Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [81,9,Mod(26,81)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(81, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("81.26");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 81.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: | \(32.9976674150\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 26.2 | ||
Character | \(\chi\) | \(=\) | 81.26 |
Dual form | 81.9.d.g.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 \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −22.2403 | − | 12.8404i | −1.39002 | − | 0.802527i | −0.396700 | − | 0.917948i | \(-0.629845\pi\) |
−0.993317 | + | 0.115422i | \(0.963178\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 201.753 | + | 349.447i | 0.788098 | + | 1.36503i | ||||
\(5\) | 176.989 | − | 102.185i | 0.283183 | − | 0.163496i | −0.351681 | − | 0.936120i | \(-0.614390\pi\) |
0.634863 | + | 0.772624i | \(0.281056\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1851.21 | − | 3206.39i | 0.771017 | − | 1.33544i | −0.165990 | − | 0.986127i | \(-0.553082\pi\) |
0.937006 | − | 0.349312i | \(-0.113585\pi\) | |||||||
\(8\) | − | 3788.08i | − | 0.924825i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5248.38 | −0.524838 | ||||||||
\(11\) | −13951.7 | − | 8054.99i | −0.952917 | − | 0.550167i | −0.0589310 | − | 0.998262i | \(-0.518769\pi\) |
−0.893986 | + | 0.448095i | \(0.852103\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18463.8 | + | 31980.2i | 0.646468 | + | 1.11972i | 0.983960 | + | 0.178387i | \(0.0570880\pi\) |
−0.337492 | + | 0.941328i | \(0.609579\pi\) | |||||||
\(14\) | −82342.9 | + | 47540.7i | −2.14345 | + | 1.23752i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3008.19 | − | 5210.35i | 0.0459014 | − | 0.0795036i | ||||
\(17\) | − | 47526.9i | − | 0.569041i | −0.958670 | − | 0.284520i | \(-0.908166\pi\) | ||
0.958670 | − | 0.284520i | \(-0.0918344\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 213962. | 1.64181 | 0.820904 | − | 0.571066i | \(-0.193470\pi\) | ||||
0.820904 | + | 0.571066i | \(0.193470\pi\) | |||||||
\(20\) | 71416.2 | + | 41232.2i | 0.446351 | + | 0.257701i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 206859. | + | 358290.i | 0.883047 | + | 1.52948i | ||||
\(23\) | 143902. | − | 83082.0i | 0.514229 | − | 0.296890i | −0.220342 | − | 0.975423i | \(-0.570717\pi\) |
0.734570 | + | 0.678533i | \(0.237384\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −174429. | + | 302120.i | −0.446538 | + | 0.773427i | ||||
\(26\) | − | 948331.i | − | 2.07523i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.49395e6 | 2.43055 | ||||||||
\(29\) | 1.17848e6 | + | 680393.i | 1.66621 | + | 0.961984i | 0.969655 | + | 0.244476i | \(0.0786161\pi\) |
0.696550 | + | 0.717508i | \(0.254717\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 109298. | + | 189309.i | 0.118349 | + | 0.204986i | 0.919114 | − | 0.393993i | \(-0.128907\pi\) |
−0.800765 | + | 0.598979i | \(0.795573\pi\) | |||||||
\(32\) | −973633. | + | 562128.i | −0.928529 | + | 0.536087i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −610265. | + | 1.05701e6i | −0.456670 | + | 0.790976i | ||||
\(35\) | − | 756662.i | − | 0.504231i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.15091e6 | 0.614093 | 0.307046 | − | 0.951695i | \(-0.400659\pi\) | ||||
0.307046 | + | 0.951695i | \(0.400659\pi\) | |||||||
\(38\) | −4.75857e6 | − | 2.74736e6i | −2.28214 | − | 1.31759i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −387084. | − | 670449.i | −0.151205 | − | 0.261894i | ||||
\(41\) | −643528. | + | 371541.i | −0.227736 | + | 0.131484i | −0.609527 | − | 0.792765i | \(-0.708641\pi\) |
0.381791 | + | 0.924249i | \(0.375307\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.46517e6 | − | 2.53774e6i | 0.428562 | − | 0.742291i | −0.568184 | − | 0.822902i | \(-0.692354\pi\) |
0.996746 | + | 0.0806110i | \(0.0256871\pi\) | |||||||
\(44\) | − | 6.50048e6i | − | 1.73434i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.26723e6 | −0.953048 | ||||||||
\(47\) | −6.31706e6 | − | 3.64716e6i | −1.29456 | − | 0.747417i | −0.315105 | − | 0.949057i | \(-0.602040\pi\) |
−0.979460 | + | 0.201640i | \(0.935373\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.97156e6 | − | 6.87895e6i | −0.688933 | − | 1.19327i | ||||
\(50\) | 7.75870e6 | − | 4.47949e6i | 1.24139 | − | 0.716718i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.45025e6 | + | 1.29042e7i | −1.01896 | + | 1.76489i | ||||
\(53\) | 2.55324e6i | 0.323585i | 0.986825 | + | 0.161792i | \(0.0517275\pi\) | ||||
−0.986825 | + | 0.161792i | \(0.948273\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.29239e6 | −0.359799 | ||||||||
\(56\) | −1.21461e7 | − | 7.01254e6i | −1.23505 | − | 0.713055i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.74731e7 | − | 3.02643e7i | −1.54404 | − | 2.67435i | ||||
\(59\) | 4.44279e6 | − | 2.56505e6i | 0.366647 | − | 0.211684i | −0.305346 | − | 0.952242i | \(-0.598772\pi\) |
0.671993 | + | 0.740558i | \(0.265439\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.34768e6 | − | 2.33425e6i | 0.0973346 | − | 0.168588i | −0.813246 | − | 0.581920i | \(-0.802302\pi\) |
0.910581 | + | 0.413332i | \(0.135635\pi\) | |||||||
\(62\) | − | 5.61372e6i | − | 0.379913i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.73316e7 | 1.62909 | ||||||||
\(65\) | 6.53578e6 | + | 3.77343e6i | 0.366137 | + | 0.211389i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −319308. | − | 553057.i | −0.0158456 | − | 0.0274455i | 0.857994 | − | 0.513660i | \(-0.171711\pi\) |
−0.873839 | + | 0.486214i | \(0.838377\pi\) | |||||||
\(68\) | 1.66081e7 | − | 9.58869e6i | 0.776755 | − | 0.448460i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −9.71586e6 | + | 1.68284e7i | −0.404659 | + | 0.700890i | ||||
\(71\) | − | 3.72932e7i | − | 1.46756i | −0.679387 | − | 0.733780i | \(-0.737754\pi\) | ||
0.679387 | − | 0.733780i | \(-0.262246\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.13898e7 | −0.753209 | −0.376604 | − | 0.926374i | \(-0.622908\pi\) | ||||
−0.376604 | + | 0.926374i | \(0.622908\pi\) | |||||||
\(74\) | −2.55965e7 | − | 1.47782e7i | −0.853599 | − | 0.492826i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.31675e7 | + | 7.47683e7i | 1.29391 | + | 2.24111i | ||||
\(77\) | −5.16549e7 | + | 2.98230e7i | −1.46943 | + | 0.848375i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.50309e7 | − | 4.33548e7i | 0.642641 | − | 1.11309i | −0.342200 | − | 0.939627i | \(-0.611172\pi\) |
0.984841 | − | 0.173460i | \(-0.0554946\pi\) | |||||||
\(80\) | − | 1.22957e6i | − | 0.0300187i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.90830e7 | 0.422076 | ||||||||
\(83\) | 2.83851e7 | + | 1.63882e7i | 0.598106 | + | 0.345317i | 0.768296 | − | 0.640094i | \(-0.221105\pi\) |
−0.170190 | + | 0.985411i | \(0.554438\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.85652e6 | − | 8.41174e6i | −0.0930357 | − | 0.161142i | ||||
\(86\) | −6.51714e7 | + | 3.76267e7i | −1.19142 | + | 0.687864i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.05130e7 | + | 5.28500e7i | −0.508808 | + | 0.881281i | ||||
\(89\) | − | 6.85873e6i | − | 0.109316i | −0.998505 | − | 0.0546580i | \(-0.982593\pi\) | ||
0.998505 | − | 0.0546580i | \(-0.0174069\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.36721e8 | 1.99375 | ||||||||
\(92\) | 5.80654e7 | + | 3.35241e7i | 0.810525 | + | 0.467957i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.36621e7 | + | 1.62228e8i | 1.19964 | + | 2.07785i | ||||
\(95\) | 3.78689e7 | − | 2.18636e7i | 0.464931 | − | 0.268428i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.14058e7 | − | 7.17170e7i | 0.467708 | − | 0.810093i | −0.531612 | − | 0.846988i | \(-0.678413\pi\) |
0.999319 | + | 0.0368950i | \(0.0117467\pi\) | |||||||
\(98\) | 2.03986e8i | 2.21155i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.40766e8 | −1.40766 | ||||||||
\(101\) | 1.71673e8 | + | 9.91154e7i | 1.64974 | + | 0.952480i | 0.977173 | + | 0.212447i | \(0.0681434\pi\) |
0.672571 | + | 0.740033i | \(0.265190\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.05983e8 | − | 1.83567e8i | −0.941641 | − | 1.63097i | −0.762340 | − | 0.647177i | \(-0.775950\pi\) |
−0.179302 | − | 0.983794i | \(-0.557384\pi\) | |||||||
\(104\) | 1.21144e8 | − | 6.99423e7i | 1.03554 | − | 0.597870i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.27847e7 | − | 5.67847e7i | 0.259685 | − | 0.449788i | ||||
\(107\) | − | 1.63763e8i | − | 1.24934i | −0.780887 | − | 0.624672i | \(-0.785233\pi\) | ||
0.780887 | − | 0.624672i | \(-0.214767\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.21458e8 | −1.56887 | −0.784434 | − | 0.620213i | \(-0.787046\pi\) | ||||
−0.784434 | + | 0.620213i | \(0.787046\pi\) | |||||||
\(110\) | 7.32236e7 | + | 4.22757e7i | 0.500127 | + | 0.288748i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.11376e7 | − | 1.92909e7i | −0.0707815 | − | 0.122597i | ||||
\(113\) | 6.14338e7 | − | 3.54688e7i | 0.376785 | − | 0.217537i | −0.299634 | − | 0.954054i | \(-0.596864\pi\) |
0.676418 | + | 0.736518i | \(0.263531\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.69794e7 | − | 2.94092e7i | 0.0970804 | − | 0.168148i | ||||
\(116\) | 5.49086e8i | 3.03255i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.31745e8 | −0.679527 | ||||||||
\(119\) | −1.52390e8 | − | 8.79822e7i | −0.759920 | − | 0.438740i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.25863e7 | + | 3.91207e7i | 0.105367 | + | 0.182501i | ||||
\(122\) | −5.99455e7 | + | 3.46096e7i | −0.270593 | + | 0.156227i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.41023e7 | + | 7.63875e7i | −0.186541 | + | 0.323099i | ||||
\(125\) | 1.51128e8i | 0.619019i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.24298e8 | −0.862205 | −0.431102 | − | 0.902303i | \(-0.641875\pi\) | ||||
−0.431102 | + | 0.902303i | \(0.641875\pi\) | |||||||
\(128\) | −3.58613e8 | − | 2.07045e8i | −1.33594 | − | 0.771303i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.69049e7 | − | 1.67844e8i | −0.339291 | − | 0.587669i | ||||
\(131\) | −3.07378e8 | + | 1.77465e8i | −1.04373 | + | 0.602596i | −0.920887 | − | 0.389830i | \(-0.872534\pi\) |
−0.122841 | + | 0.992426i | \(0.539200\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.96089e8 | − | 6.86046e8i | 1.26586 | − | 2.19254i | ||||
\(134\) | 1.64002e7i | 0.0508662i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.80036e8 | −0.526263 | ||||||||
\(137\) | 6.45816e7 | + | 3.72862e7i | 0.183327 | + | 0.105844i | 0.588855 | − | 0.808239i | \(-0.299579\pi\) |
−0.405528 | + | 0.914083i | \(0.632912\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.16583e6 | − | 7.21542e6i | −0.0111594 | − | 0.0193287i | 0.860392 | − | 0.509633i | \(-0.170219\pi\) |
−0.871551 | + | 0.490305i | \(0.836886\pi\) | |||||||
\(140\) | 2.64413e8 | − | 1.52659e8i | 0.688288 | − | 0.397383i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.78860e8 | + | 8.29410e8i | −1.17776 | + | 2.03993i | ||||
\(143\) | − | 5.94902e8i | − | 1.42266i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.78103e8 | 0.629121 | ||||||||
\(146\) | 4.75715e8 | + | 2.74654e8i | 1.04697 | + | 0.604470i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.32199e8 | + | 4.02181e8i | 0.483965 | + | 0.838252i | ||||
\(149\) | 5.91209e8 | − | 3.41334e8i | 1.19949 | − | 0.692524i | 0.239046 | − | 0.971008i | \(-0.423165\pi\) |
0.960441 | + | 0.278484i | \(0.0898319\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.08390e7 | + | 1.05376e8i | −0.117024 | + | 0.202691i | −0.918587 | − | 0.395219i | \(-0.870669\pi\) |
0.801563 | + | 0.597910i | \(0.204002\pi\) | |||||||
\(152\) | − | 8.10506e8i | − | 1.51838i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.53176e9 | 2.72338 | ||||||||
\(155\) | 3.86890e7 | + | 2.23371e7i | 0.0670288 | + | 0.0386991i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.73425e7 | + | 6.46792e7i | 0.0614618 | + | 0.106455i | 0.895119 | − | 0.445827i | \(-0.147090\pi\) |
−0.833657 | + | 0.552282i | \(0.813757\pi\) | |||||||
\(158\) | −1.11339e9 | + | 6.42815e8i | −1.78656 | + | 1.03147i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.14882e8 | + | 1.98981e8i | −0.175296 | + | 0.303621i | ||||
\(161\) | − | 6.15209e8i | − | 0.915628i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.65546e8 | 0.801157 | 0.400578 | − | 0.916262i | \(-0.368809\pi\) | ||||
0.400578 | + | 0.916262i | \(0.368809\pi\) | |||||||
\(164\) | −2.59667e8 | − | 1.49919e8i | −0.358957 | − | 0.207244i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.20862e8 | − | 7.28954e8i | −0.554252 | − | 0.959992i | ||||
\(167\) | 2.18287e8 | − | 1.26028e8i | 0.280648 | − | 0.162032i | −0.353069 | − | 0.935597i | \(-0.614862\pi\) |
0.633717 | + | 0.773565i | \(0.281529\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.73957e8 | + | 4.74507e8i | −0.335842 | + | 0.581696i | ||||
\(170\) | 2.49439e8i | 0.298654i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.18241e9 | 1.35099 | ||||||||
\(173\) | 2.42772e8 | + | 1.40164e8i | 0.271028 | + | 0.156478i | 0.629355 | − | 0.777118i | \(-0.283319\pi\) |
−0.358327 | + | 0.933596i | \(0.616653\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.45810e8 | + | 1.11858e9i | 0.688577 | + | 1.19265i | ||||
\(176\) | −8.39386e7 | + | 4.84620e7i | −0.0874804 | + | 0.0505069i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.80690e7 | + | 1.52540e8i | −0.0877290 | + | 0.151951i | ||||
\(179\) | − | 4.01384e8i | − | 0.390974i | −0.980706 | − | 0.195487i | \(-0.937371\pi\) | ||
0.980706 | − | 0.195487i | \(-0.0626287\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.39158e9 | −1.29657 | −0.648284 | − | 0.761399i | \(-0.724513\pi\) | ||||
−0.648284 | + | 0.761399i | \(0.724513\pi\) | |||||||
\(182\) | −3.04072e9 | − | 1.75556e9i | −2.77135 | − | 1.60004i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.14721e8 | − | 5.45113e8i | −0.274571 | − | 0.475571i | ||||
\(185\) | 2.03698e8 | − | 1.17605e8i | 0.173900 | − | 0.100401i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.82829e8 | + | 6.63078e8i | −0.313067 | + | 0.542249i | ||||
\(188\) | − | 2.94330e9i | − | 2.35615i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.12295e9 | −0.861683 | ||||||||
\(191\) | 1.47287e8 | + | 8.50360e7i | 0.110670 | + | 0.0638953i | 0.554313 | − | 0.832308i | \(-0.312981\pi\) |
−0.443643 | + | 0.896203i | \(0.646314\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.90945e8 | + | 5.03932e8i | 0.209692 | + | 0.363198i | 0.951618 | − | 0.307285i | \(-0.0994205\pi\) |
−0.741925 | + | 0.670483i | \(0.766087\pi\) | |||||||
\(194\) | −1.84175e9 | + | 1.06334e9i | −1.30024 | + | 0.750695i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.60255e9 | − | 2.77570e9i | 1.08589 | − | 1.88082i | ||||
\(197\) | 1.19043e9i | 0.790385i | 0.918598 | + | 0.395193i | \(0.129322\pi\) | ||||
−0.918598 | + | 0.395193i | \(0.870678\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.88525e9 | −1.20214 | −0.601071 | − | 0.799196i | \(-0.705259\pi\) | ||||
−0.601071 | + | 0.799196i | \(0.705259\pi\) | |||||||
\(200\) | 1.14446e9 | + | 6.60752e8i | 0.715285 | + | 0.412970i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.54537e9 | − | 4.40871e9i | −1.52878 | − | 2.64793i | ||||
\(203\) | 4.36321e9 | − | 2.51910e9i | 2.56934 | − | 1.48341i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.59316e7 | + | 1.31517e8i | −0.0429939 | + | 0.0744677i | ||||
\(206\) | 5.44345e9i | 3.02277i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.22171e8 | 0.118695 | ||||||||
\(209\) | −2.98512e9 | − | 1.72346e9i | −1.56451 | − | 0.903268i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.98576e8 | + | 3.43944e8i | 0.100184 | + | 0.173524i | 0.911760 | − | 0.410723i | \(-0.134724\pi\) |
−0.811576 | + | 0.584246i | \(0.801390\pi\) | |||||||
\(212\) | −8.92220e8 | + | 5.15123e8i | −0.441701 | + | 0.255016i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.10279e9 | + | 3.64214e9i | −1.00263 | + | 1.73661i | ||||
\(215\) | − | 5.98871e8i | − | 0.280272i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.09333e8 | 0.364996 | ||||||||
\(218\) | 4.92530e9 | + | 2.84362e9i | 2.18075 | + | 1.25906i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.64249e8 | − | 1.15051e9i | −0.283557 | − | 0.491135i | ||||
\(221\) | 1.51992e9 | − | 8.77526e8i | 0.637164 | − | 0.367867i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.30529e8 | − | 1.61172e9i | 0.376279 | − | 0.651735i | −0.614238 | − | 0.789121i | \(-0.710537\pi\) |
0.990518 | + | 0.137386i | \(0.0438699\pi\) | |||||||
\(224\) | 4.16247e9i | 1.65333i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.82174e9 | −0.698316 | ||||||||
\(227\) | 1.89595e9 | + | 1.09463e9i | 0.714041 | + | 0.412252i | 0.812556 | − | 0.582884i | \(-0.198076\pi\) |
−0.0985143 | + | 0.995136i | \(0.531409\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.07525e9 | + | 1.86238e9i | 0.390990 | + | 0.677215i | 0.992580 | − | 0.121590i | \(-0.0387993\pi\) |
−0.601590 | + | 0.798805i | \(0.705466\pi\) | |||||||
\(230\) | −7.55254e8 | + | 4.36046e8i | −0.269887 | + | 0.155819i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.57739e9 | − | 4.46416e9i | 0.889667 | − | 1.54095i | ||||
\(233\) | − | 3.41313e9i | − | 1.15805i | −0.815308 | − | 0.579027i | \(-0.803433\pi\) | ||
0.815308 | − | 0.579027i | \(-0.196567\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.49074e9 | −0.488798 | ||||||||
\(236\) | 1.79269e9 | + | 1.03501e9i | 0.577907 | + | 0.333655i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.25946e9 | + | 3.91350e9i | 0.704201 | + | 1.21971i | ||||
\(239\) | −2.84547e9 | + | 1.64283e9i | −0.872091 | + | 0.503502i | −0.868042 | − | 0.496490i | \(-0.834622\pi\) |
−0.00404838 | + | 0.999992i | \(0.501289\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.01741e9 | + | 3.49426e9i | −0.598035 | + | 1.03583i | 0.395076 | + | 0.918648i | \(0.370718\pi\) |
−0.993111 | + | 0.117178i | \(0.962615\pi\) | |||||||
\(242\) | − | 1.16007e9i | − | 0.338239i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.08759e9 | 0.306837 | ||||||||
\(245\) | −1.40585e9 | − | 8.11666e8i | −0.390188 | − | 0.225275i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.95055e9 | + | 6.84255e9i | 1.06138 | + | 1.83836i | ||||
\(248\) | 7.17119e8 | − | 4.14029e8i | 0.189577 | − | 0.109452i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.94054e9 | − | 3.36112e9i | 0.496779 | − | 0.860447i | ||||
\(251\) | 4.69477e9i | 1.18282i | 0.806371 | + | 0.591411i | \(0.201429\pi\) | ||||
−0.806371 | + | 0.591411i | \(0.798571\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.67690e9 | −0.653356 | ||||||||
\(254\) | 4.98845e9 | + | 2.88008e9i | 1.19848 | + | 0.691942i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.81865e9 | + | 3.14999e9i | 0.423437 | + | 0.733414i | ||||
\(257\) | −1.10426e8 | + | 6.37546e7i | −0.0253128 | + | 0.0146143i | −0.512603 | − | 0.858626i | \(-0.671319\pi\) |
0.487290 | + | 0.873240i | \(0.337985\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.13057e9 | − | 3.69026e9i | 0.473476 | − | 0.820084i | ||||
\(260\) | 3.04521e9i | 0.666382i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.11488e9 | 1.93440 | ||||||||
\(263\) | −2.01039e9 | − | 1.16070e9i | −0.420201 | − | 0.242603i | 0.274962 | − | 0.961455i | \(-0.411335\pi\) |
−0.695163 | + | 0.718852i | \(0.744668\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.60902e8 | + | 4.51895e8i | 0.0529046 | + | 0.0916335i | ||||
\(266\) | −1.76182e10 | + | 1.01719e10i | −3.51914 | + | 2.03177i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.28843e8 | − | 2.23162e8i | 0.0249758 | − | 0.0432594i | ||||
\(269\) | − | 7.86019e9i | − | 1.50115i | −0.660785 | − | 0.750575i | \(-0.729777\pi\) | ||
0.660785 | − | 0.750575i | \(-0.270223\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.14381e9 | 0.397474 | 0.198737 | − | 0.980053i | \(-0.436316\pi\) | ||||
0.198737 | + | 0.980053i | \(0.436316\pi\) | |||||||
\(272\) | −2.47631e8 | − | 1.42970e8i | −0.0452408 | − | 0.0261198i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.57541e8 | − | 1.65851e9i | −0.169885 | − | 0.294249i | ||||
\(275\) | 4.86715e9 | − | 2.81005e9i | 0.851028 | − | 0.491341i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.87519e8 | + | 6.71202e8i | −0.0658224 | + | 0.114008i | −0.897059 | − | 0.441912i | \(-0.854300\pi\) |
0.831236 | + | 0.555920i | \(0.187634\pi\) | |||||||
\(278\) | 2.13964e8i | 0.0358229i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.86630e9 | −0.466325 | ||||||||
\(281\) | 6.89145e9 | + | 3.97878e9i | 1.10531 | + | 0.638153i | 0.937611 | − | 0.347685i | \(-0.113032\pi\) |
0.167702 | + | 0.985838i | \(0.446366\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.79004e8 | − | 1.69568e9i | −0.152630 | − | 0.264362i | 0.779564 | − | 0.626323i | \(-0.215441\pi\) |
−0.932193 | + | 0.361961i | \(0.882107\pi\) | |||||||
\(284\) | 1.30320e10 | − | 7.52401e9i | 2.00326 | − | 1.15658i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.63880e9 | + | 1.32308e10i | −1.14172 | + | 1.97752i | ||||
\(287\) | 2.75120e9i | 0.405504i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.71695e9 | 0.676192 | ||||||||
\(290\) | −6.18509e9 | − | 3.57096e9i | −0.874488 | − | 0.504886i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.31546e9 | − | 7.47459e9i | −0.593602 | − | 1.02815i | ||||
\(293\) | 1.07304e10 | − | 6.19523e9i | 1.45595 | − | 0.840595i | 0.457144 | − | 0.889393i | \(-0.348872\pi\) |
0.998809 | + | 0.0487979i | \(0.0155390\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.24217e8 | − | 9.07971e8i | 0.0692187 | − | 0.119890i | ||||
\(296\) | − | 4.35974e9i | − | 0.567928i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.75315e10 | −2.22308 | ||||||||
\(299\) | 5.31396e9 | + | 3.06801e9i | 0.664865 | + | 0.383860i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.42467e9 | − | 9.39580e9i | −0.660856 | − | 1.14464i | ||||
\(302\) | 2.70615e9 | − | 1.56240e9i | 0.325330 | − | 0.187829i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.43639e8 | − | 1.11482e9i | 0.0753613 | − | 0.130530i | ||||
\(305\) | − | 5.50849e8i | − | 0.0636551i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.61263e8 | −0.0406696 | −0.0203348 | − | 0.999793i | \(-0.506473\pi\) | ||||
−0.0203348 | + | 0.999793i | \(0.506473\pi\) | |||||||
\(308\) | −2.08431e10 | − | 1.20338e10i | −2.31611 | − | 1.33721i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.73636e8 | − | 9.93567e8i | −0.0621141 | − | 0.107585i | ||||
\(311\) | −4.51507e9 | + | 2.60677e9i | −0.482639 | + | 0.278652i | −0.721516 | − | 0.692398i | \(-0.756554\pi\) |
0.238876 | + | 0.971050i | \(0.423221\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.25733e9 | − | 1.25701e10i | 0.756136 | − | 1.30967i | −0.188672 | − | 0.982040i | \(-0.560418\pi\) |
0.944808 | − | 0.327625i | \(-0.106248\pi\) | |||||||
\(314\) | − | 1.91798e9i | − | 0.197299i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.02003e10 | 2.02586 | ||||||||
\(317\) | −9.91318e9 | − | 5.72338e9i | −0.981694 | − | 0.566781i | −0.0789126 | − | 0.996882i | \(-0.525145\pi\) |
−0.902781 | + | 0.430100i | \(0.858478\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.09611e10 | − | 1.89852e10i | −1.05850 | − | 1.83338i | ||||
\(320\) | 4.83740e9 | − | 2.79287e9i | 0.461331 | − | 0.266349i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.89955e9 | + | 1.36824e10i | −0.734816 | + | 1.27274i | ||||
\(323\) | − | 1.01689e10i | − | 0.934256i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.28825e10 | −1.15469 | ||||||||
\(326\) | −1.25779e10 | − | 7.26185e9i | −1.11362 | − | 0.642950i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.40743e9 | + | 2.43774e9i | 0.121599 | + | 0.210616i | ||||
\(329\) | −2.33884e10 | + | 1.35033e10i | −1.99626 | + | 1.15254i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.60298e9 | + | 1.14367e10i | −0.550083 | + | 0.952771i | 0.448185 | + | 0.893941i | \(0.352071\pi\) |
−0.998268 | + | 0.0588306i | \(0.981263\pi\) | |||||||
\(332\) | 1.32254e10i | 1.08857i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.47301e9 | −0.520140 | ||||||||
\(335\) | −1.13028e8 | − | 6.52567e7i | −0.00897442 | − | 0.00518139i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.96753e9 | + | 1.03361e10i | 0.462674 | + | 0.801375i | 0.999093 | − | 0.0425770i | \(-0.0135568\pi\) |
−0.536419 | + | 0.843952i | \(0.680223\pi\) | |||||||
\(338\) | 1.21857e10 | − | 7.03544e9i | 0.933653 | − | 0.539045i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.95964e9 | − | 3.39419e9i | 0.146642 | − | 0.253992i | ||||
\(341\) | − | 3.52157e9i | − | 0.260447i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.06507e9 | −0.582682 | ||||||||
\(344\) | −9.61318e9 | − | 5.55017e9i | −0.686489 | − | 0.396344i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.59954e9 | − | 6.23458e9i | −0.251155 | − | 0.435014i | ||||
\(347\) | −7.95396e9 | + | 4.59222e9i | −0.548612 | + | 0.316741i | −0.748562 | − | 0.663065i | \(-0.769255\pi\) |
0.199950 | + | 0.979806i | \(0.435922\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.04434e10 | − | 1.80886e10i | 0.703950 | − | 1.21928i | −0.263119 | − | 0.964763i | \(-0.584751\pi\) |
0.967069 | − | 0.254514i | \(-0.0819155\pi\) | |||||||
\(350\) | − | 3.31699e10i | − | 2.21041i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.81117e10 | 1.17975 | ||||||||
\(353\) | 9.50403e9 | + | 5.48716e9i | 0.612081 | + | 0.353385i | 0.773780 | − | 0.633455i | \(-0.218364\pi\) |
−0.161698 | + | 0.986840i | \(0.551697\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.81079e9 | − | 6.60049e9i | −0.239940 | − | 0.415588i | ||||
\(356\) | 2.39676e9 | − | 1.38377e9i | 0.149219 | − | 0.0861517i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.15394e9 | + | 8.92688e9i | −0.313767 | + | 0.543460i | ||||
\(359\) | − | 1.19761e10i | − | 0.721001i | −0.932759 | − | 0.360501i | \(-0.882606\pi\) | ||
0.932759 | − | 0.360501i | \(-0.117394\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.87962e10 | 1.69553 | ||||||||
\(362\) | 3.09492e10 | + | 1.78685e10i | 1.80225 | + | 1.04053i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.75840e10 | + | 4.77768e10i | 1.57127 | + | 2.72152i | ||||
\(365\) | −3.78576e9 | + | 2.18571e9i | −0.213296 | + | 0.123146i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.11074e9 | − | 5.38796e9i | 0.171474 | − | 0.297002i | −0.767461 | − | 0.641096i | \(-0.778480\pi\) |
0.938936 | + | 0.344093i | \(0.111814\pi\) | |||||||
\(368\) | − | 9.99707e8i | − | 0.0545107i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.04041e9 | −0.322299 | ||||||||
\(371\) | 8.18668e9 | + | 4.72658e9i | 0.432128 | + | 0.249489i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.15140e9 | + | 1.06545e10i | 0.317789 | + | 0.550427i | 0.980026 | − | 0.198867i | \(-0.0637263\pi\) |
−0.662237 | + | 0.749294i | \(0.730393\pi\) | |||||||
\(374\) | 1.70284e10 | − | 9.83136e9i | 0.870338 | − | 0.502490i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.38157e10 | + | 2.39296e10i | −0.691230 | + | 1.19725i | ||||
\(377\) | 5.02505e10i | 2.48757i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.26268e10 | 1.09665 | 0.548324 | − | 0.836266i | \(-0.315266\pi\) | ||||
0.548324 | + | 0.836266i | \(0.315266\pi\) | |||||||
\(380\) | 1.52804e10 | + | 8.82212e9i | 0.732823 | + | 0.423095i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.18380e9 | − | 3.78245e9i | −0.102555 | − | 0.177631i | ||||
\(383\) | 9.94555e9 | − | 5.74206e9i | 0.462204 | − | 0.266854i | −0.250767 | − | 0.968048i | \(-0.580683\pi\) |
0.712971 | + | 0.701194i | \(0.247349\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.09490e9 | + | 1.05567e10i | −0.277411 | + | 0.480490i | ||||
\(386\) | − | 1.49435e10i | − | 0.673134i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.34150e10 | 1.47440 | ||||||||
\(389\) | 6.51932e8 | + | 3.76393e8i | 0.0284711 | + | 0.0164378i | 0.514168 | − | 0.857690i | \(-0.328101\pi\) |
−0.485697 | + | 0.874127i | \(0.661434\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.94863e9 | − | 6.83922e9i | −0.168943 | − | 0.292617i | ||||
\(392\) | −2.60580e10 | + | 1.50446e10i | −1.10356 | + | 0.637142i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.52856e10 | − | 2.64755e10i | 0.634305 | − | 1.09865i | ||||
\(395\) | − | 1.02311e10i | − | 0.420276i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.67666e9 | −0.228524 | −0.114262 | − | 0.993451i | \(-0.536450\pi\) | ||||
−0.114262 | + | 0.993451i | \(0.536450\pi\) | |||||||
\(398\) | 4.19284e10 | + | 2.42074e10i | 1.67100 | + | 0.964751i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.04943e9 | + | 1.81767e9i | 0.0409935 | + | 0.0710028i | ||||
\(401\) | −3.63092e10 | + | 2.09631e10i | −1.40423 | + | 0.810735i | −0.994824 | − | 0.101615i | \(-0.967599\pi\) |
−0.409410 | + | 0.912350i | \(0.634266\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.03610e9 | + | 6.99073e9i | −0.153018 | + | 0.265034i | ||||
\(404\) | 7.99874e10i | 3.00259i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.29385e11 | −4.76191 | ||||||||
\(407\) | −1.60571e10 | − | 9.27056e9i | −0.585179 | − | 0.337853i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.25068e10 | − | 2.16625e10i | −0.446946 | − | 0.774133i | 0.551240 | − | 0.834347i | \(-0.314155\pi\) |
−0.998185 | + | 0.0602143i | \(0.980822\pi\) | |||||||
\(410\) | 3.37748e9 | − | 1.94999e9i | 0.119525 | − | 0.0690075i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.27646e10 | − | 7.40705e10i | 1.48421 | − | 2.57073i | ||||
\(413\) | − | 1.89938e10i | − | 0.652846i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.69848e9 | 0.225831 | ||||||||
\(416\) | −3.59539e10 | − | 2.07580e10i | −1.20053 | − | 0.693126i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.42600e10 | + | 7.66605e10i | 1.44979 | + | 2.51112i | ||||
\(419\) | −4.37377e9 | + | 2.52520e9i | −0.141906 | + | 0.0819294i | −0.569272 | − | 0.822149i | \(-0.692775\pi\) |
0.427366 | + | 0.904079i | \(0.359442\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.11594e9 | + | 1.23252e10i | −0.226519 | + | 0.392342i | −0.956774 | − | 0.290832i | \(-0.906068\pi\) |
0.730255 | + | 0.683174i | \(0.239401\pi\) | |||||||
\(422\) | − | 1.01992e10i | − | 0.321601i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.67187e9 | 0.299259 | ||||||||
\(425\) | 1.43588e10 | + | 8.29007e9i | 0.440112 | + | 0.254099i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.98968e9 | − | 8.64237e9i | −0.150093 | − | 0.259969i | ||||
\(428\) | 5.72266e10 | − | 3.30398e10i | 1.70539 | − | 0.984605i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.68975e9 | + | 1.33190e10i | −0.224925 | + | 0.389582i | ||||
\(431\) | 3.72124e10i | 1.07840i | 0.842179 | + | 0.539199i | \(0.181273\pi\) | ||||
−0.842179 | + | 0.539199i | \(0.818727\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.76284e10 | −1.07044 | −0.535222 | − | 0.844711i | \(-0.679772\pi\) | ||||
−0.535222 | + | 0.844711i | \(0.679772\pi\) | |||||||
\(434\) | −1.79998e10 | − | 1.03922e10i | −0.507351 | − | 0.292919i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.46799e10 | − | 7.73879e10i | −1.23642 | − | 2.14154i | ||||
\(437\) | 3.07896e10 | − | 1.77764e10i | 0.844264 | − | 0.487436i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.68277e9 | + | 4.64669e9i | −0.0722312 | + | 0.125108i | −0.899879 | − | 0.436140i | \(-0.856345\pi\) |
0.827648 | + | 0.561248i | \(0.189679\pi\) | |||||||
\(440\) | 1.24718e10i | 0.332751i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.50712e10 | −1.18089 | ||||||||
\(443\) | −2.08109e10 | − | 1.20152e10i | −0.540350 | − | 0.311971i | 0.204871 | − | 0.978789i | \(-0.434323\pi\) |
−0.745221 | + | 0.666818i | \(0.767656\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.00857e8 | − | 1.21392e9i | −0.0178727 | − | 0.0309564i | ||||
\(446\) | −4.13904e10 | + | 2.38968e10i | −1.04607 | + | 0.603949i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.05966e10 | − | 8.76359e10i | 1.25606 | − | 2.17555i | ||||
\(449\) | 7.28050e10i | 1.79133i | 0.444729 | + | 0.895665i | \(0.353300\pi\) | ||||
−0.444729 | + | 0.895665i | \(0.646700\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.19710e10 | 0.289351 | ||||||||
\(452\) | 2.47889e10 | + | 1.43119e10i | 0.593886 | + | 0.342881i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.81110e10 | − | 4.86896e10i | −0.661686 | − | 1.14607i | ||||
\(455\) | 2.41982e10 | − | 1.39708e10i | 0.564595 | − | 0.325969i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.09877e10 | + | 5.36723e10i | −0.710436 | + | 1.23051i | 0.254258 | + | 0.967137i | \(0.418169\pi\) |
−0.964694 | + | 0.263375i | \(0.915164\pi\) | |||||||
\(458\) | − | 5.52265e10i | − | 1.25512i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.37026e10 | 0.306035 | ||||||||
\(461\) | −1.04284e10 | − | 6.02087e9i | −0.230896 | − | 0.133308i | 0.380090 | − | 0.924950i | \(-0.375893\pi\) |
−0.610985 | + | 0.791642i | \(0.709227\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.96311e9 | + | 5.13225e9i | 0.0644797 | + | 0.111682i | 0.896463 | − | 0.443118i | \(-0.146128\pi\) |
−0.831983 | + | 0.554801i | \(0.812795\pi\) | |||||||
\(464\) | 7.09017e9 | − | 4.09351e9i | 0.152962 | − | 0.0883129i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.38260e10 | + | 7.59089e10i | −0.929369 | + | 1.60971i | ||||
\(467\) | 5.80782e10i | 1.22109i | 0.791983 | + | 0.610543i | \(0.209049\pi\) | ||||
−0.791983 | + | 0.610543i | \(0.790951\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.36442e9 | −0.0488690 | ||||||||
\(470\) | 3.31544e10 | + | 1.91417e10i | 0.679437 | + | 0.392273i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.71661e9 | − | 1.68297e10i | −0.195770 | − | 0.339084i | ||||
\(473\) | −4.08830e10 | + | 2.36038e10i | −0.816767 | + | 0.471561i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.73212e10 | + | 6.46422e10i | −0.733130 | + | 1.26982i | ||||
\(476\) | − | 7.10027e10i | − | 1.38308i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.43786e10 | 1.61629 | ||||||||
\(479\) | 3.99551e10 | + | 2.30681e10i | 0.758980 | + | 0.438197i | 0.828929 | − | 0.559353i | \(-0.188950\pi\) |
−0.0699495 | + | 0.997551i | \(0.522284\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.12501e10 | + | 3.68063e10i | 0.396991 | + | 0.687609i | ||||
\(482\) | 8.97356e10 | − | 5.18088e10i | 1.66256 | − | 0.959877i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.11372e9 | + | 1.57854e10i | −0.166079 | + | 0.287657i | ||||
\(485\) | − | 1.69242e10i | − | 0.305872i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.55813e10 | 1.52147 | 0.760735 | − | 0.649063i | \(-0.224839\pi\) | ||||
0.760735 | + | 0.649063i | \(0.224839\pi\) | |||||||
\(488\) | −8.84233e9 | − | 5.10512e9i | −0.155915 | − | 0.0900174i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.08443e10 | + | 3.61033e10i | 0.361578 | + | 0.626272i | ||||
\(491\) | −2.58098e10 | + | 1.49013e10i | −0.444077 | + | 0.256388i | −0.705326 | − | 0.708884i | \(-0.749199\pi\) |
0.261248 | + | 0.965272i | \(0.415866\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.23370e10 | − | 5.60093e10i | 0.547408 | − | 0.948139i | ||||
\(494\) | − | 2.02907e11i | − | 3.40713i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.31516e9 | 0.0217295 | ||||||||
\(497\) | −1.19576e11 | − | 6.90375e10i | −1.95984 | − | 1.13151i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.57266e10 | + | 4.45598e10i | 0.414936 | + | 0.718690i | 0.995422 | − | 0.0955806i | \(-0.0304708\pi\) |
−0.580486 | + | 0.814270i | \(0.697137\pi\) | |||||||
\(500\) | −5.28111e10 | + | 3.04905e10i | −0.844977 | + | 0.487848i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.02828e10 | − | 1.04413e11i | 0.949246 | − | 1.64414i | ||||
\(503\) | − | 1.97425e10i | − | 0.308412i | −0.988039 | − | 0.154206i | \(-0.950718\pi\) | ||
0.988039 | − | 0.154206i | \(-0.0492819\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.05123e10 | 0.622905 | ||||||||
\(506\) | 5.95350e10 | + | 3.43725e10i | 0.908176 | + | 0.524336i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.52528e10 | − | 7.83801e10i | −0.679502 | − | 1.17693i | ||||
\(509\) | −2.46734e10 | + | 1.42452e10i | −0.367586 | + | 0.212226i | −0.672403 | − | 0.740185i | \(-0.734738\pi\) |
0.304817 | + | 0.952411i | \(0.401405\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.95970e10 | + | 6.85841e10i | −0.580736 | + | 1.00586i | ||||
\(512\) | 1.25983e10i | 0.183330i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.27455e9 | 0.0469136 | ||||||||
\(515\) | −3.75155e10 | − | 2.16596e10i | −0.533313 | − | 0.307908i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.87557e10 | + | 1.01768e11i | 0.822408 | + | 1.42445i | ||||
\(518\) | −9.47691e10 | + | 5.47150e10i | −1.31628 | + | 0.759954i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.42941e10 | − | 2.47581e10i | 0.195498 | − | 0.338613i | ||||
\(521\) | − | 1.19310e11i | − | 1.61929i | −0.586919 | − | 0.809646i | \(-0.699659\pi\) | ||
0.586919 | − | 0.809646i | \(-0.300341\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.33461e10 | −1.11398 | −0.556992 | − | 0.830518i | \(-0.688044\pi\) | ||||
−0.556992 | + | 0.830518i | \(0.688044\pi\) | |||||||
\(524\) | −1.24029e11 | − | 7.16081e10i | −1.64512 | − | 0.949810i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.98077e10 | + | 5.16285e10i | 0.389391 | + | 0.674445i | ||||
\(527\) | 8.99728e9 | − | 5.19458e9i | 0.116646 | − | 0.0673454i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.53503e10 | + | 4.39079e10i | −0.323713 | + | 0.560687i | ||||
\(530\) | − | 1.34004e10i | − | 0.169829i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.19648e11 | 3.99049 | ||||||||
\(533\) | −2.37639e10 | − | 1.37201e10i | −0.294448 | − | 0.170000i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.67341e10 | − | 2.89843e10i | −0.204262 | − | 0.353792i | ||||
\(536\) | −2.09503e9 | + | 1.20956e9i | −0.0253822 | + | 0.0146544i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.00928e11 | + | 1.74813e11i | −1.20471 | + | 2.08662i | ||||
\(539\) | 1.27964e11i | 1.51611i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.38210e11 | −1.61343 | −0.806717 | − | 0.590937i | \(-0.798758\pi\) | ||||
−0.806717 | + | 0.590937i | \(0.798758\pi\) | |||||||
\(542\) | −4.76789e10 | − | 2.75274e10i | −0.552495 | − | 0.318983i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.67162e10 | + | 4.62737e10i | 0.305055 | + | 0.528371i | ||||
\(545\) | −3.91957e10 | + | 2.26297e10i | −0.444276 | + | 0.256503i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.95682e10 | − | 6.85341e10i | 0.441974 | − | 0.765522i | −0.555862 | − | 0.831275i | \(-0.687612\pi\) |
0.997836 | + | 0.0657529i | \(0.0209449\pi\) | |||||||
\(548\) | 3.00904e10i | 0.333661i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.44329e11 | −1.57726 | ||||||||
\(551\) | 2.52149e11 | + | 1.45578e11i | 2.73559 | + | 1.57939i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.26750e10 | − | 1.60518e11i | −0.990974 | − | 1.71642i | ||||
\(554\) | 1.72370e10 | − | 9.95182e9i | 0.182989 | − | 0.105648i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.68094e9 | − | 2.91147e9i | 0.0175894 | − | 0.0304658i | ||||
\(557\) | − | 1.12395e11i | − | 1.16769i | −0.811865 | − | 0.583846i | \(-0.801547\pi\) | ||
0.811865 | − | 0.583846i | \(-0.198453\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.08210e11 | 1.10821 | ||||||||
\(560\) | −3.94247e9 | − | 2.27619e9i | −0.0400882 | − | 0.0231449i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.02178e11 | − | 1.76978e11i | −1.02427 | − | 1.77409i | ||||
\(563\) | 1.03943e11 | − | 6.00113e10i | 1.03457 | − | 0.597310i | 0.116280 | − | 0.993216i | \(-0.462903\pi\) |
0.918291 | + | 0.395906i | \(0.129570\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.24874e9 | − | 1.25552e10i | 0.0711326 | − | 0.123205i | ||||
\(566\) | 5.02833e10i | 0.489957i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.41270e11 | −1.35724 | ||||||||
\(569\) | −1.32890e11 | − | 7.67240e10i | −1.26778 | − | 0.731951i | −0.293210 | − | 0.956048i | \(-0.594723\pi\) |
−0.974567 | + | 0.224097i | \(0.928057\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.33391e10 | − | 4.04245e10i | −0.219553 | − | 0.380277i | 0.735118 | − | 0.677939i | \(-0.237127\pi\) |
−0.954671 | + | 0.297662i | \(0.903793\pi\) | |||||||
\(572\) | 2.07887e11 | − | 1.20023e11i | 1.94197 | − | 1.12120i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.53266e10 | − | 6.11875e10i | 0.325428 | − | 0.563657i | ||||
\(575\) | 5.79677e10i | 0.530291i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.25710e10 | 0.835164 | 0.417582 | − | 0.908639i | \(-0.362878\pi\) | ||||
0.417582 | + | 0.908639i | \(0.362878\pi\) | |||||||
\(578\) | −1.04906e11 | − | 6.05677e10i | −0.939919 | − | 0.542662i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.61082e10 | + | 9.71822e10i | 0.495809 | + | 0.858766i | ||||
\(581\) | 1.05094e11 | − | 6.06759e10i | 0.922300 | − | 0.532490i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.05663e10 | − | 3.56219e10i | 0.178025 | − | 0.308349i | ||||
\(584\) | 8.10263e10i | 0.696586i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.18197e11 | −2.69840 | ||||||||
\(587\) | 6.72211e10 | + | 3.88101e10i | 0.566178 | + | 0.326883i | 0.755621 | − | 0.655009i | \(-0.227335\pi\) |
−0.189443 | + | 0.981892i | \(0.560668\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.33856e10 | + | 4.05050e10i | 0.194306 | + | 0.336548i | ||||
\(590\) | −2.33175e10 | + | 1.34623e10i | −0.192430 | + | 0.111100i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.46216e9 | − | 5.99663e9i | 0.0281877 | − | 0.0488226i | ||||
\(593\) | 2.09190e11i | 1.69169i | 0.533427 | + | 0.845846i | \(0.320904\pi\) | ||||
−0.533427 | + | 0.845846i | \(0.679096\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.59618e10 | −0.286928 | ||||||||
\(596\) | 2.38556e11 | + | 1.37731e11i | 1.89063 | + | 1.09155i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.87892e10 | − | 1.36467e11i | −0.616116 | − | 1.06714i | ||||
\(599\) | 8.07861e10 | − | 4.66419e10i | 0.627523 | − | 0.362300i | −0.152269 | − | 0.988339i | \(-0.548658\pi\) |
0.779792 | + | 0.626039i | \(0.215325\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.06269e10 | − | 7.03678e10i | 0.311398 | − | 0.539357i | −0.667267 | − | 0.744818i | \(-0.732536\pi\) |
0.978665 | + | 0.205461i | \(0.0658695\pi\) | |||||||
\(602\) | 2.78620e11i | 2.12142i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.90978e10 | −0.368905 | ||||||||
\(605\) | 7.99507e9 | + | 4.61596e9i | 0.0596762 | + | 0.0344540i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.06162e10 | − | 3.57084e10i | −0.151864 | − | 0.263036i | 0.780049 | − | 0.625719i | \(-0.215194\pi\) |
−0.931913 | + | 0.362683i | \(0.881861\pi\) | |||||||
\(608\) | −2.08321e11 | + | 1.20274e11i | −1.52447 | + | 0.880151i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.07313e9 | + | 1.22510e10i | −0.0510849 | + | 0.0884816i | ||||
\(611\) | − | 2.69361e11i | − | 1.93273i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.01264e10 | 0.142536 | 0.0712681 | − | 0.997457i | \(-0.477295\pi\) | ||||
0.0712681 | + | 0.997457i | \(0.477295\pi\) | |||||||
\(614\) | 8.03459e9 | + | 4.63877e9i | 0.0565315 | + | 0.0326385i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.12972e11 | + | 1.95673e11i | 0.784599 | + | 1.35896i | ||||
\(617\) | −1.18902e11 | + | 6.86484e10i | −0.820446 | + | 0.473685i | −0.850570 | − | 0.525861i | \(-0.823743\pi\) |
0.0301240 | + | 0.999546i | \(0.490410\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.85200e10 | − | 8.40391e10i | 0.330490 | − | 0.572425i | −0.652118 | − | 0.758117i | \(-0.726119\pi\) |
0.982608 | + | 0.185692i | \(0.0594527\pi\) | |||||||
\(620\) | 1.80263e10i | 0.121995i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.33888e11 | 0.894502 | ||||||||
\(623\) | −2.19918e10 | − | 1.26970e10i | −0.145985 | − | 0.0842845i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.26934e10 | − | 9.12677e10i | −0.345332 | − | 0.598132i | ||||
\(626\) | −3.22810e11 | + | 1.86375e11i | −2.10208 | + | 1.21364i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.50679e10 | + | 2.60984e10i | −0.0968758 | + | 0.167794i | ||||
\(629\) | − | 5.46991e10i | − | 0.349444i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.86142e11 | −1.80495 | −0.902473 | − | 0.430747i | \(-0.858250\pi\) | ||||
−0.902473 | + | 0.430747i | \(0.858250\pi\) | |||||||
\(632\) | −1.64232e11 | − | 9.48192e10i | −1.02941 | − | 0.594330i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.46981e11 | + | 2.54579e11i | 0.909714 | + | 1.57567i | ||||
\(635\) | −3.96983e10 | + | 2.29198e10i | −0.244161 | + | 0.140967i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.46660e11 | − | 2.54023e11i | 0.890747 | − | 1.54282i | ||||
\(638\) | 5.62982e11i | 3.39791i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.46274e10 | −0.504418 | ||||||||
\(641\) | −4.96090e10 | − | 2.86417e10i | −0.293852 | − | 0.169655i | 0.345826 | − | 0.938299i | \(-0.387599\pi\) |
−0.639678 | + | 0.768643i | \(0.720932\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.72328e10 | + | 1.16451e11i | 0.393312 | + | 0.681236i | 0.992884 | − | 0.119084i | \(-0.0379959\pi\) |
−0.599572 | + | 0.800321i | \(0.704663\pi\) | |||||||
\(644\) | 2.14983e11 | − | 1.24120e11i | 1.24986 | − | 0.721605i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.30574e11 | + | 2.26160e11i | −0.749765 | + | 1.29863i | ||||
\(647\) | − | 2.98401e11i | − | 1.70288i | −0.524454 | − | 0.851439i | \(-0.675731\pi\) | ||
0.524454 | − | 0.851439i | \(-0.324269\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.26457e10 | −0.465845 | ||||||||
\(650\) | 2.86510e11 | + | 1.65417e11i | 1.60504 | + | 0.926671i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.14101e11 | + | 1.97628e11i | 0.631390 | + | 1.09360i | ||||
\(653\) | −8.81880e10 | + | 5.09154e10i | −0.485017 | + | 0.280025i | −0.722505 | − | 0.691366i | \(-0.757009\pi\) |
0.237488 | + | 0.971390i | \(0.423676\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.62683e10 | + | 6.28186e10i | −0.197044 | + | 0.341290i | ||||
\(656\) | 4.47067e9i | 0.0241411i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.93553e11 | 3.69978 | ||||||||
\(659\) | 2.09636e11 | + | 1.21033e11i | 1.11154 | + | 0.641746i | 0.939227 | − | 0.343296i | \(-0.111544\pi\) |
0.172310 | + | 0.985043i | \(0.444877\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.53401e11 | + | 2.65699e11i | 0.803570 | + | 1.39182i | 0.917252 | + | 0.398307i | \(0.130402\pi\) |
−0.113682 | + | 0.993517i | \(0.536265\pi\) | |||||||
\(662\) | 2.93704e11 | − | 1.69570e11i | 1.52925 | − | 0.882912i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.20797e10 | − | 1.07525e11i | 0.319358 | − | 0.553143i | ||||
\(665\) | − | 1.61897e11i | − | 0.827850i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.26114e11 | 1.14241 | ||||||||
\(668\) | 8.80800e10 | + | 5.08530e10i | 0.442356 | + | 0.255394i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.67585e9 | + | 2.90265e9i | 0.00831640 | + | 0.0144044i | ||||
\(671\) | −3.76047e10 | + | 2.17111e10i | −0.185504 | + | 0.107101i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.97126e10 | − | 1.55387e11i | 0.437314 | − | 0.757450i | −0.560168 | − | 0.828379i | \(-0.689263\pi\) |
0.997481 | + | 0.0709297i | \(0.0225966\pi\) | |||||||
\(674\) | − | 3.06502e11i | − | 1.48523i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.21086e11 | −1.05871 | ||||||||
\(677\) | 1.27199e11 | + | 7.34384e10i | 0.605521 | + | 0.349597i | 0.771210 | − | 0.636580i | \(-0.219652\pi\) |
−0.165690 | + | 0.986178i | \(0.552985\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.53302e11 | − | 2.65526e11i | −0.721220 | − | 1.24919i | ||||
\(680\) | −3.18644e10 | + | 1.83969e10i | −0.149029 | + | 0.0860417i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.52185e10 | + | 7.83207e10i | −0.209015 | + | 0.362025i | ||||
\(683\) | − | 5.39354e10i | − | 0.247851i | −0.992291 | − | 0.123926i | \(-0.960452\pi\) | ||
0.992291 | − | 0.123926i | \(-0.0395485\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.52403e10 | 0.0692200 | ||||||||
\(686\) | 1.79369e11 | + | 1.03559e11i | 0.809938 | + | 0.467618i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.81501e9 | − | 1.52681e10i | −0.0393432 | − | 0.0681444i | ||||
\(689\) | −8.16531e10 | + | 4.71424e10i | −0.362323 | + | 0.209187i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.19287e10 | + | 8.99432e10i | −0.227769 | + | 0.394508i | −0.957147 | − | 0.289603i | \(-0.906477\pi\) |
0.729377 | + | 0.684112i | \(0.239810\pi\) | |||||||
\(692\) | 1.13114e11i | 0.493279i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.35864e11 | 1.01677 | ||||||||
\(695\) | −1.47461e9 | − | 8.51367e8i | −0.00632031 | − | 0.00364903i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.76582e10 | + | 3.05849e10i | 0.0748195 | + | 0.129591i | ||||
\(698\) | −4.64530e11 | + | 2.68196e11i | −1.95700 | + | 1.12988i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.60588e11 | + | 4.51352e11i | −1.08533 | + | 1.87985i | ||||
\(701\) | − | 1.65918e11i | − | 0.687103i | −0.939134 | − | 0.343552i | \(-0.888370\pi\) | ||
0.939134 | − | 0.343552i | \(-0.111630\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.46251e11 | 1.00822 | ||||||||
\(704\) | −3.81321e11 | − | 2.20156e11i | −1.55239 | − | 0.896272i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.40915e11 | − | 2.44072e11i | −0.567202 | − | 0.982423i | ||||
\(707\) | 6.35606e11 | − | 3.66967e11i | 2.54396 | − | 1.46876i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.63444e10 | − | 1.32232e11i | 0.302129 | − | 0.523303i | −0.674489 | − | 0.738285i | \(-0.735636\pi\) |
0.976618 | + | 0.214982i | \(0.0689693\pi\) | |||||||
\(710\) | 1.95729e11i | 0.770232i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.59814e10 | −0.101098 | ||||||||
\(713\) | 3.14564e10 | + | 1.81614e10i | 0.121717 | + | 0.0702733i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.07899e10 | − | 1.05291e11i | −0.232599 | − | 0.402873i | ||||
\(716\) | 1.40262e11 | − | 8.09804e10i | 0.533689 | − | 0.308125i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.53778e11 | + | 2.66351e11i | −0.578623 | + | 1.00220i | ||||
\(719\) | 2.64075e11i | 0.988125i | 0.869427 | + | 0.494062i | \(0.164489\pi\) | ||||
−0.869427 | + | 0.494062i | \(0.835511\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.84784e11 | −2.90408 | ||||||||
\(722\) | −6.40435e11 | − | 3.69755e11i | −2.35682 | − | 1.36071i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.80756e11 | − | 4.86284e11i | −1.02182 | − | 1.76985i | ||||
\(725\) | −4.11121e11 | + | 2.37361e11i | −1.48805 | + | 0.859126i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.28330e11 | − | 2.22274e11i | 0.459399 | − | 0.795703i | −0.539530 | − | 0.841966i | \(-0.681398\pi\) |
0.998929 | + | 0.0462634i | \(0.0147314\pi\) | |||||||
\(728\) | − | 5.17912e11i | − | 1.84387i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.12262e11 | 0.395313 | ||||||||
\(731\) | −1.20611e11 | − | 6.96348e10i | −0.422394 | − | 0.243869i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.38206e11 | + | 2.39380e11i | 0.478752 | + | 0.829223i | 0.999703 | − | 0.0243635i | \(-0.00775591\pi\) |
−0.520951 | + | 0.853587i | \(0.674423\pi\) | |||||||
\(734\) | −1.38367e11 | + | 7.98864e10i | −0.476705 | + | 0.275226i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.34053e10 | + | 1.61783e11i | −0.318317 | + | 0.551342i | ||||
\(737\) | 1.02881e10i | 0.0348710i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.69193e11 | 1.23787 | 0.618935 | − | 0.785442i | \(-0.287564\pi\) | ||||
0.618935 | + | 0.785442i | \(0.287564\pi\) | |||||||
\(740\) | 8.21935e10 | + | 4.74545e10i | 0.274101 | + | 0.158252i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.21383e11 | − | 2.10241e11i | −0.400443 | − | 0.693588i | ||||
\(743\) | 4.52457e11 | − | 2.61226e11i | 1.48464 | − | 0.857160i | 0.484797 | − | 0.874627i | \(-0.338894\pi\) |
0.999847 | + | 0.0174674i | \(0.00556032\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.97583e10 | − | 1.20825e11i | 0.226449 | − | 0.392222i | ||||
\(746\) | − | 3.15947e11i | − | 1.02014i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.08947e11 | −0.986911 | ||||||||
\(749\) | −5.25090e11 | − | 3.03161e11i | −1.66842 | − | 0.963265i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.11747e11 | − | 1.93552e11i | −0.351300 | − | 0.608469i | 0.635178 | − | 0.772366i | \(-0.280927\pi\) |
−0.986477 | + | 0.163897i | \(0.947594\pi\) | |||||||
\(752\) | −3.80059e10 | + | 2.19427e10i | −0.118845 | + | 0.0686150i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.45238e11 | − | 1.11758e12i | 1.99634 | − | 3.45776i | ||||
\(755\) | 2.48673e10i | 0.0765315i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.44183e11 | −0.743588 | −0.371794 | − | 0.928315i | \(-0.621257\pi\) | ||||
−0.371794 | + | 0.928315i | \(0.621257\pi\) | |||||||
\(758\) | −5.03227e11 | − | 2.90538e11i | −1.52436 | − | 0.880089i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.28213e10 | − | 1.43451e11i | −0.248249 | − | 0.429980i | ||||
\(761\) | 1.94881e11 | − | 1.12515e11i | 0.581073 | − | 0.335483i | −0.180487 | − | 0.983577i | \(-0.557767\pi\) |
0.761560 | + | 0.648095i | \(0.224434\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.09966e11 | + | 7.10082e11i | −1.20962 | + | 2.09513i | ||||
\(764\) | 6.86251e10i | 0.201423i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.94922e11 | −0.856628 | ||||||||
\(767\) | 1.64061e11 | + | 9.47209e10i | 0.474051 | + | 0.273693i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.41526e11 | + | 4.18336e11i | 0.690652 | + | 1.19624i | 0.971625 | + | 0.236528i | \(0.0760095\pi\) |
−0.280973 | + | 0.959716i | \(0.590657\pi\) | |||||||
\(770\) | 2.71105e11 | − | 1.56522e11i | 0.771212 | − | 0.445260i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.17398e11 | + | 2.03340e11i | −0.330516 | + | 0.572470i | ||||
\(773\) | − | 1.32482e10i | − | 0.0371056i | −0.999828 | − | 0.0185528i | \(-0.994094\pi\) | ||
0.999828 | − | 0.0185528i | \(-0.00590588\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.62588e10 | −0.211390 | ||||||||
\(776\) | −2.71670e11 | − | 1.56849e11i | −0.749194 | − | 0.432547i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.66609e9 | − | 1.67422e10i | −0.0263835 | − | 0.0456976i | ||||
\(779\) | −1.37691e11 | + | 7.94957e10i | −0.373899 | + | 0.215871i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.00396e11 | + | 5.20301e11i | −0.807403 | + | 1.39846i | ||||
\(782\) | 2.02808e11i | 0.542324i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.77889e10 | −0.126492 | ||||||||
\(785\) | 1.32184e10 | + | 7.63167e9i | 0.0348098 | + | 0.0200975i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.37300e11 | − | 4.11015e11i | −0.618584 | − | 1.07142i | −0.989744 | − | 0.142850i | \(-0.954373\pi\) |
0.371161 | − | 0.928569i | \(-0.378960\pi\) | |||||||
\(788\) | −4.15992e11 | + | 2.40173e11i | −1.07890 | + | 0.622901i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.31372e11 | + | 2.27543e11i | −0.337282 | + | 0.584190i | ||||
\(791\) | − | 2.62641e11i | − | 0.670898i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.95330e10 | 0.251695 | ||||||||
\(794\) | 1.26250e11 | + | 7.28907e10i | 0.317652 | + | 0.183396i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.80354e11 | − | 6.58792e11i | −0.947405 | − | 1.64095i | ||||
\(797\) | 2.58248e11 | − | 1.49100e11i | 0.640035 | − | 0.369524i | −0.144593 | − | 0.989491i | \(-0.546187\pi\) |
0.784628 | + | 0.619967i | \(0.212854\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.73338e11 | + | 3.00230e11i | −0.425311 | + | 0.736660i | ||||
\(800\) | − | 3.92206e11i | − | 0.957533i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.07670e12 | 2.60255 | ||||||||
\(803\) | 2.98423e11 | + | 1.72295e11i | 0.717745 | + | 0.414390i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.28650e10 | − | 1.08885e11i | −0.149701 | − | 0.259290i | ||||
\(806\) | 1.79528e11 | − | 1.03650e11i | 0.425394 | − | 0.245602i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.75457e11 | − | 6.50311e11i | 0.880877 | − | 1.52572i | ||||
\(809\) | 3.19136e11i | 0.745044i | 0.928023 | + | 0.372522i | \(0.121507\pi\) | ||||
−0.928023 | + | 0.372522i | \(0.878493\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.94415e11 | 0.680575 | 0.340288 | − | 0.940321i | \(-0.389476\pi\) | ||||
0.340288 | + | 0.940321i | \(0.389476\pi\) | |||||||
\(812\) | 1.76058e12 | + | 1.01647e12i | 4.04979 | + | 2.33815i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.38076e11 | + | 4.12360e11i | 0.542273 | + | 0.939244i | ||||
\(815\) | 1.00095e11 | − | 5.77902e10i | 0.226874 | − | 0.130986i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.13490e11 | − | 5.42981e11i | 0.703616 | − | 1.21870i | ||||
\(818\) | 6.42373e11i | 1.43474i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.12777e10 | −0.135534 | ||||||||
\(821\) | −5.33500e10 | − | 3.08016e10i | −0.117425 | − | 0.0677956i | 0.440137 | − | 0.897931i | \(-0.354930\pi\) |
−0.557562 | + | 0.830135i | \(0.688263\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.35526e11 | + | 4.07944e11i | 0.513381 | + | 0.889203i | 0.999880 | + | 0.0155212i | \(0.00494074\pi\) |
−0.486498 | + | 0.873682i | \(0.661726\pi\) | |||||||
\(824\) | −6.95368e11 | + | 4.01471e11i | −1.50836 | + | 0.870853i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.43888e11 | + | 4.22427e11i | −0.523927 | + | 0.907467i | ||||
\(827\) | 4.35038e11i | 0.930048i | 0.885298 | + | 0.465024i | \(0.153954\pi\) | ||||
−0.885298 | + | 0.465024i | \(0.846046\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.07438e11 | 0.439208 | 0.219604 | − | 0.975589i | \(-0.429524\pi\) | ||||
0.219604 | + | 0.975589i | \(0.429524\pi\) | |||||||
\(830\) | −1.48976e11 | − | 8.60113e10i | −0.313909 | − | 0.181235i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.04645e11 | + | 8.74071e11i | 1.05316 | + | 1.82412i | ||||
\(833\) | −3.26935e11 | + | 1.88756e11i | −0.679018 | + | 0.392031i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.57562e10 | − | 4.46111e10i | 0.0529830 | − | 0.0917693i | ||||
\(836\) | − | 1.39086e12i | − | 2.84745i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.29699e11 | 0.263002 | ||||||||
\(839\) | −2.06839e11 | − | 1.19419e11i | −0.417431 | − | 0.241004i | 0.276546 | − | 0.961001i | \(-0.410810\pi\) |
−0.693978 | + | 0.719996i | \(0.744143\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.75747e11 | + | 1.17043e12i | 1.35083 | + | 2.33970i | ||||
\(842\) | 3.16521e11 | − | 1.82743e11i | 0.629730 | − | 0.363575i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.01268e10 | + | 1.38784e11i | −0.157909 | + | 0.273507i | ||||
\(845\) | 1.11977e11i | 0.219635i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.67248e11 | 0.324959 | ||||||||
\(848\) | 1.33033e10 | + | 7.68064e9i | 0.0257261 | + | 0.0148530i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.12896e11 | − | 3.68747e11i | −0.407842 | − | 0.706403i | ||||
\(851\) | 1.65618e11 | − | 9.56198e10i | 0.315784 | − | 0.182318i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.57842e11 | − | 2.73391e11i | 0.298144 | − | 0.516401i | −0.677567 | − | 0.735461i | \(-0.736966\pi\) |
0.975711 | + | 0.219060i | \(0.0702990\pi\) | |||||||
\(854\) | 2.56278e11i | 0.481815i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.20349e11 | −1.15542 | ||||||||
\(857\) | −4.18908e11 | − | 2.41857e11i | −0.776597 | − | 0.448369i | 0.0586257 | − | 0.998280i | \(-0.481328\pi\) |
−0.835223 | + | 0.549911i | \(0.814661\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.84594e11 | + | 4.92930e11i | 0.522700 | + | 0.905343i | 0.999651 | + | 0.0264130i | \(0.00840849\pi\) |
−0.476951 | + | 0.878930i | \(0.658258\pi\) | |||||||
\(860\) | 2.09273e11 | − | 1.20824e11i | 0.382578 | − | 0.220882i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.77823e11 | − | 8.27614e11i | 0.865443 | − | 1.49899i | ||||
\(863\) | 1.70442e11i | 0.307279i | 0.988127 | + | 0.153639i | \(0.0490994\pi\) | ||||
−0.988127 | + | 0.153639i | \(0.950901\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.72906e10 | 0.102334 | ||||||||
\(866\) | 8.36865e11 | + | 4.83164e11i | 1.48793 | + | 0.859060i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.63285e11 | + | 2.82819e11i | 0.287653 | + | 0.498229i | ||||
\(869\) | −6.98445e11 | + | 4.03248e11i | −1.22477 | + | 0.707119i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.17912e10 | − | 2.04230e10i | 0.0204874 | − | 0.0354852i | ||||
\(872\) | 8.38903e11i | 1.45093i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.13026e11 | −1.56472 | ||||||||
\(875\) | 4.84575e11 | + | 2.79769e11i | 0.826663 | + | 0.477274i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.49396e11 | − | 6.05172e11i | −0.590636 | − | 1.02301i | −0.994147 | − | 0.108037i | \(-0.965544\pi\) |
0.403511 | − | 0.914975i | \(-0.367790\pi\) | |||||||
\(878\) | 1.19331e11 | − | 6.88957e10i | 0.200805 | − | 0.115935i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.90414e9 | + | 1.71545e10i | −0.0165153 | + | 0.0286053i | ||||
\(881\) | − | 2.05065e11i | − | 0.340399i | −0.985410 | − | 0.170199i | \(-0.945559\pi\) | ||
0.985410 | − | 0.170199i | \(-0.0544412\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.79882e11 | −1.28288 | −0.641440 | − | 0.767173i | \(-0.721663\pi\) | ||||
−0.641440 | + | 0.767173i | \(0.721663\pi\) | |||||||
\(884\) | 6.13296e11 | + | 3.54087e11i | 1.00430 | + | 0.579830i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.08559e11 | + | 5.34441e11i | 0.500730 | + | 0.867290i | ||||
\(887\) | −4.20319e11 | + | 2.42671e11i | −0.679023 | + | 0.392034i | −0.799487 | − | 0.600684i | \(-0.794895\pi\) |
0.120464 | + | 0.992718i | \(0.461562\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.15223e11 | + | 7.19187e11i | −0.664774 | + | 1.15142i | ||||
\(890\) | 3.59972e10i | 0.0573732i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.50948e11 | 1.18618 | ||||||||
\(893\) | −1.35161e12 | − | 7.80353e11i | −2.12543 | − | 1.22712i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.10153e10 | − | 7.10405e10i | −0.0639224 | − | 0.110717i | ||||
\(896\) | −1.32774e12 | + | 7.66568e11i | −2.06006 | + | 1.18938i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.34847e11 | − | 1.61920e12i | 1.43759 | − | 2.48998i | ||||
\(899\) | 2.97462e11i | 0.455400i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.21347e11 | 0.184133 | ||||||||
\(902\) | −2.66239e11 | − | 1.53713e11i | −0.402203 | − | 0.232212i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.34359e11 | − | 2.32716e11i | −0.201183 | − | 0.348460i | ||||
\(905\) | −2.46295e11 | + | 1.42199e11i | −0.367165 | + | 0.211983i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.68722e11 | + | 6.38645e11i | −0.544841 | + | 0.943693i | 0.453776 | + | 0.891116i | \(0.350077\pi\) |
−0.998617 | + | 0.0525767i | \(0.983257\pi\) | |||||||
\(908\) | 8.83377e11i | 1.29958i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.17566e11 | −1.04640 | ||||||||
\(911\) | 5.44603e11 | + | 3.14427e11i | 0.790691 | + | 0.456506i | 0.840206 | − | 0.542268i | \(-0.182434\pi\) |
−0.0495146 | + | 0.998773i | \(0.515767\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.64013e11 | − | 4.57284e11i | −0.379964 | − | 0.658116i | ||||
\(914\) | 1.37835e12 | − | 7.95791e11i | 1.97504 | − | 1.14029i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.33868e11 | + | 7.51482e11i | −0.616277 | + | 1.06742i | ||||
\(917\) | 1.31410e12i | 1.85845i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.48346e11 | 0.488370 | 0.244185 | − | 0.969729i | \(-0.421480\pi\) | ||||
0.244185 | + | 0.969729i | \(0.421480\pi\) | |||||||
\(920\) | −1.11405e11 | − | 6.43194e10i | −0.155508 | − | 0.0897823i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.54621e11 | + | 2.67811e11i | 0.213966 | + | 0.370600i | ||||
\(923\) | 1.19264e12 | − | 6.88573e11i | 1.64325 | − | 0.948731i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.00752e11 | + | 3.47713e11i | −0.274216 | + | 0.474956i | ||||
\(926\) | − | 1.52190e11i | − | 0.206987i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.52987e12 | −2.06283 | ||||||||
\(929\) | 5.27095e8 | + | 3.04319e8i | 0.000707663 | + | 0.000408569i | 0.500354 | − | 0.865821i | \(-0.333203\pi\) |
−0.499646 | + | 0.866230i | \(0.666537\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.49763e11 | − | 1.47183e12i | −1.13110 | − | 1.95912i | ||||
\(932\) | 1.19271e12 | − | 6.88609e11i | 1.58077 | − | 0.912660i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.45749e11 | − | 1.29168e12i | 0.979953 | − | 1.69733i | ||||
\(935\) | 1.56477e11i | 0.204740i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.98470e10 | 0.0776398 | 0.0388199 | − | 0.999246i | \(-0.487640\pi\) | ||||
0.0388199 | + | 0.999246i | \(0.487640\pi\) | |||||||
\(938\) | 5.25854e10 | + | 3.03602e10i | 0.0679288 | + | 0.0392187i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.00760e11 | − | 5.20932e11i | −0.385220 | − | 0.667221i | ||||
\(941\) | −1.12529e12 | + | 6.49688e11i | −1.43518 | + | 0.828603i | −0.997510 | − | 0.0705309i | \(-0.977531\pi\) |
−0.437673 | + | 0.899134i | \(0.644197\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.17367e10 | + | 1.06931e11i | −0.0780723 | + | 0.135225i | ||||
\(944\) | − | 3.08646e10i | − | 0.0388663i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.21233e12 | 1.51376 | ||||||||
\(947\) | 1.13710e12 | + | 6.56502e11i | 1.41383 | + | 0.816275i | 0.995747 | − | 0.0921343i | \(-0.0293689\pi\) |
0.418083 | + | 0.908409i | \(0.362702\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.94937e11 | − | 6.84050e11i | −0.486925 | − | 0.843380i | ||||
\(950\) | 1.66007e12 | − | 9.58440e11i | 2.03813 | − | 1.17671i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.33284e11 | + | 5.77265e11i | −0.405758 | + | 0.702793i | ||||
\(953\) | − | 1.49915e12i | − | 1.81750i | −0.417341 | − | 0.908750i | \(-0.637038\pi\) | ||
0.417341 | − | 0.908750i | \(-0.362962\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.47575e10 | 0.0417864 | ||||||||
\(956\) | −1.14816e12 | − | 6.62892e11i | −1.37459 | − | 0.793618i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.92408e11 | − | 1.02608e12i | −0.703330 | − | 1.21820i | ||||
\(959\) | 2.39108e11 | − | 1.38049e11i | 0.282696 | − | 0.163215i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.02554e11 | − | 6.97243e11i | 0.471987 | − | 0.817506i | ||||
\(962\) | − | 1.09144e12i | − | 1.27438i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.62808e12 | −1.88524 | ||||||||
\(965\) | 1.02988e11 | + | 5.94604e10i | 0.118762 | + | 0.0685675i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.29701e11 | + | 2.24648e11i | 0.148332 | + | 0.256919i | 0.930611 | − | 0.366009i | \(-0.119276\pi\) |
−0.782279 | + | 0.622928i | \(0.785943\pi\) | |||||||
\(968\) | 1.48192e11 | − | 8.55589e10i | 0.168781 | − | 0.0974459i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.17313e11 | + | 3.76398e11i | −0.245471 | + | 0.425168i | ||||
\(971\) | 1.15804e12i | 1.30271i | 0.758772 | + | 0.651356i | \(0.225800\pi\) | ||||
−0.758772 | + | 0.651356i | \(0.774200\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.08473e10 | −0.0344164 | ||||||||
\(974\) | −1.90335e12 | − | 1.09890e12i | −2.11487 | − | 1.22102i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.10816e9 | − | 1.40437e10i | −0.00893559 | − | 0.0154769i | ||||
\(977\) | 7.79343e10 | − | 4.49954e10i | 0.0855363 | − | 0.0493844i | −0.456622 | − | 0.889661i | \(-0.650941\pi\) |
0.542158 | + | 0.840277i | \(0.317607\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.52470e10 | + | 9.56907e10i | −0.0601420 | + | 0.104169i | ||||
\(980\) | − | 6.55024e11i | − | 0.710155i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.65356e11 | 0.823033 | ||||||||
\(983\) | 1.42514e12 | + | 8.22805e11i | 1.52631 | + | 0.881217i | 0.999512 | + | 0.0312278i | \(0.00994174\pi\) |
0.526800 | + | 0.849989i | \(0.323392\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.21644e11 | + | 2.10693e11i | 0.129224 | + | 0.223823i | ||||
\(986\) | −1.43837e12 | + | 8.30441e11i | −1.52181 | + | 0.878620i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.59407e12 | + | 2.76101e12i | −1.67294 | + | 2.89761i | ||||
\(989\) | − | 4.86916e11i | − | 0.508943i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.39028e11 | 0.662560 | 0.331280 | − | 0.943533i | \(-0.392520\pi\) | ||||
0.331280 | + | 0.943533i | \(0.392520\pi\) | |||||||
\(992\) | −2.12832e11 | − | 1.22879e11i | −0.219781 | − | 0.126891i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.77294e12 | + | 3.07083e12i | 1.81614 | + | 3.14564i | ||||
\(995\) | −3.33668e11 | + | 1.92643e11i | −0.340426 | + | 0.196545i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.46173e11 | − | 7.72795e11i | 0.451568 | − | 0.782139i | −0.546916 | − | 0.837188i | \(-0.684198\pi\) |
0.998484 | + | 0.0550490i | \(0.0175315\pi\) | |||||||
\(998\) | − | 1.32136e12i | − | 1.33199i | ||||||
\(999\) | 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 | 81.9.d.g.26.2 | 32 | ||
3.2 | odd | 2 | inner | 81.9.d.g.26.15 | 32 | ||
9.2 | odd | 6 | 81.9.b.b.80.2 | ✓ | 16 | ||
9.4 | even | 3 | inner | 81.9.d.g.53.15 | 32 | ||
9.5 | odd | 6 | inner | 81.9.d.g.53.2 | 32 | ||
9.7 | even | 3 | 81.9.b.b.80.15 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
81.9.b.b.80.2 | ✓ | 16 | 9.2 | odd | 6 | ||
81.9.b.b.80.15 | yes | 16 | 9.7 | even | 3 | ||
81.9.d.g.26.2 | 32 | 1.1 | even | 1 | trivial | ||
81.9.d.g.26.15 | 32 | 3.2 | odd | 2 | inner | ||
81.9.d.g.53.2 | 32 | 9.5 | odd | 6 | inner | ||
81.9.d.g.53.15 | 32 | 9.4 | even | 3 | inner |