Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [140,15,Mod(41,140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(140, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("140.41");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 140 = 2^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 140.d (of order \(2\), degree \(1\), 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: | \(174.060555413\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 41.18 | ||
Character | \(\chi\) | \(=\) | 140.41 |
Dual form | 140.15.d.a.41.19 |
$q$-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 \(\left(\mathbb{Z}/140\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(101\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 303.599i | − | 0.138820i | −0.997588 | − | 0.0694098i | \(-0.977888\pi\) | ||
0.997588 | − | 0.0694098i | \(-0.0221116\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 34938.6i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −415571. | + | 711002.i | −0.504613 | + | 0.863345i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.69080e6 | 0.980729 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.67561e7 | 0.859851 | 0.429925 | − | 0.902864i | \(-0.358540\pi\) | ||||
0.429925 | + | 0.902864i | \(0.358540\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.13953e8i | 1.81603i | 0.418934 | + | 0.908017i | \(0.362404\pi\) | ||||
−0.418934 | + | 0.908017i | \(0.637596\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.06073e7 | 0.0620821 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.03769e8i | 1.71509i | 0.514406 | + | 0.857547i | \(0.328013\pi\) | ||||
−0.514406 | + | 0.857547i | \(0.671987\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.27331e8i | 0.589940i | 0.955506 | + | 0.294970i | \(0.0953097\pi\) | ||||
−0.955506 | + | 0.294970i | \(0.904690\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.15859e8 | + | 1.26167e8i | 0.119849 | + | 0.0700503i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.75456e9 | −1.10272 | −0.551358 | − | 0.834269i | \(-0.685890\pi\) | ||||
−0.551358 | + | 0.834269i | \(0.685890\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.22070e9 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.87622e9i | − | 0.274964i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.44902e9 | 0.431830 | 0.215915 | − | 0.976412i | \(-0.430727\pi\) | ||||
0.215915 | + | 0.976412i | \(0.430727\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.18796e10i | 1.52220i | 0.648636 | + | 0.761099i | \(0.275340\pi\) | ||||
−0.648636 | + | 0.761099i | \(0.724660\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 5.08712e9i | − | 0.119364i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.48414e10 | − | 1.45194e10i | −0.386100 | − | 0.225670i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.57759e11 | 1.66182 | 0.830908 | − | 0.556410i | \(-0.187821\pi\) | ||||
0.830908 | + | 0.556410i | \(0.187821\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.45961e10 | 0.252101 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.56891e10i | − | 0.0805586i | −0.999188 | − | 0.0402793i | \(-0.987175\pi\) | ||
0.999188 | − | 0.0402793i | \(-0.0128248\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.48374e11 | 1.28164 | 0.640821 | − | 0.767690i | \(-0.278594\pi\) | ||||
0.640821 | + | 0.767690i | \(0.278594\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.63890e11i | 0.438595i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.96594e11i | 1.17759i | 0.808282 | + | 0.588795i | \(0.200398\pi\) | ||||
−0.808282 | + | 0.588795i | \(0.799602\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.32825e11 | − | 5.90943e11i | −0.490731 | − | 0.871311i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.13663e11 | 0.238089 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.35416e12 | −1.15276 | −0.576378 | − | 0.817183i | \(-0.695534\pi\) | ||||
−0.576378 | + | 0.817183i | \(0.695534\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.85433e11i | 0.384537i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.60097e11 | 0.0818953 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 2.06767e11i | − | 0.0830841i | −0.999137 | − | 0.0415421i | \(-0.986773\pi\) | ||
0.999137 | − | 0.0415421i | \(-0.0132271\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 5.42825e12i | − | 1.72723i | −0.504148 | − | 0.863617i | \(-0.668193\pi\) | ||
0.504148 | − | 0.863617i | \(-0.331807\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.94936e12 | + | 3.33517e12i | −0.494889 | + | 0.846708i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.98137e12 | −0.812155 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.85879e12 | −0.636689 | −0.318345 | − | 0.947975i | \(-0.603127\pi\) | ||||
−0.318345 | + | 0.947975i | \(0.603127\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.13988e12i | 0.153079i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.27085e13 | 1.39729 | 0.698646 | − | 0.715468i | \(-0.253786\pi\) | ||||
0.698646 | + | 0.715468i | \(0.253786\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.67859e12i | − | 0.514021i | −0.966409 | − | 0.257011i | \(-0.917263\pi\) | ||
0.966409 | − | 0.257011i | \(-0.0827375\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.70604e11i | 0.0277639i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.96333e12 | + | 1.19136e13i | −0.433892 | + | 0.742348i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.24296e13 | 1.16797 | 0.583985 | − | 0.811765i | \(-0.301493\pi\) | ||||
0.583985 | + | 0.811765i | \(0.301493\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.15627e13 | 0.942559 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.87401e12i | 0.327019i | 0.986542 | + | 0.163510i | \(0.0522815\pi\) | ||||
−0.986542 | + | 0.163510i | \(0.947719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.45887e13 | −0.767013 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 2.26151e12i | − | 0.0599465i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5.93459e13i | − | 1.34172i | −0.741586 | − | 0.670858i | \(-0.765926\pi\) | ||
0.741586 | − | 0.670858i | \(-0.234074\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.10211e13 | − | 4.73557e13i | −1.56786 | − | 0.916395i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.27146e13 | 0.211311 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.84242e13 | −0.263829 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.97418e13i | 0.368099i | 0.982917 | + | 0.184050i | \(0.0589207\pi\) | ||||
−0.982917 | + | 0.184050i | \(0.941079\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.85993e13 | 0.843281 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.69586e13i | 0.158176i | 0.996868 | + | 0.0790881i | \(0.0252008\pi\) | ||||
−0.996868 | + | 0.0790881i | \(0.974799\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.51463e14i | 1.23153i | 0.787930 | + | 0.615765i | \(0.211153\pi\) | ||||
−0.787930 | + | 0.615765i | \(0.788847\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.40809e12 | + | 7.54181e12i | −0.0313274 | + | 0.0535983i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.73318e14 | −1.70209 | −0.851043 | − | 0.525096i | \(-0.824029\pi\) | ||||
−0.851043 | + | 0.525096i | \(0.824029\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.26975e14 | 0.694594 | 0.347297 | − | 0.937755i | \(-0.387100\pi\) | ||||
0.347297 | + | 0.937755i | \(0.387100\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 4.78955e13i | − | 0.230693i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.12851e14 | 1.32981 | 0.664903 | − | 0.746930i | \(-0.268473\pi\) | ||||
0.664903 | + | 0.746930i | \(0.268473\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.31179e14i | − | 0.493150i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.34532e14i | 1.78104i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.00381e14 | − | 2.92466e14i | −1.48072 | − | 0.865459i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.89843e13 | −0.260656 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.76320e12 | −0.0111831 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 4.26496e13i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00611e14 | 0.376469 | 0.188235 | − | 0.982124i | \(-0.439723\pi\) | ||||
0.188235 | + | 0.982124i | \(0.439723\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 1.05766e14i | − | 0.177917i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 7.24410e13i | − | 0.109417i | −0.998502 | − | 0.0547085i | \(-0.982577\pi\) | ||
0.998502 | − | 0.0547085i | \(-0.0174230\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.74933e14 | − | 2.19143e14i | −0.509322 | − | 0.297692i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00491e14 | 0.122968 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.46428e15 | 1.61652 | 0.808261 | − | 0.588825i | \(-0.200409\pi\) | ||||
0.808261 | + | 0.588825i | \(0.200409\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.84937e14i | 0.184467i | 0.995737 | + | 0.0922337i | \(0.0294007\pi\) | ||||
−0.995737 | + | 0.0922337i | \(0.970599\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.81125e14 | 0.163473 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.90941e15i | 1.56152i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.60258e14i | 0.193120i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.79410e14 | + | 1.01045e14i | −0.120955 | + | 0.0681231i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.76431e15 | −1.08211 | −0.541055 | − | 0.840987i | \(-0.681975\pi\) | ||||
−0.541055 | + | 0.840987i | \(0.681975\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.45390e14 | −0.192962 | −0.0964808 | − | 0.995335i | \(-0.530759\pi\) | ||||
−0.0964808 | + | 0.995335i | \(0.530759\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.30124e15i | 1.68204i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.46321e15 | −0.680748 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 4.63544e15i | − | 1.97148i | −0.168264 | − | 0.985742i | \(-0.553816\pi\) | ||
0.168264 | − | 0.985742i | \(-0.446184\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.11120e14i | 0.160025i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.56028e15 | − | 2.66950e15i | 0.556446 | − | 0.952025i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.99814e15 | −1.96202 | −0.981010 | − | 0.193957i | \(-0.937868\pi\) | ||||
−0.981010 | + | 0.193957i | \(0.937868\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.77737e14 | 0.0533813 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3.50351e15i | − | 0.967138i | −0.875306 | − | 0.483569i | \(-0.839340\pi\) | ||
0.875306 | − | 0.483569i | \(-0.160660\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.04800e15 | −2.29798 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.47360e15i | 0.578572i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.27794e15i | 1.13800i | 0.822338 | + | 0.568999i | \(0.192669\pi\) | ||||
−0.822338 | + | 0.568999i | \(0.807331\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.07289e14 | − | 8.67922e14i | 0.100923 | − | 0.172669i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.27743e13 | −0.0115337 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.27090e15 | 1.06502 | 0.532511 | − | 0.846423i | \(-0.321249\pi\) | ||||
0.532511 | + | 0.846423i | \(0.321249\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.20214e14i | 0.113165i | 0.998398 | + | 0.0565825i | \(0.0180204\pi\) | ||||
−0.998398 | + | 0.0565825i | \(0.981980\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.64801e15 | −0.239774 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.51188e15i | 0.743187i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.17924e16i | 1.47472i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.04500e15 | + | 1.19527e15i | 0.237389 | + | 0.138751i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.75823e15 | 1.05229 | 0.526147 | − | 0.850393i | \(-0.323636\pi\) | ||||
0.526147 | + | 0.850393i | \(0.323636\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.24929e16 | −1.25246 | −0.626230 | − | 0.779639i | \(-0.715403\pi\) | ||||
−0.626230 | + | 0.779639i | \(0.715403\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.20874e15i | 0.112743i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.75841e15 | −0.326393 | −0.163196 | − | 0.986594i | \(-0.552180\pi\) | ||||
−0.163196 | + | 0.986594i | \(0.552180\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.08791e15i | − | 0.249858i | −0.992166 | − | 0.124929i | \(-0.960130\pi\) | ||
0.992166 | − | 0.124929i | \(-0.0398703\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.17152e15i | 0.0883850i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.09559e15 | + | 5.29627e15i | −0.217907 | + | 0.372819i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.48156e14 | 0.0360269 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.76119e16 | −1.08147 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.83599e15i | 0.507261i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.71504e15 | −0.360638 | −0.180319 | − | 0.983608i | \(-0.557713\pi\) | ||||
−0.180319 | + | 0.983608i | \(0.557713\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 3.85829e15i | − | 0.193972i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.21717e16i | 0.573168i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.97765e16 | − | 1.74040e16i | −1.31418 | − | 0.768122i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.72401e15 | −0.0713562 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.01969e16 | −3.11467 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.03931e16i | − | 0.378977i | −0.981883 | − | 0.189489i | \(-0.939317\pi\) | ||
0.981883 | − | 0.189489i | \(-0.0606830\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.72607e15 | −0.196146 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.42849e16i | 1.74783i | 0.486082 | + | 0.873913i | \(0.338425\pi\) | ||||
−0.486082 | + | 0.873913i | \(0.661575\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.13192e16i | 0.645539i | 0.946478 | + | 0.322770i | \(0.104614\pi\) | ||||
−0.946478 | + | 0.322770i | \(0.895386\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.61695e15 | + | 2.11406e15i | 0.103053 | + | 0.0602328i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.50693e16 | 0.672435 | 0.336218 | − | 0.941784i | \(-0.390852\pi\) | ||||
0.336218 | + | 0.941784i | \(0.390852\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.08442e16 | −0.526634 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 6.80959e15i | − | 0.162137i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.81043e15 | −0.0855439 | −0.0427719 | − | 0.999085i | \(-0.513619\pi\) | ||||
−0.0427719 | + | 0.999085i | \(0.513619\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.77294e16i | 0.587248i | 0.955921 | + | 0.293624i | \(0.0948614\pi\) | ||||
−0.955921 | + | 0.293624i | \(0.905139\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 2.03033e16i | − | 0.405810i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.06467e16 | − | 1.16284e16i | 0.389662 | − | 0.219461i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.00912e16 | −1.07135 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.69414e15 | 0.0453967 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 3.53313e16i | − | 0.562916i | −0.959573 | − | 0.281458i | \(-0.909182\pi\) | ||
0.959573 | − | 0.281458i | \(-0.0908181\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.29116e16 | −0.948172 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.46509e15i | 0.106477i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.07557e16i | 0.820455i | 0.911983 | + | 0.410228i | \(0.134551\pi\) | ||||
−0.911983 | + | 0.410228i | \(0.865449\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.55602e16 | + | 1.12167e17i | −0.838575 | + | 1.43472i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.49418e16 | 0.423508 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.71447e16 | −1.00127 | −0.500635 | − | 0.865659i | \(-0.666900\pi\) | ||||
−0.500635 | + | 0.865659i | \(0.666900\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.73122e16i | − | 0.515528i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.80173e16 | −0.186257 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 2.05481e15i | − | 0.0201607i | −0.999949 | − | 0.0100804i | \(-0.996791\pi\) | ||
0.999949 | − | 0.0100804i | \(-0.00320874\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.63939e16i | 0.618504i | 0.950980 | + | 0.309252i | \(0.100079\pi\) | ||||
−0.950980 | + | 0.309252i | \(0.899921\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.43771e16 | + | 2.45979e16i | −0.127214 | + | 0.217650i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.04542e16 | −0.171970 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.72127e17 | 1.37560 | 0.687798 | − | 0.725903i | \(-0.258578\pi\) | ||||
0.687798 | + | 0.725903i | \(0.258578\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.96449e17i | 1.49286i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.56765e17 | −1.13320 | −0.566599 | − | 0.823994i | \(-0.691741\pi\) | ||||
−0.566599 | + | 0.823994i | \(0.691741\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.04416e17i | 0.718224i | 0.933294 | + | 0.359112i | \(0.116920\pi\) | ||||
−0.933294 | + | 0.359112i | \(0.883080\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.59356e15i | 0.0366247i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.11550e16 | + | 6.51995e15i | 0.0695499 | + | 0.0406510i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.26913e17 | −1.94155 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.02957e15 | 0.0510994 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.22909e17i | 0.662996i | 0.943456 | + | 0.331498i | \(0.107554\pi\) | ||||
−0.943456 | + | 0.331498i | \(0.892446\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.22416e15 | 0.0371563 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 4.81942e16i | − | 0.236428i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 4.27845e17i | − | 2.00257i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.44774e17 | + | 2.47695e17i | −0.646734 | + | 1.10650i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.14862e15 | 0.0219580 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.89655e17 | 0.772443 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.65358e16i | 0.103244i | 0.998667 | + | 0.0516219i | \(0.0164391\pi\) | ||||
−0.998667 | + | 0.0516219i | \(0.983561\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.59839e16 | 0.170961 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 5.75983e16i | − | 0.204685i | −0.994749 | − | 0.102343i | \(-0.967366\pi\) | ||
0.994749 | − | 0.102343i | \(-0.0326338\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4.04739e17i | − | 1.37520i | −0.726092 | − | 0.687598i | \(-0.758665\pi\) | ||
0.726092 | − | 0.687598i | \(-0.241335\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.16526e17 | − | 6.81078e16i | −0.378659 | − | 0.221321i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.23747e17 | 0.384699 | 0.192349 | − | 0.981327i | \(-0.438389\pi\) | ||||
0.192349 | + | 0.981327i | \(0.438389\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.24816e17 | 0.371309 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.29789e16i | 0.236283i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.71119e17 | −1.01180 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.39103e17i | − | 0.363207i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 3.85493e16i | − | 0.0964234i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.24180e17 | − | 2.47927e17i | −1.01667 | − | 0.594228i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.51196e16 | −0.0806778 | −0.0403389 | − | 0.999186i | \(-0.512844\pi\) | ||||
−0.0403389 | + | 0.999186i | \(0.512844\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.40017e17 | 1.62979 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 1.34821e17i | − | 0.284736i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.67045e17 | −0.540973 | −0.270486 | − | 0.962724i | \(-0.587185\pi\) | ||||
−0.270486 | + | 0.962724i | \(0.587185\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 9.49811e16i | − | 0.184603i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.01738e17i | 1.30886i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.58474e17 | + | 8.93980e15i | 0.999872 | + | 0.0160055i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.98257e16 | −0.0684589 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.24503e17 | −1.19601 | −0.598004 | − | 0.801493i | \(-0.704039\pi\) | ||||
−0.598004 | + | 0.801493i | \(0.704039\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.68419e17i | 0.425633i | 0.977092 | + | 0.212817i | \(0.0682637\pi\) | ||||
−0.977092 | + | 0.212817i | \(0.931736\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.27755e17 | 0.499344 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 2.88463e16i | − | 0.0422346i | −0.999777 | − | 0.0211173i | \(-0.993278\pi\) | ||
0.999777 | − | 0.0211173i | \(-0.00672234\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.44018e17i | 0.624888i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.87923e16 | + | 1.51915e17i | −0.120143 | + | 0.205553i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.09399e18 | 1.42348 | 0.711739 | − | 0.702444i | \(-0.247908\pi\) | ||||
0.711739 | + | 0.702444i | \(0.247908\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.20929e17 | 0.651970 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.00515e16i | 0.0361843i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.98402e17 | 0.229877 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 8.66474e17i | − | 0.966258i | −0.875549 | − | 0.483129i | \(-0.839500\pi\) | ||
0.875549 | − | 0.483129i | \(-0.160500\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 7.35946e16i | − | 0.0790062i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.62747e17 | − | 9.62807e17i | 0.581696 | − | 0.995226i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.29444e18 | 1.28860 | 0.644302 | − | 0.764771i | \(-0.277148\pi\) | ||||
0.644302 | + | 0.764771i | \(0.277148\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.29484e16 | −0.0124164 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.48841e17i | 0.784218i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.18349e17 | 0.283419 | 0.141710 | − | 0.989908i | \(-0.454740\pi\) | ||||
0.141710 | + | 0.989908i | \(0.454740\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 6.09053e16i | − | 0.0522613i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.48862e16i | 0.0371297i | 0.999828 | + | 0.0185648i | \(0.00590971\pi\) | ||||
−0.999828 | + | 0.0185648i | \(0.994090\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.16244e17 | − | 2.43289e17i | −0.331988 | − | 0.194043i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.63415e18 | 1.25694 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.44079e18 | 1.06894 | 0.534471 | − | 0.845187i | \(-0.320511\pi\) | ||||
0.534471 | + | 0.845187i | \(0.320511\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.64234e18i | − | 1.89126i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.19930e16 | −0.0151892 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.83657e17i | 0.522332i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 2.32098e18i | − | 1.49327i | −0.665236 | − | 0.746633i | \(-0.731669\pi\) | ||
0.665236 | − | 0.746633i | \(-0.268331\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.65316e16 | + | 1.13829e17i | −0.0413255 | + | 0.0707040i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.46571e17 | 0.447776 | 0.223888 | − | 0.974615i | \(-0.428125\pi\) | ||||
0.223888 | + | 0.974615i | \(0.428125\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.77233e18 | −2.76436 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.53370e17i | 0.421525i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.64343e18 | 1.42891 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 2.71052e18i | − | 1.41576i | −0.706334 | − | 0.707879i | \(-0.749652\pi\) | ||
0.706334 | − | 0.707879i | \(-0.250348\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 4.44555e17i | − | 0.224405i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.47012e17 | + | 8.59265e16i | 0.0717303 | + | 0.0419254i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.10045e17 | −0.146248 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.61466e16 | 0.0256077 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.72227e18i | 0.759632i | 0.925062 | + | 0.379816i | \(0.124013\pi\) | ||||
−0.925062 | + | 0.379816i | \(0.875987\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.49543e18 | 0.637957 | 0.318978 | − | 0.947762i | \(-0.396660\pi\) | ||||
0.318978 | + | 0.947762i | \(0.396660\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.79850e18i | 1.15490i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 8.59093e17i | − | 0.343019i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.85950e18 | + | 2.25582e18i | 1.49120 | + | 0.871586i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.79694e17 | 0.216769 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.34090e18 | 0.485349 | 0.242675 | − | 0.970108i | \(-0.421975\pi\) | ||||
0.242675 | + | 0.970108i | \(0.421975\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.11557e18i | − | 1.09175i | −0.837867 | − | 0.545874i | \(-0.816198\pi\) | ||
0.837867 | − | 0.545874i | \(-0.183802\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.90140e16 | 0.0268089 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1.97989e18i | − | 0.650537i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.73894e18i | 1.50810i | 0.656818 | + | 0.754049i | \(0.271902\pi\) | ||||
−0.656818 | + | 0.754049i | \(0.728098\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.56121e18 | − | 2.77200e18i | −0.481274 | − | 0.854520i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.25427e18 | 0.374597 | 0.187298 | − | 0.982303i | \(-0.440027\pi\) | ||||
0.187298 | + | 0.982303i | \(0.440027\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.07346e18 | 0.600034 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.35643e17i | 0.150218i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.61692e18 | −0.711322 | −0.355661 | − | 0.934615i | \(-0.615744\pi\) | ||||
−0.355661 | + | 0.934615i | \(0.615744\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.62888e17i | − | 0.0692684i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.04860e17i | 0.0267869i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.65454e18 | − | 2.83076e18i | 0.409824 | − | 0.701170i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.08592e18 | 0.260846 | 0.130423 | − | 0.991458i | \(-0.458366\pi\) | ||||
0.130423 | + | 0.991458i | \(0.458366\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.02420e18 | 0.471589 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 8.75216e18i | − | 1.97792i | −0.148185 | − | 0.988960i | \(-0.547343\pi\) | ||
0.148185 | − | 0.988960i | \(-0.452657\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.63944e18 | 0.359442 | 0.179721 | − | 0.983718i | \(-0.442480\pi\) | ||||
0.179721 | + | 0.983718i | \(0.442480\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.44230e17i | 0.0945012i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 8.89533e18i | − | 1.83630i | −0.396232 | − | 0.918151i | \(-0.629682\pi\) | ||
0.396232 | − | 0.918151i | \(-0.370318\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.60360e18 | − | 2.74361e18i | 0.321282 | − | 0.549683i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.40731e18 | −0.273681 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.83738e18 | 1.10202 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6.43715e17i | − | 0.117988i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.35207e18 | −1.13054 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.35669e18i | 0.407337i | 0.979040 | + | 0.203669i | \(0.0652865\pi\) | ||||
−0.979040 | + | 0.203669i | \(0.934713\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.79772e19i | 3.01791i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.10456e17 | − | 4.73700e17i | −0.132160 | − | 0.0772456i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.03914e18 | −0.164619 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.09589e18 | 1.40005 | 0.700023 | − | 0.714120i | \(-0.253173\pi\) | ||||
0.700023 | + | 0.714120i | \(0.253173\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.82103e18i | 0.272367i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.07479e18 | −1.17371 | −0.586855 | − | 0.809692i | \(-0.699634\pi\) | ||||
−0.586855 | + | 0.809692i | \(0.699634\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.24239e18i | 0.740629i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.74615e18i | 0.377127i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.28130e18 | + | 9.03580e18i | −0.705092 | + | 1.20635i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.10936e19 | −1.44002 | −0.720008 | − | 0.693966i | \(-0.755862\pi\) | ||||
−0.720008 | + | 0.693966i | \(0.755862\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.06366e18 | −0.134258 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 8.61754e18i | − | 1.05781i | −0.848681 | − | 0.528905i | \(-0.822603\pi\) | ||
0.848681 | − | 0.528905i | \(-0.177397\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.92510e17 | −0.0707386 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.74696e18i | 0.319004i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 9.44910e18i | − | 1.06749i | −0.845644 | − | 0.533747i | \(-0.820783\pi\) | ||
0.845644 | − | 0.533747i | \(-0.179217\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.03749e18 | + | 2.35986e18i | 0.443778 | + | 0.259382i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.51672e18 | 0.162212 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.29189e18 | −0.550757 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.99657e18i | 1.01255i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.60238e18 | 0.157977 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.04200e19i | 1.00000i | 0.866024 | + | 0.500002i | \(0.166668\pi\) | ||||
−0.866024 | + | 0.500002i | \(0.833332\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 7.90486e18i | − | 0.738555i | −0.929319 | − | 0.369277i | \(-0.879605\pi\) | ||
0.929319 | − | 0.369277i | \(-0.120395\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.63500e17 | − | 1.54012e17i | −0.0239699 | − | 0.0140101i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.94736e19 | −2.61071 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.50387e18 | 0.215984 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 9.69904e17i | − | 0.0814830i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.78783e18 | 0.146297 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 9.54933e18i | − | 0.761196i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 1.90384e18i | − | 0.147846i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.57683e18 | − | 9.90189e18i | −0.421955 | − | 0.749198i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.66413e18 | 0.565044 | 0.282522 | − | 0.959261i | \(-0.408829\pi\) | ||||
0.282522 | + | 0.959261i | \(0.408829\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.18656e17 | 0.0157095 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.43631e18i | 0.310632i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.75508e19 | 1.19780 | 0.598900 | − | 0.800824i | \(-0.295605\pi\) | ||||
0.598900 | + | 0.800824i | \(0.295605\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 2.54628e19i | − | 1.69395i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.92810e18i | 0.254754i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.32108e18 | + | 1.59475e19i | −0.589373 | + | 1.00836i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.67340e18 | 0.103169 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.24906e19 | −0.750924 | −0.375462 | − | 0.926838i | \(-0.622516\pi\) | ||||
−0.375462 | + | 0.926838i | \(0.622516\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.96984e19i | 2.32750i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.58016e18 | 0.204721 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.19445e19i | 1.22396i | 0.790874 | + | 0.611979i | \(0.209626\pi\) | ||||
−0.790874 | + | 0.611979i | \(0.790374\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.09306e19i | 0.594707i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.96084e18 | + | 1.53311e19i | −0.475628 | + | 0.813754i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.92000e19 | 0.994294 | 0.497147 | − | 0.867666i | \(-0.334381\pi\) | ||||
0.497147 | + | 0.867666i | \(0.334381\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.75307e19 | −0.885824 | −0.442912 | − | 0.896565i | \(-0.646055\pi\) | ||||
−0.442912 | + | 0.896565i | \(0.646055\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 2.96259e18i | − | 0.146079i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.58320e18 | 0.220543 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 2.86957e18i | − | 0.134768i | −0.997727 | − | 0.0673840i | \(-0.978535\pi\) | ||
0.997727 | − | 0.0673840i | \(-0.0214652\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.79284e18i | 0.173866i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.30944e18 | − | 3.68778e18i | −0.282331 | − | 0.165018i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.26903e19 | −0.991198 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.86758e19 | −0.796504 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.52698e19i | 0.635868i | 0.948113 | + | 0.317934i | \(0.102989\pi\) | ||||
−0.948113 | + | 0.317934i | \(0.897011\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.20844e19 | −0.898006 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.14105e18i | 0.0453098i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 2.76713e19i | − | 1.07312i | −0.843863 | − | 0.536559i | \(-0.819724\pi\) | ||
0.843863 | − | 0.536559i | \(-0.180276\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.02183e19 | − | 1.74826e19i | 0.387045 | − | 0.662197i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.37487e17 | −0.0346852 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.04578e19 | −1.46223 | −0.731113 | − | 0.682256i | \(-0.760999\pi\) | ||||
−0.731113 | + | 0.682256i | \(0.760999\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 2.10600e19i | − | 0.743595i | −0.928314 | − | 0.371797i | \(-0.878742\pi\) | ||
0.928314 | − | 0.371797i | \(-0.121258\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.81008e19 | −0.624420 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 3.45837e18i | − | 0.116569i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.49208e19i | − | 0.491442i | −0.969341 | − | 0.245721i | \(-0.920975\pi\) | ||
0.969341 | − | 0.245721i | \(-0.0790247\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.60794e18 | + | 9.39818e17i | 0.0517546 | + | 0.0302498i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.79840e19 | −2.13854 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.61547e19 | −0.804129 | −0.402065 | − | 0.915611i | \(-0.631707\pi\) | ||||
−0.402065 | + | 0.915611i | \(0.631707\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 1.66419e17i | − | 0.00500125i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.65280e18 | 0.107307 | 0.0536537 | − | 0.998560i | \(-0.482913\pi\) | ||||
0.0536537 | + | 0.998560i | \(0.482913\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.85715e18i | 0.0533352i | 0.999644 | + | 0.0266676i | \(0.00848956\pi\) | ||||
−0.999644 | + | 0.0266676i | \(0.991510\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.07989e19i | 0.303208i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.21951e19 | + | 2.46624e19i | 1.15836 | + | 0.677048i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.49012e18 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.68260e18 | 0.0704178 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.11026e20i | 2.85017i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.86578e19 | −0.719511 | −0.359755 | − | 0.933047i | \(-0.617140\pi\) | ||||
−0.359755 | + | 0.933047i | \(0.617140\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.03868e18i | 0.0500636i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.00907e18i | 0.168362i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.73400e19 | − | 3.79265e19i | 1.58233 | − | 0.891183i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.96132e19 | 1.37036 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.72028e19 | 1.06160 | 0.530801 | − | 0.847496i | \(-0.321891\pi\) | ||||
0.530801 | + | 0.847496i | \(0.321891\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 3.74689e19i | − | 0.824507i | −0.911069 | − | 0.412253i | \(-0.864742\pi\) | ||
0.911069 | − | 0.412253i | \(-0.135258\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.69531e18 | 0.0795670 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.28437e19i | 1.11343i | 0.830704 | + | 0.556715i | \(0.187938\pi\) | ||||
−0.830704 | + | 0.556715i | \(0.812062\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 3.46461e18i | − | 0.0714399i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.28382e18 | + | 9.04011e18i | −0.106630 | + | 0.182434i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.17691e19 | 0.825017 | 0.412509 | − | 0.910954i | \(-0.364653\pi\) | ||||
0.412509 | + | 0.910954i | \(0.364653\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.53098e18 | 0.0489328 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 2.66371e19i | − | 0.504115i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.20234e19 | −0.222757 | −0.111378 | − | 0.993778i | \(-0.535527\pi\) | ||||
−0.111378 | + | 0.993778i | \(0.535527\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 3.50077e19i | − | 0.634970i | −0.948263 | − | 0.317485i | \(-0.897162\pi\) | ||
0.948263 | − | 0.317485i | \(-0.102838\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.43477e19i | 0.432377i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.65656e18 | − | 1.30996e19i | 0.133132 | − | 0.227776i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.79678e19 | −0.476186 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.15535e18 | −0.0526095 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 9.09561e19i | − | 1.48516i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.60462e19 | −1.37602 | −0.688012 | − | 0.725699i | \(-0.741516\pi\) | ||||
−0.688012 | + | 0.725699i | \(0.741516\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.51101e18i | 0.0549928i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.68945e19i | 1.33313i | 0.745448 | + | 0.666564i | \(0.232236\pi\) | ||||
−0.745448 | + | 0.666564i | \(0.767764\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.11465e19 | − | 1.23598e19i | −0.317797 | − | 0.185748i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.64808e19 | 0.242633 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.93433e19 | 0.711677 | 0.355839 | − | 0.934547i | \(-0.384195\pi\) | ||||
0.355839 | + | 0.934547i | \(0.384195\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.11600e19i | 0.722931i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.47248e18 | 0.0896136 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1.54311e20i | − | 2.09344i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1.34242e20i | − | 1.78461i | −0.451433 | − | 0.892305i | \(-0.649087\pi\) | ||
0.451433 | − | 0.892305i | \(-0.350913\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.26636e19 | + | 5.58842e19i | −0.425531 | + | 0.728043i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.46143e18 | −0.0824963 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.10415e19 | 0.138166 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 7.61100e18i | − | 0.0933473i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.76404e19 | 1.17383 | 0.586913 | − | 0.809650i | \(-0.300343\pi\) | ||||
0.586913 | + | 0.809650i | \(0.300343\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.31914e19i | 0.980373i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.32826e18i | 0.0731072i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.20576e19 | − | 7.04751e18i | −0.136561 | − | 0.0798178i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.73303e19 | 0.747630 | 0.373815 | − | 0.927503i | \(-0.378050\pi\) | ||||
0.373815 | + | 0.927503i | \(0.378050\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.05213e20 | 1.14546 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.57240e20i | − | 1.67855i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.67120e19 | −0.698332 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.15684e18i | 0.0118752i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.34330e19i | 0.638576i | 0.947658 | + | 0.319288i | \(0.103444\pi\) | ||||
−0.947658 | + | 0.319288i | \(0.896556\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.07690e20 | − | 6.29435e19i | −1.06324 | − | 0.621447i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.41862e18 | 0.0815216 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.09304e18 | −0.0863660 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.16939e20i | − | 1.08948i | −0.838606 | − | 0.544739i | \(-0.816629\pi\) | ||
0.838606 | − | 0.544739i | \(-0.183371\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.69698e19 | 0.886224 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.45175e20i | 2.19814i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.13181e19i | 0.363423i | 0.983352 | + | 0.181712i | \(0.0581638\pi\) | ||||
−0.983352 | + | 0.181712i | \(0.941836\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.53037e18 | − | 6.26832e18i | −0.0304656 | − | 0.0540928i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.46581e19 | −0.547458 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.68737e20 | 1.40184 | 0.700921 | − | 0.713239i | \(-0.252773\pi\) | ||||
0.700921 | + | 0.713239i | \(0.252773\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.82436e19i | 0.148725i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.44810e20 | 1.15845 | 0.579223 | − | 0.815169i | \(-0.303356\pi\) | ||||
0.579223 | + | 0.815169i | \(0.303356\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 6.16425e19i | − | 0.483934i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.16262e19i | 0.320717i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.13583e20 | − | 1.94330e20i | 0.858895 | − | 1.46949i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.26508e19 | 0.390774 | 0.195387 | − | 0.980726i | \(-0.437404\pi\) | ||||
0.195387 | + | 0.980726i | \(0.437404\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.07265e19 | −0.0781439 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1.20674e19i | − | 0.0862951i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.67968e20 | 1.17911 | 0.589557 | − | 0.807727i | \(-0.299303\pi\) | ||||
0.589557 | + | 0.807727i | \(0.299303\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.90999e19i | 0.131625i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2.33435e20i | − | 1.57933i | −0.613539 | − | 0.789664i | \(-0.710255\pi\) | ||
0.613539 | − | 0.789664i | \(-0.289745\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.27669e19 | + | 9.02792e19i | −0.350502 | + | 0.599675i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.15341e20 | −0.752232 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.35618e19 | 0.150884 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.19790e19i | 0.0753248i | 0.999291 | + | 0.0376624i | \(0.0119911\pi\) | ||||
−0.999291 | + | 0.0376624i | \(0.988009\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.84453e19 | 0.113895 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 3.79396e19i | − | 0.230058i | −0.993362 | − | 0.115029i | \(-0.963304\pi\) | ||
0.993362 | − | 0.115029i | \(-0.0366960\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 5.11226e19i | − | 0.304440i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.40538e19 | + | 1.99040e19i | 0.199168 | + | 0.116411i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.27337e18 | 0.0475248 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.12945e20 | 1.20146 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 2.14250e19i | − | 0.118738i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.61956e20 | 0.881674 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.98290e19i | 0.212998i | 0.994313 | + | 0.106499i | \(0.0339642\pi\) | ||||
−0.994313 | + | 0.106499i | \(0.966036\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.64570e19i | 0.138996i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.30012e20 | + | 2.22438e20i | −0.671038 | + | 1.14808i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.18568e20 | 3.13671 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.43639e19 | −0.0715654 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.42042e20i | 0.695356i | 0.937614 | + | 0.347678i | \(0.113030\pi\) | ||||
−0.937614 | + | 0.347678i | \(0.886970\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.19865e20 | −2.01968 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 2.78380e20i | − | 1.31586i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 9.51509e19i | − | 0.441981i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.32684e19 | + | 5.45141e19i | 0.425759 | + | 0.248850i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.23839e17 | −0.00279871 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.55543e20 | 0.685819 | 0.342910 | − | 0.939368i | \(-0.388588\pi\) | ||||
0.342910 | + | 0.939368i | \(0.388588\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 4.05657e19i | − | 0.175797i | −0.996129 | − | 0.0878987i | \(-0.971985\pi\) | ||
0.996129 | − | 0.0878987i | \(-0.0280152\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.01571e19 | 0.0858606 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 2.09566e20i | − | 0.877442i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.83708e20i | 0.756092i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.80053e20 | − | 2.22136e20i | −1.53765 | − | 0.898735i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.62216e20 | −1.44067 | −0.720337 | − | 0.693625i | \(-0.756013\pi\) | ||||
−0.720337 | + | 0.693625i | \(0.756013\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.04171e20 | −1.97142 | −0.985710 | − | 0.168450i | \(-0.946124\pi\) | ||||
−0.985710 | + | 0.168450i | \(0.946124\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.20986e18i | 0.0238728i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.49173e20 | 1.31978 | 0.659890 | − | 0.751362i | \(-0.270603\pi\) | ||||
0.659890 | + | 0.751362i | \(0.270603\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.72366e20i | 1.01221i | 0.862472 | + | 0.506105i | \(0.168915\pi\) | ||||
−0.862472 | + | 0.506105i | \(0.831085\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 5.22575e19i | − | 0.190960i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.15888e20 | − | 2.34232e20i | 1.49438 | − | 0.841649i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.22408e20 | 0.432517 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.20455e20 | 0.418550 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.74521e20i | 0.596368i | 0.954508 | + | 0.298184i | \(0.0963809\pi\) | ||||
−0.954508 | + | 0.298184i | \(0.903619\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.42070e20 | −0.813523 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.75938e19i | 0.157310i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 3.16124e20i | − | 1.02769i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.11350e19 | − | 7.03780e19i | 0.131531 | − | 0.225037i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.17004e19 | 0.0997037 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.92317e20 | −1.83251 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 4.51180e20i | − | 1.37311i | −0.727076 | − | 0.686557i | \(-0.759121\pi\) | ||
0.727076 | − | 0.686557i | \(-0.240879\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.64241e19 | −0.258745 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.31340e20i | 0.975905i | 0.872870 | + | 0.487952i | \(0.162256\pi\) | ||||
−0.872870 | + | 0.487952i | \(0.837744\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.95753e20i | 1.43652i | 0.695773 | + | 0.718262i | \(0.255062\pi\) | ||||
−0.695773 | + | 0.718262i | \(0.744938\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.97945e18 | − | 3.38665e18i | 0.00564316 | − | 0.00965490i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.50051e19 | −0.0420886 | −0.0210443 | − | 0.999779i | \(-0.506699\pi\) | ||||
−0.0210443 | + | 0.999779i | \(0.506699\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.84404e20 | −0.508928 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.92505e19i | 0.269525i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.75831e20 | 1.00428 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 4.39722e20i | − | 1.15625i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.39513e20i | 0.361006i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.03240e19 | + | 1.77239e19i | 0.0772200 | + | 0.0451340i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.44892e19 | −0.236802 | −0.118401 | − | 0.992966i | \(-0.537777\pi\) | ||||
−0.118401 | + | 0.992966i | \(0.537777\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.73150e19 | 0.0920369 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.92647e20i | 0.710416i | 0.934787 | + | 0.355208i | \(0.115590\pi\) | ||||
−0.934787 | + | 0.355208i | \(0.884410\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.14106e20 | −1.94516 | −0.972582 | − | 0.232561i | \(-0.925289\pi\) | ||||
−0.972582 | + | 0.232561i | \(0.925289\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 2.19324e18i | − | 0.00515803i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.73996e19i | 0.0402785i | 0.999797 | + | 0.0201392i | \(0.00641095\pi\) | ||||
−0.999797 | + | 0.0201392i | \(0.993589\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.33682e19 | + | 1.42635e20i | −0.189971 | + | 0.325023i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.61306e20 | 0.810460 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.14603e20 | −0.694708 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.19096e20i | 0.476292i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.29893e20 | −0.277996 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.11962e20i | 0.657331i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 9.53013e20i | − | 1.97708i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.51998e19 | + | 4.39532e19i | 0.153604 | + | 0.0897794i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.51633e19 | −0.0506089 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.34150e20 | 1.25586 | 0.627930 | − | 0.778270i | \(-0.283902\pi\) | ||||
0.627930 | + | 0.778270i | \(0.283902\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.95495e19i | 0.155128i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.49270e20 | −1.43883 | −0.719415 | − | 0.694581i | \(-0.755590\pi\) | ||||
−0.719415 | + | 0.694581i | \(0.755590\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.48694e20i | 0.281188i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 5.75791e19i | − | 0.107230i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.15057e19 | + | 3.01044e19i | 0.0944647 | + | 0.0552133i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.04762e20 | 1.09238 | 0.546192 | − | 0.837660i | \(-0.316077\pi\) | ||||
0.546192 | + | 0.837660i | \(0.316077\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.05624e18 | 0.0143323 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.44818e21i | 2.53753i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.92577e20 | −0.332363 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.10481e20i | 1.20780i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.82789e19i | 0.131079i | 0.997850 | + | 0.0655397i | \(0.0208769\pi\) | ||||
−0.997850 | + | 0.0655397i | \(0.979123\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.11623e20 | − | 1.75509e20i | 0.514022 | − | 0.289502i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.74868e19 | −0.0284143 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.12010e20 | −0.659517 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.26304e20i | 1.46075i | 0.683045 | + | 0.730376i | \(0.260655\pi\) | ||||
−0.683045 | + | 0.730376i | \(0.739345\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.22878e20 | −0.190904 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 3.61063e20i | − | 0.552657i | −0.961063 | − | 0.276329i | \(-0.910882\pi\) | ||
0.961063 | − | 0.276329i | \(-0.0891178\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.89058e19i | 0.0888334i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.17612e19 | + | 7.14494e19i | −0.0620512 | + | 0.106164i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.18296e21 | −1.73189 | −0.865944 | − | 0.500141i | \(-0.833282\pi\) | ||||
−0.865944 | + | 0.500141i | \(0.833282\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.47095e20 | 0.933479 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 3.75695e19i | − | 0.0534037i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.82570e20 | 0.675943 | 0.337971 | − | 0.941156i | \(-0.390259\pi\) | ||||
0.337971 | + | 0.941156i | \(0.390259\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.40938e20i | 0.470601i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 3.78940e19i | − | 0.0515451i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.08514e20 | + | 1.04111e21i | −0.815719 | + | 1.39562i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.96961e20 | −1.31709 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.28208e21 | −1.66929 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 4.36485e20i | − | 0.560117i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.01512e20 | −0.887257 | −0.443629 | − | 0.896211i | \(-0.646309\pi\) | ||||
−0.443629 | + | 0.896211i | \(0.646309\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.12671e20i | 0.140458i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 6.31484e20i | − | 0.775939i | −0.921672 | − | 0.387970i | \(-0.873177\pi\) | ||
0.921672 | − | 0.387970i | \(-0.126823\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.31490e20 | − | 7.68543e19i | −0.159259 | − | 0.0930847i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.22316e19 | −0.0504202 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.01865e20 | −0.237574 | −0.118787 | − | 0.992920i | \(-0.537901\pi\) | ||||
−0.118787 | + | 0.992920i | \(0.537901\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 9.94404e20i | − | 1.15368i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.95612e20 | 0.681209 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 4.07405e20i | − | 0.459358i | −0.973266 | − | 0.229679i | \(-0.926232\pi\) | ||
0.973266 | − | 0.229679i | \(-0.0737676\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 1.31314e20i | − | 0.145967i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.52704e19 | + | 1.28780e20i | −0.0824905 | + | 0.141133i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.30799e21 | −1.41329 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.37255e20 | 0.359288 | 0.179644 | − | 0.983732i | \(-0.442505\pi\) | ||||
0.179644 | + | 0.983732i | \(0.442505\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.06623e19i | 0.0111997i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.07887e20 | 0.111740 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.09145e20i | 0.315715i | 0.987462 | + | 0.157858i | \(0.0504587\pi\) | ||||
−0.987462 | + | 0.157858i | \(0.949541\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 4.53751e20i | − | 0.456940i |
(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 | 140.15.d.a.41.18 | ✓ | 36 | |
7.6 | odd | 2 | inner | 140.15.d.a.41.19 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.15.d.a.41.18 | ✓ | 36 | 1.1 | even | 1 | trivial | |
140.15.d.a.41.19 | yes | 36 | 7.6 | odd | 2 | inner |