Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(949,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.949");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.l (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(0.500000 - 1.41036i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.961 |
Dual form | 1764.2.l.f.949.1 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.09097 | − | 1.34528i | −0.629873 | − | 0.776698i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.239123 | −0.106939 | −0.0534696 | − | 0.998569i | \(-0.517028\pi\) | ||||
−0.0534696 | + | 0.998569i | \(0.517028\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.619562 | + | 2.93533i | −0.206521 | + | 0.978442i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.12476 | −1.54517 | −0.772587 | − | 0.634909i | \(-0.781038\pi\) | ||||
−0.772587 | + | 0.634909i | \(0.781038\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.44282 | − | 4.23109i | −0.677516 | − | 1.17349i | −0.975727 | − | 0.218993i | \(-0.929723\pi\) |
0.298210 | − | 0.954500i | \(-0.403610\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.260877 | + | 0.321688i | 0.0673581 | + | 0.0830595i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.85185 | + | 3.20750i | 0.449139 | + | 0.777932i | 0.998330 | − | 0.0577649i | \(-0.0183974\pi\) |
−0.549191 | + | 0.835697i | \(0.685064\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.83009 | − | 3.16982i | 0.419853 | − | 0.727206i | −0.576072 | − | 0.817399i | \(-0.695415\pi\) |
0.995924 | + | 0.0901932i | \(0.0287484\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.42107 | 1.54740 | 0.773700 | − | 0.633553i | \(-0.218404\pi\) | ||||
0.773700 | + | 0.633553i | \(0.218404\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.94282 | −0.988564 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.62476 | − | 2.36887i | 0.890036 | − | 0.455890i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.73229 | + | 3.00041i | −0.321678 | + | 0.557162i | −0.980834 | − | 0.194844i | \(-0.937580\pi\) |
0.659157 | + | 0.752006i | \(0.270913\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.358685 | + | 0.621261i | −0.0644217 | + | 0.111582i | −0.896437 | − | 0.443171i | \(-0.853854\pi\) |
0.832016 | + | 0.554752i | \(0.187187\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.59097 | + | 6.89425i | 0.973263 | + | 1.20013i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.30150 | + | 3.98632i | −0.378365 | + | 0.655348i | −0.990825 | − | 0.135154i | \(-0.956847\pi\) |
0.612459 | + | 0.790502i | \(0.290180\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.02696 | + | 7.90228i | −0.484701 | + | 1.26538i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.80150 | + | 4.85235i | 0.437522 | + | 0.757810i | 0.997498 | − | 0.0706992i | \(-0.0225230\pi\) |
−0.559976 | + | 0.828509i | \(0.689190\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.24433 | + | 10.8155i | −0.952251 | + | 1.64935i | −0.211713 | + | 0.977332i | \(0.567904\pi\) |
−0.740538 | + | 0.672015i | \(0.765429\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.148152 | − | 0.701905i | 0.0220851 | − | 0.104634i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.16991 | + | 3.75839i | 0.316513 | + | 0.548217i | 0.979758 | − | 0.200186i | \(-0.0641545\pi\) |
−0.663245 | + | 0.748403i | \(0.730821\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.29467 | − | 5.99054i | 0.321318 | − | 0.838844i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.471410 | + | 0.816506i | 0.0647531 | + | 0.112156i | 0.896584 | − | 0.442873i | \(-0.146041\pi\) |
−0.831831 | + | 0.555029i | \(0.812707\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.22545 | 0.165240 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.26088 | + | 0.996189i | −0.829273 | + | 0.131948i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.78947 | − | 6.56355i | 0.493347 | − | 0.854501i | −0.506624 | − | 0.862167i | \(-0.669107\pi\) |
0.999971 | + | 0.00766579i | \(0.00244012\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.75404 | + | 4.77014i | 0.352619 | + | 0.610754i | 0.986707 | − | 0.162507i | \(-0.0519579\pi\) |
−0.634089 | + | 0.773260i | \(0.718625\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.584135 | + | 1.01175i | 0.0724530 | + | 0.125492i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.330095 | − | 0.571741i | 0.0403275 | − | 0.0698493i | −0.845157 | − | 0.534518i | \(-0.820493\pi\) |
0.885485 | + | 0.464669i | \(0.153827\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.09617 | − | 9.98342i | −0.974665 | − | 1.20186i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.7414 | 1.63081 | 0.815405 | − | 0.578891i | \(-0.196514\pi\) | ||||
0.815405 | + | 0.578891i | \(0.196514\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.83009 | − | 3.16982i | −0.214196 | − | 0.370999i | 0.738827 | − | 0.673895i | \(-0.235380\pi\) |
−0.953024 | + | 0.302896i | \(0.902047\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.39248 | + | 6.64948i | 0.622670 | + | 0.767816i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.11273 | + | 5.39140i | 0.350209 | + | 0.606580i | 0.986286 | − | 0.165046i | \(-0.0527772\pi\) |
−0.636077 | + | 0.771626i | \(0.719444\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.23229 | − | 3.63723i | −0.914699 | − | 0.404137i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.85185 | − | 8.40365i | 0.532560 | − | 0.922420i | −0.466718 | − | 0.884406i | \(-0.654564\pi\) |
0.999277 | − | 0.0380138i | \(-0.0121031\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.442820 | − | 0.766987i | −0.0480306 | − | 0.0831914i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.92627 | − | 0.942948i | 0.635363 | − | 0.101095i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.74433 | + | 6.48536i | −0.396898 | + | 0.687447i | −0.993341 | − | 0.115208i | \(-0.963247\pi\) |
0.596444 | + | 0.802655i | \(0.296580\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.22708 | − | 0.195246i | 0.127243 | − | 0.0202460i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.437618 | + | 0.757977i | −0.0448987 | + | 0.0777668i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.57442 | + | 14.8513i | −0.870600 | + | 1.50792i | −0.00922376 | + | 0.999957i | \(0.502936\pi\) |
−0.861377 | + | 0.507967i | \(0.830397\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.17511 | − | 15.0429i | 0.319110 | − | 1.51186i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.18194 | −0.714630 | −0.357315 | − | 0.933984i | \(-0.616308\pi\) | ||||
−0.357315 | + | 0.933984i | \(0.616308\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.8285 | 1.26403 | 0.632013 | − | 0.774958i | \(-0.282229\pi\) | ||||
0.632013 | + | 0.774958i | \(0.282229\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.78263 | + | 6.55171i | −0.365681 | + | 0.633377i | −0.988885 | − | 0.148681i | \(-0.952497\pi\) |
0.623204 | + | 0.782059i | \(0.285830\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.49028 | + | 6.04535i | 0.334309 | + | 0.579040i | 0.983352 | − | 0.181712i | \(-0.0581639\pi\) |
−0.649043 | + | 0.760752i | \(0.724831\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.87360 | − | 1.25280i | 0.747329 | − | 0.118910i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.78495 | + | 16.9480i | 0.920491 | + | 1.59434i | 0.798657 | + | 0.601787i | \(0.205544\pi\) |
0.121834 | + | 0.992550i | \(0.461122\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.77455 | −0.165478 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.9331 | − | 4.54906i | 1.28812 | − | 0.420560i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.2632 | 1.38756 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.47141 | − | 9.06259i | 0.313007 | − | 0.817146i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.37756 | 0.212655 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.8090 | −1.49156 | −0.745780 | − | 0.666192i | \(-0.767923\pi\) | ||||
−0.745780 | + | 0.666192i | \(0.767923\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 21.3623 | − | 3.39902i | 1.88084 | − | 0.299267i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.89931 | −0.428055 | −0.214027 | − | 0.976828i | \(-0.568658\pi\) | ||||
−0.214027 | + | 0.976828i | \(0.568658\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.10589 | + | 0.566453i | −0.0951797 | + | 0.0487525i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.44514 | 0.465210 | 0.232605 | − | 0.972571i | \(-0.425275\pi\) | ||||
0.232605 | + | 0.972571i | \(0.425275\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.83009 | + | 4.90187i | 0.240046 | + | 0.415771i | 0.960727 | − | 0.277495i | \(-0.0895043\pi\) |
−0.720681 | + | 0.693266i | \(0.756171\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.68878 | − | 7.01942i | 0.226436 | − | 0.591142i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.5189 | + | 21.6833i | 1.04688 | + | 1.81325i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.414230 | − | 0.717468i | 0.0343999 | − | 0.0595824i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.28263 | 0.187000 | 0.0935002 | − | 0.995619i | \(-0.470194\pi\) | ||||
0.0935002 | + | 0.995619i | \(0.470194\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.2632 | 0.916586 | 0.458293 | − | 0.888801i | \(-0.348461\pi\) | ||||
0.458293 | + | 0.888801i | \(0.348461\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.5624 | + | 3.44854i | −0.853918 | + | 0.278798i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0857699 | − | 0.148558i | 0.00688921 | − | 0.0119325i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.77292 | − | 4.80283i | 0.221303 | − | 0.383308i | −0.733901 | − | 0.679256i | \(-0.762302\pi\) |
0.955204 | + | 0.295949i | \(0.0956358\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.584135 | − | 1.52496i | 0.0463249 | − | 0.120938i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.33009 | + | 5.76789i | −0.260833 | + | 0.451776i | −0.966464 | − | 0.256804i | \(-0.917331\pi\) |
0.705630 | + | 0.708580i | \(0.250664\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.33693 | − | 1.64857i | −0.104080 | − | 0.128341i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.20370 | + | 3.81691i | 0.170527 | + | 0.295362i | 0.938604 | − | 0.344996i | \(-0.112120\pi\) |
−0.768077 | + | 0.640357i | \(0.778786\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.43474 | + | 9.41325i | −0.418057 | + | 0.724096i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.17059 | + | 7.33582i | 0.624821 | + | 0.560984i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.6654 | + | 21.9371i | 0.962932 | + | 1.66785i | 0.715072 | + | 0.699051i | \(0.246394\pi\) |
0.247860 | + | 0.968796i | \(0.420273\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.9640 | + | 2.06275i | −0.974435 | + | 0.155046i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.77292 | − | 8.26693i | −0.356744 | − | 0.617899i | 0.630670 | − | 0.776051i | \(-0.282780\pi\) |
−0.987415 | + | 0.158151i | \(0.949447\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.3743 | −0.919774 | −0.459887 | − | 0.887978i | \(-0.652110\pi\) | ||||
−0.459887 | + | 0.887978i | \(0.652110\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.41260 | − | 8.90904i | 0.252266 | − | 0.658575i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.550343 | − | 0.953223i | 0.0404621 | − | 0.0700823i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.49028 | − | 16.4377i | −0.693998 | − | 1.20204i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.58414 | − | 11.4041i | −0.476411 | − | 0.825169i | 0.523223 | − | 0.852196i | \(-0.324729\pi\) |
−0.999635 | + | 0.0270270i | \(0.991396\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.57442 | + | 9.65518i | −0.401256 | + | 0.694995i | −0.993878 | − | 0.110486i | \(-0.964759\pi\) |
0.592622 | + | 0.805481i | \(0.298093\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.723815 | − | 1.88962i | 0.0518335 | − | 0.135318i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.144194 | −0.0102734 | −0.00513669 | − | 0.999987i | \(-0.501635\pi\) | ||||
−0.00513669 | + | 0.999987i | \(0.501635\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.73461 | − | 16.8608i | −0.690068 | − | 1.19523i | −0.971815 | − | 0.235744i | \(-0.924247\pi\) |
0.281747 | − | 0.959489i | \(-0.409086\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.12928 | + | 0.179683i | −0.0796530 | + | 0.0126739i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.669905 | − | 1.16031i | −0.0467882 | − | 0.0810395i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.59781 | + | 21.7833i | −0.319570 | + | 1.51404i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.37880 | + | 16.2446i | −0.648745 | + | 1.12366i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.61436 | + | 2.79615i | 0.111137 | + | 0.192495i | 0.916229 | − | 0.400655i | \(-0.131217\pi\) |
−0.805092 | + | 0.593150i | \(0.797884\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.9915 | − | 18.4861i | −1.02720 | − | 1.26665i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.49316 | − | 2.58623i | 0.101833 | − | 0.176380i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.26771 | + | 5.92017i | −0.153238 | + | 0.400048i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.04746 | − | 15.6707i | 0.608598 | − | 1.05412i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.3856 | − | 17.9885i | 0.695474 | − | 1.20460i | −0.274547 | − | 0.961574i | \(-0.588528\pi\) |
0.970021 | − | 0.243022i | \(-0.0781389\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.06238 | − | 14.5088i | 0.204159 | − | 0.967253i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.9428 | −1.45640 | −0.728198 | − | 0.685367i | \(-0.759642\pi\) | ||||
−0.728198 | + | 0.685367i | \(0.759642\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.7713 | −1.50477 | −0.752384 | − | 0.658724i | \(-0.771096\pi\) | ||||
−0.752384 | + | 0.658724i | \(0.771096\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.8908 | − | 22.3276i | 0.844507 | − | 1.46273i | −0.0415414 | − | 0.999137i | \(-0.513227\pi\) |
0.886049 | − | 0.463592i | \(-0.153440\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.518875 | − | 0.898718i | −0.0338477 | − | 0.0586259i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.85705 | − | 10.0694i | 0.250542 | − | 0.654075i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.6488 | + | 23.6405i | 0.882870 | + | 1.52918i | 0.848136 | + | 0.529779i | \(0.177725\pi\) |
0.0347345 | + | 0.999397i | \(0.488941\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0345 | −0.646378 | −0.323189 | − | 0.946334i | \(-0.604755\pi\) | ||||
−0.323189 | + | 0.946334i | \(0.604755\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.08809 | + | 15.0429i | 0.262251 | + | 0.965000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.8824 | −1.13783 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.5985 | + | 2.64104i | −1.05189 | + | 0.167369i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.3171 | 1.78736 | 0.893680 | − | 0.448705i | \(-0.148115\pi\) | ||||
0.893680 | + | 0.448705i | \(0.148115\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −38.0312 | −2.39100 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.548709 | + | 1.43248i | −0.0343615 | + | 0.0897053i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −28.8629 | −1.80042 | −0.900210 | − | 0.435455i | \(-0.856587\pi\) | ||||
−0.900210 | + | 0.435455i | \(0.856587\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.73392 | − | 6.94377i | −0.478718 | − | 0.429808i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.20929 | −0.0745680 | −0.0372840 | − | 0.999305i | \(-0.511871\pi\) | ||||
−0.0372840 | + | 0.999305i | \(0.511871\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.112725 | − | 0.195246i | −0.00692465 | − | 0.0119938i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.8096 | − | 2.03818i | 0.783934 | − | 0.124734i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.50684 | + | 7.80607i | 0.274787 | + | 0.475944i | 0.970081 | − | 0.242780i | \(-0.0780594\pi\) |
−0.695295 | + | 0.718725i | \(0.744726\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.80150 | − | 15.2447i | 0.534653 | − | 0.926047i | −0.464527 | − | 0.885559i | \(-0.653776\pi\) |
0.999180 | − | 0.0404876i | \(-0.0128911\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 25.3308 | 1.52750 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.45417 | 0.0873726 | 0.0436863 | − | 0.999045i | \(-0.486090\pi\) | ||||
0.0436863 | + | 0.999045i | \(0.486090\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.60138 | − | 1.43777i | −0.0958718 | − | 0.0860768i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.1482 | − | 17.5771i | 0.605388 | − | 1.04856i | −0.386602 | − | 0.922247i | \(-0.626351\pi\) |
0.991990 | − | 0.126316i | \(-0.0403154\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.30150 | + | 3.98632i | −0.136810 | + | 0.236962i | −0.926288 | − | 0.376817i | \(-0.877018\pi\) |
0.789477 | + | 0.613780i | \(0.210352\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.49712 | − | 0.238212i | 0.0886818 | − | 0.0141105i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.64132 | − | 2.84284i | 0.0965479 | − | 0.167226i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 29.3337 | − | 4.66738i | 1.71957 | − | 0.273607i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.53667 | − | 6.12569i | −0.206614 | − | 0.357867i | 0.744031 | − | 0.668145i | \(-0.232911\pi\) |
−0.950646 | + | 0.310278i | \(0.899578\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.906150 | + | 1.56950i | −0.0527581 | + | 0.0913797i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −23.7008 | + | 12.1399i | −1.37526 | + | 0.704430i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.1283 | − | 31.3992i | −1.04839 | − | 1.81586i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.83530 | + | 9.66173i | 0.450126 | + | 0.555052i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.658555 | − | 1.14065i | −0.0377088 | − | 0.0653135i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.7518 | −0.899006 | −0.449503 | − | 0.893279i | \(-0.648399\pi\) | ||||
−0.449503 | + | 0.893279i | \(0.648399\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.9955 | − | 17.2579i | −0.796175 | − | 0.981767i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.81191 | + | 16.9947i | −0.556382 | + | 0.963682i | 0.441412 | + | 0.897304i | \(0.354478\pi\) |
−0.997795 | + | 0.0663780i | \(0.978856\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.7427 | − | 22.0710i | −0.720259 | − | 1.24753i | −0.960896 | − | 0.276911i | \(-0.910689\pi\) |
0.240636 | − | 0.970615i | \(-0.422644\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.14132 | − | 7.17297i | −0.232599 | − | 0.402874i | 0.725973 | − | 0.687723i | \(-0.241390\pi\) |
−0.958572 | + | 0.284849i | \(0.908056\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.87756 | − | 15.3764i | 0.497048 | − | 0.860912i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.9406 | − | 2.05903i | 0.722276 | − | 0.114924i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.5562 | 0.754289 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.0744 | + | 20.9135i | 0.669768 | + | 1.16007i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.32489 | − | 11.2907i | 0.239167 | − | 0.624378i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.99028 | + | 10.3755i | 0.329256 | + | 0.570288i | 0.982364 | − | 0.186976i | \(-0.0598688\pi\) |
−0.653109 | + | 0.757264i | \(0.726535\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.2752 | − | 9.22544i | −0.563080 | − | 0.505551i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.0789334 | + | 0.136717i | −0.00431259 | + | 0.00746963i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.46006 | + | 11.1892i | 0.351902 | + | 0.609512i | 0.986583 | − | 0.163262i | \(-0.0522017\pi\) |
−0.634681 | + | 0.772774i | \(0.718868\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.1248 | − | 31.6533i | 0.658527 | − | 1.71917i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.83818 | − | 3.18381i | 0.0995428 | − | 0.172413i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.93598 | + | 2.38727i | 0.104230 | + | 0.128526i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.09329 | + | 14.0180i | −0.434471 | + | 0.752526i | −0.997252 | − | 0.0740802i | \(-0.976398\pi\) |
0.562781 | + | 0.826606i | \(0.309731\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.05718 | + | 15.6875i | −0.484820 | + | 0.839732i | −0.999848 | − | 0.0174409i | \(-0.994448\pi\) |
0.515028 | + | 0.857173i | \(0.327781\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −21.3204 | − | 13.7811i | −1.13800 | − | 0.735578i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.6979 | 0.622618 | 0.311309 | − | 0.950309i | \(-0.399233\pi\) | ||||
0.311309 | + | 0.950309i | \(0.399233\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.28590 | −0.174397 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.8623 | + | 30.9383i | −0.942734 | + | 1.63286i | −0.182507 | + | 0.983205i | \(0.558421\pi\) |
−0.760227 | + | 0.649658i | \(0.774912\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.80150 | + | 4.85235i | 0.147448 | + | 0.255387i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.6517 | − | 20.5333i | −0.873989 | − | 1.07772i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.437618 | + | 0.757977i | 0.0229060 | + | 0.0396743i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.0539 | −0.890207 | −0.445103 | − | 0.895479i | \(-0.646833\pi\) | ||||
−0.445103 | + | 0.895479i | \(0.646833\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −15.9789 | + | 5.21700i | −0.831830 | + | 0.271586i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.9234 | −1.34226 | −0.671131 | − | 0.741339i | \(-0.734191\pi\) | ||||
−0.671131 | + | 0.741339i | \(0.734191\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.59385 | − | 3.19849i | −0.133946 | − | 0.165169i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.9267 | 0.871767 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.8446 | 1.37892 | 0.689458 | − | 0.724326i | \(-0.257849\pi\) | ||||
0.689458 | + | 0.724326i | \(0.257849\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.3382 | + | 22.6129i | 0.939493 | + | 1.15849i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.8525 | −1.26991 | −0.634953 | − | 0.772551i | \(-0.718980\pi\) | ||||
−0.634953 | + | 0.772551i | \(0.718980\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −27.8782 | − | 25.0300i | −1.41713 | − | 1.27235i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.2528 | −0.925454 | −0.462727 | − | 0.886501i | \(-0.653129\pi\) | ||||
−0.462727 | + | 0.886501i | \(0.653129\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.7427 | + | 23.8030i | 0.694998 | + | 1.20377i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.34501 | + | 6.59095i | 0.269620 | + | 0.332470i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.744325 | − | 1.28921i | −0.0374511 | − | 0.0648671i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.18715 | − | 10.7164i | 0.310524 | − | 0.537843i | −0.667952 | − | 0.744204i | \(-0.732829\pi\) |
0.978476 | + | 0.206361i | \(0.0661622\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.9623 | −0.547429 | −0.273714 | − | 0.961811i | \(-0.588252\pi\) | ||||
−0.273714 | + | 0.961811i | \(0.588252\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.50481 | 0.174587 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.96853 | + | 0.869747i | 0.0978171 | + | 0.0432181i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.7947 | − | 20.4290i | 0.584640 | − | 1.01263i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.66019 | + | 11.5358i | −0.329325 | + | 0.570408i | −0.982378 | − | 0.186904i | \(-0.940155\pi\) |
0.653053 | + | 0.757312i | \(0.273488\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.94050 | − | 7.32525i | −0.293023 | − | 0.361328i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.16019 | + | 2.00951i | −0.0569515 | + | 0.0986429i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.50684 | − | 9.15507i | 0.171731 | − | 0.448326i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.35705 | + | 4.08253i | 0.115149 | + | 0.199445i | 0.917839 | − | 0.396952i | \(-0.129932\pi\) |
−0.802690 | + | 0.596396i | \(0.796599\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.65856 | + | 16.7291i | −0.470729 | + | 0.815327i | −0.999440 | − | 0.0334755i | \(-0.989342\pi\) |
0.528710 | + | 0.848802i | \(0.322676\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.3765 | + | 4.04083i | −0.601765 | + | 0.196472i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.15335 | − | 15.8541i | −0.444003 | − | 0.769036i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 15.5124 | − | 40.4973i | 0.748947 | − | 1.95523i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.1397 | + | 26.2227i | 0.729253 | + | 1.26310i | 0.957199 | + | 0.289429i | \(0.0934655\pi\) |
−0.227947 | + | 0.973674i | \(0.573201\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.2060 | −1.64384 | −0.821918 | − | 0.569606i | \(-0.807096\pi\) | ||||
−0.821918 | + | 0.569606i | \(0.807096\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.41711 | + | 0.225481i | −0.0679452 | + | 0.0108110i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.5813 | − | 23.5234i | 0.649680 | − | 1.12528i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.311220 | − | 0.539049i | −0.0148537 | − | 0.0257274i | 0.858503 | − | 0.512809i | \(-0.171395\pi\) |
−0.873357 | + | 0.487081i | \(0.838062\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.58934 | + | 4.48486i | 0.123023 | + | 0.213082i | 0.920958 | − | 0.389661i | \(-0.127408\pi\) |
−0.797935 | + | 0.602743i | \(0.794074\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.895355 | − | 1.55080i | 0.0424439 | − | 0.0735150i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.49028 | − | 3.07078i | −0.117786 | − | 0.145243i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.4977 | −0.495416 | −0.247708 | − | 0.968835i | \(-0.579677\pi\) | ||||
−0.247708 | + | 0.968835i | \(0.579677\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.3571 | − | 24.8671i | −0.676047 | − | 1.17095i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.2878 | − | 15.1522i | −0.577333 | − | 0.711911i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.60464 | + | 2.77933i | 0.0750621 | + | 0.130011i | 0.901113 | − | 0.433584i | \(-0.142751\pi\) |
−0.826051 | + | 0.563595i | \(0.809418\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.1625 | + | 10.4471i | 0.754402 | + | 0.487629i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.1150 | + | 31.3762i | −0.843702 | + | 1.46133i | 0.0430418 | + | 0.999073i | \(0.486295\pi\) |
−0.886744 | + | 0.462261i | \(0.847038\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.5253 | − | 25.1586i | −0.675049 | − | 1.16922i | −0.976455 | − | 0.215723i | \(-0.930789\pi\) |
0.301406 | − | 0.953496i | \(-0.402544\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.293425 | + | 0.0466878i | −0.0136072 | + | 0.00216509i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.7466 | + | 32.4701i | −0.867491 | + | 1.50254i | −0.00293952 | + | 0.999996i | \(0.500936\pi\) |
−0.864552 | + | 0.502544i | \(0.832398\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.48633 | + | 1.50940i | −0.437107 | + | 0.0695495i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 32.0007 | − | 55.4268i | 1.47139 | − | 2.54853i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.04583 | + | 15.6678i | −0.415051 | + | 0.718890i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.68878 | + | 0.877867i | −0.123111 | + | 0.0401948i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.9097 | −1.36661 | −0.683305 | − | 0.730133i | \(-0.739458\pi\) | ||||
−0.683305 | + | 0.730133i | \(0.739458\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.4887 | 1.02539 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.05034 | − | 3.55130i | 0.0931013 | − | 0.161256i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.6316 | − | 18.4145i | −0.481764 | − | 0.834439i | 0.518017 | − | 0.855370i | \(-0.326670\pi\) |
−0.999781 | + | 0.0209309i | \(0.993337\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.3925 | − | 1.81270i | 0.515186 | − | 0.0819729i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.6985 | + | 18.5303i | 0.482816 | + | 0.836262i | 0.999805 | − | 0.0197296i | \(-0.00628054\pi\) |
−0.516989 | + | 0.855992i | \(0.672947\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.8317 | −0.577912 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.759242 | + | 3.59710i | −0.0341254 | + | 0.161677i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.5653 | 0.652031 | 0.326015 | − | 0.945364i | \(-0.394294\pi\) | ||||
0.326015 | + | 0.945364i | \(0.394294\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.73065 | − | 7.12874i | 0.121997 | − | 0.318488i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.92339 | −0.130348 | −0.0651738 | − | 0.997874i | \(-0.520760\pi\) | ||||
−0.0651738 | + | 0.997874i | \(0.520760\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.71737 | 0.0764220 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.5926 | − | 2.95833i | 0.825727 | − | 0.131384i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.2405 | 0.852820 | 0.426410 | − | 0.904530i | \(-0.359778\pi\) | ||||
0.426410 | + | 0.904530i | \(0.359778\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.954858 | − | 18.9949i | 0.0421580 | − | 0.838646i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.06758 | −0.135174 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.1202 | − | 19.2608i | −0.489068 | − | 0.847091i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.6940 | − | 40.9713i | 0.688889 | − | 1.79844i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.8743 | + | 24.0310i | 0.607844 | + | 1.05282i | 0.991595 | + | 0.129380i | \(0.0412986\pi\) |
−0.383751 | + | 0.923436i | \(0.625368\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.36840 | + | 2.37014i | −0.0598360 | + | 0.103639i | −0.894392 | − | 0.447285i | \(-0.852391\pi\) |
0.834556 | + | 0.550924i | \(0.185724\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.65692 | −0.115737 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32.0722 | 1.39444 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.9184 | + | 15.1898i | 0.734194 | + | 0.659183i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.6871 | − | 23.7068i | 0.592856 | − | 1.02686i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.904515 | − | 1.56667i | 0.0391056 | − | 0.0677329i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.91423 | + | 15.4399i | −0.255218 | + | 0.666281i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.98865 | − | 10.3726i | 0.257472 | − | 0.445955i | −0.708092 | − | 0.706120i | \(-0.750444\pi\) |
0.965564 | + | 0.260165i | \(0.0837771\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.5000 | + | 16.6469i | 0.579340 | + | 0.714387i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.834608 | − | 1.44558i | −0.0357507 | − | 0.0619220i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.7346 | − | 18.5929i | 0.458979 | − | 0.794975i | −0.539928 | − | 0.841711i | \(-0.681549\pi\) |
0.998907 | + | 0.0467363i | \(0.0148821\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.7082 | + | 5.12861i | −0.670410 | + | 0.218884i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.34050 | + | 10.9821i | 0.270114 | + | 0.467852i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.88276 | + | 0.299573i | −0.0799188 | + | 0.0127161i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.9246 | + | 27.5823i | 0.674748 | + | 1.16870i | 0.976542 | + | 0.215325i | \(0.0690812\pi\) |
−0.301794 | + | 0.953373i | \(0.597585\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 61.0150 | 2.58066 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.7596 | + | 30.7001i | −0.496492 | + | 1.29616i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.7742 | − | 30.7857i | 0.749091 | − | 1.29746i | −0.199167 | − | 0.979966i | \(-0.563824\pi\) |
0.948259 | − | 0.317499i | \(-0.102843\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.33981 | − | 4.05267i | −0.0984366 | − | 0.170497i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.8743 | − | 18.8348i | −0.455874 | − | 0.789597i | 0.542864 | − | 0.839821i | \(-0.317340\pi\) |
−0.998738 | + | 0.0502237i | \(0.984007\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.79987 | − | 8.31362i | 0.200868 | − | 0.347914i | −0.747940 | − | 0.663766i | \(-0.768957\pi\) |
0.948808 | + | 0.315852i | \(0.102290\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.15856 | + | 21.2990i | −0.340829 | + | 0.889779i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −36.6810 | −1.52970 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.50916 | + | 11.2742i | 0.270980 | + | 0.469351i | 0.969113 | − | 0.246617i | \(-0.0793190\pi\) |
−0.698133 | + | 0.715968i | \(0.745986\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.0705 | − | 3.03437i | 0.792541 | − | 0.126104i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.41586 | − | 4.18440i | −0.100055 | − | 0.173300i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.33173 | + | 1.08778i | −0.137750 | + | 0.0449744i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.64364 | − | 14.9712i | 0.356761 | − | 0.617928i | −0.630657 | − | 0.776062i | \(-0.717214\pi\) |
0.987418 | + | 0.158134i | \(0.0505477\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.31285 | + | 2.27393i | 0.0540952 | + | 0.0936957i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.157311 | + | 0.193981i | 0.00647092 | + | 0.00797931i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.20765 | − | 10.7520i | 0.254918 | − | 0.441531i | −0.709955 | − | 0.704247i | \(-0.751285\pi\) |
0.964873 | + | 0.262716i | \(0.0846182\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.0624 | + | 31.4905i | −0.493680 | + | 1.28882i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.94282 | − | 6.82916i | 0.161099 | − | 0.279032i | −0.774164 | − | 0.632985i | \(-0.781829\pi\) |
0.935263 | + | 0.353953i | \(0.115163\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.1413 | − | 19.2973i | 0.454464 | − | 0.787154i | −0.544193 | − | 0.838960i | \(-0.683164\pi\) |
0.998657 | + | 0.0518055i | \(0.0164976\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.47373 | + | 1.32317i | 0.0600151 | + | 0.0538835i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.64979 | −0.148385 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.0917 | −0.896673 | −0.448336 | − | 0.893865i | \(-0.647983\pi\) | ||||
−0.448336 | + | 0.893865i | \(0.647983\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.6014 | − | 18.3621i | 0.428886 | − | 0.742852i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.7632 | + | 25.5706i | 0.596280 | + | 1.03279i | 0.993365 | + | 0.115005i | \(0.0366885\pi\) |
−0.397085 | + | 0.917782i | \(0.629978\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.830095 | + | 2.16708i | −0.0334727 | + | 0.0873849i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.01655 | + | 8.68892i | 0.201959 | + | 0.349803i | 0.949159 | − | 0.314796i | \(-0.101936\pi\) |
−0.747201 | + | 0.664598i | \(0.768603\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.2567 | 1.53767 | 0.768833 | − | 0.639450i | \(-0.220838\pi\) | ||||
0.768833 | + | 0.639450i | \(0.220838\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 34.3207 | − | 17.5796i | 1.37724 | − | 0.705444i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.1456 | 0.965823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 32.0855 | − | 5.10523i | 1.28137 | − | 0.203883i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.0482 | −0.679754 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.0377 | −0.917118 | −0.458559 | − | 0.888664i | \(-0.651634\pi\) | ||||
−0.458559 | + | 0.888664i | \(0.651634\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.00039 | − | 5.22229i | 0.0795084 | − | 0.207567i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.01943 | 0.159506 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.51367 | + | 40.3356i | −0.336796 | + | 1.59565i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.3729 | −0.686189 | −0.343094 | − | 0.939301i | \(-0.611475\pi\) | ||||
−0.343094 | + | 0.939301i | \(0.611475\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.47949 | − | 16.4190i | −0.373835 | − | 0.647501i | 0.616317 | − | 0.787498i | \(-0.288624\pi\) |
−0.990152 | + | 0.139997i | \(0.955291\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.10821 | + | 0.812785i | −0.201136 | + | 0.0320034i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.50972 | + | 16.4713i | 0.373865 | + | 0.647554i | 0.990157 | − | 0.139964i | \(-0.0446988\pi\) |
−0.616291 | + | 0.787518i | \(0.711366\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.4201 | + | 33.6366i | −0.762306 | + | 1.32035i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.18659 | −0.281233 | −0.140616 | − | 0.990064i | \(-0.544908\pi\) | ||||
−0.140616 | + | 0.990064i | \(0.544908\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.17154 | 0.0457758 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.4383 | − | 3.40803i | 0.407237 | − | 0.132960i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.7261 | + | 22.0423i | −0.495740 | + | 0.858647i | −0.999988 | − | 0.00491209i | \(-0.998436\pi\) |
0.504248 | + | 0.863559i | \(0.331770\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.14295 | − | 7.17580i | 0.161142 | − | 0.279106i | −0.774136 | − | 0.633019i | \(-0.781816\pi\) |
0.935279 | + | 0.353912i | \(0.115149\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −30.9520 | + | 4.92487i | −1.20208 | + | 0.191266i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.8554 | + | 22.2662i | −0.497764 | + | 0.862152i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −35.5300 | + | 5.65329i | −1.37367 | + | 0.218569i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.1138 | − | 24.4458i | −0.544857 | − | 0.943721i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.91586 | − | 10.2466i | 0.228040 | − | 0.394977i | −0.729187 | − | 0.684314i | \(-0.760102\pi\) |
0.957227 | + | 0.289338i | \(0.0934350\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −22.8594 | + | 11.7089i | −0.879858 | + | 0.450676i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.80314 | + | 11.7834i | 0.261466 | + | 0.452872i | 0.966632 | − | 0.256170i | \(-0.0824608\pi\) |
−0.705166 | + | 0.709042i | \(0.749127\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.9390 | + | 29.5193i | 0.917344 | + | 1.13118i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.79071 | − | 3.10160i | −0.0685196 | − | 0.118679i | 0.829730 | − | 0.558165i | \(-0.188494\pi\) |
−0.898250 | + | 0.439485i | \(0.855161\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.30206 | −0.0497492 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.8428 | + | 30.6338i | 0.947813 | + | 1.16875i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.30314 | − | 3.98916i | 0.0877426 | − | 0.151975i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.85868 | + | 10.1475i | 0.222875 | + | 0.386031i | 0.955680 | − | 0.294408i | \(-0.0951225\pi\) |
−0.732805 | + | 0.680439i | \(0.761789\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.676742 | − | 1.17215i | −0.0256703 | − | 0.0444622i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.3759 | + | 17.9716i | −0.393016 | + | 0.680724i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −44.1004 | + | 7.01697i | −1.66803 | + | 0.265406i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.5926 | −0.400077 | −0.200039 | − | 0.979788i | \(-0.564107\pi\) | ||||
−0.200039 | + | 0.979788i | \(0.564107\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.42395 | + | 14.5907i | 0.317715 | + | 0.550299i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.642950 | + | 1.67851i | −0.0242149 | + | 0.0632163i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.1488 | − | 33.1668i | −0.719150 | − | 1.24560i | −0.961337 | − | 0.275374i | \(-0.911198\pi\) |
0.242187 | − | 0.970230i | \(-0.422135\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.7540 | + | 5.79656i | −0.665829 | + | 0.217388i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.66182 | + | 4.61042i | −0.0996861 | + | 0.172661i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.99355 | − | 5.18499i | −0.111953 | − | 0.193908i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.9126 | − | 44.1526i | 0.631612 | − | 1.64891i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.8376 | − | 36.0918i | 0.777112 | − | 1.34600i | −0.156488 | − | 0.987680i | \(-0.550017\pi\) |
0.933600 | − | 0.358318i | \(-0.116650\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.9473 | + | 13.4992i | 0.407136 | + | 0.502040i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.56238 | − | 14.8305i | 0.317999 | − | 0.550790i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.4126 | + | 28.4274i | −0.608709 | + | 1.05432i | 0.382744 | + | 0.923854i | \(0.374979\pi\) |
−0.991453 | + | 0.130461i | \(0.958354\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.7769 | − | 21.9110i | 0.584329 | − | 0.811517i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −46.2542 | −1.71077 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.29768 | −0.343418 | −0.171709 | − | 0.985148i | \(-0.554929\pi\) | ||||
−0.171709 | + | 0.985148i | \(0.554929\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.69166 | + | 2.93004i | −0.0623130 | + | 0.107929i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.68878 | − | 9.85326i | −0.209265 | − | 0.362458i | 0.742218 | − | 0.670158i | \(-0.233774\pi\) |
−0.951483 | + | 0.307701i | \(0.900441\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19.5092 | + | 24.0568i | 0.716687 | + | 0.883749i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.16182 | + | 2.01234i | 0.0426232 | + | 0.0738256i | 0.886550 | − | 0.462633i | \(-0.153095\pi\) |
−0.843927 | + | 0.536458i | \(0.819762\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.545830 | −0.0199977 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.6614 | + | 19.4483i | 0.792550 | + | 0.711577i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.1338 | −0.406278 | −0.203139 | − | 0.979150i | \(-0.565114\pi\) | ||||
−0.203139 | + | 0.979150i | \(0.565114\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −30.8932 | − | 38.0945i | −1.12581 | − | 1.38824i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.69329 | −0.0980190 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 52.1639 | 1.89593 | 0.947964 | − | 0.318376i | \(-0.103138\pi\) | ||||
0.947964 | + | 0.318376i | \(0.103138\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 41.4910 | + | 51.1627i | 1.50603 | + | 1.85709i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 47.0255 | 1.70467 | 0.852336 | − | 0.522995i | \(-0.175185\pi\) | ||||
0.852336 | + | 0.522995i | \(0.175185\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.52571 | − | 0.824626i | 0.0913173 | − | 0.0298144i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −37.0279 | −1.33700 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.30314 | − | 5.72121i | −0.119114 | − | 0.206312i | 0.800303 | − | 0.599596i | \(-0.204672\pi\) |
−0.919417 | + | 0.393284i | \(0.871339\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.4887 | + | 38.8288i | 1.13404 | + | 1.39838i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.54351 | + | 16.5298i | 0.343256 | + | 0.594537i | 0.985035 | − | 0.172352i | \(-0.0551368\pi\) |
−0.641779 | + | 0.766889i | \(0.721803\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.77292 | − | 3.07078i | 0.0636850 | − | 0.110306i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.5081 | 0.734778 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −70.4217 | −2.51989 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.903827 | + | 17.9797i | −0.0323001 | + | 0.642544i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.663069 | + | 1.14847i | −0.0236659 | + | 0.0409906i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.4503 | − | 44.0813i | 0.907207 | − | 1.57133i | 0.0892796 | − | 0.996007i | \(-0.471544\pi\) |
0.817927 | − | 0.575322i | \(-0.195123\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.31930 | + | 1.62683i | 0.0469683 | + | 0.0579168i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.4552 | − | 23.3052i | 0.477810 | − | 0.827591i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.139680 | + | 0.364654i | −0.00495395 | + | 0.0129330i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.38727 | + | 7.59898i | 0.155405 | + | 0.269170i | 0.933207 | − | 0.359341i | \(-0.116998\pi\) |
−0.777801 | + | 0.628510i | \(0.783665\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.03667 | + | 13.9199i | −0.284317 | + | 0.492451i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.7168 | − | 15.0089i | −0.590660 | − | 0.530313i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.37880 | + | 16.2446i | 0.330971 | + | 0.573258i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.58453 | − | 14.5792i | 0.196585 | − | 0.513211i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.75692 | + | 8.23923i | 0.167244 | + | 0.289676i | 0.937450 | − | 0.348120i | \(-0.113180\pi\) |
−0.770206 | + | 0.637796i | \(0.779846\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.0118 | 0.878282 | 0.439141 | − | 0.898418i | \(-0.355283\pi\) | ||||
0.439141 | + | 0.898418i | \(0.355283\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −30.1105 | + | 4.79099i | −1.05602 | + | 0.168027i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.796303 | − | 1.37924i | 0.0278933 | − | 0.0483126i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.8554 | + | 39.5867i | 0.799610 | + | 1.38496i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.7970 | + | 30.8253i | 0.621119 | + | 1.07581i | 0.989278 | + | 0.146047i | \(0.0466551\pi\) |
−0.368158 | + | 0.929763i | \(0.620012\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.00000 | + | 13.8564i | −0.278862 | + | 0.483004i | −0.971102 | − | 0.238664i | \(-0.923291\pi\) |
0.692240 | + | 0.721668i | \(0.256624\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −27.6352 | − | 34.0770i | −0.962133 | − | 1.18641i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.4531 | −0.885090 | −0.442545 | − | 0.896746i | \(-0.645924\pi\) | ||||
−0.442545 | + | 0.896746i | \(0.645924\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.77292 | − | 15.1951i | −0.304696 | − | 0.527749i | 0.672498 | − | 0.740099i | \(-0.265222\pi\) |
−0.977194 | + | 0.212350i | \(0.931888\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.58646 | − | 1.95627i | −0.0550336 | − | 0.0678622i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.526955 | − | 0.912713i | −0.0182360 | − | 0.0315857i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.187145 | + | 3.72286i | −0.00646868 | + | 0.128681i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.0562 | − | 20.8820i | 0.416227 | − | 0.720927i | −0.579329 | − | 0.815094i | \(-0.696685\pi\) |
0.995556 | + | 0.0941668i | \(0.0300187\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.49837 | + | 14.7196i | 0.293047 | + | 0.507572i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −34.7175 | + | 5.52402i | −1.19573 | + | 0.190257i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.29957 | − | 2.25093i | 0.0447067 | − | 0.0774342i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.87360 | − | 1.25280i | 0.270221 | − | 0.0429958i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.0796 | + | 29.5828i | −0.585482 | + | 1.01408i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.2616 | − | 28.1659i | 0.556785 | − | 0.964381i | −0.440977 | − | 0.897518i | \(-0.645368\pi\) |
0.997762 | − | 0.0668621i | \(-0.0212988\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.95378 | − | 1.75417i | −0.0668178 | − | 0.0599912i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.599740 | 0.0204867 | 0.0102434 | − | 0.999948i | \(-0.496739\pi\) | ||||
0.0102434 | + | 0.999948i | \(0.496739\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.4347 | 0.901942 | 0.450971 | − | 0.892539i | \(-0.351078\pi\) | ||||
0.450971 | + | 0.892539i | \(0.351078\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.92270 | + | 17.1866i | −0.337773 | + | 0.585039i | −0.984013 | − | 0.178094i | \(-0.943007\pi\) |
0.646241 | + | 0.763134i | \(0.276340\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.02859 | − | 5.24567i | −0.102975 | − | 0.178358i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.61505 | + | 0.893429i | −0.190697 | + | 0.0303424i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.9520 | − | 27.6296i | −0.541134 | − | 0.937271i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.22545 | −0.109290 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −38.2811 | − | 34.3700i | −1.29562 | − | 1.16325i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.4703 | 0.691234 | 0.345617 | − | 0.938376i | \(-0.387670\pi\) | ||||
0.345617 | + | 0.938376i | \(0.387670\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.38237 | + | 11.4408i | −0.147814 | + | 0.385888i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.1683 | 1.05009 | 0.525043 | − | 0.851076i | \(-0.324049\pi\) | ||||
0.525043 | + | 0.851076i | \(0.324049\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.64187 | −0.0889060 | −0.0444530 | − | 0.999011i | \(-0.514154\pi\) | ||||
−0.0444530 | + | 0.999011i | \(0.514154\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.10000 | − | 0.493251i | 0.104205 | − | 0.0165805i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.1650 | 0.777805 | 0.388902 | − | 0.921279i | \(-0.372854\pi\) | ||||
0.388902 | + | 0.921279i | \(0.372854\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 42.1885 | + | 18.6400i | 1.41337 | + | 0.624462i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.8845 | 0.531555 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.14132 | + | 1.97682i | 0.0381500 | + | 0.0660777i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.4632 | + | 58.6433i | −0.750026 | + | 1.95804i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.24269 | − | 2.15240i | −0.0414460 | − | 0.0717866i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.74596 | + | 3.02409i | −0.0581664 | + | 0.100747i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.95898 | 0.0983599 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −50.0528 | −1.66198 | −0.830988 | − | 0.556290i | \(-0.812224\pi\) | ||||
−0.830988 | + | 0.556290i | \(0.812224\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.44966 | − | 21.0814i | 0.147586 | − | 0.699224i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.42231 | − | 9.39172i | 0.179649 | − | 0.311161i | −0.762111 | − | 0.647446i | \(-0.775837\pi\) |
0.941760 | + | 0.336285i | \(0.109170\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.8646 | + | 43.0667i | −0.822897 | + | 1.42530i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.816031 | + | 2.13036i | −0.0269772 | + | 0.0704275i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.59549 | + | 9.69166i | −0.184578 | + | 0.319699i | −0.943434 | − | 0.331560i | \(-0.892425\pi\) |
0.758856 | + | 0.651258i | \(0.225759\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.1848 | + | 21.1907i | 0.566259 | + | 0.698256i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.5679 | − | 58.1413i | −1.10490 | − | 1.91374i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.3759 | − | 19.7037i | 0.374038 | − | 0.647853i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.94802 | + | 37.6557i | −0.261047 | + | 1.23678i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.6478 | + | 35.7630i | 0.677431 | + | 1.17335i | 0.975752 | + | 0.218879i | \(0.0702401\pi\) |
−0.298321 | + | 0.954466i | \(0.596427\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33.5672 | − | 5.34099i | 1.09894 | − | 0.174856i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.26935 | + | 3.93063i | 0.0742156 | + | 0.128545i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.5620 | 1.09642 | 0.548211 | − | 0.836340i | \(-0.315309\pi\) | ||||
0.548211 | + | 0.836340i | \(0.315309\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.7898 | + | 41.2213i | −0.515279 | + | 1.34521i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.2112 | − | 43.6671i | 0.821862 | − | 1.42351i | −0.0824315 | − | 0.996597i | \(-0.526269\pi\) |
0.904294 | − | 0.426911i | \(-0.140398\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.7902 | + | 36.0096i | 0.677021 | + | 1.17263i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.1212 | − | 17.5304i | −0.328895 | − | 0.569662i | 0.653398 | − | 0.757014i | \(-0.273343\pi\) |
−0.982293 | + | 0.187352i | \(0.940009\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.94119 | + | 15.4866i | −0.290243 | + | 0.502716i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.13160 | + | 13.3967i | −0.166404 | + | 0.434419i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.3685 | −0.951340 | −0.475670 | − | 0.879624i | \(-0.657794\pi\) | ||||
−0.475670 | + | 0.879624i | \(0.657794\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.57442 | + | 2.72698i | 0.0509470 | + | 0.0882429i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −30.3707 | + | 4.83239i | −0.981746 | + | 0.156209i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.2427 | + | 26.4011i | 0.491700 | + | 0.851649i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.8878 | − | 15.1624i | −0.544203 | − | 0.488603i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.33297 | − | 2.30878i | 0.0429099 | − | 0.0743222i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.2157 | + | 26.3544i | 0.489305 | + | 0.847501i | 0.999924 | − | 0.0123057i | \(-0.00391714\pi\) |
−0.510619 | + | 0.859807i | \(0.670584\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.7895 | − | 18.2369i | −0.475106 | − | 0.585855i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.59329 | − | 6.22377i | 0.115314 | − | 0.199730i | −0.802591 | − | 0.596530i | \(-0.796546\pi\) |
0.917905 | + | 0.396799i | \(0.129879\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.9617 | − | 39.0595i | 0.479158 | − | 1.25091i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.2713 | + | 24.7186i | −0.456579 | + | 0.790818i | −0.998777 | − | 0.0494328i | \(-0.984259\pi\) |
0.542199 | + | 0.840250i | \(0.317592\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.1888 | − | 33.2359i | 0.613276 | − | 1.06223i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.9075 | + | 6.49966i | −0.635598 | + | 0.207518i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.41642 | −0.140862 | −0.0704310 | − | 0.997517i | \(-0.522437\pi\) | ||||
−0.0704310 | + | 0.997517i | \(0.522437\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.0344801 | 0.00109863 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −46.3396 | + | 80.2625i | −1.47351 | + | 2.55220i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.90671 | + | 5.03456i | 0.0923345 | + | 0.159928i | 0.908493 | − | 0.417900i | \(-0.137234\pi\) |
−0.816159 | + | 0.577828i | \(0.803900\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.42270 | − | 19.3780i | 0.235552 | − | 0.614941i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.32777 | + | 4.03182i | 0.0737953 | + | 0.127817i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52.6408 | 1.66715 | 0.833575 | − | 0.552407i | \(-0.186290\pi\) | ||||
0.833575 | + | 0.552407i | \(0.186290\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.20082 | + | 23.8878i | −0.0379922 | + | 0.755776i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))