Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,21,Mod(3,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 21, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.3");
S:= CuspForms(chi, 21);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 21 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(20.2811012082\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 66008406614424 x^{16} + \cdots + 53\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{153}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.1 | ||
Root | \(16622.8 - 2.05933e6i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.3 |
Dual form | 8.21.d.b.3.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −998.751 | − | 225.992i | −0.975343 | − | 0.220696i | ||||
\(3\) | 60145.3 | 1.01857 | 0.509283 | − | 0.860599i | \(-0.329911\pi\) | ||||
0.509283 | + | 0.860599i | \(0.329911\pi\) | |||||||
\(4\) | 946431. | + | 451420.i | 0.902587 | + | 0.430508i | ||||
\(5\) | 8.23733e6i | 0.843502i | 0.906712 | + | 0.421751i | \(0.138584\pi\) | ||||
−0.906712 | + | 0.421751i | \(0.861416\pi\) | |||||||
\(6\) | −6.00701e7 | − | 1.35924e7i | −0.993450 | − | 0.224793i | ||||
\(7\) | 5.26995e8i | 1.86563i | 0.360351 | + | 0.932817i | \(0.382657\pi\) | ||||
−0.360351 | + | 0.932817i | \(0.617343\pi\) | |||||||
\(8\) | −8.43231e8 | − | 6.64742e8i | −0.785320 | − | 0.619090i | ||||
\(9\) | 1.30668e8 | 0.0374752 | ||||||||
\(10\) | 1.86157e9 | − | 8.22704e9i | 0.186157 | − | 0.822704i | ||||
\(11\) | 6.02652e9 | 0.232348 | 0.116174 | − | 0.993229i | \(-0.462937\pi\) | ||||
0.116174 | + | 0.993229i | \(0.462937\pi\) | |||||||
\(12\) | 5.69233e10 | + | 2.71508e10i | 0.919344 | + | 0.438500i | ||||
\(13\) | − | 1.38203e11i | − | 1.00250i | −0.865304 | − | 0.501248i | \(-0.832874\pi\) | ||
0.865304 | − | 0.501248i | \(-0.167126\pi\) | |||||||
\(14\) | 1.19097e11 | − | 5.26337e11i | 0.411737 | − | 1.81963i | ||||
\(15\) | 4.95436e11i | 0.859162i | ||||||||
\(16\) | 6.91951e11 | + | 8.54476e11i | 0.629326 | + | 0.777141i | ||||
\(17\) | −1.98685e12 | −0.985546 | −0.492773 | − | 0.870158i | \(-0.664017\pi\) | ||||
−0.492773 | + | 0.870158i | \(0.664017\pi\) | |||||||
\(18\) | −1.30505e11 | − | 2.95300e10i | −0.0365512 | − | 0.00827062i | ||||
\(19\) | −8.88192e12 | −1.44867 | −0.724337 | − | 0.689446i | \(-0.757854\pi\) | ||||
−0.724337 | + | 0.689446i | \(0.757854\pi\) | |||||||
\(20\) | −3.71850e12 | + | 7.79606e12i | −0.363134 | + | 0.761334i | ||||
\(21\) | 3.16963e13i | 1.90027i | ||||||||
\(22\) | −6.01899e12 | − | 1.36195e12i | −0.226619 | − | 0.0512783i | ||||
\(23\) | − | 2.01771e13i | − | 0.487057i | −0.969894 | − | 0.243529i | \(-0.921695\pi\) | ||
0.969894 | − | 0.243529i | \(-0.0783050\pi\) | |||||||
\(24\) | −5.07164e13 | − | 3.99811e13i | −0.799900 | − | 0.630583i | ||||
\(25\) | 2.75139e13 | 0.288504 | ||||||||
\(26\) | −3.12327e13 | + | 1.38030e14i | −0.221246 | + | 0.977777i | ||||
\(27\) | −2.01854e14 | −0.980394 | ||||||||
\(28\) | −2.37896e14 | + | 4.98765e14i | −0.803170 | + | 1.68390i | ||||
\(29\) | − | 2.99333e14i | − | 0.711499i | −0.934581 | − | 0.355749i | \(-0.884226\pi\) | ||
0.934581 | − | 0.355749i | \(-0.115774\pi\) | |||||||
\(30\) | 1.11965e14 | − | 4.94817e14i | 0.189613 | − | 0.837978i | ||||
\(31\) | 1.39233e15i | 1.69873i | 0.527805 | + | 0.849366i | \(0.323015\pi\) | ||||
−0.527805 | + | 0.849366i | \(0.676985\pi\) | |||||||
\(32\) | −4.97982e14 | − | 1.00978e15i | −0.442297 | − | 0.896869i | ||||
\(33\) | 3.62466e14 | 0.236662 | ||||||||
\(34\) | 1.98437e15 | + | 4.49014e14i | 0.961245 | + | 0.217506i | ||||
\(35\) | −4.34103e15 | −1.57367 | ||||||||
\(36\) | 1.23668e14 | + | 5.89862e13i | 0.0338246 | + | 0.0161334i | ||||
\(37\) | 1.32225e15i | 0.274976i | 0.990503 | + | 0.137488i | \(0.0439029\pi\) | ||||
−0.990503 | + | 0.137488i | \(0.956097\pi\) | |||||||
\(38\) | 8.87083e15 | + | 2.00725e15i | 1.41295 | + | 0.319716i | ||||
\(39\) | − | 8.31223e15i | − | 1.02111i | ||||||
\(40\) | 5.47570e15 | − | 6.94597e15i | 0.522204 | − | 0.662420i | ||||
\(41\) | 1.06415e16 | 0.792798 | 0.396399 | − | 0.918078i | \(-0.370260\pi\) | ||||
0.396399 | + | 0.918078i | \(0.370260\pi\) | |||||||
\(42\) | 7.16311e15 | − | 3.16567e16i | 0.419381 | − | 1.85341i | ||||
\(43\) | −1.54318e15 | −0.0714056 | −0.0357028 | − | 0.999362i | \(-0.511367\pi\) | ||||
−0.0357028 | + | 0.999362i | \(0.511367\pi\) | |||||||
\(44\) | 5.70368e15 | + | 2.72049e15i | 0.209715 | + | 0.100028i | ||||
\(45\) | 1.07636e15i | 0.0316104i | ||||||||
\(46\) | −4.55987e15 | + | 2.01519e16i | −0.107491 | + | 0.475048i | ||||
\(47\) | 6.01114e16i | 1.14282i | 0.820664 | + | 0.571411i | \(0.193604\pi\) | ||||
−0.820664 | + | 0.571411i | \(0.806396\pi\) | |||||||
\(48\) | 4.16176e16 | + | 5.13927e16i | 0.641010 | + | 0.791569i | ||||
\(49\) | −1.97932e17 | −2.48059 | ||||||||
\(50\) | −2.74795e16 | − | 6.21792e15i | −0.281390 | − | 0.0636715i | ||||
\(51\) | −1.19500e17 | −1.00384 | ||||||||
\(52\) | 6.23874e16 | − | 1.30799e17i | 0.431582 | − | 0.904840i | ||||
\(53\) | 2.12573e17i | 1.21549i | 0.794134 | + | 0.607743i | \(0.207925\pi\) | ||||
−0.794134 | + | 0.607743i | \(0.792075\pi\) | |||||||
\(54\) | 2.01602e17 | + | 4.56176e16i | 0.956220 | + | 0.216369i | ||||
\(55\) | 4.96424e16i | 0.195986i | ||||||||
\(56\) | 3.50316e17 | − | 4.44379e17i | 1.15499 | − | 1.46512i | ||||
\(57\) | −5.34206e17 | −1.47557 | ||||||||
\(58\) | −6.76469e16 | + | 2.98959e17i | −0.157025 | + | 0.693955i | ||||
\(59\) | 4.77160e15 | 0.00933563 | 0.00466782 | − | 0.999989i | \(-0.498514\pi\) | ||||
0.00466782 | + | 0.999989i | \(0.498514\pi\) | |||||||
\(60\) | −2.23650e17 | + | 4.68896e17i | −0.369876 | + | 0.775469i | ||||
\(61\) | − | 3.65093e16i | − | 0.0511805i | −0.999673 | − | 0.0255903i | \(-0.991853\pi\) | ||
0.999673 | − | 0.0255903i | \(-0.00814652\pi\) | |||||||
\(62\) | 3.14655e17 | − | 1.39059e18i | 0.374903 | − | 1.65685i | ||||
\(63\) | 6.88615e16i | 0.0699151i | ||||||||
\(64\) | 2.69157e17 | + | 1.12106e18i | 0.233456 | + | 0.972367i | ||||
\(65\) | 1.13842e18 | 0.845608 | ||||||||
\(66\) | −3.62014e17 | − | 8.19146e16i | −0.230826 | − | 0.0522303i | ||||
\(67\) | 6.78003e17 | 0.371949 | 0.185975 | − | 0.982555i | \(-0.440456\pi\) | ||||
0.185975 | + | 0.982555i | \(0.440456\pi\) | |||||||
\(68\) | −1.88042e18 | − | 8.96906e17i | −0.889541 | − | 0.424285i | ||||
\(69\) | − | 1.21356e18i | − | 0.496100i | ||||||
\(70\) | 4.33561e18 | + | 9.81040e17i | 1.53486 | + | 0.347301i | ||||
\(71\) | − | 2.60562e18i | − | 0.800439i | −0.916419 | − | 0.400220i | \(-0.868934\pi\) | ||
0.916419 | − | 0.400220i | \(-0.131066\pi\) | |||||||
\(72\) | −1.10183e17 | − | 8.68606e16i | −0.0294301 | − | 0.0232005i | ||||
\(73\) | 2.08057e18 | 0.484121 | 0.242061 | − | 0.970261i | \(-0.422177\pi\) | ||||
0.242061 | + | 0.970261i | \(0.422177\pi\) | |||||||
\(74\) | 2.98817e17 | − | 1.32059e18i | 0.0606860 | − | 0.268196i | ||||
\(75\) | 1.65483e18 | 0.293860 | ||||||||
\(76\) | −8.40613e18 | − | 4.00948e18i | −1.30756 | − | 0.623666i | ||||
\(77\) | 3.17595e18i | 0.433477i | ||||||||
\(78\) | −1.87850e18 | + | 8.30185e18i | −0.225354 | + | 0.995930i | ||||
\(79\) | 4.99331e18i | 0.527372i | 0.964609 | + | 0.263686i | \(0.0849383\pi\) | ||||
−0.964609 | + | 0.263686i | \(0.915062\pi\) | |||||||
\(80\) | −7.03860e18 | + | 5.69983e18i | −0.655520 | + | 0.530838i | ||||
\(81\) | −1.25962e19 | −1.03607 | ||||||||
\(82\) | −1.06282e19 | − | 2.40489e18i | −0.773250 | − | 0.174967i | ||||
\(83\) | 2.79468e19 | 1.80115 | 0.900577 | − | 0.434696i | \(-0.143144\pi\) | ||||
0.900577 | + | 0.434696i | \(0.143144\pi\) | |||||||
\(84\) | −1.43083e19 | + | 2.99983e19i | −0.818081 | + | 1.71516i | ||||
\(85\) | − | 1.63664e19i | − | 0.831310i | ||||||
\(86\) | 1.54125e18 | + | 3.48747e17i | 0.0696449 | + | 0.0157589i | ||||
\(87\) | − | 1.80034e19i | − | 0.724708i | ||||||
\(88\) | −5.08175e18 | − | 4.00608e18i | −0.182468 | − | 0.143844i | ||||
\(89\) | −2.07280e19 | −0.664748 | −0.332374 | − | 0.943148i | \(-0.607850\pi\) | ||||
−0.332374 | + | 0.943148i | \(0.607850\pi\) | |||||||
\(90\) | 2.43248e17 | − | 1.07501e18i | 0.00697629 | − | 0.0308310i | ||||
\(91\) | 7.28321e19 | 1.87029 | ||||||||
\(92\) | 9.10834e18 | − | 1.90962e19i | 0.209682 | − | 0.439611i | ||||
\(93\) | 8.37419e19i | 1.73027i | ||||||||
\(94\) | 1.35847e19 | − | 6.00363e19i | 0.252216 | − | 1.11464i | ||||
\(95\) | − | 7.31633e19i | − | 1.22196i | ||||||
\(96\) | −2.99513e19 | − | 6.07337e19i | −0.450508 | − | 0.913519i | ||||
\(97\) | −9.97818e19 | −1.35311 | −0.676557 | − | 0.736391i | \(-0.736529\pi\) | ||||
−0.676557 | + | 0.736391i | \(0.736529\pi\) | |||||||
\(98\) | 1.97685e20 | + | 4.47311e19i | 2.41942 | + | 0.547455i | ||||
\(99\) | 7.87473e17 | 0.00870731 | ||||||||
\(100\) | 2.60400e19 | + | 1.24203e19i | 0.260400 | + | 0.124203i | ||||
\(101\) | − | 1.23930e20i | − | 1.12192i | −0.827843 | − | 0.560960i | \(-0.810432\pi\) | ||
0.827843 | − | 0.560960i | \(-0.189568\pi\) | |||||||
\(102\) | 1.19351e20 | + | 2.70060e19i | 0.979091 | + | 0.221544i | ||||
\(103\) | 1.90114e20i | 1.41463i | 0.706901 | + | 0.707313i | \(0.250093\pi\) | ||||
−0.706901 | + | 0.707313i | \(0.749907\pi\) | |||||||
\(104\) | −9.18691e19 | + | 1.16537e20i | −0.620635 | + | 0.787280i | ||||
\(105\) | −2.61093e20 | −1.60288 | ||||||||
\(106\) | 4.80399e19 | − | 2.12308e20i | 0.268252 | − | 1.18551i | ||||
\(107\) | −2.21231e18 | −0.0112463 | −0.00562314 | − | 0.999984i | \(-0.501790\pi\) | ||||
−0.00562314 | + | 0.999984i | \(0.501790\pi\) | |||||||
\(108\) | −1.91041e20 | − | 9.11212e19i | −0.884891 | − | 0.422067i | ||||
\(109\) | 2.92007e20i | 1.23347i | 0.787171 | + | 0.616734i | \(0.211545\pi\) | ||||
−0.787171 | + | 0.616734i | \(0.788455\pi\) | |||||||
\(110\) | 1.12188e19 | − | 4.95804e19i | 0.0432533 | − | 0.191154i | ||||
\(111\) | 7.95268e19i | 0.280081i | ||||||||
\(112\) | −4.50305e20 | + | 3.64655e20i | −1.44986 | + | 1.17409i | ||||
\(113\) | −1.48679e20 | −0.437990 | −0.218995 | − | 0.975726i | \(-0.570278\pi\) | ||||
−0.218995 | + | 0.975726i | \(0.570278\pi\) | |||||||
\(114\) | 5.33538e20 | + | 1.20726e20i | 1.43919 | + | 0.325652i | ||||
\(115\) | 1.66205e20 | 0.410834 | ||||||||
\(116\) | 1.35125e20 | − | 2.83298e20i | 0.306306 | − | 0.642189i | ||||
\(117\) | − | 1.80587e19i | − | 0.0375688i | ||||||
\(118\) | −4.76564e18 | − | 1.07834e18i | −0.00910544 | − | 0.00206033i | ||||
\(119\) | − | 1.04706e21i | − | 1.83867i | ||||||
\(120\) | 3.29337e20 | − | 4.17767e20i | 0.531898 | − | 0.674718i | ||||
\(121\) | −6.36431e20 | −0.946014 | ||||||||
\(122\) | −8.25081e18 | + | 3.64637e19i | −0.0112953 | + | 0.0499185i | ||||
\(123\) | 6.40033e20 | 0.807516 | ||||||||
\(124\) | −6.28525e20 | + | 1.31774e21i | −0.731317 | + | 1.53325i | ||||
\(125\) | 1.01221e21i | 1.08686i | ||||||||
\(126\) | 1.55622e19 | − | 6.87754e19i | 0.0154299 | − | 0.0681911i | ||||
\(127\) | 1.29687e21i | 1.18812i | 0.804422 | + | 0.594058i | \(0.202475\pi\) | ||||
−0.804422 | + | 0.594058i | \(0.797525\pi\) | |||||||
\(128\) | −1.54688e19 | − | 1.18049e21i | −0.0131026 | − | 0.999914i | ||||
\(129\) | −9.28150e19 | −0.0727313 | ||||||||
\(130\) | −1.13700e21 | − | 2.57274e20i | −0.824757 | − | 0.186622i | ||||
\(131\) | 2.73520e21 | 1.83770 | 0.918852 | − | 0.394603i | \(-0.129118\pi\) | ||||
0.918852 | + | 0.394603i | \(0.129118\pi\) | |||||||
\(132\) | 3.43049e20 | + | 1.63625e20i | 0.213608 | + | 0.101885i | ||||
\(133\) | − | 4.68073e21i | − | 2.70270i | ||||||
\(134\) | −6.77156e20 | − | 1.53223e20i | −0.362778 | − | 0.0820875i | ||||
\(135\) | − | 1.66274e21i | − | 0.826965i | ||||||
\(136\) | 1.67538e21 | + | 1.32075e21i | 0.773969 | + | 0.610141i | ||||
\(137\) | 3.47180e21 | 1.49056 | 0.745279 | − | 0.666753i | \(-0.232316\pi\) | ||||
0.745279 | + | 0.666753i | \(0.232316\pi\) | |||||||
\(138\) | −2.74254e20 | + | 1.21204e21i | −0.109487 | + | 0.483867i | ||||
\(139\) | −2.01290e19 | −0.00747607 | −0.00373804 | − | 0.999993i | \(-0.501190\pi\) | ||||
−0.00373804 | + | 0.999993i | \(0.501190\pi\) | |||||||
\(140\) | −4.10849e21 | − | 1.95963e21i | −1.42037 | − | 0.677476i | ||||
\(141\) | 3.61542e21i | 1.16404i | ||||||||
\(142\) | −5.88851e20 | + | 2.60237e21i | −0.176653 | + | 0.780703i | ||||
\(143\) | − | 8.32880e20i | − | 0.232928i | ||||||
\(144\) | 9.04159e19 | + | 1.11653e20i | 0.0235841 | + | 0.0291235i | ||||
\(145\) | 2.46570e21 | 0.600151 | ||||||||
\(146\) | −2.07797e21 | − | 4.70193e20i | −0.472184 | − | 0.106843i | ||||
\(147\) | −1.19047e22 | −2.52664 | ||||||||
\(148\) | −5.96888e20 | + | 1.25141e21i | −0.118379 | + | 0.248190i | ||||
\(149\) | 4.96578e21i | 0.920714i | 0.887734 | + | 0.460357i | \(0.152279\pi\) | ||||
−0.887734 | + | 0.460357i | \(0.847721\pi\) | |||||||
\(150\) | −1.65276e21 | − | 3.73979e20i | −0.286614 | − | 0.0648536i | ||||
\(151\) | 5.02251e21i | 0.814988i | 0.913208 | + | 0.407494i | \(0.133597\pi\) | ||||
−0.913208 | + | 0.407494i | \(0.866403\pi\) | |||||||
\(152\) | 7.48952e21 | + | 5.90419e21i | 1.13767 | + | 0.896860i | ||||
\(153\) | −2.59618e20 | −0.0369335 | ||||||||
\(154\) | 7.17740e20 | − | 3.17198e21i | 0.0956664 | − | 0.422789i | ||||
\(155\) | −1.14691e22 | −1.43288 | ||||||||
\(156\) | 3.75231e21 | − | 7.86695e21i | 0.439595 | − | 0.921638i | ||||
\(157\) | − | 1.25764e22i | − | 1.38216i | −0.722777 | − | 0.691081i | \(-0.757135\pi\) | ||
0.722777 | − | 0.691081i | \(-0.242865\pi\) | |||||||
\(158\) | 1.12845e21 | − | 4.98707e21i | 0.116389 | − | 0.514369i | ||||
\(159\) | 1.27853e22i | 1.23805i | ||||||||
\(160\) | 8.31792e21 | − | 4.10204e21i | 0.756511 | − | 0.373079i | ||||
\(161\) | 1.06332e22 | 0.908670 | ||||||||
\(162\) | 1.25805e22 | + | 2.84664e21i | 1.01052 | + | 0.228656i | ||||
\(163\) | −5.79110e20 | −0.0437406 | −0.0218703 | − | 0.999761i | \(-0.506962\pi\) | ||||
−0.0218703 | + | 0.999761i | \(0.506962\pi\) | |||||||
\(164\) | 1.00714e22 | + | 4.80377e21i | 0.715569 | + | 0.341306i | ||||
\(165\) | 2.98575e21i | 0.199625i | ||||||||
\(166\) | −2.79119e22 | − | 6.31576e21i | −1.75674 | − | 0.397507i | ||||
\(167\) | − | 2.14950e22i | − | 1.27401i | −0.770861 | − | 0.637004i | \(-0.780174\pi\) | ||
0.770861 | − | 0.637004i | \(-0.219826\pi\) | |||||||
\(168\) | 2.10699e22 | − | 2.67273e22i | 1.17644 | − | 1.49232i | ||||
\(169\) | −9.49847e19 | −0.00499789 | ||||||||
\(170\) | −3.69867e21 | + | 1.63459e22i | −0.183466 | + | 0.810812i | ||||
\(171\) | −1.16058e21 | −0.0542894 | ||||||||
\(172\) | −1.46051e21 | − | 6.96623e20i | −0.0644498 | − | 0.0307407i | ||||
\(173\) | − | 7.43145e21i | − | 0.309466i | −0.987956 | − | 0.154733i | \(-0.950548\pi\) | ||
0.987956 | − | 0.154733i | \(-0.0494517\pi\) | |||||||
\(174\) | −4.06864e21 | + | 1.79810e22i | −0.159940 | + | 0.706839i | ||||
\(175\) | 1.44997e22i | 0.538242i | ||||||||
\(176\) | 4.17006e21 | + | 5.14951e21i | 0.146223 | + | 0.180567i | ||||
\(177\) | 2.86989e20 | 0.00950895 | ||||||||
\(178\) | 2.07021e22 | + | 4.68437e21i | 0.648357 | + | 0.146707i | ||||
\(179\) | −3.33062e21 | −0.0986267 | −0.0493134 | − | 0.998783i | \(-0.515703\pi\) | ||||
−0.0493134 | + | 0.998783i | \(0.515703\pi\) | |||||||
\(180\) | −4.85888e20 | + | 1.01870e21i | −0.0136085 | + | 0.0285312i | ||||
\(181\) | 5.92307e22i | 1.56950i | 0.619813 | + | 0.784750i | \(0.287209\pi\) | ||||
−0.619813 | + | 0.784750i | \(0.712791\pi\) | |||||||
\(182\) | −7.27411e22 | − | 1.64595e22i | −1.82417 | − | 0.412765i | ||||
\(183\) | − | 2.19586e21i | − | 0.0521307i | ||||||
\(184\) | −1.34126e22 | + | 1.70139e22i | −0.301532 | + | 0.382496i | ||||
\(185\) | −1.08918e22 | −0.231943 | ||||||||
\(186\) | 1.89250e22 | − | 8.36373e22i | 0.381863 | − | 1.68760i | ||||
\(187\) | −1.19738e22 | −0.228990 | ||||||||
\(188\) | −2.71355e22 | + | 5.68913e22i | −0.491994 | + | 1.03150i | ||||
\(189\) | − | 1.06376e23i | − | 1.82906i | ||||||
\(190\) | −1.65343e22 | + | 7.30719e22i | −0.269681 | + | 1.19183i | ||||
\(191\) | 1.05814e22i | 0.163761i | 0.996642 | + | 0.0818806i | \(0.0260926\pi\) | ||||
−0.996642 | + | 0.0818806i | \(0.973907\pi\) | |||||||
\(192\) | 1.61885e22 | + | 6.74266e22i | 0.237790 | + | 0.990420i | ||||
\(193\) | 4.43070e22 | 0.617873 | 0.308937 | − | 0.951083i | \(-0.400027\pi\) | ||||
0.308937 | + | 0.951083i | \(0.400027\pi\) | |||||||
\(194\) | 9.96572e22 | + | 2.25499e22i | 1.31975 | + | 0.298626i | ||||
\(195\) | 6.84706e22 | 0.861307 | ||||||||
\(196\) | −1.87329e23 | − | 8.93504e22i | −2.23895 | − | 1.06791i | ||||
\(197\) | 2.36624e22i | 0.268779i | 0.990929 | + | 0.134390i | \(0.0429074\pi\) | ||||
−0.990929 | + | 0.134390i | \(0.957093\pi\) | |||||||
\(198\) | −7.86490e20 | − | 1.77963e20i | −0.00849261 | − | 0.00192166i | ||||
\(199\) | − | 7.89983e22i | − | 0.811123i | −0.914068 | − | 0.405562i | \(-0.867076\pi\) | ||
0.914068 | − | 0.405562i | \(-0.132924\pi\) | |||||||
\(200\) | −2.32006e22 | − | 1.82896e22i | −0.226568 | − | 0.178610i | ||||
\(201\) | 4.07787e22 | 0.378854 | ||||||||
\(202\) | −2.80072e22 | + | 1.23775e23i | −0.247603 | + | 1.09426i | ||||
\(203\) | 1.57747e23 | 1.32740 | ||||||||
\(204\) | −1.13098e23 | − | 5.39446e22i | −0.906055 | − | 0.432162i | ||||
\(205\) | 8.76572e22i | 0.668727i | ||||||||
\(206\) | 4.29643e22 | − | 1.89876e23i | 0.312202 | − | 1.37974i | ||||
\(207\) | − | 2.63650e21i | − | 0.0182526i | ||||||
\(208\) | 1.18091e23 | − | 9.56295e22i | 0.779081 | − | 0.630897i | ||||
\(209\) | −5.35271e22 | −0.336597 | ||||||||
\(210\) | 2.60766e23 | + | 5.90049e22i | 1.56336 | + | 0.353749i | ||||
\(211\) | 1.91400e22 | 0.109425 | 0.0547127 | − | 0.998502i | \(-0.482576\pi\) | ||||
0.0547127 | + | 0.998502i | \(0.482576\pi\) | |||||||
\(212\) | −9.59598e22 | + | 2.01186e23i | −0.523276 | + | 1.09708i | ||||
\(213\) | − | 1.56716e23i | − | 0.815300i | ||||||
\(214\) | 2.20955e21 | + | 4.99966e20i | 0.0109690 | + | 0.00248200i | ||||
\(215\) | − | 1.27117e22i | − | 0.0602308i | ||||||
\(216\) | 1.70210e23 | + | 1.34181e23i | 0.769924 | + | 0.606952i | ||||
\(217\) | −7.33751e23 | −3.16921 | ||||||||
\(218\) | 6.59913e22 | − | 2.91642e23i | 0.272221 | − | 1.20305i | ||||
\(219\) | 1.25137e23 | 0.493109 | ||||||||
\(220\) | −2.24096e22 | + | 4.69831e22i | −0.0843736 | + | 0.176895i | ||||
\(221\) | 2.74588e23i | 0.988005i | ||||||||
\(222\) | 1.79725e22 | − | 7.94275e22i | 0.0618127 | − | 0.273175i | ||||
\(223\) | 5.23366e22i | 0.172090i | 0.996291 | + | 0.0860452i | \(0.0274230\pi\) | ||||
−0.996291 | + | 0.0860452i | \(0.972577\pi\) | |||||||
\(224\) | 5.32152e23 | − | 2.62434e23i | 1.67323 | − | 0.825164i | ||||
\(225\) | 3.59518e21 | 0.0108117 | ||||||||
\(226\) | 1.48493e23 | + | 3.36003e22i | 0.427191 | + | 0.0966626i | ||||
\(227\) | 8.58318e22 | 0.236260 | 0.118130 | − | 0.992998i | \(-0.462310\pi\) | ||||
0.118130 | + | 0.992998i | \(0.462310\pi\) | |||||||
\(228\) | −5.05589e23 | − | 2.41151e23i | −1.33183 | − | 0.635244i | ||||
\(229\) | 3.17833e23i | 0.801391i | 0.916211 | + | 0.400695i | \(0.131231\pi\) | ||||
−0.916211 | + | 0.400695i | \(0.868769\pi\) | |||||||
\(230\) | −1.65998e23 | − | 3.75611e22i | −0.400704 | − | 0.0906692i | ||||
\(231\) | 1.91018e23i | 0.441525i | ||||||||
\(232\) | −1.98979e23 | + | 2.52407e23i | −0.440481 | + | 0.558754i | ||||
\(233\) | −3.29360e23 | −0.698411 | −0.349206 | − | 0.937046i | \(-0.613549\pi\) | ||||
−0.349206 | + | 0.937046i | \(0.613549\pi\) | |||||||
\(234\) | −4.08112e21 | + | 1.80361e22i | −0.00829126 | + | 0.0366424i | ||||
\(235\) | −4.95158e23 | −0.963973 | ||||||||
\(236\) | 4.51599e21 | + | 2.15400e21i | 0.00842622 | + | 0.00401906i | ||||
\(237\) | 3.00324e23i | 0.537163i | ||||||||
\(238\) | −2.36628e23 | + | 1.04576e24i | −0.405786 | + | 1.79333i | ||||
\(239\) | − | 5.66048e23i | − | 0.930839i | −0.885090 | − | 0.465419i | \(-0.845904\pi\) | ||
0.885090 | − | 0.465419i | \(-0.154096\pi\) | |||||||
\(240\) | −4.23338e23 | + | 3.42818e23i | −0.667690 | + | 0.540693i | ||||
\(241\) | 3.83872e23 | 0.580786 | 0.290393 | − | 0.956907i | \(-0.406214\pi\) | ||||
0.290393 | + | 0.956907i | \(0.406214\pi\) | |||||||
\(242\) | 6.35636e23 | + | 1.43829e23i | 0.922688 | + | 0.208781i | ||||
\(243\) | −5.37788e22 | −0.0749115 | ||||||||
\(244\) | 1.64810e22 | − | 3.45535e22i | 0.0220336 | − | 0.0461949i | ||||
\(245\) | − | 1.63043e24i | − | 2.09238i | ||||||
\(246\) | −6.39234e23 | − | 1.44643e23i | −0.787605 | − | 0.178215i | ||||
\(247\) | 1.22750e24i | 1.45229i | ||||||||
\(248\) | 9.25540e23 | − | 1.17405e24i | 1.05167 | − | 1.33405i | ||||
\(249\) | 1.68087e24 | 1.83459 | ||||||||
\(250\) | 2.28752e23 | − | 1.01095e24i | 0.239864 | − | 1.06006i | ||||
\(251\) | 1.74402e23 | 0.175717 | 0.0878586 | − | 0.996133i | \(-0.471998\pi\) | ||||
0.0878586 | + | 0.996133i | \(0.471998\pi\) | |||||||
\(252\) | −3.10854e22 | + | 6.51726e22i | −0.0300990 | + | 0.0631044i | ||||
\(253\) | − | 1.21598e23i | − | 0.113167i | ||||||
\(254\) | 2.93082e23 | − | 1.29525e24i | 0.262212 | − | 1.15882i | ||||
\(255\) | − | 9.84359e23i | − | 0.846744i | ||||||
\(256\) | −2.51332e23 | + | 1.18251e24i | −0.207897 | + | 0.978151i | ||||
\(257\) | 2.21521e24 | 1.76231 | 0.881157 | − | 0.472824i | \(-0.156765\pi\) | ||||
0.881157 | + | 0.472824i | \(0.156765\pi\) | |||||||
\(258\) | 9.26991e22 | + | 2.09755e22i | 0.0709379 | + | 0.0160515i | ||||
\(259\) | −6.96818e23 | −0.513005 | ||||||||
\(260\) | 1.07744e24 | + | 5.13906e23i | 0.763234 | + | 0.364041i | ||||
\(261\) | − | 3.91132e22i | − | 0.0266636i | ||||||
\(262\) | −2.73178e24 | − | 6.18133e23i | −1.79239 | − | 0.405573i | ||||
\(263\) | − | 5.35900e23i | − | 0.338475i | −0.985575 | − | 0.169237i | \(-0.945870\pi\) | ||
0.985575 | − | 0.169237i | \(-0.0541305\pi\) | |||||||
\(264\) | −3.05643e23 | − | 2.40947e23i | −0.185855 | − | 0.146515i | ||||
\(265\) | −1.75103e24 | −1.02526 | ||||||||
\(266\) | −1.05781e24 | + | 4.67489e24i | −0.596473 | + | 2.63606i | ||||
\(267\) | −1.24669e24 | −0.677089 | ||||||||
\(268\) | 6.41683e23 | + | 3.06064e23i | 0.335716 | + | 0.160127i | ||||
\(269\) | 1.60976e24i | 0.811408i | 0.914004 | + | 0.405704i | \(0.132974\pi\) | ||||
−0.914004 | + | 0.405704i | \(0.867026\pi\) | |||||||
\(270\) | −3.75767e23 | + | 1.66066e24i | −0.182508 | + | 0.806574i | ||||
\(271\) | 2.62551e22i | 0.0122891i | 0.999981 | + | 0.00614457i | \(0.00195589\pi\) | ||||
−0.999981 | + | 0.00614457i | \(0.998044\pi\) | |||||||
\(272\) | −1.37481e24 | − | 1.69772e24i | −0.620230 | − | 0.765908i | ||||
\(273\) | 4.38051e24 | 1.90501 | ||||||||
\(274\) | −3.46746e24 | − | 7.84600e23i | −1.45380 | − | 0.328960i | ||||
\(275\) | 1.65813e23 | 0.0670334 | ||||||||
\(276\) | 5.47823e23 | − | 1.14855e24i | 0.213575 | − | 0.447773i | ||||
\(277\) | − | 5.84599e22i | − | 0.0219817i | −0.999940 | − | 0.0109908i | \(-0.996501\pi\) | ||
0.999940 | − | 0.0109908i | \(-0.00349856\pi\) | |||||||
\(278\) | 2.01038e22 | + | 4.54899e21i | 0.00729173 | + | 0.00164994i | ||||
\(279\) | 1.81933e23i | 0.0636603i | ||||||||
\(280\) | 3.66050e24 | + | 2.88567e24i | 1.23583 | + | 0.974241i | ||||
\(281\) | −5.61456e24 | −1.82916 | −0.914581 | − | 0.404402i | \(-0.867480\pi\) | ||||
−0.914581 | + | 0.404402i | \(0.867480\pi\) | |||||||
\(282\) | 8.17057e23 | − | 3.61090e24i | 0.256898 | − | 1.13534i | ||||
\(283\) | 1.26250e24 | 0.383149 | 0.191574 | − | 0.981478i | \(-0.438641\pi\) | ||||
0.191574 | + | 0.981478i | \(0.438641\pi\) | |||||||
\(284\) | 1.17623e24 | − | 2.46604e24i | 0.344595 | − | 0.722466i | ||||
\(285\) | − | 4.40043e24i | − | 1.24465i | ||||||
\(286\) | −1.88225e23 | + | 8.31840e23i | −0.0514062 | + | 0.227185i | ||||
\(287\) | 5.60800e24i | 1.47907i | ||||||||
\(288\) | −6.50704e22 | − | 1.31947e23i | −0.0165752 | − | 0.0336104i | ||||
\(289\) | −1.16643e23 | −0.0286998 | ||||||||
\(290\) | −2.46262e24 | − | 5.57230e23i | −0.585353 | − | 0.132451i | ||||
\(291\) | −6.00141e24 | −1.37823 | ||||||||
\(292\) | 1.96912e24 | + | 9.39212e23i | 0.436962 | + | 0.208418i | ||||
\(293\) | 4.18336e24i | 0.897117i | 0.893753 | + | 0.448559i | \(0.148062\pi\) | ||||
−0.893753 | + | 0.448559i | \(0.851938\pi\) | |||||||
\(294\) | 1.18898e25 | + | 2.69036e24i | 2.46434 | + | 0.557619i | ||||
\(295\) | 3.93052e22i | 0.00787463i | ||||||||
\(296\) | 8.78953e23 | − | 1.11496e24i | 0.170235 | − | 0.215944i | ||||
\(297\) | −1.21648e24 | −0.227793 | ||||||||
\(298\) | 1.12223e24 | − | 4.95958e24i | 0.203198 | − | 0.898012i | ||||
\(299\) | −2.78852e24 | −0.488273 | ||||||||
\(300\) | 1.56618e24 | + | 7.47023e23i | 0.265234 | + | 0.126509i | ||||
\(301\) | − | 8.13249e23i | − | 0.133217i | ||||||
\(302\) | 1.13505e24 | − | 5.01624e24i | 0.179864 | − | 0.794893i | ||||
\(303\) | − | 7.45378e24i | − | 1.14275i | ||||||
\(304\) | −6.14586e24 | − | 7.58939e24i | −0.911689 | − | 1.12583i | ||||
\(305\) | 3.00739e23 | 0.0431709 | ||||||||
\(306\) | 2.59294e23 | + | 5.86717e22i | 0.0360229 | + | 0.00815107i | ||||
\(307\) | 7.79220e24 | 1.04780 | 0.523898 | − | 0.851781i | \(-0.324477\pi\) | ||||
0.523898 | + | 0.851781i | \(0.324477\pi\) | |||||||
\(308\) | −1.43369e24 | + | 3.00581e24i | −0.186615 | + | 0.391251i | ||||
\(309\) | 1.14344e25i | 1.44089i | ||||||||
\(310\) | 1.14547e25 | + | 2.59192e24i | 1.39755 | + | 0.316231i | ||||
\(311\) | − | 3.44553e24i | − | 0.407054i | −0.979069 | − | 0.203527i | \(-0.934760\pi\) | ||
0.979069 | − | 0.203527i | \(-0.0652404\pi\) | |||||||
\(312\) | −5.52549e24 | + | 7.00913e24i | −0.632157 | + | 0.801896i | ||||
\(313\) | 1.01897e24 | 0.112906 | 0.0564531 | − | 0.998405i | \(-0.482021\pi\) | ||||
0.0564531 | + | 0.998405i | \(0.482021\pi\) | |||||||
\(314\) | −2.84217e24 | + | 1.25607e25i | −0.305037 | + | 1.34808i | ||||
\(315\) | −5.67234e23 | −0.0589735 | ||||||||
\(316\) | −2.25408e24 | + | 4.72582e24i | −0.227038 | + | 0.475999i | ||||
\(317\) | − | 1.18213e25i | − | 1.15365i | −0.816868 | − | 0.576825i | \(-0.804292\pi\) | ||
0.816868 | − | 0.576825i | \(-0.195708\pi\) | |||||||
\(318\) | 2.88937e24 | − | 1.27693e25i | 0.273232 | − | 1.20752i | ||||
\(319\) | − | 1.80393e24i | − | 0.165316i | ||||||
\(320\) | −9.23456e24 | + | 2.21713e24i | −0.820194 | + | 0.196921i | ||||
\(321\) | −1.33060e23 | −0.0114551 | ||||||||
\(322\) | −1.06199e25 | − | 2.40303e24i | −0.886265 | − | 0.200540i | ||||
\(323\) | 1.76471e25 | 1.42774 | ||||||||
\(324\) | −1.19214e25 | − | 5.68618e24i | −0.935144 | − | 0.446037i | ||||
\(325\) | − | 3.80249e24i | − | 0.289224i | ||||||
\(326\) | 5.78387e23 | + | 1.30874e23i | 0.0426621 | + | 0.00965336i | ||||
\(327\) | 1.75628e25i | 1.25637i | ||||||||
\(328\) | −8.97321e24 | − | 7.07383e24i | −0.622600 | − | 0.490813i | ||||
\(329\) | −3.16784e25 | −2.13209 | ||||||||
\(330\) | 6.74758e23 | − | 2.98203e24i | 0.0440563 | − | 0.194703i | ||||
\(331\) | 2.48437e25 | 1.57375 | 0.786877 | − | 0.617110i | \(-0.211697\pi\) | ||||
0.786877 | + | 0.617110i | \(0.211697\pi\) | |||||||
\(332\) | 2.64497e25 | + | 1.26157e25i | 1.62570 | + | 0.775411i | ||||
\(333\) | 1.72775e23i | 0.0103048i | ||||||||
\(334\) | −4.85770e24 | + | 2.14681e25i | −0.281168 | + | 1.24259i | ||||
\(335\) | 5.58493e24i | 0.313740i | ||||||||
\(336\) | −2.70837e25 | + | 2.19323e25i | −1.47678 | + | 1.19589i | ||||
\(337\) | −2.67940e24 | −0.141821 | −0.0709103 | − | 0.997483i | \(-0.522590\pi\) | ||||
−0.0709103 | + | 0.997483i | \(0.522590\pi\) | |||||||
\(338\) | 9.48661e22 | + | 2.14658e22i | 0.00487466 | + | 0.00110301i | ||||
\(339\) | −8.94233e24 | −0.446122 | ||||||||
\(340\) | 7.38811e24 | − | 1.54896e25i | 0.357885 | − | 0.750330i | ||||
\(341\) | 8.39089e24i | 0.394697i | ||||||||
\(342\) | 1.15913e24 | + | 2.62283e23i | 0.0529508 | + | 0.0119814i | ||||
\(343\) | − | 6.22590e25i | − | 2.76224i | ||||||
\(344\) | 1.30126e24 | + | 1.02582e24i | 0.0560763 | + | 0.0442065i | ||||
\(345\) | 9.99646e24 | 0.418461 | ||||||||
\(346\) | −1.67945e24 | + | 7.42216e24i | −0.0682977 | + | 0.301835i | ||||
\(347\) | 9.41337e24 | 0.371921 | 0.185960 | − | 0.982557i | \(-0.440460\pi\) | ||||
0.185960 | + | 0.982557i | \(0.440460\pi\) | |||||||
\(348\) | 8.12712e24 | − | 1.70390e25i | 0.311992 | − | 0.654112i | ||||
\(349\) | 3.63487e25i | 1.35592i | 0.735098 | + | 0.677960i | \(0.237136\pi\) | ||||
−0.735098 | + | 0.677960i | \(0.762864\pi\) | |||||||
\(350\) | 3.27682e24 | − | 1.44816e25i | 0.118788 | − | 0.524971i | ||||
\(351\) | 2.78968e25i | 0.982841i | ||||||||
\(352\) | −3.00110e24 | − | 6.08548e24i | −0.102767 | − | 0.208386i | ||||
\(353\) | 1.59639e25 | 0.531364 | 0.265682 | − | 0.964061i | \(-0.414403\pi\) | ||||
0.265682 | + | 0.964061i | \(0.414403\pi\) | |||||||
\(354\) | −2.86631e23 | − | 6.48573e22i | −0.00927449 | − | 0.00209858i | ||||
\(355\) | 2.14634e25 | 0.675172 | ||||||||
\(356\) | −1.96176e25 | − | 9.35703e24i | −0.599993 | − | 0.286179i | ||||
\(357\) | − | 6.29759e25i | − | 1.87280i | ||||||
\(358\) | 3.32646e24 | + | 7.52694e23i | 0.0961949 | + | 0.0217665i | ||||
\(359\) | − | 3.25820e24i | − | 0.0916292i | −0.998950 | − | 0.0458146i | \(-0.985412\pi\) | ||
0.998950 | − | 0.0458146i | \(-0.0145883\pi\) | |||||||
\(360\) | 7.15499e23 | − | 9.07617e23i | 0.0195697 | − | 0.0248243i | ||||
\(361\) | 4.12986e25 | 1.09866 | ||||||||
\(362\) | 1.33857e25 | − | 5.91567e25i | 0.346382 | − | 1.53080i | ||||
\(363\) | −3.82783e25 | −0.963577 | ||||||||
\(364\) | 6.89306e25 | + | 3.28779e25i | 1.68810 | + | 0.805174i | ||||
\(365\) | 1.71384e25i | 0.408358i | ||||||||
\(366\) | −4.96247e23 | + | 2.19312e24i | −0.0115050 | + | 0.0508453i | ||||
\(367\) | 2.00995e25i | 0.453445i | 0.973959 | + | 0.226722i | \(0.0728010\pi\) | ||||
−0.973959 | + | 0.226722i | \(0.927199\pi\) | |||||||
\(368\) | 1.72408e25 | − | 1.39616e25i | 0.378512 | − | 0.306518i | ||||
\(369\) | 1.39050e24 | 0.0297103 | ||||||||
\(370\) | 1.08782e25 | + | 2.46146e24i | 0.226224 | + | 0.0511888i | ||||
\(371\) | −1.12025e26 | −2.26765 | ||||||||
\(372\) | −3.78028e25 | + | 7.92560e25i | −0.744894 | + | 1.56172i | ||||
\(373\) | − | 5.49354e25i | − | 1.05381i | −0.849923 | − | 0.526907i | \(-0.823352\pi\) | ||
0.849923 | − | 0.526907i | \(-0.176648\pi\) | |||||||
\(374\) | 1.19589e25 | + | 2.70599e24i | 0.223344 | + | 0.0505371i | ||||
\(375\) | 6.08798e25i | 1.10703i | ||||||||
\(376\) | 3.99586e25 | − | 5.06878e25i | 0.707509 | − | 0.897481i | ||||
\(377\) | −4.13685e25 | −0.713275 | ||||||||
\(378\) | −2.40402e25 | + | 1.06244e26i | −0.403665 | + | 1.78396i | ||||
\(379\) | −8.50762e25 | −1.39129 | −0.695643 | − | 0.718388i | \(-0.744880\pi\) | ||||
−0.695643 | + | 0.718388i | \(0.744880\pi\) | |||||||
\(380\) | 3.30274e25 | − | 6.92440e25i | 0.526064 | − | 1.10293i | ||||
\(381\) | 7.80005e25i | 1.21017i | ||||||||
\(382\) | 2.39132e24 | − | 1.05682e25i | 0.0361414 | − | 0.159723i | ||||
\(383\) | 4.26912e25i | 0.628565i | 0.949330 | + | 0.314282i | \(0.101764\pi\) | ||||
−0.949330 | + | 0.314282i | \(0.898236\pi\) | |||||||
\(384\) | −9.30377e23 | − | 7.10009e25i | −0.0133459 | − | 1.01848i | ||||
\(385\) | −2.61613e25 | −0.365639 | ||||||||
\(386\) | −4.42517e25 | − | 1.00130e25i | −0.602638 | − | 0.136362i | ||||
\(387\) | −2.01644e23 | −0.00267594 | ||||||||
\(388\) | −9.44366e25 | − | 4.50435e25i | −1.22130 | − | 0.582526i | ||||
\(389\) | 1.17009e26i | 1.47477i | 0.675472 | + | 0.737386i | \(0.263940\pi\) | ||||
−0.675472 | + | 0.737386i | \(0.736060\pi\) | |||||||
\(390\) | −6.83850e25 | − | 1.54738e25i | −0.840069 | − | 0.190087i | ||||
\(391\) | 4.00889e25i | 0.480017i | ||||||||
\(392\) | 1.66902e26 | + | 1.31574e26i | 1.94806 | + | 1.53571i | ||||
\(393\) | 1.64509e26 | 1.87182 | ||||||||
\(394\) | 5.34751e24 | − | 2.36328e25i | 0.0593184 | − | 0.262152i | ||||
\(395\) | −4.11315e25 | −0.444840 | ||||||||
\(396\) | 7.45289e23 | + | 3.55481e23i | 0.00785910 | + | 0.00374856i | ||||
\(397\) | − | 1.54508e26i | − | 1.58872i | −0.607450 | − | 0.794358i | \(-0.707807\pi\) | ||
0.607450 | − | 0.794358i | \(-0.292193\pi\) | |||||||
\(398\) | −1.78530e25 | + | 7.88996e25i | −0.179011 | + | 0.791123i | ||||
\(399\) | − | 2.81524e26i | − | 2.75287i | ||||||
\(400\) | 1.90383e25 | + | 2.35099e25i | 0.181563 | + | 0.224208i | ||||
\(401\) | −6.14125e25 | −0.571232 | −0.285616 | − | 0.958344i | \(-0.592198\pi\) | ||||
−0.285616 | + | 0.958344i | \(0.592198\pi\) | |||||||
\(402\) | −4.07277e25 | − | 9.21566e24i | −0.369513 | − | 0.0836115i | ||||
\(403\) | 1.92423e26 | 1.70297 | ||||||||
\(404\) | 5.59443e25 | − | 1.17291e26i | 0.482995 | − | 1.01263i | ||||
\(405\) | − | 1.03759e26i | − | 0.873928i | ||||||
\(406\) | −1.57550e26 | − | 3.56496e25i | −1.29467 | − | 0.292951i | ||||
\(407\) | 7.96854e24i | 0.0638903i | ||||||||
\(408\) | 1.00766e26 | + | 7.94366e25i | 0.788338 | + | 0.621468i | ||||
\(409\) | 1.42600e26 | 1.08865 | 0.544323 | − | 0.838876i | \(-0.316787\pi\) | ||||
0.544323 | + | 0.838876i | \(0.316787\pi\) | |||||||
\(410\) | 1.98098e25 | − | 8.75477e25i | 0.147585 | − | 0.652238i | ||||
\(411\) | 2.08812e26 | 1.51823 | ||||||||
\(412\) | −8.58212e25 | + | 1.79930e26i | −0.609007 | + | 1.27682i | ||||
\(413\) | 2.51461e24i | 0.0174169i | ||||||||
\(414\) | −5.95829e23 | + | 2.63321e24i | −0.00402826 | + | 0.0178025i | ||||
\(415\) | 2.30207e26i | 1.51928i | ||||||||
\(416\) | −1.39555e26 | + | 6.88224e25i | −0.899107 | + | 0.443401i | ||||
\(417\) | −1.21066e24 | −0.00761487 | ||||||||
\(418\) | 5.34602e25 | + | 1.20967e25i | 0.328298 | + | 0.0742855i | ||||
\(419\) | −1.80660e26 | −1.08323 | −0.541616 | − | 0.840626i | \(-0.682187\pi\) | ||||
−0.541616 | + | 0.840626i | \(0.682187\pi\) | |||||||
\(420\) | −2.47106e26 | − | 1.17862e26i | −1.44674 | − | 0.690053i | ||||
\(421\) | 8.46001e25i | 0.483671i | 0.970317 | + | 0.241835i | \(0.0777494\pi\) | ||||
−0.970317 | + | 0.241835i | \(0.922251\pi\) | |||||||
\(422\) | −1.91161e25 | − | 4.32550e24i | −0.106727 | − | 0.0241497i | ||||
\(423\) | 7.85464e24i | 0.0428275i | ||||||||
\(424\) | 1.41306e26 | − | 1.79248e26i | 0.752494 | − | 0.954546i | ||||
\(425\) | −5.46660e25 | −0.284334 | ||||||||
\(426\) | −3.54166e25 | + | 1.56520e26i | −0.179933 | + | 0.795197i | ||||
\(427\) | 1.92402e25 | 0.0954841 | ||||||||
\(428\) | −2.09380e24 | − | 9.98682e23i | −0.0101507 | − | 0.00484161i | ||||
\(429\) | − | 5.00938e25i | − | 0.237253i | ||||||
\(430\) | −2.87274e24 | + | 1.26958e25i | −0.0132927 | + | 0.0587457i | ||||
\(431\) | − | 2.88333e26i | − | 1.30353i | −0.758420 | − | 0.651766i | \(-0.774028\pi\) | ||
0.758420 | − | 0.651766i | \(-0.225972\pi\) | |||||||
\(432\) | −1.39674e26 | − | 1.72480e26i | −0.616988 | − | 0.761905i | ||||
\(433\) | −9.66878e25 | −0.417343 | −0.208671 | − | 0.977986i | \(-0.566914\pi\) | ||||
−0.208671 | + | 0.977986i | \(0.566914\pi\) | |||||||
\(434\) | 7.32834e26 | + | 1.65822e26i | 3.09107 | + | 0.699431i | ||||
\(435\) | 1.48300e26 | 0.611293 | ||||||||
\(436\) | −1.31818e26 | + | 2.76364e26i | −0.531018 | + | 1.11331i | ||||
\(437\) | 1.79211e26i | 0.705588i | ||||||||
\(438\) | −1.24980e26 | − | 2.82799e25i | −0.480951 | − | 0.108827i | ||||
\(439\) | − | 6.67083e25i | − | 0.250920i | −0.992099 | − | 0.125460i | \(-0.959959\pi\) | ||
0.992099 | − | 0.125460i | \(-0.0400406\pi\) | |||||||
\(440\) | 3.29994e25 | − | 4.18600e25i | 0.121333 | − | 0.153912i | ||||
\(441\) | −2.58634e25 | −0.0929607 | ||||||||
\(442\) | 6.20548e25 | − | 2.74245e26i | 0.218048 | − | 0.963644i | ||||
\(443\) | −2.09664e26 | −0.720257 | −0.360129 | − | 0.932903i | \(-0.617267\pi\) | ||||
−0.360129 | + | 0.932903i | \(0.617267\pi\) | |||||||
\(444\) | −3.59000e25 | + | 7.52667e25i | −0.120577 | + | 0.252798i | ||||
\(445\) | − | 1.70743e26i | − | 0.560717i | ||||||
\(446\) | 1.18277e25 | − | 5.22712e25i | 0.0379796 | − | 0.167847i | ||||
\(447\) | 2.98668e26i | 0.937808i | ||||||||
\(448\) | −5.90795e26 | + | 1.41844e26i | −1.81408 | + | 0.435544i | ||||
\(449\) | −5.39396e26 | −1.61974 | −0.809868 | − | 0.586613i | \(-0.800461\pi\) | ||||
−0.809868 | + | 0.586613i | \(0.800461\pi\) | |||||||
\(450\) | −3.59069e24 | − | 8.12484e23i | −0.0105452 | − | 0.00238610i | ||||
\(451\) | 6.41309e25 | 0.184205 | ||||||||
\(452\) | −1.40714e26 | − | 6.71166e25i | −0.395324 | − | 0.188558i | ||||
\(453\) | 3.02080e26i | 0.830118i | ||||||||
\(454\) | −8.57246e25 | − | 1.93973e25i | −0.230434 | − | 0.0521415i | ||||
\(455\) | 5.99942e26i | 1.57759i | ||||||||
\(456\) | 4.50459e26 | + | 3.55109e26i | 1.15880 | + | 0.913510i | ||||
\(457\) | 1.14132e25 | 0.0287240 | 0.0143620 | − | 0.999897i | \(-0.495428\pi\) | ||||
0.0143620 | + | 0.999897i | \(0.495428\pi\) | |||||||
\(458\) | 7.18278e25 | − | 3.17436e26i | 0.176863 | − | 0.781631i | ||||
\(459\) | 4.01055e26 | 0.966223 | ||||||||
\(460\) | 1.57302e26 | + | 7.50284e25i | 0.370813 | + | 0.176867i | ||||
\(461\) | − | 4.34604e25i | − | 0.100250i | −0.998743 | − | 0.0501250i | \(-0.984038\pi\) | ||
0.998743 | − | 0.0501250i | \(-0.0159620\pi\) | |||||||
\(462\) | 4.31686e25 | − | 1.90780e26i | 0.0974425 | − | 0.430638i | ||||
\(463\) | − | 7.99415e26i | − | 1.76588i | −0.469482 | − | 0.882942i | \(-0.655559\pi\) | ||
0.469482 | − | 0.882942i | \(-0.344441\pi\) | |||||||
\(464\) | 2.55773e26 | − | 2.07124e26i | 0.552935 | − | 0.447765i | ||||
\(465\) | −6.89810e26 | −1.45949 | ||||||||
\(466\) | 3.28948e26 | + | 7.44328e25i | 0.681191 | + | 0.154136i | ||||
\(467\) | 2.20079e26 | 0.446077 | 0.223039 | − | 0.974810i | \(-0.428402\pi\) | ||||
0.223039 | + | 0.974810i | \(0.428402\pi\) | |||||||
\(468\) | 8.15204e24 | − | 1.70913e25i | 0.0161736 | − | 0.0339091i | ||||
\(469\) | 3.57304e26i | 0.693921i | ||||||||
\(470\) | 4.94539e26 | + | 1.11902e26i | 0.940204 | + | 0.212745i | ||||
\(471\) | − | 7.56410e26i | − | 1.40782i | ||||||
\(472\) | −4.02356e24 | − | 3.17188e24i | −0.00733146 | − | 0.00577959i | ||||
\(473\) | −9.30001e24 | −0.0165910 | ||||||||
\(474\) | 6.78709e25 | − | 2.99949e26i | 0.118550 | − | 0.523918i | ||||
\(475\) | −2.44376e26 | −0.417948 | ||||||||
\(476\) | 4.72665e26 | − | 9.90973e26i | 0.791560 | − | 1.65956i | ||||
\(477\) | 2.77765e25i | 0.0455506i | ||||||||
\(478\) | −1.27923e26 | + | 5.65341e26i | −0.205432 | + | 0.907887i | ||||
\(479\) | 1.06198e27i | 1.67017i | 0.550122 | + | 0.835084i | \(0.314581\pi\) | ||||
−0.550122 | + | 0.835084i | \(0.685419\pi\) | |||||||
\(480\) | 5.00284e26 | − | 2.46718e26i | 0.770556 | − | 0.380005i | ||||
\(481\) | 1.82738e26 | 0.275662 | ||||||||
\(482\) | −3.83393e26 | − | 8.67522e25i | −0.566466 | − | 0.128177i | ||||
\(483\) | 6.39538e26 | 0.925540 | ||||||||
\(484\) | −6.02338e26 | − | 2.87298e26i | −0.853860 | − | 0.407266i | ||||
\(485\) | − | 8.21936e26i | − | 1.14135i | ||||||
\(486\) | 5.37116e25 | + | 1.21536e25i | 0.0730644 | + | 0.0165326i | ||||
\(487\) | − | 2.80248e26i | − | 0.373468i | −0.982411 | − | 0.186734i | \(-0.940210\pi\) | ||
0.982411 | − | 0.186734i | \(-0.0597902\pi\) | |||||||
\(488\) | −2.42693e25 | + | 3.07858e25i | −0.0316853 | + | 0.0401931i | ||||
\(489\) | −3.48307e25 | −0.0445527 | ||||||||
\(490\) | −3.68465e26 | + | 1.62839e27i | −0.461780 | + | 2.04079i | ||||
\(491\) | −5.74718e26 | −0.705732 | −0.352866 | − | 0.935674i | \(-0.614793\pi\) | ||||
−0.352866 | + | 0.935674i | \(0.614793\pi\) | |||||||
\(492\) | 6.05747e26 | + | 2.88924e26i | 0.728854 | + | 0.347642i | ||||
\(493\) | 5.94730e26i | 0.701215i | ||||||||
\(494\) | 2.77407e26 | − | 1.22597e27i | 0.320514 | − | 1.41648i | ||||
\(495\) | 6.48667e24i | 0.00734463i | ||||||||
\(496\) | −1.18971e27 | + | 9.63424e26i | −1.32015 | + | 1.06906i | ||||
\(497\) | 1.37315e27 | 1.49333 | ||||||||
\(498\) | −1.67877e27 | − | 3.79863e26i | −1.78936 | − | 0.404887i | ||||
\(499\) | −5.06644e26 | −0.529295 | −0.264648 | − | 0.964345i | \(-0.585256\pi\) | ||||
−0.264648 | + | 0.964345i | \(0.585256\pi\) | |||||||
\(500\) | −4.56934e26 | + | 9.57990e26i | −0.467900 | + | 0.980982i | ||||
\(501\) | − | 1.29282e27i | − | 1.29766i | ||||||
\(502\) | −1.74184e26 | − | 3.94135e25i | −0.171385 | − | 0.0387800i | ||||
\(503\) | 2.15458e26i | 0.207818i | 0.994587 | + | 0.103909i | \(0.0331351\pi\) | ||||
−0.994587 | + | 0.103909i | \(0.966865\pi\) | |||||||
\(504\) | 4.57751e25 | − | 5.80661e25i | 0.0432837 | − | 0.0549057i | ||||
\(505\) | 1.02085e27 | 0.946342 | ||||||||
\(506\) | −2.74801e25 | + | 1.21446e26i | −0.0249754 | + | 0.110377i | ||||
\(507\) | −5.71288e24 | −0.00509068 | ||||||||
\(508\) | −5.85432e26 | + | 1.22740e27i | −0.511493 | + | 1.07238i | ||||
\(509\) | 2.11869e26i | 0.181506i | 0.995873 | + | 0.0907528i | \(0.0289273\pi\) | ||||
−0.995873 | + | 0.0907528i | \(0.971073\pi\) | |||||||
\(510\) | −2.22458e26 | + | 9.83130e26i | −0.186873 | + | 0.825865i | ||||
\(511\) | 1.09645e27i | 0.903193i | ||||||||
\(512\) | 5.18257e26 | − | 1.12424e27i | 0.418645 | − | 0.908150i | ||||
\(513\) | 1.79286e27 | 1.42027 | ||||||||
\(514\) | −2.21244e27 | − | 5.00620e26i | −1.71886 | − | 0.388935i | ||||
\(515\) | −1.56603e27 | −1.19324 | ||||||||
\(516\) | −8.78430e25 | − | 4.18986e25i | −0.0656463 | − | 0.0313114i | ||||
\(517\) | 3.62263e26i | 0.265533i | ||||||||
\(518\) | 6.95947e26 | + | 1.57475e26i | 0.500356 | + | 0.113218i | ||||
\(519\) | − | 4.46966e26i | − | 0.315211i | ||||||
\(520\) | −9.59951e26 | − | 7.56756e26i | −0.664073 | − | 0.523507i | ||||
\(521\) | −4.14659e26 | −0.281393 | −0.140697 | − | 0.990053i | \(-0.544934\pi\) | ||||
−0.140697 | + | 0.990053i | \(0.544934\pi\) | |||||||
\(522\) | −8.83929e24 | + | 3.90644e25i | −0.00588453 | + | 0.0260061i | ||||
\(523\) | −8.08616e26 | −0.528111 | −0.264056 | − | 0.964507i | \(-0.585060\pi\) | ||||
−0.264056 | + | 0.964507i | \(0.585060\pi\) | |||||||
\(524\) | 2.58867e27 | + | 1.23472e27i | 1.65869 | + | 0.791145i | ||||
\(525\) | 8.72087e26i | 0.548235i | ||||||||
\(526\) | −1.21109e26 | + | 5.35231e26i | −0.0746999 | + | 0.330129i | ||||
\(527\) | − | 2.76635e27i | − | 1.67418i | ||||||
\(528\) | 2.50809e26 | + | 3.09719e26i | 0.148938 | + | 0.183920i | ||||
\(529\) | 1.30904e27 | 0.762775 | ||||||||
\(530\) | 1.74885e27 | + | 3.95720e26i | 0.999985 | + | 0.226271i | ||||
\(531\) | 6.23495e23 | 0.000349855 | ||||||||
\(532\) | 2.11298e27 | − | 4.42999e27i | 1.16353 | − | 2.43942i | ||||
\(533\) | − | 1.47068e27i | − | 0.794777i | ||||||
\(534\) | 1.24513e27 | + | 2.81742e26i | 0.660394 | + | 0.149431i | ||||
\(535\) | − | 1.82235e25i | − | 0.00948626i | ||||||
\(536\) | −5.71713e26 | − | 4.50697e26i | −0.292099 | − | 0.230270i | ||||
\(537\) | −2.00321e26 | −0.100458 | ||||||||
\(538\) | 3.63794e26 | − | 1.60775e27i | 0.179074 | − | 0.791401i | ||||
\(539\) | −1.19284e27 | −0.576361 | ||||||||
\(540\) | 7.50595e26 | − | 1.57367e27i | 0.356015 | − | 0.746408i | ||||
\(541\) | − | 3.78702e26i | − | 0.176330i | −0.996106 | − | 0.0881648i | \(-0.971900\pi\) | ||
0.996106 | − | 0.0881648i | \(-0.0281002\pi\) | |||||||
\(542\) | 5.93346e24 | − | 2.62223e25i | 0.00271216 | − | 0.0119861i | ||||
\(543\) | 3.56245e27i | 1.59864i | ||||||||
\(544\) | 9.89418e26 | + | 2.00629e27i | 0.435904 | + | 0.883905i | ||||
\(545\) | −2.40536e27 | −1.04043 | ||||||||
\(546\) | −4.37503e27 | − | 9.89961e26i | −1.85804 | − | 0.420428i | ||||
\(547\) | 3.78029e27 | 1.57635 | 0.788173 | − | 0.615453i | \(-0.211027\pi\) | ||||
0.788173 | + | 0.615453i | \(0.211027\pi\) | |||||||
\(548\) | 3.28582e27 | + | 1.56724e27i | 1.34536 | + | 0.641697i | ||||
\(549\) | − | 4.77059e24i | − | 0.00191800i | ||||||
\(550\) | −1.65606e26 | − | 3.74724e25i | −0.0653805 | − | 0.0147940i | ||||
\(551\) | 2.65865e27i | 1.03073i | ||||||||
\(552\) | −8.06702e26 | + | 1.02331e27i | −0.307130 | + | 0.389597i | ||||
\(553\) | −2.63145e27 | −0.983884 | ||||||||
\(554\) | −1.32115e25 | + | 5.83869e25i | −0.00485126 | + | 0.0214397i | ||||
\(555\) | −6.55089e26 | −0.236249 | ||||||||
\(556\) | −1.90507e25 | − | 9.08662e24i | −0.00674781 | − | 0.00321851i | ||||
\(557\) | 1.66373e27i | 0.578803i | 0.957208 | + | 0.289401i | \(0.0934563\pi\) | ||||
−0.957208 | + | 0.289401i | \(0.906544\pi\) | |||||||
\(558\) | 4.11154e25 | − | 1.81706e26i | 0.0140496 | − | 0.0620907i | ||||
\(559\) | 2.13272e26i | 0.0715838i | ||||||||
\(560\) | −3.00378e27 | − | 3.70931e27i | −0.990350 | − | 1.22296i | ||||
\(561\) | −7.20168e26 | −0.233241 | ||||||||
\(562\) | 5.60754e27 | + | 1.26885e27i | 1.78406 | + | 0.403688i | ||||
\(563\) | −1.91718e27 | −0.599211 | −0.299606 | − | 0.954063i | \(-0.596855\pi\) | ||||
−0.299606 | + | 0.954063i | \(0.596855\pi\) | |||||||
\(564\) | −1.63207e27 | + | 3.42174e27i | −0.501128 | + | 1.05065i | ||||
\(565\) | − | 1.22472e27i | − | 0.369446i | ||||||
\(566\) | −1.26092e27 | − | 2.85316e26i | −0.373701 | − | 0.0845593i | ||||
\(567\) | − | 6.63814e27i | − | 1.93293i | ||||||
\(568\) | −1.73207e27 | + | 2.19714e27i | −0.495544 | + | 0.628601i | ||||
\(569\) | −4.08427e27 | −1.14813 | −0.574066 | − | 0.818809i | \(-0.694635\pi\) | ||||
−0.574066 | + | 0.818809i | \(0.694635\pi\) | |||||||
\(570\) | −9.94462e26 | + | 4.39493e27i | −0.274688 | + | 1.21396i | ||||
\(571\) | −5.81506e26 | −0.157831 | −0.0789157 | − | 0.996881i | \(-0.525146\pi\) | ||||
−0.0789157 | + | 0.996881i | \(0.525146\pi\) | |||||||
\(572\) | 3.75979e26 | − | 7.88264e26i | 0.100277 | − | 0.210238i | ||||
\(573\) | 6.36423e26i | 0.166801i | ||||||||
\(574\) | 1.26736e27 | − | 5.60099e27i | 0.326424 | − | 1.44260i | ||||
\(575\) | − | 5.55150e26i | − | 0.140518i | ||||||
\(576\) | 3.51702e25 | + | 1.46487e26i | 0.00874883 | + | 0.0364397i | ||||
\(577\) | 2.69062e27 | 0.657801 | 0.328901 | − | 0.944365i | \(-0.393322\pi\) | ||||
0.328901 | + | 0.944365i | \(0.393322\pi\) | |||||||
\(578\) | 1.16497e26 | + | 2.63603e25i | 0.0279921 | + | 0.00633392i | ||||
\(579\) | 2.66486e27 | 0.629344 | ||||||||
\(580\) | 2.33362e27 | + | 1.11307e27i | 0.541688 | + | 0.258370i | ||||
\(581\) | 1.47278e28i | 3.36030i | ||||||||
\(582\) | 5.99391e27 | + | 1.35627e27i | 1.34425 | + | 0.304170i | ||||
\(583\) | 1.28108e27i | 0.282416i | ||||||||
\(584\) | −1.75440e27 | − | 1.38304e27i | −0.380190 | − | 0.299715i | ||||
\(585\) | 1.48755e26 | 0.0316893 | ||||||||
\(586\) | 9.45408e26 | − | 4.17814e27i | 0.197990 | − | 0.874997i | ||||
\(587\) | −8.87574e26 | −0.182736 | −0.0913678 | − | 0.995817i | \(-0.529124\pi\) | ||||
−0.0913678 | + | 0.995817i | \(0.529124\pi\) | |||||||
\(588\) | −1.12669e28 | − | 5.37400e27i | −2.28051 | − | 1.08774i | ||||
\(589\) | − | 1.23666e28i | − | 2.46091i | ||||||
\(590\) | 8.88268e24 | − | 3.92561e25i | 0.00173790 | − | 0.00768046i | ||||
\(591\) | 1.42318e27i | 0.273769i | ||||||||
\(592\) | −1.12983e27 | + | 9.14930e26i | −0.213695 | + | 0.173050i | ||||
\(593\) | 2.28118e27 | 0.424241 | 0.212120 | − | 0.977244i | \(-0.431963\pi\) | ||||
0.212120 | + | 0.977244i | \(0.431963\pi\) | |||||||
\(594\) | 1.21496e27 | + | 2.74915e26i | 0.222176 | + | 0.0502729i | ||||
\(595\) | 8.62500e27 | 1.55092 | ||||||||
\(596\) | −2.24165e27 | + | 4.69977e27i | −0.396375 | + | 0.831025i | ||||
\(597\) | − | 4.75137e27i | − | 0.826182i | ||||||
\(598\) | 2.78504e27 | + | 6.30185e26i | 0.476233 | + | 0.107760i | ||||
\(599\) | 4.01414e27i | 0.675032i | 0.941320 | + | 0.337516i | \(0.109587\pi\) | ||||
−0.941320 | + | 0.337516i | \(0.890413\pi\) | |||||||
\(600\) | −1.39540e27 | − | 1.10003e27i | −0.230774 | − | 0.181926i | ||||
\(601\) | −9.03918e27 | −1.47023 | −0.735114 | − | 0.677944i | \(-0.762871\pi\) | ||||
−0.735114 | + | 0.677944i | \(0.762871\pi\) | |||||||
\(602\) | −1.83788e26 | + | 8.12234e26i | −0.0294003 | + | 0.129932i | ||||
\(603\) | 8.85933e25 | 0.0139389 | ||||||||
\(604\) | −2.26726e27 | + | 4.75346e27i | −0.350859 | + | 0.735597i | ||||
\(605\) | − | 5.24249e27i | − | 0.797965i | ||||||
\(606\) | −1.68450e27 | + | 7.44447e27i | −0.252199 | + | 1.11457i | ||||
\(607\) | − | 9.64789e27i | − | 1.42084i | −0.703777 | − | 0.710421i | \(-0.748505\pi\) | ||
0.703777 | − | 0.710421i | \(-0.251495\pi\) | |||||||
\(608\) | 4.42304e27 | + | 8.96883e27i | 0.640745 | + | 1.29927i | ||||
\(609\) | 9.48773e27 | 1.35204 | ||||||||
\(610\) | −3.00363e26 | − | 6.79646e25i | −0.0421064 | − | 0.00952763i | ||||
\(611\) | 8.30755e27 | 1.14567 | ||||||||
\(612\) | −2.45711e26 | − | 1.17197e26i | −0.0333357 | − | 0.0159002i | ||||
\(613\) | 3.72539e26i | 0.0497241i | 0.999691 | + | 0.0248620i | \(0.00791465\pi\) | ||||
−0.999691 | + | 0.0248620i | \(0.992085\pi\) | |||||||
\(614\) | −7.78247e27 | − | 1.76098e27i | −1.02196 | − | 0.231244i | ||||
\(615\) | 5.27216e27i | 0.681142i | ||||||||
\(616\) | 2.11119e27 | − | 2.67806e27i | 0.268361 | − | 0.340418i | ||||
\(617\) | 4.15904e27 | 0.520165 | 0.260083 | − | 0.965586i | \(-0.416250\pi\) | ||||
0.260083 | + | 0.965586i | \(0.416250\pi\) | |||||||
\(618\) | 2.58410e27 | − | 1.14202e28i | 0.317998 | − | 1.40536i | ||||
\(619\) | 1.08544e28 | 1.31431 | 0.657154 | − | 0.753756i | \(-0.271760\pi\) | ||||
0.657154 | + | 0.753756i | \(0.271760\pi\) | |||||||
\(620\) | −1.08547e28 | − | 5.17737e27i | −1.29330 | − | 0.616868i | ||||
\(621\) | 4.07283e27i | 0.477508i | ||||||||
\(622\) | −7.78662e26 | + | 3.44122e27i | −0.0898349 | + | 0.397017i | ||||
\(623\) | − | 1.09236e28i | − | 1.24018i | ||||||
\(624\) | 7.10260e27 | − | 5.75166e27i | 0.793545 | − | 0.642610i | ||||
\(625\) | −5.71401e27 | −0.628262 | ||||||||
\(626\) | −1.01770e27 | − | 2.30279e26i | −0.110122 | − | 0.0249179i | ||||
\(627\) | −3.21940e27 | −0.342846 | ||||||||
\(628\) | 5.67723e27 | − | 1.19027e28i | 0.595032 | − | 1.24752i | ||||
\(629\) | − | 2.62711e27i | − | 0.271002i | ||||||
\(630\) | 5.66526e26 | + | 1.28191e26i | 0.0575194 | + | 0.0130152i | ||||
\(631\) | 3.07267e27i | 0.307060i | 0.988144 | + | 0.153530i | \(0.0490641\pi\) | ||||
−0.988144 | + | 0.153530i | \(0.950936\pi\) | |||||||
\(632\) | 3.31926e27 | − | 4.21051e27i | 0.326491 | − | 0.414156i | ||||
\(633\) | 1.15118e27 | 0.111457 | ||||||||
\(634\) | −2.67153e27 | + | 1.18066e28i | −0.254605 | + | 1.12520i | ||||
\(635\) | −1.06827e28 | −1.00218 | ||||||||
\(636\) | −5.77153e27 | + | 1.21004e28i | −0.532991 | + | 1.11745i | ||||
\(637\) | 2.73547e28i | 2.48678i | ||||||||
\(638\) | −4.07675e26 | + | 1.80168e27i | −0.0364844 | + | 0.161239i | ||||
\(639\) | − | 3.40472e26i | − | 0.0299966i | ||||||
\(640\) | 9.72409e27 | − | 1.27422e26i | 0.843430 | − | 0.0110521i | ||||
\(641\) | −1.90529e28 | −1.62697 | −0.813485 | − | 0.581586i | \(-0.802433\pi\) | ||||
−0.813485 | + | 0.581586i | \(0.802433\pi\) | |||||||
\(642\) | 1.32894e26 | + | 3.00706e25i | 0.0111726 | + | 0.00252808i | ||||
\(643\) | −1.05796e28 | −0.875711 | −0.437856 | − | 0.899045i | \(-0.644262\pi\) | ||||
−0.437856 | + | 0.899045i | \(0.644262\pi\) | |||||||
\(644\) | 1.00636e28 | + | 4.80005e27i | 0.820154 | + | 0.391190i | ||||
\(645\) | − | 7.64548e26i | − | 0.0613490i | ||||||
\(646\) | −1.76250e28 | − | 3.98810e27i | −1.39253 | − | 0.315095i | ||||
\(647\) | 3.30511e27i | 0.257124i | 0.991701 | + | 0.128562i | \(0.0410361\pi\) | ||||
−0.991701 | + | 0.128562i | \(0.958964\pi\) | |||||||
\(648\) | 1.06215e28 | + | 8.37323e27i | 0.813648 | + | 0.641421i | ||||
\(649\) | 2.87561e25 | 0.00216912 | ||||||||
\(650\) | −8.59333e26 | + | 3.79774e27i | −0.0638304 | + | 0.282092i | ||||
\(651\) | −4.41316e28 | −3.22805 | ||||||||
\(652\) | −5.48087e26 | − | 2.61422e26i | −0.0394797 | − | 0.0188307i | ||||
\(653\) | − | 1.75915e28i | − | 1.24787i | −0.781475 | − | 0.623937i | \(-0.785532\pi\) | ||
0.781475 | − | 0.623937i | \(-0.214468\pi\) | |||||||
\(654\) | 3.96906e27 | − | 1.75409e28i | 0.277275 | − | 1.22539i | ||||
\(655\) | 2.25307e28i | 1.55011i | ||||||||
\(656\) | 7.36337e27 | + | 9.09287e27i | 0.498928 | + | 0.616116i | ||||
\(657\) | 2.71864e26 | 0.0181426 | ||||||||
\(658\) | 3.16389e28 | + | 7.15909e27i | 2.07952 | + | 0.470542i | ||||
\(659\) | 1.99713e28 | 1.29287 | 0.646433 | − | 0.762971i | \(-0.276260\pi\) | ||||
0.646433 | + | 0.762971i | \(0.276260\pi\) | |||||||
\(660\) | −1.34783e27 | + | 2.82581e27i | −0.0859401 | + | 0.180179i | ||||
\(661\) | − | 9.97708e27i | − | 0.626598i | −0.949655 | − | 0.313299i | \(-0.898566\pi\) | ||
0.949655 | − | 0.313299i | \(-0.101434\pi\) | |||||||
\(662\) | −2.48127e28 | − | 5.61449e27i | −1.53495 | − | 0.347320i | ||||
\(663\) | 1.65152e28i | 1.00635i | ||||||||
\(664\) | −2.35656e28 | − | 1.85774e28i | −1.41448 | − | 1.11508i | ||||
\(665\) | 3.85567e28 | 2.27973 | ||||||||
\(666\) | 3.90459e25 | − | 1.72560e26i | 0.00227422 | − | 0.0100507i | ||||
\(667\) | −6.03966e27 | −0.346541 | ||||||||
\(668\) | 9.70326e27 | − | 2.03435e28i | 0.548470 | − | 1.14990i | ||||
\(669\) | 3.14780e27i | 0.175285i | ||||||||
\(670\) | 1.26215e27 | − | 5.57796e27i | 0.0692410 | − | 0.306004i | ||||
\(671\) | − | 2.20024e26i | − | 0.0118917i | ||||||
\(672\) | 3.20064e28 | − | 1.57842e28i | 1.70429 | − | 0.840484i | ||||
\(673\) | 1.56242e28 | 0.819683 | 0.409841 | − | 0.912157i | \(-0.365584\pi\) | ||||
0.409841 | + | 0.912157i | \(0.365584\pi\) | |||||||
\(674\) | 2.67606e27 | + | 6.05525e26i | 0.138324 | + | 0.0312992i | ||||
\(675\) | −5.55380e27 | −0.282847 | ||||||||
\(676\) | −8.98965e25 | − | 4.28780e25i | −0.00451103 | − | 0.00215163i | ||||
\(677\) | − | 2.96609e28i | − | 1.46655i | −0.679932 | − | 0.733275i | \(-0.737991\pi\) | ||
0.679932 | − | 0.733275i | \(-0.262009\pi\) | |||||||
\(678\) | 8.93116e27 | + | 2.02090e27i | 0.435122 | + | 0.0984571i | ||||
\(679\) | − | 5.25846e28i | − | 2.52441i | ||||||
\(680\) | −1.08794e28 | + | 1.38006e28i | −0.514655 | + | 0.652845i | ||||
\(681\) | 5.16238e27 | 0.240646 | ||||||||
\(682\) | 1.89628e27 | − | 8.38041e27i | 0.0871080 | − | 0.384965i | ||||
\(683\) | −8.85063e27 | −0.400652 | −0.200326 | − | 0.979729i | \(-0.564200\pi\) | ||||
−0.200326 | + | 0.979729i | \(0.564200\pi\) | |||||||
\(684\) | −1.09841e27 | − | 5.23911e26i | −0.0490009 | − | 0.0233720i | ||||
\(685\) | 2.85983e28i | 1.25729i | ||||||||
\(686\) | −1.40701e28 | + | 6.21813e28i | −0.609614 | + | 2.69413i | ||||
\(687\) | 1.91162e28i | 0.816269i | ||||||||
\(688\) | −1.06781e27 | − | 1.31861e27i | −0.0449374 | − | 0.0554923i | ||||
\(689\) | 2.93782e28 | 1.21852 | ||||||||
\(690\) | −9.98397e27 | − | 2.25912e27i | −0.408143 | − | 0.0923525i | ||||
\(691\) | 2.99742e27 | 0.120772 | 0.0603862 | − | 0.998175i | \(-0.480767\pi\) | ||||
0.0603862 | + | 0.998175i | \(0.480767\pi\) | |||||||
\(692\) | 3.35470e27 | − | 7.03335e27i | 0.133227 | − | 0.279320i | ||||
\(693\) | 4.14995e26i | 0.0162446i | ||||||||
\(694\) | −9.40161e27 | − | 2.12735e27i | −0.362750 | − | 0.0820813i | ||||
\(695\) | − | 1.65809e26i | − | 0.00630609i | ||||||
\(696\) | −1.19677e28 | + | 1.51811e28i | −0.448659 | + | 0.569128i | ||||
\(697\) | −2.11430e28 | −0.781339 | ||||||||
\(698\) | 8.21452e27 | − | 3.63033e28i | 0.299246 | − | 1.32249i | ||||
\(699\) | −1.98094e28 | −0.711378 | ||||||||
\(700\) | −6.54545e27 | + | 1.37229e28i | −0.231718 | + | 0.485811i | ||||
\(701\) | 3.99234e26i | 0.0139331i | 0.999976 | + | 0.00696655i | \(0.00221754\pi\) | ||||
−0.999976 | + | 0.00696655i | \(0.997782\pi\) | |||||||
\(702\) | 6.30446e27 | − | 2.78620e28i | 0.216909 | − | 0.958607i | ||||
\(703\) | − | 1.17441e28i | − | 0.398351i | ||||||
\(704\) | 1.62208e27 | + | 6.75611e27i | 0.0542432 | + | 0.225928i | ||||
\(705\) | −2.97814e28 | −0.981869 | ||||||||
\(706\) | −1.59440e28 | − | 3.60772e27i | −0.518262 | − | 0.117270i | ||||
\(707\) | 6.53104e28 | 2.09309 | ||||||||
\(708\) | 2.71615e26 | + | 1.29553e26i | 0.00858265 | + | 0.00409368i | ||||
\(709\) | 2.52620e28i | 0.787055i | 0.919313 | + | 0.393528i | \(0.128745\pi\) | ||||
−0.919313 | + | 0.393528i | \(0.871255\pi\) | |||||||
\(710\) | −2.14366e28 | − | 4.85056e27i | −0.658524 | − | 0.149008i | ||||
\(711\) | 6.52466e26i | 0.0197634i | ||||||||
\(712\) | 1.74785e28 | + | 1.37788e28i | 0.522040 | + | 0.411539i | ||||
\(713\) | 2.80931e28 | 0.827379 | ||||||||
\(714\) | −1.42321e28 | + | 6.28972e28i | −0.413319 | + | 1.82662i | ||||
\(715\) | 6.86071e27 | 0.196476 | ||||||||
\(716\) | −3.15220e27 | − | 1.50351e27i | −0.0890192 | − | 0.0424596i | ||||
\(717\) | − | 3.40451e28i | − | 0.948120i | ||||||
\(718\) | −7.36329e26 | + | 3.25413e27i | −0.0202222 | + | 0.0893699i | ||||
\(719\) | 2.54621e28i | 0.689612i | 0.938674 | + | 0.344806i | \(0.112055\pi\) | ||||
−0.938674 | + | 0.344806i | \(0.887945\pi\) | |||||||
\(720\) | −9.19720e26 | + | 7.44786e26i | −0.0245658 | + | 0.0198933i | ||||
\(721\) | −1.00189e29 | −2.63917 | ||||||||
\(722\) | −4.12470e28 | − | 9.33316e27i | −1.07157 | − | 0.242469i | ||||
\(723\) | 2.30881e28 | 0.591569 | ||||||||
\(724\) | −2.67379e28 | + | 5.60578e28i | −0.675682 | + | 1.41661i | ||||
\(725\) | − | 8.23580e27i | − | 0.205270i | ||||||
\(726\) | 3.82305e28 | + | 8.65060e27i | 0.939818 | + | 0.212657i | ||||
\(727\) | 4.09725e28i | 0.993455i | 0.867907 | + | 0.496728i | \(0.165465\pi\) | ||||
−0.867907 | + | 0.496728i | \(0.834535\pi\) | |||||||
\(728\) | −6.14143e28 | − | 4.84146e28i | −1.46878 | − | 1.15788i | ||||
\(729\) | 4.06857e28 | 0.959769 | ||||||||
\(730\) | 3.87314e27 | − | 1.71170e28i | 0.0901227 | − | 0.398289i | ||||
\(731\) | 3.06608e27 | 0.0703735 | ||||||||
\(732\) | 9.91255e26 | − | 2.07823e27i | 0.0224427 | − | 0.0470525i | ||||
\(733\) | − | 1.43241e28i | − | 0.319911i | −0.987124 | − | 0.159955i | \(-0.948865\pi\) | ||
0.987124 | − | 0.159955i | \(-0.0511350\pi\) | |||||||
\(734\) | 4.54233e27 | − | 2.00744e28i | 0.100073 | − | 0.442264i | ||||
\(735\) | − | 9.80626e28i | − | 2.13123i | ||||||
\(736\) | −2.03745e28 | + | 1.00478e28i | −0.436826 | + | 0.215424i | ||||
\(737\) | 4.08600e27 | 0.0864217 | ||||||||
\(738\) | −1.38876e27 | − | 3.14242e26i | −0.0289777 | − | 0.00655693i | ||||
\(739\) | 7.87579e28 | 1.62125 | 0.810624 | − | 0.585567i | \(-0.199128\pi\) | ||||
0.810624 | + | 0.585567i | \(0.199128\pi\) | |||||||
\(740\) | −1.03083e28 | − | 4.91677e27i | −0.209349 | − | 0.0998533i | ||||
\(741\) | 7.38286e28i | 1.47925i | ||||||||
\(742\) | 1.11885e29 | + | 2.53168e28i | 2.21174 | + | 0.500461i | ||||
\(743\) | − | 5.32560e28i | − | 1.03868i | −0.854569 | − | 0.519338i | \(-0.826178\pi\) | ||
0.854569 | − | 0.519338i | \(-0.173822\pi\) | |||||||
\(744\) | 5.56668e28 | − | 7.06138e28i | 1.07119 | − | 1.35882i | ||||
\(745\) | −4.09048e28 | −0.776625 | ||||||||
\(746\) | −1.24150e28 | + | 5.48668e28i | −0.232572 | + | 1.02783i | ||||
\(747\) | 3.65175e27 | 0.0674987 | ||||||||
\(748\) | −1.13324e28 | − | 5.40522e27i | −0.206683 | − | 0.0985819i | ||||
\(749\) | − | 1.16588e27i | − | 0.0209814i | ||||||
\(750\) | 1.37584e28 | − | 6.08038e28i | 0.244318 | − | 1.07974i | ||||
\(751\) | 9.40055e28i | 1.64723i | 0.567151 | + | 0.823614i | \(0.308046\pi\) | ||||
−0.567151 | + | 0.823614i | \(0.691954\pi\) | |||||||
\(752\) | −5.13638e28 | + | 4.15942e28i | −0.888134 | + | 0.719208i | ||||
\(753\) | 1.04895e28 | 0.178979 | ||||||||
\(754\) | 4.13169e28 | + | 9.34897e27i | 0.695687 | + | 0.157417i | ||||
\(755\) | −4.13720e28 | −0.687444 | ||||||||
\(756\) | 4.80204e28 | − | 1.00678e29i | 0.787423 | − | 1.65088i | ||||
\(757\) | − | 5.34938e28i | − | 0.865654i | −0.901477 | − | 0.432827i | \(-0.857516\pi\) | ||
0.901477 | − | 0.432827i | \(-0.142484\pi\) | |||||||
\(758\) | 8.49700e28 | + | 1.92266e28i | 1.35698 | + | 0.307051i | ||||
\(759\) | − | 7.31352e27i | − | 0.115268i | ||||||
\(760\) | −4.86347e28 | + | 6.16936e28i | −0.756503 | + | 0.959631i | ||||
\(761\) | −2.22827e28 | −0.342074 | −0.171037 | − | 0.985265i | \(-0.554712\pi\) | ||||
−0.171037 | + | 0.985265i | \(0.554712\pi\) | |||||||
\(762\) | 1.76275e28 | − | 7.79031e28i | 0.267080 | − | 1.18033i | ||||
\(763\) | −1.53886e29 | −2.30120 | ||||||||
\(764\) | −4.77667e27 | + | 1.00146e28i | −0.0705004 | + | 0.147809i | ||||
\(765\) | − | 2.13856e27i | − | 0.0311535i | ||||||
\(766\) | 9.64787e27 | − | 4.26378e28i | 0.138722 | − | 0.613066i | ||||
\(767\) | − | 6.59447e26i | − | 0.00935893i | ||||||
\(768\) | −1.51164e28 | + | 7.11225e28i | −0.211757 | + | 0.996310i | ||||
\(769\) | −8.54432e28 | −1.18145 | −0.590723 | − | 0.806874i | \(-0.701157\pi\) | ||||
−0.590723 | + | 0.806874i | \(0.701157\pi\) | |||||||
\(770\) | 2.61286e28 | + | 5.91226e27i | 0.356623 | + | 0.0806949i | ||||
\(771\) | 1.33234e29 | 1.79503 | ||||||||
\(772\) | 4.19335e28 | + | 2.00011e28i | 0.557684 | + | 0.265999i | ||||
\(773\) | 1.08746e29i | 1.42764i | 0.700330 | + | 0.713819i | \(0.253036\pi\) | ||||
−0.700330 | + | 0.713819i | \(0.746964\pi\) | |||||||
\(774\) | 2.01393e26 | + | 4.55701e25i | 0.00260996 | + | 0.000590569i | ||||
\(775\) | 3.83083e28i | 0.490090i | ||||||||
\(776\) | 8.41392e28 | + | 6.63292e28i | 1.06263 | + | 0.837698i | ||||
\(777\) | −4.19103e28 | −0.522529 | ||||||||
\(778\) | 2.64432e28 | − | 1.16863e29i | 0.325476 | − | 1.43841i | ||||
\(779\) | −9.45166e28 | −1.14851 | ||||||||
\(780\) | 6.48027e28 | + | 3.09090e28i | 0.777404 | + | 0.370799i | ||||
\(781\) | − | 1.57028e28i | − | 0.185981i | ||||||
\(782\) | 9.05979e27 | − | 4.00388e28i | 0.105938 | − | 0.468181i | ||||
\(783\) | 6.04216e28i | 0.697549i | ||||||||
\(784\) | −1.36959e29 | − | 1.69128e29i | −1.56110 | − | 1.92777i | ||||
\(785\) | 1.03596e29 | 1.16586 | ||||||||
\(786\) | −1.64304e29 | − | 3.71778e28i | −1.82567 | − | 0.413103i | ||||
\(787\) | 1.07439e29 | 1.17873 | 0.589364 | − | 0.807867i | \(-0.299378\pi\) | ||||
0.589364 | + | 0.807867i | \(0.299378\pi\) | |||||||
\(788\) | −1.06817e28 | + | 2.23948e28i | −0.115712 | + | 0.242597i | ||||
\(789\) | − | 3.22319e28i | − | 0.344759i | ||||||
\(790\) | 4.10801e28 | + | 9.29540e27i | 0.433871 | + | 0.0981742i | ||||
\(791\) | − | 7.83530e28i | − | 0.817130i | ||||||
\(792\) | −6.64022e26 | − | 5.23467e26i | −0.00683803 | − | 0.00539060i | ||||
\(793\) | −5.04567e27 | −0.0513083 | ||||||||
\(794\) | −3.49177e28 | + | 1.54315e29i | −0.350623 | + | 1.54954i | ||||
\(795\) | −1.05316e29 | −1.04430 | ||||||||
\(796\) | 3.56614e28 | − | 7.47664e28i | 0.349195 | − | 0.732109i | ||||
\(797\) | − | 7.13483e28i | − | 0.689923i | −0.938617 | − | 0.344961i | \(-0.887892\pi\) | ||
0.938617 | − | 0.344961i | \(-0.112108\pi\) | |||||||
\(798\) | −6.36222e28 | + | 2.81172e29i | −0.607547 | + | 2.68499i | ||||
\(799\) | − | 1.19433e29i | − | 1.12630i | ||||||
\(800\) | −1.37014e28 | − | 2.77831e28i | −0.127604 | − | 0.258750i | ||||
\(801\) | −2.70849e27 | −0.0249116 | ||||||||
\(802\) | 6.13358e28 | + | 1.38787e28i | 0.557147 | + | 0.126068i | ||||
\(803\) | 1.25386e28 | 0.112485 | ||||||||
\(804\) | 3.85942e28 | + | 1.84083e28i | 0.341949 | + | 0.163100i | ||||
\(805\) | 8.75894e28i | 0.766466i | ||||||||
\(806\) | −1.92183e29 | − | 4.34862e28i | −1.66098 | − | 0.375838i | ||||
\(807\) | 9.68197e28i | 0.826472i | ||||||||
\(808\) | −8.23813e28 | + | 1.04501e29i | −0.694569 | + | 0.881066i | ||||
\(809\) | 6.54964e28 | 0.545422 | 0.272711 | − | 0.962096i | \(-0.412080\pi\) | ||||
0.272711 | + | 0.962096i | \(0.412080\pi\) | |||||||
\(810\) | −2.34487e28 | + | 1.03629e29i | −0.192872 | + | 0.852379i | ||||
\(811\) | 9.88172e28 | 0.802831 | 0.401415 | − | 0.915896i | \(-0.368518\pi\) | ||||
0.401415 | + | 0.915896i | \(0.368518\pi\) | |||||||
\(812\) | 1.49297e29 | + | 7.12101e28i | 1.19809 | + | 0.571454i | ||||
\(813\) | 1.57912e27i | 0.0125173i | ||||||||
\(814\) | 1.80083e27 | − | 7.95859e27i | 0.0141003 | − | 0.0623149i | ||||
\(815\) | − | 4.77032e27i | − | 0.0368953i | ||||||
\(816\) | −8.26881e28 | − | 1.02110e29i | −0.631744 | − | 0.780127i | ||||
\(817\) | 1.37064e28 | 0.103444 | ||||||||
\(818\) | −1.42422e29 | − | 3.22265e28i | −1.06180 | − | 0.240259i | ||||
\(819\) | 9.51683e27 | 0.0700895 | ||||||||
\(820\) | −3.95702e28 | + | 8.29615e28i | −0.287892 | + | 0.603584i | ||||
\(821\) | − | 9.44155e28i | − | 0.678596i | −0.940679 | − | 0.339298i | \(-0.889810\pi\) | ||
0.940679 | − | 0.339298i | \(-0.110190\pi\) | |||||||
\(822\) | −2.08551e29 | − | 4.71899e28i | −1.48079 | − | 0.335067i | ||||
\(823\) | 8.48654e28i | 0.595295i | 0.954676 | + | 0.297647i | \(0.0962020\pi\) | ||||
−0.954676 | + | 0.297647i | \(0.903798\pi\) | |||||||
\(824\) | 1.26377e29 | − | 1.60310e29i | 0.875780 | − | 1.11093i | ||||
\(825\) | 9.97285e27 | 0.0682779 | ||||||||
\(826\) | 5.68283e26 | − | 2.51147e27i | 0.00384383 | − | 0.0169874i | ||||
\(827\) | −1.42055e29 | −0.949296 | −0.474648 | − | 0.880176i | \(-0.657425\pi\) | ||||
−0.474648 | + | 0.880176i | \(0.657425\pi\) | |||||||
\(828\) | 1.19017e27 | − | 2.49526e27i | 0.00785788 | − | 0.0164745i | ||||
\(829\) | 5.53248e28i | 0.360890i | 0.983585 | + | 0.180445i | \(0.0577537\pi\) | ||||
−0.983585 | + | 0.180445i | \(0.942246\pi\) | |||||||
\(830\) | 5.20250e28 | − | 2.29919e29i | 0.335298 | − | 1.48182i | ||||
\(831\) | − | 3.51609e27i | − | 0.0223898i | ||||||
\(832\) | 1.54934e29 | − | 3.71981e28i | 0.974794 | − | 0.234039i | ||||
\(833\) | 3.93262e29 | 2.44473 | ||||||||
\(834\) | 1.20915e27 | + | 2.73600e26i | 0.00742711 | + | 0.00168057i | ||||
\(835\) | 1.77061e29 | 1.07463 | ||||||||
\(836\) | −5.06597e28 | − | 2.41632e28i | −0.303808 | − | 0.144908i | ||||
\(837\) | − | 2.81048e29i | − | 1.66543i | ||||||
\(838\) | 1.80434e29 | + | 4.08277e28i | 1.05652 | + | 0.239064i | ||||
\(839\) | 6.58676e28i | 0.381111i | 0.981676 | + | 0.190556i | \(0.0610290\pi\) | ||||
−0.981676 | + | 0.190556i | \(0.938971\pi\) | |||||||
\(840\) | 2.20161e29 | + | 1.73559e29i | 1.25878 | + | 0.992328i | ||||
\(841\) | 8.73945e28 | 0.493770 | ||||||||
\(842\) | 1.91190e28 | − | 8.44944e28i | 0.106744 | − | 0.471745i | ||||
\(843\) | −3.37689e29 | −1.86312 | ||||||||
\(844\) | 1.81147e28 | + | 8.64020e27i | 0.0987660 | + | 0.0471085i | ||||
\(845\) | − | 7.82420e26i | − | 0.00421573i | ||||||
\(846\) | 1.77509e27 | − | 7.84483e27i | 0.00945184 | − | 0.0417715i | ||||
\(847\) | − | 3.35396e29i | − | 1.76492i | ||||||
\(848\) | −1.81639e29 | + | 1.47090e29i | −0.944604 | + | 0.764937i | ||||
\(849\) | 7.59335e28 | 0.390262 | ||||||||
\(850\) | 5.45978e28 | + | 1.23541e28i | 0.277323 | + | 0.0627512i | ||||
\(851\) | 2.66791e28 | 0.133929 | ||||||||
\(852\) | 7.07447e28 | − | 1.48321e29i | 0.350993 | − | 0.735879i | ||||
\(853\) | − | 9.95133e28i | − | 0.487968i | −0.969779 | − | 0.243984i | \(-0.921546\pi\) | ||
0.969779 | − | 0.243984i | \(-0.0784544\pi\) | |||||||
\(854\) | −1.92162e28 | − | 4.34814e27i | −0.0931297 | − | 0.0210729i | ||||
\(855\) | − | 9.56011e27i | − | 0.0457933i | ||||||
\(856\) | 1.86549e27 | + | 1.47062e27i | 0.00883193 | + | 0.00696245i | ||||
\(857\) | −1.09474e29 | −0.512275 | −0.256138 | − | 0.966640i | \(-0.582450\pi\) | ||||
−0.256138 | + | 0.966640i | \(0.582450\pi\) | |||||||
\(858\) | −1.13208e28 | + | 5.00312e28i | −0.0523606 | + | 0.231403i | ||||
\(859\) | −1.09959e29 | −0.502690 | −0.251345 | − | 0.967898i | \(-0.580873\pi\) | ||||
−0.251345 | + | 0.967898i | \(0.580873\pi\) | |||||||
\(860\) | 5.73831e27 | − | 1.20307e28i | 0.0259298 | − | 0.0543635i | ||||
\(861\) | 3.37295e29i | 1.50653i | ||||||||
\(862\) | −6.51611e28 | + | 2.87973e29i | −0.287684 | + | 1.27139i | ||||
\(863\) | 2.72249e29i | 1.18811i | 0.804423 | + | 0.594057i | \(0.202475\pi\) | ||||
−0.804423 | + | 0.594057i | \(0.797525\pi\) | |||||||
\(864\) | 1.00520e29 | + | 2.03830e29i | 0.433625 | + | 0.879285i | ||||
\(865\) | 6.12153e28 | 0.261035 | ||||||||
\(866\) | 9.65670e28 | + | 2.18507e28i | 0.407052 | + | 0.0921057i | ||||
\(867\) | −7.01550e27 | −0.0292326 | ||||||||
\(868\) | −6.94444e29 | − | 3.31230e29i | −2.86049 | − | 1.36437i | ||||
\(869\) | 3.00922e28i | 0.122534i | ||||||||
\(870\) | −1.48115e29 | − | 3.35147e28i | −0.596220 | − | 0.134910i | ||||
\(871\) | − | 9.37017e28i | − | 0.372877i | ||||||
\(872\) | 1.94109e29 | − | 2.46229e29i | 0.763628 | − | 0.968668i | ||||
\(873\) | −1.30383e28 | −0.0507082 | ||||||||
\(874\) | 4.05004e28 | − | 1.78987e29i | 0.155720 | − | 0.688190i | ||||
\(875\) | −5.33432e29 | −2.02768 | ||||||||
\(876\) | 1.18433e29 | + | 5.64892e28i | 0.445074 | + | 0.212287i | ||||
\(877\) | 4.13929e29i | 1.53791i | 0.639305 | + | 0.768953i | \(0.279222\pi\) | ||||
−0.639305 | + | 0.768953i | \(0.720778\pi\) | |||||||
\(878\) | −1.50756e28 | + | 6.66250e28i | −0.0553769 | + | 0.244733i | ||||
\(879\) | 2.51609e29i | 0.913772i | ||||||||
\(880\) | −4.24182e28 | + | 3.43501e28i | −0.152309 | + | 0.123339i | ||||
\(881\) | −2.41396e29 | −0.856979 | −0.428489 | − | 0.903547i | \(-0.640954\pi\) | ||||
−0.428489 | + | 0.903547i | \(0.640954\pi\) | |||||||
\(882\) | 2.58311e28 | + | 5.84492e27i | 0.0906685 | + | 0.0205160i | ||||
\(883\) | 4.40744e29 | 1.52960 | 0.764802 | − | 0.644265i | \(-0.222837\pi\) | ||||
0.764802 | + | 0.644265i | \(0.222837\pi\) | |||||||
\(884\) | −1.23955e29 | + | 2.59879e29i | −0.425344 | + | 0.891761i | ||||
\(885\) | 2.36402e27i | 0.00802082i | ||||||||
\(886\) | 2.09403e29 | + | 4.73826e28i | 0.702498 | + | 0.158958i | ||||
\(887\) | 2.33752e29i | 0.775387i | 0.921788 | + | 0.387693i | \(0.126728\pi\) | ||||
−0.921788 | + | 0.387693i | \(0.873272\pi\) | |||||||
\(888\) | 5.28649e28 | − | 6.70595e28i | 0.173395 | − | 0.219953i | ||||
\(889\) | −6.83444e29 | −2.21659 | ||||||||
\(890\) | −3.85867e28 | + | 1.70530e29i | −0.123748 | + | 0.546891i | ||||
\(891\) | −7.59112e28 | −0.240729 | ||||||||
\(892\) | −2.36258e28 | + | 4.95330e28i | −0.0740863 | + | 0.155327i | ||||
\(893\) | − | 5.33905e29i | − | 1.65558i | ||||||
\(894\) | 6.74967e28 | − | 2.98295e29i | 0.206970 | − | 0.914684i | ||||
\(895\) | − | 2.74354e28i | − | 0.0831919i | ||||||
\(896\) | 6.22113e29 | − | 8.15201e27i | 1.86547 | − | 0.0244447i | ||||
\(897\) | −1.67717e29 | −0.497338 | ||||||||
\(898\) | 5.38722e29 | + | 1.21899e29i | 1.57980 | + | 0.357469i | ||||
\(899\) | 4.16769e29 | 1.20865 | ||||||||
\(900\) | 3.40259e27 | + | 1.62294e27i | 0.00975854 | + | 0.00465454i | ||||
\(901\) | − | 4.22352e29i | − | 1.19792i | ||||||
\(902\) | −6.40508e28 | − | 1.44931e28i | −0.179663 | − | 0.0406533i | ||||
\(903\) | − | 4.89131e28i | − | 0.135690i | ||||||
\(904\) | 1.25371e29 | + | 9.88331e28i | 0.343963 | + | 0.271155i | ||||
\(905\) | −4.87903e29 | −1.32388 | ||||||||
\(906\) | 6.82678e28 | − | 3.01703e29i | 0.183204 | − | 0.809650i | ||||
\(907\) | 4.46010e29 | 1.18378 | 0.591891 | − | 0.806018i | \(-0.298382\pi\) | ||||
0.591891 | + | 0.806018i | \(0.298382\pi\) | |||||||
\(908\) | 8.12339e28 | + | 3.87462e28i | 0.213245 | + | 0.101712i | ||||
\(909\) | − | 1.61936e28i | − | 0.0420442i | ||||||
\(910\) | 1.35582e29 | − | 5.99193e29i | 0.348168 | − | 1.53869i | ||||
\(911\) | − | 4.01750e29i | − | 1.02040i | −0.860054 | − | 0.510202i | \(-0.829570\pi\) | ||
0.860054 | − | 0.510202i | \(-0.170430\pi\) | |||||||
\(912\) | −3.69644e29 | − | 4.56466e29i | −0.928615 | − | 1.14673i | ||||
\(913\) | 1.68422e29 | 0.418495 | ||||||||
\(914\) | −1.13989e28 | − | 2.57929e27i | −0.0280158 | − | 0.00633927i | ||||
\(915\) | 1.80880e28 | 0.0439724 | ||||||||
\(916\) | −1.43476e29 | + | 3.00807e29i | −0.345005 | + | 0.723325i | ||||
\(917\) | 1.44144e30i | 3.42848i | ||||||||
\(918\) | −4.00554e29 | − | 9.06354e28i | −0.942399 | − | 0.213241i | ||||
\(919\) | − | 4.30423e29i | − | 1.00171i | −0.865532 | − | 0.500854i | \(-0.833020\pi\) | ||
0.865532 | − | 0.500854i | \(-0.166980\pi\) | |||||||
\(920\) | −1.40149e29 | − | 1.10484e29i | −0.322636 | − | 0.254343i | ||||
\(921\) | 4.68664e29 | 1.06725 | ||||||||
\(922\) | −9.82172e27 | + | 4.34061e28i | −0.0221247 | + | 0.0977781i | ||||
\(923\) | −3.60104e29 | −0.802437 | ||||||||
\(924\) | −8.62294e28 | + | 1.80785e29i | −0.190080 | + | 0.398514i | ||||
\(925\) | 3.63801e28i | 0.0793317i | ||||||||
\(926\) | −1.80662e29 | + | 7.98416e29i | −0.389723 | + | 1.72234i | ||||
\(927\) | 2.48418e28i | 0.0530134i | ||||||||
\(928\) | −3.02261e29 | + | 1.49062e29i | −0.638121 | + | 0.314694i | ||||
\(929\) | −5.72927e28 | −0.119658 | −0.0598291 | − | 0.998209i | \(-0.519056\pi\) | ||||
−0.0598291 | + | 0.998209i | \(0.519056\pi\) | |||||||
\(930\) | 6.88948e29 | + | 1.55892e29i | 1.42350 | + | 0.322102i | ||||
\(931\) | 1.75802e30 | 3.59357 | ||||||||
\(932\) | −3.11716e29 | − | 1.48680e29i | −0.630377 | − | 0.300672i | ||||
\(933\) | − | 2.07232e29i | − | 0.414611i | ||||||
\(934\) | −2.19804e29 | − | 4.97362e28i | −0.435078 | − | 0.0984473i | ||||
\(935\) | − | 9.86322e28i | − | 0.193153i | ||||||
\(936\) | −1.20044e28 | + | 1.52276e28i | −0.0232584 | + | 0.0295035i | ||||
\(937\) | −4.30339e29 | −0.824926 | −0.412463 | − | 0.910974i | \(-0.635331\pi\) | ||||
−0.412463 | + | 0.910974i | \(0.635331\pi\) | |||||||
\(938\) | 8.07480e28 | − | 3.56858e29i | 0.153145 | − | 0.676811i | ||||
\(939\) | 6.12861e28 | 0.115002 | ||||||||
\(940\) | −4.68632e29 | − | 2.23524e29i | −0.870069 | − | 0.414998i | ||||
\(941\) | − | 9.52735e29i | − | 1.75015i | −0.483985 | − | 0.875076i | \(-0.660811\pi\) | ||
0.483985 | − | 0.875076i | \(-0.339189\pi\) | |||||||
\(942\) | −1.70943e29 | + | 7.55465e29i | −0.310700 | + | 1.37311i | ||||
\(943\) | − | 2.14714e29i | − | 0.386138i | ||||||
\(944\) | 3.30171e27 | + | 4.07722e27i | 0.00587516 | + | 0.00725511i | ||||
\(945\) | 8.76257e29 | 1.54281 | ||||||||
\(946\) | 9.28839e27 | + | 2.10173e27i | 0.0161819 | + | 0.00366156i | ||||
\(947\) | −9.71257e29 | −1.67430 | −0.837152 | − | 0.546970i | \(-0.815781\pi\) | ||||
−0.837152 | + | 0.546970i | \(0.815781\pi\) | |||||||
\(948\) | −1.35572e29 | + | 2.84236e29i | −0.231253 | + | 0.484836i | ||||
\(949\) | − | 2.87541e29i | − | 0.485330i | ||||||
\(950\) | 2.44071e29 | + | 5.52271e28i | 0.407643 | + | 0.0922393i | ||||
\(951\) | − | 7.10997e29i | − | 1.17507i | ||||||
\(952\) | −6.96027e29 | + | 8.82916e29i | −1.13830 | + | 1.44394i | ||||
\(953\) | 8.45826e29 | 1.36884 | 0.684419 | − | 0.729089i | \(-0.260056\pi\) | ||||
0.684419 | + | 0.729089i | \(0.260056\pi\) | |||||||
\(954\) | 6.27728e27 | − | 2.77418e28i | 0.0100528 | − | 0.0444274i | ||||
\(955\) | −8.71627e28 | −0.138133 | ||||||||
\(956\) | 2.55526e29 | − | 5.35726e29i | 0.400733 | − | 0.840163i | ||||
\(957\) | − | 1.08498e29i | − | 0.168385i | ||||||
\(958\) | 2.39999e29 | − | 1.06065e30i | 0.368599 | − | 1.62899i | ||||
\(959\) | 1.82962e30i | 2.78083i | ||||||||
\(960\) | −5.55415e29 | + | 1.33350e29i | −0.835421 | + | 0.200577i | ||||
\(961\) | −1.26679e30 | −1.88569 | ||||||||
\(962\) | −1.82510e29 | − | 4.12973e28i | −0.268865 | − | 0.0608375i | ||||
\(963\) | −2.89079e26 | −0.000421457 | ||||||||
\(964\) | 3.63309e29 | + | 1.73288e29i | 0.524210 | + | 0.250033i | ||||
\(965\) | 3.64971e29i | 0.521177i | ||||||||
\(966\) | −6.38740e29 | − | 1.44531e29i | −0.902719 | − | 0.204263i | ||||
\(967\) | 5.87774e29i | 0.822140i | 0.911604 | + | 0.411070i | \(0.134845\pi\) | ||||
−0.911604 | + | 0.411070i | \(0.865155\pi\) | |||||||
\(968\) | 5.36659e29 | + | 4.23063e29i | 0.742924 | + | 0.585668i | ||||
\(969\) | 1.06139e30 | 1.45424 | ||||||||
\(970\) | −1.85751e29 | + | 8.20909e29i | −0.251892 | + | 1.11321i | ||||
\(971\) | −2.67719e29 | −0.359324 | −0.179662 | − | 0.983728i | \(-0.557500\pi\) | ||||
−0.179662 | + | 0.983728i | \(0.557500\pi\) | |||||||
\(972\) | −5.08979e28 | − | 2.42768e28i | −0.0676141 | − | 0.0322500i | ||||
\(973\) | − | 1.06079e28i | − | 0.0139476i | ||||||
\(974\) | −6.33339e28 | + | 2.79898e29i | −0.0824227 | + | 0.364259i | ||||
\(975\) | − | 2.28702e29i | − | 0.294593i | ||||||
\(976\) | 3.11963e28 | − | 2.52626e28i | 0.0397745 | − | 0.0322092i | ||||
\(977\) | −1.25089e30 | −1.57860 | −0.789301 | − | 0.614006i | \(-0.789557\pi\) | ||||
−0.789301 | + | 0.614006i | \(0.789557\pi\) | |||||||
\(978\) | 3.47872e28 | + | 7.87147e27i | 0.0434541 | + | 0.00983258i | ||||
\(979\) | −1.24918e29 | −0.154453 | ||||||||
\(980\) | 7.36009e29 | − | 1.54309e30i | 0.900787 | − | 1.88856i | ||||
\(981\) | 3.81560e28i | 0.0462245i | ||||||||
\(982\) | 5.74000e29 | + | 1.29882e29i | 0.688330 | + | 0.155752i | ||||
\(983\) | − | 5.43017e29i | − | 0.644582i | −0.946641 | − | 0.322291i | \(-0.895547\pi\) | ||
0.946641 | − | 0.322291i | \(-0.104453\pi\) | |||||||
\(984\) | −5.39696e29 | − | 4.25457e29i | −0.634159 | − | 0.499925i | ||||
\(985\) | −1.94915e29 | −0.226716 | ||||||||
\(986\) | 1.34404e29 | − | 5.93987e29i | 0.154755 | − | 0.683924i | ||||
\(987\) | −1.90531e30 | −2.17167 | ||||||||
\(988\) | −5.54120e29 | + | 1.16175e30i | −0.625222 | + | 1.31082i | ||||
\(989\) | 3.11369e28i | 0.0347786i | ||||||||
\(990\) | 1.46594e27 | − | 6.47857e27i | 0.00162093 | − | 0.00716353i | ||||
\(991\) | 1.86839e29i | 0.204518i | 0.994758 | + | 0.102259i | \(0.0326070\pi\) | ||||
−0.994758 | + | 0.102259i | \(0.967393\pi\) | |||||||
\(992\) | 1.40595e30 | − | 6.93355e29i | 1.52354 | − | 0.751344i | ||||
\(993\) | 1.49423e30 | 1.60297 | ||||||||
\(994\) | −1.37144e30 | − | 3.10322e29i | −1.45651 | − | 0.329571i | ||||
\(995\) | 6.50735e29 | 0.684184 | ||||||||
\(996\) | 1.59082e30 | + | 7.58777e29i | 1.65588 | + | 0.789807i | ||||
\(997\) | 9.13788e29i | 0.941659i | 0.882224 | + | 0.470830i | \(0.156045\pi\) | ||||
−0.882224 | + | 0.470830i | \(0.843955\pi\) | |||||||
\(998\) | 5.06012e29 | + | 1.14498e29i | 0.516244 | + | 0.116813i | ||||
\(999\) | − | 2.66901e29i | − | 0.269585i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8.21.d.b.3.1 | ✓ | 18 | |
3.2 | odd | 2 | 72.21.b.b.19.18 | 18 | |||
4.3 | odd | 2 | 32.21.d.b.15.4 | 18 | |||
8.3 | odd | 2 | inner | 8.21.d.b.3.2 | yes | 18 | |
8.5 | even | 2 | 32.21.d.b.15.3 | 18 | |||
24.11 | even | 2 | 72.21.b.b.19.17 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.21.d.b.3.1 | ✓ | 18 | 1.1 | even | 1 | trivial | |
8.21.d.b.3.2 | yes | 18 | 8.3 | odd | 2 | inner | |
32.21.d.b.15.3 | 18 | 8.5 | even | 2 | |||
32.21.d.b.15.4 | 18 | 4.3 | odd | 2 | |||
72.21.b.b.19.17 | 18 | 24.11 | even | 2 | |||
72.21.b.b.19.18 | 18 | 3.2 | odd | 2 |