Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [841,2,Mod(840,841)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(841, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("841.840");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 841 = 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 841.b (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: | \(6.71541880999\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 29) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 840.2 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 841.840 |
Dual form | 841.2.b.a.840.3 |
$q$-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 \(\left(\mathbb{Z}/841\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 0.414214i | − 0.292893i | −0.989219 | − | 0.146447i | \(-0.953216\pi\) | ||||
0.989219 | − | 0.146447i | \(-0.0467837\pi\) | |||||||
\(3\) | 0.414214i | 0.239146i | 0.992825 | + | 0.119573i | \(0.0381526\pi\) | ||||
−0.992825 | + | 0.119573i | \(0.961847\pi\) | |||||||
\(4\) | 1.82843 | 0.914214 | ||||||||
\(5\) | 1.00000 | 0.447214 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(6\) | 0.171573 | 0.0700443 | ||||||||
\(7\) | 2.82843 | 1.06904 | 0.534522 | − | 0.845154i | \(-0.320491\pi\) | ||||
0.534522 | + | 0.845154i | \(0.320491\pi\) | |||||||
\(8\) | − 1.58579i | − 0.560660i | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | − 0.414214i | − 0.130986i | ||||||||
\(11\) | − 2.41421i | − 0.727913i | −0.931416 | − | 0.363956i | \(-0.881426\pi\) | ||||
0.931416 | − | 0.363956i | \(-0.118574\pi\) | |||||||
\(12\) | 0.757359i | 0.218631i | ||||||||
\(13\) | −1.82843 | −0.507114 | −0.253557 | − | 0.967320i | \(-0.581601\pi\) | ||||
−0.253557 | + | 0.967320i | \(0.581601\pi\) | |||||||
\(14\) | − 1.17157i | − 0.313116i | ||||||||
\(15\) | 0.414214i | 0.106949i | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 4.82843i | 1.17107i | 0.810649 | + | 0.585533i | \(0.199115\pi\) | ||||
−0.810649 | + | 0.585533i | \(0.800885\pi\) | |||||||
\(18\) | − 1.17157i | − 0.276142i | ||||||||
\(19\) | − 6.00000i | − 1.37649i | −0.725476 | − | 0.688247i | \(-0.758380\pi\) | ||||
0.725476 | − | 0.688247i | \(-0.241620\pi\) | |||||||
\(20\) | 1.82843 | 0.408849 | ||||||||
\(21\) | 1.17157i | 0.255658i | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −7.65685 | −1.59656 | −0.798282 | − | 0.602284i | \(-0.794258\pi\) | ||||
−0.798282 | + | 0.602284i | \(0.794258\pi\) | |||||||
\(24\) | 0.656854 | 0.134080 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 0.757359i | 0.148530i | ||||||||
\(27\) | 2.41421i | 0.464616i | ||||||||
\(28\) | 5.17157 | 0.977335 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | 0.171573 | 0.0313248 | ||||||||
\(31\) | 4.07107i | 0.731185i | 0.930775 | + | 0.365593i | \(0.119134\pi\) | ||||
−0.930775 | + | 0.365593i | \(0.880866\pi\) | |||||||
\(32\) | − 4.41421i | − 0.780330i | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 2.82843 | 0.478091 | ||||||||
\(36\) | 5.17157 | 0.861929 | ||||||||
\(37\) | − 4.00000i | − 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | −2.48528 | −0.403166 | ||||||||
\(39\) | − 0.757359i | − 0.121275i | ||||||||
\(40\) | − 1.58579i | − 0.250735i | ||||||||
\(41\) | 12.4853i | 1.94987i | 0.222483 | + | 0.974937i | \(0.428584\pi\) | ||||
−0.222483 | + | 0.974937i | \(0.571416\pi\) | |||||||
\(42\) | 0.485281 | 0.0748805 | ||||||||
\(43\) | − 6.41421i | − 0.978158i | −0.872239 | − | 0.489079i | \(-0.837333\pi\) | ||||
0.872239 | − | 0.489079i | \(-0.162667\pi\) | |||||||
\(44\) | − 4.41421i | − 0.665468i | ||||||||
\(45\) | 2.82843 | 0.421637 | ||||||||
\(46\) | 3.17157i | 0.467623i | ||||||||
\(47\) | 5.24264i | 0.764718i | 0.924014 | + | 0.382359i | \(0.124888\pi\) | ||||
−0.924014 | + | 0.382359i | \(0.875112\pi\) | |||||||
\(48\) | 1.24264i | 0.179360i | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.65685i | 0.234315i | ||||||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | −3.34315 | −0.463611 | ||||||||
\(53\) | −7.48528 | −1.02818 | −0.514091 | − | 0.857736i | \(-0.671871\pi\) | ||||
−0.514091 | + | 0.857736i | \(0.671871\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | − 2.41421i | − 0.325532i | ||||||||
\(56\) | − 4.48528i | − 0.599371i | ||||||||
\(57\) | 2.48528 | 0.329184 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.65685 | 0.996838 | 0.498419 | − | 0.866936i | \(-0.333914\pi\) | ||||
0.498419 | + | 0.866936i | \(0.333914\pi\) | |||||||
\(60\) | 0.757359i | 0.0977747i | ||||||||
\(61\) | − 0.828427i | − 0.106069i | −0.998593 | − | 0.0530346i | \(-0.983111\pi\) | ||||
0.998593 | − | 0.0530346i | \(-0.0168894\pi\) | |||||||
\(62\) | 1.68629 | 0.214159 | ||||||||
\(63\) | 8.00000 | 1.00791 | ||||||||
\(64\) | 4.17157 | 0.521447 | ||||||||
\(65\) | −1.82843 | −0.226788 | ||||||||
\(66\) | − 0.414214i | − 0.0509862i | ||||||||
\(67\) | 5.65685 | 0.691095 | 0.345547 | − | 0.938401i | \(-0.387693\pi\) | ||||
0.345547 | + | 0.938401i | \(0.387693\pi\) | |||||||
\(68\) | 8.82843i | 1.07060i | ||||||||
\(69\) | − 3.17157i | − 0.381813i | ||||||||
\(70\) | − 1.17157i | − 0.140030i | ||||||||
\(71\) | 3.17157 | 0.376396 | 0.188198 | − | 0.982131i | \(-0.439735\pi\) | ||||
0.188198 | + | 0.982131i | \(0.439735\pi\) | |||||||
\(72\) | − 4.48528i | − 0.528595i | ||||||||
\(73\) | 4.00000i | 0.468165i | 0.972217 | + | 0.234082i | \(0.0752085\pi\) | ||||
−0.972217 | + | 0.234082i | \(0.924791\pi\) | |||||||
\(74\) | −1.65685 | −0.192605 | ||||||||
\(75\) | − 1.65685i | − 0.191317i | ||||||||
\(76\) | − 10.9706i | − 1.25841i | ||||||||
\(77\) | − 6.82843i | − 0.778171i | ||||||||
\(78\) | −0.313708 | −0.0355205 | ||||||||
\(79\) | − 0.414214i | − 0.0466027i | −0.999728 | − | 0.0233013i | \(-0.992582\pi\) | ||||
0.999728 | − | 0.0233013i | \(-0.00741772\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | 5.17157 | 0.571105 | ||||||||
\(83\) | −3.65685 | −0.401392 | −0.200696 | − | 0.979654i | \(-0.564320\pi\) | ||||
−0.200696 | + | 0.979654i | \(0.564320\pi\) | |||||||
\(84\) | 2.14214i | 0.233726i | ||||||||
\(85\) | 4.82843i | 0.523716i | ||||||||
\(86\) | −2.65685 | −0.286496 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.82843 | −0.408112 | ||||||||
\(89\) | − 4.48528i | − 0.475439i | −0.971334 | − | 0.237719i | \(-0.923600\pi\) | ||||
0.971334 | − | 0.237719i | \(-0.0763999\pi\) | |||||||
\(90\) | − 1.17157i | − 0.123495i | ||||||||
\(91\) | −5.17157 | −0.542128 | ||||||||
\(92\) | −14.0000 | −1.45960 | ||||||||
\(93\) | −1.68629 | −0.174860 | ||||||||
\(94\) | 2.17157 | 0.223981 | ||||||||
\(95\) | − 6.00000i | − 0.615587i | ||||||||
\(96\) | 1.82843 | 0.186613 | ||||||||
\(97\) | − 12.4853i | − 1.26769i | −0.773461 | − | 0.633844i | \(-0.781476\pi\) | ||||
0.773461 | − | 0.633844i | \(-0.218524\pi\) | |||||||
\(98\) | − 0.414214i | − 0.0418419i | ||||||||
\(99\) | − 6.82843i | − 0.686283i | ||||||||
\(100\) | −7.31371 | −0.731371 | ||||||||
\(101\) | 13.6569i | 1.35891i | 0.733718 | + | 0.679454i | \(0.237783\pi\) | ||||
−0.733718 | + | 0.679454i | \(0.762217\pi\) | |||||||
\(102\) | 0.828427i | 0.0820265i | ||||||||
\(103\) | 0.828427 | 0.0816274 | 0.0408137 | − | 0.999167i | \(-0.487005\pi\) | ||||
0.0408137 | + | 0.999167i | \(0.487005\pi\) | |||||||
\(104\) | 2.89949i | 0.284319i | ||||||||
\(105\) | 1.17157i | 0.114334i | ||||||||
\(106\) | 3.10051i | 0.301148i | ||||||||
\(107\) | −9.17157 | −0.886649 | −0.443325 | − | 0.896361i | \(-0.646201\pi\) | ||||
−0.443325 | + | 0.896361i | \(0.646201\pi\) | |||||||
\(108\) | 4.41421i | 0.424758i | ||||||||
\(109\) | −1.34315 | −0.128650 | −0.0643250 | − | 0.997929i | \(-0.520489\pi\) | ||||
−0.0643250 | + | 0.997929i | \(0.520489\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | 1.65685 | 0.157262 | ||||||||
\(112\) | 8.48528 | 0.801784 | ||||||||
\(113\) | 9.31371i | 0.876160i | 0.898936 | + | 0.438080i | \(0.144341\pi\) | ||||
−0.898936 | + | 0.438080i | \(0.855659\pi\) | |||||||
\(114\) | − 1.02944i | − 0.0964156i | ||||||||
\(115\) | −7.65685 | −0.714005 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.17157 | −0.478112 | ||||||||
\(118\) | − 3.17157i | − 0.291967i | ||||||||
\(119\) | 13.6569i | 1.25192i | ||||||||
\(120\) | 0.656854 | 0.0599623 | ||||||||
\(121\) | 5.17157 | 0.470143 | ||||||||
\(122\) | −0.343146 | −0.0310670 | ||||||||
\(123\) | −5.17157 | −0.466305 | ||||||||
\(124\) | 7.44365i | 0.668460i | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | − 3.31371i | − 0.295209i | ||||||||
\(127\) | 15.6569i | 1.38932i | 0.719338 | + | 0.694661i | \(0.244445\pi\) | ||||
−0.719338 | + | 0.694661i | \(0.755555\pi\) | |||||||
\(128\) | − 10.5563i | − 0.933058i | ||||||||
\(129\) | 2.65685 | 0.233923 | ||||||||
\(130\) | 0.757359i | 0.0664248i | ||||||||
\(131\) | − 1.31371i | − 0.114779i | −0.998352 | − | 0.0573896i | \(-0.981722\pi\) | ||||
0.998352 | − | 0.0573896i | \(-0.0182777\pi\) | |||||||
\(132\) | 1.82843 | 0.159144 | ||||||||
\(133\) | − 16.9706i | − 1.47153i | ||||||||
\(134\) | − 2.34315i | − 0.202417i | ||||||||
\(135\) | 2.41421i | 0.207782i | ||||||||
\(136\) | 7.65685 | 0.656570 | ||||||||
\(137\) | − 12.0000i | − 1.02523i | −0.858619 | − | 0.512615i | \(-0.828677\pi\) | ||||
0.858619 | − | 0.512615i | \(-0.171323\pi\) | |||||||
\(138\) | −1.31371 | −0.111830 | ||||||||
\(139\) | 14.0000 | 1.18746 | 0.593732 | − | 0.804663i | \(-0.297654\pi\) | ||||
0.593732 | + | 0.804663i | \(0.297654\pi\) | |||||||
\(140\) | 5.17157 | 0.437078 | ||||||||
\(141\) | −2.17157 | −0.182879 | ||||||||
\(142\) | − 1.31371i | − 0.110244i | ||||||||
\(143\) | 4.41421i | 0.369135i | ||||||||
\(144\) | 8.48528 | 0.707107 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.65685 | 0.137122 | ||||||||
\(147\) | 0.414214i | 0.0341638i | ||||||||
\(148\) | − 7.31371i | − 0.601183i | ||||||||
\(149\) | 2.17157 | 0.177902 | 0.0889511 | − | 0.996036i | \(-0.471649\pi\) | ||||
0.0889511 | + | 0.996036i | \(0.471649\pi\) | |||||||
\(150\) | −0.686292 | −0.0560355 | ||||||||
\(151\) | −14.1421 | −1.15087 | −0.575435 | − | 0.817847i | \(-0.695167\pi\) | ||||
−0.575435 | + | 0.817847i | \(0.695167\pi\) | |||||||
\(152\) | −9.51472 | −0.771746 | ||||||||
\(153\) | 13.6569i | 1.10409i | ||||||||
\(154\) | −2.82843 | −0.227921 | ||||||||
\(155\) | 4.07107i | 0.326996i | ||||||||
\(156\) | − 1.38478i | − 0.110871i | ||||||||
\(157\) | − 8.48528i | − 0.677199i | −0.940931 | − | 0.338600i | \(-0.890047\pi\) | ||||
0.940931 | − | 0.338600i | \(-0.109953\pi\) | |||||||
\(158\) | −0.171573 | −0.0136496 | ||||||||
\(159\) | − 3.10051i | − 0.245886i | ||||||||
\(160\) | − 4.41421i | − 0.348974i | ||||||||
\(161\) | −21.6569 | −1.70680 | ||||||||
\(162\) | − 3.10051i | − 0.243599i | ||||||||
\(163\) | 18.0711i | 1.41544i | 0.706495 | + | 0.707718i | \(0.250275\pi\) | ||||
−0.706495 | + | 0.707718i | \(0.749725\pi\) | |||||||
\(164\) | 22.8284i | 1.78260i | ||||||||
\(165\) | 1.00000 | 0.0778499 | ||||||||
\(166\) | 1.51472i | 0.117565i | ||||||||
\(167\) | 8.82843 | 0.683164 | 0.341582 | − | 0.939852i | \(-0.389037\pi\) | ||||
0.341582 | + | 0.939852i | \(0.389037\pi\) | |||||||
\(168\) | 1.85786 | 0.143337 | ||||||||
\(169\) | −9.65685 | −0.742835 | ||||||||
\(170\) | 2.00000 | 0.153393 | ||||||||
\(171\) | − 16.9706i | − 1.29777i | ||||||||
\(172\) | − 11.7279i | − 0.894246i | ||||||||
\(173\) | −23.6569 | −1.79860 | −0.899299 | − | 0.437335i | \(-0.855922\pi\) | ||||
−0.899299 | + | 0.437335i | \(0.855922\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.3137 | −0.855236 | ||||||||
\(176\) | − 7.24264i | − 0.545935i | ||||||||
\(177\) | 3.17157i | 0.238390i | ||||||||
\(178\) | −1.85786 | −0.139253 | ||||||||
\(179\) | −10.4853 | −0.783707 | −0.391853 | − | 0.920028i | \(-0.628166\pi\) | ||||
−0.391853 | + | 0.920028i | \(0.628166\pi\) | |||||||
\(180\) | 5.17157 | 0.385466 | ||||||||
\(181\) | −14.3137 | −1.06393 | −0.531965 | − | 0.846766i | \(-0.678546\pi\) | ||||
−0.531965 | + | 0.846766i | \(0.678546\pi\) | |||||||
\(182\) | 2.14214i | 0.158786i | ||||||||
\(183\) | 0.343146 | 0.0253661 | ||||||||
\(184\) | 12.1421i | 0.895130i | ||||||||
\(185\) | − 4.00000i | − 0.294086i | ||||||||
\(186\) | 0.698485i | 0.0512154i | ||||||||
\(187\) | 11.6569 | 0.852434 | ||||||||
\(188\) | 9.58579i | 0.699115i | ||||||||
\(189\) | 6.82843i | 0.496695i | ||||||||
\(190\) | −2.48528 | −0.180301 | ||||||||
\(191\) | − 2.68629i | − 0.194373i | −0.995266 | − | 0.0971866i | \(-0.969016\pi\) | ||||
0.995266 | − | 0.0971866i | \(-0.0309844\pi\) | |||||||
\(192\) | 1.72792i | 0.124702i | ||||||||
\(193\) | 10.8284i | 0.779447i | 0.920932 | + | 0.389724i | \(0.127429\pi\) | ||||
−0.920932 | + | 0.389724i | \(0.872571\pi\) | |||||||
\(194\) | −5.17157 | −0.371297 | ||||||||
\(195\) | − 0.757359i | − 0.0542356i | ||||||||
\(196\) | 1.82843 | 0.130602 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | −2.82843 | −0.201008 | ||||||||
\(199\) | 16.4853 | 1.16861 | 0.584305 | − | 0.811534i | \(-0.301367\pi\) | ||||
0.584305 | + | 0.811534i | \(0.301367\pi\) | |||||||
\(200\) | 6.34315i | 0.448528i | ||||||||
\(201\) | 2.34315i | 0.165273i | ||||||||
\(202\) | 5.65685 | 0.398015 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.65685 | −0.256031 | ||||||||
\(205\) | 12.4853i | 0.872010i | ||||||||
\(206\) | − 0.343146i | − 0.0239081i | ||||||||
\(207\) | −21.6569 | −1.50526 | ||||||||
\(208\) | −5.48528 | −0.380336 | ||||||||
\(209\) | −14.4853 | −1.00197 | ||||||||
\(210\) | 0.485281 | 0.0334876 | ||||||||
\(211\) | 17.3848i | 1.19682i | 0.801191 | + | 0.598409i | \(0.204200\pi\) | ||||
−0.801191 | + | 0.598409i | \(0.795800\pi\) | |||||||
\(212\) | −13.6863 | −0.939978 | ||||||||
\(213\) | 1.31371i | 0.0900138i | ||||||||
\(214\) | 3.79899i | 0.259694i | ||||||||
\(215\) | − 6.41421i | − 0.437446i | ||||||||
\(216\) | 3.82843 | 0.260491 | ||||||||
\(217\) | 11.5147i | 0.781670i | ||||||||
\(218\) | 0.556349i | 0.0376807i | ||||||||
\(219\) | −1.65685 | −0.111960 | ||||||||
\(220\) | − 4.41421i | − 0.297606i | ||||||||
\(221\) | − 8.82843i | − 0.593864i | ||||||||
\(222\) | − 0.686292i | − 0.0460609i | ||||||||
\(223\) | −8.82843 | −0.591195 | −0.295598 | − | 0.955313i | \(-0.595519\pi\) | ||||
−0.295598 | + | 0.955313i | \(0.595519\pi\) | |||||||
\(224\) | − 12.4853i | − 0.834208i | ||||||||
\(225\) | −11.3137 | −0.754247 | ||||||||
\(226\) | 3.85786 | 0.256621 | ||||||||
\(227\) | 20.1421 | 1.33688 | 0.668440 | − | 0.743766i | \(-0.266962\pi\) | ||||
0.668440 | + | 0.743766i | \(0.266962\pi\) | |||||||
\(228\) | 4.54416 | 0.300944 | ||||||||
\(229\) | − 20.4853i | − 1.35371i | −0.736118 | − | 0.676853i | \(-0.763343\pi\) | ||||
0.736118 | − | 0.676853i | \(-0.236657\pi\) | |||||||
\(230\) | 3.17157i | 0.209127i | ||||||||
\(231\) | 2.82843 | 0.186097 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.31371 | −0.282600 | −0.141300 | − | 0.989967i | \(-0.545128\pi\) | ||||
−0.141300 | + | 0.989967i | \(0.545128\pi\) | |||||||
\(234\) | 2.14214i | 0.140036i | ||||||||
\(235\) | 5.24264i | 0.341992i | ||||||||
\(236\) | 14.0000 | 0.911322 | ||||||||
\(237\) | 0.171573 | 0.0111449 | ||||||||
\(238\) | 5.65685 | 0.366679 | ||||||||
\(239\) | −8.34315 | −0.539673 | −0.269837 | − | 0.962906i | \(-0.586970\pi\) | ||||
−0.269837 | + | 0.962906i | \(0.586970\pi\) | |||||||
\(240\) | 1.24264i | 0.0802121i | ||||||||
\(241\) | −4.31371 | −0.277870 | −0.138935 | − | 0.990301i | \(-0.544368\pi\) | ||||
−0.138935 | + | 0.990301i | \(0.544368\pi\) | |||||||
\(242\) | − 2.14214i | − 0.137702i | ||||||||
\(243\) | 10.3431i | 0.663513i | ||||||||
\(244\) | − 1.51472i | − 0.0969699i | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 2.14214i | 0.136578i | ||||||||
\(247\) | 10.9706i | 0.698040i | ||||||||
\(248\) | 6.45584 | 0.409947 | ||||||||
\(249\) | − 1.51472i | − 0.0959914i | ||||||||
\(250\) | 3.72792i | 0.235774i | ||||||||
\(251\) | − 5.92893i | − 0.374231i | −0.982338 | − | 0.187115i | \(-0.940086\pi\) | ||||
0.982338 | − | 0.187115i | \(-0.0599138\pi\) | |||||||
\(252\) | 14.6274 | 0.921441 | ||||||||
\(253\) | 18.4853i | 1.16216i | ||||||||
\(254\) | 6.48528 | 0.406923 | ||||||||
\(255\) | −2.00000 | −0.125245 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | −23.8284 | −1.48638 | −0.743188 | − | 0.669082i | \(-0.766687\pi\) | ||||
−0.743188 | + | 0.669082i | \(0.766687\pi\) | |||||||
\(258\) | − 1.10051i | − 0.0685145i | ||||||||
\(259\) | − 11.3137i | − 0.703000i | ||||||||
\(260\) | −3.34315 | −0.207333 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.544156 | −0.0336181 | ||||||||
\(263\) | − 11.2426i | − 0.693251i | −0.938004 | − | 0.346625i | \(-0.887327\pi\) | ||||
0.938004 | − | 0.346625i | \(-0.112673\pi\) | |||||||
\(264\) | − 1.58579i | − 0.0975984i | ||||||||
\(265\) | −7.48528 | −0.459817 | ||||||||
\(266\) | −7.02944 | −0.431002 | ||||||||
\(267\) | 1.85786 | 0.113699 | ||||||||
\(268\) | 10.3431 | 0.631808 | ||||||||
\(269\) | − 19.4558i | − 1.18624i | −0.805113 | − | 0.593122i | \(-0.797895\pi\) | ||||
0.805113 | − | 0.593122i | \(-0.202105\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | − 14.5563i | − 0.884235i | −0.896957 | − | 0.442118i | \(-0.854227\pi\) | ||||
0.896957 | − | 0.442118i | \(-0.145773\pi\) | |||||||
\(272\) | 14.4853i | 0.878299i | ||||||||
\(273\) | − 2.14214i | − 0.129648i | ||||||||
\(274\) | −4.97056 | −0.300283 | ||||||||
\(275\) | 9.65685i | 0.582330i | ||||||||
\(276\) | − 5.79899i | − 0.349058i | ||||||||
\(277\) | 5.31371 | 0.319270 | 0.159635 | − | 0.987176i | \(-0.448968\pi\) | ||||
0.159635 | + | 0.987176i | \(0.448968\pi\) | |||||||
\(278\) | − 5.79899i | − 0.347800i | ||||||||
\(279\) | 11.5147i | 0.689368i | ||||||||
\(280\) | − 4.48528i | − 0.268047i | ||||||||
\(281\) | −1.97056 | −0.117554 | −0.0587770 | − | 0.998271i | \(-0.518720\pi\) | ||||
−0.0587770 | + | 0.998271i | \(0.518720\pi\) | |||||||
\(282\) | 0.899495i | 0.0535641i | ||||||||
\(283\) | −0.343146 | −0.0203979 | −0.0101989 | − | 0.999948i | \(-0.503246\pi\) | ||||
−0.0101989 | + | 0.999948i | \(0.503246\pi\) | |||||||
\(284\) | 5.79899 | 0.344107 | ||||||||
\(285\) | 2.48528 | 0.147215 | ||||||||
\(286\) | 1.82843 | 0.108117 | ||||||||
\(287\) | 35.3137i | 2.08450i | ||||||||
\(288\) | − 12.4853i | − 0.735702i | ||||||||
\(289\) | −6.31371 | −0.371395 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.17157 | 0.303163 | ||||||||
\(292\) | 7.31371i | 0.428002i | ||||||||
\(293\) | 3.65685i | 0.213636i | 0.994279 | + | 0.106818i | \(0.0340662\pi\) | ||||
−0.994279 | + | 0.106818i | \(0.965934\pi\) | |||||||
\(294\) | 0.171573 | 0.0100063 | ||||||||
\(295\) | 7.65685 | 0.445799 | ||||||||
\(296\) | −6.34315 | −0.368688 | ||||||||
\(297\) | 5.82843 | 0.338200 | ||||||||
\(298\) | − 0.899495i | − 0.0521063i | ||||||||
\(299\) | 14.0000 | 0.809641 | ||||||||
\(300\) | − 3.02944i | − 0.174905i | ||||||||
\(301\) | − 18.1421i | − 1.04570i | ||||||||
\(302\) | 5.85786i | 0.337082i | ||||||||
\(303\) | −5.65685 | −0.324978 | ||||||||
\(304\) | − 18.0000i | − 1.03237i | ||||||||
\(305\) | − 0.828427i | − 0.0474356i | ||||||||
\(306\) | 5.65685 | 0.323381 | ||||||||
\(307\) | 16.8995i | 0.964505i | 0.876032 | + | 0.482253i | \(0.160181\pi\) | ||||
−0.876032 | + | 0.482253i | \(0.839819\pi\) | |||||||
\(308\) | − 12.4853i | − 0.711415i | ||||||||
\(309\) | 0.343146i | 0.0195209i | ||||||||
\(310\) | 1.68629 | 0.0957749 | ||||||||
\(311\) | − 25.3137i | − 1.43541i | −0.696348 | − | 0.717704i | \(-0.745193\pi\) | ||||
0.696348 | − | 0.717704i | \(-0.254807\pi\) | |||||||
\(312\) | −1.20101 | −0.0679938 | ||||||||
\(313\) | 4.17157 | 0.235791 | 0.117896 | − | 0.993026i | \(-0.462385\pi\) | ||||
0.117896 | + | 0.993026i | \(0.462385\pi\) | |||||||
\(314\) | −3.51472 | −0.198347 | ||||||||
\(315\) | 8.00000 | 0.450749 | ||||||||
\(316\) | − 0.757359i | − 0.0426048i | ||||||||
\(317\) | 19.4558i | 1.09275i | 0.837541 | + | 0.546375i | \(0.183992\pi\) | ||||
−0.837541 | + | 0.546375i | \(0.816008\pi\) | |||||||
\(318\) | −1.28427 | −0.0720184 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 4.17157 | 0.233198 | ||||||||
\(321\) | − 3.79899i | − 0.212039i | ||||||||
\(322\) | 8.97056i | 0.499910i | ||||||||
\(323\) | 28.9706 | 1.61197 | ||||||||
\(324\) | 13.6863 | 0.760350 | ||||||||
\(325\) | 7.31371 | 0.405692 | ||||||||
\(326\) | 7.48528 | 0.414571 | ||||||||
\(327\) | − 0.556349i | − 0.0307662i | ||||||||
\(328\) | 19.7990 | 1.09322 | ||||||||
\(329\) | 14.8284i | 0.817518i | ||||||||
\(330\) | − 0.414214i | − 0.0228017i | ||||||||
\(331\) | 0.414214i | 0.0227672i | 0.999935 | + | 0.0113836i | \(0.00362360\pi\) | ||||
−0.999935 | + | 0.0113836i | \(0.996376\pi\) | |||||||
\(332\) | −6.68629 | −0.366958 | ||||||||
\(333\) | − 11.3137i | − 0.619987i | ||||||||
\(334\) | − 3.65685i | − 0.200094i | ||||||||
\(335\) | 5.65685 | 0.309067 | ||||||||
\(336\) | 3.51472i | 0.191744i | ||||||||
\(337\) | − 17.7990i | − 0.969573i | −0.874633 | − | 0.484786i | \(-0.838897\pi\) | ||||
0.874633 | − | 0.484786i | \(-0.161103\pi\) | |||||||
\(338\) | 4.00000i | 0.217571i | ||||||||
\(339\) | −3.85786 | −0.209530 | ||||||||
\(340\) | 8.82843i | 0.478789i | ||||||||
\(341\) | 9.82843 | 0.532239 | ||||||||
\(342\) | −7.02944 | −0.380108 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | −10.1716 | −0.548414 | ||||||||
\(345\) | − 3.17157i | − 0.170752i | ||||||||
\(346\) | 9.79899i | 0.526797i | ||||||||
\(347\) | 14.4853 | 0.777611 | 0.388805 | − | 0.921320i | \(-0.372888\pi\) | ||||
0.388805 | + | 0.921320i | \(0.372888\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.1421 | 1.23877 | 0.619385 | − | 0.785087i | \(-0.287382\pi\) | ||||
0.619385 | + | 0.785087i | \(0.287382\pi\) | |||||||
\(350\) | 4.68629i | 0.250493i | ||||||||
\(351\) | − 4.41421i | − 0.235613i | ||||||||
\(352\) | −10.6569 | −0.568012 | ||||||||
\(353\) | 6.97056 | 0.371006 | 0.185503 | − | 0.982644i | \(-0.440609\pi\) | ||||
0.185503 | + | 0.982644i | \(0.440609\pi\) | |||||||
\(354\) | 1.31371 | 0.0698228 | ||||||||
\(355\) | 3.17157 | 0.168330 | ||||||||
\(356\) | − 8.20101i | − 0.434653i | ||||||||
\(357\) | −5.65685 | −0.299392 | ||||||||
\(358\) | 4.34315i | 0.229542i | ||||||||
\(359\) | − 18.0711i | − 0.953754i | −0.878970 | − | 0.476877i | \(-0.841769\pi\) | ||||
0.878970 | − | 0.476877i | \(-0.158231\pi\) | |||||||
\(360\) | − 4.48528i | − 0.236395i | ||||||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | 5.92893i | 0.311618i | ||||||||
\(363\) | 2.14214i | 0.112433i | ||||||||
\(364\) | −9.45584 | −0.495621 | ||||||||
\(365\) | 4.00000i | 0.209370i | ||||||||
\(366\) | − 0.142136i | − 0.00742955i | ||||||||
\(367\) | − 18.0000i | − 0.939592i | −0.882775 | − | 0.469796i | \(-0.844327\pi\) | ||||
0.882775 | − | 0.469796i | \(-0.155673\pi\) | |||||||
\(368\) | −22.9706 | −1.19742 | ||||||||
\(369\) | 35.3137i | 1.83836i | ||||||||
\(370\) | −1.65685 | −0.0861358 | ||||||||
\(371\) | −21.1716 | −1.09917 | ||||||||
\(372\) | −3.08326 | −0.159860 | ||||||||
\(373\) | −3.68629 | −0.190869 | −0.0954345 | − | 0.995436i | \(-0.530424\pi\) | ||||
−0.0954345 | + | 0.995436i | \(0.530424\pi\) | |||||||
\(374\) | − 4.82843i | − 0.249672i | ||||||||
\(375\) | − 3.72792i | − 0.192509i | ||||||||
\(376\) | 8.31371 | 0.428747 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2.82843 | 0.145479 | ||||||||
\(379\) | − 26.9706i | − 1.38538i | −0.721233 | − | 0.692692i | \(-0.756424\pi\) | ||||
0.721233 | − | 0.692692i | \(-0.243576\pi\) | |||||||
\(380\) | − 10.9706i | − 0.562778i | ||||||||
\(381\) | −6.48528 | −0.332251 | ||||||||
\(382\) | −1.11270 | −0.0569306 | ||||||||
\(383\) | 20.4853 | 1.04675 | 0.523374 | − | 0.852103i | \(-0.324673\pi\) | ||||
0.523374 | + | 0.852103i | \(0.324673\pi\) | |||||||
\(384\) | 4.37258 | 0.223137 | ||||||||
\(385\) | − 6.82843i | − 0.348009i | ||||||||
\(386\) | 4.48528 | 0.228295 | ||||||||
\(387\) | − 18.1421i | − 0.922217i | ||||||||
\(388\) | − 22.8284i | − 1.15894i | ||||||||
\(389\) | 36.9706i | 1.87448i | 0.348682 | + | 0.937241i | \(0.386629\pi\) | ||||
−0.348682 | + | 0.937241i | \(0.613371\pi\) | |||||||
\(390\) | −0.313708 | −0.0158852 | ||||||||
\(391\) | − 36.9706i | − 1.86968i | ||||||||
\(392\) | − 1.58579i | − 0.0800943i | ||||||||
\(393\) | 0.544156 | 0.0274490 | ||||||||
\(394\) | − 0.828427i | − 0.0417356i | ||||||||
\(395\) | − 0.414214i | − 0.0208413i | ||||||||
\(396\) | − 12.4853i | − 0.627409i | ||||||||
\(397\) | 30.6569 | 1.53862 | 0.769312 | − | 0.638874i | \(-0.220599\pi\) | ||||
0.769312 | + | 0.638874i | \(0.220599\pi\) | |||||||
\(398\) | − 6.82843i | − 0.342278i | ||||||||
\(399\) | 7.02944 | 0.351912 | ||||||||
\(400\) | −12.0000 | −0.600000 | ||||||||
\(401\) | −7.34315 | −0.366699 | −0.183350 | − | 0.983048i | \(-0.558694\pi\) | ||||
−0.183350 | + | 0.983048i | \(0.558694\pi\) | |||||||
\(402\) | 0.970563 | 0.0484073 | ||||||||
\(403\) | − 7.44365i | − 0.370795i | ||||||||
\(404\) | 24.9706i | 1.24233i | ||||||||
\(405\) | 7.48528 | 0.371947 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.65685 | −0.478672 | ||||||||
\(408\) | 3.17157i | 0.157016i | ||||||||
\(409\) | − 14.9706i | − 0.740247i | −0.928983 | − | 0.370123i | \(-0.879315\pi\) | ||||
0.928983 | − | 0.370123i | \(-0.120685\pi\) | |||||||
\(410\) | 5.17157 | 0.255406 | ||||||||
\(411\) | 4.97056 | 0.245180 | ||||||||
\(412\) | 1.51472 | 0.0746248 | ||||||||
\(413\) | 21.6569 | 1.06566 | ||||||||
\(414\) | 8.97056i | 0.440879i | ||||||||
\(415\) | −3.65685 | −0.179508 | ||||||||
\(416\) | 8.07107i | 0.395717i | ||||||||
\(417\) | 5.79899i | 0.283978i | ||||||||
\(418\) | 6.00000i | 0.293470i | ||||||||
\(419\) | 26.4853 | 1.29389 | 0.646945 | − | 0.762536i | \(-0.276046\pi\) | ||||
0.646945 | + | 0.762536i | \(0.276046\pi\) | |||||||
\(420\) | 2.14214i | 0.104526i | ||||||||
\(421\) | − 25.1127i | − 1.22392i | −0.790889 | − | 0.611959i | \(-0.790382\pi\) | ||||
0.790889 | − | 0.611959i | \(-0.209618\pi\) | |||||||
\(422\) | 7.20101 | 0.350540 | ||||||||
\(423\) | 14.8284i | 0.720983i | ||||||||
\(424\) | 11.8701i | 0.576461i | ||||||||
\(425\) | − 19.3137i | − 0.936852i | ||||||||
\(426\) | 0.544156 | 0.0263644 | ||||||||
\(427\) | − 2.34315i | − 0.113393i | ||||||||
\(428\) | −16.7696 | −0.810587 | ||||||||
\(429\) | −1.82843 | −0.0882773 | ||||||||
\(430\) | −2.65685 | −0.128125 | ||||||||
\(431\) | 8.34315 | 0.401875 | 0.200938 | − | 0.979604i | \(-0.435601\pi\) | ||||
0.200938 | + | 0.979604i | \(0.435601\pi\) | |||||||
\(432\) | 7.24264i | 0.348462i | ||||||||
\(433\) | − 14.6274i | − 0.702949i | −0.936197 | − | 0.351474i | \(-0.885680\pi\) | ||||
0.936197 | − | 0.351474i | \(-0.114320\pi\) | |||||||
\(434\) | 4.76955 | 0.228946 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.45584 | −0.117614 | ||||||||
\(437\) | 45.9411i | 2.19766i | ||||||||
\(438\) | 0.686292i | 0.0327923i | ||||||||
\(439\) | 11.6569 | 0.556351 | 0.278176 | − | 0.960530i | \(-0.410270\pi\) | ||||
0.278176 | + | 0.960530i | \(0.410270\pi\) | |||||||
\(440\) | −3.82843 | −0.182513 | ||||||||
\(441\) | 2.82843 | 0.134687 | ||||||||
\(442\) | −3.65685 | −0.173939 | ||||||||
\(443\) | − 35.6569i | − 1.69411i | −0.531507 | − | 0.847054i | \(-0.678374\pi\) | ||||
0.531507 | − | 0.847054i | \(-0.321626\pi\) | |||||||
\(444\) | 3.02944 | 0.143771 | ||||||||
\(445\) | − 4.48528i | − 0.212623i | ||||||||
\(446\) | 3.65685i | 0.173157i | ||||||||
\(447\) | 0.899495i | 0.0425447i | ||||||||
\(448\) | 11.7990 | 0.557450 | ||||||||
\(449\) | 1.02944i | 0.0485821i | 0.999705 | + | 0.0242911i | \(0.00773285\pi\) | ||||
−0.999705 | + | 0.0242911i | \(0.992267\pi\) | |||||||
\(450\) | 4.68629i | 0.220914i | ||||||||
\(451\) | 30.1421 | 1.41934 | ||||||||
\(452\) | 17.0294i | 0.800997i | ||||||||
\(453\) | − 5.85786i | − 0.275226i | ||||||||
\(454\) | − 8.34315i | − 0.391563i | ||||||||
\(455\) | −5.17157 | −0.242447 | ||||||||
\(456\) | − 3.94113i | − 0.184560i | ||||||||
\(457\) | −34.9706 | −1.63585 | −0.817927 | − | 0.575322i | \(-0.804877\pi\) | ||||
−0.817927 | + | 0.575322i | \(0.804877\pi\) | |||||||
\(458\) | −8.48528 | −0.396491 | ||||||||
\(459\) | −11.6569 | −0.544095 | ||||||||
\(460\) | −14.0000 | −0.652753 | ||||||||
\(461\) | 14.0000i | 0.652045i | 0.945362 | + | 0.326023i | \(0.105709\pi\) | ||||
−0.945362 | + | 0.326023i | \(0.894291\pi\) | |||||||
\(462\) | − 1.17157i | − 0.0545065i | ||||||||
\(463\) | 26.0000 | 1.20832 | 0.604161 | − | 0.796862i | \(-0.293508\pi\) | ||||
0.604161 | + | 0.796862i | \(0.293508\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.68629 | −0.0781999 | ||||||||
\(466\) | 1.78680i | 0.0827718i | ||||||||
\(467\) | − 32.3553i | − 1.49723i | −0.663007 | − | 0.748613i | \(-0.730720\pi\) | ||||
0.663007 | − | 0.748613i | \(-0.269280\pi\) | |||||||
\(468\) | −9.45584 | −0.437097 | ||||||||
\(469\) | 16.0000 | 0.738811 | ||||||||
\(470\) | 2.17157 | 0.100167 | ||||||||
\(471\) | 3.51472 | 0.161950 | ||||||||
\(472\) | − 12.1421i | − 0.558887i | ||||||||
\(473\) | −15.4853 | −0.712014 | ||||||||
\(474\) | − 0.0710678i | − 0.00326425i | ||||||||
\(475\) | 24.0000i | 1.10120i | ||||||||
\(476\) | 24.9706i | 1.14452i | ||||||||
\(477\) | −21.1716 | −0.969380 | ||||||||
\(478\) | 3.45584i | 0.158067i | ||||||||
\(479\) | − 12.8995i | − 0.589393i | −0.955591 | − | 0.294696i | \(-0.904781\pi\) | ||||
0.955591 | − | 0.294696i | \(-0.0952185\pi\) | |||||||
\(480\) | 1.82843 | 0.0834559 | ||||||||
\(481\) | 7.31371i | 0.333476i | ||||||||
\(482\) | 1.78680i | 0.0813864i | ||||||||
\(483\) | − 8.97056i | − 0.408175i | ||||||||
\(484\) | 9.45584 | 0.429811 | ||||||||
\(485\) | − 12.4853i | − 0.566927i | ||||||||
\(486\) | 4.28427 | 0.194338 | ||||||||
\(487\) | −28.4853 | −1.29079 | −0.645396 | − | 0.763848i | \(-0.723307\pi\) | ||||
−0.645396 | + | 0.763848i | \(0.723307\pi\) | |||||||
\(488\) | −1.31371 | −0.0594688 | ||||||||
\(489\) | −7.48528 | −0.338496 | ||||||||
\(490\) | − 0.414214i | − 0.0187123i | ||||||||
\(491\) | − 12.7574i | − 0.575732i | −0.957671 | − | 0.287866i | \(-0.907054\pi\) | ||||
0.957671 | − | 0.287866i | \(-0.0929457\pi\) | |||||||
\(492\) | −9.45584 | −0.426302 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 4.54416 | 0.204451 | ||||||||
\(495\) | − 6.82843i | − 0.306915i | ||||||||
\(496\) | 12.2132i | 0.548389i | ||||||||
\(497\) | 8.97056 | 0.402385 | ||||||||
\(498\) | −0.627417 | −0.0281152 | ||||||||
\(499\) | 14.9706 | 0.670174 | 0.335087 | − | 0.942187i | \(-0.391234\pi\) | ||||
0.335087 | + | 0.942187i | \(0.391234\pi\) | |||||||
\(500\) | −16.4558 | −0.735928 | ||||||||
\(501\) | 3.65685i | 0.163376i | ||||||||
\(502\) | −2.45584 | −0.109610 | ||||||||
\(503\) | 25.7279i | 1.14715i | 0.819153 | + | 0.573576i | \(0.194444\pi\) | ||||
−0.819153 | + | 0.573576i | \(0.805556\pi\) | |||||||
\(504\) | − 12.6863i | − 0.565092i | ||||||||
\(505\) | 13.6569i | 0.607722i | ||||||||
\(506\) | 7.65685 | 0.340389 | ||||||||
\(507\) | − 4.00000i | − 0.177646i | ||||||||
\(508\) | 28.6274i | 1.27014i | ||||||||
\(509\) | −27.4853 | −1.21826 | −0.609132 | − | 0.793069i | \(-0.708482\pi\) | ||||
−0.609132 | + | 0.793069i | \(0.708482\pi\) | |||||||
\(510\) | 0.828427i | 0.0366834i | ||||||||
\(511\) | 11.3137i | 0.500489i | ||||||||
\(512\) | − 22.7574i | − 1.00574i | ||||||||
\(513\) | 14.4853 | 0.639541 | ||||||||
\(514\) | 9.87006i | 0.435350i | ||||||||
\(515\) | 0.828427 | 0.0365049 | ||||||||
\(516\) | 4.85786 | 0.213856 | ||||||||
\(517\) | 12.6569 | 0.556648 | ||||||||
\(518\) | −4.68629 | −0.205904 | ||||||||
\(519\) | − 9.79899i | − 0.430128i | ||||||||
\(520\) | 2.89949i | 0.127151i | ||||||||
\(521\) | 0.857864 | 0.0375837 | 0.0187919 | − | 0.999823i | \(-0.494018\pi\) | ||||
0.0187919 | + | 0.999823i | \(0.494018\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.3137 | 1.19435 | 0.597173 | − | 0.802113i | \(-0.296291\pi\) | ||||
0.597173 | + | 0.802113i | \(0.296291\pi\) | |||||||
\(524\) | − 2.40202i | − 0.104933i | ||||||||
\(525\) | − 4.68629i | − 0.204527i | ||||||||
\(526\) | −4.65685 | −0.203048 | ||||||||
\(527\) | −19.6569 | −0.856266 | ||||||||
\(528\) | 3.00000 | 0.130558 | ||||||||
\(529\) | 35.6274 | 1.54902 | ||||||||
\(530\) | 3.10051i | 0.134677i | ||||||||
\(531\) | 21.6569 | 0.939827 | ||||||||
\(532\) | − 31.0294i | − 1.34530i | ||||||||
\(533\) | − 22.8284i | − 0.988809i | ||||||||
\(534\) | − 0.769553i | − 0.0333018i | ||||||||
\(535\) | −9.17157 | −0.396522 | ||||||||
\(536\) | − 8.97056i | − 0.387469i | ||||||||
\(537\) | − 4.34315i | − 0.187421i | ||||||||
\(538\) | −8.05887 | −0.347443 | ||||||||
\(539\) | − 2.41421i | − 0.103988i | ||||||||
\(540\) | 4.41421i | 0.189958i | ||||||||
\(541\) | 21.6569i | 0.931101i | 0.885021 | + | 0.465550i | \(0.154144\pi\) | ||||
−0.885021 | + | 0.465550i | \(0.845856\pi\) | |||||||
\(542\) | −6.02944 | −0.258987 | ||||||||
\(543\) | − 5.92893i | − 0.254435i | ||||||||
\(544\) | 21.3137 | 0.913818 | ||||||||
\(545\) | −1.34315 | −0.0575340 | ||||||||
\(546\) | −0.887302 | −0.0379730 | ||||||||
\(547\) | −3.79899 | −0.162433 | −0.0812165 | − | 0.996696i | \(-0.525881\pi\) | ||||
−0.0812165 | + | 0.996696i | \(0.525881\pi\) | |||||||
\(548\) | − 21.9411i | − 0.937278i | ||||||||
\(549\) | − 2.34315i | − 0.100003i | ||||||||
\(550\) | 4.00000 | 0.170561 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −5.02944 | −0.214067 | ||||||||
\(553\) | − 1.17157i | − 0.0498203i | ||||||||
\(554\) | − 2.20101i | − 0.0935120i | ||||||||
\(555\) | 1.65685 | 0.0703295 | ||||||||
\(556\) | 25.5980 | 1.08560 | ||||||||
\(557\) | −5.31371 | −0.225149 | −0.112575 | − | 0.993643i | \(-0.535910\pi\) | ||||
−0.112575 | + | 0.993643i | \(0.535910\pi\) | |||||||
\(558\) | 4.76955 | 0.201911 | ||||||||
\(559\) | 11.7279i | 0.496038i | ||||||||
\(560\) | 8.48528 | 0.358569 | ||||||||
\(561\) | 4.82843i | 0.203856i | ||||||||
\(562\) | 0.816234i | 0.0344307i | ||||||||
\(563\) | − 9.24264i | − 0.389531i | −0.980850 | − | 0.194765i | \(-0.937605\pi\) | ||||
0.980850 | − | 0.194765i | \(-0.0623946\pi\) | |||||||
\(564\) | −3.97056 | −0.167191 | ||||||||
\(565\) | 9.31371i | 0.391831i | ||||||||
\(566\) | 0.142136i | 0.00597441i | ||||||||
\(567\) | 21.1716 | 0.889122 | ||||||||
\(568\) | − 5.02944i | − 0.211030i | ||||||||
\(569\) | − 28.3431i | − 1.18821i | −0.804389 | − | 0.594103i | \(-0.797507\pi\) | ||||
0.804389 | − | 0.594103i | \(-0.202493\pi\) | |||||||
\(570\) | − 1.02944i | − 0.0431184i | ||||||||
\(571\) | −30.6274 | −1.28172 | −0.640859 | − | 0.767659i | \(-0.721422\pi\) | ||||
−0.640859 | + | 0.767659i | \(0.721422\pi\) | |||||||
\(572\) | 8.07107i | 0.337468i | ||||||||
\(573\) | 1.11270 | 0.0464836 | ||||||||
\(574\) | 14.6274 | 0.610537 | ||||||||
\(575\) | 30.6274 | 1.27725 | ||||||||
\(576\) | 11.7990 | 0.491625 | ||||||||
\(577\) | 9.79899i | 0.407937i | 0.978977 | + | 0.203969i | \(0.0653841\pi\) | ||||
−0.978977 | + | 0.203969i | \(0.934616\pi\) | |||||||
\(578\) | 2.61522i | 0.108779i | ||||||||
\(579\) | −4.48528 | −0.186402 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.3431 | −0.429106 | ||||||||
\(582\) | − 2.14214i | − 0.0887944i | ||||||||
\(583\) | 18.0711i | 0.748427i | ||||||||
\(584\) | 6.34315 | 0.262481 | ||||||||
\(585\) | −5.17157 | −0.213818 | ||||||||
\(586\) | 1.51472 | 0.0625724 | ||||||||
\(587\) | −3.65685 | −0.150935 | −0.0754673 | − | 0.997148i | \(-0.524045\pi\) | ||||
−0.0754673 | + | 0.997148i | \(0.524045\pi\) | |||||||
\(588\) | 0.757359i | 0.0312330i | ||||||||
\(589\) | 24.4264 | 1.00647 | ||||||||
\(590\) | − 3.17157i | − 0.130572i | ||||||||
\(591\) | 0.828427i | 0.0340769i | ||||||||
\(592\) | − 12.0000i | − 0.493197i | ||||||||
\(593\) | 2.51472 | 0.103267 | 0.0516336 | − | 0.998666i | \(-0.483557\pi\) | ||||
0.0516336 | + | 0.998666i | \(0.483557\pi\) | |||||||
\(594\) | − 2.41421i | − 0.0990564i | ||||||||
\(595\) | 13.6569i | 0.559876i | ||||||||
\(596\) | 3.97056 | 0.162641 | ||||||||
\(597\) | 6.82843i | 0.279469i | ||||||||
\(598\) | − 5.79899i | − 0.237138i | ||||||||
\(599\) | 43.8701i | 1.79248i | 0.443567 | + | 0.896241i | \(0.353713\pi\) | ||||
−0.443567 | + | 0.896241i | \(0.646287\pi\) | |||||||
\(600\) | −2.62742 | −0.107264 | ||||||||
\(601\) | 22.8284i | 0.931191i | 0.884998 | + | 0.465595i | \(0.154160\pi\) | ||||
−0.884998 | + | 0.465595i | \(0.845840\pi\) | |||||||
\(602\) | −7.51472 | −0.306277 | ||||||||
\(603\) | 16.0000 | 0.651570 | ||||||||
\(604\) | −25.8579 | −1.05214 | ||||||||
\(605\) | 5.17157 | 0.210254 | ||||||||
\(606\) | 2.34315i | 0.0951838i | ||||||||
\(607\) | 17.7279i | 0.719554i | 0.933038 | + | 0.359777i | \(0.117147\pi\) | ||||
−0.933038 | + | 0.359777i | \(0.882853\pi\) | |||||||
\(608\) | −26.4853 | −1.07412 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.343146 | −0.0138936 | ||||||||
\(611\) | − 9.58579i | − 0.387799i | ||||||||
\(612\) | 24.9706i | 1.00938i | ||||||||
\(613\) | 9.00000 | 0.363507 | 0.181753 | − | 0.983344i | \(-0.441823\pi\) | ||||
0.181753 | + | 0.983344i | \(0.441823\pi\) | |||||||
\(614\) | 7.00000 | 0.282497 | ||||||||
\(615\) | −5.17157 | −0.208538 | ||||||||
\(616\) | −10.8284 | −0.436290 | ||||||||
\(617\) | 23.3137i | 0.938575i | 0.883046 | + | 0.469287i | \(0.155489\pi\) | ||||
−0.883046 | + | 0.469287i | \(0.844511\pi\) | |||||||
\(618\) | 0.142136 | 0.00571753 | ||||||||
\(619\) | 36.4142i | 1.46361i | 0.681514 | + | 0.731805i | \(0.261322\pi\) | ||||
−0.681514 | + | 0.731805i | \(0.738678\pi\) | |||||||
\(620\) | 7.44365i | 0.298944i | ||||||||
\(621\) | − 18.4853i | − 0.741789i | ||||||||
\(622\) | −10.4853 | −0.420421 | ||||||||
\(623\) | − 12.6863i | − 0.508266i | ||||||||
\(624\) | − 2.27208i | − 0.0909559i | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | − 1.72792i | − 0.0690617i | ||||||||
\(627\) | − 6.00000i | − 0.239617i | ||||||||
\(628\) | − 15.5147i | − 0.619105i | ||||||||
\(629\) | 19.3137 | 0.770088 | ||||||||
\(630\) | − 3.31371i | − 0.132021i | ||||||||
\(631\) | 31.1716 | 1.24092 | 0.620460 | − | 0.784238i | \(-0.286946\pi\) | ||||
0.620460 | + | 0.784238i | \(0.286946\pi\) | |||||||
\(632\) | −0.656854 | −0.0261283 | ||||||||
\(633\) | −7.20101 | −0.286214 | ||||||||
\(634\) | 8.05887 | 0.320059 | ||||||||
\(635\) | 15.6569i | 0.621323i | ||||||||
\(636\) | − 5.66905i | − 0.224792i | ||||||||
\(637\) | −1.82843 | −0.0724449 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.97056 | 0.354870 | ||||||||
\(640\) | − 10.5563i | − 0.417276i | ||||||||
\(641\) | 21.7990i | 0.861008i | 0.902589 | + | 0.430504i | \(0.141664\pi\) | ||||
−0.902589 | + | 0.430504i | \(0.858336\pi\) | |||||||
\(642\) | −1.57359 | −0.0621048 | ||||||||
\(643\) | −15.5147 | −0.611841 | −0.305920 | − | 0.952057i | \(-0.598964\pi\) | ||||
−0.305920 | + | 0.952057i | \(0.598964\pi\) | |||||||
\(644\) | −39.5980 | −1.56038 | ||||||||
\(645\) | 2.65685 | 0.104614 | ||||||||
\(646\) | − 12.0000i | − 0.472134i | ||||||||
\(647\) | −28.3431 | −1.11428 | −0.557142 | − | 0.830417i | \(-0.688102\pi\) | ||||
−0.557142 | + | 0.830417i | \(0.688102\pi\) | |||||||
\(648\) | − 11.8701i | − 0.466300i | ||||||||
\(649\) | − 18.4853i | − 0.725611i | ||||||||
\(650\) | − 3.02944i | − 0.118824i | ||||||||
\(651\) | −4.76955 | −0.186934 | ||||||||
\(652\) | 33.0416i | 1.29401i | ||||||||
\(653\) | − 1.85786i | − 0.0727039i | −0.999339 | − | 0.0363519i | \(-0.988426\pi\) | ||||
0.999339 | − | 0.0363519i | \(-0.0115737\pi\) | |||||||
\(654\) | −0.230447 | −0.00901121 | ||||||||
\(655\) | − 1.31371i | − 0.0513308i | ||||||||
\(656\) | 37.4558i | 1.46241i | ||||||||
\(657\) | 11.3137i | 0.441390i | ||||||||
\(658\) | 6.14214 | 0.239445 | ||||||||
\(659\) | − 11.5858i | − 0.451318i | −0.974206 | − | 0.225659i | \(-0.927546\pi\) | ||||
0.974206 | − | 0.225659i | \(-0.0724535\pi\) | |||||||
\(660\) | 1.82843 | 0.0711714 | ||||||||
\(661\) | 10.6863 | 0.415649 | 0.207824 | − | 0.978166i | \(-0.433362\pi\) | ||||
0.207824 | + | 0.978166i | \(0.433362\pi\) | |||||||
\(662\) | 0.171573 | 0.00666837 | ||||||||
\(663\) | 3.65685 | 0.142020 | ||||||||
\(664\) | 5.79899i | 0.225044i | ||||||||
\(665\) | − 16.9706i | − 0.658090i | ||||||||
\(666\) | −4.68629 | −0.181590 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 16.1421 | 0.624558 | ||||||||
\(669\) | − 3.65685i | − 0.141382i | ||||||||
\(670\) | − 2.34315i | − 0.0905236i | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | 5.17157 | 0.199498 | ||||||||
\(673\) | −23.6274 | −0.910770 | −0.455385 | − | 0.890295i | \(-0.650498\pi\) | ||||
−0.455385 | + | 0.890295i | \(0.650498\pi\) | |||||||
\(674\) | −7.37258 | −0.283981 | ||||||||
\(675\) | − 9.65685i | − 0.371692i | ||||||||
\(676\) | −17.6569 | −0.679110 | ||||||||
\(677\) | − 22.0000i | − 0.845529i | −0.906240 | − | 0.422764i | \(-0.861060\pi\) | ||||
0.906240 | − | 0.422764i | \(-0.138940\pi\) | |||||||
\(678\) | 1.59798i | 0.0613700i | ||||||||
\(679\) | − 35.3137i | − 1.35522i | ||||||||
\(680\) | 7.65685 | 0.293627 | ||||||||
\(681\) | 8.34315i | 0.319710i | ||||||||
\(682\) | − 4.07107i | − 0.155889i | ||||||||
\(683\) | −12.9706 | −0.496305 | −0.248152 | − | 0.968721i | \(-0.579823\pi\) | ||||
−0.248152 | + | 0.968721i | \(0.579823\pi\) | |||||||
\(684\) | − 31.0294i | − 1.18644i | ||||||||
\(685\) | − 12.0000i | − 0.458496i | ||||||||
\(686\) | 7.02944i | 0.268385i | ||||||||
\(687\) | 8.48528 | 0.323734 | ||||||||
\(688\) | − 19.2426i | − 0.733619i | ||||||||
\(689\) | 13.6863 | 0.521406 | ||||||||
\(690\) | −1.31371 | −0.0500120 | ||||||||
\(691\) | 48.0000 | 1.82601 | 0.913003 | − | 0.407953i | \(-0.133757\pi\) | ||||
0.913003 | + | 0.407953i | \(0.133757\pi\) | |||||||
\(692\) | −43.2548 | −1.64430 | ||||||||
\(693\) | − 19.3137i | − 0.733667i | ||||||||
\(694\) | − 6.00000i | − 0.227757i | ||||||||
\(695\) | 14.0000 | 0.531050 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −60.2843 | −2.28343 | ||||||||
\(698\) | − 9.58579i | − 0.362827i | ||||||||
\(699\) | − 1.78680i | − 0.0675829i | ||||||||
\(700\) | −20.6863 | −0.781868 | ||||||||
\(701\) | −22.1127 | −0.835185 | −0.417593 | − | 0.908634i | \(-0.637126\pi\) | ||||
−0.417593 | + | 0.908634i | \(0.637126\pi\) | |||||||
\(702\) | −1.82843 | −0.0690095 | ||||||||
\(703\) | −24.0000 | −0.905177 | ||||||||
\(704\) | − 10.0711i | − 0.379568i | ||||||||
\(705\) | −2.17157 | −0.0817862 | ||||||||
\(706\) | − 2.88730i | − 0.108665i | ||||||||
\(707\) | 38.6274i | 1.45273i | ||||||||
\(708\) | 5.79899i | 0.217939i | ||||||||
\(709\) | −0.857864 | −0.0322178 | −0.0161089 | − | 0.999870i | \(-0.505128\pi\) | ||||
−0.0161089 | + | 0.999870i | \(0.505128\pi\) | |||||||
\(710\) | − 1.31371i | − 0.0493026i | ||||||||
\(711\) | − 1.17157i | − 0.0439374i | ||||||||
\(712\) | −7.11270 | −0.266560 | ||||||||
\(713\) | − 31.1716i | − 1.16738i | ||||||||
\(714\) | 2.34315i | 0.0876900i | ||||||||
\(715\) | 4.41421i | 0.165082i | ||||||||
\(716\) | −19.1716 | −0.716475 | ||||||||
\(717\) | − 3.45584i | − 0.129061i | ||||||||
\(718\) | −7.48528 | −0.279348 | ||||||||
\(719\) | 8.14214 | 0.303650 | 0.151825 | − | 0.988407i | \(-0.451485\pi\) | ||||
0.151825 | + | 0.988407i | \(0.451485\pi\) | |||||||
\(720\) | 8.48528 | 0.316228 | ||||||||
\(721\) | 2.34315 | 0.0872633 | ||||||||
\(722\) | 7.04163i | 0.262062i | ||||||||
\(723\) | − 1.78680i | − 0.0664517i | ||||||||
\(724\) | −26.1716 | −0.972659 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.887302 | 0.0329309 | ||||||||
\(727\) | 21.3137i | 0.790482i | 0.918578 | + | 0.395241i | \(0.129339\pi\) | ||||
−0.918578 | + | 0.395241i | \(0.870661\pi\) | |||||||
\(728\) | 8.20101i | 0.303950i | ||||||||
\(729\) | 18.1716 | 0.673021 | ||||||||
\(730\) | 1.65685 | 0.0613229 | ||||||||
\(731\) | 30.9706 | 1.14549 | ||||||||
\(732\) | 0.627417 | 0.0231900 | ||||||||
\(733\) | 49.2548i | 1.81927i | 0.415410 | + | 0.909634i | \(0.363638\pi\) | ||||
−0.415410 | + | 0.909634i | \(0.636362\pi\) | |||||||
\(734\) | −7.45584 | −0.275200 | ||||||||
\(735\) | 0.414214i | 0.0152785i | ||||||||
\(736\) | 33.7990i | 1.24585i | ||||||||
\(737\) | − 13.6569i | − 0.503057i | ||||||||
\(738\) | 14.6274 | 0.538443 | ||||||||
\(739\) | 10.0711i | 0.370470i | 0.982694 | + | 0.185235i | \(0.0593047\pi\) | ||||
−0.982694 | + | 0.185235i | \(0.940695\pi\) | |||||||
\(740\) | − 7.31371i | − 0.268857i | ||||||||
\(741\) | −4.54416 | −0.166934 | ||||||||
\(742\) | 8.76955i | 0.321940i | ||||||||
\(743\) | 12.3431i | 0.452826i | 0.974031 | + | 0.226413i | \(0.0726999\pi\) | ||||
−0.974031 | + | 0.226413i | \(0.927300\pi\) | |||||||
\(744\) | 2.67410i | 0.0980372i | ||||||||
\(745\) | 2.17157 | 0.0795603 | ||||||||
\(746\) | 1.52691i | 0.0559042i | ||||||||
\(747\) | −10.3431 | −0.378436 | ||||||||
\(748\) | 21.3137 | 0.779306 | ||||||||
\(749\) | −25.9411 | −0.947868 | ||||||||
\(750\) | −1.54416 | −0.0563846 | ||||||||
\(751\) | 2.68629i | 0.0980242i | 0.998798 | + | 0.0490121i | \(0.0156073\pi\) | ||||
−0.998798 | + | 0.0490121i | \(0.984393\pi\) | |||||||
\(752\) | 15.7279i | 0.573538i | ||||||||
\(753\) | 2.45584 | 0.0894959 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.1421 | −0.514685 | ||||||||
\(756\) | 12.4853i | 0.454085i | ||||||||
\(757\) | − 42.4853i | − 1.54415i | −0.635529 | − | 0.772077i | \(-0.719218\pi\) | ||||
0.635529 | − | 0.772077i | \(-0.280782\pi\) | |||||||
\(758\) | −11.1716 | −0.405770 | ||||||||
\(759\) | −7.65685 | −0.277926 | ||||||||
\(760\) | −9.51472 | −0.345135 | ||||||||
\(761\) | −33.5980 | −1.21793 | −0.608963 | − | 0.793199i | \(-0.708414\pi\) | ||||
−0.608963 | + | 0.793199i | \(0.708414\pi\) | |||||||
\(762\) | 2.68629i | 0.0973141i | ||||||||
\(763\) | −3.79899 | −0.137533 | ||||||||
\(764\) | − 4.91169i | − 0.177699i | ||||||||
\(765\) | 13.6569i | 0.493765i | ||||||||
\(766\) | − 8.48528i | − 0.306586i | ||||||||
\(767\) | −14.0000 | −0.505511 | ||||||||
\(768\) | 1.64466i | 0.0593466i | ||||||||
\(769\) | 13.1127i | 0.472856i | 0.971649 | + | 0.236428i | \(0.0759767\pi\) | ||||
−0.971649 | + | 0.236428i | \(0.924023\pi\) | |||||||
\(770\) | −2.82843 | −0.101929 | ||||||||
\(771\) | − 9.87006i | − 0.355461i | ||||||||
\(772\) | 19.7990i | 0.712581i | ||||||||
\(773\) | 36.4853i | 1.31228i | 0.754637 | + | 0.656142i | \(0.227813\pi\) | ||||
−0.754637 | + | 0.656142i | \(0.772187\pi\) | |||||||
\(774\) | −7.51472 | −0.270111 | ||||||||
\(775\) | − 16.2843i | − 0.584948i | ||||||||
\(776\) | −19.7990 | −0.710742 | ||||||||
\(777\) | 4.68629 | 0.168120 | ||||||||
\(778\) | 15.3137 | 0.549023 | ||||||||
\(779\) | 74.9117 | 2.68399 | ||||||||
\(780\) | − 1.38478i | − 0.0495829i | ||||||||
\(781\) | − 7.65685i | − 0.273984i | ||||||||
\(782\) | −15.3137 | −0.547617 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | − 8.48528i | − 0.302853i | ||||||||
\(786\) | − 0.225397i | − 0.00803964i | ||||||||
\(787\) | −42.0833 | −1.50011 | −0.750053 | − | 0.661378i | \(-0.769972\pi\) | ||||
−0.750053 | + | 0.661378i | \(0.769972\pi\) | |||||||
\(788\) | 3.65685 | 0.130270 | ||||||||
\(789\) | 4.65685 | 0.165788 | ||||||||
\(790\) | −0.171573 | −0.00610429 | ||||||||
\(791\) | 26.3431i | 0.936654i | ||||||||
\(792\) | −10.8284 | −0.384771 | ||||||||
\(793\) | 1.51472i | 0.0537892i | ||||||||
\(794\) | − 12.6985i | − 0.450652i | ||||||||
\(795\) | − 3.10051i | − 0.109964i | ||||||||
\(796\) | 30.1421 | 1.06836 | ||||||||
\(797\) | 55.7401i | 1.97442i | 0.159437 | + | 0.987208i | \(0.449032\pi\) | ||||
−0.159437 | + | 0.987208i | \(0.550968\pi\) | |||||||
\(798\) | − 2.91169i | − 0.103073i | ||||||||
\(799\) | −25.3137 | −0.895535 | ||||||||
\(800\) | 17.6569i | 0.624264i | ||||||||
\(801\) | − 12.6863i | − 0.448248i | ||||||||
\(802\) | 3.04163i | 0.107404i | ||||||||
\(803\) | 9.65685 | 0.340783 | ||||||||
\(804\) | 4.28427i | 0.151095i | ||||||||
\(805\) | −21.6569 | −0.763304 | ||||||||
\(806\) | −3.08326 | −0.108603 | ||||||||
\(807\) | 8.05887 | 0.283686 | ||||||||
\(808\) | 21.6569 | 0.761885 | ||||||||
\(809\) | − 20.2843i | − 0.713157i | −0.934265 | − | 0.356578i | \(-0.883943\pi\) | ||||
0.934265 | − | 0.356578i | \(-0.116057\pi\) | |||||||
\(810\) | − 3.10051i | − 0.108941i | ||||||||
\(811\) | −5.17157 | −0.181598 | −0.0907992 | − | 0.995869i | \(-0.528942\pi\) | ||||
−0.0907992 | + | 0.995869i | \(0.528942\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.02944 | 0.211462 | ||||||||
\(814\) | 4.00000i | 0.140200i | ||||||||
\(815\) | 18.0711i | 0.633002i | ||||||||
\(816\) | −6.00000 | −0.210042 | ||||||||
\(817\) | −38.4853 | −1.34643 | ||||||||
\(818\) | −6.20101 | −0.216813 | ||||||||
\(819\) | −14.6274 | −0.511123 | ||||||||
\(820\) | 22.8284i | 0.797203i | ||||||||
\(821\) | −15.4853 | −0.540440 | −0.270220 | − | 0.962799i | \(-0.587096\pi\) | ||||
−0.270220 | + | 0.962799i | \(0.587096\pi\) | |||||||
\(822\) | − 2.05887i | − 0.0718115i | ||||||||
\(823\) | − 2.28427i | − 0.0796247i | −0.999207 | − | 0.0398123i | \(-0.987324\pi\) | ||||
0.999207 | − | 0.0398123i | \(-0.0126760\pi\) | |||||||
\(824\) | − 1.31371i | − 0.0457652i | ||||||||
\(825\) | −4.00000 | −0.139262 | ||||||||
\(826\) | − 8.97056i | − 0.312126i | ||||||||
\(827\) | 13.1005i | 0.455549i | 0.973714 | + | 0.227775i | \(0.0731449\pi\) | ||||
−0.973714 | + | 0.227775i | \(0.926855\pi\) | |||||||
\(828\) | −39.5980 | −1.37612 | ||||||||
\(829\) | − 9.79899i | − 0.340333i | −0.985415 | − | 0.170166i | \(-0.945569\pi\) | ||||
0.985415 | − | 0.170166i | \(-0.0544306\pi\) | |||||||
\(830\) | 1.51472i | 0.0525767i | ||||||||
\(831\) | 2.20101i | 0.0763522i | ||||||||
\(832\) | −7.62742 | −0.264433 | ||||||||
\(833\) | 4.82843i | 0.167295i | ||||||||
\(834\) | 2.40202 | 0.0831752 | ||||||||
\(835\) | 8.82843 | 0.305520 | ||||||||
\(836\) | −26.4853 | −0.916013 | ||||||||
\(837\) | −9.82843 | −0.339720 | ||||||||
\(838\) | − 10.9706i | − 0.378972i | ||||||||
\(839\) | − 22.0711i | − 0.761978i | −0.924580 | − | 0.380989i | \(-0.875584\pi\) | ||||
0.924580 | − | 0.380989i | \(-0.124416\pi\) | |||||||
\(840\) | 1.85786 | 0.0641024 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | −10.4020 | −0.358477 | ||||||||
\(843\) | − 0.816234i | − 0.0281126i | ||||||||
\(844\) | 31.7868i | 1.09415i | ||||||||
\(845\) | −9.65685 | −0.332206 | ||||||||
\(846\) | 6.14214 | 0.211171 | ||||||||
\(847\) | 14.6274 | 0.502604 | ||||||||
\(848\) | −22.4558 | −0.771137 | ||||||||
\(849\) | − 0.142136i | − 0.00487808i | ||||||||
\(850\) | −8.00000 | −0.274398 | ||||||||
\(851\) | 30.6274i | 1.04989i | ||||||||
\(852\) | 2.40202i | 0.0822919i | ||||||||
\(853\) | 10.9706i | 0.375625i | 0.982205 | + | 0.187812i | \(0.0601397\pi\) | ||||
−0.982205 | + | 0.187812i | \(0.939860\pi\) | |||||||
\(854\) | −0.970563 | −0.0332120 | ||||||||
\(855\) | − 16.9706i | − 0.580381i | ||||||||
\(856\) | 14.5442i | 0.497109i | ||||||||
\(857\) | −11.8284 | −0.404051 | −0.202026 | − | 0.979380i | \(-0.564752\pi\) | ||||
−0.202026 | + | 0.979380i | \(0.564752\pi\) | |||||||
\(858\) | 0.757359i | 0.0258558i | ||||||||
\(859\) | − 5.72792i | − 0.195434i | −0.995214 | − | 0.0977171i | \(-0.968846\pi\) | ||||
0.995214 | − | 0.0977171i | \(-0.0311540\pi\) | |||||||
\(860\) | − 11.7279i | − 0.399919i | ||||||||
\(861\) | −14.6274 | −0.498501 | ||||||||
\(862\) | − 3.45584i | − 0.117707i | ||||||||
\(863\) | 45.1127 | 1.53565 | 0.767827 | − | 0.640657i | \(-0.221338\pi\) | ||||
0.767827 | + | 0.640657i | \(0.221338\pi\) | |||||||
\(864\) | 10.6569 | 0.362554 | ||||||||
\(865\) | −23.6569 | −0.804357 | ||||||||
\(866\) | −6.05887 | −0.205889 | ||||||||
\(867\) | − 2.61522i | − 0.0888177i | ||||||||
\(868\) | 21.0538i | 0.714613i | ||||||||
\(869\) | −1.00000 | −0.0339227 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.3431 | −0.350464 | ||||||||
\(872\) | 2.12994i | 0.0721289i | ||||||||
\(873\) | − 35.3137i | − 1.19519i | ||||||||
\(874\) | 19.0294 | 0.643680 | ||||||||
\(875\) | −25.4558 | −0.860565 | ||||||||
\(876\) | −3.02944 | −0.102355 | ||||||||
\(877\) | −8.85786 | −0.299109 | −0.149554 | − | 0.988753i | \(-0.547784\pi\) | ||||
−0.149554 | + | 0.988753i | \(0.547784\pi\) | |||||||
\(878\) | − 4.82843i | − 0.162952i | ||||||||
\(879\) | −1.51472 | −0.0510902 | ||||||||
\(880\) | − 7.24264i | − 0.244149i | ||||||||
\(881\) | − 14.0000i | − 0.471672i | −0.971793 | − | 0.235836i | \(-0.924217\pi\) | ||||
0.971793 | − | 0.235836i | \(-0.0757828\pi\) | |||||||
\(882\) | − 1.17157i | − 0.0394489i | ||||||||
\(883\) | 46.4264 | 1.56237 | 0.781186 | − | 0.624298i | \(-0.214615\pi\) | ||||
0.781186 | + | 0.624298i | \(0.214615\pi\) | |||||||
\(884\) | − 16.1421i | − 0.542919i | ||||||||
\(885\) | 3.17157i | 0.106611i | ||||||||
\(886\) | −14.7696 | −0.496193 | ||||||||
\(887\) | − 36.8995i | − 1.23896i | −0.785011 | − | 0.619482i | \(-0.787343\pi\) | ||||
0.785011 | − | 0.619482i | \(-0.212657\pi\) | |||||||
\(888\) | − 2.62742i | − 0.0881703i | ||||||||
\(889\) | 44.2843i | 1.48525i | ||||||||
\(890\) | −1.85786 | −0.0622758 | ||||||||
\(891\) | − 18.0711i | − 0.605404i | ||||||||
\(892\) | −16.1421 | −0.540479 | ||||||||
\(893\) | 31.4558 | 1.05263 | ||||||||
\(894\) | 0.372583 | 0.0124610 | ||||||||
\(895\) | −10.4853 | −0.350484 | ||||||||
\(896\) | − 29.8579i | − 0.997481i | ||||||||
\(897\) | 5.79899i | 0.193623i | ||||||||
\(898\) | 0.426407 | 0.0142294 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −20.6863 | −0.689543 | ||||||||
\(901\) | − 36.1421i | − 1.20407i | ||||||||
\(902\) | − 12.4853i | − 0.415714i | ||||||||
\(903\) | 7.51472 | 0.250074 | ||||||||
\(904\) | 14.7696 | 0.491228 | ||||||||
\(905\) | −14.3137 | −0.475804 | ||||||||
\(906\) | −2.42641 | −0.0806120 | ||||||||
\(907\) | − 34.2843i | − 1.13839i | −0.822202 | − | 0.569195i | \(-0.807255\pi\) | ||||
0.822202 | − | 0.569195i | \(-0.192745\pi\) | |||||||
\(908\) | 36.8284 | 1.22219 | ||||||||
\(909\) | 38.6274i | 1.28119i | ||||||||
\(910\) | 2.14214i | 0.0710111i | ||||||||
\(911\) | − 46.5563i | − 1.54248i | −0.636544 | − | 0.771240i | \(-0.719637\pi\) | ||||
0.636544 | − | 0.771240i | \(-0.280363\pi\) | |||||||
\(912\) | 7.45584 | 0.246888 | ||||||||
\(913\) | 8.82843i | 0.292178i | ||||||||
\(914\) | 14.4853i | 0.479131i | ||||||||
\(915\) | 0.343146 | 0.0113440 | ||||||||
\(916\) | − 37.4558i | − 1.23758i | ||||||||
\(917\) | − 3.71573i | − 0.122704i | ||||||||
\(918\) | 4.82843i | 0.159362i | ||||||||
\(919\) | −20.1421 | −0.664428 | −0.332214 | − | 0.943204i | \(-0.607796\pi\) | ||||
−0.332214 | + | 0.943204i | \(0.607796\pi\) | |||||||
\(920\) | 12.1421i | 0.400314i | ||||||||
\(921\) | −7.00000 | −0.230658 | ||||||||
\(922\) | 5.79899 | 0.190980 | ||||||||
\(923\) | −5.79899 | −0.190876 | ||||||||
\(924\) | 5.17157 | 0.170132 | ||||||||
\(925\) | 16.0000i | 0.526077i | ||||||||
\(926\) | − 10.7696i | − 0.353909i | ||||||||
\(927\) | 2.34315 | 0.0769590 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41.3137 | 1.35546 | 0.677729 | − | 0.735311i | \(-0.262964\pi\) | ||||
0.677729 | + | 0.735311i | \(0.262964\pi\) | |||||||
\(930\) | 0.698485i | 0.0229042i | ||||||||
\(931\) | − 6.00000i | − 0.196642i | ||||||||
\(932\) | −7.88730 | −0.258357 | ||||||||
\(933\) | 10.4853 | 0.343273 | ||||||||
\(934\) | −13.4020 | −0.438527 | ||||||||
\(935\) | 11.6569 | 0.381220 | ||||||||
\(936\) | 8.20101i | 0.268058i | ||||||||
\(937\) | −28.6274 | −0.935217 | −0.467608 | − | 0.883936i | \(-0.654884\pi\) | ||||
−0.467608 | + | 0.883936i | \(0.654884\pi\) | |||||||
\(938\) | − 6.62742i | − 0.216393i | ||||||||
\(939\) | 1.72792i | 0.0563886i | ||||||||
\(940\) | 9.58579i | 0.312654i | ||||||||
\(941\) | −22.5980 | −0.736673 | −0.368337 | − | 0.929693i | \(-0.620073\pi\) | ||||
−0.368337 | + | 0.929693i | \(0.620073\pi\) | |||||||
\(942\) | − 1.45584i | − 0.0474340i | ||||||||
\(943\) | − 95.5980i | − 3.11310i | ||||||||
\(944\) | 22.9706 | 0.747628 | ||||||||
\(945\) | 6.82843i | 0.222129i | ||||||||
\(946\) | 6.41421i | 0.208544i | ||||||||
\(947\) | − 39.3848i | − 1.27983i | −0.768444 | − | 0.639917i | \(-0.778969\pi\) | ||||
0.768444 | − | 0.639917i | \(-0.221031\pi\) | |||||||
\(948\) | 0.313708 | 0.0101888 | ||||||||
\(949\) | − 7.31371i | − 0.237413i | ||||||||
\(950\) | 9.94113 | 0.322533 | ||||||||
\(951\) | −8.05887 | −0.261327 | ||||||||
\(952\) | 21.6569 | 0.701903 | ||||||||
\(953\) | 9.62742 | 0.311863 | 0.155931 | − | 0.987768i | \(-0.450162\pi\) | ||||
0.155931 | + | 0.987768i | \(0.450162\pi\) | |||||||
\(954\) | 8.76955i | 0.283925i | ||||||||
\(955\) | − 2.68629i | − 0.0869264i | ||||||||
\(956\) | −15.2548 | −0.493377 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.34315 | −0.172629 | ||||||||
\(959\) | − 33.9411i | − 1.09602i | ||||||||
\(960\) | 1.72792i | 0.0557684i | ||||||||
\(961\) | 14.4264 | 0.465368 | ||||||||
\(962\) | 3.02944 | 0.0976730 | ||||||||
\(963\) | −25.9411 | −0.835941 | ||||||||
\(964\) | −7.88730 | −0.254033 | ||||||||
\(965\) | 10.8284i | 0.348579i | ||||||||
\(966\) | −3.71573 | −0.119552 | ||||||||
\(967\) | − 26.7574i | − 0.860459i | −0.902720 | − | 0.430229i | \(-0.858433\pi\) | ||||
0.902720 | − | 0.430229i | \(-0.141567\pi\) | |||||||
\(968\) | − 8.20101i | − 0.263590i | ||||||||
\(969\) | 12.0000i | 0.385496i | ||||||||
\(970\) | −5.17157 | −0.166049 | ||||||||
\(971\) | 4.34315i | 0.139378i | 0.997569 | + | 0.0696891i | \(0.0222007\pi\) | ||||
−0.997569 | + | 0.0696891i | \(0.977799\pi\) | |||||||
\(972\) | 18.9117i | 0.606593i | ||||||||
\(973\) | 39.5980 | 1.26945 | ||||||||
\(974\) | 11.7990i | 0.378064i | ||||||||
\(975\) | 3.02944i | 0.0970196i | ||||||||
\(976\) | − 2.48528i | − 0.0795519i | ||||||||
\(977\) | 41.8284 | 1.33821 | 0.669105 | − | 0.743168i | \(-0.266678\pi\) | ||||
0.669105 | + | 0.743168i | \(0.266678\pi\) | |||||||
\(978\) | 3.10051i | 0.0991432i | ||||||||
\(979\) | −10.8284 | −0.346078 | ||||||||
\(980\) | 1.82843 | 0.0584070 | ||||||||
\(981\) | −3.79899 | −0.121292 | ||||||||
\(982\) | −5.28427 | −0.168628 | ||||||||
\(983\) | 31.8701i | 1.01650i | 0.861210 | + | 0.508248i | \(0.169707\pi\) | ||||
−0.861210 | + | 0.508248i | \(0.830293\pi\) | |||||||
\(984\) | 8.20101i | 0.261439i | ||||||||
\(985\) | 2.00000 | 0.0637253 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.14214 | −0.195506 | ||||||||
\(988\) | 20.0589i | 0.638158i | ||||||||
\(989\) | 49.1127i | 1.56169i | ||||||||
\(990\) | −2.82843 | −0.0898933 | ||||||||
\(991\) | 7.17157 | 0.227813 | 0.113906 | − | 0.993492i | \(-0.463664\pi\) | ||||
0.113906 | + | 0.993492i | \(0.463664\pi\) | |||||||
\(992\) | 17.9706 | 0.570566 | ||||||||
\(993\) | −0.171573 | −0.00544470 | ||||||||
\(994\) | − 3.71573i | − 0.117856i | ||||||||
\(995\) | 16.4853 | 0.522619 | ||||||||
\(996\) | − 2.76955i | − 0.0877566i | ||||||||
\(997\) | 28.2843i | 0.895772i | 0.894091 | + | 0.447886i | \(0.147823\pi\) | ||||
−0.894091 | + | 0.447886i | \(0.852177\pi\) | |||||||
\(998\) | − 6.20101i | − 0.196290i | ||||||||
\(999\) | 9.65685 | 0.305529 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))