Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,9,Mod(74,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.74");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(30.5533957546\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 3278 x^{18} + 4245491 x^{16} + 2854629536 x^{14} + 1117319469691 x^{12} + 266849787342054 x^{10} + \cdots + 89\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{22}\cdot 5^{26} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 74.12 | ||
Root | \(-15.0371i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.74 |
Dual form | 75.9.d.d.74.11 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.03414 | 0.189634 | 0.0948170 | − | 0.995495i | \(-0.469773\pi\) | ||||
0.0948170 | + | 0.995495i | \(0.469773\pi\) | |||||||
\(3\) | 79.6728 | + | 14.6031i | 0.983614 | + | 0.180286i | ||||
\(4\) | −246.794 | −0.964039 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 241.739 | + | 44.3080i | 0.186527 | + | 0.0341882i | ||||
\(7\) | − | 59.7348i | − | 0.0248791i | −0.999923 | − | 0.0124396i | \(-0.996040\pi\) | ||
0.999923 | − | 0.0124396i | \(-0.00395974\pi\) | |||||||
\(8\) | −1525.55 | −0.372448 | ||||||||
\(9\) | 6134.50 | + | 2326.94i | 0.934994 | + | 0.354663i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 21885.6i | − | 1.49482i | −0.664366 | − | 0.747408i | \(-0.731298\pi\) | ||
0.664366 | − | 0.747408i | \(-0.268702\pi\) | |||||||
\(12\) | −19662.8 | − | 3603.96i | −0.948243 | − | 0.173802i | ||||
\(13\) | 38460.5i | 1.34661i | 0.739366 | + | 0.673304i | \(0.235125\pi\) | ||||
−0.739366 | + | 0.673304i | \(0.764875\pi\) | |||||||
\(14\) | − | 181.244i | − | 0.00471792i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 58550.5 | 0.893410 | ||||||||
\(17\) | 36101.0 | 0.432238 | 0.216119 | − | 0.976367i | \(-0.430660\pi\) | ||||
0.216119 | + | 0.976367i | \(0.430660\pi\) | |||||||
\(18\) | 18612.9 | + | 7060.28i | 0.177307 | + | 0.0672561i | ||||
\(19\) | 136807. | 1.04977 | 0.524884 | − | 0.851174i | \(-0.324109\pi\) | ||||
0.524884 | + | 0.851174i | \(0.324109\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 872.314 | − | 4759.23i | 0.00448534 | − | 0.0244715i | ||||
\(22\) | − | 66404.0i | − | 0.283468i | ||||||
\(23\) | 235710. | 0.842300 | 0.421150 | − | 0.906991i | \(-0.361627\pi\) | ||||
0.421150 | + | 0.906991i | \(0.361627\pi\) | |||||||
\(24\) | −121545. | − | 22277.8i | −0.366346 | − | 0.0671470i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 116695.i | 0.255363i | ||||||||
\(27\) | 454772. | + | 274977.i | 0.855733 | + | 0.517417i | ||||
\(28\) | 14742.2i | 0.0239844i | ||||||||
\(29\) | 896225.i | 1.26714i | 0.773685 | + | 0.633571i | \(0.218412\pi\) | ||||
−0.773685 | + | 0.633571i | \(0.781588\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 68043.4 | 0.0736782 | 0.0368391 | − | 0.999321i | \(-0.488271\pi\) | ||||
0.0368391 | + | 0.999321i | \(0.488271\pi\) | |||||||
\(32\) | 568191. | 0.541869 | ||||||||
\(33\) | 319598. | − | 1.74369e6i | 0.269493 | − | 1.47032i | ||||
\(34\) | 109535. | 0.0819670 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.51396e6 | − | 574275.i | −0.901371 | − | 0.341909i | ||||
\(37\) | − | 66517.7i | − | 0.0354920i | −0.999843 | − | 0.0177460i | \(-0.994351\pi\) | ||
0.999843 | − | 0.0177460i | \(-0.00564902\pi\) | |||||||
\(38\) | 415091. | 0.199071 | ||||||||
\(39\) | −561643. | + | 3.06425e6i | −0.242774 | + | 1.32454i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.76632e6i | − | 1.33285i | −0.745572 | − | 0.666425i | \(-0.767824\pi\) | ||
0.745572 | − | 0.666425i | \(-0.232176\pi\) | |||||||
\(42\) | 2646.73 | − | 14440.2i | 0.000850573 | − | 0.00464062i | ||||
\(43\) | 2.03993e6i | 0.596679i | 0.954460 | + | 0.298339i | \(0.0964327\pi\) | ||||
−0.954460 | + | 0.298339i | \(0.903567\pi\) | |||||||
\(44\) | 5.40123e6i | 1.44106i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 715178. | 0.159729 | ||||||||
\(47\) | 5.93447e6 | 1.21616 | 0.608080 | − | 0.793876i | \(-0.291940\pi\) | ||||
0.608080 | + | 0.793876i | \(0.291940\pi\) | |||||||
\(48\) | 4.66488e6 | + | 855021.i | 0.878771 | + | 0.161069i | ||||
\(49\) | 5.76123e6 | 0.999381 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.87626e6 | + | 527187.i | 0.425156 | + | 0.0779263i | ||||
\(52\) | − | 9.49181e6i | − | 1.29818i | ||||||
\(53\) | 1.31066e7 | 1.66107 | 0.830534 | − | 0.556969i | \(-0.188036\pi\) | ||||
0.830534 | + | 0.556969i | \(0.188036\pi\) | |||||||
\(54\) | 1.37984e6 | + | 834319.i | 0.162276 | + | 0.0981199i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 91128.3i | 0.00926619i | ||||||||
\(57\) | 1.08998e7 | + | 1.99781e6i | 1.03257 | + | 0.189258i | ||||
\(58\) | 2.71928e6i | 0.240293i | ||||||||
\(59\) | 1.58410e7i | 1.30730i | 0.756799 | + | 0.653648i | \(0.226762\pi\) | ||||
−0.756799 | + | 0.653648i | \(0.773238\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.51489e6 | −0.253859 | −0.126929 | − | 0.991912i | \(-0.540512\pi\) | ||||
−0.126929 | + | 0.991912i | \(0.540512\pi\) | |||||||
\(62\) | 206453. | 0.0139719 | ||||||||
\(63\) | 138999. | − | 366443.i | 0.00882370 | − | 0.0232618i | ||||
\(64\) | −1.32650e7 | −0.790653 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 969706. | − | 5.29059e6i | 0.0511051 | − | 0.278823i | ||||
\(67\) | 1.39297e7i | 0.691263i | 0.938370 | + | 0.345632i | \(0.112335\pi\) | ||||
−0.938370 | + | 0.345632i | \(0.887665\pi\) | |||||||
\(68\) | −8.90950e6 | −0.416695 | ||||||||
\(69\) | 1.87797e7 | + | 3.44210e6i | 0.828498 | + | 0.151854i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.51547e7i | − | 0.596367i | −0.954508 | − | 0.298184i | \(-0.903619\pi\) | ||
0.954508 | − | 0.298184i | \(-0.0963808\pi\) | |||||||
\(72\) | −9.35847e6 | − | 3.54986e6i | −0.348237 | − | 0.132094i | ||||
\(73\) | − | 3.93167e7i | − | 1.38448i | −0.721669 | − | 0.692238i | \(-0.756625\pi\) | ||
0.721669 | − | 0.692238i | \(-0.243375\pi\) | |||||||
\(74\) | − | 201824.i | − | 0.00673049i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.37631e7 | −1.01202 | ||||||||
\(77\) | −1.30733e6 | −0.0371897 | ||||||||
\(78\) | −1.70411e6 | + | 9.29738e6i | −0.0460382 | + | 0.251178i | ||||
\(79\) | −3.15613e7 | −0.810301 | −0.405151 | − | 0.914250i | \(-0.632781\pi\) | ||||
−0.405151 | + | 0.914250i | \(0.632781\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.22174e7 | + | 2.85492e7i | 0.748429 | + | 0.663215i | ||||
\(82\) | − | 1.14275e7i | − | 0.252754i | ||||||
\(83\) | −4.88680e7 | −1.02970 | −0.514852 | − | 0.857279i | \(-0.672153\pi\) | ||||
−0.514852 | + | 0.857279i | \(0.672153\pi\) | |||||||
\(84\) | −215282. | + | 1.17455e6i | −0.00432405 | + | 0.0235914i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.18943e6i | 0.113151i | ||||||||
\(87\) | −1.30877e7 | + | 7.14048e7i | −0.228447 | + | 1.24638i | ||||
\(88\) | 3.33875e7i | 0.556741i | ||||||||
\(89\) | − | 1.09263e8i | − | 1.74145i | −0.491766 | − | 0.870727i | \(-0.663648\pi\) | ||
0.491766 | − | 0.870727i | \(-0.336352\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.29743e6 | 0.0335024 | ||||||||
\(92\) | −5.81718e7 | −0.812010 | ||||||||
\(93\) | 5.42120e6 | + | 993646.i | 0.0724709 | + | 0.0132831i | ||||
\(94\) | 1.80060e7 | 0.230625 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 4.52694e7 | + | 8.29737e6i | 0.532990 | + | 0.0976912i | ||||
\(97\) | − | 1.16098e8i | − | 1.31140i | −0.755020 | − | 0.655702i | \(-0.772373\pi\) | ||
0.755020 | − | 0.655702i | \(-0.227627\pi\) | |||||||
\(98\) | 1.74804e7 | 0.189517 | ||||||||
\(99\) | 5.09265e7 | − | 1.34257e8i | 0.530155 | − | 1.39764i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.46015e8i | 1.40318i | 0.712582 | + | 0.701589i | \(0.247526\pi\) | ||||
−0.712582 | + | 0.701589i | \(0.752474\pi\) | |||||||
\(102\) | 8.72700e6 | + | 1.59956e6i | 0.0806239 | + | 0.0147775i | ||||
\(103\) | 1.60527e8i | 1.42626i | 0.701032 | + | 0.713130i | \(0.252723\pi\) | ||||
−0.701032 | + | 0.713130i | \(0.747277\pi\) | |||||||
\(104\) | − | 5.86733e7i | − | 0.501542i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.97673e7 | 0.314995 | ||||||||
\(107\) | −1.10586e8 | −0.843654 | −0.421827 | − | 0.906676i | \(-0.638611\pi\) | ||||
−0.421827 | + | 0.906676i | \(0.638611\pi\) | |||||||
\(108\) | −1.12235e8 | − | 6.78626e7i | −0.824960 | − | 0.498810i | ||||
\(109\) | −1.53065e8 | −1.08435 | −0.542176 | − | 0.840265i | \(-0.682400\pi\) | ||||
−0.542176 | + | 0.840265i | \(0.682400\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 971367. | − | 5.29965e6i | 0.00639869 | − | 0.0349104i | ||||
\(112\) | − | 3.49750e6i | − | 0.0222273i | ||||||
\(113\) | −1.01707e8 | −0.623791 | −0.311895 | − | 0.950116i | \(-0.600964\pi\) | ||||
−0.311895 | + | 0.950116i | \(0.600964\pi\) | |||||||
\(114\) | 3.30714e7 | + | 6.06163e6i | 0.195810 | + | 0.0358897i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 2.21183e8i | − | 1.22157i | ||||||
\(117\) | −8.94953e7 | + | 2.35936e8i | −0.477592 | + | 1.25907i | ||||
\(118\) | 4.80638e7i | 0.247908i | ||||||||
\(119\) | − | 2.15648e6i | − | 0.0107537i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.64620e8 | −1.23447 | ||||||||
\(122\) | −1.06647e7 | −0.0481402 | ||||||||
\(123\) | 5.50000e7 | − | 3.00073e8i | 0.240294 | − | 1.31101i | ||||
\(124\) | −1.67927e7 | −0.0710287 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 421744. | − | 1.11184e6i | 0.00167327 | − | 0.00441123i | ||||
\(127\) | − | 4.85620e8i | − | 1.86673i | −0.358928 | − | 0.933365i | \(-0.616858\pi\) | ||
0.358928 | − | 0.933365i | \(-0.383142\pi\) | |||||||
\(128\) | −1.85705e8 | −0.691804 | ||||||||
\(129\) | −2.97893e7 | + | 1.62527e8i | −0.107573 | + | 0.586902i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.26001e8i | 0.767407i | 0.923456 | + | 0.383704i | \(0.125352\pi\) | ||||
−0.923456 | + | 0.383704i | \(0.874648\pi\) | |||||||
\(132\) | −7.88749e7 | + | 4.30331e8i | −0.259802 | + | 1.41745i | ||||
\(133\) | − | 8.17211e6i | − | 0.0261173i | ||||||
\(134\) | 4.22648e7i | 0.131087i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.50738e7 | −0.160986 | ||||||||
\(137\) | 5.46283e8 | 1.55073 | 0.775364 | − | 0.631515i | \(-0.217566\pi\) | ||||
0.775364 | + | 0.631515i | \(0.217566\pi\) | |||||||
\(138\) | 5.69802e7 | + | 1.04438e7i | 0.157111 | + | 0.0287967i | ||||
\(139\) | −2.15686e8 | −0.577779 | −0.288890 | − | 0.957362i | \(-0.593286\pi\) | ||||
−0.288890 | + | 0.957362i | \(0.593286\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.72816e8 | + | 8.66618e7i | 1.19623 | + | 0.219256i | ||||
\(142\) | − | 4.59815e7i | − | 0.113091i | ||||||
\(143\) | 8.41730e8 | 2.01293 | ||||||||
\(144\) | 3.59178e8 | + | 1.36244e8i | 0.835333 | + | 0.316859i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 1.19292e8i | − | 0.262544i | ||||||
\(147\) | 4.59013e8 | + | 8.41320e7i | 0.983005 | + | 0.180174i | ||||
\(148\) | 1.64162e7i | 0.0342157i | ||||||||
\(149\) | 4.32442e8i | 0.877371i | 0.898641 | + | 0.438685i | \(0.144556\pi\) | ||||
−0.898641 | + | 0.438685i | \(0.855444\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.22279e8 | −0.619904 | −0.309952 | − | 0.950752i | \(-0.600313\pi\) | ||||
−0.309952 | + | 0.950752i | \(0.600313\pi\) | |||||||
\(152\) | −2.08705e8 | −0.390984 | ||||||||
\(153\) | 2.21461e8 | + | 8.40049e7i | 0.404140 | + | 0.153299i | ||||
\(154\) | −3.96663e6 | −0.00705242 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.38610e8 | − | 7.56239e8i | 0.234043 | − | 1.27691i | ||||
\(157\) | − | 5.59602e8i | − | 0.921045i | −0.887648 | − | 0.460522i | \(-0.847662\pi\) | ||
0.887648 | − | 0.460522i | \(-0.152338\pi\) | |||||||
\(158\) | −9.57615e7 | −0.153661 | ||||||||
\(159\) | 1.04424e9 | + | 1.91398e8i | 1.63385 | + | 0.299466i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.40801e7i | − | 0.0209557i | ||||||
\(162\) | 9.77522e7 | + | 8.66225e7i | 0.141927 | + | 0.125768i | ||||
\(163\) | 4.67465e8i | 0.662215i | 0.943593 | + | 0.331107i | \(0.107422\pi\) | ||||
−0.943593 | + | 0.331107i | \(0.892578\pi\) | |||||||
\(164\) | 9.29504e8i | 1.28492i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.48273e8 | −0.195267 | ||||||||
\(167\) | 4.54837e8 | 0.584776 | 0.292388 | − | 0.956300i | \(-0.405550\pi\) | ||||
0.292388 | + | 0.956300i | \(0.405550\pi\) | |||||||
\(168\) | −1.33076e6 | + | 7.26044e6i | −0.00167056 | + | 0.00911435i | ||||
\(169\) | −6.63477e8 | −0.813353 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.39240e8 | + | 3.18341e8i | 0.981526 | + | 0.372313i | ||||
\(172\) | − | 5.03442e8i | − | 0.575222i | ||||||
\(173\) | 8.28969e8 | 0.925452 | 0.462726 | − | 0.886501i | \(-0.346871\pi\) | ||||
0.462726 | + | 0.886501i | \(0.346871\pi\) | |||||||
\(174\) | −3.97099e7 | + | 2.16652e8i | −0.0433214 | + | 0.236356i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 1.28141e9i | − | 1.33548i | ||||||
\(177\) | −2.31328e8 | + | 1.26209e9i | −0.235686 | + | 1.28587i | ||||
\(178\) | − | 3.31519e8i | − | 0.330239i | ||||||
\(179\) | − | 1.84168e8i | − | 0.179392i | −0.995969 | − | 0.0896959i | \(-0.971410\pi\) | ||
0.995969 | − | 0.0896959i | \(-0.0285895\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.14139e9 | −1.06345 | −0.531727 | − | 0.846916i | \(-0.678457\pi\) | ||||
−0.531727 | + | 0.846916i | \(0.678457\pi\) | |||||||
\(182\) | 6.97072e6 | 0.00635319 | ||||||||
\(183\) | −2.80041e8 | − | 5.13283e7i | −0.249699 | − | 0.0457670i | ||||
\(184\) | −3.59587e8 | −0.313713 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.64487e7 | + | 3.01486e6i | 0.0137429 | + | 0.00251893i | ||||
\(187\) | − | 7.90091e8i | − | 0.646116i | ||||||
\(188\) | −1.46459e9 | −1.17243 | ||||||||
\(189\) | 1.64257e7 | − | 2.71657e7i | 0.0128729 | − | 0.0212899i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.62451e9i | 1.22064i | 0.792153 | + | 0.610322i | \(0.208960\pi\) | ||||
−0.792153 | + | 0.610322i | \(0.791040\pi\) | |||||||
\(192\) | −1.05686e9 | − | 1.93710e8i | −0.777698 | − | 0.142543i | ||||
\(193\) | − | 1.50247e9i | − | 1.08287i | −0.840743 | − | 0.541434i | \(-0.817882\pi\) | ||
0.840743 | − | 0.541434i | \(-0.182118\pi\) | |||||||
\(194\) | − | 3.52257e8i | − | 0.248687i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.42184e9 | −0.963442 | ||||||||
\(197\) | 1.00297e9 | 0.665924 | 0.332962 | − | 0.942940i | \(-0.391952\pi\) | ||||
0.332962 | + | 0.942940i | \(0.391952\pi\) | |||||||
\(198\) | 1.54518e8 | − | 4.07355e8i | 0.100535 | − | 0.265041i | ||||
\(199\) | −6.24974e8 | −0.398520 | −0.199260 | − | 0.979947i | \(-0.563854\pi\) | ||||
−0.199260 | + | 0.979947i | \(0.563854\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.03418e8 | + | 1.10982e9i | −0.124625 | + | 0.679936i | ||||
\(202\) | 4.43031e8i | 0.266090i | ||||||||
\(203\) | 5.35358e7 | 0.0315254 | ||||||||
\(204\) | −7.09845e8 | − | 1.30107e8i | −0.409867 | − | 0.0751240i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.87061e8i | 0.270467i | ||||||||
\(207\) | 1.44596e9 | + | 5.48484e8i | 0.787545 | + | 0.298732i | ||||
\(208\) | 2.25188e9i | 1.20307i | ||||||||
\(209\) | − | 2.99410e9i | − | 1.56921i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.84677e9 | 1.94073 | 0.970367 | − | 0.241636i | \(-0.0776839\pi\) | ||||
0.970367 | + | 0.241636i | \(0.0776839\pi\) | |||||||
\(212\) | −3.23463e9 | −1.60133 | ||||||||
\(213\) | 2.21306e8 | − | 1.20742e9i | 0.107516 | − | 0.586596i | ||||
\(214\) | −3.35533e8 | −0.159985 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.93776e8 | − | 4.19490e8i | −0.318716 | − | 0.192711i | ||||
\(217\) | − | 4.06455e6i | − | 0.00183305i | ||||||
\(218\) | −4.64422e8 | −0.205630 | ||||||||
\(219\) | 5.74147e8 | − | 3.13247e9i | 0.249601 | − | 1.36179i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.38846e9i | 0.582055i | ||||||||
\(222\) | 2.94727e6 | − | 1.60799e7i | 0.00121341 | − | 0.00662020i | ||||
\(223\) | 3.37297e9i | 1.36393i | 0.731383 | + | 0.681967i | \(0.238875\pi\) | ||||
−0.731383 | + | 0.681967i | \(0.761125\pi\) | |||||||
\(224\) | − | 3.39408e7i | − | 0.0134812i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.08595e8 | −0.118292 | ||||||||
\(227\) | −2.59338e9 | −0.976705 | −0.488352 | − | 0.872646i | \(-0.662402\pi\) | ||||
−0.488352 | + | 0.872646i | \(0.662402\pi\) | |||||||
\(228\) | −2.69000e9 | − | 4.93046e8i | −0.995434 | − | 0.182452i | ||||
\(229\) | 2.81270e9 | 1.02278 | 0.511389 | − | 0.859349i | \(-0.329131\pi\) | ||||
0.511389 | + | 0.859349i | \(0.329131\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.04159e8 | − | 1.90911e7i | −0.0365803 | − | 0.00670476i | ||||
\(232\) | − | 1.36724e9i | − | 0.471945i | ||||||
\(233\) | −3.25957e9 | −1.10595 | −0.552977 | − | 0.833196i | \(-0.686508\pi\) | ||||
−0.552977 | + | 0.833196i | \(0.686508\pi\) | |||||||
\(234\) | −2.71542e8 | + | 7.15862e8i | −0.0905676 | + | 0.238762i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 3.90946e9i | − | 1.26028i | ||||||
\(237\) | −2.51458e9 | − | 4.60894e8i | −0.797024 | − | 0.146086i | ||||
\(238\) | − | 6.54308e6i | − | 0.00203927i | ||||||
\(239\) | − | 1.97409e9i | − | 0.605028i | −0.953145 | − | 0.302514i | \(-0.902174\pi\) | ||
0.953145 | − | 0.302514i | \(-0.0978260\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.48773e8 | 0.133033 | 0.0665163 | − | 0.997785i | \(-0.478812\pi\) | ||||
0.0665163 | + | 0.997785i | \(0.478812\pi\) | |||||||
\(242\) | −8.02895e8 | −0.234098 | ||||||||
\(243\) | 2.14994e9 | + | 2.74507e9i | 0.616597 | + | 0.787279i | ||||
\(244\) | 8.67453e8 | 0.244730 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.66878e8 | − | 9.10464e8i | 0.0455678 | − | 0.248612i | ||||
\(247\) | 5.26165e9i | 1.41362i | ||||||||
\(248\) | −1.03803e8 | −0.0274413 | ||||||||
\(249\) | −3.89345e9 | − | 7.13626e8i | −1.01283 | − | 0.185641i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.31424e9i | 0.583060i | 0.956562 | + | 0.291530i | \(0.0941644\pi\) | ||||
−0.956562 | + | 0.291530i | \(0.905836\pi\) | |||||||
\(252\) | −3.43042e7 | + | 9.04359e7i | −0.00850639 | + | 0.0224253i | ||||
\(253\) | − | 5.15865e9i | − | 1.25908i | ||||||
\(254\) | − | 1.47344e9i | − | 0.353995i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.83238e9 | 0.659464 | ||||||||
\(257\) | 5.64145e9 | 1.29318 | 0.646589 | − | 0.762839i | \(-0.276195\pi\) | ||||
0.646589 | + | 0.762839i | \(0.276195\pi\) | |||||||
\(258\) | −9.03850e7 | + | 4.93129e8i | −0.0203994 | + | 0.111296i | ||||
\(259\) | −3.97342e6 | −0.000883010 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.08547e9 | + | 5.49789e9i | −0.449408 | + | 1.18477i | ||||
\(262\) | 6.85721e8i | 0.145526i | ||||||||
\(263\) | 3.58501e9 | 0.749320 | 0.374660 | − | 0.927162i | \(-0.377760\pi\) | ||||
0.374660 | + | 0.927162i | \(0.377760\pi\) | |||||||
\(264\) | −4.87562e8 | + | 2.66008e9i | −0.100372 | + | 0.547619i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 2.47954e7i | − | 0.00495272i | ||||||
\(267\) | 1.59558e9 | − | 8.70527e9i | 0.313959 | − | 1.71292i | ||||
\(268\) | − | 3.43777e9i | − | 0.666405i | ||||||
\(269\) | 6.68399e9i | 1.27652i | 0.769822 | + | 0.638259i | \(0.220345\pi\) | ||||
−0.769822 | + | 0.638259i | \(0.779655\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.71996e9 | −0.689702 | −0.344851 | − | 0.938658i | \(-0.612070\pi\) | ||||
−0.344851 | + | 0.938658i | \(0.612070\pi\) | |||||||
\(272\) | 2.11373e9 | 0.386166 | ||||||||
\(273\) | 1.83042e8 | + | 3.35496e7i | 0.0329535 | + | 0.00604000i | ||||
\(274\) | 1.65750e9 | 0.294071 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.63471e9 | − | 8.49490e8i | −0.798704 | − | 0.146394i | ||||
\(277\) | 3.64024e9i | 0.618317i | 0.951011 | + | 0.309158i | \(0.100047\pi\) | ||||
−0.951011 | + | 0.309158i | \(0.899953\pi\) | |||||||
\(278\) | −6.54421e8 | −0.109567 | ||||||||
\(279\) | 4.17412e8 | + | 1.58333e8i | 0.0688887 | + | 0.0261309i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.06642e9i | − | 0.171041i | −0.996336 | − | 0.0855207i | \(-0.972745\pi\) | ||
0.996336 | − | 0.0855207i | \(-0.0272554\pi\) | |||||||
\(282\) | 1.43459e9 | + | 2.62944e8i | 0.226846 | + | 0.0415784i | ||||
\(283\) | − | 4.50485e9i | − | 0.702319i | −0.936316 | − | 0.351160i | \(-0.885787\pi\) | ||
0.936316 | − | 0.351160i | \(-0.114213\pi\) | |||||||
\(284\) | 3.74009e9i | 0.574921i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.55393e9 | 0.381720 | ||||||||
\(287\) | −2.24980e8 | −0.0331601 | ||||||||
\(288\) | 3.48557e9 | + | 1.32215e9i | 0.506645 | + | 0.192181i | ||||
\(289\) | −5.67248e9 | −0.813170 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.69539e9 | − | 9.24982e9i | 0.236427 | − | 1.28992i | ||||
\(292\) | 9.70312e9i | 1.33469i | ||||||||
\(293\) | 7.62525e9 | 1.03463 | 0.517313 | − | 0.855796i | \(-0.326932\pi\) | ||||
0.517313 | + | 0.855796i | \(0.326932\pi\) | |||||||
\(294\) | 1.39271e9 | + | 2.55268e8i | 0.186411 | + | 0.0341671i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.01476e8i | 0.0132189i | ||||||||
\(297\) | 6.01803e9 | − | 9.95295e9i | 0.773443 | − | 1.27916i | ||||
\(298\) | 1.31209e9i | 0.166379i | ||||||||
\(299\) | 9.06552e9i | 1.13425i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.21855e8 | 0.0148448 | ||||||||
\(302\) | −9.77840e8 | −0.117555 | ||||||||
\(303\) | −2.13228e9 | + | 1.16334e10i | −0.252972 | + | 1.38019i | ||||
\(304\) | 8.01010e9 | 0.937873 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.71945e8 | + | 2.54883e8i | 0.0766387 | + | 0.0290707i | ||||
\(307\) | − | 5.35640e9i | − | 0.603003i | −0.953466 | − | 0.301501i | \(-0.902512\pi\) | ||
0.953466 | − | 0.301501i | \(-0.0974878\pi\) | |||||||
\(308\) | 3.22641e8 | 0.0358523 | ||||||||
\(309\) | −2.34419e9 | + | 1.27896e10i | −0.257134 | + | 1.40289i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 8.46968e9i | − | 0.905369i | −0.891671 | − | 0.452685i | \(-0.850466\pi\) | ||
0.891671 | − | 0.452685i | \(-0.149534\pi\) | |||||||
\(312\) | 8.56814e8 | − | 4.67466e9i | 0.0904207 | − | 0.493324i | ||||
\(313\) | − | 3.96394e9i | − | 0.413000i | −0.978447 | − | 0.206500i | \(-0.933793\pi\) | ||
0.978447 | − | 0.206500i | \(-0.0662073\pi\) | |||||||
\(314\) | − | 1.69791e9i | − | 0.174661i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.78914e9 | 0.781162 | ||||||||
\(317\) | 1.64274e9 | 0.162679 | 0.0813393 | − | 0.996686i | \(-0.474080\pi\) | ||||
0.0813393 | + | 0.996686i | \(0.474080\pi\) | |||||||
\(318\) | 3.16837e9 | + | 5.80728e8i | 0.309833 | + | 0.0567890i | ||||
\(319\) | 1.96144e10 | 1.89414 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.81067e9 | − | 1.61490e9i | −0.829830 | − | 0.152099i | ||||
\(322\) | − | 4.27210e7i | − | 0.00397391i | ||||||
\(323\) | 4.93885e9 | 0.453750 | ||||||||
\(324\) | −7.95106e9 | − | 7.04578e9i | −0.721514 | − | 0.639365i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.41836e9i | 0.125578i | ||||||||
\(327\) | −1.21951e10 | − | 2.23523e9i | −1.06658 | − | 0.195493i | ||||
\(328\) | 5.74570e9i | 0.496418i | ||||||||
\(329\) | − | 3.54494e8i | − | 0.0302570i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.10076e9 | 0.591552 | 0.295776 | − | 0.955257i | \(-0.404422\pi\) | ||||
0.295776 | + | 0.955257i | \(0.404422\pi\) | |||||||
\(332\) | 1.20603e10 | 0.992675 | ||||||||
\(333\) | 1.54783e8 | − | 4.08053e8i | 0.0125877 | − | 0.0331848i | ||||
\(334\) | 1.38004e9 | 0.110893 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.10745e7 | − | 2.78656e8i | 0.00400725 | − | 0.0218630i | ||||
\(337\) | 2.32757e10i | 1.80461i | 0.431099 | + | 0.902305i | \(0.358126\pi\) | ||||
−0.431099 | + | 0.902305i | \(0.641874\pi\) | |||||||
\(338\) | −2.01308e9 | −0.154239 | ||||||||
\(339\) | −8.10331e9 | − | 1.48525e9i | −0.613569 | − | 0.112460i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.48917e9i | − | 0.110135i | ||||||
\(342\) | 2.54637e9 | + | 9.65893e8i | 0.186131 | + | 0.0706032i | ||||
\(343\) | − | 6.88505e8i | − | 0.0497428i | ||||||
\(344\) | − | 3.11201e9i | − | 0.222232i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.51521e9 | 0.175497 | ||||||||
\(347\) | −1.85680e9 | −0.128070 | −0.0640351 | − | 0.997948i | \(-0.520397\pi\) | ||||
−0.0640351 | + | 0.997948i | \(0.520397\pi\) | |||||||
\(348\) | 3.22996e9 | − | 1.76223e10i | 0.220232 | − | 1.20156i | ||||
\(349\) | −1.48512e10 | −1.00106 | −0.500529 | − | 0.865720i | \(-0.666861\pi\) | ||||
−0.500529 | + | 0.865720i | \(0.666861\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.05757e10 | + | 1.74907e10i | −0.696758 | + | 1.15234i | ||||
\(352\) | − | 1.24352e10i | − | 0.809994i | ||||||
\(353\) | −1.49807e10 | −0.964791 | −0.482396 | − | 0.875954i | \(-0.660233\pi\) | ||||
−0.482396 | + | 0.875954i | \(0.660233\pi\) | |||||||
\(354\) | −7.01881e8 | + | 3.82937e9i | −0.0446941 | + | 0.243845i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.69654e10i | 1.67883i | ||||||||
\(357\) | 3.14914e7 | − | 1.71813e8i | 0.00193874 | − | 0.0105775i | ||||
\(358\) | − | 5.58793e8i | − | 0.0340188i | ||||||
\(359\) | − | 2.40350e10i | − | 1.44699i | −0.690327 | − | 0.723497i | \(-0.742534\pi\) | ||
0.690327 | − | 0.723497i | \(-0.257466\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.73251e9 | 0.102011 | ||||||||
\(362\) | −3.46313e9 | −0.201667 | ||||||||
\(363\) | −2.10830e10 | − | 3.86428e9i | −1.21424 | − | 0.222557i | ||||
\(364\) | −5.66991e8 | −0.0322976 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8.49683e8 | − | 1.55737e8i | −0.0473514 | − | 0.00867898i | ||||
\(367\) | 6.35979e9i | 0.350573i | 0.984517 | + | 0.175287i | \(0.0560852\pi\) | ||||
−0.984517 | + | 0.175287i | \(0.943915\pi\) | |||||||
\(368\) | 1.38009e10 | 0.752519 | ||||||||
\(369\) | 8.76400e9 | − | 2.31045e10i | 0.472712 | − | 1.24621i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 7.82921e8i | − | 0.0413259i | ||||||
\(372\) | −1.33792e9 | − | 2.45226e8i | −0.0698648 | − | 0.0128054i | ||||
\(373\) | − | 9.55992e9i | − | 0.493877i | −0.969031 | − | 0.246939i | \(-0.920575\pi\) | ||
0.969031 | − | 0.246939i | \(-0.0794246\pi\) | |||||||
\(374\) | − | 2.39725e9i | − | 0.122526i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.05333e9 | −0.452957 | ||||||||
\(377\) | −3.44693e10 | −1.70634 | ||||||||
\(378\) | 4.98378e7 | − | 8.24245e7i | 0.00244114 | − | 0.00403728i | ||||
\(379\) | −1.47270e9 | −0.0713767 | −0.0356883 | − | 0.999363i | \(-0.511362\pi\) | ||||
−0.0356883 | + | 0.999363i | \(0.511362\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.09157e9 | − | 3.86907e10i | 0.336544 | − | 1.83614i | ||||
\(382\) | 4.92900e9i | 0.231476i | ||||||||
\(383\) | −3.53991e10 | −1.64512 | −0.822559 | − | 0.568680i | \(-0.807454\pi\) | ||||
−0.822559 | + | 0.568680i | \(0.807454\pi\) | |||||||
\(384\) | −1.47956e10 | − | 2.71187e9i | −0.680468 | − | 0.124722i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 4.55870e9i | − | 0.205349i | ||||||
\(387\) | −4.74679e9 | + | 1.25139e10i | −0.211620 | + | 0.557891i | ||||
\(388\) | 2.86522e10i | 1.26424i | ||||||||
\(389\) | 1.00866e10i | 0.440502i | 0.975443 | + | 0.220251i | \(0.0706877\pi\) | ||||
−0.975443 | + | 0.220251i | \(0.929312\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.50936e9 | 0.364074 | ||||||||
\(392\) | −8.78904e9 | −0.372218 | ||||||||
\(393\) | −3.30033e9 | + | 1.80062e10i | −0.138352 | + | 0.754833i | ||||
\(394\) | 3.04316e9 | 0.126282 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.25684e10 | + | 3.31338e10i | −0.511090 | + | 1.34738i | ||||
\(397\) | − | 1.16090e10i | − | 0.467339i | −0.972316 | − | 0.233670i | \(-0.924927\pi\) | ||
0.972316 | − | 0.233670i | \(-0.0750734\pi\) | |||||||
\(398\) | −1.89626e9 | −0.0755729 | ||||||||
\(399\) | 1.19338e8 | − | 6.51095e8i | 0.00470857 | − | 0.0256893i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.62151e10i | − | 0.627108i | −0.949570 | − | 0.313554i | \(-0.898480\pi\) | ||
0.949570 | − | 0.313554i | \(-0.101520\pi\) | |||||||
\(402\) | −6.17198e8 | + | 3.36735e9i | −0.0236331 | + | 0.128939i | ||||
\(403\) | 2.61698e9i | 0.0992157i | ||||||||
\(404\) | − | 3.60357e10i | − | 1.35272i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.62435e8 | 0.00597828 | ||||||||
\(407\) | −1.45578e9 | −0.0530540 | ||||||||
\(408\) | −4.38788e9 | − | 8.04249e8i | −0.158349 | − | 0.0290235i | ||||
\(409\) | 8.05756e9 | 0.287945 | 0.143973 | − | 0.989582i | \(-0.454012\pi\) | ||||
0.143973 | + | 0.989582i | \(0.454012\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.35239e10 | + | 7.97744e9i | 1.52532 | + | 0.279574i | ||||
\(412\) | − | 3.96171e10i | − | 1.37497i | ||||||
\(413\) | 9.46257e8 | 0.0325244 | ||||||||
\(414\) | 4.38726e9 | + | 1.66418e9i | 0.149345 | + | 0.0566498i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.18529e10i | 0.729685i | ||||||||
\(417\) | −1.71843e10 | − | 3.14969e9i | −0.568312 | − | 0.104165i | ||||
\(418\) | − | 9.08451e9i | − | 0.297575i | ||||||
\(419\) | − | 1.33632e10i | − | 0.433567i | −0.976220 | − | 0.216783i | \(-0.930443\pi\) | ||
0.976220 | − | 0.216783i | \(-0.0695565\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.39642e10 | −1.39949 | −0.699747 | − | 0.714391i | \(-0.746704\pi\) | ||||
−0.699747 | + | 0.714391i | \(0.746704\pi\) | |||||||
\(422\) | 1.16716e10 | 0.368029 | ||||||||
\(423\) | 3.64050e10 | + | 1.38092e10i | 1.13710 | + | 0.431327i | ||||
\(424\) | −1.99948e10 | −0.618662 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.71474e8 | − | 3.66347e9i | 0.0203888 | − | 0.111238i | ||||
\(427\) | 2.09961e8i | 0.00631578i | ||||||||
\(428\) | 2.72919e10 | 0.813315 | ||||||||
\(429\) | 6.70630e10 | + | 1.22919e10i | 1.97995 | + | 0.362902i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 1.47674e10i | − | 0.427950i | −0.976839 | − | 0.213975i | \(-0.931359\pi\) | ||
0.976839 | − | 0.213975i | \(-0.0686412\pi\) | |||||||
\(432\) | 2.66271e10 | + | 1.61000e10i | 0.764521 | + | 0.462266i | ||||
\(433\) | 1.57125e8i | 0.00446986i | 0.999998 | + | 0.00223493i | \(0.000711401\pi\) | ||||
−0.999998 | + | 0.00223493i | \(0.999289\pi\) | |||||||
\(434\) | − | 1.23324e7i | − | 0.000347608i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.77756e10 | 1.04536 | ||||||||
\(437\) | 3.22467e10 | 0.884219 | ||||||||
\(438\) | 1.74204e9 | − | 9.50436e9i | 0.0473328 | − | 0.258242i | ||||
\(439\) | −6.17824e10 | −1.66344 | −0.831719 | − | 0.555197i | \(-0.812643\pi\) | ||||
−0.831719 | + | 0.555197i | \(0.812643\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.53423e10 | + | 1.34061e10i | 0.934416 | + | 0.354443i | ||||
\(442\) | 4.21279e9i | 0.110377i | ||||||||
\(443\) | −8.26926e9 | −0.214710 | −0.107355 | − | 0.994221i | \(-0.534238\pi\) | ||||
−0.107355 | + | 0.994221i | \(0.534238\pi\) | |||||||
\(444\) | −2.39727e8 | + | 1.30792e9i | −0.00616859 | + | 0.0336550i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.02341e10i | 0.258648i | ||||||||
\(447\) | −6.31501e9 | + | 3.44539e10i | −0.158177 | + | 0.862995i | ||||
\(448\) | 7.92379e8i | 0.0196708i | ||||||||
\(449\) | 7.95461e10i | 1.95719i | 0.205788 | + | 0.978597i | \(0.434024\pi\) | ||||
−0.205788 | + | 0.978597i | \(0.565976\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.24281e10 | −1.99236 | ||||||||
\(452\) | 2.51008e10 | 0.601358 | ||||||||
\(453\) | −2.56769e10 | − | 4.70628e9i | −0.609746 | − | 0.111760i | ||||
\(454\) | −7.86870e9 | −0.185216 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.66281e10 | − | 3.04775e9i | −0.384578 | − | 0.0704888i | ||||
\(457\) | − | 2.02591e10i | − | 0.464467i | −0.972660 | − | 0.232234i | \(-0.925397\pi\) | ||
0.972660 | − | 0.232234i | \(-0.0746034\pi\) | |||||||
\(458\) | 8.53413e9 | 0.193953 | ||||||||
\(459\) | 1.64177e10 | + | 9.92693e9i | 0.369881 | + | 0.223648i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 3.97783e10i | − | 0.880729i | −0.897819 | − | 0.440364i | \(-0.854849\pi\) | ||
0.897819 | − | 0.440364i | \(-0.145151\pi\) | |||||||
\(462\) | −3.16032e8 | − | 5.79251e7i | −0.00693687 | − | 0.00127145i | ||||
\(463\) | − | 3.84754e10i | − | 0.837258i | −0.908157 | − | 0.418629i | \(-0.862511\pi\) | ||
0.908157 | − | 0.418629i | \(-0.137489\pi\) | |||||||
\(464\) | 5.24745e10i | 1.13208i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.89001e9 | −0.209726 | ||||||||
\(467\) | −2.20915e10 | −0.464470 | −0.232235 | − | 0.972660i | \(-0.574604\pi\) | ||||
−0.232235 | + | 0.972660i | \(0.574604\pi\) | |||||||
\(468\) | 2.20869e10 | − | 5.82275e10i | 0.460417 | − | 1.21379i | ||||
\(469\) | 8.32089e8 | 0.0171980 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.17194e9 | − | 4.45850e10i | 0.166051 | − | 0.905953i | ||||
\(472\) | − | 2.41662e10i | − | 0.486900i | ||||||
\(473\) | 4.46450e10 | 0.891925 | ||||||||
\(474\) | −7.62958e9 | − | 1.39842e9i | −0.151143 | − | 0.0277028i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.32207e8i | 0.0103670i | ||||||||
\(477\) | 8.04025e10 | + | 3.04984e10i | 1.55309 | + | 0.589119i | ||||
\(478\) | − | 5.98968e9i | − | 0.114734i | ||||||
\(479\) | 2.39823e10i | 0.455564i | 0.973712 | + | 0.227782i | \(0.0731473\pi\) | ||||
−0.973712 | + | 0.227782i | \(0.926853\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.55830e9 | 0.0477938 | ||||||||
\(482\) | 1.36164e9 | 0.0252275 | ||||||||
\(483\) | 2.05613e8 | − | 1.12180e9i | 0.00377800 | − | 0.0206123i | ||||
\(484\) | 6.53066e10 | 1.19008 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 6.52323e9 | + | 8.32894e9i | 0.116928 | + | 0.149295i | ||||
\(487\) | − | 4.42866e10i | − | 0.787329i | −0.919254 | − | 0.393664i | \(-0.871207\pi\) | ||
0.919254 | − | 0.393664i | \(-0.128793\pi\) | |||||||
\(488\) | 5.36213e9 | 0.0945492 | ||||||||
\(489\) | −6.82645e9 | + | 3.72442e10i | −0.119388 | + | 0.651364i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3.70873e10i | − | 0.638116i | −0.947735 | − | 0.319058i | \(-0.896634\pi\) | ||
0.947735 | − | 0.319058i | \(-0.103366\pi\) | |||||||
\(492\) | −1.35737e10 | + | 7.40562e10i | −0.231652 | + | 1.26387i | ||||
\(493\) | 3.23546e10i | 0.547707i | ||||||||
\(494\) | 1.59646e10i | 0.268071i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.98398e9 | 0.0658249 | ||||||||
\(497\) | −9.05262e8 | −0.0148371 | ||||||||
\(498\) | −1.18133e10 | − | 2.16524e9i | −0.192067 | − | 0.0352038i | ||||
\(499\) | −4.56047e10 | −0.735541 | −0.367771 | − | 0.929917i | \(-0.619879\pi\) | ||||
−0.367771 | + | 0.929917i | \(0.619879\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.62381e10 | + | 6.64204e9i | 0.575194 | + | 0.105427i | ||||
\(502\) | 7.02173e9i | 0.110568i | ||||||||
\(503\) | −3.73919e10 | −0.584125 | −0.292063 | − | 0.956399i | \(-0.594342\pi\) | ||||
−0.292063 | + | 0.956399i | \(0.594342\pi\) | |||||||
\(504\) | −2.12050e8 | + | 5.59026e8i | −0.00328637 | + | 0.00866383i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 1.56521e10i | − | 0.238765i | ||||||
\(507\) | −5.28610e10 | − | 9.68884e9i | −0.800026 | − | 0.146636i | ||||
\(508\) | 1.19848e11i | 1.79960i | ||||||||
\(509\) | − | 4.63948e9i | − | 0.0691192i | −0.999403 | − | 0.0345596i | \(-0.988997\pi\) | ||
0.999403 | − | 0.0345596i | \(-0.0110029\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.34857e9 | −0.0344445 | ||||||||
\(512\) | 5.61342e10 | 0.816861 | ||||||||
\(513\) | 6.22158e10 | + | 3.76187e10i | 0.898321 | + | 0.543168i | ||||
\(514\) | 1.71170e10 | 0.245230 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.35182e9 | − | 4.01106e10i | 0.103704 | − | 0.565796i | ||||
\(517\) | − | 1.29879e11i | − | 1.81793i | ||||||
\(518\) | −1.20559e7 | −0.000167449 | ||||||||
\(519\) | 6.60462e10 | + | 1.21055e10i | 0.910288 | + | 0.166846i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.90088e10i | 0.800877i | 0.916324 | + | 0.400439i | \(0.131142\pi\) | ||||
−0.916324 | + | 0.400439i | \(0.868858\pi\) | |||||||
\(522\) | −6.32760e9 | + | 1.66814e10i | −0.0852230 | + | 0.224673i | ||||
\(523\) | 6.02622e9i | 0.0805449i | 0.999189 | + | 0.0402725i | \(0.0128226\pi\) | ||||
−0.999189 | + | 0.0402725i | \(0.987177\pi\) | |||||||
\(524\) | − | 5.57758e10i | − | 0.739811i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.08774e10 | 0.142096 | ||||||||
\(527\) | 2.45643e9 | 0.0318465 | ||||||||
\(528\) | 1.87126e10 | − | 1.02094e11i | 0.240768 | − | 1.31360i | ||||
\(529\) | −2.27518e10 | −0.290531 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.68610e10 | + | 9.71764e10i | −0.463649 | + | 1.22231i | ||||
\(532\) | 2.01683e9i | 0.0251781i | ||||||||
\(533\) | 1.44854e11 | 1.79483 | ||||||||
\(534\) | 4.84121e9 | − | 2.64130e10i | 0.0595373 | − | 0.324828i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 2.12505e10i | − | 0.257460i | ||||||
\(537\) | 2.68943e9 | − | 1.46732e10i | 0.0323417 | − | 0.176452i | ||||
\(538\) | 2.02802e10i | 0.242071i | ||||||||
\(539\) | − | 1.26088e11i | − | 1.49389i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.00361e10 | 0.467372 | 0.233686 | − | 0.972312i | \(-0.424921\pi\) | ||||
0.233686 | + | 0.972312i | \(0.424921\pi\) | |||||||
\(542\) | −1.12869e10 | −0.130791 | ||||||||
\(543\) | −9.09374e10 | − | 1.66678e10i | −1.04603 | − | 0.191725i | ||||
\(544\) | 2.05123e10 | 0.234217 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.55377e8 | + | 1.01794e8i | 0.00624909 | + | 0.00114539i | ||||
\(547\) | 7.70856e10i | 0.861041i | 0.902581 | + | 0.430521i | \(0.141670\pi\) | ||||
−0.902581 | + | 0.430521i | \(0.858330\pi\) | |||||||
\(548\) | −1.34819e11 | −1.49496 | ||||||||
\(549\) | −2.15621e10 | − | 8.17894e9i | −0.237356 | − | 0.0900342i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.22610e11i | 1.33020i | ||||||||
\(552\) | −2.86493e10 | − | 5.25109e9i | −0.308573 | − | 0.0565579i | ||||
\(553\) | 1.88531e9i | 0.0201596i | ||||||||
\(554\) | 1.10450e10i | 0.117254i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.32299e10 | 0.557002 | ||||||||
\(557\) | −1.00834e10 | −0.104758 | −0.0523789 | − | 0.998627i | \(-0.516680\pi\) | ||||
−0.0523789 | + | 0.998627i | \(0.516680\pi\) | |||||||
\(558\) | 1.26649e9 | + | 4.80405e8i | 0.0130636 | + | 0.00495531i | ||||
\(559\) | −7.84565e10 | −0.803492 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.15378e10 | − | 6.29487e10i | 0.116485 | − | 0.635529i | ||||
\(562\) | − | 3.23566e9i | − | 0.0324352i | ||||||
\(563\) | −1.17038e11 | −1.16492 | −0.582458 | − | 0.812861i | \(-0.697909\pi\) | ||||
−0.582458 | + | 0.812861i | \(0.697909\pi\) | |||||||
\(564\) | −1.16688e11 | − | 2.13876e10i | −1.15321 | − | 0.211371i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 1.36684e10i | − | 0.133184i | ||||||
\(567\) | 1.70538e9 | − | 1.92450e9i | 0.0165002 | − | 0.0186202i | ||||
\(568\) | 2.31192e10i | 0.222116i | ||||||||
\(569\) | − | 2.10738e10i | − | 0.201045i | −0.994935 | − | 0.100522i | \(-0.967949\pi\) | ||
0.994935 | − | 0.100522i | \(-0.0320514\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.66672e11 | −1.56790 | −0.783949 | − | 0.620826i | \(-0.786798\pi\) | ||||
−0.783949 | + | 0.620826i | \(0.786798\pi\) | |||||||
\(572\) | −2.07734e11 | −1.94054 | ||||||||
\(573\) | −2.37229e10 | + | 1.29429e11i | −0.220065 | + | 1.20064i | ||||
\(574\) | −6.82621e8 | −0.00628829 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.13739e10 | − | 3.08668e10i | −0.739256 | − | 0.280415i | ||||
\(577\) | 9.88790e10i | 0.892074i | 0.895014 | + | 0.446037i | \(0.147165\pi\) | ||||
−0.895014 | + | 0.446037i | \(0.852835\pi\) | |||||||
\(578\) | −1.72111e10 | −0.154205 | ||||||||
\(579\) | 2.19407e10 | − | 1.19706e11i | 0.195225 | − | 1.06512i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.91912e9i | 0.0256181i | ||||||||
\(582\) | 5.14405e9 | − | 2.80653e10i | 0.0448346 | − | 0.244612i | ||||
\(583\) | − | 2.86846e11i | − | 2.48299i | ||||||
\(584\) | 5.99795e10i | 0.515646i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.31361e10 | 0.196200 | ||||||||
\(587\) | −4.94023e10 | −0.416097 | −0.208049 | − | 0.978118i | \(-0.566711\pi\) | ||||
−0.208049 | + | 0.978118i | \(0.566711\pi\) | |||||||
\(588\) | −1.13282e11 | − | 2.07633e10i | −0.947656 | − | 0.173695i | ||||
\(589\) | 9.30879e9 | 0.0773450 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.99097e10 | + | 1.46465e10i | 0.655012 | + | 0.120056i | ||||
\(592\) | − | 3.89465e9i | − | 0.0317089i | ||||||
\(593\) | −5.39077e10 | −0.435945 | −0.217973 | − | 0.975955i | \(-0.569944\pi\) | ||||
−0.217973 | + | 0.975955i | \(0.569944\pi\) | |||||||
\(594\) | 1.82596e10 | − | 3.01987e10i | 0.146671 | − | 0.242573i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 1.06724e11i | − | 0.845820i | ||||||
\(597\) | −4.97934e10 | − | 9.12658e9i | −0.391990 | − | 0.0718474i | ||||
\(598\) | 2.75061e10i | 0.215092i | ||||||||
\(599\) | − | 1.84260e11i | − | 1.43128i | −0.698469 | − | 0.715640i | \(-0.746135\pi\) | ||
0.698469 | − | 0.715640i | \(-0.253865\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.09269e9 | −0.0313698 | −0.0156849 | − | 0.999877i | \(-0.504993\pi\) | ||||
−0.0156849 | + | 0.999877i | \(0.504993\pi\) | |||||||
\(602\) | 3.69724e8 | 0.00281509 | ||||||||
\(603\) | −3.24137e10 | + | 8.54519e10i | −0.245165 | + | 0.646327i | ||||
\(604\) | 7.95365e10 | 0.597611 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.46964e9 | + | 3.52975e10i | −0.0479722 | + | 0.261730i | ||||
\(607\) | 1.45907e11i | 1.07478i | 0.843333 | + | 0.537392i | \(0.180590\pi\) | ||||
−0.843333 | + | 0.537392i | \(0.819410\pi\) | |||||||
\(608\) | 7.77323e10 | 0.568836 | ||||||||
\(609\) | 4.26535e9 | + | 7.81790e8i | 0.0310088 | + | 0.00568357i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.28243e11i | 1.63769i | ||||||||
\(612\) | −5.46553e10 | − | 2.07319e10i | −0.389607 | − | 0.147786i | ||||
\(613\) | − | 9.26923e10i | − | 0.656450i | −0.944600 | − | 0.328225i | \(-0.893550\pi\) | ||
0.944600 | − | 0.328225i | \(-0.106450\pi\) | |||||||
\(614\) | − | 1.62521e10i | − | 0.114350i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.99440e9 | 0.0138512 | ||||||||
\(617\) | 2.27799e11 | 1.57185 | 0.785925 | − | 0.618322i | \(-0.212187\pi\) | ||||
0.785925 | + | 0.618322i | \(0.212187\pi\) | |||||||
\(618\) | −7.11262e9 | + | 3.88055e10i | −0.0487613 | + | 0.266036i | ||||
\(619\) | −1.05797e11 | −0.720627 | −0.360313 | − | 0.932831i | \(-0.617330\pi\) | ||||
−0.360313 | + | 0.932831i | \(0.617330\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.07194e11 | + | 6.48148e10i | 0.720784 | + | 0.435820i | ||||
\(622\) | − | 2.56982e10i | − | 0.171689i | ||||||
\(623\) | −6.52679e9 | −0.0433259 | ||||||||
\(624\) | −3.28845e10 | + | 1.79414e11i | −0.216897 | + | 1.18336i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 1.20272e10i | − | 0.0783187i | ||||||
\(627\) | 4.37231e10 | − | 2.38548e11i | 0.282905 | − | 1.54350i | ||||
\(628\) | 1.38106e11i | 0.887923i | ||||||||
\(629\) | − | 2.40135e9i | − | 0.0153410i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.99698e11 | 1.89045 | 0.945227 | − | 0.326414i | \(-0.105840\pi\) | ||||
0.945227 | + | 0.326414i | \(0.105840\pi\) | |||||||
\(632\) | 4.81483e10 | 0.301795 | ||||||||
\(633\) | 3.06483e11 | + | 5.61748e10i | 1.90893 | + | 0.349886i | ||||
\(634\) | 4.98429e9 | 0.0308494 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.57712e11 | − | 4.72358e10i | −1.57509 | − | 0.288697i | ||||
\(637\) | 2.21580e11i | 1.34577i | ||||||||
\(638\) | 5.95129e10 | 0.359194 | ||||||||
\(639\) | 3.52641e10 | − | 9.29665e10i | 0.211509 | − | 0.557600i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 7.79955e10i | − | 0.461995i | −0.972954 | − | 0.230998i | \(-0.925801\pi\) | ||
0.972954 | − | 0.230998i | \(-0.0741989\pi\) | |||||||
\(642\) | −2.67328e10 | − | 4.89983e9i | −0.157364 | − | 0.0288430i | ||||
\(643\) | 1.10441e11i | 0.646081i | 0.946385 | + | 0.323041i | \(0.104705\pi\) | ||||
−0.946385 | + | 0.323041i | \(0.895295\pi\) | |||||||
\(644\) | 3.47488e9i | 0.0202021i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.49852e10 | 0.0860463 | ||||||||
\(647\) | −1.12591e11 | −0.642521 | −0.321261 | − | 0.946991i | \(-0.604107\pi\) | ||||
−0.321261 | + | 0.946991i | \(0.604107\pi\) | |||||||
\(648\) | −4.91492e10 | − | 4.35533e10i | −0.278751 | − | 0.247014i | ||||
\(649\) | 3.46689e11 | 1.95417 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.93552e7 | − | 3.23834e8i | 0.000330472 | − | 0.00180301i | ||||
\(652\) | − | 1.15368e11i | − | 0.638401i | ||||||
\(653\) | 1.11018e11 | 0.610578 | 0.305289 | − | 0.952260i | \(-0.401247\pi\) | ||||
0.305289 | + | 0.952260i | \(0.401247\pi\) | |||||||
\(654\) | −3.70018e10 | − | 6.78201e9i | −0.202261 | − | 0.0370721i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 2.20520e11i | − | 1.19078i | ||||||
\(657\) | 9.14877e10 | − | 2.41188e11i | 0.491022 | − | 1.29448i | ||||
\(658\) | − | 1.07559e9i | − | 0.00573775i | ||||||
\(659\) | 1.20450e11i | 0.638653i | 0.947645 | + | 0.319326i | \(0.103457\pi\) | ||||
−0.947645 | + | 0.319326i | \(0.896543\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.14150e10 | −0.164563 | −0.0822813 | − | 0.996609i | \(-0.526221\pi\) | ||||
−0.0822813 | + | 0.996609i | \(0.526221\pi\) | |||||||
\(662\) | 2.15447e10 | 0.112178 | ||||||||
\(663\) | −2.02759e10 | + | 1.10622e11i | −0.104936 | + | 0.572518i | ||||
\(664\) | 7.45506e10 | 0.383512 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.69634e8 | − | 1.23809e9i | 0.00238705 | − | 0.00629297i | ||||
\(667\) | 2.11249e11i | 1.06731i | ||||||||
\(668\) | −1.12251e11 | −0.563747 | ||||||||
\(669\) | −4.92559e10 | + | 2.68734e11i | −0.245897 | + | 1.34158i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.69253e10i | 0.379472i | ||||||||
\(672\) | 4.95641e8 | − | 2.70415e9i | 0.00243047 | − | 0.0132603i | ||||
\(673\) | − | 3.66345e11i | − | 1.78579i | −0.450265 | − | 0.892895i | \(-0.648671\pi\) | ||
0.450265 | − | 0.892895i | \(-0.351329\pi\) | |||||||
\(674\) | 7.06218e10i | 0.342215i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.63742e11 | 0.784104 | ||||||||
\(677\) | 2.51302e11 | 1.19630 | 0.598152 | − | 0.801382i | \(-0.295902\pi\) | ||||
0.598152 | + | 0.801382i | \(0.295902\pi\) | |||||||
\(678\) | −2.45866e10 | − | 4.50645e9i | −0.116354 | − | 0.0213263i | ||||
\(679\) | −6.93506e9 | −0.0326266 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.06622e11 | − | 3.78715e10i | −0.960701 | − | 0.176086i | ||||
\(682\) | − | 4.51835e9i | − | 0.0208854i | ||||||
\(683\) | 2.45748e11 | 1.12929 | 0.564646 | − | 0.825333i | \(-0.309013\pi\) | ||||
0.564646 | + | 0.825333i | \(0.309013\pi\) | |||||||
\(684\) | −2.07119e11 | − | 7.85647e10i | −0.946230 | − | 0.358925i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 2.08902e9i | − | 0.00943293i | ||||||
\(687\) | 2.24095e11 | + | 4.10742e10i | 1.00602 | + | 0.184392i | ||||
\(688\) | 1.19439e11i | 0.533079i | ||||||||
\(689\) | 5.04087e11i | 2.23681i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.44391e11 | −0.633326 | −0.316663 | − | 0.948538i | \(-0.602562\pi\) | ||||
−0.316663 | + | 0.948538i | \(0.602562\pi\) | |||||||
\(692\) | −2.04584e11 | −0.892171 | ||||||||
\(693\) | −8.01981e9 | − | 3.04208e9i | −0.0347721 | − | 0.0131898i | ||||
\(694\) | −5.63381e9 | −0.0242864 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.99659e10 | − | 1.08931e11i | 0.0850848 | − | 0.464212i | ||||
\(697\) | − | 1.35968e11i | − | 0.576109i | ||||||
\(698\) | −4.50606e10 | −0.189835 | ||||||||
\(699\) | −2.59699e11 | − | 4.76000e10i | −1.08783 | − | 0.199388i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.23367e11i | − | 0.925009i | −0.886617 | − | 0.462505i | \(-0.846951\pi\) | ||
0.886617 | − | 0.462505i | \(-0.153049\pi\) | |||||||
\(702\) | −3.20883e10 | + | 5.30694e10i | −0.132129 | + | 0.218522i | ||||
\(703\) | − | 9.10007e9i | − | 0.0372583i | ||||||
\(704\) | 2.90312e11i | 1.18188i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.54536e10 | −0.182957 | ||||||||
\(707\) | 8.72218e9 | 0.0349098 | ||||||||
\(708\) | 5.70903e10 | − | 3.11477e11i | 0.227211 | − | 1.23963i | ||||
\(709\) | 8.44074e9 | 0.0334038 | 0.0167019 | − | 0.999861i | \(-0.494683\pi\) | ||||
0.0167019 | + | 0.999861i | \(0.494683\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.93613e11 | − | 7.34414e10i | −0.757627 | − | 0.287384i | ||||
\(712\) | 1.66686e11i | 0.648602i | ||||||||
\(713\) | 1.60385e10 | 0.0620591 | ||||||||
\(714\) | 9.55494e7 | − | 5.21305e8i | 0.000367650 | − | 0.00200585i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.54516e10i | 0.172941i | ||||||||
\(717\) | 2.88279e10 | − | 1.57281e11i | 0.109078 | − | 0.595115i | ||||
\(718\) | − | 7.29257e10i | − | 0.274399i | ||||||
\(719\) | − | 3.06358e11i | − | 1.14634i | −0.819436 | − | 0.573171i | \(-0.805713\pi\) | ||
0.819436 | − | 0.573171i | \(-0.194287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.58903e9 | 0.0354841 | ||||||||
\(722\) | 5.25668e9 | 0.0193447 | ||||||||
\(723\) | 3.57550e10 | + | 6.55348e9i | 0.130853 | + | 0.0239839i | ||||
\(724\) | 2.81687e11 | 1.02521 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −6.39689e10 | − | 1.17248e10i | −0.230262 | − | 0.0422044i | ||||
\(727\) | 2.35218e10i | 0.0842040i | 0.999113 | + | 0.0421020i | \(0.0134054\pi\) | ||||
−0.999113 | + | 0.0421020i | \(0.986595\pi\) | |||||||
\(728\) | −3.50484e9 | −0.0124779 | ||||||||
\(729\) | 1.31205e11 | + | 2.50103e11i | 0.464559 | + | 0.885542i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.36433e10i | 0.257907i | ||||||||
\(732\) | 6.91123e10 | + | 1.26675e10i | 0.240719 | + | 0.0441212i | ||||
\(733\) | 6.21715e10i | 0.215365i | 0.994185 | + | 0.107683i | \(0.0343430\pi\) | ||||
−0.994185 | + | 0.107683i | \(0.965657\pi\) | |||||||
\(734\) | 1.92965e10i | 0.0664806i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.33928e11 | 0.456416 | ||||||||
\(737\) | 3.04860e11 | 1.03331 | ||||||||
\(738\) | 2.65912e10 | − | 7.01022e10i | 0.0896423 | − | 0.236323i | ||||
\(739\) | 3.85080e10 | 0.129114 | 0.0645570 | − | 0.997914i | \(-0.479437\pi\) | ||||
0.0645570 | + | 0.997914i | \(0.479437\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.68365e10 | + | 4.19210e11i | −0.254856 | + | 1.39046i | ||||
\(742\) | − | 2.37549e9i | − | 0.00783679i | ||||||
\(743\) | −1.81380e10 | −0.0595160 | −0.0297580 | − | 0.999557i | \(-0.509474\pi\) | ||||
−0.0297580 | + | 0.999557i | \(0.509474\pi\) | |||||||
\(744\) | −8.27031e9 | − | 1.51586e9i | −0.0269917 | − | 0.00494727i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 2.90062e10i | − | 0.0936558i | ||||||
\(747\) | −2.99781e11 | − | 1.13713e11i | −0.962767 | − | 0.365198i | ||||
\(748\) | 1.94990e11i | 0.622881i | ||||||||
\(749\) | 6.60582e9i | 0.0209894i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.66054e11 | 1.46513 | 0.732566 | − | 0.680696i | \(-0.238323\pi\) | ||||
0.732566 | + | 0.680696i | \(0.238323\pi\) | |||||||
\(752\) | 3.47466e11 | 1.08653 | ||||||||
\(753\) | −3.37951e10 | + | 1.84382e11i | −0.105117 | + | 0.573506i | ||||
\(754\) | −1.04585e11 | −0.323581 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.05376e9 | + | 6.70433e9i | −0.0124100 | + | 0.0205243i | ||||
\(757\) | 1.01684e11i | 0.309649i | 0.987942 | + | 0.154825i | \(0.0494812\pi\) | ||||
−0.987942 | + | 0.154825i | \(0.950519\pi\) | |||||||
\(758\) | −4.46837e9 | −0.0135354 | ||||||||
\(759\) | 7.53324e10 | − | 4.11004e11i | 0.226994 | − | 1.23845i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1.11642e9i | − | 0.00332880i | −0.999999 | − | 0.00166440i | \(-0.999470\pi\) | ||
0.999999 | − | 0.00166440i | \(-0.000529796\pi\) | |||||||
\(762\) | 2.15168e10 | − | 1.17393e11i | 0.0638202 | − | 0.348195i | ||||
\(763\) | 9.14331e9i | 0.0269777i | ||||||||
\(764\) | − | 4.00920e11i | − | 1.17675i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.07406e11 | −0.311970 | ||||||||
\(767\) | −6.09251e11 | −1.76041 | ||||||||
\(768\) | 2.25663e11 | + | 4.13615e10i | 0.648658 | + | 0.118892i | ||||
\(769\) | −5.25128e11 | −1.50162 | −0.750810 | − | 0.660519i | \(-0.770336\pi\) | ||||
−0.750810 | + | 0.660519i | \(0.770336\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.49470e11 | + | 8.23828e10i | 1.27199 | + | 0.233141i | ||||
\(772\) | 3.70800e11i | 1.04393i | ||||||||
\(773\) | 1.88899e11 | 0.529067 | 0.264534 | − | 0.964376i | \(-0.414782\pi\) | ||||
0.264534 | + | 0.964376i | \(0.414782\pi\) | |||||||
\(774\) | −1.44024e10 | + | 3.79690e10i | −0.0401303 | + | 0.105795i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.77113e11i | 0.488430i | ||||||||
\(777\) | −3.16573e8 | − | 5.80244e7i | −0.000868541 | − | 0.000159194i | ||||
\(778\) | 3.06043e10i | 0.0835342i | ||||||||
\(779\) | − | 5.15257e11i | − | 1.39918i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.31670e11 | −0.891459 | ||||||||
\(782\) | 2.58186e10 | 0.0690408 | ||||||||
\(783\) | −2.46441e11 | + | 4.07578e11i | −0.655641 | + | 1.08434i | ||||
\(784\) | 3.37323e11 | 0.892857 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.00137e10 | + | 5.46333e10i | −0.0262363 | + | 0.143142i | ||||
\(787\) | − | 6.60029e11i | − | 1.72054i | −0.509842 | − | 0.860268i | \(-0.670296\pi\) | ||
0.509842 | − | 0.860268i | \(-0.329704\pi\) | |||||||
\(788\) | −2.47528e11 | −0.641977 | ||||||||
\(789\) | 2.85627e11 | + | 5.23523e10i | 0.737042 | + | 0.135091i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.07547e9i | 0.0155194i | ||||||||
\(792\) | −7.76909e10 | + | 2.04816e11i | −0.197455 | + | 0.520550i | ||||
\(793\) | − | 1.35184e11i | − | 0.341848i | ||||||
\(794\) | − | 3.52233e10i | − | 0.0886234i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.54240e11 | 0.384189 | ||||||||
\(797\) | −5.73881e11 | −1.42229 | −0.711146 | − | 0.703044i | \(-0.751824\pi\) | ||||
−0.711146 | + | 0.703044i | \(0.751824\pi\) | |||||||
\(798\) | 3.62090e8 | − | 1.97551e9i | 0.000892904 | − | 0.00487157i | ||||
\(799\) | 2.14240e11 | 0.525671 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.54248e11 | − | 6.70272e11i | 0.617629 | − | 1.62825i | ||||
\(802\) | − | 4.91990e10i | − | 0.118921i | ||||||
\(803\) | −8.60469e11 | −2.06954 | ||||||||
\(804\) | 5.02022e10 | − | 2.73897e11i | 0.120143 | − | 0.655485i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.94029e9i | 0.0188147i | ||||||||
\(807\) | −9.76071e10 | + | 5.32532e11i | −0.230138 | + | 1.25560i | ||||
\(808\) | − | 2.22753e11i | − | 0.522611i | ||||||
\(809\) | 2.07320e11i | 0.484002i | 0.970276 | + | 0.242001i | \(0.0778038\pi\) | ||||
−0.970276 | + | 0.242001i | \(0.922196\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.06207e11 | −1.40132 | −0.700660 | − | 0.713495i | \(-0.747111\pi\) | ||||
−0.700660 | + | 0.713495i | \(0.747111\pi\) | |||||||
\(812\) | −1.32123e10 | −0.0303917 | ||||||||
\(813\) | −2.96380e11 | − | 5.43231e10i | −0.678400 | − | 0.124343i | ||||
\(814\) | −4.41704e9 | −0.0100608 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.68407e11 | + | 3.08671e10i | 0.379838 | + | 0.0696201i | ||||
\(817\) | 2.79076e11i | 0.626374i | ||||||||
\(818\) | 2.44478e10 | 0.0546042 | ||||||||
\(819\) | 1.40936e10 | + | 5.34598e9i | 0.0313246 | + | 0.0118821i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1.56657e11i | − | 0.344808i | −0.985026 | − | 0.172404i | \(-0.944846\pi\) | ||
0.985026 | − | 0.172404i | \(-0.0551535\pi\) | |||||||
\(822\) | 1.32058e11 | + | 2.42047e10i | 0.289252 | + | 0.0530167i | ||||
\(823\) | 3.65723e11i | 0.797173i | 0.917131 | + | 0.398587i | \(0.130499\pi\) | ||||
−0.917131 | + | 0.398587i | \(0.869501\pi\) | |||||||
\(824\) | − | 2.44892e11i | − | 0.531208i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.87108e9 | 0.00616772 | ||||||||
\(827\) | −5.22532e11 | −1.11710 | −0.558549 | − | 0.829472i | \(-0.688642\pi\) | ||||
−0.558549 | + | 0.829472i | \(0.688642\pi\) | |||||||
\(828\) | −3.56855e11 | − | 1.35362e11i | −0.759224 | − | 0.287990i | ||||
\(829\) | −7.56111e11 | −1.60091 | −0.800456 | − | 0.599391i | \(-0.795409\pi\) | ||||
−0.800456 | + | 0.599391i | \(0.795409\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.31589e10 | + | 2.90028e11i | −0.111474 | + | 0.608185i | ||||
\(832\) | − | 5.10177e11i | − | 1.06470i | ||||||
\(833\) | 2.07986e11 | 0.431971 | ||||||||
\(834\) | −5.21395e10 | − | 9.55659e9i | −0.107771 | − | 0.0197533i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.38925e11i | 1.51278i | ||||||||
\(837\) | 3.09442e10 | + | 1.87103e10i | 0.0630489 | + | 0.0381224i | ||||
\(838\) | − | 4.05460e10i | − | 0.0822189i | ||||||
\(839\) | − | 4.63197e11i | − | 0.934799i | −0.884046 | − | 0.467400i | \(-0.845191\pi\) | ||
0.884046 | − | 0.467400i | \(-0.154809\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.02974e11 | −0.605649 | ||||||||
\(842\) | −1.33394e11 | −0.265391 | ||||||||
\(843\) | 1.55730e10 | − | 8.49642e10i | 0.0308363 | − | 0.168239i | ||||
\(844\) | −9.49359e11 | −1.87094 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.10458e11 | + | 4.18990e10i | 0.215633 | + | 0.0817942i | ||||
\(847\) | 1.58070e10i | 0.0307126i | ||||||||
\(848\) | 7.67399e11 | 1.48401 | ||||||||
\(849\) | 6.57849e10 | − | 3.58914e11i | 0.126618 | − | 0.690811i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.56789e10i | − | 0.0298949i | ||||||
\(852\) | −5.46170e10 | + | 2.97983e11i | −0.103650 | + | 0.565501i | ||||
\(853\) | − | 6.78685e11i | − | 1.28195i | −0.767561 | − | 0.640976i | \(-0.778530\pi\) | ||
0.767561 | − | 0.640976i | \(-0.221470\pi\) | |||||||
\(854\) | 6.37051e8i | 0.00119769i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.68704e11 | 0.314217 | ||||||||
\(857\) | 1.02265e12 | 1.89584 | 0.947921 | − | 0.318506i | \(-0.103181\pi\) | ||||
0.947921 | + | 0.318506i | \(0.103181\pi\) | |||||||
\(858\) | 2.03479e11 | + | 3.72953e10i | 0.375465 | + | 0.0688185i | ||||
\(859\) | 1.64678e11 | 0.302457 | 0.151228 | − | 0.988499i | \(-0.451677\pi\) | ||||
0.151228 | + | 0.988499i | \(0.451677\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.79248e10 | − | 3.28541e9i | −0.0326168 | − | 0.00597829i | ||||
\(862\) | − | 4.48062e10i | − | 0.0811539i | ||||||
\(863\) | −9.97986e11 | −1.79921 | −0.899604 | − | 0.436707i | \(-0.856145\pi\) | ||||
−0.899604 | + | 0.436707i | \(0.856145\pi\) | |||||||
\(864\) | 2.58397e11 | + | 1.56239e11i | 0.463695 | + | 0.280373i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.76740e8i | 0.000847637i | ||||||||
\(867\) | −4.51942e11 | − | 8.28359e10i | −0.799846 | − | 0.146603i | ||||
\(868\) | 1.00311e9i | 0.00176713i | ||||||||
\(869\) | 6.90738e11i | 1.21125i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.35744e11 | −0.930861 | ||||||||
\(872\) | 2.33508e11 | 0.403865 | ||||||||
\(873\) | 2.70153e11 | − | 7.12201e11i | 0.465106 | − | 1.22616i | ||||
\(874\) | 9.78411e10 | 0.167678 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.41696e11 | + | 7.73075e11i | −0.240625 | + | 1.31282i | ||||
\(877\) | 2.30212e10i | 0.0389160i | 0.999811 | + | 0.0194580i | \(0.00619407\pi\) | ||||
−0.999811 | + | 0.0194580i | \(0.993806\pi\) | |||||||
\(878\) | −1.87457e11 | −0.315444 | ||||||||
\(879\) | 6.07525e11 | + | 1.11352e11i | 1.01767 | + | 0.186528i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 4.23415e10i | − | 0.0702851i | −0.999382 | − | 0.0351425i | \(-0.988811\pi\) | ||
0.999382 | − | 0.0351425i | \(-0.0111885\pi\) | |||||||
\(882\) | 1.07233e11 | + | 4.06759e10i | 0.177197 | + | 0.0672145i | ||||
\(883\) | 8.49512e11i | 1.39742i | 0.715406 | + | 0.698709i | \(0.246242\pi\) | ||||
−0.715406 | + | 0.698709i | \(0.753758\pi\) | |||||||
\(884\) | − | 3.42664e11i | − | 0.561124i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.50901e10 | −0.0407162 | ||||||||
\(887\) | 2.62546e11 | 0.424142 | 0.212071 | − | 0.977254i | \(-0.431979\pi\) | ||||
0.212071 | + | 0.977254i | \(0.431979\pi\) | |||||||
\(888\) | −1.48187e9 | + | 8.08488e9i | −0.00238318 | + | 0.0130023i | ||||
\(889\) | −2.90084e10 | −0.0464426 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.24817e11 | − | 7.05097e11i | 0.991384 | − | 1.11876i | ||||
\(892\) | − | 8.32429e11i | − | 1.31489i | ||||||
\(893\) | 8.11876e11 | 1.27668 | ||||||||
\(894\) | −1.91606e10 | + | 1.04538e11i | −0.0299958 | + | 0.163653i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.10930e10i | 0.0172115i | ||||||||
\(897\) | −1.32385e11 | + | 7.22275e11i | −0.204488 | + | 1.11566i | ||||
\(898\) | 2.41354e11i | 0.371150i | ||||||||
\(899\) | 6.09822e10i | 0.0933608i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.73162e11 | 0.717977 | ||||||||
\(902\) | −2.50098e11 | −0.377820 | ||||||||
\(903\) | 9.70848e9 | + | 1.77946e9i | 0.0146016 | + | 0.00267631i | ||||
\(904\) | 1.55160e11 | 0.232330 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7.79072e10 | − | 1.42795e10i | −0.115629 | − | 0.0211934i | ||||
\(907\) | − | 8.67841e11i | − | 1.28236i | −0.767389 | − | 0.641182i | \(-0.778445\pi\) | ||
0.767389 | − | 0.641182i | \(-0.221555\pi\) | |||||||
\(908\) | 6.40032e11 | 0.941582 | ||||||||
\(909\) | −3.39769e11 | + | 8.95730e11i | −0.497655 | + | 1.31196i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 7.78413e11i | − | 1.13015i | −0.825039 | − | 0.565075i | \(-0.808847\pi\) | ||
0.825039 | − | 0.565075i | \(-0.191153\pi\) | |||||||
\(912\) | 6.38187e11 | + | 1.16973e11i | 0.922505 | + | 0.169085i | ||||
\(913\) | 1.06951e12i | 1.53922i | ||||||||
\(914\) | − | 6.14690e10i | − | 0.0880787i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.94157e11 | −0.985998 | ||||||||
\(917\) | 1.35001e10 | 0.0190924 | ||||||||
\(918\) | 4.98136e10 | + | 3.01197e10i | 0.0701419 | + | 0.0424112i | ||||
\(919\) | 3.08965e11 | 0.433159 | 0.216579 | − | 0.976265i | \(-0.430510\pi\) | ||||
0.216579 | + | 0.976265i | \(0.430510\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.82202e10 | − | 4.26759e11i | 0.108713 | − | 0.593122i | ||||
\(922\) | − | 1.20693e11i | − | 0.167016i | ||||||
\(923\) | 5.82857e11 | 0.803073 | ||||||||
\(924\) | 2.57057e10 | + | 4.71157e9i | 0.0352648 | + | 0.00646365i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 1.16740e11i | − | 0.158772i | ||||||
\(927\) | −3.73537e11 | + | 9.84752e11i | −0.505842 | + | 1.33355i | ||||
\(928\) | 5.09227e11i | 0.686625i | ||||||||
\(929\) | 1.36481e12i | 1.83235i | 0.400781 | + | 0.916174i | \(0.368739\pi\) | ||||
−0.400781 | + | 0.916174i | \(0.631261\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.88175e11 | 1.04912 | ||||||||
\(932\) | 8.04443e11 | 1.06618 | ||||||||
\(933\) | 1.23684e11 | − | 6.74803e11i | 0.163225 | − | 0.890534i | ||||
\(934\) | −6.70288e10 | −0.0880793 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.36529e11 | − | 3.59931e11i | 0.177878 | − | 0.468939i | ||||
\(937\) | − | 9.26920e11i | − | 1.20250i | −0.799062 | − | 0.601249i | \(-0.794670\pi\) | ||
0.799062 | − | 0.601249i | \(-0.205330\pi\) | |||||||
\(938\) | 2.52468e9 | 0.00326133 | ||||||||
\(939\) | 5.78859e10 | − | 3.15818e11i | 0.0744578 | − | 0.406232i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 4.30760e11i | − | 0.549385i | −0.961532 | − | 0.274692i | \(-0.911424\pi\) | ||
0.961532 | − | 0.274692i | \(-0.0885761\pi\) | |||||||
\(942\) | 2.47948e10 | − | 1.35277e11i | 0.0314889 | − | 0.171799i | ||||
\(943\) | − | 8.87758e11i | − | 1.12266i | ||||||
\(944\) | 9.27497e11i | 1.16795i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.35459e11 | 0.169139 | ||||||||
\(947\) | −5.20879e11 | −0.647645 | −0.323823 | − | 0.946118i | \(-0.604968\pi\) | ||||
−0.323823 | + | 0.946118i | \(0.604968\pi\) | |||||||
\(948\) | 6.20582e11 | + | 1.13746e11i | 0.768362 | + | 0.140832i | ||||
\(949\) | 1.51214e12 | 1.86435 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.30881e11 | + | 2.39891e10i | 0.160013 | + | 0.0293286i | ||||
\(952\) | 3.28982e9i | 0.00400520i | ||||||||
\(953\) | −1.01657e12 | −1.23243 | −0.616217 | − | 0.787576i | \(-0.711336\pi\) | ||||
−0.616217 | + | 0.787576i | \(0.711336\pi\) | |||||||
\(954\) | 2.43953e11 | + | 9.25363e10i | 0.294518 | + | 0.111717i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.87194e11i | 0.583271i | ||||||||
\(957\) | 1.56274e12 | + | 2.86432e11i | 1.86311 | + | 0.341487i | ||||
\(958\) | 7.27658e10i | 0.0863903i | ||||||||
\(959\) | − | 3.26321e10i | − | 0.0385807i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.48261e11 | −0.994572 | ||||||||
\(962\) | 7.76226e9 | 0.00906333 | ||||||||
\(963\) | −6.78388e11 | − | 2.57327e11i | −0.788811 | − | 0.299213i | ||||
\(964\) | −1.10754e11 | −0.128249 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.23860e8 | − | 3.40370e9i | 0.000716438 | − | 0.00390879i | ||||
\(967\) | 1.25609e12i | 1.43653i | 0.695769 | + | 0.718266i | \(0.255064\pi\) | ||||
−0.695769 | + | 0.718266i | \(0.744936\pi\) | |||||||
\(968\) | 4.03691e11 | 0.459777 | ||||||||
\(969\) | 3.93492e11 | + | 7.21227e10i | 0.446315 | + | 0.0818045i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 3.77457e11i | − | 0.424610i | −0.977203 | − | 0.212305i | \(-0.931903\pi\) | ||
0.977203 | − | 0.212305i | \(-0.0680971\pi\) | |||||||
\(972\) | −5.30592e11 | − | 6.77467e11i | −0.594423 | − | 0.758968i | ||||
\(973\) | 1.28839e10i | 0.0143746i | ||||||||
\(974\) | − | 1.34372e11i | − | 0.149304i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.05798e11 | −0.226800 | ||||||||
\(977\) | −4.90276e11 | −0.538100 | −0.269050 | − | 0.963126i | \(-0.586710\pi\) | ||||
−0.269050 | + | 0.963126i | \(0.586710\pi\) | |||||||
\(978\) | −2.07124e10 | + | 1.13004e11i | −0.0226400 | + | 0.123521i | ||||
\(979\) | −2.39128e12 | −2.60315 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.38978e11 | − | 3.56174e11i | −1.01386 | − | 0.384580i | ||||
\(982\) | − | 1.12528e11i | − | 0.121008i | ||||||
\(983\) | 8.66068e11 | 0.927551 | 0.463775 | − | 0.885953i | \(-0.346494\pi\) | ||||
0.463775 | + | 0.885953i | \(0.346494\pi\) | |||||||
\(984\) | −8.39052e10 | + | 4.57776e11i | −0.0894970 | + | 0.488284i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.81685e10i | 0.103864i | ||||||||
\(987\) | 5.17672e9 | − | 2.82435e10i | 0.00545490 | − | 0.0297612i | ||||
\(988\) | − | 1.29854e12i | − | 1.36279i | ||||||
\(989\) | 4.80831e11i | 0.502582i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.45022e10 | 0.0565093 | 0.0282546 | − | 0.999601i | \(-0.491005\pi\) | ||||
0.0282546 | + | 0.999601i | \(0.491005\pi\) | |||||||
\(992\) | 3.86616e10 | 0.0399240 | ||||||||
\(993\) | 5.65737e11 | + | 1.03693e11i | 0.581859 | + | 0.106648i | ||||
\(994\) | −2.74669e9 | −0.00281362 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 9.60880e11 | + | 1.76119e11i | 0.976409 | + | 0.178965i | ||||
\(997\) | 7.54906e10i | 0.0764033i | 0.999270 | + | 0.0382017i | \(0.0121629\pi\) | ||||
−0.999270 | + | 0.0382017i | \(0.987837\pi\) | |||||||
\(998\) | −1.38371e11 | −0.139484 | ||||||||
\(999\) | 1.82908e10 | − | 3.02504e10i | 0.0183642 | − | 0.0303717i |
(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 | 75.9.d.d.74.12 | 20 | ||
3.2 | odd | 2 | inner | 75.9.d.d.74.10 | 20 | ||
5.2 | odd | 4 | 75.9.c.f.26.6 | yes | 10 | ||
5.3 | odd | 4 | 75.9.c.e.26.5 | ✓ | 10 | ||
5.4 | even | 2 | inner | 75.9.d.d.74.9 | 20 | ||
15.2 | even | 4 | 75.9.c.f.26.5 | yes | 10 | ||
15.8 | even | 4 | 75.9.c.e.26.6 | yes | 10 | ||
15.14 | odd | 2 | inner | 75.9.d.d.74.11 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.9.c.e.26.5 | ✓ | 10 | 5.3 | odd | 4 | ||
75.9.c.e.26.6 | yes | 10 | 15.8 | even | 4 | ||
75.9.c.f.26.5 | yes | 10 | 15.2 | even | 4 | ||
75.9.c.f.26.6 | yes | 10 | 5.2 | odd | 4 | ||
75.9.d.d.74.9 | 20 | 5.4 | even | 2 | inner | ||
75.9.d.d.74.10 | 20 | 3.2 | odd | 2 | inner | ||
75.9.d.d.74.11 | 20 | 15.14 | odd | 2 | inner | ||
75.9.d.d.74.12 | 20 | 1.1 | even | 1 | trivial |