Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(253,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.253");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.j (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 253.2 | ||
Root | \(0.500000 - 1.41036i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.253 |
Dual form | 756.2.j.b.505.2 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.119562 | − | 0.207087i | 0.0534696 | − | 0.0926120i | −0.838052 | − | 0.545591i | \(-0.816305\pi\) |
0.891521 | + | 0.452979i | \(0.149639\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.56238 | − | 4.43818i | −0.772587 | − | 1.33816i | −0.936141 | − | 0.351626i | \(-0.885629\pi\) |
0.163554 | − | 0.986534i | \(-0.447704\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.44282 | − | 4.23109i | 0.677516 | − | 1.17349i | −0.298210 | − | 0.954500i | \(-0.596390\pi\) |
0.975727 | − | 0.218993i | \(-0.0702770\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.70370 | −0.898278 | −0.449139 | − | 0.893462i | \(-0.648269\pi\) | ||||
−0.449139 | + | 0.893462i | \(0.648269\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.66019 | 0.839705 | 0.419853 | − | 0.907592i | \(-0.362082\pi\) | ||||
0.419853 | + | 0.907592i | \(0.362082\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.71053 | − | 6.42683i | 0.773700 | − | 1.34009i | −0.161823 | − | 0.986820i | \(-0.551737\pi\) |
0.935522 | − | 0.353267i | \(-0.114929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.47141 | + | 4.28061i | 0.494282 | + | 0.856122i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.73229 | + | 3.00041i | 0.321678 | + | 0.557162i | 0.980834 | − | 0.194844i | \(-0.0624200\pi\) |
−0.659157 | + | 0.752006i | \(0.729087\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.358685 | − | 0.621261i | 0.0644217 | − | 0.111582i | −0.832016 | − | 0.554752i | \(-0.812813\pi\) |
0.896437 | + | 0.443171i | \(0.146146\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.239123 | 0.0404192 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.60301 | 0.756730 | 0.378365 | − | 0.925656i | \(-0.376486\pi\) | ||||
0.378365 | + | 0.925656i | \(0.376486\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.80150 | − | 4.85235i | 0.437522 | − | 0.757810i | −0.559976 | − | 0.828509i | \(-0.689190\pi\) |
0.997498 | + | 0.0706992i | \(0.0225230\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.24433 | − | 10.8155i | −0.952251 | − | 1.64935i | −0.740538 | − | 0.672015i | \(-0.765429\pi\) |
−0.211713 | − | 0.977332i | \(-0.567904\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.16991 | + | 3.75839i | 0.316513 | + | 0.548217i | 0.979758 | − | 0.200186i | \(-0.0641545\pi\) |
−0.663245 | + | 0.748403i | \(0.730821\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.942820 | 0.129506 | 0.0647531 | − | 0.997901i | \(-0.479374\pi\) | ||||
0.0647531 | + | 0.997901i | \(0.479374\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.22545 | −0.165240 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.78947 | − | 6.56355i | 0.493347 | − | 0.854501i | −0.506624 | − | 0.862167i | \(-0.669107\pi\) |
0.999971 | + | 0.00766579i | \(0.00244012\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.75404 | − | 4.77014i | −0.352619 | − | 0.610754i | 0.634089 | − | 0.773260i | \(-0.281375\pi\) |
−0.986707 | + | 0.162507i | \(0.948042\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.584135 | − | 1.01175i | −0.0724530 | − | 0.125492i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.330095 | − | 0.571741i | 0.0403275 | − | 0.0698493i | −0.845157 | − | 0.534518i | \(-0.820493\pi\) |
0.885485 | + | 0.464669i | \(0.153827\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.7414 | −1.63081 | −0.815405 | − | 0.578891i | \(-0.803486\pi\) | ||||
−0.815405 | + | 0.578891i | \(0.803486\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.66019 | −0.428393 | −0.214196 | − | 0.976791i | \(-0.568713\pi\) | ||||
−0.214196 | + | 0.976791i | \(0.568713\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.56238 | − | 4.43818i | 0.292010 | − | 0.505777i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.11273 | + | 5.39140i | 0.350209 | + | 0.606580i | 0.986286 | − | 0.165046i | \(-0.0527772\pi\) |
−0.636077 | + | 0.771626i | \(0.719444\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.85185 | + | 8.40365i | 0.532560 | + | 0.922420i | 0.999277 | + | 0.0380138i | \(0.0121031\pi\) |
−0.466718 | + | 0.884406i | \(0.654564\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.442820 | + | 0.766987i | −0.0480306 | + | 0.0831914i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.48865 | 0.793795 | 0.396898 | − | 0.917863i | \(-0.370087\pi\) | ||||
0.396898 | + | 0.917863i | \(0.370087\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.88564 | 0.512154 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.437618 | − | 0.757977i | 0.0448987 | − | 0.0777668i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.57442 | + | 14.8513i | 0.870600 | + | 1.50792i | 0.861377 | + | 0.507967i | \(0.169603\pi\) |
0.00922376 | + | 0.999957i | \(0.497064\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.59097 | + | 6.21975i | 0.357315 | + | 0.618888i | 0.987511 | − | 0.157548i | \(-0.0503589\pi\) |
−0.630196 | + | 0.776436i | \(0.717026\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.41423 | − | 11.1098i | 0.632013 | − | 1.09468i | −0.355127 | − | 0.934818i | \(-0.615562\pi\) |
0.987140 | − | 0.159860i | \(-0.0511044\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.56526 | −0.731361 | −0.365681 | − | 0.930740i | \(-0.619164\pi\) | ||||
−0.365681 | + | 0.930740i | \(0.619164\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.98057 | −0.668617 | −0.334309 | − | 0.942464i | \(-0.608503\pi\) | ||||
−0.334309 | + | 0.942464i | \(0.608503\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.78495 | + | 16.9480i | −0.920491 | + | 1.59434i | −0.121834 | + | 0.992550i | \(0.538878\pi\) |
−0.798657 | + | 0.601787i | \(0.794456\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.887275 | − | 1.53681i | −0.0827388 | − | 0.143308i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.85185 | − | 3.20750i | −0.169759 | − | 0.294031i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.63160 | + | 13.2183i | −0.693782 | + | 1.20167i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.37756 | 0.212655 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.8090 | −1.49156 | −0.745780 | − | 0.666192i | \(-0.767923\pi\) | ||||
−0.745780 | + | 0.666192i | \(0.767923\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.44966 | − | 4.24293i | 0.214027 | − | 0.370706i | −0.738944 | − | 0.673767i | \(-0.764675\pi\) |
0.952971 | + | 0.303061i | \(0.0980085\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.83009 | + | 3.16982i | 0.158689 | + | 0.274858i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.72257 | + | 4.71563i | 0.232605 | + | 0.402884i | 0.958574 | − | 0.284844i | \(-0.0919417\pi\) |
−0.725969 | + | 0.687727i | \(0.758608\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.83009 | + | 4.90187i | −0.240046 | + | 0.415771i | −0.960727 | − | 0.277495i | \(-0.910496\pi\) |
0.720681 | + | 0.693266i | \(0.243829\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −25.0377 | −2.09376 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.828460 | 0.0687999 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.14132 | − | 1.97682i | 0.0935002 | − | 0.161947i | −0.815481 | − | 0.578783i | \(-0.803528\pi\) |
0.908982 | + | 0.416836i | \(0.136861\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.63160 | − | 9.75422i | −0.458293 | − | 0.793787i | 0.540578 | − | 0.841294i | \(-0.318206\pi\) |
−0.998871 | + | 0.0475071i | \(0.984872\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.0857699 | − | 0.148558i | −0.00688921 | − | 0.0119325i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.77292 | + | 4.80283i | −0.221303 | + | 0.383308i | −0.955204 | − | 0.295949i | \(-0.904364\pi\) |
0.733901 | + | 0.679256i | \(0.237698\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.42107 | 0.584862 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.66019 | 0.521666 | 0.260833 | − | 0.965384i | \(-0.416003\pi\) | ||||
0.260833 | + | 0.965384i | \(0.416003\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.20370 | − | 3.81691i | 0.170527 | − | 0.295362i | −0.768077 | − | 0.640357i | \(-0.778786\pi\) |
0.938604 | + | 0.344996i | \(0.112120\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.43474 | − | 9.41325i | −0.418057 | − | 0.724096i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.6654 | + | 21.9371i | 0.962932 | + | 1.66785i | 0.715072 | + | 0.699051i | \(0.246394\pi\) |
0.247860 | + | 0.968796i | \(0.420273\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.47141 | + | 4.28061i | −0.186821 | + | 0.323584i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.54583 | −0.713489 | −0.356744 | − | 0.934202i | \(-0.616113\pi\) | ||||
−0.356744 | + | 0.934202i | \(0.616113\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.3743 | 0.919774 | 0.459887 | − | 0.887978i | \(-0.347890\pi\) | ||||
0.459887 | + | 0.887978i | \(0.347890\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.550343 | − | 0.953223i | 0.0404621 | − | 0.0700823i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.49028 | + | 16.4377i | 0.693998 | + | 1.20204i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.58414 | + | 11.4041i | 0.476411 | + | 0.825169i | 0.999635 | − | 0.0270270i | \(-0.00860400\pi\) |
−0.523223 | + | 0.852196i | \(0.675271\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.57442 | + | 9.65518i | −0.401256 | + | 0.694995i | −0.993878 | − | 0.110486i | \(-0.964759\pi\) |
0.592622 | + | 0.805481i | \(0.298093\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.144194 | 0.0102734 | 0.00513669 | − | 0.999987i | \(-0.498365\pi\) | ||||
0.00513669 | + | 0.999987i | \(0.498365\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.4692 | −1.38014 | −0.690068 | − | 0.723744i | \(-0.742419\pi\) | ||||
−0.690068 | + | 0.723744i | \(0.742419\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.73229 | + | 3.00041i | −0.121583 | + | 0.210587i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.669905 | − | 1.16031i | −0.0467882 | − | 0.0810395i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.37880 | − | 16.2446i | −0.648745 | − | 1.12366i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.61436 | − | 2.79615i | 0.111137 | − | 0.192495i | −0.805092 | − | 0.593150i | \(-0.797884\pi\) |
0.916229 | + | 0.400655i | \(0.131217\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.98633 | −0.203666 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.717370 | 0.0486982 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.04746 | + | 15.6707i | −0.608598 | + | 1.05412i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.3856 | − | 17.9885i | −0.695474 | − | 1.20460i | −0.970021 | − | 0.243022i | \(-0.921861\pi\) |
0.274547 | − | 0.961574i | \(-0.411472\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.9714 | + | 19.0030i | 0.728198 | + | 1.26128i | 0.957644 | + | 0.287955i | \(0.0929752\pi\) |
−0.229446 | + | 0.973321i | \(0.573691\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.3856 | + | 19.7205i | −0.752384 | + | 1.30317i | 0.194280 | + | 0.980946i | \(0.437763\pi\) |
−0.946664 | + | 0.322222i | \(0.895570\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.7817 | 1.68901 | 0.844507 | − | 0.535544i | \(-0.179894\pi\) | ||||
0.844507 | + | 0.535544i | \(0.179894\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.03775 | 0.0676953 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.6488 | + | 23.6405i | −0.882870 | + | 1.52918i | −0.0347345 | + | 0.999397i | \(0.511059\pi\) |
−0.848136 | + | 0.529779i | \(0.822275\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.01724 | − | 8.69011i | −0.323189 | − | 0.559779i | 0.657955 | − | 0.753057i | \(-0.271422\pi\) |
−0.981144 | + | 0.193277i | \(0.938088\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.119562 | + | 0.207087i | 0.00763851 | + | 0.0132303i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.94119 | − | 15.4866i | 0.568914 | − | 0.985388i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.3171 | 1.78736 | 0.893680 | − | 0.448705i | \(-0.148115\pi\) | ||||
0.893680 | + | 0.448705i | \(0.148115\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −38.0312 | −2.39100 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.4315 | − | 24.9960i | 0.900210 | − | 1.55921i | 0.0729899 | − | 0.997333i | \(-0.476746\pi\) |
0.827221 | − | 0.561877i | \(-0.189921\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.30150 | + | 3.98632i | 0.143009 | + | 0.247698i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.604645 | − | 1.04728i | −0.0372840 | − | 0.0645778i | 0.846781 | − | 0.531941i | \(-0.178537\pi\) |
−0.884065 | + | 0.467363i | \(0.845204\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.112725 | − | 0.195246i | 0.00692465 | − | 0.0119938i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.01367 | −0.549573 | −0.274787 | − | 0.961505i | \(-0.588607\pi\) | ||||
−0.274787 | + | 0.961505i | \(0.588607\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.6030 | 1.06931 | 0.534653 | − | 0.845071i | \(-0.320442\pi\) | ||||
0.534653 | + | 0.845071i | \(0.320442\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.6654 | − | 21.9371i | 0.763752 | − | 1.32286i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.727085 | − | 1.25935i | −0.0436863 | − | 0.0756669i | 0.843355 | − | 0.537356i | \(-0.180577\pi\) |
−0.887042 | + | 0.461689i | \(0.847244\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.1482 | − | 17.5771i | −0.605388 | − | 1.04856i | −0.991990 | − | 0.126316i | \(-0.959685\pi\) |
0.386602 | − | 0.922247i | \(-0.373649\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.30150 | − | 3.98632i | 0.136810 | − | 0.236962i | −0.789477 | − | 0.613780i | \(-0.789648\pi\) |
0.926288 | + | 0.376817i | \(0.122982\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.60301 | 0.330735 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.28263 | −0.193096 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.53667 | + | 6.12569i | −0.206614 | + | 0.357867i | −0.950646 | − | 0.310278i | \(-0.899578\pi\) |
0.744031 | + | 0.668145i | \(0.232911\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.906150 | − | 1.56950i | −0.0527581 | − | 0.0913797i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.1283 | − | 31.3992i | −1.04839 | − | 1.81586i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.24433 | − | 10.8155i | 0.359917 | − | 0.623394i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.31711 | −0.0754175 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.7518 | 0.899006 | 0.449503 | − | 0.893279i | \(-0.351601\pi\) | ||||
0.449503 | + | 0.893279i | \(0.351601\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.81191 | + | 16.9947i | −0.556382 | + | 0.963682i | 0.441412 | + | 0.897304i | \(0.354478\pi\) |
−0.997795 | + | 0.0663780i | \(0.978856\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.7427 | + | 22.0710i | 0.720259 | + | 1.24753i | 0.960896 | + | 0.276911i | \(0.0893106\pi\) |
−0.240636 | + | 0.970615i | \(0.577356\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.14132 | + | 7.17297i | 0.232599 | + | 0.402874i | 0.958572 | − | 0.284849i | \(-0.0919436\pi\) |
−0.725973 | + | 0.687723i | \(0.758610\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.87756 | − | 15.3764i | 0.497048 | − | 0.860912i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.5562 | −0.754289 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24.1488 | 1.33954 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.16991 | + | 3.75839i | −0.119631 | + | 0.207207i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.99028 | + | 10.3755i | 0.329256 | + | 0.570288i | 0.982364 | − | 0.186976i | \(-0.0598688\pi\) |
−0.653109 | + | 0.757264i | \(0.726535\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.0789334 | − | 0.136717i | −0.00431259 | − | 0.00746963i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.46006 | − | 11.1892i | 0.351902 | − | 0.609512i | −0.634681 | − | 0.772774i | \(-0.718868\pi\) |
0.986583 | + | 0.163262i | \(0.0522017\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.67635 | −0.199086 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.09329 | − | 14.0180i | 0.434471 | − | 0.752526i | −0.562781 | − | 0.826606i | \(-0.690269\pi\) |
0.997252 | + | 0.0740802i | \(0.0236021\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.05718 | + | 15.6875i | 0.484820 | + | 0.839732i | 0.999848 | − | 0.0174409i | \(-0.00555188\pi\) |
−0.515028 | + | 0.857173i | \(0.672219\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.84897 | − | 10.1307i | −0.311309 | − | 0.539203i | 0.667337 | − | 0.744756i | \(-0.267434\pi\) |
−0.978646 | + | 0.205553i | \(0.934101\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.64295 | + | 2.84567i | −0.0871987 | + | 0.151033i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −35.7245 | −1.88547 | −0.942734 | − | 0.333547i | \(-0.891755\pi\) | ||||
−0.942734 | + | 0.333547i | \(0.891755\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.60301 | −0.294895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.437618 | + | 0.757977i | −0.0229060 | + | 0.0396743i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.52696 | − | 14.7691i | −0.445103 | − | 0.770942i | 0.552956 | − | 0.833210i | \(-0.313500\pi\) |
−0.998059 | + | 0.0622687i | \(0.980166\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.471410 | + | 0.816506i | 0.0244744 | + | 0.0423909i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.9617 | − | 22.4503i | 0.671131 | − | 1.16243i | −0.306453 | − | 0.951886i | \(-0.599142\pi\) |
0.977584 | − | 0.210547i | \(-0.0675246\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.9267 | 0.871767 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.8446 | 1.37892 | 0.689458 | − | 0.724326i | \(-0.257849\pi\) | ||||
0.689458 | + | 0.724326i | \(0.257849\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.4263 | − | 21.5229i | 0.634953 | − | 1.09977i | −0.351573 | − | 0.936161i | \(-0.614353\pi\) |
0.986525 | − | 0.163610i | \(-0.0523137\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.612725 | − | 1.06127i | −0.0312274 | − | 0.0540874i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.12640 | − | 15.8074i | −0.462727 | − | 0.801466i | 0.536369 | − | 0.843984i | \(-0.319796\pi\) |
−0.999096 | + | 0.0425174i | \(0.986462\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.7427 | + | 23.8030i | −0.694998 | + | 1.20377i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.48865 | 0.0749021 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.3743 | 0.621048 | 0.310524 | − | 0.950566i | \(-0.399496\pi\) | ||||
0.310524 | + | 0.950566i | \(0.399496\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.48113 | + | 9.49359i | −0.273714 | + | 0.474087i | −0.969810 | − | 0.243862i | \(-0.921586\pi\) |
0.696096 | + | 0.717949i | \(0.254919\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.75241 | − | 3.03526i | −0.0872935 | − | 0.151197i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.7947 | − | 20.4290i | −0.584640 | − | 1.01263i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.66019 | − | 11.5358i | 0.329325 | − | 0.570408i | −0.653053 | − | 0.757312i | \(-0.726512\pi\) |
0.982378 | + | 0.186904i | \(0.0598454\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.57893 | 0.372935 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.32038 | 0.113903 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.35705 | − | 4.08253i | 0.115149 | − | 0.199445i | −0.802690 | − | 0.596396i | \(-0.796599\pi\) |
0.917839 | + | 0.396952i | \(0.129932\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.65856 | − | 16.7291i | −0.470729 | − | 0.815327i | 0.528710 | − | 0.848802i | \(-0.322676\pi\) |
−0.999440 | + | 0.0334755i | \(0.989342\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.15335 | − | 15.8541i | −0.444003 | − | 0.769036i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.75404 | − | 4.77014i | 0.133277 | − | 0.230843i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.2794 | 1.45851 | 0.729253 | − | 0.684244i | \(-0.239868\pi\) | ||||
0.729253 | + | 0.684244i | \(0.239868\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.2060 | 1.64384 | 0.821918 | − | 0.569606i | \(-0.192904\pi\) | ||||
0.821918 | + | 0.569606i | \(0.192904\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.5813 | − | 23.5234i | 0.649680 | − | 1.12528i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.311220 | + | 0.539049i | 0.0148537 | + | 0.0257274i | 0.873357 | − | 0.487081i | \(-0.161938\pi\) |
−0.858503 | + | 0.512809i | \(0.828605\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.58934 | − | 4.48486i | −0.123023 | − | 0.213082i | 0.797935 | − | 0.602743i | \(-0.205926\pi\) |
−0.920958 | + | 0.389661i | \(0.872592\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.895355 | − | 1.55080i | 0.0424439 | − | 0.0735150i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.4977 | 0.495416 | 0.247708 | − | 0.968835i | \(-0.420323\pi\) | ||||
0.247708 | + | 0.968835i | \(0.420323\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.7141 | −1.35209 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.584135 | − | 1.01175i | 0.0273847 | − | 0.0474317i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.60464 | + | 2.77933i | 0.0750621 | + | 0.130011i | 0.901113 | − | 0.433584i | \(-0.142751\pi\) |
−0.826051 | + | 0.563595i | \(0.809418\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.1150 | − | 31.3762i | −0.843702 | − | 1.46133i | −0.886744 | − | 0.462261i | \(-0.847038\pi\) |
0.0430418 | − | 0.999073i | \(-0.486295\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.5253 | + | 25.1586i | −0.675049 | + | 1.16922i | 0.301406 | + | 0.953496i | \(0.402544\pi\) |
−0.976455 | + | 0.215723i | \(0.930789\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 37.4933 | 1.73498 | 0.867491 | − | 0.497452i | \(-0.165731\pi\) | ||||
0.867491 | + | 0.497452i | \(0.165731\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.660190 | 0.0304847 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −32.0007 | + | 55.4268i | −1.47139 | + | 2.54853i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.04583 | + | 15.6678i | 0.415051 | + | 0.718890i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.9549 | + | 25.9026i | 0.683305 | + | 1.18352i | 0.973966 | + | 0.226693i | \(0.0727914\pi\) |
−0.290661 | + | 0.956826i | \(0.593875\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.2443 | − | 19.4757i | 0.512697 | − | 0.888017i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.10069 | 0.186203 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.2632 | 0.963528 | 0.481764 | − | 0.876301i | \(-0.339996\pi\) | ||||
0.481764 | + | 0.876301i | \(0.339996\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.6985 | + | 18.5303i | −0.482816 | + | 0.836262i | −0.999805 | − | 0.0197296i | \(-0.993719\pi\) |
0.516989 | + | 0.855992i | \(0.327053\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.41586 | − | 11.1126i | −0.288956 | − | 0.500487i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.87072 | − | 11.9004i | −0.308194 | − | 0.533808i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.28263 | + | 12.6139i | −0.326015 | + | 0.564675i | −0.981717 | − | 0.190345i | \(-0.939039\pi\) |
0.655702 | + | 0.755020i | \(0.272373\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.92339 | −0.130348 | −0.0651738 | − | 0.997874i | \(-0.520760\pi\) | ||||
−0.0651738 | + | 0.997874i | \(0.520760\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.71737 | 0.0764220 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.62025 | + | 16.6628i | −0.426410 | + | 0.738564i | −0.996551 | − | 0.0829830i | \(-0.973555\pi\) |
0.570141 | + | 0.821547i | \(0.306889\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.83009 | − | 3.16982i | −0.0809586 | − | 0.140224i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.53379 | − | 2.65661i | −0.0675869 | − | 0.117064i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.1202 | − | 19.2608i | 0.489068 | − | 0.847091i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.7486 | −1.21569 | −0.607844 | − | 0.794057i | \(-0.707965\pi\) | ||||
−0.607844 | + | 0.794057i | \(0.707965\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.73680 | −0.119672 | −0.0598360 | − | 0.998208i | \(-0.519058\pi\) | ||||
−0.0598360 | + | 0.998208i | \(0.519058\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.32846 | + | 2.30096i | −0.0578686 | + | 0.100231i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.0361 | − | 27.7754i | −0.697222 | − | 1.20762i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.6871 | − | 23.7068i | −0.592856 | − | 1.02686i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.904515 | + | 1.56667i | −0.0391056 | + | 0.0677329i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.12476 | 0.220739 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.9773 | −0.514944 | −0.257472 | − | 0.966286i | \(-0.582890\pi\) | ||||
−0.257472 | + | 0.966286i | \(0.582890\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.834608 | + | 1.44558i | −0.0357507 | + | 0.0619220i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.7346 | + | 18.5929i | 0.458979 | + | 0.794975i | 0.998907 | − | 0.0467363i | \(-0.0148821\pi\) |
−0.539928 | + | 0.841711i | \(0.681549\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.34050 | + | 10.9821i | 0.270114 | + | 0.467852i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.11273 | + | 5.39140i | −0.132367 | + | 0.229266i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.8493 | 1.34950 | 0.674748 | − | 0.738048i | \(-0.264252\pi\) | ||||
0.674748 | + | 0.738048i | \(0.264252\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −61.0150 | −2.58066 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.7742 | − | 30.7857i | 0.749091 | − | 1.29746i | −0.199167 | − | 0.979966i | \(-0.563824\pi\) |
0.948259 | − | 0.317499i | \(-0.102843\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.33981 | + | 4.05267i | 0.0984366 | + | 0.170497i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.8743 | + | 18.8348i | 0.455874 | + | 0.789597i | 0.998738 | − | 0.0502237i | \(-0.0159934\pi\) |
−0.542864 | + | 0.839821i | \(0.682660\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.79987 | − | 8.31362i | 0.200868 | − | 0.347914i | −0.747940 | − | 0.663766i | \(-0.768957\pi\) |
0.948808 | + | 0.315852i | \(0.102290\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.6810 | 1.52970 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.0183 | 0.541960 | 0.270980 | − | 0.962585i | \(-0.412652\pi\) | ||||
0.270980 | + | 0.962585i | \(0.412652\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.85185 | + | 8.40365i | −0.201289 | + | 0.348642i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.41586 | − | 4.18440i | −0.100055 | − | 0.173300i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.64364 | + | 14.9712i | 0.356761 | + | 0.617928i | 0.987418 | − | 0.158134i | \(-0.0505477\pi\) |
−0.630657 | + | 0.776062i | \(0.717214\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.31285 | − | 2.27393i | 0.0540952 | − | 0.0936957i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.4153 | −0.509836 | −0.254918 | − | 0.966963i | \(-0.582048\pi\) | ||||
−0.254918 | + | 0.966963i | \(0.582048\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.885640 | −0.0363077 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.94282 | + | 6.82916i | −0.161099 | + | 0.279032i | −0.935263 | − | 0.353953i | \(-0.884837\pi\) |
0.774164 | + | 0.632985i | \(0.218171\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.1413 | − | 19.2973i | −0.454464 | − | 0.787154i | 0.544193 | − | 0.838960i | \(-0.316836\pi\) |
−0.998657 | + | 0.0518055i | \(0.983502\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.82489 | + | 3.16081i | 0.0741925 | + | 0.128505i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.0458 | + | 19.1319i | −0.448336 | + | 0.776541i | −0.998278 | − | 0.0586617i | \(-0.981317\pi\) |
0.549942 | + | 0.835203i | \(0.314650\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.2028 | 0.857771 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.5264 | −1.19256 | −0.596280 | − | 0.802777i | \(-0.703355\pi\) | ||||
−0.596280 | + | 0.802777i | \(0.703355\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.01655 | + | 8.68892i | −0.201959 | + | 0.349803i | −0.949159 | − | 0.314796i | \(-0.898064\pi\) |
0.747201 | + | 0.664598i | \(0.231397\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.1283 | + | 33.1312i | 0.768833 | + | 1.33166i | 0.938196 | + | 0.346103i | \(0.112495\pi\) |
−0.169364 | + | 0.985554i | \(0.554171\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.74433 | + | 6.48536i | 0.150013 | + | 0.259831i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.0728 | + | 20.9107i | −0.482911 | + | 0.836427i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.0482 | −0.679754 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.0377 | −0.917118 | −0.458559 | − | 0.888664i | \(-0.651634\pi\) | ||||
−0.458559 | + | 0.888664i | \(0.651634\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.00972 | + | 3.48093i | −0.0797531 | + | 0.138136i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.44282 | + | 4.23109i | 0.0967881 | + | 0.167642i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.68646 | − | 15.0454i | −0.343094 | − | 0.594257i | 0.641911 | − | 0.766779i | \(-0.278142\pi\) |
−0.985006 | + | 0.172522i | \(0.944808\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.47949 | − | 16.4190i | 0.373835 | − | 0.647501i | −0.616317 | − | 0.787498i | \(-0.711376\pi\) |
0.990152 | + | 0.139997i | \(0.0447094\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.0194 | −0.747731 | −0.373865 | − | 0.927483i | \(-0.621968\pi\) | ||||
−0.373865 | + | 0.927483i | \(0.621968\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −38.8402 | −1.52461 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.59329 | + | 6.22377i | −0.140616 | + | 0.243555i | −0.927729 | − | 0.373255i | \(-0.878242\pi\) |
0.787112 | + | 0.616810i | \(0.211575\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.585770 | − | 1.01458i | −0.0228879 | − | 0.0396430i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.7261 | + | 22.0423i | 0.495740 | + | 0.858647i | 0.999988 | − | 0.00491209i | \(-0.00156357\pi\) |
−0.504248 | + | 0.863559i | \(0.668230\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.14295 | + | 7.17580i | −0.161142 | + | 0.279106i | −0.935279 | − | 0.353912i | \(-0.884851\pi\) |
0.774136 | + | 0.633019i | \(0.218184\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.875237 | 0.0339402 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.7108 | 0.995527 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.1138 | + | 24.4458i | −0.544857 | + | 0.943721i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.91586 | + | 10.2466i | 0.228040 | + | 0.394977i | 0.957227 | − | 0.289338i | \(-0.0934350\pi\) |
−0.729187 | + | 0.684314i | \(0.760102\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.80314 | + | 11.7834i | 0.261466 | + | 0.452872i | 0.966632 | − | 0.256170i | \(-0.0824608\pi\) |
−0.705166 | + | 0.709042i | \(0.749127\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.57442 | + | 14.8513i | −0.329056 | + | 0.569942i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.58142 | −0.137039 | −0.0685196 | − | 0.997650i | \(-0.521828\pi\) | ||||
−0.0685196 | + | 0.997650i | \(0.521828\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.30206 | 0.0497492 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.30314 | − | 3.98916i | 0.0877426 | − | 0.151975i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.85868 | − | 10.1475i | −0.222875 | − | 0.386031i | 0.732805 | − | 0.680439i | \(-0.238211\pi\) |
−0.955680 | + | 0.294408i | \(0.904877\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.676742 | + | 1.17215i | 0.0256703 | + | 0.0444622i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.3759 | + | 17.9716i | −0.393016 | + | 0.680724i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.5926 | 0.400077 | 0.200039 | − | 0.979788i | \(-0.435893\pi\) | ||||
0.200039 | + | 0.979788i | \(0.435893\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.8479 | 0.635430 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.59097 | + | 6.21975i | −0.135052 | + | 0.233918i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.1488 | − | 33.1668i | −0.719150 | − | 1.24560i | −0.961337 | − | 0.275374i | \(-0.911198\pi\) |
0.242187 | − | 0.970230i | \(-0.422135\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.66182 | − | 4.61042i | −0.0996861 | − | 0.172661i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.99355 | + | 5.18499i | −0.111953 | + | 0.193908i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −41.6752 | −1.55422 | −0.777112 | − | 0.629362i | \(-0.783316\pi\) | ||||
−0.777112 | + | 0.629362i | \(0.783316\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.8285 | 0.477757 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.56238 | + | 14.8305i | −0.317999 | + | 0.550790i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.4126 | + | 28.4274i | 0.608709 | + | 1.05432i | 0.991453 | + | 0.130461i | \(0.0416458\pi\) |
−0.382744 | + | 0.923854i | \(0.625021\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.1271 | + | 40.0573i | 0.855386 | + | 1.48157i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.64884 | + | 8.05203i | −0.171709 | + | 0.297408i | −0.939017 | − | 0.343870i | \(-0.888262\pi\) |
0.767309 | + | 0.641278i | \(0.221595\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.38332 | −0.124626 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.3776 | 0.418530 | 0.209265 | − | 0.977859i | \(-0.432893\pi\) | ||||
0.209265 | + | 0.977859i | \(0.432893\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.16182 | + | 2.01234i | −0.0426232 | + | 0.0738256i | −0.886550 | − | 0.462633i | \(-0.846905\pi\) |
0.843927 | + | 0.536458i | \(0.180238\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.272915 | − | 0.472703i | −0.00999883 | − | 0.0173185i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.78263 | − | 6.55171i | −0.138214 | − | 0.239394i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.56690 | − | 9.64215i | 0.203139 | − | 0.351847i | −0.746399 | − | 0.665498i | \(-0.768219\pi\) |
0.949538 | + | 0.313652i | \(0.101552\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.69329 | −0.0980190 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 52.1639 | 1.89593 | 0.947964 | − | 0.318376i | \(-0.103138\pi\) | ||||
0.947964 | + | 0.318376i | \(0.103138\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.5127 | + | 40.7252i | −0.852336 | + | 1.47629i | 0.0267592 | + | 0.999642i | \(0.491481\pi\) |
−0.879095 | + | 0.476647i | \(0.841852\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.49028 | − | 6.04535i | −0.126357 | − | 0.218856i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.5140 | − | 32.0671i | −0.668501 | − | 1.15788i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.30314 | − | 5.72121i | 0.119114 | − | 0.206312i | −0.800303 | − | 0.599596i | \(-0.795328\pi\) |
0.919417 | + | 0.393284i | \(0.128661\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.0870 | −0.686512 | −0.343256 | − | 0.939242i | \(-0.611530\pi\) | ||||
−0.343256 | + | 0.939242i | \(0.611530\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.54583 | 0.127370 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.2540 | − | 17.7605i | 0.367389 | − | 0.636337i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.2108 | + | 60.9869i | 1.25994 | + | 2.18228i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.663069 | + | 1.14847i | 0.0236659 | + | 0.0409906i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.4503 | + | 44.0813i | −0.907207 | + | 1.57133i | −0.0892796 | + | 0.996007i | \(0.528456\pi\) |
−0.817927 | + | 0.575322i | \(0.804877\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.5699 | −0.695826 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26.9105 | −0.955620 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.38727 | − | 7.59898i | 0.155405 | − | 0.269170i | −0.777801 | − | 0.628510i | \(-0.783665\pi\) |
0.933207 | + | 0.359341i | \(0.116998\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.03667 | − | 13.9199i | −0.284317 | − | 0.492451i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.37880 | + | 16.2446i | 0.330971 | + | 0.573258i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.887275 | − | 1.53681i | 0.0312723 | − | 0.0541653i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.51384 | 0.334489 | 0.167244 | − | 0.985915i | \(-0.446513\pi\) | ||||
0.167244 | + | 0.985915i | \(0.446513\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.0118 | −0.878282 | −0.439141 | − | 0.898418i | \(-0.644717\pi\) | ||||
−0.439141 | + | 0.898418i | \(0.644717\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.796303 | − | 1.37924i | 0.0278933 | − | 0.0483126i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.8554 | − | 39.5867i | −0.799610 | − | 1.38496i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.7970 | − | 30.8253i | −0.621119 | − | 1.07581i | −0.989278 | − | 0.146047i | \(-0.953345\pi\) |
0.368158 | − | 0.929763i | \(-0.379988\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.00000 | + | 13.8564i | −0.278862 | + | 0.483004i | −0.971102 | − | 0.238664i | \(-0.923291\pi\) |
0.692240 | + | 0.721668i | \(0.256624\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.4531 | 0.885090 | 0.442545 | − | 0.896746i | \(-0.354076\pi\) | ||||
0.442545 | + | 0.896746i | \(0.354076\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.5458 | −0.609392 | −0.304696 | − | 0.952450i | \(-0.598555\pi\) | ||||
−0.304696 | + | 0.952450i | \(0.598555\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.85185 | − | 3.20750i | 0.0641627 | − | 0.111133i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.526955 | − | 0.912713i | −0.0182360 | − | 0.0315857i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.0562 | + | 20.8820i | 0.416227 | + | 0.720927i | 0.995556 | − | 0.0941668i | \(-0.0300187\pi\) |
−0.579329 | + | 0.815094i | \(0.696685\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.49837 | − | 14.7196i | 0.293047 | − | 0.507572i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.59915 | −0.0894133 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.2632 | −0.524450 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.0796 | − | 29.5828i | 0.585482 | − | 1.01408i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.2616 | − | 28.1659i | −0.556785 | − | 0.964381i | −0.997762 | − | 0.0668621i | \(-0.978701\pi\) |
0.440977 | − | 0.897518i | \(-0.354632\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.299870 | − | 0.519390i | −0.0102434 | − | 0.0177420i | 0.860858 | − | 0.508845i | \(-0.169927\pi\) |
−0.871102 | + | 0.491103i | \(0.836594\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.2174 | − | 22.8932i | 0.450971 | − | 0.781104i | −0.547476 | − | 0.836822i | \(-0.684411\pi\) |
0.998447 | + | 0.0557171i | \(0.0177445\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.8454 | −0.675545 | −0.337773 | − | 0.941228i | \(-0.609674\pi\) | ||||
−0.337773 | + | 0.941228i | \(0.609674\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.05718 | 0.205950 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.9520 | − | 27.6296i | 0.541134 | − | 0.937271i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.61273 | − | 2.79332i | −0.0546451 | − | 0.0946481i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.18878 | + | 2.05903i | 0.0401881 | + | 0.0696078i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.2352 | + | 17.7278i | −0.345617 | + | 0.598626i | −0.985466 | − | 0.169875i | \(-0.945664\pi\) |
0.639849 | + | 0.768501i | \(0.278997\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.1683 | 1.05009 | 0.525043 | − | 0.851076i | \(-0.324049\pi\) | ||||
0.525043 | + | 0.851076i | \(0.324049\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.64187 | −0.0889060 | −0.0444530 | − | 0.999011i | \(-0.514154\pi\) | ||||
−0.0444530 | + | 0.999011i | \(0.514154\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.5825 | + | 20.0615i | −0.388902 | + | 0.673599i | −0.992302 | − | 0.123840i | \(-0.960479\pi\) |
0.603400 | + | 0.797439i | \(0.293812\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.40451 | − | 14.5570i | −0.281878 | − | 0.488228i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.94226 | + | 13.7564i | 0.265778 | + | 0.460341i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.14132 | + | 1.97682i | −0.0381500 | + | 0.0660777i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.48538 | 0.0828921 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.49192 | −0.116333 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.47949 | − | 2.56255i | 0.0491799 | − | 0.0851821i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.0264 | + | 43.3470i | 0.830988 | + | 1.43931i | 0.897256 | + | 0.441511i | \(0.145558\pi\) |
−0.0662676 | + | 0.997802i | \(0.521109\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.42231 | − | 9.39172i | −0.179649 | − | 0.311161i | 0.762111 | − | 0.647446i | \(-0.224163\pi\) |
−0.941760 | + | 0.336285i | \(0.890830\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.8646 | − | 43.0667i | 0.822897 | − | 1.42530i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.89931 | 0.161790 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.1910 | 0.369156 | 0.184578 | − | 0.982818i | \(-0.440908\pi\) | ||||
0.184578 | + | 0.982818i | \(0.440908\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.5679 | + | 58.1413i | −1.10490 | + | 1.91374i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.3759 | + | 19.7037i | 0.374038 | + | 0.647853i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.6478 | + | 35.7630i | 0.677431 | + | 1.17335i | 0.975752 | + | 0.218879i | \(0.0702401\pi\) |
−0.298321 | + | 0.954466i | \(0.596427\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.83009 | + | 3.16982i | −0.0599789 | + | 0.103887i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.53870 | 0.148431 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.5620 | −1.09642 | −0.548211 | − | 0.836340i | \(-0.684691\pi\) | ||||
−0.548211 | + | 0.836340i | \(0.684691\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.2112 | − | 43.6671i | 0.821862 | − | 1.42351i | −0.0824315 | − | 0.996597i | \(-0.526269\pi\) |
0.904294 | − | 0.426911i | \(-0.140398\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.7902 | − | 36.0096i | −0.677021 | − | 1.17263i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.1212 | + | 17.5304i | 0.328895 | + | 0.569662i | 0.982293 | − | 0.187352i | \(-0.0599905\pi\) |
−0.653398 | + | 0.757014i | \(0.726657\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.94119 | + | 15.4866i | −0.290243 | + | 0.502716i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.3685 | 0.951340 | 0.475670 | − | 0.879624i | \(-0.342206\pi\) | ||||
0.475670 | + | 0.879624i | \(0.342206\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.14884 | 0.101894 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.72257 | + | 4.71563i | −0.0879164 | + | 0.152276i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.2427 | + | 26.4011i | 0.491700 | + | 0.851649i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.33297 | + | 2.30878i | 0.0429099 | + | 0.0743222i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.2157 | − | 26.3544i | 0.489305 | − | 0.847501i | −0.510619 | − | 0.859807i | \(-0.670584\pi\) |
0.999924 | + | 0.0123057i | \(0.00391714\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.18659 | −0.230629 | −0.115314 | − | 0.993329i | \(-0.536788\pi\) | ||||
−0.115314 | + | 0.993329i | \(0.536788\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.66019 | −0.181457 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.2713 | − | 24.7186i | 0.456579 | − | 0.790818i | −0.542199 | − | 0.840250i | \(-0.682408\pi\) |
0.998777 | + | 0.0494328i | \(0.0157414\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.1888 | − | 33.2359i | −0.613276 | − | 1.06223i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.20821 | + | 3.82473i | 0.0704310 | + | 0.121990i | 0.899090 | − | 0.437763i | \(-0.144229\pi\) |
−0.828659 | + | 0.559753i | \(0.810896\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.0172400 | − | 0.0298606i | 0.000549313 | − | 0.000951438i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −92.6791 | −2.94702 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.81341 | −0.184669 | −0.0923345 | − | 0.995728i | \(-0.529433\pi\) | ||||
−0.0923345 | + | 0.995728i | \(0.529433\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.32777 | + | 4.03182i | −0.0737953 | + | 0.127817i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.3204 | + | 45.5882i | 0.833575 | + | 1.44379i | 0.895186 | + | 0.445694i | \(0.147043\pi\) |
−0.0616108 | + | 0.998100i | \(0.519624\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))