Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1156,2,Mod(733,1156)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1156, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([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("1156.733");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1156 = 2^{2} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1156.h (of order \(8\), degree \(4\), 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: | \(9.23070647366\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\Q(\zeta_{48})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 68) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 757.3 | ||
Root | \(0.991445 - 0.130526i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1156.757 |
Dual form | 1156.2.h.f.733.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1156\mathbb{Z}\right)^\times\).
\(n\) | \(579\) | \(581\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{8}\right)\) |
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 | ||||||||
\(3\) | 0.676327 | + | 0.280144i | 0.390477 | + | 0.161741i | 0.569280 | − | 0.822144i | \(-0.307222\pi\) |
−0.178802 | + | 0.983885i | \(0.557222\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.32565 | − | 3.20041i | 0.592851 | − | 1.43127i | −0.287887 | − | 0.957664i | \(-0.592953\pi\) |
0.880738 | − | 0.473604i | \(-0.157047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.280144 | + | 0.676327i | 0.105884 | + | 0.255627i | 0.967938 | − | 0.251190i | \(-0.0808219\pi\) |
−0.862053 | + | 0.506817i | \(0.830822\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.74238 | − | 1.74238i | −0.580794 | − | 0.580794i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.37184 | + | 1.81088i | −1.31816 | + | 0.546000i | −0.927255 | − | 0.374431i | \(-0.877838\pi\) |
−0.390906 | + | 0.920431i | \(0.627838\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.46410i | − | 0.406069i | −0.979172 | − | 0.203034i | \(-0.934920\pi\) | ||
0.979172 | − | 0.203034i | \(-0.0650803\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.79315 | − | 1.79315i | 0.462990 | − | 0.462990i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.86370 | − | 3.86370i | 0.886394 | − | 0.886394i | −0.107780 | − | 0.994175i | \(-0.534374\pi\) |
0.994175 | + | 0.107780i | \(0.0343743\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.535898i | 0.116943i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.37184 | − | 1.81088i | 0.911593 | − | 0.377594i | 0.122927 | − | 0.992416i | \(-0.460772\pi\) |
0.788666 | + | 0.614822i | \(0.210772\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.94975 | − | 4.94975i | −0.989949 | − | 0.989949i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.53073 | − | 3.69552i | −0.294590 | − | 0.711203i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.32565 | − | 3.20041i | 0.246168 | − | 0.594302i | −0.751704 | − | 0.659500i | \(-0.770768\pi\) |
0.997872 | + | 0.0651984i | \(0.0207680\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.72450 | − | 2.37116i | −1.02815 | − | 0.425874i | −0.196106 | − | 0.980583i | \(-0.562830\pi\) |
−0.832044 | + | 0.554709i | \(0.812830\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.46410 | −0.603023 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.53590 | 0.428645 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.5914 | − | 4.38712i | −1.74122 | − | 0.721238i | −0.998676 | − | 0.0514451i | \(-0.983617\pi\) |
−0.742548 | − | 0.669793i | \(-0.766383\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.410159 | − | 0.990211i | 0.0656780 | − | 0.158561i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.29610 | − | 5.54328i | −0.358591 | − | 0.865714i | −0.995499 | − | 0.0947747i | \(-0.969787\pi\) |
0.636908 | − | 0.770940i | \(-0.280213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.76268 | + | 8.76268i | 1.33630 | + | 1.33630i | 0.899617 | + | 0.436679i | \(0.143846\pi\) |
0.436679 | + | 0.899617i | \(0.356154\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.88614 | + | 3.26655i | −1.17560 | + | 0.486948i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.92820i | 1.01058i | 0.862949 | + | 0.505291i | \(0.168615\pi\) | ||||
−0.862949 | + | 0.505291i | \(0.831385\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.57081 | − | 4.57081i | 0.652973 | − | 0.652973i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.656339 | + | 0.656339i | −0.0901551 | + | 0.0901551i | −0.750746 | − | 0.660591i | \(-0.770306\pi\) |
0.660591 | + | 0.750746i | \(0.270306\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.3923i | 2.21034i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.69552 | − | 1.53073i | 0.489483 | − | 0.202751i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.69213 | − | 6.69213i | −0.871241 | − | 0.871241i | 0.121367 | − | 0.992608i | \(-0.461272\pi\) |
−0.992608 | + | 0.121367i | \(0.961272\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.85639 | + | 6.89593i | 0.365723 | + | 0.882933i | 0.994441 | + | 0.105300i | \(0.0335802\pi\) |
−0.628718 | + | 0.777634i | \(0.716420\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.690303 | − | 1.66654i | 0.0869700 | − | 0.209964i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.68573 | − | 1.94089i | −0.581193 | − | 0.240738i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.07180 | −0.130941 | −0.0654704 | − | 0.997855i | \(-0.520855\pi\) | ||||
−0.0654704 | + | 0.997855i | \(0.520855\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.46410 | 0.417029 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.02898 | − | 0.840431i | −0.240796 | − | 0.0997408i | 0.259022 | − | 0.965871i | \(-0.416600\pi\) |
−0.499818 | + | 0.866131i | \(0.666600\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.765367 | − | 1.84776i | 0.0895794 | − | 0.216264i | −0.872740 | − | 0.488185i | \(-0.837659\pi\) |
0.962319 | + | 0.271921i | \(0.0876591\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.96101 | − | 4.73429i | −0.226437 | − | 0.546668i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.44949 | − | 2.44949i | −0.279145 | − | 0.279145i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.66654 | + | 0.690303i | −0.187500 | + | 0.0776651i | −0.474458 | − | 0.880278i | \(-0.657356\pi\) |
0.286958 | + | 0.957943i | \(0.407356\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.46410i | 0.496011i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.69213 | − | 6.69213i | 0.734557 | − | 0.734557i | −0.236962 | − | 0.971519i | \(-0.576152\pi\) |
0.971519 | + | 0.236962i | \(0.0761517\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.79315 | − | 1.79315i | 0.192246 | − | 0.192246i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 9.46410i | − | 1.00319i | −0.865102 | − | 0.501596i | \(-0.832746\pi\) | ||
0.865102 | − | 0.501596i | \(-0.167254\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.990211 | − | 0.410159i | 0.103802 | − | 0.0429963i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.20736 | − | 3.20736i | −0.332588 | − | 0.332588i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.24351 | − | 17.4874i | −0.743168 | − | 1.79417i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.41668 | + | 8.24858i | −0.346911 | + | 0.837517i | 0.650070 | + | 0.759874i | \(0.274739\pi\) |
−0.996981 | + | 0.0776429i | \(0.975261\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.7727 | + | 4.46219i | 1.08269 | + | 0.448467i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.46410 | 0.941713 | 0.470857 | − | 0.882210i | \(-0.343945\pi\) | ||||
0.470857 | + | 0.882210i | \(0.343945\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.92820 | 0.288524 | 0.144262 | − | 0.989539i | \(-0.453919\pi\) | ||||
0.144262 | + | 0.989539i | \(0.453919\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.71510 | + | 0.710416i | 0.167376 | + | 0.0693295i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.78132 | − | 6.71471i | 0.268881 | − | 0.649135i | −0.730550 | − | 0.682859i | \(-0.760736\pi\) |
0.999431 | + | 0.0337232i | \(0.0107365\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.44623 | + | 5.90572i | 0.234306 | + | 0.565665i | 0.996675 | − | 0.0814773i | \(-0.0259638\pi\) |
−0.762369 | + | 0.647143i | \(0.775964\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.93426 | − | 5.93426i | −0.563255 | − | 0.563255i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.25837 | + | 3.00652i | −0.682810 | + | 0.282829i | −0.697001 | − | 0.717070i | \(-0.745483\pi\) |
0.0141908 | + | 0.999899i | \(0.495483\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 16.3923i | − | 1.52859i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.55103 | + | 2.55103i | −0.235842 | + | 0.235842i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.05558 | − | 8.05558i | 0.732325 | − | 0.732325i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 4.39230i | − | 0.396041i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.40083 | + | 2.65131i | −0.572507 | + | 0.237140i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.4195 | + | 14.4195i | 1.27953 | + | 1.27953i | 0.940932 | + | 0.338595i | \(0.109952\pi\) |
0.338595 | + | 0.940932i | \(0.390048\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.47163 | + | 8.38125i | 0.305660 | + | 0.737928i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.46219 | − | 10.7727i | 0.389863 | − | 0.941213i | −0.600105 | − | 0.799921i | \(-0.704875\pi\) |
0.989968 | − | 0.141291i | \(-0.0451254\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.69552 | + | 1.53073i | 0.320442 | + | 0.132731i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.8564 | −1.19257 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.46410 | 0.808573 | 0.404286 | − | 0.914632i | \(-0.367520\pi\) | ||||
0.404286 | + | 0.914632i | \(0.367520\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.4102 | + | 4.31206i | 0.882984 | + | 0.365744i | 0.777653 | − | 0.628693i | \(-0.216410\pi\) |
0.105331 | + | 0.994437i | \(0.466410\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.94089 | + | 4.68573i | −0.163453 | + | 0.394610i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.65131 | + | 6.40083i | 0.221714 | + | 0.535264i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.48528 | − | 8.48528i | −0.704664 | − | 0.704664i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.37184 | − | 1.81088i | 0.360584 | − | 0.149359i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.00000i | 0.491539i | 0.969328 | + | 0.245770i | \(0.0790407\pi\) | ||||
−0.969328 | + | 0.245770i | \(0.920959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.62158 | − | 4.62158i | 0.376099 | − | 0.376099i | −0.493594 | − | 0.869693i | \(-0.664317\pi\) |
0.869693 | + | 0.493594i | \(0.164317\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.1774 | + | 15.1774i | −1.21908 | + | 1.21908i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2.00000i | − | 0.159617i | −0.996810 | − | 0.0798087i | \(-0.974569\pi\) | ||
0.996810 | − | 0.0798087i | \(-0.0254309\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.627769 | + | 0.260030i | −0.0497853 | + | 0.0206217i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.44949 | + | 2.44949i | 0.193047 | + | 0.193047i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.05203 | + | 9.78246i | 0.317379 | + | 0.766221i | 0.999391 | + | 0.0348805i | \(0.0111051\pi\) |
−0.682012 | + | 0.731341i | \(0.738895\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.59220 | + | 11.0866i | −0.357502 | + | 0.863087i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.7727 | − | 4.46219i | −0.833614 | − | 0.345294i | −0.0752818 | − | 0.997162i | \(-0.523986\pi\) |
−0.758332 | + | 0.651868i | \(0.773986\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.8564 | 0.835108 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.4641 | −1.02963 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.88614 | + | 3.26655i | 0.599572 | + | 0.248351i | 0.661763 | − | 0.749713i | \(-0.269809\pi\) |
−0.0621905 | + | 0.998064i | \(0.519809\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.96101 | − | 4.73429i | 0.148238 | − | 0.357878i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.65131 | − | 6.40083i | −0.199285 | − | 0.481115i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.1774 | + | 15.1774i | 1.13441 | + | 1.13441i | 0.989435 | + | 0.144978i | \(0.0463112\pi\) |
0.144978 | + | 0.989435i | \(0.453689\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5914 | − | 4.38712i | 0.787256 | − | 0.326092i | 0.0474163 | − | 0.998875i | \(-0.484901\pi\) |
0.739840 | + | 0.672783i | \(0.234901\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.46410i | 0.403918i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −28.0812 | + | 28.0812i | −2.06457 | + | 2.06457i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.07055 | − | 2.07055i | 0.150611 | − | 0.150611i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 12.0000i | − | 0.868290i | −0.900843 | − | 0.434145i | \(-0.857051\pi\) | ||
0.900843 | − | 0.434145i | \(-0.142949\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.53349 | + | 2.70626i | −0.470291 | + | 0.194801i | −0.605226 | − | 0.796054i | \(-0.706917\pi\) |
0.134935 | + | 0.990854i | \(0.456917\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.62536 | − | 2.62536i | −0.188006 | − | 0.188006i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.32565 | + | 3.20041i | 0.0944490 | + | 0.228020i | 0.964042 | − | 0.265748i | \(-0.0856191\pi\) |
−0.869593 | + | 0.493768i | \(0.835619\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.37116 | − | 5.72450i | 0.168087 | − | 0.405799i | −0.817280 | − | 0.576240i | \(-0.804519\pi\) |
0.985368 | + | 0.170441i | \(0.0545193\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.724885 | − | 0.300257i | −0.0511294 | − | 0.0211785i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.53590 | 0.177985 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.7846 | −1.45166 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.7727 | − | 4.46219i | −0.748752 | − | 0.310143i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.89482 | + | 23.8882i | −0.684439 | + | 1.65238i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.52365 | + | 18.1637i | 0.517950 | + | 1.25044i | 0.939161 | + | 0.343478i | \(0.111605\pi\) |
−0.421211 | + | 0.906963i | \(0.638395\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.13681 | − | 1.13681i | −0.0778931 | − | 0.0778931i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 39.6605 | − | 16.4279i | 2.70482 | − | 1.12037i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 4.53590i | − | 0.307917i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.03528 | − | 1.03528i | 0.0699575 | − | 0.0699575i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.93426 | + | 5.93426i | −0.397387 | + | 0.397387i | −0.877310 | − | 0.479923i | \(-0.840664\pi\) |
0.479923 | + | 0.877310i | \(0.340664\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 17.2487i | 1.14991i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.05757 | − | 3.75177i | 0.601172 | − | 0.249014i | −0.0612766 | − | 0.998121i | \(-0.519517\pi\) |
0.662449 | + | 0.749107i | \(0.269517\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.277401 | − | 0.277401i | −0.0183312 | − | 0.0183312i | 0.697882 | − | 0.716213i | \(-0.254126\pi\) |
−0.716213 | + | 0.697882i | \(0.754126\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.970446 | − | 2.34286i | −0.0638507 | − | 0.154149i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.29610 | + | 5.54328i | −0.150423 | + | 0.363152i | −0.981072 | − | 0.193644i | \(-0.937969\pi\) |
0.830649 | + | 0.556796i | \(0.187969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.1731 | + | 9.18440i | 1.44641 | + | 0.599124i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.32051 | −0.0857762 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.7846 | −1.34444 | −0.672222 | − | 0.740349i | \(-0.734660\pi\) | ||||
−0.672222 | + | 0.740349i | \(0.734660\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.84776 | − | 0.765367i | −0.119025 | − | 0.0493016i | 0.322376 | − | 0.946612i | \(-0.395518\pi\) |
−0.441401 | + | 0.897310i | \(0.645518\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.84279 | + | 14.1057i | −0.374815 | + | 0.904884i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.56916 | − | 20.6878i | −0.547464 | − | 1.32169i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.65685 | − | 5.65685i | −0.359937 | − | 0.359937i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.40083 | − | 2.65131i | 0.405636 | − | 0.168020i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 6.92820i | − | 0.437304i | −0.975803 | − | 0.218652i | \(-0.929834\pi\) | ||
0.975803 | − | 0.218652i | \(-0.0701660\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.8338 | + | 15.8338i | −0.995459 | + | 0.995459i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.37945 | + | 5.37945i | −0.335561 | + | 0.335561i | −0.854694 | − | 0.519133i | \(-0.826255\pi\) |
0.519133 | + | 0.854694i | \(0.326255\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 8.39230i | − | 0.521472i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.88614 | + | 3.26655i | −0.488140 | + | 0.202194i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.4901 | + | 16.4901i | 1.01682 | + | 1.01682i | 0.999856 | + | 0.0169664i | \(0.00540084\pi\) |
0.0169664 | + | 0.999856i | \(0.494599\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.23048 | + | 2.97063i | 0.0755876 | + | 0.182485i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.65131 | − | 6.40083i | 0.162257 | − | 0.391724i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.9727 | − | 7.85875i | −1.15679 | − | 0.479156i | −0.279982 | − | 0.960005i | \(-0.590329\pi\) |
−0.876803 | + | 0.480849i | \(0.840329\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.9282 | −0.906824 | −0.453412 | − | 0.891301i | \(-0.649793\pi\) | ||||
−0.453412 | + | 0.891301i | \(0.649793\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.784610 | 0.0474867 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 30.6029 | + | 12.6761i | 1.84543 | + | 0.764400i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.50770 | + | 13.2968i | −0.330925 | + | 0.798925i | 0.667594 | + | 0.744526i | \(0.267324\pi\) |
−0.998519 | + | 0.0543990i | \(0.982676\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.84279 | + | 14.1057i | 0.349799 | + | 0.844489i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.55532 | + | 5.55532i | 0.331403 | + | 0.331403i | 0.853119 | − | 0.521716i | \(-0.174708\pi\) |
−0.521716 | + | 0.853119i | \(0.674708\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.78246 | + | 4.05203i | −0.581507 | + | 0.240868i | −0.653992 | − | 0.756501i | \(-0.726907\pi\) |
0.0724852 | + | 0.997369i | \(0.476907\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 13.8564i | − | 0.820783i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.10583 | − | 3.10583i | 0.183331 | − | 0.183331i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.62158 | + | 4.62158i | −0.270922 | + | 0.270922i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 30.0000i | − | 1.75262i | −0.481749 | − | 0.876309i | \(-0.659998\pi\) | ||
0.481749 | − | 0.876309i | \(-0.340002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −30.2890 | + | 12.5461i | −1.76350 | + | 0.730464i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.3843 | + | 13.3843i | 0.776634 | + | 0.776634i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.65131 | − | 6.40083i | −0.153329 | − | 0.370169i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.47163 | + | 8.38125i | −0.200101 | + | 0.483087i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.40083 | + | 2.65131i | 0.367718 | + | 0.152314i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 25.8564 | 1.48053 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.7846 | 0.957948 | 0.478974 | − | 0.877829i | \(-0.341009\pi\) | ||||
0.478974 | + | 0.877829i | \(0.341009\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.98042 | + | 0.820318i | 0.112662 | + | 0.0466662i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.08394 | − | 19.5164i | 0.458398 | − | 1.10667i | −0.510648 | − | 0.859790i | \(-0.670594\pi\) |
0.969046 | − | 0.246881i | \(-0.0794057\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.70626 | + | 6.53349i | 0.152967 | + | 0.369295i | 0.981723 | − | 0.190315i | \(-0.0609510\pi\) |
−0.828756 | + | 0.559610i | \(0.810951\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.41851 | − | 4.41851i | −0.248955 | − | 0.248955i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.2870 | − | 5.91786i | 0.802436 | − | 0.332380i | 0.0565043 | − | 0.998402i | \(-0.482005\pi\) |
0.745932 | + | 0.666022i | \(0.232005\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.3923i | 0.917793i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.76217 | − | 3.76217i | 0.209984 | − | 0.209984i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.24693 | + | 7.24693i | −0.401988 | + | 0.401988i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.67949i | 0.258776i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.68573 | + | 1.94089i | −0.258333 | + | 0.107005i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.8332 | + | 10.8332i | 0.595448 | + | 0.595448i | 0.939098 | − | 0.343650i | \(-0.111663\pi\) |
−0.343650 | + | 0.939098i | \(0.611663\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.8103 | + | 26.0984i | 0.592402 | + | 1.43018i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.42083 | + | 3.43019i | −0.0776283 | + | 0.187411i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.1368 | + | 13.3115i | 1.75060 | + | 0.725123i | 0.997758 | + | 0.0669248i | \(0.0213187\pi\) |
0.752844 | + | 0.658199i | \(0.228681\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.75129 | −0.312367 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29.3205 | 1.58779 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.10613 | + | 3.77188i | 0.491685 | + | 0.203663i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.59220 | − | 11.0866i | 0.247236 | − | 0.596880i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.55085 | + | 3.74408i | 0.0832538 | + | 0.200993i | 0.960024 | − | 0.279916i | \(-0.0903068\pi\) |
−0.876771 | + | 0.480909i | \(0.840307\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.7680 | − | 21.7680i | −1.16521 | − | 1.16521i | −0.983318 | − | 0.181897i | \(-0.941776\pi\) |
−0.181897 | − | 0.983318i | \(-0.558224\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.41061 | + | 2.24115i | −0.288797 | + | 0.119624i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.85641i | 0.418154i | 0.977899 | + | 0.209077i | \(0.0670460\pi\) | ||||
−0.977899 | + | 0.209077i | \(0.932954\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.37945 | + | 5.37945i | −0.285512 | + | 0.285512i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.00481 | − | 8.00481i | 0.422478 | − | 0.422478i | −0.463578 | − | 0.886056i | \(-0.653435\pi\) |
0.886056 | + | 0.463578i | \(0.153435\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 10.8564i | − | 0.571390i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.70492 | − | 3.19148i | 0.404403 | − | 0.167509i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.89898 | − | 4.89898i | −0.256424 | − | 0.256424i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.52365 | − | 18.1637i | −0.392732 | − | 0.948138i | −0.989342 | − | 0.145607i | \(-0.953486\pi\) |
0.596611 | − | 0.802531i | \(-0.296514\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.65783 | + | 13.6592i | −0.294535 | + | 0.711069i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.627769 | − | 0.260030i | −0.0325921 | − | 0.0135001i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.3923 | −0.641649 | −0.320825 | − | 0.947139i | \(-0.603960\pi\) | ||||
−0.320825 | + | 0.947139i | \(0.603960\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.07180 | −0.261906 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.68573 | − | 1.94089i | −0.241327 | − | 0.0999611i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.34161 | + | 8.06736i | −0.171647 | + | 0.414393i | −0.986170 | − | 0.165739i | \(-0.946999\pi\) |
0.814523 | + | 0.580132i | \(0.196999\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.71278 | + | 13.7919i | 0.292674 | + | 0.706578i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.69213 | − | 6.69213i | −0.341952 | − | 0.341952i | 0.515149 | − | 0.857101i | \(-0.327737\pi\) |
−0.857101 | + | 0.515149i | \(0.827737\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.0866 | + | 4.59220i | −0.565023 | + | 0.234040i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 30.5359i | − | 1.55223i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.8028 | − | 17.8028i | 0.902636 | − | 0.902636i | −0.0930274 | − | 0.995664i | \(-0.529654\pi\) |
0.995664 | + | 0.0930274i | \(0.0296544\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.03579 | − | 6.03579i | 0.304465 | − | 0.304465i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.24871i | 0.314407i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.3833 | − | 10.0999i | 1.22376 | − | 0.506899i | 0.325159 | − | 0.945659i | \(-0.394582\pi\) |
0.898604 | + | 0.438760i | \(0.144582\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.07055 | + | 2.07055i | 0.103657 | + | 0.103657i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.58568 | − | 3.82818i | −0.0791853 | − | 0.191170i | 0.879329 | − | 0.476215i | \(-0.157992\pi\) |
−0.958514 | + | 0.285045i | \(0.907992\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.47163 | + | 8.38125i | −0.172934 | + | 0.417500i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.2870 | + | 5.91786i | 0.709925 | + | 0.294061i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 54.2487 | 2.68901 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −37.7128 | −1.86478 | −0.932389 | − | 0.361456i | \(-0.882280\pi\) | ||||
−0.932389 | + | 0.361456i | \(0.882280\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.40083 | + | 2.65131i | 0.315729 | + | 0.130779i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.65131 | − | 6.40083i | 0.130462 | − | 0.314964i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.5461 | − | 30.2890i | −0.615865 | − | 1.48683i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.83272 | + | 5.83272i | 0.285630 | + | 0.285630i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.08694 | − | 2.52129i | 0.297367 | − | 0.123173i | −0.229012 | − | 0.973424i | \(-0.573550\pi\) |
0.526379 | + | 0.850250i | \(0.323550\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.2487i | 1.27928i | 0.768673 | + | 0.639642i | \(0.220917\pi\) | ||||
−0.768673 | + | 0.639642i | \(0.779083\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.0716 | − | 12.0716i | 0.586940 | − | 0.586940i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.86370 | + | 3.86370i | −0.186978 | + | 0.186978i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.07180i | 0.244869i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.313884 | + | 0.130015i | −0.0151193 | + | 0.00626261i | −0.390230 | − | 0.920717i | \(-0.627605\pi\) |
0.375111 | + | 0.926980i | \(0.377605\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.2480 | − | 17.2480i | −0.828884 | − | 0.828884i | 0.158478 | − | 0.987362i | \(-0.449341\pi\) |
−0.987362 | + | 0.158478i | \(0.949341\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.36172 | − | 8.11592i | −0.161182 | − | 0.389129i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.89482 | − | 23.8882i | 0.473333 | − | 1.14273i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.7531 | − | 5.28250i | −0.608672 | − | 0.252120i | 0.0569887 | − | 0.998375i | \(-0.481850\pi\) |
−0.665661 | + | 0.746255i | \(0.731850\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.9282 | −0.758486 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.7846 | 0.987507 | 0.493753 | − | 0.869602i | \(-0.335625\pi\) | ||||
0.493753 | + | 0.869602i | \(0.335625\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.2890 | − | 12.5461i | −1.43584 | − | 0.594743i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.68086 | + | 4.05796i | −0.0795021 | + | 0.191935i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.29610 | + | 5.54328i | 0.108360 | + | 0.261603i | 0.968753 | − | 0.248027i | \(-0.0797822\pi\) |
−0.860393 | + | 0.509630i | \(0.829782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.0764 | + | 20.0764i | 0.945360 | + | 0.945360i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.42040 | − | 1.83099i | 0.207689 | − | 0.0860275i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 3.71281i | − | 0.174059i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.277401 | + | 0.277401i | −0.0129763 | + | 0.0129763i | −0.713565 | − | 0.700589i | \(-0.752921\pi\) |
0.700589 | + | 0.713565i | \(0.252921\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.4543 | + | 10.4543i | −0.486905 | + | 0.486905i | −0.907328 | − | 0.420423i | \(-0.861882\pi\) |
0.420423 | + | 0.907328i | \(0.361882\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.8564i | 1.38754i | 0.720194 | + | 0.693772i | \(0.244053\pi\) | ||||
−0.720194 | + | 0.693772i | \(0.755947\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.5167 | + | 6.01303i | −0.673198 | + | 0.278848i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.1774 | − | 15.1774i | −0.702327 | − | 0.702327i | 0.262583 | − | 0.964910i | \(-0.415426\pi\) |
−0.964910 | + | 0.262583i | \(0.915426\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.300257 | − | 0.724885i | −0.0138646 | − | 0.0334721i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.560287 | − | 1.35265i | 0.0258167 | − | 0.0623270i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −54.1772 | − | 22.4409i | −2.49107 | − | 1.03184i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −38.2487 | −1.75497 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.28719 | 0.104723 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.313884 | + | 0.130015i | 0.0143417 | + | 0.00594054i | 0.389843 | − | 0.920881i | \(-0.372529\pi\) |
−0.375501 | + | 0.926822i | \(0.622529\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.42319 | + | 15.5070i | −0.292872 | + | 0.707056i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.970446 | + | 2.34286i | 0.0441568 | + | 0.106604i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.8695 | + | 21.8695i | 0.993045 | + | 0.993045i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.6127 | + | 12.2660i | −1.34188 | + | 0.555825i | −0.934020 | − | 0.357220i | \(-0.883725\pi\) |
−0.407859 | + | 0.913045i | \(0.633725\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.75129i | 0.350525i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.8028 | + | 17.8028i | −0.803428 | + | 0.803428i | −0.983630 | − | 0.180202i | \(-0.942325\pi\) |
0.180202 | + | 0.983630i | \(0.442325\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 28.5617 | − | 28.5617i | 1.28375 | − | 1.28375i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1.60770i | − | 0.0721150i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.9270 | − | 10.3251i | 1.11588 | − | 0.462215i | 0.252924 | − | 0.967486i | \(-0.418608\pi\) |
0.862960 | + | 0.505272i | \(0.168608\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.03579 | − | 6.03579i | −0.269659 | − | 0.269659i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.10046 | − | 2.65675i | −0.0490672 | − | 0.118459i | 0.897445 | − | 0.441125i | \(-0.145421\pi\) |
−0.946513 | + | 0.322667i | \(0.895421\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.5461 | − | 30.2890i | 0.558295 | − | 1.34784i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.34248 | + | 3.04135i | 0.326091 | + | 0.135071i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −33.7128 | −1.49429 | −0.747147 | − | 0.664659i | \(-0.768577\pi\) | ||||
−0.747147 | + | 0.664659i | \(0.768577\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.46410 | 0.0647680 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −20.1927 | − | 8.36408i | −0.891529 | − | 0.369283i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.88179 | − | 9.37146i | 0.171052 | − | 0.412956i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.5461 | − | 30.2890i | −0.551778 | − | 1.33211i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.41851 | + | 4.41851i | 0.193951 | + | 0.193951i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.54328 | + | 2.29610i | −0.242855 | + | 0.100594i | −0.500791 | − | 0.865568i | \(-0.666958\pi\) |
0.257936 | + | 0.966162i | \(0.416958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.7846i | 1.25866i | 0.777137 | + | 0.629332i | \(0.216671\pi\) | ||||
−0.777137 | + | 0.629332i | \(0.783329\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.65256 | − | 2.65256i | 0.115767 | − | 0.115767i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.429705 | + | 0.429705i | −0.0186828 | + | 0.0186828i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 23.3205i | 1.01202i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.11592 | + | 3.36172i | −0.351540 | + | 0.145612i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.8028 | − | 17.8028i | −0.769681 | − | 0.769681i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.01303 | + | 14.5167i | 0.259482 | + | 0.626444i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.7057 | + | 28.2600i | −0.504200 | + | 1.21725i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.21020 | − | 0.915495i | −0.0950240 | − | 0.0393602i | 0.334665 | − | 0.942337i | \(-0.391377\pi\) |
−0.429689 | + | 0.902977i | \(0.641377\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.39230 | 0.360148 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 22.1436 | 0.948527 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.2789 | − | 15.0272i | −1.55117 | − | 0.642516i | −0.567644 | − | 0.823274i | \(-0.692145\pi\) |
−0.983528 | + | 0.180758i | \(0.942145\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.03843 | − | 16.9923i | 0.300393 | − | 0.725213i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.24351 | − | 17.4874i | −0.308584 | − | 0.744987i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.933740 | − | 0.933740i | −0.0397067 | − | 0.0397067i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −26.8588 | + | 11.1253i | −1.14009 | + | 0.472242i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 33.4641i | − | 1.41792i | −0.705249 | − | 0.708960i | \(-0.749165\pi\) | ||
0.705249 | − | 0.708960i | \(-0.250835\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.8295 | − | 12.8295i | 0.542628 | − | 0.542628i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.480473 | + | 0.480473i | −0.0202495 | + | 0.0202495i | −0.717159 | − | 0.696910i | \(-0.754558\pi\) |
0.696910 | + | 0.717159i | \(0.254558\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.2154i | 1.14496i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.01919 | + | 1.25059i | −0.126794 | + | 0.0525198i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.0406 | − | 14.0406i | −0.588613 | − | 0.588613i | 0.348643 | − | 0.937256i | \(-0.386643\pi\) |
−0.937256 | + | 0.348643i | \(0.886643\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.02247 | + | 12.1253i | 0.210184 | + | 0.507429i | 0.993451 | − | 0.114256i | \(-0.0364484\pi\) |
−0.783267 | + | 0.621685i | \(0.786448\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.36172 | − | 8.11592i | 0.140438 | − | 0.339047i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.6029 | − | 12.6761i | −1.27623 | − | 0.528632i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.53590 | 0.272093 | 0.136047 | − | 0.990702i | \(-0.456560\pi\) | ||||
0.136047 | + | 0.990702i | \(0.456560\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.17691 | −0.215145 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.40083 | + | 2.65131i | 0.265551 | + | 0.109995i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.68086 | − | 4.05796i | 0.0696142 | − | 0.168064i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.78256 | + | 11.5461i | 0.197734 | + | 0.477373i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.37945 | + | 5.37945i | 0.222034 | + | 0.222034i | 0.809354 | − | 0.587321i | \(-0.199817\pi\) |
−0.587321 | + | 0.809354i | \(0.699817\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.2792 | + | 12.9563i | −1.28884 | + | 0.533854i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.53590i | 0.104313i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.5259 | − | 22.5259i | 0.925027 | − | 0.925027i | −0.0723521 | − | 0.997379i | \(-0.523051\pi\) |
0.997379 | + | 0.0723521i | \(0.0230505\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.20736 | − | 3.20736i | 0.131269 | − | 0.131269i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 27.7128i | − | 1.13231i | −0.824297 | − | 0.566157i | \(-0.808429\pi\) | ||
0.824297 | − | 0.566157i | \(-0.191571\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.4413 | − | 11.7808i | 1.16014 | − | 0.480547i | 0.282221 | − | 0.959349i | \(-0.408929\pi\) |
0.877923 | + | 0.478802i | \(0.158929\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.86748 | + | 1.86748i | 0.0760497 | + | 0.0760497i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.1023 | − | 36.4601i | −0.613994 | − | 1.48231i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.4965 | − | 32.5833i | 0.547804 | − | 1.32252i | −0.371304 | − | 0.928511i | \(-0.621089\pi\) |
0.919108 | − | 0.394005i | \(-0.128911\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.71510 | + | 0.710416i | 0.0694992 | + | 0.0287875i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.1436 | 0.410366 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.1436 | −0.813592 | −0.406796 | − | 0.913519i | \(-0.633354\pi\) | ||||
−0.406796 | + | 0.913519i | \(0.633354\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.0572 | − | 5.82268i | −0.566841 | − | 0.234793i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.2040 | − | 43.9482i | 0.732864 | − | 1.76929i | 0.100053 | − | 0.994982i | \(-0.468099\pi\) |
0.632810 | − | 0.774307i | \(-0.281901\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.49410 | + | 20.5066i | 0.341407 | + | 0.824229i | 0.997574 | + | 0.0696133i | \(0.0221765\pi\) |
−0.656167 | + | 0.754615i | \(0.727823\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.3843 | − | 13.3843i | −0.537092 | − | 0.537092i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.40083 | − | 2.65131i | 0.256444 | − | 0.106222i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 11.0000i | − | 0.440000i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.3843 | + | 13.3843i | −0.534516 | + | 0.534516i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.4206 | − | 24.4206i | 0.972167 | − | 0.972167i | −0.0274556 | − | 0.999623i | \(-0.508740\pi\) |
0.999623 | + | 0.0274556i | \(0.00874048\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.3923i | 0.572043i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 65.2638 | − | 27.0331i | 2.58991 | − | 1.07278i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.69213 | − | 6.69213i | −0.265152 | − | 0.265152i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.07091 | + | 4.99961i | 0.0819238 | + | 0.197782i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.355208 | + | 0.857548i | −0.0140299 | + | 0.0338711i | −0.930739 | − | 0.365684i | \(-0.880835\pi\) |
0.916709 | + | 0.399555i | \(0.130835\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.30410 | + | 0.540174i | 0.0514285 | + | 0.0213024i | 0.408249 | − | 0.912870i | \(-0.366139\pi\) |
−0.356821 | + | 0.934173i | \(0.616139\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 31.4256 | 1.23738 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.9282 | 1.21591 | 0.607957 | − | 0.793970i | \(-0.291989\pi\) | ||||
0.607957 | + | 0.793970i | \(0.291989\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 41.3756 | + | 17.1383i | 1.62413 | + | 0.672738i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.27070 | − | 3.06775i | 0.0498028 | − | 0.120235i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.97696 | + | 9.60124i | 0.155631 | + | 0.375725i | 0.982393 | − | 0.186826i | \(-0.0598199\pi\) |
−0.826763 | + | 0.562551i | \(0.809820\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −28.5617 | − | 28.5617i | −1.11600 | − | 1.11600i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.55307 | + | 1.88594i | −0.177632 | + | 0.0735776i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.0718i | 1.13248i | 0.824242 | + | 0.566238i | \(0.191602\pi\) | ||||
−0.824242 | + | 0.566238i | \(0.808398\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.4553 | − | 20.4553i | 0.795620 | − | 0.795620i | −0.186781 | − | 0.982401i | \(-0.559806\pi\) |
0.982401 | + | 0.186781i | \(0.0598056\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.79796 | − | 9.79796i | 0.379949 | − | 0.379949i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 16.3923i | − | 0.634713i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.67594 | + | 2.35105i | −0.219445 | + | 0.0908969i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.9754 | − | 24.9754i | −0.964163 | − | 0.964163i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.6602 | − | 25.7360i | −0.410920 | − | 0.992048i | −0.984891 | − | 0.173173i | \(-0.944598\pi\) |
0.573971 | − | 0.818875i | \(-0.305402\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.7151 | + | 25.8686i | −0.412426 | + | 0.995684i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.4029 | + | 9.27958i | 0.861013 | + | 0.356643i | 0.769104 | − | 0.639124i | \(-0.220703\pi\) |
0.0919093 | + | 0.995767i | \(0.470703\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.53590 | −0.250825 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.17691 | 0.275020 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.34248 | + | 3.04135i | 0.280952 | + | 0.116374i | 0.518710 | − | 0.854950i | \(-0.326412\pi\) |
−0.237758 | + | 0.971324i | \(0.576412\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.5461 | − | 30.2890i | 0.479363 | − | 1.15728i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.109902 | − | 0.265326i | −0.00419301 | − | 0.0101228i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.960947 | + | 0.960947i | 0.0366092 | + | 0.0366092i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.8396 | + | 9.87470i | −0.906903 | + | 0.375651i | −0.786870 | − | 0.617118i | \(-0.788300\pi\) |
−0.120033 | + | 0.992770i | \(0.538300\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.53590i | 0.324252i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 27.6007 | − | 27.6007i | 1.04696 | − | 1.04696i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.10583 | + | 3.10583i | −0.117473 | + | 0.117473i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 4.39230i | − | 0.165895i | −0.996554 | − | 0.0829475i | \(-0.973567\pi\) | ||
0.996554 | − | 0.0829475i | \(-0.0264334\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −57.8728 | + | 23.9717i | −2.18271 | + | 0.904109i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.4233 | + | 12.4233i | 0.467889 | + | 0.467889i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.65131 | + | 6.40083i | 0.0997127 | + | 0.240728i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.3410 | + | 29.7939i | −0.463478 | + | 1.11893i | 0.503482 | + | 0.864006i | \(0.332052\pi\) |
−0.966960 | + | 0.254929i | \(0.917948\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.10652 | + | 1.70098i | 0.154006 | + | 0.0637916i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −29.3205 | −1.09806 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.0000 | 0.897549 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.0572 | − | 5.82268i | −0.524975 | − | 0.217452i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.580401 | + | 1.40121i | −0.0216453 | + | 0.0522564i | −0.934333 | − | 0.356402i | \(-0.884003\pi\) |
0.912687 | + | 0.408659i | \(0.134003\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.820318 | + | 1.98042i | 0.0305502 | + | 0.0737548i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.03528 | − | 1.03528i | −0.0385023 | − | 0.0385023i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −22.4029 | + | 9.27958i | −0.832022 | + | 0.344635i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 36.7846i | − | 1.36427i | −0.731228 | − | 0.682133i | \(-0.761053\pi\) | ||
0.731228 | − | 0.682133i | \(-0.238947\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.56652 | − | 1.56652i | 0.0580192 | − | 0.0580192i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.1112 | − | 16.1112i | 0.595079 | − | 0.595079i | −0.343920 | − | 0.938999i | \(-0.611755\pi\) |
0.938999 | + | 0.343920i | \(0.111755\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 16.3923i | − | 0.604639i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.68573 | − | 1.94089i | 0.172601 | − | 0.0714937i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.93426 | + | 5.93426i | 0.218295 | + | 0.218295i | 0.807780 | − | 0.589485i | \(-0.200669\pi\) |
−0.589485 | + | 0.807780i | \(0.700669\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.24115 | − | 5.41061i | −0.0823307 | − | 0.198764i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.0379 | − | 38.7188i | 0.588372 | − | 1.42046i | −0.296686 | − | 0.954975i | \(-0.595881\pi\) |
0.885058 | − | 0.465481i | \(-0.154119\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.2025 | + | 7.95393i | 0.703524 | + | 0.291409i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −23.3205 | −0.853253 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.32051 | 0.194407 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.1057 | − | 5.84279i | −0.514726 | − | 0.213206i | 0.110173 | − | 0.993912i | \(-0.464860\pi\) |
−0.624899 | + | 0.780706i | \(0.714860\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.94089 | − | 4.68573i | 0.0707301 | − | 0.170757i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.66434 | − | 20.9176i | −0.315328 | − | 0.761268i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.45001 | + | 7.45001i | 0.270775 | + | 0.270775i | 0.829412 | − | 0.558637i | \(-0.188676\pi\) |
−0.558637 | + | 0.829412i | \(0.688676\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.1445 | + | 6.27306i | −0.549711 | + | 0.227698i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4.39230i | − | 0.159221i | −0.996826 | − | 0.0796105i | \(-0.974632\pi\) | ||
0.996826 | − | 0.0796105i | \(-0.0253676\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.30890 | + | 3.30890i | −0.119790 | + | 0.119790i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.79796 | + | 9.79796i | −0.353784 | + | 0.353784i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.3923i | 0.735365i | 0.929951 | + | 0.367683i | \(0.119849\pi\) | ||||
−0.929951 | + | 0.367683i | \(0.880151\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.14529 | + | 2.13125i | −0.185303 | + | 0.0767550i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.9754 | + | 24.9754i | 0.898302 | + | 0.898302i | 0.995286 | − | 0.0969843i | \(-0.0309197\pi\) |
−0.0969843 | + | 0.995286i | \(0.530920\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.5982 | + | 40.0715i | 0.596223 | + | 1.43941i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.35105 | − | 5.67594i | 0.0843435 | − | 0.203623i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30.2890 | − | 12.5461i | −1.08522 | − | 0.449512i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.3923 | 0.371866 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13.8564 | −0.495188 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.40083 | − | 2.65131i | −0.228455 | − | 0.0946293i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.430272 | + | 1.03877i | −0.0153376 | + | 0.0370281i | −0.931363 | − | 0.364093i | \(-0.881379\pi\) |
0.916025 | + | 0.401121i | \(0.131379\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.53309 | + | 15.7723i | 0.232584 | + | 0.561508i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.06678 | − | 4.06678i | −0.144598 | − | 0.144598i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.0963 | − | 4.18204i | 0.358532 | − | 0.148509i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.35383i | 0.0834817i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.4249 | + | 27.4249i | −0.971438 | + | 0.971438i | −0.999603 | − | 0.0281649i | \(-0.991034\pi\) |
0.0281649 | + | 0.999603i | \(0.491034\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.4901 | + | 16.4901i | −0.582649 | + | 0.582649i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.46410i | 0.333981i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.0866 | − | 4.59220i | 0.390750 | − | 0.161854i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.6302 | − | 10.6302i | −0.374199 | − | 0.374199i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.59872 | − | 18.3449i | −0.267157 | − | 0.644973i | 0.732191 | − | 0.681100i | \(-0.238498\pi\) |
−0.999347 | + | 0.0361266i | \(0.988498\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.5367 | + | 32.6805i | −0.475337 | + | 1.14757i | 0.486435 | + | 0.873717i | \(0.338297\pi\) |
−0.961773 | + | 0.273849i | \(0.911703\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.0963 | − | 4.18204i | −0.354094 | − | 0.146671i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 36.6795 | 1.28483 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 67.7128 | 2.36897 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.43998 | − | 1.01067i | −0.0852598 | − | 0.0353158i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.2335 | + | 41.6054i | −0.601454 | + | 1.45204i | 0.270632 | + | 0.962683i | \(0.412767\pi\) |
−0.872085 | + | 0.489354i | \(0.837233\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.99292 | − | 14.4682i | −0.208900 | − | 0.504329i | 0.784350 | − | 0.620318i | \(-0.212996\pi\) |
−0.993251 | + | 0.115989i | \(0.962996\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 17.1464 | + | 17.1464i | 0.596962 | + | 0.596962i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.5743 | − | 9.76480i | 0.819759 | − | 0.339555i | 0.0669189 | − | 0.997758i | \(-0.478683\pi\) |
0.752841 | + | 0.658203i | \(0.228683\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.1436i | 0.421764i | 0.977511 | + | 0.210882i | \(0.0676337\pi\) | ||||
−0.977511 | + | 0.210882i | \(0.932366\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.45001 | + | 7.45001i | −0.258438 | + | 0.258438i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.5617 | + | 28.5617i | −0.988417 | + | 0.988417i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 24.7846i | 0.856681i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45.7474 | + | 18.9492i | −1.57938 | + | 0.654199i | −0.988315 | − | 0.152427i | \(-0.951291\pi\) |
−0.591062 | + | 0.806626i | \(0.701291\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.0208 | + | 12.0208i | 0.414511 | + | 0.414511i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.20092 | + | 5.31350i | 0.0758038 | + | 0.183007i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.3918 | − | 34.7450i | 0.495094 | − | 1.19526i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.70492 | + | 3.19148i | 0.264744 | + | 0.109661i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.75129 | −0.266024 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −54.2487 | −1.85962 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.1850 | + | 15.4025i | 1.27319 | + | 0.527372i | 0.913932 | − | 0.405867i | \(-0.133030\pi\) |
0.359257 | + | 0.933239i | \(0.383030\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −17.8487 | + | 43.0907i | −0.610414 | + | 1.47367i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.1448 | − | 48.6340i | −0.688135 | − | 1.66130i | −0.748506 | − | 0.663128i | \(-0.769228\pi\) |
0.0603709 | − | 0.998176i | \(-0.480772\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.17638 | + | 5.17638i | 0.176616 | + | 0.176616i | 0.789879 | − | 0.613263i | \(-0.210143\pi\) |
−0.613263 | + | 0.789879i | \(0.710143\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.97063 | − | 1.23048i | 0.101239 | − | 0.0419345i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.8564i | 1.28865i | 0.764753 | + | 0.644324i | \(0.222861\pi\) | ||||
−0.764753 | + | 0.644324i | \(0.777139\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.9086 | − | 20.9086i | 0.710914 | − | 0.710914i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.03579 | − | 6.03579i | 0.204750 | − | 0.204750i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.56922i | 0.0531710i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.3253 | − | 8.41904i | 0.687909 | − | 0.284941i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.58630 | − | 3.58630i | −0.121239 | − | 0.121239i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.6306 | − | 28.0788i | −0.392739 | − | 0.948155i | −0.989341 | − | 0.145618i | \(-0.953483\pi\) |
0.596602 | − | 0.802537i | \(-0.296517\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.40431 | − | 20.2898i | 0.283470 | − | 0.684358i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.57264 | + | 1.06562i | 0.0866746 | + | 0.0359018i | 0.425599 | − | 0.904912i | \(-0.360063\pi\) |
−0.338925 | + | 0.940813i | \(0.610063\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.0000 | −0.673054 | −0.336527 | − | 0.941674i | \(-0.609252\pi\) | ||||
−0.336527 | + | 0.941674i | \(0.609252\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −24.0000 | −0.806751 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.3466 | − | 16.2979i | −1.32113 | − | 0.547230i | −0.393018 | − | 0.919531i | \(-0.628569\pi\) |
−0.928112 | + | 0.372301i | \(0.878569\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.71278 | + | 13.7919i | −0.191600 | + | 0.462564i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.08394 | − | 19.5164i | −0.270822 | − | 0.653823i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.7685 | + | 26.7685i | 0.895774 | + | 0.895774i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 68.6940 | − | 28.4540i | 2.29619 | − | 0.951112i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 5.07180i | − | 0.169342i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.1774 | + | 15.1774i | −0.506195 | + | 0.506195i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.69591 | + | 4.69591i | −0.156270 | + | 0.156270i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 39.7128i | − | 1.32010i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.5841 | − | 9.35464i | 0.749893 | − | 0.310616i | 0.0251951 | − | 0.999683i | \(-0.491979\pi\) |
0.724698 | + | 0.689067i | \(0.241979\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.4901 | − | 16.4901i | −0.546942 | − | 0.546942i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.0248 | + | 24.2021i | 0.332138 | + | 0.801851i | 0.998422 | + | 0.0561534i | \(0.0178836\pi\) |
−0.666285 | + | 0.745698i | \(0.732116\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.1383 | + | 41.3756i | −0.567196 | + | 1.36933i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17.4874 | + | 7.24351i | 0.578115 | + | 0.239463i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.53590 | 0.281880 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −52.0000 | −1.71532 | −0.857661 | − | 0.514216i | \(-0.828083\pi\) | ||||
−0.857661 | + | 0.514216i | \(0.828083\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.3519 | + | 4.70210i | 0.374057 | + | 0.154940i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.23048 | + | 2.97063i | −0.0405016 | + | 0.0977796i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.7099 | + | 74.1401i | 1.00973 | + | 2.43771i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.10205 | − | 5.10205i | −0.167573 | − | 0.167573i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42.2331 | − | 17.4935i | 1.38562 | − | 0.573944i | 0.439645 | − | 0.898172i | \(-0.355104\pi\) |
0.945979 | + | 0.324227i | \(0.105104\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 35.3205i | − | 1.15758i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.9348 | − | 10.9348i | 0.357988 | − | 0.357988i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.6975 | − | 19.6975i | 0.643488 | − | 0.643488i | −0.307923 | − | 0.951411i | \(-0.599634\pi\) |
0.951411 | + | 0.307923i | \(0.0996340\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.17691i | 0.168942i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.17105 | + | 2.55613i | −0.201170 | + | 0.0833275i | −0.480994 | − | 0.876724i | \(-0.659724\pi\) |
0.279823 | + | 0.960051i | \(0.409724\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.0764 | − | 20.0764i | −0.653777 | − | 0.653777i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.88179 | − | 9.37146i | −0.126274 | − | 0.304854i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.1797 | + | 48.7181i | −0.655752 | + | 1.58312i | 0.148551 | + | 0.988905i | \(0.452539\pi\) |
−0.804303 | + | 0.594220i | \(0.797461\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.70531 | − | 1.12057i | −0.0878180 | − | 0.0363754i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.3205 | 0.367093 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.2487 | −1.36857 | −0.684285 | − | 0.729215i | \(-0.739886\pi\) | ||||
−0.684285 | + | 0.729215i | \(0.739886\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −38.4050 | − | 15.9079i | −1.24276 | − | 0.514766i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.59220 | + | 11.0866i | −0.148445 | + | 0.358377i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.65131 | + | 6.40083i | 0.0856152 | + | 0.206693i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.22715 | + | 5.22715i | 0.168618 | + | 0.168618i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.5457 | + | 6.85346i | −0.533179 | + | 0.220850i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.4974i | 0.788600i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.2185 | + | 34.2185i | −1.10039 | + | 1.10039i | −0.106031 | + | 0.994363i | \(0.533814\pi\) |
−0.994363 | + | 0.106031i | \(0.966186\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.6723 | + | 39.6723i | −1.27314 | + | 1.27314i | −0.328716 | + | 0.944429i | \(0.606616\pi\) |
−0.944429 | + | 0.328716i | \(0.893384\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.24871i | 0.264442i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.93148 | + | 2.87111i | −0.221985 | + | 0.0919492i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.6985 | + | 29.6985i | 0.950139 | + | 0.950139i | 0.998815 | − | 0.0486759i | \(-0.0155002\pi\) |
−0.0486759 | + | 0.998815i | \(0.515500\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.1383 | + | 41.3756i | 0.547743 | + | 1.32237i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.02776 | − | 14.5523i | 0.192451 | − | 0.464619i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.6323 | + | 11.4457i | 0.881333 | + | 0.365060i | 0.777014 | − | 0.629484i | \(-0.216734\pi\) |
0.104319 | + | 0.994544i | \(0.466734\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.0000 | 0.382352 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.71281 | −0.118180 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 54.1772 | + | 22.4409i | 1.72274 | + | 0.713581i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.90190 | − | 9.42002i | 0.123948 | − | 0.299237i | −0.849710 | − | 0.527250i | \(-0.823223\pi\) |
0.973658 | + | 0.228014i | \(0.0732230\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.29194 | + | 10.3617i | 0.136201 | + | 0.328818i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.1774 | − | 15.1774i | −0.481156 | − | 0.481156i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.1654 | − | 16.2228i | 1.24038 | − | 0.513782i | 0.336547 | − | 0.941667i | \(-0.390741\pi\) |
0.903833 | + | 0.427885i | \(0.140741\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 45.8564i | 1.45083i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))