Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,18,Mod(4,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.4");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.b (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: | \(9.16110436723\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 203459x^{6} + 12362849196x^{4} + 237701205446144x^{2} + 1320400799499206656 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{8}\cdot 5^{12}\cdot 11 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4.8 | ||
Root | \(330.281i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.4 |
Dual form | 5.18.b.a.4.1 |
$q$-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 \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 660.562i | 1.82456i | 0.409564 | + | 0.912282i | \(0.365681\pi\) | ||||
−0.409564 | + | 0.912282i | \(0.634319\pi\) | |||||||
\(3\) | 11309.3i | 0.995184i | 0.867411 | + | 0.497592i | \(0.165782\pi\) | ||||
−0.867411 | + | 0.497592i | \(0.834218\pi\) | |||||||
\(4\) | −305271. | −2.32903 | ||||||||
\(5\) | −21187.7 | − | 873207.i | −0.0242571 | − | 0.999706i | ||||
\(6\) | −7.47047e6 | −1.81578 | ||||||||
\(7\) | 2.37065e7i | 1.55429i | 0.629319 | + | 0.777147i | \(0.283334\pi\) | ||||
−0.629319 | + | 0.777147i | \(0.716666\pi\) | |||||||
\(8\) | − | 1.15069e8i | − | 2.42490i | ||||||
\(9\) | 1.24087e6 | 0.00960874 | ||||||||
\(10\) | 5.76808e8 | − | 1.39958e7i | 1.82403 | − | 0.0442587i | ||||
\(11\) | −3.40136e8 | −0.478425 | −0.239213 | − | 0.970967i | \(-0.576889\pi\) | ||||
−0.239213 | + | 0.970967i | \(0.576889\pi\) | |||||||
\(12\) | − | 3.45238e9i | − | 2.31781i | ||||||
\(13\) | − | 6.20461e8i | − | 0.210958i | −0.994422 | − | 0.105479i | \(-0.966362\pi\) | ||
0.994422 | − | 0.105479i | \(-0.0336376\pi\) | |||||||
\(14\) | −1.56596e10 | −2.83591 | ||||||||
\(15\) | 9.87532e9 | − | 2.39618e8i | 0.994891 | − | 0.0241403i | ||||
\(16\) | 3.59979e10 | 2.09535 | ||||||||
\(17\) | 9.78165e9i | 0.340092i | 0.985436 | + | 0.170046i | \(0.0543916\pi\) | ||||
−0.985436 | + | 0.170046i | \(0.945608\pi\) | |||||||
\(18\) | 8.19675e8i | 0.0175317i | ||||||||
\(19\) | −3.92941e10 | −0.530789 | −0.265395 | − | 0.964140i | \(-0.585502\pi\) | ||||
−0.265395 | + | 0.964140i | \(0.585502\pi\) | |||||||
\(20\) | 6.46800e9 | + | 2.66565e11i | 0.0564956 | + | 2.32835i | ||||
\(21\) | −2.68102e11 | −1.54681 | ||||||||
\(22\) | − | 2.24681e11i | − | 0.872917i | ||||||
\(23\) | − | 2.44514e11i | − | 0.651055i | −0.945533 | − | 0.325527i | \(-0.894458\pi\) | ||
0.945533 | − | 0.325527i | \(-0.105542\pi\) | |||||||
\(24\) | 1.30135e12 | 2.41322 | ||||||||
\(25\) | −7.62042e11 | + | 3.70026e10i | −0.998823 | + | 0.0485000i | ||||
\(26\) | 4.09853e11 | 0.384906 | ||||||||
\(27\) | 1.47451e12i | 1.00475i | ||||||||
\(28\) | − | 7.23689e12i | − | 3.62000i | ||||||
\(29\) | −3.98521e12 | −1.47934 | −0.739670 | − | 0.672970i | \(-0.765018\pi\) | ||||
−0.739670 | + | 0.672970i | \(0.765018\pi\) | |||||||
\(30\) | 1.58282e11 | + | 6.52327e12i | 0.0440455 | + | 1.81524i | ||||
\(31\) | 2.84863e12 | 0.599877 | 0.299939 | − | 0.953959i | \(-0.403034\pi\) | ||||
0.299939 | + | 0.953959i | \(0.403034\pi\) | |||||||
\(32\) | 8.69651e12i | 1.39820i | ||||||||
\(33\) | − | 3.84668e12i | − | 0.476121i | ||||||
\(34\) | −6.46139e12 | −0.620519 | ||||||||
\(35\) | 2.07006e13 | − | 5.02286e11i | 1.55384 | − | 0.0377028i | ||||
\(36\) | −3.78802e11 | −0.0223790 | ||||||||
\(37\) | 2.87331e13i | 1.34483i | 0.740173 | + | 0.672417i | \(0.234744\pi\) | ||||
−0.740173 | + | 0.672417i | \(0.765256\pi\) | |||||||
\(38\) | − | 2.59562e13i | − | 0.968459i | ||||||
\(39\) | 7.01695e12 | 0.209942 | ||||||||
\(40\) | −1.00479e14 | + | 2.43806e12i | −2.42419 | + | 0.0588212i | ||||
\(41\) | 2.58650e13 | 0.505882 | 0.252941 | − | 0.967482i | \(-0.418602\pi\) | ||||
0.252941 | + | 0.967482i | \(0.418602\pi\) | |||||||
\(42\) | − | 1.77098e14i | − | 2.82225i | ||||||
\(43\) | 7.92427e13i | 1.03390i | 0.856016 | + | 0.516949i | \(0.172932\pi\) | ||||
−0.856016 | + | 0.516949i | \(0.827068\pi\) | |||||||
\(44\) | 1.03833e14 | 1.11427 | ||||||||
\(45\) | −2.62913e10 | − | 1.08354e12i | −0.000233081 | − | 0.00960591i | ||||
\(46\) | 1.61517e14 | 1.18789 | ||||||||
\(47\) | 3.42344e13i | 0.209716i | 0.994487 | + | 0.104858i | \(0.0334388\pi\) | ||||
−0.994487 | + | 0.104858i | \(0.966561\pi\) | |||||||
\(48\) | 4.07109e14i | 2.08526i | ||||||||
\(49\) | −3.29366e14 | −1.41583 | ||||||||
\(50\) | −2.44425e13 | − | 5.03376e14i | −0.0884913 | − | 1.82242i | ||||
\(51\) | −1.10623e14 | −0.338454 | ||||||||
\(52\) | 1.89408e14i | 0.491327i | ||||||||
\(53\) | 6.28298e14i | 1.38618i | 0.720850 | + | 0.693091i | \(0.243752\pi\) | ||||
−0.720850 | + | 0.693091i | \(0.756248\pi\) | |||||||
\(54\) | −9.74008e14 | −1.83322 | ||||||||
\(55\) | 7.20671e12 | + | 2.97009e14i | 0.0116052 | + | 0.478285i | ||||
\(56\) | 2.72788e15 | 3.76901 | ||||||||
\(57\) | − | 4.44388e14i | − | 0.528233i | ||||||
\(58\) | − | 2.63248e15i | − | 2.69915i | ||||||
\(59\) | 1.43672e15 | 1.27389 | 0.636943 | − | 0.770911i | \(-0.280199\pi\) | ||||
0.636943 | + | 0.770911i | \(0.280199\pi\) | |||||||
\(60\) | −3.01465e15 | + | 7.31483e13i | −2.31713 | + | 0.0562236i | ||||
\(61\) | −1.41408e15 | −0.944428 | −0.472214 | − | 0.881484i | \(-0.656545\pi\) | ||||
−0.472214 | + | 0.881484i | \(0.656545\pi\) | |||||||
\(62\) | 1.88170e15i | 1.09451i | ||||||||
\(63\) | 2.94167e13i | 0.0149348i | ||||||||
\(64\) | −1.02627e15 | −0.455757 | ||||||||
\(65\) | −5.41791e14 | + | 1.31462e13i | −0.210896 | + | 0.00511724i | ||||
\(66\) | 2.54097e15 | 0.868713 | ||||||||
\(67\) | − | 3.52003e14i | − | 0.105904i | −0.998597 | − | 0.0529518i | \(-0.983137\pi\) | ||
0.998597 | − | 0.0529518i | \(-0.0168630\pi\) | |||||||
\(68\) | − | 2.98605e15i | − | 0.792084i | ||||||
\(69\) | 2.76527e15 | 0.647919 | ||||||||
\(70\) | 3.31792e14 | + | 1.36741e16i | 0.0687910 | + | 2.83507i | ||||
\(71\) | 5.76817e15 | 1.06009 | 0.530044 | − | 0.847970i | \(-0.322175\pi\) | ||||
0.530044 | + | 0.847970i | \(0.322175\pi\) | |||||||
\(72\) | − | 1.42786e14i | − | 0.0233002i | ||||||
\(73\) | − | 1.24525e15i | − | 0.180723i | −0.995909 | − | 0.0903613i | \(-0.971198\pi\) | ||
0.995909 | − | 0.0903613i | \(-0.0288022\pi\) | |||||||
\(74\) | −1.89800e16 | −2.45373 | ||||||||
\(75\) | −4.18472e14 | − | 8.61812e15i | −0.0482664 | − | 0.994013i | ||||
\(76\) | 1.19953e16 | 1.23622 | ||||||||
\(77\) | − | 8.06341e15i | − | 0.743614i | ||||||
\(78\) | 4.63513e15i | 0.383052i | ||||||||
\(79\) | −8.16669e15 | −0.605642 | −0.302821 | − | 0.953048i | \(-0.597928\pi\) | ||||
−0.302821 | + | 0.953048i | \(0.597928\pi\) | |||||||
\(80\) | −7.62714e14 | − | 3.14336e16i | −0.0508273 | − | 2.09474i | ||||
\(81\) | −1.65154e16 | −0.990299 | ||||||||
\(82\) | 1.70854e16i | 0.923013i | ||||||||
\(83\) | 2.09840e16i | 1.02264i | 0.859389 | + | 0.511322i | \(0.170844\pi\) | ||||
−0.859389 | + | 0.511322i | \(0.829156\pi\) | |||||||
\(84\) | 8.18438e16 | 3.60257 | ||||||||
\(85\) | 8.54140e15 | − | 2.07251e14i | 0.339992 | − | 0.00824966i | ||||
\(86\) | −5.23447e16 | −1.88641 | ||||||||
\(87\) | − | 4.50697e16i | − | 1.47222i | ||||||
\(88\) | 3.91391e16i | 1.16013i | ||||||||
\(89\) | −2.91132e16 | −0.783926 | −0.391963 | − | 0.919981i | \(-0.628204\pi\) | ||||
−0.391963 | + | 0.919981i | \(0.628204\pi\) | |||||||
\(90\) | 7.15746e14 | − | 1.73671e13i | 0.0175266 | − | 0.000425270i | ||||
\(91\) | 1.47089e16 | 0.327891 | ||||||||
\(92\) | 7.46430e16i | 1.51633i | ||||||||
\(93\) | 3.22159e16i | 0.596988i | ||||||||
\(94\) | −2.26140e16 | −0.382640 | ||||||||
\(95\) | 8.32554e14 | + | 3.43119e16i | 0.0128754 | + | 0.530633i | ||||
\(96\) | −9.83511e16 | −1.39147 | ||||||||
\(97\) | − | 4.58585e16i | − | 0.594100i | −0.954862 | − | 0.297050i | \(-0.903997\pi\) | ||
0.954862 | − | 0.297050i | \(-0.0960029\pi\) | |||||||
\(98\) | − | 2.17567e17i | − | 2.58327i | ||||||
\(99\) | −4.22065e14 | −0.00459706 | ||||||||
\(100\) | 2.32629e17 | − | 1.12958e16i | 2.32629 | − | 0.112958i | ||||
\(101\) | 1.53390e17 | 1.40950 | 0.704752 | − | 0.709454i | \(-0.251058\pi\) | ||||
0.704752 | + | 0.709454i | \(0.251058\pi\) | |||||||
\(102\) | − | 7.30735e16i | − | 0.617531i | ||||||
\(103\) | 1.35527e17i | 1.05416i | 0.849815 | + | 0.527082i | \(0.176714\pi\) | ||||
−0.849815 | + | 0.527082i | \(0.823286\pi\) | |||||||
\(104\) | −7.13958e16 | −0.511552 | ||||||||
\(105\) | 5.68049e15 | + | 2.34109e17i | 0.0375212 | + | 1.54635i | ||||
\(106\) | −4.15030e17 | −2.52918 | ||||||||
\(107\) | − | 1.40345e17i | − | 0.789649i | −0.918757 | − | 0.394824i | \(-0.870805\pi\) | ||
0.918757 | − | 0.394824i | \(-0.129195\pi\) | |||||||
\(108\) | − | 4.50125e17i | − | 2.34009i | ||||||
\(109\) | 2.67560e17 | 1.28616 | 0.643081 | − | 0.765798i | \(-0.277656\pi\) | ||||
0.643081 | + | 0.765798i | \(0.277656\pi\) | |||||||
\(110\) | −1.96193e17 | + | 4.76048e15i | −0.872660 | + | 0.0211745i | ||||
\(111\) | −3.24950e17 | −1.33836 | ||||||||
\(112\) | 8.53382e17i | 3.25680i | ||||||||
\(113\) | − | 9.95662e16i | − | 0.352326i | −0.984361 | − | 0.176163i | \(-0.943631\pi\) | ||
0.984361 | − | 0.176163i | \(-0.0563687\pi\) | |||||||
\(114\) | 2.93546e17 | 0.963795 | ||||||||
\(115\) | −2.13512e17 | + | 5.18070e15i | −0.650863 | + | 0.0157927i | ||||
\(116\) | 1.21657e18 | 3.44543 | ||||||||
\(117\) | − | 7.69913e14i | − | 0.00202704i | ||||||
\(118\) | 9.49044e17i | 2.32428i | ||||||||
\(119\) | −2.31888e17 | −0.528603 | ||||||||
\(120\) | −2.75726e16 | − | 1.13634e18i | −0.0585379 | − | 2.41251i | ||||
\(121\) | −3.89755e17 | −0.771109 | ||||||||
\(122\) | − | 9.34085e17i | − | 1.72317i | ||||||
\(123\) | 2.92513e17i | 0.503445i | ||||||||
\(124\) | −8.69605e17 | −1.39713 | ||||||||
\(125\) | 4.84569e16 | + | 6.64636e17i | 0.0727143 | + | 0.997353i | ||||
\(126\) | −1.94316e16 | −0.0272495 | ||||||||
\(127\) | − | 1.33130e18i | − | 1.74559i | −0.488084 | − | 0.872797i | \(-0.662304\pi\) | ||
0.488084 | − | 0.872797i | \(-0.337696\pi\) | |||||||
\(128\) | 4.61951e17i | 0.566645i | ||||||||
\(129\) | −8.96176e17 | −1.02892 | ||||||||
\(130\) | −8.68386e15 | − | 3.57886e17i | −0.00933672 | − | 0.384793i | ||||
\(131\) | 1.65183e18 | 1.66402 | 0.832010 | − | 0.554760i | \(-0.187190\pi\) | ||||
0.832010 | + | 0.554760i | \(0.187190\pi\) | |||||||
\(132\) | 1.17428e18i | 1.10890i | ||||||||
\(133\) | − | 9.31525e17i | − | 0.825003i | ||||||
\(134\) | 2.32520e17 | 0.193228 | ||||||||
\(135\) | 1.28755e18 | − | 3.12416e16i | 1.00445 | − | 0.0243723i | ||||
\(136\) | 1.12557e18 | 0.824689 | ||||||||
\(137\) | − | 8.57280e17i | − | 0.590198i | −0.955467 | − | 0.295099i | \(-0.904647\pi\) | ||
0.955467 | − | 0.295099i | \(-0.0953527\pi\) | |||||||
\(138\) | 1.82664e18i | 1.18217i | ||||||||
\(139\) | 1.70531e18 | 1.03795 | 0.518976 | − | 0.854789i | \(-0.326313\pi\) | ||||
0.518976 | + | 0.854789i | \(0.326313\pi\) | |||||||
\(140\) | −6.31930e18 | + | 1.53333e17i | −3.61893 | + | 0.0878109i | ||||
\(141\) | −3.87166e17 | −0.208706 | ||||||||
\(142\) | 3.81024e18i | 1.93420i | ||||||||
\(143\) | 2.11041e17i | 0.100928i | ||||||||
\(144\) | 4.46688e16 | 0.0201337 | ||||||||
\(145\) | 8.44376e16 | + | 3.47991e18i | 0.0358846 | + | 1.47890i | ||||
\(146\) | 8.22566e17 | 0.329740 | ||||||||
\(147\) | − | 3.72488e18i | − | 1.40901i | ||||||
\(148\) | − | 8.77139e18i | − | 3.13216i | ||||||
\(149\) | −1.88380e18 | −0.635259 | −0.317629 | − | 0.948215i | \(-0.602887\pi\) | ||||
−0.317629 | + | 0.948215i | \(0.602887\pi\) | |||||||
\(150\) | 5.69281e18 | − | 2.76427e17i | 1.81364 | − | 0.0880652i | ||||
\(151\) | −3.21839e18 | −0.969024 | −0.484512 | − | 0.874785i | \(-0.661003\pi\) | ||||
−0.484512 | + | 0.874785i | \(0.661003\pi\) | |||||||
\(152\) | 4.52154e18i | 1.28711i | ||||||||
\(153\) | 1.21378e16i | 0.00326785i | ||||||||
\(154\) | 5.32638e18 | 1.35677 | ||||||||
\(155\) | −6.03561e16 | − | 2.48745e18i | −0.0145513 | − | 0.599701i | ||||
\(156\) | −2.14207e18 | −0.488961 | ||||||||
\(157\) | 5.70488e18i | 1.23339i | 0.787204 | + | 0.616693i | \(0.211528\pi\) | ||||
−0.787204 | + | 0.616693i | \(0.788472\pi\) | |||||||
\(158\) | − | 5.39461e18i | − | 1.10503i | ||||||
\(159\) | −7.10558e18 | −1.37951 | ||||||||
\(160\) | 7.59386e18 | − | 1.84259e17i | 1.39779 | − | 0.0339164i | ||||
\(161\) | 5.79657e18 | 1.01193 | ||||||||
\(162\) | − | 1.09094e19i | − | 1.80686i | ||||||
\(163\) | 2.76799e18i | 0.435080i | 0.976051 | + | 0.217540i | \(0.0698033\pi\) | ||||
−0.976051 | + | 0.217540i | \(0.930197\pi\) | |||||||
\(164\) | −7.89581e18 | −1.17821 | ||||||||
\(165\) | −3.35895e18 | + | 8.15025e16i | −0.475981 | + | 0.0115493i | ||||
\(166\) | −1.38613e19 | −1.86588 | ||||||||
\(167\) | 2.96598e18i | 0.379384i | 0.981844 | + | 0.189692i | \(0.0607489\pi\) | ||||
−0.981844 | + | 0.189692i | \(0.939251\pi\) | |||||||
\(168\) | 3.08503e19i | 3.75086i | ||||||||
\(169\) | 8.26544e18 | 0.955497 | ||||||||
\(170\) | 1.36902e17 | + | 5.64213e18i | 0.0150520 | + | 0.620336i | ||||
\(171\) | −4.87591e16 | −0.00510021 | ||||||||
\(172\) | − | 2.41905e19i | − | 2.40798i | ||||||
\(173\) | 1.22679e19i | 1.16246i | 0.813740 | + | 0.581228i | \(0.197428\pi\) | ||||
−0.813740 | + | 0.581228i | \(0.802572\pi\) | |||||||
\(174\) | 2.97714e19 | 2.68615 | ||||||||
\(175\) | −8.77200e17 | − | 1.80653e19i | −0.0753833 | − | 1.55247i | ||||
\(176\) | −1.22442e19 | −1.00247 | ||||||||
\(177\) | 1.62482e19i | 1.26775i | ||||||||
\(178\) | − | 1.92311e19i | − | 1.43032i | ||||||
\(179\) | 1.05059e19 | 0.745048 | 0.372524 | − | 0.928023i | \(-0.378492\pi\) | ||||
0.372524 | + | 0.928023i | \(0.378492\pi\) | |||||||
\(180\) | 8.02597e15 | + | 3.30773e17i | 0.000542852 | + | 0.0223725i | ||||
\(181\) | −6.36140e18 | −0.410473 | −0.205236 | − | 0.978712i | \(-0.565796\pi\) | ||||
−0.205236 | + | 0.978712i | \(0.565796\pi\) | |||||||
\(182\) | 9.71616e18i | 0.598257i | ||||||||
\(183\) | − | 1.59921e19i | − | 0.939880i | ||||||
\(184\) | −2.81360e19 | −1.57874 | ||||||||
\(185\) | 2.50900e19 | − | 6.08791e17i | 1.34444 | − | 0.0326218i | ||||
\(186\) | −2.12806e19 | −1.08924 | ||||||||
\(187\) | − | 3.32709e18i | − | 0.162709i | ||||||
\(188\) | − | 1.04508e19i | − | 0.488435i | ||||||
\(189\) | −3.49555e19 | −1.56167 | ||||||||
\(190\) | −2.26652e19 | + | 5.49954e17i | −0.968174 | + | 0.0234920i | ||||
\(191\) | 2.68237e19 | 1.09581 | 0.547905 | − | 0.836541i | \(-0.315426\pi\) | ||||
0.547905 | + | 0.836541i | \(0.315426\pi\) | |||||||
\(192\) | − | 1.16064e19i | − | 0.453562i | ||||||
\(193\) | 1.22468e19i | 0.457916i | 0.973436 | + | 0.228958i | \(0.0735319\pi\) | ||||
−0.973436 | + | 0.228958i | \(0.926468\pi\) | |||||||
\(194\) | 3.02924e19 | 1.08397 | ||||||||
\(195\) | −1.48673e17 | − | 6.12725e18i | −0.00509259 | − | 0.209880i | ||||
\(196\) | 1.00546e20 | 3.29751 | ||||||||
\(197\) | 1.20855e19i | 0.379580i | 0.981825 | + | 0.189790i | \(0.0607807\pi\) | ||||
−0.981825 | + | 0.189790i | \(0.939219\pi\) | |||||||
\(198\) | − | 2.78800e17i | − | 0.00838763i | ||||||
\(199\) | −6.55776e19 | −1.89018 | −0.945092 | − | 0.326804i | \(-0.894028\pi\) | ||||
−0.945092 | + | 0.326804i | \(0.894028\pi\) | |||||||
\(200\) | 4.25785e18 | + | 8.76874e19i | 0.117608 | + | 2.42205i | ||||
\(201\) | 3.98090e18 | 0.105394 | ||||||||
\(202\) | 1.01324e20i | 2.57173i | ||||||||
\(203\) | − | 9.44751e19i | − | 2.29933i | ||||||
\(204\) | 3.37700e19 | 0.788270 | ||||||||
\(205\) | −5.48020e17 | − | 2.25855e19i | −0.0122712 | − | 0.505733i | ||||
\(206\) | −8.95237e19 | −1.92339 | ||||||||
\(207\) | − | 3.03411e17i | − | 0.00625581i | ||||||
\(208\) | − | 2.23353e19i | − | 0.442031i | ||||||
\(209\) | 1.33653e19 | 0.253943 | ||||||||
\(210\) | −1.54644e20 | + | 3.75232e18i | −2.82142 | + | 0.0684598i | ||||
\(211\) | −2.90167e19 | −0.508449 | −0.254224 | − | 0.967145i | \(-0.581820\pi\) | ||||
−0.254224 | + | 0.967145i | \(0.581820\pi\) | |||||||
\(212\) | − | 1.91801e20i | − | 3.22846i | ||||||
\(213\) | 6.52337e19i | 1.05498i | ||||||||
\(214\) | 9.27065e19 | 1.44076 | ||||||||
\(215\) | 6.91953e19 | − | 1.67897e18i | 1.03359 | − | 0.0250794i | ||||
\(216\) | 1.69671e20 | 2.43641 | ||||||||
\(217\) | 6.75310e19i | 0.932386i | ||||||||
\(218\) | 1.76740e20i | 2.34668i | ||||||||
\(219\) | 1.40829e19 | 0.179852 | ||||||||
\(220\) | −2.20000e18 | − | 9.06681e19i | −0.0270289 | − | 1.11394i | ||||
\(221\) | 6.06913e18 | 0.0717450 | ||||||||
\(222\) | − | 2.14650e20i | − | 2.44192i | ||||||
\(223\) | − | 1.00403e20i | − | 1.09940i | −0.835363 | − | 0.549699i | \(-0.814742\pi\) | ||
0.835363 | − | 0.549699i | \(-0.185258\pi\) | |||||||
\(224\) | −2.06163e20 | −2.17322 | ||||||||
\(225\) | −9.45597e17 | + | 4.59155e16i | −0.00959743 | + | 0.000466024i | ||||
\(226\) | 6.57697e19 | 0.642842 | ||||||||
\(227\) | 7.25392e19i | 0.682894i | 0.939901 | + | 0.341447i | \(0.110917\pi\) | ||||
−0.939901 | + | 0.341447i | \(0.889083\pi\) | |||||||
\(228\) | 1.35658e20i | 1.23027i | ||||||||
\(229\) | −1.05419e20 | −0.921124 | −0.460562 | − | 0.887628i | \(-0.652352\pi\) | ||||
−0.460562 | + | 0.887628i | \(0.652352\pi\) | |||||||
\(230\) | −3.42218e18 | − | 1.41038e20i | −0.0288148 | − | 1.18754i | ||||
\(231\) | 9.11912e19 | 0.740033 | ||||||||
\(232\) | 4.58574e20i | 3.58725i | ||||||||
\(233\) | 1.19870e20i | 0.904037i | 0.892008 | + | 0.452019i | \(0.149296\pi\) | ||||
−0.892008 | + | 0.452019i | \(0.850704\pi\) | |||||||
\(234\) | 5.08576e17 | 0.00369846 | ||||||||
\(235\) | 2.98937e19 | − | 7.25350e17i | 0.209654 | − | 0.00508711i | ||||
\(236\) | −4.38589e20 | −2.96692 | ||||||||
\(237\) | − | 9.23592e19i | − | 0.602725i | ||||||
\(238\) | − | 1.53177e20i | − | 0.964469i | ||||||
\(239\) | 8.27461e19 | 0.502766 | 0.251383 | − | 0.967888i | \(-0.419115\pi\) | ||||
0.251383 | + | 0.967888i | \(0.419115\pi\) | |||||||
\(240\) | 3.55491e20 | − | 8.62573e18i | 2.08465 | − | 0.0505825i | ||||
\(241\) | 8.99963e19 | 0.509425 | 0.254712 | − | 0.967017i | \(-0.418019\pi\) | ||||
0.254712 | + | 0.967017i | \(0.418019\pi\) | |||||||
\(242\) | − | 2.57457e20i | − | 1.40694i | ||||||
\(243\) | 3.64195e18i | 0.0192168i | ||||||||
\(244\) | 4.31676e20 | 2.19960 | ||||||||
\(245\) | 6.97851e18 | + | 2.87604e20i | 0.0343440 | + | 1.41541i | ||||
\(246\) | −1.93223e20 | −0.918568 | ||||||||
\(247\) | 2.43805e19i | 0.111974i | ||||||||
\(248\) | − | 3.27790e20i | − | 1.45464i | ||||||
\(249\) | −2.37314e20 | −1.01772 | ||||||||
\(250\) | −4.39034e20 | + | 3.20088e19i | −1.81973 | + | 0.132672i | ||||
\(251\) | −5.05233e19 | −0.202425 | −0.101213 | − | 0.994865i | \(-0.532272\pi\) | ||||
−0.101213 | + | 0.994865i | \(0.532272\pi\) | |||||||
\(252\) | − | 8.98006e18i | − | 0.0347836i | ||||||
\(253\) | 8.31680e19i | 0.311481i | ||||||||
\(254\) | 8.79404e20 | 3.18495 | ||||||||
\(255\) | 2.34386e18 | + | 9.65969e19i | 0.00820993 | + | 0.338354i | ||||
\(256\) | −4.39663e20 | −1.48964 | ||||||||
\(257\) | − | 5.06773e20i | − | 1.66105i | −0.556984 | − | 0.830524i | \(-0.688041\pi\) | ||
0.556984 | − | 0.830524i | \(-0.311959\pi\) | |||||||
\(258\) | − | 5.91980e20i | − | 1.87733i | ||||||
\(259\) | −6.81161e20 | −2.09027 | ||||||||
\(260\) | 1.65393e20 | − | 4.01314e18i | 0.491183 | − | 0.0119182i | ||||
\(261\) | −4.94514e18 | −0.0142146 | ||||||||
\(262\) | 1.09114e21i | 3.03611i | ||||||||
\(263\) | 5.09531e19i | 0.137261i | 0.997642 | + | 0.0686305i | \(0.0218629\pi\) | ||||
−0.997642 | + | 0.0686305i | \(0.978137\pi\) | |||||||
\(264\) | −4.42634e20 | −1.15455 | ||||||||
\(265\) | 5.48634e20 | − | 1.33122e19i | 1.38577 | − | 0.0336248i | ||||
\(266\) | 6.15330e20 | 1.50527 | ||||||||
\(267\) | − | 3.29249e20i | − | 0.780151i | ||||||
\(268\) | 1.07456e20i | 0.246653i | ||||||||
\(269\) | −9.13493e19 | −0.203147 | −0.101574 | − | 0.994828i | \(-0.532388\pi\) | ||||
−0.101574 | + | 0.994828i | \(0.532388\pi\) | |||||||
\(270\) | 2.06370e19 | + | 8.50510e20i | 0.0444688 | + | 1.83268i | ||||
\(271\) | 3.85248e19 | 0.0804455 | 0.0402227 | − | 0.999191i | \(-0.487193\pi\) | ||||
0.0402227 | + | 0.999191i | \(0.487193\pi\) | |||||||
\(272\) | 3.52119e20i | 0.712612i | ||||||||
\(273\) | 1.66347e20i | 0.326312i | ||||||||
\(274\) | 5.66287e20 | 1.07685 | ||||||||
\(275\) | 2.59197e20 | − | 1.25859e19i | 0.477862 | − | 0.0232036i | ||||
\(276\) | −8.44157e20 | −1.50902 | ||||||||
\(277\) | − | 8.52898e20i | − | 1.47849i | −0.673435 | − | 0.739246i | \(-0.735182\pi\) | ||
0.673435 | − | 0.739246i | \(-0.264818\pi\) | |||||||
\(278\) | 1.12646e21i | 1.89381i | ||||||||
\(279\) | 3.53480e18 | 0.00576406 | ||||||||
\(280\) | −5.77976e19 | − | 2.38200e21i | −0.0914254 | − | 3.76790i | ||||
\(281\) | 7.66403e20 | 1.17612 | 0.588062 | − | 0.808816i | \(-0.299891\pi\) | ||||
0.588062 | + | 0.808816i | \(0.299891\pi\) | |||||||
\(282\) | − | 2.55747e20i | − | 0.380797i | ||||||
\(283\) | 6.44868e20i | 0.931721i | 0.884858 | + | 0.465860i | \(0.154255\pi\) | ||||
−0.884858 | + | 0.465860i | \(0.845745\pi\) | |||||||
\(284\) | −1.76085e21 | −2.46898 | ||||||||
\(285\) | −3.88042e20 | + | 9.41557e18i | −0.528078 | + | 0.0128134i | ||||
\(286\) | −1.39406e20 | −0.184149 | ||||||||
\(287\) | 6.13167e20i | 0.786289i | ||||||||
\(288\) | 1.07913e19i | 0.0134350i | ||||||||
\(289\) | 7.31560e20 | 0.884338 | ||||||||
\(290\) | −2.29870e21 | + | 5.57763e19i | −2.69835 | + | 0.0654737i | ||||
\(291\) | 5.18625e20 | 0.591239 | ||||||||
\(292\) | 3.80139e20i | 0.420908i | ||||||||
\(293\) | − | 1.05852e21i | − | 1.13847i | −0.822173 | − | 0.569237i | \(-0.807239\pi\) | ||
0.822173 | − | 0.569237i | \(-0.192761\pi\) | |||||||
\(294\) | 2.46052e21 | 2.57083 | ||||||||
\(295\) | −3.04409e19 | − | 1.25455e21i | −0.0309008 | − | 1.27351i | ||||
\(296\) | 3.30630e21 | 3.26109 | ||||||||
\(297\) | − | 5.01534e20i | − | 0.480696i | ||||||
\(298\) | − | 1.24436e21i | − | 1.15907i | ||||||
\(299\) | −1.51711e20 | −0.137345 | ||||||||
\(300\) | 1.27747e20 | + | 2.63086e21i | 0.112414 | + | 2.31509i | ||||
\(301\) | −1.87856e21 | −1.60698 | ||||||||
\(302\) | − | 2.12595e21i | − | 1.76805i | ||||||
\(303\) | 1.73473e21i | 1.40272i | ||||||||
\(304\) | −1.41451e21 | −1.11219 | ||||||||
\(305\) | 2.99611e19 | + | 1.23478e21i | 0.0229091 | + | 0.944150i | ||||
\(306\) | −8.01777e18 | −0.00596240 | ||||||||
\(307\) | 2.20525e21i | 1.59508i | 0.603268 | + | 0.797538i | \(0.293865\pi\) | ||||
−0.603268 | + | 0.797538i | \(0.706135\pi\) | |||||||
\(308\) | 2.46152e21i | 1.73190i | ||||||||
\(309\) | −1.53270e21 | −1.04909 | ||||||||
\(310\) | 1.64311e21 | − | 3.98690e19i | 1.09419 | − | 0.0265498i | ||||
\(311\) | −1.67631e21 | −1.08615 | −0.543077 | − | 0.839683i | \(-0.682741\pi\) | ||||
−0.543077 | + | 0.839683i | \(0.682741\pi\) | |||||||
\(312\) | − | 8.07434e20i | − | 0.509088i | ||||||
\(313\) | − | 1.91815e21i | − | 1.17695i | −0.808517 | − | 0.588473i | \(-0.799729\pi\) | ||
0.808517 | − | 0.588473i | \(-0.200271\pi\) | |||||||
\(314\) | −3.76843e21 | −2.25039 | ||||||||
\(315\) | 2.56869e19 | − | 6.23274e17i | 0.0149304 | − | 0.000362276i | ||||
\(316\) | 2.49305e21 | 1.41056 | ||||||||
\(317\) | − | 2.94101e20i | − | 0.161992i | −0.996714 | − | 0.0809959i | \(-0.974190\pi\) | ||
0.996714 | − | 0.0809959i | \(-0.0258101\pi\) | |||||||
\(318\) | − | 4.69368e21i | − | 2.51700i | ||||||
\(319\) | 1.35551e21 | 0.707754 | ||||||||
\(320\) | 2.17444e19 | + | 8.96150e20i | 0.0110554 | + | 0.455623i | ||||
\(321\) | 1.58719e21 | 0.785846 | ||||||||
\(322\) | 3.82899e21i | 1.84633i | ||||||||
\(323\) | − | 3.84361e20i | − | 0.180517i | ||||||
\(324\) | 5.04167e21 | 2.30644 | ||||||||
\(325\) | 2.29586e19 | + | 4.72817e20i | 0.0102315 | + | 0.210710i | ||||
\(326\) | −1.82843e21 | −0.793831 | ||||||||
\(327\) | 3.02590e21i | 1.27997i | ||||||||
\(328\) | − | 2.97626e21i | − | 1.22671i | ||||||
\(329\) | −8.11577e20 | −0.325960 | ||||||||
\(330\) | −5.38375e19 | − | 2.21879e21i | −0.0210725 | − | 0.868458i | ||||
\(331\) | 3.51653e21 | 1.34145 | 0.670727 | − | 0.741704i | \(-0.265982\pi\) | ||||
0.670727 | + | 0.741704i | \(0.265982\pi\) | |||||||
\(332\) | − | 6.40581e21i | − | 2.38177i | ||||||
\(333\) | 3.56542e19i | 0.0129221i | ||||||||
\(334\) | −1.95922e21 | −0.692210 | ||||||||
\(335\) | −3.07372e20 | + | 7.45816e18i | −0.105873 | + | 0.00256892i | ||||
\(336\) | −9.65112e21 | −3.24111 | ||||||||
\(337\) | − | 1.06259e21i | − | 0.347947i | −0.984750 | − | 0.173973i | \(-0.944339\pi\) | ||
0.984750 | − | 0.173973i | \(-0.0556607\pi\) | |||||||
\(338\) | 5.45984e21i | 1.74336i | ||||||||
\(339\) | 1.12602e21 | 0.350630 | ||||||||
\(340\) | −2.60744e21 | + | 6.32677e19i | −0.791851 | + | 0.0192137i | ||||
\(341\) | −9.68922e20 | −0.286996 | ||||||||
\(342\) | − | 3.22084e19i | − | 0.00930566i | ||||||
\(343\) | − | 2.29325e21i | − | 0.646325i | ||||||
\(344\) | 9.11838e21 | 2.50710 | ||||||||
\(345\) | −5.85899e19 | − | 2.41466e21i | −0.0157167 | − | 0.647729i | ||||
\(346\) | −8.10369e21 | −2.12098 | ||||||||
\(347\) | 6.26207e21i | 1.59925i | 0.600498 | + | 0.799626i | \(0.294969\pi\) | ||||
−0.600498 | + | 0.799626i | \(0.705031\pi\) | |||||||
\(348\) | 1.37585e22i | 3.42883i | ||||||||
\(349\) | 4.92952e21 | 1.19891 | 0.599457 | − | 0.800407i | \(-0.295383\pi\) | ||||
0.599457 | + | 0.800407i | \(0.295383\pi\) | |||||||
\(350\) | 1.19333e22 | − | 5.79445e20i | 2.83257 | − | 0.137542i | ||||
\(351\) | 9.14877e20 | 0.211959 | ||||||||
\(352\) | − | 2.95799e21i | − | 0.668936i | ||||||
\(353\) | − | 1.65310e21i | − | 0.364934i | −0.983212 | − | 0.182467i | \(-0.941592\pi\) | ||
0.983212 | − | 0.182467i | \(-0.0584083\pi\) | |||||||
\(354\) | −1.07330e22 | −2.31309 | ||||||||
\(355\) | −1.22215e20 | − | 5.03681e21i | −0.0257147 | − | 1.05978i | ||||
\(356\) | 8.88742e21 | 1.82579 | ||||||||
\(357\) | − | 2.62248e21i | − | 0.526057i | ||||||
\(358\) | 6.93983e21i | 1.35939i | ||||||||
\(359\) | −5.64380e21 | −1.07961 | −0.539807 | − | 0.841789i | \(-0.681503\pi\) | ||||
−0.539807 | + | 0.841789i | \(0.681503\pi\) | |||||||
\(360\) | −1.24682e20 | + | 3.02532e18i | −0.0232934 | + | 0.000565197i | ||||
\(361\) | −3.93636e21 | −0.718263 | ||||||||
\(362\) | − | 4.20210e21i | − | 0.748934i | ||||||
\(363\) | − | 4.40784e21i | − | 0.767396i | ||||||
\(364\) | −4.49020e21 | −0.763667 | ||||||||
\(365\) | −1.08736e21 | + | 2.63841e19i | −0.180669 | + | 0.00438381i | ||||
\(366\) | 1.05638e22 | 1.71487 | ||||||||
\(367\) | − | 7.92023e20i | − | 0.125625i | −0.998025 | − | 0.0628125i | \(-0.979993\pi\) | ||
0.998025 | − | 0.0628125i | \(-0.0200070\pi\) | |||||||
\(368\) | − | 8.80199e21i | − | 1.36419i | ||||||
\(369\) | 3.20952e19 | 0.00486088 | ||||||||
\(370\) | 4.02144e20 | + | 1.65735e22i | 0.0595206 | + | 2.45301i | ||||
\(371\) | −1.48947e22 | −2.15454 | ||||||||
\(372\) | − | 9.83458e21i | − | 1.39040i | ||||||
\(373\) | 5.60332e21i | 0.774320i | 0.922012 | + | 0.387160i | \(0.126544\pi\) | ||||
−0.922012 | + | 0.387160i | \(0.873456\pi\) | |||||||
\(374\) | 2.19775e21 | 0.296872 | ||||||||
\(375\) | −7.51654e21 | + | 5.48011e20i | −0.992550 | + | 0.0723642i | ||||
\(376\) | 3.93932e21 | 0.508540 | ||||||||
\(377\) | 2.47266e21i | 0.312078i | ||||||||
\(378\) | − | 2.30903e22i | − | 2.84937i | ||||||
\(379\) | 1.12046e22 | 1.35195 | 0.675977 | − | 0.736923i | \(-0.263722\pi\) | ||||
0.675977 | + | 0.736923i | \(0.263722\pi\) | |||||||
\(380\) | −2.54154e20 | − | 1.04744e22i | −0.0299873 | − | 1.23586i | ||||
\(381\) | 1.50560e22 | 1.73719 | ||||||||
\(382\) | 1.77187e22i | 1.99937i | ||||||||
\(383\) | − | 7.07404e21i | − | 0.780689i | −0.920669 | − | 0.390344i | \(-0.872356\pi\) | ||
0.920669 | − | 0.390344i | \(-0.127644\pi\) | |||||||
\(384\) | −5.22432e21 | −0.563916 | ||||||||
\(385\) | −7.04103e21 | + | 1.70845e20i | −0.743395 | + | 0.0180380i | ||||
\(386\) | −8.08979e21 | −0.835497 | ||||||||
\(387\) | 9.83302e19i | 0.00993444i | ||||||||
\(388\) | 1.39992e22i | 1.38368i | ||||||||
\(389\) | 1.85301e22 | 1.79187 | 0.895937 | − | 0.444182i | \(-0.146506\pi\) | ||||
0.895937 | + | 0.444182i | \(0.146506\pi\) | |||||||
\(390\) | 4.04743e21 | − | 9.82080e19i | 0.382939 | − | 0.00929175i | ||||
\(391\) | 2.39175e21 | 0.221418 | ||||||||
\(392\) | 3.78998e22i | 3.43325i | ||||||||
\(393\) | 1.86809e22i | 1.65601i | ||||||||
\(394\) | −7.98326e21 | −0.692568 | ||||||||
\(395\) | 1.73034e20 | + | 7.13121e21i | 0.0146911 | + | 0.605463i | ||||
\(396\) | 1.28844e20 | 0.0107067 | ||||||||
\(397\) | − | 2.32134e22i | − | 1.88807i | −0.329840 | − | 0.944037i | \(-0.606995\pi\) | ||
0.329840 | − | 0.944037i | \(-0.393005\pi\) | |||||||
\(398\) | − | 4.33181e22i | − | 3.44876i | ||||||
\(399\) | 1.05349e22 | 0.821030 | ||||||||
\(400\) | −2.74319e22 | + | 1.33201e21i | −2.09289 | + | 0.101625i | ||||
\(401\) | −1.49395e22 | −1.11586 | −0.557928 | − | 0.829890i | \(-0.688403\pi\) | ||||
−0.557928 | + | 0.829890i | \(0.688403\pi\) | |||||||
\(402\) | 2.62963e21i | 0.192297i | ||||||||
\(403\) | − | 1.76747e21i | − | 0.126549i | ||||||
\(404\) | −4.68256e22 | −3.28278 | ||||||||
\(405\) | 3.49924e20 | + | 1.44214e22i | 0.0240218 | + | 0.990008i | ||||
\(406\) | 6.24067e22 | 4.19527 | ||||||||
\(407\) | − | 9.77316e21i | − | 0.643402i | ||||||
\(408\) | 1.27293e22i | 0.820717i | ||||||||
\(409\) | −2.14032e22 | −1.35155 | −0.675774 | − | 0.737109i | \(-0.736190\pi\) | ||||
−0.675774 | + | 0.737109i | \(0.736190\pi\) | |||||||
\(410\) | 1.49191e22 | − | 3.62002e20i | 0.922742 | − | 0.0223897i | ||||
\(411\) | 9.69520e21 | 0.587356 | ||||||||
\(412\) | − | 4.13723e22i | − | 2.45518i | ||||||
\(413\) | 3.40596e22i | 1.97999i | ||||||||
\(414\) | 2.00422e20 | 0.0114141 | ||||||||
\(415\) | 1.83234e22 | − | 4.44604e20i | 1.02234 | − | 0.0248064i | ||||
\(416\) | 5.39584e21 | 0.294962 | ||||||||
\(417\) | 1.92858e22i | 1.03295i | ||||||||
\(418\) | 8.82864e21i | 0.463335i | ||||||||
\(419\) | −4.94779e20 | −0.0254444 | −0.0127222 | − | 0.999919i | \(-0.504050\pi\) | ||||
−0.0127222 | + | 0.999919i | \(0.504050\pi\) | |||||||
\(420\) | −1.73409e21 | − | 7.14666e22i | −0.0873880 | − | 3.60151i | ||||
\(421\) | −2.45451e22 | −1.21218 | −0.606091 | − | 0.795395i | \(-0.707263\pi\) | ||||
−0.606091 | + | 0.795395i | \(0.707263\pi\) | |||||||
\(422\) | − | 1.91673e22i | − | 0.927696i | ||||||
\(423\) | 4.24806e19i | 0.00201510i | ||||||||
\(424\) | 7.22976e22 | 3.36135 | ||||||||
\(425\) | −3.61946e20 | − | 7.45402e21i | −0.0164945 | − | 0.339692i | ||||
\(426\) | −4.30910e22 | −1.92488 | ||||||||
\(427\) | − | 3.35227e22i | − | 1.46792i | ||||||
\(428\) | 4.28431e22i | 1.83912i | ||||||||
\(429\) | −2.38671e21 | −0.100442 | ||||||||
\(430\) | 1.10907e21 | + | 4.57078e22i | 0.0457589 | + | 1.88586i | ||||
\(431\) | 2.21018e22 | 0.894067 | 0.447033 | − | 0.894517i | \(-0.352480\pi\) | ||||
0.447033 | + | 0.894517i | \(0.352480\pi\) | |||||||
\(432\) | 5.30793e22i | 2.10530i | ||||||||
\(433\) | − | 2.47754e22i | − | 0.963549i | −0.876295 | − | 0.481774i | \(-0.839992\pi\) | ||
0.876295 | − | 0.481774i | \(-0.160008\pi\) | |||||||
\(434\) | −4.46085e22 | −1.70120 | ||||||||
\(435\) | −3.93552e22 | + | 9.54926e20i | −1.47178 | + | 0.0357117i | ||||
\(436\) | −8.16781e22 | −2.99551 | ||||||||
\(437\) | 9.60798e21i | 0.345573i | ||||||||
\(438\) | 9.30261e21i | 0.328152i | ||||||||
\(439\) | −7.72167e21 | −0.267155 | −0.133577 | − | 0.991038i | \(-0.542646\pi\) | ||||
−0.133577 | + | 0.991038i | \(0.542646\pi\) | |||||||
\(440\) | 3.41765e22 | − | 8.29269e20i | 1.15979 | − | 0.0281415i | ||||
\(441\) | −4.08701e20 | −0.0136044 | ||||||||
\(442\) | 4.00904e21i | 0.130903i | ||||||||
\(443\) | 3.47364e21i | 0.111264i | 0.998451 | + | 0.0556318i | \(0.0177173\pi\) | ||||
−0.998451 | + | 0.0556318i | \(0.982283\pi\) | |||||||
\(444\) | 9.91979e22 | 3.11707 | ||||||||
\(445\) | 6.16844e20 | + | 2.54219e22i | 0.0190158 | + | 0.783696i | ||||
\(446\) | 6.63224e22 | 2.00592 | ||||||||
\(447\) | − | 2.13043e22i | − | 0.632199i | ||||||
\(448\) | − | 2.43293e22i | − | 0.708381i | ||||||
\(449\) | 3.35625e22 | 0.958871 | 0.479435 | − | 0.877577i | \(-0.340841\pi\) | ||||
0.479435 | + | 0.877577i | \(0.340841\pi\) | |||||||
\(450\) | −3.03301e19 | − | 6.24626e20i | −0.000850290 | − | 0.0175111i | ||||
\(451\) | −8.79759e21 | −0.242027 | ||||||||
\(452\) | 3.03946e22i | 0.820579i | ||||||||
\(453\) | − | 3.63976e22i | − | 0.964357i | ||||||
\(454\) | −4.79167e22 | −1.24598 | ||||||||
\(455\) | −3.11649e20 | − | 1.28439e22i | −0.00795369 | − | 0.327794i | ||||
\(456\) | −5.11353e22 | −1.28091 | ||||||||
\(457\) | 3.47799e22i | 0.855146i | 0.903981 | + | 0.427573i | \(0.140631\pi\) | ||||
−0.903981 | + | 0.427573i | \(0.859369\pi\) | |||||||
\(458\) | − | 6.96359e22i | − | 1.68065i | ||||||
\(459\) | −1.44232e22 | −0.341706 | ||||||||
\(460\) | 6.51788e22 | − | 1.58152e21i | 1.51588 | − | 0.0367818i | ||||
\(461\) | 4.25534e22 | 0.971574 | 0.485787 | − | 0.874077i | \(-0.338533\pi\) | ||||
0.485787 | + | 0.874077i | \(0.338533\pi\) | |||||||
\(462\) | 6.02375e22i | 1.35024i | ||||||||
\(463\) | − | 4.02870e22i | − | 0.886597i | −0.896374 | − | 0.443299i | \(-0.853808\pi\) | ||
0.896374 | − | 0.443299i | \(-0.146192\pi\) | |||||||
\(464\) | −1.43459e23 | −3.09974 | ||||||||
\(465\) | 2.81312e22 | − | 6.82583e20i | 0.596813 | − | 0.0144812i | ||||
\(466\) | −7.91818e22 | −1.64947 | ||||||||
\(467\) | − | 1.32049e21i | − | 0.0270110i | −0.999909 | − | 0.0135055i | \(-0.995701\pi\) | ||
0.999909 | − | 0.0135055i | \(-0.00429907\pi\) | |||||||
\(468\) | 2.35032e20i | 0.00472103i | ||||||||
\(469\) | 8.34476e21 | 0.164606 | ||||||||
\(470\) | 4.79139e20 | + | 1.97467e22i | 0.00928175 | + | 0.382527i | ||||
\(471\) | −6.45179e22 | −1.22745 | ||||||||
\(472\) | − | 1.65322e23i | − | 3.08904i | ||||||
\(473\) | − | 2.69533e22i | − | 0.494643i | ||||||
\(474\) | 6.10090e22 | 1.09971 | ||||||||
\(475\) | 2.99438e22 | − | 1.45398e21i | 0.530165 | − | 0.0257433i | ||||
\(476\) | 7.07887e22 | 1.23113 | ||||||||
\(477\) | 7.79638e20i | 0.0133195i | ||||||||
\(478\) | 5.46590e22i | 0.917328i | ||||||||
\(479\) | 4.98795e22 | 0.822375 | 0.411188 | − | 0.911551i | \(-0.365114\pi\) | ||||
0.411188 | + | 0.911551i | \(0.365114\pi\) | |||||||
\(480\) | 2.08384e21 | + | 8.58809e22i | 0.0337531 | + | 1.39106i | ||||
\(481\) | 1.78278e22 | 0.283703 | ||||||||
\(482\) | 5.94482e22i | 0.929477i | ||||||||
\(483\) | 6.55548e22i | 1.00706i | ||||||||
\(484\) | 1.18981e23 | 1.79594 | ||||||||
\(485\) | −4.00439e22 | + | 9.71638e20i | −0.593926 | + | 0.0144112i | ||||
\(486\) | −2.40574e21 | −0.0350623 | ||||||||
\(487\) | − | 1.58494e22i | − | 0.226996i | −0.993538 | − | 0.113498i | \(-0.963794\pi\) | ||
0.993538 | − | 0.113498i | \(-0.0362055\pi\) | |||||||
\(488\) | 1.62716e23i | 2.29014i | ||||||||
\(489\) | −3.13039e22 | −0.432985 | ||||||||
\(490\) | −1.89981e23 | + | 4.60974e21i | −2.58251 | + | 0.0626629i | ||||
\(491\) | 6.29353e22 | 0.840817 | 0.420409 | − | 0.907335i | \(-0.361887\pi\) | ||||
0.420409 | + | 0.907335i | \(0.361887\pi\) | |||||||
\(492\) | − | 8.92958e22i | − | 1.17254i | ||||||
\(493\) | − | 3.89819e22i | − | 0.503111i | ||||||
\(494\) | −1.61048e22 | −0.204304 | ||||||||
\(495\) | 8.94261e18 | + | 3.68550e20i | 0.000111512 | + | 0.00459571i | ||||
\(496\) | 1.02545e23 | 1.25695 | ||||||||
\(497\) | 1.36743e23i | 1.64769i | ||||||||
\(498\) | − | 1.56760e23i | − | 1.85689i | ||||||
\(499\) | −1.06080e23 | −1.23532 | −0.617660 | − | 0.786445i | \(-0.711919\pi\) | ||||
−0.617660 | + | 0.786445i | \(0.711919\pi\) | |||||||
\(500\) | −1.47925e22 | − | 2.02894e23i | −0.169354 | − | 2.32287i | ||||
\(501\) | −3.35431e22 | −0.377557 | ||||||||
\(502\) | − | 3.33738e22i | − | 0.369338i | ||||||
\(503\) | 9.88915e22i | 1.07605i | 0.842930 | + | 0.538024i | \(0.180829\pi\) | ||||
−0.842930 | + | 0.538024i | \(0.819171\pi\) | |||||||
\(504\) | 3.38496e21 | 0.0362154 | ||||||||
\(505\) | −3.24999e21 | − | 1.33941e23i | −0.0341905 | − | 1.40909i | ||||
\(506\) | −5.49376e22 | −0.568317 | ||||||||
\(507\) | 9.34760e22i | 0.950895i | ||||||||
\(508\) | 4.06406e23i | 4.06554i | ||||||||
\(509\) | −1.44169e23 | −1.41831 | −0.709156 | − | 0.705051i | \(-0.750924\pi\) | ||||
−0.709156 | + | 0.705051i | \(0.750924\pi\) | |||||||
\(510\) | −6.38083e22 | + | 1.54826e21i | −0.617349 | + | 0.0149795i | ||||
\(511\) | 2.95205e22 | 0.280896 | ||||||||
\(512\) | − | 2.29876e23i | − | 2.15129i | ||||||
\(513\) | − | 5.79397e22i | − | 0.533309i | ||||||
\(514\) | 3.34755e23 | 3.03069 | ||||||||
\(515\) | 1.18343e23 | − | 2.87150e21i | 1.05385 | − | 0.0255710i | ||||
\(516\) | 2.73576e23 | 2.39638 | ||||||||
\(517\) | − | 1.16443e22i | − | 0.100333i | ||||||
\(518\) | − | 4.49949e23i | − | 3.81382i | ||||||
\(519\) | −1.38740e23 | −1.15686 | ||||||||
\(520\) | 1.51272e21 | + | 6.23433e22i | 0.0124088 | + | 0.511401i | ||||
\(521\) | −2.14130e22 | −0.172805 | −0.0864025 | − | 0.996260i | \(-0.527537\pi\) | ||||
−0.0864025 | + | 0.996260i | \(0.527537\pi\) | |||||||
\(522\) | − | 3.26657e21i | − | 0.0259354i | ||||||
\(523\) | 8.29652e22i | 0.648084i | 0.946043 | + | 0.324042i | \(0.105042\pi\) | ||||
−0.946043 | + | 0.324042i | \(0.894958\pi\) | |||||||
\(524\) | −5.04255e23 | −3.87556 | ||||||||
\(525\) | 2.04305e23 | − | 9.92048e21i | 1.54499 | − | 0.0750203i | ||||
\(526\) | −3.36577e22 | −0.250441 | ||||||||
\(527\) | 2.78643e22i | 0.204013i | ||||||||
\(528\) | − | 1.38472e23i | − | 0.997642i | ||||||
\(529\) | 8.12628e22 | 0.576128 | ||||||||
\(530\) | 8.79355e21 | + | 3.62407e23i | 0.0613506 | + | 2.52843i | ||||
\(531\) | 1.78279e21 | 0.0122404 | ||||||||
\(532\) | 2.84367e23i | 1.92146i | ||||||||
\(533\) | − | 1.60482e22i | − | 0.106720i | ||||||
\(534\) | 2.17490e23 | 1.42343 | ||||||||
\(535\) | −1.22550e23 | + | 2.97359e21i | −0.789417 | + | 0.0191546i | ||||
\(536\) | −4.05047e22 | −0.256806 | ||||||||
\(537\) | 1.18814e23i | 0.741460i | ||||||||
\(538\) | − | 6.03419e22i | − | 0.370655i | ||||||
\(539\) | 1.12029e23 | 0.677370 | ||||||||
\(540\) | −3.93053e23 | + | 9.53714e21i | −2.33940 | + | 0.0567638i | ||||
\(541\) | 4.66901e22 | 0.273557 | 0.136779 | − | 0.990602i | \(-0.456325\pi\) | ||||
0.136779 | + | 0.990602i | \(0.456325\pi\) | |||||||
\(542\) | 2.54480e22i | 0.146778i | ||||||||
\(543\) | − | 7.19427e22i | − | 0.408496i | ||||||
\(544\) | −8.50662e22 | −0.475517 | ||||||||
\(545\) | −5.66899e21 | − | 2.33635e23i | −0.0311986 | − | 1.28578i | ||||
\(546\) | −1.09883e23 | −0.595376 | ||||||||
\(547\) | 2.17735e22i | 0.116155i | 0.998312 | + | 0.0580773i | \(0.0184970\pi\) | ||||
−0.998312 | + | 0.0580773i | \(0.981503\pi\) | |||||||
\(548\) | 2.61702e23i | 1.37459i | ||||||||
\(549\) | −1.75469e21 | −0.00907476 | ||||||||
\(550\) | 8.31377e21 | + | 1.71216e23i | 0.0423365 | + | 0.871890i | ||||
\(551\) | 1.56595e23 | 0.785218 | ||||||||
\(552\) | − | 3.18198e23i | − | 1.57114i | ||||||
\(553\) | − | 1.93603e23i | − | 0.941345i | ||||||
\(554\) | 5.63392e23 | 2.69760 | ||||||||
\(555\) | 6.88497e21 | + | 2.83749e23i | 0.0324647 | + | 1.33796i | ||||
\(556\) | −5.20581e23 | −2.41742 | ||||||||
\(557\) | − | 3.95082e23i | − | 1.80683i | −0.428763 | − | 0.903417i | \(-0.641051\pi\) | ||
0.428763 | − | 0.903417i | \(-0.358949\pi\) | |||||||
\(558\) | 2.33495e21i | 0.0105169i | ||||||||
\(559\) | 4.91670e22 | 0.218109 | ||||||||
\(560\) | 7.45179e23 | − | 1.80812e22i | 3.25584 | − | 0.0790006i | ||||
\(561\) | 3.76269e22 | 0.161925 | ||||||||
\(562\) | 5.06257e23i | 2.14591i | ||||||||
\(563\) | 1.57683e23i | 0.658359i | 0.944267 | + | 0.329180i | \(0.106772\pi\) | ||||
−0.944267 | + | 0.329180i | \(0.893228\pi\) | |||||||
\(564\) | 1.18190e23 | 0.486082 | ||||||||
\(565\) | −8.69419e22 | + | 2.10958e21i | −0.352223 | + | 0.00854643i | ||||
\(566\) | −4.25975e23 | −1.69998 | ||||||||
\(567\) | − | 3.91522e23i | − | 1.53922i | ||||||
\(568\) | − | 6.63738e23i | − | 2.57061i | ||||||
\(569\) | −2.40022e23 | −0.915791 | −0.457896 | − | 0.889006i | \(-0.651397\pi\) | ||||
−0.457896 | + | 0.889006i | \(0.651397\pi\) | |||||||
\(570\) | −6.21957e21 | − | 2.56326e23i | −0.0233789 | − | 0.963511i | ||||
\(571\) | 1.03536e23 | 0.383428 | 0.191714 | − | 0.981451i | \(-0.438595\pi\) | ||||
0.191714 | + | 0.981451i | \(0.438595\pi\) | |||||||
\(572\) | − | 6.44245e22i | − | 0.235063i | ||||||
\(573\) | 3.03356e23i | 1.09053i | ||||||||
\(574\) | −4.05035e23 | −1.43463 | ||||||||
\(575\) | 9.04766e21 | + | 1.86330e23i | 0.0315762 | + | 0.650289i | ||||
\(576\) | −1.27348e21 | −0.00437925 | ||||||||
\(577\) | 5.37249e22i | 0.182046i | 0.995849 | + | 0.0910229i | \(0.0290137\pi\) | ||||
−0.995849 | + | 0.0910229i | \(0.970986\pi\) | |||||||
\(578\) | 4.83241e23i | 1.61353i | ||||||||
\(579\) | −1.38502e23 | −0.455711 | ||||||||
\(580\) | −2.57763e22 | − | 1.06231e24i | −0.0835762 | − | 3.44441i | ||||
\(581\) | −4.97457e23 | −1.58949 | ||||||||
\(582\) | 3.42584e23i | 1.07875i | ||||||||
\(583\) | − | 2.13706e23i | − | 0.663185i | ||||||
\(584\) | −1.43290e23 | −0.438234 | ||||||||
\(585\) | −6.72294e20 | + | 1.63127e19i | −0.00202644 | + | 4.91702e-5i | ||||
\(586\) | 6.99217e23 | 2.07722 | ||||||||
\(587\) | 7.97439e22i | 0.233493i | 0.993162 | + | 0.116746i | \(0.0372465\pi\) | ||||
−0.993162 | + | 0.116746i | \(0.962753\pi\) | |||||||
\(588\) | 1.13710e24i | 3.28163i | ||||||||
\(589\) | −1.11935e23 | −0.318408 | ||||||||
\(590\) | 8.28712e23 | − | 2.01081e22i | 2.32360 | − | 0.0563805i | ||||
\(591\) | −1.36679e23 | −0.377752 | ||||||||
\(592\) | 1.03433e24i | 2.81790i | ||||||||
\(593\) | − | 2.92994e22i | − | 0.0786854i | −0.999226 | − | 0.0393427i | \(-0.987474\pi\) | ||
0.999226 | − | 0.0393427i | \(-0.0125264\pi\) | |||||||
\(594\) | 3.31295e23 | 0.877061 | ||||||||
\(595\) | 4.91319e21 | + | 2.02486e23i | 0.0128224 | + | 0.528447i | ||||
\(596\) | 5.75068e23 | 1.47954 | ||||||||
\(597\) | − | 7.41634e23i | − | 1.88108i | ||||||
\(598\) | − | 1.00215e23i | − | 0.250595i | ||||||
\(599\) | −2.14554e23 | −0.528942 | −0.264471 | − | 0.964394i | \(-0.585197\pi\) | ||||
−0.264471 | + | 0.964394i | \(0.585197\pi\) | |||||||
\(600\) | −9.91680e23 | + | 4.81532e22i | −2.41038 | + | 0.117041i | ||||
\(601\) | 3.54004e23 | 0.848351 | 0.424175 | − | 0.905580i | \(-0.360564\pi\) | ||||
0.424175 | + | 0.905580i | \(0.360564\pi\) | |||||||
\(602\) | − | 1.24091e24i | − | 2.93204i | ||||||
\(603\) | − | 4.36792e20i | − | 0.00101760i | ||||||
\(604\) | 9.82480e23 | 2.25689 | ||||||||
\(605\) | 8.25803e21 | + | 3.40337e23i | 0.0187049 | + | 0.770882i | ||||
\(606\) | −1.14590e24 | −2.55934 | ||||||||
\(607\) | 2.65810e23i | 0.585419i | 0.956201 | + | 0.292710i | \(0.0945569\pi\) | ||||
−0.956201 | + | 0.292710i | \(0.905443\pi\) | |||||||
\(608\) | − | 3.41722e23i | − | 0.742151i | ||||||
\(609\) | 1.06844e24 | 2.28826 | ||||||||
\(610\) | −8.15650e23 | + | 1.97912e22i | −1.72266 | + | 0.0417992i | ||||
\(611\) | 2.12411e22 | 0.0442412 | ||||||||
\(612\) | − | 3.70531e21i | − | 0.00761093i | ||||||
\(613\) | 6.38443e23i | 1.29333i | 0.762776 | + | 0.646663i | \(0.223836\pi\) | ||||
−0.762776 | + | 0.646663i | \(0.776164\pi\) | |||||||
\(614\) | −1.45670e24 | −2.91032 | ||||||||
\(615\) | 2.55425e23 | − | 6.19770e21i | 0.503297 | − | 0.0122122i | ||||
\(616\) | −9.27849e23 | −1.80319 | ||||||||
\(617\) | 8.39922e23i | 1.60996i | 0.593301 | + | 0.804980i | \(0.297824\pi\) | ||||
−0.593301 | + | 0.804980i | \(0.702176\pi\) | |||||||
\(618\) | − | 1.01245e24i | − | 1.91412i | ||||||
\(619\) | −1.78611e23 | −0.333072 | −0.166536 | − | 0.986035i | \(-0.553258\pi\) | ||||
−0.166536 | + | 0.986035i | \(0.553258\pi\) | |||||||
\(620\) | 1.84250e22 | + | 7.59345e23i | 0.0338904 | + | 1.39672i | ||||
\(621\) | 3.60539e23 | 0.654145 | ||||||||
\(622\) | − | 1.10731e24i | − | 1.98175i | ||||||
\(623\) | − | 6.90172e23i | − | 1.21845i | ||||||
\(624\) | 2.52595e23 | 0.439902 | ||||||||
\(625\) | 5.79338e23 | − | 5.63950e22i | 0.995295 | − | 0.0968859i | ||||
\(626\) | 1.26706e24 | 2.14741 | ||||||||
\(627\) | 1.51152e23i | 0.252720i | ||||||||
\(628\) | − | 1.74153e24i | − | 2.87260i | ||||||
\(629\) | −2.81057e23 | −0.457367 | ||||||||
\(630\) | 4.11711e20 | + | 1.69678e22i | 0.000660995 | + | 0.0272415i | ||||
\(631\) | 4.46452e23 | 0.707173 | 0.353586 | − | 0.935402i | \(-0.384962\pi\) | ||||
0.353586 | + | 0.935402i | \(0.384962\pi\) | |||||||
\(632\) | 9.39733e23i | 1.46862i | ||||||||
\(633\) | − | 3.28157e23i | − | 0.506000i | ||||||
\(634\) | 1.94272e23 | 0.295564 | ||||||||
\(635\) | −1.16250e24 | + | 2.82072e22i | −1.74508 | + | 0.0423431i | ||||
\(636\) | 2.16912e24 | 3.21291 | ||||||||
\(637\) | 2.04358e23i | 0.298681i | ||||||||
\(638\) | 8.95399e23i | 1.29134i | ||||||||
\(639\) | 7.15757e21 | 0.0101861 | ||||||||
\(640\) | 4.03379e23 | − | 9.78770e21i | 0.566479 | − | 0.0137452i | ||||
\(641\) | −5.46949e23 | −0.757973 | −0.378987 | − | 0.925402i | \(-0.623727\pi\) | ||||
−0.378987 | + | 0.925402i | \(0.623727\pi\) | |||||||
\(642\) | 1.04844e24i | 1.43383i | ||||||||
\(643\) | 7.19921e23i | 0.971609i | 0.874067 | + | 0.485805i | \(0.161473\pi\) | ||||
−0.874067 | + | 0.485805i | \(0.838527\pi\) | |||||||
\(644\) | −1.76952e24 | −2.35682 | ||||||||
\(645\) | 1.89879e22 | + | 7.82547e23i | 0.0249586 | + | 1.02862i | ||||
\(646\) | 2.53895e23 | 0.329365 | ||||||||
\(647\) | − | 1.25975e24i | − | 1.61287i | −0.591324 | − | 0.806434i | \(-0.701395\pi\) | ||
0.591324 | − | 0.806434i | \(-0.298605\pi\) | |||||||
\(648\) | 1.90041e24i | 2.40138i | ||||||||
\(649\) | −4.88680e23 | −0.609459 | ||||||||
\(650\) | −3.12325e23 | + | 1.51656e22i | −0.384453 | + | 0.0186679i | ||||
\(651\) | −7.63726e23 | −0.927895 | ||||||||
\(652\) | − | 8.44985e23i | − | 1.01332i | ||||||
\(653\) | − | 5.58543e23i | − | 0.661142i | −0.943781 | − | 0.330571i | \(-0.892759\pi\) | ||
0.943781 | − | 0.330571i | \(-0.107241\pi\) | |||||||
\(654\) | −1.99880e24 | −2.33538 | ||||||||
\(655\) | −3.49985e22 | − | 1.44239e24i | −0.0403644 | − | 1.66353i | ||||
\(656\) | 9.31084e23 | 1.06000 | ||||||||
\(657\) | − | 1.54520e21i | − | 0.00173652i | ||||||
\(658\) | − | 5.36097e23i | − | 0.594735i | ||||||
\(659\) | 1.40175e24 | 1.53513 | 0.767563 | − | 0.640973i | \(-0.221469\pi\) | ||||
0.767563 | + | 0.640973i | \(0.221469\pi\) | |||||||
\(660\) | 1.02539e24 | − | 2.48803e22i | 1.10857 | − | 0.0268988i | ||||
\(661\) | −1.56535e24 | −1.67070 | −0.835349 | − | 0.549720i | \(-0.814734\pi\) | ||||
−0.835349 | + | 0.549720i | \(0.814734\pi\) | |||||||
\(662\) | 2.32288e24i | 2.44757i | ||||||||
\(663\) | 6.86373e22i | 0.0713995i | ||||||||
\(664\) | 2.41461e24 | 2.47981 | ||||||||
\(665\) | −8.13414e23 | + | 1.97369e22i | −0.824760 | + | 0.0200122i | ||||
\(666\) | −2.35518e22 | −0.0235773 | ||||||||
\(667\) | 9.74440e23i | 0.963131i | ||||||||
\(668\) | − | 9.05428e23i | − | 0.883596i | ||||||
\(669\) | 1.13548e24 | 1.09410 | ||||||||
\(670\) | −4.92658e21 | − | 2.03038e23i | −0.00468716 | − | 0.193171i | ||||
\(671\) | 4.80977e23 | 0.451838 | ||||||||
\(672\) | − | 2.33156e24i | − | 2.16275i | ||||||
\(673\) | 1.06512e24i | 0.975593i | 0.872957 | + | 0.487797i | \(0.162199\pi\) | ||||
−0.872957 | + | 0.487797i | \(0.837801\pi\) | |||||||
\(674\) | 7.01909e23 | 0.634851 | ||||||||
\(675\) | −5.45608e22 | − | 1.12364e24i | −0.0487302 | − | 1.00356i | ||||
\(676\) | −2.52320e24 | −2.22538 | ||||||||
\(677\) | 1.35343e23i | 0.117878i | 0.998262 | + | 0.0589389i | \(0.0187717\pi\) | ||||
−0.998262 | + | 0.0589389i | \(0.981228\pi\) | |||||||
\(678\) | 7.43806e23i | 0.639746i | ||||||||
\(679\) | 1.08714e24 | 0.923407 | ||||||||
\(680\) | −2.38482e22 | − | 9.82852e23i | −0.0200046 | − | 0.824446i | ||||
\(681\) | −8.20365e23 | −0.679605 | ||||||||
\(682\) | − | 6.40033e23i | − | 0.523643i | ||||||
\(683\) | − | 6.70521e23i | − | 0.541797i | −0.962608 | − | 0.270898i | \(-0.912679\pi\) | ||
0.962608 | − | 0.270898i | \(-0.0873207\pi\) | |||||||
\(684\) | 1.48847e22 | 0.0118786 | ||||||||
\(685\) | −7.48583e23 | + | 1.81638e22i | −0.590024 | + | 0.0143165i | ||||
\(686\) | 1.51483e24 | 1.17926 | ||||||||
\(687\) | − | 1.19221e24i | − | 0.916687i | ||||||
\(688\) | 2.85257e24i | 2.16638i | ||||||||
\(689\) | 3.89834e23 | 0.292426 | ||||||||
\(690\) | 1.59503e24 | − | 3.87023e22i | 1.18182 | − | 0.0286761i | ||||
\(691\) | 1.91000e24 | 1.39788 | 0.698941 | − | 0.715179i | \(-0.253655\pi\) | ||||
0.698941 | + | 0.715179i | \(0.253655\pi\) | |||||||
\(692\) | − | 3.74502e24i | − | 2.70740i | ||||||
\(693\) | − | 1.00057e22i | − | 0.00714519i | ||||||
\(694\) | −4.13649e24 | −2.91794 | ||||||||
\(695\) | −3.61317e22 | − | 1.48909e24i | −0.0251778 | − | 1.03765i | ||||
\(696\) | −5.18613e24 | −3.56998 | ||||||||
\(697\) | 2.53002e23i | 0.172046i | ||||||||
\(698\) | 3.25625e24i | 2.18750i | ||||||||
\(699\) | −1.35564e24 | −0.899684 | ||||||||
\(700\) | 2.67783e23 | + | 5.51481e24i | 0.175570 | + | 3.61574i | ||||
\(701\) | 2.38901e24 | 1.54745 | 0.773723 | − | 0.633524i | \(-0.218392\pi\) | ||||
0.773723 | + | 0.633524i | \(0.218392\pi\) | |||||||
\(702\) | 6.04333e23i | 0.386733i | ||||||||
\(703\) | − | 1.12904e24i | − | 0.713823i | ||||||
\(704\) | 3.49072e23 | 0.218046 | ||||||||
\(705\) | 8.20317e21 | + | 3.38076e23i | 0.00506261 | + | 0.208644i | ||||
\(706\) | 1.09198e24 | 0.665845 | ||||||||
\(707\) | 3.63634e24i | 2.19078i | ||||||||
\(708\) | − | 4.96011e24i | − | 2.95263i | ||||||
\(709\) | 1.18830e24 | 0.698926 | 0.349463 | − | 0.936950i | \(-0.386364\pi\) | ||||
0.349463 | + | 0.936950i | \(0.386364\pi\) | |||||||
\(710\) | 3.32713e24 | − | 8.07304e22i | 1.93363 | − | 0.0469182i | ||||
\(711\) | −1.01338e22 | −0.00581945 | ||||||||
\(712\) | 3.35003e24i | 1.90094i | ||||||||
\(713\) | − | 6.96532e23i | − | 0.390553i | ||||||
\(714\) | 1.73231e24 | 0.959824 | ||||||||
\(715\) | 1.84282e23 | − | 4.47148e21i | 0.100898 | − | 0.00244822i | ||||
\(716\) | −3.20716e24 | −1.73524 | ||||||||
\(717\) | 9.35797e23i | 0.500344i | ||||||||
\(718\) | − | 3.72808e24i | − | 1.96983i | ||||||
\(719\) | −7.00134e23 | −0.365583 | −0.182791 | − | 0.983152i | \(-0.558513\pi\) | ||||
−0.182791 | + | 0.983152i | \(0.558513\pi\) | |||||||
\(720\) | −9.46432e20 | − | 3.90051e22i | −0.000488386 | − | 0.0201278i | ||||
\(721\) | −3.21285e24 | −1.63848 | ||||||||
\(722\) | − | 2.60021e24i | − | 1.31052i | ||||||
\(723\) | 1.01779e24i | 0.506971i | ||||||||
\(724\) | 1.94195e24 | 0.956004 | ||||||||
\(725\) | 3.03689e24 | − | 1.47463e23i | 1.47760 | − | 0.0717480i | ||||
\(726\) | 2.91165e24 | 1.40016 | ||||||||
\(727\) | 6.64217e23i | 0.315695i | 0.987464 | + | 0.157847i | \(0.0504554\pi\) | ||||
−0.987464 | + | 0.157847i | \(0.949545\pi\) | |||||||
\(728\) | − | 1.69254e24i | − | 0.795102i | ||||||
\(729\) | −2.17399e24 | −1.00942 | ||||||||
\(730\) | −1.74283e22 | − | 7.18270e23i | −0.00799855 | − | 0.329643i | ||||
\(731\) | −7.75124e23 | −0.351620 | ||||||||
\(732\) | 4.88193e24i | 2.18901i | ||||||||
\(733\) | 1.04024e24i | 0.461054i | 0.973066 | + | 0.230527i | \(0.0740450\pi\) | ||||
−0.973066 | + | 0.230527i | \(0.925955\pi\) | |||||||
\(734\) | 5.23181e23 | 0.229211 | ||||||||
\(735\) | −3.25259e24 | + | 7.89218e22i | −1.40860 | + | 0.0341786i | ||||
\(736\) | 2.12642e24 | 0.910307 | ||||||||
\(737\) | 1.19729e23i | 0.0506670i | ||||||||
\(738\) | 2.12008e22i | 0.00886899i | ||||||||
\(739\) | −7.14037e23 | −0.295286 | −0.147643 | − | 0.989041i | \(-0.547169\pi\) | ||||
−0.147643 | + | 0.989041i | \(0.547169\pi\) | |||||||
\(740\) | −7.65924e24 | + | 1.85846e23i | −3.13124 | + | 0.0759772i | ||||
\(741\) | −2.75725e23 | −0.111435 | ||||||||
\(742\) | − | 9.83889e24i | − | 3.93109i | ||||||
\(743\) | − | 3.15273e24i | − | 1.24532i | −0.782492 | − | 0.622661i | \(-0.786052\pi\) | ||
0.782492 | − | 0.622661i | \(-0.213948\pi\) | |||||||
\(744\) | 3.70706e24 | 1.44764 | ||||||||
\(745\) | 3.99134e22 | + | 1.64494e24i | 0.0154096 | + | 0.635072i | ||||
\(746\) | −3.70134e24 | −1.41280 | ||||||||
\(747\) | 2.60385e22i | 0.00982632i | ||||||||
\(748\) | 1.01566e24i | 0.378953i | ||||||||
\(749\) | 3.32708e24 | 1.22735 | ||||||||
\(750\) | −3.61995e23 | − | 4.96514e24i | −0.132033 | − | 1.81097i | ||||
\(751\) | −9.62214e21 | −0.00347002 | −0.00173501 | − | 0.999998i | \(-0.500552\pi\) | ||||
−0.00173501 | + | 0.999998i | \(0.500552\pi\) | |||||||
\(752\) | 1.23237e24i | 0.439429i | ||||||||
\(753\) | − | 5.71381e23i | − | 0.201451i | ||||||
\(754\) | −1.63335e24 | −0.569407 | ||||||||
\(755\) | 6.81904e22 | + | 2.81032e24i | 0.0235058 | + | 0.968739i | ||||
\(756\) | 1.06709e25 | 3.63718 | ||||||||
\(757\) | − | 2.06888e24i | − | 0.697302i | −0.937253 | − | 0.348651i | \(-0.886640\pi\) | ||
0.937253 | − | 0.348651i | \(-0.113360\pi\) | |||||||
\(758\) | 7.40132e24i | 2.46672i | ||||||||
\(759\) | −9.40568e23 | −0.309981 | ||||||||
\(760\) | 3.94824e24 | − | 9.58013e22i | 1.28673 | − | 0.0312216i | ||||
\(761\) | −1.54775e24 | −0.498807 | −0.249404 | − | 0.968400i | \(-0.580235\pi\) | ||||
−0.249404 | + | 0.968400i | \(0.580235\pi\) | |||||||
\(762\) | 9.94541e24i | 3.16961i | ||||||||
\(763\) | 6.34289e24i | 1.99907i | ||||||||
\(764\) | −8.18849e24 | −2.55218 | ||||||||
\(765\) | 1.05988e22 | − | 2.57172e20i | 0.00326689 | − | 7.92688e-5i | ||||
\(766\) | 4.67284e24 | 1.42442 | ||||||||
\(767\) | − | 8.91429e23i | − | 0.268736i | ||||||
\(768\) | − | 4.97227e24i | − | 1.48246i | ||||||
\(769\) | 1.41912e24 | 0.418451 | 0.209226 | − | 0.977867i | \(-0.432906\pi\) | ||||
0.209226 | + | 0.977867i | \(0.432906\pi\) | |||||||
\(770\) | −1.12854e23 | − | 4.65104e24i | −0.0329114 | − | 1.35637i | ||||
\(771\) | 5.73123e24 | 1.65305 | ||||||||
\(772\) | − | 3.73859e24i | − | 1.06650i | ||||||
\(773\) | 7.68448e23i | 0.216815i | 0.994107 | + | 0.108407i | \(0.0345751\pi\) | ||||
−0.994107 | + | 0.108407i | \(0.965425\pi\) | |||||||
\(774\) | −6.49532e22 | −0.0181260 | ||||||||
\(775\) | −2.17078e24 | + | 1.05407e23i | −0.599171 | + | 0.0290941i | ||||
\(776\) | −5.27689e24 | −1.44063 | ||||||||
\(777\) | − | 7.70343e24i | − | 2.08020i | ||||||
\(778\) | 1.22403e25i | 3.26939i | ||||||||
\(779\) | −1.01634e24 | −0.268517 | ||||||||
\(780\) | 4.53856e22 | + | 1.87047e24i | 0.0118608 | + | 0.488817i | ||||
\(781\) | −1.96196e24 | −0.507173 | ||||||||
\(782\) | 1.57990e24i | 0.403992i | ||||||||
\(783\) | − | 5.87624e24i | − | 1.48636i | ||||||
\(784\) | −1.18565e25 | −2.96667 | ||||||||
\(785\) | 4.98154e24 | − | 1.20873e23i | 1.23302 | − | 0.0299184i | ||||
\(786\) | −1.23399e25 | −3.02149 | ||||||||
\(787\) | 1.67424e24i | 0.405539i | 0.979226 | + | 0.202769i | \(0.0649942\pi\) | ||||
−0.979226 | + | 0.202769i | \(0.935006\pi\) | |||||||
\(788\) | − | 3.68936e24i | − | 0.884053i | ||||||
\(789\) | −5.76242e23 | −0.136600 | ||||||||
\(790\) | −4.71061e24 | + | 1.14300e23i | −1.10471 | + | 0.0268049i | ||||
\(791\) | 2.36036e24 | 0.547619 | ||||||||
\(792\) | 4.85667e22i | 0.0111474i | ||||||||
\(793\) | 8.77378e23i | 0.199235i | ||||||||
\(794\) | 1.53339e25 | 3.44491 | ||||||||
\(795\) | 1.50551e23 | + | 6.20464e24i | 0.0334629 | + | 1.37910i | ||||
\(796\) | 2.00189e25 | 4.40230 | ||||||||
\(797\) | − | 4.21412e24i | − | 0.916877i | −0.888726 | − | 0.458439i | \(-0.848409\pi\) | ||
0.888726 | − | 0.458439i | \(-0.151591\pi\) | |||||||
\(798\) | 6.95893e24i | 1.49802i | ||||||||
\(799\) | −3.34869e23 | −0.0713226 | ||||||||
\(800\) | −3.21793e23 | − | 6.62710e24i | −0.0678129 | − | 1.39656i | ||||
\(801\) | −3.61258e22 | −0.00753254 | ||||||||
\(802\) | − | 9.86845e24i | − | 2.03595i | ||||||
\(803\) | 4.23554e23i | 0.0864623i | ||||||||
\(804\) | −1.21525e24 | −0.245465 | ||||||||
\(805\) | −1.22816e23 | − | 5.06160e24i | −0.0245466 | − | 1.01163i | ||||
\(806\) | 1.16752e24 | 0.230896 | ||||||||
\(807\) | − | 1.03309e24i | − | 0.202169i | ||||||
\(808\) | − | 1.76505e25i | − | 3.41791i | ||||||
\(809\) | −6.29496e23 | −0.120623 | −0.0603116 | − | 0.998180i | \(-0.519209\pi\) | ||||
−0.0603116 | + | 0.998180i | \(0.519209\pi\) | |||||||
\(810\) | −9.52621e24 | + | 2.31147e23i | −1.80633 | + | 0.0438293i | ||||
\(811\) | −1.97375e24 | −0.370352 | −0.185176 | − | 0.982705i | \(-0.559286\pi\) | ||||
−0.185176 | + | 0.982705i | \(0.559286\pi\) | |||||||
\(812\) | 2.88405e25i | 5.35521i | ||||||||
\(813\) | 4.35687e23i | 0.0800581i | ||||||||
\(814\) | 6.45578e24 | 1.17393 | ||||||||
\(815\) | 2.41703e24 | − | 5.86474e22i | 0.434952 | − | 0.0105538i | ||||
\(816\) | −3.98220e24 | −0.709180 | ||||||||
\(817\) | − | 3.11377e24i | − | 0.548782i | ||||||
\(818\) | − | 1.41382e25i | − | 2.46598i | ||||||
\(819\) | 1.82519e22 | 0.00315061 | ||||||||
\(820\) | 1.67295e23 | + | 6.89468e24i | 0.0285801 | + | 1.17787i | ||||
\(821\) | −9.78759e24 | −1.65485 | −0.827426 | − | 0.561575i | \(-0.810196\pi\) | ||||
−0.827426 | + | 0.561575i | \(0.810196\pi\) | |||||||
\(822\) | 6.40428e24i | 1.07167i | ||||||||
\(823\) | 2.29900e23i | 0.0380750i | 0.999819 | + | 0.0190375i | \(0.00606019\pi\) | ||||
−0.999819 | + | 0.0190375i | \(0.993940\pi\) | |||||||
\(824\) | 1.55949e25 | 2.55624 | ||||||||
\(825\) | 1.42337e23 | + | 2.93133e24i | 0.0230919 | + | 0.475561i | ||||
\(826\) | −2.24985e25 | −3.61262 | ||||||||
\(827\) | 4.00653e24i | 0.636754i | 0.947964 | + | 0.318377i | \(0.103138\pi\) | ||||
−0.947964 | + | 0.318377i | \(0.896862\pi\) | |||||||
\(828\) | 9.26226e22i | 0.0145700i | ||||||||
\(829\) | −7.23311e24 | −1.12619 | −0.563095 | − | 0.826392i | \(-0.690389\pi\) | ||||
−0.563095 | + | 0.826392i | \(0.690389\pi\) | |||||||
\(830\) | 2.93689e23 | + | 1.21037e25i | 0.0452609 | + | 1.86533i | ||||
\(831\) | 9.64564e24 | 1.47137 | ||||||||
\(832\) | 6.36763e23i | 0.0961456i | ||||||||
\(833\) | − | 3.22174e24i | − | 0.481513i | ||||||
\(834\) | −1.27395e25 | −1.88469 | ||||||||
\(835\) | 2.58992e24 | − | 6.28425e22i | 0.379272 | − | 0.00920277i | ||||
\(836\) | −4.08004e24 | −0.591441 | ||||||||
\(837\) | 4.20035e24i | 0.602724i | ||||||||
\(838\) | − | 3.26832e23i | − | 0.0464249i | ||||||
\(839\) | −8.73556e24 | −1.22833 | −0.614163 | − | 0.789179i | \(-0.710506\pi\) | ||||
−0.614163 | + | 0.789179i | \(0.710506\pi\) | |||||||
\(840\) | 2.69387e25 | − | 6.53648e23i | 3.74975 | − | 0.0909851i | ||||
\(841\) | 8.62473e24 | 1.18845 | ||||||||
\(842\) | − | 1.62136e25i | − | 2.21170i | ||||||
\(843\) | 8.66745e24i | 1.17046i | ||||||||
\(844\) | 8.85794e24 | 1.18419 | ||||||||
\(845\) | −1.75126e23 | − | 7.21744e24i | −0.0231776 | − | 0.955216i | ||||
\(846\) | −2.80611e22 | −0.00367668 | ||||||||
\(847\) | − | 9.23971e24i | − | 1.19853i | ||||||
\(848\) | 2.26174e25i | 2.90454i | ||||||||
\(849\) | −7.29297e24 | −0.927234 | ||||||||
\(850\) | 4.92385e24 | − | 2.39088e23i | 0.619789 | − | 0.0300952i | ||||
\(851\) | 7.02566e24 | 0.875560 | ||||||||
\(852\) | − | 1.99140e25i | − | 2.45709i | ||||||
\(853\) | − | 2.48651e24i | − | 0.303755i | −0.988399 | − | 0.151878i | \(-0.951468\pi\) | ||
0.988399 | − | 0.151878i | \(-0.0485320\pi\) | |||||||
\(854\) | 2.21438e25 | 2.67831 | ||||||||
\(855\) | 1.03309e21 | + | 4.25768e22i | 0.000123717 | + | 0.00509871i | ||||
\(856\) | −1.61493e25 | −1.91482 | ||||||||
\(857\) | 7.73588e24i | 0.908181i | 0.890955 | + | 0.454091i | \(0.150036\pi\) | ||||
−0.890955 | + | 0.454091i | \(0.849964\pi\) | |||||||
\(858\) | − | 1.57657e24i | − | 0.183262i | ||||||
\(859\) | −9.34602e24 | −1.07568 | −0.537842 | − | 0.843045i | \(-0.680760\pi\) | ||||
−0.537842 | + | 0.843045i | \(0.680760\pi\) | |||||||
\(860\) | −2.11233e25 | + | 5.12542e23i | −2.40727 | + | 0.0584107i | ||||
\(861\) | −6.93446e24 | −0.782502 | ||||||||
\(862\) | 1.45996e25i | 1.63128i | ||||||||
\(863\) | 9.26216e24i | 1.02476i | 0.858760 | + | 0.512378i | \(0.171235\pi\) | ||||
−0.858760 | + | 0.512378i | \(0.828765\pi\) | |||||||
\(864\) | −1.28231e25 | −1.40484 | ||||||||
\(865\) | 1.07124e25 | − | 2.59928e23i | 1.16211 | − | 0.0281979i | ||||
\(866\) | 1.63657e25 | 1.75806 | ||||||||
\(867\) | 8.27340e24i | 0.880079i | ||||||||
\(868\) | − | 2.06152e25i | − | 2.17156i | ||||||
\(869\) | 2.77778e24 | 0.289754 | ||||||||
\(870\) | −6.30788e23 | − | 2.59966e25i | −0.0651583 | − | 2.68536i | ||||
\(871\) | −2.18404e23 | −0.0223412 | ||||||||
\(872\) | − | 3.07879e25i | − | 3.11881i | ||||||
\(873\) | − | 5.69046e22i | − | 0.00570855i | ||||||
\(874\) | −6.34667e24 | −0.630520 | ||||||||
\(875\) | −1.57562e25 | + | 1.14874e24i | −1.55018 | + | 0.113020i | ||||
\(876\) | −4.29908e24 | −0.418881 | ||||||||
\(877\) | 1.25978e25i | 1.21562i | 0.794082 | + | 0.607810i | \(0.207952\pi\) | ||||
−0.794082 | + | 0.607810i | \(0.792048\pi\) | |||||||
\(878\) | − | 5.10065e24i | − | 0.487441i | ||||||
\(879\) | 1.19710e25 | 1.13299 | ||||||||
\(880\) | 2.59426e23 | + | 1.06917e25i | 0.0243171 | + | 1.00217i | ||||
\(881\) | −6.10480e24 | −0.566730 | −0.283365 | − | 0.959012i | \(-0.591451\pi\) | ||||
−0.283365 | + | 0.959012i | \(0.591451\pi\) | |||||||
\(882\) | − | 2.69973e23i | − | 0.0248220i | ||||||
\(883\) | 7.68576e24i | 0.699876i | 0.936773 | + | 0.349938i | \(0.113797\pi\) | ||||
−0.936773 | + | 0.349938i | \(0.886203\pi\) | |||||||
\(884\) | −1.85273e24 | −0.167096 | ||||||||
\(885\) | 1.41881e25 | − | 3.44264e23i | 1.26738 | − | 0.0307520i | ||||
\(886\) | −2.29456e24 | −0.203008 | ||||||||
\(887\) | − | 1.57170e25i | − | 1.37727i | −0.725110 | − | 0.688633i | \(-0.758211\pi\) | ||
0.725110 | − | 0.688633i | \(-0.241789\pi\) | |||||||
\(888\) | 3.73918e25i | 3.24538i | ||||||||
\(889\) | 3.15603e25 | 2.71317 | ||||||||
\(890\) | −1.67927e25 | + | 4.07464e23i | −1.42990 | + | 0.0346956i | ||||
\(891\) | 5.61747e24 | 0.473784 | ||||||||
\(892\) | 3.06501e25i | 2.56053i | ||||||||
\(893\) | − | 1.34521e24i | − | 0.111315i | ||||||
\(894\) | 1.40728e25 | 1.15349 | ||||||||
\(895\) | −2.22597e23 | − | 9.17386e24i | −0.0180727 | − | 0.744829i | ||||
\(896\) | −1.09512e25 | −0.880734 | ||||||||
\(897\) | − | 1.71574e24i | − | 0.136684i | ||||||
\(898\) | 2.21701e25i | 1.74952i | ||||||||
\(899\) | −1.13524e25 | −0.887422 | ||||||||
\(900\) | 2.88663e23 | − | 1.40167e22i | 0.0223527 | − | 0.00108538i | ||||
\(901\) | −6.14579e24 | −0.471429 | ||||||||
\(902\) | − | 5.81136e24i | − | 0.441593i | ||||||
\(903\) | − | 2.12452e25i | − | 1.59924i | ||||||
\(904\) | −1.14570e25 | −0.854356 | ||||||||
\(905\) | 1.34784e23 | + | 5.55482e24i | 0.00995690 | + | 0.410352i | ||||
\(906\) | 2.40429e25 | 1.75953 | ||||||||
\(907\) | 2.48686e24i | 0.180297i | 0.995928 | + | 0.0901486i | \(0.0287342\pi\) | ||||
−0.995928 | + | 0.0901486i | \(0.971266\pi\) | |||||||
\(908\) | − | 2.21441e25i | − | 1.59048i | ||||||
\(909\) | 1.90338e23 | 0.0135435 | ||||||||
\(910\) | 8.48422e24 | − | 2.05864e23i | 0.598081 | − | 0.0145120i | ||||
\(911\) | 1.32000e25 | 0.921867 | 0.460933 | − | 0.887435i | \(-0.347515\pi\) | ||||
0.460933 | + | 0.887435i | \(0.347515\pi\) | |||||||
\(912\) | − | 1.59970e25i | − | 1.10683i | ||||||
\(913\) | − | 7.13741e24i | − | 0.489259i | ||||||
\(914\) | −2.29743e25 | −1.56027 | ||||||||
\(915\) | −1.39645e25 | + | 3.38837e23i | −0.939603 | + | 0.0227988i | ||||
\(916\) | 3.21814e25 | 2.14532 | ||||||||
\(917\) | 3.91590e25i | 2.58638i | ||||||||
\(918\) | − | 9.52740e24i | − | 0.623464i | ||||||
\(919\) | −2.58452e25 | −1.67571 | −0.837853 | − | 0.545896i | \(-0.816189\pi\) | ||||
−0.837853 | + | 0.545896i | \(0.816189\pi\) | |||||||
\(920\) | 5.96139e23 | + | 2.45686e25i | 0.0382958 | + | 1.57828i | ||||
\(921\) | −2.49397e25 | −1.58739 | ||||||||
\(922\) | 2.81092e25i | 1.77270i | ||||||||
\(923\) | − | 3.57892e24i | − | 0.223634i | ||||||
\(924\) | −2.78380e25 | −1.72356 | ||||||||
\(925\) | −1.06320e24 | − | 2.18959e25i | −0.0652244 | − | 1.34325i | ||||
\(926\) | 2.66121e25 | 1.61765 | ||||||||
\(927\) | 1.68171e23i | 0.0101292i | ||||||||
\(928\) | − | 3.46574e25i | − | 2.06842i | ||||||
\(929\) | −1.29245e25 | −0.764331 | −0.382165 | − | 0.924094i | \(-0.624822\pi\) | ||||
−0.382165 | + | 0.924094i | \(0.624822\pi\) | |||||||
\(930\) | 4.50889e23 | + | 1.85824e25i | 0.0264219 | + | 1.08892i | ||||
\(931\) | 1.29421e25 | 0.751508 | ||||||||
\(932\) | − | 3.65929e25i | − | 2.10553i | ||||||
\(933\) | − | 1.89578e25i | − | 1.08092i | ||||||
\(934\) | 8.72265e23 | 0.0492833 | ||||||||
\(935\) | −2.90524e24 | + | 7.04935e22i | −0.162661 | + | 0.00394685i | ||||
\(936\) | −8.85932e22 | −0.00491537 | ||||||||
\(937\) | − | 3.51601e24i | − | 0.193314i | −0.995318 | − | 0.0966570i | \(-0.969185\pi\) | ||
0.995318 | − | 0.0966570i | \(-0.0308150\pi\) | |||||||
\(938\) | 5.51223e24i | 0.300333i | ||||||||
\(939\) | 2.16929e25 | 1.17128 | ||||||||
\(940\) | −9.12568e24 | + | 2.21428e23i | −0.488291 | + | 0.0118480i | ||||
\(941\) | −6.77453e24 | −0.359225 | −0.179613 | − | 0.983737i | \(-0.557484\pi\) | ||||
−0.179613 | + | 0.983737i | \(0.557484\pi\) | |||||||
\(942\) | − | 4.26181e25i | − | 2.23955i | ||||||
\(943\) | − | 6.32435e24i | − | 0.329357i | ||||||
\(944\) | 5.17189e25 | 2.66924 | ||||||||
\(945\) | 7.40628e23 | + | 3.05234e25i | 0.0378817 | + | 1.56121i | ||||
\(946\) | 1.78043e25 | 0.902507 | ||||||||
\(947\) | − | 1.57938e25i | − | 0.793438i | −0.917940 | − | 0.396719i | \(-0.870149\pi\) | ||
0.917940 | − | 0.396719i | \(-0.129851\pi\) | |||||||
\(948\) | 2.81945e25i | 1.40376i | ||||||||
\(949\) | −7.72629e23 | −0.0381249 | ||||||||
\(950\) | 9.60448e23 | + | 1.97797e25i | 0.0469703 | + | 0.967319i | ||||
\(951\) | 3.32606e24 | 0.161212 | ||||||||
\(952\) | 2.66832e25i | 1.28181i | ||||||||
\(953\) | − | 1.60725e25i | − | 0.765232i | −0.923908 | − | 0.382616i | \(-0.875023\pi\) | ||
0.923908 | − | 0.382616i | \(-0.124977\pi\) | |||||||
\(954\) | −5.15000e23 | −0.0243022 | ||||||||
\(955\) | −5.68334e23 | − | 2.34227e25i | −0.0265812 | − | 1.09549i | ||||
\(956\) | −2.52600e25 | −1.17096 | ||||||||
\(957\) | 1.53298e25i | 0.704345i | ||||||||
\(958\) | 3.29485e25i | 1.50048i | ||||||||
\(959\) | 2.03231e25 | 0.917342 | ||||||||
\(960\) | −1.01348e25 | + | 2.45913e23i | −0.453429 | + | 0.0110021i | ||||
\(961\) | −1.44354e25 | −0.640147 | ||||||||
\(962\) | 1.17764e25i | 0.517634i | ||||||||
\(963\) | − | 1.74150e23i | − | 0.00758753i | ||||||
\(964\) | −2.74732e25 | −1.18647 | ||||||||
\(965\) | 1.06940e25 | − | 2.59482e23i | 0.457782 | − | 0.0111077i | ||||
\(966\) | −4.33031e25 | −1.83744 | ||||||||
\(967\) | − | 1.43849e25i | − | 0.605037i | −0.953143 | − | 0.302519i | \(-0.902173\pi\) | ||
0.953143 | − | 0.302519i | \(-0.0978275\pi\) | |||||||
\(968\) | 4.48487e25i | 1.86986i | ||||||||
\(969\) | 4.34684e24 | 0.179648 | ||||||||
\(970\) | −6.41827e23 | − | 2.64515e25i | −0.0262941 | − | 1.08365i | ||||
\(971\) | 3.71146e23 | 0.0150724 | 0.00753618 | − | 0.999972i | \(-0.497601\pi\) | ||||
0.00753618 | + | 0.999972i | \(0.497601\pi\) | |||||||
\(972\) | − | 1.11178e24i | − | 0.0447565i | ||||||
\(973\) | 4.04268e25i | 1.61328i | ||||||||
\(974\) | 1.04695e25 | 0.414168 | ||||||||
\(975\) | −5.34721e24 | + | 2.59645e23i | −0.209695 | + | 0.0101822i | ||||
\(976\) | −5.09037e25 | −1.97891 | ||||||||
\(977\) | 5.02948e24i | 0.193829i | 0.995293 | + | 0.0969146i | \(0.0308974\pi\) | ||||
−0.995293 | + | 0.0969146i | \(0.969103\pi\) | |||||||
\(978\) | − | 2.06782e25i | − | 0.790008i | ||||||
\(979\) | 9.90244e24 | 0.375050 | ||||||||
\(980\) | −2.13034e24 | − | 8.77972e25i | −0.0799883 | − | 3.29654i | ||||
\(981\) | 3.32008e23 | 0.0123584 | ||||||||
\(982\) | 4.15727e25i | 1.53412i | ||||||||
\(983\) | − | 6.31866e23i | − | 0.0231164i | −0.999933 | − | 0.0115582i | \(-0.996321\pi\) | ||
0.999933 | − | 0.0115582i | \(-0.00367917\pi\) | |||||||
\(984\) | 3.36593e25 | 1.22080 | ||||||||
\(985\) | 1.05532e25 | − | 2.56065e23i | 0.379468 | − | 0.00920753i | ||||
\(986\) | 2.57500e25 | 0.917958 | ||||||||
\(987\) | − | 9.17833e24i | − | 0.324390i | ||||||
\(988\) | − | 7.44264e24i | − | 0.260791i | ||||||
\(989\) | 1.93760e25 | 0.673124 | ||||||||
\(990\) | −2.43451e23 | + | 5.90715e21i | −0.00838516 | + | 0.000203460i | ||||
\(991\) | 4.61468e25 | 1.57585 | 0.787927 | − | 0.615769i | \(-0.211155\pi\) | ||||
0.787927 | + | 0.615769i | \(0.211155\pi\) | |||||||
\(992\) | 2.47732e25i | 0.838750i | ||||||||
\(993\) | 3.97693e25i | 1.33499i | ||||||||
\(994\) | −9.03272e25 | −3.00632 | ||||||||
\(995\) | 1.38944e24 | + | 5.72628e25i | 0.0458505 | + | 1.88963i | ||||
\(996\) | 7.24449e25 | 2.37030 | ||||||||
\(997\) | − | 4.92727e25i | − | 1.59844i | −0.601037 | − | 0.799222i | \(-0.705245\pi\) | ||
0.601037 | − | 0.799222i | \(-0.294755\pi\) | |||||||
\(998\) | − | 7.00725e25i | − | 2.25392i | ||||||
\(999\) | −4.23674e25 | −1.35122 |
(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 | 5.18.b.a.4.8 | yes | 8 | |
3.2 | odd | 2 | 45.18.b.b.19.1 | 8 | |||
4.3 | odd | 2 | 80.18.c.b.49.3 | 8 | |||
5.2 | odd | 4 | 25.18.a.f.1.1 | 8 | |||
5.3 | odd | 4 | 25.18.a.f.1.8 | 8 | |||
5.4 | even | 2 | inner | 5.18.b.a.4.1 | ✓ | 8 | |
15.14 | odd | 2 | 45.18.b.b.19.8 | 8 | |||
20.19 | odd | 2 | 80.18.c.b.49.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.18.b.a.4.1 | ✓ | 8 | 5.4 | even | 2 | inner | |
5.18.b.a.4.8 | yes | 8 | 1.1 | even | 1 | trivial | |
25.18.a.f.1.1 | 8 | 5.2 | odd | 4 | |||
25.18.a.f.1.8 | 8 | 5.3 | odd | 4 | |||
45.18.b.b.19.1 | 8 | 3.2 | odd | 2 | |||
45.18.b.b.19.8 | 8 | 15.14 | odd | 2 | |||
80.18.c.b.49.3 | 8 | 4.3 | odd | 2 | |||
80.18.c.b.49.6 | 8 | 20.19 | odd | 2 |