Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,10,Mod(10,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.10");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.c (of order \(3\), 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: | \(13.9059675764\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 1984 x^{14} - 13748 x^{13} + 1552498 x^{12} - 9136628 x^{11} + 609566956 x^{10} + \cdots + 13\!\cdots\!25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{40}\cdot 17^{2} \) |
Twist minimal: | no (minimal twist has level 9) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 10.4 | ||
Root | \(0.500000 - 3.55897i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 27.10 |
Dual form | 27.10.c.a.19.4 |
$q$-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 \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.83216 | − | 6.63749i | −0.169359 | − | 0.293339i | 0.768836 | − | 0.639447i | \(-0.220836\pi\) |
−0.938195 | + | 0.346108i | \(0.887503\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 226.629 | − | 392.533i | 0.442635 | − | 0.766666i | ||||
\(5\) | 1105.48 | − | 1914.74i | 0.791014 | − | 1.37008i | −0.134326 | − | 0.990937i | \(-0.542887\pi\) |
0.925340 | − | 0.379139i | \(-0.123780\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3116.58 | + | 5398.07i | 0.490610 | + | 0.849762i | 0.999942 | − | 0.0108087i | \(-0.00344058\pi\) |
−0.509331 | + | 0.860570i | \(0.670107\pi\) | |||||||
\(8\) | −7398.05 | −0.638575 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −16945.4 | −0.535862 | ||||||||
\(11\) | 9312.12 | + | 16129.1i | 0.191770 | + | 0.332156i | 0.945837 | − | 0.324642i | \(-0.105244\pi\) |
−0.754067 | + | 0.656798i | \(0.771910\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 84699.6 | − | 146704.i | 0.822501 | − | 1.42461i | −0.0813133 | − | 0.996689i | \(-0.525911\pi\) |
0.903814 | − | 0.427925i | \(-0.140755\pi\) | |||||||
\(14\) | 23886.4 | − | 41372.5i | 0.166179 | − | 0.287830i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −87683.6 | − | 151872.i | −0.334486 | − | 0.579347i | ||||
\(17\) | −433113. | −1.25771 | −0.628856 | − | 0.777522i | \(-0.716476\pi\) | ||||
−0.628856 | + | 0.777522i | \(0.716476\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 51200.2 | 0.0901322 | 0.0450661 | − | 0.998984i | \(-0.485650\pi\) | ||||
0.0450661 | + | 0.998984i | \(0.485650\pi\) | |||||||
\(20\) | −501066. | − | 867871.i | −0.700261 | − | 1.21289i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 71371.1 | − | 123618.i | 0.0649561 | − | 0.112507i | ||||
\(23\) | 152281. | − | 263759.i | 0.113468 | − | 0.196532i | −0.803699 | − | 0.595037i | \(-0.797138\pi\) |
0.917166 | + | 0.398505i | \(0.130471\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.46759e6 | − | 2.54194e6i | −0.751406 | − | 1.30147i | ||||
\(26\) | −1.29833e6 | −0.557192 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.82523e6 | 0.868645 | ||||||||
\(29\) | −568995. | − | 985528.i | −0.149389 | − | 0.258749i | 0.781613 | − | 0.623764i | \(-0.214397\pi\) |
−0.931002 | + | 0.365015i | \(0.881064\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 389293. | − | 674275.i | 0.0757092 | − | 0.131132i | −0.825685 | − | 0.564131i | \(-0.809211\pi\) |
0.901394 | + | 0.432999i | \(0.142545\pi\) | |||||||
\(32\) | −2.56594e6 | + | 4.44433e6i | −0.432584 | + | 0.749258i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.65976e6 | + | 2.87479e6i | 0.213005 | + | 0.368935i | ||||
\(35\) | 1.37812e7 | 1.55232 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.32050e6 | −0.554426 | −0.277213 | − | 0.960808i | \(-0.589411\pi\) | ||||
−0.277213 | + | 0.960808i | \(0.589411\pi\) | |||||||
\(38\) | −196207. | − | 339841.i | −0.0152647 | − | 0.0264393i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.17836e6 | + | 1.41653e7i | −0.505122 | + | 0.874897i | ||||
\(41\) | −1.23991e6 | + | 2.14759e6i | −0.0685271 | + | 0.118692i | −0.898253 | − | 0.439478i | \(-0.855163\pi\) |
0.829726 | + | 0.558171i | \(0.188497\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.56300e7 | + | 2.70719e7i | 0.697189 | + | 1.20757i | 0.969437 | + | 0.245339i | \(0.0788993\pi\) |
−0.272249 | + | 0.962227i | \(0.587767\pi\) | |||||||
\(44\) | 8.44159e6 | 0.339537 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.33427e6 | −0.0768671 | ||||||||
\(47\) | 5.07040e6 | + | 8.78219e6i | 0.151566 | + | 0.262520i | 0.931803 | − | 0.362964i | \(-0.118235\pi\) |
−0.780237 | + | 0.625484i | \(0.784902\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 750710. | − | 1.30027e6i | 0.0186033 | − | 0.0322219i | ||||
\(50\) | −1.12481e7 | + | 1.94822e7i | −0.254515 | + | 0.440832i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.83908e7 | − | 6.64948e7i | −0.728135 | − | 1.26117i | ||||
\(53\) | 3.32278e7 | 0.578442 | 0.289221 | − | 0.957262i | \(-0.406604\pi\) | ||||
0.289221 | + | 0.957262i | \(0.406604\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.11773e7 | 0.606772 | ||||||||
\(56\) | −2.30566e7 | − | 3.99352e7i | −0.313292 | − | 0.542637i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.36096e6 | + | 7.55340e6i | −0.0506007 | + | 0.0876429i | ||||
\(59\) | −2.33603e7 | + | 4.04612e7i | −0.250983 | + | 0.434715i | −0.963797 | − | 0.266639i | \(-0.914087\pi\) |
0.712814 | + | 0.701353i | \(0.247420\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.06902e7 | + | 5.31570e7i | 0.283802 | + | 0.491560i | 0.972318 | − | 0.233662i | \(-0.0750708\pi\) |
−0.688516 | + | 0.725221i | \(0.741737\pi\) | |||||||
\(62\) | −5.96733e6 | −0.0512882 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.04557e7 | −0.375924 | ||||||||
\(65\) | −1.87267e8 | − | 3.24355e8i | −1.30122 | − | 2.25378i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.37409e8 | − | 2.37999e8i | 0.833062 | − | 1.44291i | −0.0625367 | − | 0.998043i | \(-0.519919\pi\) |
0.895599 | − | 0.444863i | \(-0.146748\pi\) | |||||||
\(68\) | −9.81560e7 | + | 1.70011e8i | −0.556707 | + | 0.964245i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.28117e7 | − | 9.14726e7i | −0.262899 | − | 0.455355i | ||||
\(71\) | 2.93935e8 | 1.37274 | 0.686372 | − | 0.727251i | \(-0.259202\pi\) | ||||
0.686372 | + | 0.727251i | \(0.259202\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.55084e8 | −0.639168 | −0.319584 | − | 0.947558i | \(-0.603543\pi\) | ||||
−0.319584 | + | 0.947558i | \(0.603543\pi\) | |||||||
\(74\) | 2.42212e7 | + | 4.19523e7i | 0.0938971 | + | 0.162635i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.16034e7 | − | 2.00978e7i | 0.0398957 | − | 0.0691013i | ||||
\(77\) | −5.80439e7 | + | 1.00535e8i | −0.188169 | + | 0.325918i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.17883e8 | + | 2.04180e8i | 0.340511 | + | 0.589782i | 0.984528 | − | 0.175230i | \(-0.0560668\pi\) |
−0.644017 | + | 0.765011i | \(0.722733\pi\) | |||||||
\(80\) | −3.87728e8 | −1.05833 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.90061e7 | 0.0464228 | ||||||||
\(83\) | 1.68070e8 | + | 2.91106e8i | 0.388722 | + | 0.673287i | 0.992278 | − | 0.124034i | \(-0.0395832\pi\) |
−0.603556 | + | 0.797321i | \(0.706250\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.78796e8 | + | 8.29299e8i | −0.994867 | + | 1.72316i | ||||
\(86\) | 1.19793e8 | − | 2.07488e8i | 0.236150 | − | 0.409025i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.88915e7 | − | 1.19324e8i | −0.122460 | − | 0.212107i | ||||
\(89\) | 1.03812e9 | 1.75384 | 0.876922 | − | 0.480633i | \(-0.159593\pi\) | ||||
0.876922 | + | 0.480633i | \(0.159593\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.05589e9 | 1.61411 | ||||||||
\(92\) | −6.90228e7 | − | 1.19551e8i | −0.100449 | − | 0.173983i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.88611e7 | − | 6.73095e7i | 0.0513382 | − | 0.0889203i | ||||
\(95\) | 5.66005e7 | − | 9.80350e7i | 0.0712958 | − | 0.123488i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.34786e8 | + | 2.33457e8i | 0.154587 | + | 0.267753i | 0.932909 | − | 0.360113i | \(-0.117262\pi\) |
−0.778321 | + | 0.627866i | \(0.783929\pi\) | |||||||
\(98\) | −1.15074e7 | −0.0126026 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.33039e9 | −1.33039 | ||||||||
\(101\) | 4.90047e8 | + | 8.48786e8i | 0.468588 | + | 0.811618i | 0.999355 | − | 0.0358992i | \(-0.0114295\pi\) |
−0.530767 | + | 0.847518i | \(0.678096\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.36838e7 | − | 1.44945e8i | 0.0732611 | − | 0.126892i | −0.827068 | − | 0.562102i | \(-0.809993\pi\) |
0.900329 | + | 0.435210i | \(0.143326\pi\) | |||||||
\(104\) | −6.26612e8 | + | 1.08532e9i | −0.525229 | + | 0.909723i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.27334e8 | − | 2.20549e8i | −0.0979644 | − | 0.169679i | ||||
\(107\) | −1.91944e9 | −1.41563 | −0.707813 | − | 0.706400i | \(-0.750318\pi\) | ||||
−0.707813 | + | 0.706400i | \(0.750318\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.60871e8 | 0.177013 | 0.0885066 | − | 0.996076i | \(-0.471791\pi\) | ||||
0.0885066 | + | 0.996076i | \(0.471791\pi\) | |||||||
\(110\) | −1.57798e8 | − | 2.73314e8i | −0.102762 | − | 0.177990i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.46545e8 | − | 9.46644e8i | 0.328205 | − | 0.568468i | ||||
\(113\) | 1.63303e9 | − | 2.82850e9i | 0.942197 | − | 1.63193i | 0.180929 | − | 0.983496i | \(-0.442089\pi\) |
0.761268 | − | 0.648438i | \(-0.224577\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.36687e8 | − | 5.83159e8i | −0.179509 | − | 0.310918i | ||||
\(116\) | −5.15803e8 | −0.264499 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.58081e8 | 0.170025 | ||||||||
\(119\) | −1.34983e9 | − | 2.33797e9i | −0.617046 | − | 1.06876i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00554e9 | − | 1.74165e9i | 0.426448 | − | 0.738630i | ||||
\(122\) | 2.35220e8 | − | 4.07412e8i | 0.0961290 | − | 0.166500i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.76450e8 | − | 3.05621e8i | −0.0670231 | − | 0.116087i | ||||
\(125\) | −2.17127e9 | −0.795461 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.25753e9 | −0.428944 | −0.214472 | − | 0.976730i | \(-0.568803\pi\) | ||||
−0.214472 | + | 0.976730i | \(0.568803\pi\) | |||||||
\(128\) | 1.50711e9 | + | 2.61040e9i | 0.496251 | + | 0.859531i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.43527e9 | + | 2.48596e9i | −0.440747 | + | 0.763396i | ||||
\(131\) | −9.06758e8 | + | 1.57055e9i | −0.269011 | + | 0.465941i | −0.968607 | − | 0.248598i | \(-0.920030\pi\) |
0.699596 | + | 0.714539i | \(0.253364\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.59569e8 | + | 2.76382e8i | 0.0442198 | + | 0.0765909i | ||||
\(134\) | −2.10629e9 | −0.564347 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.20419e9 | 0.803144 | ||||||||
\(137\) | 3.25621e9 | + | 5.63992e9i | 0.789714 | + | 1.36783i | 0.926142 | + | 0.377175i | \(0.123104\pi\) |
−0.136428 | + | 0.990650i | \(0.543562\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.16659e8 | − | 1.58770e9i | 0.208277 | − | 0.360746i | −0.742895 | − | 0.669408i | \(-0.766548\pi\) |
0.951172 | + | 0.308662i | \(0.0998811\pi\) | |||||||
\(140\) | 3.12322e9 | − | 5.40957e9i | 0.687110 | − | 1.19011i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.12641e9 | − | 1.95099e9i | −0.232487 | − | 0.402679i | ||||
\(143\) | 3.15493e9 | 0.630925 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.51604e9 | −0.472674 | ||||||||
\(146\) | 5.94308e8 | + | 1.02937e9i | 0.108249 | + | 0.187493i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.43241e9 | + | 2.48101e9i | −0.245408 | + | 0.425060i | ||||
\(149\) | −5.34302e8 | + | 9.25439e8i | −0.0888074 | + | 0.153819i | −0.907007 | − | 0.421115i | \(-0.861639\pi\) |
0.818200 | + | 0.574934i | \(0.194972\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.03980e9 | + | 6.99713e9i | 0.632358 | + | 1.09528i | 0.987068 | + | 0.160300i | \(0.0512463\pi\) |
−0.354710 | + | 0.934976i | \(0.615420\pi\) | |||||||
\(152\) | −3.78781e8 | −0.0575562 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.89733e8 | 0.127473 | ||||||||
\(155\) | −8.60707e8 | − | 1.49079e9i | −0.119774 | − | 0.207455i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.62446e9 | + | 6.27775e9i | −0.476096 | + | 0.824623i | −0.999625 | − | 0.0273849i | \(-0.991282\pi\) |
0.523528 | + | 0.852008i | \(0.324615\pi\) | |||||||
\(158\) | 9.03496e8 | − | 1.56490e9i | 0.115337 | − | 0.199770i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.67316e9 | + | 9.82619e9i | 0.684360 | + | 1.18535i | ||||
\(161\) | 1.89839e9 | 0.222673 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.25726e10 | −1.39502 | −0.697511 | − | 0.716574i | \(-0.745709\pi\) | ||||
−0.697511 | + | 0.716574i | \(0.745709\pi\) | |||||||
\(164\) | 5.61999e8 | + | 9.73411e8i | 0.0606650 | + | 0.105075i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.28814e9 | − | 2.23113e9i | 0.131667 | − | 0.228054i | ||||
\(167\) | −7.07474e9 | + | 1.22538e10i | −0.703860 | + | 1.21912i | 0.263241 | + | 0.964730i | \(0.415209\pi\) |
−0.967101 | + | 0.254392i | \(0.918125\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.04581e9 | − | 1.56678e10i | −0.853016 | − | 1.47747i | ||||
\(170\) | 7.33929e9 | 0.673959 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.41688e10 | 1.23440 | ||||||||
\(173\) | −6.14075e9 | − | 1.06361e10i | −0.521211 | − | 0.902764i | −0.999696 | − | 0.0246683i | \(-0.992147\pi\) |
0.478484 | − | 0.878096i | \(-0.341186\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.14771e9 | − | 1.58443e10i | 0.737294 | − | 1.27703i | ||||
\(176\) | 1.63304e9 | − | 2.82851e9i | 0.128289 | − | 0.222203i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.97823e9 | − | 6.89049e9i | −0.297030 | − | 0.514470i | ||||
\(179\) | 5.47007e8 | 0.0398249 | 0.0199124 | − | 0.999802i | \(-0.493661\pi\) | ||||
0.0199124 | + | 0.999802i | \(0.493661\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.46578e9 | 0.586291 | 0.293146 | − | 0.956068i | \(-0.405298\pi\) | ||||
0.293146 | + | 0.956068i | \(0.405298\pi\) | |||||||
\(182\) | −4.04634e9 | − | 7.00847e9i | −0.273364 | − | 0.473481i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.12659e9 | + | 1.95130e9i | −0.0724576 | + | 0.125500i | ||||
\(185\) | −6.98716e9 | + | 1.21021e10i | −0.438559 | + | 0.759606i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.03320e9 | − | 6.98571e9i | −0.241192 | − | 0.417757i | ||||
\(188\) | 4.59640e9 | 0.268354 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.67609e8 | −0.0482984 | ||||||||
\(191\) | −1.45905e10 | − | 2.52716e10i | −0.793271 | − | 1.37399i | −0.923932 | − | 0.382558i | \(-0.875043\pi\) |
0.130661 | − | 0.991427i | \(-0.458290\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.06260e10 | + | 1.84048e10i | −0.551268 | + | 0.954824i | 0.446915 | + | 0.894576i | \(0.352522\pi\) |
−0.998183 | + | 0.0602479i | \(0.980811\pi\) | |||||||
\(194\) | 1.03305e9 | − | 1.78929e9i | 0.0523615 | − | 0.0906928i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.40266e8 | − | 5.89357e8i | −0.0164689 | − | 0.0285251i | ||||
\(197\) | −1.91891e10 | −0.907728 | −0.453864 | − | 0.891071i | \(-0.649955\pi\) | ||||
−0.453864 | + | 0.891071i | \(0.649955\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.01109e9 | 0.271716 | 0.135858 | − | 0.990728i | \(-0.456621\pi\) | ||||
0.135858 | + | 0.990728i | \(0.456621\pi\) | |||||||
\(200\) | 1.08573e10 | + | 1.88054e10i | 0.479829 | + | 0.831088i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.75587e9 | − | 6.50536e9i | 0.158719 | − | 0.274910i | ||||
\(203\) | 3.54663e9 | − | 6.14295e9i | 0.146583 | − | 0.253889i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.74138e9 | + | 4.74821e9i | 0.108412 | + | 0.187775i | ||||
\(206\) | −1.28276e9 | −0.0496298 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.97071e10 | −1.10046 | ||||||||
\(209\) | 4.76782e8 | + | 8.25811e8i | 0.0172847 | + | 0.0299380i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.05024e9 | − | 1.04793e10i | 0.210137 | − | 0.363967i | −0.741621 | − | 0.670820i | \(-0.765942\pi\) |
0.951757 | + | 0.306852i | \(0.0992758\pi\) | |||||||
\(212\) | 7.53038e9 | − | 1.30430e10i | 0.256039 | − | 0.443472i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.35562e9 | + | 1.27403e10i | 0.239749 | + | 0.415258i | ||||
\(215\) | 6.91142e10 | 2.20594 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.85304e9 | 0.148575 | ||||||||
\(218\) | −9.99697e8 | − | 1.73153e9i | −0.0299788 | − | 0.0519248i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.33197e9 | − | 1.61634e10i | 0.268579 | − | 0.465192i | ||||
\(221\) | −3.66845e10 | + | 6.35395e10i | −1.03447 | + | 1.79175i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.63189e10 | + | 4.55857e10i | 0.712682 | + | 1.23440i | 0.963847 | + | 0.266457i | \(0.0858530\pi\) |
−0.251165 | + | 0.967944i | \(0.580814\pi\) | |||||||
\(224\) | −3.19877e10 | −0.848921 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.50322e10 | −0.638279 | ||||||||
\(227\) | 6.19793e9 | + | 1.07351e10i | 0.154928 | + | 0.268343i | 0.933033 | − | 0.359791i | \(-0.117152\pi\) |
−0.778105 | + | 0.628135i | \(0.783819\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.20676e10 | + | 3.82222e10i | −0.530268 | + | 0.918451i | 0.469108 | + | 0.883141i | \(0.344575\pi\) |
−0.999376 | + | 0.0353106i | \(0.988758\pi\) | |||||||
\(230\) | −2.58047e9 | + | 4.46951e9i | −0.0608029 | + | 0.105314i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.20945e9 | + | 7.29099e9i | 0.0953959 | + | 0.165231i | ||||
\(233\) | 5.44229e10 | 1.20971 | 0.604853 | − | 0.796337i | \(-0.293232\pi\) | ||||
0.604853 | + | 0.796337i | \(0.293232\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.24208e10 | 0.479563 | ||||||||
\(236\) | 1.05882e10 | + | 1.83393e10i | 0.222187 | + | 0.384840i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.03455e10 | + | 1.79190e10i | −0.209005 | + | 0.362007i | ||||
\(239\) | 4.21933e10 | − | 7.30809e10i | 0.836474 | − | 1.44882i | −0.0563504 | − | 0.998411i | \(-0.517946\pi\) |
0.892825 | − | 0.450405i | \(-0.148720\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.24645e10 | − | 5.62302e10i | −0.619916 | − | 1.07373i | −0.989501 | − | 0.144528i | \(-0.953833\pi\) |
0.369585 | − | 0.929197i | \(-0.379500\pi\) | |||||||
\(242\) | −1.54136e10 | −0.288892 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.78212e10 | 0.502483 | ||||||||
\(245\) | −1.65978e9 | − | 2.87483e9i | −0.0294309 | − | 0.0509759i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.33663e9 | − | 7.51127e9i | 0.0741338 | − | 0.128404i | ||||
\(248\) | −2.88001e9 | + | 4.98832e9i | −0.0483460 | + | 0.0837378i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.32065e9 | + | 1.44118e10i | 0.134719 | + | 0.233339i | ||||
\(251\) | −4.84990e10 | −0.771260 | −0.385630 | − | 0.922654i | \(-0.626016\pi\) | ||||
−0.385630 | + | 0.922654i | \(0.626016\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.67225e9 | 0.0870389 | ||||||||
\(254\) | 4.81904e9 | + | 8.34682e9i | 0.0726455 | + | 0.125826i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.36567e9 | + | 2.36541e9i | −0.0198731 | + | 0.0344213i | ||||
\(257\) | 1.82031e10 | − | 3.15287e10i | 0.260284 | − | 0.450824i | −0.706034 | − | 0.708178i | \(-0.749517\pi\) |
0.966317 | + | 0.257354i | \(0.0828506\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.96983e10 | − | 3.41185e10i | −0.272007 | − | 0.471130i | ||||
\(260\) | −1.69760e11 | −2.30386 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.38994e10 | 0.182238 | ||||||||
\(263\) | −1.36692e10 | − | 2.36758e10i | −0.176174 | − | 0.305143i | 0.764393 | − | 0.644751i | \(-0.223039\pi\) |
−0.940567 | + | 0.339608i | \(0.889706\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.67325e10 | − | 6.36225e10i | 0.457556 | − | 0.792509i | ||||
\(266\) | 1.22299e9 | − | 2.11828e9i | 0.0149780 | − | 0.0259427i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.22816e10 | − | 1.07875e11i | −0.737485 | − | 1.27736i | ||||
\(269\) | −1.34342e9 | −0.0156432 | −0.00782159 | − | 0.999969i | \(-0.502490\pi\) | ||||
−0.00782159 | + | 0.999969i | \(0.502490\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.98471e10 | −0.223530 | −0.111765 | − | 0.993735i | \(-0.535650\pi\) | ||||
−0.111765 | + | 0.993735i | \(0.535650\pi\) | |||||||
\(272\) | 3.79769e10 | + | 6.57780e10i | 0.420688 | + | 0.728652i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.49566e10 | − | 4.32262e10i | 0.267491 | − | 0.463307i | ||||
\(275\) | 2.73327e10 | − | 4.73417e10i | 0.288195 | − | 0.499168i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.66879e10 | + | 1.15507e11i | 0.680594 | + | 1.17882i | 0.974800 | + | 0.223081i | \(0.0716113\pi\) |
−0.294206 | + | 0.955742i | \(0.595055\pi\) | |||||||
\(278\) | −1.40511e10 | −0.141094 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.01954e11 | −0.991272 | ||||||||
\(281\) | 3.21667e9 | + | 5.57144e9i | 0.0307772 | + | 0.0533076i | 0.881004 | − | 0.473109i | \(-0.156868\pi\) |
−0.850227 | + | 0.526417i | \(0.823535\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.92398e10 | − | 3.33244e10i | 0.178305 | − | 0.308833i | −0.762995 | − | 0.646404i | \(-0.776272\pi\) |
0.941300 | + | 0.337571i | \(0.109605\pi\) | |||||||
\(284\) | 6.66143e10 | − | 1.15379e11i | 0.607624 | − | 1.05244i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.20902e10 | − | 2.09408e10i | −0.106853 | − | 0.185075i | ||||
\(287\) | −1.54571e10 | −0.134480 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.89991e10 | 0.581839 | ||||||||
\(290\) | 9.64187e9 | + | 1.67002e10i | 0.0800516 | + | 0.138653i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.51466e10 | + | 6.08757e10i | −0.282918 | + | 0.490028i | ||||
\(293\) | −9.29644e10 | + | 1.61019e11i | −0.736906 | + | 1.27636i | 0.216976 | + | 0.976177i | \(0.430381\pi\) |
−0.953882 | + | 0.300182i | \(0.902953\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.16484e10 | + | 8.94576e10i | 0.397061 | + | 0.687730i | ||||
\(296\) | 4.67594e10 | 0.354043 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.19013e9 | 0.0601613 | ||||||||
\(299\) | −2.57964e10 | − | 4.46806e10i | −0.186654 | − | 0.323295i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.74240e10 | + | 1.68743e11i | −0.684096 | + | 1.18489i | ||||
\(302\) | 3.09623e10 | − | 5.36283e10i | 0.214191 | − | 0.370990i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.48941e9 | − | 7.77589e9i | −0.0301480 | − | 0.0522179i | ||||
\(305\) | 1.35709e11 | 0.897966 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.44816e11 | 0.930450 | 0.465225 | − | 0.885192i | \(-0.345973\pi\) | ||||
0.465225 | + | 0.885192i | \(0.345973\pi\) | |||||||
\(308\) | 2.63089e10 | + | 4.55683e10i | 0.166580 | + | 0.288526i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.59673e9 | + | 1.14259e10i | −0.0405697 | + | 0.0702687i | ||||
\(311\) | 8.64353e9 | − | 1.49710e10i | 0.0523925 | − | 0.0907465i | −0.838640 | − | 0.544687i | \(-0.816649\pi\) |
0.891032 | + | 0.453940i | \(0.149982\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.03029e10 | − | 5.24862e10i | −0.178457 | − | 0.309097i | 0.762895 | − | 0.646522i | \(-0.223777\pi\) |
−0.941352 | + | 0.337425i | \(0.890444\pi\) | |||||||
\(314\) | 5.55580e10 | 0.322525 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.06863e11 | 0.602887 | ||||||||
\(317\) | 1.23929e11 | + | 2.14652e11i | 0.689298 | + | 1.19390i | 0.972065 | + | 0.234710i | \(0.0754140\pi\) |
−0.282768 | + | 0.959188i | \(0.591253\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.05971e10 | − | 1.83547e10i | 0.0572966 | − | 0.0992407i | ||||
\(320\) | −5.57776e10 | + | 9.66096e10i | −0.297361 | + | 0.515045i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.27492e9 | − | 1.26005e10i | −0.0377118 | − | 0.0653187i | ||||
\(323\) | −2.21755e10 | −0.113360 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.97217e11 | −2.47213 | ||||||||
\(326\) | 4.81803e10 | + | 8.34507e10i | 0.236260 | + | 0.409214i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.17290e9 | − | 1.58879e10i | 0.0437597 | − | 0.0757941i | ||||
\(329\) | −3.16046e10 | + | 5.47407e10i | −0.148720 | + | 0.257590i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.52348e10 | − | 2.63875e10i | −0.0697607 | − | 0.120829i | 0.829035 | − | 0.559196i | \(-0.188890\pi\) |
−0.898796 | + | 0.438367i | \(0.855557\pi\) | |||||||
\(332\) | 1.52358e11 | 0.688248 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.08446e11 | 0.476821 | ||||||||
\(335\) | −3.03804e11 | − | 5.26203e11i | −1.31793 | − | 2.28272i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.66771e10 | + | 4.62062e10i | −0.112669 | + | 0.195149i | −0.916846 | − | 0.399242i | \(-0.869273\pi\) |
0.804177 | + | 0.594391i | \(0.202607\pi\) | |||||||
\(338\) | −6.93299e10 | + | 1.20083e11i | −0.288932 | + | 0.500445i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.17018e11 | + | 3.75886e11i | 0.880726 | + | 1.52546i | ||||
\(341\) | 1.45006e10 | 0.0580751 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.60889e11 | 1.01773 | ||||||||
\(344\) | −1.15631e11 | − | 2.00279e11i | −0.445207 | − | 0.771122i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.70646e10 | + | 8.15184e10i | −0.176544 | + | 0.305783i | ||||
\(347\) | −6.25615e10 | + | 1.08360e11i | −0.231646 | + | 0.401222i | −0.958293 | − | 0.285789i | \(-0.907744\pi\) |
0.726647 | + | 0.687011i | \(0.241078\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.27508e11 | − | 2.20851e11i | −0.460070 | − | 0.796865i | 0.538894 | − | 0.842374i | \(-0.318842\pi\) |
−0.998964 | + | 0.0455090i | \(0.985509\pi\) | |||||||
\(350\) | −1.40222e11 | −0.499470 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9.55772e10 | −0.331827 | ||||||||
\(353\) | 1.66531e10 | + | 2.88441e10i | 0.0570834 | + | 0.0988713i | 0.893155 | − | 0.449749i | \(-0.148487\pi\) |
−0.836072 | + | 0.548620i | \(0.815153\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.24938e11 | − | 5.62810e11i | 1.08586 | − | 1.88076i | ||||
\(356\) | 2.35267e11 | − | 4.07495e11i | 0.776313 | − | 1.34461i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.09622e9 | − | 3.63076e9i | −0.00674471 | − | 0.0116822i | ||||
\(359\) | 8.10854e10 | 0.257643 | 0.128821 | − | 0.991668i | \(-0.458881\pi\) | ||||
0.128821 | + | 0.991668i | \(0.458881\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.20066e11 | −0.991876 | ||||||||
\(362\) | −3.24422e10 | − | 5.61916e10i | −0.0992938 | − | 0.171982i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.39296e11 | − | 4.14472e11i | 0.714461 | − | 1.23748i | ||||
\(365\) | −1.71442e11 | + | 2.96946e11i | −0.505590 | + | 0.875708i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.35647e11 | − | 4.08152e11i | −0.678054 | − | 1.17442i | −0.975566 | − | 0.219706i | \(-0.929490\pi\) |
0.297512 | − | 0.954718i | \(-0.403843\pi\) | |||||||
\(368\) | −5.34103e10 | −0.151813 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.07104e11 | 0.297096 | ||||||||
\(371\) | 1.03557e11 | + | 1.79366e11i | 0.283790 | + | 0.491538i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.53168e11 | + | 4.38500e11i | −0.677204 | + | 1.17295i | 0.298616 | + | 0.954373i | \(0.403475\pi\) |
−0.975819 | + | 0.218578i | \(0.929858\pi\) | |||||||
\(374\) | −3.09117e10 | + | 5.35407e10i | −0.0816961 | + | 0.141502i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.75110e10 | − | 6.49710e10i | −0.0967863 | − | 0.167639i | ||||
\(377\) | −1.92775e11 | −0.491489 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.43255e11 | 0.854557 | 0.427278 | − | 0.904120i | \(-0.359472\pi\) | ||||
0.427278 | + | 0.904120i | \(0.359472\pi\) | |||||||
\(380\) | −2.56546e10 | − | 4.44351e10i | −0.0631161 | − | 0.109320i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.11827e11 | + | 1.93689e11i | −0.268695 | + | 0.465394i | ||||
\(383\) | −2.19794e11 | + | 3.80695e11i | −0.521942 | + | 0.904030i | 0.477732 | + | 0.878506i | \(0.341459\pi\) |
−0.999674 | + | 0.0255246i | \(0.991874\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.28332e11 | + | 2.22278e11i | 0.297689 | + | 0.515612i | ||||
\(386\) | 1.62882e11 | 0.373449 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.22186e11 | 0.273703 | ||||||||
\(389\) | −2.52265e11 | − | 4.36935e11i | −0.558577 | − | 0.967484i | −0.997616 | − | 0.0690158i | \(-0.978014\pi\) |
0.439038 | − | 0.898468i | \(-0.355319\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.59551e10 | + | 1.14238e11i | −0.142709 | + | 0.247180i | ||||
\(392\) | −5.55379e9 | + | 9.61945e9i | −0.0118796 | + | 0.0205761i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.35356e10 | + | 1.27367e11i | 0.153732 | + | 0.266272i | ||||
\(395\) | 5.21269e11 | 1.07739 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.62244e11 | −0.529844 | −0.264922 | − | 0.964270i | \(-0.585346\pi\) | ||||
−0.264922 | + | 0.964270i | \(0.585346\pi\) | |||||||
\(398\) | −2.30355e10 | − | 3.98986e10i | −0.0460175 | − | 0.0797047i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.57367e11 | + | 4.45773e11i | −0.502670 | + | 0.870650i | ||||
\(401\) | 1.23763e11 | − | 2.14363e11i | 0.239023 | − | 0.414000i | −0.721411 | − | 0.692507i | \(-0.756506\pi\) |
0.960434 | + | 0.278507i | \(0.0898395\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.59459e10 | − | 1.14222e11i | −0.124542 | − | 0.215713i | ||||
\(404\) | 4.44235e11 | 0.829654 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.43651e10 | −0.0993008 | ||||||||
\(407\) | −5.88573e10 | − | 1.01944e11i | −0.106323 | − | 0.184156i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.78721e10 | + | 1.34878e11i | −0.137603 | + | 0.238335i | −0.926589 | − | 0.376076i | \(-0.877273\pi\) |
0.788986 | + | 0.614411i | \(0.210606\pi\) | |||||||
\(410\) | 2.10108e10 | − | 3.63918e10i | 0.0367210 | − | 0.0636027i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.79304e10 | − | 6.56973e10i | −0.0648559 | − | 0.112334i | ||||
\(413\) | −2.91216e11 | −0.492538 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.43190e11 | 1.22994 | ||||||||
\(416\) | 4.34668e11 | + | 7.52866e11i | 0.711602 | + | 1.23253i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.65421e9 | − | 6.32928e9i | 0.00585464 | − | 0.0101405i | ||||
\(419\) | 4.60177e11 | − | 7.97051e11i | 0.729394 | − | 1.26335i | −0.227746 | − | 0.973721i | \(-0.573135\pi\) |
0.957140 | − | 0.289627i | \(-0.0935312\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.28419e11 | + | 7.42043e11i | 0.664660 | + | 1.15122i | 0.979377 | + | 0.202039i | \(0.0647567\pi\) |
−0.314718 | + | 0.949185i | \(0.601910\pi\) | |||||||
\(422\) | −9.27419e10 | −0.142354 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.45821e11 | −0.369379 | ||||||||
\(425\) | 6.35632e11 | + | 1.10095e12i | 0.945052 | + | 1.63688i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.91297e11 | + | 3.31336e11i | −0.278472 | + | 0.482328i | ||||
\(428\) | −4.35002e11 | + | 7.53446e11i | −0.626606 | + | 1.08531i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.64857e11 | − | 4.58745e11i | −0.373597 | − | 0.647088i | ||||
\(431\) | −5.94731e11 | −0.830181 | −0.415090 | − | 0.909780i | \(-0.636250\pi\) | ||||
−0.415090 | + | 0.909780i | \(0.636250\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.28268e12 | −1.75357 | −0.876787 | − | 0.480880i | \(-0.840317\pi\) | ||||
−0.876787 | + | 0.480880i | \(0.840317\pi\) | |||||||
\(434\) | −1.85976e10 | − | 3.22120e10i | −0.0251625 | − | 0.0435827i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.91209e10 | − | 1.02400e11i | 0.0783522 | − | 0.135710i | ||||
\(437\) | 7.79683e9 | − | 1.35045e10i | 0.0102271 | − | 0.0177138i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.00633e11 | + | 6.93916e11i | 0.514821 | + | 0.891696i | 0.999852 | + | 0.0171991i | \(0.00547493\pi\) |
−0.485031 | + | 0.874497i | \(0.661192\pi\) | |||||||
\(440\) | −3.04631e11 | −0.387470 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.62324e11 | 0.700787 | ||||||||
\(443\) | 3.57521e11 | + | 6.19245e11i | 0.441047 | + | 0.763916i | 0.997767 | − | 0.0667840i | \(-0.0212739\pi\) |
−0.556720 | + | 0.830700i | \(0.687941\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.14761e12 | − | 1.98772e12i | 1.38731 | − | 2.40290i | ||||
\(446\) | 2.01716e11 | − | 3.49383e11i | 0.241398 | − | 0.418114i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.57249e11 | − | 2.72363e11i | −0.184432 | − | 0.319446i | ||||
\(449\) | −8.30808e11 | −0.964700 | −0.482350 | − | 0.875979i | \(-0.660217\pi\) | ||||
−0.482350 | + | 0.875979i | \(0.660217\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.61847e10 | −0.0525659 | ||||||||
\(452\) | −7.40185e11 | − | 1.28204e12i | −0.834099 | − | 1.44470i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.75029e10 | − | 8.22774e10i | 0.0524770 | − | 0.0908928i | ||||
\(455\) | 1.16726e12 | − | 2.02176e12i | 1.27678 | − | 2.21145i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.80720e11 | − | 4.86221e11i | −0.301058 | − | 0.521447i | 0.675318 | − | 0.737527i | \(-0.264006\pi\) |
−0.976376 | + | 0.216079i | \(0.930673\pi\) | |||||||
\(458\) | 3.38266e11 | 0.359223 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.05212e11 | −0.317827 | ||||||||
\(461\) | 2.67794e11 | + | 4.63834e11i | 0.276151 | + | 0.478308i | 0.970425 | − | 0.241403i | \(-0.0776075\pi\) |
−0.694274 | + | 0.719711i | \(0.744274\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.33673e11 | + | 1.09755e12i | −0.640841 | + | 1.10997i | 0.344404 | + | 0.938822i | \(0.388081\pi\) |
−0.985245 | + | 0.171148i | \(0.945252\pi\) | |||||||
\(464\) | −9.97831e10 | + | 1.72829e11i | −0.0999369 | + | 0.173096i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.08557e11 | − | 3.61231e11i | −0.204875 | − | 0.354853i | ||||
\(467\) | −9.53957e11 | −0.928117 | −0.464059 | − | 0.885804i | \(-0.653607\pi\) | ||||
−0.464059 | + | 0.885804i | \(0.653607\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.71298e12 | 1.63483 | ||||||||
\(470\) | −8.59201e10 | − | 1.48818e11i | −0.0812184 | − | 0.140674i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.72820e11 | − | 2.99333e11i | 0.160271 | − | 0.277598i | ||||
\(473\) | −2.91096e11 | + | 5.04194e11i | −0.267400 | + | 0.463151i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.51408e10 | − | 1.30148e11i | −0.0677258 | − | 0.117305i | ||||
\(476\) | −1.22364e12 | −1.09251 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.46765e11 | −0.566658 | ||||||||
\(479\) | −6.43441e11 | − | 1.11447e12i | −0.558469 | − | 0.967297i | −0.997625 | − | 0.0688858i | \(-0.978056\pi\) |
0.439155 | − | 0.898411i | \(-0.355278\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.35344e11 | + | 9.27243e11i | −0.456016 | + | 0.789843i | ||||
\(482\) | −2.48819e11 | + | 4.30966e11i | −0.209977 | + | 0.363690i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.55770e11 | − | 7.89418e11i | −0.377522 | − | 0.653887i | ||||
\(485\) | 5.96012e11 | 0.489122 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.22356e12 | −0.985704 | −0.492852 | − | 0.870113i | \(-0.664046\pi\) | ||||
−0.492852 | + | 0.870113i | \(0.664046\pi\) | |||||||
\(488\) | −2.27048e11 | − | 3.93258e11i | −0.181229 | − | 0.313898i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.27211e10 | + | 2.20336e10i | −0.00996880 | + | 0.0172665i | ||||
\(491\) | −5.85291e11 | + | 1.01375e12i | −0.454470 | + | 0.787165i | −0.998658 | − | 0.0517987i | \(-0.983505\pi\) |
0.544188 | + | 0.838963i | \(0.316838\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.46439e11 | + | 4.26845e11i | 0.187888 | + | 0.325431i | ||||
\(494\) | −6.64747e10 | −0.0502210 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.36538e11 | −0.101295 | ||||||||
\(497\) | 9.16072e11 | + | 1.58668e12i | 0.673482 | + | 1.16650i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.10884e12 | − | 1.92057e12i | 0.800602 | − | 1.38668i | −0.118619 | − | 0.992940i | \(-0.537847\pi\) |
0.919221 | − | 0.393743i | \(-0.128820\pi\) | |||||||
\(500\) | −4.92073e11 | + | 8.52296e11i | −0.352099 | + | 0.609853i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.85856e11 | + | 3.21912e11i | 0.130620 | + | 0.226240i | ||||
\(503\) | 2.31868e12 | 1.61505 | 0.807524 | − | 0.589834i | \(-0.200807\pi\) | ||||
0.807524 | + | 0.589834i | \(0.200807\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.16694e12 | 1.48264 | ||||||||
\(506\) | −2.17370e10 | − | 3.76495e10i | −0.0147408 | − | 0.0255319i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.84992e11 | + | 4.93621e11i | −0.189866 | + | 0.328857i | ||||
\(509\) | 1.26661e12 | − | 2.19383e12i | 0.836396 | − | 1.44868i | −0.0564927 | − | 0.998403i | \(-0.517992\pi\) |
0.892889 | − | 0.450277i | \(-0.148675\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.83332e11 | − | 8.37155e11i | −0.313582 | − | 0.543140i | ||||
\(512\) | 1.56422e12 | 1.00596 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.79029e11 | −0.176326 | ||||||||
\(515\) | −1.85021e11 | − | 3.20465e11i | −0.115901 | − | 0.200747i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.44323e10 | + | 1.63562e11i | −0.0581317 | + | 0.100687i | ||||
\(518\) | −1.50974e11 | + | 2.61495e11i | −0.0921338 | + | 0.159580i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.38541e12 | + | 2.39960e12i | 0.830926 | + | 1.43921i | ||||
\(521\) | −9.44125e11 | −0.561384 | −0.280692 | − | 0.959798i | \(-0.590564\pi\) | ||||
−0.280692 | + | 0.959798i | \(0.590564\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.67874e12 | −0.981128 | −0.490564 | − | 0.871405i | \(-0.663209\pi\) | ||||
−0.490564 | + | 0.871405i | \(0.663209\pi\) | |||||||
\(524\) | 4.10995e11 | + | 7.11865e11i | 0.238148 | + | 0.412484i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.04765e11 | + | 1.81459e11i | −0.0596735 | + | 0.103358i | ||||
\(527\) | −1.68608e11 | + | 2.92037e11i | −0.0952204 | + | 0.164927i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.54197e11 | + | 1.47951e12i | 0.474250 | + | 0.821425i | ||||
\(530\) | −5.63059e11 | −0.309965 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.44652e11 | 0.0782929 | ||||||||
\(533\) | 2.10040e11 | + | 3.63799e11i | 0.112727 | + | 0.195249i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.12190e12 | + | 3.67524e12i | −1.11978 | + | 1.93952i | ||||
\(536\) | −1.01656e12 | + | 1.76073e12i | −0.531973 | + | 0.921404i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.14818e9 | + | 8.91691e9i | 0.00264932 | + | 0.00458875i | ||||
\(539\) | 2.79628e10 | 0.0142703 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.34365e12 | −0.674372 | −0.337186 | − | 0.941438i | \(-0.609475\pi\) | ||||
−0.337186 | + | 0.941438i | \(0.609475\pi\) | |||||||
\(542\) | 7.60574e10 | + | 1.31735e11i | 0.0378569 | + | 0.0655700i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.11134e12 | − | 1.92490e12i | 0.544066 | − | 0.942351i | ||||
\(545\) | 2.88386e11 | − | 4.99499e11i | 0.140020 | − | 0.242522i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.04392e11 | + | 5.27222e11i | 0.145375 | + | 0.251797i | 0.929513 | − | 0.368790i | \(-0.120228\pi\) |
−0.784138 | + | 0.620587i | \(0.786894\pi\) | |||||||
\(548\) | 2.95181e12 | 1.39822 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.18974e11 | −0.195234 | ||||||||
\(551\) | −2.91326e10 | − | 5.04592e10i | −0.0134647 | − | 0.0233216i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.34785e11 | + | 1.27268e12i | −0.334116 | + | 0.578706i | ||||
\(554\) | 5.11117e11 | − | 8.85281e11i | 0.230529 | − | 0.399289i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.15483e11 | − | 7.19638e11i | −0.184381 | − | 0.319358i | ||||
\(557\) | 6.12226e11 | 0.269503 | 0.134751 | − | 0.990879i | \(-0.456976\pi\) | ||||
0.134751 | + | 0.990879i | \(0.456976\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.29541e12 | 2.29375 | ||||||||
\(560\) | −1.20838e12 | − | 2.09298e12i | −0.519229 | − | 0.899331i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.46536e10 | − | 4.27013e10i | 0.0104248 | − | 0.0180563i | ||||
\(563\) | −2.12194e12 | + | 3.67531e12i | −0.890114 | + | 1.54172i | −0.0503772 | + | 0.998730i | \(0.516042\pi\) |
−0.839737 | + | 0.542993i | \(0.817291\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.61055e12 | − | 6.25366e12i | −1.49058 | − | 2.58176i | ||||
\(566\) | −2.94921e11 | −0.120790 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.17455e12 | −0.876600 | ||||||||
\(569\) | −2.05395e12 | − | 3.55754e12i | −0.821456 | − | 1.42280i | −0.904598 | − | 0.426265i | \(-0.859829\pi\) |
0.0831427 | − | 0.996538i | \(-0.473504\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.90871e12 | − | 3.30597e12i | 0.751409 | − | 1.30148i | −0.195731 | − | 0.980658i | \(-0.562708\pi\) |
0.947140 | − | 0.320821i | \(-0.103959\pi\) | |||||||
\(572\) | 7.15000e11 | − | 1.23842e12i | 0.279270 | − | 0.483709i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.92340e10 | + | 1.02596e11i | 0.0227755 | + | 0.0394483i | ||||
\(575\) | −8.93946e11 | −0.341041 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.58536e12 | 0.595440 | 0.297720 | − | 0.954653i | \(-0.403774\pi\) | ||||
0.297720 | + | 0.954653i | \(0.403774\pi\) | |||||||
\(578\) | −2.64415e11 | − | 4.57981e11i | −0.0985398 | − | 0.170676i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.70208e11 | + | 9.87629e11i | −0.209222 | + | 0.362383i | ||||
\(581\) | −1.04761e12 | + | 1.81451e12i | −0.381422 | + | 0.660643i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.09421e11 | + | 5.35933e11i | 0.110928 | + | 0.192133i | ||||
\(584\) | 1.14732e12 | 0.408157 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.42502e12 | 0.499207 | ||||||||
\(587\) | 7.16024e11 | + | 1.24019e12i | 0.248918 | + | 0.431139i | 0.963226 | − | 0.268693i | \(-0.0865917\pi\) |
−0.714308 | + | 0.699832i | \(0.753258\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.99318e10 | − | 3.45230e10i | 0.00682384 | − | 0.0118192i | ||||
\(590\) | 3.95850e11 | − | 6.85632e11i | 0.134492 | − | 0.232947i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.54204e11 | + | 9.59910e11i | 0.185448 | + | 0.321205i | ||||
\(593\) | −4.74549e12 | −1.57592 | −0.787961 | − | 0.615725i | \(-0.788863\pi\) | ||||
−0.787961 | + | 0.615725i | \(0.788863\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.96881e12 | −1.95237 | ||||||||
\(596\) | 2.42177e11 | + | 4.19463e11i | 0.0786185 | + | 0.136171i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.97712e11 | + | 3.42446e11i | −0.0632232 | + | 0.109506i | ||||
\(599\) | 7.86184e10 | − | 1.36171e11i | 0.0249519 | − | 0.0432179i | −0.853280 | − | 0.521453i | \(-0.825390\pi\) |
0.878232 | + | 0.478235i | \(0.158723\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.65008e12 | + | 2.85803e12i | 0.515906 | + | 0.893576i | 0.999830 | + | 0.0184653i | \(0.00587803\pi\) |
−0.483923 | + | 0.875110i | \(0.660789\pi\) | |||||||
\(602\) | 1.49338e12 | 0.463431 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.66214e12 | 1.11962 | ||||||||
\(605\) | −2.22321e12 | − | 3.85070e12i | −0.674653 | − | 1.16853i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.95171e12 | − | 3.38046e12i | 0.583534 | − | 1.01071i | −0.411522 | − | 0.911400i | \(-0.635003\pi\) |
0.995056 | − | 0.0993113i | \(-0.0316640\pi\) | |||||||
\(608\) | −1.31376e11 | + | 2.27550e11i | −0.0389898 | + | 0.0675323i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.20059e11 | − | 9.00768e11i | −0.152079 | − | 0.263408i | ||||
\(611\) | 1.71784e12 | 0.498653 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.67659e12 | −0.765615 | −0.382807 | − | 0.923828i | \(-0.625043\pi\) | ||||
−0.382807 | + | 0.923828i | \(0.625043\pi\) | |||||||
\(614\) | −5.54957e11 | − | 9.61214e11i | −0.157580 | − | 0.272937i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.29411e11 | − | 7.43762e11i | 0.120160 | − | 0.208123i | ||||
\(617\) | 1.82429e12 | − | 3.15976e12i | 0.506769 | − | 0.877750i | −0.493200 | − | 0.869916i | \(-0.664173\pi\) |
0.999969 | − | 0.00783384i | \(-0.00249362\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.83256e11 | − | 8.37024e11i | −0.132303 | − | 0.229155i | 0.792261 | − | 0.610182i | \(-0.208904\pi\) |
−0.924564 | + | 0.381027i | \(0.875571\pi\) | |||||||
\(620\) | −7.80245e11 | −0.212065 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.32493e11 | −0.0354926 | ||||||||
\(623\) | 3.23537e12 | + | 5.60382e12i | 0.860454 | + | 1.49035i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.66099e11 | − | 8.07307e11i | 0.122185 | − | 0.211631i | ||||
\(626\) | −2.32251e11 | + | 4.02271e11i | −0.0604468 | + | 0.104697i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.64282e12 | + | 2.84544e12i | 0.421474 | + | 0.730014i | ||||
\(629\) | 2.73749e12 | 0.697308 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.92249e12 | −1.23610 | −0.618049 | − | 0.786139i | \(-0.712077\pi\) | ||||
−0.618049 | + | 0.786139i | \(0.712077\pi\) | |||||||
\(632\) | −8.72106e11 | − | 1.51053e12i | −0.217442 | − | 0.376620i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.49832e11 | − | 1.64516e12i | 0.233478 | − | 0.404395i | ||||
\(635\) | −1.39016e12 | + | 2.40784e12i | −0.339300 | + | 0.587686i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.27170e11 | − | 2.20265e11i | −0.0306025 | − | 0.0530050i | ||||
\(638\) | −1.62439e11 | −0.0388148 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.66431e12 | 1.57016 | ||||||||
\(641\) | 2.40584e12 | + | 4.16704e12i | 0.562866 | + | 0.974913i | 0.997245 | + | 0.0741828i | \(0.0236348\pi\) |
−0.434378 | + | 0.900731i | \(0.643032\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.66650e12 | + | 4.61852e12i | −0.615167 | + | 1.06550i | 0.375189 | + | 0.926948i | \(0.377578\pi\) |
−0.990355 | + | 0.138551i | \(0.955755\pi\) | |||||||
\(644\) | 4.30230e11 | − | 7.45180e11i | 0.0985630 | − | 0.170716i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.49799e10 | + | 1.47189e11i | 0.0191986 | + | 0.0332530i | ||||
\(647\) | −6.50961e12 | −1.46045 | −0.730223 | − | 0.683209i | \(-0.760584\pi\) | ||||
−0.730223 | + | 0.683209i | \(0.760584\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.70134e11 | −0.192524 | ||||||||
\(650\) | 1.90541e12 | + | 3.30028e12i | 0.418677 | + | 0.725170i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.84932e12 | + | 4.93517e12i | −0.617486 | + | 1.06952i | ||||
\(653\) | 2.67842e12 | − | 4.63916e12i | 0.576460 | − | 0.998458i | −0.419421 | − | 0.907792i | \(-0.637767\pi\) |
0.995881 | − | 0.0906665i | \(-0.0288997\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.00480e12 | + | 3.47241e12i | 0.425583 | + | 0.737132i | ||||
\(656\) | 4.34879e11 | 0.0916856 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.84455e11 | 0.100748 | ||||||||
\(659\) | 6.53510e11 | + | 1.13191e12i | 0.134980 | + | 0.233791i | 0.925590 | − | 0.378529i | \(-0.123570\pi\) |
−0.790610 | + | 0.612320i | \(0.790236\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.08403e10 | + | 1.05379e11i | −0.0123961 | + | 0.0214707i | −0.872157 | − | 0.489226i | \(-0.837279\pi\) |
0.859761 | + | 0.510697i | \(0.170613\pi\) | |||||||
\(662\) | −1.16764e11 | + | 2.02242e11i | −0.0236292 | + | 0.0409270i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.24339e12 | − | 2.15362e12i | −0.248228 | − | 0.429944i | ||||
\(665\) | 7.05599e11 | 0.139914 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.46590e11 | −0.0678030 | ||||||||
\(668\) | 3.20668e12 | + | 5.55414e12i | 0.623106 | + | 1.07925i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.32845e12 | + | 4.03299e12i | −0.446406 | + | 0.773198i | ||||
\(671\) | −5.71582e11 | + | 9.90009e11i | −0.108850 | + | 0.188533i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.64753e12 | − | 2.85361e12i | −0.309575 | − | 0.536200i | 0.668694 | − | 0.743538i | \(-0.266854\pi\) |
−0.978269 | + | 0.207337i | \(0.933520\pi\) | |||||||
\(674\) | 4.08924e11 | 0.0763261 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.20017e12 | −1.51030 | ||||||||
\(677\) | 5.84161e11 | + | 1.01180e12i | 0.106877 | + | 0.185116i | 0.914503 | − | 0.404578i | \(-0.132582\pi\) |
−0.807627 | + | 0.589694i | \(0.799248\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.40145e11 | + | 1.45517e12i | −0.151684 | + | 0.262725i | ||||
\(680\) | 3.54215e12 | − | 6.13519e12i | 0.635298 | − | 1.10037i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.55685e10 | − | 9.62474e10i | −0.00983555 | − | 0.0170357i | ||||
\(683\) | −7.05520e11 | −0.124055 | −0.0620277 | − | 0.998074i | \(-0.519757\pi\) | ||||
−0.0620277 | + | 0.998074i | \(0.519757\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.43986e13 | 2.49870 | ||||||||
\(686\) | −9.99767e11 | − | 1.73165e12i | −0.172362 | − | 0.298539i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.74099e12 | − | 4.74753e12i | 0.466400 | − | 0.807829i | ||||
\(689\) | 2.81438e12 | − | 4.87465e12i | 0.475769 | − | 0.824056i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.84563e12 | + | 4.92877e12i | 0.474817 | + | 0.822408i | 0.999584 | − | 0.0288384i | \(-0.00918082\pi\) |
−0.524767 | + | 0.851246i | \(0.675847\pi\) | |||||||
\(692\) | −5.56669e12 | −0.922825 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.58982e11 | 0.156925 | ||||||||
\(695\) | −2.02669e12 | − | 3.51033e12i | −0.329500 | − | 0.570711i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.37021e11 | − | 9.30147e11i | 0.0861874 | − | 0.149281i | ||||
\(698\) | −9.77264e11 | + | 1.69267e12i | −0.155834 | + | 0.269913i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.14627e12 | − | 7.18155e12i | −0.652705 | − | 1.13052i | ||||
\(701\) | 3.75961e12 | 0.588046 | 0.294023 | − | 0.955798i | \(-0.405006\pi\) | ||||
0.294023 | + | 0.955798i | \(0.405006\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.23611e11 | −0.0499717 | ||||||||
\(704\) | −4.69850e11 | − | 8.13804e11i | −0.0720912 | − | 0.124866i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.27635e11 | − | 2.21070e11i | 0.0193352 | − | 0.0334895i | ||||
\(707\) | −3.05454e12 | + | 5.29061e12i | −0.459788 | + | 0.796376i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.85253e12 | + | 3.20868e12i | 0.275333 | + | 0.476890i | 0.970219 | − | 0.242229i | \(-0.0778787\pi\) |
−0.694886 | + | 0.719120i | \(0.744545\pi\) | |||||||
\(710\) | −4.98086e12 | −0.735600 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.68003e12 | −1.11996 | ||||||||
\(713\) | −1.18564e11 | − | 2.05359e11i | −0.0171811 | − | 0.0297585i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.48770e12 | − | 6.04087e12i | 0.499071 | − | 0.864416i | ||||
\(716\) | 1.23968e11 | − | 2.14718e11i | 0.0176279 | − | 0.0305324i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.10732e11 | − | 5.38204e11i | −0.0436341 | − | 0.0755765i | ||||
\(719\) | 1.23468e11 | 0.0172296 | 0.00861478 | − | 0.999963i | \(-0.497258\pi\) | ||||
0.00861478 | + | 0.999963i | \(0.497258\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.04323e12 | 0.143771 | ||||||||
\(722\) | 1.22654e12 | + | 2.12444e12i | 0.167983 | + | 0.290956i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.91859e12 | − | 3.32310e12i | 0.259513 | − | 0.449490i | ||||
\(725\) | −1.67010e12 | + | 2.89270e12i | −0.224503 | + | 0.388850i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.89947e12 | − | 1.02182e13i | −0.783264 | − | 1.35665i | −0.930031 | − | 0.367482i | \(-0.880220\pi\) |
0.146766 | − | 0.989171i | \(-0.453113\pi\) | |||||||
\(728\) | −7.81153e12 | −1.03073 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.62797e12 | 0.342505 | ||||||||
\(731\) | −6.76955e12 | − | 1.17252e13i | −0.876862 | − | 1.51877i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.53411e12 | − | 6.12126e12i | 0.452181 | − | 0.783200i | −0.546341 | − | 0.837563i | \(-0.683980\pi\) |
0.998521 | + | 0.0543633i | \(0.0173129\pi\) | |||||||
\(734\) | −1.80607e12 | + | 3.12821e12i | −0.229669 | + | 0.397799i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.81489e11 | + | 1.35358e12i | 0.0981686 | + | 0.170033i | ||||
\(737\) | 5.11826e12 | 0.639026 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.61726e12 | −0.569488 | −0.284744 | − | 0.958604i | \(-0.591909\pi\) | ||||
−0.284744 | + | 0.958604i | \(0.591909\pi\) | |||||||
\(740\) | 3.16699e12 | + | 5.48538e12i | 0.388243 | + | 0.672456i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.93693e11 | − | 1.37472e12i | 0.0961247 | − | 0.166493i | ||||
\(743\) | −7.55678e11 | + | 1.30887e12i | −0.0909677 | + | 0.157561i | −0.907919 | − | 0.419147i | \(-0.862329\pi\) |
0.816951 | + | 0.576707i | \(0.195663\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.18132e12 | + | 2.04610e12i | 0.140496 | + | 0.243346i | ||||
\(746\) | 3.88072e12 | 0.458763 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.65616e12 | −0.427040 | ||||||||
\(749\) | −5.98209e12 | − | 1.03613e13i | −0.694521 | − | 1.20294i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.49028e12 | + | 1.29735e13i | −0.859247 | + | 1.48826i | 0.0134003 | + | 0.999910i | \(0.495734\pi\) |
−0.872648 | + | 0.488350i | \(0.837599\pi\) | |||||||
\(752\) | 8.89182e11 | − | 1.54011e12i | 0.101394 | − | 0.175619i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.38743e11 | + | 1.27954e12i | 0.0832382 | + | 0.144173i | ||||
\(755\) | 1.78636e13 | 2.00082 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.27715e12 | 0.362714 | 0.181357 | − | 0.983417i | \(-0.441951\pi\) | ||||
0.181357 | + | 0.983417i | \(0.441951\pi\) | |||||||
\(758\) | −1.31541e12 | − | 2.27836e12i | −0.144727 | − | 0.250674i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.18733e11 | + | 7.25267e11i | −0.0455278 | + | 0.0788564i | ||||
\(761\) | 2.91809e12 | − | 5.05428e12i | 0.315404 | − | 0.546296i | −0.664119 | − | 0.747627i | \(-0.731193\pi\) |
0.979523 | + | 0.201331i | \(0.0645265\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.13023e11 | + | 1.40820e12i | 0.0868445 | + | 0.150419i | ||||
\(764\) | −1.32266e13 | −1.40452 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.36915e12 | 0.353583 | ||||||||
\(767\) | 3.95721e12 | + | 6.85409e12i | 0.412867 | + | 0.715106i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.88296e11 | − | 1.36537e12i | 0.0812870 | − | 0.140793i | −0.822516 | − | 0.568742i | \(-0.807430\pi\) |
0.903803 | + | 0.427949i | \(0.140764\pi\) | |||||||
\(770\) | 9.83578e11 | − | 1.70361e12i | 0.100833 | − | 0.174647i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.81633e12 | + | 8.34213e12i | 0.488021 | + | 0.845277i | ||||
\(773\) | −1.49007e13 | −1.50106 | −0.750529 | − | 0.660837i | \(-0.770201\pi\) | ||||
−0.750529 | + | 0.660837i | \(0.770201\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.28529e12 | −0.227553 | ||||||||
\(776\) | −9.97157e11 | − | 1.72713e12i | −0.0987156 | − | 0.170980i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.93344e12 | + | 3.34881e12i | −0.189200 | + | 0.327705i | ||||
\(779\) | −6.34835e10 | + | 1.09957e11i | −0.00617650 | + | 0.0106980i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.73716e12 | + | 4.74090e12i | 0.263251 | + | 0.455965i | ||||
\(782\) | 1.01100e12 | 0.0966766 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.63300e11 | −0.0248902 | ||||||||
\(785\) | 8.01350e12 | + | 1.38798e13i | 0.753198 | + | 1.30458i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.94718e12 | + | 8.56877e12i | −0.459697 | + | 0.796219i | −0.998945 | − | 0.0459287i | \(-0.985375\pi\) |
0.539248 | + | 0.842147i | \(0.318709\pi\) | |||||||
\(788\) | −4.34880e12 | + | 7.53234e12i | −0.401792 | + | 0.695925i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.99758e12 | − | 3.45992e12i | −0.182466 | − | 0.316041i | ||||
\(791\) | 2.03579e13 | 1.84901 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.03978e13 | 0.933710 | ||||||||
\(794\) | 1.00496e12 | + | 1.74064e12i | 0.0897339 | + | 0.155424i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.36229e12 | − | 2.35955e12i | 0.120271 | − | 0.208315i | ||||
\(797\) | 1.27503e11 | − | 2.20842e11i | 0.0111933 | − | 0.0193874i | −0.860374 | − | 0.509662i | \(-0.829770\pi\) |
0.871568 | + | 0.490275i | \(0.163104\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.19606e12 | − | 3.80368e12i | −0.190626 | − | 0.330174i | ||||
\(800\) | 1.50630e13 | 1.30018 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.89711e12 | −0.161923 | ||||||||
\(803\) | −1.44416e12 | − | 2.50136e12i | −0.122573 | − | 0.212303i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.09862e12 | − | 3.63492e12i | 0.176138 | − | 0.305079i | ||||
\(806\) | −5.05430e11 | + | 8.75431e11i | −0.0421846 | + | 0.0730658i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.62539e12 | − | 6.27936e12i | −0.299229 | − | 0.518279i | ||||
\(809\) | 1.62301e13 | 1.33215 | 0.666075 | − | 0.745885i | \(-0.267973\pi\) | ||||
0.666075 | + | 0.745885i | \(0.267973\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.16753e12 | −0.338287 | −0.169143 | − | 0.985591i | \(-0.554100\pi\) | ||||
−0.169143 | + | 0.985591i | \(0.554100\pi\) | |||||||
\(812\) | −1.60754e12 | − | 2.78434e12i | −0.129766 | − | 0.224761i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.51101e11 | + | 7.81330e11i | −0.0360134 | + | 0.0623770i | ||||
\(815\) | −1.38987e13 | + | 2.40733e13i | −1.10348 | + | 1.91129i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.00257e11 | + | 1.38609e12i | 0.0628392 | + | 0.108841i | ||||
\(818\) | 1.19367e12 | 0.0932171 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.48510e12 | 0.191947 | ||||||||
\(821\) | −1.10895e12 | − | 1.92075e12i | −0.0851855 | − | 0.147546i | 0.820285 | − | 0.571955i | \(-0.193815\pi\) |
−0.905470 | + | 0.424410i | \(0.860482\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.36686e11 | − | 4.09953e11i | 0.0179835 | − | 0.0311483i | −0.856894 | − | 0.515493i | \(-0.827609\pi\) |
0.874877 | + | 0.484345i | \(0.160942\pi\) | |||||||
\(824\) | −6.19096e11 | + | 1.07231e12i | −0.0467828 | + | 0.0810301i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.11599e12 | + | 1.93295e12i | 0.0834159 | + | 0.144481i | ||||
\(827\) | 3.43656e12 | 0.255475 | 0.127738 | − | 0.991808i | \(-0.459228\pi\) | ||||
0.127738 | + | 0.991808i | \(0.459228\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.73227e13 | −1.27386 | −0.636929 | − | 0.770922i | \(-0.719796\pi\) | ||||
−0.636929 | + | 0.770922i | \(0.719796\pi\) | |||||||
\(830\) | −2.84802e12 | − | 4.93292e12i | −0.208301 | − | 0.360788i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.27358e12 | + | 7.40206e12i | −0.309198 | + | 0.535547i | ||||
\(833\) | −3.25143e11 | + | 5.63163e11i | −0.0233976 | + | 0.0405258i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.56419e13 | + | 2.70926e13i | 1.11353 | + | 1.92868i | ||||
\(836\) | 4.32211e11 | 0.0306032 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.05389e12 | −0.494118 | ||||||||
\(839\) | −1.22497e13 | − | 2.12171e13i | −0.853486 | − | 1.47828i | −0.878043 | − | 0.478583i | \(-0.841151\pi\) |
0.0245567 | − | 0.999698i | \(-0.492183\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.60606e12 | − | 1.14420e13i | 0.455366 | − | 0.788717i | ||||
\(842\) | 3.28354e12 | − | 5.68726e12i | 0.225132 | − | 0.389941i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.74232e12 | − | 4.74984e12i | −0.186028 | − | 0.322209i | ||||
\(845\) | −3.99997e13 | −2.69899 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.25354e13 | 0.836879 | ||||||||
\(848\) | −2.91353e12 | − | 5.04638e12i | −0.193481 | − | 0.335119i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.87169e12 | − | 8.43801e12i | 0.320106 | − | 0.554440i | ||||
\(851\) | −9.62495e11 | + | 1.66709e12i | −0.0629094 | + | 0.108962i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.92703e12 | − | 3.33772e12i | −0.124629 | − | 0.215863i | 0.796959 | − | 0.604033i | \(-0.206441\pi\) |
−0.921588 | + | 0.388170i | \(0.873107\pi\) | |||||||
\(854\) | 2.93232e12 | 0.188647 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.42001e13 | 0.903984 | ||||||||
\(857\) | −1.88200e12 | − | 3.25971e12i | −0.119181 | − | 0.206427i | 0.800263 | − | 0.599650i | \(-0.204693\pi\) |
−0.919443 | + | 0.393223i | \(0.871360\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.17704e12 | − | 2.03869e12i | 0.0737599 | − | 0.127756i | −0.826786 | − | 0.562516i | \(-0.809833\pi\) |
0.900546 | + | 0.434760i | \(0.143167\pi\) | |||||||
\(860\) | 1.56633e13 | − | 2.71296e13i | 0.976428 | − | 1.69122i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.27910e12 | + | 3.94752e12i | 0.140599 | + | 0.243524i | ||||
\(863\) | 1.83375e13 | 1.12536 | 0.562680 | − | 0.826675i | \(-0.309770\pi\) | ||||
0.562680 | + | 0.826675i | \(0.309770\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.71538e13 | −1.64914 | ||||||||
\(866\) | 4.91545e12 | + | 8.51380e12i | 0.296984 | + | 0.514391i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.09984e12 | − | 1.90498e12i | 0.0657644 | − | 0.113907i | ||||
\(869\) | −2.19549e12 | + | 3.80270e12i | −0.130600 | + | 0.226205i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.32769e13 | − | 4.03168e13i | −1.37039 | − | 2.37358i | ||||
\(872\) | −1.92993e12 | −0.113036 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.19515e11 | −0.00692820 | ||||||||
\(875\) | −6.76693e12 | − | 1.17207e13i | −0.390261 | − | 0.675952i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.75313e11 | + | 9.96472e11i | −0.0328402 | + | 0.0568809i | −0.881978 | − | 0.471290i | \(-0.843789\pi\) |
0.849138 | + | 0.528171i | \(0.177122\pi\) | |||||||
\(878\) | 3.07058e12 | − | 5.31840e12i | 0.174379 | − | 0.302034i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.61057e12 | − | 6.25370e12i | −0.202957 | − | 0.351532i | ||||
\(881\) | −2.37153e13 | −1.32628 | −0.663142 | − | 0.748494i | \(-0.730777\pi\) | ||||
−0.663142 | + | 0.748494i | \(0.730777\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.59683e13 | 1.43754 | 0.718771 | − | 0.695247i | \(-0.244705\pi\) | ||||
0.718771 | + | 0.695247i | \(0.244705\pi\) | |||||||
\(884\) | 1.66276e13 | + | 2.87998e13i | 0.915785 | + | 1.58619i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.74016e12 | − | 4.74609e12i | 0.149391 | − | 0.258752i | ||||
\(887\) | −7.91049e12 | + | 1.37014e13i | −0.429089 | + | 0.743204i | −0.996793 | − | 0.0800293i | \(-0.974499\pi\) |
0.567704 | + | 0.823233i | \(0.307832\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.91918e12 | − | 6.78821e12i | −0.210444 | − | 0.364500i | ||||
\(890\) | −1.75913e13 | −0.939818 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.38585e13 | 1.26183 | ||||||||
\(893\) | 2.59605e11 | + | 4.49649e11i | 0.0136610 | + | 0.0236615i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.04703e11 | − | 1.04738e12i | 0.0315020 | − | 0.0545631i | ||||
\(896\) | −9.39407e12 | + | 1.62710e13i | −0.486931 | + | 0.843389i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.18379e12 | + | 5.51449e12i | 0.163381 | + | 0.282984i | ||||
\(899\) | −8.86023e11 | −0.0452404 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.43914e13 | −0.727513 | ||||||||
\(902\) | 1.76987e11 | + | 3.06551e11i | 0.00890251 | + | 0.0154196i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.20813e13 | + | 2.09253e13i | −0.601664 | + | 1.04211i | ||||
\(905\) | 9.35871e12 | − | 1.62098e13i | 0.463765 | − | 0.803264i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.76777e12 | − | 1.34542e13i | −0.381122 | − | 0.660122i | 0.610101 | − | 0.792323i | \(-0.291129\pi\) |
−0.991223 | + | 0.132202i | \(0.957795\pi\) | |||||||
\(908\) | 5.61852e12 | 0.274306 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.78925e13 | −0.864939 | ||||||||
\(911\) | 2.56238e12 | + | 4.43818e12i | 0.123257 | + | 0.213487i | 0.921050 | − | 0.389444i | \(-0.127333\pi\) |
−0.797793 | + | 0.602931i | \(0.793999\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.13018e12 | + | 5.42163e12i | −0.149091 | + | 0.258233i | ||||
\(914\) | −2.15152e12 | + | 3.72655e12i | −0.101974 | + | 0.176624i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.00023e13 | + | 1.73245e13i | 0.469430 | + | 0.813077i | ||||
\(917\) | −1.13039e13 | −0.527919 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.60261e13 | 1.20362 | 0.601810 | − | 0.798639i | \(-0.294446\pi\) | ||||
0.601810 | + | 0.798639i | \(0.294446\pi\) | |||||||
\(920\) | 2.49082e12 | + | 4.31423e12i | 0.114630 | + | 0.198545i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.05246e12 | − | 3.55497e12i | 0.0935375 | − | 0.162012i | ||||
\(923\) | 2.48962e13 | − | 4.31215e13i | 1.12908 | − | 1.95563i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.27590e12 | + | 1.60663e13i | 0.416599 | + | 0.721570i | ||||
\(926\) | 9.71334e12 | 0.434129 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.84002e12 | 0.258493 | ||||||||
\(929\) | 2.01836e13 | + | 3.49590e13i | 0.889052 | + | 1.53988i | 0.840998 | + | 0.541039i | \(0.181969\pi\) |
0.0480546 | + | 0.998845i | \(0.484698\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.84365e10 | − | 6.65740e10i | 0.00167676 | − | 0.00290423i | ||||
\(932\) | 1.23338e13 | − | 2.13628e13i | 0.535458 | − | 0.927440i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.65572e12 | + | 6.33188e12i | 0.157185 | + | 0.272253i | ||||
\(935\) | −1.78344e13 | −0.763144 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.54039e12 | −0.0652835 | −0.0326418 | − | 0.999467i | \(-0.510392\pi\) | ||||
−0.0326418 | + | 0.999467i | \(0.510392\pi\) | |||||||
\(938\) | −6.56440e12 | − | 1.13699e13i | −0.276874 | − | 0.479560i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.08121e12 | − | 8.80091e12i | 0.212271 | − | 0.367665i | ||||
\(941\) | −2.77277e12 | + | 4.80258e12i | −0.115282 | + | 0.199674i | −0.917892 | − | 0.396829i | \(-0.870110\pi\) |
0.802611 | + | 0.596503i | \(0.203444\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.77630e11 | + | 6.54075e11i | 0.0155512 | + | 0.0269355i | ||||
\(944\) | 8.19325e12 | 0.335801 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.46211e12 | 0.181147 | ||||||||
\(947\) | 8.80699e12 | + | 1.52542e13i | 0.355838 | + | 0.616330i | 0.987261 | − | 0.159109i | \(-0.0508621\pi\) |
−0.631423 | + | 0.775439i | \(0.717529\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.31356e13 | + | 2.27515e13i | −0.525716 | + | 0.910567i | ||||
\(950\) | −5.75903e11 | + | 9.97493e11i | −0.0229400 | + | 0.0397332i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.98610e12 | + | 1.72964e13i | 0.394031 | + | 0.682481i | ||||
\(953\) | 4.21531e13 | 1.65543 | 0.827717 | − | 0.561146i | \(-0.189639\pi\) | ||||
0.827717 | + | 0.561146i | \(0.189639\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.45180e13 | −2.50995 | ||||||||
\(956\) | −1.91244e13 | − | 3.31245e13i | −0.740505 | − | 1.28259i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.93154e12 | + | 8.54168e12i | −0.189164 | + | 0.327641i | ||||
\(959\) | −2.02965e13 | + | 3.51545e13i | −0.774884 | + | 1.34214i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.29167e13 | + | 2.23724e13i | 0.488536 | + | 0.846170i | ||||
\(962\) | 8.20609e12 | 0.308922 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.94296e13 | −1.09759 | ||||||||
\(965\) | 2.34936e13 | + | 4.06921e13i | 0.872121 | + | 1.51056i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.62577e13 | − | 2.81592e13i | 0.597918 | − | 1.03562i | −0.395210 | − | 0.918591i | \(-0.629328\pi\) |
0.993128 | − | 0.117033i | \(-0.0373383\pi\) | |||||||
\(968\) | −7.43905e12 | + | 1.28848e13i | −0.272319 | + | 0.471671i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.28401e12 | − | 3.95603e12i | −0.0828373 | − | 0.143478i | ||||
\(971\) | −4.38405e13 | −1.58266 | −0.791332 | − | 0.611386i | \(-0.790612\pi\) | ||||
−0.791332 | + | 0.611386i | \(0.790612\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.14274e13 | 0.408731 | ||||||||
\(974\) | 4.68889e12 | + | 8.12140e12i | 0.166938 | + | 0.289145i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.38206e12 | − | 9.32200e12i | 0.189856 | − | 0.328840i | ||||
\(977\) | 6.56481e12 | − | 1.13706e13i | 0.230514 | − | 0.399261i | −0.727446 | − | 0.686165i | \(-0.759293\pi\) |
0.957959 | + | 0.286904i | \(0.0926260\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.66707e12 | + | 1.67438e13i | 0.336335 | + | 0.582550i | ||||
\(980\) | −1.50462e12 | −0.0521087 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.97171e12 | 0.307874 | ||||||||
\(983\) | −9.26273e12 | − | 1.60435e13i | −0.316408 | − | 0.548035i | 0.663328 | − | 0.748329i | \(-0.269144\pi\) |
−0.979736 | + | 0.200294i | \(0.935810\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.12130e13 | + | 3.67421e13i | −0.718025 | + | 1.24366i | ||||
\(986\) | 1.88879e12 | − | 3.27148e12i | 0.0636410 | − | 0.110230i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.96562e12 | − | 3.40455e12i | −0.0656285 | − | 0.113672i | ||||
\(989\) | 9.52062e12 | 0.316433 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.95986e13 | 1.30421 | 0.652106 | − | 0.758127i | \(-0.273885\pi\) | ||||
0.652106 | + | 0.758127i | \(0.273885\pi\) | |||||||
\(992\) | 1.99780e12 | + | 3.46029e12i | 0.0655012 | + | 0.113451i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.02107e12 | − | 1.21608e13i | 0.228121 | − | 0.395116i | ||||
\(995\) | 6.64512e12 | − | 1.15097e13i | 0.214931 | − | 0.372271i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.39753e13 | − | 4.15264e13i | −0.768485 | − | 1.33105i | −0.938385 | − | 0.345593i | \(-0.887678\pi\) |
0.169900 | − | 0.985461i | \(-0.445656\pi\) | |||||||
\(998\) | −1.69970e13 | −0.542357 | ||||||||
\(999\) | 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 | 27.10.c.a.10.4 | 16 | ||
3.2 | odd | 2 | 9.10.c.a.4.5 | ✓ | 16 | ||
9.2 | odd | 6 | 9.10.c.a.7.5 | yes | 16 | ||
9.4 | even | 3 | 81.10.a.d.1.5 | 8 | |||
9.5 | odd | 6 | 81.10.a.c.1.4 | 8 | |||
9.7 | even | 3 | inner | 27.10.c.a.19.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.10.c.a.4.5 | ✓ | 16 | 3.2 | odd | 2 | ||
9.10.c.a.7.5 | yes | 16 | 9.2 | odd | 6 | ||
27.10.c.a.10.4 | 16 | 1.1 | even | 1 | trivial | ||
27.10.c.a.19.4 | 16 | 9.7 | even | 3 | inner | ||
81.10.a.c.1.4 | 8 | 9.5 | odd | 6 | |||
81.10.a.d.1.5 | 8 | 9.4 | even | 3 |