Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,11,Mod(53,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.53");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.d (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: | \(102.927874933\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.17318914560000.97 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 82x^{6} + 260x^{5} + 2477x^{4} - 5392x^{3} - 31616x^{2} + 34356x + 161859 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{24}\cdot 3^{16} \) |
Twist minimal: | no (minimal twist has level 6) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 107.2 | ||
Root | \(3.88503 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.107 |
Dual form | 162.11.d.d.53.2 |
$q$-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 \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −19.5959 | − | 11.3137i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 256.000 | + | 443.405i | 0.250000 | + | 0.433013i | ||||
\(5\) | 4172.87 | − | 2409.21i | 1.33532 | − | 0.770946i | 0.349209 | − | 0.937045i | \(-0.386450\pi\) |
0.986109 | + | 0.166099i | \(0.0531171\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −335.265 | + | 580.696i | −0.0199479 | + | 0.0345508i | −0.875827 | − | 0.482625i | \(-0.839683\pi\) |
0.855879 | + | 0.517176i | \(0.173017\pi\) | |||||||
\(8\) | − | 11585.2i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −109028. | −1.09028 | ||||||||
\(11\) | 202016. | + | 116634.i | 1.25436 | + | 0.724206i | 0.971973 | − | 0.235093i | \(-0.0755396\pi\) |
0.282390 | + | 0.959300i | \(0.408873\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −153890. | − | 266546.i | −0.414471 | − | 0.717885i | 0.580901 | − | 0.813974i | \(-0.302700\pi\) |
−0.995373 | + | 0.0960885i | \(0.969367\pi\) | |||||||
\(14\) | 13139.6 | − | 7586.18i | 0.0244311 | − | 0.0141053i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −131072. | + | 227023.i | −0.125000 | + | 0.216506i | ||||
\(17\) | − | 672324.i | − | 0.473515i | −0.971569 | − | 0.236758i | \(-0.923915\pi\) | ||
0.971569 | − | 0.236758i | \(-0.0760847\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.55119e6 | −0.626465 | −0.313233 | − | 0.949676i | \(-0.601412\pi\) | ||||
−0.313233 | + | 0.949676i | \(0.601412\pi\) | |||||||
\(20\) | 2.13651e6 | + | 1.23351e6i | 0.667659 | + | 0.385473i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.63913e6 | − | 4.57111e6i | −0.512091 | − | 0.886968i | ||||
\(23\) | −4.82854e6 | + | 2.78776e6i | −0.750199 | + | 0.433127i | −0.825766 | − | 0.564013i | \(-0.809257\pi\) |
0.0755670 | + | 0.997141i | \(0.475923\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.72574e6 | − | 1.16493e7i | 0.688716 | − | 1.19289i | ||||
\(26\) | 6.96428e6i | 0.586151i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −343311. | −0.0199479 | ||||||||
\(29\) | −2.57481e7 | − | 1.48657e7i | −1.25532 | − | 0.724760i | −0.283160 | − | 0.959073i | \(-0.591383\pi\) |
−0.972161 | + | 0.234313i | \(0.924716\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.54684e7 | − | 2.67921e7i | −0.540303 | − | 0.935832i | −0.998886 | − | 0.0471804i | \(-0.984976\pi\) |
0.458584 | − | 0.888651i | \(-0.348357\pi\) | |||||||
\(32\) | 5.13695e6 | − | 2.96582e6i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.60648e6 | + | 1.31748e7i | −0.167413 | + | 0.289968i | ||||
\(35\) | 3.23089e6i | 0.0615151i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.56690e7 | −1.23542 | −0.617711 | − | 0.786406i | \(-0.711940\pi\) | ||||
−0.617711 | + | 0.786406i | \(0.711940\pi\) | |||||||
\(38\) | 3.03970e7 | + | 1.75497e7i | 0.383630 | + | 0.221489i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.79112e7 | − | 4.83437e7i | −0.272571 | − | 0.472106i | ||||
\(41\) | −3.10950e7 | + | 1.79527e7i | −0.268393 | + | 0.154957i | −0.628157 | − | 0.778087i | \(-0.716190\pi\) |
0.359764 | + | 0.933043i | \(0.382857\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.83126e7 | − | 3.17184e7i | 0.124569 | − | 0.215759i | −0.796996 | − | 0.603985i | \(-0.793579\pi\) |
0.921564 | + | 0.388226i | \(0.126912\pi\) | |||||||
\(44\) | 1.19433e8i | 0.724206i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.26159e8 | 0.612535 | ||||||||
\(47\) | 2.84816e7 | + | 1.64438e7i | 0.124187 | + | 0.0716992i | 0.560806 | − | 0.827947i | \(-0.310491\pi\) |
−0.436620 | + | 0.899646i | \(0.643825\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.41013e8 | + | 2.44241e8i | 0.499204 | + | 0.864647i | ||||
\(50\) | −2.63594e8 | + | 1.52186e8i | −0.843501 | + | 0.486996i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.87918e7 | − | 1.36471e8i | 0.207236 | − | 0.358943i | ||||
\(53\) | − | 4.59194e8i | − | 1.09804i | −0.835810 | − | 0.549019i | \(-0.815002\pi\) | ||
0.835810 | − | 0.549019i | \(-0.184998\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.12398e9 | 2.23330 | ||||||||
\(56\) | 6.72750e6 | + | 3.88412e6i | 0.0122156 | + | 0.00705266i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.36372e8 | + | 5.82613e8i | 0.512483 | + | 0.887646i | ||||
\(59\) | 4.23189e8 | − | 2.44328e8i | 0.591936 | − | 0.341754i | −0.173927 | − | 0.984759i | \(-0.555646\pi\) |
0.765863 | + | 0.643004i | \(0.222312\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.06464e7 | − | 5.30811e7i | 0.0362852 | − | 0.0628479i | −0.847312 | − | 0.531095i | \(-0.821781\pi\) |
0.883598 | + | 0.468247i | \(0.155114\pi\) | |||||||
\(62\) | 7.00020e8i | 0.764103i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.34218e8 | −0.125000 | ||||||||
\(65\) | −1.28433e9 | − | 7.41507e8i | −1.10690 | − | 0.639070i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.35388e8 | + | 5.80909e8i | 0.248413 | + | 0.430263i | 0.963086 | − | 0.269196i | \(-0.0867578\pi\) |
−0.714673 | + | 0.699459i | \(0.753424\pi\) | |||||||
\(68\) | 2.98112e8 | − | 1.72115e8i | 0.205038 | − | 0.118379i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.65533e7 | − | 6.33122e7i | 0.0217489 | − | 0.0376702i | ||||
\(71\) | − | 1.23330e9i | − | 0.683561i | −0.939780 | − | 0.341781i | \(-0.888970\pi\) | ||
0.939780 | − | 0.341781i | \(-0.111030\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.08126e9 | 0.521573 | 0.260787 | − | 0.965396i | \(-0.416018\pi\) | ||||
0.260787 | + | 0.965396i | \(0.416018\pi\) | |||||||
\(74\) | 1.67876e9 | + | 9.69234e8i | 0.756538 | + | 0.436787i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.97104e8 | − | 6.87805e8i | −0.156616 | − | 0.271267i | ||||
\(77\) | −1.35458e8 | + | 7.82067e7i | −0.0500439 | + | 0.0288928i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.33141e8 | − | 1.61625e9i | 0.303258 | − | 0.525258i | −0.673614 | − | 0.739083i | \(-0.735259\pi\) |
0.976872 | + | 0.213826i | \(0.0685924\pi\) | |||||||
\(80\) | 1.26312e9i | 0.385473i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.12446e8 | 0.219142 | ||||||||
\(83\) | −9.48838e8 | − | 5.47812e8i | −0.240880 | − | 0.139072i | 0.374701 | − | 0.927146i | \(-0.377745\pi\) |
−0.615581 | + | 0.788073i | \(0.711079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.61977e9 | − | 2.80552e9i | −0.365055 | − | 0.632293i | ||||
\(86\) | −7.17706e8 | + | 4.14368e8i | −0.152565 | + | 0.0880833i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.35123e9 | − | 2.34041e9i | 0.256046 | − | 0.443484i | ||||
\(89\) | − | 5.19876e9i | − | 0.931000i | −0.885048 | − | 0.465500i | \(-0.845874\pi\) | ||
0.885048 | − | 0.465500i | \(-0.154126\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.06376e8 | 0.0330714 | ||||||||
\(92\) | −2.47221e9 | − | 1.42733e9i | −0.375099 | − | 0.216564i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.72082e8 | − | 6.44464e8i | −0.0506990 | − | 0.0878132i | ||||
\(95\) | −6.47291e9 | + | 3.73714e9i | −0.836530 | + | 0.482971i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.37353e9 | − | 9.30722e9i | 0.625750 | − | 1.08383i | −0.362645 | − | 0.931927i | \(-0.618126\pi\) |
0.988395 | − | 0.151904i | \(-0.0485403\pi\) | |||||||
\(98\) | − | 6.38151e9i | − | 0.705981i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.88716e9 | 0.688716 | ||||||||
\(101\) | −9.36643e9 | − | 5.40771e9i | −0.891183 | − | 0.514525i | −0.0168540 | − | 0.999858i | \(-0.505365\pi\) |
−0.874329 | + | 0.485333i | \(0.838698\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.41723e9 | + | 2.45471e9i | 0.122251 | + | 0.211746i | 0.920655 | − | 0.390377i | \(-0.127655\pi\) |
−0.798404 | + | 0.602122i | \(0.794322\pi\) | |||||||
\(104\) | −3.08800e9 | + | 1.78286e9i | −0.253811 | + | 0.146538i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.19519e9 | + | 8.99834e9i | −0.388215 | + | 0.672408i | ||||
\(107\) | 2.41202e10i | 1.71974i | 0.510515 | + | 0.859869i | \(0.329455\pi\) | ||||
−0.510515 | + | 0.859869i | \(0.670545\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.43424e9 | −0.353188 | −0.176594 | − | 0.984284i | \(-0.556508\pi\) | ||||
−0.176594 | + | 0.984284i | \(0.556508\pi\) | |||||||
\(110\) | −2.20255e10 | − | 1.27164e10i | −1.36761 | − | 0.789590i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.78877e7 | − | 1.52226e8i | −0.00498698 | − | 0.00863771i | ||||
\(113\) | −1.20642e10 | + | 6.96526e9i | −0.654795 | + | 0.378046i | −0.790291 | − | 0.612732i | \(-0.790071\pi\) |
0.135496 | + | 0.990778i | \(0.456737\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.34326e10 | + | 2.32659e10i | −0.667836 | + | 1.15673i | ||||
\(116\) | − | 1.52224e10i | − | 0.724760i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.10570e10 | −0.483313 | ||||||||
\(119\) | 3.90416e8 | + | 2.25407e8i | 0.0163603 | + | 0.00944565i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.42383e10 | + | 2.46615e10i | 0.548950 | + | 0.950809i | ||||
\(122\) | −1.20109e9 | + | 6.93449e8i | −0.0444402 | + | 0.0256575i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.91982e9 | − | 1.37175e10i | 0.270151 | − | 0.467916i | ||||
\(125\) | − | 1.77600e10i | − | 0.581958i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.08412e10 | 1.23617 | 0.618087 | − | 0.786110i | \(-0.287908\pi\) | ||||
0.618087 | + | 0.786110i | \(0.287908\pi\) | |||||||
\(128\) | 2.63012e9 | + | 1.51850e9i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.67784e10 | + | 2.90610e10i | 0.451891 | + | 0.782698i | ||||
\(131\) | −3.59831e10 | + | 2.07749e10i | −0.932701 | + | 0.538495i | −0.887665 | − | 0.460490i | \(-0.847674\pi\) |
−0.0450365 | + | 0.998985i | \(0.514340\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.20059e8 | − | 9.00769e8i | 0.0124967 | − | 0.0216449i | ||||
\(134\) | − | 1.51779e10i | − | 0.351308i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.78903e9 | −0.167413 | ||||||||
\(137\) | −8.01534e10 | − | 4.62766e10i | −1.66081 | − | 0.958867i | −0.972331 | − | 0.233609i | \(-0.924946\pi\) |
−0.688477 | − | 0.725259i | \(-0.741720\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.97788e10 | − | 6.88989e10i | −0.766615 | − | 1.32782i | −0.939388 | − | 0.342855i | \(-0.888606\pi\) |
0.172773 | − | 0.984962i | \(-0.444727\pi\) | |||||||
\(140\) | −1.43259e9 | + | 8.27107e8i | −0.0266368 | + | 0.0153788i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.39532e10 | + | 2.41677e10i | −0.241675 | + | 0.418594i | ||||
\(143\) | − | 7.17955e10i | − | 1.20065i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.43258e11 | −2.23500 | ||||||||
\(146\) | −2.11883e10 | − | 1.22330e10i | −0.319397 | − | 0.184404i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.19313e10 | − | 3.79861e10i | −0.308855 | − | 0.534953i | ||||
\(149\) | −6.99579e10 | + | 4.03902e10i | −0.952589 | + | 0.549977i | −0.893884 | − | 0.448298i | \(-0.852030\pi\) |
−0.0587047 | + | 0.998275i | \(0.518697\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.54327e10 | + | 2.67302e10i | −0.196588 | + | 0.340501i | −0.947420 | − | 0.319993i | \(-0.896320\pi\) |
0.750832 | + | 0.660493i | \(0.229653\pi\) | |||||||
\(152\) | 1.79709e10i | 0.221489i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.53923e9 | 0.0408606 | ||||||||
\(155\) | −1.29095e11 | − | 7.45332e10i | −1.44295 | − | 0.833088i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.85661e10 | − | 8.41190e10i | −0.509138 | − | 0.881852i | −0.999944 | − | 0.0105835i | \(-0.996631\pi\) |
0.490806 | − | 0.871269i | \(-0.336702\pi\) | |||||||
\(158\) | −3.65715e10 | + | 2.11146e10i | −0.371413 | + | 0.214435i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.42905e10 | − | 2.47520e10i | 0.136285 | − | 0.236053i | ||||
\(161\) | − | 3.73855e9i | − | 0.0345600i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.39440e11 | −1.21185 | −0.605927 | − | 0.795520i | \(-0.707198\pi\) | ||||
−0.605927 | + | 0.795520i | \(0.707198\pi\) | |||||||
\(164\) | −1.59206e10 | − | 9.19178e9i | −0.134196 | − | 0.0774784i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.23956e10 | + | 2.14698e10i | 0.0983390 | + | 0.170328i | ||||
\(167\) | 1.08981e11 | − | 6.29200e10i | 0.839009 | − | 0.484402i | −0.0179180 | − | 0.999839i | \(-0.505704\pi\) |
0.856927 | + | 0.515437i | \(0.172370\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.15648e10 | − | 3.73513e10i | 0.156427 | − | 0.270940i | ||||
\(170\) | 7.33023e10i | 0.516265i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.87521e10 | 0.124569 | ||||||||
\(173\) | −1.09342e11 | − | 6.31284e10i | −0.705594 | − | 0.407375i | 0.103833 | − | 0.994595i | \(-0.466889\pi\) |
−0.809428 | + | 0.587220i | \(0.800222\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.50981e9 | + | 7.81121e9i | 0.0274769 | + | 0.0475914i | ||||
\(176\) | −5.29574e10 | + | 3.05749e10i | −0.313591 | + | 0.181052i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.88173e10 | + | 1.01875e11i | −0.329158 | + | 0.570119i | ||||
\(179\) | − | 2.96543e11i | − | 1.61370i | −0.590758 | − | 0.806848i | \(-0.701171\pi\) | ||
0.590758 | − | 0.806848i | \(-0.298829\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.48451e11 | 1.27893 | 0.639466 | − | 0.768819i | \(-0.279155\pi\) | ||||
0.639466 | + | 0.768819i | \(0.279155\pi\) | |||||||
\(182\) | −4.04413e9 | − | 2.33488e9i | −0.0202520 | − | 0.0116925i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.22968e10 | + | 5.59397e10i | 0.153134 | + | 0.265235i | ||||
\(185\) | −3.57485e11 | + | 2.06394e11i | −1.64968 | + | 0.952443i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.84159e10 | − | 1.35820e11i | 0.342923 | − | 0.593960i | ||||
\(188\) | 1.68385e10i | 0.0716992i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.69123e11 | 0.683024 | ||||||||
\(191\) | −1.36876e11 | − | 7.90252e10i | −0.538468 | − | 0.310884i | 0.205990 | − | 0.978554i | \(-0.433959\pi\) |
−0.744458 | + | 0.667670i | \(0.767292\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.89185e11 | + | 3.27677e11i | 0.706479 | + | 1.22366i | 0.966155 | + | 0.257962i | \(0.0830508\pi\) |
−0.259676 | + | 0.965696i | \(0.583616\pi\) | |||||||
\(194\) | −2.10598e11 | + | 1.21589e11i | −0.766384 | + | 0.442472i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.21986e10 | + | 1.25052e11i | −0.249602 | + | 0.432323i | ||||
\(197\) | 1.89406e11i | 0.638356i | 0.947695 | + | 0.319178i | \(0.103407\pi\) | ||||
−0.947695 | + | 0.319178i | \(0.896593\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.02942e10 | 0.161158 | 0.0805791 | − | 0.996748i | \(-0.474323\pi\) | ||||
0.0805791 | + | 0.996748i | \(0.474323\pi\) | |||||||
\(200\) | −1.34960e11 | − | 7.79193e10i | −0.421750 | − | 0.243498i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.22362e11 | + | 2.11938e11i | 0.363824 | + | 0.630162i | ||||
\(203\) | 1.72649e10 | − | 9.96787e9i | 0.0500821 | − | 0.0289149i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.65035e10 | + | 1.49828e11i | −0.238927 | + | 0.413833i | ||||
\(206\) | − | 6.41365e10i | − | 0.172890i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 8.06828e10 | 0.207236 | ||||||||
\(209\) | −3.13366e11 | − | 1.80922e11i | −0.785814 | − | 0.453690i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.37485e11 | − | 4.11336e11i | −0.567837 | − | 0.983522i | −0.996780 | − | 0.0801907i | \(-0.974447\pi\) |
0.428943 | − | 0.903332i | \(-0.358886\pi\) | |||||||
\(212\) | 2.03609e11 | − | 1.17554e11i | 0.475464 | − | 0.274509i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.72889e11 | − | 4.72658e11i | 0.608019 | − | 1.05312i | ||||
\(215\) | − | 1.76476e11i | − | 0.384143i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.07440e10 | 0.0431117 | ||||||||
\(218\) | 1.06489e11 | + | 6.14814e10i | 0.216283 | + | 0.124871i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.87740e11 | + | 4.98380e11i | 0.558324 | + | 0.967046i | ||||
\(221\) | −1.79205e11 | + | 1.03464e11i | −0.339930 | + | 0.196258i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.17790e11 | − | 2.04018e11i | 0.213592 | − | 0.369951i | −0.739244 | − | 0.673437i | \(-0.764817\pi\) |
0.952836 | + | 0.303486i | \(0.0981505\pi\) | |||||||
\(224\) | 3.97734e9i | 0.00705266i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.15211e11 | 0.534638 | ||||||||
\(227\) | 3.69815e11 | + | 2.13513e11i | 0.613557 | + | 0.354238i | 0.774356 | − | 0.632750i | \(-0.218074\pi\) |
−0.160799 | + | 0.986987i | \(0.551407\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.18356e11 | − | 8.97819e11i | −0.823096 | − | 1.42564i | −0.903366 | − | 0.428871i | \(-0.858911\pi\) |
0.0802696 | − | 0.996773i | \(-0.474422\pi\) | |||||||
\(230\) | 5.26447e11 | − | 3.03944e11i | 0.817928 | − | 0.472231i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.72222e11 | + | 2.98298e11i | −0.256241 | + | 0.443823i | ||||
\(233\) | 1.03766e12i | 1.51103i | 0.655130 | + | 0.755516i | \(0.272614\pi\) | ||||
−0.655130 | + | 0.755516i | \(0.727386\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.58466e11 | 0.221105 | ||||||||
\(236\) | 2.16673e11 | + | 1.25096e11i | 0.295968 | + | 0.170877i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.10037e9 | − | 8.83410e9i | −0.00667908 | − | 0.0115685i | ||||
\(239\) | 1.07116e12 | − | 6.18437e11i | 1.37362 | − | 0.793060i | 0.382238 | − | 0.924064i | \(-0.375153\pi\) |
0.991382 | + | 0.131004i | \(0.0418202\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.19560e11 | − | 8.99904e11i | 0.639072 | − | 1.10691i | −0.346564 | − | 0.938026i | \(-0.612652\pi\) |
0.985637 | − | 0.168880i | \(-0.0540149\pi\) | |||||||
\(242\) | − | 6.44354e11i | − | 0.776333i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.13819e10 | 0.0362852 | ||||||||
\(245\) | 1.17686e12 | + | 6.79458e11i | 1.33319 | + | 0.769719i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.38713e11 | + | 4.13463e11i | 0.259652 | + | 0.449730i | ||||
\(248\) | −3.10392e11 | + | 1.79205e11i | −0.330866 | + | 0.191026i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.00931e11 | + | 3.48023e11i | −0.205753 | + | 0.356375i | ||||
\(251\) | − | 5.66781e11i | − | 0.568914i | −0.958689 | − | 0.284457i | \(-0.908187\pi\) | ||
0.958689 | − | 0.284457i | \(-0.0918133\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.30059e12 | −1.25469 | ||||||||
\(254\) | −8.00320e11 | − | 4.62065e11i | −0.756999 | − | 0.437053i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.43597e10 | − | 5.95128e10i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −1.10802e12 | + | 6.39713e11i | −0.988281 | + | 0.570584i | −0.904760 | − | 0.425922i | \(-0.859950\pi\) |
−0.0835208 | + | 0.996506i | \(0.526617\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.87218e10 | − | 4.97476e10i | 0.0246441 | − | 0.0426848i | ||||
\(260\) | − | 7.59303e11i | − | 0.639070i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.40164e11 | 0.761548 | ||||||||
\(263\) | 1.45997e12 | + | 8.42915e11i | 1.16029 | + | 0.669892i | 0.951373 | − | 0.308042i | \(-0.0996737\pi\) |
0.208914 | + | 0.977934i | \(0.433007\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.10629e12 | − | 1.91616e12i | −0.846528 | − | 1.46623i | ||||
\(266\) | −2.03821e10 | + | 1.17676e10i | −0.0153052 | + | 0.00883649i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.71719e11 | + | 2.97426e11i | −0.124206 | + | 0.215132i | ||||
\(269\) | 1.34023e12i | 0.951523i | 0.879574 | + | 0.475761i | \(0.157827\pi\) | ||||
−0.879574 | + | 0.475761i | \(0.842173\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.75349e12 | −1.19966 | −0.599829 | − | 0.800129i | \(-0.704765\pi\) | ||||
−0.599829 | + | 0.800129i | \(0.704765\pi\) | |||||||
\(272\) | 1.52633e11 | + | 8.81228e10i | 0.102519 | + | 0.0591894i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.04712e12 | + | 1.81366e12i | 0.678022 | + | 1.17437i | ||||
\(275\) | 2.71742e12 | − | 1.56890e12i | 1.72780 | − | 0.997545i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.47898e11 | + | 1.46860e12i | −0.519930 | + | 0.900545i | 0.479802 | + | 0.877377i | \(0.340709\pi\) |
−0.999732 | + | 0.0231681i | \(0.992625\pi\) | |||||||
\(278\) | 1.80018e12i | 1.08416i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.74306e10 | 0.0217489 | ||||||||
\(281\) | 2.11462e11 | + | 1.22088e11i | 0.120698 | + | 0.0696851i | 0.559134 | − | 0.829078i | \(-0.311134\pi\) |
−0.438435 | + | 0.898763i | \(0.644467\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.98205e11 | + | 8.62916e11i | 0.274458 | + | 0.475375i | 0.969998 | − | 0.243112i | \(-0.0781683\pi\) |
−0.695540 | + | 0.718487i | \(0.744835\pi\) | |||||||
\(284\) | 5.46852e11 | − | 3.15725e11i | 0.295991 | − | 0.170890i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.12273e11 | + | 1.40690e12i | −0.424494 | + | 0.735246i | ||||
\(287\) | − | 2.40756e10i | − | 0.0123643i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.56397e12 | 0.775783 | ||||||||
\(290\) | 2.80727e12 | + | 1.62078e12i | 1.36865 | + | 0.790193i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.76802e11 | + | 4.79435e11i | 0.130393 | + | 0.225848i | ||||
\(293\) | 1.36461e12 | − | 7.87855e11i | 0.631930 | − | 0.364845i | −0.149569 | − | 0.988751i | \(-0.547789\pi\) |
0.781499 | + | 0.623906i | \(0.214455\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.17728e12 | − | 2.03910e12i | 0.526948 | − | 0.912701i | ||||
\(296\) | 9.92496e11i | 0.436787i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.82785e12 | 0.777786 | ||||||||
\(299\) | 1.48613e12 | + | 8.58017e11i | 0.621872 | + | 0.359038i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.22792e10 | + | 2.12681e10i | 0.00496977 | + | 0.00860790i | ||||
\(302\) | 6.04836e11 | − | 3.49202e11i | 0.240770 | − | 0.139009i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.03317e11 | − | 3.52156e11i | 0.0783081 | − | 0.135634i | ||||
\(305\) | − | 2.95334e11i | − | 0.111896i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.29823e12 | −1.20945 | −0.604726 | − | 0.796434i | \(-0.706717\pi\) | ||||
−0.604726 | + | 0.796434i | \(0.706717\pi\) | |||||||
\(308\) | −6.93545e10 | − | 4.00418e10i | −0.0250219 | − | 0.0144464i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.68649e12 | + | 2.92109e12i | 0.589082 | + | 1.02032i | ||||
\(311\) | −1.44887e12 | + | 8.36504e11i | −0.497997 | + | 0.287519i | −0.727886 | − | 0.685698i | \(-0.759497\pi\) |
0.229889 | + | 0.973217i | \(0.426164\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.66592e11 | + | 1.50098e12i | −0.288465 | + | 0.499636i | −0.973444 | − | 0.228927i | \(-0.926478\pi\) |
0.684979 | + | 0.728563i | \(0.259812\pi\) | |||||||
\(314\) | 2.19785e12i | 0.720029i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.55536e11 | 0.303258 | ||||||||
\(317\) | −1.15268e12 | − | 6.65501e11i | −0.360092 | − | 0.207899i | 0.309029 | − | 0.951053i | \(-0.399996\pi\) |
−0.669121 | + | 0.743154i | \(0.733329\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.46769e12 | − | 6.00621e12i | −1.04975 | − | 1.81822i | ||||
\(320\) | −5.60073e11 | + | 3.23358e11i | −0.166915 | + | 0.0963683i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.22968e10 | + | 7.32603e10i | −0.0122188 | + | 0.0211636i | ||||
\(323\) | 1.04290e12i | 0.296641i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.14010e12 | −1.14181 | ||||||||
\(326\) | 2.73246e12 | + | 1.57759e12i | 0.742107 | + | 0.428455i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.07986e11 | + | 3.60243e11i | 0.0547855 | + | 0.0948912i | ||||
\(329\) | −1.90977e10 | + | 1.10261e10i | −0.00495453 | + | 0.00286050i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.35980e12 | + | 4.08730e12i | −0.593931 | + | 1.02872i | 0.399766 | + | 0.916617i | \(0.369092\pi\) |
−0.993697 | + | 0.112102i | \(0.964242\pi\) | |||||||
\(332\) | − | 5.60959e11i | − | 0.139072i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.84743e12 | −0.685048 | ||||||||
\(335\) | 2.79906e12 | + | 1.61604e12i | 0.663420 | + | 0.383025i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.07642e12 | − | 3.59646e12i | −0.477711 | − | 0.827419i | 0.521963 | − | 0.852968i | \(-0.325200\pi\) |
−0.999674 | + | 0.0255489i | \(0.991867\pi\) | |||||||
\(338\) | −8.45164e11 | + | 4.87956e11i | −0.191583 | + | 0.110611i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.29321e11 | − | 1.43643e12i | 0.182527 | − | 0.316147i | ||||
\(341\) | − | 7.21658e12i | − | 1.56516i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.78515e11 | −0.0797282 | ||||||||
\(344\) | −3.67466e11 | − | 2.12156e11i | −0.0762824 | − | 0.0440417i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.42843e12 | + | 2.47412e12i | 0.288058 | + | 0.498931i | ||||
\(347\) | 3.80998e12 | − | 2.19969e12i | 0.757313 | − | 0.437235i | −0.0710170 | − | 0.997475i | \(-0.522624\pi\) |
0.828330 | + | 0.560240i | \(0.189291\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.62001e12 | − | 8.00209e12i | 0.892310 | − | 1.54553i | 0.0552116 | − | 0.998475i | \(-0.482417\pi\) |
0.837099 | − | 0.547052i | \(-0.184250\pi\) | |||||||
\(350\) | − | 2.04091e11i | − | 0.0388582i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.38366e12 | 0.256046 | ||||||||
\(353\) | 7.97378e11 | + | 4.60367e11i | 0.145476 | + | 0.0839905i | 0.570971 | − | 0.820970i | \(-0.306567\pi\) |
−0.425495 | + | 0.904961i | \(0.639900\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.97128e12 | − | 5.14640e12i | −0.526989 | − | 0.912771i | ||||
\(356\) | 2.30516e12 | − | 1.33088e12i | 0.403135 | − | 0.232750i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.35500e12 | + | 5.81103e12i | −0.570528 | + | 0.988184i | ||||
\(359\) | 6.17595e12i | 1.03569i | 0.855473 | + | 0.517847i | \(0.173267\pi\) | ||||
−0.855473 | + | 0.517847i | \(0.826733\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.72488e12 | −0.607542 | ||||||||
\(362\) | −4.86862e12 | − | 2.81090e12i | −0.783183 | − | 0.452171i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.28323e10 | + | 9.15082e10i | 0.00826784 | + | 0.0143203i | ||||
\(365\) | 4.51195e12 | − | 2.60497e12i | 0.696466 | − | 0.402105i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.09689e12 | − | 7.09603e12i | 0.615353 | − | 1.06582i | −0.374969 | − | 0.927037i | \(-0.622347\pi\) |
0.990322 | − | 0.138786i | \(-0.0443199\pi\) | |||||||
\(368\) | − | 1.46159e12i | − | 0.216564i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.34034e12 | 1.34696 | ||||||||
\(371\) | 2.66652e11 | + | 1.53952e11i | 0.0379381 | + | 0.0219036i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.53661e12 | + | 7.85764e12i | 0.628329 | + | 1.08830i | 0.987887 | + | 0.155176i | \(0.0495943\pi\) |
−0.359557 | + | 0.933123i | \(0.617072\pi\) | |||||||
\(374\) | −3.07326e12 | + | 1.77435e12i | −0.419993 | + | 0.242483i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.90506e11 | − | 3.29966e11i | 0.0253495 | − | 0.0439066i | ||||
\(377\) | 9.15072e12i | 1.20157i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.17817e13 | 1.50665 | 0.753324 | − | 0.657650i | \(-0.228449\pi\) | ||||
0.753324 | + | 0.657650i | \(0.228449\pi\) | |||||||
\(380\) | −3.31413e12 | − | 1.91341e12i | −0.418265 | − | 0.241485i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.78814e12 | + | 3.09714e12i | 0.219828 | + | 0.380754i | ||||
\(383\) | −5.90920e12 | + | 3.41168e12i | −0.717026 | + | 0.413975i | −0.813657 | − | 0.581345i | \(-0.802527\pi\) |
0.0966310 | + | 0.995320i | \(0.469193\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.76832e11 | + | 6.52692e11i | −0.0445496 | + | 0.0771622i | ||||
\(386\) | − | 8.56152e12i | − | 0.999112i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.50249e12 | 0.625750 | ||||||||
\(389\) | 6.12985e11 | + | 3.53907e11i | 0.0688180 | + | 0.0397321i | 0.534014 | − | 0.845476i | \(-0.320683\pi\) |
−0.465196 | + | 0.885208i | \(0.654016\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.87428e12 | + | 3.24634e12i | 0.205092 | + | 0.355230i | ||||
\(392\) | 2.82959e12 | − | 1.63367e12i | 0.305699 | − | 0.176495i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.14289e12 | − | 3.71159e12i | 0.225693 | − | 0.390912i | ||||
\(395\) | − | 8.99251e12i | − | 0.935181i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.26553e12 | 0.128328 | 0.0641639 | − | 0.997939i | \(-0.479562\pi\) | ||||
0.0641639 | + | 0.997939i | \(0.479562\pi\) | |||||||
\(398\) | −9.85560e11 | − | 5.69013e11i | −0.0986888 | − | 0.0569780i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.76311e12 | + | 3.05380e12i | 0.172179 | + | 0.298223i | ||||
\(401\) | −1.30128e13 | + | 7.51294e12i | −1.25501 | + | 0.724583i | −0.972101 | − | 0.234562i | \(-0.924634\pi\) |
−0.282914 | + | 0.959145i | \(0.591301\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.76087e12 | + | 8.24608e12i | −0.447880 | + | 0.775751i | ||||
\(404\) | − | 5.53749e12i | − | 0.514525i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.51094e11 | −0.0408919 | ||||||||
\(407\) | −1.73065e13 | − | 9.99193e12i | −1.54967 | − | 0.894700i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.51808e11 | + | 1.47537e12i | 0.0744261 | + | 0.128910i | 0.900837 | − | 0.434158i | \(-0.142954\pi\) |
−0.826410 | + | 0.563068i | \(0.809621\pi\) | |||||||
\(410\) | 3.39023e12 | − | 1.95735e12i | 0.292624 | − | 0.168947i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.25622e11 | + | 1.25681e12i | −0.0611257 | + | 0.105873i | ||||
\(413\) | 3.27659e11i | 0.0272692i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.27917e12 | −0.428869 | ||||||||
\(416\) | −1.58105e12 | − | 9.12822e11i | −0.126905 | − | 0.0732689i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.09379e12 | + | 7.09065e12i | 0.320807 | + | 0.555655i | ||||
\(419\) | −1.92646e13 | + | 1.11224e13i | −1.49173 | + | 0.861248i | −0.999955 | − | 0.00947693i | \(-0.996983\pi\) |
−0.491770 | + | 0.870725i | \(0.663650\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.14739e10 | + | 1.58437e11i | −0.00691650 | + | 0.0119797i | −0.869463 | − | 0.493998i | \(-0.835535\pi\) |
0.862546 | + | 0.505978i | \(0.168868\pi\) | |||||||
\(422\) | 1.07473e13i | 0.803043i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.31988e12 | −0.388215 | ||||||||
\(425\) | −7.83212e12 | − | 4.52187e12i | −0.564852 | − | 0.326117i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.05493e10 | + | 3.55924e10i | 0.00144763 | + | 0.00250737i | ||||
\(428\) | −1.06950e13 | + | 6.17477e12i | −0.744668 | + | 0.429934i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.99660e12 | + | 3.45820e12i | −0.135815 | + | 0.235239i | ||||
\(431\) | − | 6.64491e12i | − | 0.446789i | −0.974728 | − | 0.223395i | \(-0.928286\pi\) | ||
0.974728 | − | 0.223395i | \(-0.0717139\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.28337e12 | 0.478512 | 0.239256 | − | 0.970956i | \(-0.423096\pi\) | ||||
0.239256 | + | 0.970956i | \(0.423096\pi\) | |||||||
\(434\) | −4.06499e11 | − | 2.34692e11i | −0.0264004 | − | 0.0152423i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.39116e12 | − | 2.40957e12i | −0.0882970 | − | 0.152935i | ||||
\(437\) | 7.48997e12 | − | 4.32434e12i | 0.469973 | − | 0.271339i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.63002e12 | − | 1.32156e13i | 0.467954 | − | 0.810520i | −0.531376 | − | 0.847136i | \(-0.678325\pi\) |
0.999329 | + | 0.0366167i | \(0.0116581\pi\) | |||||||
\(440\) | − | 1.30216e13i | − | 0.789590i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.68225e12 | 0.277551 | ||||||||
\(443\) | −1.58746e13 | − | 9.16520e12i | −0.930430 | − | 0.537184i | −0.0434825 | − | 0.999054i | \(-0.513845\pi\) |
−0.886948 | + | 0.461870i | \(0.847179\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.25249e13 | − | 2.16937e13i | −0.717751 | − | 1.24318i | ||||
\(446\) | −4.61641e12 | + | 2.66528e12i | −0.261595 | + | 0.151032i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.49985e10 | − | 7.79397e10i | 0.00249349 | − | 0.00431885i | ||||
\(449\) | − | 8.33876e12i | − | 0.456951i | −0.973550 | − | 0.228475i | \(-0.926626\pi\) | ||
0.973550 | − | 0.228475i | \(-0.0733741\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.37559e12 | −0.448883 | ||||||||
\(452\) | −6.17686e12 | − | 3.56621e12i | −0.327398 | − | 0.189023i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.83124e12 | − | 8.36796e12i | −0.250484 | − | 0.433851i | ||||
\(455\) | 8.61180e11 | − | 4.97202e11i | 0.0441608 | − | 0.0254962i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.06144e11 | + | 3.57052e11i | −0.0103416 | + | 0.0179123i | −0.871150 | − | 0.491017i | \(-0.836625\pi\) |
0.860808 | + | 0.508929i | \(0.169959\pi\) | |||||||
\(458\) | 2.34581e13i | 1.16403i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.37549e13 | −0.667836 | ||||||||
\(461\) | 1.43974e11 | + | 8.31235e10i | 0.00691480 | + | 0.00399226i | 0.503453 | − | 0.864022i | \(-0.332063\pi\) |
−0.496539 | + | 0.868015i | \(0.665396\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.36616e12 | − | 1.10265e13i | −0.299208 | − | 0.518243i | 0.676747 | − | 0.736216i | \(-0.263389\pi\) |
−0.975955 | + | 0.217972i | \(0.930056\pi\) | |||||||
\(464\) | 6.74970e12 | − | 3.89694e12i | 0.313830 | − | 0.181190i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.17397e13 | − | 2.03338e13i | 0.534230 | − | 0.925314i | ||||
\(467\) | 2.26689e13i | 1.02058i | 0.860004 | + | 0.510288i | \(0.170461\pi\) | ||||
−0.860004 | + | 0.510288i | \(0.829539\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.49775e11 | −0.0198213 | ||||||||
\(470\) | −3.10530e12 | − | 1.79284e12i | −0.135398 | − | 0.0781723i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.83060e12 | − | 4.90275e12i | −0.120828 | − | 0.209281i | ||||
\(473\) | 7.39891e12 | − | 4.27176e12i | 0.312508 | − | 0.180427i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.04329e13 | + | 1.80703e13i | −0.431456 | + | 0.747304i | ||||
\(476\) | 2.30816e11i | 0.00944565i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.79873e13 | −1.12156 | ||||||||
\(479\) | −2.07547e13 | − | 1.19827e13i | −0.823073 | − | 0.475201i | 0.0284023 | − | 0.999597i | \(-0.490958\pi\) |
−0.851475 | + | 0.524395i | \(0.824291\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.31836e13 | + | 2.28347e13i | 0.512047 | + | 0.886891i | ||||
\(482\) | −2.03625e13 | + | 1.17563e13i | −0.782701 | + | 0.451892i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.29004e12 | + | 1.26267e13i | −0.274475 | + | 0.475405i | ||||
\(485\) | − | 5.17838e13i | − | 1.92968i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.13824e13 | −0.415516 | −0.207758 | − | 0.978180i | \(-0.566617\pi\) | ||||
−0.207758 | + | 0.978180i | \(0.566617\pi\) | |||||||
\(488\) | −6.14957e11 | − | 3.55046e11i | −0.0222201 | − | 0.0128288i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.53744e13 | − | 2.66292e13i | −0.544273 | − | 0.942709i | ||||
\(491\) | −3.11346e13 | + | 1.79756e13i | −1.09103 | + | 0.629906i | −0.933850 | − | 0.357664i | \(-0.883573\pi\) |
−0.157179 | + | 0.987570i | \(0.550240\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.99454e12 | + | 1.73110e13i | −0.343185 | + | 0.594414i | ||||
\(494\) | − | 1.08029e13i | − | 0.367203i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.10990e12 | 0.270151 | ||||||||
\(497\) | 7.16172e11 | + | 4.13482e11i | 0.0236176 | + | 0.0136356i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.68148e12 | + | 1.15727e13i | 0.215958 | + | 0.374051i | 0.953569 | − | 0.301176i | \(-0.0973791\pi\) |
−0.737610 | + | 0.675227i | \(0.764046\pi\) | |||||||
\(500\) | 7.87485e12 | − | 4.54655e12i | 0.251995 | − | 0.145490i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.41239e12 | + | 1.11066e13i | −0.201141 | + | 0.348387i | ||||
\(503\) | − | 3.54934e13i | − | 1.10232i | −0.834399 | − | 0.551160i | \(-0.814185\pi\) | ||
0.834399 | − | 0.551160i | \(-0.185815\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.21132e13 | −1.58668 | ||||||||
\(506\) | 2.54863e13 | + | 1.47145e13i | 0.768340 | + | 0.443602i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.04553e13 | + | 1.81092e13i | 0.309043 | + | 0.535279i | ||||
\(509\) | 5.25969e13 | − | 3.03668e13i | 1.53947 | − | 0.888813i | 0.540600 | − | 0.841280i | \(-0.318197\pi\) |
0.998870 | − | 0.0475339i | \(-0.0151362\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.62508e11 | + | 6.27882e11i | −0.0104043 | + | 0.0180208i | ||||
\(512\) | 1.55494e12i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.89501e13 | 0.806928 | ||||||||
\(515\) | 1.18278e13 | + | 6.82880e12i | 0.326489 | + | 0.188499i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.83583e12 | + | 6.64385e12i | 0.103850 | + | 0.179873i | ||||
\(518\) | −1.12566e12 | + | 6.49900e11i | −0.0301827 | + | 0.0174260i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.59053e12 | + | 1.48792e13i | −0.225945 | + | 0.391349i | ||||
\(521\) | 2.06244e13i | 0.537270i | 0.963242 | + | 0.268635i | \(0.0865726\pi\) | ||||
−0.963242 | + | 0.268635i | \(0.913427\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.24376e13 | 1.34009 | 0.670045 | − | 0.742320i | \(-0.266275\pi\) | ||||
0.670045 | + | 0.742320i | \(0.266275\pi\) | |||||||
\(524\) | −1.84234e13 | − | 1.06367e13i | −0.466351 | − | 0.269248i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.90730e13 | − | 3.30354e13i | −0.473685 | − | 0.820447i | ||||
\(527\) | −1.80129e13 | + | 1.03998e13i | −0.443130 | + | 0.255841i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.17008e12 | + | 8.95484e12i | −0.124801 | + | 0.216162i | ||||
\(530\) | 5.00652e13i | 1.19717i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.32541e11 | 0.0124967 | ||||||||
\(533\) | 9.57043e12 | + | 5.52549e12i | 0.222482 | + | 0.128450i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.81106e13 | + | 1.00650e14i | 1.32582 | + | 2.29640i | ||||
\(536\) | 6.72997e12 | − | 3.88555e12i | 0.152121 | − | 0.0878271i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.51630e13 | − | 2.62631e13i | 0.336414 | − | 0.582686i | ||||
\(539\) | 6.57877e13i | 1.44611i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.20249e13 | 1.76994 | 0.884972 | − | 0.465645i | \(-0.154178\pi\) | ||||
0.884972 | + | 0.465645i | \(0.154178\pi\) | |||||||
\(542\) | 3.43613e13 | + | 1.98385e13i | 0.734637 | + | 0.424143i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.99399e12 | − | 3.45370e12i | −0.0418532 | − | 0.0724919i | ||||
\(545\) | −2.26764e13 | + | 1.30922e13i | −0.471618 | + | 0.272289i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.11661e12 | − | 1.40584e13i | 0.165744 | − | 0.287077i | −0.771175 | − | 0.636623i | \(-0.780331\pi\) |
0.936919 | + | 0.349546i | \(0.113664\pi\) | |||||||
\(548\) | − | 4.73872e13i | − | 0.958867i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.10004e13 | −1.41074 | ||||||||
\(551\) | 3.99401e13 | + | 2.30595e13i | 0.786415 | + | 0.454037i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.25698e11 | + | 1.08374e12i | 0.0120987 | + | 0.0209556i | ||||
\(554\) | 3.32307e13 | − | 1.91857e13i | 0.636782 | − | 0.367646i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.03667e13 | − | 3.52762e13i | 0.383308 | − | 0.663908i | ||||
\(557\) | 1.12168e13i | 0.209215i | 0.994514 | + | 0.104608i | \(0.0333587\pi\) | ||||
−0.994514 | + | 0.104608i | \(0.966641\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.12726e13 | −0.206521 | ||||||||
\(560\) | −7.33487e11 | − | 4.23479e11i | −0.0133184 | − | 0.00768939i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.76253e12 | − | 4.78484e12i | −0.0492748 | − | 0.0853465i | ||||
\(563\) | 6.91540e13 | − | 3.99261e13i | 1.22258 | − | 0.705854i | 0.257109 | − | 0.966382i | \(-0.417230\pi\) |
0.965466 | + | 0.260528i | \(0.0838968\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.35615e13 | + | 5.81302e13i | −0.582906 | + | 1.00962i | ||||
\(566\) | − | 2.25462e13i | − | 0.388142i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.42881e13 | −0.241675 | ||||||||
\(569\) | −8.62210e11 | − | 4.97797e11i | −0.0144561 | − | 0.00834624i | 0.492755 | − | 0.870168i | \(-0.335990\pi\) |
−0.507211 | + | 0.861822i | \(0.669323\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.39178e13 | − | 9.33883e13i | −0.888283 | − | 1.53855i | −0.841904 | − | 0.539627i | \(-0.818565\pi\) |
−0.0463786 | − | 0.998924i | \(-0.514768\pi\) | |||||||
\(572\) | 3.18345e13 | − | 1.83796e13i | 0.519897 | − | 0.300163i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.72385e11 | + | 4.71784e11i | −0.00437143 | + | 0.00757153i | ||||
\(575\) | 7.49989e13i | 1.19321i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.31000e13 | 0.517546 | 0.258773 | − | 0.965938i | \(-0.416682\pi\) | ||||
0.258773 | + | 0.965938i | \(0.416682\pi\) | |||||||
\(578\) | −3.06475e13 | − | 1.76944e13i | −0.475068 | − | 0.274281i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.66740e13 | − | 6.35212e13i | −0.558751 | − | 0.967785i | ||||
\(581\) | 6.36224e11 | − | 3.67324e11i | 0.00961013 | − | 0.00554841i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.35578e13 | − | 9.27648e13i | 0.795206 | − | 1.37734i | ||||
\(584\) | − | 1.25266e13i | − | 0.184404i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.56543e13 | −0.515969 | ||||||||
\(587\) | 1.04808e14 | + | 6.05110e13i | 1.50385 | + | 0.868248i | 0.999990 | + | 0.00446213i | \(0.00142035\pi\) |
0.503859 | + | 0.863786i | \(0.331913\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.39944e13 | + | 4.15596e13i | 0.338481 | + | 0.586266i | ||||
\(590\) | −4.61396e13 | + | 2.66387e13i | −0.645377 | + | 0.372609i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.12288e13 | − | 1.94489e13i | 0.154428 | − | 0.267477i | ||||
\(593\) | 8.43944e12i | 0.115091i | 0.998343 | + | 0.0575453i | \(0.0183274\pi\) | ||||
−0.998343 | + | 0.0575453i | \(0.981673\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.17220e12 | 0.0291283 | ||||||||
\(596\) | −3.58185e13 | − | 2.06798e13i | −0.476294 | − | 0.274989i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.94147e13 | − | 3.36273e13i | −0.253878 | − | 0.439730i | ||||
\(599\) | −2.70098e13 | + | 1.55941e13i | −0.350258 | + | 0.202221i | −0.664799 | − | 0.747023i | \(-0.731483\pi\) |
0.314541 | + | 0.949244i | \(0.398149\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.43700e13 | + | 2.48896e13i | −0.183267 | + | 0.317428i | −0.942991 | − | 0.332817i | \(-0.892001\pi\) |
0.759724 | + | 0.650246i | \(0.225334\pi\) | |||||||
\(602\) | − | 5.55692e11i | − | 0.00702832i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.58031e13 | −0.196588 | ||||||||
\(605\) | 1.18830e14 | + | 6.86062e13i | 1.46605 | + | 0.846422i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.23768e13 | + | 3.87578e13i | 0.271553 | + | 0.470344i | 0.969260 | − | 0.246040i | \(-0.0791295\pi\) |
−0.697707 | + | 0.716384i | \(0.745796\pi\) | |||||||
\(608\) | −7.96839e12 | + | 4.60055e12i | −0.0959075 | + | 0.0553722i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.34132e12 | + | 5.78734e12i | −0.0395612 | + | 0.0685219i | ||||
\(611\) | − | 1.01222e13i | − | 0.118869i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.78051e13 | 0.783358 | 0.391679 | − | 0.920102i | \(-0.371894\pi\) | ||||
0.391679 | + | 0.920102i | \(0.371894\pi\) | |||||||
\(614\) | 6.46318e13 | + | 3.73152e13i | 0.740635 | + | 0.427606i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.06043e11 | + | 1.56931e12i | 0.0102152 | + | 0.0176932i | ||||
\(617\) | 2.15001e12 | − | 1.24131e12i | 0.0240444 | − | 0.0138820i | −0.487930 | − | 0.872883i | \(-0.662248\pi\) |
0.511974 | + | 0.859001i | \(0.328914\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.20000e12 | + | 1.42028e13i | −0.0902320 | + | 0.156286i | −0.907609 | − | 0.419817i | \(-0.862094\pi\) |
0.817377 | + | 0.576104i | \(0.195428\pi\) | |||||||
\(620\) | − | 7.63220e13i | − | 0.833088i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.78559e13 | 0.406613 | ||||||||
\(623\) | 3.01890e12 | + | 1.74296e12i | 0.0321668 | + | 0.0185715i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.28936e13 | + | 3.96529e13i | 0.240057 | + | 0.415791i | ||||
\(626\) | 3.39633e13 | − | 1.96087e13i | 0.353296 | − | 0.203976i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.48659e13 | − | 4.30689e13i | 0.254569 | − | 0.440926i | ||||
\(629\) | 5.75973e13i | 0.584991i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.37258e13 | −0.137211 | −0.0686056 | − | 0.997644i | \(-0.521855\pi\) | ||||
−0.0686056 | + | 0.997644i | \(0.521855\pi\) | |||||||
\(632\) | −1.87246e13 | − | 1.08107e13i | −0.185707 | − | 0.107218i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.50586e13 | + | 2.60822e13i | 0.147007 | + | 0.254623i | ||||
\(635\) | 1.70425e14 | − | 9.83948e13i | 1.65068 | − | 0.953023i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.34010e13 | − | 7.51728e13i | 0.413812 | − | 0.716743i | ||||
\(638\) | 1.56930e14i | 1.48457i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.46335e13 | 0.136285 | ||||||||
\(641\) | −4.69687e13 | − | 2.71174e13i | −0.434029 | − | 0.250587i | 0.267033 | − | 0.963687i | \(-0.413957\pi\) |
−0.701061 | + | 0.713101i | \(0.747290\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.77346e13 | + | 4.80378e13i | 0.252329 | + | 0.437047i | 0.964167 | − | 0.265297i | \(-0.0854700\pi\) |
−0.711837 | + | 0.702344i | \(0.752137\pi\) | |||||||
\(644\) | 1.65769e12 | − | 9.57068e11i | 0.0149649 | − | 0.00863999i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.17991e13 | − | 2.04366e13i | 0.104878 | − | 0.181655i | ||||
\(647\) | − | 5.56652e13i | − | 0.490979i | −0.969399 | − | 0.245489i | \(-0.921051\pi\) | ||
0.969399 | − | 0.245489i | \(-0.0789486\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.13988e14 | 0.990002 | ||||||||
\(650\) | 8.11291e13 | + | 4.68399e13i | 0.699214 | + | 0.403691i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.56967e13 | − | 6.18286e13i | −0.302964 | − | 0.524749i | ||||
\(653\) | 4.82196e13 | − | 2.78396e13i | 0.406123 | − | 0.234475i | −0.283000 | − | 0.959120i | \(-0.591329\pi\) |
0.689123 | + | 0.724645i | \(0.257996\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.00102e14 | + | 1.73382e14i | −0.830302 | + | 1.43813i | ||||
\(656\) | − | 9.41238e12i | − | 0.0774784i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.98984e11 | 0.00404536 | ||||||||
\(659\) | 1.32241e14 | + | 7.63495e13i | 1.06399 | + | 0.614298i | 0.926535 | − | 0.376210i | \(-0.122773\pi\) |
0.137460 | + | 0.990507i | \(0.456106\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.04018e14 | + | 1.80164e14i | 0.824329 | + | 1.42778i | 0.902431 | + | 0.430834i | \(0.141780\pi\) |
−0.0781026 | + | 0.996945i | \(0.524886\pi\) | |||||||
\(662\) | 9.24851e13 | − | 5.33963e13i | 0.727414 | − | 0.419973i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.34653e12 | + | 1.09925e13i | −0.0491695 | + | 0.0851641i | ||||
\(665\) | − | 5.01172e12i | − | 0.0385371i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.65767e14 | 1.25565 | ||||||||
\(668\) | 5.57981e13 | + | 3.22150e13i | 0.419505 | + | 0.242201i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.65668e13 | − | 6.33355e13i | −0.270840 | − | 0.469108i | ||||
\(671\) | 1.23821e13 | − | 7.14883e12i | 0.0910297 | − | 0.0525560i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.72630e13 | − | 8.18619e13i | 0.342331 | − | 0.592934i | −0.642534 | − | 0.766257i | \(-0.722117\pi\) |
0.984865 | + | 0.173323i | \(0.0554503\pi\) | |||||||
\(674\) | 9.39679e13i | 0.675585i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.20824e13 | 0.156427 | ||||||||
\(677\) | −1.47316e14 | − | 8.50528e13i | −1.03587 | − | 0.598060i | −0.117210 | − | 0.993107i | \(-0.537395\pi\) |
−0.918661 | + | 0.395047i | \(0.870728\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.60311e12 | + | 6.24077e12i | 0.0249648 | + | 0.0432404i | ||||
\(680\) | −3.25026e13 | + | 1.87654e13i | −0.223549 | + | 0.129066i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.16463e13 | + | 1.41415e14i | −0.553369 | + | 0.958462i | ||||
\(683\) | − | 2.23578e14i | − | 1.50427i | −0.659009 | − | 0.752135i | \(-0.729024\pi\) | ||
0.659009 | − | 0.752135i | \(-0.270976\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.45960e14 | −2.95694 | ||||||||
\(686\) | 7.41734e12 | + | 4.28240e12i | 0.0488234 | + | 0.0281882i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.80055e12 | + | 8.31480e12i | 0.0311422 | + | 0.0539398i | ||||
\(689\) | −1.22396e14 | + | 7.06656e13i | −0.788265 | + | 0.455105i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.50672e12 | − | 9.53792e12i | 0.0349545 | − | 0.0605429i | −0.848019 | − | 0.529966i | \(-0.822205\pi\) |
0.882973 | + | 0.469423i | \(0.155538\pi\) | |||||||
\(692\) | − | 6.46435e13i | − | 0.407375i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.95468e13 | −0.618344 | ||||||||
\(695\) | −3.31983e14 | − | 1.91671e14i | −2.04735 | − | 1.18204i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.20700e13 | + | 2.09059e13i | 0.0733744 | + | 0.127088i | ||||
\(698\) | −1.81067e14 | + | 1.04539e14i | −1.09285 | + | 0.630959i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.30902e12 | + | 3.99934e12i | −0.0137384 | + | 0.0237957i | ||||
\(701\) | 1.10962e14i | 0.655516i | 0.944762 | + | 0.327758i | \(0.106293\pi\) | ||||
−0.944762 | + | 0.327758i | \(0.893707\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.32889e14 | 0.773948 | ||||||||
\(704\) | −2.71142e13 | − | 1.56544e13i | −0.156795 | − | 0.0905258i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.04169e13 | − | 1.80426e13i | −0.0593903 | − | 0.102867i | ||||
\(707\) | 6.28047e12 | − | 3.62603e12i | 0.0355545 | − | 0.0205274i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.04110e14 | + | 1.80323e14i | −0.581112 | + | 1.00652i | 0.414236 | + | 0.910169i | \(0.364049\pi\) |
−0.995348 | + | 0.0963458i | \(0.969285\pi\) | |||||||
\(710\) | 1.34465e14i | 0.745275i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.02289e13 | −0.329158 | ||||||||
\(713\) | 1.49380e14 | + | 8.62443e13i | 0.810669 | + | 0.468040i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.72970e14 | − | 2.99593e14i | −0.925637 | − | 1.60325i | ||||
\(716\) | 1.31488e14 | − | 7.59149e13i | 0.698751 | − | 0.403424i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.98730e13 | − | 1.21024e14i | 0.366173 | − | 0.634231i | ||||
\(719\) | − | 2.74910e14i | − | 1.43069i | −0.698771 | − | 0.715346i | \(-0.746269\pi\) | ||
0.698771 | − | 0.715346i | \(-0.253731\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.90059e12 | −0.00975465 | ||||||||
\(722\) | 7.29924e13 | + | 4.21422e13i | 0.372042 | + | 0.214798i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.36034e13 | + | 1.10164e14i | 0.319733 | + | 0.553794i | ||||
\(725\) | −3.46350e14 | + | 1.99965e14i | −1.72912 | + | 0.998307i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.49536e14 | − | 2.59003e14i | 0.736330 | − | 1.27536i | −0.217807 | − | 0.975992i | \(-0.569890\pi\) |
0.954137 | − | 0.299370i | \(-0.0967764\pi\) | |||||||
\(728\) | − | 2.39092e12i | − | 0.0116925i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.17888e14 | −0.568662 | ||||||||
\(731\) | −2.13251e13 | − | 1.23120e13i | −0.102165 | − | 0.0589852i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.99610e13 | − | 1.03856e14i | −0.283367 | − | 0.490806i | 0.688845 | − | 0.724909i | \(-0.258118\pi\) |
−0.972212 | + | 0.234103i | \(0.924785\pi\) | |||||||
\(734\) | −1.60565e14 | + | 9.27021e13i | −0.753651 | + | 0.435120i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.65360e13 | + | 2.86411e13i | −0.0765668 | + | 0.132618i | ||||
\(737\) | 1.56471e14i | 0.719608i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.29345e13 | −0.330911 | −0.165455 | − | 0.986217i | \(-0.552909\pi\) | ||||
−0.165455 | + | 0.986217i | \(0.552909\pi\) | |||||||
\(740\) | −1.83033e14 | − | 1.05674e14i | −0.824840 | − | 0.476221i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.48353e12 | − | 6.03365e12i | −0.0154882 | − | 0.0268263i | ||||
\(743\) | 9.27173e13 | − | 5.35303e13i | 0.409465 | − | 0.236405i | −0.281095 | − | 0.959680i | \(-0.590698\pi\) |
0.690560 | + | 0.723275i | \(0.257364\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.94617e14 | + | 3.37086e14i | −0.848006 | + | 1.46879i | ||||
\(746\) | − | 2.05304e14i | − | 0.888592i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.02979e13 | 0.342923 | ||||||||
\(749\) | −1.40065e13 | − | 8.08666e12i | −0.0594183 | − | 0.0343052i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.18885e13 | − | 1.59156e14i | −0.384646 | − | 0.666227i | 0.607074 | − | 0.794645i | \(-0.292343\pi\) |
−0.991720 | + | 0.128419i | \(0.959010\pi\) | |||||||
\(752\) | −7.46627e12 | + | 4.31065e12i | −0.0310466 | + | 0.0179248i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.03529e14 | − | 1.79317e14i | 0.424819 | − | 0.735808i | ||||
\(755\) | 1.48722e14i | 0.606236i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.73049e14 | −0.696130 | −0.348065 | − | 0.937470i | \(-0.613161\pi\) | ||||
−0.348065 | + | 0.937470i | \(0.613161\pi\) | |||||||
\(758\) | −2.30873e14 | − | 1.33295e14i | −0.922629 | − | 0.532680i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.32956e13 | + | 7.49902e13i | 0.170756 | + | 0.295758i | ||||
\(761\) | 9.53979e13 | − | 5.50780e13i | 0.373780 | − | 0.215802i | −0.301329 | − | 0.953520i | \(-0.597430\pi\) |
0.675108 | + | 0.737719i | \(0.264097\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.82191e12 | − | 3.15564e12i | 0.00704537 | − | 0.0122029i | ||||
\(764\) | − | 8.09218e13i | − | 0.310884i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.54395e14 | 0.585449 | ||||||||
\(767\) | −1.30249e14 | − | 7.51995e13i | −0.490681 | − | 0.283295i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.15229e14 | − | 1.99583e14i | −0.428480 | − | 0.742149i | 0.568259 | − | 0.822850i | \(-0.307617\pi\) |
−0.996738 | + | 0.0807014i | \(0.974284\pi\) | |||||||
\(770\) | 1.47687e13 | − | 8.52674e12i | 0.0545619 | − | 0.0315013i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.68625e13 | + | 1.67771e14i | −0.353239 | + | 0.611829i | ||||
\(773\) | 1.50965e14i | 0.546991i | 0.961873 | + | 0.273495i | \(0.0881798\pi\) | ||||
−0.961873 | + | 0.273495i | \(0.911820\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.16146e14 | −1.48846 | ||||||||
\(776\) | −1.07826e14 | − | 6.22536e13i | −0.383192 | − | 0.221236i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.00801e12 | − | 1.38703e13i | −0.0280948 | − | 0.0486617i | ||||
\(779\) | 4.82342e13 | − | 2.78480e13i | 0.168139 | − | 0.0970750i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.43845e14 | − | 2.49147e14i | 0.495039 | − | 0.857433i | ||||
\(782\) | − | 8.48200e13i | − | 0.290044i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.39313e13 | −0.249602 | ||||||||
\(785\) | −4.05320e14 | − | 2.34012e14i | −1.35972 | − | 0.785035i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.71040e14 | + | 2.96250e14i | 0.566532 | + | 0.981263i | 0.996905 | + | 0.0786117i | \(0.0250487\pi\) |
−0.430373 | + | 0.902651i | \(0.641618\pi\) | |||||||
\(788\) | −8.39837e13 | + | 4.84880e13i | −0.276416 | + | 0.159589i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.01739e14 | + | 1.76217e14i | −0.330636 | + | 0.572679i | ||||
\(791\) | − | 9.34082e12i | − | 0.0301649i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.88647e13 | −0.0601568 | ||||||||
\(794\) | −2.47993e13 | − | 1.43179e13i | −0.0785844 | − | 0.0453707i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.28753e13 | + | 2.23007e13i | 0.0402895 | + | 0.0697835i | ||||
\(797\) | −4.52919e14 | + | 2.61493e14i | −1.40841 | + | 0.813146i | −0.995235 | − | 0.0975050i | \(-0.968914\pi\) |
−0.413176 | + | 0.910651i | \(0.635580\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.10556e13 | − | 1.91488e13i | 0.0339506 | − | 0.0588042i | ||||
\(800\) | − | 7.97893e13i | − | 0.243498i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.39997e14 | 1.02472 | ||||||||
\(803\) | 2.18432e14 | + | 1.26112e14i | 0.654242 | + | 0.377727i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.00693e12 | − | 1.56005e13i | −0.0266439 | − | 0.0461486i | ||||
\(806\) | 1.86587e14 | − | 1.07726e14i | 0.548539 | − | 0.316699i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.26496e13 | + | 1.08512e14i | −0.181912 | + | 0.315081i | ||||
\(809\) | − | 3.45374e14i | − | 0.996661i | −0.866987 | − | 0.498331i | \(-0.833947\pi\) | ||
0.866987 | − | 0.498331i | \(-0.166053\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.60870e14 | 1.02860 | 0.514301 | − | 0.857610i | \(-0.328052\pi\) | ||||
0.514301 | + | 0.857610i | \(0.328052\pi\) | |||||||
\(812\) | 8.83960e12 | + | 5.10355e12i | 0.0250411 | + | 0.0144575i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.26092e14 | + | 3.91602e14i | 0.632648 | + | 1.09578i | ||||
\(815\) | −5.81866e14 | + | 3.35941e14i | −1.61821 | + | 0.934275i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.84064e13 | + | 4.92013e13i | −0.0780379 | + | 0.135166i | ||||
\(818\) | − | 3.85484e13i | − | 0.105254i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.85796e13 | −0.238927 | ||||||||
\(821\) | −5.78784e14 | − | 3.34161e14i | −1.55168 | − | 0.895860i | −0.998006 | − | 0.0631235i | \(-0.979894\pi\) |
−0.553669 | − | 0.832737i | \(-0.686773\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.17665e13 | − | 3.77008e13i | −0.0576488 | − | 0.0998506i | 0.835761 | − | 0.549094i | \(-0.185027\pi\) |
−0.893410 | + | 0.449243i | \(0.851694\pi\) | |||||||
\(824\) | 2.84384e13 | − | 1.64189e13i | 0.0748634 | − | 0.0432224i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.70704e12 | − | 6.42078e12i | 0.00964110 | − | 0.0166989i | ||||
\(827\) | 2.21008e13i | 0.0571321i | 0.999592 | + | 0.0285661i | \(0.00909409\pi\) | ||||
−0.999592 | + | 0.0285661i | \(0.990906\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.62973e14 | 1.94866 | 0.974331 | − | 0.225119i | \(-0.0722770\pi\) | ||||
0.974331 | + | 0.225119i | \(0.0722770\pi\) | |||||||
\(830\) | 1.03450e14 | + | 5.97270e13i | 0.262628 | + | 0.151628i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.06548e13 | + | 3.57752e13i | 0.0518089 | + | 0.0897357i | ||||
\(833\) | 1.64209e14 | − | 9.48063e13i | 0.409423 | − | 0.236381i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.03174e14 | − | 5.25113e14i | 0.746896 | − | 1.29366i | ||||
\(836\) | − | 1.85264e14i | − | 0.453690i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.03342e14 | 1.21799 | ||||||||
\(839\) | −7.40702e13 | − | 4.27644e13i | −0.178170 | − | 0.102866i | 0.408263 | − | 0.912864i | \(-0.366135\pi\) |
−0.586432 | + | 0.809998i | \(0.699468\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.31622e14 | + | 4.01181e14i | 0.550554 | + | 0.953588i | ||||
\(842\) | 3.58503e12 | − | 2.06982e12i | 0.00847095 | − | 0.00489071i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.21592e14 | − | 2.10604e14i | 0.283918 | − | 0.491761i | ||||
\(845\) | − | 2.07816e14i | − | 0.482387i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.90945e13 | −0.0438017 | ||||||||
\(848\) | 1.04248e14 | + | 6.01875e13i | 0.237732 | + | 0.137255i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.02318e14 | + | 1.77221e14i | 0.230600 | + | 0.399411i | ||||
\(851\) | 4.13656e14 | − | 2.38824e14i | 0.926811 | − | 0.535095i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.10893e13 | + | 1.57771e14i | −0.201708 | + | 0.349368i | −0.949079 | − | 0.315039i | \(-0.897982\pi\) |
0.747371 | + | 0.664407i | \(0.231316\pi\) | |||||||
\(854\) | − | 9.29956e11i | − | 0.00204726i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.79438e14 | 0.608019 | ||||||||
\(857\) | 7.38198e14 | + | 4.26199e14i | 1.59687 | + | 0.921952i | 0.992086 | + | 0.125560i | \(0.0400727\pi\) |
0.604781 | + | 0.796392i | \(0.293261\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.30031e14 | − | 2.25220e14i | −0.278023 | − | 0.481550i | 0.692870 | − | 0.721062i | \(-0.256346\pi\) |
−0.970893 | + | 0.239512i | \(0.923013\pi\) | |||||||
\(860\) | 7.82502e13 | − | 4.51778e13i | 0.166339 | − | 0.0960357i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.51786e13 | + | 1.30213e14i | −0.157964 | + | 0.273601i | ||||
\(863\) | 2.71494e14i | 0.567161i | 0.958948 | + | 0.283580i | \(0.0915223\pi\) | ||||
−0.958948 | + | 0.283580i | \(0.908478\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.08358e14 | −1.25626 | ||||||||
\(866\) | −1.42724e14 | − | 8.24020e13i | −0.293028 | − | 0.169180i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.31048e12 | + | 9.19801e12i | 0.0107779 | + | 0.0186679i | ||||
\(869\) | 3.77019e14 | − | 2.17672e14i | 0.760790 | − | 0.439242i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.03226e14 | − | 1.78793e14i | 0.205920 | − | 0.356664i | ||||
\(872\) | 6.29569e13i | 0.124871i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.95697e14 | −0.383732 | ||||||||
\(875\) | 1.03131e13 | + | 5.95429e12i | 0.0201071 | + | 0.0116089i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.50609e13 | − | 1.64650e14i | −0.183233 | − | 0.317369i | 0.759747 | − | 0.650219i | \(-0.225323\pi\) |
−0.942980 | + | 0.332850i | \(0.891990\pi\) | |||||||
\(878\) | −2.99034e14 | + | 1.72648e14i | −0.573124 | + | 0.330893i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.47323e14 | + | 2.55170e14i | −0.279162 | + | 0.483523i | ||||
\(881\) | − | 6.12829e14i | − | 1.15468i | −0.816506 | − | 0.577338i | \(-0.804092\pi\) | ||
0.816506 | − | 0.577338i | \(-0.195908\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.57367e14 | −0.852042 | −0.426021 | − | 0.904713i | \(-0.640085\pi\) | ||||
−0.426021 | + | 0.904713i | \(0.640085\pi\) | |||||||
\(884\) | −9.17530e13 | − | 5.29736e13i | −0.169965 | − | 0.0981292i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.07385e14 | + | 3.59201e14i | 0.379847 | + | 0.657913i | ||||
\(887\) | −5.17143e14 | + | 2.98573e14i | −0.941874 | + | 0.543791i | −0.890547 | − | 0.454891i | \(-0.849678\pi\) |
−0.0513267 | + | 0.998682i | \(0.516345\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.36926e13 | + | 2.37163e13i | −0.0246591 | + | 0.0427108i | ||||
\(890\) | 5.66812e14i | 1.01505i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.20617e14 | 0.213592 | ||||||||
\(893\) | −4.41803e13 | − | 2.55075e13i | −0.0777985 | − | 0.0449170i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.14432e14 | − | 1.23743e15i | −1.24407 | − | 2.15480i | ||||
\(896\) | −1.76357e12 | + | 1.01820e12i | −0.00305389 | + | 0.00176316i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.43423e13 | + | 1.63406e14i | −0.161557 | + | 0.279824i | ||||
\(899\) | 9.19792e14i | 1.56636i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.08727e14 | −0.519938 | ||||||||
\(902\) | 1.64127e14 | + | 9.47590e13i | 0.274883 | + | 0.158704i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.06941e13 | + | 1.39766e14i | 0.133659 | + | 0.231505i | ||||
\(905\) | 1.03675e15 | − | 5.98569e14i | 1.70778 | − | 0.985988i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.98099e14 | − | 6.89528e14i | 0.648567 | − | 1.12335i | −0.334898 | − | 0.942254i | \(-0.608702\pi\) |
0.983465 | − | 0.181097i | \(-0.0579647\pi\) | |||||||
\(908\) | 2.18637e14i | 0.354238i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.25008e13 | −0.0360571 | ||||||||
\(911\) | −5.15739e14 | − | 2.97762e14i | −0.821936 | − | 0.474545i | 0.0291479 | − | 0.999575i | \(-0.490721\pi\) |
−0.851083 | + | 0.525030i | \(0.824054\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.27787e14 | − | 2.21334e14i | −0.201434 | − | 0.348894i | ||||
\(914\) | 8.07916e12 | − | 4.66451e12i | 0.0126659 | − | 0.00731265i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.65398e14 | − | 4.59683e14i | 0.411548 | − | 0.712822i | ||||
\(917\) | − | 2.78603e13i | − | 0.0429675i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.55318e14 | 0.847157 | 0.423579 | − | 0.905859i | \(-0.360774\pi\) | ||||
0.423579 | + | 0.905859i | \(0.360774\pi\) | |||||||
\(920\) | 2.69541e14 | + | 1.55619e14i | 0.408964 | + | 0.236116i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.88087e12 | − | 3.25776e12i | −0.00282296 | − | 0.00488950i | ||||
\(923\) | −3.28731e14 | + | 1.89793e14i | −0.490718 | + | 0.283316i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.76187e14 | + | 9.97986e14i | −0.850854 | + | 1.47372i | ||||
\(926\) | 2.88100e14i | 0.423144i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.76356e14 | −0.256241 | ||||||||
\(929\) | −1.29291e14 | − | 7.46462e13i | −0.186849 | − | 0.107877i | 0.403658 | − | 0.914910i | \(-0.367739\pi\) |
−0.590506 | + | 0.807033i | \(0.701072\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.18738e14 | − | 3.78865e14i | −0.312734 | − | 0.541671i | ||||
\(932\) | −4.60102e14 | + | 2.65640e14i | −0.654296 | + | 0.377758i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.56469e14 | − | 4.44217e14i | 0.360828 | − | 0.624972i | ||||
\(935\) | − | 7.55681e14i | − | 1.05750i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.07315e14 | −0.425487 | −0.212743 | − | 0.977108i | \(-0.568240\pi\) | ||||
−0.212743 | + | 0.977108i | \(0.568240\pi\) | |||||||
\(938\) | 8.81376e12 | + | 5.08863e12i | 0.0121380 | + | 0.00700788i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.05674e13 | + | 7.02648e13i | 0.0552762 | + | 0.0957412i | ||||
\(941\) | −2.27895e14 | + | 1.31575e14i | −0.308877 | + | 0.178330i | −0.646424 | − | 0.762978i | \(-0.723736\pi\) |
0.337547 | + | 0.941309i | \(0.390403\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.00096e14 | − | 1.73371e14i | 0.134232 | − | 0.232497i | ||||
\(944\) | 1.28098e14i | 0.170877i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.93318e14 | −0.255162 | ||||||||
\(947\) | 1.04028e15 | + | 6.00604e14i | 1.36584 | + | 0.788566i | 0.990393 | − | 0.138279i | \(-0.0441572\pi\) |
0.375443 | + | 0.926845i | \(0.377491\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.66395e14 | − | 2.88205e14i | −0.216177 | − | 0.374430i | ||||
\(950\) | 4.08884e14 | − | 2.36069e14i | 0.528424 | − | 0.305086i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.61139e12 | − | 4.52306e12i | 0.00333954 | − | 0.00578425i | ||||
\(953\) | − | 3.27942e13i | − | 0.0417189i | −0.999782 | − | 0.0208594i | \(-0.993360\pi\) | ||
0.999782 | − | 0.0208594i | \(-0.00664025\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.61552e14 | −0.958700 | ||||||||
\(956\) | 5.48436e14 | + | 3.16640e14i | 0.686810 | + | 0.396530i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.71138e14 | + | 4.69624e14i | 0.336018 | + | 0.582000i | ||||
\(959\) | 5.37452e13 | − | 3.10298e13i | 0.0662593 | − | 0.0382548i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.87290e13 | + | 1.19042e14i | −0.0838538 | + | 0.145239i | ||||
\(962\) | − | 5.96623e14i | − | 0.724143i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.32029e14 | 0.639072 | ||||||||
\(965\) | 1.57888e15 | + | 9.11569e14i | 1.88675 | + | 1.08931i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.93527e14 | + | 8.54813e14i | 0.583684 | + | 1.01097i | 0.995038 | + | 0.0994953i | \(0.0317228\pi\) |
−0.411354 | + | 0.911476i | \(0.634944\pi\) | |||||||
\(968\) | 2.85710e14 | − | 1.64955e14i | 0.336162 | − | 0.194083i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.85866e14 | + | 1.01475e15i | −0.682244 | + | 1.18168i | ||||
\(971\) | 5.42431e14i | 0.628418i | 0.949354 | + | 0.314209i | \(0.101739\pi\) | ||||
−0.949354 | + | 0.314209i | \(0.898261\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.33457e13 | 0.0611695 | ||||||||
\(974\) | 2.23048e14 | + | 1.28777e14i | 0.254451 | + | 0.146907i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.03377e12 | + | 1.39149e13i | 0.00907131 | + | 0.0157120i | ||||
\(977\) | 8.26067e14 | − | 4.76930e14i | 0.927988 | − | 0.535774i | 0.0418131 | − | 0.999125i | \(-0.486687\pi\) |
0.886175 | + | 0.463352i | \(0.153353\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.06353e14 | − | 1.05023e15i | 0.674237 | − | 1.16781i | ||||
\(980\) | 6.95765e14i | 0.769719i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.13482e14 | 0.890821 | ||||||||
\(983\) | −5.46361e14 | − | 3.15442e14i | −0.595268 | − | 0.343678i | 0.171910 | − | 0.985113i | \(-0.445006\pi\) |
−0.767178 | + | 0.641435i | \(0.778340\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.56319e14 | + | 7.90367e14i | 0.492138 | + | 0.852409i | ||||
\(986\) | 3.91704e14 | − | 2.26151e14i | 0.420314 | − | 0.242668i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.22221e14 | + | 2.11693e14i | −0.129826 | + | 0.224865i | ||||
\(989\) | 2.04205e14i | 0.215816i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.94498e14 | 0.517364 | 0.258682 | − | 0.965963i | \(-0.416712\pi\) | ||||
0.258682 | + | 0.965963i | \(0.416712\pi\) | |||||||
\(992\) | −1.58921e14 | − | 9.17530e13i | −0.165433 | − | 0.0955129i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.35604e12 | − | 1.62051e13i | −0.00964184 | − | 0.0167002i | ||||
\(995\) | 2.09871e14 | − | 1.21169e14i | 0.215197 | − | 0.124244i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.14965e14 | + | 1.41156e15i | −0.827301 | + | 1.43293i | 0.0728476 | + | 0.997343i | \(0.476791\pi\) |
−0.900148 | + | 0.435584i | \(0.856542\pi\) | |||||||
\(998\) | − | 3.02369e14i | − | 0.305411i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 162.11.d.d.107.2 | 8 | ||
3.2 | odd | 2 | inner | 162.11.d.d.107.3 | 8 | ||
9.2 | odd | 6 | 6.11.b.a.5.2 | ✓ | 4 | ||
9.4 | even | 3 | inner | 162.11.d.d.53.3 | 8 | ||
9.5 | odd | 6 | inner | 162.11.d.d.53.2 | 8 | ||
9.7 | even | 3 | 6.11.b.a.5.4 | yes | 4 | ||
36.7 | odd | 6 | 48.11.e.d.17.1 | 4 | |||
36.11 | even | 6 | 48.11.e.d.17.2 | 4 | |||
45.2 | even | 12 | 150.11.b.a.149.5 | 8 | |||
45.7 | odd | 12 | 150.11.b.a.149.3 | 8 | |||
45.29 | odd | 6 | 150.11.d.a.101.3 | 4 | |||
45.34 | even | 6 | 150.11.d.a.101.1 | 4 | |||
45.38 | even | 12 | 150.11.b.a.149.4 | 8 | |||
45.43 | odd | 12 | 150.11.b.a.149.6 | 8 | |||
72.11 | even | 6 | 192.11.e.h.65.3 | 4 | |||
72.29 | odd | 6 | 192.11.e.g.65.2 | 4 | |||
72.43 | odd | 6 | 192.11.e.h.65.4 | 4 | |||
72.61 | even | 6 | 192.11.e.g.65.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.11.b.a.5.2 | ✓ | 4 | 9.2 | odd | 6 | ||
6.11.b.a.5.4 | yes | 4 | 9.7 | even | 3 | ||
48.11.e.d.17.1 | 4 | 36.7 | odd | 6 | |||
48.11.e.d.17.2 | 4 | 36.11 | even | 6 | |||
150.11.b.a.149.3 | 8 | 45.7 | odd | 12 | |||
150.11.b.a.149.4 | 8 | 45.38 | even | 12 | |||
150.11.b.a.149.5 | 8 | 45.2 | even | 12 | |||
150.11.b.a.149.6 | 8 | 45.43 | odd | 12 | |||
150.11.d.a.101.1 | 4 | 45.34 | even | 6 | |||
150.11.d.a.101.3 | 4 | 45.29 | odd | 6 | |||
162.11.d.d.53.2 | 8 | 9.5 | odd | 6 | inner | ||
162.11.d.d.53.3 | 8 | 9.4 | even | 3 | inner | ||
162.11.d.d.107.2 | 8 | 1.1 | even | 1 | trivial | ||
162.11.d.d.107.3 | 8 | 3.2 | odd | 2 | inner | ||
192.11.e.g.65.1 | 4 | 72.61 | even | 6 | |||
192.11.e.g.65.2 | 4 | 72.29 | odd | 6 | |||
192.11.e.h.65.3 | 4 | 72.11 | even | 6 | |||
192.11.e.h.65.4 | 4 | 72.43 | odd | 6 |