Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,3,Mod(377,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.377");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.m (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.6567211305\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 24) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 593.1 | ||
Root | \(-1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.593 |
Dual form | 648.3.m.d.377.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(487\) | \(569\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.89898 | + | 2.82843i | −0.979796 | + | 0.565685i | −0.902209 | − | 0.431300i | \(-0.858055\pi\) |
−0.0775874 | + | 0.996986i | \(0.524722\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00000 | − | 5.19615i | 0.428571 | − | 0.742307i | −0.568175 | − | 0.822908i | \(-0.692350\pi\) |
0.996747 | + | 0.0806002i | \(0.0256837\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.89898 | + | 2.82843i | 0.445362 | + | 0.257130i | 0.705869 | − | 0.708342i | \(-0.250557\pi\) |
−0.260508 | + | 0.965472i | \(0.583890\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.00000 | − | 8.66025i | −0.384615 | − | 0.666173i | 0.607100 | − | 0.794625i | \(-0.292333\pi\) |
−0.991716 | + | 0.128452i | \(0.958999\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 22.6274i | 1.33102i | 0.746387 | + | 0.665512i | \(0.231787\pi\) | ||||
−0.746387 | + | 0.665512i | \(0.768213\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.105263 | 0.0526316 | − | 0.998614i | \(-0.483239\pi\) | ||||
0.0526316 | + | 0.998614i | \(0.483239\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.79796 | − | 5.65685i | 0.425998 | − | 0.245950i | −0.271642 | − | 0.962398i | \(-0.587567\pi\) |
0.697640 | + | 0.716448i | \(0.254233\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.50000 | − | 6.06218i | 0.140000 | − | 0.242487i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 14.6969 | + | 8.48528i | 0.506791 | + | 0.292596i | 0.731514 | − | 0.681827i | \(-0.238814\pi\) |
−0.224723 | + | 0.974423i | \(0.572148\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 11.0000 | + | 19.0526i | 0.354839 | + | 0.614599i | 0.987090 | − | 0.160164i | \(-0.0512024\pi\) |
−0.632252 | + | 0.774763i | \(0.717869\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 33.9411i | 0.969746i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.162162 | −0.0810811 | − | 0.996708i | \(-0.525837\pi\) | ||||
−0.0810811 | + | 0.996708i | \(0.525837\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −29.3939 | + | 16.9706i | −0.716924 | + | 0.413916i | −0.813619 | − | 0.581398i | \(-0.802506\pi\) |
0.0966956 | + | 0.995314i | \(0.469173\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −41.0000 | + | 71.0141i | −0.953488 | + | 1.65149i | −0.215698 | + | 0.976460i | \(0.569203\pi\) |
−0.737790 | + | 0.675030i | \(0.764131\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 58.7878 | + | 33.9411i | 1.25080 | + | 0.722152i | 0.971269 | − | 0.237984i | \(-0.0764866\pi\) |
0.279534 | + | 0.960136i | \(0.409820\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.50000 | + | 11.2583i | 0.132653 | + | 0.229762i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 62.2254i | 1.17406i | 0.809564 | + | 0.587032i | \(0.199704\pi\) | ||||
−0.809564 | + | 0.587032i | \(0.800296\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −32.0000 | −0.581818 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −63.6867 | + | 36.7696i | −1.07944 | + | 0.623213i | −0.930744 | − | 0.365671i | \(-0.880840\pi\) |
−0.148692 | + | 0.988884i | \(0.547506\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 43.0000 | − | 74.4782i | 0.704918 | − | 1.22095i | −0.261803 | − | 0.965121i | \(-0.584317\pi\) |
0.966721 | − | 0.255833i | \(-0.0823496\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 48.9898 | + | 28.2843i | 0.753689 | + | 0.435143i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | − | 1.73205i | −0.0149254 | − | 0.0258515i | 0.858466 | − | 0.512870i | \(-0.171418\pi\) |
−0.873392 | + | 0.487019i | \(0.838084\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 124.451i | 1.75283i | 0.481558 | + | 0.876414i | \(0.340071\pi\) | ||||
−0.481558 | + | 0.876414i | \(0.659929\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 82.0000 | 1.12329 | 0.561644 | − | 0.827379i | \(-0.310169\pi\) | ||||
0.561644 | + | 0.827379i | \(0.310169\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 29.3939 | − | 16.9706i | 0.381739 | − | 0.220397i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.00000 | + | 8.66025i | −0.0632911 | + | 0.109623i | −0.895935 | − | 0.444186i | \(-0.853493\pi\) |
0.832644 | + | 0.553809i | \(0.186826\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −63.6867 | − | 36.7696i | −0.767310 | − | 0.443007i | 0.0646041 | − | 0.997911i | \(-0.479422\pi\) |
−0.831914 | + | 0.554904i | \(0.812755\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −64.0000 | − | 110.851i | −0.752941 | − | 1.30413i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 33.9411i | 0.381361i | 0.981652 | + | 0.190680i | \(0.0610694\pi\) | ||||
−0.981652 | + | 0.190680i | \(0.938931\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −60.0000 | −0.659341 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.79796 | + | 5.65685i | −0.103136 | + | 0.0595458i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 47.0000 | − | 81.4064i | 0.484536 | − | 0.839241i | −0.515306 | − | 0.857006i | \(-0.672322\pi\) |
0.999842 | + | 0.0177651i | \(0.00565510\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 44.0908 | + | 25.4558i | 0.436543 | + | 0.252038i | 0.702130 | − | 0.712049i | \(-0.252233\pi\) |
−0.265587 | + | 0.964087i | \(0.585566\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 67.0000 | + | 116.047i | 0.650485 | + | 1.12667i | 0.983005 | + | 0.183578i | \(0.0587678\pi\) |
−0.332520 | + | 0.943096i | \(0.607899\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 50.9117i | − | 0.475810i | −0.971288 | − | 0.237905i | \(-0.923539\pi\) | ||
0.971288 | − | 0.237905i | \(-0.0764607\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.0917431 | 0.0458716 | − | 0.998947i | \(-0.485394\pi\) | ||||
0.0458716 | + | 0.998947i | \(0.485394\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 58.7878 | − | 33.9411i | 0.520246 | − | 0.300364i | −0.216790 | − | 0.976218i | \(-0.569559\pi\) |
0.737035 | + | 0.675854i | \(0.236225\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −32.0000 | + | 55.4256i | −0.278261 | + | 0.481962i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 117.576 | + | 67.8823i | 0.988029 | + | 0.570439i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −44.5000 | − | 77.0763i | −0.367769 | − | 0.636994i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 101.823i | − | 0.814587i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 106.000 | 0.834646 | 0.417323 | − | 0.908758i | \(-0.362968\pi\) | ||||
0.417323 | + | 0.908758i | \(0.362968\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.89898 | − | 2.82843i | 0.0373968 | − | 0.0215910i | −0.481185 | − | 0.876619i | \(-0.659793\pi\) |
0.518582 | + | 0.855028i | \(0.326460\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | − | 10.3923i | 0.0451128 | − | 0.0781376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −88.1816 | − | 50.9117i | −0.643662 | − | 0.371618i | 0.142362 | − | 0.989815i | \(-0.454530\pi\) |
−0.786024 | + | 0.618196i | \(0.787864\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 39.0000 | + | 67.5500i | 0.280576 | + | 0.485971i | 0.971527 | − | 0.236930i | \(-0.0761413\pi\) |
−0.690951 | + | 0.722902i | \(0.742808\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 56.5685i | − | 0.395584i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −96.0000 | −0.662069 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −142.070 | + | 82.0244i | −0.953493 | + | 0.550499i | −0.894164 | − | 0.447739i | \(-0.852229\pi\) |
−0.0593285 | + | 0.998239i | \(0.518896\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −109.000 | + | 188.794i | −0.721854 | + | 1.25029i | 0.238401 | + | 0.971167i | \(0.423377\pi\) |
−0.960256 | + | 0.279122i | \(0.909957\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −107.778 | − | 62.2254i | −0.695339 | − | 0.401454i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 43.0000 | + | 74.4782i | 0.273885 | + | 0.474383i | 0.969853 | − | 0.243690i | \(-0.0783578\pi\) |
−0.695968 | + | 0.718073i | \(0.745024\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 67.8823i | − | 0.421629i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −222.000 | −1.36196 | −0.680982 | − | 0.732301i | \(-0.738447\pi\) | ||||
−0.680982 | + | 0.732301i | \(0.738447\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 146.969 | − | 84.8528i | 0.880056 | − | 0.508101i | 0.00937926 | − | 0.999956i | \(-0.497014\pi\) |
0.870677 | + | 0.491855i | \(0.163681\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 34.5000 | − | 59.7558i | 0.204142 | − | 0.353584i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −161.666 | − | 93.3381i | −0.934487 | − | 0.539527i | −0.0462594 | − | 0.998929i | \(-0.514730\pi\) |
−0.888228 | + | 0.459403i | \(0.848063\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.0000 | − | 36.3731i | −0.120000 | − | 0.207846i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 152.735i | − | 0.853269i | −0.904424 | − | 0.426634i | \(-0.859699\pi\) | ||
0.904424 | − | 0.426634i | \(-0.140301\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 90.0000 | 0.497238 | 0.248619 | − | 0.968601i | \(-0.420023\pi\) | ||||
0.248619 | + | 0.968601i | \(0.420023\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 29.3939 | − | 16.9706i | 0.158886 | − | 0.0917328i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −64.0000 | + | 110.851i | −0.342246 | + | 0.592787i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −235.151 | − | 135.765i | −1.23116 | − | 0.710809i | −0.263886 | − | 0.964554i | \(-0.585004\pi\) |
−0.967271 | + | 0.253745i | \(0.918338\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | − | 1.73205i | −0.00518135 | − | 0.00897436i | 0.863423 | − | 0.504480i | \(-0.168316\pi\) |
−0.868604 | + | 0.495506i | \(0.834983\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 84.8528i | 0.430725i | 0.976534 | + | 0.215362i | \(0.0690933\pi\) | ||||
−0.976534 | + | 0.215362i | \(0.930907\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 250.000 | 1.25628 | 0.628141 | − | 0.778100i | \(-0.283816\pi\) | ||||
0.628141 | + | 0.778100i | \(0.283816\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 88.1816 | − | 50.9117i | 0.434392 | − | 0.250796i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 96.0000 | − | 166.277i | 0.468293 | − | 0.811107i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.79796 | + | 5.65685i | 0.0468802 | + | 0.0270663i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.0000 | − | 29.4449i | −0.0805687 | − | 0.139549i | 0.822926 | − | 0.568149i | \(-0.192340\pi\) |
−0.903494 | + | 0.428600i | \(0.859007\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 463.862i | − | 2.15750i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 132.000 | 0.608295 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 195.959 | − | 113.137i | 0.886693 | − | 0.511933i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 139.000 | − | 240.755i | 0.623318 | − | 1.07962i | −0.365545 | − | 0.930794i | \(-0.619117\pi\) |
0.988863 | − | 0.148825i | \(-0.0475493\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 191.060 | + | 110.309i | 0.841675 | + | 0.485941i | 0.857833 | − | 0.513928i | \(-0.171810\pi\) |
−0.0161583 | + | 0.999869i | \(0.505144\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −29.0000 | − | 50.2295i | −0.126638 | − | 0.219343i | 0.795734 | − | 0.605646i | \(-0.207085\pi\) |
−0.922372 | + | 0.386303i | \(0.873752\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 395.980i | − | 1.69948i | −0.527199 | − | 0.849742i | \(-0.676758\pi\) | ||
0.527199 | − | 0.849742i | \(-0.323242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −384.000 | −1.63404 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.5959 | − | 11.3137i | 0.0819913 | − | 0.0473377i | −0.458444 | − | 0.888723i | \(-0.651593\pi\) |
0.540435 | + | 0.841386i | \(0.318260\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.0000 | − | 25.9808i | 0.0622407 | − | 0.107804i | −0.833226 | − | 0.552933i | \(-0.813509\pi\) |
0.895467 | + | 0.445129i | \(0.146842\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −63.6867 | − | 36.7696i | −0.259946 | − | 0.150080i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.0000 | − | 17.3205i | −0.0404858 | − | 0.0701235i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 107.480i | 0.428208i | 0.976811 | + | 0.214104i | \(0.0686832\pi\) | ||||
−0.976811 | + | 0.214104i | \(0.931317\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 64.0000 | 0.252964 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −156.767 | + | 90.5097i | −0.609990 | + | 0.352178i | −0.772961 | − | 0.634453i | \(-0.781225\pi\) |
0.162972 | + | 0.986631i | \(0.447892\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.0000 | + | 31.1769i | −0.0694981 | + | 0.120374i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −186.161 | − | 107.480i | −0.707837 | − | 0.408670i | 0.102422 | − | 0.994741i | \(-0.467341\pi\) |
−0.810260 | + | 0.586071i | \(0.800674\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −176.000 | − | 304.841i | −0.664151 | − | 1.15034i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 401.637i | − | 1.49307i | −0.665344 | − | 0.746537i | \(-0.731715\pi\) | ||
0.665344 | − | 0.746537i | \(-0.268285\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 266.000 | 0.981550 | 0.490775 | − | 0.871286i | \(-0.336714\pi\) | ||||
0.490775 | + | 0.871286i | \(0.336714\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 34.2929 | − | 19.7990i | 0.124701 | − | 0.0719963i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −173.000 | + | 299.645i | −0.624549 | + | 1.08175i | 0.364079 | + | 0.931368i | \(0.381384\pi\) |
−0.988628 | + | 0.150382i | \(0.951950\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −107.778 | − | 62.2254i | −0.383550 | − | 0.221443i | 0.295812 | − | 0.955246i | \(-0.404410\pi\) |
−0.679362 | + | 0.733804i | \(0.737743\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.0000 | + | 39.8372i | 0.0812721 | + | 0.140767i | 0.903797 | − | 0.427962i | \(-0.140768\pi\) |
−0.822525 | + | 0.568730i | \(0.807435\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 203.647i | 0.709571i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −223.000 | −0.771626 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 191.060 | − | 110.309i | 0.652083 | − | 0.376480i | −0.137171 | − | 0.990547i | \(-0.543801\pi\) |
0.789254 | + | 0.614067i | \(0.210468\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 208.000 | − | 360.267i | 0.705085 | − | 1.22124i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −97.9796 | − | 56.5685i | −0.327691 | − | 0.189192i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 246.000 | + | 426.084i | 0.817276 | + | 1.41556i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 486.489i | 1.59505i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.0000 | −0.0977199 | −0.0488599 | − | 0.998806i | \(-0.515559\pi\) | ||||
−0.0488599 | + | 0.998806i | \(0.515559\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −499.696 | + | 288.500i | −1.60674 | + | 0.927651i | −0.616646 | + | 0.787241i | \(0.711509\pi\) |
−0.990093 | + | 0.140411i | \(0.955158\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −105.000 | + | 181.865i | −0.335463 | + | 0.581039i | −0.983574 | − | 0.180507i | \(-0.942226\pi\) |
0.648110 | + | 0.761546i | \(0.275560\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 132.272 | + | 76.3675i | 0.417263 | + | 0.240907i | 0.693906 | − | 0.720066i | \(-0.255888\pi\) |
−0.276642 | + | 0.960973i | \(0.589222\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 48.0000 | + | 83.1384i | 0.150470 | + | 0.260622i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 45.2548i | 0.140108i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −70.0000 | −0.215385 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 352.727 | − | 203.647i | 1.07212 | − | 0.618987i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −217.000 | + | 375.855i | −0.655589 | + | 1.13551i | 0.326157 | + | 0.945316i | \(0.394246\pi\) |
−0.981746 | + | 0.190198i | \(0.939087\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.79796 | + | 5.65685i | 0.0292476 | + | 0.0168861i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 255.000 | + | 441.673i | 0.756677 | + | 1.31060i | 0.944537 | + | 0.328406i | \(0.106512\pi\) |
−0.187860 | + | 0.982196i | \(0.560155\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 124.451i | 0.364958i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 372.000 | 1.08455 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 132.272 | − | 76.3675i | 0.381189 | − | 0.220079i | −0.297147 | − | 0.954832i | \(-0.596035\pi\) |
0.678335 | + | 0.734752i | \(0.262702\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −213.000 | + | 368.927i | −0.610315 | + | 1.05710i | 0.380872 | + | 0.924628i | \(0.375624\pi\) |
−0.991187 | + | 0.132469i | \(0.957709\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 39.1918 | + | 22.6274i | 0.111025 | + | 0.0641003i | 0.554484 | − | 0.832194i | \(-0.312916\pi\) |
−0.443459 | + | 0.896295i | \(0.646249\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −352.000 | − | 609.682i | −0.991549 | − | 1.71741i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 441.235i | 1.22907i | 0.788891 | + | 0.614533i | \(0.210655\pi\) | ||||
−0.788891 | + | 0.614533i | \(0.789345\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −357.000 | −0.988920 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −401.716 | + | 231.931i | −1.10059 | + | 0.635427i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 283.000 | − | 490.170i | 0.771117 | − | 1.33561i | −0.165834 | − | 0.986154i | \(-0.553032\pi\) |
0.936951 | − | 0.349460i | \(-0.113635\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 323.333 | + | 186.676i | 0.871517 | + | 0.503170i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −109.000 | − | 188.794i | −0.292225 | − | 0.506149i | 0.682110 | − | 0.731249i | \(-0.261062\pi\) |
−0.974336 | + | 0.225100i | \(0.927729\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 169.706i | − | 0.450148i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −142.000 | −0.374670 | −0.187335 | − | 0.982296i | \(-0.559985\pi\) | ||||
−0.187335 | + | 0.982296i | \(0.559985\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −96.0000 | + | 166.277i | −0.249351 | + | 0.431888i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 475.201 | + | 274.357i | 1.22160 | + | 0.705289i | 0.965258 | − | 0.261298i | \(-0.0841506\pi\) |
0.256338 | + | 0.966587i | \(0.417484\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 128.000 | + | 221.703i | 0.327366 | + | 0.567014i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 56.5685i | − | 0.143211i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −310.000 | −0.780856 | −0.390428 | − | 0.920633i | \(-0.627673\pi\) | ||||
−0.390428 | + | 0.920633i | \(0.627673\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −293.939 | + | 169.706i | −0.733014 | + | 0.423206i | −0.819524 | − | 0.573045i | \(-0.805762\pi\) |
0.0865095 | + | 0.996251i | \(0.472429\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 110.000 | − | 190.526i | 0.272953 | − | 0.472768i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −29.3939 | − | 16.9706i | −0.0722208 | − | 0.0416967i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 135.000 | + | 233.827i | 0.330073 | + | 0.571704i | 0.982526 | − | 0.186126i | \(-0.0595932\pi\) |
−0.652453 | + | 0.757830i | \(0.726260\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 441.235i | 1.06836i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 416.000 | 1.00241 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 44.0908 | − | 25.4558i | 0.105229 | − | 0.0607538i | −0.446462 | − | 0.894803i | \(-0.647316\pi\) |
0.551691 | + | 0.834049i | \(0.313983\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 227.000 | − | 393.176i | 0.539192 | − | 0.933909i | −0.459755 | − | 0.888046i | \(-0.652063\pi\) |
0.998948 | − | 0.0458630i | \(-0.0146038\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 137.171 | + | 79.1960i | 0.322756 | + | 0.186343i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −258.000 | − | 446.869i | −0.604215 | − | 1.04653i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 248.902i | − | 0.577498i | −0.957405 | − | 0.288749i | \(-0.906761\pi\) | ||
0.957405 | − | 0.288749i | \(-0.0932393\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 706.000 | 1.63048 | 0.815242 | − | 0.579120i | \(-0.196604\pi\) | ||||
0.815242 | + | 0.579120i | \(0.196604\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.5959 | − | 11.3137i | 0.0448419 | − | 0.0258895i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 243.000 | − | 420.888i | 0.553531 | − | 0.958743i | −0.444485 | − | 0.895786i | \(-0.646613\pi\) |
0.998016 | − | 0.0629573i | \(-0.0200532\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 612.372 | + | 353.553i | 1.38233 | + | 0.798089i | 0.992435 | − | 0.122770i | \(-0.0391778\pi\) |
0.389895 | + | 0.920859i | \(0.372511\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −96.0000 | − | 166.277i | −0.215730 | − | 0.373656i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 724.077i | 1.61264i | 0.591477 | + | 0.806322i | \(0.298545\pi\) | ||||
−0.591477 | + | 0.806322i | \(0.701455\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −192.000 | −0.425721 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 293.939 | − | 169.706i | 0.646019 | − | 0.372979i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −169.000 | + | 292.717i | −0.369803 | + | 0.640518i | −0.989535 | − | 0.144296i | \(-0.953908\pi\) |
0.619731 | + | 0.784814i | \(0.287242\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −671.160 | − | 387.495i | −1.45588 | − | 0.840552i | −0.457074 | − | 0.889429i | \(-0.651103\pi\) |
−0.998805 | + | 0.0488765i | \(0.984436\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −37.0000 | − | 64.0859i | −0.0799136 | − | 0.138414i | 0.823299 | − | 0.567608i | \(-0.192131\pi\) |
−0.903212 | + | 0.429194i | \(0.858798\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 797.616i | 1.70796i | 0.520307 | + | 0.853979i | \(0.325817\pi\) | ||||
−0.520307 | + | 0.853979i | \(0.674183\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.0000 | −0.0255864 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −401.716 | + | 231.931i | −0.849295 | + | 0.490340i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.00000 | − | 12.1244i | 0.0147368 | − | 0.0255250i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 274.343 | + | 158.392i | 0.572741 | + | 0.330672i | 0.758243 | − | 0.651972i | \(-0.226058\pi\) |
−0.185502 | + | 0.982644i | \(0.559391\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 30.0000 | + | 51.9615i | 0.0623701 | + | 0.108028i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 531.744i | 1.09638i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −134.000 | −0.275154 | −0.137577 | − | 0.990491i | \(-0.543931\pi\) | ||||
−0.137577 | + | 0.990491i | \(0.543931\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −44.0908 | + | 25.4558i | −0.0897980 | + | 0.0518449i | −0.544227 | − | 0.838938i | \(-0.683177\pi\) |
0.454429 | + | 0.890783i | \(0.349843\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −192.000 | + | 332.554i | −0.389452 | + | 0.674551i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 646.665 | + | 373.352i | 1.30114 | + | 0.751212i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.0000 | + | 25.9808i | 0.0300601 | + | 0.0520657i | 0.880664 | − | 0.473741i | \(-0.157097\pi\) |
−0.850604 | + | 0.525807i | \(0.823763\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 237.588i | 0.472342i | 0.971712 | + | 0.236171i | \(0.0758925\pi\) | ||||
−0.971712 | + | 0.236171i | \(0.924107\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −288.000 | −0.570297 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 102.879 | − | 59.3970i | 0.202119 | − | 0.116693i | −0.395524 | − | 0.918455i | \(-0.629437\pi\) |
0.597643 | + | 0.801762i | \(0.296104\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 246.000 | − | 426.084i | 0.481409 | − | 0.833825i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −656.463 | − | 379.009i | −1.27469 | − | 0.735940i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 192.000 | + | 332.554i | 0.371373 | + | 0.643237i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 79.1960i | − | 0.152008i | −0.997108 | − | 0.0760038i | \(-0.975784\pi\) | ||
0.997108 | − | 0.0760038i | \(-0.0242161\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −494.000 | −0.944551 | −0.472275 | − | 0.881451i | \(-0.656567\pi\) | ||||
−0.472275 | + | 0.881451i | \(0.656567\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −431.110 | + | 248.902i | −0.818046 | + | 0.472299i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −200.500 | + | 347.276i | −0.379017 | + | 0.656477i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 293.939 | + | 169.706i | 0.551480 | + | 0.318397i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 144.000 | + | 249.415i | 0.269159 | + | 0.466197i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 73.5391i | 0.136436i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 234.000 | 0.432532 | 0.216266 | − | 0.976334i | \(-0.430612\pi\) | ||||
0.216266 | + | 0.976334i | \(0.430612\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −48.9898 | + | 28.2843i | −0.0898895 | + | 0.0518977i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −145.000 | + | 251.147i | −0.265082 | + | 0.459136i | −0.967585 | − | 0.252545i | \(-0.918732\pi\) |
0.702503 | + | 0.711681i | \(0.252066\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 29.3939 | + | 16.9706i | 0.0533464 | + | 0.0307996i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.0000 | + | 51.9615i | 0.0542495 | + | 0.0939630i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 175.362i | − | 0.314834i | −0.987532 | − | 0.157417i | \(-0.949683\pi\) | ||
0.987532 | − | 0.157417i | \(-0.0503167\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 820.000 | 1.46691 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −210.656 | + | 121.622i | −0.374167 | + | 0.216026i | −0.675277 | − | 0.737564i | \(-0.735976\pi\) |
0.301110 | + | 0.953589i | \(0.402643\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −192.000 | + | 332.554i | −0.339823 | + | 0.588591i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −538.888 | − | 311.127i | −0.947079 | − | 0.546796i | −0.0549064 | − | 0.998492i | \(-0.517486\pi\) |
−0.892172 | + | 0.451695i | \(0.850819\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −201.000 | − | 348.142i | −0.352014 | − | 0.609706i | 0.634588 | − | 0.772850i | \(-0.281170\pi\) |
−0.986602 | + | 0.163144i | \(0.947836\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 79.1960i | − | 0.137732i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 98.0000 | 0.169844 | 0.0849220 | − | 0.996388i | \(-0.472936\pi\) | ||||
0.0849220 | + | 0.996388i | \(0.472936\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −382.120 | + | 220.617i | −0.657694 | + | 0.379720i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −176.000 | + | 304.841i | −0.301887 | + | 0.522883i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 475.201 | + | 274.357i | 0.809542 | + | 0.467389i | 0.846797 | − | 0.531917i | \(-0.178528\pi\) |
−0.0372550 | + | 0.999306i | \(0.511861\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.0000 | + | 38.1051i | 0.0373514 | + | 0.0646946i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 701.450i | − | 1.18288i | −0.806348 | − | 0.591442i | \(-0.798559\pi\) | ||
0.806348 | − | 0.591442i | \(-0.201441\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −768.000 | −1.29076 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 558.484 | − | 322.441i | 0.932360 | − | 0.538298i | 0.0448028 | − | 0.998996i | \(-0.485734\pi\) |
0.887557 | + | 0.460698i | \(0.152401\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 199.000 | − | 344.678i | 0.331115 | − | 0.573508i | −0.651616 | − | 0.758549i | \(-0.725909\pi\) |
0.982731 | + | 0.185041i | \(0.0592419\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 436.009 | + | 251.730i | 0.720676 | + | 0.416083i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −85.0000 | − | 147.224i | −0.140033 | − | 0.242544i | 0.787476 | − | 0.616346i | \(-0.211388\pi\) |
−0.927509 | + | 0.373801i | \(0.878054\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 678.823i | − | 1.11100i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1030.00 | −1.68026 | −0.840131 | − | 0.542384i | \(-0.817522\pi\) | ||||
−0.840131 | + | 0.542384i | \(0.817522\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 911.210 | − | 526.087i | 1.47684 | − | 0.852654i | 0.477182 | − | 0.878805i | \(-0.341658\pi\) |
0.999658 | + | 0.0261507i | \(0.00832498\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.00000 | − | 12.1244i | 0.0113086 | − | 0.0195870i | −0.860316 | − | 0.509762i | \(-0.829734\pi\) |
0.871624 | + | 0.490175i | \(0.163067\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 176.363 | + | 101.823i | 0.283087 | + | 0.163440i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 375.500 | + | 650.385i | 0.600800 | + | 1.04062i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 135.765i | − | 0.215842i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1114.00 | 1.76545 | 0.882726 | − | 0.469888i | \(-0.155706\pi\) | ||||
0.882726 | + | 0.469888i | \(0.155706\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −519.292 | + | 299.813i | −0.817782 | + | 0.472147i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 65.0000 | − | 112.583i | 0.102041 | − | 0.176740i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −391.918 | − | 226.274i | −0.611417 | − | 0.353002i | 0.162103 | − | 0.986774i | \(-0.448172\pi\) |
−0.773520 | + | 0.633772i | \(0.781506\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 399.000 | + | 691.088i | 0.620529 | + | 1.07479i | 0.989387 | + | 0.145302i | \(0.0464153\pi\) |
−0.368859 | + | 0.929486i | \(0.620251\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 147.078i | − | 0.227323i | −0.993520 | − | 0.113662i | \(-0.963742\pi\) | ||
0.993520 | − | 0.113662i | \(-0.0362580\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −416.000 | −0.640986 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 279.242 | − | 161.220i | 0.427629 | − | 0.246892i | −0.270707 | − | 0.962662i | \(-0.587257\pi\) |
0.698336 | + | 0.715770i | \(0.253924\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.0000 | + | 27.7128i | −0.0244275 | + | 0.0423096i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −690.756 | − | 398.808i | −1.04819 | − | 0.605172i | −0.126047 | − | 0.992024i | \(-0.540229\pi\) |
−0.922142 | + | 0.386852i | \(0.873562\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −493.000 | − | 853.901i | −0.745840 | − | 1.29183i | −0.949801 | − | 0.312853i | \(-0.898715\pi\) |
0.203962 | − | 0.978979i | \(-0.434618\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 67.8823i | 0.102079i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 192.000 | 0.287856 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 421.312 | − | 243.245i | 0.627887 | − | 0.362511i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.0000 | + | 29.4449i | −0.0252600 | + | 0.0437517i | −0.878379 | − | 0.477965i | \(-0.841375\pi\) |
0.853119 | + | 0.521716i | \(0.174708\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −347.828 | − | 200.818i | −0.513778 | − | 0.296630i | 0.220607 | − | 0.975363i | \(-0.429196\pi\) |
−0.734385 | + | 0.678733i | \(0.762529\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −282.000 | − | 488.438i | −0.415317 | − | 0.719350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 130.108i | 0.190494i | 0.995454 | + | 0.0952472i | \(0.0303641\pi\) | ||||
−0.995454 | + | 0.0952472i | \(0.969636\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 576.000 | 0.840876 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 538.888 | − | 311.127i | 0.782130 | − | 0.451563i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −289.000 | + | 500.563i | −0.418234 | + | 0.724403i | −0.995762 | − | 0.0919679i | \(-0.970684\pi\) |
0.577528 | + | 0.816371i | \(0.304018\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −382.120 | − | 220.617i | −0.549814 | − | 0.317435i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −384.000 | − | 665.108i | −0.550933 | − | 0.954243i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1238.85i | − | 1.76726i | −0.468183 | − | 0.883631i | \(-0.655091\pi\) | ||
0.468183 | − | 0.883631i | \(-0.344909\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.0000 | −0.0170697 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 264.545 | − | 152.735i | 0.374179 | − | 0.216033i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 611.000 | − | 1058.28i | 0.861777 | − | 1.49264i | −0.00843489 | − | 0.999964i | \(-0.502685\pi\) |
0.870212 | − | 0.492677i | \(-0.163982\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 215.555 | + | 124.451i | 0.302321 | + | 0.174545i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 160.000 | + | 277.128i | 0.223776 | + | 0.387592i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 248.902i | 0.346177i | 0.984906 | + | 0.173089i | \(0.0553747\pi\) | ||||
−0.984906 | + | 0.173089i | \(0.944625\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 804.000 | 1.11512 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 102.879 | − | 59.3970i | 0.141901 | − | 0.0819269i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 435.000 | − | 753.442i | 0.598349 | − | 1.03637i | −0.394715 | − | 0.918803i | \(-0.629157\pi\) |
0.993065 | − | 0.117568i | \(-0.0375098\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1606.87 | − | 927.724i | −2.19817 | − | 1.26912i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 107.000 | + | 185.329i | 0.145975 | + | 0.252837i | 0.929736 | − | 0.368226i | \(-0.120035\pi\) |
−0.783761 | + | 0.621063i | \(0.786701\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 11.3137i | − | 0.0153510i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −958.000 | −1.29635 | −0.648173 | − | 0.761493i | \(-0.724467\pi\) | ||||
−0.648173 | + | 0.761493i | \(0.724467\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −872.018 | + | 503.460i | −1.17365 | + | 0.677604i | −0.954536 | − | 0.298096i | \(-0.903648\pi\) |
−0.219109 | + | 0.975700i | \(0.570315\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 464.000 | − | 803.672i | 0.622819 | − | 1.07875i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −264.545 | − | 152.735i | −0.353197 | − | 0.203919i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 315.000 | + | 545.596i | 0.419441 | + | 0.726493i | 0.995883 | − | 0.0906450i | \(-0.0288929\pi\) |
−0.576443 | + | 0.817138i | \(0.695560\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1233.19i | − | 1.63337i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 602.000 | 0.795244 | 0.397622 | − | 0.917549i | \(-0.369835\pi\) | ||||
0.397622 | + | 0.917549i | \(0.369835\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −950.402 | + | 548.715i | −1.24889 | + | 0.721044i | −0.970887 | − | 0.239537i | \(-0.923004\pi\) |
−0.277998 | + | 0.960582i | \(0.589671\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.0000 | − | 51.9615i | 0.0393185 | − | 0.0681016i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 636.867 | + | 367.696i | 0.830336 | + | 0.479394i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −385.000 | − | 666.840i | −0.500650 | − | 0.867152i | −1.00000 | 0.000750943i | \(-0.999761\pi\) | |
0.499350 | − | 0.866401i | \(-0.333572\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 186.676i | − | 0.241496i | −0.992683 | − | 0.120748i | \(-0.961471\pi\) | ||
0.992683 | − | 0.120748i | \(-0.0385293\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 154.000 | 0.198710 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −58.7878 | + | 33.9411i | −0.0754657 | + | 0.0435701i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −352.000 | + | 609.682i | −0.450704 | + | 0.780643i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −421.312 | − | 243.245i | −0.536703 | − | 0.309866i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −257.000 | − | 445.137i | −0.326557 | − | 0.565613i | 0.655270 | − | 0.755395i | \(-0.272555\pi\) |
−0.981826 | + | 0.189783i | \(0.939222\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 407.294i | − | 0.514910i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −860.000 | −1.08449 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 612.372 | − | 353.553i | 0.768347 | − | 0.443605i | −0.0639377 | − | 0.997954i | \(-0.520366\pi\) |
0.832285 | + | 0.554349i | \(0.187033\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −768.000 | + | 1330.22i | −0.961202 | + | 1.66485i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 401.716 | + | 231.931i | 0.500269 | + | 0.288831i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 192.000 | + | 332.554i | 0.238509 | + | 0.413110i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 758.018i | − | 0.936982i | −0.883468 | − | 0.468491i | \(-0.844798\pi\) | ||
0.883468 | − | 0.468491i | \(-0.155202\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1454.00 | −1.79285 | −0.896424 | − | 0.443197i | \(-0.853844\pi\) | ||||
−0.896424 | + | 0.443197i | \(0.853844\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1087.57 | − | 627.911i | 1.33445 | − | 0.770443i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −82.0000 | + | 142.028i | −0.100367 | + | 0.173841i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −837.725 | − | 483.661i | −1.02037 | − | 0.589112i | −0.106160 | − | 0.994349i | \(-0.533856\pi\) |
−0.914212 | + | 0.405237i | \(0.867189\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 83.0000 | + | 143.760i | 0.100851 | + | 0.174678i | 0.912035 | − | 0.410112i | \(-0.134510\pi\) |
−0.811185 | + | 0.584790i | \(0.801177\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 978.636i | − | 1.18336i | −0.806174 | − | 0.591678i | \(-0.798466\pi\) | ||
0.806174 | − | 0.591678i | \(-0.201534\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1258.00 | 1.51749 | 0.758745 | − | 0.651387i | \(-0.225813\pi\) | ||||
0.758745 | + | 0.651387i | \(0.225813\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −254.747 | + | 147.078i | −0.305819 | + | 0.176564i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −480.000 | + | 831.384i | −0.574850 | + | 0.995670i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1146.36 | + | 661.852i | 1.36634 | + | 0.788858i | 0.990459 | − | 0.137809i | \(-0.0440060\pi\) |
0.375883 | + | 0.926667i | \(0.377339\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −276.500 | − | 478.912i | −0.328775 | − | 0.569455i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 390.323i | 0.461921i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −534.000 | −0.630460 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −58.7878 | + | 33.9411i | −0.0690808 | + | 0.0398838i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 371.000 | − | 642.591i | 0.434936 | − | 0.753330i | −0.562355 | − | 0.826896i | \(-0.690104\pi\) |
0.997290 | + | 0.0735656i | \(0.0234378\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 205.757 | + | 118.794i | 0.240090 | + | 0.138616i | 0.615218 | − | 0.788357i | \(-0.289068\pi\) |
−0.375128 | + | 0.926973i | \(0.622401\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 615.000 | + | 1065.21i | 0.715949 | + | 1.24006i | 0.962592 | + | 0.270953i | \(0.0873389\pi\) |
−0.246644 | + | 0.969106i | \(0.579328\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.2548i | 0.0524390i | 0.999656 | + | 0.0262195i | \(0.00834688\pi\) | ||||
−0.999656 | + | 0.0262195i | \(0.991653\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1056.00 | 1.22081 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48.9898 | + | 28.2843i | −0.0563749 | + | 0.0325481i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.0000 | + | 17.3205i | −0.0114811 | + | 0.0198858i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −529.090 | − | 305.470i | −0.604674 | − | 0.349109i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 411.000 | + | 711.873i | 0.468643 | + | 0.811714i | 0.999358 | − | 0.0358370i | \(-0.0114097\pi\) |
−0.530715 | + | 0.847551i | \(0.678076\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 656.195i | − | 0.744830i | −0.928066 | − | 0.372415i | \(-0.878530\pi\) | ||
0.928066 | − | 0.372415i | \(-0.121470\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 962.000 | 1.08947 | 0.544734 | − | 0.838609i | \(-0.316631\pi\) | ||||
0.544734 | + | 0.838609i | \(0.316631\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 989.594 | − | 571.342i | 1.11566 | − | 0.644129i | 0.175373 | − | 0.984502i | \(-0.443887\pi\) |
0.940290 | + | 0.340373i | \(0.110553\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 318.000 | − | 550.792i | 0.357705 | − | 0.619564i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 117.576 | + | 67.8823i | 0.131664 | + | 0.0760160i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 432.000 | + | 748.246i | 0.482682 | + | 0.836029i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 373.352i | 0.415297i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1408.00 | −1.56271 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −440.908 | + | 254.558i | −0.487191 | + | 0.281280i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −521.000 | + | 902.398i | −0.574421 | + | 0.994927i | 0.421683 | + | 0.906743i | \(0.361439\pi\) |
−0.996104 | + | 0.0881834i | \(0.971894\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1391.31 | − | 803.273i | −1.52723 | − | 0.881749i | −0.999476 | − | 0.0323539i | \(-0.989700\pi\) |
−0.527758 | − | 0.849395i | \(-0.676967\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −208.000 | − | 360.267i | −0.227820 | − | 0.394596i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 33.9411i | − | 0.0370132i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −614.000 | −0.668118 | −0.334059 | − | 0.942552i | \(-0.608418\pi\) | ||||
−0.334059 | + | 0.942552i | \(0.608418\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1077.78 | − | 622.254i | 1.16769 | − | 0.674165i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.0000 | + | 36.3731i | −0.0227027 | + | 0.0393222i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.1918 | + | 22.6274i | 0.0421871 | + | 0.0243567i | 0.520945 | − | 0.853590i | \(-0.325580\pi\) |
−0.478758 | + | 0.877947i | \(0.658913\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.0000 | + | 22.5167i | 0.0139635 | + | 0.0241855i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 724.077i | − | 0.774414i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −462.000 | −0.493063 | −0.246531 | − | 0.969135i | \(-0.579291\pi\) | ||||
−0.246531 | + | 0.969135i | \(0.579291\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −308.636 | + | 178.191i | −0.327987 | + | 0.189363i | −0.654947 | − | 0.755675i | \(-0.727309\pi\) |
0.326960 | + | 0.945038i | \(0.393976\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −192.000 | + | 332.554i | −0.203606 | + | 0.352655i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 602.574 | + | 347.897i | 0.636298 | + | 0.367367i | 0.783187 | − | 0.621786i | \(-0.213593\pi\) |
−0.146889 | + | 0.989153i | \(0.546926\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −410.000 | − | 710.141i | −0.432034 | − | 0.748304i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1527.35i | 1.60268i | 0.598212 | + | 0.801338i | \(0.295878\pi\) | ||||
−0.598212 | + | 0.801338i | \(0.704122\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1536.00 | 1.60838 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −529.090 | + | 305.470i | −0.551710 | + | 0.318530i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 238.500 | − | 413.094i | 0.248179 | − | 0.429859i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.79796 | + | 5.65685i | 0.0101533 | + | 0.00586203i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.0000 | + | 60.6218i | 0.0361944 | + | 0.0626906i | 0.883555 | − | 0.468327i | \(-0.155143\pi\) |
−0.847361 | + | 0.531018i | \(0.821810\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 627.911i | 0.646664i | 0.946286 | + | 0.323332i | \(0.104803\pi\) | ||||
−0.946286 | + | 0.323332i | \(0.895197\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 468.000 | 0.480987 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 881.816 | − | 509.117i | 0.902576 | − | 0.521102i | 0.0245406 | − | 0.999699i | \(-0.492188\pi\) |
0.878035 | + | 0.478597i | \(0.158854\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −96.0000 | + | 166.277i | −0.0980592 | + | 0.169844i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −558.484 | − | 322.441i | −0.568142 | − | 0.328017i | 0.188265 | − | 0.982118i | \(-0.439714\pi\) |
−0.756407 | + | 0.654101i | \(0.773047\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −240.000 | − | 415.692i | −0.243655 | − | 0.422023i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 927.724i | 0.938043i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −854.000 | −0.861756 | −0.430878 | − | 0.902410i | \(-0.641796\pi\) | ||||
−0.430878 | + | 0.902410i | \(0.641796\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1224.74 | + | 707.107i | −1.23090 | + | 0.710660i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 259.000 | − | 448.601i | 0.259779 | − | 0.449951i | −0.706403 | − | 0.707810i | \(-0.749684\pi\) |
0.966183 | + | 0.257858i | \(0.0830168\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))