Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(1685,1764)]
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, 1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.1685");
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.bm (of order \(6\), 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: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3x^{14} - 9x^{12} - 9x^{10} + 225x^{8} - 81x^{6} - 729x^{4} - 2187x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1685.2 | ||
Root | \(-1.69483 - 0.357142i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1685 |
Dual form | 1764.2.bm.b.1697.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | −1.69483 | − | 0.357142i | −0.978511 | − | 0.206196i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.42488 | −1.08444 | −0.542220 | − | 0.840237i | \(-0.682416\pi\) | ||||
−0.542220 | + | 0.840237i | \(0.682416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.74490 | + | 1.21059i | 0.914967 | + | 0.403530i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.42118i | − | 0.730013i | −0.931005 | − | 0.365006i | \(-0.881067\pi\) | ||
0.931005 | − | 0.365006i | \(-0.118933\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.73574 | + | 2.73418i | −1.31346 | + | 0.758325i | −0.982667 | − | 0.185380i | \(-0.940648\pi\) |
−0.330790 | + | 0.943704i | \(0.607315\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.10976 | + | 0.866025i | 1.06114 | + | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.29034 | − | 2.23494i | −0.312954 | − | 0.542053i | 0.666046 | − | 0.745911i | \(-0.267985\pi\) |
−0.979001 | + | 0.203858i | \(0.934652\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.348755 | + | 0.201354i | 0.0800100 | + | 0.0461938i | 0.539471 | − | 0.842004i | \(-0.318624\pi\) |
−0.459461 | + | 0.888198i | \(0.651957\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.54372i | 0.738916i | 0.929247 | + | 0.369458i | \(0.120457\pi\) | ||||
−0.929247 | + | 0.369458i | \(0.879543\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.880040 | 0.176008 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.21979 | − | 3.03206i | −0.812098 | − | 0.583520i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.31784 | − | 3.64761i | −1.17319 | − | 0.677343i | −0.218763 | − | 0.975778i | \(-0.570202\pi\) |
−0.954430 | + | 0.298435i | \(0.903535\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.63732 | + | 2.10001i | 0.653282 | + | 0.377172i | 0.789712 | − | 0.613477i | \(-0.210230\pi\) |
−0.136431 | + | 0.990650i | \(0.543563\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.864703 | + | 4.10349i | −0.150526 | + | 0.714325i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.59680 | − | 2.76574i | 0.262513 | − | 0.454685i | −0.704396 | − | 0.709807i | \(-0.748782\pi\) |
0.966909 | + | 0.255122i | \(0.0821155\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.00276 | − | 2.94264i | 1.44159 | − | 0.471199i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.03924 | + | 6.99618i | 0.630824 | + | 1.09262i | 0.987384 | + | 0.158346i | \(0.0506163\pi\) |
−0.356560 | + | 0.934273i | \(0.616050\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.22573 | + | 7.31918i | −0.644418 | + | 1.11616i | 0.340018 | + | 0.940419i | \(0.389567\pi\) |
−0.984436 | + | 0.175745i | \(0.943766\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.65605 | − | 2.93553i | −0.992225 | − | 0.437603i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.25769 | − | 3.91043i | −0.329317 | − | 0.570395i | 0.653059 | − | 0.757307i | \(-0.273485\pi\) |
−0.982377 | + | 0.186912i | \(0.940152\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.38872 | + | 4.24868i | 0.194460 | + | 0.594934i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.1493 | − | 7.01442i | 1.66884 | − | 0.963505i | 0.700575 | − | 0.713579i | \(-0.252927\pi\) |
0.968265 | − | 0.249926i | \(-0.0804065\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.87106i | 0.791654i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.519169 | − | 0.465816i | −0.0687657 | − | 0.0616989i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.0779043 | + | 0.134934i | −0.0101423 | + | 0.0175669i | −0.871052 | − | 0.491191i | \(-0.836562\pi\) |
0.860910 | + | 0.508758i | \(0.169895\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.2288 | − | 5.90561i | 1.30967 | − | 0.756136i | 0.327626 | − | 0.944808i | \(-0.393752\pi\) |
0.982040 | + | 0.188672i | \(0.0604182\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.4836 | − | 6.63005i | 1.42436 | − | 0.822357i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.53682 | − | 4.39390i | 0.309922 | − | 0.536801i | −0.668423 | − | 0.743781i | \(-0.733030\pi\) |
0.978345 | + | 0.206981i | \(0.0663637\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.26561 | − | 6.00600i | 0.152361 | − | 0.723037i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.73987i | 1.03723i | 0.855007 | + | 0.518616i | \(0.173552\pi\) | ||||
−0.855007 | + | 0.518616i | \(0.826448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.62339 | + | 4.40137i | −0.892251 | + | 0.515141i | −0.874678 | − | 0.484704i | \(-0.838927\pi\) |
−0.0175727 | + | 0.999846i | \(0.505594\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.49152 | − | 0.314299i | −0.172226 | − | 0.0362921i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.66575 | + | 9.81337i | 0.637447 | + | 1.10409i | 0.985991 | + | 0.166798i | \(0.0533427\pi\) |
−0.348544 | + | 0.937292i | \(0.613324\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.06895 | + | 6.64589i | 0.674328 | + | 0.738432i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.50937 | − | 13.0066i | 0.824260 | − | 1.42766i | −0.0782227 | − | 0.996936i | \(-0.524925\pi\) |
0.902483 | − | 0.430725i | \(-0.141742\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.12893 | + | 5.41946i | 0.339380 | + | 0.587823i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.40495 | + | 8.43843i | 1.00832 | + | 0.904695i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.83339 | − | 13.5678i | 0.830338 | − | 1.43819i | −0.0674328 | − | 0.997724i | \(-0.521481\pi\) |
0.897771 | − | 0.440463i | \(-0.145186\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.41464 | − | 4.85819i | −0.561472 | − | 0.503771i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.845690 | − | 0.488259i | −0.0867660 | − | 0.0500944i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.97713 | + | 2.87355i | 0.505351 | + | 0.291765i | 0.730921 | − | 0.682462i | \(-0.239091\pi\) |
−0.225569 | + | 0.974227i | \(0.572424\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.93105 | − | 6.64589i | 0.294582 | − | 0.667937i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.67675 | 0.962873 | 0.481436 | − | 0.876481i | \(-0.340115\pi\) | ||||
0.481436 | + | 0.876481i | \(0.340115\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.2676i | 1.89850i | 0.314526 | + | 0.949249i | \(0.398155\pi\) | ||||
−0.314526 | + | 0.949249i | \(0.601845\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.944715 | + | 0.545431i | 0.0913290 | + | 0.0527288i | 0.544969 | − | 0.838456i | \(-0.316541\pi\) |
−0.453640 | + | 0.891185i | \(0.649875\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.15678 | − | 2.00360i | −0.110800 | − | 0.191910i | 0.805293 | − | 0.592877i | \(-0.202008\pi\) |
−0.916093 | + | 0.400966i | \(0.868674\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.69407 | + | 4.11718i | −0.350626 | + | 0.390785i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.8868 | − | 8.01754i | 1.30636 | − | 0.754227i | 0.324872 | − | 0.945758i | \(-0.394679\pi\) |
0.981487 | + | 0.191531i | \(0.0613453\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 8.59309i | − | 0.801309i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16.3091 | + | 1.77202i | −1.50778 | + | 0.163823i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.13790 | 0.467082 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.34721 | − | 13.2999i | −0.391974 | − | 1.19921i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.99041 | 0.893569 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.06425 | −0.271909 | −0.135954 | − | 0.990715i | \(-0.543410\pi\) | ||||
−0.135954 | + | 0.990715i | \(0.543410\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.77588 | − | 10.8956i | 0.860718 | − | 0.959303i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.4630 | 1.00153 | 0.500765 | − | 0.865584i | \(-0.333052\pi\) | ||||
0.500765 | + | 0.865584i | \(0.333052\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.2325 | + | 7.35238i | 0.880671 | + | 0.632792i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1.97456i | − | 0.168698i | −0.996436 | − | 0.0843488i | \(-0.973119\pi\) | ||
0.996436 | − | 0.0843488i | \(-0.0268810\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.37804 | − | 3.10501i | 0.456159 | − | 0.263364i | −0.254269 | − | 0.967134i | \(-0.581835\pi\) |
0.710428 | + | 0.703770i | \(0.248501\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.42982 | + | 7.43383i | 0.204628 | + | 0.626041i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.61993 | + | 11.4661i | 0.553587 | + | 0.958840i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.3200 | + | 8.84500i | 1.27226 | + | 0.734537i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.1692i | 0.996943i | 0.866906 | + | 0.498472i | \(0.166105\pi\) | ||||
−0.866906 | + | 0.498472i | \(0.833895\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.6357 | 0.865519 | 0.432759 | − | 0.901509i | \(-0.357540\pi\) | ||||
0.432759 | + | 0.901509i | \(0.357540\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.836270 | − | 7.69677i | −0.0676084 | − | 0.622247i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.82006 | − | 5.09226i | −0.708444 | − | 0.409021i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.06154 | − | 1.76758i | −0.244337 | − | 0.141068i | 0.372831 | − | 0.927899i | \(-0.378387\pi\) |
−0.617169 | + | 0.786831i | \(0.711720\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −23.0962 | + | 7.54922i | −1.83165 | + | 0.598692i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.16575 | + | 5.48324i | −0.247961 | + | 0.429481i | −0.962960 | − | 0.269645i | \(-0.913094\pi\) |
0.714999 | + | 0.699125i | \(0.246427\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.09680 | − | 9.95046i | 0.163236 | − | 0.774642i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.39779 | − | 14.5454i | −0.649840 | − | 1.12556i | −0.983161 | − | 0.182743i | \(-0.941502\pi\) |
0.333320 | − | 0.942814i | \(-0.391831\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.45146 | − | 14.6384i | 0.650112 | − | 1.12603i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.713542 | + | 0.974896i | 0.0545659 | + | 0.0745522i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.30850 | − | 14.3907i | −0.631684 | − | 1.09411i | −0.987207 | − | 0.159441i | \(-0.949031\pi\) |
0.355524 | − | 0.934667i | \(-0.384303\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.180225 | − | 0.200868i | 0.0135466 | − | 0.0150981i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.6082 | + | 7.27937i | −0.942384 | + | 0.544086i | −0.890707 | − | 0.454578i | \(-0.849790\pi\) |
−0.0516773 | + | 0.998664i | \(0.516457\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.02355i | 0.299068i | 0.988757 | + | 0.149534i | \(0.0477774\pi\) | ||||
−0.988757 | + | 0.149534i | \(0.952223\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.4452 | + | 6.35587i | −1.43743 | + | 0.469839i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.87205 | + | 6.70659i | −0.284679 | + | 0.493078i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.41119 | + | 3.12415i | −0.395705 | + | 0.228461i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.28998 | + | 4.20887i | −0.527485 | + | 0.304543i | −0.739992 | − | 0.672616i | \(-0.765171\pi\) |
0.212507 | + | 0.977160i | \(0.431837\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.31784 | − | 7.47871i | 0.310805 | − | 0.538330i | −0.667732 | − | 0.744402i | \(-0.732735\pi\) |
0.978537 | + | 0.206072i | \(0.0660681\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −21.8306 | + | 7.13555i | −1.56332 | + | 0.510987i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.3303i | 1.66221i | 0.556112 | + | 0.831107i | \(0.312292\pi\) | ||||
−0.556112 | + | 0.831107i | \(0.687708\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.2441 | + | 7.06913i | −0.867960 | + | 0.501117i | −0.866670 | − | 0.498882i | \(-0.833744\pi\) |
−0.00129041 | + | 0.999999i | \(0.500411\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.86873 | + | 6.54092i | −0.413948 | + | 0.461361i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.79468 | − | 16.9649i | −0.684090 | − | 1.18488i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.28998 | + | 9.72715i | −0.298175 | + | 0.676083i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.487514 | − | 0.844399i | 0.0337221 | − | 0.0584083i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.75786 | − | 11.7050i | −0.465230 | − | 0.805802i | 0.533982 | − | 0.845496i | \(-0.320695\pi\) |
−0.999212 | + | 0.0396938i | \(0.987362\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.12137 | − | 14.8126i | 0.213873 | − | 1.01494i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.2469 | − | 17.7481i | 0.698832 | − | 1.21041i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.4923 | − | 4.73694i | 0.979297 | − | 0.320093i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.2215 | + | 7.05606i | 0.822104 | + | 0.474642i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.4054 | + | 7.73961i | 0.897692 | + | 0.518283i | 0.876451 | − | 0.481492i | \(-0.159905\pi\) |
0.0212411 | + | 0.999774i | \(0.493238\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.41562 | + | 1.06537i | 0.161041 | + | 0.0710245i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.0167 | −0.996694 | −0.498347 | − | 0.866978i | \(-0.666059\pi\) | ||||
−0.498347 | + | 0.866978i | \(0.666059\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.5935i | 1.29478i | 0.762160 | + | 0.647389i | \(0.224139\pi\) | ||||
−0.762160 | + | 0.647389i | \(0.775861\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.9283 | − | 9.77356i | −1.10901 | − | 0.640287i | −0.170437 | − | 0.985369i | \(-0.554518\pi\) |
−0.938573 | + | 0.345081i | \(0.887851\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.47462 | + | 9.48232i | 0.357125 | + | 0.618558i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.09772 | − | 18.6555i | −0.396090 | − | 1.21180i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.36210 | − | 4.25051i | 0.476215 | − | 0.274943i | −0.242623 | − | 0.970121i | \(-0.578008\pi\) |
0.718838 | + | 0.695178i | \(0.244674\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 8.33094i | − | 0.536643i | −0.963329 | − | 0.268321i | \(-0.913531\pi\) | ||
0.963329 | − | 0.268321i | \(-0.0864689\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.91231 | − | 13.4311i | −0.507575 | − | 0.861607i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.20215 | −0.140120 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.3723 | + | 19.3621i | −1.10093 | + | 1.22702i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.5763 | 0.856928 | 0.428464 | − | 0.903559i | \(-0.359055\pi\) | ||||
0.428464 | + | 0.903559i | \(0.359055\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.57997 | 0.539418 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.36749 | − | 10.3025i | −0.210880 | − | 0.645170i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.98060 | −0.373059 | −0.186530 | − | 0.982449i | \(-0.559724\pi\) | ||||
−0.186530 | + | 0.982449i | \(0.559724\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.9261 | − | 17.6606i | −0.800104 | − | 1.09316i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.36602i | 0.207558i | 0.994600 | + | 0.103779i | \(0.0330934\pi\) | ||||
−0.994600 | + | 0.103779i | \(0.966907\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −29.4607 | + | 17.0091i | −1.80976 | + | 1.04486i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.1219 | + | 20.1975i | −1.10904 | + | 1.23607i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.14112 | + | 10.6367i | 0.374431 | + | 0.648533i | 0.990242 | − | 0.139361i | \(-0.0445048\pi\) |
−0.615811 | + | 0.787894i | \(0.711171\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.4823 | + | 14.7122i | 1.54794 | + | 0.893703i | 0.998299 | + | 0.0583012i | \(0.0185684\pi\) |
0.549640 | + | 0.835402i | \(0.314765\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 2.13073i | − | 0.128488i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.20215 | −0.552904 | −0.276452 | − | 0.961028i | \(-0.589159\pi\) | ||||
−0.276452 | + | 0.961028i | \(0.589159\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.44183 | + | 10.1676i | 0.445531 | + | 0.608719i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.05254 | + | 0.607682i | 0.0627891 | + | 0.0362513i | 0.531066 | − | 0.847331i | \(-0.321792\pi\) |
−0.468277 | + | 0.883582i | \(0.655125\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.5776 | + | 6.10696i | 0.628771 | + | 0.363021i | 0.780276 | − | 0.625435i | \(-0.215079\pi\) |
−0.151505 | + | 0.988457i | \(0.548412\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.25892 | + | 1.12955i | 0.0745722 | + | 0.0669086i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.17002 | − | 8.95475i | 0.304119 | − | 0.526750i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.40913 | − | 6.64772i | −0.434331 | − | 0.389696i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.15082 | + | 5.45739i | 0.184073 | + | 0.318824i | 0.943264 | − | 0.332044i | \(-0.107738\pi\) |
−0.759191 | + | 0.650868i | \(0.774405\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.188909 | − | 0.327199i | 0.0109987 | − | 0.0190503i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.34116 | + | 10.2169i | −0.425977 | + | 0.592842i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.68915 | − | 16.7821i | −0.560338 | − | 0.970534i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.4004 | − | 3.45597i | −0.942181 | − | 0.198540i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −24.8036 | + | 14.3204i | −1.42025 | + | 0.819983i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.7264i | 1.63950i | 0.572721 | + | 0.819750i | \(0.305888\pi\) | ||||
−0.572721 | + | 0.819750i | \(0.694112\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.88128 | − | 32.6554i | 0.391462 | − | 1.85770i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.86623 | − | 15.3568i | 0.502758 | − | 0.870802i | −0.497237 | − | 0.867615i | \(-0.665652\pi\) |
0.999995 | − | 0.00318766i | \(-0.00101467\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.4526 | − | 13.5404i | 1.32562 | − | 0.765348i | 0.341003 | − | 0.940062i | \(-0.389233\pi\) |
0.984619 | + | 0.174714i | \(0.0559001\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.65389 | − | 2.68692i | 0.261388 | − | 0.150913i | −0.363579 | − | 0.931563i | \(-0.618445\pi\) |
0.624968 | + | 0.780651i | \(0.285112\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.83150 | + | 15.2966i | −0.494469 | + | 0.856446i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.40633 | − | 1.26181i | −0.0784940 | − | 0.0704274i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.03926i | − | 0.0578262i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.16764 | + | 2.40619i | −0.231179 | + | 0.133471i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.24498 | + | 3.80890i | 0.0688474 | + | 0.210633i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.72104 | + | 6.44502i | 0.204527 | + | 0.354250i | 0.949982 | − | 0.312305i | \(-0.101101\pi\) |
−0.745455 | + | 0.666556i | \(0.767768\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.73124 | − | 5.65861i | 0.423669 | − | 0.310090i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.15149 | + | 10.6547i | −0.336092 | + | 0.582128i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.31784 | − | 9.21076i | −0.289681 | − | 0.501742i | 0.684053 | − | 0.729433i | \(-0.260216\pi\) |
−0.973734 | + | 0.227690i | \(0.926883\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −26.3991 | + | 8.62882i | −1.43380 | + | 0.468653i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.08449 | − | 8.80660i | 0.275341 | − | 0.476904i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.06895 | + | 14.5638i | −0.165227 | + | 0.784090i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.63842 | + | 0.945944i | 0.0879552 | + | 0.0507809i | 0.543332 | − | 0.839518i | \(-0.317162\pi\) |
−0.455377 | + | 0.890299i | \(0.650496\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.1105 | − | 9.30140i | −0.862375 | − | 0.497892i | 0.00243201 | − | 0.999997i | \(-0.499226\pi\) |
−0.864807 | + | 0.502105i | \(0.832559\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 28.2740 | + | 2.82139i | 1.50915 | + | 0.150595i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.89010 | 0.207049 | 0.103525 | − | 0.994627i | \(-0.466988\pi\) | ||||
0.103525 | + | 0.994627i | \(0.466988\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 21.1931i | − | 1.12481i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.46992 | + | 4.31276i | 0.394248 | + | 0.227619i | 0.683999 | − | 0.729483i | \(-0.260239\pi\) |
−0.289751 | + | 0.957102i | \(0.593573\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.41891 | − | 16.3140i | −0.495732 | − | 0.858633i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.70786 | − | 1.83496i | −0.457044 | − | 0.0963103i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.4858 | − | 10.6728i | 0.967592 | − | 0.558639i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.3252i | 0.956568i | 0.878205 | + | 0.478284i | \(0.158741\pi\) | ||||
−0.878205 | + | 0.478284i | \(0.841259\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.61783 | + | 24.0937i | 0.136279 | + | 1.25427i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.69583 | −0.398475 | −0.199237 | − | 0.979951i | \(-0.563846\pi\) | ||||
−0.199237 | + | 0.979951i | \(0.563846\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −16.9320 | − | 3.56799i | −0.874367 | − | 0.184250i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 39.8928 | 2.05458 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.52510 | −0.386539 | −0.193269 | − | 0.981146i | \(-0.561909\pi\) | ||||
−0.193269 | + | 0.981146i | \(0.561909\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.19339 | + | 1.09437i | 0.266065 | + | 0.0560664i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.40934 | 0.174209 | 0.0871047 | − | 0.996199i | \(-0.472239\pi\) | ||||
0.0871047 | + | 0.996199i | \(0.472239\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.4597 | + | 14.9748i | −1.04003 | + | 0.761211i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 9.62356i | − | 0.487934i | −0.969784 | − | 0.243967i | \(-0.921551\pi\) | ||
0.969784 | − | 0.243967i | \(-0.0784489\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.92000 | − | 4.57261i | 0.400532 | − | 0.231247i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.4279 | − | 4.09392i | −0.980007 | − | 0.206511i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.7388 | − | 23.7962i | −0.691272 | − | 1.19732i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.3349 | − | 11.7404i | −1.02058 | − | 0.589232i | −0.106308 | − | 0.994333i | \(-0.533903\pi\) |
−0.914272 | + | 0.405101i | \(0.867236\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 25.6365i | − | 1.28023i | −0.768281 | − | 0.640113i | \(-0.778887\pi\) | ||
0.768281 | − | 0.640113i | \(-0.221113\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.9672 | −1.14408 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −14.7165 | − | 16.1155i | −0.731267 | − | 0.800785i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.69635 | − | 3.86614i | −0.331926 | − | 0.191637i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.3646 | − | 7.71603i | −0.660835 | − | 0.381533i | 0.131760 | − | 0.991282i | \(-0.457937\pi\) |
−0.792595 | + | 0.609748i | \(0.791270\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.705196 | + | 3.34654i | −0.0347848 | + | 0.165073i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.2093 | + | 31.5395i | −0.893860 | + | 1.54821i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.2238 | + | 3.34175i | −0.500661 | + | 0.163646i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.10643 | + | 12.3087i | 0.347172 | + | 0.601319i | 0.985746 | − | 0.168241i | \(-0.0538088\pi\) |
−0.638574 | + | 0.769560i | \(0.720475\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.849964 | + | 1.47218i | −0.0414247 | + | 0.0717497i | −0.885994 | − | 0.463696i | \(-0.846523\pi\) |
0.844570 | + | 0.535446i | \(0.179856\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.46320 | − | 13.4669i | −0.0711433 | − | 0.654781i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.13555 | − | 1.96684i | −0.0550825 | − | 0.0954057i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.12465 | − | 21.7973i | −0.343982 | − | 1.05238i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.2868 | + | 16.3314i | −1.36253 | + | 0.786656i | −0.989960 | − | 0.141349i | \(-0.954856\pi\) |
−0.372568 | + | 0.928005i | \(0.621523\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.6919i | 0.657992i | 0.944331 | + | 0.328996i | \(0.106710\pi\) | ||||
−0.944331 | + | 0.328996i | \(0.893290\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.8059 | − | 20.4622i | −1.09346 | − | 0.981087i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.713542 | + | 1.23589i | −0.0341333 | + | 0.0591207i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.64139 | − | 4.41176i | 0.364704 | − | 0.210562i | −0.306438 | − | 0.951890i | \(-0.599137\pi\) |
0.671142 | + | 0.741329i | \(0.265804\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.3562 | + | 12.3300i | −1.01466 | + | 0.585816i | −0.912554 | − | 0.408957i | \(-0.865893\pi\) |
−0.102109 | + | 0.994773i | \(0.532559\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.9950 | + | 32.9004i | −0.900451 | + | 1.55963i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.34614 | − | 20.6248i | 0.205566 | − | 0.975520i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 4.61306i | − | 0.217704i | −0.994058 | − | 0.108852i | \(-0.965283\pi\) | ||
0.994058 | − | 0.108852i | \(-0.0347174\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.9390 | − | 9.77973i | 0.797626 | − | 0.460509i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.0257 | − | 3.79844i | −0.846920 | − | 0.178466i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.85935 | − | 6.68460i | −0.180533 | − | 0.312692i | 0.761529 | − | 0.648131i | \(-0.224449\pi\) |
−0.942062 | + | 0.335438i | \(0.891116\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.33150 | + | 13.3434i | −0.0621491 | + | 0.622816i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.28621 | − | 16.0842i | 0.432502 | − | 0.749115i | −0.564586 | − | 0.825374i | \(-0.690964\pi\) |
0.997088 | + | 0.0762589i | \(0.0242975\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7046 | + | 30.6653i | 0.822804 | + | 1.42514i | 0.903586 | + | 0.428406i | \(0.140925\pi\) |
−0.0807828 | + | 0.996732i | \(0.525742\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.1298 | + | 11.7805i | 0.608882 | + | 0.546309i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.92166 | + | 13.7207i | −0.366571 | + | 0.634919i | −0.989027 | − | 0.147736i | \(-0.952802\pi\) |
0.622456 | + | 0.782655i | \(0.286135\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.55751 | + | 4.08915i | 0.209999 | + | 0.188418i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.7210 | + | 10.2312i | 0.814814 | + | 0.470433i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.306919 | + | 0.177200i | 0.0140824 | + | 0.00813048i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 41.8403 | − | 4.54603i | 1.91574 | − | 0.208149i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.5025 | 1.21093 | 0.605465 | − | 0.795872i | \(-0.292987\pi\) | ||||
0.605465 | + | 0.795872i | \(0.292987\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.4638i | 0.796279i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.0689 | − | 6.96801i | −0.548023 | − | 0.316401i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.50469 | + | 6.07031i | 0.158813 | + | 0.275072i | 0.934441 | − | 0.356118i | \(-0.115900\pi\) |
−0.775628 | + | 0.631190i | \(0.782567\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.32370 | − | 8.16254i | 0.331189 | − | 0.369123i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.4508 | + | 9.49785i | −0.742413 | + | 0.428632i | −0.822946 | − | 0.568120i | \(-0.807671\pi\) |
0.0805333 | + | 0.996752i | \(0.474338\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.8267i | 0.847910i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.10745 | + | 16.1155i | −0.319456 | + | 0.724337i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.25786 | 0.0563094 | 0.0281547 | − | 0.999604i | \(-0.491037\pi\) | ||||
0.0281547 | + | 0.999604i | \(0.491037\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.03806 | + | 27.6512i | 0.403791 | + | 1.23536i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −37.9507 | −1.69214 | −0.846070 | − | 0.533072i | \(-0.821037\pi\) | ||||
−0.846070 | + | 0.533072i | \(0.821037\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.4650 | −1.04418 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.5518 | + | 21.7912i | −0.868324 | + | 0.967780i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.80942 | −0.257498 | −0.128749 | − | 0.991677i | \(-0.541096\pi\) | ||||
−0.128749 | + | 0.991677i | \(0.541096\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.861156 | − | 1.90712i | −0.0380210 | − | 0.0842014i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 46.7217i | − | 2.05881i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.46784 | + | 5.46626i | −0.416395 | + | 0.240406i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.94197 | + | 27.3572i | 0.392509 | + | 1.20085i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.84995 | + | 11.8645i | 0.300102 | + | 0.519791i | 0.976159 | − | 0.217058i | \(-0.0696461\pi\) |
−0.676057 | + | 0.736849i | \(0.736313\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.2073 | + | 12.2440i | 0.927330 | + | 0.535394i | 0.885966 | − | 0.463750i | \(-0.153496\pi\) |
0.0413640 | + | 0.999144i | \(0.486830\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 10.8389i | − | 0.472151i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.4421 | 0.454003 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.377189 | + | 0.276071i | −0.0163686 | + | 0.0119805i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −38.2576 | − | 22.0880i | −1.65712 | − | 0.956739i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.29082 | − | 1.32261i | −0.0990408 | − | 0.0571812i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23.9686 | − | 7.83437i | 1.03432 | − | 0.338078i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.5804 | − | 32.1822i | 0.798833 | − | 1.38362i | −0.121543 | − | 0.992586i | \(-0.538784\pi\) |
0.920376 | − | 0.391034i | \(-0.127882\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.43698 | − | 6.81924i | 0.0616666 | − | 0.292641i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.80506 | + | 4.85850i | 0.120155 | + | 0.208115i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.31826 | + | 5.74739i | −0.141878 | + | 0.245741i | −0.928204 | − | 0.372072i | \(-0.878648\pi\) |
0.786326 | + | 0.617812i | \(0.211981\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 35.2263 | − | 3.82741i | 1.50342 | − | 0.163350i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.46892 | − | 2.54424i | −0.0625781 | − | 0.108388i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.95767 | − | 9.98366i | 0.380232 | − | 0.423783i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.3205 | + | 12.3094i | −0.903378 | + | 0.521565i | −0.878295 | − | 0.478120i | \(-0.841318\pi\) |
−0.0250832 | + | 0.999685i | \(0.507985\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 46.2156i | − | 1.95471i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.2868 | − | 3.36235i | 0.434310 | − | 0.141958i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.28555 | − | 10.8869i | 0.264904 | − | 0.458828i | −0.702634 | − | 0.711551i | \(-0.747993\pi\) |
0.967539 | + | 0.252724i | \(0.0813263\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33.6738 | + | 19.4416i | −1.41667 | + | 0.817913i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.8872 | − | 7.44043i | 0.540260 | − | 0.311919i | −0.204924 | − | 0.978778i | \(-0.565695\pi\) |
0.745184 | + | 0.666859i | \(0.232362\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.45573 | − | 14.6458i | 0.353861 | − | 0.612906i | −0.633061 | − | 0.774102i | \(-0.718202\pi\) |
0.986922 | + | 0.161196i | \(0.0515351\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.8585 | − | 4.52977i | 0.578945 | − | 0.189234i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.11861i | 0.130055i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.1011 | − | 10.4507i | 0.753558 | − | 0.435067i | −0.0734203 | − | 0.997301i | \(-0.523391\pi\) |
0.826978 | + | 0.562234i | \(0.190058\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.98896 | + | 11.1331i | −0.415127 | + | 0.462675i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.9832 | − | 29.4157i | −0.703371 | − | 1.21827i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 39.5476 | − | 4.29692i | 1.63509 | − | 0.177656i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.8542 | − | 25.7283i | 0.613100 | − | 1.06192i | −0.377615 | − | 0.925963i | \(-0.623256\pi\) |
0.990715 | − | 0.135957i | \(-0.0434109\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.845690 | + | 1.46478i | 0.0348461 | + | 0.0603551i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.33222 | − | 39.5409i | 0.342742 | − | 1.62649i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.89603 | + | 10.2122i | −0.242121 | + | 0.419365i | −0.961318 | − | 0.275440i | \(-0.911176\pi\) |
0.719197 | + | 0.694806i | \(0.244510\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 23.2763 | − | 7.60810i | 0.952637 | − | 0.311379i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.7991 | + | 16.0498i | 1.13584 | + | 0.655778i | 0.945397 | − | 0.325921i | \(-0.105674\pi\) |
0.190443 | + | 0.981698i | \(0.439008\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.1636 | + | 9.33208i | 0.659329 | + | 0.380664i | 0.792021 | − | 0.610494i | \(-0.209029\pi\) |
−0.132692 | + | 0.991157i | \(0.542362\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.2825 | − | 8.98978i | 0.500183 | − | 0.366092i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.4588 | −0.506522 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 13.8684i | − | 0.562900i | −0.959576 | − | 0.281450i | \(-0.909185\pi\) | ||
0.959576 | − | 0.281450i | \(-0.0908154\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.3836 | + | 12.3458i | 0.865089 | + | 0.499459i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.4510 | + | 18.1017i | 0.422114 | + | 0.731122i | 0.996146 | − | 0.0877104i | \(-0.0279550\pi\) |
−0.574032 | + | 0.818833i | \(0.694622\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.5415 | + | 32.2507i | 0.425072 | + | 1.30047i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.2904 | − | 8.82792i | 0.615569 | − | 0.355399i | −0.159573 | − | 0.987186i | \(-0.551012\pi\) |
0.775142 | + | 0.631787i | \(0.217678\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.52857i | 0.222212i | 0.993809 | + | 0.111106i | \(0.0354393\pi\) | ||||
−0.993809 | + | 0.111106i | \(0.964561\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.7448 | − | 14.9537i | 0.431173 | − | 0.600073i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.6257 | −1.14503 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.12782 | + | 1.25700i | −0.0450409 | + | 0.0501998i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.24169 | −0.328618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.3544 | 0.969533 | 0.484766 | − | 0.874644i | \(-0.338905\pi\) | ||||
0.484766 | + | 0.874644i | \(0.338905\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.27310 | + | 22.2514i | 0.289080 | + | 0.884415i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.43045 | 0.294868 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.5804 | + | 23.9901i | −0.418554 | + | 0.949032i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 29.2340i | − | 1.15467i | −0.816506 | − | 0.577337i | \(-0.804092\pi\) | ||
0.816506 | − | 0.577337i | \(-0.195908\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.6535 | − | 20.0072i | 1.36660 | − | 0.789008i | 0.376109 | − | 0.926575i | \(-0.377262\pi\) |
0.990492 | + | 0.137567i | \(0.0439284\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −23.7053 | + | 26.4205i | −0.933396 | + | 1.04031i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.78276 | − | 6.55194i | −0.148716 | − | 0.257583i | 0.782037 | − | 0.623232i | \(-0.214181\pi\) |
−0.930753 | + | 0.365648i | \(0.880847\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.326700 | + | 0.188620i | 0.0128241 | + | 0.00740399i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.1877i | 1.53353i | 0.641927 | + | 0.766766i | \(0.278135\pi\) | ||||
−0.641927 | + | 0.766766i | \(0.721865\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.7965 | −1.08610 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −26.2537 | + | 2.85252i | −1.02425 | + | 0.111287i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.8594 | − | 13.1979i | −0.890474 | − | 0.514115i | −0.0163765 | − | 0.999866i | \(-0.505213\pi\) |
−0.874098 | + | 0.485751i | \(0.838546\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.3501 | − | 15.7906i | −1.06380 | − | 0.614184i | −0.137317 | − | 0.990527i | \(-0.543848\pi\) |
−0.926480 | + | 0.376343i | \(0.877181\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18.1933 | − | 16.3236i | −0.706568 | − | 0.633957i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.9261 | − | 22.3886i | 0.500500 | − | 0.866891i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.9557 | − | 17.9049i | −0.771533 | − | 0.692245i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.2985 | − | 24.7658i | −0.551989 | − | 0.956073i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.21676 | + | 12.4998i | −0.278186 | + | 0.481832i | −0.970934 | − | 0.239348i | \(-0.923066\pi\) |
0.692748 | + | 0.721180i | \(0.256400\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.71358 | − | 2.66834i | −0.142936 | − | 0.102704i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.2099 | + | 29.8084i | 0.661430 | + | 1.14563i | 0.980240 | + | 0.197812i | \(0.0633837\pi\) |
−0.318809 | + | 0.947819i | \(0.603283\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.4508 | + | 5.36309i | 0.975275 | + | 0.205514i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.4694 | − | 9.50861i | 0.630184 | − | 0.363837i | −0.150639 | − | 0.988589i | \(-0.548133\pi\) |
0.780823 | + | 0.624752i | \(0.214800\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.78806i | 0.182942i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.99767 | − | 33.2077i | 0.266978 | − | 1.26695i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −38.3574 | + | 66.4369i | −1.46130 | + | 2.53104i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.7795 | + | 9.68764i | −0.638321 | + | 0.368535i | −0.783968 | − | 0.620802i | \(-0.786807\pi\) |
0.145646 | + | 0.989337i | \(0.453474\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.0411 | + | 7.52928i | −0.494677 | + | 0.285602i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.4240 | − | 18.0549i | 0.394838 | − | 0.683880i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.2001 | + | 22.6103i | 0.953154 | + | 0.855201i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.0297i | 0.869819i | 0.900474 | + | 0.434910i | \(0.143220\pi\) | ||||
−0.900474 | + | 0.434910i | \(0.856780\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.11379 | − | 0.643045i | 0.0420073 | − | 0.0242529i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.89202 | − | 18.0261i | −0.221906 | − | 0.678903i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.4119 | + | 35.3544i | 0.766585 | + | 1.32776i | 0.939405 | + | 0.342810i | \(0.111379\pi\) |
−0.172820 | + | 0.984953i | \(0.555288\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.67196 | + | 33.7956i | 0.137709 | + | 1.26743i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.44183 | + | 12.8896i | −0.278699 | + | 0.482720i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.0525 | − | 27.8038i | −0.600331 | − | 1.03980i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.9955 | + | 4.57458i | −0.522673 | + | 0.170841i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.1578 | − | 36.6464i | 0.789054 | − | 1.36668i | −0.137494 | − | 0.990503i | \(-0.543905\pi\) |
0.926547 | − | 0.376178i | \(-0.122762\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.97532 | + | 14.1195i | −0.110654 | + | 0.525111i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.55995 | − | 3.21004i | −0.206491 | − | 0.119218i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.58754 | − | 2.64862i | −0.170142 | − | 0.0982318i | 0.412511 | − | 0.910953i | \(-0.364652\pi\) |
−0.582653 | + | 0.812721i | \(0.697985\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.61321 | + | 25.5893i | 0.319008 | + | 0.947752i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.8106 | 0.806694 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 18.6499i | − | 0.688852i | −0.938814 | − | 0.344426i | \(-0.888074\pi\) | ||
0.938814 | − | 0.344426i | \(-0.111926\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.6384 | − | 6.14210i | −0.391871 | − | 0.226247i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.5918 | − | 35.6661i | −0.757483 | − | 1.31200i | −0.944131 | − | 0.329572i | \(-0.893096\pi\) |
0.186648 | − | 0.982427i | \(-0.440238\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.73227 | + | 0.786480i | 0.137108 | + | 0.0288921i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.5831 | − | 11.8837i | 0.755122 | − | 0.435970i | −0.0724196 | − | 0.997374i | \(-0.523072\pi\) |
0.827542 | + | 0.561404i | \(0.189739\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 29.5089i | − | 1.08112i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 36.3581 | − | 26.6111i | 1.33027 | − | 0.973649i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.1230 | 0.661318 | 0.330659 | − | 0.943750i | \(-0.392729\pi\) | ||||
0.330659 | + | 0.943750i | \(0.392729\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −23.0095 | − | 4.84866i | −0.838513 | − | 0.176695i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.7902 | −0.938603 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.1059 | 1.34864 | 0.674319 | − | 0.738440i | \(-0.264437\pi\) | ||||
0.674319 | + | 0.738440i | \(0.264437\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −14.5416 | − | 3.06426i | −0.527826 | − | 0.111226i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.8107 | 0.428139 | 0.214070 | − | 0.976818i | \(-0.431328\pi\) | ||||
0.214070 | + | 0.976818i | \(0.431328\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.02785 | + | 18.6637i | 0.0733172 | + | 0.674789i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 0.852017i | − | 0.0307646i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.14015 | − | 1.81297i | 0.113237 | − | 0.0653773i | −0.442312 | − | 0.896861i | \(-0.645842\pi\) |
0.555549 | + | 0.831484i | \(0.312508\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.1361 | + | 2.13592i | 0.365043 | + | 0.0769233i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.05553 | + | 10.4885i | 0.217802 | + | 0.377245i | 0.954136 | − | 0.299374i | \(-0.0967778\pi\) |
−0.736333 | + | 0.676619i | \(0.763445\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.20099 | + | 1.84809i | 0.114983 | + | 0.0663854i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.25327i | 0.116561i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.1608 | 0.757192 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.6002 | + | 34.5482i | 0.557505 | + | 1.23465i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.42386 | + | 4.28617i | 0.264969 | + | 0.152980i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.5995 | + | 10.1611i | 0.627354 | + | 0.362203i | 0.779727 | − | 0.626120i | \(-0.215358\pi\) |
−0.152372 | + | 0.988323i | \(0.548691\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.20215 | − | 5.70483i | 0.0427975 | − | 0.203097i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.2940 | + | 55.9348i | −1.14679 | + | 1.98630i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 56.0055 | − | 18.3060i | 1.98631 | − | 0.649245i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.8973 | + | 29.2669i | 0.598532 | + | 1.03669i | 0.993038 | + | 0.117795i | \(0.0375824\pi\) |
−0.394506 | + | 0.918893i | \(0.629084\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.82639 | + | 10.0916i | −0.206123 | + | 0.357015i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 37.9269 | − | 27.7593i | 1.34008 | − | 0.980827i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.6565 | + | 18.4576i | 0.376060 | + | 0.651354i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.60934 | − | 20.2207i | −0.232660 | − | 0.711803i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.19308 | − | 2.42087i | 0.147421 | − | 0.0851134i | −0.424475 | − | 0.905440i | \(-0.639541\pi\) |
0.571896 | + | 0.820326i | \(0.306208\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.493486i | 0.0173286i | 0.999962 | + | 0.00866432i | \(0.00275797\pi\) | ||||
−0.999962 | + | 0.00866432i | \(0.997242\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −37.9338 | − | 34.0355i | −1.33040 | − | 1.19368i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.67656 | − | 13.2962i | 0.268898 | − | 0.465745i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.94749 | + | 1.70174i | −0.103120 | + | 0.0595362i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.6931 | − | 15.4113i | 0.931595 | − | 0.537857i | 0.0442792 | − | 0.999019i | \(-0.485901\pi\) |
0.887316 | + | 0.461163i | \(0.152568\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.94249 | − | 13.7568i | 0.276858 | − | 0.479532i | −0.693744 | − | 0.720221i | \(-0.744040\pi\) |
0.970602 | + | 0.240690i | \(0.0773736\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.760974 | + | 3.61123i | −0.0264937 | + | 0.125727i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.6756i | 1.24056i | 0.784379 | + | 0.620282i | \(0.212982\pi\) | ||||
−0.784379 | + | 0.620282i | \(0.787018\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.87997 | + | 1.66275i | −0.100026 | + | 0.0577498i | −0.549178 | − | 0.835705i | \(-0.685059\pi\) |
0.449153 | + | 0.893455i | \(0.351726\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.5961 | + | 3.28647i | 0.541022 | + | 0.114006i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.3636 | + | 35.2708i | 0.704712 | + | 1.22060i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.98136 | − | 19.8902i | −0.310441 | − | 0.687504i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.9689 | + | 36.3192i | −0.723926 | + | 1.25388i | 0.235488 | + | 0.971877i | \(0.424331\pi\) |
−0.959414 | + | 0.282000i | \(0.909002\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.1100 | + | 20.9752i | 0.417588 | + | 0.723283i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.56684 | − | 1.40582i | −0.0539649 | − | 0.0484191i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −20.4938 | + | 35.4963i | −0.705007 | + | 1.22111i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.7461 | − | 14.1280i | −0.540406 | − | 0.484870i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.80100 | + | 5.65861i | 0.335974 | + | 0.193975i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.5330 | − | 7.23594i | −0.429122 | − | 0.247754i | 0.269851 | − | 0.962902i | \(-0.413026\pi\) |
−0.698973 | + | 0.715149i | \(0.746359\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.73025 | − | 2.36401i | −0.0591734 | − | 0.0808473i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −47.4657 | −1.62140 | −0.810699 | − | 0.585463i | \(-0.800913\pi\) | ||||
−0.810699 | + | 0.585463i | \(0.800913\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 6.00809i | − | 0.204993i | −0.994733 | − | 0.102497i | \(-0.967317\pi\) | ||
0.994733 | − | 0.102497i | \(-0.0326831\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.1064 | + | 15.6499i | 0.922714 | + | 0.532729i | 0.884500 | − | 0.466540i | \(-0.154500\pi\) |
0.0382141 | + | 0.999270i | \(0.487833\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.1471 | + | 34.8958i | 0.685022 | + | 1.18649i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.9604 | + | 13.3303i | −0.406197 | + | 0.452722i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23.7599 | − | 13.7178i | 0.806000 | − | 0.465344i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.7445i | 0.940086i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.1830 | + | 13.9129i | 0.344644 | + | 0.470879i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.3764 | 1.39718 | 0.698591 | − | 0.715521i | \(-0.253811\pi\) | ||||
0.698591 | + | 0.715521i | \(0.253811\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.39105 | − | 10.3746i | −0.114377 | − | 0.349928i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.7350 | −1.33870 | −0.669352 | − | 0.742945i | \(-0.733428\pi\) | ||||
−0.669352 | + | 0.742945i | \(0.733428\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.1324 | −1.61978 | −0.809892 | − | 0.586579i | \(-0.800474\pi\) | ||||
−0.809892 | + | 0.586579i | \(0.800474\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.437024 | + | 0.487080i | −0.0146904 | + | 0.0163730i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.1122 | −0.943916 | −0.471958 | − | 0.881621i | \(-0.656453\pi\) | ||||
−0.471958 | + | 0.881621i | \(0.656453\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.0909 | − | 14.6940i | 0.539065 | − | 0.492268i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1.81838i | − | 0.0608497i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.5735 | − | 17.6516i | 1.02196 | − | 0.590028i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.4279 | + | 31.9032i | 0.348177 | + | 1.06522i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.3200 | − | 26.5350i | −0.510950 | − | 0.884992i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.3537 | − | 18.1020i | −1.04454 | − | 0.603066i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 9.75663i | − | 0.324321i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 59.4859 | 1.97520 | 0.987599 | − | 0.156997i | \(-0.0501812\pi\) | ||||
0.987599 | + | 0.156997i | \(0.0501812\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 26.5617 | + | 11.7146i | 0.880996 | + | 0.388548i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.4502 | + | 14.6937i | 0.843204 | + | 0.486824i | 0.858352 | − | 0.513061i | \(-0.171489\pi\) |
−0.0151480 | + | 0.999885i | \(0.504822\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.4913 | − | 18.1815i | −1.04221 | − | 0.601721i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 47.1524 | − | 15.4122i | 1.55881 | − | 0.509512i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.7994 | − | 36.0256i | 0.686108 | − | 1.18837i | −0.286979 | − | 0.957937i | \(-0.592651\pi\) |
0.973087 | − | 0.230437i | \(-0.0740156\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.2594 | − | 48.6863i | 0.338058 | − | 1.60427i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.8964 | − | 41.3897i | −0.786558 | − | 1.36236i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.40525 | − | 2.43396i | 0.0462043 | − | 0.0800282i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −23.3252 | + | 52.8878i | −0.766100 | + | 1.73706i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.21614 | − | 2.10641i | −0.0399002 | − | 0.0691092i | 0.845386 | − | 0.534156i | \(-0.179371\pi\) |
−0.885286 | + | 0.465047i | \(0.846037\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.5113 | + | 22.8606i | −0.671510 | + | 0.748423i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.1215 | − | 7.57569i | 0.429118 | − | 0.247752i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.29837i | 0.238427i | 0.992869 | + | 0.119214i | \(0.0380374\pi\) | ||||
−0.992869 | + | 0.119214i | \(0.961963\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −44.5841 | + | 14.5728i | −1.45495 | + | 0.475564i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.2367 | − | 36.7831i | 0.692298 | − | 1.19910i | −0.278785 | − | 0.960354i | \(-0.589932\pi\) |
0.971083 | − | 0.238742i | \(-0.0767350\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.7925 | + | 14.3139i | −0.807354 | + | 0.466126i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.3119 | − | 27.3155i | 1.53743 | − | 0.887636i | 0.538443 | − | 0.842662i | \(-0.319013\pi\) |
0.998988 | − | 0.0449739i | \(-0.0143205\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0683 | − | 41.6874i | 0.781288 | − | 1.35323i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.84717 | + | 2.89178i | −0.286889 | + | 0.0937725i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.1877i | 0.556764i | 0.960470 | + | 0.278382i | \(0.0897981\pi\) | ||||
−0.960470 | + | 0.278382i | \(0.910202\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.6773 | − | 10.2060i | 0.572025 | − | 0.330259i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.4310 | − | 22.7711i | 0.660439 | − | 0.736084i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.67994 | − | 11.5700i | −0.215482 | − | 0.373226i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.93285 | + | 2.64082i | 0.0622854 | + | 0.0850991i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.4702 | + | 18.1350i | −0.337049 | + | 0.583786i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.1546 | − | 19.3203i | −0.358706 | − | 0.621298i | 0.629039 | − | 0.777374i | \(-0.283449\pi\) |
−0.987745 | + | 0.156076i | \(0.950115\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.371164 | + | 1.76138i | −0.0119235 | + | 0.0565836i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.1241 | + | 46.9803i | −0.870453 | + | 1.50767i | −0.00892375 | + | 0.999960i | \(0.502841\pi\) |
−0.861529 | + | 0.507708i | \(0.830493\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.92279 | − | 2.58964i | 0.253732 | − | 0.0829349i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 35.6936 | + | 20.6077i | 1.14194 | + | 0.659299i | 0.946910 | − | 0.321498i | \(-0.104186\pi\) |
0.195029 | + | 0.980797i | \(0.437520\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.8501 | − | 18.9660i | −1.04989 | − | 0.606157i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.749708 | − | 6.90008i | −0.0239363 | − | 0.220303i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.4394 | −0.588125 | −0.294062 | − | 0.955786i | \(-0.595007\pi\) | ||||
−0.294062 | + | 0.955786i | \(0.595007\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 56.5731i | − | 1.80257i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25.9371 | − | 14.9748i | −0.824752 | − | 0.476171i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.86116 | + | 3.22362i | 0.0591216 | + | 0.102402i | 0.894071 | − | 0.447925i | \(-0.147837\pi\) |
−0.834950 | + | 0.550326i | \(0.814503\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.00474 | − | 12.2522i | −0.127087 | − | 0.388810i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 29.6904 | − | 17.1418i | 0.941250 | − | 0.543431i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.475330i | 0.0150539i | 0.999972 | + | 0.00752693i | \(0.00239592\pi\) | ||||
−0.999972 | + | 0.00752693i | \(0.997604\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −15.1241 | + | 6.82924i | −0.478504 | + | 0.216068i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))