Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,30,Mod(20,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 30, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.20");
S:= CuspForms(chi, 30);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 30 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.c (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: | \(111.883889004\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 20.17 | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.30.c.a.20.18 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3217.48i | − | 0.138861i | −0.997587 | − | 0.0694306i | \(-0.977882\pi\) | ||
0.997587 | − | 0.0694306i | \(-0.0221182\pi\) | |||||||
\(3\) | 7.29657e6 | − | 3.92306e6i | 0.880766 | − | 0.473551i | ||||
\(4\) | 5.26519e8 | 0.980718 | ||||||||
\(5\) | 1.29709e10 | 0.950396 | 0.475198 | − | 0.879879i | \(-0.342376\pi\) | ||||
0.475198 | + | 0.879879i | \(0.342376\pi\) | |||||||
\(6\) | −1.26224e10 | − | 2.34766e10i | −0.0657579 | − | 0.122304i | ||||
\(7\) | 5.86304e11 | − | 1.69592e12i | 0.326739 | − | 0.945115i | ||||
\(8\) | − | 3.42144e12i | − | 0.275045i | ||||||
\(9\) | 3.78496e13 | − | 5.72498e13i | 0.551499 | − | 0.834176i | ||||
\(10\) | − | 4.17336e13i | − | 0.131973i | ||||||
\(11\) | 2.57206e14i | 0.204215i | 0.994773 | + | 0.102107i | \(0.0325585\pi\) | ||||
−0.994773 | + | 0.102107i | \(0.967442\pi\) | |||||||
\(12\) | 3.84178e15 | − | 2.06557e15i | 0.863783 | − | 0.464420i | ||||
\(13\) | 2.26248e15i | 0.159370i | 0.996820 | + | 0.0796849i | \(0.0253914\pi\) | ||||
−0.996820 | + | 0.0796849i | \(0.974609\pi\) | |||||||
\(14\) | −5.45660e15 | − | 1.88642e15i | −0.131240 | − | 0.0453714i | ||||
\(15\) | 9.46430e16 | − | 5.08856e16i | 0.837077 | − | 0.450061i | ||||
\(16\) | 2.71664e17 | 0.942524 | ||||||||
\(17\) | 2.95368e17 | 0.425456 | 0.212728 | − | 0.977111i | \(-0.431765\pi\) | ||||
0.212728 | + | 0.977111i | \(0.431765\pi\) | |||||||
\(18\) | −1.84200e17 | − | 1.21780e17i | −0.115835 | − | 0.0765818i | ||||
\(19\) | 7.21413e17i | 0.207137i | 0.994622 | + | 0.103568i | \(0.0330260\pi\) | ||||
−0.994622 | + | 0.103568i | \(0.966974\pi\) | |||||||
\(20\) | 6.82942e18 | 0.932070 | ||||||||
\(21\) | −2.37520e18 | − | 1.46745e19i | −0.159779 | − | 0.987153i | ||||
\(22\) | 8.27555e17 | 0.0283575 | ||||||||
\(23\) | − | 7.82034e18i | − | 0.140661i | −0.997524 | − | 0.0703303i | \(-0.977595\pi\) | ||
0.997524 | − | 0.0703303i | \(-0.0224053\pi\) | |||||||
\(24\) | −1.34225e19 | − | 2.49648e19i | −0.130248 | − | 0.242250i | ||||
\(25\) | −1.80205e19 | −0.0967468 | ||||||||
\(26\) | 7.27948e18 | 0.0221303 | ||||||||
\(27\) | 5.15776e19 | − | 5.66213e20i | 0.0907166 | − | 0.995877i | ||||
\(28\) | 3.08700e20 | − | 8.92935e20i | 0.320439 | − | 0.926890i | ||||
\(29\) | − | 1.31886e21i | − | 0.823056i | −0.911397 | − | 0.411528i | \(-0.864995\pi\) | ||
0.911397 | − | 0.411528i | \(-0.135005\pi\) | |||||||
\(30\) | −1.63723e20 | − | 3.04512e20i | −0.0624961 | − | 0.116238i | ||||
\(31\) | − | 8.21072e20i | − | 0.194821i | −0.995244 | − | 0.0974107i | \(-0.968944\pi\) | ||
0.995244 | − | 0.0974107i | \(-0.0310560\pi\) | |||||||
\(32\) | − | 2.71094e21i | − | 0.405925i | ||||||
\(33\) | 1.00903e21 | + | 1.87672e21i | 0.0967060 | + | 0.179865i | ||||
\(34\) | − | 9.50341e20i | − | 0.0590793i | ||||||
\(35\) | 7.60488e21 | − | 2.19976e22i | 0.310532 | − | 0.898233i | ||||
\(36\) | 1.99285e22 | − | 3.01431e22i | 0.540864 | − | 0.818091i | ||||
\(37\) | 2.70371e22 | 0.493213 | 0.246607 | − | 0.969116i | \(-0.420684\pi\) | ||||
0.246607 | + | 0.969116i | \(0.420684\pi\) | |||||||
\(38\) | 2.32113e21 | 0.0287632 | ||||||||
\(39\) | 8.87584e21 | + | 1.65083e22i | 0.0754697 | + | 0.140368i | ||||
\(40\) | − | 4.43791e22i | − | 0.261402i | ||||||
\(41\) | 8.94365e22 | 0.368255 | 0.184128 | − | 0.982902i | \(-0.441054\pi\) | ||||
0.184128 | + | 0.982902i | \(0.441054\pi\) | |||||||
\(42\) | −4.72150e22 | + | 7.64216e21i | −0.137077 | + | 0.0221871i | ||||
\(43\) | −4.21105e23 | −0.869157 | −0.434578 | − | 0.900634i | \(-0.643103\pi\) | ||||
−0.434578 | + | 0.900634i | \(0.643103\pi\) | |||||||
\(44\) | 1.35424e23i | 0.200277i | ||||||||
\(45\) | 4.90943e23 | − | 7.42581e23i | 0.524142 | − | 0.792798i | ||||
\(46\) | −2.51618e22 | −0.0195323 | ||||||||
\(47\) | 2.58177e24 | 1.46723 | 0.733614 | − | 0.679566i | \(-0.237832\pi\) | ||||
0.733614 | + | 0.679566i | \(0.237832\pi\) | |||||||
\(48\) | 1.98222e24 | − | 1.06576e24i | 0.830144 | − | 0.446334i | ||||
\(49\) | −2.53240e24 | − | 1.98865e24i | −0.786483 | − | 0.617612i | ||||
\(50\) | 5.79806e22i | 0.0134344i | ||||||||
\(51\) | 2.15518e24 | − | 1.15875e24i | 0.374727 | − | 0.201475i | ||||
\(52\) | 1.19124e24i | 0.156297i | ||||||||
\(53\) | 3.95452e24i | 0.393635i | 0.980440 | + | 0.196817i | \(0.0630606\pi\) | ||||
−0.980440 | + | 0.196817i | \(0.936939\pi\) | |||||||
\(54\) | −1.82178e24 | − | 1.65950e23i | −0.138289 | − | 0.0125970i | ||||
\(55\) | 3.33619e24i | 0.194085i | ||||||||
\(56\) | −5.80249e24 | − | 2.00600e24i | −0.259949 | − | 0.0898679i | ||||
\(57\) | 2.83015e24 | + | 5.26384e24i | 0.0980898 | + | 0.182439i | ||||
\(58\) | −4.24342e24 | −0.114291 | ||||||||
\(59\) | −4.28869e25 | −0.901510 | −0.450755 | − | 0.892648i | \(-0.648845\pi\) | ||||
−0.450755 | + | 0.892648i | \(0.648845\pi\) | |||||||
\(60\) | 4.98313e25 | − | 2.67922e25i | 0.820936 | − | 0.441383i | ||||
\(61\) | 1.02071e26i | 1.32319i | 0.749862 | + | 0.661594i | \(0.230120\pi\) | ||||
−0.749862 | + | 0.661594i | \(0.769880\pi\) | |||||||
\(62\) | −2.64178e24 | −0.0270531 | ||||||||
\(63\) | −7.48999e25 | − | 9.77557e25i | −0.608195 | − | 0.793787i | ||||
\(64\) | 1.37126e26 | 0.886157 | ||||||||
\(65\) | 2.93464e25i | 0.151464i | ||||||||
\(66\) | 6.03831e24 | − | 3.24655e24i | 0.0249763 | − | 0.0134287i | ||||
\(67\) | −2.28970e26 | −0.761541 | −0.380771 | − | 0.924670i | \(-0.624341\pi\) | ||||
−0.380771 | + | 0.924670i | \(0.624341\pi\) | |||||||
\(68\) | 1.55517e26 | 0.417252 | ||||||||
\(69\) | −3.06797e25 | − | 5.70617e25i | −0.0666099 | − | 0.123889i | ||||
\(70\) | −7.07770e25 | − | 2.44686e25i | −0.124730 | − | 0.0431208i | ||||
\(71\) | 9.93970e26i | 1.42603i | 0.701151 | + | 0.713013i | \(0.252670\pi\) | ||||
−0.701151 | + | 0.713013i | \(0.747330\pi\) | |||||||
\(72\) | −1.95877e26 | − | 1.29500e26i | −0.229436 | − | 0.151687i | ||||
\(73\) | − | 3.22830e26i | − | 0.309594i | −0.987946 | − | 0.154797i | \(-0.950528\pi\) | ||
0.987946 | − | 0.154797i | \(-0.0494723\pi\) | |||||||
\(74\) | − | 8.69912e25i | − | 0.0684882i | ||||||
\(75\) | −1.31488e26 | + | 7.06955e25i | −0.0852114 | + | 0.0458146i | ||||
\(76\) | 3.79837e26i | 0.203142i | ||||||||
\(77\) | 4.36201e26 | + | 1.50801e26i | 0.193006 | + | 0.0667249i | ||||
\(78\) | 5.31153e25 | − | 2.85579e25i | 0.0194916 | − | 0.0104798i | ||||
\(79\) | 2.91142e27 | 0.888203 | 0.444101 | − | 0.895977i | \(-0.353523\pi\) | ||||
0.444101 | + | 0.895977i | \(0.353523\pi\) | |||||||
\(80\) | 3.52373e27 | 0.895772 | ||||||||
\(81\) | −1.84495e27 | − | 4.33376e27i | −0.391698 | − | 0.920094i | ||||
\(82\) | − | 2.87760e26i | − | 0.0511364i | ||||||
\(83\) | 5.01961e26 | 0.0748235 | 0.0374117 | − | 0.999300i | \(-0.488089\pi\) | ||||
0.0374117 | + | 0.999300i | \(0.488089\pi\) | |||||||
\(84\) | −1.25059e27 | − | 7.72641e27i | −0.156698 | − | 0.968118i | ||||
\(85\) | 3.83119e27 | 0.404351 | ||||||||
\(86\) | 1.35490e27i | 0.120692i | ||||||||
\(87\) | −5.17399e27 | − | 9.62319e27i | −0.389759 | − | 0.724920i | ||||
\(88\) | 8.80013e26 | 0.0561682 | ||||||||
\(89\) | −1.01997e28 | −0.552626 | −0.276313 | − | 0.961068i | \(-0.589113\pi\) | ||||
−0.276313 | + | 0.961068i | \(0.589113\pi\) | |||||||
\(90\) | −2.38924e27 | − | 1.57960e27i | −0.110089 | − | 0.0727831i | ||||
\(91\) | 3.83699e27 | + | 1.32650e27i | 0.150623 | + | 0.0520723i | ||||
\(92\) | − | 4.11756e27i | − | 0.137948i | ||||||
\(93\) | −3.22111e27 | − | 5.99101e27i | −0.0922579 | − | 0.171592i | ||||
\(94\) | − | 8.30678e27i | − | 0.203741i | ||||||
\(95\) | 9.35737e27i | 0.196862i | ||||||||
\(96\) | −1.06352e28 | − | 1.97806e28i | −0.192226 | − | 0.357525i | ||||
\(97\) | 1.12210e29i | 1.74519i | 0.488449 | + | 0.872593i | \(0.337563\pi\) | ||||
−0.488449 | + | 0.872593i | \(0.662437\pi\) | |||||||
\(98\) | −6.39845e27 | + | 8.14795e27i | −0.0857624 | + | 0.109212i | ||||
\(99\) | 1.47250e28 | + | 9.73512e27i | 0.170351 | + | 0.112624i | ||||
\(100\) | −9.48813e27 | −0.0948813 | ||||||||
\(101\) | −7.98606e28 | −0.691310 | −0.345655 | − | 0.938362i | \(-0.612343\pi\) | ||||
−0.345655 | + | 0.938362i | \(0.612343\pi\) | |||||||
\(102\) | −3.72825e27 | − | 6.93424e27i | −0.0279771 | − | 0.0520351i | ||||
\(103\) | 1.82681e29i | 1.19002i | 0.803719 | + | 0.595009i | \(0.202852\pi\) | ||||
−0.803719 | + | 0.595009i | \(0.797148\pi\) | |||||||
\(104\) | 7.74093e27 | 0.0438338 | ||||||||
\(105\) | −3.08085e28 | − | 1.90342e29i | −0.151854 | − | 0.938186i | ||||
\(106\) | 1.27236e28 | 0.0546606 | ||||||||
\(107\) | − | 2.80806e29i | − | 1.05279i | −0.850240 | − | 0.526395i | \(-0.823543\pi\) | ||
0.850240 | − | 0.526395i | \(-0.176457\pi\) | |||||||
\(108\) | 2.71566e28 | − | 2.98122e29i | 0.0889674 | − | 0.976674i | ||||
\(109\) | 2.27472e29 | 0.651994 | 0.325997 | − | 0.945371i | \(-0.394300\pi\) | ||||
0.325997 | + | 0.945371i | \(0.394300\pi\) | |||||||
\(110\) | 1.07341e28 | 0.0269509 | ||||||||
\(111\) | 1.97278e29 | − | 1.06068e29i | 0.434405 | − | 0.233562i | ||||
\(112\) | 1.59278e29 | − | 4.60721e29i | 0.307960 | − | 0.890794i | ||||
\(113\) | − | 1.08391e30i | − | 1.84228i | −0.389236 | − | 0.921138i | \(-0.627261\pi\) | ||
0.389236 | − | 0.921138i | \(-0.372739\pi\) | |||||||
\(114\) | 1.69363e28 | − | 9.10595e27i | 0.0253337 | − | 0.0136209i | ||||
\(115\) | − | 1.01437e29i | − | 0.133683i | ||||||
\(116\) | − | 6.94407e29i | − | 0.807185i | ||||||
\(117\) | 1.29526e29 | + | 8.56338e28i | 0.132942 | + | 0.0878922i | ||||
\(118\) | 1.37988e29i | 0.125185i | ||||||||
\(119\) | 1.73175e29 | − | 5.00922e29i | 0.139013 | − | 0.402104i | ||||
\(120\) | −1.74102e29 | − | 3.23815e29i | −0.123787 | − | 0.230234i | ||||
\(121\) | 1.52015e30 | 0.958296 | ||||||||
\(122\) | 3.28413e29 | 0.183740 | ||||||||
\(123\) | 6.52580e29 | − | 3.50865e29i | 0.324347 | − | 0.174388i | ||||
\(124\) | − | 4.32310e29i | − | 0.191065i | ||||||
\(125\) | −2.64976e30 | −1.04234 | ||||||||
\(126\) | −3.14527e29 | + | 2.40989e29i | −0.110226 | + | 0.0844548i | ||||
\(127\) | 3.05221e30 | 0.953808 | 0.476904 | − | 0.878955i | \(-0.341759\pi\) | ||||
0.476904 | + | 0.878955i | \(0.341759\pi\) | |||||||
\(128\) | − | 1.89663e30i | − | 0.528978i | ||||||
\(129\) | −3.07263e30 | + | 1.65202e30i | −0.765524 | + | 0.411590i | ||||
\(130\) | 9.44214e28 | 0.0210325 | ||||||||
\(131\) | −6.25257e30 | −1.24631 | −0.623153 | − | 0.782100i | \(-0.714149\pi\) | ||||
−0.623153 | + | 0.782100i | \(0.714149\pi\) | |||||||
\(132\) | 5.31275e29 | + | 9.88128e29i | 0.0948413 | + | 0.176397i | ||||
\(133\) | 1.22346e30 | + | 4.22967e29i | 0.195768 | + | 0.0676796i | ||||
\(134\) | 7.36706e29i | 0.105749i | ||||||||
\(135\) | 6.69008e29 | − | 7.34429e30i | 0.0862167 | − | 0.946478i | ||||
\(136\) | − | 1.01058e30i | − | 0.117019i | ||||||
\(137\) | − | 1.45077e31i | − | 1.51060i | −0.655377 | − | 0.755302i | \(-0.727490\pi\) | ||
0.655377 | − | 0.755302i | \(-0.272510\pi\) | |||||||
\(138\) | −1.83595e29 | + | 9.87113e28i | −0.0172034 | + | 0.00924954i | ||||
\(139\) | − | 1.14481e31i | − | 0.966096i | −0.875594 | − | 0.483048i | \(-0.839530\pi\) | ||
0.875594 | − | 0.483048i | \(-0.160470\pi\) | |||||||
\(140\) | 4.00411e30 | − | 1.15822e31i | 0.304544 | − | 0.880913i | ||||
\(141\) | 1.88380e31 | − | 1.01284e31i | 1.29229 | − | 0.694808i | ||||
\(142\) | 3.19808e30 | 0.198020 | ||||||||
\(143\) | −5.81923e29 | −0.0325456 | ||||||||
\(144\) | 1.02824e31 | − | 1.55527e31i | 0.519801 | − | 0.786231i | ||||
\(145\) | − | 1.71069e31i | − | 0.782229i | ||||||
\(146\) | −1.03870e30 | −0.0429906 | ||||||||
\(147\) | −2.62795e31 | − | 4.57558e30i | −0.985179 | − | 0.171532i | ||||
\(148\) | 1.42355e31 | 0.483703 | ||||||||
\(149\) | − | 9.22813e30i | − | 0.284389i | −0.989839 | − | 0.142195i | \(-0.954584\pi\) | ||
0.989839 | − | 0.142195i | \(-0.0454159\pi\) | |||||||
\(150\) | 2.27462e29 | + | 4.23060e29i | 0.00636187 | + | 0.0118326i | ||||
\(151\) | −2.71070e31 | −0.688518 | −0.344259 | − | 0.938875i | \(-0.611870\pi\) | ||||
−0.344259 | + | 0.938875i | \(0.611870\pi\) | |||||||
\(152\) | 2.46827e30 | 0.0569719 | ||||||||
\(153\) | 1.11796e31 | − | 1.69098e31i | 0.234638 | − | 0.354905i | ||||
\(154\) | 4.85198e29 | − | 1.40347e30i | 0.00926550 | − | 0.0268011i | ||||
\(155\) | − | 1.06500e31i | − | 0.185157i | ||||||
\(156\) | 4.67330e30 | + | 8.69195e30i | 0.0740145 | + | 0.137661i | ||||
\(157\) | 2.72110e31i | 0.392826i | 0.980521 | + | 0.196413i | \(0.0629293\pi\) | ||||
−0.980521 | + | 0.196413i | \(0.937071\pi\) | |||||||
\(158\) | − | 9.36744e30i | − | 0.123337i | ||||||
\(159\) | 1.55138e31 | + | 2.88544e31i | 0.186406 | + | 0.346700i | ||||
\(160\) | − | 3.51634e31i | − | 0.385790i | ||||||
\(161\) | −1.32627e31 | − | 4.58510e30i | −0.132940 | − | 0.0459593i | ||||
\(162\) | −1.39438e31 | + | 5.93609e30i | −0.127765 | + | 0.0543917i | ||||
\(163\) | 7.61162e31 | 0.637907 | 0.318953 | − | 0.947770i | \(-0.396669\pi\) | ||||
0.318953 | + | 0.947770i | \(0.396669\pi\) | |||||||
\(164\) | 4.70900e31 | 0.361155 | ||||||||
\(165\) | 1.30881e31 | + | 2.43427e31i | 0.0919091 | + | 0.170943i | ||||
\(166\) | − | 1.61505e30i | − | 0.0103901i | ||||||
\(167\) | −1.11448e32 | −0.657181 | −0.328591 | − | 0.944472i | \(-0.606574\pi\) | ||||
−0.328591 | + | 0.944472i | \(0.606574\pi\) | |||||||
\(168\) | −5.02080e31 | + | 8.12659e30i | −0.271511 | + | 0.0439465i | ||||
\(169\) | 1.96419e32 | 0.974601 | ||||||||
\(170\) | − | 1.23268e31i | − | 0.0561488i | ||||||
\(171\) | 4.13008e31 | + | 2.73052e31i | 0.172788 | + | 0.114236i | ||||
\(172\) | −2.21720e32 | −0.852397 | ||||||||
\(173\) | −2.52800e32 | −0.893527 | −0.446764 | − | 0.894652i | \(-0.647424\pi\) | ||||
−0.446764 | + | 0.894652i | \(0.647424\pi\) | |||||||
\(174\) | −3.09624e31 | + | 1.66472e31i | −0.100663 | + | 0.0541224i | ||||
\(175\) | −1.05655e31 | + | 3.05614e31i | −0.0316110 | + | 0.0914369i | ||||
\(176\) | 6.98736e31i | 0.192477i | ||||||||
\(177\) | −3.12927e32 | + | 1.68248e32i | −0.794020 | + | 0.426911i | ||||
\(178\) | 3.28172e31i | 0.0767383i | ||||||||
\(179\) | 2.57937e32i | 0.556089i | 0.960568 | + | 0.278045i | \(0.0896863\pi\) | ||||
−0.960568 | + | 0.278045i | \(0.910314\pi\) | |||||||
\(180\) | 2.58490e32 | − | 3.90983e32i | 0.514036 | − | 0.777510i | ||||
\(181\) | 8.15388e32i | 1.49632i | 0.663517 | + | 0.748161i | \(0.269063\pi\) | ||||
−0.663517 | + | 0.748161i | \(0.730937\pi\) | |||||||
\(182\) | 4.26799e30 | − | 1.23454e31i | 0.00723083 | − | 0.0209157i | ||||
\(183\) | 4.00433e32 | + | 7.44772e32i | 0.626598 | + | 1.16542i | ||||
\(184\) | −2.67568e31 | −0.0386880 | ||||||||
\(185\) | 3.50695e32 | 0.468748 | ||||||||
\(186\) | −1.92760e31 | + | 1.03639e31i | −0.0238275 | + | 0.0128110i | ||||
\(187\) | 7.59704e31i | 0.0868842i | ||||||||
\(188\) | 1.35935e33 | 1.43894 | ||||||||
\(189\) | −9.30014e32 | − | 4.19445e32i | −0.911577 | − | 0.411130i | ||||
\(190\) | 3.01072e31 | 0.0273365 | ||||||||
\(191\) | 1.32812e33i | 1.11751i | 0.829332 | + | 0.558756i | \(0.188721\pi\) | ||||
−0.829332 | + | 0.558756i | \(0.811279\pi\) | |||||||
\(192\) | 1.00055e33 | − | 5.37954e32i | 0.780497 | − | 0.419641i | ||||
\(193\) | −2.18985e33 | −1.58429 | −0.792144 | − | 0.610334i | \(-0.791035\pi\) | ||||
−0.792144 | + | 0.610334i | \(0.791035\pi\) | |||||||
\(194\) | 3.61034e32 | 0.242339 | ||||||||
\(195\) | 1.15128e32 | + | 2.14128e32i | 0.0717262 | + | 0.133405i | ||||
\(196\) | −1.33336e33 | − | 1.04706e33i | −0.771318 | − | 0.605703i | ||||
\(197\) | 3.55117e33i | 1.90814i | 0.299576 | + | 0.954072i | \(0.403155\pi\) | ||||
−0.299576 | + | 0.954072i | \(0.596845\pi\) | |||||||
\(198\) | 3.13226e31 | − | 4.73773e31i | 0.0156391 | − | 0.0236551i | ||||
\(199\) | 7.79968e32i | 0.361999i | 0.983483 | + | 0.180999i | \(0.0579332\pi\) | ||||
−0.983483 | + | 0.180999i | \(0.942067\pi\) | |||||||
\(200\) | 6.16560e31i | 0.0266097i | ||||||||
\(201\) | −1.67069e33 | + | 8.98262e32i | −0.670740 | + | 0.360629i | ||||
\(202\) | 2.56950e32i | 0.0959962i | ||||||||
\(203\) | −2.23669e33 | − | 7.73256e32i | −0.777882 | − | 0.268925i | ||||
\(204\) | 1.13474e33 | − | 6.10102e32i | 0.367501 | − | 0.197590i | ||||
\(205\) | 1.16007e33 | 0.349989 | ||||||||
\(206\) | 5.87773e32 | 0.165247 | ||||||||
\(207\) | −4.47713e32 | − | 2.95997e32i | −0.117336 | − | 0.0775741i | ||||
\(208\) | 6.14635e32i | 0.150210i | ||||||||
\(209\) | −1.85552e32 | −0.0423003 | ||||||||
\(210\) | −6.12421e32 | + | 9.91256e31i | −0.130278 | + | 0.0210866i | ||||
\(211\) | 4.62986e33 | 0.919331 | 0.459666 | − | 0.888092i | \(-0.347969\pi\) | ||||
0.459666 | + | 0.888092i | \(0.347969\pi\) | |||||||
\(212\) | 2.08213e33i | 0.386044i | ||||||||
\(213\) | 3.89941e33 | + | 7.25258e33i | 0.675296 | + | 1.25600i | ||||
\(214\) | −9.03489e32 | −0.146192 | ||||||||
\(215\) | −5.46211e33 | −0.826043 | ||||||||
\(216\) | −1.93726e33 | − | 1.76470e32i | −0.273911 | − | 0.0249511i | ||||
\(217\) | −1.39247e33 | − | 4.81397e32i | −0.184128 | − | 0.0636557i | ||||
\(218\) | − | 7.31887e32i | − | 0.0905367i | ||||||
\(219\) | −1.26648e33 | − | 2.35555e33i | −0.146609 | − | 0.272680i | ||||
\(220\) | 1.75657e33i | 0.190342i | ||||||||
\(221\) | 6.68264e32i | 0.0678048i | ||||||||
\(222\) | −3.41272e32 | − | 6.34738e32i | −0.0324327 | − | 0.0603221i | ||||
\(223\) | − | 1.31423e34i | − | 1.17017i | −0.810972 | − | 0.585085i | \(-0.801061\pi\) | ||
0.810972 | − | 0.585085i | \(-0.198939\pi\) | |||||||
\(224\) | −4.59755e33 | − | 1.58944e33i | −0.383646 | − | 0.132632i | ||||
\(225\) | −6.82068e32 | + | 1.03167e33i | −0.0533558 | + | 0.0807039i | ||||
\(226\) | −3.48745e33 | −0.255821 | ||||||||
\(227\) | 2.31063e34 | 1.58985 | 0.794924 | − | 0.606709i | \(-0.207511\pi\) | ||||
0.794924 | + | 0.606709i | \(0.207511\pi\) | |||||||
\(228\) | 1.49013e33 | + | 2.77151e33i | 0.0961983 | + | 0.178921i | ||||
\(229\) | − | 1.98937e34i | − | 1.20532i | −0.797998 | − | 0.602660i | \(-0.794108\pi\) | ||
0.797998 | − | 0.602660i | \(-0.205892\pi\) | |||||||
\(230\) | −3.26371e32 | −0.0185634 | ||||||||
\(231\) | 3.77437e33 | − | 6.10915e32i | 0.201591 | − | 0.0326292i | ||||
\(232\) | −4.51241e33 | −0.226377 | ||||||||
\(233\) | − | 3.32558e34i | − | 1.56749i | −0.621080 | − | 0.783747i | \(-0.713306\pi\) | ||
0.621080 | − | 0.783747i | \(-0.286694\pi\) | |||||||
\(234\) | 2.75525e32 | − | 4.16749e32i | 0.0122048 | − | 0.0184605i | ||||
\(235\) | 3.34878e34 | 1.39445 | ||||||||
\(236\) | −2.25808e34 | −0.884127 | ||||||||
\(237\) | 2.12434e34 | − | 1.14217e34i | 0.782299 | − | 0.420609i | ||||
\(238\) | −1.61171e33 | − | 5.57189e32i | −0.0558367 | − | 0.0193035i | ||||
\(239\) | − | 4.36685e34i | − | 1.42364i | −0.702364 | − | 0.711818i | \(-0.747872\pi\) | ||
0.702364 | − | 0.711818i | \(-0.252128\pi\) | |||||||
\(240\) | 2.57111e34 | − | 1.38238e34i | 0.788966 | − | 0.424194i | ||||
\(241\) | 2.66808e34i | 0.770819i | 0.922746 | + | 0.385409i | \(0.125940\pi\) | ||||
−0.922746 | + | 0.385409i | \(0.874060\pi\) | |||||||
\(242\) | − | 4.89107e33i | − | 0.133070i | ||||||
\(243\) | −3.04634e34 | − | 2.43837e34i | −0.780706 | − | 0.624898i | ||||
\(244\) | 5.37426e34i | 1.29767i | ||||||||
\(245\) | −3.28475e34 | − | 2.57946e34i | −0.747471 | − | 0.586976i | ||||
\(246\) | −1.12890e33 | − | 2.09966e33i | −0.0242157 | − | 0.0450392i | ||||
\(247\) | −1.63218e33 | −0.0330113 | ||||||||
\(248\) | −2.80924e33 | −0.0535846 | ||||||||
\(249\) | 3.66260e33 | − | 1.96923e33i | 0.0659020 | − | 0.0354327i | ||||
\(250\) | 8.52555e33i | 0.144741i | ||||||||
\(251\) | −3.22018e34 | −0.515954 | −0.257977 | − | 0.966151i | \(-0.583056\pi\) | ||||
−0.257977 | + | 0.966151i | \(0.583056\pi\) | |||||||
\(252\) | −3.94362e34 | − | 5.14702e34i | −0.596468 | − | 0.778481i | ||||
\(253\) | 2.01144e33 | 0.0287249 | ||||||||
\(254\) | − | 9.82044e33i | − | 0.132447i | ||||||
\(255\) | 2.79545e34 | − | 1.50300e34i | 0.356139 | − | 0.191481i | ||||
\(256\) | 6.75167e34 | 0.812703 | ||||||||
\(257\) | −1.24082e34 | −0.141149 | −0.0705747 | − | 0.997506i | \(-0.522483\pi\) | ||||
−0.0705747 | + | 0.997506i | \(0.522483\pi\) | |||||||
\(258\) | 5.31535e33 | + | 9.88611e33i | 0.0571539 | + | 0.106302i | ||||
\(259\) | 1.58519e34 | − | 4.58528e34i | 0.161152 | − | 0.466143i | ||||
\(260\) | 1.54514e34i | 0.148544i | ||||||||
\(261\) | −7.55048e34 | − | 4.99185e34i | −0.686573 | − | 0.453914i | ||||
\(262\) | 2.01175e34i | 0.173064i | ||||||||
\(263\) | 1.47335e35i | 1.19935i | 0.800242 | + | 0.599677i | \(0.204704\pi\) | ||||
−0.800242 | + | 0.599677i | \(0.795296\pi\) | |||||||
\(264\) | 6.42108e33 | − | 3.45234e33i | 0.0494710 | − | 0.0265985i | ||||
\(265\) | 5.12936e34i | 0.374109i | ||||||||
\(266\) | 1.36089e33 | − | 3.93646e33i | 0.00939808 | − | 0.0271846i | ||||
\(267\) | −7.44226e34 | + | 4.00139e34i | −0.486734 | + | 0.261696i | ||||
\(268\) | −1.20557e35 | −0.746857 | ||||||||
\(269\) | 2.28593e35 | 1.34170 | 0.670849 | − | 0.741594i | \(-0.265930\pi\) | ||||
0.670849 | + | 0.741594i | \(0.265930\pi\) | |||||||
\(270\) | −2.36301e34 | − | 2.15252e33i | −0.131429 | − | 0.0119722i | ||||
\(271\) | 1.26940e34i | 0.0669180i | 0.999440 | + | 0.0334590i | \(0.0106523\pi\) | ||||
−0.999440 | + | 0.0334590i | \(0.989348\pi\) | |||||||
\(272\) | 8.02409e34 | 0.401002 | ||||||||
\(273\) | 3.32008e34 | − | 5.37384e33i | 0.157322 | − | 0.0254640i | ||||
\(274\) | −4.66783e34 | −0.209764 | ||||||||
\(275\) | − | 4.63498e33i | − | 0.0197571i | ||||||
\(276\) | −1.61534e34 | − | 3.00441e34i | −0.0653255 | − | 0.121500i | ||||
\(277\) | 2.72044e35 | 1.04396 | 0.521978 | − | 0.852959i | \(-0.325194\pi\) | ||||
0.521978 | + | 0.852959i | \(0.325194\pi\) | |||||||
\(278\) | −3.68342e34 | −0.134153 | ||||||||
\(279\) | −4.70062e34 | − | 3.10772e34i | −0.162515 | − | 0.107444i | ||||
\(280\) | −7.52635e34 | − | 2.60196e34i | −0.247055 | − | 0.0854102i | ||||
\(281\) | 1.17283e35i | 0.365589i | 0.983151 | + | 0.182794i | \(0.0585143\pi\) | ||||
−0.983151 | + | 0.182794i | \(0.941486\pi\) | |||||||
\(282\) | −3.25880e34 | − | 6.06110e34i | −0.0964819 | − | 0.179448i | ||||
\(283\) | 5.84019e34i | 0.164257i | 0.996622 | + | 0.0821284i | \(0.0261718\pi\) | ||||
−0.996622 | + | 0.0821284i | \(0.973828\pi\) | |||||||
\(284\) | 5.23344e35i | 1.39853i | ||||||||
\(285\) | 3.67095e34 | + | 6.82767e34i | 0.0932241 | + | 0.173389i | ||||
\(286\) | 1.87232e33i | 0.00451933i | ||||||||
\(287\) | 5.24370e34 | − | 1.51677e35i | 0.120323 | − | 0.348044i | ||||
\(288\) | −1.55201e35 | − | 1.02608e35i | −0.338613 | − | 0.223867i | ||||
\(289\) | −3.94726e35 | −0.818987 | ||||||||
\(290\) | −5.50410e34 | −0.108621 | ||||||||
\(291\) | 4.40207e35 | + | 8.18749e35i | 0.826434 | + | 1.53710i | ||||
\(292\) | − | 1.69976e35i | − | 0.303624i | ||||||
\(293\) | 3.25348e35 | 0.553054 | 0.276527 | − | 0.961006i | \(-0.410817\pi\) | ||||
0.276527 | + | 0.961006i | \(0.410817\pi\) | |||||||
\(294\) | −1.47218e34 | + | 8.45536e34i | −0.0238191 | + | 0.136803i | ||||
\(295\) | −5.56281e35 | −0.856792 | ||||||||
\(296\) | − | 9.25056e34i | − | 0.135656i | ||||||
\(297\) | 1.45633e35 | + | 1.32661e34i | 0.203373 | + | 0.0185257i | ||||
\(298\) | −2.96913e34 | −0.0394906 | ||||||||
\(299\) | 1.76934e34 | 0.0224170 | ||||||||
\(300\) | −6.92309e34 | + | 3.72225e34i | −0.0835683 | + | 0.0449312i | ||||
\(301\) | −2.46896e35 | + | 7.14162e35i | −0.283988 | + | 0.821453i | ||||
\(302\) | 8.72162e34i | 0.0956085i | ||||||||
\(303\) | −5.82709e35 | + | 3.13298e35i | −0.608883 | + | 0.327371i | ||||
\(304\) | 1.95982e35i | 0.195231i | ||||||||
\(305\) | 1.32396e36i | 1.25755i | ||||||||
\(306\) | −5.44069e34 | − | 3.59700e34i | −0.0492825 | − | 0.0325822i | ||||
\(307\) | − | 2.09803e35i | − | 0.181261i | −0.995885 | − | 0.0906307i | \(-0.971112\pi\) | ||
0.995885 | − | 0.0906307i | \(-0.0288883\pi\) | |||||||
\(308\) | 2.29668e35 | + | 7.93994e34i | 0.189285 | + | 0.0654383i | ||||
\(309\) | 7.16669e35 | + | 1.33295e36i | 0.563535 | + | 1.04813i | ||||
\(310\) | −3.42663e34 | −0.0257112 | ||||||||
\(311\) | −1.97774e36 | −1.41626 | −0.708130 | − | 0.706083i | \(-0.750461\pi\) | ||||
−0.708130 | + | 0.706083i | \(0.750461\pi\) | |||||||
\(312\) | 5.64822e34 | − | 3.03681e34i | 0.0386074 | − | 0.0207576i | ||||
\(313\) | 1.48050e36i | 0.966085i | 0.875597 | + | 0.483042i | \(0.160468\pi\) | ||||
−0.875597 | + | 0.483042i | \(0.839532\pi\) | |||||||
\(314\) | 8.75509e34 | 0.0545483 | ||||||||
\(315\) | −9.71518e35 | − | 1.26798e36i | −0.578027 | − | 0.754413i | ||||
\(316\) | 1.53292e36 | 0.871076 | ||||||||
\(317\) | − | 2.47386e36i | − | 1.34282i | −0.741088 | − | 0.671408i | \(-0.765690\pi\) | ||
0.741088 | − | 0.671408i | \(-0.234310\pi\) | |||||||
\(318\) | 9.28385e34 | − | 4.99154e34i | 0.0481432 | − | 0.0258846i | ||||
\(319\) | 3.39220e35 | 0.168080 | ||||||||
\(320\) | 1.77865e36 | 0.842201 | ||||||||
\(321\) | −1.10162e36 | − | 2.04892e36i | −0.498550 | − | 0.927263i | ||||
\(322\) | −1.47525e34 | + | 4.26725e34i | −0.00638197 | + | 0.0184603i | ||||
\(323\) | 2.13082e35i | 0.0881274i | ||||||||
\(324\) | −9.71401e35 | − | 2.28181e36i | −0.384145 | − | 0.902352i | ||||
\(325\) | − | 4.07710e34i | − | 0.0154185i | ||||||
\(326\) | − | 2.44903e35i | − | 0.0885805i | ||||||
\(327\) | 1.65977e36 | − | 8.92386e35i | 0.574254 | − | 0.308753i | ||||
\(328\) | − | 3.06001e35i | − | 0.101287i | ||||||
\(329\) | 1.51370e36 | − | 4.37847e36i | 0.479401 | − | 1.38670i | ||||
\(330\) | 7.83223e34 | − | 4.21106e34i | 0.0237374 | − | 0.0127626i | ||||
\(331\) | 2.11214e36 | 0.612655 | 0.306327 | − | 0.951926i | \(-0.400900\pi\) | ||||
0.306327 | + | 0.951926i | \(0.400900\pi\) | |||||||
\(332\) | 2.64292e35 | 0.0733807 | ||||||||
\(333\) | 1.02334e36 | − | 1.54787e36i | 0.272006 | − | 0.411426i | ||||
\(334\) | 3.58583e35i | 0.0912570i | ||||||||
\(335\) | −2.96994e36 | −0.723766 | ||||||||
\(336\) | −6.45257e35 | − | 3.98654e36i | −0.150596 | − | 0.930416i | ||||
\(337\) | 7.11308e36 | 1.59010 | 0.795050 | − | 0.606544i | \(-0.207445\pi\) | ||||
0.795050 | + | 0.606544i | \(0.207445\pi\) | |||||||
\(338\) | − | 6.31975e35i | − | 0.135334i | ||||||
\(339\) | −4.25223e36 | − | 7.90881e36i | −0.872412 | − | 1.62261i | ||||
\(340\) | 2.01719e36 | 0.396555 | ||||||||
\(341\) | 2.11184e35 | 0.0397853 | ||||||||
\(342\) | 8.78539e34 | − | 1.32884e35i | 0.0158629 | − | 0.0239936i | ||||
\(343\) | −4.85736e36 | + | 3.12880e36i | −0.840689 | + | 0.541519i | ||||
\(344\) | 1.44078e36i | 0.239057i | ||||||||
\(345\) | −3.97943e35 | − | 7.40141e35i | −0.0633058 | − | 0.117744i | ||||
\(346\) | 8.13378e35i | 0.124076i | ||||||||
\(347\) | 5.05695e36i | 0.739795i | 0.929073 | + | 0.369897i | \(0.120607\pi\) | ||||
−0.929073 | + | 0.369897i | \(0.879393\pi\) | |||||||
\(348\) | −2.72420e36 | − | 5.06679e36i | −0.382244 | − | 0.710942i | ||||
\(349\) | 1.34312e37i | 1.80778i | 0.427769 | + | 0.903888i | \(0.359300\pi\) | ||||
−0.427769 | + | 0.903888i | \(0.640700\pi\) | |||||||
\(350\) | 9.83307e34 | + | 3.39943e34i | 0.0126970 | + | 0.00438954i | ||||
\(351\) | 1.28105e36 | + | 1.16693e35i | 0.158713 | + | 0.0144575i | ||||
\(352\) | 6.97270e35 | 0.0828958 | ||||||||
\(353\) | −7.98024e36 | −0.910506 | −0.455253 | − | 0.890362i | \(-0.650451\pi\) | ||||
−0.455253 | + | 0.890362i | \(0.650451\pi\) | |||||||
\(354\) | 5.41335e35 | + | 1.00684e36i | 0.0592814 | + | 0.110259i | ||||
\(355\) | 1.28927e37i | 1.35529i | ||||||||
\(356\) | −5.37032e36 | −0.541970 | ||||||||
\(357\) | −7.01558e35 | − | 4.33439e36i | −0.0679790 | − | 0.419990i | ||||
\(358\) | 8.29907e35 | 0.0772193 | ||||||||
\(359\) | − | 1.28647e37i | − | 1.14956i | −0.818309 | − | 0.574778i | \(-0.805088\pi\) | ||
0.818309 | − | 0.574778i | \(-0.194912\pi\) | |||||||
\(360\) | −2.54069e36 | − | 1.67973e36i | −0.218055 | − | 0.144163i | ||||
\(361\) | 1.16094e37 | 0.957094 | ||||||||
\(362\) | 2.62350e36 | 0.207781 | ||||||||
\(363\) | 1.10919e37 | − | 5.96366e36i | 0.844035 | − | 0.453802i | ||||
\(364\) | 2.02025e36 | + | 6.98427e35i | 0.147718 | + | 0.0510683i | ||||
\(365\) | − | 4.18739e36i | − | 0.294237i | ||||||
\(366\) | 2.39629e36 | − | 1.28838e36i | 0.161832 | − | 0.0870101i | ||||
\(367\) | − | 7.74016e36i | − | 0.502449i | −0.967929 | − | 0.251225i | \(-0.919167\pi\) | ||
0.967929 | − | 0.251225i | \(-0.0808333\pi\) | |||||||
\(368\) | − | 2.12451e36i | − | 0.132576i | ||||||
\(369\) | 3.38513e36 | − | 5.12022e36i | 0.203092 | − | 0.307190i | ||||
\(370\) | − | 1.12835e36i | − | 0.0650909i | ||||||
\(371\) | 6.70655e36 | + | 2.31855e36i | 0.372030 | + | 0.128616i | ||||
\(372\) | −1.69598e36 | − | 3.15438e36i | −0.0904789 | − | 0.168283i | ||||
\(373\) | −1.54845e37 | −0.794548 | −0.397274 | − | 0.917700i | \(-0.630044\pi\) | ||||
−0.397274 | + | 0.917700i | \(0.630044\pi\) | |||||||
\(374\) | 2.44433e35 | 0.0120649 | ||||||||
\(375\) | −1.93342e37 | + | 1.03952e37i | −0.918062 | + | 0.493603i | ||||
\(376\) | − | 8.83335e36i | − | 0.403554i | ||||||
\(377\) | 2.98390e36 | 0.131170 | ||||||||
\(378\) | −1.34956e36 | + | 2.99230e36i | −0.0570900 | + | 0.126583i | ||||
\(379\) | −1.12893e37 | −0.459621 | −0.229811 | − | 0.973235i | \(-0.573811\pi\) | ||||
−0.229811 | + | 0.973235i | \(0.573811\pi\) | |||||||
\(380\) | 4.92683e36i | 0.193066i | ||||||||
\(381\) | 2.22707e37 | − | 1.19740e37i | 0.840082 | − | 0.451677i | ||||
\(382\) | 4.27319e36 | 0.155179 | ||||||||
\(383\) | 9.37924e36 | 0.327933 | 0.163967 | − | 0.986466i | \(-0.447571\pi\) | ||||
0.163967 | + | 0.986466i | \(0.447571\pi\) | |||||||
\(384\) | −7.44059e36 | − | 1.38389e37i | −0.250498 | − | 0.465906i | ||||
\(385\) | 5.65792e36 | + | 1.95602e36i | 0.183432 | + | 0.0634151i | ||||
\(386\) | 7.04581e36i | 0.219996i | ||||||||
\(387\) | −1.59387e37 | + | 2.41082e37i | −0.479339 | + | 0.725030i | ||||
\(388\) | 5.90807e37i | 1.71153i | ||||||||
\(389\) | 3.17539e37i | 0.886192i | 0.896474 | + | 0.443096i | \(0.146120\pi\) | ||||
−0.896474 | + | 0.443096i | \(0.853880\pi\) | |||||||
\(390\) | 6.88953e35 | − | 3.70421e35i | 0.0185248 | − | 0.00995998i | ||||
\(391\) | − | 2.30988e36i | − | 0.0598448i | ||||||
\(392\) | −6.80405e36 | + | 8.66445e36i | −0.169871 | + | 0.216318i | ||||
\(393\) | −4.56223e37 | + | 2.45292e37i | −1.09770 | + | 0.590189i | ||||
\(394\) | 1.14258e37 | 0.264967 | ||||||||
\(395\) | 3.77637e37 | 0.844145 | ||||||||
\(396\) | 7.75298e36 | + | 5.12573e36i | 0.167066 | + | 0.110452i | ||||
\(397\) | 5.96515e37i | 1.23925i | 0.784898 | + | 0.619625i | \(0.212715\pi\) | ||||
−0.784898 | + | 0.619625i | \(0.787285\pi\) | |||||||
\(398\) | 2.50953e36 | 0.0502676 | ||||||||
\(399\) | 1.05864e37 | − | 1.71350e36i | 0.204475 | − | 0.0330961i | ||||
\(400\) | −4.89553e36 | −0.0911863 | ||||||||
\(401\) | 6.33950e37i | 1.13884i | 0.822048 | + | 0.569418i | \(0.192832\pi\) | ||||
−0.822048 | + | 0.569418i | \(0.807168\pi\) | |||||||
\(402\) | 2.89014e36 | + | 5.37543e36i | 0.0500773 | + | 0.0931398i | ||||
\(403\) | 1.85766e36 | 0.0310486 | ||||||||
\(404\) | −4.20481e37 | −0.677980 | ||||||||
\(405\) | −2.39306e37 | − | 5.62127e37i | −0.372269 | − | 0.874454i | ||||
\(406\) | −2.48794e36 | + | 7.19652e36i | −0.0373432 | + | 0.108018i | ||||
\(407\) | 6.95409e36i | 0.100721i | ||||||||
\(408\) | −3.96458e36 | − | 7.37379e36i | −0.0554147 | − | 0.103067i | ||||
\(409\) | 6.96108e37i | 0.939050i | 0.882919 | + | 0.469525i | \(0.155575\pi\) | ||||
−0.882919 | + | 0.469525i | \(0.844425\pi\) | |||||||
\(410\) | − | 3.73251e36i | − | 0.0485998i | ||||||
\(411\) | −5.69146e37 | − | 1.05857e38i | −0.715348 | − | 1.33049i | ||||
\(412\) | 9.61850e37i | 1.16707i | ||||||||
\(413\) | −2.51448e37 | + | 7.27329e37i | −0.294559 | + | 0.852030i | ||||
\(414\) | −9.52363e35 | + | 1.44051e36i | −0.0107720 | + | 0.0162934i | ||||
\(415\) | 6.51089e36 | 0.0711120 | ||||||||
\(416\) | 6.13345e36 | 0.0646922 | ||||||||
\(417\) | −4.49118e37 | − | 8.35322e37i | −0.457496 | − | 0.850905i | ||||
\(418\) | 5.97009e35i | 0.00587387i | ||||||||
\(419\) | 8.00971e37 | 0.761226 | 0.380613 | − | 0.924734i | \(-0.375713\pi\) | ||||
0.380613 | + | 0.924734i | \(0.375713\pi\) | |||||||
\(420\) | −1.62212e37 | − | 1.00218e38i | −0.148925 | − | 0.920096i | ||||
\(421\) | −1.28915e37 | −0.114344 | −0.0571718 | − | 0.998364i | \(-0.518208\pi\) | ||||
−0.0571718 | + | 0.998364i | \(0.518208\pi\) | |||||||
\(422\) | − | 1.48965e37i | − | 0.127659i | ||||||
\(423\) | 9.77187e37 | − | 1.47806e38i | 0.809175 | − | 1.22393i | ||||
\(424\) | 1.35301e37 | 0.108267 | ||||||||
\(425\) | −5.32268e36 | −0.0411615 | ||||||||
\(426\) | 2.33350e37 | − | 1.25463e37i | 0.174409 | − | 0.0937724i | ||||
\(427\) | 1.73105e38 | + | 5.98449e37i | 1.25057 | + | 0.432338i | ||||
\(428\) | − | 1.47850e38i | − | 1.03249i | ||||||
\(429\) | −4.24604e36 | + | 2.28292e36i | −0.0286651 | + | 0.0154120i | ||||
\(430\) | 1.75742e37i | 0.114705i | ||||||||
\(431\) | − | 1.28079e38i | − | 0.808270i | −0.914699 | − | 0.404135i | \(-0.867573\pi\) | ||
0.914699 | − | 0.404135i | \(-0.132427\pi\) | |||||||
\(432\) | 1.40118e37 | − | 1.53820e38i | 0.0855026 | − | 0.938638i | ||||
\(433\) | 2.45977e38i | 1.45151i | 0.687954 | + | 0.725754i | \(0.258509\pi\) | ||||
−0.687954 | + | 0.725754i | \(0.741491\pi\) | |||||||
\(434\) | −1.54889e36 | + | 4.48026e36i | −0.00883932 | + | 0.0255683i | ||||
\(435\) | −6.71112e37 | − | 1.24821e38i | −0.370426 | − | 0.688961i | ||||
\(436\) | 1.19768e38 | 0.639422 | ||||||||
\(437\) | 5.64170e36 | 0.0291359 | ||||||||
\(438\) | −7.57894e36 | + | 4.07488e36i | −0.0378647 | + | 0.0203582i | ||||
\(439\) | 1.65194e38i | 0.798471i | 0.916848 | + | 0.399236i | \(0.130724\pi\) | ||||
−0.916848 | + | 0.399236i | \(0.869276\pi\) | |||||||
\(440\) | 1.14146e37 | 0.0533820 | ||||||||
\(441\) | −2.09700e38 | + | 6.97099e37i | −0.948941 | + | 0.315453i | ||||
\(442\) | 2.15013e36 | 0.00941546 | ||||||||
\(443\) | 1.08261e38i | 0.458794i | 0.973333 | + | 0.229397i | \(0.0736753\pi\) | ||||
−0.973333 | + | 0.229397i | \(0.926325\pi\) | |||||||
\(444\) | 1.03871e38 | − | 5.58468e37i | 0.426029 | − | 0.229058i | ||||
\(445\) | −1.32299e38 | −0.525213 | ||||||||
\(446\) | −4.22849e37 | −0.162491 | ||||||||
\(447\) | −3.62025e37 | − | 6.73337e37i | −0.134673 | − | 0.250480i | ||||
\(448\) | 8.03976e37 | − | 2.32555e38i | 0.289542 | − | 0.837520i | ||||
\(449\) | − | 6.91070e37i | − | 0.240963i | −0.992716 | − | 0.120481i | \(-0.961556\pi\) | ||
0.992716 | − | 0.120481i | \(-0.0384438\pi\) | |||||||
\(450\) | 3.31938e36 | + | 2.19454e36i | 0.0112066 | + | 0.00740905i | ||||
\(451\) | 2.30036e37i | 0.0752031i | ||||||||
\(452\) | − | 5.70697e38i | − | 1.80675i | ||||||
\(453\) | −1.97788e38 | + | 1.06342e38i | −0.606424 | + | 0.326049i | ||||
\(454\) | − | 7.43441e37i | − | 0.220768i | ||||||
\(455\) | 4.97692e37 | + | 1.72059e37i | 0.143151 | + | 0.0494894i | ||||
\(456\) | 1.80099e37 | − | 9.68317e36i | 0.0501789 | − | 0.0269791i | ||||
\(457\) | 4.86788e38 | 1.31388 | 0.656939 | − | 0.753944i | \(-0.271851\pi\) | ||||
0.656939 | + | 0.753944i | \(0.271851\pi\) | |||||||
\(458\) | −6.40077e37 | −0.167372 | ||||||||
\(459\) | 1.52344e37 | − | 1.67241e38i | 0.0385959 | − | 0.423701i | ||||
\(460\) | − | 5.34084e37i | − | 0.131105i | ||||||
\(461\) | −6.17936e38 | −1.46987 | −0.734937 | − | 0.678135i | \(-0.762788\pi\) | ||||
−0.734937 | + | 0.678135i | \(0.762788\pi\) | |||||||
\(462\) | −1.96561e36 | − | 1.21440e37i | −0.00453094 | − | 0.0279932i | ||||
\(463\) | 2.51806e38 | 0.562524 | 0.281262 | − | 0.959631i | \(-0.409247\pi\) | ||||
0.281262 | + | 0.959631i | \(0.409247\pi\) | |||||||
\(464\) | − | 3.58288e38i | − | 0.775750i | ||||||
\(465\) | −4.17807e37 | − | 7.77087e37i | −0.0876815 | − | 0.163080i | ||||
\(466\) | −1.07000e38 | −0.217664 | ||||||||
\(467\) | 2.04785e38 | 0.403833 | 0.201917 | − | 0.979403i | \(-0.435283\pi\) | ||||
0.201917 | + | 0.979403i | \(0.435283\pi\) | |||||||
\(468\) | 6.81981e37 | + | 4.50878e37i | 0.130379 | + | 0.0861974i | ||||
\(469\) | −1.34246e38 | + | 3.88315e38i | −0.248825 | + | 0.719744i | ||||
\(470\) | − | 1.07746e38i | − | 0.193635i | ||||||
\(471\) | 1.06750e38 | + | 1.98547e38i | 0.186023 | + | 0.345988i | ||||
\(472\) | 1.46735e38i | 0.247956i | ||||||||
\(473\) | − | 1.08311e38i | − | 0.177494i | ||||||
\(474\) | −3.67490e37 | − | 6.83502e37i | −0.0584064 | − | 0.108631i | ||||
\(475\) | − | 1.30002e37i | − | 0.0200398i | ||||||
\(476\) | 9.11801e37 | − | 2.63745e38i | 0.136333 | − | 0.394351i | ||||
\(477\) | 2.26395e38 | + | 1.49677e38i | 0.328360 | + | 0.217089i | ||||
\(478\) | −1.40503e38 | −0.197688 | ||||||||
\(479\) | −2.36182e38 | −0.322390 | −0.161195 | − | 0.986923i | \(-0.551535\pi\) | ||||
−0.161195 | + | 0.986923i | \(0.551535\pi\) | |||||||
\(480\) | −1.37948e38 | − | 2.56572e38i | −0.182691 | − | 0.339791i | ||||
\(481\) | 6.11708e37i | 0.0786032i | ||||||||
\(482\) | 8.58451e37 | 0.107037 | ||||||||
\(483\) | −1.14760e38 | + | 1.85749e37i | −0.138853 | + | 0.0224746i | ||||
\(484\) | 8.00390e38 | 0.939818 | ||||||||
\(485\) | 1.45546e39i | 1.65862i | ||||||||
\(486\) | −7.84542e37 | + | 9.80155e37i | −0.0867742 | + | 0.108410i | ||||
\(487\) | −1.51291e39 | −1.62422 | −0.812109 | − | 0.583505i | \(-0.801681\pi\) | ||||
−0.812109 | + | 0.583505i | \(0.801681\pi\) | |||||||
\(488\) | 3.49231e38 | 0.363936 | ||||||||
\(489\) | 5.55388e38 | − | 2.98609e38i | 0.561847 | − | 0.302081i | ||||
\(490\) | −8.29936e37 | + | 1.05686e38i | −0.0815082 | + | 0.103795i | ||||
\(491\) | 1.85806e39i | 1.77166i | 0.464014 | + | 0.885828i | \(0.346409\pi\) | ||||
−0.464014 | + | 0.885828i | \(0.653591\pi\) | |||||||
\(492\) | 3.43596e38 | − | 1.84737e38i | 0.318093 | − | 0.171025i | ||||
\(493\) | − | 3.89551e38i | − | 0.350174i | ||||||
\(494\) | 5.25151e36i | 0.00458399i | ||||||||
\(495\) | 1.90996e38 | + | 1.26273e38i | 0.161901 | + | 0.107037i | ||||
\(496\) | − | 2.23056e38i | − | 0.183624i | ||||||
\(497\) | 1.68570e39 | + | 5.82769e38i | 1.34776 | + | 0.465938i | ||||
\(498\) | −6.33595e36 | − | 1.17843e37i | −0.00492024 | − | 0.00915124i | ||||
\(499\) | −1.21670e39 | −0.917750 | −0.458875 | − | 0.888501i | \(-0.651747\pi\) | ||||
−0.458875 | + | 0.888501i | \(0.651747\pi\) | |||||||
\(500\) | −1.39515e39 | −1.02225 | ||||||||
\(501\) | −8.13192e38 | + | 4.37219e38i | −0.578823 | + | 0.311209i | ||||
\(502\) | 1.03609e38i | 0.0716460i | ||||||||
\(503\) | 6.50422e38 | 0.436978 | 0.218489 | − | 0.975839i | \(-0.429887\pi\) | ||||
0.218489 | + | 0.975839i | \(0.429887\pi\) | |||||||
\(504\) | −3.34465e38 | + | 2.56265e38i | −0.218327 | + | 0.167281i | ||||
\(505\) | −1.03586e39 | −0.657018 | ||||||||
\(506\) | − | 6.47176e36i | − | 0.00398878i | ||||||
\(507\) | 1.43319e39 | − | 7.70565e38i | 0.858396 | − | 0.461524i | ||||
\(508\) | 1.60705e39 | 0.935416 | ||||||||
\(509\) | 2.73105e39 | 1.54498 | 0.772488 | − | 0.635029i | \(-0.219012\pi\) | ||||
0.772488 | + | 0.635029i | \(0.219012\pi\) | |||||||
\(510\) | −4.83587e37 | − | 8.99432e37i | −0.0265893 | − | 0.0494539i | ||||
\(511\) | −5.47495e38 | − | 1.89276e38i | −0.292602 | − | 0.101156i | ||||
\(512\) | − | 1.23548e39i | − | 0.641831i | ||||||
\(513\) | 4.08474e38 | + | 3.72088e37i | 0.206282 | + | 0.0187907i | ||||
\(514\) | 3.99232e37i | 0.0196002i | ||||||||
\(515\) | 2.36954e39i | 1.13099i | ||||||||
\(516\) | −1.61779e39 | + | 8.69820e38i | −0.750763 | + | 0.403654i | ||||
\(517\) | 6.64045e38i | 0.299629i | ||||||||
\(518\) | −1.47530e38 | − | 5.10033e37i | −0.0647292 | − | 0.0223778i | ||||
\(519\) | −1.84457e39 | + | 9.91748e38i | −0.786989 | + | 0.423131i | ||||
\(520\) | 1.00407e38 | 0.0416595 | ||||||||
\(521\) | −3.15327e39 | −1.27237 | −0.636185 | − | 0.771536i | \(-0.719489\pi\) | ||||
−0.636185 | + | 0.771536i | \(0.719489\pi\) | |||||||
\(522\) | −1.60612e38 | + | 2.42935e38i | −0.0630311 | + | 0.0953384i | ||||
\(523\) | 1.46480e39i | 0.559118i | 0.960128 | + | 0.279559i | \(0.0901883\pi\) | ||||
−0.960128 | + | 0.279559i | \(0.909812\pi\) | |||||||
\(524\) | −3.29209e39 | −1.22227 | ||||||||
\(525\) | 4.28023e37 | + | 2.64442e38i | 0.0154581 | + | 0.0955039i | ||||
\(526\) | 4.74047e38 | 0.166544 | ||||||||
\(527\) | − | 2.42518e38i | − | 0.0828878i | ||||||
\(528\) | 2.74118e38 | + | 5.09838e38i | 0.0911478 | + | 0.169527i | ||||
\(529\) | 3.02990e39 | 0.980215 | ||||||||
\(530\) | 1.65036e38 | 0.0519492 | ||||||||
\(531\) | −1.62325e39 | + | 2.45527e39i | −0.497182 | + | 0.752018i | ||||
\(532\) | 6.44175e38 | + | 2.22700e38i | 0.191993 | + | 0.0663746i | ||||
\(533\) | 2.02348e38i | 0.0586888i | ||||||||
\(534\) | 1.28744e38 | + | 2.39453e38i | 0.0363395 | + | 0.0675885i | ||||
\(535\) | − | 3.64231e39i | − | 1.00057i | ||||||
\(536\) | 7.83405e38i | 0.209458i | ||||||||
\(537\) | 1.01190e39 | + | 1.88206e39i | 0.263337 | + | 0.489785i | ||||
\(538\) | − | 7.35493e38i | − | 0.186310i | ||||||
\(539\) | 5.11493e38 | − | 6.51348e38i | 0.126125 | − | 0.160611i | ||||
\(540\) | 3.52245e38 | − | 3.86691e39i | 0.0845543 | − | 0.928227i | ||||
\(541\) | −7.22197e39 | −1.68770 | −0.843851 | − | 0.536578i | \(-0.819717\pi\) | ||||
−0.843851 | + | 0.536578i | \(0.819717\pi\) | |||||||
\(542\) | 4.08426e37 | 0.00929231 | ||||||||
\(543\) | 3.19882e39 | + | 5.94954e39i | 0.708585 | + | 1.31791i | ||||
\(544\) | − | 8.00727e38i | − | 0.172703i | ||||||
\(545\) | 2.95051e39 | 0.619653 | ||||||||
\(546\) | −1.72902e37 | − | 1.06823e38i | −0.00353596 | − | 0.0218460i | ||||
\(547\) | −2.19338e39 | −0.436815 | −0.218407 | − | 0.975858i | \(-0.570086\pi\) | ||||
−0.218407 | + | 0.975858i | \(0.570086\pi\) | |||||||
\(548\) | − | 7.63858e39i | − | 1.48148i | ||||||
\(549\) | 5.84357e39 | + | 3.86336e39i | 1.10377 | + | 0.729737i | ||||
\(550\) | −1.49130e37 | −0.00274350 | ||||||||
\(551\) | 9.51446e38 | 0.170485 | ||||||||
\(552\) | −1.95233e38 | + | 1.04969e38i | −0.0340751 | + | 0.0183207i | ||||
\(553\) | 1.70698e39 | − | 4.93754e39i | 0.290211 | − | 0.839453i | ||||
\(554\) | − | 8.75296e38i | − | 0.144965i | ||||||
\(555\) | 2.55887e39 | − | 1.37580e39i | 0.412857 | − | 0.221976i | ||||
\(556\) | − | 6.02766e39i | − | 0.947468i | ||||||
\(557\) | − | 1.22987e37i | − | 0.00188347i | −1.00000 | 0.000941736i | \(-0.999700\pi\) | |||
1.00000 | 0.000941736i | \(-0.000299764\pi\) | ||||||||
\(558\) | −9.99903e37 | + | 1.51242e38i | −0.0149198 | + | 0.0225671i | ||||
\(559\) | − | 9.52742e38i | − | 0.138517i | ||||||
\(560\) | 2.06597e39 | − | 5.97597e39i | 0.292684 | − | 0.846607i | ||||
\(561\) | 2.98036e38 | + | 5.54323e38i | 0.0411441 | + | 0.0765247i | ||||
\(562\) | 3.77355e38 | 0.0507661 | ||||||||
\(563\) | −5.88591e39 | −0.771689 | −0.385844 | − | 0.922564i | \(-0.626090\pi\) | ||||
−0.385844 | + | 0.922564i | \(0.626090\pi\) | |||||||
\(564\) | 9.91858e39 | − | 5.33280e39i | 1.26737 | − | 0.681410i | ||||
\(565\) | − | 1.40592e40i | − | 1.75089i | ||||||
\(566\) | 1.87907e38 | 0.0228089 | ||||||||
\(567\) | −8.43142e39 | + | 5.87992e38i | −0.997577 | + | 0.0695692i | ||||
\(568\) | 3.40081e39 | 0.392221 | ||||||||
\(569\) | − | 4.90530e39i | − | 0.551490i | −0.961231 | − | 0.275745i | \(-0.911076\pi\) | ||
0.961231 | − | 0.275745i | \(-0.0889245\pi\) | |||||||
\(570\) | 2.19679e38 | − | 1.18112e38i | 0.0240771 | − | 0.0129452i | ||||
\(571\) | −6.72248e38 | −0.0718300 | −0.0359150 | − | 0.999355i | \(-0.511435\pi\) | ||||
−0.0359150 | + | 0.999355i | \(0.511435\pi\) | |||||||
\(572\) | −3.06393e38 | −0.0319181 | ||||||||
\(573\) | 5.21028e39 | + | 9.69070e39i | 0.529199 | + | 0.984267i | ||||
\(574\) | −4.88019e38 | − | 1.68715e38i | −0.0483298 | − | 0.0167083i | ||||
\(575\) | 1.40927e38i | 0.0136085i | ||||||||
\(576\) | 5.19017e39 | − | 7.85045e39i | 0.488715 | − | 0.739211i | ||||
\(577\) | 3.64717e39i | 0.334894i | 0.985881 | + | 0.167447i | \(0.0535523\pi\) | ||||
−0.985881 | + | 0.167447i | \(0.946448\pi\) | |||||||
\(578\) | 1.27002e39i | 0.113726i | ||||||||
\(579\) | −1.59784e40 | + | 8.59093e39i | −1.39539 | + | 0.750241i | ||||
\(580\) | − | 9.00708e39i | − | 0.767146i | ||||||
\(581\) | 2.94302e38 | − | 8.51288e38i | 0.0244478 | − | 0.0707168i | ||||
\(582\) | 2.63431e39 | − | 1.41636e39i | 0.213444 | − | 0.114760i | ||||
\(583\) | −1.01712e39 | −0.0803859 | ||||||||
\(584\) | −1.10454e39 | −0.0851522 | ||||||||
\(585\) | 1.68007e39 | + | 1.11075e39i | 0.126348 | + | 0.0835324i | ||||
\(586\) | − | 1.04680e39i | − | 0.0767977i | ||||||
\(587\) | −1.29836e40 | −0.929269 | −0.464634 | − | 0.885503i | \(-0.653814\pi\) | ||||
−0.464634 | + | 0.885503i | \(0.653814\pi\) | |||||||
\(588\) | −1.38366e40 | − | 2.40913e39i | −0.966182 | − | 0.168224i | ||||
\(589\) | 5.92332e38 | 0.0403546 | ||||||||
\(590\) | 1.78982e39i | 0.118975i | ||||||||
\(591\) | 1.39315e40 | + | 2.59114e40i | 0.903604 | + | 1.68063i | ||||
\(592\) | 7.34500e39 | 0.464865 | ||||||||
\(593\) | 6.27708e39 | 0.387672 | 0.193836 | − | 0.981034i | \(-0.437907\pi\) | ||||
0.193836 | + | 0.981034i | \(0.437907\pi\) | |||||||
\(594\) | 4.26833e37 | − | 4.68573e38i | 0.00257250 | − | 0.0282406i | ||||
\(595\) | 2.24624e39 | − | 6.49740e39i | 0.132117 | − | 0.382158i | ||||
\(596\) | − | 4.85879e39i | − | 0.278905i | ||||||
\(597\) | 3.05986e39 | + | 5.69109e39i | 0.171425 | + | 0.318836i | ||||
\(598\) | − | 5.69281e37i | − | 0.00311286i | ||||||
\(599\) | 2.19238e40i | 1.17011i | 0.810993 | + | 0.585056i | \(0.198927\pi\) | ||||
−0.810993 | + | 0.585056i | \(0.801073\pi\) | |||||||
\(600\) | 2.41880e38 | + | 4.49878e38i | 0.0126011 | + | 0.0234370i | ||||
\(601\) | − | 2.47937e40i | − | 1.26084i | −0.776253 | − | 0.630421i | \(-0.782882\pi\) | ||
0.776253 | − | 0.630421i | \(-0.217118\pi\) | |||||||
\(602\) | 2.29780e39 | + | 7.94382e38i | 0.114068 | + | 0.0394349i | ||||
\(603\) | −8.66640e39 | + | 1.31085e40i | −0.419989 | + | 0.635259i | ||||
\(604\) | −1.42723e40 | −0.675242 | ||||||||
\(605\) | 1.97178e40 | 0.910761 | ||||||||
\(606\) | 1.00803e39 | + | 1.87485e39i | 0.0454591 | + | 0.0845502i | ||||
\(607\) | 1.61926e39i | 0.0712984i | 0.999364 | + | 0.0356492i | \(0.0113499\pi\) | ||||
−0.999364 | + | 0.0356492i | \(0.988650\pi\) | |||||||
\(608\) | 1.95571e39 | 0.0840819 | ||||||||
\(609\) | −1.93537e40 | + | 3.13257e39i | −0.812482 | + | 0.131507i | ||||
\(610\) | 4.25981e39 | 0.174626 | ||||||||
\(611\) | 5.84119e39i | 0.233832i | ||||||||
\(612\) | 5.88625e39 | − | 8.90331e39i | 0.230114 | − | 0.348061i | ||||
\(613\) | −3.40740e40 | −1.30091 | −0.650454 | − | 0.759546i | \(-0.725421\pi\) | ||||
−0.650454 | + | 0.759546i | \(0.725421\pi\) | |||||||
\(614\) | −6.75037e38 | −0.0251702 | ||||||||
\(615\) | 8.46455e39 | − | 4.55103e39i | 0.308258 | − | 0.165737i | ||||
\(616\) | 5.15955e38 | − | 1.49243e39i | 0.0183523 | − | 0.0530854i | ||||
\(617\) | 1.61001e40i | 0.559363i | 0.960093 | + | 0.279681i | \(0.0902288\pi\) | ||||
−0.960093 | + | 0.279681i | \(0.909771\pi\) | |||||||
\(618\) | 4.28873e39 | − | 2.30587e39i | 0.145544 | − | 0.0782531i | ||||
\(619\) | 2.35307e40i | 0.780045i | 0.920805 | + | 0.390023i | \(0.127533\pi\) | ||||
−0.920805 | + | 0.390023i | \(0.872467\pi\) | |||||||
\(620\) | − | 5.60744e39i | − | 0.181587i | ||||||
\(621\) | −4.42798e39 | − | 4.03355e38i | −0.140081 | − | 0.0127602i | ||||
\(622\) | 6.36333e39i | 0.196664i | ||||||||
\(623\) | −5.98010e39 | + | 1.72978e40i | −0.180564 | + | 0.522294i | ||||
\(624\) | 2.41125e39 | + | 4.48473e39i | 0.0711321 | + | 0.132300i | ||||
\(625\) | −3.10132e40 | −0.893893 | ||||||||
\(626\) | 4.76348e39 | 0.134152 | ||||||||
\(627\) | −1.35389e39 | + | 7.27930e38i | −0.0372567 | + | 0.0200314i | ||||
\(628\) | 1.43271e40i | 0.385251i | ||||||||
\(629\) | 7.98589e39 | 0.209840 | ||||||||
\(630\) | −4.07970e39 | + | 3.12584e39i | −0.104759 | + | 0.0802655i | ||||
\(631\) | 2.90046e40 | 0.727848 | 0.363924 | − | 0.931429i | \(-0.381437\pi\) | ||||
0.363924 | + | 0.931429i | \(0.381437\pi\) | |||||||
\(632\) | − | 9.96124e39i | − | 0.244296i | ||||||
\(633\) | 3.37821e40 | − | 1.81632e40i | 0.809716 | − | 0.435350i | ||||
\(634\) | −7.95961e39 | −0.186465 | ||||||||
\(635\) | 3.95899e40 | 0.906495 | ||||||||
\(636\) | 8.16831e39 | + | 1.51924e40i | 0.182812 | + | 0.340015i | ||||
\(637\) | 4.49928e39 | − | 5.72951e39i | 0.0984287 | − | 0.125342i | ||||
\(638\) | − | 1.09143e39i | − | 0.0233398i | ||||||
\(639\) | 5.69046e40 | + | 3.76213e40i | 1.18956 | + | 0.786451i | ||||
\(640\) | − | 2.46010e40i | − | 0.502739i | ||||||
\(641\) | − | 4.21824e40i | − | 0.842733i | −0.906890 | − | 0.421367i | \(-0.861551\pi\) | ||
0.906890 | − | 0.421367i | \(-0.138449\pi\) | |||||||
\(642\) | −6.59237e39 | + | 3.54444e39i | −0.128761 | + | 0.0692293i | ||||
\(643\) | 4.98422e40i | 0.951783i | 0.879504 | + | 0.475891i | \(0.157874\pi\) | ||||
−0.879504 | + | 0.475891i | \(0.842126\pi\) | |||||||
\(644\) | −6.98306e39 | − | 2.41414e39i | −0.130377 | − | 0.0450731i | ||||
\(645\) | −3.98547e40 | + | 2.14282e40i | −0.727551 | + | 0.391174i | ||||
\(646\) | 6.85589e38 | 0.0122375 | ||||||||
\(647\) | −8.00928e40 | −1.39792 | −0.698959 | − | 0.715162i | \(-0.746353\pi\) | ||||
−0.698959 | + | 0.715162i | \(0.746353\pi\) | |||||||
\(648\) | −1.48277e40 | + | 6.31238e39i | −0.253067 | + | 0.107735i | ||||
\(649\) | − | 1.10308e40i | − | 0.184101i | ||||||
\(650\) | −1.31180e38 | −0.00214104 | ||||||||
\(651\) | −1.20488e40 | + | 1.95021e39i | −0.192318 | + | 0.0311284i | ||||
\(652\) | 4.00766e40 | 0.625606 | ||||||||
\(653\) | 1.21175e41i | 1.85000i | 0.379968 | + | 0.925000i | \(0.375935\pi\) | ||||
−0.379968 | + | 0.925000i | \(0.624065\pi\) | |||||||
\(654\) | −2.87124e39 | − | 5.34027e39i | −0.0428738 | − | 0.0797417i | ||||
\(655\) | −8.11014e40 | −1.18448 | ||||||||
\(656\) | 2.42967e40 | 0.347090 | ||||||||
\(657\) | −1.84819e40 | − | 1.22190e40i | −0.258256 | − | 0.170741i | ||||
\(658\) | −1.40877e40 | − | 4.87030e39i | −0.192559 | − | 0.0665702i | ||||
\(659\) | 1.29051e40i | 0.172553i | 0.996271 | + | 0.0862766i | \(0.0274969\pi\) | ||||
−0.996271 | + | 0.0862766i | \(0.972503\pi\) | |||||||
\(660\) | 6.89111e39 | + | 1.28169e40i | 0.0901368 | + | 0.167647i | ||||
\(661\) | − | 1.74223e39i | − | 0.0222938i | −0.999938 | − | 0.0111469i | \(-0.996452\pi\) | ||
0.999938 | − | 0.0111469i | \(-0.00354824\pi\) | |||||||
\(662\) | − | 6.79576e39i | − | 0.0850740i | ||||||
\(663\) | 2.62164e39 | + | 4.87604e39i | 0.0321090 | + | 0.0597202i | ||||
\(664\) | − | 1.71743e39i | − | 0.0205798i | ||||||
\(665\) | 1.58694e40 | + | 5.48626e39i | 0.186057 | + | 0.0643225i | ||||
\(666\) | −4.98023e39 | − | 3.29258e39i | −0.0571312 | − | 0.0377711i | ||||
\(667\) | −1.03140e40 | −0.115771 | ||||||||
\(668\) | −5.86797e40 | −0.644509 | ||||||||
\(669\) | −5.15579e40 | − | 9.58934e40i | −0.554136 | − | 1.03065i | ||||
\(670\) | 9.55573e39i | 0.100503i | ||||||||
\(671\) | −2.62534e40 | −0.270214 | ||||||||
\(672\) | −3.97818e40 | + | 6.43903e39i | −0.400710 | + | 0.0648584i | ||||
\(673\) | 3.44565e40 | 0.339667 | 0.169833 | − | 0.985473i | \(-0.445677\pi\) | ||||
0.169833 | + | 0.985473i | \(0.445677\pi\) | |||||||
\(674\) | − | 2.28862e40i | − | 0.220803i | ||||||
\(675\) | −9.29455e38 | + | 1.02035e40i | −0.00877655 | + | 0.0963479i | ||||
\(676\) | 1.03418e41 | 0.955809 | ||||||||
\(677\) | 1.05965e41 | 0.958575 | 0.479287 | − | 0.877658i | \(-0.340895\pi\) | ||||
0.479287 | + | 0.877658i | \(0.340895\pi\) | |||||||
\(678\) | −2.54464e40 | + | 1.36815e40i | −0.225318 | + | 0.121144i | ||||
\(679\) | 1.90300e41 | + | 6.57892e40i | 1.64940 | + | 0.570220i | ||||
\(680\) | − | 1.31082e40i | − | 0.111215i | ||||||
\(681\) | 1.68597e41 | − | 9.06474e40i | 1.40028 | − | 0.752874i | ||||
\(682\) | − | 6.79482e38i | − | 0.00552464i | ||||||
\(683\) | − | 1.41522e41i | − | 1.12648i | −0.826294 | − | 0.563239i | \(-0.809555\pi\) | ||
0.826294 | − | 0.563239i | \(-0.190445\pi\) | |||||||
\(684\) | 2.17456e40 | + | 1.43767e40i | 0.169457 | + | 0.112033i | ||||
\(685\) | − | 1.88178e41i | − | 1.43567i | ||||||
\(686\) | 1.00669e40 | + | 1.56285e40i | 0.0751960 | + | 0.116739i | ||||
\(687\) | −7.80444e40 | − | 1.45156e41i | −0.570780 | − | 1.06160i | ||||
\(688\) | −1.14399e41 | −0.819202 | ||||||||
\(689\) | −8.94701e39 | −0.0627334 | ||||||||
\(690\) | −2.38139e39 | + | 1.28037e39i | −0.0163500 | + | 0.00879073i | ||||
\(691\) | 1.54342e41i | 1.03765i | 0.854880 | + | 0.518826i | \(0.173631\pi\) | ||||
−0.854880 | + | 0.518826i | \(0.826369\pi\) | |||||||
\(692\) | −1.33104e41 | −0.876298 | ||||||||
\(693\) | 2.51433e40 | − | 1.92647e40i | 0.162103 | − | 0.124202i | ||||
\(694\) | 1.62706e40 | 0.102729 | ||||||||
\(695\) | − | 1.48493e41i | − | 0.918174i | ||||||
\(696\) | −3.29251e40 | + | 1.77025e40i | −0.199386 | + | 0.107201i | ||||
\(697\) | 2.64167e40 | 0.156676 | ||||||||
\(698\) | 4.32145e40 | 0.251030 | ||||||||
\(699\) | −1.30464e41 | − | 2.42653e41i | −0.742289 | − | 1.38060i | ||||
\(700\) | −5.56293e39 | + | 1.60911e40i | −0.0310014 | + | 0.0896737i | ||||
\(701\) | − | 3.15774e41i | − | 1.72371i | −0.507151 | − | 0.861857i | \(-0.669301\pi\) | ||
0.507151 | − | 0.861857i | \(-0.330699\pi\) | |||||||
\(702\) | 3.75459e38 | − | 4.12174e39i | 0.00200758 | − | 0.0220390i | ||||
\(703\) | 1.95049e40i | 0.102162i | ||||||||
\(704\) | 3.52696e40i | 0.180966i | ||||||||
\(705\) | 2.44346e41 | − | 1.31375e41i | 1.22818 | − | 0.660343i | ||||
\(706\) | 2.56763e40i | 0.126434i | ||||||||
\(707\) | −4.68226e40 | + | 1.35437e41i | −0.225878 | + | 0.653367i | ||||
\(708\) | −1.64762e41 | + | 8.85857e40i | −0.778709 | + | 0.418679i | ||||
\(709\) | 1.69570e40 | 0.0785197 | 0.0392598 | − | 0.999229i | \(-0.487500\pi\) | ||||
0.0392598 | + | 0.999229i | \(0.487500\pi\) | |||||||
\(710\) | 4.14820e40 | 0.188197 | ||||||||
\(711\) | 1.10196e41 | − | 1.66678e41i | 0.489843 | − | 0.740917i | ||||
\(712\) | 3.48975e40i | 0.151997i | ||||||||
\(713\) | −6.42106e39 | −0.0274037 | ||||||||
\(714\) | −1.39458e40 | + | 2.25725e39i | −0.0583203 | + | 0.00943965i | ||||
\(715\) | −7.54805e39 | −0.0309312 | ||||||||
\(716\) | 1.35809e41i | 0.545367i | ||||||||
\(717\) | −1.71314e41 | − | 3.18630e41i | −0.674164 | − | 1.25389i | ||||
\(718\) | −4.13919e40 | −0.159629 | ||||||||
\(719\) | −6.55101e40 | −0.247594 | −0.123797 | − | 0.992308i | \(-0.539507\pi\) | ||||
−0.123797 | + | 0.992308i | \(0.539507\pi\) | |||||||
\(720\) | 1.33372e41 | − | 2.01733e41i | 0.494017 | − | 0.747231i | ||||
\(721\) | 3.09813e41 | + | 1.07107e41i | 1.12470 | + | 0.388826i | ||||
\(722\) | − | 3.73530e40i | − | 0.132903i | ||||||
\(723\) | 1.04671e41 | + | 1.94679e41i | 0.365022 | + | 0.678911i | ||||
\(724\) | 4.29317e41i | 1.46747i | ||||||||
\(725\) | 2.37666e40i | 0.0796281i | ||||||||
\(726\) | −1.91880e40 | − | 3.56880e40i | −0.0630156 | − | 0.117204i | ||||
\(727\) | 3.70792e41i | 1.19366i | 0.802367 | + | 0.596831i | \(0.203574\pi\) | ||||
−0.802367 | + | 0.596831i | \(0.796426\pi\) | |||||||
\(728\) | 4.53854e39 | − | 1.31280e40i | 0.0143222 | − | 0.0414280i | ||||
\(729\) | −3.17937e41 | − | 5.84079e40i | −0.983541 | − | 0.180685i | ||||
\(730\) | −1.34729e40 | −0.0408581 | ||||||||
\(731\) | −1.24381e41 | −0.369788 | ||||||||
\(732\) | 2.10835e41 | + | 3.92136e41i | 0.614515 | + | 1.14295i | ||||
\(733\) | 5.21653e41i | 1.49064i | 0.666705 | + | 0.745322i | \(0.267704\pi\) | ||||
−0.666705 | + | 0.745322i | \(0.732296\pi\) | |||||||
\(734\) | −2.49038e40 | −0.0697707 | ||||||||
\(735\) | −3.40868e41 | − | 5.93493e40i | −0.936310 | − | 0.163023i | ||||
\(736\) | −2.12005e40 | −0.0570976 | ||||||||
\(737\) | − | 5.88923e40i | − | 0.155518i | ||||||
\(738\) | −1.64742e40 | − | 1.08916e40i | −0.0426567 | − | 0.0282017i | ||||
\(739\) | −1.44058e41 | −0.365758 | −0.182879 | − | 0.983135i | \(-0.558542\pi\) | ||||
−0.182879 | + | 0.983135i | \(0.558542\pi\) | |||||||
\(740\) | 1.84647e41 | 0.459709 | ||||||||
\(741\) | −1.19093e40 | + | 6.40315e39i | −0.0290752 | + | 0.0156325i | ||||
\(742\) | 7.45988e39 | − | 2.15782e40i | 0.0178598 | − | 0.0516605i | ||||
\(743\) | 4.59109e41i | 1.07790i | 0.842338 | + | 0.538949i | \(0.181179\pi\) | ||||
−0.842338 | + | 0.538949i | \(0.818821\pi\) | |||||||
\(744\) | −2.04979e40 | + | 1.10208e40i | −0.0471955 | + | 0.0253751i | ||||
\(745\) | − | 1.19697e41i | − | 0.270282i | ||||||
\(746\) | 4.98212e40i | 0.110332i | ||||||||
\(747\) | 1.89990e40 | − | 2.87372e40i | 0.0412651 | − | 0.0624159i | ||||
\(748\) | 3.99998e40i | 0.0852089i | ||||||||
\(749\) | −4.76226e41 | − | 1.64638e41i | −0.995008 | − | 0.343988i | ||||
\(750\) | 3.34462e40 | + | 6.22073e40i | 0.0685424 | + | 0.127483i | ||||
\(751\) | −1.27894e41 | −0.257081 | −0.128541 | − | 0.991704i | \(-0.541029\pi\) | ||||
−0.128541 | + | 0.991704i | \(0.541029\pi\) | |||||||
\(752\) | 7.01373e41 | 1.38290 | ||||||||
\(753\) | −2.34963e41 | + | 1.26330e41i | −0.454435 | + | 0.244330i | ||||
\(754\) | − | 9.60066e39i | − | 0.0182145i | ||||||
\(755\) | −3.51602e41 | −0.654365 | ||||||||
\(756\) | −4.89670e41 | − | 2.20846e41i | −0.894000 | − | 0.403202i | ||||
\(757\) | 7.05869e41 | 1.26425 | 0.632126 | − | 0.774865i | \(-0.282182\pi\) | ||||
0.632126 | + | 0.774865i | \(0.282182\pi\) | |||||||
\(758\) | 3.63233e40i | 0.0638236i | ||||||||
\(759\) | 1.46766e40 | − | 7.89099e39i | 0.0252999 | − | 0.0136027i | ||||
\(760\) | 3.20156e40 | 0.0541458 | ||||||||
\(761\) | 4.62680e41 | 0.767720 | 0.383860 | − | 0.923391i | \(-0.374594\pi\) | ||||
0.383860 | + | 0.923391i | \(0.374594\pi\) | |||||||
\(762\) | −3.85262e40 | − | 7.16555e40i | −0.0627204 | − | 0.116655i | ||||
\(763\) | 1.33368e41 | − | 3.85775e41i | 0.213032 | − | 0.616209i | ||||
\(764\) | 6.99278e41i | 1.09596i | ||||||||
\(765\) | 1.45009e41 | − | 2.19335e41i | 0.222999 | − | 0.337300i | ||||
\(766\) | − | 3.01775e40i | − | 0.0455372i | ||||||
\(767\) | − | 9.70307e40i | − | 0.143673i | ||||||
\(768\) | 4.92640e41 | − | 2.64872e41i | 0.715801 | − | 0.384856i | ||||
\(769\) | 6.74788e40i | 0.0962134i | 0.998842 | + | 0.0481067i | \(0.0153188\pi\) | ||||
−0.998842 | + | 0.0481067i | \(0.984681\pi\) | |||||||
\(770\) | 6.29346e39 | − | 1.82042e40i | 0.00880590 | − | 0.0254716i | ||||
\(771\) | −9.05375e40 | + | 4.86782e40i | −0.124320 | + | 0.0668415i | ||||
\(772\) | −1.15300e42 | −1.55374 | ||||||||
\(773\) | 1.34279e42 | 1.77585 | 0.887926 | − | 0.459987i | \(-0.152146\pi\) | ||||
0.887926 | + | 0.459987i | \(0.152146\pi\) | |||||||
\(774\) | 7.75677e40 | + | 5.12823e40i | 0.100679 | + | 0.0665616i | ||||
\(775\) | 1.47961e40i | 0.0188483i | ||||||||
\(776\) | 3.83919e41 | 0.480004 | ||||||||
\(777\) | −6.42184e40 | − | 3.96756e41i | −0.0788052 | − | 0.486877i | ||||
\(778\) | 1.02168e41 | 0.123058 | ||||||||
\(779\) | 6.45207e40i | 0.0762792i | ||||||||
\(780\) | 6.06168e40 | + | 1.12742e41i | 0.0703431 | + | 0.130832i | ||||
\(781\) | −2.55655e41 | −0.291215 | ||||||||
\(782\) | −7.43200e39 | −0.00831013 | ||||||||
\(783\) | −7.46759e41 | − | 6.80239e40i | −0.819662 | − | 0.0746649i | ||||
\(784\) | −6.87963e41 | − | 5.40245e41i | −0.741280 | − | 0.582114i | ||||
\(785\) | 3.52951e41i | 0.373340i | ||||||||
\(786\) | 7.89222e40 | + | 1.46789e41i | 0.0819544 | + | 0.152429i | ||||
\(787\) | 8.75892e41i | 0.892929i | 0.894801 | + | 0.446465i | \(0.147317\pi\) | ||||
−0.894801 | + | 0.446465i | \(0.852683\pi\) | |||||||
\(788\) | 1.86976e42i | 1.87135i | ||||||||
\(789\) | 5.78004e41 | + | 1.07504e42i | 0.567955 | + | 1.05635i | ||||
\(790\) | − | 1.21504e41i | − | 0.117219i | ||||||
\(791\) | −1.83822e42 | − | 6.35499e41i | −1.74116 | − | 0.601944i | ||||
\(792\) | 3.33081e40 | − | 5.03806e40i | 0.0309767 | − | 0.0468541i | ||||
\(793\) | −2.30935e41 | −0.210876 | ||||||||
\(794\) | 1.91928e41 | 0.172084 | ||||||||
\(795\) | 2.01228e41 | + | 3.74267e41i | 0.177160 | + | 0.329502i | ||||
\(796\) | 4.10668e41i | 0.355019i | ||||||||
\(797\) | −9.86993e41 | −0.837854 | −0.418927 | − | 0.908020i | \(-0.637594\pi\) | ||||
−0.418927 | + | 0.908020i | \(0.637594\pi\) | |||||||
\(798\) | −5.51315e39 | − | 3.40615e40i | −0.00459577 | − | 0.0283937i | ||||
\(799\) | 7.62571e41 | 0.624241 | ||||||||
\(800\) | 4.88526e40i | 0.0392720i | ||||||||
\(801\) | −3.86053e41 | + | 5.83929e41i | −0.304772 | + | 0.460987i | ||||
\(802\) | 2.03972e41 | 0.158140 | ||||||||
\(803\) | 8.30337e40 | 0.0632236 | ||||||||
\(804\) | −8.79652e41 | + | 4.72952e41i | −0.657806 | + | 0.353675i | ||||
\(805\) | −1.72029e41 | − | 5.94728e40i | −0.126346 | − | 0.0436795i | ||||
\(806\) | − | 5.97698e39i | − | 0.00431145i | ||||||
\(807\) | 1.66794e42 | − | 8.96784e41i | 1.18172 | − | 0.635362i | ||||
\(808\) | 2.73238e41i | 0.190141i | ||||||||
\(809\) | − | 1.12421e42i | − | 0.768410i | −0.923248 | − | 0.384205i | \(-0.874476\pi\) | ||
0.923248 | − | 0.384205i | \(-0.125524\pi\) | |||||||
\(810\) | −1.80863e41 | + | 7.69964e40i | −0.121428 | + | 0.0516937i | ||||
\(811\) | − | 2.02846e42i | − | 1.33771i | −0.743391 | − | 0.668857i | \(-0.766784\pi\) | ||
0.743391 | − | 0.668857i | \(-0.233216\pi\) | |||||||
\(812\) | −1.17766e42 | − | 4.07134e41i | −0.762883 | − | 0.263739i | ||||
\(813\) | 4.97992e40 | + | 9.26225e40i | 0.0316891 | + | 0.0589391i | ||||
\(814\) | 2.23746e40 | 0.0139863 | ||||||||
\(815\) | 9.87296e41 | 0.606264 | ||||||||
\(816\) | 5.85484e41 | − | 3.14790e41i | 0.353189 | − | 0.189895i | ||||
\(817\) | − | 3.03791e41i | − | 0.180034i | ||||||
\(818\) | 2.23972e41 | 0.130398 | ||||||||
\(819\) | 2.21170e41 | − | 1.69459e41i | 0.126506 | − | 0.0969280i | ||||
\(820\) | 6.10799e41 | 0.343240 | ||||||||
\(821\) | − | 2.80127e42i | − | 1.54660i | −0.634038 | − | 0.773302i | \(-0.718604\pi\) | ||
0.634038 | − | 0.773302i | \(-0.281396\pi\) | |||||||
\(822\) | −3.40592e41 | + | 1.83122e41i | −0.184753 | + | 0.0993342i | ||||
\(823\) | 8.17526e41 | 0.435716 | 0.217858 | − | 0.975980i | \(-0.430093\pi\) | ||||
0.217858 | + | 0.975980i | \(0.430093\pi\) | |||||||
\(824\) | 6.25032e41 | 0.327309 | ||||||||
\(825\) | −1.81833e40 | − | 3.38194e40i | −0.00935600 | − | 0.0174014i | ||||
\(826\) | 2.34017e41 | + | 8.09028e40i | 0.118314 | + | 0.0409028i | ||||
\(827\) | − | 3.21875e42i | − | 1.59903i | −0.600645 | − | 0.799516i | \(-0.705090\pi\) | ||
0.600645 | − | 0.799516i | \(-0.294910\pi\) | |||||||
\(828\) | −2.35729e41 | − | 1.55848e41i | −0.115073 | − | 0.0760783i | ||||
\(829\) | − | 1.91498e42i | − | 0.918594i | −0.888283 | − | 0.459297i | \(-0.848101\pi\) | ||
0.888283 | − | 0.459297i | \(-0.151899\pi\) | |||||||
\(830\) | − | 2.09487e40i | − | 0.00987470i | ||||||
\(831\) | 1.98499e42 | − | 1.06724e42i | 0.919482 | − | 0.494367i | ||||
\(832\) | 3.10245e41i | 0.141227i | ||||||||
\(833\) | −7.47991e41 | − | 5.87384e41i | −0.334614 | − | 0.262766i | ||||
\(834\) | −2.68763e41 | + | 1.44503e41i | −0.118158 | + | 0.0635285i | ||||
\(835\) | −1.44559e42 | −0.624583 | ||||||||
\(836\) | −9.76964e40 | −0.0414846 | ||||||||
\(837\) | −4.64902e41 | − | 4.23489e40i | −0.194018 | − | 0.0176735i | ||||
\(838\) | − | 2.57711e41i | − | 0.105705i | ||||||
\(839\) | −2.49900e42 | −1.00744 | −0.503719 | − | 0.863867i | \(-0.668035\pi\) | ||||
−0.503719 | + | 0.863867i | \(0.668035\pi\) | |||||||
\(840\) | −6.51242e41 | + | 1.05409e41i | −0.258043 | + | 0.0417666i | ||||
\(841\) | 8.28281e41 | 0.322579 | ||||||||
\(842\) | 4.14781e40i | 0.0158779i | ||||||||
\(843\) | 4.60108e41 | + | 8.55763e41i | 0.173125 | + | 0.321998i | ||||
\(844\) | 2.43771e42 | 0.901604 | ||||||||
\(845\) | 2.54773e42 | 0.926257 | ||||||||
\(846\) | −4.75562e41 | − | 3.14408e41i | −0.169956 | − | 0.112363i | ||||
\(847\) | 8.91272e41 | − | 2.57806e42i | 0.313113 | − | 0.905700i | ||||
\(848\) | 1.07430e42i | 0.371010i | ||||||||
\(849\) | 2.29114e41 | + | 4.26133e41i | 0.0777840 | + | 0.144672i | ||||
\(850\) | 1.71256e40i | 0.00571574i | ||||||||
\(851\) | − | 2.11439e41i | − | 0.0693756i | ||||||
\(852\) | 2.05311e42 | + | 3.81862e42i | 0.662275 | + | 1.23178i | ||||
\(853\) | − | 4.89339e42i | − | 1.55185i | −0.630828 | − | 0.775923i | \(-0.717285\pi\) | ||
0.630828 | − | 0.775923i | \(-0.282715\pi\) | |||||||
\(854\) | 1.92550e41 | − | 5.56963e41i | 0.0600349 | − | 0.173655i | ||||
\(855\) | 5.35708e41 | + | 3.54172e41i | 0.164217 | + | 0.108569i | ||||
\(856\) | −9.60761e41 | −0.289565 | ||||||||
\(857\) | 1.70966e42 | 0.506628 | 0.253314 | − | 0.967384i | \(-0.418479\pi\) | ||||
0.253314 | + | 0.967384i | \(0.418479\pi\) | |||||||
\(858\) | 7.34524e39 | + | 1.36616e40i | 0.00214013 | + | 0.00398047i | ||||
\(859\) | 4.97270e42i | 1.42459i | 0.701878 | + | 0.712297i | \(0.252345\pi\) | ||||
−0.701878 | + | 0.712297i | \(0.747655\pi\) | |||||||
\(860\) | −2.87590e42 | −0.810115 | ||||||||
\(861\) | −2.12430e41 | − | 1.31244e42i | −0.0588396 | − | 0.363524i | ||||
\(862\) | −4.12091e41 | −0.112237 | ||||||||
\(863\) | 2.28155e42i | 0.611045i | 0.952185 | + | 0.305522i | \(0.0988311\pi\) | ||||
−0.952185 | + | 0.305522i | \(0.901169\pi\) | |||||||
\(864\) | −1.53497e42 | − | 1.39824e41i | −0.404251 | − | 0.0368242i | ||||
\(865\) | −3.27904e42 | −0.849205 | ||||||||
\(866\) | 7.91426e41 | 0.201558 | ||||||||
\(867\) | −2.88015e42 | + | 1.54854e42i | −0.721337 | + | 0.387832i | ||||
\(868\) | −7.33164e41 | − | 2.53465e41i | −0.180578 | − | 0.0624283i | ||||
\(869\) | 7.48834e41i | 0.181384i | ||||||||
\(870\) | −4.01611e41 | + | 2.15929e41i | −0.0956700 | + | 0.0514378i | ||||
\(871\) | − | 5.18039e41i | − | 0.121367i | ||||||
\(872\) | − | 7.78281e41i | − | 0.179328i | ||||||
\(873\) | 6.42400e42 | + | 4.24710e42i | 1.45579 | + | 0.962467i | ||||
\(874\) | − | 1.81521e40i | − | 0.00404585i | ||||||
\(875\) | −1.55356e42 | + | 4.49379e42i | −0.340575 | + | 0.985135i | ||||
\(876\) | −6.66826e41 | − | 1.24024e42i | −0.143782 | − | 0.267422i | ||||
\(877\) | 3.39192e42 | 0.719368 | 0.359684 | − | 0.933074i | \(-0.382885\pi\) | ||||
0.359684 | + | 0.933074i | \(0.382885\pi\) | |||||||
\(878\) | 5.31509e41 | 0.110877 | ||||||||
\(879\) | 2.37392e42 | − | 1.27636e42i | 0.487111 | − | 0.261899i | ||||
\(880\) | 9.06323e41i | 0.182930i | ||||||||
\(881\) | −6.58043e42 | −1.30648 | −0.653242 | − | 0.757150i | \(-0.726591\pi\) | ||||
−0.653242 | + | 0.757150i | \(0.726591\pi\) | |||||||
\(882\) | 2.24290e41 | + | 6.74706e41i | 0.0438042 | + | 0.131771i | ||||
\(883\) | −9.49026e42 | −1.82326 | −0.911628 | − | 0.411016i | \(-0.865174\pi\) | ||||
−0.911628 | + | 0.411016i | \(0.865174\pi\) | |||||||
\(884\) | 3.51854e41i | 0.0664973i | ||||||||
\(885\) | −4.05895e42 | + | 2.18233e42i | −0.754633 | + | 0.405735i | ||||
\(886\) | 3.48327e41 | 0.0637086 | ||||||||
\(887\) | 9.58180e42 | 1.72407 | 0.862034 | − | 0.506850i | \(-0.169190\pi\) | ||||
0.862034 | + | 0.506850i | \(0.169190\pi\) | |||||||
\(888\) | −3.62905e41 | − | 6.74974e41i | −0.0642399 | − | 0.119481i | ||||
\(889\) | 1.78952e42 | − | 5.17632e42i | 0.311646 | − | 0.901458i | ||||
\(890\) | 4.25669e41i | 0.0729318i | ||||||||
\(891\) | 1.11467e42 | − | 4.74532e41i | 0.187897 | − | 0.0799905i | ||||
\(892\) | − | 6.91964e42i | − | 1.14761i | ||||||
\(893\) | 1.86252e42i | 0.303917i | ||||||||
\(894\) | −2.16645e41 | + | 1.16481e41i | −0.0347820 | + | 0.0187008i | ||||
\(895\) | 3.34567e42i | 0.528505i | ||||||||
\(896\) | −3.21653e42 | − | 1.11200e42i | −0.499945 | − | 0.172838i | ||||
\(897\) | 1.29101e41 | − | 6.94121e40i | 0.0197442 | − | 0.0106156i | ||||
\(898\) | −2.22350e41 | −0.0334604 | ||||||||
\(899\) | −1.08288e42 | −0.160349 | ||||||||
\(900\) | −3.59122e41 | + | 5.43194e41i | −0.0523269 | + | 0.0791477i | ||||
\(901\) | 1.16804e42i | 0.167474i | ||||||||
\(902\) | 7.40136e40 | 0.0104428 | ||||||||
\(903\) | 1.00021e42 | + | 6.17952e42i | 0.138873 | + | 0.857991i | ||||
\(904\) | −3.70852e42 | −0.506709 | ||||||||
\(905\) | 1.05763e43i | 1.42210i | ||||||||
\(906\) | 3.42154e41 | + | 6.36379e41i | 0.0452755 | + | 0.0842087i | ||||
\(907\) | −8.47440e42 | −1.10358 | −0.551789 | − | 0.833984i | \(-0.686055\pi\) | ||||
−0.551789 | + | 0.833984i | \(0.686055\pi\) | |||||||
\(908\) | 1.21659e43 | 1.55919 | ||||||||
\(909\) | −3.02269e42 | + | 4.57200e42i | −0.381257 | + | 0.576674i | ||||
\(910\) | 5.53596e40 | − | 1.60131e41i | 0.00687215 | − | 0.0198782i | ||||
\(911\) | 2.87271e42i | 0.350975i | 0.984482 | + | 0.175487i | \(0.0561501\pi\) | ||||
−0.984482 | + | 0.175487i | \(0.943850\pi\) | |||||||
\(912\) | 7.68850e41 | + | 1.43000e42i | 0.0924520 | + | 0.171953i | ||||
\(913\) | 1.29107e41i | 0.0152800i | ||||||||
\(914\) | − | 1.56623e42i | − | 0.182447i | ||||||
\(915\) | 5.19397e42 | + | 9.66036e42i | 0.595516 | + | 1.10761i | ||||
\(916\) | − | 1.04744e43i | − | 1.18208i | ||||||
\(917\) | −3.66590e42 | + | 1.06039e43i | −0.407217 | + | 1.17790i | ||||
\(918\) | −5.38096e41 | − | 4.90164e40i | −0.0588357 | − | 0.00535948i | ||||
\(919\) | −2.67726e42 | −0.288148 | −0.144074 | − | 0.989567i | \(-0.546020\pi\) | ||||
−0.144074 | + | 0.989567i | \(0.546020\pi\) | |||||||
\(920\) | −3.47060e41 | −0.0367689 | ||||||||
\(921\) | −8.23070e41 | − | 1.53084e42i | −0.0858366 | − | 0.159649i | ||||
\(922\) | 1.98820e42i | 0.204109i | ||||||||
\(923\) | −2.24884e42 | −0.227265 | ||||||||
\(924\) | 1.98728e42 | − | 3.21658e41i | 0.197704 | − | 0.0320001i | ||||
\(925\) | −4.87222e41 | −0.0477168 | ||||||||
\(926\) | − | 8.10180e41i | − | 0.0781128i | ||||||
\(927\) | 1.04585e43 | + | 6.91440e42i | 0.992685 | + | 0.656294i | ||||
\(928\) | −3.57537e42 | −0.334099 | ||||||||
\(929\) | 1.62876e43 | 1.49840 | 0.749201 | − | 0.662342i | \(-0.230438\pi\) | ||||
0.749201 | + | 0.662342i | \(0.230438\pi\) | |||||||
\(930\) | −2.50026e41 | + | 1.34429e41i | −0.0226456 | + | 0.0121756i | ||||
\(931\) | 1.43464e42 | − | 1.82691e42i | 0.127930 | − | 0.162909i | ||||
\(932\) | − | 1.75098e43i | − | 1.53727i | ||||||
\(933\) | −1.44307e43 | + | 7.75878e42i | −1.24739 | + | 0.670671i | ||||
\(934\) | − | 6.58890e41i | − | 0.0560768i | ||||||
\(935\) | 9.85403e41i | 0.0825745i | ||||||||
\(936\) | 2.92991e41 | − | 4.43167e41i | 0.0241743 | − | 0.0365651i | ||||
\(937\) | − | 1.22135e43i | − | 0.992236i | −0.868255 | − | 0.496118i | \(-0.834758\pi\) | ||
0.868255 | − | 0.496118i | \(-0.165242\pi\) | |||||||
\(938\) | 1.24940e42 | + | 4.31933e41i | 0.0999445 | + | 0.0345522i | ||||
\(939\) | 5.80809e42 | + | 1.08026e43i | 0.457490 | + | 0.850895i | ||||
\(940\) | 1.76320e43 | 1.36756 | ||||||||
\(941\) | 2.83113e41 | 0.0216227 | 0.0108114 | − | 0.999942i | \(-0.496559\pi\) | ||||
0.0108114 | + | 0.999942i | \(0.496559\pi\) | |||||||
\(942\) | 6.38822e41 | − | 3.43468e41i | 0.0480443 | − | 0.0258314i | ||||
\(943\) | − | 6.99424e41i | − | 0.0517990i | ||||||
\(944\) | −1.16508e43 | −0.849695 | ||||||||
\(945\) | −1.20631e43 | − | 5.44057e42i | −0.866359 | − | 0.390736i | ||||
\(946\) | −3.48488e41 | −0.0246471 | ||||||||
\(947\) | − | 6.26788e42i | − | 0.436562i | −0.975886 | − | 0.218281i | \(-0.929955\pi\) | ||
0.975886 | − | 0.218281i | \(-0.0700449\pi\) | |||||||
\(948\) | 1.11850e43 | − | 6.01373e42i | 0.767215 | − | 0.412499i | ||||
\(949\) | 7.30396e41 | 0.0493399 | ||||||||
\(950\) | −4.18280e40 | −0.00278275 | ||||||||
\(951\) | −9.70512e42 | − | 1.80507e43i | −0.635892 | − | 1.18271i | ||||
\(952\) | −1.71387e42 | − | 5.92509e41i | −0.110597 | − | 0.0382348i | ||||
\(953\) | 9.58697e42i | 0.609304i | 0.952464 | + | 0.304652i | \(0.0985402\pi\) | ||||
−0.952464 | + | 0.304652i | \(0.901460\pi\) | |||||||
\(954\) | 4.81582e41 | − | 7.28422e41i | 0.0301452 | − | 0.0455965i | ||||
\(955\) | 1.72269e43i | 1.06208i | ||||||||
\(956\) | − | 2.29923e43i | − | 1.39618i | ||||||
\(957\) | 2.47514e42 | − | 1.33078e42i | 0.148039 | − | 0.0795945i | ||||
\(958\) | 7.59910e41i | 0.0447674i | ||||||||
\(959\) | −2.46040e43 | − | 8.50593e42i | −1.42769 | − | 0.493574i | ||||
\(960\) | 1.29780e43 | − | 6.97775e42i | 0.741782 | − | 0.398825i | ||||
\(961\) | 1.70877e43 | 0.962045 | ||||||||
\(962\) | 1.96816e41 | 0.0109149 | ||||||||
\(963\) | −1.60761e43 | − | 1.06284e43i | −0.878213 | − | 0.580613i | ||||
\(964\) | 1.40480e43i | 0.755956i | ||||||||
\(965\) | −2.84043e43 | −1.50570 | ||||||||
\(966\) | 5.97643e40 | + | 3.69238e41i | 0.00312085 | + | 0.0192814i | ||||
\(967\) | 1.82993e43 | 0.941350 | 0.470675 | − | 0.882307i | \(-0.344010\pi\) | ||||
0.470675 | + | 0.882307i | \(0.344010\pi\) | |||||||
\(968\) | − | 5.20111e42i | − | 0.263575i | ||||||
\(969\) | 8.35935e41 | + | 1.55477e42i | 0.0417328 | + | 0.0776197i | ||||
\(970\) | 4.68293e42 | 0.230318 | ||||||||
\(971\) | 3.22871e43 | 1.56441 | 0.782204 | − | 0.623022i | \(-0.214095\pi\) | ||||
0.782204 | + | 0.623022i | \(0.214095\pi\) | |||||||
\(972\) | −1.60396e43 | − | 1.28385e43i | −0.765652 | − | 0.612849i | ||||
\(973\) | −1.94152e43 | − | 6.71209e42i | −0.913072 | − | 0.315661i | ||||
\(974\) | 4.86777e42i | 0.225541i | ||||||||
\(975\) | −1.59947e41 | − | 2.97489e41i | −0.00730146 | − | 0.0135801i | ||||
\(976\) | 2.77292e43i | 1.24714i | ||||||||
\(977\) | − | 1.39873e43i | − | 0.619815i | −0.950767 | − | 0.309908i | \(-0.899702\pi\) | ||
0.950767 | − | 0.309908i | \(-0.100298\pi\) | |||||||
\(978\) | −9.60768e41 | − | 1.78695e42i | −0.0419474 | − | 0.0780187i | ||||
\(979\) | − | 2.62341e42i | − | 0.112854i | ||||||
\(980\) | −1.72948e43 | − | 1.35813e43i | −0.733058 | − | 0.575658i | ||||
\(981\) | 8.60971e42 | − | 1.30227e43i | 0.359574 | − | 0.543878i | ||||
\(982\) | 5.97829e42 | 0.246014 | ||||||||
\(983\) | 2.38457e43 | 0.966904 | 0.483452 | − | 0.875371i | \(-0.339383\pi\) | ||||
0.483452 | + | 0.875371i | \(0.339383\pi\) | |||||||
\(984\) | −1.20046e42 | − | 2.23276e42i | −0.0479645 | − | 0.0892100i | ||||
\(985\) | 4.60619e43i | 1.81349i | ||||||||
\(986\) | −1.25337e42 | −0.0486256 | ||||||||
\(987\) | −6.13221e42 | − | 3.78862e43i | −0.234433 | − | 1.44838i | ||||
\(988\) | −8.59374e41 | −0.0323748 | ||||||||
\(989\) | 3.29319e42i | 0.122256i | ||||||||
\(990\) | 4.06282e41 | − | 6.14526e41i | 0.0148634 | − | 0.0224817i | ||||
\(991\) | 1.69193e43 | 0.609977 | 0.304988 | − | 0.952356i | \(-0.401347\pi\) | ||||
0.304988 | + | 0.952356i | \(0.401347\pi\) | |||||||
\(992\) | −2.22588e42 | −0.0790829 | ||||||||
\(993\) | 1.54113e43 | − | 8.28604e42i | 0.539606 | − | 0.290123i | ||||
\(994\) | 1.87505e42 | − | 5.42370e42i | 0.0647008 | − | 0.187151i | ||||
\(995\) | 1.01169e43i | 0.344042i | ||||||||
\(996\) | 1.92843e42 | − | 1.03683e42i | 0.0646313 | − | 0.0347495i | ||||
\(997\) | − | 1.31265e42i | − | 0.0433581i | −0.999765 | − | 0.0216790i | \(-0.993099\pi\) | ||
0.999765 | − | 0.0216790i | \(-0.00690119\pi\) | |||||||
\(998\) | 3.91470e42i | 0.127440i | ||||||||
\(999\) | 1.39451e42 | − | 1.53087e43i | 0.0447426 | − | 0.491179i |
(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 | 21.30.c.a.20.17 | ✓ | 76 | |
3.2 | odd | 2 | inner | 21.30.c.a.20.60 | yes | 76 | |
7.6 | odd | 2 | inner | 21.30.c.a.20.59 | yes | 76 | |
21.20 | even | 2 | inner | 21.30.c.a.20.18 | yes | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.30.c.a.20.17 | ✓ | 76 | 1.1 | even | 1 | trivial | |
21.30.c.a.20.18 | yes | 76 | 21.20 | even | 2 | inner | |
21.30.c.a.20.59 | yes | 76 | 7.6 | odd | 2 | inner | |
21.30.c.a.20.60 | yes | 76 | 3.2 | odd | 2 | inner |