Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(2239,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.2239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6x^{14} + 28x^{12} + 16x^{10} - 40x^{8} + 610x^{6} + 1625x^{4} - 524x^{2} + 1444 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2239.4 | ||
Root | \(-1.61596 + 1.02509i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.2239 |
Dual form | 2240.2.e.f.2239.15 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.13578i | − | 1.23309i | −0.787319 | − | 0.616546i | \(-0.788531\pi\) | ||
0.787319 | − | 0.616546i | \(-0.211469\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.94442 | + | 1.10418i | 0.869572 | + | 0.493806i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.35829 | + | 1.19935i | 0.891352 | + | 0.453313i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.56155 | −0.520518 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.33205i | − | 0.703139i | −0.936162 | − | 0.351569i | \(-0.885648\pi\) | ||
0.936162 | − | 0.351569i | \(-0.114352\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.09190 | 0.302837 | 0.151419 | − | 0.988470i | \(-0.451616\pi\) | ||||
0.151419 | + | 0.988470i | \(0.451616\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.35829 | − | 4.15286i | 0.608909 | − | 1.07226i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.98074 | 1.20801 | 0.604003 | − | 0.796982i | \(-0.293571\pi\) | ||||
0.604003 | + | 0.796982i | \(0.293571\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.57501 | −0.590748 | −0.295374 | − | 0.955382i | \(-0.595444\pi\) | ||||
−0.295374 | + | 0.955382i | \(0.595444\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.56155 | − | 5.03680i | 0.558977 | − | 1.09912i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.04090 | −1.25961 | −0.629807 | − | 0.776752i | \(-0.716866\pi\) | ||||
−0.629807 | + | 0.776752i | \(0.716866\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.56155 | + | 4.29400i | 0.512311 | + | 0.858800i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 3.07221i | − | 0.591246i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.561553 | −0.104278 | −0.0521389 | − | 0.998640i | \(-0.516604\pi\) | ||||
−0.0521389 | + | 0.998640i | \(0.516604\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.59603 | 1.18468 | 0.592341 | − | 0.805688i | \(-0.298204\pi\) | ||||
0.592341 | + | 0.805688i | \(0.298204\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.98074 | −0.867035 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.26121 | + | 4.93604i | 0.551246 | + | 0.834343i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.49966i | 0.904138i | 0.891983 | + | 0.452069i | \(0.149314\pi\) | ||||
−0.891983 | + | 0.452069i | \(0.850686\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 2.33205i | − | 0.373427i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 8.48528i | − | 1.32518i | −0.748983 | − | 0.662589i | \(-0.769458\pi\) | ||
0.748983 | − | 0.662589i | \(-0.230542\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.32431 | −0.201955 | −0.100977 | − | 0.994889i | \(-0.532197\pi\) | ||||
−0.100977 | + | 0.994889i | \(0.532197\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.03632 | − | 1.72424i | −0.452627 | − | 0.257035i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 9.74247i | − | 1.42109i | −0.703654 | − | 0.710543i | \(-0.748450\pi\) | ||
0.703654 | − | 0.710543i | \(-0.251550\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.12311 | + | 5.65685i | 0.589015 | + | 0.808122i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 10.6378i | − | 1.48958i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.58800i | 1.17965i | 0.807530 | + | 0.589826i | \(0.200804\pi\) | ||||
−0.807530 | + | 0.589826i | \(0.799196\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.57501 | − | 4.53448i | 0.347214 | − | 0.611430i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.49966i | 0.728447i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.3211 | 1.86444 | 0.932222 | − | 0.361888i | \(-0.117868\pi\) | ||||
0.932222 | + | 0.361888i | \(0.117868\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.620058i | 0.0793903i | 0.999212 | + | 0.0396951i | \(0.0126387\pi\) | ||||
−0.999212 | + | 0.0396951i | \(0.987361\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.68260 | − | 1.87285i | −0.463964 | − | 0.235957i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.12311 | + | 1.20565i | 0.263339 | + | 0.149543i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.71659 | 0.576223 | 0.288112 | − | 0.957597i | \(-0.406973\pi\) | ||||
0.288112 | + | 0.957597i | \(0.406973\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.9020i | 1.55322i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.9473i | 1.41789i | 0.705265 | + | 0.708943i | \(0.250828\pi\) | ||||
−0.705265 | + | 0.708943i | \(0.749172\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.96148 | 1.16590 | 0.582951 | − | 0.812507i | \(-0.301898\pi\) | ||||
0.582951 | + | 0.812507i | \(0.301898\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.17104 | − | 5.47091i | 1.05898 | − | 0.631726i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.79695 | − | 5.49966i | 0.318742 | − | 0.626744i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 10.6378i | − | 1.19684i | −0.801182 | − | 0.598421i | \(-0.795795\pi\) | ||
0.801182 | − | 0.598421i | \(-0.204205\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2462 | −1.24958 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.86098i | 0.423798i | 0.977292 | + | 0.211899i | \(0.0679648\pi\) | ||||
−0.977292 | + | 0.211899i | \(0.932035\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.68466 | + | 5.49966i | 1.05045 | + | 0.596521i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.19935i | 0.128584i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.82843i | 0.299813i | 0.988700 | + | 0.149906i | \(0.0478972\pi\) | ||||
−0.988700 | + | 0.149906i | \(0.952103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.57501 | + | 1.30957i | 0.269935 | + | 0.137280i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 14.0877i | − | 1.46082i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.00691 | − | 2.84329i | −0.513698 | − | 0.291715i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.9422 | −1.51715 | −0.758576 | − | 0.651584i | \(-0.774105\pi\) | ||||
−0.758576 | + | 0.651584i | \(0.774105\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.64162i | 0.365996i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 15.1104i | − | 1.50354i | −0.659425 | − | 0.751770i | \(-0.729200\pi\) | ||
0.659425 | − | 0.751770i | \(-0.270800\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.47091i | 0.539065i | 0.962991 | + | 0.269532i | \(0.0868691\pi\) | ||||
−0.962991 | + | 0.269532i | \(0.913131\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.5423 | − | 6.96523i | 1.02882 | − | 0.679737i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.0138 | −0.968072 | −0.484036 | − | 0.875048i | \(-0.660830\pi\) | ||||
−0.484036 | + | 0.875048i | \(0.660830\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.56155 | −0.436918 | −0.218459 | − | 0.975846i | \(-0.570103\pi\) | ||||
−0.218459 | + | 0.975846i | \(0.570103\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.7460 | 1.11489 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.49966i | − | 0.517364i | −0.965963 | − | 0.258682i | \(-0.916712\pi\) | ||
0.965963 | − | 0.258682i | \(-0.0832882\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.7460 | − | 6.67026i | −1.09532 | − | 0.622005i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.70505 | −0.157632 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.7460 | + | 5.97366i | 1.07676 | + | 0.547605i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.56155 | 0.505596 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −18.1227 | −1.63407 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.239369 | + | 11.1778i | 0.0214098 | + | 0.999771i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.29723 | −0.470053 | −0.235026 | − | 0.971989i | \(-0.575518\pi\) | ||||
−0.235026 | + | 0.971989i | \(0.575518\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.82843i | 0.249029i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.57501 | 0.224980 | 0.112490 | − | 0.993653i | \(-0.464117\pi\) | ||||
0.112490 | + | 0.993653i | \(0.464117\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.07263 | − | 3.08835i | −0.526564 | − | 0.267794i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.39228 | − | 5.97366i | 0.291961 | − | 0.514131i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.08835i | 0.263855i | 0.991259 | + | 0.131928i | \(0.0421167\pi\) | ||||
−0.991259 | + | 0.131928i | \(0.957883\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.02102 | 0.341058 | 0.170529 | − | 0.985353i | \(-0.445452\pi\) | ||||
0.170529 | + | 0.985353i | \(0.445452\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −20.8078 | −1.75233 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 2.54635i | − | 0.212937i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.09190 | − | 0.620058i | −0.0906770 | − | 0.0514930i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.0818 | − | 8.80604i | 0.996489 | − | 0.726310i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.00000 | 0.163846 | 0.0819232 | − | 0.996639i | \(-0.473894\pi\) | ||||
0.0819232 | + | 0.996639i | \(0.473894\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.95118i | − | 0.402922i | −0.979497 | − | 0.201461i | \(-0.935431\pi\) | ||
0.979497 | − | 0.201461i | \(-0.0645689\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.77769 | −0.628789 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.8255 | + | 7.28323i | 1.03017 | + | 0.585003i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.88884 | 0.310364 | 0.155182 | − | 0.987886i | \(-0.450404\pi\) | ||||
0.155182 | + | 0.987886i | \(0.450404\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 18.3421 | 1.45462 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.2462 | − | 7.24517i | −1.12276 | − | 0.570999i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.5012 | −0.900840 | −0.450420 | − | 0.892817i | \(-0.648726\pi\) | ||||
−0.450420 | + | 0.892817i | \(0.648726\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.68466 | − | 5.49966i | −0.753950 | − | 0.428148i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.673500i | 0.0521170i | 0.999660 | + | 0.0260585i | \(0.00829562\pi\) | ||||
−0.999660 | + | 0.0260585i | \(0.991704\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8078 | −0.908290 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.02102 | 0.307495 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.0534 | −0.840372 | −0.420186 | − | 0.907438i | \(-0.638035\pi\) | ||||
−0.420186 | + | 0.907438i | \(0.638035\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.890873 | + | 13.1987i | 0.0673437 | + | 0.997730i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 30.5866i | − | 2.29903i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 8.30571i | − | 0.620798i | −0.950606 | − | 0.310399i | \(-0.899537\pi\) | ||
0.950606 | − | 0.310399i | \(-0.100463\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.44849i | − | 0.256324i | −0.991753 | − | 0.128162i | \(-0.959092\pi\) | ||
0.991753 | − | 0.128162i | \(-0.0409077\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.32431 | 0.0978956 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.07263 | + | 10.6937i | −0.446469 | + | 0.786213i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 11.6153i | − | 0.849396i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.68466 | − | 7.24517i | 0.268019 | − | 0.527008i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 19.9660i | − | 1.44469i | −0.691535 | − | 0.722343i | \(-0.743065\pi\) | ||
0.691535 | − | 0.722343i | \(-0.256935\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.49966i | 0.395874i | 0.980215 | + | 0.197937i | \(0.0634241\pi\) | ||||
−0.980215 | + | 0.197937i | \(0.936576\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.57501 | − | 4.53448i | 0.184400 | − | 0.324721i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 16.4990i | − | 1.17550i | −0.809042 | − | 0.587751i | \(-0.800013\pi\) | ||
0.809042 | − | 0.587751i | \(-0.199987\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.3421 | −1.30024 | −0.650118 | − | 0.759834i | \(-0.725280\pi\) | ||||
−0.650118 | + | 0.759834i | \(0.725280\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 10.0736i | − | 0.710536i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.32431 | − | 0.673500i | −0.0929481 | − | 0.0472704i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.36932 | − | 16.4990i | 0.654381 | − | 1.15234i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.43318 | 0.655651 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.00505i | 0.415378i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 0.287088i | − | 0.0197640i | −0.999951 | − | 0.00988198i | \(-0.996854\pi\) | ||
0.999951 | − | 0.00988198i | \(-0.00314558\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 25.5169 | 1.74839 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.57501 | − | 1.46228i | −0.175614 | − | 0.0997266i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.5554 | + | 7.91096i | 1.05597 | + | 0.537031i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 21.2755i | − | 1.43767i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.43845 | 0.365830 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 0.147647i | − | 0.00988718i | −0.999988 | − | 0.00494359i | \(-0.998426\pi\) | ||
0.999988 | − | 0.00494359i | \(-0.00157360\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.00000 | − | 6.70531i | −0.266667 | − | 0.447021i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.1530i | 0.673881i | 0.941526 | + | 0.336941i | \(0.109392\pi\) | ||||
−0.941526 | + | 0.336941i | \(0.890608\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.45353i | 0.624707i | 0.949966 | + | 0.312354i | \(0.101117\pi\) | ||||
−0.949966 | + | 0.312354i | \(0.898883\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.7460 | − | 5.97366i | −0.772833 | − | 0.393038i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.9993i | 0.720589i | 0.932839 | + | 0.360294i | \(0.117324\pi\) | ||||
−0.932839 | + | 0.360294i | \(0.882676\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.7575 | − | 18.9435i | 0.701741 | − | 1.23574i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −22.7199 | −1.47582 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.33205i | 0.150848i | 0.997152 | + | 0.0754238i | \(0.0240310\pi\) | ||||
−0.997152 | + | 0.0754238i | \(0.975969\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 16.0786i | − | 1.03572i | −0.855466 | − | 0.517858i | \(-0.826729\pi\) | ||
0.855466 | − | 0.517858i | \(-0.173271\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.8028i | 0.949601i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.77085 | + | 15.5520i | 0.113135 | + | 0.993580i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.81164 | −0.178901 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.24621 | 0.522582 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.17104 | 0.578871 | 0.289435 | − | 0.957198i | \(-0.406532\pi\) | ||||
0.289435 | + | 0.957198i | \(0.406532\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.0877i | 0.885683i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.7460 | − | 20.6843i | 0.735566 | − | 1.29530i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.55137 | 0.408663 | 0.204332 | − | 0.978902i | \(-0.434498\pi\) | ||||
0.204332 | + | 0.978902i | \(0.434498\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.59603 | + | 12.9698i | −0.409857 | + | 0.805905i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.876894 | 0.0542784 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.5829 | −1.45419 | −0.727093 | − | 0.686539i | \(-0.759129\pi\) | ||||
−0.727093 | + | 0.686539i | \(0.759129\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.48274 | + | 16.6987i | −0.582520 | + | 1.02579i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.04090 | 0.369697 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 0.968253i | − | 0.0590354i | −0.999564 | − | 0.0295177i | \(-0.990603\pi\) | ||
0.999564 | − | 0.0295177i | \(-0.00939715\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.59603 | −0.400680 | −0.200340 | − | 0.979726i | \(-0.564205\pi\) | ||||
−0.200340 | + | 0.979726i | \(0.564205\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.79695 | − | 5.49966i | 0.169279 | − | 0.332854i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.0138 | − | 5.97366i | 0.603856 | − | 0.360225i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.5873i | 1.17689i | 0.808538 | + | 0.588444i | \(0.200259\pi\) | ||||
−0.808538 | + | 0.588444i | \(0.799741\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.3000 | −0.616648 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.0540 | 1.01735 | 0.508677 | − | 0.860957i | \(-0.330135\pi\) | ||||
0.508677 | + | 0.860957i | \(0.330135\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.45904i | 0.443394i | 0.975116 | + | 0.221697i | \(0.0711596\pi\) | ||||
−0.975116 | + | 0.221697i | \(0.928840\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.07263 | + | 10.6937i | −0.359712 | + | 0.633437i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.1768 | − | 20.0108i | 0.600720 | − | 1.18120i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.80776 | 0.459280 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 31.9133i | 1.87079i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.4635 | −0.844965 | −0.422483 | − | 0.906371i | \(-0.638841\pi\) | ||||
−0.422483 | + | 0.906371i | \(0.638841\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.8462 | + | 15.8131i | 1.62127 | + | 0.920674i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.16453 | −0.415728 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.59603 | −0.381458 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.12311 | − | 1.58831i | −0.180013 | − | 0.0915487i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −32.2725 | −1.85400 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.684658 | + | 1.20565i | −0.0392034 | + | 0.0690356i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.8987i | 0.793243i | 0.917982 | + | 0.396622i | \(0.129818\pi\) | ||||
−0.917982 | + | 0.396622i | \(0.870182\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.6847 | 0.664717 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.44600 | −0.0819954 | −0.0409977 | − | 0.999159i | \(-0.513054\pi\) | ||||
−0.0409977 | + | 0.999159i | \(0.513054\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.16453 | −0.404963 | −0.202482 | − | 0.979286i | \(-0.564901\pi\) | ||||
−0.202482 | + | 0.979286i | \(0.564901\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.09256 | − | 7.70789i | −0.286933 | − | 0.434290i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.4099i | 1.37100i | 0.728073 | + | 0.685499i | \(0.240416\pi\) | ||||
−0.728073 | + | 0.685499i | \(0.759584\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.30957i | 0.0733217i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.3873i | 1.19372i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.8255 | −0.713628 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.79695 | + | 4.68860i | 0.155147 | + | 0.260077i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.74247i | 0.538760i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.6847 | − | 22.9756i | 0.644196 | − | 1.26669i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 8.30571i | − | 0.456523i | −0.973600 | − | 0.228262i | \(-0.926696\pi\) | ||
0.973600 | − | 0.228262i | \(-0.0733041\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 8.58800i | − | 0.470620i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.17104 | + | 5.20798i | 0.501067 | + | 0.284543i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.5866i | 1.66616i | 0.553153 | + | 0.833080i | \(0.313425\pi\) | ||||
−0.553153 | + | 0.833080i | \(0.686575\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.7460 | −0.637958 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 15.3823i | − | 0.832996i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.93893 | + | 18.2856i | 0.158687 | + | 0.987329i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −14.2462 | + | 25.0870i | −0.766990 | + | 1.35064i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.32431 | −0.0710925 | −0.0355463 | − | 0.999368i | \(-0.511317\pi\) | ||||
−0.0355463 | + | 0.999368i | \(0.511317\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 18.8307i | − | 1.00799i | −0.863708 | − | 0.503993i | \(-0.831864\pi\) | ||
0.863708 | − | 0.503993i | \(-0.168136\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 3.35453i | − | 0.179051i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.1685 | 0.860564 | 0.430282 | − | 0.902694i | \(-0.358414\pi\) | ||||
0.430282 | + | 0.902694i | \(0.358414\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.1921 | + | 23.2306i | −0.700162 | + | 1.23295i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.7584 | − | 25.0870i | 0.675248 | − | 1.32774i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.3507i | 0.546288i | 0.961973 | + | 0.273144i | \(0.0880635\pi\) | ||||
−0.961973 | + | 0.273144i | \(0.911937\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.3693 | −0.651017 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 11.8782i | − | 0.623446i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.3693 | + | 10.9993i | 1.01384 | + | 0.575730i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.3783i | 1.22034i | 0.792272 | + | 0.610168i | \(0.208898\pi\) | ||||
−0.792272 | + | 0.610168i | \(0.791102\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.2502i | 0.689779i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.3000 | + | 20.2530i | −0.534752 | + | 1.05149i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.6763i | 0.604578i | 0.953216 | + | 0.302289i | \(0.0977508\pi\) | ||||
−0.953216 | + | 0.302289i | \(0.902249\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 23.8733 | − | 0.511240i | 1.23281 | − | 0.0264003i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.613157 | −0.0315792 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.9171i | 1.27991i | 0.768414 | + | 0.639954i | \(0.221046\pi\) | ||||
−0.768414 | + | 0.639954i | \(0.778954\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.3137i | 0.579619i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.6638i | 0.953675i | 0.878991 | + | 0.476838i | \(0.158217\pi\) | ||||
−0.878991 | + | 0.476838i | \(0.841783\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.5111 | − | 7.60530i | 0.586659 | − | 0.387602i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.06798 | 0.105121 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.9309 | 0.604919 | 0.302460 | − | 0.953162i | \(-0.402192\pi\) | ||||
0.302460 | + | 0.953162i | \(0.402192\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.0881 | −1.52162 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 5.49966i | − | 0.277421i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.7460 | − | 20.6843i | 0.591008 | − | 1.04074i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.0149 | 1.05471 | 0.527353 | − | 0.849647i | \(-0.323185\pi\) | ||||
0.527353 | + | 0.849647i | \(0.323185\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.59603 | + | 12.9698i | −0.330214 | + | 0.649303i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.4384 | 0.671084 | 0.335542 | − | 0.942025i | \(-0.391081\pi\) | ||||
0.335542 | + | 0.942025i | \(0.391081\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.20217 | 0.358766 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −21.8674 | − | 12.4179i | −1.08660 | − | 0.617050i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.8255 | 0.635734 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 30.2208i | − | 1.49432i | −0.664643 | − | 0.747161i | \(-0.731417\pi\) | ||
0.664643 | − | 0.747161i | \(-0.268583\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.59603 | 0.325358 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 33.7733 | + | 17.1760i | 1.66187 | + | 0.845176i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.26324 | + | 7.50738i | −0.209274 | + | 0.368523i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 8.58800i | − | 0.420556i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.3631 | −1.09251 | −0.546254 | − | 0.837619i | \(-0.683947\pi\) | ||||
−0.546254 | + | 0.837619i | \(0.683947\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.5616 | −0.612213 | −0.306106 | − | 0.951997i | \(-0.599026\pi\) | ||||
−0.306106 | + | 0.951997i | \(0.599026\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15.2134i | 0.739700i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.7584 | + | 21.3873i | 0.618875 | + | 1.03744i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.743668 | + | 1.46228i | −0.0359886 | + | 0.0707647i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.43845 | −0.262571 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.6602i | 0.561654i | 0.959758 | + | 0.280827i | \(0.0906087\pi\) | ||||
−0.959758 | + | 0.280827i | \(0.909391\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.00400 | −0.432705 | −0.216352 | − | 0.976315i | \(-0.569416\pi\) | ||||
−0.216352 | + | 0.976315i | \(0.569416\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.32431 | + | 2.33205i | −0.0634957 | + | 0.111813i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.5554 | 0.744114 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.5341 | −1.50504 | −0.752521 | − | 0.658568i | \(-0.771162\pi\) | ||||
−0.752521 | + | 0.658568i | \(0.771162\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.43845 | − | 8.83348i | −0.306593 | − | 0.420642i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.5420 | −0.833448 | −0.416724 | − | 0.909033i | \(-0.636822\pi\) | ||||
−0.416724 | + | 0.909033i | \(0.636822\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.12311 | + | 5.49966i | −0.148049 | + | 0.260709i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 4.27156i | − | 0.202038i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.31534 | 0.298039 | 0.149020 | − | 0.988834i | \(-0.452388\pi\) | ||||
0.149020 | + | 0.988834i | \(0.452388\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.7881 | −0.931784 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.5746 | −0.496840 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.56090 | + | 5.38964i | 0.166938 | + | 0.252670i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 10.3223i | − | 0.482856i | −0.970419 | − | 0.241428i | \(-0.922384\pi\) | ||
0.970419 | − | 0.241428i | \(-0.0776157\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 15.3019i | − | 0.714229i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.1154i | 0.983444i | 0.870752 | + | 0.491722i | \(0.163632\pi\) | ||||
−0.870752 | + | 0.491722i | \(0.836368\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.3266 | −1.13055 | −0.565277 | − | 0.824901i | \(-0.691231\pi\) | ||||
−0.565277 | + | 0.824901i | \(0.691231\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15.5554 | − | 27.3924i | 0.721363 | − | 1.27029i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 23.1983i | − | 1.07349i | −0.843745 | − | 0.536744i | \(-0.819654\pi\) | ||
0.843745 | − | 0.536744i | \(-0.180346\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.1231 | + | 5.65685i | 0.513617 | + | 0.261209i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 8.30571i | − | 0.382707i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.08835i | 0.142002i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.59603 | − | 11.0571i | −0.302646 | − | 0.507335i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 13.4106i | − | 0.614030i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.0881 | 1.37476 | 0.687381 | − | 0.726297i | \(-0.258760\pi\) | ||||
0.687381 | + | 0.726297i | \(0.258760\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.00505i | 0.273807i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.4741 | + | 30.4268i | −0.704095 | + | 1.38447i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −29.0540 | − | 16.4990i | −1.31927 | − | 0.749179i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.16128 | 0.0526225 | 0.0263112 | − | 0.999654i | \(-0.491624\pi\) | ||||
0.0263112 | + | 0.999654i | \(0.491624\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.5639i | 1.11082i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.2794i | 0.644419i | 0.946668 | + | 0.322210i | \(0.104426\pi\) | ||||
−0.946668 | + | 0.322210i | \(0.895574\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.79695 | −0.125968 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.02102 | + | 7.08084i | −0.180731 | + | 0.318260i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.3291 | + | 28.1753i | −0.642746 | + | 1.26384i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.6525i | 1.14836i | 0.818727 | + | 0.574182i | \(0.194680\pi\) | ||||
−0.818727 | + | 0.574182i | \(0.805320\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.43845 | 0.0642651 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.8114i | 0.838761i | 0.907811 | + | 0.419380i | \(0.137753\pi\) | ||||
−0.907811 | + | 0.419380i | \(0.862247\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.6847 | − | 29.3810i | 0.742458 | − | 1.30744i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 25.2188i | 1.12001i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 28.0124i | − | 1.24163i | −0.783958 | − | 0.620814i | \(-0.786802\pi\) | ||
0.783958 | − | 0.620814i | \(-0.213198\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.4921 | + | 11.9473i | 1.03923 | + | 0.528519i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.91096i | 0.349278i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.04090 | + | 10.6378i | −0.266194 | + | 0.468756i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.7199 | −0.999220 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.6076i | 1.03626i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 2.82843i | − | 0.123916i | −0.998079 | − | 0.0619578i | \(-0.980266\pi\) | ||
0.998079 | − | 0.0619578i | \(-0.0197344\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.9472i | 0.915958i | 0.888963 | + | 0.457979i | \(0.151426\pi\) | ||||
−0.888963 | + | 0.457979i | \(0.848574\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 28.1896 | − | 1.90271i | 1.23029 | − | 0.0830410i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 32.8531 | 1.43110 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.4924 | 0.586627 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.3631 | −0.970476 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 9.26504i | − | 0.401313i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.4711 | − | 11.0571i | −0.841808 | − | 0.478040i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17.7392 | −0.765502 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.1921 | − | 9.61528i | 0.568222 | − | 0.414159i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.4384 | 0.835724 | 0.417862 | − | 0.908510i | \(-0.362780\pi\) | ||||
0.417862 | + | 0.908510i | \(0.362780\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.36520 | −0.316071 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.86958 | − | 5.03680i | −0.379931 | − | 0.215753i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.4337 | 1.42952 | 0.714762 | − | 0.699368i | \(-0.246535\pi\) | ||||
0.714762 | + | 0.699368i | \(0.246535\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 0.968253i | − | 0.0413240i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.44600 | 0.0616019 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.7584 | − | 25.0870i | 0.542543 | − | 1.06681i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 22.8393 | + | 12.9698i | 0.969473 | + | 0.550538i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 8.58800i | − | 0.363885i | −0.983309 | − | 0.181943i | \(-0.941761\pi\) | ||
0.983309 | − | 0.181943i | \(-0.0582385\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.44600 | −0.0611595 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.8078 | −1.04738 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.78554i | 0.285977i | 0.989724 | + | 0.142988i | \(0.0456711\pi\) | ||||
−0.989724 | + | 0.142988i | \(0.954329\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.07263 | − | 10.6937i | 0.255478 | − | 0.449885i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −26.5219 | − | 13.4882i | −1.11381 | − | 0.566450i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −43.8617 | −1.83878 | −0.919390 | − | 0.393347i | \(-0.871317\pi\) | ||||
−0.919390 | + | 0.393347i | \(0.871317\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 15.5889i | − | 0.652377i | −0.945305 | − | 0.326188i | \(-0.894236\pi\) | ||
0.945305 | − | 0.326188i | \(-0.105764\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −42.6429 | −1.78143 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.4741 | − | 25.9396i | −0.645313 | − | 1.08176i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.0915 | 1.50251 | 0.751254 | − | 0.660013i | \(-0.229449\pi\) | ||||
0.751254 | + | 0.660013i | \(0.229449\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.7460 | 0.488149 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.63068 | + | 9.10534i | −0.192113 | + | 0.377753i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.0276 | 0.829460 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.31534 | − | 1.88269i | −0.137073 | − | 0.0778398i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 2.80928i | − | 0.115951i | −0.998318 | − | 0.0579757i | \(-0.981535\pi\) | ||
0.998318 | − | 0.0579757i | \(-0.0184646\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.9848 | −0.699848 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −35.2381 | −1.44950 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.20705 | −0.254893 | −0.127447 | − | 0.991845i | \(-0.540678\pi\) | ||||
−0.127447 | + | 0.991845i | \(0.540678\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.2432 | + | 24.5851i | 0.665908 | + | 1.00789i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 39.1746i | 1.60331i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 17.9210i | − | 0.732232i | −0.930569 | − | 0.366116i | \(-0.880687\pi\) | ||
0.930569 | − | 0.366116i | \(-0.119313\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.2309i | 1.72263i | 0.508068 | + | 0.861317i | \(0.330360\pi\) | ||||
−0.508068 | + | 0.861317i | \(0.669640\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.36520 | −0.299934 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.8140 | + | 6.14098i | 0.439652 | + | 0.249666i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 44.9666i | − | 1.82514i | −0.408921 | − | 0.912570i | \(-0.634095\pi\) | ||
0.408921 | − | 0.912570i | \(-0.365905\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.43845 | + | 2.82843i | −0.0582888 | + | 0.114614i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 10.6378i | − | 0.430358i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 47.7626i | − | 1.92911i | −0.263874 | − | 0.964557i | \(-0.585000\pi\) | ||
0.263874 | − | 0.964557i | \(-0.415000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −35.2381 | − | 20.0108i | −1.42094 | − | 0.806913i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 14.7647i | − | 0.594404i | −0.954815 | − | 0.297202i | \(-0.903946\pi\) | ||
0.954815 | − | 0.297202i | \(-0.0960535\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.0671 | −1.04773 | −0.523863 | − | 0.851803i | \(-0.675510\pi\) | ||||
−0.523863 | + | 0.851803i | \(0.675510\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.5589i | 0.744742i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.39228 | + | 6.67026i | −0.135909 | + | 0.267238i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.8769 | + | 21.9986i | −0.475076 | + | 0.879945i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.8255 | 0.512200 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.3924i | 1.09220i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.9582i | 1.35186i | 0.736968 | + | 0.675928i | \(0.236257\pi\) | ||||
−0.736968 | + | 0.675928i | \(0.763743\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.613157 | −0.0243708 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.3000 | − | 5.84912i | −0.408745 | − | 0.232115i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.50200 | + | 6.17669i | 0.178376 | + | 0.244730i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 18.6564i | − | 0.738035i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.8617 | 1.57444 | 0.787222 | − | 0.616670i | \(-0.211519\pi\) | ||||
0.787222 | + | 0.616670i | \(0.211519\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.8341i | 1.45260i | 0.687380 | + | 0.726298i | \(0.258761\pi\) | ||||
−0.687380 | + | 0.726298i | \(0.741239\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.12311 | + | 5.49966i | −0.122972 | + | 0.216549i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.5712i | 1.43776i | 0.695134 | + | 0.718881i | \(0.255345\pi\) | ||||
−0.695134 | + | 0.718881i | \(0.744655\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 33.3974i | − | 1.31096i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.8961 | − | 33.2228i | 0.662209 | − | 1.30211i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 16.4990i | − | 0.645654i | −0.946458 | − | 0.322827i | \(-0.895367\pi\) | ||
0.946458 | − | 0.322827i | \(-0.104633\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.00691 | + | 2.84329i | 0.195636 | + | 0.111096i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.5554 | −0.606873 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 42.8381i | − | 1.66874i | −0.551207 | − | 0.834368i | \(-0.685833\pi\) | ||
0.551207 | − | 0.834368i | \(-0.314167\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.51198i | 0.0588092i | 0.999568 | + | 0.0294046i | \(0.00936112\pi\) | ||||
−0.999568 | + | 0.0294046i | \(0.990639\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 11.6153i | − | 0.451102i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.39766 | − | 12.7104i | −0.325647 | − | 0.492887i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.39228 | 0.131350 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.315342 | −0.0121918 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.44600 | 0.0558224 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.0877i | 0.543039i | 0.962433 | + | 0.271520i | \(0.0875262\pi\) | ||||
−0.962433 | + | 0.271520i | \(0.912474\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.1921 | − | 7.86962i | 0.507762 | − | 0.302902i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −46.5317 | −1.78836 | −0.894179 | − | 0.447709i | \(-0.852240\pi\) | ||||
−0.894179 | + | 0.447709i | \(0.852240\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −35.2381 | − | 17.9210i | −1.35232 | − | 0.687745i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.6847 | 0.830958 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.1907 | −0.772574 | −0.386287 | − | 0.922379i | \(-0.626243\pi\) | ||||
−0.386287 | + | 0.922379i | \(0.626243\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.41011 | + | 6.00505i | −0.130293 | + | 0.229441i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.1907 | 0.770322 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.37720i | 0.357243i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.8132 | −1.43848 | −0.719240 | − | 0.694761i | \(-0.755510\pi\) | ||||
−0.719240 | + | 0.694761i | \(0.755510\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.36758 | + | 8.58800i | −0.165911 | + | 0.326231i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.81855 | + | 4.43994i | 0.296575 | + | 0.168417i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 42.2630i | − | 1.60082i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.4921 | 0.888553 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.6695 | 1.15837 | 0.579186 | − | 0.815196i | \(-0.303371\pi\) | ||||
0.579186 | + | 0.815196i | \(0.303371\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 14.1617i | − | 0.534118i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −40.4591 | − | 22.9756i | −1.52378 | − | 0.865312i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.1227 | − | 35.6347i | 0.681574 | − | 1.34018i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.8078 | −1.15701 | −0.578505 | − | 0.815679i | \(-0.696364\pi\) | ||||
−0.578505 | + | 0.815679i | \(0.696364\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.6114i | 0.622977i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −39.8459 | −1.49224 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.81164 | − | 4.95118i | 0.105150 | − | 0.185164i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.98074 | 0.186009 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.1961 | −1.01424 | −0.507122 | − | 0.861874i | \(-0.669291\pi\) | ||||
−0.507122 | + | 0.861874i | \(0.669291\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.56155 | + | 12.9020i | −0.244365 | + | 0.480496i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −34.3404 | −1.27713 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.43845 | − | 2.41131i | −0.0534226 | − | 0.0895537i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.8255i | 1.21743i | 0.793389 | + | 0.608715i | \(0.208315\pi\) | ||||
−0.793389 | + | 0.608715i | \(0.791685\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.12311 | −0.0786335 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.59603 | −0.243963 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.4250 | 0.902156 | 0.451078 | − | 0.892484i | \(-0.351040\pi\) | ||||
0.451078 | + | 0.892484i | \(0.351040\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 33.2156 | − | 3.78213i | 1.22518 | − | 0.139506i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 10.9993i | − | 0.405165i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 49.5472i | 1.82262i | 0.411718 | + | 0.911311i | \(0.364929\pi\) | ||||
−0.411718 | + | 0.911311i | \(0.635071\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.00505i | 0.220601i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.43318 | −0.346070 | −0.173035 | − | 0.984916i | \(-0.555357\pi\) | ||||
−0.173035 | + | 0.984916i | \(0.555357\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.88884 | + | 2.20837i | 0.142476 | + | 0.0809084i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 6.02913i | − | 0.220594i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.6155 | − | 12.0101i | −0.862893 | − | 0.438839i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.5999i | 1.37204i | 0.727584 | + | 0.686019i | \(0.240643\pi\) | ||||
−0.727584 | + | 0.686019i | \(0.759357\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 19.5873i | − | 0.713801i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.46702 | − | 9.62719i | 0.198965 | − | 0.350369i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 25.7640i | − | 0.936409i | −0.883620 | − | 0.468204i | \(-0.844901\pi\) | ||
0.883620 | − | 0.468204i | \(-0.155099\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 30.0881 | 1.09213 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.1228i | 1.56320i | 0.623780 | + | 0.781600i | \(0.285596\pi\) | ||||
−0.623780 | + | 0.781600i | \(0.714404\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.7575 | − | 5.47091i | −0.389447 | − | 0.198060i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.1231 | − | 8.58800i | −0.546777 | − | 0.310500i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.6371 | 0.564623 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.4903i | 0.522535i | 0.965266 | + | 0.261267i | \(0.0841404\pi\) | ||||
−0.965266 | + | 0.261267i | \(0.915860\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 13.9923i | − | 0.503920i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.6898 | 0.564323 | 0.282161 | − | 0.959367i | \(-0.408949\pi\) | ||||
0.282161 | + | 0.959367i | \(0.408949\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.8961 | + | 28.3234i | 0.606925 | + | 1.01740i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 27.7006 | + | 14.0877i | 0.993755 | + | 0.505392i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21.8497i | 0.782847i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.8617 | 0.996971 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.72521i | 0.0616538i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.56155 | + | 4.29400i | 0.269883 | + | 0.153259i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.8578i | 1.17126i | 0.810580 | + | 0.585628i | \(0.199152\pi\) | ||||
−0.810580 | + | 0.585628i | \(0.800848\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 50.3680i | 1.79315i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.59603 | − | 12.9698i | 0.234528 | − | 0.461153i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.677039i | 0.0240423i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 35.6647 | + | 20.2530i | 1.26490 | + | 0.718301i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.04937 | 0.0725925 | 0.0362963 | − | 0.999341i | \(-0.488444\pi\) | ||||
0.0362963 | + | 0.999341i | \(0.488444\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 48.5247i | − | 1.71668i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 4.41674i | − | 0.156058i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 23.2306i | − | 0.819792i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.7006 | − | 29.8181i | −0.694356 | − | 1.05095i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.06798 | −0.0727962 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.0540 | −0.951167 | −0.475584 | − | 0.879671i | \(-0.657763\pi\) | ||||
−0.475584 | + | 0.879671i | \(0.657763\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.17104 | −0.322039 | −0.161019 | − | 0.986951i | \(-0.551478\pi\) | ||||
−0.161019 | + | 0.986951i | \(0.551478\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.0877i | 0.494076i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.3631 | − | 12.6994i | −0.783345 | − | 0.444840i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.41011 | 0.119304 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.02102 | − | 2.04496i | −0.140506 | − | 0.0714567i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.9309 | 1.25400 | 0.626998 | − | 0.779021i | \(-0.284283\pi\) | ||||
0.626998 | + | 0.779021i | \(0.284283\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.8393 | −0.796127 | −0.398064 | − | 0.917358i | \(-0.630318\pi\) | ||||
−0.398064 | + | 0.917358i | \(0.630318\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.7584 | − | 21.3873i | −0.444191 | − | 0.744610i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.71659 | 0.164012 | 0.0820059 | − | 0.996632i | \(-0.473867\pi\) | ||||
0.0820059 | + | 0.996632i | \(0.473867\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 43.3947i | − | 1.50716i | −0.657357 | − | 0.753579i | \(-0.728326\pi\) | ||
0.657357 | − | 0.753579i | \(-0.271674\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 41.8342 | 1.45121 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.5361 | + | 28.1753i | 0.711534 | + | 0.976217i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.743668 | + | 1.30957i | −0.0257357 | + | 0.0453195i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 20.2644i | − | 0.700438i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.3461 | 1.11671 | 0.558356 | − | 0.829601i | \(-0.311432\pi\) | ||||
0.558356 | + | 0.829601i | \(0.311432\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6847 | −0.989126 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 36.4235i | − | 1.25449i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.9593 | − | 13.0380i | −0.789823 | − | 0.448519i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.1158 | + | 6.67026i | 0.450664 | + | 0.229193i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.9309 | 0.546746 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 33.2228i | − | 1.13886i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.93137 | −0.100368 | −0.0501840 | − | 0.998740i | \(-0.515981\pi\) | ||||
−0.0501840 | + | 0.998740i | \(0.515981\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.81855 | + | 4.43994i | 0.267389 | + | 0.151843i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.59390 | −0.191084 | −0.0955419 | − | 0.995425i | \(-0.530458\pi\) | ||||
−0.0955419 | + | 0.995425i | \(0.530458\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.17104 | 0.312912 | 0.156456 | − | 0.987685i | \(-0.449993\pi\) | ||||
0.156456 | + | 0.987685i | \(0.449993\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −42.7386 | − | 21.7355i | −1.45653 | − | 0.740744i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.7851 | −1.04794 | −0.523969 | − | 0.851737i | \(-0.675549\pi\) | ||||
−0.523969 | + | 0.851737i | \(0.675549\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.4924 | − | 12.2050i | −0.730764 | − | 0.414981i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 16.6757i | − | 0.566335i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.8078 | −0.841546 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.15002 | 0.174502 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 23.3331 | 0.789705 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.8416 | + | 26.6476i | −0.434125 | + | 0.900853i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 5.49966i | − | 0.185710i | −0.995680 | − | 0.0928551i | \(-0.970401\pi\) | ||
0.995680 | − | 0.0928551i | \(-0.0295993\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30.8908i | 1.04192i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 30.7645i | − | 1.03648i | −0.855234 | − | 0.518241i | \(-0.826587\pi\) | ||
0.855234 | − | 0.518241i | \(-0.173413\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.4902 | −1.63183 | −0.815913 | − | 0.578175i | \(-0.803765\pi\) | ||||
−0.815913 | + | 0.578175i | \(0.803765\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 33.7733 | − | 59.4733i | 1.13528 | − | 1.99917i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 31.7738i | − | 1.06686i | −0.845845 | − | 0.533429i | \(-0.820903\pi\) | ||
0.845845 | − | 0.533429i | \(-0.179097\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.4924 | − | 6.35324i | −0.418982 | − | 0.213081i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26.2267i | 0.878628i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.0870i | 0.839503i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.17104 | − | 16.1498i | 0.306554 | − | 0.539829i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.0877i | 0.470373i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.70402 | −0.123536 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.7746i | 1.42503i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.39228 | + | 6.67026i | −0.112888 | + | 0.221972i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.80776 | − | 6.70531i | 0.126574 | − | 0.222892i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −53.7874 | −1.78598 | −0.892991 | − | 0.450074i | \(-0.851397\pi\) | ||||
−0.892991 | + | 0.450074i | \(0.851397\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 23.5957i | 0.782619i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 56.0950i | − | 1.85851i | −0.369438 | − | 0.929255i | \(-0.620450\pi\) | ||
0.369438 | − | 0.929255i | \(-0.379550\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.00400 | 0.297989 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.57501 | + | 1.46228i | 0.0851272 | + | 0.0483415i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.07263 | + | 3.08835i | 0.200536 | + | 0.101986i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.1965i | 1.29297i | 0.762925 | + | 0.646487i | \(0.223762\pi\) | ||||
−0.762925 | + | 0.646487i | \(0.776238\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.6847 | 0.978143 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.0452i | 0.429389i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.6155 | + | 14.0877i | −0.776474 | + | 0.463199i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 8.54312i | − | 0.280593i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.9807i | 0.950825i | 0.879763 | + | 0.475412i | \(0.157701\pi\) | ||||
−0.879763 | + | 0.475412i | \(0.842299\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.6170 | − | 14.5665i | −0.347960 | − | 0.477397i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.08835i | 0.101108i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.8255 | − | 22.5851i | 0.419437 | − | 0.738611i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.4631 | −1.61589 | −0.807944 | − | 0.589259i | \(-0.799420\pi\) | ||||
−0.807944 | + | 0.589259i | \(0.799420\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.3019i | 0.499357i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 8.75714i | − | 0.285475i | −0.989761 | − | 0.142737i | \(-0.954410\pi\) | ||
0.989761 | − | 0.142737i | \(-0.0455904\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 51.2587i | 1.66921i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 15.1645 | − | 10.0191i | 0.493302 | − | 0.325922i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 52.6261 | 1.71012 | 0.855060 | − | 0.518529i | \(-0.173520\pi\) | ||||
0.855060 | + | 0.518529i | \(0.173520\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.8769 | 0.353079 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 52.1342 | 1.69057 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 31.2637i | − | 1.01273i | −0.862319 | − | 0.506365i | \(-0.830989\pi\) | ||
0.862319 | − | 0.506365i | \(-0.169011\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.0461 | − | 38.8222i | 0.713395 | − | 1.25626i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.79695 | 0.0904125 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.70402 | + | 7.28323i | −0.119609 | + | 0.235188i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.5076 | 0.403470 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.6371 | 0.503899 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.07263 | + | 10.6937i | −0.195485 | + | 0.344241i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.2177 | −0.521527 | −0.260764 | − | 0.965403i | \(-0.583974\pi\) | ||||
−0.260764 | + | 0.965403i | \(0.583974\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 27.3924i | 0.879969i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.3672 | 1.16708 | 0.583539 | − | 0.812085i | \(-0.301668\pi\) | ||||
0.583539 | + | 0.812085i | \(0.301668\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.48274 | + | 4.82262i | 0.304003 | + | 0.154606i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.0138 | − | 5.97366i | 0.320699 | − | 0.191310i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.0877i | 0.450704i | 0.974277 | + | 0.225352i | \(0.0723532\pi\) | ||||
−0.974277 | + | 0.225352i | \(0.927647\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.59603 | 0.210810 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.12311 | 0.227423 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 44.7361i | − | 1.42686i | −0.700727 | − | 0.713430i | \(-0.747141\pi\) | ||
0.700727 | − | 0.713430i | \(-0.252859\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.2179 | − | 32.0810i | 0.580471 | − | 1.02218i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −49.0708 | − | 24.9559i | −1.56194 | − | 0.794353i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.00000 | 0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.574176i | 0.0182393i | 0.999958 | + | 0.00911966i | \(0.00290292\pi\) | ||||
−0.999958 | + | 0.00911966i | \(0.997097\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.7392 | −0.562935 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −35.6647 | − | 20.2530i | −1.13065 | − | 0.642065i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 47.7580 | 1.51251 | 0.756256 | − | 0.654276i | \(-0.227027\pi\) | ||||
0.756256 | + | 0.654276i | \(0.227027\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.8961 | 0.534568 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))