Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,2,Mod(1009,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("1440.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.d (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: | \(11.4984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.839056.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 6x^{4} + 8x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1009.5 | ||
Root | \(2.02852i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1440.1009 |
Dual form | 1440.2.d.f.1009.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.11491 | − | 0.726062i | 0.945815 | − | 0.324705i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.05705i | − | 1.53342i | −0.641994 | − | 0.766710i | \(-0.721893\pi\) | ||
0.641994 | − | 0.766710i | \(-0.278107\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.985939i | 0.297272i | 0.988892 | + | 0.148636i | \(0.0474882\pi\) | ||||
−0.988892 | + | 0.148636i | \(0.952512\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.94567 | 1.37168 | 0.685841 | − | 0.727752i | \(-0.259435\pi\) | ||||
0.685841 | + | 0.727752i | \(0.259435\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.52323i | 1.09704i | 0.836136 | + | 0.548522i | \(0.184809\pi\) | ||||
−0.836136 | + | 0.548522i | \(0.815191\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.60492i | − | 0.597610i | −0.954314 | − | 0.298805i | \(-0.903412\pi\) | ||
0.954314 | − | 0.298805i | \(-0.0965881\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 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 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.59434i | − | 1.41023i | −0.709091 | − | 0.705117i | \(-0.750895\pi\) | ||
0.709091 | − | 0.705117i | \(-0.249105\pi\) | |||||||
\(30\) | 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 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.94567 | − | 8.58028i | −0.497909 | − | 1.45033i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.945668 | −0.155467 | −0.0777334 | − | 0.996974i | \(-0.524768\pi\) | ||||
−0.0777334 | + | 0.996974i | \(0.524768\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.568295 | −0.0887527 | −0.0443763 | − | 0.999015i | \(-0.514130\pi\) | ||||
−0.0443763 | + | 0.999015i | \(0.514130\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.45963 | −1.29008 | −0.645041 | − | 0.764148i | \(-0.723160\pi\) | ||||
−0.645041 | + | 0.764148i | \(0.723160\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 2.60492i | − | 0.379967i | −0.981787 | − | 0.189984i | \(-0.939157\pi\) | ||
0.981787 | − | 0.189984i | \(-0.0608435\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.45963 | −1.35138 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.229815 | −0.0315675 | −0.0157838 | − | 0.999875i | \(-0.505024\pi\) | ||||
−0.0157838 | + | 0.999875i | \(0.505024\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.715853 | + | 2.08517i | 0.0965256 | + | 0.281164i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 9.10003i | − | 1.18472i | −0.805672 | − | 0.592362i | \(-0.798196\pi\) | ||
0.805672 | − | 0.592362i | \(-0.201804\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 11.0183i | − | 1.41075i | −0.708832 | − | 0.705377i | \(-0.750778\pi\) | ||
0.708832 | − | 0.705377i | \(-0.249222\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.4596 | − | 3.59086i | 1.29736 | − | 0.445392i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.45963 | 1.03351 | 0.516754 | − | 0.856134i | \(-0.327140\pi\) | ||||
0.516754 | + | 0.856134i | \(0.327140\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | \(0.246533\pi\) | ||||
−0.714767 | + | 0.699363i | \(0.753467\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.28415 | −0.369495 | −0.184748 | − | 0.982786i | \(-0.559147\pi\) | ||||
−0.184748 | + | 0.982786i | \(0.559147\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.89134 | 1.08572 | 0.542858 | − | 0.839825i | \(-0.317342\pi\) | ||||
0.542858 | + | 0.839825i | \(0.317342\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.28415 | + | 9.56622i | 0.356216 | + | 1.03760i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.3510 | −1.30920 | −0.654600 | − | 0.755976i | \(-0.727163\pi\) | ||||
−0.654600 | + | 0.755976i | \(0.727163\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 20.0648i | − | 2.10336i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 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 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.35637i | 0.433475i | 0.976230 | + | 0.216738i | \(0.0695416\pi\) | ||||
−0.976230 | + | 0.216738i | \(0.930458\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.0754i | 1.48542i | 0.669612 | + | 0.742711i | \(0.266460\pi\) | ||||
−0.669612 | + | 0.742711i | \(0.733540\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 4.17034i | − | 0.399446i | −0.979852 | − | 0.199723i | \(-0.935996\pi\) | ||
0.979852 | − | 0.199723i | \(-0.0640042\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.28526i | 0.120907i | 0.998171 | + | 0.0604537i | \(0.0192548\pi\) | ||||
−0.998171 | + | 0.0604537i | \(0.980745\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.56829 | + | 7.48105i | 0.239495 | + | 0.697611i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.3510 | 1.68223 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.0279 | 0.911630 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.11491 | − | 9.35991i | 0.546934 | − | 0.837176i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.15280i | − | 0.102294i | −0.998691 | − | 0.0511472i | \(-0.983712\pi\) | ||
0.998691 | − | 0.0511472i | \(-0.0162878\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.89019i | 0.339887i | 0.985454 | + | 0.169944i | \(0.0543586\pi\) | ||||
−0.985454 | + | 0.169944i | \(0.945641\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.5683 | −0.916387 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 17.5135i | − | 1.49628i | −0.663544 | − | 0.748138i | \(-0.730948\pi\) | ||
0.663544 | − | 0.748138i | \(-0.269052\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.8612i | 1.43015i | 0.699047 | + | 0.715076i | \(0.253608\pi\) | ||||
−0.699047 | + | 0.715076i | \(0.746392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.87613i | 0.407762i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.51396 | − | 16.0613i | −0.457910 | − | 1.33382i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 10.4986i | − | 0.860078i | −0.902810 | − | 0.430039i | \(-0.858500\pi\) | ||
0.902810 | − | 0.430039i | \(-0.141500\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.71585 | −0.383771 | −0.191885 | − | 0.981417i | \(-0.561460\pi\) | ||||
−0.191885 | + | 0.981417i | \(0.561460\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.94567 | − | 2.38449i | 0.557889 | − | 0.191527i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.94567 | −0.713942 | −0.356971 | − | 0.934115i | \(-0.616191\pi\) | ||||
−0.356971 | + | 0.934115i | \(0.616191\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.3510 | 1.13101 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.7827 | 1.23619 | 0.618097 | − | 0.786102i | \(-0.287904\pi\) | ||||
0.618097 | + | 0.786102i | \(0.287904\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 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 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.3385 | −0.786020 | −0.393010 | − | 0.919534i | \(-0.628566\pi\) | ||||
−0.393010 | + | 0.919534i | \(0.628566\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.4596 | − | 16.0078i | −0.941860 | − | 1.21007i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.1746i | 1.20895i | 0.796625 | + | 0.604474i | \(0.206617\pi\) | ||||
−0.796625 | + | 0.604474i | \(0.793383\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 8.11409i | − | 0.603116i | −0.953448 | − | 0.301558i | \(-0.902493\pi\) | ||
0.953448 | − | 0.301558i | \(-0.0975067\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.00000 | + | 0.686614i | −0.147043 | + | 0.0504808i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.45963 | −0.326120 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.9193 | −1.80309 | −0.901547 | − | 0.432681i | \(-0.857568\pi\) | ||||
−0.901547 | + | 0.432681i | \(0.857568\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.03951i | 0.0748254i | 0.999300 | + | 0.0374127i | \(0.0119116\pi\) | ||||
−0.999300 | + | 0.0374127i | \(0.988088\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.66152 | −0.688355 | −0.344177 | − | 0.938905i | \(-0.611842\pi\) | ||||
−0.344177 | + | 0.938905i | \(0.611842\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.0668 | 1.63516 | 0.817582 | − | 0.575813i | \(-0.195314\pi\) | ||||
0.817582 | + | 0.575813i | \(0.195314\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −30.8106 | −2.16248 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.20189 | + | 0.412617i | −0.0839437 | + | 0.0288184i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.56829 | 0.177653 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.44154i | 0.443454i | 0.975109 | + | 0.221727i | \(0.0711694\pi\) | ||||
−0.975109 | + | 0.221727i | \(0.928831\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.8913 | + | 6.14222i | −1.22018 | + | 0.418896i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 13.3239i | − | 0.904488i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.3704i | 1.50480i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.9796i | 1.20401i | 0.798494 | + | 0.602003i | \(0.205630\pi\) | ||||
−0.798494 | + | 0.602003i | \(0.794370\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.02792 | 0.466460 | 0.233230 | − | 0.972422i | \(-0.425071\pi\) | ||||
0.233230 | + | 0.972422i | \(0.425071\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.17034i | 0.275584i | 0.990461 | + | 0.137792i | \(0.0440005\pi\) | ||||
−0.990461 | + | 0.137792i | \(0.955999\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.9894i | 1.57160i | 0.618483 | + | 0.785799i | \(0.287748\pi\) | ||||
−0.618483 | + | 0.785799i | \(0.712252\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.89134 | − | 5.50917i | −0.123377 | − | 0.359379i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.91926 | 0.576939 | 0.288469 | − | 0.957489i | \(-0.406854\pi\) | ||||
0.288469 | + | 0.957489i | \(0.406854\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.3510 | −1.05326 | −0.526629 | − | 0.850095i | \(-0.676544\pi\) | ||||
−0.526629 | + | 0.850095i | \(0.676544\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −20.0062 | + | 6.86828i | −1.27815 | + | 0.438798i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 12.8831i | − | 0.819731i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.22391i | 0.266611i | 0.991075 | + | 0.133305i | \(0.0425591\pi\) | ||||
−0.991075 | + | 0.133305i | \(0.957441\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.48755 | −0.219261 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.6952i | 1.54044i | 0.637777 | + | 0.770221i | \(0.279854\pi\) | ||||
−0.637777 | + | 0.770221i | \(0.720146\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.83662i | 0.238396i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.5381i | 0.703490i | 0.936096 | + | 0.351745i | \(0.114412\pi\) | ||||
−0.936096 | + | 0.351745i | \(0.885588\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.63511 | −0.342309 | −0.171154 | − | 0.985244i | \(-0.554750\pi\) | ||||
−0.171154 | + | 0.985244i | \(0.554750\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.02792 | + | 3.89019i | 0.182591 | + | 0.234587i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.4053 | 1.04578 | 0.522892 | − | 0.852399i | \(-0.324853\pi\) | ||||
0.522892 | + | 0.852399i | \(0.324853\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.7827 | −1.29945 | −0.649723 | − | 0.760171i | \(-0.725115\pi\) | ||||
−0.649723 | + | 0.760171i | \(0.725115\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.5962 | −1.28376 | −0.641881 | − | 0.766804i | \(-0.721846\pi\) | ||||
−0.641881 | + | 0.766804i | \(0.721846\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.30560i | 0.136095i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.45963 | −0.203508 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 32.0125 | 1.87019 | 0.935095 | − | 0.354398i | \(-0.115314\pi\) | ||||
0.935095 | + | 0.354398i | \(0.115314\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.60719 | − | 19.2457i | −0.384685 | − | 1.12053i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.4943i | 1.01172i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 34.3211i | 1.97824i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.00000 | − | 23.3028i | −0.458079 | − | 1.33431i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.13659 | 0.0648686 | 0.0324343 | − | 0.999474i | \(-0.489674\pi\) | ||||
0.0324343 | + | 0.999474i | \(0.489674\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 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 | \(0.226142\pi\) | ||||
−0.758071 | + | 0.652172i | \(0.773858\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.66152 | −0.0933203 | −0.0466601 | − | 0.998911i | \(-0.514858\pi\) | ||||
−0.0466601 | + | 0.998911i | \(0.514858\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.48755 | 0.419223 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.7827 | 0.655605 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.5140 | − | 15.1887i | 1.08244 | − | 0.842516i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.5683 | −0.582649 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.9077i | 1.42402i | 0.702171 | + | 0.712008i | \(0.252214\pi\) | ||||
−0.702171 | + | 0.712008i | \(0.747786\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.23797i | 0.175346i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.97884i | 0.538806i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.0279 | −1.23620 | −0.618102 | − | 0.786098i | \(-0.712098\pi\) | ||||
−0.618102 | + | 0.786098i | \(0.712098\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.4380i | 1.14755i | 0.819012 | + | 0.573776i | \(0.194522\pi\) | ||||
−0.819012 | + | 0.573776i | \(0.805478\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.52323i | 0.240747i | 0.992729 | + | 0.120374i | \(0.0384093\pi\) | ||||
−0.992729 | + | 0.120374i | \(0.961591\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.02792 | − | 1.03951i | 0.160706 | − | 0.0551713i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.67696 | + | 25.2747i | 0.454173 | + | 1.32294i | ||||
\(366\) | 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 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.932371i | 0.0484063i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.0823 | −1.55760 | −0.778800 | − | 0.627272i | \(-0.784171\pi\) | ||||
−0.778800 | + | 0.627272i | \(0.784171\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 37.5591i | − | 1.93439i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 33.6881i | − | 1.73044i | −0.501392 | − | 0.865220i | \(-0.667179\pi\) | ||
0.501392 | − | 0.865220i | \(-0.332821\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 5.17545i | − | 0.264453i | −0.991220 | − | 0.132227i | \(-0.957787\pi\) | ||
0.991220 | − | 0.132227i | \(-0.0422127\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.45963 | − | 2.90425i | 0.431143 | − | 0.148014i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.6408i | 0.843722i | 0.906660 | + | 0.421861i | \(0.138623\pi\) | ||||
−0.906660 | + | 0.421861i | \(0.861377\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.94567 | + | 2.38449i | −0.349474 | + | 0.119977i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.4332 | 1.02551 | 0.512757 | − | 0.858534i | \(-0.328624\pi\) | ||||
0.512757 | + | 0.858534i | \(0.328624\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.56829 | 0.228130 | 0.114065 | − | 0.993473i | \(-0.463613\pi\) | ||||
0.114065 | + | 0.993473i | \(0.463613\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.2423 | 0.809087 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.932371i | − | 0.0462159i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.8913 | −0.983563 | −0.491782 | − | 0.870719i | \(-0.663654\pi\) | ||||
−0.491782 | + | 0.870719i | \(0.663654\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −36.9193 | −1.81668 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.9193 | − | 7.18172i | 1.02689 | − | 0.352537i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 0.387288i | − | 0.0189203i | −0.999955 | − | 0.00946013i | \(-0.996989\pi\) | ||
0.999955 | − | 0.00946013i | \(-0.00301130\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.0578i | 0.587664i | 0.955857 | + | 0.293832i | \(0.0949306\pi\) | ||||
−0.955857 | + | 0.293832i | \(0.905069\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.8913 | + | 17.8472i | 0.673829 | + | 0.865715i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −44.7019 | −2.16328 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 40.4068 | 1.94633 | 0.973164 | − | 0.230113i | \(-0.0739096\pi\) | ||||
0.973164 | + | 0.230113i | \(0.0739096\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.1859i | 1.73898i | 0.493949 | + | 0.869491i | \(0.335553\pi\) | ||||
−0.493949 | + | 0.869491i | \(0.664447\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.21438 | 0.440783 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.4178 | −1.21312 | −0.606562 | − | 0.795036i | \(-0.707452\pi\) | ||||
−0.606562 | + | 0.795036i | \(0.707452\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.02792 | −0.333907 | −0.166953 | − | 0.985965i | \(-0.553393\pi\) | ||||
−0.166953 | + | 0.985965i | \(0.553393\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −26.1212 | + | 8.96757i | −1.23826 | + | 0.425103i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.00000 | −0.0943858 | −0.0471929 | − | 0.998886i | \(-0.515028\pi\) | ||||
−0.0471929 | + | 0.998886i | \(0.515028\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 0.560304i | − | 0.0263837i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.5683 | − | 42.4352i | −0.682972 | − | 1.98939i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 25.2747i | − | 1.18230i | −0.806562 | − | 0.591149i | \(-0.798674\pi\) | ||
0.806562 | − | 0.591149i | \(-0.201326\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 41.0902i | − | 1.91376i | −0.290479 | − | 0.956881i | \(-0.593815\pi\) | ||
0.290479 | − | 0.956881i | \(-0.406185\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.2106i | 0.613951i | 0.951717 | + | 0.306975i | \(0.0993169\pi\) | ||||
−0.951717 | + | 0.306975i | \(0.900683\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.89134 | −0.0875206 | −0.0437603 | − | 0.999042i | \(-0.513934\pi\) | ||||
−0.0437603 | + | 0.999042i | \(0.513934\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 34.3211i | − | 1.58480i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 8.34068i | − | 0.383505i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.00000 | − | 10.2782i | −0.367065 | − | 0.471594i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.4876 | −1.43870 | −0.719352 | − | 0.694646i | \(-0.755561\pi\) | ||||
−0.719352 | + | 0.694646i | \(0.755561\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.67696 | −0.213251 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.35097 | + | 6.84800i | 0.106752 | + | 0.310952i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.9964i | 0.588922i | 0.955664 | + | 0.294461i | \(0.0951401\pi\) | ||||
−0.955664 | + | 0.294461i | \(0.904860\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 14.9085i | − | 0.672812i | −0.941717 | − | 0.336406i | \(-0.890788\pi\) | ||
0.941717 | − | 0.336406i | \(-0.109212\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 34.3510 | 1.54709 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 5.80850i | − | 0.260547i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.6599i | 1.59636i | 0.602420 | + | 0.798179i | \(0.294203\pi\) | ||||
−0.602420 | + | 0.798179i | \(0.705797\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.7366i | 0.608862i | 0.952534 | + | 0.304431i | \(0.0984663\pi\) | ||||
−0.952534 | + | 0.304431i | \(0.901534\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 48.4846 | 2.14483 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.9457 | + | 31.8831i | 0.482324 | + | 1.40494i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.56829 | 0.112953 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.9193 | 1.35460 | 0.677299 | − | 0.735708i | \(-0.263150\pi\) | ||||
0.677299 | + | 0.735708i | \(0.263150\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.8385 | −0.954932 | −0.477466 | − | 0.878650i | \(-0.658445\pi\) | ||||
−0.477466 | + | 0.878650i | \(0.658445\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.8550i | 0.647092i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.4876 | 0.455981 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.81060 | −0.121740 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.45963 | − | 2.90425i | 0.365742 | − | 0.125562i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 9.32662i | − | 0.401726i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 24.3423i | − | 1.04656i | −0.852162 | − | 0.523278i | \(-0.824709\pi\) | ||
0.852162 | − | 0.523278i | \(-0.175291\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.02792 | − | 8.81988i | −0.129702 | − | 0.377802i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.3789 | 1.42718 | 0.713589 | − | 0.700564i | \(-0.247068\pi\) | ||||
0.713589 | + | 0.700564i | \(0.247068\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.7827 | −0.842770 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.3239i | 0.566592i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.5808 | 1.29575 | 0.647875 | − | 0.761747i | \(-0.275658\pi\) | ||||
0.647875 | + | 0.761747i | \(0.275658\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.8385 | −1.76958 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.02792 | 0.296192 | 0.148096 | − | 0.988973i | \(-0.452686\pi\) | ||||
0.148096 | + | 0.988973i | \(0.452686\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.933181 | + | 2.71821i | 0.0392592 | + | 0.114356i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.3510 | 1.02085 | 0.510423 | − | 0.859924i | \(-0.329489\pi\) | ||||
0.510423 | + | 0.859924i | \(0.329489\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0992i | 0.841125i | 0.907263 | + | 0.420563i | \(0.138167\pi\) | ||||
−0.907263 | + | 0.420563i | \(0.861833\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 40.1296i | − | 1.66486i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 0.226584i | − | 0.00938413i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.21733 | 0.339165 | 0.169583 | − | 0.985516i | \(-0.445758\pi\) | ||||
0.169583 | + | 0.985516i | \(0.445758\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 8.55495i | − | 0.352501i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.76120i | 0.318714i | 0.987221 | + | 0.159357i | \(0.0509421\pi\) | ||||
−0.987221 | + | 0.159357i | \(0.949058\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 38.8106 | − | 13.3239i | 1.59108 | − | 0.546228i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 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 | \(-0.779503\pi\) | ||||
−0.769516 | + | 0.638627i | \(0.779503\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.2081 | − | 7.28090i | 0.862233 | − | 0.296010i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 0.113292i | − | 0.00459837i | −0.999997 | − | 0.00229919i | \(-0.999268\pi\) | ||
0.999997 | − | 0.00229919i | \(-0.000731854\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 12.8831i | − | 0.521194i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.703366 | −0.0284087 | −0.0142044 | − | 0.999899i | \(-0.504522\pi\) | ||||
−0.0142044 | + | 0.999899i | \(0.504522\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.4809i | 0.985564i | 0.870153 | + | 0.492782i | \(0.164020\pi\) | ||||
−0.870153 | + | 0.492782i | \(0.835980\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 39.4966i | − | 1.58750i | −0.608243 | − | 0.793751i | \(-0.708126\pi\) | ||
0.608243 | − | 0.793751i | \(-0.291874\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 50.1084i | 2.00755i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.13659 | − | 24.2351i | 0.245464 | − | 0.969406i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 4.27748i | − | 0.170554i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.3400 | −0.690294 | −0.345147 | − | 0.938549i | \(-0.612171\pi\) | ||||
−0.345147 | + | 0.938549i | \(0.612171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.837003 | − | 2.43806i | −0.0332155 | − | 0.0967516i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −46.7842 | −1.85366 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.7019 | −1.52863 | −0.764317 | − | 0.644840i | \(-0.776924\pi\) | ||||
−0.764317 | + | 0.644840i | \(0.776924\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.13659 | 0.0448227 | 0.0224113 | − | 0.999749i | \(-0.492866\pi\) | ||||
0.0224113 | + | 0.999749i | \(0.492866\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 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 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.74226 | −0.342111 | −0.171056 | − | 0.985261i | \(-0.554718\pi\) | ||||
−0.171056 | + | 0.985261i | \(0.554718\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.82452 | + | 8.22739i | 0.110363 | + | 0.321471i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 35.5336i | − | 1.38419i | −0.721804 | − | 0.692097i | \(-0.756687\pi\) | ||
0.721804 | − | 0.692097i | \(-0.243313\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.3028i | 0.906373i | 0.891416 | + | 0.453186i | \(0.149713\pi\) | ||||
−0.891416 | + | 0.453186i | \(0.850287\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.3510 | + | 7.67324i | −0.866733 | + | 0.297555i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.8634 | 1.04016 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.3076 | −0.934217 | −0.467109 | − | 0.884200i | \(-0.654704\pi\) | ||||
−0.467109 | + | 0.884200i | \(0.654704\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.1366 | 0.504136 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.5933 | 1.47673 | 0.738365 | − | 0.674401i | \(-0.235598\pi\) | ||||
0.738365 | + | 0.674401i | \(0.235598\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.7159 | − | 37.0393i | −0.485848 | − | 1.41520i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.13659 | −0.0433006 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.4090i | 0.510102i | 0.966928 | + | 0.255051i | \(0.0820923\pi\) | ||||
−0.966928 | + | 0.255051i | \(0.917908\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.2423 | + | 35.6599i | 0.464377 | + | 1.35266i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 2.57053i | − | 0.0973657i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 15.6013i | − | 0.589253i | −0.955613 | − | 0.294626i | \(-0.904805\pi\) | ||
0.955613 | − | 0.294626i | \(-0.0951952\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.46339i | 0.0929086i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.6740 | 0.664699 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.7873i | 0.592906i | 0.955047 | + | 0.296453i | \(0.0958038\pi\) | ||||
−0.955047 | + | 0.296453i | \(0.904196\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.6170i | 0.435060i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.54037 | + | 10.3126i | 0.132402 | + | 0.385668i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.5683 | −0.841655 | −0.420828 | − | 0.907141i | \(-0.638260\pi\) | ||||
−0.420828 | + | 0.907141i | \(0.638260\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 61.1616 | 2.27778 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.3230 | − | 29.9647i | −0.866196 | − | 1.11286i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.79096i | 0.103511i | 0.998660 | + | 0.0517554i | \(0.0164816\pi\) | ||||
−0.998660 | + | 0.0517554i | \(0.983518\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 38.2649i | − | 1.41528i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.4860 | 0.608926 | 0.304463 | − | 0.952524i | \(-0.401523\pi\) | ||||
0.304463 | + | 0.952524i | \(0.401523\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.34068i | 0.307233i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 14.8894i | − | 0.547714i | −0.961770 | − | 0.273857i | \(-0.911701\pi\) | ||
0.961770 | − | 0.273857i | \(-0.0882995\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 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 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 16.2282i | − | 0.592965i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.5544 | −1.11494 | −0.557472 | − | 0.830195i | \(-0.688229\pi\) | ||||
−0.557472 | + | 0.830195i | \(0.688229\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.97359 | + | 3.42400i | −0.362976 | + | 0.124612i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.433223 | −0.0157457 | −0.00787287 | − | 0.999969i | \(-0.502506\pi\) | ||||
−0.00787287 | + | 0.999969i | \(0.502506\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.9193 | 0.540823 | 0.270411 | − | 0.962745i | \(-0.412840\pi\) | ||||
0.270411 | + | 0.962745i | \(0.412840\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.9193 | −0.612518 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.4192 | 0.482656 | 0.241328 | − | 0.970444i | \(-0.422417\pi\) | ||||
0.241328 | + | 0.970444i | \(0.422417\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.9582 | − | 10.0860i | 0.465471 | − | 0.362299i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.48036i | 0.0530395i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.41157i | 0.0505101i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.9193 | + | 6.49511i | −0.675257 | + | 0.231820i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.4846 | 1.30054 | 0.650268 | − | 0.759705i | \(-0.274657\pi\) | ||||
0.650268 | + | 0.759705i | \(0.274657\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.21438 | 0.185402 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 54.4931i | − | 1.93511i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.0683 | −0.923388 | −0.461694 | − | 0.887039i | \(-0.652758\pi\) | ||||
−0.461694 | + | 0.887039i | \(0.652758\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.7827 | 0.416841 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.7827 | −0.415801 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 30.3510 | − | 10.4197i | 1.06973 | − | 0.367246i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.6212 | 1.25237 | 0.626187 | − | 0.779673i | \(-0.284615\pi\) | ||||
0.626187 | + | 0.779673i | \(0.284615\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 43.8935i | − | 1.54131i | −0.637253 | − | 0.770654i | \(-0.719929\pi\) | ||
0.637253 | − | 0.770654i | \(-0.280071\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 33.3789 | − | 11.4592i | 1.16921 | − | 0.401398i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.0367i | 0.770966i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.8058i | 1.00533i | 0.864482 | + | 0.502665i | \(0.167647\pi\) | ||||
−0.864482 | + | 0.502665i | \(0.832353\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 27.9585i | − | 0.974571i | −0.873243 | − | 0.487286i | \(-0.837987\pi\) | ||
0.873243 | − | 0.487286i | \(-0.162013\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.8634 | −0.516851 | −0.258426 | − | 0.966031i | \(-0.583204\pi\) | ||||
−0.258426 | + | 0.966031i | \(0.583204\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 41.7678i | − | 1.45065i | −0.688404 | − | 0.725327i | \(-0.741688\pi\) | ||
0.688404 | − | 0.725327i | \(-0.258312\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 42.7881i | − | 1.48252i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.00000 | − | 11.6514i | −0.138426 | − | 0.403213i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24.2361 | − | 8.32040i | 0.833746 | − | 0.286231i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 40.6838i | − | 1.39791i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 3.34510i | − | 0.114669i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −49.1880 | −1.68416 | −0.842082 | − | 0.539350i | \(-0.818670\pi\) | ||||
−0.842082 | + | 0.539350i | \(0.818670\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 2.65849i | − | 0.0908123i | −0.998969 | − | 0.0454062i | \(-0.985542\pi\) | ||
0.998969 | − | 0.0454062i | \(-0.0144582\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.57680i | 0.156158i | 0.996947 | + | 0.0780792i | \(0.0248787\pi\) | ||||
−0.996947 | + | 0.0780792i | \(0.975121\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 34.0218i | − | 1.15812i | −0.815287 | − | 0.579058i | \(-0.803421\pi\) | ||
0.815287 | − | 0.579058i | \(-0.196579\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.8649 | + | 7.50638i | −0.743430 | + | 0.255224i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 3.23797i | − | 0.109841i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 41.8385 | 1.41764 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −37.9736 | − | 24.8085i | −1.28374 | − | 0.838679i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.7563 | 0.396981 | 0.198490 | − | 0.980103i | \(-0.436396\pi\) | ||||
0.198490 | + | 0.980103i | \(0.436396\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.2702 | −0.447085 | −0.223543 | − | 0.974694i | \(-0.571762\pi\) | ||||
−0.223543 | + | 0.974694i | \(0.571762\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.1366 | 0.576692 | 0.288346 | − | 0.957526i | \(-0.406895\pi\) | ||||
0.288346 | + | 0.957526i | \(0.406895\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 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 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.78562 | −0.227072 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.7438 | + | 34.2078i | 0.392551 | + | 1.14344i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 24.9409i | − | 0.831827i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.03951i | − | 0.0346310i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.89134 | − | 17.1606i | −0.195835 | − | 0.570436i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.4596 | −1.34344 | −0.671720 | − | 0.740805i | \(-0.734444\pi\) | ||||
−0.671720 | + | 0.740805i | \(0.734444\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.0000 | 0.530104 | 0.265052 | − | 0.964234i | \(-0.414611\pi\) | ||||
0.265052 | + | 0.964234i | \(0.414611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.75225i | 0.322752i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.7827 | 0.521190 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.8495 | 1.67737 | 0.838685 | − | 0.544617i | \(-0.183325\pi\) | ||||
0.838685 | + | 0.544617i | \(0.183325\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.08074 | 0.233065 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.73129 | + | 2.90425i | −0.122684 | + | 0.0954911i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.6461 | 0.414904 | 0.207452 | − | 0.978245i | \(-0.433483\pi\) | ||||
0.207452 | + | 0.978245i | \(0.433483\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.6416i | 0.807596i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.43171 | + | 3.23797i | −0.308450 | + | 0.105893i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.7971i | 1.33278i | 0.745603 | + | 0.666391i | \(0.232162\pi\) | ||||
−0.745603 | + | 0.666391i | \(0.767838\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.1086i | 0.459928i | 0.973199 | + | 0.229964i | \(0.0738608\pi\) | ||||
−0.973199 | + | 0.229964i | \(0.926139\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.01022i | − | 0.0654619i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45.8385 | 1.48955 | 0.744776 | − | 0.667315i | \(-0.232556\pi\) | ||||
0.744776 | + | 0.667315i | \(0.232556\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 59.1043i | 1.91861i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.9104i | 0.709747i | 0.934914 | + | 0.354873i | \(0.115476\pi\) | ||||
−0.934914 | + | 0.354873i | \(0.884524\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −52.7019 | + | 18.0929i | −1.70539 | + | 0.585473i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −71.0529 | −2.29442 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.2144 | −0.652077 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.754747 | + | 2.19846i | 0.0242962 | + | 0.0707710i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.0359i | 0.451364i | 0.974201 | + | 0.225682i | \(0.0724610\pi\) | ||||
−0.974201 | + | 0.225682i | \(0.927539\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.6494i | 0.694762i | 0.937724 | + | 0.347381i | \(0.112929\pi\) | ||||
−0.937724 | + | 0.347381i | \(0.887071\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 68.4068 | 2.19302 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.60225i | 0.211225i | 0.994407 | + | 0.105612i | \(0.0336802\pi\) | ||||
−0.994407 | + | 0.105612i | \(0.966320\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 12.1773i | − | 0.389188i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 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 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 29.9242i | − | 0.951534i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.7129 | −0.943861 | −0.471931 | − | 0.881636i | \(-0.656443\pi\) | ||||
−0.471931 | + | 0.881636i | \(0.656443\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 48.7842 | − | 16.7479i | 1.54656 | − | 0.530945i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.6506 | 0.527328 | 0.263664 | − | 0.964615i | \(-0.415069\pi\) | ||||
0.263664 | + | 0.964615i | \(0.415069\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))