Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,13,Mod(3,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 13, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.3");
S:= CuspForms(chi, 13);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.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: | \(7.31195053821\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 5 x^{9} + 468 x^{8} + 1496 x^{7} + 710096 x^{6} + 29155008 x^{5} + 143571008 x^{4} + \cdots + 824967906703360 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{45}\cdot 3^{3}\cdot 23 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.5 | ||
Root | \(-10.5406 + 27.3936i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.3 |
Dual form | 8.13.d.b.3.6 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −33.0812 | − | 54.7872i | −0.516893 | − | 0.856050i | ||||
\(3\) | −875.418 | −1.20085 | −0.600424 | − | 0.799682i | \(-0.705002\pi\) | ||||
−0.600424 | + | 0.799682i | \(0.705002\pi\) | |||||||
\(4\) | −1907.27 | + | 3624.85i | −0.465642 | + | 0.884973i | ||||
\(5\) | 2272.99i | 0.145471i | 0.997351 | + | 0.0727356i | \(0.0231729\pi\) | ||||
−0.997351 | + | 0.0727356i | \(0.976827\pi\) | |||||||
\(6\) | 28959.9 | + | 47961.7i | 0.620711 | + | 1.02799i | ||||
\(7\) | − | 92079.6i | − | 0.782664i | −0.920250 | − | 0.391332i | \(-0.872014\pi\) | ||
0.920250 | − | 0.391332i | \(-0.127986\pi\) | |||||||
\(8\) | 261690. | − | 15420.3i | 0.998268 | − | 0.0588238i | ||||
\(9\) | 234916. | 0.442037 | ||||||||
\(10\) | 124531. | − | 75193.1i | 0.124531 | − | 0.0751931i | ||||
\(11\) | 2.60172e6 | 1.46861 | 0.734303 | − | 0.678822i | \(-0.237509\pi\) | ||||
0.734303 | + | 0.678822i | \(0.237509\pi\) | |||||||
\(12\) | 1.66966e6 | − | 3.17326e6i | 0.559166 | − | 1.06272i | ||||
\(13\) | 8.33004e6i | 1.72579i | 0.505387 | + | 0.862893i | \(0.331350\pi\) | ||||
−0.505387 | + | 0.862893i | \(0.668650\pi\) | |||||||
\(14\) | −5.04478e6 | + | 3.04610e6i | −0.669999 | + | 0.404554i | ||||
\(15\) | − | 1.98981e6i | − | 0.174689i | ||||||
\(16\) | −9.50185e6 | − | 1.38271e7i | −0.566355 | − | 0.824162i | ||||
\(17\) | −7.99706e6 | −0.331312 | −0.165656 | − | 0.986184i | \(-0.552974\pi\) | ||||
−0.165656 | + | 0.986184i | \(0.552974\pi\) | |||||||
\(18\) | −7.77131e6 | − | 1.28704e7i | −0.228486 | − | 0.378405i | ||||
\(19\) | 1.09745e7 | 0.233272 | 0.116636 | − | 0.993175i | \(-0.462789\pi\) | ||||
0.116636 | + | 0.993175i | \(0.462789\pi\) | |||||||
\(20\) | −8.23923e6 | − | 4.33520e6i | −0.128738 | − | 0.0677375i | ||||
\(21\) | 8.06082e7i | 0.939861i | ||||||||
\(22\) | −8.60681e7 | − | 1.42541e8i | −0.759113 | − | 1.25720i | ||||
\(23\) | 2.00098e8i | 1.35169i | 0.737045 | + | 0.675844i | \(0.236221\pi\) | ||||
−0.737045 | + | 0.675844i | \(0.763779\pi\) | |||||||
\(24\) | −2.29088e8 | + | 1.34992e7i | −1.19877 | + | 0.0706385i | ||||
\(25\) | 2.38974e8 | 0.978838 | ||||||||
\(26\) | 4.56379e8 | − | 2.75567e8i | 1.47736 | − | 0.892047i | ||||
\(27\) | 2.59583e8 | 0.670029 | ||||||||
\(28\) | 3.33775e8 | + | 1.75621e8i | 0.692636 | + | 0.364441i | ||||
\(29\) | 1.82066e8i | 0.306085i | 0.988220 | + | 0.153042i | \(0.0489071\pi\) | ||||
−0.988220 | + | 0.153042i | \(0.951093\pi\) | |||||||
\(30\) | −1.09016e8 | + | 6.58254e7i | −0.149542 | + | 0.0902955i | ||||
\(31\) | − | 1.49678e9i | − | 1.68650i | −0.537518 | − | 0.843252i | \(-0.680638\pi\) | ||
0.537518 | − | 0.843252i | \(-0.319362\pi\) | |||||||
\(32\) | −4.43217e8 | + | 9.77998e8i | −0.412778 | + | 0.910831i | ||||
\(33\) | −2.27760e9 | −1.76357 | ||||||||
\(34\) | 2.64552e8 | + | 4.38136e8i | 0.171253 | + | 0.283619i | ||||
\(35\) | 2.09296e8 | 0.113855 | ||||||||
\(36\) | −4.48049e8 | + | 8.51536e8i | −0.205831 | + | 0.391190i | ||||
\(37\) | 3.12728e9i | 1.21887i | 0.792837 | + | 0.609434i | \(0.208603\pi\) | ||||
−0.792837 | + | 0.609434i | \(0.791397\pi\) | |||||||
\(38\) | −3.63048e8 | − | 6.01260e8i | −0.120577 | − | 0.199692i | ||||
\(39\) | − | 7.29227e9i | − | 2.07241i | ||||||
\(40\) | 3.50502e7 | + | 5.94818e8i | 0.00855717 | + | 0.145219i | ||||
\(41\) | −2.93948e9 | −0.618825 | −0.309412 | − | 0.950928i | \(-0.600132\pi\) | ||||
−0.309412 | + | 0.950928i | \(0.600132\pi\) | |||||||
\(42\) | 4.41630e9 | − | 2.66661e9i | 0.804567 | − | 0.485808i | ||||
\(43\) | 4.63601e9 | 0.733388 | 0.366694 | − | 0.930342i | \(-0.380490\pi\) | ||||
0.366694 | + | 0.930342i | \(0.380490\pi\) | |||||||
\(44\) | −4.96219e9 | + | 9.43086e9i | −0.683845 | + | 1.29968i | ||||
\(45\) | 5.33962e8i | 0.0643035i | ||||||||
\(46\) | 1.09628e10 | − | 6.61949e9i | 1.15711 | − | 0.698679i | ||||
\(47\) | 3.74487e9i | 0.347416i | 0.984797 | + | 0.173708i | \(0.0555749\pi\) | ||||
−0.984797 | + | 0.173708i | \(0.944425\pi\) | |||||||
\(48\) | 8.31810e9 | + | 1.21045e10i | 0.680106 | + | 0.989693i | ||||
\(49\) | 5.36263e9 | 0.387437 | ||||||||
\(50\) | −7.90555e9 | − | 1.30927e10i | −0.505955 | − | 0.837934i | ||||
\(51\) | 7.00077e9 | 0.397855 | ||||||||
\(52\) | −3.01951e10 | − | 1.58876e10i | −1.52727 | − | 0.803599i | ||||
\(53\) | 3.11048e10i | 1.40337i | 0.712487 | + | 0.701685i | \(0.247569\pi\) | ||||
−0.712487 | + | 0.701685i | \(0.752431\pi\) | |||||||
\(54\) | −8.58732e9 | − | 1.42218e10i | −0.346334 | − | 0.573579i | ||||
\(55\) | 5.91368e9i | 0.213640i | ||||||||
\(56\) | −1.41990e9 | − | 2.40963e10i | −0.0460393 | − | 0.781309i | ||||
\(57\) | −9.60725e9 | −0.280124 | ||||||||
\(58\) | 9.97490e9 | − | 6.02297e9i | 0.262024 | − | 0.158213i | ||||
\(59\) | −2.18545e9 | −0.0518118 | −0.0259059 | − | 0.999664i | \(-0.508247\pi\) | ||||
−0.0259059 | + | 0.999664i | \(0.508247\pi\) | |||||||
\(60\) | 7.21278e9 | + | 3.79511e9i | 0.154595 | + | 0.0813425i | ||||
\(61\) | − | 3.86145e9i | − | 0.0749500i | −0.999298 | − | 0.0374750i | \(-0.988069\pi\) | ||
0.999298 | − | 0.0374750i | \(-0.0119315\pi\) | |||||||
\(62\) | −8.20043e10 | + | 4.95152e10i | −1.44373 | + | 0.871743i | ||||
\(63\) | − | 2.16310e10i | − | 0.345966i | ||||||
\(64\) | 6.82439e10 | − | 8.07069e9i | 0.993080 | − | 0.117444i | ||||
\(65\) | −1.89341e10 | −0.251052 | ||||||||
\(66\) | 7.53456e10 | + | 1.24783e11i | 0.911579 | + | 1.50971i | ||||
\(67\) | −1.29631e10 | −0.143304 | −0.0716521 | − | 0.997430i | \(-0.522827\pi\) | ||||
−0.0716521 | + | 0.997430i | \(0.522827\pi\) | |||||||
\(68\) | 1.52526e10 | − | 2.89881e10i | 0.154273 | − | 0.293202i | ||||
\(69\) | − | 1.75170e11i | − | 1.62317i | ||||||
\(70\) | −6.92375e9 | − | 1.14667e10i | −0.0588509 | − | 0.0974655i | ||||
\(71\) | 9.21267e10i | 0.719176i | 0.933111 | + | 0.359588i | \(0.117083\pi\) | ||||
−0.933111 | + | 0.359588i | \(0.882917\pi\) | |||||||
\(72\) | 6.14753e10 | − | 3.62248e9i | 0.441271 | − | 0.0260023i | ||||
\(73\) | 2.54860e11 | 1.68409 | 0.842045 | − | 0.539408i | \(-0.181352\pi\) | ||||
0.842045 | + | 0.539408i | \(0.181352\pi\) | |||||||
\(74\) | 1.71335e11 | − | 1.03454e11i | 1.04341 | − | 0.630025i | ||||
\(75\) | −2.09202e11 | −1.17544 | ||||||||
\(76\) | −2.09313e10 | + | 3.97808e10i | −0.108621 | + | 0.206439i | ||||
\(77\) | − | 2.39566e11i | − | 1.14942i | ||||||
\(78\) | −3.99523e11 | + | 2.41237e11i | −1.77408 | + | 1.07121i | ||||
\(79\) | 2.54108e11i | 1.04534i | 0.852536 | + | 0.522669i | \(0.175064\pi\) | ||||
−0.852536 | + | 0.522669i | \(0.824936\pi\) | |||||||
\(80\) | 3.14289e10 | − | 2.15976e10i | 0.119892 | − | 0.0823882i | ||||
\(81\) | −3.52088e11 | −1.24664 | ||||||||
\(82\) | 9.72416e10 | + | 1.61046e11i | 0.319867 | + | 0.529745i | ||||
\(83\) | −1.71927e11 | −0.525868 | −0.262934 | − | 0.964814i | \(-0.584690\pi\) | ||||
−0.262934 | + | 0.964814i | \(0.584690\pi\) | |||||||
\(84\) | −2.92193e11 | − | 1.53742e11i | −0.831751 | − | 0.437639i | ||||
\(85\) | − | 1.81772e10i | − | 0.0481963i | ||||||
\(86\) | −1.53365e11 | − | 2.53994e11i | −0.379083 | − | 0.627816i | ||||
\(87\) | − | 1.59384e11i | − | 0.367561i | ||||||
\(88\) | 6.80845e11 | − | 4.01194e10i | 1.46606 | − | 0.0863890i | ||||
\(89\) | 5.29026e11 | 1.06448 | 0.532240 | − | 0.846594i | \(-0.321351\pi\) | ||||
0.532240 | + | 0.846594i | \(0.321351\pi\) | |||||||
\(90\) | 2.92542e10 | − | 1.76641e10i | 0.0550470 | − | 0.0332381i | ||||
\(91\) | 7.67027e11 | 1.35071 | ||||||||
\(92\) | −7.25326e11 | − | 3.81642e11i | −1.19621 | − | 0.629403i | ||||
\(93\) | 1.31031e12i | 2.02524i | ||||||||
\(94\) | 2.05171e11 | − | 1.23885e11i | 0.297406 | − | 0.179577i | ||||
\(95\) | 2.49448e10i | 0.0339343i | ||||||||
\(96\) | 3.88001e11 | − | 8.56157e11i | 0.495684 | − | 1.09377i | ||||
\(97\) | −4.13049e11 | −0.495874 | −0.247937 | − | 0.968776i | \(-0.579753\pi\) | ||||
−0.247937 | + | 0.968776i | \(0.579753\pi\) | |||||||
\(98\) | −1.77402e11 | − | 2.93803e11i | −0.200264 | − | 0.331666i | ||||
\(99\) | 6.11188e11 | 0.649177 | ||||||||
\(100\) | −4.55788e11 | + | 8.66245e11i | −0.455788 | + | 0.866245i | ||||
\(101\) | 3.09648e11i | 0.291703i | 0.989307 | + | 0.145851i | \(0.0465921\pi\) | ||||
−0.989307 | + | 0.145851i | \(0.953408\pi\) | |||||||
\(102\) | −2.31594e11 | − | 3.83552e11i | −0.205649 | − | 0.340584i | ||||
\(103\) | − | 4.72305e11i | − | 0.395548i | −0.980248 | − | 0.197774i | \(-0.936629\pi\) | ||
0.980248 | − | 0.197774i | \(-0.0633712\pi\) | |||||||
\(104\) | 1.28452e11 | + | 2.17989e12i | 0.101517 | + | 1.72280i | ||||
\(105\) | −1.83221e11 | −0.136723 | ||||||||
\(106\) | 1.70414e12 | − | 1.02898e12i | 1.20135 | − | 0.725393i | ||||
\(107\) | −1.18389e12 | −0.788873 | −0.394436 | − | 0.918923i | \(-0.629060\pi\) | ||||
−0.394436 | + | 0.918923i | \(0.629060\pi\) | |||||||
\(108\) | −4.95095e11 | + | 9.40950e11i | −0.311994 | + | 0.592958i | ||||
\(109\) | − | 1.92014e12i | − | 1.14492i | −0.819933 | − | 0.572459i | \(-0.805989\pi\) | ||
0.819933 | − | 0.572459i | \(-0.194011\pi\) | |||||||
\(110\) | 3.23994e11 | − | 1.95632e11i | 0.182886 | − | 0.110429i | ||||
\(111\) | − | 2.73768e12i | − | 1.46367i | ||||||
\(112\) | −1.27320e12 | + | 8.74927e11i | −0.645042 | + | 0.443265i | ||||
\(113\) | −2.99243e12 | −1.43732 | −0.718659 | − | 0.695362i | \(-0.755244\pi\) | ||||
−0.718659 | + | 0.695362i | \(0.755244\pi\) | |||||||
\(114\) | 3.17819e11 | + | 5.26354e11i | 0.144794 | + | 0.239800i | ||||
\(115\) | −4.54821e11 | −0.196632 | ||||||||
\(116\) | −6.59963e11 | − | 3.47250e11i | −0.270877 | − | 0.142526i | ||||
\(117\) | 1.95686e12i | 0.762860i | ||||||||
\(118\) | 7.22973e10 | + | 1.19735e11i | 0.0267812 | + | 0.0443535i | ||||
\(119\) | 7.36366e11i | 0.259306i | ||||||||
\(120\) | −3.06836e10 | − | 5.20714e11i | −0.0102759 | − | 0.174386i | ||||
\(121\) | 3.63054e12 | 1.15680 | ||||||||
\(122\) | −2.11558e11 | + | 1.27741e11i | −0.0641610 | + | 0.0387412i | ||||
\(123\) | 2.57328e12 | 0.743115 | ||||||||
\(124\) | 5.42560e12 | + | 2.85476e12i | 1.49251 | + | 0.785308i | ||||
\(125\) | 1.09811e12i | 0.287864i | ||||||||
\(126\) | −1.18510e12 | + | 7.15579e11i | −0.296164 | + | 0.178828i | ||||
\(127\) | − | 3.66709e11i | − | 0.0873976i | −0.999045 | − | 0.0436988i | \(-0.986086\pi\) | ||
0.999045 | − | 0.0436988i | \(-0.0139142\pi\) | |||||||
\(128\) | −2.69976e12 | − | 3.47190e12i | −0.613854 | − | 0.789419i | ||||
\(129\) | −4.05845e12 | −0.880687 | ||||||||
\(130\) | 6.26361e11 | + | 1.03734e12i | 0.129767 | + | 0.214913i | ||||
\(131\) | 2.64308e12 | 0.522977 | 0.261489 | − | 0.965207i | \(-0.415787\pi\) | ||||
0.261489 | + | 0.965207i | \(0.415787\pi\) | |||||||
\(132\) | 4.34400e12 | − | 8.25595e12i | 0.821194 | − | 1.56071i | ||||
\(133\) | − | 1.01052e12i | − | 0.182573i | ||||||
\(134\) | 4.28834e11 | + | 7.10210e11i | 0.0740730 | + | 0.122676i | ||||
\(135\) | 5.90029e11i | 0.0974699i | ||||||||
\(136\) | −2.09275e12 | + | 1.23317e11i | −0.330738 | + | 0.0194890i | ||||
\(137\) | 1.01637e13 | 1.53719 | 0.768593 | − | 0.639737i | \(-0.220957\pi\) | ||||
0.768593 | + | 0.639737i | \(0.220957\pi\) | |||||||
\(138\) | −9.59706e12 | + | 5.79482e12i | −1.38952 | + | 0.839007i | ||||
\(139\) | −9.07912e12 | −1.25879 | −0.629397 | − | 0.777084i | \(-0.716698\pi\) | ||||
−0.629397 | + | 0.777084i | \(0.716698\pi\) | |||||||
\(140\) | −3.99184e11 | + | 7.58665e11i | −0.0530157 | + | 0.100759i | ||||
\(141\) | − | 3.27833e12i | − | 0.417194i | ||||||
\(142\) | 5.04736e12 | − | 3.04766e12i | 0.615651 | − | 0.371737i | ||||
\(143\) | 2.16725e13i | 2.53450i | ||||||||
\(144\) | −2.23214e12 | − | 3.24822e12i | −0.250349 | − | 0.364310i | ||||
\(145\) | −4.13834e11 | −0.0445265 | ||||||||
\(146\) | −8.43108e12 | − | 1.39631e13i | −0.870495 | − | 1.44166i | ||||
\(147\) | −4.69455e12 | −0.465253 | ||||||||
\(148\) | −1.13359e13 | − | 5.96457e12i | −1.07866 | − | 0.567556i | ||||
\(149\) | − | 8.38360e12i | − | 0.766148i | −0.923718 | − | 0.383074i | \(-0.874865\pi\) | ||
0.923718 | − | 0.383074i | \(-0.125135\pi\) | |||||||
\(150\) | 6.92066e12 | + | 1.14616e13i | 0.607575 | + | 1.00623i | ||||
\(151\) | 5.12336e12i | 0.432208i | 0.976370 | + | 0.216104i | \(0.0693351\pi\) | ||||
−0.976370 | + | 0.216104i | \(0.930665\pi\) | |||||||
\(152\) | 2.87191e12 | − | 1.69230e11i | 0.232868 | − | 0.0137219i | ||||
\(153\) | −1.87864e12 | −0.146452 | ||||||||
\(154\) | −1.31251e13 | + | 7.92512e12i | −0.983965 | + | 0.594130i | ||||
\(155\) | 3.40216e12 | 0.245338 | ||||||||
\(156\) | 2.64334e13 | + | 1.39083e13i | 1.83402 | + | 0.965000i | ||||
\(157\) | − | 9.44792e12i | − | 0.630868i | −0.948948 | − | 0.315434i | \(-0.897850\pi\) | ||
0.948948 | − | 0.315434i | \(-0.102150\pi\) | |||||||
\(158\) | 1.39219e13 | − | 8.40621e12i | 0.894861 | − | 0.540328i | ||||
\(159\) | − | 2.72297e13i | − | 1.68523i | ||||||
\(160\) | −2.22298e12 | − | 1.00743e12i | −0.132500 | − | 0.0600473i | ||||
\(161\) | 1.84250e13 | 1.05792 | ||||||||
\(162\) | 1.16475e13 | + | 1.92899e13i | 0.644380 | + | 1.06719i | ||||
\(163\) | −1.31168e12 | −0.0699363 | −0.0349681 | − | 0.999388i | \(-0.511133\pi\) | ||||
−0.0349681 | + | 0.999388i | \(0.511133\pi\) | |||||||
\(164\) | 5.60639e12 | − | 1.06552e13i | 0.288151 | − | 0.547643i | ||||
\(165\) | − | 5.17695e12i | − | 0.256549i | ||||||
\(166\) | 5.68756e12 | + | 9.41942e12i | 0.271818 | + | 0.450169i | ||||
\(167\) | − | 9.67497e12i | − | 0.446016i | −0.974817 | − | 0.223008i | \(-0.928412\pi\) | ||
0.974817 | − | 0.223008i | \(-0.0715877\pi\) | |||||||
\(168\) | 1.24300e12 | + | 2.10944e13i | 0.0552862 | + | 0.938233i | ||||
\(169\) | −4.60914e13 | −1.97834 | ||||||||
\(170\) | −9.95877e11 | + | 6.01323e11i | −0.0412584 | + | 0.0249123i | ||||
\(171\) | 2.57808e12 | 0.103115 | ||||||||
\(172\) | −8.84213e12 | + | 1.68048e13i | −0.341496 | + | 0.649028i | ||||
\(173\) | 4.81822e13i | 1.79725i | 0.438713 | + | 0.898627i | \(0.355435\pi\) | ||||
−0.438713 | + | 0.898627i | \(0.644565\pi\) | |||||||
\(174\) | −8.73221e12 | + | 5.27262e12i | −0.314651 | + | 0.189990i | ||||
\(175\) | − | 2.20046e13i | − | 0.766101i | ||||||
\(176\) | −2.47212e13 | − | 3.59744e13i | −0.831751 | − | 1.21037i | ||||
\(177\) | 1.91318e12 | 0.0622181 | ||||||||
\(178\) | −1.75008e13 | − | 2.89839e13i | −0.550222 | − | 0.911247i | ||||
\(179\) | 3.22905e13 | 0.981649 | 0.490825 | − | 0.871258i | \(-0.336696\pi\) | ||||
0.490825 | + | 0.871258i | \(0.336696\pi\) | |||||||
\(180\) | −1.93553e12 | − | 1.01841e12i | −0.0569069 | − | 0.0299424i | ||||
\(181\) | 1.37019e13i | 0.389682i | 0.980835 | + | 0.194841i | \(0.0624191\pi\) | ||||
−0.980835 | + | 0.194841i | \(0.937581\pi\) | |||||||
\(182\) | −2.53741e13 | − | 4.20232e13i | −0.698173 | − | 1.15627i | ||||
\(183\) | 3.38039e12i | 0.0900036i | ||||||||
\(184\) | 3.08558e12 | + | 5.23637e13i | 0.0795115 | + | 1.34935i | ||||
\(185\) | −7.10826e12 | −0.177310 | ||||||||
\(186\) | 7.17881e13 | − | 4.33465e13i | 1.73370 | − | 1.04683i | ||||
\(187\) | −2.08061e13 | −0.486566 | ||||||||
\(188\) | −1.35746e13 | − | 7.14249e12i | −0.307454 | − | 0.161772i | ||||
\(189\) | − | 2.39023e13i | − | 0.524408i | ||||||
\(190\) | 1.36666e12 | − | 8.25204e11i | 0.0290494 | − | 0.0175404i | ||||
\(191\) | 4.48830e13i | 0.924446i | 0.886764 | + | 0.462223i | \(0.152948\pi\) | ||||
−0.886764 | + | 0.462223i | \(0.847052\pi\) | |||||||
\(192\) | −5.97420e13 | + | 7.06523e12i | −1.19254 | + | 0.141032i | ||||
\(193\) | 2.98766e13 | 0.578080 | 0.289040 | − | 0.957317i | \(-0.406664\pi\) | ||||
0.289040 | + | 0.957317i | \(0.406664\pi\) | |||||||
\(194\) | 1.36641e13 | + | 2.26298e13i | 0.256314 | + | 0.424492i | ||||
\(195\) | 1.65752e13 | 0.301475 | ||||||||
\(196\) | −1.02280e13 | + | 1.94387e13i | −0.180407 | + | 0.342872i | ||||
\(197\) | 7.29068e13i | 1.24730i | 0.781704 | + | 0.623650i | \(0.214351\pi\) | ||||
−0.781704 | + | 0.623650i | \(0.785649\pi\) | |||||||
\(198\) | −2.02188e13 | − | 3.34852e13i | −0.335556 | − | 0.555728i | ||||
\(199\) | − | 5.06713e13i | − | 0.815912i | −0.913001 | − | 0.407956i | \(-0.866242\pi\) | ||
0.913001 | − | 0.407956i | \(-0.133758\pi\) | |||||||
\(200\) | 6.25372e13 | − | 3.68506e12i | 0.977143 | − | 0.0575790i | ||||
\(201\) | 1.13481e13 | 0.172087 | ||||||||
\(202\) | 1.69647e13 | − | 1.02435e13i | 0.249712 | − | 0.150779i | ||||
\(203\) | 1.67646e13 | 0.239561 | ||||||||
\(204\) | −1.33524e13 | + | 2.53767e13i | −0.185258 | + | 0.352091i | ||||
\(205\) | − | 6.68140e12i | − | 0.0900211i | ||||||
\(206\) | −2.58763e13 | + | 1.56244e13i | −0.338609 | + | 0.204456i | ||||
\(207\) | 4.70064e13i | 0.597495i | ||||||||
\(208\) | 1.15181e14 | − | 7.91508e13i | 1.42233 | − | 0.977406i | ||||
\(209\) | 2.85525e13 | 0.342584 | ||||||||
\(210\) | 6.06118e12 | + | 1.00382e13i | 0.0706710 | + | 0.117041i | ||||
\(211\) | 8.53415e13 | 0.967087 | 0.483543 | − | 0.875320i | \(-0.339350\pi\) | ||||
0.483543 | + | 0.875320i | \(0.339350\pi\) | |||||||
\(212\) | −1.12750e14 | − | 5.93253e13i | −1.24194 | − | 0.653468i | ||||
\(213\) | − | 8.06494e13i | − | 0.863622i | ||||||
\(214\) | 3.91643e13 | + | 6.48617e13i | 0.407763 | + | 0.675314i | ||||
\(215\) | 1.05376e13i | 0.106687i | ||||||||
\(216\) | 6.79303e13 | − | 4.00285e12i | 0.668869 | − | 0.0394137i | ||||
\(217\) | −1.37823e14 | −1.31997 | ||||||||
\(218\) | −1.05199e14 | + | 6.35206e13i | −0.980107 | + | 0.591801i | ||||
\(219\) | −2.23109e14 | −2.02234 | ||||||||
\(220\) | −2.14362e13 | − | 1.12790e13i | −0.189065 | − | 0.0994797i | ||||
\(221\) | − | 6.66158e13i | − | 0.571773i | ||||||
\(222\) | −1.49990e14 | + | 9.05656e13i | −1.25298 | + | 0.756564i | ||||
\(223\) | − | 1.82903e14i | − | 1.48728i | −0.668582 | − | 0.743638i | \(-0.733099\pi\) | ||
0.668582 | − | 0.743638i | \(-0.266901\pi\) | |||||||
\(224\) | 9.00537e13 | + | 4.08113e13i | 0.712875 | + | 0.323067i | ||||
\(225\) | 5.61389e13 | 0.432682 | ||||||||
\(226\) | 9.89931e13 | + | 1.63947e14i | 0.742941 | + | 1.23042i | ||||
\(227\) | −8.07643e13 | −0.590289 | −0.295144 | − | 0.955453i | \(-0.595368\pi\) | ||||
−0.295144 | + | 0.955453i | \(0.595368\pi\) | |||||||
\(228\) | 1.83236e13 | − | 3.48248e13i | 0.130437 | − | 0.247902i | ||||
\(229\) | − | 7.52407e13i | − | 0.521723i | −0.965376 | − | 0.260861i | \(-0.915993\pi\) | ||
0.965376 | − | 0.260861i | \(-0.0840066\pi\) | |||||||
\(230\) | 1.50460e13 | + | 2.49183e13i | 0.101638 | + | 0.168326i | ||||
\(231\) | 2.09720e14i | 1.38028i | ||||||||
\(232\) | 2.80752e12 | + | 4.76450e13i | 0.0180051 | + | 0.305555i | ||||
\(233\) | 4.65372e13 | 0.290847 | 0.145423 | − | 0.989369i | \(-0.453546\pi\) | ||||
0.145423 | + | 0.989369i | \(0.453546\pi\) | |||||||
\(234\) | 1.07211e14 | − | 6.47353e13i | 0.653046 | − | 0.394317i | ||||
\(235\) | −8.51205e12 | −0.0505390 | ||||||||
\(236\) | 4.16824e12 | − | 7.92193e12i | 0.0241258 | − | 0.0458521i | ||||
\(237\) | − | 2.22451e14i | − | 1.25529i | ||||||
\(238\) | 4.03434e13 | − | 2.43599e13i | 0.221978 | − | 0.134033i | ||||
\(239\) | 2.31124e14i | 1.24010i | 0.784561 | + | 0.620051i | \(0.212888\pi\) | ||||
−0.784561 | + | 0.620051i | \(0.787112\pi\) | |||||||
\(240\) | −2.75134e13 | + | 1.89069e13i | −0.143972 | + | 0.0989357i | ||||
\(241\) | 2.35479e14 | 1.20185 | 0.600925 | − | 0.799306i | \(-0.294799\pi\) | ||||
0.600925 | + | 0.799306i | \(0.294799\pi\) | |||||||
\(242\) | −1.20103e14 | − | 1.98907e14i | −0.597944 | − | 0.990281i | ||||
\(243\) | 1.70271e14 | 0.826996 | ||||||||
\(244\) | 1.39972e13 | + | 7.36484e12i | 0.0663288 | + | 0.0348999i | ||||
\(245\) | 1.21892e13i | 0.0563609i | ||||||||
\(246\) | −8.51270e13 | − | 1.40983e14i | −0.384111 | − | 0.636143i | ||||
\(247\) | 9.14177e13i | 0.402577i | ||||||||
\(248\) | −2.30808e13 | − | 3.91692e14i | −0.0992067 | − | 1.68358i | ||||
\(249\) | 1.50508e14 | 0.631488 | ||||||||
\(250\) | 6.01625e13 | − | 3.63269e13i | 0.246426 | − | 0.148795i | ||||
\(251\) | −3.74367e13 | −0.149711 | −0.0748557 | − | 0.997194i | \(-0.523850\pi\) | ||||
−0.0748557 | + | 0.997194i | \(0.523850\pi\) | |||||||
\(252\) | 7.84091e13 | + | 4.12562e13i | 0.306171 | + | 0.161096i | ||||
\(253\) | 5.20601e14i | 1.98510i | ||||||||
\(254\) | −2.00910e13 | + | 1.21312e13i | −0.0748167 | + | 0.0451753i | ||||
\(255\) | 1.59127e13i | 0.0578764i | ||||||||
\(256\) | −1.00905e14 | + | 2.62767e14i | −0.358485 | + | 0.933535i | ||||
\(257\) | −3.57288e14 | −1.23999 | −0.619996 | − | 0.784605i | \(-0.712866\pi\) | ||||
−0.619996 | + | 0.784605i | \(0.712866\pi\) | |||||||
\(258\) | 1.34258e14 | + | 2.22351e14i | 0.455222 | + | 0.753912i | ||||
\(259\) | 2.87959e14 | 0.953963 | ||||||||
\(260\) | 3.61124e13 | − | 6.86331e13i | 0.116900 | − | 0.222174i | ||||
\(261\) | 4.27704e13i | 0.135301i | ||||||||
\(262\) | −8.74362e13 | − | 1.44807e14i | −0.270323 | − | 0.447694i | ||||
\(263\) | − | 4.28675e14i | − | 1.29537i | −0.761908 | − | 0.647685i | \(-0.775737\pi\) | ||
0.761908 | − | 0.647685i | \(-0.224263\pi\) | |||||||
\(264\) | −5.96025e14 | + | 3.51213e13i | −1.76052 | + | 0.103740i | ||||
\(265\) | −7.07008e13 | −0.204150 | ||||||||
\(266\) | −5.53638e13 | + | 3.34293e13i | −0.156292 | + | 0.0943709i | ||||
\(267\) | −4.63119e14 | −1.27828 | ||||||||
\(268\) | 2.47241e13 | − | 4.69892e13i | 0.0667285 | − | 0.126820i | ||||
\(269\) | 1.10224e14i | 0.290913i | 0.989365 | + | 0.145456i | \(0.0464651\pi\) | ||||
−0.989365 | + | 0.145456i | \(0.953535\pi\) | |||||||
\(270\) | 3.23260e13 | − | 1.95189e13i | 0.0834391 | − | 0.0503816i | ||||
\(271\) | − | 4.03212e14i | − | 1.01793i | −0.860788 | − | 0.508964i | \(-0.830028\pi\) | ||
0.860788 | − | 0.508964i | \(-0.169972\pi\) | |||||||
\(272\) | 7.59868e13 | + | 1.10576e14i | 0.187640 | + | 0.273054i | ||||
\(273\) | −6.71469e14 | −1.62200 | ||||||||
\(274\) | −3.36226e14 | − | 5.56838e14i | −0.794562 | − | 1.31591i | ||||
\(275\) | 6.21745e14 | 1.43753 | ||||||||
\(276\) | 6.34964e14 | + | 3.34096e14i | 1.43646 | + | 0.755817i | ||||
\(277\) | 3.12608e14i | 0.692025i | 0.938230 | + | 0.346013i | \(0.112465\pi\) | ||||
−0.938230 | + | 0.346013i | \(0.887535\pi\) | |||||||
\(278\) | 3.00348e14 | + | 4.97419e14i | 0.650663 | + | 1.07759i | ||||
\(279\) | − | 3.51618e14i | − | 0.745497i | ||||||
\(280\) | 5.47706e13 | − | 3.22741e12i | 0.113658 | − | 0.00669739i | ||||
\(281\) | 6.30960e14 | 1.28163 | 0.640817 | − | 0.767693i | \(-0.278596\pi\) | ||||
0.640817 | + | 0.767693i | \(0.278596\pi\) | |||||||
\(282\) | −1.79611e14 | + | 1.08451e14i | −0.357139 | + | 0.215645i | ||||
\(283\) | 1.63451e13 | 0.0318178 | 0.0159089 | − | 0.999873i | \(-0.494936\pi\) | ||||
0.0159089 | + | 0.999873i | \(0.494936\pi\) | |||||||
\(284\) | −3.33945e14 | − | 1.75711e14i | −0.636452 | − | 0.334879i | ||||
\(285\) | − | 2.18371e13i | − | 0.0407499i | ||||||
\(286\) | 1.18737e15 | − | 7.16951e14i | 2.16966 | − | 1.31007i | ||||
\(287\) | 2.70666e14i | 0.484332i | ||||||||
\(288\) | −1.04119e14 | + | 2.29748e14i | −0.182463 | + | 0.402621i | ||||
\(289\) | −5.18669e14 | −0.890233 | ||||||||
\(290\) | 1.36901e13 | + | 2.26728e13i | 0.0230155 | + | 0.0381169i | ||||
\(291\) | 3.61590e14 | 0.595469 | ||||||||
\(292\) | −4.86088e14 | + | 9.23830e14i | −0.784183 | + | 1.49037i | ||||
\(293\) | − | 6.63426e14i | − | 1.04854i | −0.851551 | − | 0.524272i | \(-0.824337\pi\) | ||
0.851551 | − | 0.524272i | \(-0.175663\pi\) | |||||||
\(294\) | 1.55301e14 | + | 2.57201e14i | 0.240486 | + | 0.398280i | ||||
\(295\) | − | 4.96750e12i | − | 0.00753712i | ||||||
\(296\) | 4.82236e13 | + | 8.18378e14i | 0.0716984 | + | 1.21676i | ||||
\(297\) | 6.75364e14 | 0.984009 | ||||||||
\(298\) | −4.59314e14 | + | 2.77339e14i | −0.655861 | + | 0.396017i | ||||
\(299\) | −1.66683e15 | −2.33272 | ||||||||
\(300\) | 3.99006e14 | − | 7.58327e14i | 0.547333 | − | 1.04023i | ||||
\(301\) | − | 4.26882e14i | − | 0.573996i | ||||||
\(302\) | 2.80695e14 | − | 1.69487e14i | 0.369992 | − | 0.223406i | ||||
\(303\) | − | 2.71072e14i | − | 0.350290i | ||||||
\(304\) | −1.04278e14 | − | 1.51745e14i | −0.132114 | − | 0.192253i | ||||
\(305\) | 8.77703e12 | 0.0109031 | ||||||||
\(306\) | 6.21476e13 | + | 1.02925e14i | 0.0757000 | + | 0.125370i | ||||
\(307\) | 9.56153e14 | 1.14208 | 0.571041 | − | 0.820922i | \(-0.306540\pi\) | ||||
0.571041 | + | 0.820922i | \(0.306540\pi\) | |||||||
\(308\) | 8.68390e14 | + | 4.56917e14i | 1.01721 | + | 0.535221i | ||||
\(309\) | 4.13464e14i | 0.474993i | ||||||||
\(310\) | −1.12547e14 | − | 1.86395e14i | −0.126813 | − | 0.210021i | ||||
\(311\) | 7.61532e14i | 0.841639i | 0.907144 | + | 0.420819i | \(0.138257\pi\) | ||||
−0.907144 | + | 0.420819i | \(0.861743\pi\) | |||||||
\(312\) | −1.12449e14 | − | 1.90831e15i | −0.121907 | − | 2.06882i | ||||
\(313\) | −8.18040e14 | −0.869978 | −0.434989 | − | 0.900436i | \(-0.643248\pi\) | ||||
−0.434989 | + | 0.900436i | \(0.643248\pi\) | |||||||
\(314\) | −5.17625e14 | + | 3.12548e14i | −0.540054 | + | 0.326091i | ||||
\(315\) | 4.91670e13 | 0.0503281 | ||||||||
\(316\) | −9.21105e14 | − | 4.84654e14i | −0.925095 | − | 0.486753i | ||||
\(317\) | − | 8.53575e14i | − | 0.841175i | −0.907252 | − | 0.420587i | \(-0.861824\pi\) | ||
0.907252 | − | 0.420587i | \(-0.138176\pi\) | |||||||
\(318\) | −1.49184e15 | + | 9.00791e14i | −1.44264 | + | 0.871087i | ||||
\(319\) | 4.73687e14i | 0.449518i | ||||||||
\(320\) | 1.83446e13 | + | 1.55117e14i | 0.0170847 | + | 0.144464i | ||||
\(321\) | 1.03639e15 | 0.947316 | ||||||||
\(322\) | −6.09520e14 | − | 1.00945e15i | −0.546830 | − | 0.905630i | ||||
\(323\) | −8.77634e13 | −0.0772856 | ||||||||
\(324\) | 6.71527e14 | − | 1.27627e15i | 0.580488 | − | 1.10324i | ||||
\(325\) | 1.99066e15i | 1.68926i | ||||||||
\(326\) | 4.33920e13 | + | 7.18633e13i | 0.0361496 | + | 0.0598689i | ||||
\(327\) | 1.68093e15i | 1.37487i | ||||||||
\(328\) | −7.69233e14 | + | 4.53277e13i | −0.617753 | + | 0.0364016i | ||||
\(329\) | 3.44827e14 | 0.271910 | ||||||||
\(330\) | −2.83630e14 | + | 1.71260e14i | −0.219619 | + | 0.132608i | ||||
\(331\) | −1.36071e15 | −1.03466 | −0.517329 | − | 0.855787i | \(-0.673074\pi\) | ||||
−0.517329 | + | 0.855787i | \(0.673074\pi\) | |||||||
\(332\) | 3.27912e14 | − | 6.23211e14i | 0.244866 | − | 0.465379i | ||||
\(333\) | 7.34649e14i | 0.538784i | ||||||||
\(334\) | −5.30064e14 | + | 3.20059e14i | −0.381812 | + | 0.230543i | ||||
\(335\) | − | 2.94649e13i | − | 0.0208466i | ||||||
\(336\) | 1.11458e15 | − | 7.65927e14i | 0.774597 | − | 0.532294i | ||||
\(337\) | 7.72413e14 | 0.527315 | 0.263657 | − | 0.964616i | \(-0.415071\pi\) | ||||
0.263657 | + | 0.964616i | \(0.415071\pi\) | |||||||
\(338\) | 1.52476e15 | + | 2.52522e15i | 1.02259 | + | 1.69355i | ||||
\(339\) | 2.61963e15 | 1.72600 | ||||||||
\(340\) | 6.58896e13 | + | 3.46688e13i | 0.0426524 | + | 0.0224422i | ||||
\(341\) | − | 3.89421e15i | − | 2.47681i | ||||||
\(342\) | −8.52860e13 | − | 1.41246e14i | −0.0532992 | − | 0.0882712i | ||||
\(343\) | − | 1.76829e15i | − | 1.08590i | ||||||
\(344\) | 1.21320e15 | − | 7.14887e13i | 0.732118 | − | 0.0431407i | ||||
\(345\) | 3.98158e14 | 0.236125 | ||||||||
\(346\) | 2.63976e15 | − | 1.59392e15i | 1.53854 | − | 0.928989i | ||||
\(347\) | −1.82105e15 | −1.04315 | −0.521574 | − | 0.853206i | \(-0.674655\pi\) | ||||
−0.521574 | + | 0.853206i | \(0.674655\pi\) | |||||||
\(348\) | 5.77744e14 | + | 3.03989e14i | 0.325282 | + | 0.171152i | ||||
\(349\) | − | 6.54823e14i | − | 0.362386i | −0.983448 | − | 0.181193i | \(-0.942004\pi\) | ||
0.983448 | − | 0.181193i | \(-0.0579959\pi\) | |||||||
\(350\) | −1.20557e15 | + | 7.27940e14i | −0.655821 | + | 0.395993i | ||||
\(351\) | 2.16234e15i | 1.15633i | ||||||||
\(352\) | −1.15313e15 | + | 2.54448e15i | −0.606209 | + | 1.33765i | ||||
\(353\) | −5.87304e13 | −0.0303539 | −0.0151769 | − | 0.999885i | \(-0.504831\pi\) | ||||
−0.0151769 | + | 0.999885i | \(0.504831\pi\) | |||||||
\(354\) | −6.32904e13 | − | 1.04818e14i | −0.0321601 | − | 0.0532618i | ||||
\(355\) | −2.09403e14 | −0.104619 | ||||||||
\(356\) | −1.00900e15 | + | 1.91764e15i | −0.495667 | + | 0.942036i | ||||
\(357\) | − | 6.44628e14i | − | 0.311387i | ||||||
\(358\) | −1.06821e15 | − | 1.76910e15i | −0.507408 | − | 0.840340i | ||||
\(359\) | − | 8.71047e14i | − | 0.406888i | −0.979087 | − | 0.203444i | \(-0.934786\pi\) | ||
0.979087 | − | 0.203444i | \(-0.0652135\pi\) | |||||||
\(360\) | 8.23385e12 | + | 1.39732e14i | 0.00378258 | + | 0.0641922i | ||||
\(361\) | −2.09288e15 | −0.945584 | ||||||||
\(362\) | 7.50690e14 | − | 4.53276e14i | 0.333587 | − | 0.201424i | ||||
\(363\) | −3.17824e15 | −1.38914 | ||||||||
\(364\) | −1.46293e15 | + | 2.78036e15i | −0.628948 | + | 1.19534i | ||||
\(365\) | 5.79294e14i | 0.244986i | ||||||||
\(366\) | 1.85202e14 | − | 1.11827e14i | 0.0770476 | − | 0.0465223i | ||||
\(367\) | − | 2.14035e15i | − | 0.875966i | −0.898983 | − | 0.437983i | \(-0.855693\pi\) | ||
0.898983 | − | 0.437983i | \(-0.144307\pi\) | |||||||
\(368\) | 2.76679e15 | − | 1.90130e15i | 1.11401 | − | 0.765535i | ||||
\(369\) | −6.90532e14 | −0.273543 | ||||||||
\(370\) | 2.35150e14 | + | 3.89442e14i | 0.0916504 | + | 0.151786i | ||||
\(371\) | 2.86412e15 | 1.09837 | ||||||||
\(372\) | −4.74967e15 | − | 2.49911e15i | −1.79228 | − | 0.943036i | ||||
\(373\) | 4.21640e15i | 1.56563i | 0.622255 | + | 0.782815i | \(0.286217\pi\) | ||||
−0.622255 | + | 0.782815i | \(0.713783\pi\) | |||||||
\(374\) | 6.88292e14 | + | 1.13991e15i | 0.251503 | + | 0.416525i | ||||
\(375\) | − | 9.61308e14i | − | 0.345681i | ||||||
\(376\) | 5.77472e13 | + | 9.79997e14i | 0.0204364 | + | 0.346815i | ||||
\(377\) | −1.51662e15 | −0.528237 | ||||||||
\(378\) | −1.30954e15 | + | 7.90717e14i | −0.448919 | + | 0.271063i | ||||
\(379\) | 1.96185e15 | 0.661959 | 0.330979 | − | 0.943638i | \(-0.392621\pi\) | ||||
0.330979 | + | 0.943638i | \(0.392621\pi\) | |||||||
\(380\) | −9.04212e13 | − | 4.75765e13i | −0.0300309 | − | 0.0158012i | ||||
\(381\) | 3.21024e14i | 0.104951i | ||||||||
\(382\) | 2.45901e15 | − | 1.48478e15i | 0.791371 | − | 0.477840i | ||||
\(383\) | − | 3.87397e15i | − | 1.22734i | −0.789564 | − | 0.613668i | \(-0.789693\pi\) | ||
0.789564 | − | 0.613668i | \(-0.210307\pi\) | |||||||
\(384\) | 2.36342e15 | + | 3.03937e15i | 0.737146 | + | 0.947973i | ||||
\(385\) | 5.44530e14 | 0.167208 | ||||||||
\(386\) | −9.88354e14 | − | 1.63686e15i | −0.298806 | − | 0.494865i | ||||
\(387\) | 1.08907e15 | 0.324184 | ||||||||
\(388\) | 7.87796e14 | − | 1.49724e15i | 0.230900 | − | 0.438835i | ||||
\(389\) | − | 1.38328e14i | − | 0.0399220i | −0.999801 | − | 0.0199610i | \(-0.993646\pi\) | ||
0.999801 | − | 0.0199610i | \(-0.00635421\pi\) | |||||||
\(390\) | −5.48328e14 | − | 9.08110e14i | −0.155831 | − | 0.258078i | ||||
\(391\) | − | 1.60020e15i | − | 0.447830i | ||||||
\(392\) | 1.40335e15 | − | 8.26935e13i | 0.386766 | − | 0.0227905i | ||||
\(393\) | −2.31380e15 | −0.628016 | ||||||||
\(394\) | 3.99436e15 | − | 2.41184e15i | 1.06775 | − | 0.644721i | ||||
\(395\) | −5.77585e14 | −0.152066 | ||||||||
\(396\) | −1.16570e15 | + | 2.21546e15i | −0.302284 | + | 0.574504i | ||||
\(397\) | 7.26952e15i | 1.85679i | 0.371595 | + | 0.928395i | \(0.378811\pi\) | ||||
−0.371595 | + | 0.928395i | \(0.621189\pi\) | |||||||
\(398\) | −2.77614e15 | + | 1.67627e15i | −0.698462 | + | 0.421740i | ||||
\(399\) | 8.84632e14i | 0.219243i | ||||||||
\(400\) | −2.27070e15 | − | 3.30433e15i | −0.554369 | − | 0.806721i | ||||
\(401\) | 3.70403e15 | 0.890857 | 0.445428 | − | 0.895318i | \(-0.353051\pi\) | ||||
0.445428 | + | 0.895318i | \(0.353051\pi\) | |||||||
\(402\) | −3.75409e14 | − | 6.21731e14i | −0.0889505 | − | 0.147315i | ||||
\(403\) | 1.24682e16 | 2.91055 | ||||||||
\(404\) | −1.12243e15 | − | 5.90583e14i | −0.258149 | − | 0.135829i | ||||
\(405\) | − | 8.00291e14i | − | 0.181350i | ||||||
\(406\) | −5.54593e14 | − | 9.18485e14i | −0.123828 | − | 0.205077i | ||||
\(407\) | 8.13632e15i | 1.79004i | ||||||||
\(408\) | 1.83203e15 | − | 1.07954e14i | 0.397166 | − | 0.0234034i | ||||
\(409\) | −2.06826e15 | −0.441841 | −0.220920 | − | 0.975292i | \(-0.570906\pi\) | ||||
−0.220920 | + | 0.975292i | \(0.570906\pi\) | |||||||
\(410\) | −3.66055e14 | + | 2.21029e14i | −0.0770626 | + | 0.0465313i | ||||
\(411\) | −8.89745e15 | −1.84593 | ||||||||
\(412\) | 1.71203e15 | + | 9.00813e14i | 0.350049 | + | 0.184184i | ||||
\(413\) | 2.01235e14i | 0.0405512i | ||||||||
\(414\) | 2.57535e15 | − | 1.55503e15i | 0.511486 | − | 0.308841i | ||||
\(415\) | − | 3.90789e14i | − | 0.0764986i | ||||||
\(416\) | −8.14676e15 | − | 3.69202e15i | −1.57190 | − | 0.712367i | ||||
\(417\) | 7.94803e15 | 1.51162 | ||||||||
\(418\) | −9.44552e14 | − | 1.56431e15i | −0.177079 | − | 0.293269i | ||||
\(419\) | −9.81366e15 | −1.81362 | −0.906811 | − | 0.421536i | \(-0.861491\pi\) | ||||
−0.906811 | + | 0.421536i | \(0.861491\pi\) | |||||||
\(420\) | 3.49453e14 | − | 6.64150e14i | 0.0636638 | − | 0.120996i | ||||
\(421\) | − | 1.57841e15i | − | 0.283483i | −0.989904 | − | 0.141741i | \(-0.954730\pi\) | ||
0.989904 | − | 0.141741i | \(-0.0452701\pi\) | |||||||
\(422\) | −2.82320e15 | − | 4.67562e15i | −0.499881 | − | 0.827874i | ||||
\(423\) | 8.79732e14i | 0.153571i | ||||||||
\(424\) | 4.79646e14 | + | 8.13982e15i | 0.0825516 | + | 1.40094i | ||||
\(425\) | −1.91109e15 | −0.324300 | ||||||||
\(426\) | −4.41855e15 | + | 2.66798e15i | −0.739303 | + | 0.446400i | ||||
\(427\) | −3.55561e14 | −0.0586607 | ||||||||
\(428\) | 2.25799e15 | − | 4.29141e15i | 0.367332 | − | 0.698131i | ||||
\(429\) | − | 1.89725e16i | − | 3.04355i | ||||||
\(430\) | 5.77325e14 | − | 3.48596e14i | 0.0913291 | − | 0.0551457i | ||||
\(431\) | 6.30496e15i | 0.983600i | 0.870708 | + | 0.491800i | \(0.163661\pi\) | ||||
−0.870708 | + | 0.491800i | \(0.836339\pi\) | |||||||
\(432\) | −2.46652e15 | − | 3.58929e15i | −0.379474 | − | 0.552213i | ||||
\(433\) | −5.54487e15 | −0.841325 | −0.420663 | − | 0.907217i | \(-0.638202\pi\) | ||||
−0.420663 | + | 0.907217i | \(0.638202\pi\) | |||||||
\(434\) | 4.55934e15 | + | 7.55093e15i | 0.682282 | + | 1.12996i | ||||
\(435\) | 3.62278e14 | 0.0534696 | ||||||||
\(436\) | 6.96023e15 | + | 3.66223e15i | 1.01322 | + | 0.533123i | ||||
\(437\) | 2.19597e15i | 0.315310i | ||||||||
\(438\) | 7.38072e15 | + | 1.22235e16i | 1.04533 | + | 1.73122i | ||||
\(439\) | − | 1.32422e16i | − | 1.85001i | −0.379956 | − | 0.925005i | \(-0.624061\pi\) | ||
0.379956 | − | 0.925005i | \(-0.375939\pi\) | |||||||
\(440\) | 9.11909e13 | + | 1.54755e15i | 0.0125671 | + | 0.213270i | ||||
\(441\) | 1.25977e15 | 0.171261 | ||||||||
\(442\) | −3.64969e15 | + | 2.20373e15i | −0.489466 | + | 0.295546i | ||||
\(443\) | 3.53113e15 | 0.467188 | 0.233594 | − | 0.972334i | \(-0.424951\pi\) | ||||
0.233594 | + | 0.972334i | \(0.424951\pi\) | |||||||
\(444\) | 9.92367e15 | + | 5.22149e15i | 1.29531 | + | 0.681549i | ||||
\(445\) | 1.20247e15i | 0.154851i | ||||||||
\(446\) | −1.00207e16 | + | 6.05065e15i | −1.27318 | + | 0.768763i | ||||
\(447\) | 7.33915e15i | 0.920028i | ||||||||
\(448\) | −7.43146e14 | − | 6.28387e15i | −0.0919191 | − | 0.777247i | ||||
\(449\) | −3.35658e15 | −0.409655 | −0.204828 | − | 0.978798i | \(-0.565663\pi\) | ||||
−0.204828 | + | 0.978798i | \(0.565663\pi\) | |||||||
\(450\) | −1.85714e15 | − | 3.07569e15i | −0.223651 | − | 0.370397i | ||||
\(451\) | −7.64772e15 | −0.908810 | ||||||||
\(452\) | 5.70737e15 | − | 1.08471e16i | 0.669276 | − | 1.27199i | ||||
\(453\) | − | 4.48508e15i | − | 0.519017i | ||||||
\(454\) | 2.67178e15 | + | 4.42485e15i | 0.305116 | + | 0.505316i | ||||
\(455\) | 1.74344e15i | 0.196489i | ||||||||
\(456\) | −2.51412e15 | + | 1.48147e14i | −0.279639 | + | 0.0164779i | ||||
\(457\) | 1.34065e16 | 1.47169 | 0.735847 | − | 0.677148i | \(-0.236784\pi\) | ||||
0.735847 | + | 0.677148i | \(0.236784\pi\) | |||||||
\(458\) | −4.12223e15 | + | 2.48905e15i | −0.446621 | + | 0.269675i | ||||
\(459\) | −2.07590e15 | −0.221989 | ||||||||
\(460\) | 8.67466e14 | − | 1.64866e15i | 0.0915599 | − | 0.174014i | ||||
\(461\) | 4.96899e15i | 0.517681i | 0.965920 | + | 0.258841i | \(0.0833404\pi\) | ||||
−0.965920 | + | 0.258841i | \(0.916660\pi\) | |||||||
\(462\) | 1.14900e16 | − | 6.93780e15i | 1.18159 | − | 0.713460i | ||||
\(463\) | − | 5.00187e15i | − | 0.507746i | −0.967238 | − | 0.253873i | \(-0.918295\pi\) | ||
0.967238 | − | 0.253873i | \(-0.0817045\pi\) | |||||||
\(464\) | 2.51746e15 | − | 1.72997e15i | 0.252263 | − | 0.173353i | ||||
\(465\) | −2.97831e15 | −0.294613 | ||||||||
\(466\) | −1.53951e15 | − | 2.54964e15i | −0.150337 | − | 0.248979i | ||||
\(467\) | 1.60670e16 | 1.54894 | 0.774470 | − | 0.632611i | \(-0.218017\pi\) | ||||
0.774470 | + | 0.632611i | \(0.218017\pi\) | |||||||
\(468\) | −7.09333e15 | − | 3.73226e15i | −0.675111 | − | 0.355220i | ||||
\(469\) | 1.19363e15i | 0.112159i | ||||||||
\(470\) | 2.81589e14 | + | 4.66351e14i | 0.0261233 | + | 0.0432639i | ||||
\(471\) | 8.27088e15i | 0.757576i | ||||||||
\(472\) | −5.71910e14 | + | 3.37003e13i | −0.0517221 | + | 0.00304777i | ||||
\(473\) | 1.20616e16 | 1.07706 | ||||||||
\(474\) | −1.21875e16 | + | 7.35895e15i | −1.07459 | + | 0.648852i | ||||
\(475\) | 2.62261e15 | 0.228335 | ||||||||
\(476\) | −2.66922e15 | − | 1.40445e15i | −0.229478 | − | 0.120744i | ||||
\(477\) | 7.30703e15i | 0.620341i | ||||||||
\(478\) | 1.26626e16 | − | 7.64585e15i | 1.06159 | − | 0.641001i | ||||
\(479\) | − | 5.73610e15i | − | 0.474902i | −0.971400 | − | 0.237451i | \(-0.923688\pi\) | ||
0.971400 | − | 0.237451i | \(-0.0763119\pi\) | |||||||
\(480\) | 1.94603e15 | + | 8.81920e14i | 0.159112 | + | 0.0721077i | ||||
\(481\) | −2.60504e16 | −2.10350 | ||||||||
\(482\) | −7.78992e15 | − | 1.29012e16i | −0.621228 | − | 1.02884i | ||||
\(483\) | −1.61296e16 | −1.27040 | ||||||||
\(484\) | −6.92443e15 | + | 1.31602e16i | −0.538656 | + | 1.02374i | ||||
\(485\) | − | 9.38854e14i | − | 0.0721353i | ||||||
\(486\) | −5.63277e15 | − | 9.32868e15i | −0.427469 | − | 0.707950i | ||||
\(487\) | 8.93354e15i | 0.669653i | 0.942280 | + | 0.334827i | \(0.108678\pi\) | ||||
−0.942280 | + | 0.334827i | \(0.891322\pi\) | |||||||
\(488\) | −5.95448e13 | − | 1.01050e15i | −0.00440885 | − | 0.0748203i | ||||
\(489\) | 1.14827e15 | 0.0839829 | ||||||||
\(490\) | 6.67811e14 | − | 4.03233e14i | 0.0482478 | − | 0.0291326i | ||||
\(491\) | −4.60186e15 | −0.328431 | −0.164216 | − | 0.986424i | \(-0.552509\pi\) | ||||
−0.164216 | + | 0.986424i | \(0.552509\pi\) | |||||||
\(492\) | −4.90794e15 | + | 9.32774e15i | −0.346026 | + | 0.657636i | ||||
\(493\) | − | 1.45599e15i | − | 0.101409i | ||||||
\(494\) | 5.00852e15 | − | 3.02421e15i | 0.344626 | − | 0.208089i | ||||
\(495\) | 1.38922e15i | 0.0944365i | ||||||||
\(496\) | −2.06962e16 | + | 1.42222e16i | −1.38995 | + | 0.955160i | ||||
\(497\) | 8.48299e15 | 0.562873 | ||||||||
\(498\) | −4.97900e15 | − | 8.24594e15i | −0.326412 | − | 0.540585i | ||||
\(499\) | 2.64251e14 | 0.0171164 | 0.00855821 | − | 0.999963i | \(-0.497276\pi\) | ||||
0.00855821 | + | 0.999963i | \(0.497276\pi\) | |||||||
\(500\) | −3.98049e15 | − | 2.09440e15i | −0.254752 | − | 0.134042i | ||||
\(501\) | 8.46965e15i | 0.535598i | ||||||||
\(502\) | 1.23845e15 | + | 2.05105e15i | 0.0773848 | + | 0.128160i | ||||
\(503\) | 7.33852e15i | 0.453107i | 0.973999 | + | 0.226553i | \(0.0727458\pi\) | ||||
−0.973999 | + | 0.226553i | \(0.927254\pi\) | |||||||
\(504\) | −3.33557e14 | − | 5.66062e15i | −0.0203510 | − | 0.345367i | ||||
\(505\) | −7.03826e14 | −0.0424343 | ||||||||
\(506\) | 2.85222e16 | − | 1.72221e16i | 1.69934 | − | 1.02608i | ||||
\(507\) | 4.03493e16 | 2.37568 | ||||||||
\(508\) | 1.32927e15 | + | 6.99414e14i | 0.0773446 | + | 0.0406960i | ||||
\(509\) | 1.30956e16i | 0.753041i | 0.926408 | + | 0.376520i | \(0.122880\pi\) | ||||
−0.926408 | + | 0.376520i | \(0.877120\pi\) | |||||||
\(510\) | 8.71809e14 | − | 5.26409e14i | 0.0495451 | − | 0.0299159i | ||||
\(511\) | − | 2.34674e16i | − | 1.31808i | ||||||
\(512\) | 1.77343e16 | − | 3.16436e15i | 0.984451 | − | 0.175657i | ||||
\(513\) | 2.84879e15 | 0.156299 | ||||||||
\(514\) | 1.18195e16 | + | 1.95748e16i | 0.640944 | + | 1.06150i | ||||
\(515\) | 1.07354e15 | 0.0575408 | ||||||||
\(516\) | 7.74056e15 | − | 1.47113e16i | 0.410085 | − | 0.779385i | ||||
\(517\) | 9.74313e15i | 0.510218i | ||||||||
\(518\) | −9.52602e15 | − | 1.57764e16i | −0.493097 | − | 0.816640i | ||||
\(519\) | − | 4.21795e16i | − | 2.15823i | ||||||
\(520\) | −4.95485e15 | + | 2.91969e14i | −0.250617 | + | 0.0147678i | ||||
\(521\) | −2.39785e15 | −0.119893 | −0.0599467 | − | 0.998202i | \(-0.519093\pi\) | ||||
−0.0599467 | + | 0.998202i | \(0.519093\pi\) | |||||||
\(522\) | 2.34327e15 | − | 1.41489e15i | 0.115824 | − | 0.0699360i | ||||
\(523\) | −1.38045e16 | −0.674543 | −0.337271 | − | 0.941407i | \(-0.609504\pi\) | ||||
−0.337271 | + | 0.941407i | \(0.609504\pi\) | |||||||
\(524\) | −5.04107e15 | + | 9.58077e15i | −0.243520 | + | 0.462821i | ||||
\(525\) | 1.92633e16i | 0.919971i | ||||||||
\(526\) | −2.34859e16 | + | 1.41811e16i | −1.10890 | + | 0.669568i | ||||
\(527\) | 1.19698e16i | 0.558759i | ||||||||
\(528\) | 2.16414e16 | + | 3.14927e16i | 0.998807 | + | 1.45347i | ||||
\(529\) | −1.81247e16 | −0.827060 | ||||||||
\(530\) | 2.33887e15 | + | 3.87350e15i | 0.105524 | + | 0.174762i | ||||
\(531\) | −5.13398e14 | −0.0229027 | ||||||||
\(532\) | 3.66300e15 | + | 1.92734e15i | 0.161572 | + | 0.0850138i | ||||
\(533\) | − | 2.44860e16i | − | 1.06796i | ||||||
\(534\) | 1.53205e16 | + | 2.53730e16i | 0.660734 | + | 1.09427i | ||||
\(535\) | − | 2.69095e15i | − | 0.114758i | ||||||
\(536\) | −3.39231e15 | + | 1.99895e14i | −0.143056 | + | 0.00842970i | ||||
\(537\) | −2.82677e16 | −1.17881 | ||||||||
\(538\) | 6.03887e15 | − | 3.64634e15i | 0.249036 | − | 0.150371i | ||||
\(539\) | 1.39521e16 | 0.568993 | ||||||||
\(540\) | −2.13877e15 | − | 1.12534e15i | −0.0862583 | − | 0.0453861i | ||||
\(541\) | − | 3.66448e16i | − | 1.46160i | −0.682592 | − | 0.730800i | \(-0.739147\pi\) | ||
0.682592 | − | 0.730800i | \(-0.260853\pi\) | |||||||
\(542\) | −2.20908e16 | + | 1.33387e16i | −0.871398 | + | 0.526161i | ||||
\(543\) | − | 1.19949e16i | − | 0.467949i | ||||||
\(544\) | 3.54444e15 | − | 7.82110e15i | 0.136758 | − | 0.301769i | ||||
\(545\) | 4.36446e15 | 0.166553 | ||||||||
\(546\) | 2.22130e16 | + | 3.67879e16i | 0.838400 | + | 1.38851i | ||||
\(547\) | −4.31567e16 | −1.61111 | −0.805553 | − | 0.592523i | \(-0.798132\pi\) | ||||
−0.805553 | + | 0.592523i | \(0.798132\pi\) | |||||||
\(548\) | −1.93849e16 | + | 3.68417e16i | −0.715779 | + | 1.36037i | ||||
\(549\) | − | 9.07119e14i | − | 0.0331307i | ||||||
\(550\) | −2.05681e16 | − | 3.40637e16i | −0.743048 | − | 1.23059i | ||||
\(551\) | 1.99808e15i | 0.0714009i | ||||||||
\(552\) | −2.70117e15 | − | 4.58402e16i | −0.0954812 | − | 1.62036i | ||||
\(553\) | 2.33982e16 | 0.818148 | ||||||||
\(554\) | 1.71269e16 | − | 1.03415e16i | 0.592408 | − | 0.357703i | ||||
\(555\) | 6.22270e15 | 0.212922 | ||||||||
\(556\) | 1.73163e16 | − | 3.29104e16i | 0.586148 | − | 1.11400i | ||||
\(557\) | 1.09327e16i | 0.366098i | 0.983104 | + | 0.183049i | \(0.0585966\pi\) | ||||
−0.983104 | + | 0.183049i | \(0.941403\pi\) | |||||||
\(558\) | −1.92642e16 | + | 1.16319e16i | −0.638182 | + | 0.385342i | ||||
\(559\) | 3.86181e16i | 1.26567i | ||||||||
\(560\) | −1.98870e15 | − | 2.89396e15i | −0.0644823 | − | 0.0938349i | ||||
\(561\) | 1.82141e16 | 0.584292 | ||||||||
\(562\) | −2.08729e16 | − | 3.45685e16i | −0.662469 | − | 1.09714i | ||||
\(563\) | −4.15377e16 | −1.30435 | −0.652173 | − | 0.758071i | \(-0.726142\pi\) | ||||
−0.652173 | + | 0.758071i | \(0.726142\pi\) | |||||||
\(564\) | 1.18835e16 | + | 6.25267e15i | 0.369206 | + | 0.194263i | ||||
\(565\) | − | 6.80175e15i | − | 0.209088i | ||||||
\(566\) | −5.40716e14 | − | 8.95504e14i | −0.0164464 | − | 0.0272376i | ||||
\(567\) | 3.24201e16i | 0.975700i | ||||||||
\(568\) | 1.42062e15 | + | 2.41086e16i | 0.0423047 | + | 0.717931i | ||||
\(569\) | 1.16448e16 | 0.343130 | 0.171565 | − | 0.985173i | \(-0.445118\pi\) | ||||
0.171565 | + | 0.985173i | \(0.445118\pi\) | |||||||
\(570\) | −1.19640e15 | + | 7.22398e14i | −0.0348839 | + | 0.0210634i | ||||
\(571\) | 4.58308e16 | 1.32233 | 0.661166 | − | 0.750240i | \(-0.270062\pi\) | ||||
0.661166 | + | 0.750240i | \(0.270062\pi\) | |||||||
\(572\) | −7.85594e16 | − | 4.13353e16i | −2.24296 | − | 1.18017i | ||||
\(573\) | − | 3.92914e16i | − | 1.11012i | ||||||
\(574\) | 1.48291e16 | − | 8.95397e15i | 0.414612 | − | 0.250348i | ||||
\(575\) | 4.78183e16i | 1.32308i | ||||||||
\(576\) | 1.60316e16 | − | 1.89594e15i | 0.438977 | − | 0.0519145i | ||||
\(577\) | 5.52781e16 | 1.49795 | 0.748977 | − | 0.662596i | \(-0.230546\pi\) | ||||
0.748977 | + | 0.662596i | \(0.230546\pi\) | |||||||
\(578\) | 1.71582e16 | + | 2.84164e16i | 0.460155 | + | 0.762083i | ||||
\(579\) | −2.61546e16 | −0.694186 | ||||||||
\(580\) | 7.89294e14 | − | 1.50009e15i | 0.0207334 | − | 0.0394047i | ||||
\(581\) | 1.58310e16i | 0.411578i | ||||||||
\(582\) | −1.19618e16 | − | 1.98105e16i | −0.307794 | − | 0.509751i | ||||
\(583\) | 8.09261e16i | 2.06100i | ||||||||
\(584\) | 6.66944e16 | − | 3.93003e15i | 1.68117 | − | 0.0990646i | ||||
\(585\) | −4.44792e15 | −0.110974 | ||||||||
\(586\) | −3.63473e16 | + | 2.19469e16i | −0.897606 | + | 0.541986i | ||||
\(587\) | 3.56815e16 | 0.872197 | 0.436099 | − | 0.899899i | \(-0.356360\pi\) | ||||
0.436099 | + | 0.899899i | \(0.356360\pi\) | |||||||
\(588\) | 8.95377e15 | − | 1.70170e16i | 0.216642 | − | 0.411737i | ||||
\(589\) | − | 1.64264e16i | − | 0.393414i | ||||||
\(590\) | −2.72155e14 | + | 1.64331e14i | −0.00645215 | + | 0.00389589i | ||||
\(591\) | − | 6.38240e16i | − | 1.49782i | ||||||
\(592\) | 4.32413e16 | − | 2.97150e16i | 1.00454 | − | 0.690311i | ||||
\(593\) | −1.49380e16 | −0.343530 | −0.171765 | − | 0.985138i | \(-0.554947\pi\) | ||||
−0.171765 | + | 0.985138i | \(0.554947\pi\) | |||||||
\(594\) | −2.23418e16 | − | 3.70013e16i | −0.508628 | − | 0.842361i | ||||
\(595\) | −1.67375e15 | −0.0377215 | ||||||||
\(596\) | 3.03893e16 | + | 1.59898e16i | 0.678020 | + | 0.356751i | ||||
\(597\) | 4.43586e16i | 0.979787i | ||||||||
\(598\) | 5.51406e16 | + | 9.13207e16i | 1.20577 | + | 1.99693i | ||||
\(599\) | − | 8.10969e16i | − | 1.75567i | −0.478962 | − | 0.877836i | \(-0.658987\pi\) | ||
0.478962 | − | 0.877836i | \(-0.341013\pi\) | |||||||
\(600\) | −5.47462e16 | + | 3.22597e15i | −1.17340 | + | 0.0691437i | ||||
\(601\) | 3.89715e14 | 0.00826991 | 0.00413495 | − | 0.999991i | \(-0.498684\pi\) | ||||
0.00413495 | + | 0.999991i | \(0.498684\pi\) | |||||||
\(602\) | −2.33877e16 | + | 1.41218e16i | −0.491369 | + | 0.296695i | ||||
\(603\) | −3.04524e15 | −0.0633457 | ||||||||
\(604\) | −1.85714e16 | − | 9.77164e15i | −0.382493 | − | 0.201255i | ||||
\(605\) | 8.25217e15i | 0.168281i | ||||||||
\(606\) | −1.48513e16 | + | 8.96737e15i | −0.299866 | + | 0.181063i | ||||
\(607\) | 7.80965e15i | 0.156135i | 0.996948 | + | 0.0780674i | \(0.0248749\pi\) | ||||
−0.996948 | + | 0.0780674i | \(0.975125\pi\) | |||||||
\(608\) | −4.86407e15 | + | 1.07330e16i | −0.0962895 | + | 0.212471i | ||||
\(609\) | −1.46760e16 | −0.287677 | ||||||||
\(610\) | −2.90355e14 | − | 4.80869e14i | −0.00563572 | − | 0.00933357i | ||||
\(611\) | −3.11949e16 | −0.599566 | ||||||||
\(612\) | 3.58307e15 | − | 6.80978e15i | 0.0681942 | − | 0.129606i | ||||
\(613\) | − | 3.98858e16i | − | 0.751719i | −0.926677 | − | 0.375859i | \(-0.877348\pi\) | ||
0.926677 | − | 0.375859i | \(-0.122652\pi\) | |||||||
\(614\) | −3.16307e16 | − | 5.23849e16i | −0.590334 | − | 0.977678i | ||||
\(615\) | 5.84902e15i | 0.108102i | ||||||||
\(616\) | −3.69418e15 | − | 6.26920e16i | −0.0676136 | − | 1.14743i | ||||
\(617\) | −8.61498e16 | −1.56151 | −0.780753 | − | 0.624840i | \(-0.785164\pi\) | ||||
−0.780753 | + | 0.624840i | \(0.785164\pi\) | |||||||
\(618\) | 2.26525e16 | − | 1.36779e16i | 0.406618 | − | 0.245521i | ||||
\(619\) | 3.64100e16 | 0.647257 | 0.323629 | − | 0.946184i | \(-0.395097\pi\) | ||||
0.323629 | + | 0.946184i | \(0.395097\pi\) | |||||||
\(620\) | −6.48884e15 | + | 1.23323e16i | −0.114240 | + | 0.217117i | ||||
\(621\) | 5.19421e16i | 0.905671i | ||||||||
\(622\) | 4.17222e16 | − | 2.51924e16i | 0.720485 | − | 0.435038i | ||||
\(623\) | − | 4.87125e16i | − | 0.833130i | ||||||
\(624\) | −1.00831e17 | + | 6.92900e16i | −1.70800 | + | 1.17372i | ||||
\(625\) | 5.58473e16 | 0.936962 | ||||||||
\(626\) | 2.70617e16 | + | 4.48181e16i | 0.449686 | + | 0.744745i | ||||
\(627\) | −2.49954e16 | −0.411391 | ||||||||
\(628\) | 3.42473e16 | + | 1.80197e16i | 0.558301 | + | 0.293759i | ||||
\(629\) | − | 2.50090e16i | − | 0.403825i | ||||||
\(630\) | −1.62650e15 | − | 2.69372e15i | −0.0260142 | − | 0.0430833i | ||||
\(631\) | − | 7.57937e15i | − | 0.120076i | −0.998196 | − | 0.0600381i | \(-0.980878\pi\) | ||
0.998196 | − | 0.0600381i | \(-0.0191222\pi\) | |||||||
\(632\) | 3.91843e15 | + | 6.64976e16i | 0.0614908 | + | 1.04353i | ||||
\(633\) | −7.47095e16 | −1.16132 | ||||||||
\(634\) | −4.67650e16 | + | 2.82373e16i | −0.720087 | + | 0.434798i | ||||
\(635\) | 8.33525e14 | 0.0127138 | ||||||||
\(636\) | 9.87036e16 | + | 5.19344e16i | 1.49139 | + | 0.784716i | ||||
\(637\) | 4.46709e16i | 0.668634i | ||||||||
\(638\) | 2.59519e16 | − | 1.56701e16i | 0.384810 | − | 0.232353i | ||||
\(639\) | 2.16421e16i | 0.317902i | ||||||||
\(640\) | 7.89159e15 | − | 6.13651e15i | 0.114838 | − | 0.0892980i | ||||
\(641\) | 4.69745e15 | 0.0677195 | 0.0338597 | − | 0.999427i | \(-0.489220\pi\) | ||||
0.0338597 | + | 0.999427i | \(0.489220\pi\) | |||||||
\(642\) | −3.42852e16 | − | 5.67811e16i | −0.489662 | − | 0.810950i | ||||
\(643\) | −4.04169e16 | −0.571870 | −0.285935 | − | 0.958249i | \(-0.592304\pi\) | ||||
−0.285935 | + | 0.958249i | \(0.592304\pi\) | |||||||
\(644\) | −3.51414e16 | + | 6.67878e16i | −0.492611 | + | 0.936228i | ||||
\(645\) | − | 9.22480e15i | − | 0.128115i | ||||||
\(646\) | 2.90332e15 | + | 4.80831e15i | 0.0399484 | + | 0.0661603i | ||||
\(647\) | − | 1.26950e17i | − | 1.73064i | −0.501216 | − | 0.865322i | \(-0.667114\pi\) | ||
0.501216 | − | 0.865322i | \(-0.332886\pi\) | |||||||
\(648\) | −9.21379e16 | + | 5.42931e15i | −1.24448 | + | 0.0733322i | ||||
\(649\) | −5.68594e15 | −0.0760911 | ||||||||
\(650\) | 1.09063e17 | − | 6.58535e16i | 1.44609 | − | 0.873170i | ||||
\(651\) | 1.20653e17 | 1.58508 | ||||||||
\(652\) | 2.50173e15 | − | 4.75465e15i | 0.0325653 | − | 0.0618917i | ||||
\(653\) | − | 1.07897e17i | − | 1.39165i | −0.718211 | − | 0.695826i | \(-0.755039\pi\) | ||
0.718211 | − | 0.695826i | \(-0.244961\pi\) | |||||||
\(654\) | 9.20933e16 | − | 5.56071e16i | 1.17696 | − | 0.710663i | ||||
\(655\) | 6.00769e15i | 0.0760780i | ||||||||
\(656\) | 2.79305e16 | + | 4.06446e16i | 0.350474 | + | 0.510012i | ||||
\(657\) | 5.98709e16 | 0.744429 | ||||||||
\(658\) | −1.14073e16 | − | 1.88921e16i | −0.140549 | − | 0.232769i | ||||
\(659\) | −7.56505e15 | −0.0923632 | −0.0461816 | − | 0.998933i | \(-0.514705\pi\) | ||||
−0.0461816 | + | 0.998933i | \(0.514705\pi\) | |||||||
\(660\) | 1.87657e16 | + | 9.87384e15i | 0.227039 | + | 0.119460i | ||||
\(661\) | 7.41336e15i | 0.0888804i | 0.999012 | + | 0.0444402i | \(0.0141504\pi\) | ||||
−0.999012 | + | 0.0444402i | \(0.985850\pi\) | |||||||
\(662\) | 4.50138e16 | + | 7.45493e16i | 0.534808 | + | 0.885719i | ||||
\(663\) | 5.83167e16i | 0.686612i | ||||||||
\(664\) | −4.49917e16 | + | 2.65118e15i | −0.524957 | + | 0.0309336i | ||||
\(665\) | 2.29691e15 | 0.0265591 | ||||||||
\(666\) | 4.02494e16 | − | 2.43031e16i | 0.461226 | − | 0.278494i | ||||
\(667\) | −3.64312e16 | −0.413731 | ||||||||
\(668\) | 3.50703e16 | + | 1.84528e16i | 0.394712 | + | 0.207684i | ||||
\(669\) | 1.60117e17i | 1.78599i | ||||||||
\(670\) | −1.61430e15 | + | 9.74733e14i | −0.0178457 | + | 0.0107755i | ||||
\(671\) | − | 1.00464e16i | − | 0.110072i | ||||||
\(672\) | −7.88346e16 | − | 3.57270e16i | −0.856055 | − | 0.387954i | ||||
\(673\) | 3.11706e16 | 0.335471 | 0.167736 | − | 0.985832i | \(-0.446355\pi\) | ||||
0.167736 | + | 0.985832i | \(0.446355\pi\) | |||||||
\(674\) | −2.55523e16 | − | 4.23183e16i | −0.272566 | − | 0.451408i | ||||
\(675\) | 6.20337e16 | 0.655850 | ||||||||
\(676\) | 8.79088e16 | − | 1.67074e17i | 0.921197 | − | 1.75077i | ||||
\(677\) | 1.35475e17i | 1.40711i | 0.710641 | + | 0.703555i | \(0.248405\pi\) | ||||
−0.710641 | + | 0.703555i | \(0.751595\pi\) | |||||||
\(678\) | −8.66604e16 | − | 1.43522e17i | −0.892159 | − | 1.47754i | ||||
\(679\) | 3.80334e16i | 0.388102i | ||||||||
\(680\) | −2.80298e14 | − | 4.75679e15i | −0.00283509 | − | 0.0481128i | ||||
\(681\) | 7.07026e16 | 0.708847 | ||||||||
\(682\) | −2.13353e17 | + | 1.28825e17i | −2.12027 | + | 1.28025i | ||||
\(683\) | 6.65918e16 | 0.655989 | 0.327995 | − | 0.944680i | \(-0.393627\pi\) | ||||
0.327995 | + | 0.944680i | \(0.393627\pi\) | |||||||
\(684\) | −4.91710e15 | + | 9.34515e15i | −0.0480145 | + | 0.0912536i | ||||
\(685\) | 2.31019e16i | 0.223616i | ||||||||
\(686\) | −9.68796e16 | + | 5.84971e16i | −0.929582 | + | 0.561293i | ||||
\(687\) | 6.58671e16i | 0.626510i | ||||||||
\(688\) | −4.40507e16 | − | 6.41028e16i | −0.415357 | − | 0.604430i | ||||
\(689\) | −2.59104e17 | −2.42192 | ||||||||
\(690\) | −1.31715e16 | − | 2.18140e16i | −0.122051 | − | 0.202134i | ||||
\(691\) | −6.92836e16 | −0.636447 | −0.318224 | − | 0.948016i | \(-0.603086\pi\) | ||||
−0.318224 | + | 0.948016i | \(0.603086\pi\) | |||||||
\(692\) | −1.74653e17 | − | 9.18964e16i | −1.59052 | − | 0.836878i | ||||
\(693\) | − | 5.62779e16i | − | 0.508088i | ||||||
\(694\) | 6.02426e16 | + | 9.97704e16i | 0.539196 | + | 0.892986i | ||||
\(695\) | − | 2.06367e16i | − | 0.183118i | ||||||
\(696\) | −2.45776e15 | − | 4.17093e16i | −0.0216214 | − | 0.366925i | ||||
\(697\) | 2.35072e16 | 0.205024 | ||||||||
\(698\) | −3.58759e16 | + | 2.16623e16i | −0.310221 | + | 0.187315i | ||||
\(699\) | −4.07395e16 | −0.349263 | ||||||||
\(700\) | 7.97635e16 | + | 4.19688e16i | 0.677979 | + | 0.356729i | ||||
\(701\) | − | 7.65599e15i | − | 0.0645199i | −0.999480 | − | 0.0322599i | \(-0.989730\pi\) | ||
0.999480 | − | 0.0322599i | \(-0.0102704\pi\) | |||||||
\(702\) | 1.18468e17 | − | 7.15327e16i | 0.989874 | − | 0.597698i | ||||
\(703\) | 3.43202e16i | 0.284327i | ||||||||
\(704\) | 1.77552e17 | − | 2.09977e16i | 1.45844 | − | 0.172479i | ||||
\(705\) | 7.45160e15 | 0.0606897 | ||||||||
\(706\) | 1.94287e15 | + | 3.21767e15i | 0.0156897 | + | 0.0259844i | ||||
\(707\) | 2.85123e16 | 0.228305 | ||||||||
\(708\) | −3.64896e15 | + | 6.93500e15i | −0.0289714 | + | 0.0550614i | ||||
\(709\) | − | 1.42396e17i | − | 1.12104i | −0.828140 | − | 0.560521i | \(-0.810601\pi\) | ||
0.828140 | − | 0.560521i | \(-0.189399\pi\) | |||||||
\(710\) | 6.92729e15 | + | 1.14726e16i | 0.0540771 | + | 0.0895594i | ||||
\(711\) | 5.96942e16i | 0.462077i | ||||||||
\(712\) | 1.38441e17 | − | 8.15775e15i | 1.06264 | − | 0.0626168i | ||||
\(713\) | 2.99503e17 | 2.27963 | ||||||||
\(714\) | −3.53174e16 | + | 2.13251e16i | −0.266562 | + | 0.160954i | ||||
\(715\) | −4.92612e16 | −0.368696 | ||||||||
\(716\) | −6.15867e16 | + | 1.17048e17i | −0.457097 | + | 0.868733i | ||||
\(717\) | − | 2.02330e17i | − | 1.48917i | ||||||
\(718\) | −4.77222e16 | + | 2.88153e16i | −0.348316 | + | 0.210318i | ||||
\(719\) | − | 1.68320e17i | − | 1.21833i | −0.793045 | − | 0.609163i | \(-0.791506\pi\) | ||
0.793045 | − | 0.609163i | \(-0.208494\pi\) | |||||||
\(720\) | 7.38316e15 | − | 5.07362e15i | 0.0529965 | − | 0.0364186i | ||||
\(721\) | −4.34896e16 | −0.309581 | ||||||||
\(722\) | 6.92348e16 | + | 1.14663e17i | 0.488766 | + | 0.809467i | ||||
\(723\) | −2.06143e17 | −1.44324 | ||||||||
\(724\) | −4.96674e16 | − | 2.61333e16i | −0.344858 | − | 0.181452i | ||||
\(725\) | 4.35092e16i | 0.299607i | ||||||||
\(726\) | 1.05140e17 | + | 1.74127e17i | 0.718040 | + | 1.18918i | ||||
\(727\) | 1.82317e17i | 1.23487i | 0.786622 | + | 0.617435i | \(0.211828\pi\) | ||||
−0.786622 | + | 0.617435i | \(0.788172\pi\) | |||||||
\(728\) | 2.00723e17 | − | 1.18278e16i | 1.34837 | − | 0.0794539i | ||||
\(729\) | 3.80555e16 | 0.253543 | ||||||||
\(730\) | 3.17379e16 | − | 1.91637e16i | 0.209720 | − | 0.126632i | ||||
\(731\) | −3.70744e16 | −0.242980 | ||||||||
\(732\) | −1.22534e16 | − | 6.44732e15i | −0.0796508 | − | 0.0419095i | ||||
\(733\) | − | 2.14324e17i | − | 1.38181i | −0.722947 | − | 0.690903i | \(-0.757213\pi\) | ||
0.722947 | − | 0.690903i | \(-0.242787\pi\) | |||||||
\(734\) | −1.17263e17 | + | 7.08051e16i | −0.749871 | + | 0.452781i | ||||
\(735\) | − | 1.06706e16i | − | 0.0676809i | ||||||
\(736\) | −1.95696e17 | − | 8.86871e16i | −1.23116 | − | 0.557948i | ||||
\(737\) | −3.37263e16 | −0.210457 | ||||||||
\(738\) | 2.28436e16 | + | 3.78323e16i | 0.141393 | + | 0.234167i | ||||
\(739\) | 1.40791e17 | 0.864384 | 0.432192 | − | 0.901782i | \(-0.357740\pi\) | ||||
0.432192 | + | 0.901782i | \(0.357740\pi\) | |||||||
\(740\) | 1.35574e16 | − | 2.57664e16i | 0.0825630 | − | 0.156915i | ||||
\(741\) | − | 8.00287e16i | − | 0.483433i | ||||||
\(742\) | −9.47484e16 | − | 1.56917e17i | −0.567739 | − | 0.940257i | ||||
\(743\) | 2.34527e17i | 1.39399i | 0.717077 | + | 0.696994i | \(0.245480\pi\) | ||||
−0.717077 | + | 0.696994i | \(0.754520\pi\) | |||||||
\(744\) | 2.02054e16 | + | 3.42895e17i | 0.119132 | + | 2.02173i | ||||
\(745\) | 1.90558e16 | 0.111452 | ||||||||
\(746\) | 2.31005e17 | − | 1.39484e17i | 1.34026 | − | 0.809263i | ||||
\(747\) | −4.03886e16 | −0.232453 | ||||||||
\(748\) | 3.96829e16 | − | 7.54191e16i | 0.226566 | − | 0.430598i | ||||
\(749\) | 1.09012e17i | 0.617422i | ||||||||
\(750\) | −5.26674e16 | + | 3.18012e16i | −0.295920 | + | 0.178680i | ||||
\(751\) | 1.85542e17i | 1.03420i | 0.855926 | + | 0.517099i | \(0.172988\pi\) | ||||
−0.855926 | + | 0.517099i | \(0.827012\pi\) | |||||||
\(752\) | 5.17809e16 | − | 3.55832e16i | 0.286327 | − | 0.196761i | ||||
\(753\) | 3.27727e16 | 0.179781 | ||||||||
\(754\) | 5.01716e16 | + | 8.30913e16i | 0.273042 | + | 0.452197i | ||||
\(755\) | −1.16453e16 | −0.0628738 | ||||||||
\(756\) | 8.66423e16 | + | 4.55882e16i | 0.464087 | + | 0.244186i | ||||
\(757\) | − | 6.68044e16i | − | 0.355001i | −0.984121 | − | 0.177501i | \(-0.943199\pi\) | ||
0.984121 | − | 0.177501i | \(-0.0568012\pi\) | |||||||
\(758\) | −6.49004e16 | − | 1.07484e17i | −0.342162 | − | 0.566670i | ||||
\(759\) | − | 4.55743e17i | − | 2.38380i | ||||||
\(760\) | 3.84657e14 | + | 6.52781e15i | 0.00199614 | + | 0.0338755i | ||||
\(761\) | −3.05000e16 | −0.157033 | −0.0785166 | − | 0.996913i | \(-0.525018\pi\) | ||||
−0.0785166 | + | 0.996913i | \(0.525018\pi\) | |||||||
\(762\) | 1.75880e16 | − | 1.06199e16i | 0.0898435 | − | 0.0542486i | ||||
\(763\) | −1.76806e17 | −0.896086 | ||||||||
\(764\) | −1.62694e17 | − | 8.56040e16i | −0.818110 | − | 0.430461i | ||||
\(765\) | − | 4.27012e15i | − | 0.0213045i | ||||||
\(766\) | −2.12244e17 | + | 1.28155e17i | −1.05066 | + | 0.634402i | ||||
\(767\) | − | 1.82049e16i | − | 0.0894161i | ||||||
\(768\) | 8.83337e16 | − | 2.30031e17i | 0.430486 | − | 1.12103i | ||||
\(769\) | −1.44827e17 | −0.700313 | −0.350156 | − | 0.936691i | \(-0.613872\pi\) | ||||
−0.350156 | + | 0.936691i | \(0.613872\pi\) | |||||||
\(770\) | −1.80137e16 | − | 2.98332e16i | −0.0864288 | − | 0.143138i | ||||
\(771\) | 3.12776e17 | 1.48904 | ||||||||
\(772\) | −5.69828e16 | + | 1.08298e17i | −0.269178 | + | 0.511585i | ||||
\(773\) | 2.32429e17i | 1.08946i | 0.838610 | + | 0.544732i | \(0.183369\pi\) | ||||
−0.838610 | + | 0.544732i | \(0.816631\pi\) | |||||||
\(774\) | −3.60279e16 | − | 5.96673e16i | −0.167569 | − | 0.277518i | ||||
\(775\) | − | 3.57692e17i | − | 1.65082i | ||||||
\(776\) | −1.08091e17 | + | 6.36934e15i | −0.495015 | + | 0.0291692i | ||||
\(777\) | −2.52084e17 | −1.14557 | ||||||||
\(778\) | −7.57861e15 | + | 4.57606e15i | −0.0341753 | + | 0.0206354i | ||||
\(779\) | −3.22592e16 | −0.144354 | ||||||||
\(780\) | −3.16134e16 | + | 6.00827e16i | −0.140380 | + | 0.266797i | ||||
\(781\) | 2.39688e17i | 1.05619i | ||||||||
\(782\) | −8.76703e16 | + | 5.29364e16i | −0.383365 | + | 0.231480i | ||||
\(783\) | 4.72614e16i | 0.205086i | ||||||||
\(784\) | −5.09549e16 | − | 7.41498e16i | −0.219427 | − | 0.319311i | ||||
\(785\) | 2.14750e16 | 0.0917730 | ||||||||
\(786\) | 7.65433e16 | + | 1.26767e17i | 0.324617 | + | 0.537613i | ||||
\(787\) | −6.74291e16 | −0.283791 | −0.141896 | − | 0.989882i | \(-0.545320\pi\) | ||||
−0.141896 | + | 0.989882i | \(0.545320\pi\) | |||||||
\(788\) | −2.64276e17 | − | 1.39053e17i | −1.10383 | − | 0.580795i | ||||
\(789\) | 3.75270e17i | 1.55554i | ||||||||
\(790\) | 1.91072e16 | + | 3.16442e16i | 0.0786021 | + | 0.130176i | ||||
\(791\) | 2.75542e17i | 1.12494i | ||||||||
\(792\) | 1.59942e17 | − | 9.42470e15i | 0.648053 | − | 0.0381871i | ||||
\(793\) | 3.21661e16 | 0.129348 | ||||||||
\(794\) | 3.98277e17 | − | 2.40484e17i | 1.58950 | − | 0.959763i | ||||
\(795\) | 6.18928e16 | 0.245153 | ||||||||
\(796\) | 1.83676e17 | + | 9.66439e16i | 0.722061 | + | 0.379923i | ||||
\(797\) | − | 1.81340e15i | − | 0.00707530i | −0.999994 | − | 0.00353765i | \(-0.998874\pi\) | ||
0.999994 | − | 0.00353765i | \(-0.00112607\pi\) | |||||||
\(798\) | 4.84665e16 | − | 2.92647e16i | 0.187683 | − | 0.113325i | ||||
\(799\) | − | 2.99480e16i | − | 0.115103i | ||||||
\(800\) | −1.05918e17 | + | 2.33716e17i | −0.404043 | + | 0.891557i | ||||
\(801\) | 1.24277e17 | 0.470539 | ||||||||
\(802\) | −1.22534e17 | − | 2.02933e17i | −0.460478 | − | 0.762618i | ||||
\(803\) | 6.63076e17 | 2.47326 | ||||||||
\(804\) | −2.16439e16 | + | 4.11352e16i | −0.0801308 | + | 0.152292i | ||||
\(805\) | 4.18797e16i | 0.153896i | ||||||||
\(806\) | −4.12464e17 | − | 6.83099e17i | −1.50444 | − | 2.49157i | ||||
\(807\) | − | 9.64922e16i | − | 0.349342i | ||||||
\(808\) | 4.77487e15 | + | 8.10318e16i | 0.0171591 | + | 0.291197i | ||||
\(809\) | 2.92000e17 | 1.04158 | 0.520789 | − | 0.853685i | \(-0.325638\pi\) | ||||
0.520789 | + | 0.853685i | \(0.325638\pi\) | |||||||
\(810\) | −4.38457e16 | + | 2.64746e16i | −0.155245 | + | 0.0937387i | ||||
\(811\) | −1.70120e17 | −0.597902 | −0.298951 | − | 0.954268i | \(-0.596637\pi\) | ||||
−0.298951 | + | 0.954268i | \(0.596637\pi\) | |||||||
\(812\) | −3.19746e16 | + | 6.07692e16i | −0.111550 | + | 0.212005i | ||||
\(813\) | 3.52979e17i | 1.22238i | ||||||||
\(814\) | 4.45766e17 | − | 2.69159e17i | 1.53236 | − | 0.925258i | ||||
\(815\) | − | 2.98143e15i | − | 0.0101737i | ||||||
\(816\) | −6.65203e16 | − | 9.68006e16i | −0.225327 | − | 0.327897i | ||||
\(817\) | 5.08777e16 | 0.171078 | ||||||||
\(818\) | 6.84205e16 | + | 1.13314e17i | 0.228384 | + | 0.378237i | ||||
\(819\) | 1.80187e17 | 0.597063 | ||||||||
\(820\) | 2.42191e16 | + | 1.27432e16i | 0.0796663 | + | 0.0419176i | ||||
\(821\) | − | 4.93861e17i | − | 1.61267i | −0.591459 | − | 0.806335i | \(-0.701448\pi\) | ||
0.591459 | − | 0.806335i | \(-0.298552\pi\) | |||||||
\(822\) | 2.94338e17 | + | 4.87466e17i | 0.954148 | + | 1.58021i | ||||
\(823\) | 1.34570e17i | 0.433062i | 0.976276 | + | 0.216531i | \(0.0694743\pi\) | ||||
−0.976276 | + | 0.216531i | \(0.930526\pi\) | |||||||
\(824\) | −7.28309e15 | − | 1.23597e17i | −0.0232676 | − | 0.394863i | ||||
\(825\) | −5.44287e17 | −1.72625 | ||||||||
\(826\) | 1.10251e16 | − | 6.65710e15i | 0.0347139 | − | 0.0209607i | ||||
\(827\) | −2.73538e17 | −0.855036 | −0.427518 | − | 0.904007i | \(-0.640612\pi\) | ||||
−0.427518 | + | 0.904007i | \(0.640612\pi\) | |||||||
\(828\) | −1.70391e17 | − | 8.96539e16i | −0.528767 | − | 0.278219i | ||||
\(829\) | − | 1.87428e16i | − | 0.0577441i | −0.999583 | − | 0.0288721i | \(-0.990808\pi\) | ||
0.999583 | − | 0.0288721i | \(-0.00919154\pi\) | |||||||
\(830\) | −2.14102e16 | + | 1.29278e16i | −0.0654866 | + | 0.0395416i | ||||
\(831\) | − | 2.73663e17i | − | 0.831017i | ||||||
\(832\) | 6.72291e16 | + | 5.68474e17i | 0.202683 | + | 1.71384i | ||||
\(833\) | −4.28853e16 | −0.128362 | ||||||||
\(834\) | −2.62930e17 | − | 4.35450e17i | −0.781347 | − | 1.29402i | ||||
\(835\) | 2.19911e16 | 0.0648825 | ||||||||
\(836\) | −5.44574e16 | + | 1.03499e17i | −0.159522 | + | 0.303177i | ||||
\(837\) | − | 3.88539e17i | − | 1.13001i | ||||||
\(838\) | 3.24648e17 | + | 5.37663e17i | 0.937450 | + | 1.55255i | ||||
\(839\) | 1.28127e17i | 0.367341i | 0.982988 | + | 0.183671i | \(0.0587980\pi\) | ||||
−0.982988 | + | 0.183671i | \(0.941202\pi\) | |||||||
\(840\) | −4.79472e16 | + | 2.82533e15i | −0.136486 | + | 0.00804254i | ||||
\(841\) | 3.20667e17 | 0.906312 | ||||||||
\(842\) | −8.64764e16 | + | 5.22156e16i | −0.242675 | + | 0.146530i | ||||
\(843\) | −5.52354e17 | −1.53905 | ||||||||
\(844\) | −1.62769e17 | + | 3.09350e17i | −0.450316 | + | 0.855846i | ||||
\(845\) | − | 1.04765e17i | − | 0.287791i | ||||||
\(846\) | 4.81981e16 | − | 2.91026e16i | 0.131464 | − | 0.0793797i | ||||
\(847\) | − | 3.34299e17i | − | 0.905388i | ||||||
\(848\) | 4.30090e17 | − | 2.95553e17i | 1.15660 | − | 0.794805i | ||||
\(849\) | −1.43088e16 | −0.0382083 | ||||||||
\(850\) | 6.32211e16 | + | 1.04703e17i | 0.167629 | + | 0.277617i | ||||
\(851\) | −6.25763e17 | −1.64753 | ||||||||
\(852\) | 2.92342e17 | + | 1.53820e17i | 0.764282 | + | 0.402139i | ||||
\(853\) | − | 8.33316e16i | − | 0.216329i | −0.994133 | − | 0.108165i | \(-0.965503\pi\) | ||
0.994133 | − | 0.108165i | \(-0.0344974\pi\) | |||||||
\(854\) | 1.17624e16 | + | 1.94802e16i | 0.0303213 | + | 0.0502165i | ||||
\(855\) | 5.85994e15i | 0.0150002i | ||||||||
\(856\) | −3.09811e17 | + | 1.82559e16i | −0.787507 | + | 0.0464045i | ||||
\(857\) | −3.59209e17 | −0.906696 | −0.453348 | − | 0.891334i | \(-0.649771\pi\) | ||||
−0.453348 | + | 0.891334i | \(0.649771\pi\) | |||||||
\(858\) | −1.03945e18 | + | 6.27632e17i | −2.60543 | + | 1.57319i | ||||
\(859\) | 2.17917e17 | 0.542416 | 0.271208 | − | 0.962521i | \(-0.412577\pi\) | ||||
0.271208 | + | 0.962521i | \(0.412577\pi\) | |||||||
\(860\) | −3.81972e16 | − | 2.00980e16i | −0.0944149 | − | 0.0496779i | ||||
\(861\) | − | 2.36946e17i | − | 0.581609i | ||||||
\(862\) | 3.45431e17 | − | 2.08575e17i | 0.842011 | − | 0.508416i | ||||
\(863\) | 7.88461e16i | 0.190860i | 0.995436 | + | 0.0954301i | \(0.0304226\pi\) | ||||
−0.995436 | + | 0.0954301i | \(0.969577\pi\) | |||||||
\(864\) | −1.15052e17 | + | 2.53872e17i | −0.276574 | + | 0.610284i | ||||
\(865\) | −1.09517e17 | −0.261449 | ||||||||
\(866\) | 1.83431e17 | + | 3.03788e17i | 0.434876 | + | 0.720216i | ||||
\(867\) | 4.54053e17 | 1.06903 | ||||||||
\(868\) | 2.62866e17 | − | 4.99587e17i | 0.614632 | − | 1.16813i | ||||
\(869\) | 6.61120e17i | 1.53519i | ||||||||
\(870\) | −1.19846e16 | − | 1.98482e16i | −0.0276381 | − | 0.0457726i | ||||
\(871\) | − | 1.07983e17i | − | 0.247312i | ||||||
\(872\) | −2.96092e16 | − | 5.02482e17i | −0.0673485 | − | 1.14294i | ||||
\(873\) | −9.70319e16 | −0.219194 | ||||||||
\(874\) | 1.20311e17 | − | 7.26453e16i | 0.269921 | − | 0.162982i | ||||
\(875\) | 1.01114e17 | 0.225301 | ||||||||
\(876\) | 4.25530e17 | − | 8.08738e17i | 0.941685 | − | 1.78971i | ||||
\(877\) | − | 4.87327e17i | − | 1.07108i | −0.844509 | − | 0.535541i | \(-0.820108\pi\) | ||
0.844509 | − | 0.535541i | \(-0.179892\pi\) | |||||||
\(878\) | −7.25504e17 | + | 4.38068e17i | −1.58370 | + | 0.956258i | ||||
\(879\) | 5.80776e17i | 1.25914i | ||||||||
\(880\) | 8.17693e16 | − | 5.61909e16i | 0.176074 | − | 0.120996i | ||||
\(881\) | 4.51739e17 | 0.966122 | 0.483061 | − | 0.875587i | \(-0.339525\pi\) | ||||
0.483061 | + | 0.875587i | \(0.339525\pi\) | |||||||
\(882\) | −4.16747e16 | − | 6.90192e16i | −0.0885239 | − | 0.146608i | ||||
\(883\) | 6.51124e17 | 1.37372 | 0.686862 | − | 0.726788i | \(-0.258988\pi\) | ||||
0.686862 | + | 0.726788i | \(0.258988\pi\) | |||||||
\(884\) | 2.41472e17 | + | 1.27054e17i | 0.506003 | + | 0.266242i | ||||
\(885\) | 4.34864e15i | 0.00905094i | ||||||||
\(886\) | −1.16814e17 | − | 1.93461e17i | −0.241487 | − | 0.399936i | ||||
\(887\) | 5.99033e16i | 0.123001i | 0.998107 | + | 0.0615006i | \(0.0195886\pi\) | ||||
−0.998107 | + | 0.0615006i | \(0.980411\pi\) | |||||||
\(888\) | −4.22159e16 | − | 7.16423e17i | −0.0860989 | − | 1.46114i | ||||
\(889\) | −3.37665e16 | −0.0684030 | ||||||||
\(890\) | 6.58799e16 | − | 3.97791e16i | 0.132560 | − | 0.0800415i | ||||
\(891\) | −9.16036e17 | −1.83082 | ||||||||
\(892\) | 6.62996e17 | + | 3.48845e17i | 1.31620 | + | 0.692539i | ||||
\(893\) | 4.10980e16i | 0.0810423i | ||||||||
\(894\) | 4.02092e17 | − | 2.42788e17i | 0.787589 | − | 0.475556i | ||||
\(895\) | 7.33958e16i | 0.142802i | ||||||||
\(896\) | −3.19692e17 | + | 2.48593e17i | −0.617850 | + | 0.480441i | ||||
\(897\) | 1.45917e18 | 2.80125 | ||||||||
\(898\) | 1.11040e17 | + | 1.83897e17i | 0.211748 | + | 0.350685i | ||||
\(899\) | 2.72513e17 | 0.516213 | ||||||||
\(900\) | −1.07072e17 | + | 2.03495e17i | −0.201475 | + | 0.382912i | ||||
\(901\) | − | 2.48747e17i | − | 0.464953i | ||||||
\(902\) | 2.52996e17 | + | 4.18997e17i | 0.469758 | + | 0.777986i | ||||
\(903\) | 3.73700e17i | 0.689282i | ||||||||
\(904\) | −7.83089e17 | + | 4.61442e16i | −1.43483 | + | 0.0845486i | ||||
\(905\) | −3.11443e16 | −0.0566875 | ||||||||
\(906\) | −2.45725e17 | + | 1.48372e17i | −0.444304 | + | 0.268276i | ||||
\(907\) | −8.95377e16 | −0.160828 | −0.0804141 | − | 0.996762i | \(-0.525624\pi\) | ||||
−0.0804141 | + | 0.996762i | \(0.525624\pi\) | |||||||
\(908\) | 1.54039e17 | − | 2.92759e17i | 0.274863 | − | 0.522390i | ||||
\(909\) | 7.27414e16i | 0.128943i | ||||||||
\(910\) | 9.55182e16 | − | 5.76751e16i | 0.168205 | − | 0.101564i | ||||
\(911\) | 9.69255e17i | 1.69562i | 0.530303 | + | 0.847808i | \(0.322078\pi\) | ||||
−0.530303 | + | 0.847808i | \(0.677922\pi\) | |||||||
\(912\) | 9.12866e16 | + | 1.32841e17i | 0.158649 | + | 0.230867i | ||||
\(913\) | −4.47308e17 | −0.772293 | ||||||||
\(914\) | −4.43502e17 | − | 7.34503e17i | −0.760709 | − | 1.25984i | ||||
\(915\) | −7.68357e15 | −0.0130929 | ||||||||
\(916\) | 2.72736e17 | + | 1.43504e17i | 0.461711 | + | 0.242936i | ||||
\(917\) | − | 2.43374e17i | − | 0.409315i | ||||||
\(918\) | 6.86733e16 | + | 1.13733e17i | 0.114744 | + | 0.190033i | ||||
\(919\) | − | 2.97870e17i | − | 0.494463i | −0.968956 | − | 0.247231i | \(-0.920479\pi\) | ||
0.968956 | − | 0.247231i | \(-0.0795208\pi\) | |||||||
\(920\) | −1.19022e17 | + | 7.01348e15i | −0.196291 | + | 0.0115666i | ||||
\(921\) | −8.37033e17 | −1.37147 | ||||||||
\(922\) | 2.72237e17 | − | 1.64380e17i | 0.443161 | − | 0.267586i | ||||
\(923\) | −7.67419e17 | −1.24114 | ||||||||
\(924\) | −7.60205e17 | − | 3.99993e17i | −1.22151 | − | 0.642719i | ||||
\(925\) | 7.47339e17i | 1.19307i | ||||||||
\(926\) | −2.74038e17 | + | 1.65468e17i | −0.434656 | + | 0.262451i | ||||
\(927\) | − | 1.10952e17i | − | 0.174847i | ||||||
\(928\) | −1.78061e17 | − | 8.06950e16i | −0.278792 | − | 0.126345i | ||||
\(929\) | 2.19428e17 | 0.341349 | 0.170674 | − | 0.985327i | \(-0.445405\pi\) | ||||
0.170674 | + | 0.985327i | \(0.445405\pi\) | |||||||
\(930\) | 9.85261e16 | + | 1.63173e17i | 0.152284 | + | 0.252204i | ||||
\(931\) | 5.88520e16 | 0.0903781 | ||||||||
\(932\) | −8.87590e16 | + | 1.68690e17i | −0.135431 | + | 0.257392i | ||||
\(933\) | − | 6.66659e17i | − | 1.01068i | ||||||
\(934\) | −5.31516e17 | − | 8.80268e17i | −0.800637 | − | 1.32597i | ||||
\(935\) | − | 4.72921e16i | − | 0.0707813i | ||||||
\(936\) | 3.01754e16 | + | 5.12091e17i | 0.0448744 | + | 0.761539i | ||||
\(937\) | 3.67690e17 | 0.543306 | 0.271653 | − | 0.962395i | \(-0.412430\pi\) | ||||
0.271653 | + | 0.962395i | \(0.412430\pi\) | |||||||
\(938\) | 6.53959e16 | − | 3.94868e16i | 0.0960137 | − | 0.0579743i | ||||
\(939\) | 7.16127e17 | 1.04471 | ||||||||
\(940\) | 1.62348e16 | − | 3.08549e16i | 0.0235331 | − | 0.0447257i | ||||
\(941\) | − | 9.58053e17i | − | 1.37991i | −0.723851 | − | 0.689957i | \(-0.757630\pi\) | ||
0.723851 | − | 0.689957i | \(-0.242370\pi\) | |||||||
\(942\) | 4.53138e17 | − | 2.73611e17i | 0.648523 | − | 0.391586i | ||||
\(943\) | − | 5.88185e17i | − | 0.836458i | ||||||
\(944\) | 2.07658e16 | + | 3.02185e16i | 0.0293439 | + | 0.0427013i | ||||
\(945\) | 5.43296e16 | 0.0762862 | ||||||||
\(946\) | −3.99013e17 | − | 6.60822e17i | −0.556724 | − | 0.922015i | ||||
\(947\) | 1.74200e17 | 0.241517 | 0.120758 | − | 0.992682i | \(-0.461467\pi\) | ||||
0.120758 | + | 0.992682i | \(0.461467\pi\) | |||||||
\(948\) | 8.06352e17 | + | 4.24275e17i | 1.11090 | + | 0.584517i | ||||
\(949\) | 2.12300e18i | 2.90638i | ||||||||
\(950\) | −8.67592e16 | − | 1.43686e17i | −0.118025 | − | 0.195466i | ||||
\(951\) | 7.47236e17i | 1.01012i | ||||||||
\(952\) | 1.13550e16 | + | 1.92700e17i | 0.0152533 | + | 0.258857i | ||||
\(953\) | 2.06893e17 | 0.276178 | 0.138089 | − | 0.990420i | \(-0.455904\pi\) | ||||
0.138089 | + | 0.990420i | \(0.455904\pi\) | |||||||
\(954\) | 4.00331e17 | − | 2.41725e17i | 0.531043 | − | 0.320650i | ||||
\(955\) | −1.02018e17 | −0.134480 | ||||||||
\(956\) | −8.37789e17 | − | 4.40816e17i | −1.09746 | − | 0.577444i | ||||
\(957\) | − | 4.14674e17i | − | 0.539803i | ||||||
\(958\) | −3.14265e17 | + | 1.89757e17i | −0.406540 | + | 0.245474i | ||||
\(959\) | − | 9.35866e17i | − | 1.20310i | ||||||
\(960\) | −1.60592e16 | − | 1.35793e17i | −0.0205161 | − | 0.173480i | ||||
\(961\) | −1.45269e18 | −1.84430 | ||||||||
\(962\) | 8.61777e17 | + | 1.42723e18i | 1.08729 | + | 1.80070i | ||||
\(963\) | −2.78114e17 | −0.348710 | ||||||||
\(964\) | −4.49122e17 | + | 8.53576e17i | −0.559632 | + | 1.06360i | ||||
\(965\) | 6.79092e16i | 0.0840939i | ||||||||
\(966\) | 5.33585e17 | + | 8.83693e17i | 0.656660 | + | 1.08752i | ||||
\(967\) | − | 9.40030e17i | − | 1.14970i | −0.818261 | − | 0.574848i | \(-0.805061\pi\) | ||
0.818261 | − | 0.574848i | \(-0.194939\pi\) | |||||||
\(968\) | 9.50077e17 | − | 5.59841e16i | 1.15480 | − | 0.0680476i | ||||
\(969\) | 7.68297e16 | 0.0928082 | ||||||||
\(970\) | −5.14372e16 | + | 3.10584e16i | −0.0617514 | + | 0.0372863i | ||||
\(971\) | 2.00797e17 | 0.239576 | 0.119788 | − | 0.992800i | \(-0.461779\pi\) | ||||
0.119788 | + | 0.992800i | \(0.461779\pi\) | |||||||
\(972\) | −3.24753e17 | + | 6.17207e17i | −0.385084 | + | 0.731869i | ||||
\(973\) | 8.36002e17i | 0.985213i | ||||||||
\(974\) | 4.89444e17 | − | 2.95532e17i | 0.573256 | − | 0.346139i | ||||
\(975\) | − | 1.74266e18i | − | 2.02855i | ||||||
\(976\) | −5.33929e16 | + | 3.66910e16i | −0.0617710 | + | 0.0424483i | ||||
\(977\) | −1.37968e18 | −1.58639 | −0.793197 | − | 0.608965i | \(-0.791585\pi\) | ||||
−0.793197 | + | 0.608965i | \(0.791585\pi\) | |||||||
\(978\) | −3.79861e16 | − | 6.29105e16i | −0.0434102 | − | 0.0718935i | ||||
\(979\) | 1.37638e18 | 1.56330 | ||||||||
\(980\) | −4.41840e16 | − | 2.32481e16i | −0.0498779 | − | 0.0262440i | ||||
\(981\) | − | 4.51073e17i | − | 0.506096i | ||||||
\(982\) | 1.52235e17 | + | 2.52123e17i | 0.169764 | + | 0.281154i | ||||
\(983\) | − | 1.01606e18i | − | 1.12615i | −0.826405 | − | 0.563076i | \(-0.809618\pi\) | ||
0.826405 | − | 0.563076i | \(-0.190382\pi\) | |||||||
\(984\) | 6.73401e17 | − | 3.96807e16i | 0.741828 | − | 0.0437129i | ||||
\(985\) | −1.65716e17 | −0.181446 | ||||||||
\(986\) | −7.97699e16 | + | 4.81660e16i | −0.0868115 | + | 0.0524179i | ||||
\(987\) | −3.01868e17 | −0.326523 | ||||||||
\(988\) | −3.31375e17 | − | 1.74358e17i | −0.356269 | − | 0.187457i | ||||
\(989\) | 9.27658e17i | 0.991311i | ||||||||
\(990\) | 7.61115e16 | − | 4.59571e16i | 0.0808424 | − | 0.0488136i | ||||
\(991\) | 3.04422e17i | 0.321391i | 0.987004 | + | 0.160696i | \(0.0513738\pi\) | ||||
−0.987004 | + | 0.160696i | \(0.948626\pi\) | |||||||
\(992\) | 1.46385e18 | + | 6.63399e17i | 1.53612 | + | 0.696153i | ||||
\(993\) | 1.19119e18 | 1.24247 | ||||||||
\(994\) | −2.80627e17 | − | 4.64759e17i | −0.290946 | − | 0.481847i | ||||
\(995\) | 1.15175e17 | 0.118692 | ||||||||
\(996\) | −2.87060e17 | + | 5.45571e17i | −0.294047 | + | 0.558850i | ||||
\(997\) | − | 6.03575e17i | − | 0.614554i | −0.951620 | − | 0.307277i | \(-0.900582\pi\) | ||
0.951620 | − | 0.307277i | \(-0.0994178\pi\) | |||||||
\(998\) | −8.74173e15 | − | 1.44776e16i | −0.00884737 | − | 0.0146525i | ||||
\(999\) | 8.11789e17i | 0.816677i |
(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 | 8.13.d.b.3.5 | ✓ | 10 | |
3.2 | odd | 2 | 72.13.b.b.19.6 | 10 | |||
4.3 | odd | 2 | 32.13.d.b.15.8 | 10 | |||
8.3 | odd | 2 | inner | 8.13.d.b.3.6 | yes | 10 | |
8.5 | even | 2 | 32.13.d.b.15.7 | 10 | |||
24.11 | even | 2 | 72.13.b.b.19.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.13.d.b.3.5 | ✓ | 10 | 1.1 | even | 1 | trivial | |
8.13.d.b.3.6 | yes | 10 | 8.3 | odd | 2 | inner | |
32.13.d.b.15.7 | 10 | 8.5 | even | 2 | |||
32.13.d.b.15.8 | 10 | 4.3 | odd | 2 | |||
72.13.b.b.19.5 | 10 | 24.11 | even | 2 | |||
72.13.b.b.19.6 | 10 | 3.2 | odd | 2 |