0.640067 | − | 0.537080i | 0.263972 | − | 0.964530i | \(-0.414967\pi\) |
−0.904039 | + | 0.427450i | \(0.859412\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.3676 | − | 5.99180i | 0.740430 | − | 0.358720i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.52866 | + | 0.974852i | 0.329812 | + | 0.0581548i | 0.336102 | − | 0.941825i | \(-0.390891\pi\) |
−0.00629033 | + | 0.999980i | \(0.502002\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.59448 | + | 15.3707i | −0.332558 | + | 0.913694i | 0.654887 | + | 0.755727i | \(0.272716\pi\) |
−0.987444 | + | 0.157967i | \(0.949506\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.86757 | + | 2.86834i | −0.525270 | + | 0.169906i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.31129 | − | 5.73532i | −0.195459 | − | 0.338545i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.33002 | + | 7.49982i | −0.254707 | + | 0.441166i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.957398 | − | 1.80634i | −0.0561237 | − | 0.105890i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.32574 | − | 8.73048i | −0.427975 | − | 0.510040i | 0.508362 | − | 0.861143i | \(-0.330251\pi\) |
−0.936337 | + | 0.351103i | \(0.885807\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.16561 | − | 8.69744i | −0.184309 | − | 0.506385i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.83715 | − | 0.450349i | 0.106602 | − | 0.0261319i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.55534 | − | 1.65801i | 0.263442 | − | 0.0958850i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.31818 | − | 5.30159i | 0.364174 | − | 0.305578i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.441797 | − | 12.1909i | 0.0253806 | − | 0.700350i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −20.1946 | − | 11.6593i | −1.15634 | − | 0.667612i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.20934 | + | 3.58496i | −0.354386 | + | 0.204605i | −0.666615 | − | 0.745402i | \(-0.732258\pi\) |
0.312230 | + | 0.950007i | \(0.398924\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.7193 | + | 11.8735i | −0.609801 | + | 0.675461i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.1437 | + | 7.33171i | 1.14224 | + | 0.415743i | 0.842723 | − | 0.538347i | \(-0.180951\pi\) |
0.299521 | + | 0.954090i | \(0.403173\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.26646 | − | 7.18245i | 0.0715845 | − | 0.405976i | −0.927869 | − | 0.372907i | \(-0.878361\pi\) |
0.999453 | − | 0.0330687i | \(-0.0105280\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.74786 | − | 2.66761i | −0.154825 | − | 0.150303i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.9507 | + | 17.8176i | −0.839717 | + | 1.00074i | 0.160190 | + | 0.987086i | \(0.448789\pi\) |
−0.999907 | + | 0.0136497i | \(0.995655\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.13449 | − | 0.376368i | 0.119509 | − | 0.0210726i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.0191 | + | 12.4815i | −0.894097 | + | 0.696650i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.36169 | 0.465257 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.13034 | −0.229110 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.4867 | − | 13.6251i | 0.967018 | − | 0.753467i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.72534 | + | 1.18586i | −0.370780 | + | 0.0653785i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.44461 | − | 8.87214i | 0.409193 | − | 0.487657i | −0.521607 | − | 0.853186i | \(-0.674667\pi\) |
0.930800 | + | 0.365529i | \(0.119112\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.2316 | − | 2.90470i | 0.560686 | − | 0.159177i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.61633 | + | 9.16668i | −0.0883097 | + | 0.500829i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.71533 | + | 3.53609i | 0.529228 | + | 0.192623i | 0.592793 | − | 0.805355i | \(-0.298025\pi\) |
−0.0635658 | + | 0.997978i | \(0.520247\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.2094 | + | 14.6317i | −0.717434 | + | 0.794683i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.44415 | − | 0.833783i | 0.0782053 | − | 0.0451519i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.04778 | + | 4.64639i | 0.434540 | + | 0.250882i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.211570 | + | 5.83805i | −0.0113905 | + | 0.314310i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.93967 | − | 8.34038i | 0.533590 | − | 0.447735i | −0.335749 | − | 0.941951i | \(-0.608989\pi\) |
0.869339 | + | 0.494217i | \(0.164545\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.4970 | + | 6.73235i | −0.990121 | + | 0.360375i | −0.785767 | − | 0.618522i | \(-0.787732\pi\) |
−0.204354 | + | 0.978897i | \(0.565509\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.913437 | + | 13.8491i | 0.0487557 | + | 0.739211i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.12185 | − | 3.08225i | −0.0597099 | − | 0.164052i | 0.906251 | − | 0.422740i | \(-0.138932\pi\) |
−0.965961 | + | 0.258689i | \(0.916710\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.8263 | − | 23.6281i | −1.05227 | − | 1.25405i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.60910 | + | 3.03591i | 0.0851624 | + | 0.160677i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.91834 | + | 8.51881i | −0.259580 | + | 0.449606i | −0.966129 | − | 0.258058i | \(-0.916917\pi\) |
0.706549 | + | 0.707664i | \(0.250251\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.30826 | − | 9.19417i | −0.279382 | − | 0.483904i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.9094 | + | 5.79305i | −0.940001 | + | 0.304056i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.70535 | + | 23.9177i | −0.455659 | + | 1.25191i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.4143 | − | 5.01021i | −1.48321 | − | 0.261531i | −0.627352 | − | 0.778735i | \(-0.715861\pi\) |
−0.855862 | + | 0.517205i | \(0.826973\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −23.9354 | − | 16.2366i | −1.24603 | − | 0.845242i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.536634 | + | 0.450289i | 0.0278606 | + | 0.0233778i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.186692 | + | 1.05878i | 0.00966652 | + | 0.0548216i | 0.989259 | − | 0.146170i | \(-0.0466947\pi\) |
−0.979593 | + | 0.200992i | \(0.935584\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.91932 | − | 19.5269i | 0.408952 | − | 1.00836i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.9034i | 0.819068i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 26.9955i | − | 1.38667i | −0.720617 | − | 0.693333i | \(-0.756142\pi\) | ||
0.720617 | − | 0.693333i | \(-0.243858\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.4980 | − | 2.85327i | 1.05014 | − | 0.146178i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.42477 | + | 19.4229i | 0.174998 | + | 0.992461i | 0.938147 | + | 0.346239i | \(0.112541\pi\) |
−0.763149 | + | 0.646223i | \(0.776348\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.355989 | − | 0.298710i | −0.0181429 | − | 0.0152237i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.7376 | − | 32.8678i | 0.749153 | − | 1.67076i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.2544 | − | 3.57139i | −1.02694 | − | 0.181077i | −0.365291 | − | 0.930893i | \(-0.619031\pi\) |
−0.661646 | + | 0.749817i | \(0.730142\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.79261 | − | 4.92515i | 0.0906561 | − | 0.249076i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.411991 | − | 1.92579i | 0.0207822 | − | 0.0971430i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.85676 | − | 11.8763i | −0.345001 | − | 0.597559i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.5650 | − | 20.0311i | 0.580430 | − | 1.00533i | −0.414998 | − | 0.909822i | \(-0.636218\pi\) |
0.995428 | − | 0.0955122i | \(-0.0304489\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.82938 | + | 2.91906i | −0.0915837 | + | 0.146136i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.33843 | − | 11.1291i | −0.466339 | − | 0.555761i | 0.480698 | − | 0.876886i | \(-0.340383\pi\) |
−0.947037 | + | 0.321125i | \(0.895939\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.18488 | + | 11.4979i | 0.208463 | + | 0.572749i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −15.8796 | − | 5.25226i | −0.789062 | − | 0.260987i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.21275 | − | 0.441407i | 0.0601140 | − | 0.0218797i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.2899 | + | 12.8298i | −0.756038 | + | 0.634392i | −0.937092 | − | 0.349082i | \(-0.886494\pi\) |
0.181054 | + | 0.983473i | \(0.442049\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.8092 | − | 7.40088i | −0.582507 | − | 0.365059i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.96281 | − | 1.71058i | −0.145790 | − | 0.0841721i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.26157 | + | 3.61512i | −0.307368 | + | 0.177459i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.19195 | − | 1.96647i | −0.450132 | − | 0.0962984i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.7184 | − | 8.99676i | −1.20757 | − | 0.439520i | −0.341711 | − | 0.939805i | \(-0.611006\pi\) |
−0.865861 | + | 0.500285i | \(0.833229\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.54271 | − | 8.74913i | 0.0751870 | − | 0.426407i | −0.923859 | − | 0.382733i | \(-0.874983\pi\) |
0.999046 | − | 0.0436734i | \(-0.0139061\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −24.1748 | + | 17.4669i | −1.17542 | + | 0.849269i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.87047 | + | 3.42089i | −0.139238 | + | 0.165938i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.48835 | + | 1.49673i | −0.410780 | + | 0.0724316i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.232190 | + | 1.66806i | 0.0112102 | + | 0.0805345i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.6692 | 1.71812 | 0.859062 | − | 0.511872i | \(-0.171048\pi\) | ||||
0.859062 | + | 0.511872i | \(0.171048\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.3661 | 0.978735 | 0.489367 | − | 0.872078i | \(-0.337228\pi\) | ||||
0.489367 | + | 0.872078i | \(0.337228\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.7600 | − | 7.20274i | −0.851528 | − | 0.345345i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.17506 | − | 0.912503i | 0.247557 | − | 0.0436510i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.4995 | − | 25.6222i | 1.02612 | − | 1.22288i | 0.0515759 | − | 0.998669i | \(-0.483576\pi\) |
0.974541 | − | 0.224209i | \(-0.0719800\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.5330 | + | 1.41761i | 0.930145 | + | 0.0675052i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.76559 | − | 15.6845i | 0.131397 | − | 0.745191i | −0.845904 | − | 0.533336i | \(-0.820938\pi\) |
0.977301 | − | 0.211855i | \(-0.0679506\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.4239 | − | 8.88956i | −1.15780 | − | 0.421405i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.05974 | + | 3.27623i | 0.0501240 | + | 0.154960i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.6096 | − | 12.4763i | 1.01982 | − | 0.588795i | 0.105770 | − | 0.994391i | \(-0.466269\pi\) |
0.914052 | + | 0.405596i | \(0.132936\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.03938 | − | 1.75479i | −0.143119 | − | 0.0826297i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.38936 | + | 2.32645i | −0.206230 | + | 0.109306i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.61207 | − | 2.19178i | 0.122456 | − | 0.102752i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.1920 | + | 5.89341i | −0.757431 | + | 0.275682i | −0.691729 | − | 0.722157i | \(-0.743151\pi\) |
−0.0657017 | + | 0.997839i | \(0.520929\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.1051 | + | 8.86819i | 0.565019 | + | 0.413932i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.09999 | + | 5.76968i | 0.0978065 | + | 0.268721i | 0.978941 | − | 0.204145i | \(-0.0654415\pi\) |
−0.881134 | + | 0.472866i | \(0.843219\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.43905 | + | 4.09850i | 0.159826 | + | 0.190474i | 0.840014 | − | 0.542564i | \(-0.182546\pi\) |
−0.680188 | + | 0.733038i | \(0.738102\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.7355 | − | 0.534011i | −0.683341 | − | 0.0247642i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.2724 | + | 28.1846i | −0.752995 | + | 1.30423i | 0.193370 | + | 0.981126i | \(0.438058\pi\) |
−0.946365 | + | 0.323100i | \(0.895275\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.72028 | + | 2.97960i | 0.0794349 | + | 0.137585i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.5629 | + | 14.0500i | 0.717098 | + | 0.647391i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.49492 | − | 4.10725i | 0.0687363 | − | 0.188852i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.40927 | − | 0.777474i | −0.202311 | − | 0.0356729i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.96657 | + | 0.747957i | 0.135830 | + | 0.0342466i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.7640 | − | 26.6531i | −1.45133 | − | 1.21781i | −0.931601 | − | 0.363483i | \(-0.881587\pi\) |
−0.519732 | − | 0.854330i | \(-0.673968\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.64439 | + | 9.32581i | 0.0749778 | + | 0.425220i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.32718 | + | 1.70333i | 0.0603887 | + | 0.0775042i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.19352i | 0.0996024i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 40.8059i | 1.84909i | 0.381072 | + | 0.924545i | \(0.375555\pi\) | ||||
−0.381072 | + | 0.924545i | \(0.624445\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.92906 | + | 5.04265i | 0.177678 | + | 0.228036i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.86890 | − | 27.6129i | −0.219730 | − | 1.24615i | −0.872507 | − | 0.488602i | \(-0.837507\pi\) |
0.652777 | − | 0.757550i | \(-0.273604\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.1718 | + | 11.0524i | 0.593227 | + | 0.497776i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.96795 | − | 0.496175i | −0.0884526 | − | 0.0223014i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.2278 | − | 1.97976i | −0.503634 | − | 0.0888043i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.37784 | − | 9.28054i | 0.151213 | − | 0.415454i | −0.840839 | − | 0.541286i | \(-0.817938\pi\) |
0.992052 | + | 0.125832i | \(0.0401600\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −26.6822 | − | 24.0885i | −1.19207 | − | 1.07619i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.4724 | − | 21.6029i | −0.556117 | − | 0.963224i | −0.997816 | − | 0.0660600i | \(-0.978957\pi\) |
0.441698 | − | 0.897164i | \(-0.354376\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.54442 | + | 11.3353i | −0.291223 | + | 0.504413i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.1526 | + | 0.367930i | 0.450894 | + | 0.0163403i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.22498 | − | 5.03513i | −0.187269 | − | 0.223178i | 0.664239 | − | 0.747520i | \(-0.268756\pi\) |
−0.851508 | + | 0.524342i | \(0.824311\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.21776 | + | 8.84072i | 0.142345 | + | 0.391091i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.63176 | + | 14.9563i | −0.0720440 | + | 0.660337i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.1283 | − | 5.87020i | 0.710696 | − | 0.258672i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.77232 | + | 2.32625i | −0.121927 | + | 0.102309i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.54532 | + | 5.05922i | −0.418993 | + | 0.222075i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.2065 | + | 9.93418i | 0.753831 | + | 0.435224i | 0.827076 | − | 0.562090i | \(-0.190002\pi\) |
−0.0732458 | + | 0.997314i | \(0.523336\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.5708 | − | 14.7633i | 1.11813 | − | 0.645554i | 0.177209 | − | 0.984173i | \(-0.443293\pi\) |
0.940923 | + | 0.338620i | \(0.109960\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.566225 | − | 1.75051i | −0.0247121 | − | 0.0763983i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.4313 | + | 4.52462i | 0.541515 | + | 0.197095i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.42194 | + | 19.4068i | −0.148780 | + | 0.843773i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.9021 | − | 1.08152i | −0.646694 | − | 0.0469338i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.5527 | − | 19.7268i | 0.716978 | − | 0.854461i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.4580 | − | 3.78363i | 0.927711 | − | 0.163580i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.7241 | + | 8.81043i | 0.937466 | + | 0.380198i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.37642 | 0.102360 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.0123 | −0.559444 | −0.279722 | − | 0.960081i | \(-0.590242\pi\) | ||||
−0.279722 | + | 0.960081i | \(0.590242\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.62032 | − | 11.6404i | −0.0695346 | − | 0.499538i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −23.4240 | + | 4.13028i | −1.00337 | + | 0.176922i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.8628 | + | 16.5211i | −0.592732 | + | 0.706391i | −0.976129 | − | 0.217193i | \(-0.930310\pi\) |
0.383396 | + | 0.923584i | \(0.374754\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −30.5121 | + | 22.0457i | −1.30222 | + | 0.940889i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.99358 | + | 16.9774i | −0.127531 | + | 0.723263i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.76324 | − | 1.73368i | −0.202553 | − | 0.0737234i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.1593 | − | 2.38735i | −0.473685 | − | 0.101337i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.8521 | − | 15.5031i | 1.13776 | − | 0.656886i | 0.191885 | − | 0.981417i | \(-0.438540\pi\) |
0.945875 | + | 0.324531i | \(0.105207\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.7743 | + | 16.0355i | 1.17473 | + | 0.678230i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.54291 | + | 0.966944i | 0.0651416 | + | 0.0408244i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.12175 | + | 6.81496i | −0.342291 | + | 0.287216i | −0.797686 | − | 0.603073i | \(-0.793943\pi\) |
0.455395 | + | 0.890290i | \(0.349498\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.8747 | − | 7.23382i | 0.836137 | − | 0.304329i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.74425 | + | 2.28569i | −0.241236 | + | 0.0959901i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.42133 | − | 9.40004i | −0.143430 | − | 0.394070i | 0.847088 | − | 0.531452i | \(-0.178353\pi\) |
−0.990518 | + | 0.137382i | \(0.956131\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.8465 | + | 22.4604i | 0.788702 | + | 0.939938i | 0.999291 | − | 0.0376364i | \(-0.0119829\pi\) |
−0.210590 | + | 0.977575i | \(0.567538\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.0426 | − | 24.0028i | 0.628414 | − | 1.00273i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.40322 | + | 2.43045i | −0.0585182 | + | 0.101357i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.08995 | − | 5.35195i | −0.128636 | − | 0.222805i | 0.794512 | − | 0.607248i | \(-0.207727\pi\) |
−0.923148 | + | 0.384444i | \(0.874393\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.86841 | + | 32.1053i | −0.285441 | + | 1.33425i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.914054 | + | 2.51134i | −0.0379213 | + | 0.104188i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.365597 | + | 0.0644646i | 0.0151415 | + | 0.00266985i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.09282 | − | 13.5882i | 0.251907 | − | 0.561804i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.4842 | + | 18.0274i | 0.886749 | + | 0.744071i | 0.967555 | − | 0.252659i | \(-0.0813050\pi\) |
−0.0808061 | + | 0.996730i | \(0.525749\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.30320 | + | 13.0621i | 0.0949015 | + | 0.538213i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 40.4185 | − | 5.62616i | 1.66259 | − | 0.231429i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.19379i | 0.131153i | 0.997848 | + | 0.0655767i | \(0.0208887\pi\) | ||||
−0.997848 | + | 0.0655767i | \(0.979111\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 3.68663i | − | 0.151137i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.16974 | − | 20.1444i | 0.334365 | − | 0.824454i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.65896 | − | 26.4223i | −0.190360 | − | 1.07958i | −0.918873 | − | 0.394553i | \(-0.870899\pi\) |
0.728513 | − | 0.685032i | \(-0.240212\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.5609 | + | 13.8962i | 0.675532 | + | 0.566839i | 0.914697 | − | 0.404140i | \(-0.132429\pi\) |
−0.239165 | + | 0.970979i | \(0.576874\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.4349 | + | 8.43519i | 0.506388 | + | 0.343507i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19.8894 | + | 3.50703i | 0.808617 | + | 0.142581i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.00813 | − | 16.5072i | 0.243862 | − | 0.670007i | −0.756018 | − | 0.654551i | \(-0.772858\pi\) |
0.999881 | − | 0.0154559i | \(-0.00491995\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.74013 | + | 2.18019i | −0.273124 | + | 0.0883457i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.2772 | − | 22.9968i | −0.537139 | − | 0.930353i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.8232 | − | 23.9424i | 0.558313 | − | 0.967026i | −0.439325 | − | 0.898328i | \(-0.644782\pi\) |
0.997638 | − | 0.0686979i | \(-0.0218844\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 14.5329 | + | 27.4195i | 0.586023 | + | 1.10566i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.7467 | + | 36.6425i | 1.23782 | + | 1.47517i | 0.825769 | + | 0.564008i | \(0.190741\pi\) |
0.412046 | + | 0.911163i | \(0.364814\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.6524 | + | 40.2571i | 0.588929 | + | 1.61807i | 0.772467 | + | 0.635055i | \(0.219023\pi\) |
−0.183538 | + | 0.983013i | \(0.558755\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.45966 | + | 4.16752i | 0.339474 | + | 0.167237i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.02779 | + | 3.28585i | −0.361691 | + | 0.131645i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.3966 | + | 9.56287i | −0.455863 | + | 0.382515i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.0661163 | + | 1.82441i | −0.00264043 | + | 0.0728599i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.86676 | + | 5.11923i | 0.353541 | + | 0.204117i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.97385 | + | 4.02635i | −0.277625 | + | 0.160287i | −0.632348 | − | 0.774685i | \(-0.717909\pi\) |
0.354723 | + | 0.934971i | \(0.384575\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23.0737 | − | 25.5582i | 0.917099 | − | 1.01585i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.8662 | − | 7.59469i | −0.828051 | − | 0.301386i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.02790 | + | 17.1721i | −0.119970 | + | 0.680383i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −47.8987 | + | 13.5983i | −1.89484 | + | 0.537939i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.9247 | − | 35.6629i | 1.18195 | − | 1.40860i | 0.289668 | − | 0.957127i | \(-0.406455\pi\) |
0.892286 | − | 0.451471i | \(-0.149101\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.30455 | + | 1.28799i | −0.288063 | + | 0.0507933i | −0.315813 | − | 0.948822i | \(-0.602277\pi\) |
0.0277494 | + | 0.999615i | \(0.491166\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −30.4867 | + | 23.7542i | −1.20041 | + | 0.935320i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.4394 | 0.528359 | 0.264180 | − | 0.964474i | \(-0.414899\pi\) | ||||
0.264180 | + | 0.964474i | \(0.414899\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.81301 | −0.0711669 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.29927 | + | 3.34985i | −0.168502 | + | 0.131291i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.6649 | − | 3.64379i | 0.808681 | − | 0.142592i | 0.246004 | − | 0.969269i | \(-0.420882\pi\) |
0.562678 | + | 0.826676i | \(0.309771\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.35823 | + | 1.61867i | −0.0530704 | + | 0.0632468i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.4810 | + | 28.6199i | 1.15016 | + | 1.11657i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.93840 | − | 39.3496i | 0.270282 | − | 1.53284i | −0.483279 | − | 0.875466i | \(-0.660554\pi\) |
0.753561 | − | 0.657378i | \(-0.228334\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.62964 | + | 3.14093i | 0.335654 | + | 0.122168i | 0.504348 | − | 0.863500i | \(-0.331733\pi\) |
−0.168694 | + | 0.985668i | \(0.553955\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.95304 | + | 9.91706i | −0.347707 | + | 0.385147i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.20104 | − | 1.84812i | 0.124131 | − | 0.0716670i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.35817 | + | 5.40294i | 0.362350 | + | 0.209203i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.566198 | − | 15.6237i | 0.0218905 | − | 0.604045i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.49907 | + | 2.93607i | −0.135080 | + | 0.113346i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.36707 | − | 3.40934i | 0.361074 | − | 0.131420i | −0.155112 | − | 0.987897i | \(-0.549574\pi\) |
0.516186 | + | 0.856477i | \(0.327351\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.55868 | − | 5.80190i | −0.213954 | − | 0.223315i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.1036 | − | 36.0019i | −0.503613 | − | 1.38366i | −0.887723 | − | 0.460377i | \(-0.847714\pi\) |
0.384111 | − | 0.923287i | \(-0.374508\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.521166 | + | 0.621101i | 0.0200005 | + | 0.0238357i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.8158 | − | 20.4065i | −0.414464 | − | 0.781977i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.9774 | + | 36.3339i | −0.802677 | + | 1.39028i | 0.115171 | + | 0.993346i | \(0.463258\pi\) |
−0.917848 | + | 0.396932i | \(0.870075\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.47669 | + | 12.9500i | 0.285669 | + | 0.494794i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.9813 | + | 4.84592i | −0.571574 | + | 0.184883i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.931645 | + | 2.55967i | −0.0354928 | + | 0.0975158i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.7535 | + | 3.83573i | 0.827542 | + | 0.145918i | 0.571349 | − | 0.820707i | \(-0.306420\pi\) |
0.256194 | + | 0.966625i | \(0.417531\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.675119 | + | 0.327078i | −0.0256456 | + | 0.0124247i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.72607 | + | 6.48295i | 0.293067 | + | 0.245912i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.83472 | − | 27.4191i | −0.183128 | − | 1.03857i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.63879 | + | 11.4380i | −0.175455 | + | 0.432625i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.1898i | 1.02695i | 0.858106 | + | 0.513473i | \(0.171641\pi\) | ||||
−0.858106 | + | 0.513473i | \(0.828359\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.2651i | 0.387157i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 31.6949 | − | 4.41185i | 1.19370 | − | 0.166160i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.840115 | + | 4.76453i | 0.0315958 | + | 0.179189i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.1540 | + | 28.6586i | 1.28268 | + | 1.07630i | 0.992869 | + | 0.119211i | \(0.0380366\pi\) |
0.289810 | + | 0.957084i | \(0.406408\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22.0223 | + | 2.25599i | −0.825902 | + | 0.0846063i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.18751 | + | 1.44368i | 0.306625 | + | 0.0540662i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.618029 | − | 1.69802i | 0.0231130 | − | 0.0635024i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.04232 | − | 14.2208i | 0.113618 | − | 0.531087i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.5033 | − | 37.2448i | −0.801937 | − | 1.38900i | −0.918340 | − | 0.395793i | \(-0.870470\pi\) |
0.116403 | − | 0.993202i | \(-0.462864\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.17204 | − | 5.49414i | 0.118133 | − | 0.204612i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.72544 | + | 12.3271i | −0.287312 | + | 0.458450i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.91806 | − | 7.05286i | −0.219791 | − | 0.261937i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.94324 | − | 27.3188i | −0.368775 | − | 1.01320i | −0.975828 | − | 0.218539i | \(-0.929871\pi\) |
0.607054 | − | 0.794661i | \(-0.292351\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.2246 | + | 19.9215i | −0.674984 | + | 0.737833i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 32.5835 | − | 11.8594i | 1.20515 | − | 0.438637i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.0928 | + | 10.1471i | −0.446658 | + | 0.374791i | −0.838194 | − | 0.545372i | \(-0.816388\pi\) |
0.391536 | + | 0.920163i | \(0.371944\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −17.8054 | − | 11.1587i | −0.656763 | − | 0.411595i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.57901 | + | 0.911643i | 0.0581637 | + | 0.0335808i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.2356 | − | 23.2300i | 1.48009 | − | 0.854531i | 0.480345 | − | 0.877080i | \(-0.340511\pi\) |
0.999746 | + | 0.0225487i | \(0.00717807\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.0990 | − | 2.80232i | −0.481203 | − | 0.102946i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −39.2909 | − | 14.3007i | −1.44144 | − | 0.524643i | −0.501257 | − | 0.865299i | \(-0.667129\pi\) |
−0.940188 | + | 0.340656i | \(0.889351\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.641552 | − | 3.63842i | 0.0235047 | − | 0.133302i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.18944 | + | 11.6109i | 0.0435192 | + | 0.424821i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.17694 | − | 6.16964i | 0.189161 | − | 0.225434i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.0407 | − | 5.47331i | 1.13269 | − | 0.199724i | 0.424284 | − | 0.905529i | \(-0.360526\pi\) |
0.708406 | + | 0.705805i | \(0.249415\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.47329 | − | 53.6884i | −0.272342 | − | 1.95651i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.33018 | 0.193985 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.5123 | 0.418421 | 0.209210 | − | 0.977871i | \(-0.432911\pi\) | ||||
0.209210 | + | 0.977871i | \(0.432911\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.06043 | + | 0.430067i | 0.0384911 | + | 0.0156104i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.5836 | + | 4.86373i | −0.999903 | + | 0.176310i | −0.649559 | − | 0.760311i | \(-0.725047\pi\) |
−0.350344 | + | 0.936621i | \(0.613935\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.65125 | + | 6.73489i | −0.204589 | + | 0.243820i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.01991 | − | 14.4897i | −0.253805 | − | 0.523877i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.31003 | − | 13.1009i | 0.0834105 | − | 0.473044i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.9996 | − | 9.46309i | −0.937571 | − | 0.341248i | −0.172365 | − | 0.985033i | \(-0.555141\pi\) |
−0.765206 | + | 0.643785i | \(0.777363\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.1760 | + | 34.5510i | 0.402494 | + | 1.24432i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.0220 | − | 21.3747i | 1.33159 | − | 0.768793i | 0.346045 | − | 0.938218i | \(-0.387524\pi\) |
0.985543 | + | 0.169425i | \(0.0541911\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.13454 | − | 3.54178i | −0.220359 | − | 0.127224i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.72700 | + | 1.97539i | −0.133705 | + | 0.0708666i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21.3838 | − | 17.9432i | 0.766156 | − | 0.642881i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.67747 | + | 2.06643i | −0.203156 | + | 0.0739427i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −22.3396 | + | 21.4031i | −0.798352 | + | 0.764885i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.69419 | − | 21.1396i | −0.274617 | − | 0.754505i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.9543 | − | 15.4383i | −0.461769 | − | 0.550315i | 0.484037 | − | 0.875048i | \(-0.339170\pi\) |
−0.945806 | + | 0.324733i | \(0.894726\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.6757 | − | 0.459364i | −0.451266 | − | 0.0163538i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.90889 | − | 6.77039i | 0.138984 | − | 0.240727i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.7578 | − | 29.0253i | −0.595086 | − | 1.03072i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.43655 | − | 2.19969i | −0.0864154 | − | 0.0780151i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.2695 | + | 47.4474i | −0.611716 | + | 1.68067i | 0.114684 | + | 0.993402i | \(0.463414\pi\) |
−0.726400 | + | 0.687273i | \(0.758808\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.2741 | − | 4.98548i | −1.00027 | − | 0.176374i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −29.2255 | + | 30.1048i | −1.03263 | + | 1.06370i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.81929 | + | 3.20477i | 0.134780 | + | 0.113094i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.402319 | − | 2.28166i | −0.0141799 | − | 0.0804180i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.5480 | − | 25.0884i | −0.688124 | − | 0.883154i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.20124i | 0.323498i | 0.986832 | + | 0.161749i | \(0.0517135\pi\) | ||||
−0.986832 | + | 0.161749i | \(0.948286\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 11.4571i | − | 0.402312i | −0.979559 | − | 0.201156i | \(-0.935530\pi\) | ||
0.979559 | − | 0.201156i | \(-0.0644697\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.15048 | − | 1.47655i | −0.0403489 | − | 0.0517847i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.19105 | − | 6.75478i | −0.0417206 | − | 0.236610i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.6316 | + | 22.3465i | 0.931721 | + | 0.781807i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.50328 | − | 5.29517i | −0.0525288 | − | 0.185028i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.64372 | + | 1.17147i | 0.231867 | + | 0.0408845i | 0.288374 | − | 0.957518i | \(-0.406885\pi\) |
−0.0565070 | + | 0.998402i | \(0.517996\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.31714 | − | 14.6087i | 0.185344 | − | 0.509228i | −0.811869 | − | 0.583840i | \(-0.801550\pi\) |
0.997213 | + | 0.0746118i | \(0.0237718\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.723696 | − | 0.653347i | −0.0251959 | − | 0.0227466i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.0772 | + | 31.3106i | 0.628606 | + | 1.08878i | 0.987832 | + | 0.155527i | \(0.0497075\pi\) |
−0.359226 | + | 0.933251i | \(0.616959\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.04448 | + | 12.2014i | −0.244665 | + | 0.423772i | −0.962037 | − | 0.272918i | \(-0.912011\pi\) |
0.717373 | + | 0.696690i | \(0.245345\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.0706 | + | 0.872315i | 0.835000 | + | 0.0302603i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.1182 | + | 14.4419i | 0.419871 | + | 0.500383i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.1915 | + | 36.2434i | 0.456512 | + | 1.25426i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.5190 | + | 21.3525i | −0.363589 | + | 0.738051i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.6165 | + | 5.68395i | −0.539142 | + | 0.196232i | −0.597216 | − | 0.802081i | \(-0.703726\pi\) |
0.0580737 | + | 0.998312i | \(0.481504\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.94101 | + | 4.14600i | −0.170380 | + | 0.142965i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.59147 | + | 4.55366i | −0.295906 | + | 0.156836i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.44004 | − | 5.45021i | −0.324747 | − | 0.187493i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.46498 | − | 3.73256i | 0.222139 | − | 0.128252i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.71940 | − | 26.9563i | −0.299249 | − | 0.925139i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.04631 | + | 2.20068i | 0.207265 | + | 0.0754382i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.76180 | + | 49.6906i | −0.299998 | + | 1.70138i | 0.346163 | + | 0.938174i | \(0.387484\pi\) |
−0.646161 | + | 0.763201i | \(0.723627\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.06206 | − | 13.3590i | 0.309916 | − | 0.456868i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.4251 | + | 30.3005i | −0.868506 | + | 1.03504i | 0.130543 | + | 0.991443i | \(0.458328\pi\) |
−0.999049 | + | 0.0436021i | \(0.986117\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.3052 | − | 3.22771i | 0.624567 | − | 0.110128i | 0.147597 | − | 0.989048i | \(-0.452846\pi\) |
0.476970 | + | 0.878920i | \(0.341735\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.6297 | + | 4.31099i | 0.362260 | + | 0.146918i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35.2494 | 1.19990 | 0.599952 | − | 0.800036i | \(-0.295187\pi\) | ||||
0.599952 | + | 0.800036i | \(0.295187\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.5913 | 0.394115 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.06798 | − | 14.8564i | −0.0702321 | − | 0.504550i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.64542 | + | 0.466459i | −0.0897398 | + | 0.0158235i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.59944 | + | 10.2484i | −0.291381 | + | 0.347254i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.23103 | + | 1.44876i | 0.109354 | + | 0.0490331i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.45116 | + | 8.22996i | −0.0490583 | + | 0.278223i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.9724 | − | 15.2767i | −1.41731 | − | 0.515858i | −0.484042 | − | 0.875045i | \(-0.660832\pi\) |
−0.933266 | + | 0.359187i | \(0.883054\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.3031 | + | 4.12959i | 0.651078 | + | 0.139288i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.33653 | − | 1.34900i | 0.0787198 | − | 0.0454489i | −0.460123 | − | 0.887855i | \(-0.652195\pi\) |
0.538843 | + | 0.842406i | \(0.318862\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.3880 | + | 10.0389i | 0.585151 | + | 0.337837i | 0.763178 | − | 0.646188i | \(-0.223638\pi\) |
−0.178027 | + | 0.984026i | \(0.556971\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.5840 | + | 8.51315i | 0.456622 | + | 0.286166i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.5348 | + | 14.7135i | −0.588762 | + | 0.494030i | −0.887811 | − | 0.460208i | \(-0.847775\pi\) |
0.299049 | + | 0.954238i | \(0.403331\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.71279 | + | 2.80723i | −0.258679 | + | 0.0941513i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.03064 | + | 2.57106i | −0.0680289 | + | 0.0861336i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.84507 | − | 27.0491i | −0.329453 | − | 0.905164i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.1680 | − | 19.2682i | −0.540436 | − | 0.644066i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.45881 | + | 7.11472i | −0.148875 | + | 0.237553i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.6372 | + | 23.6204i | −0.454828 | + | 0.787784i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.47254 | + | 2.55052i | 0.0490575 | + | 0.0849701i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.98855 | + | 13.9695i | −0.0994528 | + | 0.464876i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.31288 | + | 11.8495i | −0.143365 | + | 0.393892i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.29373 | + | 0.404447i | 0.0761621 | + | 0.0134294i | 0.211599 | − | 0.977356i | \(-0.432133\pi\) |
−0.135437 | + | 0.990786i | \(0.543244\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.3743 | + | 17.1265i | 0.410430 | + | 0.568050i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.41352 | − | 1.18609i | −0.0468320 | − | 0.0392968i | 0.619071 | − | 0.785335i | \(-0.287509\pi\) |
−0.665903 | + | 0.746038i | \(0.731954\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.245933 | + | 1.39476i | 0.00813920 | + | 0.0461597i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 40.0035 | − | 5.56839i | 1.32247 | − | 0.184085i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.781039i | 0.0257922i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.95591i | 0.262441i | 0.991353 | + | 0.131221i | \(0.0418896\pi\) | ||||
−0.991353 | + | 0.131221i | \(0.958110\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.66728 | − | 11.5083i | 0.153792 | − | 0.379210i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.69816 | − | 43.6585i | −0.253388 | − | 1.43704i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.19962 | − | 3.52390i | −0.138083 | − | 0.115865i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.00553 | − | 27.6339i | 0.0658702 | − | 0.907616i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.5766 | − | 5.92047i | −1.10161 | − | 0.194244i | −0.406859 | − | 0.913491i | \(-0.633376\pi\) |
−0.694755 | + | 0.719247i | \(0.744487\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.46477 | + | 17.7618i | −0.211874 | + | 0.582120i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −35.3269 | + | 11.4270i | −1.15655 | + | 0.374103i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.976848 | − | 1.69195i | −0.0319463 | − | 0.0553327i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.5356 | − | 44.2290i | 0.834213 | − | 1.44490i | −0.0604570 | − | 0.998171i | \(-0.519256\pi\) |
0.894670 | − | 0.446728i | \(-0.147411\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.91580 | + | 11.1614i | 0.193055 | + | 0.364240i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.1713 | − | 22.8475i | −0.624968 | − | 0.744808i | 0.356948 | − | 0.934124i | \(-0.383817\pi\) |
−0.981916 | + | 0.189317i | \(0.939373\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.98444 | − | 16.4421i | −0.194880 | − | 0.535429i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.59417 | + | 0.719436i | 0.214508 | + | 0.0234032i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.9500 | − | 14.5406i | 1.29820 | − | 0.472507i | 0.401791 | − | 0.915731i | \(-0.368388\pi\) |
0.896411 | + | 0.443225i | \(0.146166\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.0240 | + | 23.5150i | −0.909699 | + | 0.763328i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.45901 | − | 40.2597i | 0.0473115 | − | 1.30551i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.2227 | + | 11.6756i | 0.655078 | + | 0.378209i | 0.790399 | − | 0.612592i | \(-0.209873\pi\) |
−0.135321 | + | 0.990802i | \(0.543207\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −26.3214 | + | 15.1967i | −0.851741 | + | 0.491753i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.51564 | + | 2.78651i | −0.0813192 | + | 0.0900752i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.19389 | + | 1.89042i | 0.167719 | + | 0.0610448i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.73919 | − | 9.86344i | 0.0561029 | − | 0.318175i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.59920 | − | 34.1064i | 0.277105 | − | 1.09906i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.6434 | − | 26.9853i | 0.728916 | − | 0.868688i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.8501 | + | 5.96869i | −1.08855 | + | 0.191940i | −0.688992 | − | 0.724769i | \(-0.741947\pi\) |
−0.399555 | + | 0.916709i | \(0.630835\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.4244 | + | 8.90151i | −0.367005 | + | 0.285958i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −46.5628 | −1.49427 | −0.747136 | − | 0.664672i | \(-0.768571\pi\) | ||||
−0.747136 | + | 0.664672i | \(0.768571\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.72797 | 0.119513 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.64319 | − | 4.39699i | 0.180727 | − | 0.140816i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −53.9905 | + | 9.51998i | −1.72731 | + | 0.304571i | −0.947098 | − | 0.320944i | \(-0.896000\pi\) |
−0.780212 | + | 0.625516i | \(0.784889\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.27258 | + | 3.90011i | −0.104592 | + | 0.124648i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.38705 | + | 37.2312i | −0.299706 | + | 1.18870i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.28596 | − | 29.9782i | 0.168596 | − | 0.956156i | −0.776683 | − | 0.629892i | \(-0.783099\pi\) |
0.945279 | − | 0.326264i | \(-0.105790\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −41.1446 | − | 14.9754i | −1.31097 | − | 0.477156i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.92627 | − | 8.77973i | 0.252296 | − | 0.279462i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.8718 | − | 10.8956i | 0.600088 | − | 0.346461i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.9511 | + | 14.9829i | 0.824364 | + | 0.475946i | 0.851919 | − | 0.523674i | \(-0.175439\pi\) |
−0.0275554 | + | 0.999620i | \(0.508772\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.726501 | + | 20.0470i | −0.0230548 | + | 0.636173i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −17.8670 | + | 14.9922i | −0.566423 | + | 0.475286i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.0596 | − | 6.57315i | 0.571953 | − | 0.208174i | −0.0398208 | − | 0.999207i | \(-0.512679\pi\) |
0.611773 | + | 0.791033i | \(0.290456\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.8869 | + | 14.8607i | −0.344447 | + | 0.470172i |
(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 | 432.2.be.c.47.2 | yes | 36 | |
4.3 | odd | 2 | 432.2.be.b.47.5 | ✓ | 36 | ||
27.23 | odd | 18 | 432.2.be.b.239.5 | yes | 36 | ||
108.23 | even | 18 | inner | 432.2.be.c.239.2 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.be.b.47.5 | ✓ | 36 | 4.3 | odd | 2 | ||
432.2.be.b.239.5 | yes | 36 | 27.23 | odd | 18 | ||
432.2.be.c.47.2 | yes | 36 | 1.1 | even | 1 | trivial | |
432.2.be.c.239.2 | yes | 36 | 108.23 | even | 18 | inner |