Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(509,1764)]
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, 5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.509");
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.w (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 | 509.5 | ||
Root | \(1.69483 + 0.357142i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.509 |
Dual form | 1764.2.w.a.1109.5 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | 0.538121 | − | 1.64634i | 0.310685 | − | 0.950513i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.21244 | + | 2.10001i | 0.542220 | + | 0.939152i | 0.998776 | + | 0.0494574i | \(0.0157492\pi\) |
−0.456557 | + | 0.889694i | \(0.650917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.42085 | − | 1.77186i | −0.806950 | − | 0.590619i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.09680 | − | 1.21059i | −0.632209 | − | 0.365006i | 0.149398 | − | 0.988777i | \(-0.452267\pi\) |
−0.781607 | + | 0.623771i | \(0.785600\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.73574 | − | 2.73418i | −1.31346 | − | 0.758325i | −0.330790 | − | 0.943704i | \(-0.607315\pi\) |
−0.982667 | + | 0.185380i | \(0.940648\pi\) | |||||||
\(14\) | 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 | 0.459461 | − | 0.888198i | \(-0.348043\pi\) |
−0.539471 | + | 0.842004i | \(0.681376\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.06895 | + | 1.77186i | −0.639920 | + | 0.369458i | −0.784584 | − | 0.620023i | \(-0.787123\pi\) |
0.144664 | + | 0.989481i | \(0.453790\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.440020 | + | 0.762137i | −0.0880040 | + | 0.152427i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.21979 | + | 3.03206i | −0.812098 | + | 0.583520i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.31784 | + | 3.64761i | −1.17319 | + | 0.677343i | −0.954430 | − | 0.298435i | \(-0.903535\pi\) |
−0.218763 | + | 0.975778i | \(0.570202\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.20001i | 0.754345i | 0.926143 | + | 0.377172i | \(0.123104\pi\) | ||||
−0.926143 | + | 0.377172i | \(0.876896\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.12137 | + | 2.80060i | −0.543361 | + | 0.487522i | ||||
\(34\) | 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 | ||||||||
\(39\) | −7.04978 | + | 6.32530i | −1.12887 | + | 1.01286i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.03924 | − | 6.99618i | 0.630824 | − | 1.09262i | −0.356560 | − | 0.934273i | \(-0.616050\pi\) |
0.987384 | − | 0.158346i | \(-0.0506163\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.22573 | − | 7.31918i | −0.644418 | − | 1.11616i | −0.984436 | − | 0.175745i | \(-0.943766\pi\) |
0.340018 | − | 0.940419i | \(-0.389567\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.785780 | − | 7.23208i | 0.117137 | − | 1.07809i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.51537 | 0.658635 | 0.329317 | − | 0.944219i | \(-0.393181\pi\) | ||||
0.329317 | + | 0.944219i | \(0.393181\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.37383 | + | 0.921671i | −0.612458 | + | 0.129060i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.1493 | + | 7.01442i | −1.66884 | + | 0.963505i | −0.700575 | + | 0.713579i | \(0.747073\pi\) |
−0.968265 | + | 0.249926i | \(0.919594\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.87106i | − | 0.791654i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.519169 | + | 0.465816i | −0.0687657 | + | 0.0616989i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.155809 | 0.0202846 | 0.0101423 | − | 0.999949i | \(-0.496772\pi\) | ||||
0.0101423 | + | 0.999949i | \(0.496772\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 11.8112i | − | 1.51227i | −0.654415 | − | 0.756136i | \(-0.727085\pi\) | ||
0.654415 | − | 0.756136i | \(-0.272915\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 13.2601i | − | 1.64471i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.07364 | −0.619844 | −0.309922 | − | 0.950762i | \(-0.600303\pi\) | ||||
−0.309922 | + | 0.950762i | \(0.600303\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.26561 | + | 6.00600i | 0.152361 | + | 0.723037i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.73987i | − | 1.03723i | −0.855007 | − | 0.518616i | \(-0.826448\pi\) | ||
0.855007 | − | 0.518616i | \(-0.173552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.62339 | − | 4.40137i | 0.892251 | − | 0.515141i | 0.0175727 | − | 0.999846i | \(-0.494406\pi\) |
0.874678 | + | 0.484704i | \(0.161073\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.01795 | + | 1.13454i | 0.117543 | + | 0.131006i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.3315 | −1.27489 | −0.637447 | − | 0.770494i | \(-0.720009\pi\) | ||||
−0.637447 | + | 0.770494i | \(0.720009\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.72104 | + | 8.57881i | 0.302337 | + | 0.953201i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.50937 | + | 13.0066i | 0.824260 | + | 1.42766i | 0.902483 | + | 0.430725i | \(0.141742\pi\) |
−0.0782227 | + | 0.996936i | \(0.524925\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.12893 | − | 5.41946i | 0.339380 | − | 0.587823i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.60542 | + | 12.3641i | 0.279331 | + | 1.32558i | ||||
\(88\) | 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 | ||||||||
\(93\) | 6.91464 | + | 2.26012i | 0.717015 | + | 0.234363i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 0.976519i | − | 0.100189i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.97713 | − | 2.87355i | 0.505351 | − | 0.291765i | −0.225569 | − | 0.974227i | \(-0.572424\pi\) |
0.730921 | + | 0.682462i | \(0.239091\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.93105 | + | 6.64589i | 0.294582 | + | 0.667937i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.83838 | + | 8.38031i | −0.481436 | + | 0.833872i | −0.999773 | − | 0.0213045i | \(-0.993218\pi\) |
0.518337 | + | 0.855177i | \(0.326551\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.6863 | + | 9.63382i | −1.64415 | + | 0.949249i | −0.664811 | + | 0.747012i | \(0.731488\pi\) |
−0.979337 | + | 0.202237i | \(0.935179\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.944715 | − | 0.545431i | −0.0913290 | − | 0.0527288i | 0.453640 | − | 0.891185i | \(-0.350125\pi\) |
−0.544969 | + | 0.838456i | \(0.683459\pi\) | |||||||
\(108\) | 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 | 0.981487 | − | 0.191531i | \(-0.0613453\pi\) |
0.324872 | + | 0.945758i | \(0.394679\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.44183 | − | 4.29654i | −0.693954 | − | 0.400655i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.61993 | + | 15.0101i | 0.612013 | + | 1.38768i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.56895 | − | 4.44955i | −0.233541 | − | 0.404505i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.34446 | − | 10.4147i | −0.842561 | − | 0.939066i | ||||
\(124\) | 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 | ||||||||
\(129\) | −14.3238 | + | 3.01837i | −1.26114 | + | 0.265753i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.73151 | − | 9.92727i | −0.500765 | − | 0.867350i | −1.00000 | 0.000883062i | \(-0.999719\pi\) | |
0.499235 | − | 0.866467i | \(-0.333614\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.4836 | − | 5.18539i | −0.988350 | − | 0.446288i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.71002 | − | 0.987278i | −0.146096 | − | 0.0843488i | 0.425170 | − | 0.905114i | \(-0.360214\pi\) |
−0.571266 | + | 0.820765i | \(0.693548\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.37804 | + | 3.10501i | 0.456159 | + | 0.263364i | 0.710428 | − | 0.703770i | \(-0.248501\pi\) |
−0.254269 | + | 0.967134i | \(0.581835\pi\) | |||||||
\(140\) | 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 | ||||||||
\(149\) | −10.5389 | + | 6.08462i | −0.863378 | + | 0.498472i | −0.865142 | − | 0.501527i | \(-0.832772\pi\) |
0.00176397 | + | 0.999998i | \(0.499439\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.31784 | + | 9.21076i | −0.432759 | + | 0.749561i | −0.997110 | − | 0.0759740i | \(-0.975793\pi\) |
0.564350 | + | 0.825535i | \(0.309127\pi\) | |||||||
\(152\) | 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 | ||||||||
\(157\) | − | 3.53516i | − | 0.282136i | −0.990000 | − | 0.141068i | \(-0.954946\pi\) | ||
0.990000 | − | 0.141068i | \(-0.0450537\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.01029 | + | 23.7765i | 0.397341 | + | 1.88560i | ||||
\(160\) | 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 | ||||||||
\(165\) | −9.66575 | − | 3.15935i | −0.752478 | − | 0.245955i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.39779 | + | 14.5454i | −0.649840 | + | 1.12556i | 0.333320 | + | 0.942814i | \(0.391831\pi\) |
−0.983161 | + | 0.182743i | \(0.941502\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.45146 | + | 14.6384i | 0.650112 | + | 1.12603i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.487514 | + | 1.10539i | 0.0372811 | + | 0.0845316i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.6170 | 1.26337 | 0.631684 | − | 0.775226i | \(-0.282364\pi\) | ||||
0.631684 | + | 0.775226i | \(0.282364\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.0838440 | − | 0.256513i | 0.00630210 | − | 0.0192807i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.6082 | − | 7.27937i | 0.942384 | − | 0.544086i | 0.0516773 | − | 0.998664i | \(-0.483543\pi\) |
0.890707 | + | 0.454578i | \(0.150210\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.02355i | − | 0.299068i | −0.988757 | − | 0.149534i | \(-0.952223\pi\) | ||
0.988757 | − | 0.149534i | \(-0.0477774\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.4452 | − | 6.35587i | −1.43743 | − | 0.469839i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.74410 | 0.569358 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.24830i | 0.456921i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.41775i | 0.609087i | 0.952498 | + | 0.304543i | \(0.0985039\pi\) | ||||
−0.952498 | + | 0.304543i | \(0.901496\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.63567 | −0.621609 | −0.310805 | − | 0.950474i | \(-0.600599\pi\) | ||||
−0.310805 | + | 0.950474i | \(0.600599\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −21.8306 | − | 7.13555i | −1.56332 | − | 0.510987i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 23.3303i | − | 1.66221i | −0.556112 | − | 0.831107i | \(-0.687708\pi\) | ||
0.556112 | − | 0.831107i | \(-0.312292\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.2441 | − | 7.06913i | 0.867960 | − | 0.501117i | 0.00129041 | − | 0.999999i | \(-0.499589\pi\) |
0.866670 | + | 0.498882i | \(0.166256\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.73024 | + | 8.35293i | −0.192576 | + | 0.589170i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.5894 | 1.36818 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.5689 | + | 1.14834i | 0.734593 | + | 0.0798150i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.487514 | + | 0.844399i | 0.0337221 | + | 0.0584083i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.75786 | + | 11.7050i | −0.465230 | + | 0.805802i | −0.999212 | − | 0.0396938i | \(-0.987362\pi\) |
0.533982 | + | 0.845496i | \(0.320695\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.3888 | − | 4.70311i | −0.985902 | − | 0.322252i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.2469 | − | 17.7481i | 0.698832 | − | 1.21041i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.14382 | − | 14.9191i | −0.212440 | − | 1.00814i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.1121i | 0.949284i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.4054 | − | 7.73961i | 0.897692 | − | 0.518283i | 0.0212411 | − | 0.999774i | \(-0.493238\pi\) |
0.876451 | + | 0.481492i | \(0.159905\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.41562 | − | 1.06537i | 0.161041 | − | 0.0710245i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.50835 | − | 13.0048i | 0.498347 | − | 0.863162i | −0.501651 | − | 0.865070i | \(-0.667274\pi\) |
0.999998 | + | 0.00190793i | \(0.000607314\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.9685 | + | 9.79677i | −1.12131 | + | 0.647389i | −0.941735 | − | 0.336355i | \(-0.890806\pi\) |
−0.179575 | + | 0.983744i | \(0.557472\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.9283 | + | 9.77356i | 1.10901 | + | 0.640287i | 0.938573 | − | 0.345081i | \(-0.112149\pi\) |
0.170437 | + | 0.985369i | \(0.445482\pi\) | |||||||
\(234\) | 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 | 0.718838 | − | 0.695178i | \(-0.244674\pi\) |
−0.242623 | + | 0.970121i | \(0.578008\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.21480 | − | 4.16547i | −0.464746 | − | 0.268321i | 0.249292 | − | 0.968428i | \(-0.419802\pi\) |
−0.714038 | + | 0.700107i | \(0.753136\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5879 | + | 0.136700i | 0.999962 | + | 0.00876928i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.10108 | + | 1.90712i | 0.0700598 | + | 0.121347i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 25.4542 | − | 5.36382i | 1.61310 | − | 0.339918i | ||||
\(250\) | 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 | ||||||||
\(255\) | −7.23852 | − | 8.06760i | −0.453294 | − | 0.505213i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.99030 | + | 5.17935i | 0.186530 | + | 0.323079i | 0.944091 | − | 0.329685i | \(-0.106943\pi\) |
−0.757561 | + | 0.652764i | \(0.773609\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.7576 | + | 2.36401i | 1.34676 | + | 0.146328i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.91506 | + | 1.68301i | 0.179750 | + | 0.103779i | 0.587175 | − | 0.809460i | \(-0.300240\pi\) |
−0.407425 | + | 0.913239i | \(0.633573\pi\) | |||||||
\(264\) | 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 | \(-0.981432\pi\) |
−0.549640 | − | 0.835402i | \(-0.685235\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.84527 | − | 1.06537i | 0.111274 | − | 0.0642440i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.60108 | − | 7.96930i | 0.276452 | − | 0.478829i | −0.694049 | − | 0.719928i | \(-0.744175\pi\) |
0.970500 | + | 0.241100i | \(0.0775080\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.44183 | − | 10.1676i | 0.445531 | − | 0.608719i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.05254 | − | 0.607682i | 0.0627891 | − | 0.0362513i | −0.468277 | − | 0.883582i | \(-0.655125\pi\) |
0.531066 | + | 0.847331i | \(0.321792\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.2139i | 0.726043i | 0.931781 | + | 0.363021i | \(0.118255\pi\) | ||||
−0.931781 | + | 0.363021i | \(0.881745\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.60768 | − | 0.525486i | −0.0952307 | − | 0.0311271i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.17002 | − | 8.95475i | 0.304119 | − | 0.526750i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.05253 | − | 9.74036i | −0.120321 | − | 0.570990i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.15082 | − | 5.45739i | 0.184073 | − | 0.318824i | −0.759191 | − | 0.650868i | \(-0.774405\pi\) |
0.943264 | + | 0.332044i | \(0.107738\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.188909 | + | 0.327199i | 0.0109987 | + | 0.0190503i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.5186 | − | 1.24920i | 0.726405 | − | 0.0724860i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 19.3783 | 1.12068 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.1932 | + | 12.4752i | 0.643032 | + | 0.716683i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24.8036 | − | 14.3204i | 1.42025 | − | 0.819983i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 28.7264i | − | 1.63950i | −0.572721 | − | 0.819750i | \(-0.694112\pi\) | ||
0.572721 | − | 0.819750i | \(-0.305888\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.88128 | + | 32.6554i | 0.391462 | + | 1.85770i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.7325 | −1.00552 | −0.502758 | − | 0.864427i | \(-0.667681\pi\) | ||||
−0.502758 | + | 0.864427i | \(0.667681\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 27.0808i | − | 1.53070i | −0.643616 | − | 0.765348i | \(-0.722567\pi\) | ||
0.643616 | − | 0.765348i | \(-0.277433\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 5.37385i | − | 0.301825i | −0.988547 | − | 0.150913i | \(-0.951779\pi\) | ||
0.988547 | − | 0.150913i | \(-0.0482212\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.6630 | 0.988938 | ||||||||
\(320\) | 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 | ||||||||
\(327\) | −3.92110 | + | 0.826270i | −0.216837 | + | 0.0456928i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.44207 | −0.409053 | −0.204527 | − | 0.978861i | \(-0.565565\pi\) | ||||
−0.204527 | + | 0.978861i | \(0.565565\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.76612 | + | 3.86614i | −0.480380 | + | 0.211863i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.15149 | − | 10.6547i | −0.336092 | − | 0.582128i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.31784 | + | 9.21076i | −0.289681 | + | 0.501742i | −0.973734 | − | 0.227690i | \(-0.926883\pi\) |
0.684053 | + | 0.729433i | \(0.260216\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.6723 | − | 18.5479i | 1.12277 | − | 1.00738i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.08449 | − | 8.80660i | 0.275341 | − | 0.476904i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.0782 | + | 9.93970i | −0.596428 | + | 0.535135i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.89189i | 0.101562i | 0.998710 | + | 0.0507809i | \(0.0161710\pi\) | ||||
−0.998710 | + | 0.0507809i | \(0.983829\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.1105 | + | 9.30140i | −0.862375 | + | 0.497892i | −0.864807 | − | 0.502105i | \(-0.832559\pi\) |
0.00243201 | + | 0.999997i | \(0.499226\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 28.2740 | − | 2.82139i | 1.50915 | − | 0.150595i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.94505 | + | 3.36893i | −0.103525 | + | 0.179310i | −0.913134 | − | 0.407659i | \(-0.866345\pi\) |
0.809610 | + | 0.586968i | \(0.199679\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.3538 | − | 10.5966i | 0.974118 | − | 0.562407i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.46992 | − | 4.31276i | −0.394248 | − | 0.227619i | 0.289751 | − | 0.957102i | \(-0.406427\pi\) |
−0.683999 | + | 0.729483i | \(0.739761\pi\) | |||||||
\(360\) | 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 | ||||||||
\(367\) | 15.8701 | + | 9.16260i | 0.828412 | + | 0.478284i | 0.853309 | − | 0.521406i | \(-0.174592\pi\) |
−0.0248966 | + | 0.999690i | \(0.507926\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −22.1746 | + | 9.77973i | −1.15437 | + | 0.509112i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.84791 | + | 6.66478i | 0.199237 | + | 0.345089i | 0.948281 | − | 0.317431i | \(-0.102820\pi\) |
−0.749044 | + | 0.662520i | \(0.769487\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.37605 | − | 16.4476i | 0.277618 | − | 0.849349i | ||||
\(376\) | 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 | ||||||||
\(381\) | −1.64894 | + | 5.04479i | −0.0844778 | + | 0.258453i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.70467 | − | 2.95258i | −0.0871047 | − | 0.150870i | 0.819181 | − | 0.573534i | \(-0.194428\pi\) |
−0.906286 | + | 0.422665i | \(0.861095\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.73869 | + | 25.2060i | −0.139215 | + | 1.28129i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.33425 | − | 4.81178i | −0.422563 | − | 0.243967i | 0.273610 | − | 0.961841i | \(-0.411782\pi\) |
−0.696173 | + | 0.717874i | \(0.745116\pi\) | |||||||
\(390\) | 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 | 0.914272 | − | 0.405101i | \(-0.132764\pi\) |
0.106308 | + | 0.994333i | \(0.466097\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.2019 | − | 12.8183i | 1.10871 | − | 0.640113i | 0.170214 | − | 0.985407i | \(-0.445554\pi\) |
0.938495 | + | 0.345294i | \(0.112221\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.4836 | − | 19.8902i | 0.572038 | − | 0.990799i | ||||
\(404\) | 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 | ||||||||
\(409\) | − | 15.4321i | − | 0.763066i | −0.924355 | − | 0.381533i | \(-0.875396\pi\) | ||
0.924355 | − | 0.381533i | \(-0.124604\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.54559 | + | 2.28399i | −0.125565 | + | 0.112661i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.2093 | + | 31.5395i | −0.893860 | + | 1.54821i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.00593 | − | 7.18319i | 0.392052 | − | 0.351762i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.10643 | − | 12.3087i | 0.347172 | − | 0.601319i | −0.638574 | − | 0.769560i | \(-0.720475\pi\) |
0.985746 | + | 0.168241i | \(0.0538088\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.849964 | − | 1.47218i | −0.0414247 | − | 0.0717497i | 0.844570 | − | 0.535446i | \(-0.179856\pi\) |
−0.885994 | + | 0.463696i | \(0.846523\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.9310 | − | 8.00060i | −0.531486 | − | 0.389003i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.27111 | 0.110165 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 22.4393 | − | 4.72851i | 1.08338 | − | 0.228294i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.2868 | − | 16.3314i | 1.36253 | − | 0.786656i | 0.372568 | − | 0.928005i | \(-0.378477\pi\) |
0.989960 | + | 0.141349i | \(0.0451440\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 13.6919i | − | 0.657992i | −0.944331 | − | 0.328996i | \(-0.893290\pi\) | ||
0.944331 | − | 0.328996i | \(-0.106710\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.8059 | + | 20.4622i | −1.09346 | + | 0.981087i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.42708 | 0.0682667 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 8.82352i | − | 0.421124i | −0.977581 | − | 0.210562i | \(-0.932471\pi\) | ||
0.977581 | − | 0.210562i | \(-0.0675293\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.6600i | 1.17163i | 0.810444 | + | 0.585816i | \(0.199226\pi\) | ||||
−0.810444 | + | 0.585816i | \(0.800774\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 37.9901 | 1.80090 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.34614 | + | 20.6248i | 0.205566 | + | 0.975520i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.61306i | 0.217704i | 0.994058 | + | 0.108852i | \(0.0347174\pi\) | ||||
−0.994058 | + | 0.108852i | \(0.965283\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.9390 | + | 9.77973i | −0.797626 | + | 0.460509i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.3024 | + | 13.7115i | 0.578016 | + | 0.644221i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.71871 | 0.361066 | 0.180533 | − | 0.983569i | \(-0.442218\pi\) | ||||
0.180533 | + | 0.983569i | \(0.442218\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.2215 | + | 5.51858i | 0.570449 | + | 0.257585i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.28621 | + | 16.0842i | 0.432502 | + | 0.749115i | 0.997088 | − | 0.0762589i | \(-0.0242975\pi\) |
−0.564586 | + | 0.825374i | \(0.690964\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7046 | − | 30.6653i | 0.822804 | − | 1.42514i | −0.0807828 | − | 0.996732i | \(-0.525742\pi\) |
0.903586 | − | 0.428406i | \(-0.140925\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.63732 | + | 17.2610i | 0.168677 | + | 0.800462i | ||||
\(466\) | 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 | ||||||||
\(471\) | −5.82006 | − | 1.90234i | −0.268174 | − | 0.0876554i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.4625i | 0.940866i | ||||||||
\(474\) | 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 | ||||||||
\(479\) | −13.2512 | + | 22.9518i | −0.605465 | + | 1.04870i | 0.386513 | + | 0.922284i | \(0.373679\pi\) |
−0.991978 | + | 0.126412i | \(0.959654\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.1241 | + | 8.73188i | −0.689598 | + | 0.398139i | ||||
\(482\) | 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 | 0.0805333 | − | 0.996752i | \(-0.474338\pi\) |
−0.822946 | + | 0.568120i | \(0.807671\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.3044 | + | 9.41333i | 0.734312 | + | 0.423955i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.4027 | + | 14.2130i | −0.467566 | + | 0.638826i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.628929 | − | 1.08934i | −0.0281547 | − | 0.0487654i | 0.851605 | − | 0.524184i | \(-0.175630\pi\) |
−0.879759 | + | 0.475419i | \(0.842296\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.4276 | + | 21.6528i | 0.867961 | + | 0.967375i | ||||
\(502\) | 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 | ||||||||
\(507\) | 28.6476 | − | 6.03674i | 1.27228 | − | 0.268101i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.90471 | + | 5.03110i | 0.128749 | + | 0.223000i | 0.923192 | − | 0.384339i | \(-0.125571\pi\) |
−0.794443 | + | 0.607338i | \(0.792237\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.08219 | − | 0.207776i | 0.0919310 | − | 0.00917355i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −40.4622 | − | 23.3609i | −1.78298 | − | 1.02940i | ||||
\(516\) | 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 | −0.0413640 | − | 0.999144i | \(-0.513170\pi\) |
−0.885966 | + | 0.463750i | \(0.846504\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.38679 | − | 5.41946i | 0.408895 | − | 0.236076i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.22104 | + | 9.04310i | −0.227002 | + | 0.393178i | ||||
\(530\) | 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 | ||||||||
\(535\) | − | 2.64521i | − | 0.114362i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.19953 | − | 24.6746i | −0.224376 | − | 1.06479i | ||||
\(538\) | 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 | ||||||||
\(543\) | −6.62412 | − | 2.16516i | −0.284268 | − | 0.0929159i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.80506 | − | 4.85850i | 0.120155 | − | 0.208115i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.31826 | − | 5.74739i | −0.141878 | − | 0.245741i | 0.786326 | − | 0.617812i | \(-0.211981\pi\) |
−0.928204 | + | 0.372072i | \(0.878648\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −20.9278 | + | 28.5932i | −0.893177 | + | 1.22033i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.93784 | 0.125156 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.16727 | − | 12.7494i | 0.176891 | − | 0.541182i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.3205 | − | 12.3094i | 0.903378 | − | 0.521565i | 0.0250832 | − | 0.999685i | \(-0.492015\pi\) |
0.878295 | + | 0.478120i | \(0.158682\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46.2156i | 1.95471i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.2868 | + | 3.36235i | 0.434310 | + | 0.141958i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.5711 | −0.529808 | −0.264904 | − | 0.964275i | \(-0.585340\pi\) | ||||
−0.264904 | + | 0.964275i | \(0.585340\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 38.8831i | 1.63583i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 14.8809i | − | 0.623838i | −0.950109 | − | 0.311919i | \(-0.899028\pi\) | ||
0.950109 | − | 0.311919i | \(-0.100972\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.9115 | −0.707723 | −0.353861 | − | 0.935298i | \(-0.615132\pi\) | ||||
−0.353861 | + | 0.935298i | \(0.615132\pi\) | |||||||
\(572\) | 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 | −0.826978 | − | 0.562234i | \(-0.809942\pi\) |
0.0734203 | + | 0.997301i | \(0.476609\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.64704 | + | 14.2172i | −0.193124 | + | 0.590848i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.9663 | 1.40674 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −23.4950 | + | 32.1007i | −0.971400 | + | 1.32720i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.8542 | + | 25.7283i | 0.613100 | + | 1.06192i | 0.990715 | + | 0.135957i | \(0.0434109\pi\) |
−0.377615 | + | 0.925963i | \(0.623256\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.845690 | − | 1.46478i | 0.0348461 | − | 0.0603551i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −38.4095 | − | 12.5545i | −1.57996 | − | 0.516424i | ||||
\(592\) | 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 | ||||||||
\(597\) | −5.04936 | − | 23.9619i | −0.206657 | − | 0.980697i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.0996i | 1.31156i | 0.754954 | + | 0.655778i | \(0.227659\pi\) | ||||
−0.754954 | + | 0.655778i | \(0.772341\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.1636 | − | 9.33208i | 0.659329 | − | 0.380664i | −0.132692 | − | 0.991157i | \(-0.542362\pi\) |
0.792021 | + | 0.610494i | \(0.209029\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.2825 | + | 8.98978i | 0.500183 | + | 0.366092i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.22939 | − | 10.7896i | 0.253261 | − | 0.438661i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.0104 | − | 6.93419i | 0.487486 | − | 0.281450i | −0.236045 | − | 0.971742i | \(-0.575851\pi\) |
0.723531 | + | 0.690292i | \(0.242518\pi\) | |||||||
\(608\) | 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 | 0.775142 | − | 0.631787i | \(-0.217678\pi\) |
−0.159573 | + | 0.987186i | \(0.551012\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.78789 | + | 2.76429i | 0.192441 | + | 0.111106i | 0.593125 | − | 0.805110i | \(-0.297894\pi\) |
−0.400684 | + | 0.916216i | \(0.631227\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.57793 | − | 16.7821i | 0.304092 | − | 0.673443i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.3129 | + | 24.7906i | 0.572515 | + | 0.991624i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.65251 | − | 0.348223i | 0.0659948 | − | 0.0139067i | ||||
\(628\) | 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 | ||||||||
\(633\) | 15.6337 | + | 17.4244i | 0.621386 | + | 0.692558i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.71522 | − | 6.43496i | −0.147434 | − | 0.255363i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.4858 | + | 21.1579i | −0.612609 | + | 0.836994i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.3174 | − | 14.6170i | −0.999978 | − | 0.577337i | −0.0917361 | − | 0.995783i | \(-0.529242\pi\) |
−0.908242 | + | 0.418446i | \(0.862575\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.6535 | + | 20.0072i | 1.36660 | + | 0.789008i | 0.990492 | − | 0.137567i | \(-0.0439284\pi\) |
0.376109 | + | 0.926575i | \(0.377262\pi\) | |||||||
\(644\) | 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 | ||||||||
\(653\) | −33.9375 | + | 19.5938i | −1.32808 | + | 0.766766i | −0.985002 | − | 0.172542i | \(-0.944802\pi\) |
−0.343076 | + | 0.939308i | \(0.611469\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.8982 | − | 24.0724i | 0.543049 | − | 0.940588i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −26.2537 | − | 2.85252i | −1.02425 | − | 0.111287i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.8594 | + | 13.1979i | −0.890474 | + | 0.514115i | −0.874098 | − | 0.485751i | \(-0.838546\pi\) |
−0.0163765 | + | 0.999866i | \(0.505213\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 31.5812i | − | 1.22837i | −0.789163 | − | 0.614184i | \(-0.789485\pi\) | ||
0.789163 | − | 0.614184i | \(-0.210515\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.2333 | + | 7.59404i | 0.902307 | + | 0.294928i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.9261 | − | 22.3886i | 0.500500 | − | 0.866891i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.52827 | − | 26.2346i | −0.213735 | − | 1.01429i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.2985 | + | 24.7658i | −0.551989 | + | 0.956073i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.21676 | − | 12.4998i | −0.278186 | − | 0.481832i | 0.692748 | − | 0.721180i | \(-0.256400\pi\) |
−0.970934 | + | 0.239348i | \(0.923066\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.454055 | − | 4.55022i | −0.0174766 | − | 0.175138i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −34.4198 | −1.32286 | −0.661430 | − | 0.750006i | \(-0.730050\pi\) | ||||
−0.661430 | + | 0.750006i | \(0.730050\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.3700 | − | 19.3595i | −0.665618 | − | 0.741856i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.4694 | + | 9.50861i | −0.630184 | + | 0.363837i | −0.780823 | − | 0.624752i | \(-0.785200\pi\) |
0.150639 | + | 0.988589i | \(0.451867\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 4.78806i | − | 0.182942i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.99767 | + | 33.2077i | 0.266978 | + | 1.26695i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 76.7147 | 2.92260 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.3753i | 0.737070i | 0.929614 | + | 0.368535i | \(0.120141\pi\) | ||||
−0.929614 | + | 0.368535i | \(0.879859\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.0586i | 0.571204i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.8481 | −0.789676 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.2001 | − | 22.6103i | 0.953154 | − | 0.855201i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 23.0297i | − | 0.869819i | −0.900474 | − | 0.434910i | \(-0.856780\pi\) | ||
0.900474 | − | 0.434910i | \(-0.143220\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.11379 | + | 0.643045i | −0.0420073 | + | 0.0242529i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.5571 | − | 3.91043i | 0.698901 | − | 0.147275i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −40.8238 | −1.53317 | −0.766585 | − | 0.642143i | \(-0.778045\pi\) | ||||
−0.766585 | + | 0.642143i | \(0.778045\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27.4319 | + | 20.0778i | 1.02878 | + | 0.752977i | ||||
\(712\) | 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 | ||||||||
\(717\) | 10.9595 | − | 9.83321i | 0.409289 | − | 0.367228i | ||||
\(718\) | 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 | ||||||||
\(723\) | −10.7402 | + | 9.63647i | −0.399433 | + | 0.358384i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 6.42008i | − | 0.238436i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.58754 | + | 2.64862i | −0.170142 | + | 0.0982318i | −0.582653 | − | 0.812721i | \(-0.697985\pi\) |
0.412511 | + | 0.910953i | \(0.364652\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.61321 | − | 25.5893i | 0.319008 | − | 0.947752i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.9053 | + | 18.8885i | −0.403347 | + | 0.698617i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.1513 | − | 9.32497i | 0.596563 | − | 0.344426i | −0.171125 | − | 0.985249i | \(-0.554740\pi\) |
0.767688 | + | 0.640824i | \(0.221407\pi\) | |||||||
\(734\) | 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 | 0.827542 | − | 0.561404i | \(-0.189739\pi\) |
−0.0724196 | + | 0.997374i | \(0.523072\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25.5555 | − | 14.7545i | −0.936281 | − | 0.540562i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.86681 | − | 44.7926i | 0.178067 | − | 1.63888i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.06151 | − | 15.6950i | −0.330659 | − | 0.572718i | 0.651982 | − | 0.758234i | \(-0.273938\pi\) |
−0.982641 | + | 0.185516i | \(0.940604\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.30569 | − | 22.3511i | 0.266234 | − | 0.814521i | ||||
\(754\) | 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 | ||||||||
\(759\) | 4.61707 | − | 14.1255i | 0.167589 | − | 0.512724i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.90537 | − | 10.2284i | −0.214070 | − | 0.370779i | 0.738915 | − | 0.673799i | \(-0.235339\pi\) |
−0.952984 | + | 0.303020i | \(0.902005\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −17.1772 | + | 7.57569i | −0.621043 | + | 0.273900i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.737868 | − | 0.426009i | −0.0266429 | − | 0.0153823i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.14015 | + | 1.81297i | 0.113237 | + | 0.0653773i | 0.555549 | − | 0.831484i | \(-0.312508\pi\) |
−0.442312 | + | 0.896861i | \(0.645842\pi\) | |||||||
\(770\) | 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 | ||||||||
\(779\) | −2.81742 | + | 1.62664i | −0.100944 | + | 0.0582803i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.5804 | + | 18.3258i | −0.378596 | + | 0.655748i | ||||
\(782\) | 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 | ||||||||
\(787\) | 20.3222i | 0.724406i | 0.932099 | + | 0.362203i | \(0.117975\pi\) | ||||
−0.932099 | + | 0.362203i | \(0.882025\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.33946 | − | 3.89351i | 0.154489 | − | 0.138612i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.2940 | + | 55.9348i | −1.14679 | + | 1.98630i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −43.8562 | + | 39.3492i | −1.55542 | + | 1.39557i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.8973 | − | 29.2669i | 0.598532 | − | 1.03669i | −0.394506 | − | 0.918893i | \(-0.629084\pi\) |
0.993038 | − | 0.117795i | \(-0.0375824\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.82639 | − | 10.0916i | −0.206123 | − | 0.357015i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −43.0037 | + | 18.9660i | −1.51946 | + | 0.670132i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.3130 | −0.752119 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.8163 | − | 4.38650i | 0.732769 | − | 0.154412i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.19308 | + | 2.42087i | −0.147421 | + | 0.0851134i | −0.571896 | − | 0.820326i | \(-0.693792\pi\) |
0.424475 | + | 0.905440i | \(0.360459\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 0.493486i | − | 0.0173286i | −0.999962 | − | 0.00866432i | \(-0.997242\pi\) | ||
0.999962 | − | 0.00866432i | \(-0.00275797\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −37.9338 | + | 34.0355i | −1.33040 | + | 1.19368i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.3531 | −0.537797 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.40347i | 0.119072i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 30.8225i | − | 1.07571i | −0.843036 | − | 0.537857i | \(-0.819234\pi\) | ||
0.843036 | − | 0.537857i | \(-0.180766\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.8850 | −0.553716 | −0.276858 | − | 0.960911i | \(-0.589293\pi\) | ||||
−0.276858 | + | 0.960911i | \(0.589293\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.760974 | − | 3.61123i | −0.0264937 | − | 0.125727i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 35.6756i | − | 1.24056i | −0.784379 | − | 0.620282i | \(-0.787018\pi\) | ||
0.784379 | − | 0.620282i | \(-0.212982\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.87997 | − | 1.66275i | 0.100026 | − | 0.0577498i | −0.449153 | − | 0.893455i | \(-0.648274\pi\) |
0.549178 | + | 0.835705i | \(0.314941\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.6442 | − | 11.8634i | −0.369244 | − | 0.411536i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −40.7273 | −1.40942 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12.7347 | − | 17.7232i | −0.440176 | − | 0.612602i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.9689 | − | 36.3192i | −0.723926 | − | 1.25388i | −0.959414 | − | 0.282000i | \(-0.909002\pi\) |
0.235488 | − | 0.971877i | \(-0.424331\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.1100 | − | 20.9752i | 0.417588 | − | 0.723283i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.434057 | − | 2.05984i | −0.0149497 | − | 0.0709445i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −20.4938 | + | 35.4963i | −0.705007 | + | 1.22111i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.1082 | + | 6.57258i | 0.690113 | + | 0.225570i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.3172i | 0.387949i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.5330 | + | 7.23594i | −0.429122 | + | 0.247754i | −0.698973 | − | 0.715149i | \(-0.746359\pi\) |
0.269851 | + | 0.962902i | \(0.413026\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.73025 | + | 2.36401i | −0.0591734 | + | 0.0808473i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.7329 | − | 41.1065i | 0.810699 | − | 1.40417i | −0.101676 | − | 0.994818i | \(-0.532421\pi\) |
0.912375 | − | 0.409355i | \(-0.134246\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.20316 | − | 3.00405i | 0.177530 | − | 0.102497i | −0.408602 | − | 0.912713i | \(-0.633984\pi\) |
0.586131 | + | 0.810216i | \(0.300650\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.1064 | − | 15.6499i | −0.922714 | − | 0.532729i | −0.0382141 | − | 0.999270i | \(-0.512167\pi\) |
−0.884500 | + | 0.466540i | \(0.845500\pi\) | |||||||
\(864\) | 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 | ||||||||
\(871\) | 24.0274 | + | 13.8722i | 0.814139 | + | 0.470043i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −17.1404 | − | 1.86234i | −0.580115 | − | 0.0630307i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.6882 | − | 35.8330i | −0.698591 | − | 1.21000i | −0.968955 | − | 0.247237i | \(-0.920477\pi\) |
0.270364 | − | 0.962758i | \(-0.412856\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.28917 | − | 8.12406i | −0.245858 | − | 0.274018i | ||||
\(880\) | 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 | ||||||||
\(885\) | 0.640336 | − | 0.134934i | 0.0215247 | − | 0.00453576i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.0561 | + | 24.3459i | 0.471958 | + | 0.817456i | 0.999485 | − | 0.0320827i | \(-0.0102140\pi\) |
−0.527527 | + | 0.849538i | \(0.676881\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.67994 | − | 21.2821i | 0.156784 | − | 0.712978i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.57476 | − | 0.909189i | −0.0526974 | − | 0.0304248i | ||||
\(894\) | 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 | ||||||||
\(905\) | 8.44949 | − | 4.87831i | 0.280870 | − | 0.162161i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.7430 | + | 51.5163i | −0.987599 | + | 1.71057i | −0.357836 | + | 0.933784i | \(0.616485\pi\) |
−0.629763 | + | 0.776788i | \(0.716848\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 26.5617 | − | 11.7146i | 0.880996 | − | 0.388548i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.4502 | − | 14.6937i | 0.843204 | − | 0.486824i | −0.0151480 | − | 0.999885i | \(-0.504822\pi\) |
0.858352 | + | 0.513061i | \(0.171489\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 36.3630i | − | 1.20344i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.2288 | − | 48.5413i | −0.338154 | − | 1.60472i | ||||
\(916\) | 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 | ||||||||
\(921\) | −47.2933 | − | 15.4583i | −1.55837 | − | 0.509367i | ||||
\(922\) | 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 | ||||||||
\(927\) | 57.4648 | + | 6.24366i | 1.88739 | + | 0.205069i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.43228 | 0.0798004 | 0.0399002 | − | 0.999204i | \(-0.487296\pi\) | ||||
0.0399002 | + | 0.999204i | \(0.487296\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.54222 | + | 29.1936i | −0.312398 | + | 0.955756i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.1215 | + | 7.57569i | −0.429118 | + | 0.247752i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 7.29837i | − | 0.238427i | −0.992869 | − | 0.119214i | \(-0.961963\pi\) | ||
0.992869 | − | 0.119214i | \(-0.0380374\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −44.5841 | − | 14.5728i | −1.45495 | − | 0.475564i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.4735 | −1.38460 | −0.692298 | − | 0.721612i | \(-0.743402\pi\) | ||||
−0.692298 | + | 0.721612i | \(0.743402\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.6279i | 0.932252i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 54.6311i | − | 1.77527i | −0.460546 | − | 0.887636i | \(-0.652346\pi\) | ||
0.460546 | − | 0.887636i | \(-0.347654\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −48.1365 | −1.56258 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.84717 | − | 2.89178i | −0.286889 | − | 0.0937725i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 17.1877i | − | 0.556764i | −0.960470 | − | 0.278382i | \(-0.910202\pi\) | ||
0.960470 | − | 0.278382i | \(-0.0897981\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.6773 | + | 10.2060i | −0.572025 | + | 0.330259i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.50484 | − | 29.0793i | 0.307248 | − | 0.939999i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.3599 | 0.430964 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.32059 | + | 2.99431i | 0.0425553 | + | 0.0964902i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.4702 | − | 18.1350i | −0.337049 | − | 0.583786i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.1546 | + | 19.3203i | −0.358706 | + | 0.621298i | −0.987745 | − | 0.156076i | \(-0.950115\pi\) |
0.629039 | + | 0.777374i | \(0.283449\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.71098 | + | 0.559250i | 0.0549646 | + | 0.0179657i | ||||
\(970\) | 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 | ||||||||
\(975\) | −1.71870 | − | 8.15616i | −0.0550424 | − | 0.261206i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.2154i | 1.31860i | 0.751881 | + | 0.659299i | \(0.229147\pi\) | ||||
−0.751881 | + | 0.659299i | \(0.770853\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | 9.21969 | − | 15.9690i | 0.294062 | − | 0.509331i | −0.680704 | − | 0.732559i | \(-0.738326\pi\) |
0.974766 | + | 0.223228i | \(0.0716593\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48.9938 | − | 28.2866i | 1.56107 | − | 0.901285i | ||||
\(986\) | 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 | ||||||||
\(997\) | 0.411648 | + | 0.237665i | 0.0130370 | + | 0.00752693i | 0.506504 | − | 0.862237i | \(-0.330937\pi\) |
−0.493467 | + | 0.869764i | \(0.664271\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.64773 | + | 16.5124i | 0.0521320 | + | 0.522431i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))