Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3840,2,Mod(769,3840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3840.769");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3840 = 2^{8} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3840.f (of order \(2\), degree \(1\), 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: | \(30.6625543762\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.180227832610816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + x^{10} - 8x^{6} + 16x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.10 | ||
Root | \(1.37729 - 0.321037i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3840.769 |
Dual form | 3840.2.f.m.769.4 |
$q$-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 \(\left(\mathbb{Z}/3840\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(1537\) | \(2561\) | \(2821\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.726062 | + | 2.11491i | 0.324705 | + | 0.945815i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.05705i | 1.53342i | 0.641994 | + | 0.766710i | \(0.278107\pi\) | ||||
−0.641994 | + | 0.766710i | \(0.721893\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.985939 | −0.297272 | −0.148636 | − | 0.988892i | \(-0.547488\pi\) | ||||
−0.148636 | + | 0.988892i | \(0.547488\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.94567i | 1.37168i | 0.727752 | + | 0.685841i | \(0.240565\pi\) | ||||
−0.727752 | + | 0.685841i | \(0.759435\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.11491 | + | 0.726062i | −0.546067 | + | 0.187468i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.52323i | − | 1.09704i | −0.836136 | − | 0.548522i | \(-0.815191\pi\) | ||
0.836136 | − | 0.548522i | \(-0.184809\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.60492 | 0.597610 | 0.298805 | − | 0.954314i | \(-0.403412\pi\) | ||||
0.298805 | + | 0.954314i | \(0.403412\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.05705 | −0.885320 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.53729i | 0.737577i | 0.929513 | + | 0.368788i | \(0.120227\pi\) | ||||
−0.929513 | + | 0.368788i | \(0.879773\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.94567 | + | 3.07111i | −0.789134 | + | 0.614222i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.59434 | −1.41023 | −0.705117 | − | 0.709091i | \(-0.749105\pi\) | ||||
−0.705117 | + | 0.709091i | \(0.749105\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.28415 | 0.589850 | 0.294925 | − | 0.955520i | \(-0.404705\pi\) | ||||
0.294925 | + | 0.955520i | \(0.404705\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.985939i | − | 0.171630i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.58028 | + | 2.94567i | −1.45033 | + | 0.497909i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.945668i | 0.155467i | 0.996974 | + | 0.0777334i | \(0.0247683\pi\) | ||||
−0.996974 | + | 0.0777334i | \(0.975232\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.94567 | −0.791941 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.568295 | −0.0887527 | −0.0443763 | − | 0.999015i | \(-0.514130\pi\) | ||||
−0.0443763 | + | 0.999015i | \(0.514130\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.45963i | 1.29008i | 0.764148 | + | 0.645041i | \(0.223160\pi\) | ||||
−0.764148 | + | 0.645041i | \(0.776840\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.726062 | − | 2.11491i | −0.108235 | − | 0.315272i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.60492i | 0.379967i | 0.981787 | + | 0.189984i | \(0.0608435\pi\) | ||||
−0.981787 | + | 0.189984i | \(0.939157\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.45963 | −1.35138 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.52323 | 0.633379 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 0.229815i | − | 0.0315675i | −0.999875 | − | 0.0157838i | \(-0.994976\pi\) | ||
0.999875 | − | 0.0157838i | \(-0.00502434\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.715853 | − | 2.08517i | −0.0965256 | − | 0.281164i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.60492i | 0.345030i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.10003 | 1.18472 | 0.592362 | − | 0.805672i | \(-0.298196\pi\) | ||||
0.592362 | + | 0.805672i | \(0.298196\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.0183 | 1.41075 | 0.705377 | − | 0.708832i | \(-0.250778\pi\) | ||||
0.705377 | + | 0.708832i | \(0.250778\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 4.05705i | − | 0.511140i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.4596 | + | 3.59086i | −1.29736 | + | 0.445392i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.45963i | 1.03351i | 0.856134 | + | 0.516754i | \(0.172860\pi\) | ||||
−0.856134 | + | 0.516754i | \(0.827140\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.53729 | −0.425840 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.43171 | 0.169912 | 0.0849561 | − | 0.996385i | \(-0.472925\pi\) | ||||
0.0849561 | + | 0.996385i | \(0.472925\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 11.9507i | − | 1.39873i | −0.714767 | − | 0.699363i | \(-0.753467\pi\) | ||
0.714767 | − | 0.699363i | \(-0.246533\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.07111 | − | 3.94567i | −0.354621 | − | 0.455606i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 4.00000i | − | 0.455842i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.28415 | −0.369495 | −0.184748 | − | 0.982786i | \(-0.559147\pi\) | ||||
−0.184748 | + | 0.982786i | \(0.559147\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 9.89134i | − | 1.08572i | −0.839825 | − | 0.542858i | \(-0.817342\pi\) | ||
0.839825 | − | 0.542858i | \(-0.182658\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.56622 | − | 3.28415i | 1.03760 | − | 0.356216i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 7.59434i | − | 0.814199i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.3510 | −1.30920 | −0.654600 | − | 0.755976i | \(-0.727163\pi\) | ||||
−0.654600 | + | 0.755976i | \(0.727163\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −20.0648 | −2.10336 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.28415i | 0.340550i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.89134 | + | 5.50917i | 0.194047 | + | 0.565229i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.23797i | 0.328766i | 0.986397 | + | 0.164383i | \(0.0525633\pi\) | ||||
−0.986397 | + | 0.164383i | \(0.947437\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.985939 | 0.0990906 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.35637 | −0.433475 | −0.216738 | − | 0.976230i | \(-0.569542\pi\) | ||||
−0.216738 | + | 0.976230i | \(0.569542\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 15.0754i | − | 1.48542i | −0.669612 | − | 0.742711i | \(-0.733540\pi\) | ||
0.669612 | − | 0.742711i | \(-0.266460\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.94567 | − | 8.58028i | −0.287468 | − | 0.837350i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000i | 0.386695i | 0.981130 | + | 0.193347i | \(0.0619344\pi\) | ||||
−0.981130 | + | 0.193347i | \(0.938066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.17034 | 0.399446 | 0.199723 | − | 0.979852i | \(-0.435996\pi\) | ||||
0.199723 | + | 0.979852i | \(0.435996\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.945668 | −0.0897588 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.28526i | − | 0.120907i | −0.998171 | − | 0.0604537i | \(-0.980745\pi\) | ||
0.998171 | − | 0.0604537i | \(-0.0192548\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.48105 | + | 2.56829i | −0.697611 | + | 0.239495i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 4.94567i | − | 0.457227i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.3510 | 1.68223 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0279 | −0.911630 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 0.568295i | − | 0.0512414i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.35991 | − | 6.11491i | −0.837176 | − | 0.546934i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.15280i | − | 0.102294i | −0.998691 | − | 0.0511472i | \(-0.983712\pi\) | ||
0.998691 | − | 0.0511472i | \(-0.0162878\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.45963 | −0.744829 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.89019 | 0.339887 | 0.169944 | − | 0.985454i | \(-0.445641\pi\) | ||||
0.169944 | + | 0.985454i | \(0.445641\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.5683i | 0.916387i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.11491 | − | 0.726062i | 0.182022 | − | 0.0624895i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 17.5135i | − | 1.49628i | −0.663544 | − | 0.748138i | \(-0.730948\pi\) | ||
0.663544 | − | 0.748138i | \(-0.269052\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.8612 | 1.43015 | 0.715076 | − | 0.699047i | \(-0.246392\pi\) | ||||
0.715076 | + | 0.699047i | \(0.246392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.60492 | −0.219374 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 4.87613i | − | 0.407762i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.51396 | − | 16.0613i | −0.457910 | − | 1.33382i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 9.45963i | − | 0.780217i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.4986 | 0.860078 | 0.430039 | − | 0.902810i | \(-0.358500\pi\) | ||||
0.430039 | + | 0.902810i | \(0.358500\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.71585 | 0.383771 | 0.191885 | − | 0.981417i | \(-0.438540\pi\) | ||||
0.191885 | + | 0.981417i | \(0.438540\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.52323i | 0.365682i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.38449 | + | 6.94567i | 0.191527 | + | 0.557889i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.94567i | − | 0.713942i | −0.934115 | − | 0.356971i | \(-0.883809\pi\) | ||
0.934115 | − | 0.356971i | \(-0.116191\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.229815 | 0.0182255 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.3510 | −1.13101 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.7827i | 1.23619i | 0.786102 | + | 0.618097i | \(0.212096\pi\) | ||||
−0.786102 | + | 0.618097i | \(0.787904\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.08517 | − | 0.715853i | 0.162330 | − | 0.0557291i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 5.50917i | − | 0.426312i | −0.977018 | − | 0.213156i | \(-0.931626\pi\) | ||
0.977018 | − | 0.213156i | \(-0.0683743\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4596 | −0.881510 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.60492 | −0.199203 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.3385i | 0.786020i | 0.919534 | + | 0.393010i | \(0.128566\pi\) | ||||
−0.919534 | + | 0.393010i | \(0.871434\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.4596 | − | 16.0078i | −0.941860 | − | 1.21007i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.10003i | 0.684000i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.1746 | 1.20895 | 0.604474 | − | 0.796625i | \(-0.293383\pi\) | ||||
0.604474 | + | 0.796625i | \(0.293383\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.11409 | −0.603116 | −0.301558 | − | 0.953448i | \(-0.597507\pi\) | ||||
−0.301558 | + | 0.953448i | \(0.597507\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.0183i | 0.814499i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.00000 | + | 0.686614i | −0.147043 | + | 0.0504808i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.45963i | 0.326120i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.05705 | 0.295107 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.9193 | 1.80309 | 0.901547 | − | 0.432681i | \(-0.142432\pi\) | ||||
0.901547 | + | 0.432681i | \(0.142432\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.03951i | 0.0748254i | 0.999300 | + | 0.0374127i | \(0.0119116\pi\) | ||||
−0.999300 | + | 0.0374127i | \(0.988088\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.59086 | − | 10.4596i | −0.257147 | − | 0.749030i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 9.66152i | − | 0.688355i | −0.938905 | − | 0.344177i | \(-0.888158\pi\) | ||
0.938905 | − | 0.344177i | \(-0.111842\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.0668 | −1.63516 | −0.817582 | − | 0.575813i | \(-0.804686\pi\) | ||||
−0.817582 | + | 0.575813i | \(0.804686\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.45963 | −0.596696 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 30.8106i | − | 2.16248i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.412617 | − | 1.20189i | −0.0288184 | − | 0.0839437i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 3.53729i | − | 0.245859i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.56829 | −0.177653 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.44154 | −0.443454 | −0.221727 | − | 0.975109i | \(-0.571169\pi\) | ||||
−0.221727 | + | 0.975109i | \(0.571169\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.43171i | 0.0980988i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.8913 | + | 6.14222i | −1.22018 | + | 0.418896i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.3239i | 0.904488i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.9507 | 0.807554 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.3704 | 1.50480 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.9796i | 1.20401i | 0.798494 | + | 0.602003i | \(0.205630\pi\) | ||||
−0.798494 | + | 0.602003i | \(0.794370\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.94567 | − | 3.07111i | 0.263045 | − | 0.204741i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 7.02792i | − | 0.466460i | −0.972422 | − | 0.233230i | \(-0.925071\pi\) | ||
0.972422 | − | 0.233230i | \(-0.0749295\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.17034 | 0.275584 | 0.137792 | − | 0.990461i | \(-0.455999\pi\) | ||||
0.137792 | + | 0.990461i | \(0.455999\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.00000 | 0.263181 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.9894i | 1.57160i | 0.618483 | + | 0.785799i | \(0.287748\pi\) | ||||
−0.618483 | + | 0.785799i | \(0.712252\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.50917 | + | 1.89134i | −0.359379 | + | 0.123377i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 3.28415i | − | 0.213328i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.91926 | −0.576939 | −0.288469 | − | 0.957489i | \(-0.593146\pi\) | ||||
−0.288469 | + | 0.957489i | \(0.593146\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.3510 | −1.05326 | −0.526629 | − | 0.850095i | \(-0.676544\pi\) | ||||
−0.526629 | + | 0.850095i | \(0.676544\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.86828 | − | 20.0062i | −0.438798 | − | 1.27815i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.8831i | 0.819731i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.89134 | 0.626838 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.22391 | −0.266611 | −0.133305 | − | 0.991075i | \(-0.542559\pi\) | ||||
−0.133305 | + | 0.991075i | \(0.542559\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3.48755i | − | 0.219261i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.28415 | + | 9.56622i | 0.205661 | + | 0.599060i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 24.6952i | − | 1.54044i | −0.637777 | − | 0.770221i | \(-0.720146\pi\) | ||
0.637777 | − | 0.770221i | \(-0.279854\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.83662 | −0.238396 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.59434 | 0.470078 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.6628i | 0.904145i | 0.891981 | + | 0.452073i | \(0.149315\pi\) | ||||
−0.891981 | + | 0.452073i | \(0.850685\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.486038 | − | 0.166860i | 0.0298571 | − | 0.0102501i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 12.3510i | − | 0.755867i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.5381 | 0.703490 | 0.351745 | − | 0.936096i | \(-0.385588\pi\) | ||||
0.351745 | + | 0.936096i | \(0.385588\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.63511 | −0.342309 | −0.171154 | − | 0.985244i | \(-0.554750\pi\) | ||||
−0.171154 | + | 0.985244i | \(0.554750\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 20.0648i | − | 1.21438i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.89019 | − | 3.02792i | 0.234587 | − | 0.182591i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 17.4053i | − | 1.04578i | −0.852399 | − | 0.522892i | \(-0.824853\pi\) | ||
0.852399 | − | 0.522892i | \(-0.175147\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.28415 | −0.196617 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.7827 | −1.29945 | −0.649723 | − | 0.760171i | \(-0.725115\pi\) | ||||
−0.649723 | + | 0.760171i | \(0.725115\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.5962i | 1.28376i | 0.766804 | + | 0.641881i | \(0.221846\pi\) | ||||
−0.766804 | + | 0.641881i | \(0.778154\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.50917 | + | 1.89134i | −0.326335 | + | 0.112033i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 2.30560i | − | 0.136095i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.45963 | −0.203508 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.23797 | −0.189813 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 32.0125i | 1.87019i | 0.354398 | + | 0.935095i | \(0.384686\pi\) | ||||
−0.354398 | + | 0.935095i | \(0.615314\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.60719 | + | 19.2457i | 0.384685 | + | 1.12053i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.985939i | 0.0572100i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −17.4943 | −1.01172 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −34.3211 | −1.97824 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 4.35637i | − | 0.250267i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.00000 | + | 23.3028i | 0.458079 | + | 1.33431i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.13659i | 0.0648686i | 0.999474 | + | 0.0324343i | \(0.0103260\pi\) | ||||
−0.999474 | + | 0.0324343i | \(0.989674\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.0754 | 0.857609 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.13659 | 0.291269 | 0.145635 | − | 0.989338i | \(-0.453478\pi\) | ||||
0.145635 | + | 0.989338i | \(0.453478\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 23.0762i | − | 1.30434i | −0.758071 | − | 0.652172i | \(-0.773858\pi\) | ||
0.758071 | − | 0.652172i | \(-0.226142\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.58028 | − | 2.94567i | 0.483444 | − | 0.165970i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.66152i | 0.0933203i | 0.998911 | + | 0.0466601i | \(0.0148578\pi\) | ||||
−0.998911 | + | 0.0466601i | \(0.985142\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.48755 | 0.419223 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 11.7827i | − | 0.655605i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.1887 | − | 19.5140i | −0.842516 | − | 1.08244i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.17034i | 0.230620i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.5683 | −0.582649 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.9077 | 1.42402 | 0.712008 | − | 0.702171i | \(-0.247786\pi\) | ||||
0.712008 | + | 0.702171i | \(0.247786\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 0.945668i | − | 0.0518223i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.8913 | + | 6.14222i | −0.977508 | + | 0.335585i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 8.00696i | − | 0.436167i | −0.975930 | − | 0.218083i | \(-0.930020\pi\) | ||
0.975930 | − | 0.218083i | \(-0.0699805\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.28526 | 0.0698060 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.23797 | −0.175346 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 9.97884i | − | 0.538806i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.56829 | − | 7.48105i | −0.138272 | − | 0.402766i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 23.0279i | − | 1.23620i | −0.786098 | − | 0.618102i | \(-0.787902\pi\) | ||
0.786098 | − | 0.618102i | \(-0.212098\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.4380 | −1.14755 | −0.573776 | − | 0.819012i | \(-0.694522\pi\) | ||||
−0.573776 | + | 0.819012i | \(0.694522\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.94567 | 0.263980 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 4.52323i | − | 0.240747i | −0.992729 | − | 0.120374i | \(-0.961591\pi\) | ||
0.992729 | − | 0.120374i | \(-0.0384093\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.03951 | + | 3.02792i | 0.0551713 | + | 0.160706i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.3510i | 0.971236i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.3510 | −0.546303 | −0.273152 | − | 0.961971i | \(-0.588066\pi\) | ||||
−0.273152 | + | 0.961971i | \(0.588066\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.2144 | −0.642862 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 10.0279i | − | 0.526330i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 25.2747 | − | 8.67696i | 1.32294 | − | 0.454173i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 0.485359i | − | 0.0253355i | −0.999920 | − | 0.0126678i | \(-0.995968\pi\) | ||
0.999920 | − | 0.0126678i | \(-0.00403238\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.568295 | 0.0295842 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.932371 | 0.0484063 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.0823i | 1.55760i | 0.627272 | + | 0.778800i | \(0.284171\pi\) | ||||
−0.627272 | + | 0.778800i | \(0.715829\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.11491 | − | 9.35991i | 0.315772 | − | 0.483344i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 37.5591i | − | 1.93439i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.6881 | −1.73044 | −0.865220 | − | 0.501392i | \(-0.832821\pi\) | ||||
−0.865220 | + | 0.501392i | \(0.832821\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.15280 | 0.0590597 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.17545i | 0.264453i | 0.991220 | + | 0.132227i | \(0.0422127\pi\) | ||||
−0.991220 | + | 0.132227i | \(0.957787\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.45963 | − | 2.90425i | 0.431143 | − | 0.148014i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 8.45963i | − | 0.430027i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.6408 | −0.843722 | −0.421861 | − | 0.906660i | \(-0.638623\pi\) | ||||
−0.421861 | + | 0.906660i | \(0.638623\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0000 | 0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.89019i | 0.196234i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.38449 | − | 6.94567i | −0.119977 | − | 0.349474i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.4332i | 1.02551i | 0.858534 | + | 0.512757i | \(0.171376\pi\) | ||||
−0.858534 | + | 0.512757i | \(0.828624\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.5683 | −0.529076 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.56829 | −0.228130 | −0.114065 | − | 0.993473i | \(-0.536387\pi\) | ||||
−0.114065 | + | 0.993473i | \(0.536387\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.2423i | 0.809087i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.726062 | + | 2.11491i | 0.0360783 | + | 0.105091i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.932371i | − | 0.0462159i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.8913 | 0.983563 | 0.491782 | − | 0.870719i | \(-0.336346\pi\) | ||||
0.491782 | + | 0.870719i | \(0.336346\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.5135 | 0.863875 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 36.9193i | 1.81668i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.9193 | − | 7.18172i | 1.02689 | − | 0.352537i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.8612i | 0.825698i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.387288 | −0.0189203 | −0.00946013 | − | 0.999955i | \(-0.503011\pi\) | ||||
−0.00946013 | + | 0.999955i | \(0.503011\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.0578 | 0.587664 | 0.293832 | − | 0.955857i | \(-0.405069\pi\) | ||||
0.293832 | + | 0.955857i | \(0.405069\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 2.60492i | − | 0.126656i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.8913 | + | 17.8472i | 0.673829 | + | 0.865715i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 44.7019i | 2.16328i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.87613 | 0.235422 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −40.4068 | −1.94633 | −0.973164 | − | 0.230113i | \(-0.926090\pi\) | ||||
−0.973164 | + | 0.230113i | \(0.926090\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.1859i | 1.73898i | 0.493949 | + | 0.869491i | \(0.335553\pi\) | ||||
−0.493949 | + | 0.869491i | \(0.664447\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.0613 | − | 5.51396i | 0.770082 | − | 0.264374i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.21438i | 0.440783i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.4178 | 1.21312 | 0.606562 | − | 0.795036i | \(-0.292548\pi\) | ||||
0.606562 | + | 0.795036i | \(0.292548\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.45963 | 0.450459 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 7.02792i | − | 0.333907i | −0.985965 | − | 0.166953i | \(-0.946607\pi\) | ||
0.985965 | − | 0.166953i | \(-0.0533929\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.96757 | − | 26.1212i | −0.425103 | − | 1.23826i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.4986i | 0.496566i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.00000 | 0.0943858 | 0.0471929 | − | 0.998886i | \(-0.484972\pi\) | ||||
0.0471929 | + | 0.998886i | \(0.484972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.560304 | 0.0263837 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.71585i | 0.221570i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.5683 | − | 42.4352i | −0.682972 | − | 1.98939i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.2747i | 1.18230i | 0.806562 | + | 0.591149i | \(0.201326\pi\) | ||||
−0.806562 | + | 0.591149i | \(0.798674\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.52323 | −0.211126 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −41.0902 | −1.91376 | −0.956881 | − | 0.290479i | \(-0.906185\pi\) | ||||
−0.956881 | + | 0.290479i | \(0.906185\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.2106i | 0.613951i | 0.951717 | + | 0.306975i | \(0.0993169\pi\) | ||||
−0.951717 | + | 0.306975i | \(0.900683\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.94567 | + | 2.38449i | −0.322098 | + | 0.110578i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.89134i | 0.0875206i | 0.999042 | + | 0.0437603i | \(0.0139338\pi\) | ||||
−0.999042 | + | 0.0437603i | \(0.986066\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −34.3211 | −1.58480 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.94567 | 0.412195 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 8.34068i | − | 0.383505i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.2782 | + | 8.00000i | −0.471594 | + | 0.367065i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.229815i | 0.0105225i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.4876 | 1.43870 | 0.719352 | − | 0.694646i | \(-0.244439\pi\) | ||||
0.719352 | + | 0.694646i | \(0.244439\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.67696 | −0.213251 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 14.3510i | − | 0.652992i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.84800 | + | 2.35097i | −0.310952 | + | 0.106752i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 12.9964i | − | 0.588922i | −0.955664 | − | 0.294461i | \(-0.904860\pi\) | ||
0.955664 | − | 0.294461i | \(-0.0951401\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.7827 | −0.713717 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.9085 | 0.672812 | 0.336406 | − | 0.941717i | \(-0.390788\pi\) | ||||
0.336406 | + | 0.941717i | \(0.390788\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 34.3510i | 1.54709i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.715853 | + | 2.08517i | 0.0321752 | + | 0.0937214i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.80850i | 0.260547i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.6599 | −1.59636 | −0.798179 | − | 0.602420i | \(-0.794203\pi\) | ||||
−0.798179 | + | 0.602420i | \(0.794203\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.50917 | 0.246132 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 25.3090i | − | 1.12847i | −0.825613 | − | 0.564237i | \(-0.809170\pi\) | ||
0.825613 | − | 0.564237i | \(-0.190830\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.16300 | − | 9.21332i | −0.140751 | − | 0.409988i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 11.4596i | − | 0.508940i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.7366 | 0.608862 | 0.304431 | − | 0.952534i | \(-0.401534\pi\) | ||||
0.304431 | + | 0.952534i | \(0.401534\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 48.4846 | 2.14483 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 2.60492i | − | 0.115010i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 31.8831 | − | 10.9457i | 1.40494 | − | 0.482324i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.56829i | − | 0.112953i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.3385 | −0.453809 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.9193 | 1.35460 | 0.677299 | − | 0.735708i | \(-0.263150\pi\) | ||||
0.677299 | + | 0.735708i | \(0.263150\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.8385i | 0.954932i | 0.878650 | + | 0.477466i | \(0.158445\pi\) | ||||
−0.878650 | + | 0.477466i | \(0.841555\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16.0078 | − | 12.4596i | 0.698636 | − | 0.543783i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 14.8550i | − | 0.647092i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.4876 | 0.455981 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.10003 | −0.394908 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.81060i | − | 0.121740i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.45963 | + | 2.90425i | −0.365742 | + | 0.125562i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.1746i | 0.697986i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.32662 | 0.401726 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.3423 | 1.04656 | 0.523278 | − | 0.852162i | \(-0.324709\pi\) | ||||
0.523278 | + | 0.852162i | \(0.324709\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 8.11409i | − | 0.348209i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.02792 | + | 8.81988i | 0.129702 | + | 0.377802i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.3789i | 1.42718i | 0.700564 | + | 0.713589i | \(0.252932\pi\) | ||||
−0.700564 | + | 0.713589i | \(0.747068\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.0183 | −0.470251 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.7827 | −0.842770 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 13.3239i | − | 0.566592i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.686614 | − | 2.00000i | −0.0291451 | − | 0.0848953i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 30.5808i | − | 1.29575i | −0.761747 | − | 0.647875i | \(-0.775658\pi\) | ||
0.761747 | − | 0.647875i | \(-0.224342\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.8385 | −1.76958 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.45963 | −0.188286 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 7.02792i | − | 0.296192i | −0.988973 | − | 0.148096i | \(-0.952686\pi\) | ||
0.988973 | − | 0.148096i | \(-0.0473144\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.71821 | − | 0.933181i | 0.114356 | − | 0.0392592i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.05705i | 0.170380i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.3510 | 1.02085 | 0.510423 | − | 0.859924i | \(-0.329489\pi\) | ||||
0.510423 | + | 0.859924i | \(0.329489\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0992 | 0.841125 | 0.420563 | − | 0.907263i | \(-0.361833\pi\) | ||||
0.420563 | + | 0.907263i | \(0.361833\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.9193i | 1.04102i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.8634 | − | 13.9570i | −0.453036 | − | 0.582047i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.76899i | 0.198536i | 0.995061 | + | 0.0992678i | \(0.0316501\pi\) | ||||
−0.995061 | + | 0.0992678i | \(0.968350\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.03951 | −0.0432004 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 40.1296 | 1.66486 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.226584i | 0.00938413i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.4596 | − | 3.59086i | 0.432452 | − | 0.148464i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.21733i | 0.339165i | 0.985516 | + | 0.169583i | \(0.0542420\pi\) | ||||
−0.985516 | + | 0.169583i | \(0.945758\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.55495 | 0.352501 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.66152 | 0.397422 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 7.76120i | − | 0.318714i | −0.987221 | − | 0.159357i | \(-0.949058\pi\) | ||
0.987221 | − | 0.159357i | \(-0.0509421\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.3239 | + | 38.8106i | 0.546228 | + | 1.59108i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 23.0668i | − | 0.944062i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.64903 | 0.230813 | 0.115407 | − | 0.993318i | \(-0.463183\pi\) | ||||
0.115407 | + | 0.993318i | \(0.463183\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.7299 | 1.53903 | 0.769516 | − | 0.638627i | \(-0.220497\pi\) | ||||
0.769516 | + | 0.638627i | \(0.220497\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 8.45963i | − | 0.344503i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.28090 | − | 21.2081i | −0.296010 | − | 0.862233i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 0.113292i | − | 0.00459837i | −0.999997 | − | 0.00229919i | \(-0.999268\pi\) | ||
0.999997 | − | 0.00229919i | \(-0.000731854\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 30.8106 | 1.24851 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.8831 | −0.521194 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.703366i | 0.0284087i | 0.999899 | + | 0.0142044i | \(0.00452154\pi\) | ||||
−0.999899 | + | 0.0142044i | \(0.995478\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.20189 | − | 0.412617i | 0.0484649 | − | 0.0166383i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.4809i | 0.985564i | 0.870153 | + | 0.492782i | \(0.164020\pi\) | ||||
−0.870153 | + | 0.492782i | \(0.835980\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −39.4966 | −1.58750 | −0.793751 | − | 0.608243i | \(-0.791874\pi\) | ||||
−0.793751 | + | 0.608243i | \(0.791874\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.53729 | 0.141947 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 50.1084i | − | 2.00755i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.13659 | − | 24.2351i | 0.245464 | − | 0.969406i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 2.56829i | − | 0.102568i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.27748 | 0.170554 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.3400 | 0.690294 | 0.345147 | − | 0.938549i | \(-0.387829\pi\) | ||||
0.345147 | + | 0.938549i | \(0.387829\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 6.44154i | − | 0.256028i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.43806 | − | 0.837003i | 0.0967516 | − | 0.0332155i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 46.7842i | − | 1.85366i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.43171 | −0.0566374 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.7019 | 1.52863 | 0.764317 | − | 0.644840i | \(-0.223076\pi\) | ||||
0.764317 | + | 0.644840i | \(0.223076\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.13659i | 0.0448227i | 0.999749 | + | 0.0224113i | \(0.00713435\pi\) | ||||
−0.999749 | + | 0.0224113i | \(0.992866\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.14222 | − | 17.8913i | −0.241850 | − | 0.704471i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 6.54868i | − | 0.257455i | −0.991680 | − | 0.128728i | \(-0.958911\pi\) | ||
0.991680 | − | 0.128728i | \(-0.0410893\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.97208 | −0.352185 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.3239 | −0.522206 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.74226i | 0.342111i | 0.985261 | + | 0.171056i | \(0.0547178\pi\) | ||||
−0.985261 | + | 0.171056i | \(0.945282\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.82452 | + | 8.22739i | 0.110363 | + | 0.321471i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.9507i | 0.466242i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.5336 | −1.38419 | −0.692097 | − | 0.721804i | \(-0.743313\pi\) | ||||
−0.692097 | + | 0.721804i | \(0.743313\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.3028 | 0.906373 | 0.453186 | − | 0.891416i | \(-0.350287\pi\) | ||||
0.453186 | + | 0.891416i | \(0.350287\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 22.3704i | 0.868795i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.3510 | + | 7.67324i | −0.866733 | + | 0.297555i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 26.8634i | − | 1.04016i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.9796 | −0.695133 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.8634 | −0.419377 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 14.3634i | − | 0.553670i | −0.960917 | − | 0.276835i | \(-0.910714\pi\) | ||
0.960917 | − | 0.276835i | \(-0.0892856\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.07111 | + | 3.94567i | 0.118207 | + | 0.151869i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 24.3076i | − | 0.934217i | −0.884200 | − | 0.467109i | \(-0.845296\pi\) | ||
0.884200 | − | 0.467109i | \(-0.154704\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.1366 | −0.504136 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.02792 | 0.269311 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.5933i | 1.47673i | 0.674401 | + | 0.738365i | \(0.264402\pi\) | ||||
−0.674401 | + | 0.738365i | \(0.735598\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 37.0393 | − | 12.7159i | 1.41520 | − | 0.485848i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.17034i | 0.159108i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.13659 | 0.0433006 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.4090 | −0.510102 | −0.255051 | − | 0.966928i | \(-0.582092\pi\) | ||||
−0.255051 | + | 0.966928i | \(0.582092\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.00000i | 0.151947i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.2423 | + | 35.6599i | 0.464377 | + | 1.35266i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.57053i | 0.0973657i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.9894 | −0.907362 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.6013 | −0.589253 | −0.294626 | − | 0.955613i | \(-0.595195\pi\) | ||||
−0.294626 | + | 0.955613i | \(0.595195\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.46339i | 0.0929086i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.89134 | − | 5.50917i | −0.0712318 | − | 0.207487i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 17.6740i | − | 0.664699i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.7873 | 0.592906 | 0.296453 | − | 0.955047i | \(-0.404196\pi\) | ||||
0.296453 | + | 0.955047i | \(0.404196\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.28415 | 0.123165 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.6170i | 0.435060i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.3126 | − | 3.54037i | 0.385668 | − | 0.132402i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 8.91926i | − | 0.333096i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.5683 | 0.841655 | 0.420828 | − | 0.907141i | \(-0.361740\pi\) | ||||
0.420828 | + | 0.907141i | \(0.361740\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 61.1616 | 2.27778 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 16.3510i | − | 0.608099i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 29.9647 | − | 23.3230i | 1.11286 | − | 0.866196i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.79096i | − | 0.103511i | −0.998660 | − | 0.0517554i | \(-0.983518\pi\) | ||
0.998660 | − | 0.0517554i | \(-0.0164816\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38.2649 | 1.41528 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.4860i | 0.608926i | 0.952524 | + | 0.304463i | \(0.0984769\pi\) | ||||
−0.952524 | + | 0.304463i | \(0.901523\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 20.0062 | − | 6.86828i | 0.737941 | − | 0.253340i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 8.34068i | − | 0.307233i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.8894 | 0.547714 | 0.273857 | − | 0.961770i | \(-0.411701\pi\) | ||||
0.273857 | + | 0.961770i | \(0.411701\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.8831 | −0.473272 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.4301i | 1.51992i | 0.649968 | + | 0.759961i | \(0.274782\pi\) | ||||
−0.649968 | + | 0.759961i | \(0.725218\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.62263 | + | 22.2035i | 0.279271 | + | 0.813475i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.89134i | 0.361905i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.2282 | −0.592965 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.5544 | −1.11494 | −0.557472 | − | 0.830195i | \(-0.688229\pi\) | ||||
−0.557472 | + | 0.830195i | \(0.688229\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 4.22391i | − | 0.153928i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.42400 | + | 9.97359i | 0.124612 | + | 0.362976i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.433223i | 0.0157457i | 0.999969 | + | 0.00787287i | \(0.00250604\pi\) | ||||
−0.999969 | + | 0.00787287i | \(0.997494\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.48755 | 0.126590 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.9193 | 0.540823 | 0.270411 | − | 0.962745i | \(-0.412840\pi\) | ||||
0.270411 | + | 0.962745i | \(0.412840\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.9193i | 0.612518i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.56622 | + | 3.28415i | −0.345867 | + | 0.118739i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 45.0057i | 1.62506i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.3789 | 1.13155 | 0.565776 | − | 0.824559i | \(-0.308577\pi\) | ||||
0.565776 | + | 0.824559i | \(0.308577\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.6952 | 0.889375 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.4192i | 0.482656i | 0.970444 | + | 0.241328i | \(0.0775829\pi\) | ||||
−0.970444 | + | 0.241328i | \(0.922417\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.9582 | + | 10.0860i | −0.465471 | + | 0.362299i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 3.83662i | − | 0.137638i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.48036 | −0.0530395 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.41157 | −0.0505101 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.59434i | 0.271400i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.9193 | − | 6.49511i | 0.675257 | − | 0.231820i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.4846i | 1.30054i | 0.759705 | + | 0.650268i | \(0.225343\pi\) | ||||
−0.759705 | + | 0.650268i | \(0.774657\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.6628 | −0.522009 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.21438 | 0.185402 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 54.4931i | 1.93511i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.166860 | + | 0.486038i | 0.00591791 | + | 0.0172380i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.0683i | 0.923388i | 0.887039 | + | 0.461694i | \(0.152758\pi\) | ||||
−0.887039 | + | 0.461694i | \(0.847242\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.7827 | 0.416841 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.3510 | 0.436400 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.7827i | 0.415801i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.4197 | − | 30.3510i | −0.367246 | − | 1.06973i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.5381i | 0.406160i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.6212 | 1.25237 | 0.626187 | − | 0.779673i | \(-0.284615\pi\) | ||||
0.626187 | + | 0.779673i | \(0.284615\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.8935 | −1.54131 | −0.770654 | − | 0.637253i | \(-0.780071\pi\) | ||||
−0.770654 | + | 0.637253i | \(0.780071\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 5.63511i | − | 0.197632i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −33.3789 | + | 11.4592i | −1.16921 | + | 0.401398i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.0367i | 0.770966i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 20.0648 | 0.701121 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.8058 | −1.00533 | −0.502665 | − | 0.864482i | \(-0.667647\pi\) | ||||
−0.502665 | + | 0.864482i | \(0.667647\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.9585i | 0.974571i | 0.873243 | + | 0.487286i | \(0.162013\pi\) | ||||
−0.873243 | + | 0.487286i | \(0.837987\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.02792 | + | 3.89019i | 0.105419 | + | 0.135439i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 14.8634i | − | 0.516851i | −0.966031 | − | 0.258426i | \(-0.916796\pi\) | ||
0.966031 | − | 0.258426i | \(-0.0832037\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.7678 | 1.45065 | 0.725327 | − | 0.688404i | \(-0.241688\pi\) | ||||
0.725327 | + | 0.688404i | \(0.241688\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.4053 | 0.603783 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 42.7881i | 1.48252i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.6514 | − | 4.00000i | 0.403213 | − | 0.138426i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 3.28415i | − | 0.113517i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.6490 | 0.747408 | 0.373704 | − | 0.927548i | \(-0.378088\pi\) | ||||
0.373704 | + | 0.927548i | \(0.378088\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.6740 | 0.988759 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 21.7827i | − | 0.750235i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.32040 | − | 24.2361i | −0.286231 | − | 0.833746i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 40.6838i | − | 1.39791i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21.5962 | −0.741180 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.34510 | −0.114669 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.1880i | 1.68416i | 0.539350 | + | 0.842082i | \(0.318670\pi\) | ||||
−0.539350 | + | 0.842082i | \(0.681330\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.89134 | − | 5.50917i | −0.0646823 | − | 0.188410i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 2.65849i | − | 0.0908123i | −0.998969 | − | 0.0454062i | \(-0.985542\pi\) | ||
0.998969 | − | 0.0454062i | \(-0.0144582\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.57680 | 0.156158 | 0.0780792 | − | 0.996947i | \(-0.475121\pi\) | ||||
0.0780792 | + | 0.996947i | \(0.475121\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.30560 | 0.0785746 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.0218i | 1.15812i | 0.815287 | + | 0.579058i | \(0.196579\pi\) | ||||
−0.815287 | + | 0.579058i | \(0.803421\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.8649 | + | 7.50638i | −0.743430 | + | 0.255224i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 3.45963i | − | 0.117495i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.23797 | 0.109841 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.8385 | −1.41764 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 3.23797i | − | 0.109589i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.8085 | − | 37.9736i | 0.838679 | − | 1.28374i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.7563i | 0.396981i | 0.980103 | + | 0.198490i | \(0.0636039\pi\) | ||||
−0.980103 | + | 0.198490i | \(0.936396\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −32.0125 | −1.07975 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.2702 | 0.447085 | 0.223543 | − | 0.974694i | \(-0.428238\pi\) | ||||
0.223543 | + | 0.974694i | \(0.428238\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.1366i | 0.576692i | 0.957526 | + | 0.288346i | \(0.0931054\pi\) | ||||
−0.957526 | + | 0.288346i | \(0.906895\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19.2457 | + | 6.60719i | −0.646938 | + | 0.222098i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.0883i | 1.07742i | 0.842492 | + | 0.538709i | \(0.181088\pi\) | ||||
−0.842492 | + | 0.538709i | \(0.818912\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.67696 | 0.156860 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.985939 | −0.0330302 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.78562i | 0.227072i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.7438 | + | 34.2078i | 0.392551 | + | 1.14344i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 17.4943i | − | 0.584117i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.9409 | −0.831827 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.03951 | −0.0346310 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 34.3211i | − | 1.14214i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.89134 | − | 17.1606i | −0.195835 | − | 0.570436i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.4596i | 1.34344i | 0.740805 | + | 0.671720i | \(0.234444\pi\) | ||||
−0.740805 | + | 0.671720i | \(0.765556\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.35637 | 0.144492 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.0000 | −0.530104 | −0.265052 | − | 0.964234i | \(-0.585389\pi\) | ||||
−0.265052 | + | 0.964234i | \(0.585389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.75225i | 0.322752i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −23.3028 | + | 8.00000i | −0.770366 | + | 0.264472i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.7827i | 0.521190i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50.8495 | −1.67737 | −0.838685 | − | 0.544617i | \(-0.816675\pi\) | ||||
−0.838685 | + | 0.544617i | \(0.816675\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.13659 | −0.0374519 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.08074i | 0.233065i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.90425 | − | 3.73129i | −0.0954911 | − | 0.122684i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.0754i | 0.495141i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.6461 | −0.414904 | −0.207452 | − | 0.978245i | \(-0.566517\pi\) | ||||
−0.207452 | + | 0.978245i | \(0.566517\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.6416 | −0.807596 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.13659i | 0.168164i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.43171 | + | 3.23797i | −0.308450 | + | 0.105893i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 40.7971i | − | 1.33278i | −0.745603 | − | 0.666391i | \(-0.767838\pi\) | ||
0.745603 | − | 0.666391i | \(-0.232162\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.0762 | 0.753063 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.1086 | 0.459928 | 0.229964 | − | 0.973199i | \(-0.426139\pi\) | ||||
0.229964 | + | 0.973199i | \(0.426139\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.01022i | − | 0.0654619i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.94567 | + | 8.58028i | 0.0958226 | + | 0.279117i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 45.8385i | − | 1.48955i | −0.667315 | − | 0.744776i | \(-0.732556\pi\) | ||
0.667315 | − | 0.744776i | \(-0.267444\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 59.1043 | 1.91861 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.66152 | −0.0538785 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.9104i | 0.709747i | 0.934914 | + | 0.354873i | \(0.115476\pi\) | ||||
−0.934914 | + | 0.354873i | \(0.884524\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.0929 | + | 52.7019i | 0.585473 | + | 1.70539i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.48755i | 0.242038i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 71.0529 | 2.29442 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.2144 | −0.652077 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 4.00000i | − | 0.128898i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.19846 | + | 0.754747i | −0.0707710 | + | 0.0242962i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 14.0359i | − | 0.451364i | −0.974201 | − | 0.225682i | \(-0.927539\pi\) | ||
0.974201 | − | 0.225682i | \(-0.0724610\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.7827 | 0.378514 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.6494 | −0.694762 | −0.347381 | − | 0.937724i | \(-0.612929\pi\) | ||||
−0.347381 | + | 0.937724i | \(0.612929\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 68.4068i | 2.19302i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 19.5140 | − | 15.1887i | 0.624947 | − | 0.486427i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 6.60225i | − | 0.211225i | −0.994407 | − | 0.105612i | \(-0.966320\pi\) | ||
0.994407 | − | 0.105612i | \(-0.0336802\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.1773 | 0.389188 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.17034 | −0.133149 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 53.8600i | − | 1.71787i | −0.512087 | − | 0.858934i | \(-0.671127\pi\) | ||
0.512087 | − | 0.858934i | \(-0.328873\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.4332 | − | 7.01486i | 0.651057 | − | 0.223512i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 10.5683i | − | 0.336393i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −29.9242 | −0.951534 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.7129 | −0.943861 | −0.471931 | − | 0.881636i | \(-0.656443\pi\) | ||||
−0.471931 | + | 0.881636i | \(0.656443\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.9077i | 0.822156i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.7479 | − | 48.7842i | −0.530945 | − | 1.54656i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 16.6506i | − | 0.527328i | −0.964615 | − | 0.263664i | \(-0.915069\pi\) | ||
0.964615 | − | 0.263664i | \(-0.0849311\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.945668 | 0.0299196 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))