Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [12,13,Mod(7,12)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 13, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12.7");
S:= CuspForms(chi, 13);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.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: | \(10.9679258073\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 1570 x^{10} - 4077 x^{9} + 1884069 x^{8} - 3551868 x^{7} + 881574992 x^{6} + \cdots + 104882177440000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{57}\cdot 3^{25} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 7.5 | ||
Root | \(13.5291 + 23.4332i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 12.7 |
Dual form | 12.13.d.a.7.6 |
$q$-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 \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −35.2919 | − | 53.3899i | −0.551436 | − | 0.834217i | ||||
\(3\) | − | 420.888i | − | 0.577350i | ||||||
\(4\) | −1604.96 | + | 3768.46i | −0.391837 | + | 0.920035i | ||||
\(5\) | 8409.28 | 0.538194 | 0.269097 | − | 0.963113i | \(-0.413275\pi\) | ||||
0.269097 | + | 0.963113i | \(0.413275\pi\) | |||||||
\(6\) | −22471.2 | + | 14854.0i | −0.481636 | + | 0.318372i | ||||
\(7\) | 192052.i | 1.63242i | 0.577756 | + | 0.816210i | \(0.303929\pi\) | ||||
−0.577756 | + | 0.816210i | \(0.696071\pi\) | |||||||
\(8\) | 257840. | − | 47307.4i | 0.983582 | − | 0.180463i | ||||
\(9\) | −177147. | −0.333333 | ||||||||
\(10\) | −296780. | − | 448971.i | −0.296780 | − | 0.448971i | ||||
\(11\) | − | 748209.i | − | 0.422345i | −0.977449 | − | 0.211172i | \(-0.932272\pi\) | ||
0.977449 | − | 0.211172i | \(-0.0677281\pi\) | |||||||
\(12\) | 1.58610e6 | + | 675510.i | 0.531182 | + | 0.226227i | ||||
\(13\) | 5.80736e6 | 1.20315 | 0.601573 | − | 0.798818i | \(-0.294541\pi\) | ||||
0.601573 | + | 0.798818i | \(0.294541\pi\) | |||||||
\(14\) | 1.02537e7 | − | 6.77790e6i | 1.36179 | − | 0.900175i | ||||
\(15\) | − | 3.53937e6i | − | 0.310726i | ||||||
\(16\) | −1.16254e7 | − | 1.20965e7i | −0.692928 | − | 0.721007i | ||||
\(17\) | 2.57798e7 | 1.06804 | 0.534018 | − | 0.845473i | \(-0.320681\pi\) | ||||
0.534018 | + | 0.845473i | \(0.320681\pi\) | |||||||
\(18\) | 6.25185e6 | + | 9.45786e6i | 0.183812 | + | 0.278072i | ||||
\(19\) | − | 1.62006e7i | − | 0.344357i | −0.985066 | − | 0.172178i | \(-0.944919\pi\) | ||
0.985066 | − | 0.172178i | \(-0.0550806\pi\) | |||||||
\(20\) | −1.34966e7 | + | 3.16901e7i | −0.210884 | + | 0.495157i | ||||
\(21\) | 8.08326e7 | 0.942478 | ||||||||
\(22\) | −3.99468e7 | + | 2.64057e7i | −0.352327 | + | 0.232896i | ||||
\(23\) | 1.99788e8i | 1.34959i | 0.738003 | + | 0.674797i | \(0.235769\pi\) | ||||
−0.738003 | + | 0.674797i | \(0.764231\pi\) | |||||||
\(24\) | −1.99111e7 | − | 1.08522e8i | −0.104191 | − | 0.567871i | ||||
\(25\) | −1.73425e8 | −0.710347 | ||||||||
\(26\) | −2.04953e8 | − | 3.10054e8i | −0.663458 | − | 1.00369i | ||||
\(27\) | 7.45591e7i | 0.192450i | ||||||||
\(28\) | −7.23743e8 | − | 3.08237e8i | −1.50188 | − | 0.639642i | ||||
\(29\) | 8.06751e8 | 1.35629 | 0.678144 | − | 0.734929i | \(-0.262785\pi\) | ||||
0.678144 | + | 0.734929i | \(0.262785\pi\) | |||||||
\(30\) | −1.88967e8 | + | 1.24911e8i | −0.259213 | + | 0.171346i | ||||
\(31\) | 7.40990e8i | 0.834915i | 0.908696 | + | 0.417457i | \(0.137079\pi\) | ||||
−0.908696 | + | 0.417457i | \(0.862921\pi\) | |||||||
\(32\) | −2.35548e8 | + | 1.04759e9i | −0.219371 | + | 0.975642i | ||||
\(33\) | −3.14913e8 | −0.243841 | ||||||||
\(34\) | −9.09818e8 | − | 1.37638e9i | −0.588954 | − | 0.890974i | ||||
\(35\) | 1.61502e9i | 0.878558i | ||||||||
\(36\) | 2.84314e8 | − | 6.67572e8i | 0.130612 | − | 0.306678i | ||||
\(37\) | 4.40061e9 | 1.71515 | 0.857575 | − | 0.514358i | \(-0.171970\pi\) | ||||
0.857575 | + | 0.514358i | \(0.171970\pi\) | |||||||
\(38\) | −8.64947e8 | + | 5.71749e8i | −0.287269 | + | 0.189891i | ||||
\(39\) | − | 2.44425e9i | − | 0.694637i | ||||||
\(40\) | 2.16825e9 | − | 3.97821e8i | 0.529358 | − | 0.0971243i | ||||
\(41\) | 3.32788e9 | 0.700590 | 0.350295 | − | 0.936639i | \(-0.386081\pi\) | ||||
0.350295 | + | 0.936639i | \(0.386081\pi\) | |||||||
\(42\) | −2.85274e9 | − | 4.31565e9i | −0.519716 | − | 0.786231i | ||||
\(43\) | − | 4.43899e9i | − | 0.702220i | −0.936334 | − | 0.351110i | \(-0.885804\pi\) | ||
0.936334 | − | 0.351110i | \(-0.114196\pi\) | |||||||
\(44\) | 2.81960e9 | + | 1.20085e9i | 0.388572 | + | 0.165490i | ||||
\(45\) | −1.48968e9 | −0.179398 | ||||||||
\(46\) | 1.06667e10 | − | 7.05091e9i | 1.12585 | − | 0.744215i | ||||
\(47\) | 1.18788e10i | 1.10201i | 0.834501 | + | 0.551006i | \(0.185756\pi\) | ||||
−0.834501 | + | 0.551006i | \(0.814244\pi\) | |||||||
\(48\) | −5.09127e9 | + | 4.89300e9i | −0.416274 | + | 0.400062i | ||||
\(49\) | −2.30429e10 | −1.66479 | ||||||||
\(50\) | 6.12048e9 | + | 9.25912e9i | 0.391711 | + | 0.592584i | ||||
\(51\) | − | 1.08504e10i | − | 0.616631i | ||||||
\(52\) | −9.32060e9 | + | 2.18848e10i | −0.471437 | + | 1.10694i | ||||
\(53\) | −1.52961e10 | −0.690124 | −0.345062 | − | 0.938580i | \(-0.612142\pi\) | ||||
−0.345062 | + | 0.938580i | \(0.612142\pi\) | |||||||
\(54\) | 3.98070e9 | − | 2.63133e9i | 0.160545 | − | 0.106124i | ||||
\(55\) | − | 6.29190e9i | − | 0.227303i | ||||||
\(56\) | 9.08550e9 | + | 4.95188e10i | 0.294592 | + | 1.60562i | ||||
\(57\) | −6.81863e9 | −0.198815 | ||||||||
\(58\) | −2.84718e10 | − | 4.30724e10i | −0.747905 | − | 1.13144i | ||||
\(59\) | − | 2.87986e10i | − | 0.682746i | −0.939928 | − | 0.341373i | \(-0.889108\pi\) | ||
0.939928 | − | 0.341373i | \(-0.110892\pi\) | |||||||
\(60\) | 1.33380e10 | + | 5.68056e9i | 0.285879 | + | 0.121754i | ||||
\(61\) | −5.04818e10 | −0.979842 | −0.489921 | − | 0.871767i | \(-0.662974\pi\) | ||||
−0.489921 | + | 0.871767i | \(0.662974\pi\) | |||||||
\(62\) | 3.95614e10 | − | 2.61509e10i | 0.696500 | − | 0.460402i | ||||
\(63\) | − | 3.40215e10i | − | 0.544140i | ||||||
\(64\) | 6.42435e10 | − | 2.43955e10i | 0.934866 | − | 0.355001i | ||||
\(65\) | 4.88357e10 | 0.647526 | ||||||||
\(66\) | 1.11139e10 | + | 1.68132e10i | 0.134463 | + | 0.203416i | ||||
\(67\) | 7.04181e10i | 0.778458i | 0.921141 | + | 0.389229i | \(0.127259\pi\) | ||||
−0.921141 | + | 0.389229i | \(0.872741\pi\) | |||||||
\(68\) | −4.13756e10 | + | 9.71502e10i | −0.418496 | + | 0.982631i | ||||
\(69\) | 8.40886e10 | 0.779189 | ||||||||
\(70\) | 8.62259e10 | − | 5.69972e10i | 0.732908 | − | 0.484469i | ||||
\(71\) | − | 4.83964e10i | − | 0.377801i | −0.981996 | − | 0.188900i | \(-0.939508\pi\) | ||
0.981996 | − | 0.188900i | \(-0.0604923\pi\) | |||||||
\(72\) | −4.56756e10 | + | 8.38036e9i | −0.327861 | + | 0.0601544i | ||||
\(73\) | 2.79013e10 | 0.184369 | 0.0921844 | − | 0.995742i | \(-0.470615\pi\) | ||||
0.0921844 | + | 0.995742i | \(0.470615\pi\) | |||||||
\(74\) | −1.55306e11 | − | 2.34948e11i | −0.945796 | − | 1.43081i | ||||
\(75\) | 7.29924e10i | 0.410119i | ||||||||
\(76\) | 6.10513e10 | + | 2.60013e10i | 0.316820 | + | 0.134932i | ||||
\(77\) | 1.43695e11 | 0.689444 | ||||||||
\(78\) | −1.30498e11 | + | 8.62622e10i | −0.579478 | + | 0.383048i | ||||
\(79\) | 4.03847e11i | 1.66132i | 0.556777 | + | 0.830662i | \(0.312038\pi\) | ||||
−0.556777 | + | 0.830662i | \(0.687962\pi\) | |||||||
\(80\) | −9.77613e10 | − | 1.01723e11i | −0.372930 | − | 0.388042i | ||||
\(81\) | 3.13811e10 | 0.111111 | ||||||||
\(82\) | −1.17447e11 | − | 1.77675e11i | −0.386331 | − | 0.584445i | ||||
\(83\) | − | 3.84526e11i | − | 1.17614i | −0.808812 | − | 0.588068i | \(-0.799889\pi\) | ||
0.808812 | − | 0.588068i | \(-0.200111\pi\) | |||||||
\(84\) | −1.29733e11 | + | 3.04615e11i | −0.369297 | + | 0.867112i | ||||
\(85\) | 2.16790e11 | 0.574811 | ||||||||
\(86\) | −2.36997e11 | + | 1.56660e11i | −0.585804 | + | 0.387229i | ||||
\(87\) | − | 3.39552e11i | − | 0.783053i | ||||||
\(88\) | −3.53958e10 | − | 1.92918e11i | −0.0762177 | − | 0.415411i | ||||
\(89\) | −4.78354e11 | −0.962519 | −0.481259 | − | 0.876578i | \(-0.659820\pi\) | ||||
−0.481259 | + | 0.876578i | \(0.659820\pi\) | |||||||
\(90\) | 5.25736e10 | + | 7.95338e10i | 0.0989265 | + | 0.149657i | ||||
\(91\) | 1.11532e12i | 1.96404i | ||||||||
\(92\) | −7.52895e11 | − | 3.20653e11i | −1.24167 | − | 0.528821i | ||||
\(93\) | 3.11874e11 | 0.482038 | ||||||||
\(94\) | 6.34210e11 | − | 4.19226e11i | 0.919318 | − | 0.607689i | ||||
\(95\) | − | 1.36235e11i | − | 0.185331i | ||||||
\(96\) | 4.40917e11 | + | 9.91393e10i | 0.563287 | + | 0.126654i | ||||
\(97\) | −1.21562e12 | −1.45938 | −0.729691 | − | 0.683777i | \(-0.760336\pi\) | ||||
−0.729691 | + | 0.683777i | \(0.760336\pi\) | |||||||
\(98\) | 8.13227e11 | + | 1.23026e12i | 0.918026 | + | 1.38880i | ||||
\(99\) | 1.32543e11i | 0.140782i | ||||||||
\(100\) | 2.78340e11 | − | 6.53544e11i | 0.278340 | − | 0.653544i | ||||
\(101\) | 1.52254e12 | 1.43430 | 0.717151 | − | 0.696918i | \(-0.245446\pi\) | ||||
0.717151 | + | 0.696918i | \(0.245446\pi\) | |||||||
\(102\) | −5.79303e11 | + | 3.82932e11i | −0.514404 | + | 0.340033i | ||||
\(103\) | − | 1.02348e12i | − | 0.857147i | −0.903507 | − | 0.428574i | \(-0.859016\pi\) | ||
0.903507 | − | 0.428574i | \(-0.140984\pi\) | |||||||
\(104\) | 1.49737e12 | − | 2.74731e11i | 1.18339 | − | 0.217124i | ||||
\(105\) | 6.79744e11 | 0.507236 | ||||||||
\(106\) | 5.39830e11 | + | 8.16660e11i | 0.380559 | + | 0.575713i | ||||
\(107\) | − | 2.33951e12i | − | 1.55891i | −0.626456 | − | 0.779457i | \(-0.715495\pi\) | ||
0.626456 | − | 0.779457i | \(-0.284505\pi\) | |||||||
\(108\) | −2.80973e11 | − | 1.19665e11i | −0.177061 | − | 0.0754090i | ||||
\(109\) | −3.01919e12 | −1.80025 | −0.900123 | − | 0.435637i | \(-0.856523\pi\) | ||||
−0.900123 | + | 0.435637i | \(0.856523\pi\) | |||||||
\(110\) | −3.35924e11 | + | 2.22053e11i | −0.189620 | + | 0.125343i | ||||
\(111\) | − | 1.85216e12i | − | 0.990243i | ||||||
\(112\) | 2.32316e12 | − | 2.23269e12i | 1.17699 | − | 1.13115i | ||||
\(113\) | −4.21569e11 | −0.202487 | −0.101244 | − | 0.994862i | \(-0.532282\pi\) | ||||
−0.101244 | + | 0.994862i | \(0.532282\pi\) | |||||||
\(114\) | 2.40643e11 | + | 3.64046e11i | 0.109634 | + | 0.165855i | ||||
\(115\) | 1.68008e12i | 0.726343i | ||||||||
\(116\) | −1.29481e12 | + | 3.04021e12i | −0.531443 | + | 1.24783i | ||||
\(117\) | −1.02876e12 | −0.401049 | ||||||||
\(118\) | −1.53755e12 | + | 1.01636e12i | −0.569559 | + | 0.376491i | ||||
\(119\) | 4.95107e12i | 1.74348i | ||||||||
\(120\) | −1.67438e11 | − | 9.12591e11i | −0.0560747 | − | 0.305625i | ||||
\(121\) | 2.57861e12 | 0.821625 | ||||||||
\(122\) | 1.78160e12 | + | 2.69522e12i | 0.540320 | + | 0.817401i | ||||
\(123\) | − | 1.40066e12i | − | 0.404486i | ||||||
\(124\) | −2.79239e12 | − | 1.18926e12i | −0.768151 | − | 0.327150i | ||||
\(125\) | −3.51142e12 | −0.920499 | ||||||||
\(126\) | −1.81641e12 | + | 1.20068e12i | −0.453931 | + | 0.300058i | ||||
\(127\) | − | 1.97980e11i | − | 0.0471846i | −0.999722 | − | 0.0235923i | \(-0.992490\pi\) | ||
0.999722 | − | 0.0235923i | \(-0.00751035\pi\) | |||||||
\(128\) | −3.56975e12 | − | 2.56899e12i | −0.811667 | − | 0.584121i | ||||
\(129\) | −1.86832e12 | −0.405427 | ||||||||
\(130\) | −1.72351e12 | − | 2.60733e12i | −0.357069 | − | 0.540178i | ||||
\(131\) | 2.26629e12i | 0.448423i | 0.974541 | + | 0.224212i | \(0.0719807\pi\) | ||||
−0.974541 | + | 0.224212i | \(0.928019\pi\) | |||||||
\(132\) | 5.05423e11 | − | 1.18674e12i | 0.0955458 | − | 0.224342i | ||||
\(133\) | 3.11136e12 | 0.562135 | ||||||||
\(134\) | 3.75961e12 | − | 2.48519e12i | 0.649403 | − | 0.429270i | ||||
\(135\) | 6.26988e11i | 0.103575i | ||||||||
\(136\) | 6.64707e12 | − | 1.21957e12i | 1.05050 | − | 0.192741i | ||||
\(137\) | 1.06046e13 | 1.60388 | 0.801939 | − | 0.597406i | \(-0.203802\pi\) | ||||
0.801939 | + | 0.597406i | \(0.203802\pi\) | |||||||
\(138\) | −2.96765e12 | − | 4.48948e12i | −0.429673 | − | 0.650013i | ||||
\(139\) | − | 1.02219e12i | − | 0.141723i | −0.997486 | − | 0.0708616i | \(-0.977425\pi\) | ||
0.997486 | − | 0.0708616i | \(-0.0225749\pi\) | |||||||
\(140\) | −6.08615e12 | − | 2.59205e12i | −0.808304 | − | 0.344251i | ||||
\(141\) | 4.99966e12 | 0.636247 | ||||||||
\(142\) | −2.58388e12 | + | 1.70800e12i | −0.315168 | + | 0.208333i | ||||
\(143\) | − | 4.34512e12i | − | 0.508143i | ||||||
\(144\) | 2.05940e12 | + | 2.14286e12i | 0.230976 | + | 0.240336i | ||||
\(145\) | 6.78420e12 | 0.729946 | ||||||||
\(146\) | −9.84691e11 | − | 1.48965e12i | −0.101668 | − | 0.153804i | ||||
\(147\) | 9.69847e12i | 0.961168i | ||||||||
\(148\) | −7.06281e12 | + | 1.65835e13i | −0.672059 | + | 1.57800i | ||||
\(149\) | 4.63546e12 | 0.423619 | 0.211809 | − | 0.977311i | \(-0.432064\pi\) | ||||
0.211809 | + | 0.977311i | \(0.432064\pi\) | |||||||
\(150\) | 3.89706e12 | − | 2.57604e12i | 0.342128 | − | 0.226154i | ||||
\(151\) | − | 7.67283e12i | − | 0.647283i | −0.946180 | − | 0.323641i | \(-0.895093\pi\) | ||
0.946180 | − | 0.323641i | \(-0.104907\pi\) | |||||||
\(152\) | −7.66407e11 | − | 4.17716e12i | −0.0621438 | − | 0.338703i | ||||
\(153\) | −4.56681e12 | −0.356012 | ||||||||
\(154\) | −5.07129e12 | − | 7.67189e12i | −0.380184 | − | 0.575146i | ||||
\(155\) | 6.23119e12i | 0.449346i | ||||||||
\(156\) | 9.21106e12 | + | 3.92293e12i | 0.639090 | + | 0.272184i | ||||
\(157\) | −6.58343e12 | −0.439596 | −0.219798 | − | 0.975545i | \(-0.570540\pi\) | ||||
−0.219798 | + | 0.975545i | \(0.570540\pi\) | |||||||
\(158\) | 2.15614e13 | − | 1.42525e13i | 1.38590 | − | 0.916114i | ||||
\(159\) | 6.43797e12i | 0.398443i | ||||||||
\(160\) | −1.98079e12 | + | 8.80945e12i | −0.118064 | + | 0.525084i | ||||
\(161\) | −3.83699e13 | −2.20310 | ||||||||
\(162\) | −1.10750e12 | − | 1.67543e12i | −0.0612707 | − | 0.0926908i | ||||
\(163\) | − | 3.43265e12i | − | 0.183022i | −0.995804 | − | 0.0915112i | \(-0.970830\pi\) | ||
0.995804 | − | 0.0915112i | \(-0.0291697\pi\) | |||||||
\(164\) | −5.34112e12 | + | 1.25410e13i | −0.274517 | + | 0.644568i | ||||
\(165\) | −2.64819e12 | −0.131234 | ||||||||
\(166\) | −2.05298e13 | + | 1.35707e13i | −0.981153 | + | 0.648564i | ||||
\(167\) | − | 2.48216e13i | − | 1.14428i | −0.820157 | − | 0.572139i | \(-0.806114\pi\) | ||
0.820157 | − | 0.572139i | \(-0.193886\pi\) | |||||||
\(168\) | 2.08419e13 | − | 3.82398e12i | 0.927004 | − | 0.170083i | ||||
\(169\) | 1.04273e13 | 0.447562 | ||||||||
\(170\) | −7.65092e12 | − | 1.15744e13i | −0.316971 | − | 0.479517i | ||||
\(171\) | 2.86988e12i | 0.114786i | ||||||||
\(172\) | 1.67282e13 | + | 7.12441e12i | 0.646067 | + | 0.275156i | ||||
\(173\) | −2.52781e13 | −0.942903 | −0.471452 | − | 0.881892i | \(-0.656270\pi\) | ||||
−0.471452 | + | 0.881892i | \(0.656270\pi\) | |||||||
\(174\) | −1.81287e13 | + | 1.19834e13i | −0.653236 | + | 0.431803i | ||||
\(175\) | − | 3.33066e13i | − | 1.15958i | ||||||
\(176\) | −9.05071e12 | + | 8.69823e12i | −0.304513 | + | 0.292654i | ||||
\(177\) | −1.21210e13 | −0.394184 | ||||||||
\(178\) | 1.68820e13 | + | 2.55393e13i | 0.530767 | + | 0.802950i | ||||
\(179\) | 3.68721e13i | 1.12093i | 0.828177 | + | 0.560467i | \(0.189378\pi\) | ||||
−0.828177 | + | 0.560467i | \(0.810622\pi\) | |||||||
\(180\) | 2.39088e12 | − | 5.61380e12i | 0.0702947 | − | 0.165052i | ||||
\(181\) | 5.27764e12 | 0.150096 | 0.0750479 | − | 0.997180i | \(-0.476089\pi\) | ||||
0.0750479 | + | 0.997180i | \(0.476089\pi\) | |||||||
\(182\) | 5.95467e13 | − | 3.93617e13i | 1.63844 | − | 1.08304i | ||||
\(183\) | 2.12472e13i | 0.565712i | ||||||||
\(184\) | 9.45146e12 | + | 5.15134e13i | 0.243552 | + | 1.32744i | ||||
\(185\) | 3.70059e13 | 0.923084 | ||||||||
\(186\) | −1.10066e13 | − | 1.66509e13i | −0.265813 | − | 0.402125i | ||||
\(187\) | − | 1.92887e13i | − | 0.451080i | ||||||
\(188\) | −4.47649e13 | − | 1.90651e13i | −1.01389 | − | 0.431809i | ||||
\(189\) | −1.43193e13 | −0.314159 | ||||||||
\(190\) | −7.27358e12 | + | 4.80800e12i | −0.154606 | + | 0.102198i | ||||
\(191\) | − | 4.43177e13i | − | 0.912803i | −0.889774 | − | 0.456401i | \(-0.849138\pi\) | ||
0.889774 | − | 0.456401i | \(-0.150862\pi\) | |||||||
\(192\) | −1.02678e13 | − | 2.70393e13i | −0.204960 | − | 0.539745i | ||||
\(193\) | 3.90632e13 | 0.755831 | 0.377915 | − | 0.925840i | \(-0.376641\pi\) | ||||
0.377915 | + | 0.925840i | \(0.376641\pi\) | |||||||
\(194\) | 4.29017e13 | + | 6.49020e13i | 0.804755 | + | 1.21744i | ||||
\(195\) | − | 2.05544e13i | − | 0.373849i | ||||||
\(196\) | 3.69830e13 | − | 8.68362e13i | 0.652327 | − | 1.53167i | ||||
\(197\) | 3.41818e13 | 0.584787 | 0.292394 | − | 0.956298i | \(-0.405548\pi\) | ||||
0.292394 | + | 0.956298i | \(0.405548\pi\) | |||||||
\(198\) | 7.07646e12 | − | 4.67770e12i | 0.117442 | − | 0.0776320i | ||||
\(199\) | 5.01748e12i | 0.0807918i | 0.999184 | + | 0.0403959i | \(0.0128619\pi\) | ||||
−0.999184 | + | 0.0403959i | \(0.987138\pi\) | |||||||
\(200\) | −4.47158e13 | + | 8.20426e12i | −0.698685 | + | 0.128192i | ||||
\(201\) | 2.96381e13 | 0.449443 | ||||||||
\(202\) | −5.37334e13 | − | 8.12883e13i | −0.790926 | − | 1.19652i | ||||
\(203\) | 1.54939e14i | 2.21403i | ||||||||
\(204\) | 4.08894e13 | + | 1.74145e13i | 0.567322 | + | 0.241619i | ||||
\(205\) | 2.79851e13 | 0.377054 | ||||||||
\(206\) | −5.46434e13 | + | 3.61205e13i | −0.715047 | + | 0.472662i | ||||
\(207\) | − | 3.53919e13i | − | 0.449865i | ||||||
\(208\) | −6.75129e13 | − | 7.02486e13i | −0.833694 | − | 0.867477i | ||||
\(209\) | −1.21214e13 | −0.145437 | ||||||||
\(210\) | −2.39895e13 | − | 3.62915e13i | −0.279708 | − | 0.423145i | ||||
\(211\) | 9.35524e13i | 1.06013i | 0.847956 | + | 0.530066i | \(0.177833\pi\) | ||||
−0.847956 | + | 0.530066i | \(0.822167\pi\) | |||||||
\(212\) | 2.45498e13 | − | 5.76430e13i | 0.270416 | − | 0.634938i | ||||
\(213\) | −2.03695e13 | −0.218123 | ||||||||
\(214\) | −1.24906e14 | + | 8.25657e13i | −1.30047 | + | 0.859641i | ||||
\(215\) | − | 3.73287e13i | − | 0.377930i | ||||||
\(216\) | 3.52720e12 | + | 1.92243e13i | 0.0347302 | + | 0.189290i | ||||
\(217\) | −1.42309e14 | −1.36293 | ||||||||
\(218\) | 1.06553e14 | + | 1.61194e14i | 0.992720 | + | 1.50180i | ||||
\(219\) | − | 1.17433e13i | − | 0.106445i | ||||||
\(220\) | 2.37108e13 | + | 1.00983e13i | 0.209127 | + | 0.0890658i | ||||
\(221\) | 1.49713e14 | 1.28500 | ||||||||
\(222\) | −9.88869e13 | + | 6.53664e13i | −0.826077 | + | 0.546055i | ||||
\(223\) | − | 1.78398e13i | − | 0.145064i | −0.997366 | − | 0.0725320i | \(-0.976892\pi\) | ||
0.997366 | − | 0.0725320i | \(-0.0231080\pi\) | |||||||
\(224\) | −2.01192e14 | − | 4.52375e13i | −1.59266 | − | 0.358105i | ||||
\(225\) | 3.07217e13 | 0.236782 | ||||||||
\(226\) | 1.48780e13 | + | 2.25075e13i | 0.111659 | + | 0.168919i | ||||
\(227\) | − | 1.36751e13i | − | 0.0999485i | −0.998751 | − | 0.0499742i | \(-0.984086\pi\) | ||
0.998751 | − | 0.0499742i | \(-0.0159139\pi\) | |||||||
\(228\) | 1.09437e13 | − | 2.56958e13i | 0.0779029 | − | 0.182916i | ||||
\(229\) | −9.88118e13 | −0.685166 | −0.342583 | − | 0.939488i | \(-0.611302\pi\) | ||||
−0.342583 | + | 0.939488i | \(0.611302\pi\) | |||||||
\(230\) | 8.96991e13 | − | 5.92931e13i | 0.605928 | − | 0.400532i | ||||
\(231\) | − | 6.04797e13i | − | 0.398050i | ||||||
\(232\) | 2.08013e14 | − | 3.81653e13i | 1.33402 | − | 0.244760i | ||||
\(233\) | −7.18845e13 | −0.449262 | −0.224631 | − | 0.974444i | \(-0.572118\pi\) | ||||
−0.224631 | + | 0.974444i | \(0.572118\pi\) | |||||||
\(234\) | 3.63068e13 | + | 5.49252e13i | 0.221153 | + | 0.334562i | ||||
\(235\) | 9.98924e13i | 0.593096i | ||||||||
\(236\) | 1.08526e14 | + | 4.62207e13i | 0.628150 | + | 0.267525i | ||||
\(237\) | 1.69974e14 | 0.959166 | ||||||||
\(238\) | 2.64337e14 | − | 1.74733e14i | 1.45444 | − | 0.961419i | ||||
\(239\) | − | 2.17724e14i | − | 1.16820i | −0.811680 | − | 0.584102i | \(-0.801447\pi\) | ||
0.811680 | − | 0.584102i | \(-0.198553\pi\) | |||||||
\(240\) | −4.28139e13 | + | 4.11466e13i | −0.224036 | + | 0.215311i | ||||
\(241\) | −4.26407e13 | −0.217632 | −0.108816 | − | 0.994062i | \(-0.534706\pi\) | ||||
−0.108816 | + | 0.994062i | \(0.534706\pi\) | |||||||
\(242\) | −9.10041e13 | − | 1.37672e14i | −0.453074 | − | 0.685414i | ||||
\(243\) | − | 1.32079e13i | − | 0.0641500i | ||||||
\(244\) | 8.10215e13 | − | 1.90239e14i | 0.383938 | − | 0.901488i | ||||
\(245\) | −1.93774e14 | −0.895981 | ||||||||
\(246\) | −7.47814e13 | + | 4.94321e13i | −0.337429 | + | 0.223048i | ||||
\(247\) | − | 9.40826e13i | − | 0.414312i | ||||||
\(248\) | 3.50543e13 | + | 1.91057e14i | 0.150671 | + | 0.821207i | ||||
\(249\) | −1.61843e14 | −0.679042 | ||||||||
\(250\) | 1.23925e14 | + | 1.87475e14i | 0.507596 | + | 0.767896i | ||||
\(251\) | − | 2.51073e14i | − | 1.00406i | −0.864851 | − | 0.502028i | \(-0.832588\pi\) | ||
0.864851 | − | 0.502028i | \(-0.167412\pi\) | |||||||
\(252\) | 1.28209e14 | + | 5.46033e13i | 0.500627 | + | 0.213214i | ||||
\(253\) | 1.49484e14 | 0.569994 | ||||||||
\(254\) | −1.05702e13 | + | 6.98710e12i | −0.0393622 | + | 0.0260193i | ||||
\(255\) | − | 9.12442e13i | − | 0.331867i | ||||||
\(256\) | −1.11751e13 | + | 2.81253e14i | −0.0397018 | + | 0.999212i | ||||
\(257\) | 2.52884e13 | 0.0877652 | 0.0438826 | − | 0.999037i | \(-0.486027\pi\) | ||||
0.0438826 | + | 0.999037i | \(0.486027\pi\) | |||||||
\(258\) | 6.59365e13 | + | 9.97493e13i | 0.223567 | + | 0.338214i | ||||
\(259\) | 8.45147e14i | 2.79984i | ||||||||
\(260\) | −7.83795e13 | + | 1.84036e14i | −0.253725 | + | 0.595747i | ||||
\(261\) | −1.42914e14 | −0.452096 | ||||||||
\(262\) | 1.20997e14 | − | 7.99817e13i | 0.374082 | − | 0.247277i | ||||
\(263\) | − | 2.96423e14i | − | 0.895730i | −0.894101 | − | 0.447865i | \(-0.852184\pi\) | ||
0.894101 | − | 0.447865i | \(-0.147816\pi\) | |||||||
\(264\) | −8.11971e13 | + | 1.48977e13i | −0.239837 | + | 0.0440043i | ||||
\(265\) | −1.28630e14 | −0.371420 | ||||||||
\(266\) | −1.09806e14 | − | 1.66115e14i | −0.309981 | − | 0.468943i | ||||
\(267\) | 2.01334e14i | 0.555711i | ||||||||
\(268\) | −2.65368e14 | − | 1.13018e14i | −0.716209 | − | 0.305029i | ||||
\(269\) | −2.90107e14 | −0.765676 | −0.382838 | − | 0.923816i | \(-0.625053\pi\) | ||||
−0.382838 | + | 0.923816i | \(0.625053\pi\) | |||||||
\(270\) | 3.34749e13 | − | 2.21276e13i | 0.0864044 | − | 0.0571152i | ||||
\(271\) | − | 4.86728e14i | − | 1.22877i | −0.789007 | − | 0.614384i | \(-0.789404\pi\) | ||
0.789007 | − | 0.614384i | \(-0.210596\pi\) | |||||||
\(272\) | −2.99701e14 | − | 3.11845e14i | −0.740072 | − | 0.770062i | ||||
\(273\) | 4.69424e14 | 1.13394 | ||||||||
\(274\) | −3.74257e14 | − | 5.66179e14i | −0.884436 | − | 1.33798i | ||||
\(275\) | 1.29758e14i | 0.300011i | ||||||||
\(276\) | −1.34959e14 | + | 3.16885e14i | −0.305315 | + | 0.716881i | ||||
\(277\) | −2.87923e14 | −0.637379 | −0.318689 | − | 0.947859i | \(-0.603243\pi\) | ||||
−0.318689 | + | 0.947859i | \(0.603243\pi\) | |||||||
\(278\) | −5.45744e13 | + | 3.60749e13i | −0.118228 | + | 0.0781513i | ||||
\(279\) | − | 1.31264e14i | − | 0.278305i | ||||||
\(280\) | 7.64025e13 | + | 4.16418e14i | 0.158547 | + | 0.864134i | ||||
\(281\) | 8.35003e14 | 1.69609 | 0.848047 | − | 0.529920i | \(-0.177778\pi\) | ||||
0.848047 | + | 0.529920i | \(0.177778\pi\) | |||||||
\(282\) | −1.76448e14 | − | 2.66931e14i | −0.350850 | − | 0.530768i | ||||
\(283\) | 5.74546e13i | 0.111842i | 0.998435 | + | 0.0559212i | \(0.0178096\pi\) | ||||
−0.998435 | + | 0.0559212i | \(0.982190\pi\) | |||||||
\(284\) | 1.82380e14 | + | 7.76744e13i | 0.347590 | + | 0.148036i | ||||
\(285\) | −5.73398e13 | −0.107001 | ||||||||
\(286\) | −2.31986e14 | + | 1.53348e14i | −0.423901 | + | 0.280208i | ||||
\(287\) | 6.39127e14i | 1.14366i | ||||||||
\(288\) | 4.17266e13 | − | 1.85577e14i | 0.0731237 | − | 0.325214i | ||||
\(289\) | 8.19760e13 | 0.140702 | ||||||||
\(290\) | −2.39427e14 | − | 3.62208e14i | −0.402518 | − | 0.608933i | ||||
\(291\) | 5.11642e14i | 0.842574i | ||||||||
\(292\) | −4.47806e13 | + | 1.05145e14i | −0.0722425 | + | 0.169626i | ||||
\(293\) | 2.19620e14 | 0.347109 | 0.173554 | − | 0.984824i | \(-0.444475\pi\) | ||||
0.173554 | + | 0.984824i | \(0.444475\pi\) | |||||||
\(294\) | 5.17801e14 | − | 3.42278e14i | 0.801823 | − | 0.530023i | ||||
\(295\) | − | 2.42176e14i | − | 0.367450i | ||||||
\(296\) | 1.13465e15 | − | 2.08181e14i | 1.68699 | − | 0.309522i | ||||
\(297\) | 5.57858e13 | 0.0812803 | ||||||||
\(298\) | −1.63594e14 | − | 2.47487e14i | −0.233599 | − | 0.353390i | ||||
\(299\) | 1.16024e15i | 1.62376i | ||||||||
\(300\) | −2.75069e14 | − | 1.17150e14i | −0.377324 | − | 0.160700i | ||||
\(301\) | 8.52518e14 | 1.14632 | ||||||||
\(302\) | −4.09652e14 | + | 2.70789e14i | −0.539975 | + | 0.356935i | ||||
\(303\) | − | 6.40820e14i | − | 0.828095i | ||||||
\(304\) | −1.95970e14 | + | 1.88338e14i | −0.248284 | + | 0.238615i | ||||
\(305\) | −4.24516e14 | −0.527345 | ||||||||
\(306\) | 1.61172e14 | + | 2.43822e14i | 0.196318 | + | 0.296991i | ||||
\(307\) | − | 9.85856e14i | − | 1.17756i | −0.808293 | − | 0.588781i | \(-0.799608\pi\) | ||
0.808293 | − | 0.588781i | \(-0.200392\pi\) | |||||||
\(308\) | −2.30626e14 | + | 5.41511e14i | −0.270149 | + | 0.634312i | ||||
\(309\) | −4.30770e14 | −0.494874 | ||||||||
\(310\) | 3.32683e14 | − | 2.19911e14i | 0.374852 | − | 0.247786i | ||||
\(311\) | − | 4.46244e14i | − | 0.493185i | −0.969119 | − | 0.246593i | \(-0.920689\pi\) | ||
0.969119 | − | 0.246593i | \(-0.0793110\pi\) | |||||||
\(312\) | −1.15631e14 | − | 6.30225e14i | −0.125356 | − | 0.683232i | ||||
\(313\) | 1.29474e15 | 1.37694 | 0.688471 | − | 0.725264i | \(-0.258282\pi\) | ||||
0.688471 | + | 0.725264i | \(0.258282\pi\) | |||||||
\(314\) | 2.32342e14 | + | 3.51489e14i | 0.242409 | + | 0.366719i | ||||
\(315\) | − | 2.86097e14i | − | 0.292853i | ||||||
\(316\) | −1.52188e15 | − | 6.48160e14i | −1.52848 | − | 0.650968i | ||||
\(317\) | 2.35093e14 | 0.231678 | 0.115839 | − | 0.993268i | \(-0.463044\pi\) | ||||
0.115839 | + | 0.993268i | \(0.463044\pi\) | |||||||
\(318\) | 3.43723e14 | − | 2.27208e14i | 0.332388 | − | 0.219716i | ||||
\(319\) | − | 6.03619e14i | − | 0.572821i | ||||||
\(320\) | 5.40242e14 | − | 2.05148e14i | 0.503139 | − | 0.191059i | ||||
\(321\) | −9.84672e14 | −0.900039 | ||||||||
\(322\) | 1.35415e15 | + | 2.04856e15i | 1.21487 | + | 1.83787i | ||||
\(323\) | − | 4.17648e14i | − | 0.367786i | ||||||
\(324\) | −5.03655e13 | + | 1.18258e14i | −0.0435374 | + | 0.102226i | ||||
\(325\) | −1.00714e15 | −0.854652 | ||||||||
\(326\) | −1.83269e14 | + | 1.21145e14i | −0.152680 | + | 0.100925i | ||||
\(327\) | 1.27074e15i | 1.03937i | ||||||||
\(328\) | 8.58060e14 | − | 1.57433e14i | 0.689088 | − | 0.126431i | ||||
\(329\) | −2.28136e15 | −1.79895 | ||||||||
\(330\) | 9.34596e13 | + | 1.41387e14i | 0.0723670 | + | 0.109477i | ||||
\(331\) | − | 1.65323e14i | − | 0.125709i | −0.998023 | − | 0.0628544i | \(-0.979980\pi\) | ||
0.998023 | − | 0.0628544i | \(-0.0200204\pi\) | |||||||
\(332\) | 1.44907e15 | + | 6.17151e14i | 1.08209 | + | 0.460853i | ||||
\(333\) | −7.79554e14 | −0.571717 | ||||||||
\(334\) | −1.32522e15 | + | 8.76002e14i | −0.954576 | + | 0.630996i | ||||
\(335\) | 5.92165e14i | 0.418962i | ||||||||
\(336\) | −9.39712e14 | − | 9.77791e14i | −0.653069 | − | 0.679533i | ||||
\(337\) | −1.71469e15 | −1.17060 | −0.585298 | − | 0.810819i | \(-0.699022\pi\) | ||||
−0.585298 | + | 0.810819i | \(0.699022\pi\) | |||||||
\(338\) | −3.68000e14 | − | 5.56714e14i | −0.246802 | − | 0.373364i | ||||
\(339\) | 1.77434e14i | 0.116906i | ||||||||
\(340\) | −3.47939e14 | + | 8.16963e14i | −0.225232 | + | 0.528846i | ||||
\(341\) | 5.54416e14 | 0.352622 | ||||||||
\(342\) | 1.53223e14 | − | 1.01284e14i | 0.0957562 | − | 0.0632969i | ||||
\(343\) | − | 1.76719e15i | − | 1.08522i | ||||||
\(344\) | −2.09997e14 | − | 1.14455e15i | −0.126725 | − | 0.690691i | ||||
\(345\) | 7.07125e14 | 0.419355 | ||||||||
\(346\) | 8.92111e14 | + | 1.34959e15i | 0.519951 | + | 0.786586i | ||||
\(347\) | 1.54474e15i | 0.884870i | 0.896801 | + | 0.442435i | \(0.145885\pi\) | ||||
−0.896801 | + | 0.442435i | \(0.854115\pi\) | |||||||
\(348\) | 1.27959e15 | + | 5.44969e14i | 0.720436 | + | 0.306829i | ||||
\(349\) | 7.96922e14 | 0.441025 | 0.220513 | − | 0.975384i | \(-0.429227\pi\) | ||||
0.220513 | + | 0.975384i | \(0.429227\pi\) | |||||||
\(350\) | −1.77824e15 | + | 1.17545e15i | −0.967345 | + | 0.639437i | ||||
\(351\) | 4.32991e14i | 0.231546i | ||||||||
\(352\) | 7.83815e14 | + | 1.76239e14i | 0.412057 | + | 0.0926502i | ||||
\(353\) | −5.85455e14 | −0.302583 | −0.151292 | − | 0.988489i | \(-0.548343\pi\) | ||||
−0.151292 | + | 0.988489i | \(0.548343\pi\) | |||||||
\(354\) | 4.27773e14 | + | 6.47139e14i | 0.217367 | + | 0.328835i | ||||
\(355\) | − | 4.06979e14i | − | 0.203330i | ||||||
\(356\) | 7.67740e14 | − | 1.80266e15i | 0.377150 | − | 0.885551i | ||||
\(357\) | 2.08385e15 | 1.00660 | ||||||||
\(358\) | 1.96860e15 | − | 1.30129e15i | 0.935103 | − | 0.618123i | ||||
\(359\) | − | 2.30396e15i | − | 1.07624i | −0.842868 | − | 0.538120i | \(-0.819135\pi\) | ||
0.842868 | − | 0.538120i | \(-0.180865\pi\) | |||||||
\(360\) | −3.84099e14 | + | 7.04728e13i | −0.176453 | + | 0.0323748i | ||||
\(361\) | 1.95086e15 | 0.881418 | ||||||||
\(362\) | −1.86258e14 | − | 2.81773e14i | −0.0827682 | − | 0.125213i | ||||
\(363\) | − | 1.08531e15i | − | 0.474365i | ||||||
\(364\) | −4.20303e15 | − | 1.79004e15i | −1.80698 | − | 0.769583i | ||||
\(365\) | 2.34630e14 | 0.0992262 | ||||||||
\(366\) | 1.13439e15 | − | 7.49854e14i | 0.471927 | − | 0.311954i | ||||
\(367\) | 3.94215e15i | 1.61338i | 0.590975 | + | 0.806690i | \(0.298743\pi\) | ||||
−0.590975 | + | 0.806690i | \(0.701257\pi\) | |||||||
\(368\) | 2.41674e15 | − | 2.32262e15i | 0.973067 | − | 0.935171i | ||||
\(369\) | −5.89524e14 | −0.233530 | ||||||||
\(370\) | −1.30601e15 | − | 1.97574e15i | −0.509022 | − | 0.770052i | ||||
\(371\) | − | 2.93766e15i | − | 1.12657i | ||||||
\(372\) | −5.00546e14 | + | 1.17529e15i | −0.188880 | + | 0.443492i | ||||
\(373\) | 9.62006e14 | 0.357211 | 0.178605 | − | 0.983921i | \(-0.442841\pi\) | ||||
0.178605 | + | 0.983921i | \(0.442841\pi\) | |||||||
\(374\) | −1.02982e15 | + | 6.80735e14i | −0.376298 | + | 0.248741i | ||||
\(375\) | 1.47792e15i | 0.531450i | ||||||||
\(376\) | 5.61956e14 | + | 3.06284e15i | 0.198873 | + | 1.08392i | ||||
\(377\) | 4.68509e15 | 1.63181 | ||||||||
\(378\) | 5.05354e14 | + | 7.64504e14i | 0.173239 | + | 0.262077i | ||||
\(379\) | − | 7.38046e14i | − | 0.249028i | −0.992218 | − | 0.124514i | \(-0.960263\pi\) | ||
0.992218 | − | 0.124514i | \(-0.0397372\pi\) | |||||||
\(380\) | 5.13397e14 | + | 2.18653e14i | 0.170511 | + | 0.0726194i | ||||
\(381\) | −8.33276e13 | −0.0272420 | ||||||||
\(382\) | −2.36612e15 | + | 1.56406e15i | −0.761476 | + | 0.503352i | ||||
\(383\) | 6.59297e14i | 0.208876i | 0.994531 | + | 0.104438i | \(0.0333044\pi\) | ||||
−0.994531 | + | 0.104438i | \(0.966696\pi\) | |||||||
\(384\) | −1.08126e15 | + | 1.50246e15i | −0.337242 | + | 0.468616i | ||||
\(385\) | 1.20838e15 | 0.371054 | ||||||||
\(386\) | −1.37862e15 | − | 2.08558e15i | −0.416792 | − | 0.630527i | ||||
\(387\) | 7.86353e14i | 0.234073i | ||||||||
\(388\) | 1.95103e15 | − | 4.58103e15i | 0.571839 | − | 1.34268i | ||||
\(389\) | −1.71529e15 | −0.495040 | −0.247520 | − | 0.968883i | \(-0.579616\pi\) | ||||
−0.247520 | + | 0.968883i | \(0.579616\pi\) | |||||||
\(390\) | −1.09740e15 | + | 7.25403e14i | −0.311872 | + | 0.206154i | ||||
\(391\) | 5.15050e15i | 1.44142i | ||||||||
\(392\) | −5.94137e15 | + | 1.09010e15i | −1.63746 | + | 0.300434i | ||||
\(393\) | 9.53856e14 | 0.258897 | ||||||||
\(394\) | −1.20634e15 | − | 1.82496e15i | −0.322473 | − | 0.487839i | ||||
\(395\) | 3.39606e15i | 0.894114i | ||||||||
\(396\) | −4.99483e14 | − | 2.12727e14i | −0.129524 | − | 0.0551634i | ||||
\(397\) | −5.33258e15 | −1.36205 | −0.681027 | − | 0.732259i | \(-0.738466\pi\) | ||||
−0.681027 | + | 0.732259i | \(0.738466\pi\) | |||||||
\(398\) | 2.67883e14 | − | 1.77076e14i | 0.0673979 | − | 0.0445515i | ||||
\(399\) | − | 1.30954e15i | − | 0.324549i | ||||||
\(400\) | 2.01613e15 | + | 2.09783e15i | 0.492219 | + | 0.512165i | ||||
\(401\) | −3.28891e15 | −0.791017 | −0.395509 | − | 0.918462i | \(-0.629432\pi\) | ||||
−0.395509 | + | 0.918462i | \(0.629432\pi\) | |||||||
\(402\) | −1.04599e15 | − | 1.58238e15i | −0.247839 | − | 0.374933i | ||||
\(403\) | 4.30319e15i | 1.00452i | ||||||||
\(404\) | −2.44362e15 | + | 5.73764e15i | −0.562012 | + | 1.31961i | ||||
\(405\) | 2.63892e14 | 0.0597993 | ||||||||
\(406\) | 8.27215e15 | − | 5.46808e15i | 1.84698 | − | 1.22090i | ||||
\(407\) | − | 3.29258e15i | − | 0.724385i | ||||||
\(408\) | −5.13305e14 | − | 2.79767e15i | −0.111279 | − | 0.606507i | ||||
\(409\) | −3.11334e15 | −0.665100 | −0.332550 | − | 0.943086i | \(-0.607909\pi\) | ||||
−0.332550 | + | 0.943086i | \(0.607909\pi\) | |||||||
\(410\) | −9.87646e14 | − | 1.49412e15i | −0.207921 | − | 0.314545i | ||||
\(411\) | − | 4.46335e15i | − | 0.925999i | ||||||
\(412\) | 3.85694e15 | + | 1.64265e15i | 0.788605 | + | 0.335862i | ||||
\(413\) | 5.53084e15 | 1.11453 | ||||||||
\(414\) | −1.88957e15 | + | 1.24905e15i | −0.375285 | + | 0.248072i | ||||
\(415\) | − | 3.23359e15i | − | 0.632989i | ||||||
\(416\) | −1.36791e15 | + | 6.08371e15i | −0.263935 | + | 1.17384i | ||||
\(417\) | −4.30226e14 | −0.0818239 | ||||||||
\(418\) | 4.27788e14 | + | 6.47162e14i | 0.0801994 | + | 0.121326i | ||||
\(419\) | − | 5.08845e15i | − | 0.940376i | −0.882566 | − | 0.470188i | \(-0.844186\pi\) | ||
0.882566 | − | 0.470188i | \(-0.155814\pi\) | |||||||
\(420\) | −1.09096e15 | + | 2.56159e15i | −0.198754 | + | 0.466675i | ||||
\(421\) | 1.23557e15 | 0.221909 | 0.110954 | − | 0.993825i | \(-0.464609\pi\) | ||||
0.110954 | + | 0.993825i | \(0.464609\pi\) | |||||||
\(422\) | 4.99475e15 | − | 3.30164e15i | 0.884381 | − | 0.584595i | ||||
\(423\) | − | 2.10430e15i | − | 0.367337i | ||||||
\(424\) | −3.94396e15 | + | 7.23620e14i | −0.678793 | + | 0.124542i | ||||
\(425\) | −4.47085e15 | −0.758677 | ||||||||
\(426\) | 7.18877e14 | + | 1.08752e15i | 0.120281 | + | 0.181962i | ||||
\(427\) | − | 9.69516e15i | − | 1.59951i | ||||||
\(428\) | 8.81635e15 | + | 3.75483e15i | 1.43425 | + | 0.610840i | ||||
\(429\) | −1.82881e15 | −0.293376 | ||||||||
\(430\) | −1.99297e15 | + | 1.31740e15i | −0.315276 | + | 0.208404i | ||||
\(431\) | 1.01057e16i | 1.57653i | 0.615336 | + | 0.788265i | \(0.289020\pi\) | ||||
−0.615336 | + | 0.788265i | \(0.710980\pi\) | |||||||
\(432\) | 9.01903e14 | − | 8.66780e14i | 0.138758 | − | 0.133354i | ||||
\(433\) | −2.25070e15 | −0.341499 | −0.170750 | − | 0.985314i | \(-0.554619\pi\) | ||||
−0.170750 | + | 0.985314i | \(0.554619\pi\) | |||||||
\(434\) | 5.02235e15 | + | 7.59786e15i | 0.751569 | + | 1.13698i | ||||
\(435\) | − | 2.85539e15i | − | 0.421434i | ||||||
\(436\) | 4.84569e15 | − | 1.13777e16i | 0.705402 | − | 1.65629i | ||||
\(437\) | 3.23669e15 | 0.464742 | ||||||||
\(438\) | −6.26976e14 | + | 4.14445e14i | −0.0887986 | + | 0.0586978i | ||||
\(439\) | 1.26672e16i | 1.76967i | 0.465903 | + | 0.884836i | \(0.345729\pi\) | ||||
−0.465903 | + | 0.884836i | \(0.654271\pi\) | |||||||
\(440\) | −2.97653e14 | − | 1.62230e15i | −0.0410199 | − | 0.223571i | ||||
\(441\) | 4.08197e15 | 0.554931 | ||||||||
\(442\) | −5.28364e15 | − | 7.99314e15i | −0.708598 | − | 1.07197i | ||||
\(443\) | − | 8.26929e15i | − | 1.09407i | −0.837109 | − | 0.547036i | \(-0.815756\pi\) | ||
0.837109 | − | 0.547036i | \(-0.184244\pi\) | |||||||
\(444\) | 6.97981e15 | + | 2.97266e15i | 0.911058 | + | 0.388013i | ||||
\(445\) | −4.02261e15 | −0.518022 | ||||||||
\(446\) | −9.52463e14 | + | 6.29599e14i | −0.121015 | + | 0.0799935i | ||||
\(447\) | − | 1.95101e15i | − | 0.244576i | ||||||
\(448\) | 4.68521e15 | + | 1.23381e16i | 0.579510 | + | 1.52609i | ||||
\(449\) | −2.61387e13 | −0.00319011 | −0.00159506 | − | 0.999999i | \(-0.500508\pi\) | ||||
−0.00159506 | + | 0.999999i | \(0.500508\pi\) | |||||||
\(450\) | −1.08423e15 | − | 1.64023e15i | −0.130570 | − | 0.197528i | ||||
\(451\) | − | 2.48995e15i | − | 0.295891i | ||||||
\(452\) | 6.76603e14 | − | 1.58867e15i | 0.0793420 | − | 0.186296i | ||||
\(453\) | −3.22941e15 | −0.373709 | ||||||||
\(454\) | −7.30113e14 | + | 4.82621e14i | −0.0833787 | + | 0.0551152i | ||||
\(455\) | 9.37902e15i | 1.05703i | ||||||||
\(456\) | −1.75812e15 | + | 3.22572e14i | −0.195550 | + | 0.0358787i | ||||
\(457\) | −1.61980e15 | −0.177813 | −0.0889067 | − | 0.996040i | \(-0.528337\pi\) | ||||
−0.0889067 | + | 0.996040i | \(0.528337\pi\) | |||||||
\(458\) | 3.48726e15 | + | 5.27555e15i | 0.377825 | + | 0.571577i | ||||
\(459\) | 1.92212e15i | 0.205544i | ||||||||
\(460\) | −6.33131e15 | − | 2.69646e15i | −0.668261 | − | 0.284608i | ||||
\(461\) | 6.13058e15 | 0.638698 | 0.319349 | − | 0.947637i | \(-0.396536\pi\) | ||||
0.319349 | + | 0.947637i | \(0.396536\pi\) | |||||||
\(462\) | −3.22901e15 | + | 2.13445e15i | −0.332061 | + | 0.219499i | ||||
\(463\) | − | 5.83824e15i | − | 0.592647i | −0.955088 | − | 0.296324i | \(-0.904239\pi\) | ||
0.955088 | − | 0.296324i | \(-0.0957607\pi\) | |||||||
\(464\) | −9.37881e15 | − | 9.75886e15i | −0.939809 | − | 0.977892i | ||||
\(465\) | 2.62264e15 | 0.259430 | ||||||||
\(466\) | 2.53694e15 | + | 3.83791e15i | 0.247739 | + | 0.374782i | ||||
\(467\) | − | 1.22182e16i | − | 1.17789i | −0.808172 | − | 0.588946i | \(-0.799543\pi\) | ||
0.808172 | − | 0.588946i | \(-0.200457\pi\) | |||||||
\(468\) | 1.65112e15 | − | 3.87683e15i | 0.157146 | − | 0.368979i | ||||
\(469\) | −1.35240e16 | −1.27077 | ||||||||
\(470\) | 5.33325e15 | − | 3.52539e15i | 0.494771 | − | 0.327055i | ||||
\(471\) | 2.77089e15i | 0.253801i | ||||||||
\(472\) | −1.36239e15 | − | 7.42543e15i | −0.123211 | − | 0.671537i | ||||
\(473\) | −3.32129e15 | −0.296579 | ||||||||
\(474\) | −5.99872e15 | − | 9.07492e15i | −0.528918 | − | 0.800153i | ||||
\(475\) | 2.80958e15i | 0.244613i | ||||||||
\(476\) | −1.86579e16 | − | 7.94629e15i | −1.60407 | − | 0.683161i | ||||
\(477\) | 2.70967e15 | 0.230041 | ||||||||
\(478\) | −1.16243e16 | + | 7.68390e15i | −0.974537 | + | 0.644190i | ||||
\(479\) | 1.85726e16i | 1.53766i | 0.639455 | + | 0.768829i | \(0.279160\pi\) | ||||
−0.639455 | + | 0.768829i | \(0.720840\pi\) | |||||||
\(480\) | 3.70780e15 | + | 8.33690e14i | 0.303158 | + | 0.0681644i | ||||
\(481\) | 2.55559e16 | 2.06358 | ||||||||
\(482\) | 1.50487e15 | + | 2.27658e15i | 0.120010 | + | 0.181552i | ||||
\(483\) | 1.61494e16i | 1.27196i | ||||||||
\(484\) | −4.13858e15 | + | 9.71740e15i | −0.321943 | + | 0.755924i | ||||
\(485\) | −1.02225e16 | −0.785430 | ||||||||
\(486\) | −7.05170e14 | + | 4.66133e14i | −0.0535151 | + | 0.0353746i | ||||
\(487\) | − | 9.11126e14i | − | 0.0682975i | −0.999417 | − | 0.0341488i | \(-0.989128\pi\) | ||
0.999417 | − | 0.0341488i | \(-0.0108720\pi\) | |||||||
\(488\) | −1.30162e16 | + | 2.38816e15i | −0.963754 | + | 0.176825i | ||||
\(489\) | −1.44476e15 | −0.105668 | ||||||||
\(490\) | 6.83865e15 | + | 1.03456e16i | 0.494076 | + | 0.747443i | ||||
\(491\) | 9.34268e13i | 0.00666780i | 0.999994 | + | 0.00333390i | \(0.00106121\pi\) | ||||
−0.999994 | + | 0.00333390i | \(0.998939\pi\) | |||||||
\(492\) | 5.27835e15 | + | 2.24802e15i | 0.372141 | + | 0.158493i | ||||
\(493\) | 2.07979e16 | 1.44856 | ||||||||
\(494\) | −5.02306e15 | + | 3.32035e15i | −0.345626 | + | 0.228466i | ||||
\(495\) | 1.11459e15i | 0.0757678i | ||||||||
\(496\) | 8.96338e15 | − | 8.61431e15i | 0.601979 | − | 0.578536i | ||||
\(497\) | 9.29464e15 | 0.616729 | ||||||||
\(498\) | 5.71173e15 | + | 8.64076e15i | 0.374448 | + | 0.566469i | ||||
\(499\) | 1.60263e15i | 0.103808i | 0.998652 | + | 0.0519039i | \(0.0165289\pi\) | ||||
−0.998652 | + | 0.0519039i | \(0.983471\pi\) | |||||||
\(500\) | 5.63571e15 | − | 1.32327e16i | 0.360685 | − | 0.846891i | ||||
\(501\) | −1.04471e16 | −0.660649 | ||||||||
\(502\) | −1.34048e16 | + | 8.86085e15i | −0.837600 | + | 0.553672i | ||||
\(503\) | − | 2.08437e16i | − | 1.28696i | −0.765461 | − | 0.643482i | \(-0.777489\pi\) | ||
0.765461 | − | 0.643482i | \(-0.222511\pi\) | |||||||
\(504\) | −1.60947e15 | − | 8.77211e15i | −0.0981972 | − | 0.535206i | ||||
\(505\) | 1.28035e16 | 0.771933 | ||||||||
\(506\) | −5.27556e15 | − | 7.98091e15i | −0.314315 | − | 0.475499i | ||||
\(507\) | − | 4.38874e15i | − | 0.258400i | ||||||
\(508\) | 7.46082e14 | + | 3.17751e14i | 0.0434114 | + | 0.0184886i | ||||
\(509\) | −1.02294e15 | −0.0588223 | −0.0294112 | − | 0.999567i | \(-0.509363\pi\) | ||||
−0.0294112 | + | 0.999567i | \(0.509363\pi\) | |||||||
\(510\) | −4.87152e15 | + | 3.22018e15i | −0.276849 | + | 0.183003i | ||||
\(511\) | 5.35852e15i | 0.300967i | ||||||||
\(512\) | 1.54105e16 | − | 9.32932e15i | 0.855453 | − | 0.517881i | ||||
\(513\) | 1.20790e15 | 0.0662715 | ||||||||
\(514\) | −8.92475e14 | − | 1.35014e15i | −0.0483969 | − | 0.0732152i | ||||
\(515\) | − | 8.60672e15i | − | 0.461312i | ||||||
\(516\) | 2.99858e15 | − | 7.04069e15i | 0.158861 | − | 0.373007i | ||||
\(517\) | 8.88785e15 | 0.465429 | ||||||||
\(518\) | 4.51223e16 | − | 2.98269e16i | 2.33568 | − | 1.54393i | ||||
\(519\) | 1.06392e16i | 0.544385i | ||||||||
\(520\) | 1.25918e16 | − | 2.31029e15i | 0.636895 | − | 0.116855i | ||||
\(521\) | −2.99473e16 | −1.49738 | −0.748689 | − | 0.662921i | \(-0.769317\pi\) | ||||
−0.748689 | + | 0.662921i | \(0.769317\pi\) | |||||||
\(522\) | 5.04369e15 | + | 7.63014e15i | 0.249302 | + | 0.377146i | ||||
\(523\) | − | 3.07690e16i | − | 1.50350i | −0.659448 | − | 0.751750i | \(-0.729210\pi\) | ||
0.659448 | − | 0.751750i | \(-0.270790\pi\) | |||||||
\(524\) | −8.54043e15 | − | 3.63731e15i | −0.412565 | − | 0.175709i | ||||
\(525\) | −1.40184e16 | −0.669486 | ||||||||
\(526\) | −1.58260e16 | + | 1.04613e16i | −0.747234 | + | 0.493938i | ||||
\(527\) | 1.91026e16i | 0.891720i | ||||||||
\(528\) | 3.66099e15 | + | 3.80934e15i | 0.168964 | + | 0.175811i | ||||
\(529\) | −1.80008e16 | −0.821404 | ||||||||
\(530\) | 4.53958e15 | + | 6.86752e15i | 0.204815 | + | 0.309845i | ||||
\(531\) | 5.10159e15i | 0.227582i | ||||||||
\(532\) | −4.99362e15 | + | 1.17250e16i | −0.220265 | + | 0.517184i | ||||
\(533\) | 1.93262e16 | 0.842913 | ||||||||
\(534\) | 1.07492e16 | − | 7.10544e15i | 0.463583 | − | 0.306439i | ||||
\(535\) | − | 1.96736e16i | − | 0.838998i | ||||||
\(536\) | 3.33129e15 | + | 1.81566e16i | 0.140483 | + | 0.765677i | ||||
\(537\) | 1.55191e16 | 0.647172 | ||||||||
\(538\) | 1.02384e16 | + | 1.54888e16i | 0.422221 | + | 0.638740i | ||||
\(539\) | 1.72409e16i | 0.703116i | ||||||||
\(540\) | −2.36278e15 | − | 1.00629e15i | −0.0952930 | − | 0.0405847i | ||||
\(541\) | −9.46188e14 | −0.0377393 | −0.0188696 | − | 0.999822i | \(-0.506007\pi\) | ||||
−0.0188696 | + | 0.999822i | \(0.506007\pi\) | |||||||
\(542\) | −2.59863e16 | + | 1.71775e16i | −1.02506 | + | 0.677587i | ||||
\(543\) | − | 2.22130e15i | − | 0.0866579i | ||||||
\(544\) | −6.07238e15 | + | 2.70066e16i | −0.234296 | + | 1.04202i | ||||
\(545\) | −2.53892e16 | −0.968881 | ||||||||
\(546\) | −1.65669e16 | − | 2.50625e16i | −0.625295 | − | 0.945951i | ||||
\(547\) | − | 3.26129e15i | − | 0.121749i | −0.998145 | − | 0.0608746i | \(-0.980611\pi\) | ||
0.998145 | − | 0.0608746i | \(-0.0193890\pi\) | |||||||
\(548\) | −1.70200e16 | + | 3.99631e16i | −0.628458 | + | 1.47562i | ||||
\(549\) | 8.94270e15 | 0.326614 | ||||||||
\(550\) | 6.92776e15 | − | 4.57940e15i | 0.250275 | − | 0.165437i | ||||
\(551\) | − | 1.30698e16i | − | 0.467047i | ||||||
\(552\) | 2.16814e16 | − | 3.97801e15i | 0.766396 | − | 0.140615i | ||||
\(553\) | −7.75598e16 | −2.71198 | ||||||||
\(554\) | 1.01613e16 | + | 1.53722e16i | 0.351474 | + | 0.531712i | ||||
\(555\) | − | 1.55754e16i | − | 0.532943i | ||||||
\(556\) | 3.85207e15 | + | 1.64057e15i | 0.130390 | + | 0.0555324i | ||||
\(557\) | −1.06541e16 | −0.356768 | −0.178384 | − | 0.983961i | \(-0.557087\pi\) | ||||
−0.178384 | + | 0.983961i | \(0.557087\pi\) | |||||||
\(558\) | −7.00818e15 | + | 4.63256e15i | −0.232167 | + | 0.153467i | ||||
\(559\) | − | 2.57788e16i | − | 0.844873i | ||||||
\(560\) | 1.95361e16 | − | 1.87753e16i | 0.633446 | − | 0.608777i | ||||
\(561\) | −8.11839e15 | −0.260431 | ||||||||
\(562\) | −2.94688e16 | − | 4.45807e16i | −0.935288 | − | 1.41491i | ||||
\(563\) | 4.45857e16i | 1.40006i | 0.714116 | + | 0.700028i | \(0.246829\pi\) | ||||
−0.714116 | + | 0.700028i | \(0.753171\pi\) | |||||||
\(564\) | −8.02427e15 | + | 1.88410e16i | −0.249305 | + | 0.585369i | ||||
\(565\) | −3.54509e15 | −0.108978 | ||||||||
\(566\) | 3.06750e15 | − | 2.02768e15i | 0.0933009 | − | 0.0616739i | ||||
\(567\) | 6.02681e15i | 0.181380i | ||||||||
\(568\) | −2.28950e15 | − | 1.24785e16i | −0.0681791 | − | 0.371598i | ||||
\(569\) | 2.78386e16 | 0.820301 | 0.410150 | − | 0.912018i | \(-0.365476\pi\) | ||||
0.410150 | + | 0.912018i | \(0.365476\pi\) | |||||||
\(570\) | 2.02363e15 | + | 3.06137e15i | 0.0590041 | + | 0.0892619i | ||||
\(571\) | 3.48673e16i | 1.00601i | 0.864284 | + | 0.503004i | \(0.167772\pi\) | ||||
−0.864284 | + | 0.503004i | \(0.832228\pi\) | |||||||
\(572\) | 1.63744e16 | + | 6.97376e15i | 0.467509 | + | 0.199109i | ||||
\(573\) | −1.86528e16 | −0.527007 | ||||||||
\(574\) | 3.41229e16 | − | 2.25560e16i | 0.954059 | − | 0.630654i | ||||
\(575\) | − | 3.46482e16i | − | 0.958681i | ||||||
\(576\) | −1.13805e16 | + | 4.32158e15i | −0.311622 | + | 0.118334i | ||||
\(577\) | 6.23408e16 | 1.68934 | 0.844671 | − | 0.535285i | \(-0.179796\pi\) | ||||
0.844671 | + | 0.535285i | \(0.179796\pi\) | |||||||
\(578\) | −2.89309e15 | − | 4.37669e15i | −0.0775880 | − | 0.117376i | ||||
\(579\) | − | 1.64413e16i | − | 0.436379i | ||||||
\(580\) | −1.08884e16 | + | 2.55660e16i | −0.286019 | + | 0.671575i | ||||
\(581\) | 7.38492e16 | 1.91995 | ||||||||
\(582\) | 2.73165e16 | − | 1.80568e16i | 0.702890 | − | 0.464626i | ||||
\(583\) | 1.14447e16i | 0.291470i | ||||||||
\(584\) | 7.19408e15 | − | 1.31994e15i | 0.181342 | − | 0.0332718i | ||||
\(585\) | −8.65110e15 | −0.215842 | ||||||||
\(586\) | −7.75080e15 | − | 1.17255e16i | −0.191408 | − | 0.289564i | ||||
\(587\) | − | 6.86060e15i | − | 0.167700i | −0.996478 | − | 0.0838501i | \(-0.973278\pi\) | ||
0.996478 | − | 0.0838501i | \(-0.0267217\pi\) | |||||||
\(588\) | −3.65483e16 | − | 1.55657e16i | −0.884308 | − | 0.376621i | ||||
\(589\) | 1.20045e16 | 0.287509 | ||||||||
\(590\) | −1.29297e16 | + | 8.54684e15i | −0.306533 | + | 0.202625i | ||||
\(591\) | − | 1.43867e16i | − | 0.337627i | ||||||
\(592\) | −5.11588e16 | − | 5.32319e16i | −1.18848 | − | 1.23664i | ||||
\(593\) | −4.01477e16 | −0.923278 | −0.461639 | − | 0.887068i | \(-0.652738\pi\) | ||||
−0.461639 | + | 0.887068i | \(0.652738\pi\) | |||||||
\(594\) | −1.96879e15 | − | 2.97840e15i | −0.0448209 | − | 0.0678054i | ||||
\(595\) | 4.16350e16i | 0.938332i | ||||||||
\(596\) | −7.43974e15 | + | 1.74685e16i | −0.165989 | + | 0.389744i | ||||
\(597\) | 2.11180e15 | 0.0466451 | ||||||||
\(598\) | 6.19452e16 | − | 4.09472e16i | 1.35457 | − | 0.895399i | ||||
\(599\) | 2.96254e15i | 0.0641362i | 0.999486 | + | 0.0320681i | \(0.0102093\pi\) | ||||
−0.999486 | + | 0.0320681i | \(0.989791\pi\) | |||||||
\(600\) | 3.45308e15 | + | 1.88204e16i | 0.0740115 | + | 0.403386i | ||||
\(601\) | 9.07584e16 | 1.92593 | 0.962964 | − | 0.269631i | \(-0.0869019\pi\) | ||||
0.962964 | + | 0.269631i | \(0.0869019\pi\) | |||||||
\(602\) | −3.00870e16 | − | 4.55159e16i | −0.632120 | − | 0.956277i | ||||
\(603\) | − | 1.24743e16i | − | 0.259486i | ||||||
\(604\) | 2.89148e16 | + | 1.23146e16i | 0.595523 | + | 0.253629i | ||||
\(605\) | 2.16843e16 | 0.442194 | ||||||||
\(606\) | −3.42133e16 | + | 2.26157e16i | −0.690811 | + | 0.456641i | ||||
\(607\) | 6.47764e16i | 1.29504i | 0.762047 | + | 0.647522i | \(0.224195\pi\) | ||||
−0.762047 | + | 0.647522i | \(0.775805\pi\) | |||||||
\(608\) | 1.69715e16 | + | 3.81601e15i | 0.335969 | + | 0.0755419i | ||||
\(609\) | 6.52118e16 | 1.27827 | ||||||||
\(610\) | 1.49820e16 | + | 2.26649e16i | 0.290797 | + | 0.439920i | ||||
\(611\) | 6.89846e16i | 1.32588i | ||||||||
\(612\) | 7.32957e15 | − | 1.72099e16i | 0.139499 | − | 0.327544i | ||||
\(613\) | −1.03068e17 | −1.94251 | −0.971254 | − | 0.238046i | \(-0.923493\pi\) | ||||
−0.971254 | + | 0.238046i | \(0.923493\pi\) | |||||||
\(614\) | −5.26348e16 | + | 3.47927e16i | −0.982342 | + | 0.649350i | ||||
\(615\) | − | 1.17786e16i | − | 0.217692i | ||||||
\(616\) | 3.70504e16 | − | 6.79785e15i | 0.678124 | − | 0.124419i | ||||
\(617\) | −3.80906e16 | −0.690410 | −0.345205 | − | 0.938527i | \(-0.612191\pi\) | ||||
−0.345205 | + | 0.938527i | \(0.612191\pi\) | |||||||
\(618\) | 1.52027e16 | + | 2.29988e16i | 0.272891 | + | 0.412833i | ||||
\(619\) | − | 3.54627e16i | − | 0.630416i | −0.949023 | − | 0.315208i | \(-0.897926\pi\) | ||
0.949023 | − | 0.315208i | \(-0.102074\pi\) | |||||||
\(620\) | −2.34820e16 | − | 1.00008e16i | −0.413414 | − | 0.176070i | ||||
\(621\) | −1.48960e16 | −0.259730 | ||||||||
\(622\) | −2.38249e16 | + | 1.57488e16i | −0.411424 | + | 0.271960i | ||||
\(623\) | − | 9.18690e16i | − | 1.57123i | ||||||
\(624\) | −2.95668e16 | + | 2.84154e16i | −0.500838 | + | 0.481333i | ||||
\(625\) | 1.28114e16 | 0.214940 | ||||||||
\(626\) | −4.56938e16 | − | 6.91259e16i | −0.759296 | − | 1.14867i | ||||
\(627\) | 5.10177e15i | 0.0839683i | ||||||||
\(628\) | 1.05662e16 | − | 2.48094e16i | 0.172250 | − | 0.404444i | ||||
\(629\) | 1.13447e17 | 1.83184 | ||||||||
\(630\) | −1.52747e16 | + | 1.00969e16i | −0.244303 | + | 0.161490i | ||||
\(631\) | 2.41796e15i | 0.0383065i | 0.999817 | + | 0.0191533i | \(0.00609704\pi\) | ||||
−0.999817 | + | 0.0191533i | \(0.993903\pi\) | |||||||
\(632\) | 1.91049e16 | + | 1.04128e17i | 0.299808 | + | 1.63405i | ||||
\(633\) | 3.93751e16 | 0.612068 | ||||||||
\(634\) | −8.29689e15 | − | 1.25516e16i | −0.127756 | − | 0.193270i | ||||
\(635\) | − | 1.66487e15i | − | 0.0253944i | ||||||
\(636\) | −2.42612e16 | − | 1.03327e16i | −0.366581 | − | 0.156125i | ||||
\(637\) | −1.33818e17 | −2.00299 | ||||||||
\(638\) | −3.22271e16 | + | 2.13029e16i | −0.477857 | + | 0.315874i | ||||
\(639\) | 8.57327e15i | 0.125934i | ||||||||
\(640\) | −3.00190e16 | − | 2.16034e16i | −0.436834 | − | 0.314370i | ||||
\(641\) | −7.32646e16 | −1.05620 | −0.528100 | − | 0.849182i | \(-0.677095\pi\) | ||||
−0.528100 | + | 0.849182i | \(0.677095\pi\) | |||||||
\(642\) | 3.47510e16 | + | 5.25715e16i | 0.496314 | + | 0.750828i | ||||
\(643\) | 5.58572e16i | 0.790339i | 0.918608 | + | 0.395169i | \(0.129314\pi\) | ||||
−0.918608 | + | 0.395169i | \(0.870686\pi\) | |||||||
\(644\) | 6.15822e16 | − | 1.44595e17i | 0.863257 | − | 2.02693i | ||||
\(645\) | −1.57112e16 | −0.218198 | ||||||||
\(646\) | −2.22982e16 | + | 1.47396e16i | −0.306813 | + | 0.202810i | ||||
\(647\) | − | 8.52631e16i | − | 1.16235i | −0.813780 | − | 0.581173i | \(-0.802594\pi\) | ||
0.813780 | − | 0.581173i | \(-0.197406\pi\) | |||||||
\(648\) | 8.09129e15 | − | 1.48456e15i | 0.109287 | − | 0.0200515i | ||||
\(649\) | −2.15474e16 | −0.288354 | ||||||||
\(650\) | 3.55438e16 | + | 5.37711e16i | 0.471286 | + | 0.712965i | ||||
\(651\) | 5.98962e16i | 0.786889i | ||||||||
\(652\) | 1.29358e16 | + | 5.50928e15i | 0.168387 | + | 0.0717149i | ||||
\(653\) | −1.28375e17 | −1.65577 | −0.827887 | − | 0.560894i | \(-0.810457\pi\) | ||||
−0.827887 | + | 0.560894i | \(0.810457\pi\) | |||||||
\(654\) | 6.78448e16 | − | 4.48469e16i | 0.867062 | − | 0.573147i | ||||
\(655\) | 1.90579e16i | 0.241339i | ||||||||
\(656\) | −3.86879e16 | − | 4.02556e16i | −0.485459 | − | 0.505130i | ||||
\(657\) | −4.94264e15 | −0.0614563 | ||||||||
\(658\) | 8.05135e16 | + | 1.21802e17i | 0.992004 | + | 1.50071i | ||||
\(659\) | − | 9.03419e16i | − | 1.10300i | −0.834174 | − | 0.551501i | \(-0.814055\pi\) | ||
0.834174 | − | 0.551501i | \(-0.185945\pi\) | |||||||
\(660\) | 4.25025e15 | − | 9.97960e15i | 0.0514222 | − | 0.120740i | ||||
\(661\) | 3.76936e16 | 0.451917 | 0.225959 | − | 0.974137i | \(-0.427449\pi\) | ||||
0.225959 | + | 0.974137i | \(0.427449\pi\) | |||||||
\(662\) | −8.82659e15 | + | 5.83457e15i | −0.104868 | + | 0.0693203i | ||||
\(663\) | − | 6.30123e16i | − | 0.741898i | ||||||
\(664\) | −1.81909e16 | − | 9.91463e16i | −0.212249 | − | 1.15683i | ||||
\(665\) | 2.61643e16 | 0.302538 | ||||||||
\(666\) | 2.75120e16 | + | 4.16203e16i | 0.315265 | + | 0.476936i | ||||
\(667\) | 1.61180e17i | 1.83044i | ||||||||
\(668\) | 9.35393e16 | + | 3.98378e16i | 1.05277 | + | 0.448370i | ||||
\(669\) | −7.50855e15 | −0.0837528 | ||||||||
\(670\) | 3.16156e16 | − | 2.08986e16i | 0.349505 | − | 0.231030i | ||||
\(671\) | 3.77710e16i | 0.413831i | ||||||||
\(672\) | −1.90400e16 | + | 8.46792e16i | −0.206752 | + | 0.919520i | ||||
\(673\) | −5.56200e16 | −0.598606 | −0.299303 | − | 0.954158i | \(-0.596754\pi\) | ||||
−0.299303 | + | 0.954158i | \(0.596754\pi\) | |||||||
\(674\) | 6.05147e16 | + | 9.15472e16i | 0.645508 | + | 0.976531i | ||||
\(675\) | − | 1.29304e16i | − | 0.136706i | ||||||
\(676\) | −1.67355e16 | + | 3.92950e16i | −0.175371 | + | 0.411772i | ||||
\(677\) | 7.87952e16 | 0.818404 | 0.409202 | − | 0.912444i | \(-0.365807\pi\) | ||||
0.409202 | + | 0.912444i | \(0.365807\pi\) | |||||||
\(678\) | 9.47316e15 | − | 6.26197e15i | 0.0975252 | − | 0.0644663i | ||||
\(679\) | − | 2.33464e17i | − | 2.38232i | ||||||
\(680\) | 5.58970e16 | − | 1.02557e16i | 0.565373 | − | 0.103732i | ||||
\(681\) | −5.75570e15 | −0.0577053 | ||||||||
\(682\) | −1.95664e16 | − | 2.96002e16i | −0.194448 | − | 0.294163i | ||||
\(683\) | − | 5.12504e16i | − | 0.504862i | −0.967615 | − | 0.252431i | \(-0.918770\pi\) | ||
0.967615 | − | 0.252431i | \(-0.0812301\pi\) | |||||||
\(684\) | −1.08150e16 | − | 4.60606e15i | −0.105607 | − | 0.0449772i | ||||
\(685\) | 8.91771e16 | 0.863197 | ||||||||
\(686\) | −9.43499e16 | + | 6.23673e16i | −0.905309 | + | 0.598429i | ||||
\(687\) | 4.15887e16i | 0.395581i | ||||||||
\(688\) | −5.36961e16 | + | 5.16050e16i | −0.506305 | + | 0.486588i | ||||
\(689\) | −8.88302e16 | −0.830320 | ||||||||
\(690\) | −2.49558e16 | − | 3.77533e16i | −0.231247 | − | 0.349833i | ||||
\(691\) | − | 6.40379e16i | − | 0.588259i | −0.955766 | − | 0.294129i | \(-0.904970\pi\) | ||
0.955766 | − | 0.294129i | \(-0.0950297\pi\) | |||||||
\(692\) | 4.05704e16 | − | 9.52594e16i | 0.369464 | − | 0.867504i | ||||
\(693\) | −2.54552e16 | −0.229815 | ||||||||
\(694\) | 8.24737e16 | − | 5.45169e16i | 0.738174 | − | 0.487949i | ||||
\(695\) | − | 8.59585e15i | − | 0.0762746i | ||||||
\(696\) | −1.60633e16 | − | 8.75501e16i | −0.141312 | − | 0.770196i | ||||
\(697\) | 8.57920e16 | 0.748256 | ||||||||
\(698\) | −2.81249e16 | − | 4.25476e16i | −0.243197 | − | 0.367911i | ||||
\(699\) | 3.02553e16i | 0.259382i | ||||||||
\(700\) | 1.25515e17 | + | 5.34559e16i | 1.06686 | + | 0.454368i | ||||
\(701\) | 1.93098e17 | 1.62731 | 0.813655 | − | 0.581348i | \(-0.197474\pi\) | ||||
0.813655 | + | 0.581348i | \(0.197474\pi\) | |||||||
\(702\) | 2.31174e16 | − | 1.52811e16i | 0.193159 | − | 0.127683i | ||||
\(703\) | − | 7.12924e16i | − | 0.590624i | ||||||
\(704\) | −1.82529e16 | − | 4.80676e16i | −0.149933 | − | 0.394836i | ||||
\(705\) | 4.20436e16 | 0.342424 | ||||||||
\(706\) | 2.06618e16 | + | 3.12574e16i | 0.166855 | + | 0.252420i | ||||
\(707\) | 2.92408e17i | 2.34138i | ||||||||
\(708\) | 1.94538e16 | − | 4.56775e16i | 0.154456 | − | 0.362663i | ||||
\(709\) | −1.93068e16 | −0.151996 | −0.0759980 | − | 0.997108i | \(-0.524214\pi\) | ||||
−0.0759980 | + | 0.997108i | \(0.524214\pi\) | |||||||
\(710\) | −2.17286e16 | + | 1.43631e16i | −0.169621 | + | 0.112123i | ||||
\(711\) | − | 7.15403e16i | − | 0.553775i | ||||||
\(712\) | −1.23339e17 | + | 2.26297e16i | −0.946716 | + | 0.173699i | ||||
\(713\) | −1.48041e17 | −1.12680 | ||||||||
\(714\) | −7.35430e16 | − | 1.11257e17i | −0.555076 | − | 0.839723i | ||||
\(715\) | − | 3.65393e16i | − | 0.273479i | ||||||
\(716\) | −1.38951e17 | − | 5.91784e16i | −1.03130 | − | 0.439223i | ||||
\(717\) | −9.16375e16 | −0.674463 | ||||||||
\(718\) | −1.23008e17 | + | 8.13113e16i | −0.897818 | + | 0.593478i | ||||
\(719\) | 2.21045e17i | 1.59996i | 0.600029 | + | 0.799978i | \(0.295156\pi\) | ||||
−0.600029 | + | 0.799978i | \(0.704844\pi\) | |||||||
\(720\) | 1.73181e16 | + | 1.80199e16i | 0.124310 | + | 0.129347i | ||||
\(721\) | 1.96562e17 | 1.39922 | ||||||||
\(722\) | −6.88494e16 | − | 1.04156e17i | −0.486046 | − | 0.735294i | ||||
\(723\) | 1.79470e16i | 0.125650i | ||||||||
\(724\) | −8.47043e15 | + | 1.98886e16i | −0.0588131 | + | 0.138093i | ||||
\(725\) | −1.39911e17 | −0.963435 | ||||||||
\(726\) | −5.79445e16 | + | 3.83026e16i | −0.395724 | + | 0.261582i | ||||
\(727\) | − | 1.20160e17i | − | 0.813865i | −0.913458 | − | 0.406932i | \(-0.866598\pi\) | ||
0.913458 | − | 0.406932i | \(-0.133402\pi\) | |||||||
\(728\) | 5.27627e16 | + | 2.87574e17i | 0.354437 | + | 1.93179i | ||||
\(729\) | −5.55906e15 | −0.0370370 | ||||||||
\(730\) | −8.28054e15 | − | 1.25269e16i | −0.0547169 | − | 0.0827762i | ||||
\(731\) | − | 1.14436e17i | − | 0.749996i | ||||||
\(732\) | −8.00693e16 | − | 3.41010e16i | −0.520475 | − | 0.221667i | ||||
\(733\) | −7.58459e16 | −0.489000 | −0.244500 | − | 0.969649i | \(-0.578624\pi\) | ||||
−0.244500 | + | 0.969649i | \(0.578624\pi\) | |||||||
\(734\) | 2.10471e17 | − | 1.39126e17i | 1.34591 | − | 0.889676i | ||||
\(735\) | 8.15572e16i | 0.517295i | ||||||||
\(736\) | −2.09296e17 | − | 4.70597e16i | −1.31672 | − | 0.296062i | ||||
\(737\) | 5.26875e16 | 0.328778 | ||||||||
\(738\) | 2.08054e16 | + | 3.14746e16i | 0.128777 | + | 0.194815i | ||||
\(739\) | 2.21632e17i | 1.36071i | 0.732883 | + | 0.680355i | \(0.238174\pi\) | ||||
−0.732883 | + | 0.680355i | \(0.761826\pi\) | |||||||
\(740\) | −5.93932e16 | + | 1.39455e17i | −0.361698 | + | 0.849269i | ||||
\(741\) | −3.95983e16 | −0.239203 | ||||||||
\(742\) | −1.56842e17 | + | 1.03676e17i | −0.939805 | + | 0.621232i | ||||
\(743\) | 2.29188e17i | 1.36226i | 0.732165 | + | 0.681128i | \(0.238510\pi\) | ||||
−0.732165 | + | 0.681128i | \(0.761490\pi\) | |||||||
\(744\) | 8.04136e16 | − | 1.47539e16i | 0.474124 | − | 0.0869902i | ||||
\(745\) | 3.89809e16 | 0.227989 | ||||||||
\(746\) | −3.39510e16 | − | 5.13614e16i | −0.196979 | − | 0.297991i | ||||
\(747\) | 6.81177e16i | 0.392045i | ||||||||
\(748\) | 7.26887e16 | + | 3.09576e16i | 0.415009 | + | 0.176750i | ||||
\(749\) | 4.49309e17 | 2.54480 | ||||||||
\(750\) | 7.89059e16 | − | 5.21585e16i | 0.443345 | − | 0.293061i | ||||
\(751\) | 1.69065e17i | 0.942351i | 0.882039 | + | 0.471176i | \(0.156170\pi\) | ||||
−0.882039 | + | 0.471176i | \(0.843830\pi\) | |||||||
\(752\) | 1.43692e17 | − | 1.38096e17i | 0.794559 | − | 0.763615i | ||||
\(753\) | −1.05674e17 | −0.579692 | ||||||||
\(754\) | −1.65346e17 | − | 2.50137e17i | −0.899840 | − | 1.36129i | ||||
\(755\) | − | 6.45230e16i | − | 0.348364i | ||||||
\(756\) | 2.29819e16 | − | 5.39616e16i | 0.123099 | − | 0.289037i | ||||
\(757\) | −5.99548e15 | −0.0318602 | −0.0159301 | − | 0.999873i | \(-0.505071\pi\) | ||||
−0.0159301 | + | 0.999873i | \(0.505071\pi\) | |||||||
\(758\) | −3.94042e16 | + | 2.60471e16i | −0.207744 | + | 0.137323i | ||||
\(759\) | − | 6.29159e16i | − | 0.329086i | ||||||
\(760\) | −6.44493e15 | − | 3.51269e16i | −0.0334454 | − | 0.182288i | ||||
\(761\) | −2.35648e17 | −1.21326 | −0.606632 | − | 0.794983i | \(-0.707480\pi\) | ||||
−0.606632 | + | 0.794983i | \(0.707480\pi\) | |||||||
\(762\) | 2.94079e15 | + | 4.44885e15i | 0.0150222 | + | 0.0227258i | ||||
\(763\) | − | 5.79843e17i | − | 2.93875i | ||||||
\(764\) | 1.67010e17 | + | 7.11283e16i | 0.839810 | + | 0.357670i | ||||
\(765\) | −3.84036e16 | −0.191604 | ||||||||
\(766\) | 3.51998e16 | − | 2.32678e16i | 0.174248 | − | 0.115182i | ||||
\(767\) | − | 1.67244e17i | − | 0.821444i | ||||||
\(768\) | 1.18376e17 | + | 4.70345e15i | 0.576895 | + | 0.0229218i | ||||
\(769\) | 1.99155e17 | 0.963017 | 0.481508 | − | 0.876442i | \(-0.340089\pi\) | ||||
0.481508 | + | 0.876442i | \(0.340089\pi\) | |||||||
\(770\) | −4.26459e16 | − | 6.45151e16i | −0.204613 | − | 0.309540i | ||||
\(771\) | − | 1.06436e16i | − | 0.0506712i | ||||||
\(772\) | −6.26951e16 | + | 1.47208e17i | −0.296162 | + | 0.695390i | ||||
\(773\) | −7.95257e16 | −0.372761 | −0.186380 | − | 0.982478i | \(-0.559676\pi\) | ||||
−0.186380 | + | 0.982478i | \(0.559676\pi\) | |||||||
\(774\) | 4.19833e16 | − | 2.77519e16i | 0.195268 | − | 0.129076i | ||||
\(775\) | − | 1.28506e17i | − | 0.593080i | ||||||
\(776\) | −3.13436e17 | + | 5.75080e16i | −1.43542 | + | 0.263365i | ||||
\(777\) | 3.55713e17 | 1.61649 | ||||||||
\(778\) | 6.05358e16 | + | 9.15792e16i | 0.272983 | + | 0.412971i | ||||
\(779\) | − | 5.39135e16i | − | 0.241253i | ||||||
\(780\) | 7.74584e16 | + | 3.29890e16i | 0.343954 | + | 0.146488i | ||||
\(781\) | −3.62106e16 | −0.159562 | ||||||||
\(782\) | 2.74985e17 | − | 1.81771e17i | 1.20245 | − | 0.794848i | ||||
\(783\) | 6.01506e16i | 0.261018i | ||||||||
\(784\) | 2.67883e17 | + | 2.78738e17i | 1.15358 | + | 1.20033i | ||||
\(785\) | −5.53619e16 | −0.236588 | ||||||||
\(786\) | −3.36634e16 | − | 5.09263e16i | −0.142765 | − | 0.215976i | ||||
\(787\) | − | 5.38526e16i | − | 0.226651i | −0.993558 | − | 0.113326i | \(-0.963850\pi\) | ||
0.993558 | − | 0.113326i | \(-0.0361503\pi\) | |||||||
\(788\) | −5.48606e16 | + | 1.28813e17i | −0.229141 | + | 0.538024i | ||||
\(789\) | −1.24761e17 | −0.517150 | ||||||||
\(790\) | 1.81315e17 | − | 1.19854e17i | 0.745886 | − | 0.493047i | ||||
\(791\) | − | 8.09634e16i | − | 0.330544i | ||||||
\(792\) | 6.27026e15 | + | 3.41749e16i | 0.0254059 | + | 0.138470i | ||||
\(793\) | −2.93166e17 | −1.17889 | ||||||||
\(794\) | 1.88197e17 | + | 2.84706e17i | 0.751085 | + | 1.13625i | ||||
\(795\) | 5.41387e16i | 0.214440i | ||||||||
\(796\) | −1.89082e16 | − | 8.05287e15i | −0.0743312 | − | 0.0316572i | ||||
\(797\) | 2.45587e16 | 0.0958198 | 0.0479099 | − | 0.998852i | \(-0.484744\pi\) | ||||
0.0479099 | + | 0.998852i | \(0.484744\pi\) | |||||||
\(798\) | −6.99160e16 | + | 4.62160e16i | −0.270744 | + | 0.178968i | ||||
\(799\) | 3.06234e17i | 1.17699i | ||||||||
\(800\) | 4.08498e16 | − | 1.81677e17i | 0.155830 | − | 0.693044i | ||||
\(801\) | 8.47389e16 | 0.320840 | ||||||||
\(802\) | 1.16072e17 | + | 1.75595e17i | 0.436195 | + | 0.659880i | ||||
\(803\) | − | 2.08760e16i | − | 0.0778672i | ||||||
\(804\) | −4.75681e16 | + | 1.11690e17i | −0.176108 | + | 0.413503i | ||||
\(805\) | −3.22663e17 | −1.18570 | ||||||||
\(806\) | 2.29747e17 | − | 1.51868e17i | 0.837992 | − | 0.553931i | ||||
\(807\) | 1.22103e17i | 0.442063i | ||||||||
\(808\) | 3.92572e17 | − | 7.20274e16i | 1.41075 | − | 0.258839i | ||||
\(809\) | −4.48214e17 | −1.59880 | −0.799400 | − | 0.600799i | \(-0.794849\pi\) | ||||
−0.799400 | + | 0.600799i | \(0.794849\pi\) | |||||||
\(810\) | −9.31326e15 | − | 1.40892e16i | −0.0329755 | − | 0.0498856i | ||||
\(811\) | 2.88318e17i | 1.01332i | 0.862146 | + | 0.506660i | \(0.169120\pi\) | ||||
−0.862146 | + | 0.506660i | \(0.830880\pi\) | |||||||
\(812\) | −5.83880e17 | − | 2.48671e17i | −2.03698 | − | 0.867538i | ||||
\(813\) | −2.04858e17 | −0.709430 | ||||||||
\(814\) | −1.75790e17 | + | 1.16201e17i | −0.604294 | + | 0.399452i | ||||
\(815\) | − | 2.88661e16i | − | 0.0985015i | ||||||
\(816\) | −1.31252e17 | + | 1.26140e17i | −0.444595 | + | 0.427281i | ||||
\(817\) | −7.19141e16 | −0.241814 | ||||||||
\(818\) | 1.09876e17 | + | 1.66221e17i | 0.366760 | + | 0.554838i | ||||
\(819\) | − | 1.97575e17i | − | 0.654680i | ||||||
\(820\) | −4.49150e16 | + | 1.05461e17i | −0.147743 | + | 0.346902i | ||||
\(821\) | 3.50686e17 | 1.14514 | 0.572572 | − | 0.819855i | \(-0.305946\pi\) | ||||
0.572572 | + | 0.819855i | \(0.305946\pi\) | |||||||
\(822\) | −2.38298e17 | + | 1.57520e17i | −0.772484 | + | 0.510629i | ||||
\(823\) | 1.83144e17i | 0.589377i | 0.955593 | + | 0.294689i | \(0.0952159\pi\) | ||||
−0.955593 | + | 0.294689i | \(0.904784\pi\) | |||||||
\(824\) | −4.84181e16 | − | 2.63894e17i | −0.154684 | − | 0.843074i | ||||
\(825\) | 5.46136e16 | 0.173212 | ||||||||
\(826\) | −1.95194e17 | − | 2.95291e17i | −0.614591 | − | 0.929759i | ||||
\(827\) | − | 6.06407e17i | − | 1.89553i | −0.318968 | − | 0.947766i | \(-0.603336\pi\) | ||
0.318968 | − | 0.947766i | \(-0.396664\pi\) | |||||||
\(828\) | 1.33373e17 | + | 5.68027e16i | 0.413891 | + | 0.176274i | ||||
\(829\) | 3.25609e17 | 1.00316 | 0.501578 | − | 0.865112i | \(-0.332753\pi\) | ||||
0.501578 | + | 0.865112i | \(0.332753\pi\) | |||||||
\(830\) | −1.72641e17 | + | 1.14120e17i | −0.528050 | + | 0.349053i | ||||
\(831\) | 1.21183e17i | 0.367991i | ||||||||
\(832\) | 3.73085e17 | − | 1.41673e17i | 1.12478 | − | 0.427118i | ||||
\(833\) | −5.94041e17 | −1.77806 | ||||||||
\(834\) | 1.51835e16 | + | 2.29697e16i | 0.0451207 | + | 0.0682589i | ||||
\(835\) | − | 2.08732e17i | − | 0.615843i | ||||||
\(836\) | 1.94544e16 | − | 4.56791e16i | 0.0569877 | − | 0.133807i | ||||
\(837\) | −5.52476e16 | −0.160679 | ||||||||
\(838\) | −2.71672e17 | + | 1.79581e17i | −0.784478 | + | 0.518557i | ||||
\(839\) | − | 2.58848e17i | − | 0.742117i | −0.928610 | − | 0.371058i | \(-0.878995\pi\) | ||
0.928610 | − | 0.371058i | \(-0.121005\pi\) | |||||||
\(840\) | 1.75265e17 | − | 3.21569e16i | 0.498908 | − | 0.0915374i | ||||
\(841\) | 2.97033e17 | 0.839515 | ||||||||
\(842\) | −4.36056e16 | − | 6.59669e16i | −0.122369 | − | 0.185120i | ||||
\(843\) | − | 3.51443e17i | − | 0.979241i | ||||||
\(844\) | −3.52549e17 | − | 1.50148e17i | −0.975359 | − | 0.415399i | ||||
\(845\) | 8.76863e16 | 0.240875 | ||||||||
\(846\) | −1.12348e17 | + | 7.42647e16i | −0.306439 | + | 0.202563i | ||||
\(847\) | 4.95229e17i | 1.34124i | ||||||||
\(848\) | 1.77824e17 | + | 1.85030e17i | 0.478206 | + | 0.497584i | ||||
\(849\) | 2.41820e16 | 0.0645722 | ||||||||
\(850\) | 1.57785e17 | + | 2.38698e17i | 0.418362 | + | 0.632901i | ||||
\(851\) | 8.79190e17i | 2.31476i | ||||||||
\(852\) | 3.26923e16 | − | 7.67616e16i | 0.0854687 | − | 0.200681i | ||||
\(853\) | 6.77094e16 | 0.175774 | 0.0878870 | − | 0.996130i | \(-0.471989\pi\) | ||||
0.0878870 | + | 0.996130i | \(0.471989\pi\) | |||||||
\(854\) | −5.17623e17 | + | 3.42161e17i | −1.33434 | + | 0.882029i | ||||
\(855\) | 2.41337e16i | 0.0617770i | ||||||||
\(856\) | −1.10676e17 | − | 6.03219e17i | −0.281327 | − | 1.53332i | ||||
\(857\) | 5.69625e17 | 1.43782 | 0.718910 | − | 0.695103i | \(-0.244641\pi\) | ||||
0.718910 | + | 0.695103i | \(0.244641\pi\) | |||||||
\(858\) | 6.45422e16 | + | 9.76400e16i | 0.161778 | + | 0.244740i | ||||
\(859\) | 3.77313e16i | 0.0939168i | 0.998897 | + | 0.0469584i | \(0.0149528\pi\) | ||||
−0.998897 | + | 0.0469584i | \(0.985047\pi\) | |||||||
\(860\) | 1.40672e17 | + | 5.99112e16i | 0.347709 | + | 0.148087i | ||||
\(861\) | 2.69001e17 | 0.660291 | ||||||||
\(862\) | 5.39542e17 | − | 3.56649e17i | 1.31517 | − | 0.869355i | ||||
\(863\) | − | 5.01665e16i | − | 0.121437i | −0.998155 | − | 0.0607183i | \(-0.980661\pi\) | ||
0.998155 | − | 0.0607183i | \(-0.0193391\pi\) | |||||||
\(864\) | −7.81072e16 | − | 1.75622e16i | −0.187762 | − | 0.0422180i | ||||
\(865\) | −2.12570e17 | −0.507465 | ||||||||
\(866\) | 7.94314e16 | + | 1.20164e17i | 0.188315 | + | 0.284884i | ||||
\(867\) | − | 3.45027e16i | − | 0.0812342i | ||||||
\(868\) | 2.28401e17 | − | 5.36286e17i | 0.534046 | − | 1.25394i | ||||
\(869\) | 3.02162e17 | 0.701651 | ||||||||
\(870\) | −1.52449e17 | + | 1.00772e17i | −0.351568 | + | 0.232394i | ||||
\(871\) | 4.08943e17i | 0.936599i | ||||||||
\(872\) | −7.78468e17 | + | 1.42830e17i | −1.77069 | + | 0.324878i | ||||
\(873\) | 2.15344e17 | 0.486460 | ||||||||
\(874\) | −1.14229e17 | − | 1.72806e17i | −0.256276 | − | 0.387696i | ||||
\(875\) | − | 6.74378e17i | − | 1.50264i | ||||||
\(876\) | 4.42543e16 | + | 1.88476e16i | 0.0979335 | + | 0.0417092i | ||||
\(877\) | −3.64569e17 | −0.801275 | −0.400638 | − | 0.916237i | \(-0.631211\pi\) | ||||
−0.400638 | + | 0.916237i | \(0.631211\pi\) | |||||||
\(878\) | 6.76299e17 | − | 4.47049e17i | 1.47629 | − | 0.975860i | ||||
\(879\) | − | 9.24354e16i | − | 0.200403i | ||||||
\(880\) | −7.61099e16 | + | 7.31459e16i | −0.163887 | + | 0.157505i | ||||
\(881\) | 7.83888e17 | 1.67648 | 0.838241 | − | 0.545300i | \(-0.183584\pi\) | ||||
0.838241 | + | 0.545300i | \(0.183584\pi\) | |||||||
\(882\) | −1.44061e17 | − | 2.17936e17i | −0.306009 | − | 0.462933i | ||||
\(883\) | − | 3.30429e16i | − | 0.0697131i | −0.999392 | − | 0.0348566i | \(-0.988903\pi\) | ||
0.999392 | − | 0.0348566i | \(-0.0110974\pi\) | |||||||
\(884\) | −2.40283e17 | + | 5.64186e17i | −0.503512 | + | 1.18225i | ||||
\(885\) | −1.01929e17 | −0.212147 | ||||||||
\(886\) | −4.41497e17 | + | 2.91839e17i | −0.912694 | + | 0.603311i | ||||
\(887\) | 4.40353e17i | 0.904189i | 0.891970 | + | 0.452094i | \(0.149323\pi\) | ||||
−0.891970 | + | 0.452094i | \(0.850677\pi\) | |||||||
\(888\) | −8.76210e16 | − | 4.77562e17i | −0.178702 | − | 0.973985i | ||||
\(889\) | 3.80226e16 | 0.0770250 | ||||||||
\(890\) | 1.41966e17 | + | 2.14767e17i | 0.285656 | + | 0.432143i | ||||
\(891\) | − | 2.34796e16i | − | 0.0469272i | ||||||
\(892\) | 6.72285e16 | + | 2.86322e16i | 0.133464 | + | 0.0568414i | ||||
\(893\) | 1.92444e17 | 0.379486 | ||||||||
\(894\) | −1.04164e17 | + | 6.88549e16i | −0.204030 | + | 0.134868i | ||||
\(895\) | 3.10068e17i | 0.603280i | ||||||||
\(896\) | 4.93381e17 | − | 6.85579e17i | 0.953530 | − | 1.32498i | ||||
\(897\) | 4.88333e17 | 0.937478 | ||||||||
\(898\) | 9.22484e14 | + | 1.39554e15i | 0.00175914 | + | 0.00266125i | ||||
\(899\) | 5.97795e17i | 1.13238i | ||||||||
\(900\) | −4.93071e16 | + | 1.15773e17i | −0.0927801 | + | 0.217848i | ||||
\(901\) | −3.94332e17 | −0.737077 | ||||||||
\(902\) | −1.32938e17 | + | 8.78750e16i | −0.246837 | + | 0.163165i | ||||
\(903\) | − | 3.58815e17i | − | 0.661826i | ||||||
\(904\) | −1.08697e17 | + | 1.99433e16i | −0.199163 | + | 0.0365416i | ||||
\(905\) | 4.43812e16 | 0.0807807 | ||||||||
\(906\) | 1.13972e17 | + | 1.72418e17i | 0.206077 | + | 0.311754i | ||||
\(907\) | − | 6.33281e17i | − | 1.13750i | −0.822509 | − | 0.568752i | \(-0.807426\pi\) | ||
0.822509 | − | 0.568752i | \(-0.192574\pi\) | |||||||
\(908\) | 5.15342e16 | + | 2.19481e16i | 0.0919561 | + | 0.0391635i | ||||
\(909\) | −2.69713e17 | −0.478101 | ||||||||
\(910\) | 5.00745e17 | − | 3.31003e17i | 0.881796 | − | 0.582887i | ||||
\(911\) | 3.15684e17i | 0.552258i | 0.961121 | + | 0.276129i | \(0.0890517\pi\) | ||||
−0.961121 | + | 0.276129i | \(0.910948\pi\) | |||||||
\(912\) | 7.92694e16 | + | 8.24815e16i | 0.137764 | + | 0.143347i | ||||
\(913\) | −2.87706e17 | −0.496735 | ||||||||
\(914\) | 5.71659e16 | + | 8.64810e16i | 0.0980527 | + | 0.148335i | ||||
\(915\) | 1.78674e17i | 0.304463i | ||||||||
\(916\) | 1.58589e17 | − | 3.72369e17i | 0.268473 | − | 0.630377i | ||||
\(917\) | −4.35247e17 | −0.732014 | ||||||||
\(918\) | 1.02622e17 | − | 6.78352e16i | 0.171468 | − | 0.113344i | ||||
\(919\) | − | 8.76187e17i | − | 1.45447i | −0.686390 | − | 0.727234i | \(-0.740806\pi\) | ||
0.686390 | − | 0.727234i | \(-0.259194\pi\) | |||||||
\(920\) | 7.94800e16 | + | 4.33191e17i | 0.131078 | + | 0.714418i | ||||
\(921\) | −4.14935e17 | −0.679865 | ||||||||
\(922\) | −2.16360e17 | − | 3.27311e17i | −0.352201 | − | 0.532813i | ||||
\(923\) | − | 2.81055e17i | − | 0.454550i | ||||||
\(924\) | 2.27916e17 | + | 9.70678e16i | 0.366220 | + | 0.155971i | ||||
\(925\) | −7.63174e17 | −1.21835 | ||||||||
\(926\) | −3.11703e17 | + | 2.06043e17i | −0.494396 | + | 0.326807i | ||||
\(927\) | 1.81306e17i | 0.285716i | ||||||||
\(928\) | −1.90028e17 | + | 8.45142e17i | −0.297530 | + | 1.32325i | ||||
\(929\) | −9.68108e17 | −1.50602 | −0.753008 | − | 0.658011i | \(-0.771398\pi\) | ||||
−0.753008 | + | 0.658011i | \(0.771398\pi\) | |||||||
\(930\) | −9.25578e16 | − | 1.40022e17i | −0.143059 | − | 0.216421i | ||||
\(931\) | 3.73308e17i | 0.573283i | ||||||||
\(932\) | 1.15372e17 | − | 2.70894e17i | 0.176037 | − | 0.413337i | ||||
\(933\) | −1.87819e17 | −0.284741 | ||||||||
\(934\) | −6.52328e17 | + | 4.31203e17i | −0.982618 | + | 0.649532i | ||||
\(935\) | − | 1.62204e17i | − | 0.242768i | ||||||
\(936\) | −2.65255e17 | + | 4.86677e16i | −0.394464 | + | 0.0723746i | ||||
\(937\) | 1.29269e18 | 1.91010 | 0.955050 | − | 0.296446i | \(-0.0958014\pi\) | ||||
0.955050 | + | 0.296446i | \(0.0958014\pi\) | |||||||
\(938\) | 4.77286e17 | + | 7.22043e17i | 0.700748 | + | 1.06010i | ||||
\(939\) | − | 5.44940e17i | − | 0.794978i | ||||||
\(940\) | −3.76441e17 | − | 1.60324e17i | −0.545669 | − | 0.232397i | ||||
\(941\) | −5.54035e16 | −0.0797993 | −0.0398997 | − | 0.999204i | \(-0.512704\pi\) | ||||
−0.0398997 | + | 0.999204i | \(0.512704\pi\) | |||||||
\(942\) | 1.47937e17 | − | 9.77899e16i | 0.211725 | − | 0.139955i | ||||
\(943\) | 6.64871e17i | 0.945513i | ||||||||
\(944\) | −3.48362e17 | + | 3.34795e17i | −0.492265 | + | 0.473094i | ||||
\(945\) | −1.20415e17 | −0.169079 | ||||||||
\(946\) | 1.17215e17 | + | 1.77323e17i | 0.163544 | + | 0.247411i | ||||
\(947\) | − | 1.25165e18i | − | 1.73533i | −0.497149 | − | 0.867665i | \(-0.665620\pi\) | ||
0.497149 | − | 0.867665i | \(-0.334380\pi\) | |||||||
\(948\) | −2.72803e17 | + | 6.40542e17i | −0.375836 | + | 0.882466i | ||||
\(949\) | 1.62033e17 | 0.221823 | ||||||||
\(950\) | 1.50003e17 | − | 9.91554e16i | 0.204060 | − | 0.134888i | ||||
\(951\) | − | 9.89480e16i | − | 0.133759i | ||||||
\(952\) | 2.34222e17 | + | 1.27659e18i | 0.314635 | + | 1.71486i | ||||
\(953\) | −8.07216e17 | −1.07754 | −0.538769 | − | 0.842454i | \(-0.681110\pi\) | ||||
−0.538769 | + | 0.842454i | \(0.681110\pi\) | |||||||
\(954\) | −9.56293e16 | − | 1.44669e17i | −0.126853 | − | 0.191904i | ||||
\(955\) | − | 3.72680e17i | − | 0.491265i | ||||||
\(956\) | 8.20485e17 | + | 3.49439e17i | 1.07479 | + | 0.457746i | ||||
\(957\) | −2.54056e17 | −0.330718 | ||||||||
\(958\) | 9.91589e17 | − | 6.55462e17i | 1.28274 | − | 0.847920i | ||||
\(959\) | 2.03664e18i | 2.61820i | ||||||||
\(960\) | −8.63445e16 | − | 2.27381e17i | −0.110308 | − | 0.290488i | ||||
\(961\) | 2.38597e17 | 0.302917 | ||||||||
\(962\) | −9.01916e17 | − | 1.36443e18i | −1.13793 | − | 1.72147i | ||||
\(963\) | 4.14437e17i | 0.519638i | ||||||||
\(964\) | 6.84367e16 | − | 1.60690e17i | 0.0852761 | − | 0.200229i | ||||
\(965\) | 3.28494e17 | 0.406783 | ||||||||
\(966\) | 8.62216e17 | − | 5.69944e17i | 1.06109 | − | 0.701406i | ||||
\(967\) | − | 9.22020e17i | − | 1.12767i | −0.825888 | − | 0.563834i | \(-0.809326\pi\) | ||
0.825888 | − | 0.563834i | \(-0.190674\pi\) | |||||||
\(968\) | 6.64869e17 | − | 1.21987e17i | 0.808135 | − | 0.148273i | ||||
\(969\) | −1.75783e17 | −0.212341 | ||||||||
\(970\) | 3.60772e17 | + | 5.45779e17i | 0.433114 | + | 0.655219i | ||||
\(971\) | − | 3.21154e17i | − | 0.383176i | −0.981475 | − | 0.191588i | \(-0.938636\pi\) | ||
0.981475 | − | 0.191588i | \(-0.0613637\pi\) | |||||||
\(972\) | 4.97736e16 | + | 2.11982e16i | 0.0590203 | + | 0.0251363i | ||||
\(973\) | 1.96313e17 | 0.231352 | ||||||||
\(974\) | −4.86450e16 | + | 3.21554e16i | −0.0569750 | + | 0.0376617i | ||||
\(975\) | 4.23893e17i | 0.493433i | ||||||||
\(976\) | 5.86871e17 | + | 6.10653e17i | 0.678960 | + | 0.706473i | ||||
\(977\) | −1.05644e18 | −1.21472 | −0.607359 | − | 0.794427i | \(-0.707771\pi\) | ||||
−0.607359 | + | 0.794427i | \(0.707771\pi\) | |||||||
\(978\) | 5.09884e16 | + | 7.71358e16i | 0.0582691 | + | 0.0881501i | ||||
\(979\) | 3.57909e17i | 0.406515i | ||||||||
\(980\) | 3.11000e17 | − | 7.30230e17i | 0.351078 | − | 0.824334i | ||||
\(981\) | 5.34841e17 | 0.600082 | ||||||||
\(982\) | 4.98805e15 | − | 3.29721e15i | 0.00556239 | − | 0.00367686i | ||||
\(983\) | − | 1.65538e18i | − | 1.83475i | −0.398023 | − | 0.917375i | \(-0.630304\pi\) | ||
0.398023 | − | 0.917375i | \(-0.369696\pi\) | |||||||
\(984\) | −6.62618e16 | − | 3.61147e17i | −0.0729949 | − | 0.397845i | ||||
\(985\) | 2.87445e17 | 0.314729 | ||||||||
\(986\) | −7.33997e17 | − | 1.11040e18i | −0.798790 | − | 1.20842i | ||||
\(987\) | 9.60197e17i | 1.03862i | ||||||||
\(988\) | 3.54547e17 | + | 1.50999e17i | 0.381181 | + | 0.162343i | ||||
\(989\) | 8.86858e17 | 0.947712 | ||||||||
\(990\) | 5.95079e16 | − | 3.93361e16i | 0.0632068 | − | 0.0417811i | ||||
\(991\) | − | 1.47211e18i | − | 1.55417i | −0.629394 | − | 0.777087i | \(-0.716697\pi\) | ||
0.629394 | − | 0.777087i | \(-0.283303\pi\) | |||||||
\(992\) | −7.76252e17 | − | 1.74539e17i | −0.814578 | − | 0.183156i | ||||
\(993\) | −6.95826e16 | −0.0725780 | ||||||||
\(994\) | −3.28026e17 | − | 4.96240e17i | −0.340087 | − | 0.514486i | ||||
\(995\) | 4.21934e16i | 0.0434816i | ||||||||
\(996\) | 2.59751e17 | − | 6.09898e17i | 0.266074 | − | 0.624742i | ||||
\(997\) | 1.00149e18 | 1.01971 | 0.509855 | − | 0.860261i | \(-0.329699\pi\) | ||||
0.509855 | + | 0.860261i | \(0.329699\pi\) | |||||||
\(998\) | 8.55642e16 | − | 5.65598e16i | 0.0865982 | − | 0.0572433i | ||||
\(999\) | 3.28105e17i | 0.330081i |
(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 | 12.13.d.a.7.5 | ✓ | 12 | |
3.2 | odd | 2 | 36.13.d.d.19.8 | 12 | |||
4.3 | odd | 2 | inner | 12.13.d.a.7.6 | yes | 12 | |
8.3 | odd | 2 | 192.13.g.e.127.2 | 12 | |||
8.5 | even | 2 | 192.13.g.e.127.8 | 12 | |||
12.11 | even | 2 | 36.13.d.d.19.7 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.13.d.a.7.5 | ✓ | 12 | 1.1 | even | 1 | trivial | |
12.13.d.a.7.6 | yes | 12 | 4.3 | odd | 2 | inner | |
36.13.d.d.19.7 | 12 | 12.11 | even | 2 | |||
36.13.d.d.19.8 | 12 | 3.2 | odd | 2 | |||
192.13.g.e.127.2 | 12 | 8.3 | odd | 2 | |||
192.13.g.e.127.8 | 12 | 8.5 | even | 2 |