Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,9,Mod(17,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.17");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.q (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: | \(175.987559546\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 150208 x^{14} - 1927740 x^{13} + 8702363206 x^{12} + 239206241152 x^{11} + \cdots + 81\!\cdots\!61 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{40} \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 305.1 | ||
Root | \(220.333 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 432.305 |
Dual form | 432.9.q.c.17.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −935.250 | + | 539.967i | −1.49640 | + | 0.863947i | −0.999991 | − | 0.00414227i | \(-0.998681\pi\) |
−0.496408 | + | 0.868089i | \(0.665348\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2056.09 | − | 3561.25i | 0.856347 | − | 1.48324i | −0.0190419 | − | 0.999819i | \(-0.506062\pi\) |
0.875389 | − | 0.483419i | \(-0.160605\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8419.53 | + | 4861.02i | 0.575065 | + | 0.332014i | 0.759170 | − | 0.650893i | \(-0.225605\pi\) |
−0.184105 | + | 0.982907i | \(0.558939\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4116.02 | − | 7129.16i | −0.144113 | − | 0.249612i | 0.784928 | − | 0.619586i | \(-0.212700\pi\) |
−0.929042 | + | 0.369975i | \(0.879366\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 87809.9i | 1.05135i | 0.850685 | + | 0.525676i | \(0.176187\pi\) | ||||
−0.850685 | + | 0.525676i | \(0.823813\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −123643. | −0.948754 | −0.474377 | − | 0.880322i | \(-0.657327\pi\) | ||||
−0.474377 | + | 0.880322i | \(0.657327\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 92029.4 | − | 53133.2i | 0.328863 | − | 0.189869i | −0.326473 | − | 0.945206i | \(-0.605860\pi\) |
0.655336 | + | 0.755337i | \(0.272527\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 387816. | − | 671717.i | 0.992808 | − | 1.71959i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −430885. | − | 248772.i | −0.609213 | − | 0.351729i | 0.163444 | − | 0.986553i | \(-0.447740\pi\) |
−0.772657 | + | 0.634823i | \(0.781073\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 577977. | + | 1.00109e6i | 0.625841 | + | 1.08399i | 0.988378 | + | 0.152019i | \(0.0485775\pi\) |
−0.362536 | + | 0.931970i | \(0.618089\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.44088e6i | 2.95935i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.20145e6 | 0.641061 | 0.320531 | − | 0.947238i | \(-0.396139\pi\) | ||||
0.320531 | + | 0.947238i | \(0.396139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.53952e6 | + | 888843.i | −0.544816 | + | 0.314550i | −0.747029 | − | 0.664792i | \(-0.768520\pi\) |
0.202212 | + | 0.979342i | \(0.435187\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 528726. | − | 915780.i | 0.154652 | − | 0.267866i | −0.778280 | − | 0.627917i | \(-0.783908\pi\) |
0.932932 | + | 0.360052i | \(0.117241\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.80689e6 | − | 2.19791e6i | −0.780151 | − | 0.450420i | 0.0563327 | − | 0.998412i | \(-0.482059\pi\) |
−0.836484 | + | 0.547992i | \(0.815393\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.57261e6 | − | 9.65205e6i | −0.966662 | − | 1.67431i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.04810e6i | − | 0.132831i | −0.997792 | − | 0.0664157i | \(-0.978844\pi\) | ||
0.997792 | − | 0.0664157i | \(-0.0211563\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.04991e7 | −1.14737 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.70048e6 | + | 5.02323e6i | −0.718018 | + | 0.414548i | −0.814023 | − | 0.580833i | \(-0.802727\pi\) |
0.0960047 | + | 0.995381i | \(0.469394\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.15770e6 | + | 7.20135e6i | −0.300285 | + | 0.520109i | −0.976200 | − | 0.216870i | \(-0.930415\pi\) |
0.675915 | + | 0.736979i | \(0.263749\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.69902e6 | + | 4.44503e6i | 0.431302 | + | 0.249013i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.19183e6 | − | 1.07246e7i | −0.307270 | − | 0.532207i | 0.670494 | − | 0.741915i | \(-0.266082\pi\) |
−0.977764 | + | 0.209708i | \(0.932749\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.69579e7i | − | 0.667328i | −0.942692 | − | 0.333664i | \(-0.891715\pi\) | ||
0.942692 | − | 0.333664i | \(-0.108285\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.42736e7 | −0.854757 | −0.427378 | − | 0.904073i | \(-0.640563\pi\) | ||||
−0.427378 | + | 0.904073i | \(0.640563\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.46226e7 | − | 1.99894e7i | 0.984911 | − | 0.568639i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.39004e6 | + | 1.10679e7i | −0.164057 | + | 0.284155i | −0.936320 | − | 0.351148i | \(-0.885791\pi\) |
0.772263 | + | 0.635303i | \(0.219125\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.79188e7 | − | 1.61189e7i | −0.588281 | − | 0.339644i | 0.176136 | − | 0.984366i | \(-0.443640\pi\) |
−0.764418 | + | 0.644722i | \(0.776973\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.74144e7 | − | 8.21242e7i | −0.908312 | − | 1.57324i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.10088e7i | − | 0.334843i | −0.985885 | − | 0.167422i | \(-0.946456\pi\) | ||
0.985885 | − | 0.167422i | \(-0.0535441\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.38516e7 | −0.493644 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.15637e8 | − | 6.67629e7i | 1.41972 | − | 0.819673i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.46651e7 | + | 7.73622e7i | −0.504523 | + | 0.873860i | 0.495463 | + | 0.868629i | \(0.334998\pi\) |
−0.999986 | + | 0.00523116i | \(0.998335\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.08430e7 | + | 1.78072e7i | 0.296395 | + | 0.171124i | 0.640822 | − | 0.767689i | \(-0.278594\pi\) |
−0.344427 | + | 0.938813i | \(0.611927\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.35300e6 | + | 7.53962e6i | 0.0386759 | + | 0.0669886i | 0.884715 | − | 0.466132i | \(-0.154353\pi\) |
−0.846040 | + | 0.533120i | \(0.821019\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.34341e8i | 1.78778i | 0.448290 | + | 0.893888i | \(0.352033\pi\) | ||||
−0.448290 | + | 0.893888i | \(0.647967\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.66492e8 | 1.88789 | 0.943947 | − | 0.330098i | \(-0.107082\pi\) | ||||
0.943947 | + | 0.330098i | \(0.107082\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.47560e8 | − | 1.42929e8i | 1.51833 | − | 0.876610i | 0.518565 | − | 0.855038i | \(-0.326466\pi\) |
0.999767 | − | 0.0215714i | \(-0.00686693\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.73803e7 | + | 9.93856e7i | −0.328074 | + | 0.568241i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.12713e8 | + | 1.80545e8i | 1.55940 | + | 0.900322i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.99205e7 | − | 1.03785e8i | −0.279534 | − | 0.484166i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.15781e8i | 1.70304i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.18752e7 | 0.314730 | 0.157365 | − | 0.987541i | \(-0.449700\pi\) | ||||
0.157365 | + | 0.987541i | \(0.449700\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.27800e8 | − | 1.89256e8i | 1.11308 | − | 0.642634i | 0.173451 | − | 0.984843i | \(-0.444508\pi\) |
0.939624 | + | 0.342208i | \(0.111175\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.54220e8 | + | 4.40322e8i | −0.812463 | + | 1.40723i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.36881e7 | − | 4.83174e7i | −0.237565 | − | 0.137158i | 0.376492 | − | 0.926420i | \(-0.377130\pi\) |
−0.614057 | + | 0.789262i | \(0.710463\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.13230e8 | + | 3.69325e8i | 0.571200 | + | 0.989348i | 0.996443 | + | 0.0842686i | \(0.0268554\pi\) |
−0.425243 | + | 0.905079i | \(0.639811\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 8.00322e7i | − | 0.191391i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.37313e8 | 1.21550 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.73436e8 | + | 2.15603e8i | −0.757653 | + | 0.437431i | −0.828453 | − | 0.560059i | \(-0.810778\pi\) |
0.0707992 | + | 0.997491i | \(0.477445\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.20280e8 | − | 7.27947e8i | 0.808409 | − | 1.40021i | −0.105556 | − | 0.994413i | \(-0.533662\pi\) |
0.913965 | − | 0.405793i | \(-0.133004\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.08111e9 | − | 6.24177e8i | −1.87302 | − | 1.08139i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.10919e8 | + | 3.65323e8i | 0.347150 | + | 0.601282i | 0.985742 | − | 0.168264i | \(-0.0538160\pi\) |
−0.638592 | + | 0.769546i | \(0.720483\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 4.36987e8i | − | 0.650376i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.50818e8 | 0.780293 | 0.390146 | − | 0.920753i | \(-0.372424\pi\) | ||||
0.390146 | + | 0.920753i | \(0.372424\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.25550e8 | − | 3.03427e8i | 0.675691 | − | 0.390111i | −0.122538 | − | 0.992464i | \(-0.539103\pi\) |
0.798230 | + | 0.602353i | \(0.205770\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.73982e8 | − | 6.47756e8i | 0.458463 | − | 0.794081i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.26617e8 | + | 4.77248e8i | 0.922826 | + | 0.532794i | 0.884536 | − | 0.466473i | \(-0.154475\pi\) |
0.0382907 | + | 0.999267i | \(0.487809\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.59477e9 | − | 2.76222e9i | −1.70038 | − | 2.94514i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.44019e8i | 0.919536i | 0.888039 | + | 0.459768i | \(0.152067\pi\) | ||||
−0.888039 | + | 0.459768i | \(0.847933\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.68230e8 | −0.808948 | −0.404474 | − | 0.914550i | \(-0.632545\pi\) | ||||
−0.404474 | + | 0.914550i | \(0.632545\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.12366e9 | + | 6.48744e8i | −0.959284 | + | 0.553843i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.26845e8 | + | 7.39318e8i | −0.349063 | + | 0.604595i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.09956e7 | − | 3.52159e7i | −0.0458316 | − | 0.0264609i | 0.476909 | − | 0.878953i | \(-0.341757\pi\) |
−0.522741 | + | 0.852492i | \(0.675090\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.36871e9 | − | 2.37068e9i | −0.986467 | − | 1.70861i | −0.635225 | − | 0.772327i | \(-0.719093\pi\) |
−0.351242 | − | 0.936285i | \(-0.614241\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.47276e8i | − | 0.363364i | −0.983357 | − | 0.181682i | \(-0.941846\pi\) | ||
0.983357 | − | 0.181682i | \(-0.0581541\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.66467e9 | 1.69915 | 0.849574 | − | 0.527469i | \(-0.176859\pi\) | ||||
0.849574 | + | 0.527469i | \(0.176859\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.77188e9 | + | 1.02299e9i | −1.04340 | + | 0.602405i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.59891e8 | − | 1.66258e9i | 0.543509 | − | 0.941385i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.04101e9 | − | 6.01029e8i | −0.545595 | − | 0.315000i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.39137e8 | + | 1.62663e9i | 0.473804 | + | 0.820653i | 0.999550 | − | 0.0299884i | \(-0.00954702\pi\) |
−0.525746 | + | 0.850642i | \(0.676214\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.14198e9i | 0.534446i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.75349e9 | 2.14375 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.26011e8 | − | 3.61427e8i | 0.262430 | − | 0.151514i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.45052e9 | + | 2.51237e9i | −0.586548 | + | 1.01593i | 0.408132 | + | 0.912923i | \(0.366180\pi\) |
−0.994680 | + | 0.103009i | \(0.967153\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.60966e9 | + | 2.08404e9i | 1.35945 | + | 0.784877i | 0.989549 | − | 0.144195i | \(-0.0460594\pi\) |
0.369898 | + | 0.929072i | \(0.379393\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.80018e9 | + | 3.11801e9i | 0.654599 | + | 1.13380i | 0.981994 | + | 0.188911i | \(0.0604957\pi\) |
−0.327396 | + | 0.944887i | \(0.606171\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 2.86365e9i | − | 0.971618i | −0.874065 | − | 0.485809i | \(-0.838525\pi\) | ||
0.874065 | − | 0.485809i | \(-0.161475\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.74719e9 | 1.55656 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.21500e9 | − | 7.01479e8i | 0.372378 | − | 0.214992i | −0.302119 | − | 0.953270i | \(-0.597694\pi\) |
0.674497 | + | 0.738278i | \(0.264361\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.21808e9 | − | 3.84182e9i | 0.657519 | − | 1.13886i | −0.323737 | − | 0.946147i | \(-0.604939\pi\) |
0.981256 | − | 0.192709i | \(-0.0617273\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.04236e10 | + | 6.01805e9i | 2.89303 | + | 1.67029i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.08916e8 | + | 8.81468e8i | 0.136728 | + | 0.236820i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2.42084e9i | − | 0.609916i | −0.952366 | − | 0.304958i | \(-0.901357\pi\) | ||
0.952366 | − | 0.304958i | \(-0.0986425\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.03313e9 | 0.252157 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.08915e9 | − | 1.20617e9i | 0.478891 | − | 0.276488i | −0.241063 | − | 0.970509i | \(-0.577496\pi\) |
0.719954 | + | 0.694022i | \(0.244163\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.47029e9 | − | 4.27867e9i | 0.548971 | − | 0.950846i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.65030e9 | + | 3.26220e9i | 1.18100 | + | 0.681849i | 0.956245 | − | 0.292567i | \(-0.0945096\pi\) |
0.224752 | + | 0.974416i | \(0.427843\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.65941e8 | + | 9.80238e8i | 0.114759 | + | 0.198769i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.64127e9i | 1.26836i | 0.773186 | + | 0.634180i | \(0.218662\pi\) | ||||
−0.773186 | + | 0.634180i | \(0.781338\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.72229e9 | 0.504728 | 0.252364 | − | 0.967632i | \(-0.418792\pi\) | ||||
0.252364 | + | 0.967632i | \(0.418792\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.53045e9 | − | 3.77036e9i | 1.14186 | − | 0.659252i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.00946e9 | + | 8.67663e9i | −0.850886 | + | 1.47378i | 0.0295233 | + | 0.999564i | \(0.490601\pi\) |
−0.880410 | + | 0.474214i | \(0.842732\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.83019e9 | + | 3.94341e9i | 1.09549 | + | 0.632480i | 0.935032 | − | 0.354563i | \(-0.115370\pi\) |
0.160456 | + | 0.987043i | \(0.448704\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.86855e8 | − | 8.43258e8i | −0.0759021 | − | 0.131466i | 0.825576 | − | 0.564291i | \(-0.190850\pi\) |
−0.901478 | + | 0.432824i | \(0.857517\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.31016e9i | 1.07746i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.34822e8 | −0.105339 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.59420e9 | − | 2.65246e9i | 0.623361 | − | 0.359898i | −0.154815 | − | 0.987943i | \(-0.549478\pi\) |
0.778176 | + | 0.628046i | \(0.216145\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.42475e9 | − | 9.39595e9i | 0.716295 | − | 1.24066i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.57590e8 | − | 4.37395e8i | −0.0947871 | − | 0.0547254i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.17422e9 | − | 3.76585e9i | −0.264872 | − | 0.458772i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 8.98008e9i | − | 1.03772i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.34241e10 | −1.51124 | −0.755618 | − | 0.655013i | \(-0.772663\pi\) | ||||
−0.755618 | + | 0.655013i | \(0.772663\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.98291e9 | − | 1.14483e9i | 0.211964 | − | 0.122377i | −0.390260 | − | 0.920705i | \(-0.627615\pi\) |
0.602224 | + | 0.798327i | \(0.294282\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.94161e9 | − | 1.54873e10i | 0.931619 | − | 1.61361i | 0.151065 | − | 0.988524i | \(-0.451730\pi\) |
0.780555 | − | 0.625088i | \(-0.214937\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.77404e9 | − | 3.33364e9i | −0.571798 | − | 0.330128i | 0.186069 | − | 0.982537i | \(-0.440425\pi\) |
−0.757867 | + | 0.652409i | \(0.773758\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.41856e9 | − | 4.18908e9i | −0.233558 | − | 0.404535i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.08570e10i | − | 0.997474i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.38503e9 | −0.572308 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.56546e10 | + | 9.03820e9i | −1.33616 | + | 0.771433i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.84292e9 | − | 1.35843e10i | 0.653380 | − | 1.13169i | −0.328918 | − | 0.944359i | \(-0.606684\pi\) |
0.982297 | − | 0.187328i | \(-0.0599828\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.15818e10 | + | 6.68676e9i | 0.919597 | + | 0.530929i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.29188e9 | − | 2.23761e9i | −0.100162 | − | 0.173486i | 0.811589 | − | 0.584229i | \(-0.198603\pi\) |
−0.911751 | + | 0.410743i | \(0.865270\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.12382e10i | 0.831152i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.21253e10 | −1.59850 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.45626e10 | − | 8.40775e9i | 1.00444 | − | 0.579912i | 0.0948784 | − | 0.995489i | \(-0.469754\pi\) |
0.909558 | + | 0.415577i | \(0.136420\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.22366e10 | − | 2.11945e10i | 0.824822 | − | 1.42863i | −0.0772336 | − | 0.997013i | \(-0.524609\pi\) |
0.902055 | − | 0.431620i | \(-0.142058\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.05088e9 | + | 5.22553e9i | 0.582897 | + | 0.336536i | 0.762284 | − | 0.647243i | \(-0.224078\pi\) |
−0.179387 | + | 0.983779i | \(0.557411\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.15672e9 | + | 1.58599e10i | 0.576536 | + | 0.998590i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.37497e10i | 1.42982i | 0.699219 | + | 0.714908i | \(0.253531\pi\) | ||||
−0.699219 | + | 0.714908i | \(0.746469\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.69607e9 | −0.0998656 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.27019e10 | − | 1.31069e10i | 1.27906 | − | 0.738464i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.17433e9 | − | 8.96220e9i | 0.285226 | − | 0.494027i | −0.687438 | − | 0.726243i | \(-0.741265\pi\) |
0.972664 | + | 0.232217i | \(0.0745979\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.73256e9 | − | 2.15499e9i | −0.197020 | − | 0.113750i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.02672e9 | + | 6.97448e9i | 0.208025 | + | 0.360310i | 0.951092 | − | 0.308907i | \(-0.0999631\pi\) |
−0.743067 | + | 0.669217i | \(0.766630\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.09580e9i | 0.202756i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.63218e10 | 1.27573 | 0.637864 | − | 0.770149i | \(-0.279818\pi\) | ||||
0.637864 | + | 0.770149i | \(0.279818\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.64941e10 | + | 1.52964e10i | −1.23127 | + | 0.710876i | −0.967295 | − | 0.253653i | \(-0.918368\pi\) |
−0.263978 | + | 0.964529i | \(0.585035\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.15872e10 | + | 3.73901e10i | −0.982547 | + | 1.70182i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.76791e10 | − | 2.17540e10i | −1.64552 | − | 0.950039i | −0.978824 | − | 0.204704i | \(-0.934377\pi\) |
−0.666691 | − | 0.745334i | \(-0.732290\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.66562e9 | + | 8.08109e9i | 0.199619 | + | 0.345751i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 1.38016e10i | − | 0.566947i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.31419e10 | 1.73675 | 0.868375 | − | 0.495908i | \(-0.165165\pi\) | ||||
0.868375 | + | 0.495908i | \(0.165165\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.57455e10 | − | 9.09069e9i | 0.608948 | − | 0.351576i | −0.163606 | − | 0.986526i | \(-0.552312\pi\) |
0.772554 | + | 0.634950i | \(0.218979\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.75794e9 | − | 8.24099e9i | 0.180384 | − | 0.312434i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.01157e10 | + | 5.84028e9i | 0.368652 | + | 0.212841i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.23724e9 | + | 5.60707e9i | 0.115686 | + | 0.200374i | 0.918054 | − | 0.396456i | \(-0.129760\pi\) |
−0.802368 | + | 0.596830i | \(0.796427\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.13128e10i | 1.41999i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.48148e10 | 1.17374 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.28096e10 | + | 1.89427e10i | −1.06450 | + | 0.614589i | −0.926673 | − | 0.375868i | \(-0.877345\pi\) |
−0.137826 | + | 0.990456i | \(0.544011\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.38781e10 | − | 4.13581e10i | 0.760102 | − | 1.31654i | −0.182696 | − | 0.983170i | \(-0.558482\pi\) |
0.942798 | − | 0.333366i | \(-0.108184\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.89834e10 | + | 3.40541e10i | 1.80790 | + | 1.04379i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.70972e10 | + | 2.96133e10i | 0.514297 | + | 0.890789i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 2.73395e10i | − | 0.792285i | −0.918189 | − | 0.396143i | \(-0.870349\pi\) | ||
0.918189 | − | 0.396143i | \(-0.129651\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.96958e9 | −0.198269 | −0.0991345 | − | 0.995074i | \(-0.531607\pi\) | ||||
−0.0991345 | + | 0.995074i | \(0.531607\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.13788e10 | + | 6.56953e9i | −0.312010 | + | 0.180139i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.26214e9 | + | 7.38223e9i | −0.114754 | + | 0.198760i | −0.917682 | − | 0.397317i | \(-0.869941\pi\) |
0.802927 | + | 0.596077i | \(0.203275\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.77214e10 | − | 1.02315e10i | −0.460134 | − | 0.265658i | 0.251967 | − | 0.967736i | \(-0.418923\pi\) |
−0.712101 | + | 0.702077i | \(0.752256\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.13441e10 | + | 1.96485e10i | 0.289287 | + | 0.501060i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1.52992e10i | − | 0.376430i | −0.982128 | − | 0.188215i | \(-0.939730\pi\) | ||
0.982128 | − | 0.188215i | \(-0.0602702\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.72827e10 | −0.417740 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.16597e10 | − | 1.82788e10i | 0.738689 | − | 0.426483i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.20106e10 | + | 2.08029e10i | −0.275359 | + | 0.476935i | −0.970226 | − | 0.242203i | \(-0.922130\pi\) |
0.694867 | + | 0.719138i | \(0.255463\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.96796e10 | − | 2.86825e10i | −1.09995 | − | 0.635058i | −0.163744 | − | 0.986503i | \(-0.552357\pi\) |
−0.936209 | + | 0.351445i | \(0.885690\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.03202e10 | − | 5.25162e10i | −0.659795 | − | 1.14280i | −0.980669 | − | 0.195676i | \(-0.937310\pi\) |
0.320874 | − | 0.947122i | \(-0.396023\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.01091e10i | 0.212543i | 0.994337 | + | 0.106271i | \(0.0338912\pi\) | ||||
−0.994337 | + | 0.106271i | \(0.966109\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.09238e10 | −1.05252 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.90324e9 | − | 5.14029e9i | 0.177870 | − | 0.102693i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.79505e10 | + | 8.30528e10i | −0.941931 | + | 1.63147i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.87971e10 | + | 1.08525e10i | 0.357067 | + | 0.206153i | 0.667793 | − | 0.744347i | \(-0.267239\pi\) |
−0.310727 | + | 0.950499i | \(0.600572\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.94520e9 | − | 8.56534e9i | −0.0923855 | − | 0.160016i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 9.64707e10i | − | 1.74353i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.82792e9 | 0.103609 | 0.0518045 | − | 0.998657i | \(-0.483503\pi\) | ||||
0.0518045 | + | 0.998657i | \(0.483503\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.15718e10 | + | 1.24545e10i | −0.371159 | + | 0.214288i | −0.673964 | − | 0.738764i | \(-0.735410\pi\) |
0.302806 | + | 0.953052i | \(0.402077\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.18446e10 | − | 3.78360e10i | 0.369791 | − | 0.640497i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.03915e10 | − | 3.48670e10i | −0.989806 | − | 0.571465i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.19755e9 | + | 1.41986e10i | 0.132215 | + | 0.229004i | 0.924530 | − | 0.381109i | \(-0.124458\pi\) |
−0.792315 | + | 0.610112i | \(0.791124\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 4.61285e10i | − | 0.720606i | −0.932835 | − | 0.360303i | \(-0.882673\pi\) | ||
0.932835 | − | 0.360303i | \(-0.117327\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.84612e10 | −0.591367 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.69443e9 | − | 3.86503e9i | 0.0997339 | − | 0.0575814i | −0.449303 | − | 0.893379i | \(-0.648328\pi\) |
0.549037 | + | 0.835798i | \(0.314994\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.99087e10 | + | 8.64444e10i | −0.731969 | + | 1.26781i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.14229e9 | − | 4.70095e9i | −0.115749 | − | 0.0668278i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.13681e10 | − | 3.70107e10i | −0.299092 | − | 0.518042i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 3.97902e10i | − | 0.540039i | −0.962855 | − | 0.270019i | \(-0.912970\pi\) | ||
0.962855 | − | 0.270019i | \(-0.0870301\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.49978e10 | 0.467772 | 0.233886 | − | 0.972264i | \(-0.424856\pi\) | ||||
0.233886 | + | 0.972264i | \(0.424856\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.79053e10 | + | 5.07521e10i | −1.13965 | + | 0.657979i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.35092e10 | + | 5.80397e10i | −0.427899 | + | 0.741143i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.26734e10 | + | 7.31699e9i | 0.157031 | + | 0.0906617i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.26536e11 | − | 2.19167e11i | −1.54454 | − | 2.67523i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.08354e11i | − | 1.28378i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.34001e10 | 0.273168 | 0.136584 | − | 0.990629i | \(-0.456388\pi\) | ||||
0.136584 | + | 0.990629i | \(0.456388\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.49236e11 | + | 1.43897e11i | −2.82504 | + | 1.63104i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.16091e10 | − | 2.01075e10i | 0.129673 | − | 0.224600i | −0.793877 | − | 0.608078i | \(-0.791941\pi\) |
0.923550 | + | 0.383478i | \(0.125274\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.32757e10 | + | 3.07588e10i | 0.577994 | + | 0.333705i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.62770e10 | + | 4.55131e10i | 0.280980 | + | 0.486671i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.65617e10i | 0.379844i | 0.981799 | + | 0.189922i | \(0.0608236\pi\) | ||||
−0.981799 | + | 0.189922i | \(0.939176\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.70499e9 | −0.0891499 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.15433e11 | + | 6.66450e10i | −1.14893 | + | 0.663337i | −0.948627 | − | 0.316397i | \(-0.897527\pi\) |
−0.200306 | + | 0.979733i | \(0.564194\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.54354e11 | + | 2.67348e11i | −1.51469 | + | 2.62352i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.42643e11 | + | 8.23549e10i | 1.36082 | + | 0.785670i | 0.989733 | − | 0.142928i | \(-0.0456517\pi\) |
0.371087 | + | 0.928598i | \(0.378985\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.84597e10 | + | 1.18576e11i | 0.644007 | + | 1.11545i | 0.984530 | + | 0.175216i | \(0.0560625\pi\) |
−0.340523 | + | 0.940236i | \(0.610604\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 8.24235e10i | − | 0.754015i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.01555e11 | −0.916218 | −0.458109 | − | 0.888896i | \(-0.651473\pi\) | ||||
−0.458109 | + | 0.888896i | \(0.651473\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.14807e11 | + | 6.62840e10i | −1.00755 | + | 0.581707i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.09485e9 | − | 8.82453e9i | 0.0441018 | − | 0.0763866i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.25669e10 | − | 1.88025e10i | −0.274299 | − | 0.158367i | 0.356541 | − | 0.934280i | \(-0.383956\pi\) |
−0.630840 | + | 0.775913i | \(0.717289\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.14626e10 | − | 1.23777e11i | −0.593769 | − | 1.02844i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1.30215e11i | − | 1.05304i | −0.850163 | − | 0.526519i | \(-0.823497\pi\) | ||
0.850163 | − | 0.526519i | \(-0.176503\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.89953e11 | −3.11132 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.13848e11 | − | 6.57304e10i | 0.884341 | − | 0.510575i | 0.0122537 | − | 0.999925i | \(-0.496099\pi\) |
0.872087 | + | 0.489350i | \(0.162766\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.15092e10 | − | 3.72550e10i | 0.164864 | − | 0.285553i | −0.771743 | − | 0.635935i | \(-0.780615\pi\) |
0.936607 | + | 0.350382i | \(0.113948\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.12081e11 | + | 6.47102e10i | 0.836588 | + | 0.483004i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.29606e10 | + | 2.24485e10i | 0.0954710 | + | 0.165361i | 0.909805 | − | 0.415036i | \(-0.136231\pi\) |
−0.814334 | + | 0.580396i | \(0.802898\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.61866e10i | 0.259646i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.28485e11 | 0.909933 | 0.454967 | − | 0.890508i | \(-0.349651\pi\) | ||||
0.454967 | + | 0.890508i | \(0.349651\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.02289e11 | − | 5.90563e10i | 0.705808 | − | 0.407498i | −0.103699 | − | 0.994609i | \(-0.533068\pi\) |
0.809507 | + | 0.587110i | \(0.199735\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.40218e10 | − | 1.10889e11i | 0.436079 | − | 0.755312i | −0.561304 | − | 0.827610i | \(-0.689700\pi\) |
0.997383 | + | 0.0722982i | \(0.0230333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.48177e10 | − | 4.31960e10i | −0.496652 | − | 0.286742i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.30176e10 | − | 1.26470e11i | −0.478528 | − | 0.828835i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.05499e11i | 0.673980i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.40613e11 | 1.51775 | 0.758877 | − | 0.651233i | \(-0.225748\pi\) | ||||
0.758877 | + | 0.651233i | \(0.225748\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.65738e10 | + | 4.42099e10i | −0.470961 | + | 0.271910i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.58740e10 | + | 7.94561e10i | −0.278618 | + | 0.482580i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.87111e11 | − | 1.08029e11i | −1.10833 | − | 0.639893i | −0.169932 | − | 0.985456i | \(-0.554355\pi\) |
−0.938396 | + | 0.345563i | \(0.887688\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.85669e10 | + | 3.21588e10i | 0.108616 | + | 0.188129i | 0.915210 | − | 0.402977i | \(-0.132025\pi\) |
−0.806594 | + | 0.591106i | \(0.798691\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.88598e10i | 0.335894i | 0.985796 | + | 0.167947i | \(0.0537137\pi\) | ||||
−0.985796 | + | 0.167947i | \(0.946286\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.76719e10 | −0.550543 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.48938e11 | − | 8.59893e10i | 0.819129 | − | 0.472925i | −0.0309867 | − | 0.999520i | \(-0.509865\pi\) |
0.850116 | + | 0.526595i | \(0.176532\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.04384e11 | + | 3.54003e11i | −1.11040 | + | 1.92328i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.34850e11 | + | 1.35591e11i | 1.24523 | + | 0.718934i | 0.970154 | − | 0.242489i | \(-0.0779639\pi\) |
0.275075 | + | 0.961423i | \(0.411297\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.21597e11 | + | 2.10613e11i | 0.636968 | + | 1.10326i | 0.986095 | + | 0.166185i | \(0.0531451\pi\) |
−0.349126 | + | 0.937076i | \(0.613522\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 5.49082e11i | − | 2.80770i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.28721e10 | −0.267130 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.00118e10 | + | 4.04213e10i | −0.345367 | + | 0.199398i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.44609e10 | − | 2.50471e10i | 0.0704914 | − | 0.122095i | −0.828625 | − | 0.559804i | \(-0.810877\pi\) |
0.899117 | + | 0.437709i | \(0.144210\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.58076e11 | − | 9.12654e10i | −0.752509 | − | 0.434462i | 0.0740905 | − | 0.997252i | \(-0.476395\pi\) |
−0.826600 | + | 0.562790i | \(0.809728\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.83671e11 | + | 3.18127e11i | 0.864095 | + | 1.49666i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 3.71514e11i | − | 1.70723i | −0.520903 | − | 0.853616i | \(-0.674405\pi\) | ||
0.520903 | − | 0.853616i | \(-0.325595\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.04359e11 | 0.473989 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.47209e9 | + | 4.31401e9i | −0.0331562 | + | 0.0191428i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.88238e10 | − | 1.71168e11i | 0.433460 | − | 0.750775i | −0.563708 | − | 0.825974i | \(-0.690626\pi\) |
0.997169 | + | 0.0751987i | \(0.0239591\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.98846e11 | − | 2.30274e11i | −1.70949 | − | 0.986973i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.80492e10 | − | 1.35185e11i | −0.330702 | − | 0.572793i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.70096e10i | 0.277501i | 0.990327 | + | 0.138751i | \(0.0443087\pi\) | ||||
−0.990327 | + | 0.138751i | \(0.955691\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.48551e11 | −0.608209 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.26832e11 | − | 7.32264e10i | 0.507634 | − | 0.293083i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.70291e10 | − | 9.87774e10i | 0.225690 | − | 0.390906i | −0.730836 | − | 0.682553i | \(-0.760870\pi\) |
0.956526 | + | 0.291647i | \(0.0942031\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.06382e11 | + | 6.14196e10i | 0.411632 | + | 0.237656i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.32147e10 | + | 7.48501e10i | 0.165351 | + | 0.286397i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.31072e11i | 0.864633i | 0.901722 | + | 0.432317i | \(0.142304\pi\) | ||||
−0.901722 | + | 0.432317i | \(0.857696\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.58007e10 | 0.132480 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.34208e11 | + | 1.92955e11i | −1.20966 | + | 0.698400i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.70637e11 | + | 2.95551e11i | −0.610850 | + | 1.05802i | 0.380248 | + | 0.924885i | \(0.375839\pi\) |
−0.991097 | + | 0.133138i | \(0.957495\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.04145e10 | + | 4.64274e10i | 0.281621 | + | 0.162594i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.07203e11 | + | 3.58887e11i | 0.717763 | + | 1.24320i | 0.961884 | + | 0.273457i | \(0.0881670\pi\) |
−0.244122 | + | 0.969745i | \(0.578500\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.20394e11i | − | 0.408071i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.71838e11 | −0.911449 | −0.455725 | − | 0.890121i | \(-0.650620\pi\) | ||||
−0.455725 | + | 0.890121i | \(0.650620\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.96676e11 | + | 1.71286e11i | −0.973479 | + | 0.562039i | −0.900295 | − | 0.435280i | \(-0.856649\pi\) |
−0.0731842 | + | 0.997318i | \(0.523316\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.32837e11 | − | 4.03286e11i | 0.755835 | − | 1.30914i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.34547e11 | + | 4.81826e11i | 2.65170 | + | 1.53096i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.25839e10 | + | 9.10780e10i | 0.165308 | + | 0.286321i | 0.936765 | − | 0.349960i | \(-0.113805\pi\) |
−0.771457 | + | 0.636282i | \(0.780472\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.07750e11i | 2.79369i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.23531e11 | −1.28974 | −0.644869 | − | 0.764293i | \(-0.723088\pi\) | ||||
−0.644869 | + | 0.764293i | \(0.723088\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.62418e11 | + | 2.66977e11i | −1.37878 | + | 0.796041i | −0.992013 | − | 0.126135i | \(-0.959743\pi\) |
−0.386770 | + | 0.922176i | \(0.626409\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.47931e11 | − | 9.49044e11i | 1.61669 | − | 2.80019i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.16228e10 | + | 4.13514e10i | 0.206952 | + | 0.119484i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.66789e10 | − | 9.81707e10i | −0.162075 | − | 0.280722i | 0.773538 | − | 0.633750i | \(-0.218485\pi\) |
−0.935613 | + | 0.353028i | \(0.885152\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.83942e11i | 0.795265i | 0.917545 | + | 0.397632i | \(0.130168\pi\) | ||||
−0.917545 | + | 0.397632i | \(0.869832\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.96595e11 | 2.48536 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.90350e11 | − | 1.09899e11i | 0.516897 | − | 0.298430i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.24328e10 | − | 1.42778e11i | 0.221562 | − | 0.383757i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.94524e11 | − | 2.27779e11i | −1.03895 | − | 0.599839i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.25568e11 | − | 5.63900e11i | −0.848678 | − | 1.46995i | −0.882389 | − | 0.470521i | \(-0.844066\pi\) |
0.0337110 | − | 0.999432i | \(-0.489267\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.17550e12i | − | 3.00273i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.84528e10 | 0.173100 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.16469e11 | + | 2.40448e11i | −1.03216 | + | 0.595921i | −0.917604 | − | 0.397496i | \(-0.869879\pi\) |
−0.114561 | + | 0.993416i | \(0.536546\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.92998e11 | − | 3.34283e11i | 0.473550 | − | 0.820213i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.04372e11 | − | 1.17994e11i | −0.491541 | − | 0.283791i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.35958e11 | + | 4.08692e11i | 0.561890 | + | 0.973223i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1.97505e11i | − | 0.461089i | −0.973062 | − | 0.230545i | \(-0.925949\pi\) | ||
0.973062 | − | 0.230545i | \(-0.0740508\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.30697e11 | 0.302121 | 0.151061 | − | 0.988524i | \(-0.451731\pi\) | ||||
0.151061 | + | 0.988524i | \(0.451731\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.15152e11 | + | 2.97423e11i | −1.16763 | + | 0.674131i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.53730e10 | + | 1.13229e11i | −0.146727 | + | 0.254139i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.25465e10 | − | 1.30172e10i | −0.0496256 | − | 0.0286514i | 0.474982 | − | 0.879996i | \(-0.342455\pi\) |
−0.524608 | + | 0.851344i | \(0.675788\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.02310e11 | − | 1.77206e11i | −0.223007 | − | 0.386260i | 0.732712 | − | 0.680539i | \(-0.238254\pi\) |
−0.955720 | + | 0.294278i | \(0.904921\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 2.31574e11i | − | 0.495072i | −0.968879 | − | 0.247536i | \(-0.920379\pi\) | ||
0.968879 | − | 0.247536i | \(-0.0796208\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.98205e11 | 1.69004 | 0.845019 | − | 0.534736i | \(-0.179589\pi\) | ||||
0.845019 | + | 0.534736i | \(0.179589\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.47545e11 | − | 4.89331e11i | 1.76029 | − | 1.01630i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.27681e11 | + | 5.67559e11i | −0.674070 | + | 1.16752i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.56790e11 | + | 3.21463e11i | 1.12368 | + | 0.648758i | 0.942338 | − | 0.334662i | \(-0.108622\pi\) |
0.181343 | + | 0.983420i | \(0.441955\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.26349e11 | − | 2.18842e11i | −0.252573 | − | 0.437469i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.07752e11i | 1.58435i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.92808e11 | −0.957511 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.10569e11 | − | 6.38370e10i | 0.210821 | − | 0.121718i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.75384e10 | − | 1.68942e11i | 0.184238 | − | 0.319110i | −0.759081 | − | 0.650996i | \(-0.774352\pi\) |
0.943320 | + | 0.331886i | \(0.107685\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.84904e10 | + | 2.22224e10i | 0.0713557 | + | 0.0411972i | 0.535253 | − | 0.844692i | \(-0.320216\pi\) |
−0.463898 | + | 0.885889i | \(0.653549\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.25294e11 | + | 2.17015e11i | 0.230122 | + | 0.398582i | 0.957844 | − | 0.287290i | \(-0.0927543\pi\) |
−0.727722 | + | 0.685872i | \(0.759421\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.91558e11i | 0.705915i | 0.935639 | + | 0.352958i | \(0.114824\pi\) | ||||
−0.935639 | + | 0.352958i | \(0.885176\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.03079e12 | −1.84122 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.07602e11 | + | 6.21242e10i | −0.188687 | + | 0.108939i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.09714e10 | + | 8.82851e10i | −0.0885633 | + | 0.153396i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.48070e12 | + | 8.54884e11i | 2.52601 | + | 1.45839i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.99055e10 | + | 6.91184e10i | 0.0674582 | + | 0.116841i | 0.897782 | − | 0.440441i | \(-0.145178\pi\) |
−0.830324 | + | 0.557282i | \(0.811844\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 5.84453e11i | − | 0.970166i | −0.874468 | − | 0.485083i | \(-0.838789\pi\) | ||
0.874468 | − | 0.485083i | \(-0.161211\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.52384e10 | −0.123765 | −0.0618823 | − | 0.998083i | \(-0.519710\pi\) | ||||
−0.0618823 | + | 0.998083i | \(0.519710\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.05896e11 | − | 3.49814e11i | 0.978822 | − | 0.565123i | 0.0769076 | − | 0.997038i | \(-0.475495\pi\) |
0.901914 | + | 0.431915i | \(0.142162\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.68343e11 | − | 2.91578e11i | 0.269518 | − | 0.466819i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.70694e11 | + | 2.71755e11i | 0.740172 | + | 0.427338i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.09739e11 | − | 8.82894e11i | −0.794430 | − | 1.37599i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 5.75137e11i | − | 0.880507i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.20338e10 | 0.139652 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.12012e11 | − | 4.68815e11i | 1.21051 | − | 0.698888i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.79947e10 | − | 1.00450e11i | 0.0856958 | − | 0.148429i | −0.819992 | − | 0.572375i | \(-0.806022\pi\) |
0.905687 | + | 0.423946i | \(0.139355\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.81176e11 | + | 5.66482e11i | 1.42454 | + | 0.822456i | 0.996682 | − | 0.0813913i | \(-0.0259363\pi\) |
0.427854 | + | 0.903848i | \(0.359270\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.56709e11 | − | 2.71428e11i | −0.225533 | − | 0.390635i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 1.55651e12i | − | 2.20127i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.06256e11 | 0.429361 | 0.214680 | − | 0.976684i | \(-0.431129\pi\) | ||||
0.214680 | + | 0.976684i | \(0.431129\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.20896e11 | + | 6.97992e10i | −0.166573 | + | 0.0961709i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.65942e11 | − | 8.07035e11i | 0.636451 | − | 1.10237i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.75115e11 | + | 5.05248e11i | 1.17490 | + | 0.678331i | 0.954830 | − | 0.297152i | \(-0.0960369\pi\) |
0.220074 | + | 0.975483i | \(0.429370\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.89012e11 | + | 1.19340e12i | 0.917124 | + | 1.58851i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 9.21929e11i | − | 1.20629i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.80033e11 | −0.493018 | −0.246509 | − | 0.969141i | \(-0.579283\pi\) | ||||
−0.246509 | + | 0.969141i | \(0.579283\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.20722e11 | + | 2.42904e11i | −0.536583 | + | 0.309796i | −0.743693 | − | 0.668521i | \(-0.766928\pi\) |
0.207110 | + | 0.978318i | \(0.433594\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.44541e10 | + | 1.63599e11i | −0.119447 | + | 0.206888i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.64773e9 | + | 2.68337e9i | 0.00577885 | + | 0.00333642i | 0.502887 | − | 0.864352i | \(-0.332271\pi\) |
−0.497108 | + | 0.867689i | \(0.665605\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.99106e10 | + | 1.73050e11i | 0.123182 | + | 0.213357i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.87948e11i | 0.349094i | 0.984649 | + | 0.174547i | \(0.0558462\pi\) | ||||
−0.984649 | + | 0.174547i | \(0.944154\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.60616e10 | 0.0914433 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.44141e11 | + | 1.98690e11i | −0.406876 | + | 0.234910i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.41670e11 | + | 4.18585e11i | −0.283354 | + | 0.490784i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.56017e12 | + | 1.47812e12i | 2.95230 | + | 1.70451i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.51417e11 | + | 7.81877e11i | 0.516264 | + | 0.894195i | 0.999822 | + | 0.0188827i | \(0.00601091\pi\) |
−0.483558 | + | 0.875312i | \(0.660656\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 8.08040e11i | − | 0.908983i | −0.890751 | − | 0.454492i | \(-0.849821\pi\) | ||
0.890751 | − | 0.454492i | \(-0.150179\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.75368e12 | 1.95658 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.39658e12 | + | 8.06317e11i | −1.53281 | + | 0.884968i | −0.533579 | + | 0.845750i | \(0.679153\pi\) |
−0.999231 | + | 0.0392176i | \(0.987513\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.02124e11 | − | 1.76884e11i | 0.111173 | − | 0.192557i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.24469e12 | + | 7.18625e11i | 1.33306 | + | 0.769641i | 0.985767 | − | 0.168117i | \(-0.0537687\pi\) |
0.347290 | + | 0.937758i | \(0.387102\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.95511e11 | + | 5.11840e11i | 0.313927 | + | 0.543737i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1.12372e11i | − | 0.117455i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.11953e12 | 1.16075 | 0.580377 | − | 0.814348i | \(-0.302905\pi\) | ||||
0.580377 | + | 0.814348i | \(0.302905\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.49213e12 | + | 1.43883e12i | −2.54261 | + | 1.46797i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.45668e11 | + | 7.71920e11i | −0.451057 | + | 0.781253i | −0.998452 | − | 0.0556212i | \(-0.982286\pi\) |
0.547395 | + | 0.836874i | \(0.315619\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 432.9.q.c.305.1 | 16 | ||
3.2 | odd | 2 | 144.9.q.b.65.5 | 16 | |||
4.3 | odd | 2 | 54.9.d.a.35.1 | 16 | |||
9.4 | even | 3 | 144.9.q.b.113.5 | 16 | |||
9.5 | odd | 6 | inner | 432.9.q.c.17.1 | 16 | ||
12.11 | even | 2 | 18.9.d.a.11.6 | yes | 16 | ||
36.7 | odd | 6 | 162.9.b.c.161.9 | 16 | |||
36.11 | even | 6 | 162.9.b.c.161.8 | 16 | |||
36.23 | even | 6 | 54.9.d.a.17.1 | 16 | |||
36.31 | odd | 6 | 18.9.d.a.5.6 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
18.9.d.a.5.6 | ✓ | 16 | 36.31 | odd | 6 | ||
18.9.d.a.11.6 | yes | 16 | 12.11 | even | 2 | ||
54.9.d.a.17.1 | 16 | 36.23 | even | 6 | |||
54.9.d.a.35.1 | 16 | 4.3 | odd | 2 | |||
144.9.q.b.65.5 | 16 | 3.2 | odd | 2 | |||
144.9.q.b.113.5 | 16 | 9.4 | even | 3 | |||
162.9.b.c.161.8 | 16 | 36.11 | even | 6 | |||
162.9.b.c.161.9 | 16 | 36.7 | odd | 6 | |||
432.9.q.c.17.1 | 16 | 9.5 | odd | 6 | inner | ||
432.9.q.c.305.1 | 16 | 1.1 | even | 1 | trivial |