Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,3,Mod(1023,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1024.1023");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.c (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: | \(27.9019790705\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.653473922154496.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{10} + 13x^{8} - 28x^{6} + 52x^{4} - 64x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{30} \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1023.6 | ||
Root | \(1.35489 - 0.405301i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.1023 |
Dual form | 1024.3.c.j.1023.8 |
$q$-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 \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 0.206992i | − 0.0689974i | −0.999405 | − | 0.0344987i | \(-0.989017\pi\) | ||||
0.999405 | − | 0.0344987i | \(-0.0109834\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.21257 | 1.04251 | 0.521257 | − | 0.853400i | \(-0.325463\pi\) | ||||
0.521257 | + | 0.853400i | \(0.325463\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.66442i | 1.38063i | 0.723508 | + | 0.690316i | \(0.242528\pi\) | ||||
−0.723508 | + | 0.690316i | \(0.757472\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.95715 | 0.995239 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.80371i | 0.709428i | 0.934975 | + | 0.354714i | \(0.115422\pi\) | ||||
−0.934975 | + | 0.354714i | \(0.884578\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.86897 | −0.682228 | −0.341114 | − | 0.940022i | \(-0.610804\pi\) | ||||
−0.341114 | + | 0.940022i | \(0.610804\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 1.07896i | − 0.0719308i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.78623 | 0.399190 | 0.199595 | − | 0.979878i | \(-0.436037\pi\) | ||||
0.199595 | + | 0.979878i | \(0.436037\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.1174i | 1.00618i | 0.864234 | + | 0.503090i | \(0.167804\pi\) | ||||
−0.864234 | + | 0.503090i | \(0.832196\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00046 | 0.0952599 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 17.0790i | 0.742564i | 0.928520 | + | 0.371282i | \(0.121082\pi\) | ||||
−0.928520 | + | 0.371282i | \(0.878918\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.17092 | 0.0868370 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 3.71699i | − 0.137666i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.86851 | −0.236845 | −0.118423 | − | 0.992963i | \(-0.537784\pi\) | ||||
−0.118423 | + | 0.992963i | \(0.537784\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.25662i | 0.169568i | 0.996399 | + | 0.0847841i | \(0.0270201\pi\) | ||||
−0.996399 | + | 0.0847841i | \(0.972980\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.61531 | 0.0489487 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 50.3765i | 1.43933i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −25.7183 | −0.695090 | −0.347545 | − | 0.937663i | \(-0.612985\pi\) | ||||
−0.347545 | + | 0.937663i | \(0.612985\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.83581i | 0.0470720i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −48.2302 | −1.17635 | −0.588173 | − | 0.808735i | \(-0.700152\pi\) | ||||
−0.588173 | + | 0.808735i | \(0.700152\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 77.0907i | − 1.79281i | −0.443240 | − | 0.896403i | \(-0.646171\pi\) | ||||
0.443240 | − | 0.896403i | \(-0.353829\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 46.6898 | 1.03755 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 40.4015i | 0.859607i | 0.902922 | + | 0.429804i | \(0.141417\pi\) | ||||
−0.902922 | + | 0.429804i | \(0.858583\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −44.4011 | −0.906144 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 1.40470i | − 0.0275431i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −15.4144 | −0.290837 | −0.145419 | − | 0.989370i | \(-0.546453\pi\) | ||||
−0.145419 | + | 0.989370i | \(0.546453\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 40.6774i | 0.739590i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.95715 | 0.0694238 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 71.9690i | − 1.21981i | −0.792473 | − | 0.609907i | \(-0.791207\pi\) | ||||
0.792473 | − | 0.609907i | \(-0.208793\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 24.0624 | 0.394466 | 0.197233 | − | 0.980357i | \(-0.436804\pi\) | ||||
0.197233 | + | 0.980357i | \(0.436804\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 86.5657i | 1.37406i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −46.2302 | −0.711233 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 32.4126i | − 0.483769i | −0.970305 | − | 0.241885i | \(-0.922234\pi\) | ||||
0.970305 | − | 0.241885i | \(-0.0777656\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.53521 | 0.0512349 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 51.6047i | 0.726827i | 0.931628 | + | 0.363414i | \(0.118389\pi\) | ||||
−0.931628 | + | 0.363414i | \(0.881611\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 78.5032 | 1.07539 | 0.537693 | − | 0.843141i | \(-0.319296\pi\) | ||||
0.537693 | + | 0.843141i | \(0.319296\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 0.449364i | − 0.00599152i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −75.4184 | −0.979459 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 108.512i | 1.37357i | 0.726859 | + | 0.686787i | \(0.240979\pi\) | ||||
−0.726859 | + | 0.686787i | \(0.759021\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 79.8450 | 0.985741 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 81.0589i | 0.976613i | 0.872672 | + | 0.488307i | \(0.162385\pi\) | ||||
−0.872672 | + | 0.488307i | \(0.837615\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 35.3737 | 0.416161 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.42173i | 0.0163417i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −44.1276 | −0.495816 | −0.247908 | − | 0.968784i | \(-0.579743\pi\) | ||||
−0.247908 | + | 0.968784i | \(0.579743\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 85.7135i | − 0.941906i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.08808 | 0.0116998 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 99.6510i | 1.04896i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 112.700 | 1.16185 | 0.580926 | − | 0.813956i | \(-0.302691\pi\) | ||||
0.580926 | + | 0.813956i | \(0.302691\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 69.8991i | 0.706051i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 137.724 | 1.36361 | 0.681804 | − | 0.731534i | \(-0.261195\pi\) | ||||
0.681804 | + | 0.731534i | \(0.261195\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 138.698i | 1.34658i | 0.739379 | + | 0.673290i | \(0.235119\pi\) | ||||
−0.739379 | + | 0.673290i | \(0.764881\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.4275 | 0.0993099 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 44.8851i | − 0.419487i | −0.977756 | − | 0.209743i | \(-0.932737\pi\) | ||||
0.977756 | − | 0.209743i | \(-0.0672629\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00735 | 0.00924179 | 0.00462089 | − | 0.999989i | \(-0.498529\pi\) | ||||
0.00462089 | + | 0.999989i | \(0.498529\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.32349i | 0.0479594i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.8888 | −0.131759 | −0.0658795 | − | 0.997828i | \(-0.520985\pi\) | ||||
−0.0658795 | + | 0.997828i | \(0.520985\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 89.0253i | 0.774133i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −79.4407 | −0.678981 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 65.5850i | 0.551134i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 60.1021 | 0.496711 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.98326i | 0.0811647i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −118.998 | −0.951986 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 106.861i | − 0.841425i | −0.907194 | − | 0.420712i | \(-0.861780\pi\) | ||||
0.907194 | − | 0.420712i | \(-0.138220\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.9572 | −0.123699 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 216.655i | 1.65386i | 0.562307 | + | 0.826928i | \(0.309914\pi\) | ||||
−0.562307 | + | 0.826928i | \(0.690086\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −184.759 | −1.38916 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 19.3751i | − 0.143519i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −75.1700 | −0.548686 | −0.274343 | − | 0.961632i | \(-0.588460\pi\) | ||||
−0.274343 | + | 0.961632i | \(0.588460\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 151.922i | − 1.09297i | −0.837471 | − | 0.546483i | \(-0.815966\pi\) | ||||
0.837471 | − | 0.546483i | \(-0.184034\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.36280 | 0.0593106 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 69.2109i | − 0.483992i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −35.8026 | −0.246915 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.19067i | 0.0625216i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 206.519 | 1.38603 | 0.693017 | − | 0.720921i | \(-0.256281\pi\) | ||||
0.693017 | + | 0.720921i | \(0.256281\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 220.513i | 1.46035i | 0.683260 | + | 0.730175i | \(0.260561\pi\) | ||||
−0.683260 | + | 0.730175i | \(0.739439\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 60.7853 | 0.397290 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 27.4005i | 0.176777i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 154.942 | 0.986893 | 0.493447 | − | 0.869776i | \(-0.335737\pi\) | ||||
0.493447 | + | 0.869776i | \(0.335737\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.19066i | 0.0200670i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −165.058 | −1.02521 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 80.2963i | − 0.492615i | −0.969192 | − | 0.246308i | \(-0.920783\pi\) | ||||
0.969192 | − | 0.246308i | \(-0.0792174\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.41990 | 0.0510297 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 106.677i | − 0.638781i | −0.947623 | − | 0.319391i | \(-0.896522\pi\) | ||||
0.947623 | − | 0.319391i | \(-0.103478\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −90.3414 | −0.534564 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 171.238i | 1.00139i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 252.240 | 1.45803 | 0.729016 | − | 0.684496i | \(-0.239978\pi\) | ||||
0.729016 | + | 0.684496i | \(0.239978\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 20.9807i | 0.119890i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.8970 | −0.0841639 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 85.5065i | 0.477690i | 0.971058 | + | 0.238845i | \(0.0767688\pi\) | ||||
−0.971058 | + | 0.238845i | \(0.923231\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −208.049 | −1.14944 | −0.574721 | − | 0.818349i | \(-0.694890\pi\) | ||||
−0.574721 | + | 0.818349i | \(0.694890\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 4.98073i | − 0.0272171i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −134.059 | −0.724642 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 52.9578i | 0.283197i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 35.9225 | 0.190066 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 106.861i | 0.559481i | 0.960076 | + | 0.279741i | \(0.0902485\pi\) | ||||
−0.960076 | + | 0.279741i | \(0.909752\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 68.1873 | 0.353302 | 0.176651 | − | 0.984274i | \(-0.443474\pi\) | ||||
0.176651 | + | 0.984274i | \(0.443474\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.56927i | 0.0490732i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −87.4732 | −0.444027 | −0.222013 | − | 0.975044i | \(-0.571263\pi\) | ||||
−0.222013 | + | 0.975044i | \(0.571263\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 158.466i | 0.796310i | 0.917318 | + | 0.398155i | \(0.130349\pi\) | ||||
−0.917318 | + | 0.398155i | \(0.869651\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.70914 | −0.0333788 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 66.3802i | − 0.326996i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −251.403 | −1.22636 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 152.979i | 0.739028i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −149.187 | −0.713813 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 278.644i | − 1.32059i | −0.751007 | − | 0.660295i | \(-0.770431\pi\) | ||||
0.751007 | − | 0.660295i | \(-0.229569\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.6818 | 0.0501492 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 401.841i | − 1.86903i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −50.8022 | −0.234111 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 16.2495i | − 0.0741988i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −60.1869 | −0.272339 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 15.7698i | − 0.0707168i | −0.999375 | − | 0.0353584i | \(-0.988743\pi\) | ||||
0.999375 | − | 0.0353584i | \(-0.0112573\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 19.4453 | 0.0864236 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 281.838i | − 1.24158i | −0.783978 | − | 0.620788i | \(-0.786813\pi\) | ||||
0.783978 | − | 0.620788i | \(-0.213187\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 326.007 | 1.42361 | 0.711805 | − | 0.702377i | \(-0.247878\pi\) | ||||
0.711805 | + | 0.702377i | \(0.247878\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.6110i | 0.0675801i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 344.791 | 1.47979 | 0.739895 | − | 0.672722i | \(-0.234875\pi\) | ||||
0.739895 | + | 0.672722i | \(0.234875\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 210.596i | 0.896153i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 22.4612 | 0.0947729 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 77.1978i | − 0.323004i | −0.986872 | − | 0.161502i | \(-0.948366\pi\) | ||||
0.986872 | − | 0.161502i | \(-0.0516337\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 293.483 | 1.21777 | 0.608885 | − | 0.793259i | \(-0.291617\pi\) | ||||
0.608885 | + | 0.793259i | \(0.291617\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 49.9802i | − 0.205680i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −231.444 | −0.944669 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 169.552i | − 0.686445i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.7785 | 0.0673837 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 112.617i | − 0.448673i | −0.974512 | − | 0.224337i | \(-0.927979\pi\) | ||||
0.974512 | − | 0.224337i | \(-0.0720215\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −133.279 | −0.526796 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 7.32208i | − 0.0287140i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 221.860 | 0.863270 | 0.431635 | − | 0.902048i | \(-0.357937\pi\) | ||||
0.431635 | + | 0.902048i | \(0.357937\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 248.553i | − 0.959664i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −61.5223 | −0.235718 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 374.223i | − 1.42290i | −0.702736 | − | 0.711451i | \(-0.748039\pi\) | ||||
0.702736 | − | 0.711451i | \(-0.251961\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −80.3486 | −0.303202 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.13407i | 0.0342100i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −506.247 | −1.88196 | −0.940979 | − | 0.338465i | \(-0.890092\pi\) | ||||
−0.940979 | + | 0.338465i | \(0.890092\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 359.030i | − 1.32484i | −0.749135 | − | 0.662418i | \(-0.769530\pi\) | ||||
0.749135 | − | 0.662418i | \(-0.230470\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −17.7420 | −0.0649890 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.9413i | 0.0616046i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 497.471 | 1.79592 | 0.897961 | − | 0.440074i | \(-0.145048\pi\) | ||||
0.897961 | + | 0.440074i | \(0.145048\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 47.0843i | 0.168761i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 191.390 | 0.681103 | 0.340552 | − | 0.940226i | \(-0.389386\pi\) | ||||
0.340552 | + | 0.940226i | \(0.389386\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 44.2818i | 0.156473i | 0.996935 | + | 0.0782363i | \(0.0249289\pi\) | ||||
−0.996935 | + | 0.0782363i | \(0.975071\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 20.6270 | 0.0723753 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 466.117i | − 1.62410i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −242.947 | −0.840647 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 23.3279i | − 0.0801647i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −130.233 | −0.444483 | −0.222241 | − | 0.974992i | \(-0.571337\pi\) | ||||
−0.222241 | + | 0.974992i | \(0.571337\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 375.144i | − 1.27167i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 29.0063 | 0.0976643 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 151.473i | − 0.506598i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 745.037 | 2.47521 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 28.5079i | − 0.0940854i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 125.427 | 0.411236 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 364.254i | − 1.18649i | −0.805020 | − | 0.593247i | \(-0.797846\pi\) | ||||
0.805020 | − | 0.593247i | \(-0.202154\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 28.7093 | 0.0929104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 130.914i | − 0.420946i | −0.977600 | − | 0.210473i | \(-0.932500\pi\) | ||||
0.977600 | − | 0.210473i | \(-0.0675004\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 51.8354 | 0.165608 | 0.0828041 | − | 0.996566i | \(-0.473612\pi\) | ||||
0.0828041 | + | 0.996566i | \(0.473612\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 451.230i | 1.43248i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 155.049 | 0.489114 | 0.244557 | − | 0.969635i | \(-0.421357\pi\) | ||||
0.244557 | + | 0.969635i | \(0.421357\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 53.5999i | − 0.168025i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.29086 | −0.0289435 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 129.735i | 0.401657i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19.2539 | −0.0592426 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 0.208514i | 0 0.000637659i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −390.458 | −1.18680 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 457.111i | 1.38100i | 0.723332 | + | 0.690500i | \(0.242610\pi\) | ||||
−0.723332 | + | 0.690500i | \(0.757390\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −230.363 | −0.691781 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 168.953i | − 0.504337i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −315.159 | −0.935191 | −0.467596 | − | 0.883943i | \(-0.654880\pi\) | ||||
−0.467596 | + | 0.883943i | \(0.654880\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.08186i | 0.00909102i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −41.0211 | −0.120297 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 44.4459i | 0.129580i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.4275 | 0.0534132 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 434.967i | 1.25351i | 0.779218 | + | 0.626753i | \(0.215616\pi\) | ||||
−0.779218 | + | 0.626753i | \(0.784384\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −241.068 | −0.690740 | −0.345370 | − | 0.938467i | \(-0.612247\pi\) | ||||
−0.345370 | + | 0.938467i | \(0.612247\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 32.9659i | 0.0939198i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 238.136 | 0.674606 | 0.337303 | − | 0.941396i | \(-0.390485\pi\) | ||||
0.337303 | + | 0.941396i | \(0.390485\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 268.993i | 0.757728i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.5756 | 0.0380268 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 33.6470i | − 0.0937241i | −0.998901 | − | 0.0468620i | \(-0.985078\pi\) | ||||
0.998901 | − | 0.0468620i | \(-0.0149221\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.47577 | −0.0123983 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 12.4407i | − 0.0342718i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 409.203 | 1.12111 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 240.758i | − 0.656016i | −0.944675 | − | 0.328008i | \(-0.893623\pi\) | ||||
0.944675 | − | 0.328008i | \(-0.106377\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −432.005 | −1.17075 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 148.971i | − 0.401539i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −611.653 | −1.63982 | −0.819910 | − | 0.572492i | \(-0.805977\pi\) | ||||
−0.819910 | + | 0.572492i | \(0.805977\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24.6317i | 0.0656845i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 60.9166 | 0.161583 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 247.086i | 0.651943i | 0.945380 | + | 0.325971i | \(0.105691\pi\) | ||||
−0.945380 | + | 0.325971i | \(0.894309\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −22.1194 | −0.0580561 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 673.381i | − 1.75817i | −0.476661 | − | 0.879087i | \(-0.658153\pi\) | ||||
0.476661 | − | 0.879087i | \(-0.341847\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −393.124 | −1.02110 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 690.513i | − 1.78427i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −388.408 | −0.998478 | −0.499239 | − | 0.866464i | \(-0.666387\pi\) | ||||
−0.499239 | + | 0.866464i | \(0.666387\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 115.902i | 0.296424i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 44.8459 | 0.114112 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 565.628i | 1.43197i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −383.611 | −0.966275 | −0.483137 | − | 0.875545i | \(-0.660503\pi\) | ||||
−0.483137 | + | 0.875545i | \(0.660503\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 38.2436i | 0.0958487i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 415.193 | 1.03539 | 0.517697 | − | 0.855564i | \(-0.326790\pi\) | ||||
0.517697 | + | 0.855564i | \(0.326790\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 46.6208i | − 0.115684i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 416.198 | 1.02765 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 200.699i | − 0.493117i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −634.686 | −1.55180 | −0.775900 | − | 0.630856i | \(-0.782704\pi\) | ||||
−0.775900 | + | 0.630856i | \(0.782704\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.5596i | 0.0378579i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 695.539 | 1.68411 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 422.525i | 1.01813i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −31.4467 | −0.0754117 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 27.2500i | − 0.0650358i | −0.999471 | − | 0.0325179i | \(-0.989647\pi\) | ||||
0.999471 | − | 0.0325179i | \(-0.0103526\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 345.783 | 0.821337 | 0.410668 | − | 0.911785i | \(-0.365295\pi\) | ||||
0.410668 | + | 0.911785i | \(0.365295\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 361.883i | 0.855515i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.7324 | 0.0346644 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 232.549i | 0.544612i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.3261 | −0.0333942 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 337.331i | − 0.782670i | −0.920248 | − | 0.391335i | \(-0.872013\pi\) | ||||
0.920248 | − | 0.391335i | \(-0.127987\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 424.560 | 0.980508 | 0.490254 | − | 0.871580i | \(-0.336904\pi\) | ||||
0.490254 | + | 0.871580i | \(0.336904\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.41086i | 0.0170365i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −326.506 | −0.747153 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 162.004i | − 0.369029i | −0.982830 | − | 0.184514i | \(-0.940929\pi\) | ||||
0.982830 | − | 0.184514i | \(-0.0590712\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −397.707 | −0.901831 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 696.061i | − 1.57124i | −0.618707 | − | 0.785622i | \(-0.712343\pi\) | ||||
0.618707 | − | 0.785622i | \(-0.287657\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −230.018 | −0.516895 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 42.7478i | − 0.0956327i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 195.434 | 0.435266 | 0.217633 | − | 0.976031i | \(-0.430166\pi\) | ||||
0.217633 | + | 0.976031i | \(0.430166\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 376.374i | − 0.834533i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 45.6444 | 0.100760 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 446.788i | − 0.981951i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 386.874 | 0.846552 | 0.423276 | − | 0.906001i | \(-0.360880\pi\) | ||||
0.423276 | + | 0.906001i | \(0.360880\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 25.2243i | − 0.0549550i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −246.640 | −0.535011 | −0.267505 | − | 0.963556i | \(-0.586199\pi\) | ||||
−0.267505 | + | 0.963556i | \(0.586199\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 60.5295i | 0.130733i | 0.997861 | + | 0.0653666i | \(0.0208217\pi\) | ||||
−0.997861 | + | 0.0653666i | \(0.979178\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.67168 | 0.0121972 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 433.431i | 0.928118i | 0.885804 | + | 0.464059i | \(0.153607\pi\) | ||||
−0.885804 | + | 0.464059i | \(0.846393\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 313.249 | 0.667908 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 32.0718i | − 0.0680930i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 601.593 | 1.27187 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 41.5025i | 0.0873736i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −138.069 | −0.289453 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 376.452i | − 0.785912i | −0.919557 | − | 0.392956i | \(-0.871453\pi\) | ||||
0.919557 | − | 0.392956i | \(-0.128547\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 228.095 | 0.474210 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 34.1658i | 0.0707366i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 587.455 | 1.21125 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 77.2033i | − 0.158528i | −0.996854 | − | 0.0792641i | \(-0.974743\pi\) | ||||
0.996854 | − | 0.0792641i | \(-0.0252571\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.6207 | −0.0339892 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 822.277i | − 1.67470i | −0.546668 | − | 0.837350i | \(-0.684104\pi\) | ||||
0.546668 | − | 0.837350i | \(-0.315896\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −46.6113 | −0.0945462 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 364.354i | 0.736069i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −498.730 | −1.00348 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 246.081i | − 0.493149i | −0.969124 | − | 0.246574i | \(-0.920695\pi\) | ||||
0.969124 | − | 0.246574i | \(-0.0793050\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −22.0812 | −0.0440742 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 355.262i | − 0.706286i | −0.935569 | − | 0.353143i | \(-0.885113\pi\) | ||||
0.935569 | − | 0.353143i | \(-0.114887\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 717.899 | 1.42158 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.7000i | 0.0368835i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −395.509 | −0.777032 | −0.388516 | − | 0.921442i | \(-0.627012\pi\) | ||||
−0.388516 | + | 0.921442i | \(0.627012\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 758.688i | 1.48471i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 71.0592 | 0.138517 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 722.972i | 1.40383i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −315.282 | −0.609830 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 52.2116i | − 0.100600i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 705.745 | 1.35460 | 0.677299 | − | 0.735708i | \(-0.263151\pi\) | ||||
0.677299 | + | 0.735708i | \(0.263151\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 264.122i | − 0.505013i | −0.967595 | − | 0.252506i | \(-0.918745\pi\) | ||||
0.967595 | − | 0.252506i | \(-0.0812549\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.34284 | 0.00827208 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 35.6726i | 0.0676899i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 237.309 | 0.448599 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 644.637i | − 1.21401i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 427.752 | 0.802536 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 233.967i | − 0.437321i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.6992 | 0.0329593 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 346.493i | − 0.642845i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −168.679 | −0.311792 | −0.155896 | − | 0.987774i | \(-0.549826\pi\) | ||||
−0.155896 | + | 0.987774i | \(0.549826\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 43.0645i | 0.0793085i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.25091 | 0.00963470 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 200.072i | 0.365762i | 0.983135 | + | 0.182881i | \(0.0585422\pi\) | ||||
−0.983135 | + | 0.182881i | \(0.941458\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 215.531 | 0.392588 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 131.308i | − 0.238309i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1048.71 | −1.89640 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 27.7491i | 0.0499984i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 531.576 | 0.954355 | 0.477178 | − | 0.878807i | \(-0.341660\pi\) | ||||
0.477178 | + | 0.878807i | \(0.341660\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 683.715i | 1.22310i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.9618 | 0.0195398 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 431.828i | 0.767012i | 0.923538 | + | 0.383506i | \(0.125284\pi\) | ||||
−0.923538 | + | 0.383506i | \(0.874716\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −77.6088 | −0.137361 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 771.656i | 1.36095i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −296.778 | −0.521578 | −0.260789 | − | 0.965396i | \(-0.583983\pi\) | ||||
−0.260789 | + | 0.965396i | \(0.583983\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 491.745i | 0.861201i | 0.902543 | + | 0.430600i | \(0.141698\pi\) | ||||
−0.902543 | + | 0.430600i | \(0.858302\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.1194 | 0.0386027 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 37.0771i | 0.0644820i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −189.382 | −0.328218 | −0.164109 | − | 0.986442i | \(-0.552475\pi\) | ||||
−0.164109 | + | 0.986442i | \(0.552475\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 14.1142i | − 0.0243769i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −783.387 | −1.34834 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 120.289i | − 0.206328i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −414.091 | −0.707847 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 906.775i | − 1.54476i | −0.635160 | − | 0.772381i | \(-0.719066\pi\) | ||||
0.635160 | − | 0.772381i | \(-0.280934\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −100.493 | −0.170616 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.1063i | 0.0306367i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 127.909 | 0.215697 | 0.107849 | − | 0.994167i | \(-0.465604\pi\) | ||||
0.107849 | + | 0.994167i | \(0.465604\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 341.867i | 0.574566i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 32.8011 | 0.0549433 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 794.804i | 1.32688i | 0.748227 | + | 0.663442i | \(0.230905\pi\) | ||||
−0.748227 | + | 0.663442i | \(0.769095\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 89.2746 | 0.148543 | 0.0742717 | − | 0.997238i | \(-0.476337\pi\) | ||||
0.0742717 | + | 0.997238i | \(0.476337\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 290.324i | − 0.481466i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 313.286 | 0.517829 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 316.002i | 0.520596i | 0.965528 | + | 0.260298i | \(0.0838208\pi\) | ||||
−0.965528 | + | 0.260298i | \(0.916179\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.7402 | −0.0225619 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 358.320i | − 0.586448i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −271.534 | −0.442959 | −0.221479 | − | 0.975165i | \(-0.571089\pi\) | ||||
−0.221479 | + | 0.975165i | \(0.571089\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 52.0385i | 0.0846154i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −105.762 | −0.171413 | −0.0857066 | − | 0.996320i | \(-0.527315\pi\) | ||||
−0.0857066 | + | 0.996320i | \(0.527315\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 783.218i | 1.26530i | 0.774440 | + | 0.632648i | \(0.218032\pi\) | ||||
−0.774440 | + | 0.632648i | \(0.781968\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 63.4823 | 0.102226 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 426.468i | − 0.684539i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −674.560 | −1.07930 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 30.8805i | 0.0492512i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −174.531 | −0.277473 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 762.907i | 1.20904i | 0.796589 | + | 0.604522i | \(0.206636\pi\) | ||||
−0.796589 | + | 0.604522i | \(0.793364\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −57.6772 | −0.0911172 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 557.020i | − 0.877198i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 393.792 | 0.618197 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 462.232i | 0.723367i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −412.834 | −0.644046 | −0.322023 | − | 0.946732i | \(-0.604363\pi\) | ||||
−0.322023 | + | 0.946732i | \(0.604363\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 526.815i | 0.819308i | 0.912241 | + | 0.409654i | \(0.134351\pi\) | ||||
−0.912241 | + | 0.409654i | \(0.865649\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −83.1778 | −0.128958 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1170.94i | 1.80980i | 0.425627 | + | 0.904899i | \(0.360054\pi\) | ||||
−0.425627 | + | 0.904899i | \(0.639946\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 561.625 | 0.865370 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.5156i | 0.0161531i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.4487 | 0.0297836 | 0.0148918 | − | 0.999889i | \(-0.495260\pi\) | ||||
0.0148918 | + | 0.999889i | \(0.495260\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1129.33i | 1.72417i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 703.165 | 1.07027 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 400.433i | 0.607637i | 0.952730 | + | 0.303818i | \(0.0982616\pi\) | ||||
−0.952730 | + | 0.303818i | \(0.901738\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −406.636 | −0.615182 | −0.307591 | − | 0.951519i | \(-0.599523\pi\) | ||||
−0.307591 | + | 0.951519i | \(0.599523\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.4582i | 0.0187907i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −963.069 | −1.44822 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 117.307i | − 0.175873i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.26423 | −0.00487927 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 187.776i | 0.279845i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −45.5265 | −0.0676471 | −0.0338236 | − | 0.999428i | \(-0.510768\pi\) | ||||
−0.0338236 | + | 0.999428i | \(0.510768\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 8.06930i | − 0.0119545i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 294.639 | 0.435213 | 0.217606 | − | 0.976037i | \(-0.430175\pi\) | ||||
0.217606 | + | 0.976037i | \(0.430175\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1089.18i | 1.60409i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −58.3382 | −0.0856655 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 310.626i | − 0.454796i | −0.973802 | − | 0.227398i | \(-0.926978\pi\) | ||||
0.973802 | − | 0.227398i | \(-0.0730218\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −391.829 | −0.572013 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 67.4808i | − 0.0982254i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 136.710 | 0.198418 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 980.037i | 1.41829i | 0.705063 | + | 0.709144i | \(0.250919\pi\) | ||||
−0.705063 | + | 0.709144i | \(0.749081\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −675.534 | −0.974797 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 791.905i | − 1.13943i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −327.301 | −0.469585 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 71.3690i | − 0.102102i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −276.305 | −0.394158 | −0.197079 | − | 0.980388i | \(-0.563146\pi\) | ||||
−0.197079 | + | 0.980388i | \(0.563146\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 491.668i | − 0.699386i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 43.5917 | 0.0618322 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1331.03i | 1.88264i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 449.838 | 0.634468 | 0.317234 | − | 0.948347i | \(-0.397246\pi\) | ||||
0.317234 | + | 0.948347i | \(0.397246\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 971.962i | 1.36703i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −89.7775 | −0.125915 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 360.767i | − 0.504569i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.9793 | −0.0222864 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1122.38i | − 1.56103i | −0.625139 | − | 0.780514i | \(-0.714958\pi\) | ||||
0.625139 | − | 0.780514i | \(-0.285042\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1340.43 | −1.85913 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 60.7486i | − 0.0840229i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.9110 | −0.0205669 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 529.192i | 0.727911i | 0.931416 | + | 0.363956i | \(0.118574\pi\) | ||||
−0.931416 | + | 0.363956i | \(0.881426\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 708.260 | 0.971549 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 523.155i | − 0.715670i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 372.110 | 0.507653 | 0.253826 | − | 0.967250i | \(-0.418311\pi\) | ||||
0.253826 | + | 0.967250i | \(0.418311\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 47.9070i | 0.0651797i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 252.938 | 0.343200 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 62.9975i | 0.0852469i | 0.999091 | + | 0.0426235i | \(0.0135716\pi\) | ||||
−0.999091 | + | 0.0426235i | \(0.986428\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −35.0959 | −0.0473629 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 762.894i | − 1.02678i | −0.858157 | − | 0.513388i | \(-0.828390\pi\) | ||||
0.858157 | − | 0.513388i | \(-0.171610\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1076.50 | 1.44496 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 726.057i | 0.971964i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 433.789 | 0.579157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1342.93i | 1.78819i | 0.447876 | + | 0.894095i | \(0.352180\pi\) | ||||
−0.447876 | + | 0.894095i | \(0.647820\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −23.3108 | −0.0309573 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1149.44i | 1.52244i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 558.375 | 0.737615 | 0.368808 | − | 0.929506i | \(-0.379766\pi\) | ||||
0.368808 | + | 0.929506i | \(0.379766\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 27.5878i | 0.0363475i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 480.213 | 0.631029 | 0.315514 | − | 0.948921i | \(-0.397823\pi\) | ||||
0.315514 | + | 0.948921i | \(0.397823\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.73550i | 0.0127595i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 316.848 | 0.414180 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 638.291i | 0.832191i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 472.763 | 0.614777 | 0.307388 | − | 0.951584i | \(-0.400545\pi\) | ||||
0.307388 | + | 0.951584i | \(0.400545\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 45.9234i | − 0.0595634i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1213.02 | 1.56924 | 0.784619 | − | 0.619979i | \(-0.212859\pi\) | ||||
0.784619 | + | 0.619979i | \(0.212859\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.4117i | 0.0147248i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −51.4485 | −0.0662143 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 922.036i | − 1.18362i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −402.708 | −0.515632 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 25.5302i | 0.0326056i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 807.648 | 1.02885 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 240.919i | 0.306123i | 0.988217 | + | 0.153062i | \(0.0489133\pi\) | ||||
−0.988217 | + | 0.153062i | \(0.951087\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −77.4612 | −0.0981764 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 143.891i | − 0.181911i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −213.409 | −0.269116 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 16.6315i | 0.0209202i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1181.68 | −1.48266 | −0.741328 | − | 0.671143i | \(-0.765803\pi\) | ||||
−0.741328 | + | 0.671143i | \(0.765803\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 274.174i | 0.343147i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −395.258 | −0.493456 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 612.616i | 0.762909i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −860.379 | −1.06879 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 104.789i | 0.129850i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −371.926 | −0.459735 | −0.229868 | − | 0.973222i | \(-0.573829\pi\) | ||||
−0.229868 | + | 0.973222i | \(0.573829\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 389.798i | − 0.480639i | −0.970694 | − | 0.240320i | \(-0.922748\pi\) | ||||
0.970694 | − | 0.240320i | \(-0.0772522\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −74.3165 | −0.0914102 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 418.550i | − 0.513559i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1473.77 | 1.80389 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 767.749i | − 0.937422i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1279.76 | 1.55878 | 0.779388 | − | 0.626542i | \(-0.215530\pi\) | ||||
0.779388 | + | 0.626542i | \(0.215530\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 523.237i | 0.635768i | 0.948130 | + | 0.317884i | \(0.102972\pi\) | ||||
−0.948130 | + | 0.317884i | \(0.897028\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.50671 | 0.00425055 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1022.20i | − 1.23603i | −0.786165 | − | 0.618017i | \(-0.787936\pi\) | ||||
0.786165 | − | 0.618017i | \(-0.212064\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 405.003 | 0.488544 | 0.244272 | − | 0.969707i | \(-0.421451\pi\) | ||||
0.244272 | + | 0.969707i | \(0.421451\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 102.972i | − 0.123914i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −301.316 | −0.361724 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 556.059i | − 0.665939i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.5388 | 0.0233438 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1353.58i | − 1.61333i | −0.591008 | − | 0.806666i | \(-0.701270\pi\) | ||||
0.591008 | − | 0.806666i | \(-0.298730\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −793.824 | −0.943904 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 39.6162i | − 0.0469943i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −470.911 | −0.557291 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 580.852i | 0.685776i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.16597 | 0.0107962 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 439.243i | − 0.516149i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 945.053 | 1.10792 | 0.553958 | − | 0.832544i | \(-0.313117\pi\) | ||||
0.553958 | + | 0.832544i | \(0.313117\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 892.589i | 1.04396i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 488.688 | 0.570230 | 0.285115 | − | 0.958493i | \(-0.407968\pi\) | ||||
0.285115 | + | 0.958493i | \(0.407968\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 380.166i | 0.442568i | 0.975209 | + | 0.221284i | \(0.0710247\pi\) | ||||
−0.975209 | + | 0.221284i | \(0.928975\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −96.4824 | −0.112059 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 152.667i | − 0.176903i | −0.996080 | − | 0.0884514i | \(-0.971808\pi\) | ||||
0.996080 | − | 0.0884514i | \(-0.0281918\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1314.82 | 1.52002 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 50.2881i | 0.0580024i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −846.799 | −0.974452 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 287.466i | 0.330041i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1009.47 | 1.15632 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 1150.05i | − 1.31434i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 230.004 | 0.262262 | 0.131131 | − | 0.991365i | \(-0.458139\pi\) | ||||
0.131131 | + | 0.991365i | \(0.458139\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.9573i | 0.0306681i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −873.243 | −0.991196 | −0.495598 | − | 0.868552i | \(-0.665051\pi\) | ||||
−0.495598 | + | 0.868552i | \(0.665051\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 325.304i | − 0.368408i | −0.982888 | − | 0.184204i | \(-0.941029\pi\) | ||||
0.982888 | − | 0.184204i | \(-0.0589707\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −77.6517 | −0.0877421 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 430.685i | 0.485552i | 0.970082 | + | 0.242776i | \(0.0780580\pi\) | ||||
−0.970082 | + | 0.242776i | \(0.921942\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1032.75 | 1.16170 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 623.087i | 0.699312i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −772.373 | −0.864920 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 445.709i | 0.497999i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −31.3537 | −0.0349539 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 36.1051i | − 0.0401614i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −104.606 | −0.116099 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 154.217i | − 0.170783i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1084.47 | −1.19831 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.4326i | 0.0346556i | 0.999850 | + | 0.0173278i | \(0.00551588\pi\) | ||||
−0.999850 | + | 0.0173278i | \(0.994484\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1233.62 | 1.35712 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1399.85i | 1.53661i | 0.640083 | + | 0.768306i | \(0.278900\pi\) | ||||
−0.640083 | + | 0.768306i | \(0.721100\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −632.560 | −0.692837 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 25.9624i | − 0.0283742i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2093.85 | −2.28337 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 806.944i | − 0.878068i | −0.898470 | − | 0.439034i | \(-0.855321\pi\) | ||||
0.898470 | − | 0.439034i | \(-0.144679\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −75.3976 | −0.0818650 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 457.681i | − 0.495862i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −55.8326 | −0.0603595 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1242.34i | 1.34017i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1620.69 | −1.74455 | −0.872276 | − | 0.489013i | \(-0.837357\pi\) | ||||
−0.872276 | + | 0.489013i | \(0.837357\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 848.834i | − 0.911744i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −27.0982 | −0.0290442 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 276.046i | 0.295237i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −598.181 | −0.638400 | −0.319200 | − | 0.947687i | \(-0.603414\pi\) | ||||
−0.319200 | + | 0.947687i | \(0.603414\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 10.7295i | − 0.0114265i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1382.88 | −1.46958 | −0.734791 | − | 0.678294i | \(-0.762720\pi\) | ||||
−0.734791 | + | 0.678294i | \(0.762720\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 823.721i | − 0.873511i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 187.249 | 0.198147 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1170.80i | − 1.23633i | −0.786050 | − | 0.618163i | \(-0.787877\pi\) | ||||
0.786050 | − | 0.618163i | \(-0.212123\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −696.242 | −0.733659 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 32.0939i | − 0.0337476i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1846.78 | −1.93786 | −0.968930 | − | 0.247333i | \(-0.920446\pi\) | ||||
−0.968930 | + | 0.247333i | \(0.920446\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 557.020i | 0.583267i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.0947 | −0.0115933 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 726.475i | − 0.757534i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 933.368 | 0.971247 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 402.043i | − 0.417490i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 355.431 | 0.368323 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 363.922i | 0.376341i | 0.982136 | + | 0.188170i | \(0.0602557\pi\) | ||||
−0.982136 | + | 0.188170i | \(0.939744\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 26.8542 | 0.0277133 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1642.32i | 1.69137i | 0.533683 | + | 0.845685i | \(0.320808\pi\) | ||||
−0.533683 | + | 0.845685i | \(0.679192\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1468.24 | 1.50898 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.98540i | 0.00408759i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1159.63 | −1.18693 | −0.593467 | − | 0.804858i | \(-0.702241\pi\) | ||||
−0.593467 | + | 0.804858i | \(0.702241\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 344.359i | − 0.351746i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.02303 | 0.00919779 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1780.51i | − 1.81131i | −0.424020 | − | 0.905653i | \(-0.639382\pi\) | ||||
0.424020 | − | 0.905653i | \(-0.360618\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −455.961 | −0.462904 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 80.8216i | 0.0818861i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1316.63 | 1.33127 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 675.783i | − 0.681920i | −0.940078 | − | 0.340960i | \(-0.889248\pi\) | ||||
0.940078 | − | 0.340960i | \(-0.110752\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 94.6184 | 0.0952854 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 826.014i | 0.830165i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.3638 | 0.0134040 | 0.00670200 | − | 0.999978i | \(-0.497867\pi\) | ||||
0.00670200 | + | 0.999978i | \(0.497867\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 95.5948i | 0.0956905i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))