Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,15,Mod(12,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.12");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.c (of order \(4\), degree \(2\), 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: | \(36.0554007641\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Relative dimension: | \(34\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 12.15 | ||
Character | \(\chi\) | \(=\) | 29.12 |
Dual form | 29.15.c.a.17.15 |
$q$-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 \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −48.4316 | − | 48.4316i | −0.378372 | − | 0.378372i | 0.492143 | − | 0.870514i | \(-0.336214\pi\) |
−0.870514 | + | 0.492143i | \(0.836214\pi\) | |||||||
\(3\) | 2910.35 | + | 2910.35i | 1.33075 | + | 1.33075i | 0.904699 | + | 0.426052i | \(0.140096\pi\) |
0.426052 | + | 0.904699i | \(0.359904\pi\) | |||||||
\(4\) | − | 11692.8i | − | 0.713670i | ||||||
\(5\) | − | 56568.4i | − | 0.724075i | −0.932164 | − | 0.362038i | \(-0.882081\pi\) | ||
0.932164 | − | 0.362038i | \(-0.117919\pi\) | |||||||
\(6\) | − | 281906.i | − | 1.00704i | ||||||
\(7\) | 166969. | 0.202745 | 0.101373 | − | 0.994849i | \(-0.467677\pi\) | ||||
0.101373 | + | 0.994849i | \(0.467677\pi\) | |||||||
\(8\) | −1.35980e6 | + | 1.35980e6i | −0.648404 | + | 0.648404i | ||||
\(9\) | 1.21573e7i | 2.54180i | ||||||||
\(10\) | −2.73969e6 | + | 2.73969e6i | −0.273969 | + | 0.273969i | ||||
\(11\) | 8.97417e6 | + | 8.97417e6i | 0.460517 | + | 0.460517i | 0.898825 | − | 0.438308i | \(-0.144422\pi\) |
−0.438308 | + | 0.898825i | \(0.644422\pi\) | |||||||
\(12\) | 3.40301e7 | − | 3.40301e7i | 0.949717 | − | 0.949717i | ||||
\(13\) | − | 5.10364e7i | − | 0.813349i | −0.913573 | − | 0.406675i | \(-0.866688\pi\) | ||
0.913573 | − | 0.406675i | \(-0.133312\pi\) | |||||||
\(14\) | −8.08659e6 | − | 8.08659e6i | −0.0767130 | − | 0.0767130i | ||||
\(15\) | 1.64634e8 | − | 1.64634e8i | 0.963564 | − | 0.963564i | ||||
\(16\) | −5.98597e7 | −0.222995 | ||||||||
\(17\) | 5.50123e8 | + | 5.50123e8i | 1.34066 | + | 1.34066i | 0.895406 | + | 0.445252i | \(0.146886\pi\) |
0.445252 | + | 0.895406i | \(0.353114\pi\) | |||||||
\(18\) | 5.88798e8 | − | 5.88798e8i | 0.961743 | − | 0.961743i | ||||
\(19\) | −3.93948e8 | − | 3.93948e8i | −0.440721 | − | 0.440721i | 0.451533 | − | 0.892254i | \(-0.350877\pi\) |
−0.892254 | + | 0.451533i | \(0.850877\pi\) | |||||||
\(20\) | −6.61441e8 | −0.516751 | ||||||||
\(21\) | 4.85940e8 | + | 4.85940e8i | 0.269803 | + | 0.269803i | ||||
\(22\) | − | 8.69266e8i | − | 0.348493i | ||||||
\(23\) | 2.69461e9 | 0.791408 | 0.395704 | − | 0.918378i | \(-0.370501\pi\) | ||||
0.395704 | + | 0.918378i | \(0.370501\pi\) | |||||||
\(24\) | −7.91500e9 | −1.72573 | ||||||||
\(25\) | 2.90354e9 | 0.475715 | ||||||||
\(26\) | −2.47177e9 | + | 2.47177e9i | −0.307748 | + | 0.307748i | ||||
\(27\) | −2.14620e10 | + | 2.14620e10i | −2.05175 | + | 2.05175i | ||||
\(28\) | − | 1.95233e9i | − | 0.144693i | ||||||
\(29\) | 1.70785e10 | − | 2.42557e9i | 0.990065 | − | 0.140614i | ||||
\(30\) | −1.59469e10 | −0.729170 | ||||||||
\(31\) | −1.63564e10 | − | 1.63564e10i | −0.594504 | − | 0.594504i | 0.344341 | − | 0.938845i | \(-0.388102\pi\) |
−0.938845 | + | 0.344341i | \(0.888102\pi\) | |||||||
\(32\) | 2.51781e10 | + | 2.51781e10i | 0.732779 | + | 0.732779i | ||||
\(33\) | 5.22360e10i | 1.22567i | ||||||||
\(34\) | − | 5.32867e10i | − | 1.01453i | ||||||
\(35\) | − | 9.44519e9i | − | 0.146803i | ||||||
\(36\) | 1.42153e11 | 1.81400 | ||||||||
\(37\) | 1.82791e10 | − | 1.82791e10i | 0.192549 | − | 0.192549i | −0.604247 | − | 0.796797i | \(-0.706526\pi\) |
0.796797 | + | 0.604247i | \(0.206526\pi\) | |||||||
\(38\) | 3.81591e10i | 0.333513i | ||||||||
\(39\) | 1.48534e11 | − | 1.48534e11i | 1.08236 | − | 1.08236i | ||||
\(40\) | 7.69218e10 | + | 7.69218e10i | 0.469493 | + | 0.469493i | ||||
\(41\) | 1.65641e11 | − | 1.65641e11i | 0.850513 | − | 0.850513i | −0.139683 | − | 0.990196i | \(-0.544608\pi\) |
0.990196 | + | 0.139683i | \(0.0446084\pi\) | |||||||
\(42\) | − | 4.70696e10i | − | 0.204172i | ||||||
\(43\) | 3.51242e11 | + | 3.51242e11i | 1.29219 | + | 1.29219i | 0.933428 | + | 0.358765i | \(0.116802\pi\) |
0.358765 | + | 0.933428i | \(0.383198\pi\) | |||||||
\(44\) | 1.04933e11 | − | 1.04933e11i | 0.328657 | − | 0.328657i | ||||
\(45\) | 6.87720e11 | 1.84045 | ||||||||
\(46\) | −1.30504e11 | − | 1.30504e11i | −0.299446 | − | 0.299446i | ||||
\(47\) | −1.60441e11 | + | 1.60441e11i | −0.316686 | + | 0.316686i | −0.847493 | − | 0.530807i | \(-0.821889\pi\) |
0.530807 | + | 0.847493i | \(0.321889\pi\) | |||||||
\(48\) | −1.74213e11 | − | 1.74213e11i | −0.296751 | − | 0.296751i | ||||
\(49\) | −6.50344e11 | −0.958894 | ||||||||
\(50\) | −1.40623e11 | − | 1.40623e11i | −0.179997 | − | 0.179997i | ||||
\(51\) | 3.20211e12i | 3.56816i | ||||||||
\(52\) | −5.96757e11 | −0.580463 | ||||||||
\(53\) | 1.48615e11 | 0.126512 | 0.0632560 | − | 0.997997i | \(-0.479852\pi\) | ||||
0.0632560 | + | 0.997997i | \(0.479852\pi\) | |||||||
\(54\) | 2.07887e12 | 1.55264 | ||||||||
\(55\) | 5.07654e11 | − | 5.07654e11i | 0.333449 | − | 0.333449i | ||||
\(56\) | −2.27045e11 | + | 2.27045e11i | −0.131461 | + | 0.131461i | ||||
\(57\) | − | 2.29306e12i | − | 1.17298i | ||||||
\(58\) | −9.44612e11 | − | 7.09664e11i | −0.427816 | − | 0.321408i | ||||
\(59\) | 2.18073e12 | 0.876271 | 0.438136 | − | 0.898909i | \(-0.355639\pi\) | ||||
0.438136 | + | 0.898909i | \(0.355639\pi\) | |||||||
\(60\) | −1.92503e12 | − | 1.92503e12i | −0.687666 | − | 0.687666i | ||||
\(61\) | 4.21207e12 | + | 4.21207e12i | 1.34025 | + | 1.34025i | 0.895806 | + | 0.444446i | \(0.146600\pi\) |
0.444446 | + | 0.895806i | \(0.353400\pi\) | |||||||
\(62\) | 1.58433e12i | 0.449887i | ||||||||
\(63\) | 2.02990e12i | 0.515337i | ||||||||
\(64\) | − | 1.45809e12i | − | 0.331530i | ||||||
\(65\) | −2.88705e12 | −0.588926 | ||||||||
\(66\) | 2.52987e12 | − | 2.52987e12i | 0.463757 | − | 0.463757i | ||||
\(67\) | − | 1.29909e12i | − | 0.214346i | −0.994240 | − | 0.107173i | \(-0.965820\pi\) | ||
0.994240 | − | 0.107173i | \(-0.0341799\pi\) | |||||||
\(68\) | 6.43247e12 | − | 6.43247e12i | 0.956787 | − | 0.956787i | ||||
\(69\) | 7.84225e12 | + | 7.84225e12i | 1.05317 | + | 1.05317i | ||||
\(70\) | −4.57445e11 | + | 4.57445e11i | −0.0555460 | + | 0.0555460i | ||||
\(71\) | − | 1.80711e12i | − | 0.198691i | −0.995053 | − | 0.0993453i | \(-0.968325\pi\) | ||
0.995053 | − | 0.0993453i | \(-0.0316748\pi\) | |||||||
\(72\) | −1.65316e13 | − | 1.65316e13i | −1.64811 | − | 1.64811i | ||||
\(73\) | −3.74645e12 | + | 3.74645e12i | −0.339125 | + | 0.339125i | −0.856038 | − | 0.516913i | \(-0.827081\pi\) |
0.516913 | + | 0.856038i | \(0.327081\pi\) | |||||||
\(74\) | −1.77057e12 | −0.145710 | ||||||||
\(75\) | 8.45031e12 | + | 8.45031e12i | 0.633058 | + | 0.633058i | ||||
\(76\) | −4.60635e12 | + | 4.60635e12i | −0.314530 | + | 0.314530i | ||||
\(77\) | 1.49841e12 | + | 1.49841e12i | 0.0933676 | + | 0.0933676i | ||||
\(78\) | −1.43875e13 | −0.819072 | ||||||||
\(79\) | 6.34597e12 | + | 6.34597e12i | 0.330452 | + | 0.330452i | 0.852758 | − | 0.522306i | \(-0.174928\pi\) |
−0.522306 | + | 0.852758i | \(0.674928\pi\) | |||||||
\(80\) | 3.38617e12i | 0.161465i | ||||||||
\(81\) | −6.67757e13 | −2.91893 | ||||||||
\(82\) | −1.60445e13 | −0.643620 | ||||||||
\(83\) | −3.51297e13 | −1.29458 | −0.647289 | − | 0.762245i | \(-0.724097\pi\) | ||||
−0.647289 | + | 0.762245i | \(0.724097\pi\) | |||||||
\(84\) | 5.68198e12 | − | 5.68198e12i | 0.192551 | − | 0.192551i | ||||
\(85\) | 3.11196e13 | − | 3.11196e13i | 0.970736 | − | 0.970736i | ||||
\(86\) | − | 3.40224e13i | − | 0.977858i | ||||||
\(87\) | 5.67637e13 | + | 4.26452e13i | 1.50465 | + | 1.13041i | ||||
\(88\) | −2.44062e13 | −0.597202 | ||||||||
\(89\) | 1.49288e13 | + | 1.49288e13i | 0.337516 | + | 0.337516i | 0.855432 | − | 0.517916i | \(-0.173292\pi\) |
−0.517916 | + | 0.855432i | \(0.673292\pi\) | |||||||
\(90\) | −3.33074e13 | − | 3.33074e13i | −0.696374 | − | 0.696374i | ||||
\(91\) | − | 8.52153e12i | − | 0.164903i | ||||||
\(92\) | − | 3.15074e13i | − | 0.564804i | ||||||
\(93\) | − | 9.52055e13i | − | 1.58227i | ||||||
\(94\) | 1.55408e13 | 0.239650 | ||||||||
\(95\) | −2.22850e13 | + | 2.22850e13i | −0.319115 | + | 0.319115i | ||||
\(96\) | 1.46554e14i | 1.95029i | ||||||||
\(97\) | 4.05437e13 | − | 4.05437e13i | 0.501789 | − | 0.501789i | −0.410204 | − | 0.911994i | \(-0.634543\pi\) |
0.911994 | + | 0.410204i | \(0.134543\pi\) | |||||||
\(98\) | 3.14972e13 | + | 3.14972e13i | 0.362818 | + | 0.362818i | ||||
\(99\) | −1.09102e14 | + | 1.09102e14i | −1.17054 | + | 1.17054i | ||||
\(100\) | − | 3.39504e13i | − | 0.339504i | ||||||
\(101\) | −2.26421e13 | − | 2.26421e13i | −0.211187 | − | 0.211187i | 0.593584 | − | 0.804772i | \(-0.297712\pi\) |
−0.804772 | + | 0.593584i | \(0.797712\pi\) | |||||||
\(102\) | 1.55083e14 | − | 1.55083e14i | 1.35009 | − | 1.35009i | ||||
\(103\) | −1.31518e14 | −1.06936 | −0.534681 | − | 0.845054i | \(-0.679568\pi\) | ||||
−0.534681 | + | 0.845054i | \(0.679568\pi\) | |||||||
\(104\) | 6.93994e13 | + | 6.93994e13i | 0.527379 | + | 0.527379i | ||||
\(105\) | 2.74888e13 | − | 2.74888e13i | 0.195358 | − | 0.195358i | ||||
\(106\) | −7.19766e12 | − | 7.19766e12i | −0.0478685 | − | 0.0478685i | ||||
\(107\) | −2.04400e14 | −1.27290 | −0.636451 | − | 0.771317i | \(-0.719598\pi\) | ||||
−0.636451 | + | 0.771317i | \(0.719598\pi\) | |||||||
\(108\) | 2.50950e14 | + | 2.50950e14i | 1.46427 | + | 1.46427i | ||||
\(109\) | − | 3.03290e12i | − | 0.0165910i | −0.999966 | − | 0.00829551i | \(-0.997359\pi\) | ||
0.999966 | − | 0.00829551i | \(-0.00264057\pi\) | |||||||
\(110\) | −4.91730e13 | −0.252335 | ||||||||
\(111\) | 1.06397e14 | 0.512470 | ||||||||
\(112\) | −9.99474e12 | −0.0452111 | ||||||||
\(113\) | −1.56639e14 | + | 1.56639e14i | −0.665809 | + | 0.665809i | −0.956743 | − | 0.290934i | \(-0.906034\pi\) |
0.290934 | + | 0.956743i | \(0.406034\pi\) | |||||||
\(114\) | −1.11056e14 | + | 1.11056e14i | −0.443822 | + | 0.443822i | ||||
\(115\) | − | 1.52429e14i | − | 0.573039i | ||||||
\(116\) | −2.83616e13 | − | 1.99695e14i | −0.100352 | − | 0.706579i | ||||
\(117\) | 6.20467e14 | 2.06737 | ||||||||
\(118\) | −1.05616e14 | − | 1.05616e14i | −0.331556 | − | 0.331556i | ||||
\(119\) | 9.18538e13 | + | 9.18538e13i | 0.271812 | + | 0.271812i | ||||
\(120\) | 4.47739e14i | 1.24956i | ||||||||
\(121\) | − | 2.18678e14i | − | 0.575848i | ||||||
\(122\) | − | 4.07994e14i | − | 1.01423i | ||||||
\(123\) | 9.64147e14 | 2.26364 | ||||||||
\(124\) | −1.91251e14 | + | 1.91251e14i | −0.424279 | + | 0.424279i | ||||
\(125\) | − | 5.09514e14i | − | 1.06853i | ||||||
\(126\) | 9.83113e13 | − | 9.83113e13i | 0.194989 | − | 0.194989i | ||||
\(127\) | −2.15974e14 | − | 2.15974e14i | −0.405298 | − | 0.405298i | 0.474797 | − | 0.880095i | \(-0.342521\pi\) |
−0.880095 | + | 0.474797i | \(0.842521\pi\) | |||||||
\(128\) | 3.41900e14 | − | 3.41900e14i | 0.607337 | − | 0.607337i | ||||
\(129\) | 2.04448e15i | 3.43917i | ||||||||
\(130\) | 1.39824e14 | + | 1.39824e14i | 0.222833 | + | 0.222833i | ||||
\(131\) | 4.42781e14 | − | 4.42781e14i | 0.668791 | − | 0.668791i | −0.288646 | − | 0.957436i | \(-0.593205\pi\) |
0.957436 | + | 0.288646i | \(0.0932049\pi\) | |||||||
\(132\) | 6.10784e14 | 0.874722 | ||||||||
\(133\) | −6.57773e13 | − | 6.57773e13i | −0.0893541 | − | 0.0893541i | ||||
\(134\) | −6.29171e13 | + | 6.29171e13i | −0.0811026 | + | 0.0811026i | ||||
\(135\) | 1.21407e15 | + | 1.21407e15i | 1.48562 | + | 1.48562i | ||||
\(136\) | −1.49612e15 | −1.73857 | ||||||||
\(137\) | −7.95705e14 | − | 7.95705e14i | −0.878432 | − | 0.878432i | 0.114940 | − | 0.993372i | \(-0.463332\pi\) |
−0.993372 | + | 0.114940i | \(0.963332\pi\) | |||||||
\(138\) | − | 7.59625e14i | − | 0.796977i | ||||||
\(139\) | −5.25176e14 | −0.523843 | −0.261921 | − | 0.965089i | \(-0.584356\pi\) | ||||
−0.261921 | + | 0.965089i | \(0.584356\pi\) | |||||||
\(140\) | −1.10440e14 | −0.104769 | ||||||||
\(141\) | −9.33878e14 | −0.842862 | ||||||||
\(142\) | −8.75213e13 | + | 8.75213e13i | −0.0751788 | + | 0.0751788i | ||||
\(143\) | 4.58010e14 | − | 4.58010e14i | 0.374561 | − | 0.374561i | ||||
\(144\) | − | 7.27734e14i | − | 0.566807i | ||||||
\(145\) | −1.37211e14 | − | 9.66102e14i | −0.101815 | − | 0.716881i | ||||
\(146\) | 3.62893e14 | 0.256630 | ||||||||
\(147\) | −1.89273e15 | − | 1.89273e15i | −1.27605 | − | 1.27605i | ||||
\(148\) | −2.13733e14 | − | 2.13733e14i | −0.137417 | − | 0.137417i | ||||
\(149\) | 2.41822e15i | 1.48318i | 0.670855 | + | 0.741588i | \(0.265927\pi\) | ||||
−0.670855 | + | 0.741588i | \(0.734073\pi\) | |||||||
\(150\) | − | 8.18523e14i | − | 0.479063i | ||||||
\(151\) | − | 1.83567e15i | − | 1.02555i | −0.858524 | − | 0.512773i | \(-0.828618\pi\) | ||
0.858524 | − | 0.512773i | \(-0.171382\pi\) | |||||||
\(152\) | 1.07138e15 | 0.571531 | ||||||||
\(153\) | −6.68803e15 | + | 6.68803e15i | −3.40768 | + | 3.40768i | ||||
\(154\) | − | 1.45141e14i | − | 0.0706553i | ||||||
\(155\) | −9.25252e14 | + | 9.25252e14i | −0.430465 | + | 0.430465i | ||||
\(156\) | −1.73677e15 | − | 1.73677e15i | −0.772451 | − | 0.772451i | ||||
\(157\) | −1.33570e15 | + | 1.33570e15i | −0.568082 | + | 0.568082i | −0.931591 | − | 0.363509i | \(-0.881579\pi\) |
0.363509 | + | 0.931591i | \(0.381579\pi\) | |||||||
\(158\) | − | 6.14690e14i | − | 0.250067i | ||||||
\(159\) | 4.32522e14 | + | 4.32522e14i | 0.168356 | + | 0.168356i | ||||
\(160\) | 1.42428e15 | − | 1.42428e15i | 0.530587 | − | 0.530587i | ||||
\(161\) | 4.49917e14 | 0.160454 | ||||||||
\(162\) | 3.23405e15 | + | 3.23405e15i | 1.10444 | + | 1.10444i | ||||
\(163\) | −8.81170e13 | + | 8.81170e13i | −0.0288235 | + | 0.0288235i | −0.721372 | − | 0.692548i | \(-0.756488\pi\) |
0.692548 | + | 0.721372i | \(0.256488\pi\) | |||||||
\(164\) | −1.93680e15 | − | 1.93680e15i | −0.606986 | − | 0.606986i | ||||
\(165\) | 2.95491e15 | 0.887475 | ||||||||
\(166\) | 1.70139e15 | + | 1.70139e15i | 0.489831 | + | 0.489831i | ||||
\(167\) | − | 6.74997e15i | − | 1.86332i | −0.363336 | − | 0.931658i | \(-0.618362\pi\) | ||
0.363336 | − | 0.931658i | \(-0.381638\pi\) | |||||||
\(168\) | −1.32156e15 | −0.349883 | ||||||||
\(169\) | 1.33266e15 | 0.338463 | ||||||||
\(170\) | −3.01434e15 | −0.734598 | ||||||||
\(171\) | 4.78936e15 | − | 4.78936e15i | 1.12022 | − | 1.12022i | ||||
\(172\) | 4.10699e15 | − | 4.10699e15i | 0.922199 | − | 0.922199i | ||||
\(173\) | 1.81269e15i | 0.390841i | 0.980720 | + | 0.195421i | \(0.0626072\pi\) | ||||
−0.980720 | + | 0.195421i | \(0.937393\pi\) | |||||||
\(174\) | −6.83782e14 | − | 4.81452e15i | −0.141603 | − | 0.997031i | ||||
\(175\) | 4.84802e14 | 0.0964490 | ||||||||
\(176\) | −5.37192e14 | − | 5.37192e14i | −0.102693 | − | 0.102693i | ||||
\(177\) | 6.34670e15 | + | 6.34670e15i | 1.16610 | + | 1.16610i | ||||
\(178\) | − | 1.44605e15i | − | 0.255413i | ||||||
\(179\) | − | 7.93134e15i | − | 1.34702i | −0.739176 | − | 0.673512i | \(-0.764785\pi\) | ||
0.739176 | − | 0.673512i | \(-0.235215\pi\) | |||||||
\(180\) | − | 8.04135e15i | − | 1.31347i | ||||||
\(181\) | 2.82725e15 | 0.444236 | 0.222118 | − | 0.975020i | \(-0.428703\pi\) | ||||
0.222118 | + | 0.975020i | \(0.428703\pi\) | |||||||
\(182\) | −4.12711e14 | + | 4.12711e14i | −0.0623945 | + | 0.0623945i | ||||
\(183\) | 2.45172e16i | 3.56708i | ||||||||
\(184\) | −3.66413e15 | + | 3.66413e15i | −0.513152 | + | 0.513152i | ||||
\(185\) | −1.03402e15 | − | 1.03402e15i | −0.139420 | − | 0.139420i | ||||
\(186\) | −4.61095e15 | + | 4.61095e15i | −0.598687 | + | 0.598687i | ||||
\(187\) | 9.87381e15i | 1.23479i | ||||||||
\(188\) | 1.87600e15 | + | 1.87600e15i | 0.226010 | + | 0.226010i | ||||
\(189\) | −3.58350e15 | + | 3.58350e15i | −0.415982 | + | 0.415982i | ||||
\(190\) | 2.15860e15 | 0.241488 | ||||||||
\(191\) | 1.13864e15 | + | 1.13864e15i | 0.122787 | + | 0.122787i | 0.765830 | − | 0.643043i | \(-0.222328\pi\) |
−0.643043 | + | 0.765830i | \(0.722328\pi\) | |||||||
\(192\) | 4.24354e15 | − | 4.24354e15i | 0.441184 | − | 0.441184i | ||||
\(193\) | −5.80212e15 | − | 5.80212e15i | −0.581682 | − | 0.581682i | 0.353683 | − | 0.935365i | \(-0.384929\pi\) |
−0.935365 | + | 0.353683i | \(0.884929\pi\) | |||||||
\(194\) | −3.92719e15 | −0.379725 | ||||||||
\(195\) | −8.40233e15 | − | 8.40233e15i | −0.783713 | − | 0.783713i | ||||
\(196\) | 7.60433e15i | 0.684334i | ||||||||
\(197\) | −2.25726e16 | −1.96028 | −0.980138 | − | 0.198317i | \(-0.936452\pi\) | ||||
−0.980138 | + | 0.198317i | \(0.936452\pi\) | |||||||
\(198\) | 1.05680e16 | 0.885798 | ||||||||
\(199\) | 1.67821e16 | 1.35792 | 0.678962 | − | 0.734174i | \(-0.262430\pi\) | ||||
0.678962 | + | 0.734174i | \(0.262430\pi\) | |||||||
\(200\) | −3.94823e15 | + | 3.94823e15i | −0.308456 | + | 0.308456i | ||||
\(201\) | 3.78082e15 | − | 3.78082e15i | 0.285242 | − | 0.285242i | ||||
\(202\) | 2.19319e15i | 0.159815i | ||||||||
\(203\) | 2.85159e15 | − | 4.04996e14i | 0.200731 | − | 0.0285088i | ||||
\(204\) | 3.74415e16 | 2.54649 | ||||||||
\(205\) | −9.37004e15 | − | 9.37004e15i | −0.615835 | − | 0.615835i | ||||
\(206\) | 6.36962e15 | + | 6.36962e15i | 0.404616 | + | 0.404616i | ||||
\(207\) | 3.27592e16i | 2.01160i | ||||||||
\(208\) | 3.05503e15i | 0.181373i | ||||||||
\(209\) | − | 7.07072e15i | − | 0.405919i | ||||||
\(210\) | −2.66265e15 | −0.147836 | ||||||||
\(211\) | 1.58631e14 | − | 1.58631e14i | 0.00851946 | − | 0.00851946i | −0.702834 | − | 0.711354i | \(-0.748082\pi\) |
0.711354 | + | 0.702834i | \(0.248082\pi\) | |||||||
\(212\) | − | 1.73772e15i | − | 0.0902878i | ||||||
\(213\) | 5.25934e15 | − | 5.25934e15i | 0.264408 | − | 0.264408i | ||||
\(214\) | 9.89943e15 | + | 9.89943e15i | 0.481630 | + | 0.481630i | ||||
\(215\) | 1.98692e16 | − | 1.98692e16i | 0.935645 | − | 0.935645i | ||||
\(216\) | − | 5.83681e16i | − | 2.66072i | ||||||
\(217\) | −2.73101e15 | − | 2.73101e15i | −0.120533 | − | 0.120533i | ||||
\(218\) | −1.46888e14 | + | 1.46888e14i | −0.00627757 | + | 0.00627757i | ||||
\(219\) | −2.18070e16 | −0.902581 | ||||||||
\(220\) | −5.93589e15 | − | 5.93589e15i | −0.237972 | − | 0.237972i | ||||
\(221\) | 2.80763e16 | − | 2.80763e16i | 1.09042 | − | 1.09042i | ||||
\(222\) | −5.15297e15 | − | 5.15297e15i | −0.193904 | − | 0.193904i | ||||
\(223\) | 2.97321e16 | 1.08416 | 0.542078 | − | 0.840328i | \(-0.317638\pi\) | ||||
0.542078 | + | 0.840328i | \(0.317638\pi\) | |||||||
\(224\) | 4.20397e15 | + | 4.20397e15i | 0.148567 | + | 0.148567i | ||||
\(225\) | 3.52992e16i | 1.20917i | ||||||||
\(226\) | 1.51725e16 | 0.503846 | ||||||||
\(227\) | −5.81337e15 | −0.187175 | −0.0935874 | − | 0.995611i | \(-0.529833\pi\) | ||||
−0.0935874 | + | 0.995611i | \(0.529833\pi\) | |||||||
\(228\) | −2.68122e16 | −0.837121 | ||||||||
\(229\) | −3.68949e16 | + | 3.68949e16i | −1.11717 | + | 1.11717i | −0.125010 | + | 0.992156i | \(0.539896\pi\) |
−0.992156 | + | 0.125010i | \(0.960104\pi\) | |||||||
\(230\) | −7.38240e15 | + | 7.38240e15i | −0.216822 | + | 0.216822i | ||||
\(231\) | 8.72182e15i | 0.248498i | ||||||||
\(232\) | −1.99251e16 | + | 2.65217e16i | −0.550787 | + | 0.733136i | ||||
\(233\) | −6.60788e16 | −1.77244 | −0.886219 | − | 0.463267i | \(-0.846677\pi\) | ||||
−0.886219 | + | 0.463267i | \(0.846677\pi\) | |||||||
\(234\) | −3.00502e16 | − | 3.00502e16i | −0.782233 | − | 0.782233i | ||||
\(235\) | 9.07587e15 | + | 9.07587e15i | 0.229305 | + | 0.229305i | ||||
\(236\) | − | 2.54988e16i | − | 0.625368i | ||||||
\(237\) | 3.69380e16i | 0.879498i | ||||||||
\(238\) | − | 8.89724e15i | − | 0.205692i | ||||||
\(239\) | 4.28843e15 | 0.0962750 | 0.0481375 | − | 0.998841i | \(-0.484671\pi\) | ||||
0.0481375 | + | 0.998841i | \(0.484671\pi\) | |||||||
\(240\) | −9.85494e15 | + | 9.85494e15i | −0.214870 | + | 0.214870i | ||||
\(241\) | 6.57682e16i | 1.39282i | 0.717642 | + | 0.696412i | \(0.245222\pi\) | ||||
−0.717642 | + | 0.696412i | \(0.754778\pi\) | |||||||
\(242\) | −1.05909e16 | + | 1.05909e16i | −0.217885 | + | 0.217885i | ||||
\(243\) | −9.16889e16 | − | 9.16889e16i | −1.83262 | − | 1.83262i | ||||
\(244\) | 4.92507e16 | − | 4.92507e16i | 0.956497 | − | 0.956497i | ||||
\(245\) | 3.67889e16i | 0.694312i | ||||||||
\(246\) | −4.66952e16 | − | 4.66952e16i | −0.856498 | − | 0.856498i | ||||
\(247\) | −2.01057e16 | + | 2.01057e16i | −0.358460 | + | 0.358460i | ||||
\(248\) | 4.44828e16 | 0.770957 | ||||||||
\(249\) | −1.02240e17 | − | 1.02240e17i | −1.72276 | − | 1.72276i | ||||
\(250\) | −2.46766e16 | + | 2.46766e16i | −0.404301 | + | 0.404301i | ||||
\(251\) | −1.09046e16 | − | 1.09046e16i | −0.173738 | − | 0.173738i | 0.614882 | − | 0.788619i | \(-0.289204\pi\) |
−0.788619 | + | 0.614882i | \(0.789204\pi\) | |||||||
\(252\) | 2.37352e16 | 0.367780 | ||||||||
\(253\) | 2.41819e16 | + | 2.41819e16i | 0.364457 | + | 0.364457i | ||||
\(254\) | 2.09199e16i | 0.306707i | ||||||||
\(255\) | 1.81138e17 | 2.58362 | ||||||||
\(256\) | −5.70068e16 | −0.791129 | ||||||||
\(257\) | −8.72641e16 | −1.17843 | −0.589215 | − | 0.807977i | \(-0.700563\pi\) | ||||
−0.589215 | + | 0.807977i | \(0.700563\pi\) | |||||||
\(258\) | 9.90172e16 | − | 9.90172e16i | 1.30129 | − | 1.30129i | ||||
\(259\) | 3.05204e15 | − | 3.05204e15i | 0.0390384 | − | 0.0390384i | ||||
\(260\) | 3.37576e16i | 0.420299i | ||||||||
\(261\) | 2.94885e16 | + | 2.07629e17i | 0.357411 | + | 2.51654i | ||||
\(262\) | −4.28892e16 | −0.506103 | ||||||||
\(263\) | 1.01258e17 | + | 1.01258e17i | 1.16343 | + | 1.16343i | 0.983720 | + | 0.179706i | \(0.0575148\pi\) |
0.179706 | + | 0.983720i | \(0.442485\pi\) | |||||||
\(264\) | −7.10306e16 | − | 7.10306e16i | −0.794727 | − | 0.794727i | ||||
\(265\) | − | 8.40691e15i | − | 0.0916042i | ||||||
\(266\) | 6.37139e15i | 0.0676181i | ||||||||
\(267\) | 8.68961e16i | 0.898300i | ||||||||
\(268\) | −1.51900e16 | −0.152973 | ||||||||
\(269\) | 1.07766e17 | − | 1.07766e17i | 1.05734 | − | 1.05734i | 0.0590915 | − | 0.998253i | \(-0.481180\pi\) |
0.998253 | − | 0.0590915i | \(-0.0188204\pi\) | |||||||
\(270\) | − | 1.17599e17i | − | 1.12423i | ||||||
\(271\) | 5.97366e16 | − | 5.97366e16i | 0.556487 | − | 0.556487i | −0.371818 | − | 0.928306i | \(-0.621266\pi\) |
0.928306 | + | 0.371818i | \(0.121266\pi\) | |||||||
\(272\) | −3.29302e16 | − | 3.29302e16i | −0.298960 | − | 0.298960i | ||||
\(273\) | 2.48006e16 | − | 2.48006e16i | 0.219444 | − | 0.219444i | ||||
\(274\) | 7.70745e16i | 0.664747i | ||||||||
\(275\) | 2.60568e16 | + | 2.60568e16i | 0.219075 | + | 0.219075i | ||||
\(276\) | 9.16976e16 | − | 9.16976e16i | 0.751614 | − | 0.751614i | ||||
\(277\) | −5.66529e16 | −0.452756 | −0.226378 | − | 0.974040i | \(-0.572688\pi\) | ||||
−0.226378 | + | 0.974040i | \(0.572688\pi\) | |||||||
\(278\) | 2.54351e16 | + | 2.54351e16i | 0.198207 | + | 0.198207i | ||||
\(279\) | 1.98850e17 | − | 1.98850e17i | 1.51111 | − | 1.51111i | ||||
\(280\) | 1.28436e16 | + | 1.28436e16i | 0.0951875 | + | 0.0951875i | ||||
\(281\) | 8.39442e16 | 0.606801 | 0.303401 | − | 0.952863i | \(-0.401878\pi\) | ||||
0.303401 | + | 0.952863i | \(0.401878\pi\) | |||||||
\(282\) | 4.52292e16 | + | 4.52292e16i | 0.318915 | + | 0.318915i | ||||
\(283\) | 1.22543e15i | 0.00842915i | 0.999991 | + | 0.00421458i | \(0.00134155\pi\) | ||||
−0.999991 | + | 0.00421458i | \(0.998658\pi\) | |||||||
\(284\) | −2.11302e16 | −0.141799 | ||||||||
\(285\) | −1.29714e17 | −0.849326 | ||||||||
\(286\) | −4.43643e16 | −0.283447 | ||||||||
\(287\) | 2.76570e16 | − | 2.76570e16i | 0.172437 | − | 0.172437i | ||||
\(288\) | −3.06098e17 | + | 3.06098e17i | −1.86257 | + | 1.86257i | ||||
\(289\) | 4.36894e17i | 2.59472i | ||||||||
\(290\) | −4.01445e16 | + | 5.34352e16i | −0.232724 | + | 0.309771i | ||||
\(291\) | 2.35993e17 | 1.33551 | ||||||||
\(292\) | 4.38063e16 | + | 4.38063e16i | 0.242023 | + | 0.242023i | ||||
\(293\) | 2.38824e16 | + | 2.38824e16i | 0.128826 | + | 0.128826i | 0.768580 | − | 0.639754i | \(-0.220964\pi\) |
−0.639754 | + | 0.768580i | \(0.720964\pi\) | |||||||
\(294\) | 1.83336e17i | 0.965642i | ||||||||
\(295\) | − | 1.23361e17i | − | 0.634486i | ||||||
\(296\) | 4.97118e16i | 0.249699i | ||||||||
\(297\) | −3.85207e17 | −1.88973 | ||||||||
\(298\) | 1.17118e17 | − | 1.17118e17i | 0.561192 | − | 0.561192i | ||||
\(299\) | − | 1.37523e17i | − | 0.643691i | ||||||
\(300\) | 9.88075e16 | − | 9.88075e16i | 0.451795 | − | 0.451795i | ||||
\(301\) | 5.86467e16 | + | 5.86467e16i | 0.261986 | + | 0.261986i | ||||
\(302\) | −8.89042e16 | + | 8.89042e16i | −0.388037 | + | 0.388037i | ||||
\(303\) | − | 1.31793e17i | − | 0.562075i | ||||||
\(304\) | 2.35816e16 | + | 2.35816e16i | 0.0982785 | + | 0.0982785i | ||||
\(305\) | 2.38270e17 | − | 2.38270e17i | 0.970443 | − | 0.970443i | ||||
\(306\) | 6.47824e17 | 2.57874 | ||||||||
\(307\) | −1.74926e17 | − | 1.74926e17i | −0.680592 | − | 0.680592i | 0.279542 | − | 0.960134i | \(-0.409817\pi\) |
−0.960134 | + | 0.279542i | \(0.909817\pi\) | |||||||
\(308\) | 1.75206e16 | − | 1.75206e16i | 0.0666337 | − | 0.0666337i | ||||
\(309\) | −3.82764e17 | − | 3.82764e17i | −1.42305 | − | 1.42305i | ||||
\(310\) | 8.96228e16 | 0.325752 | ||||||||
\(311\) | 8.65927e15 | + | 8.65927e15i | 0.0307722 | + | 0.0307722i | 0.722325 | − | 0.691553i | \(-0.243073\pi\) |
−0.691553 | + | 0.722325i | \(0.743073\pi\) | |||||||
\(312\) | 4.03954e17i | 1.40362i | ||||||||
\(313\) | −2.01190e17 | −0.683589 | −0.341795 | − | 0.939775i | \(-0.611035\pi\) | ||||
−0.341795 | + | 0.939775i | \(0.611035\pi\) | |||||||
\(314\) | 1.29380e17 | 0.429892 | ||||||||
\(315\) | 1.14828e17 | 0.373143 | ||||||||
\(316\) | 7.42019e16 | − | 7.42019e16i | 0.235834 | − | 0.235834i | ||||
\(317\) | 6.95469e16 | − | 6.95469e16i | 0.216204 | − | 0.216204i | −0.590693 | − | 0.806897i | \(-0.701145\pi\) |
0.806897 | + | 0.590693i | \(0.201145\pi\) | |||||||
\(318\) | − | 4.18954e16i | − | 0.127402i | ||||||
\(319\) | 1.75033e17 | + | 1.31498e17i | 0.520697 | + | 0.391187i | ||||
\(320\) | −8.24816e16 | −0.240053 | ||||||||
\(321\) | −5.94877e17 | − | 5.94877e17i | −1.69392 | − | 1.69392i | ||||
\(322\) | −2.17902e16 | − | 2.17902e16i | −0.0607113 | − | 0.0607113i | ||||
\(323\) | − | 4.33440e17i | − | 1.18171i | ||||||
\(324\) | 7.80793e17i | 2.08315i | ||||||||
\(325\) | − | 1.48186e17i | − | 0.386923i | ||||||
\(326\) | 8.53529e15 | 0.0218120 | ||||||||
\(327\) | 8.82681e15 | − | 8.82681e15i | 0.0220785 | − | 0.0220785i | ||||
\(328\) | 4.50478e17i | 1.10295i | ||||||||
\(329\) | −2.67887e16 | + | 2.67887e16i | −0.0642067 | + | 0.0642067i | ||||
\(330\) | −1.43111e17 | − | 1.43111e17i | −0.335795 | − | 0.335795i | ||||
\(331\) | −2.38744e17 | + | 2.38744e17i | −0.548449 | + | 0.548449i | −0.925992 | − | 0.377543i | \(-0.876769\pi\) |
0.377543 | + | 0.925992i | \(0.376769\pi\) | |||||||
\(332\) | 4.10764e17i | 0.923901i | ||||||||
\(333\) | 2.22225e17 | + | 2.22225e17i | 0.489421 | + | 0.489421i | ||||
\(334\) | −3.26912e17 | + | 3.26912e17i | −0.705026 | + | 0.705026i | ||||
\(335\) | −7.34875e16 | −0.155203 | ||||||||
\(336\) | −2.90882e16 | − | 2.90882e16i | −0.0601648 | − | 0.0601648i | ||||
\(337\) | 4.05039e17 | − | 4.05039e17i | 0.820517 | − | 0.820517i | −0.165665 | − | 0.986182i | \(-0.552977\pi\) |
0.986182 | + | 0.165665i | \(0.0529771\pi\) | |||||||
\(338\) | −6.45427e16 | − | 6.45427e16i | −0.128065 | − | 0.128065i | ||||
\(339\) | −9.11747e17 | −1.77205 | ||||||||
\(340\) | −3.63874e17 | − | 3.63874e17i | −0.692785 | − | 0.692785i | ||||
\(341\) | − | 2.93570e17i | − | 0.547558i | ||||||
\(342\) | −4.63912e17 | −0.847721 | ||||||||
\(343\) | −2.21830e17 | −0.397157 | ||||||||
\(344\) | −9.55239e17 | −1.67573 | ||||||||
\(345\) | 4.43623e17 | − | 4.43623e17i | 0.762572 | − | 0.762572i | ||||
\(346\) | 8.77913e16 | − | 8.77913e16i | 0.147883 | − | 0.147883i | ||||
\(347\) | − | 4.22004e17i | − | 0.696642i | −0.937375 | − | 0.348321i | \(-0.886752\pi\) | ||
0.937375 | − | 0.348321i | \(-0.113248\pi\) | |||||||
\(348\) | 4.98640e17 | − | 6.63725e17i | 0.806738 | − | 1.07382i | ||||
\(349\) | −6.75708e17 | −1.07147 | −0.535737 | − | 0.844385i | \(-0.679966\pi\) | ||||
−0.535737 | + | 0.844385i | \(0.679966\pi\) | |||||||
\(350\) | −2.34797e16 | − | 2.34797e16i | −0.0364936 | − | 0.0364936i | ||||
\(351\) | 1.09534e18 | + | 1.09534e18i | 1.66879 | + | 1.66879i | ||||
\(352\) | 4.51905e17i | 0.674914i | ||||||||
\(353\) | 6.14165e17i | 0.899212i | 0.893227 | + | 0.449606i | \(0.148436\pi\) | ||||
−0.893227 | + | 0.449606i | \(0.851564\pi\) | |||||||
\(354\) | − | 6.14761e17i | − | 0.882437i | ||||||
\(355\) | −1.02225e17 | −0.143867 | ||||||||
\(356\) | 1.74559e17 | − | 1.74559e17i | 0.240875 | − | 0.240875i | ||||
\(357\) | 5.34654e17i | 0.723428i | ||||||||
\(358\) | −3.84127e17 | + | 3.84127e17i | −0.509676 | + | 0.509676i | ||||
\(359\) | −9.83480e17 | − | 9.83480e17i | −1.27969 | − | 1.27969i | −0.940842 | − | 0.338847i | \(-0.889963\pi\) |
−0.338847 | − | 0.940842i | \(-0.610037\pi\) | |||||||
\(360\) | −9.35163e17 | + | 9.35163e17i | −1.19336 | + | 1.19336i | ||||
\(361\) | − | 4.88616e17i | − | 0.611530i | ||||||
\(362\) | −1.36928e17 | − | 1.36928e17i | −0.168086 | − | 0.168086i | ||||
\(363\) | 6.36431e17 | − | 6.36431e17i | 0.766310 | − | 0.766310i | ||||
\(364\) | −9.96402e16 | −0.117686 | ||||||||
\(365\) | 2.11930e17 | + | 2.11930e17i | 0.245552 | + | 0.245552i | ||||
\(366\) | 1.18741e18 | − | 1.18741e18i | 1.34968 | − | 1.34968i | ||||
\(367\) | 1.19902e18 | + | 1.19902e18i | 1.33711 | + | 1.33711i | 0.898851 | + | 0.438255i | \(0.144403\pi\) |
0.438255 | + | 0.898851i | \(0.355597\pi\) | |||||||
\(368\) | −1.61298e17 | −0.176480 | ||||||||
\(369\) | 2.01375e18 | + | 2.01375e18i | 2.16183 | + | 2.16183i | ||||
\(370\) | 1.00158e17i | 0.105505i | ||||||||
\(371\) | 2.48142e16 | 0.0256497 | ||||||||
\(372\) | −1.11322e18 | −1.12922 | ||||||||
\(373\) | 1.10288e18 | 1.09791 | 0.548957 | − | 0.835851i | \(-0.315025\pi\) | ||||
0.548957 | + | 0.835851i | \(0.315025\pi\) | |||||||
\(374\) | 4.78204e17 | − | 4.78204e17i | 0.467210 | − | 0.467210i | ||||
\(375\) | 1.48287e18 | − | 1.48287e18i | 1.42195 | − | 1.42195i | ||||
\(376\) | − | 4.36335e17i | − | 0.410681i | ||||||
\(377\) | −1.23792e17 | − | 8.71626e17i | −0.114368 | − | 0.805268i | ||||
\(378\) | 3.47108e17 | 0.314791 | ||||||||
\(379\) | −1.09964e18 | − | 1.09964e18i | −0.978986 | − | 0.978986i | 0.0207973 | − | 0.999784i | \(-0.493380\pi\) |
−0.999784 | + | 0.0207973i | \(0.993380\pi\) | |||||||
\(380\) | 2.60573e17 | + | 2.60573e17i | 0.227743 | + | 0.227743i | ||||
\(381\) | − | 1.25712e18i | − | 1.07870i | ||||||
\(382\) | − | 1.10292e17i | − | 0.0929180i | ||||||
\(383\) | − | 6.00651e17i | − | 0.496856i | −0.968650 | − | 0.248428i | \(-0.920086\pi\) | ||
0.968650 | − | 0.248428i | \(-0.0799140\pi\) | |||||||
\(384\) | 1.99010e18 | 1.61643 | ||||||||
\(385\) | 8.47628e16 | − | 8.47628e16i | 0.0676052 | − | 0.0676052i | ||||
\(386\) | 5.62012e17i | 0.440184i | ||||||||
\(387\) | −4.27017e18 | + | 4.27017e18i | −3.28449 | + | 3.28449i | ||||
\(388\) | −4.74068e17 | − | 4.74068e17i | −0.358112 | − | 0.358112i | ||||
\(389\) | −6.02713e17 | + | 6.02713e17i | −0.447160 | + | 0.447160i | −0.894409 | − | 0.447249i | \(-0.852404\pi\) |
0.447249 | + | 0.894409i | \(0.352404\pi\) | |||||||
\(390\) | 8.13876e17i | 0.593070i | ||||||||
\(391\) | 1.48237e18 | + | 1.48237e18i | 1.06101 | + | 1.06101i | ||||
\(392\) | 8.84339e17 | − | 8.84339e17i | 0.621751 | − | 0.621751i | ||||
\(393\) | 2.57730e18 | 1.77999 | ||||||||
\(394\) | 1.09322e18 | + | 1.09322e18i | 0.741713 | + | 0.741713i | ||||
\(395\) | 3.58981e17 | − | 3.58981e17i | 0.239272 | − | 0.239272i | ||||
\(396\) | 1.27570e18 | + | 1.27570e18i | 0.835379 | + | 0.835379i | ||||
\(397\) | −2.37417e18 | −1.52749 | −0.763745 | − | 0.645518i | \(-0.776642\pi\) | ||||
−0.763745 | + | 0.645518i | \(0.776642\pi\) | |||||||
\(398\) | −8.12784e17 | − | 8.12784e17i | −0.513800 | − | 0.513800i | ||||
\(399\) | − | 3.82870e17i | − | 0.237816i | ||||||
\(400\) | −1.73805e17 | −0.106082 | ||||||||
\(401\) | 1.55954e18 | 0.935377 | 0.467689 | − | 0.883893i | \(-0.345087\pi\) | ||||
0.467689 | + | 0.883893i | \(0.345087\pi\) | |||||||
\(402\) | −3.66222e17 | −0.215855 | ||||||||
\(403\) | −8.34770e17 | + | 8.34770e17i | −0.483539 | + | 0.483539i | ||||
\(404\) | −2.64749e17 | + | 2.64749e17i | −0.150718 | + | 0.150718i | ||||
\(405\) | 3.77739e18i | 2.11352i | ||||||||
\(406\) | −1.57721e17 | − | 1.18492e17i | −0.0867378 | − | 0.0651639i | ||||
\(407\) | 3.28079e17 | 0.177344 | ||||||||
\(408\) | −4.35423e18 | − | 4.35423e18i | −2.31361 | − | 2.31361i | ||||
\(409\) | −6.11563e17 | − | 6.11563e17i | −0.319432 | − | 0.319432i | 0.529117 | − | 0.848549i | \(-0.322523\pi\) |
−0.848549 | + | 0.529117i | \(0.822523\pi\) | |||||||
\(410\) | 9.07611e17i | 0.466029i | ||||||||
\(411\) | − | 4.63156e18i | − | 2.33795i | ||||||
\(412\) | 1.53781e18i | 0.763171i | ||||||||
\(413\) | 3.64116e17 | 0.177660 | ||||||||
\(414\) | 1.58658e18 | − | 1.58658e18i | 0.761131 | − | 0.761131i | ||||
\(415\) | 1.98723e18i | 0.937372i | ||||||||
\(416\) | 1.28500e18 | − | 1.28500e18i | 0.596005 | − | 0.596005i | ||||
\(417\) | −1.52845e18 | − | 1.52845e18i | −0.697104 | − | 0.697104i | ||||
\(418\) | −3.42446e17 | + | 3.42446e17i | −0.153588 | + | 0.153588i | ||||
\(419\) | 2.84591e18i | 1.25523i | 0.778525 | + | 0.627614i | \(0.215968\pi\) | ||||
−0.778525 | + | 0.627614i | \(0.784032\pi\) | |||||||
\(420\) | −3.21420e17 | − | 3.21420e17i | −0.139421 | − | 0.139421i | ||||
\(421\) | −1.03009e18 | + | 1.03009e18i | −0.439439 | + | 0.439439i | −0.891823 | − | 0.452384i | \(-0.850574\pi\) |
0.452384 | + | 0.891823i | \(0.350574\pi\) | |||||||
\(422\) | −1.53655e16 | −0.00644704 | ||||||||
\(423\) | −1.95053e18 | − | 1.95053e18i | −0.804952 | − | 0.804952i | ||||
\(424\) | −2.02087e17 | + | 2.02087e17i | −0.0820309 | + | 0.0820309i | ||||
\(425\) | 1.59730e18 | + | 1.59730e18i | 0.637771 | + | 0.637771i | ||||
\(426\) | −5.09436e17 | −0.200089 | ||||||||
\(427\) | 7.03286e17 | + | 7.03286e17i | 0.271730 | + | 0.271730i | ||||
\(428\) | 2.39001e18i | 0.908433i | ||||||||
\(429\) | 2.66594e18 | 0.996895 | ||||||||
\(430\) | −1.92459e18 | −0.708043 | ||||||||
\(431\) | 3.94437e18 | 1.42770 | 0.713850 | − | 0.700298i | \(-0.246950\pi\) | ||||
0.713850 | + | 0.700298i | \(0.246950\pi\) | |||||||
\(432\) | 1.28471e18 | − | 1.28471e18i | 0.457529 | − | 0.457529i | ||||
\(433\) | −3.07603e18 | + | 3.07603e18i | −1.07789 | + | 1.07789i | −0.0811938 | + | 0.996698i | \(0.525873\pi\) |
−0.996698 | + | 0.0811938i | \(0.974127\pi\) | |||||||
\(434\) | 2.64534e17i | 0.0912124i | ||||||||
\(435\) | 2.41237e18 | − | 3.21103e18i | 0.818500 | − | 1.08948i | ||||
\(436\) | −3.54630e16 | −0.0118405 | ||||||||
\(437\) | −1.06154e18 | − | 1.06154e18i | −0.348790 | − | 0.348790i | ||||
\(438\) | 1.05615e18 | + | 1.05615e18i | 0.341511 | + | 0.341511i | ||||
\(439\) | − | 3.08389e18i | − | 0.981403i | −0.871328 | − | 0.490701i | \(-0.836741\pi\) | ||
0.871328 | − | 0.490701i | \(-0.163259\pi\) | |||||||
\(440\) | 1.38062e18i | 0.432419i | ||||||||
\(441\) | − | 7.90645e18i | − | 2.43731i | ||||||
\(442\) | −2.71956e18 | −0.825169 | ||||||||
\(443\) | 3.04279e18 | − | 3.04279e18i | 0.908754 | − | 0.908754i | −0.0874177 | − | 0.996172i | \(-0.527861\pi\) |
0.996172 | + | 0.0874177i | \(0.0278615\pi\) | |||||||
\(444\) | − | 1.24408e18i | − | 0.365735i | ||||||
\(445\) | 8.44497e17 | − | 8.44497e17i | 0.244387 | − | 0.244387i | ||||
\(446\) | −1.43997e18 | − | 1.43997e18i | −0.410214 | − | 0.410214i | ||||
\(447\) | −7.03788e18 | + | 7.03788e18i | −1.97374 | + | 1.97374i | ||||
\(448\) | − | 2.43456e17i | − | 0.0672162i | ||||||
\(449\) | −3.87645e17 | − | 3.87645e17i | −0.105368 | − | 0.105368i | 0.652457 | − | 0.757826i | \(-0.273738\pi\) |
−0.757826 | + | 0.652457i | \(0.773738\pi\) | |||||||
\(450\) | 1.70960e18 | − | 1.70960e18i | 0.457516 | − | 0.457516i | ||||
\(451\) | 2.97298e18 | 0.783351 | ||||||||
\(452\) | 1.83154e18 | + | 1.83154e18i | 0.475168 | + | 0.475168i | ||||
\(453\) | 5.34244e18 | − | 5.34244e18i | 1.36475 | − | 1.36475i | ||||
\(454\) | 2.81551e17 | + | 2.81551e17i | 0.0708216 | + | 0.0708216i | ||||
\(455\) | −4.82049e17 | −0.119402 | ||||||||
\(456\) | 3.11810e18 | + | 3.11810e18i | 0.760565 | + | 0.760565i | ||||
\(457\) | 7.84237e18i | 1.88380i | 0.335900 | + | 0.941898i | \(0.390960\pi\) | ||||
−0.335900 | + | 0.941898i | \(0.609040\pi\) | |||||||
\(458\) | 3.57375e18 | 0.845407 | ||||||||
\(459\) | −2.36135e19 | −5.50137 | ||||||||
\(460\) | −1.78232e18 | −0.408961 | ||||||||
\(461\) | 4.50214e18 | − | 4.50214e18i | 1.01745 | − | 1.01745i | 0.0176048 | − | 0.999845i | \(-0.494396\pi\) |
0.999845 | − | 0.0176048i | \(-0.00560406\pi\) | |||||||
\(462\) | 4.22411e17 | − | 4.22411e17i | 0.0940246 | − | 0.0940246i | ||||
\(463\) | 6.89151e18i | 1.51094i | 0.655183 | + | 0.755470i | \(0.272591\pi\) | ||||
−0.655183 | + | 0.755470i | \(0.727409\pi\) | |||||||
\(464\) | −1.02231e18 | + | 1.45194e17i | −0.220779 | + | 0.0313561i | ||||
\(465\) | −5.38562e18 | −1.14568 | ||||||||
\(466\) | 3.20030e18 | + | 3.20030e18i | 0.670640 | + | 0.670640i | ||||
\(467\) | −4.73454e18 | − | 4.73454e18i | −0.977371 | − | 0.977371i | 0.0223790 | − | 0.999750i | \(-0.492876\pi\) |
−0.999750 | + | 0.0223790i | \(0.992876\pi\) | |||||||
\(468\) | − | 7.25498e18i | − | 1.47542i | ||||||
\(469\) | − | 2.16909e17i | − | 0.0434577i | ||||||
\(470\) | − | 8.79117e17i | − | 0.173525i | ||||||
\(471\) | −7.77471e18 | −1.51195 | ||||||||
\(472\) | −2.96536e18 | + | 2.96536e18i | −0.568178 | + | 0.568178i | ||||
\(473\) | 6.30422e18i | 1.19015i | ||||||||
\(474\) | 1.78896e18 | − | 1.78896e18i | 0.332777 | − | 0.332777i | ||||
\(475\) | −1.14384e18 | − | 1.14384e18i | −0.209658 | − | 0.209658i | ||||
\(476\) | 1.07403e18 | − | 1.07403e18i | 0.193984 | − | 0.193984i | ||||
\(477\) | 1.80676e18i | 0.321568i | ||||||||
\(478\) | −2.07696e17 | − | 2.07696e17i | −0.0364277 | − | 0.0364277i | ||||
\(479\) | −9.73194e17 | + | 9.73194e17i | −0.168210 | + | 0.168210i | −0.786192 | − | 0.617982i | \(-0.787950\pi\) |
0.617982 | + | 0.786192i | \(0.287950\pi\) | |||||||
\(480\) | 8.29033e18 | 1.41216 | ||||||||
\(481\) | −9.32898e17 | − | 9.32898e17i | −0.156610 | − | 0.156610i | ||||
\(482\) | 3.18526e18 | − | 3.18526e18i | 0.527005 | − | 0.527005i | ||||
\(483\) | 1.30942e18 | + | 1.30942e18i | 0.213525 | + | 0.213525i | ||||
\(484\) | −2.55695e18 | −0.410965 | ||||||||
\(485\) | −2.29349e18 | − | 2.29349e18i | −0.363333 | − | 0.363333i | ||||
\(486\) | 8.88127e18i | 1.38682i | ||||||||
\(487\) | 1.36458e18 | 0.210037 | 0.105019 | − | 0.994470i | \(-0.466510\pi\) | ||||
0.105019 | + | 0.994470i | \(0.466510\pi\) | |||||||
\(488\) | −1.14551e19 | −1.73805 | ||||||||
\(489\) | −5.12903e17 | −0.0767138 | ||||||||
\(490\) | 1.78174e18 | − | 1.78174e18i | 0.262708 | − | 0.262708i | ||||
\(491\) | 3.18535e18 | − | 3.18535e18i | 0.463006 | − | 0.463006i | −0.436634 | − | 0.899639i | \(-0.643829\pi\) |
0.899639 | + | 0.436634i | \(0.143829\pi\) | |||||||
\(492\) | − | 1.12736e19i | − | 1.61549i | ||||||
\(493\) | 1.07296e19 | + | 8.06092e18i | 1.51585 | + | 1.13882i | ||||
\(494\) | 1.94750e18 | 0.271262 | ||||||||
\(495\) | 6.17172e18 | + | 6.17172e18i | 0.847559 | + | 0.847559i | ||||
\(496\) | 9.79087e17 | + | 9.79087e17i | 0.132571 | + | 0.132571i | ||||
\(497\) | − | 3.01733e17i | − | 0.0402836i | ||||||
\(498\) | 9.90327e18i | 1.30369i | ||||||||
\(499\) | 1.18259e19i | 1.53508i | 0.641003 | + | 0.767538i | \(0.278518\pi\) | ||||
−0.641003 | + | 0.767538i | \(0.721482\pi\) | |||||||
\(500\) | −5.95763e18 | −0.762577 | ||||||||
\(501\) | 1.96448e19 | − | 1.96448e19i | 2.47961 | − | 2.47961i | ||||
\(502\) | 1.05625e18i | 0.131475i | ||||||||
\(503\) | −4.52857e18 | + | 4.52857e18i | −0.555886 | + | 0.555886i | −0.928133 | − | 0.372248i | \(-0.878587\pi\) |
0.372248 | + | 0.928133i | \(0.378587\pi\) | |||||||
\(504\) | −2.76026e18 | − | 2.76026e18i | −0.334146 | − | 0.334146i | ||||
\(505\) | −1.28083e18 | + | 1.28083e18i | −0.152915 | + | 0.152915i | ||||
\(506\) | − | 2.34233e18i | − | 0.275800i | ||||||
\(507\) | 3.87850e18 | + | 3.87850e18i | 0.450410 | + | 0.450410i | ||||
\(508\) | −2.52533e18 | + | 2.52533e18i | −0.289249 | + | 0.289249i | ||||
\(509\) | 1.21817e19 | 1.37621 | 0.688104 | − | 0.725612i | \(-0.258443\pi\) | ||||
0.688104 | + | 0.725612i | \(0.258443\pi\) | |||||||
\(510\) | −8.77279e18 | − | 8.77279e18i | −0.977567 | − | 0.977567i | ||||
\(511\) | −6.25542e17 | + | 6.25542e17i | −0.0687559 | + | 0.0687559i | ||||
\(512\) | −2.84077e18 | − | 2.84077e18i | −0.307997 | − | 0.307997i | ||||
\(513\) | 1.69098e19 | 1.80850 | ||||||||
\(514\) | 4.22633e18 | + | 4.22633e18i | 0.445884 | + | 0.445884i | ||||
\(515\) | 7.43976e18i | 0.774298i | ||||||||
\(516\) | 2.39056e19 | 2.45444 | ||||||||
\(517\) | −2.87965e18 | −0.291679 | ||||||||
\(518\) | −2.95631e17 | −0.0295421 | ||||||||
\(519\) | −5.27556e18 | + | 5.27556e18i | −0.520113 | + | 0.520113i | ||||
\(520\) | 3.92581e18 | − | 3.92581e18i | 0.381862 | − | 0.381862i | ||||
\(521\) | 6.00810e18i | 0.576598i | 0.957540 | + | 0.288299i | \(0.0930896\pi\) | ||||
−0.957540 | + | 0.288299i | \(0.906910\pi\) | |||||||
\(522\) | 8.62762e18 | − | 1.14840e19i | 0.816953 | − | 1.08742i | ||||
\(523\) | 3.81122e18 | 0.356084 | 0.178042 | − | 0.984023i | \(-0.443024\pi\) | ||||
0.178042 | + | 0.984023i | \(0.443024\pi\) | |||||||
\(524\) | −5.17734e18 | − | 5.17734e18i | −0.477296 | − | 0.477296i | ||||
\(525\) | 1.41094e18 | + | 1.41094e18i | 0.128350 | + | 0.128350i | ||||
\(526\) | − | 9.80816e18i | − | 0.880415i | ||||||
\(527\) | − | 1.79960e19i | − | 1.59405i | ||||||
\(528\) | − | 3.12683e18i | − | 0.273317i | ||||||
\(529\) | −4.33193e18 | −0.373673 | ||||||||
\(530\) | −4.07160e17 | + | 4.07160e17i | −0.0346604 | + | 0.0346604i | ||||
\(531\) | 2.65119e19i | 2.22730i | ||||||||
\(532\) | −7.69119e17 | + | 7.69119e17i | −0.0637694 | + | 0.0637694i | ||||
\(533\) | −8.45373e18 | − | 8.45373e18i | −0.691764 | − | 0.691764i | ||||
\(534\) | 4.20851e18 | − | 4.20851e18i | 0.339891 | − | 0.339891i | ||||
\(535\) | 1.15626e19i | 0.921677i | ||||||||
\(536\) | 1.76651e18 | + | 1.76651e18i | 0.138983 | + | 0.138983i | ||||
\(537\) | 2.30830e19 | − | 2.30830e19i | 1.79255 | − | 1.79255i | ||||
\(538\) | −1.04386e19 | −0.800138 | ||||||||
\(539\) | −5.83630e18 | − | 5.83630e18i | −0.441587 | − | 0.441587i | ||||
\(540\) | 1.41958e19 | − | 1.41958e19i | 1.06024 | − | 1.06024i | ||||
\(541\) | −8.55903e18 | − | 8.55903e18i | −0.631021 | − | 0.631021i | 0.317303 | − | 0.948324i | \(-0.397223\pi\) |
−0.948324 | + | 0.317303i | \(0.897223\pi\) | |||||||
\(542\) | −5.78627e18 | −0.421118 | ||||||||
\(543\) | 8.22829e18 | + | 8.22829e18i | 0.591168 | + | 0.591168i | ||||
\(544\) | 2.77021e19i | 1.96481i | ||||||||
\(545\) | −1.71566e17 | −0.0120131 | ||||||||
\(546\) | −2.40227e18 | −0.166063 | ||||||||
\(547\) | −1.38137e19 | −0.942754 | −0.471377 | − | 0.881932i | \(-0.656243\pi\) | ||||
−0.471377 | + | 0.881932i | \(0.656243\pi\) | |||||||
\(548\) | −9.30399e18 | + | 9.30399e18i | −0.626911 | + | 0.626911i | ||||
\(549\) | −5.12075e19 | + | 5.12075e19i | −3.40665 | + | 3.40665i | ||||
\(550\) | − | 2.52395e18i | − | 0.165783i | ||||||
\(551\) | −7.68359e18 | − | 5.77249e18i | −0.498314 | − | 0.374371i | ||||
\(552\) | −2.13278e19 | −1.36576 | ||||||||
\(553\) | 1.05958e18 | + | 1.05958e18i | 0.0669975 | + | 0.0669975i | ||||
\(554\) | 2.74379e18 | + | 2.74379e18i | 0.171310 | + | 0.171310i | ||||
\(555\) | − | 6.01871e18i | − | 0.371067i | ||||||
\(556\) | 6.14076e18i | 0.373851i | ||||||||
\(557\) | − | 1.70604e19i | − | 1.02566i | −0.858491 | − | 0.512829i | \(-0.828598\pi\) | ||
0.858491 | − | 0.512829i | \(-0.171402\pi\) | |||||||
\(558\) | −1.92612e19 | −1.14352 | ||||||||
\(559\) | 1.79262e19 | − | 1.79262e19i | 1.05100 | − | 1.05100i | ||||
\(560\) | 5.65386e17i | 0.0327363i | ||||||||
\(561\) | −2.87363e19 | + | 2.87363e19i | −1.64320 | + | 1.64320i | ||||
\(562\) | −4.06555e18 | − | 4.06555e18i | −0.229596 | − | 0.229596i | ||||
\(563\) | 1.29732e19 | − | 1.29732e19i | 0.723585 | − | 0.723585i | −0.245748 | − | 0.969334i | \(-0.579034\pi\) |
0.969334 | + | 0.245748i | \(0.0790336\pi\) | |||||||
\(564\) | 1.09196e19i | 0.601525i | ||||||||
\(565\) | 8.86079e18 | + | 8.86079e18i | 0.482096 | + | 0.482096i | ||||
\(566\) | 5.93495e16 | − | 5.93495e16i | 0.00318935 | − | 0.00318935i | ||||
\(567\) | −1.11495e19 | −0.591799 | ||||||||
\(568\) | 2.45732e18 | + | 2.45732e18i | 0.128832 | + | 0.128832i | ||||
\(569\) | 2.15643e18 | − | 2.15643e18i | 0.111673 | − | 0.111673i | −0.649062 | − | 0.760735i | \(-0.724839\pi\) |
0.760735 | + | 0.649062i | \(0.224839\pi\) | |||||||
\(570\) | 6.28227e18 | + | 6.28227e18i | 0.321361 | + | 0.321361i | ||||
\(571\) | 5.49118e18 | 0.277468 | 0.138734 | − | 0.990330i | \(-0.455697\pi\) | ||||
0.138734 | + | 0.990330i | \(0.455697\pi\) | |||||||
\(572\) | −5.35541e18 | − | 5.35541e18i | −0.267313 | − | 0.267313i | ||||
\(573\) | 6.62766e18i | 0.326797i | ||||||||
\(574\) | −2.67894e18 | −0.130491 | ||||||||
\(575\) | 7.82388e18 | 0.376485 | ||||||||
\(576\) | 1.77264e19 | 0.842683 | ||||||||
\(577\) | 2.05903e19 | − | 2.05903e19i | 0.967011 | − | 0.967011i | −0.0324616 | − | 0.999473i | \(-0.510335\pi\) |
0.999473 | + | 0.0324616i | \(0.0103347\pi\) | |||||||
\(578\) | 2.11594e19 | − | 2.11594e19i | 0.981769 | − | 0.981769i | ||||
\(579\) | − | 3.37724e19i | − | 1.54815i | ||||||
\(580\) | −1.12964e19 | + | 1.60437e18i | −0.511616 | + | 0.0726622i | ||||
\(581\) | −5.86559e18 | −0.262470 | ||||||||
\(582\) | −1.14295e19 | − | 1.14295e19i | −0.505320 | − | 0.505320i | ||||
\(583\) | 1.33370e18 | + | 1.33370e18i | 0.0582609 | + | 0.0582609i | ||||
\(584\) | − | 1.01889e19i | − | 0.439780i | ||||||
\(585\) | − | 3.50988e19i | − | 1.49693i | ||||||
\(586\) | − | 2.31332e18i | − | 0.0974882i | ||||||
\(587\) | 2.61272e19 | 1.08799 | 0.543997 | − | 0.839087i | \(-0.316910\pi\) | ||||
0.543997 | + | 0.839087i | \(0.316910\pi\) | |||||||
\(588\) | −2.21313e19 | + | 2.21313e19i | −0.910678 | + | 0.910678i | ||||
\(589\) | 1.28871e19i | 0.524021i | ||||||||
\(590\) | −5.97454e18 | + | 5.97454e18i | −0.240071 | + | 0.240071i | ||||
\(591\) | −6.56941e19 | − | 6.56941e19i | −2.60864 | − | 2.60864i | ||||
\(592\) | −1.09418e18 | + | 1.09418e18i | −0.0429375 | + | 0.0429375i | ||||
\(593\) | 1.30386e19i | 0.505648i | 0.967512 | + | 0.252824i | \(0.0813594\pi\) | ||||
−0.967512 | + | 0.252824i | \(0.918641\pi\) | |||||||
\(594\) | 1.86562e19 | + | 1.86562e19i | 0.715019 | + | 0.715019i | ||||
\(595\) | 5.19602e18 | − | 5.19602e18i | 0.196812 | − | 0.196812i | ||||
\(596\) | 2.82757e19 | 1.05850 | ||||||||
\(597\) | 4.88419e19 | + | 4.88419e19i | 1.80706 | + | 1.80706i | ||||
\(598\) | −6.66046e18 | + | 6.66046e18i | −0.243554 | + | 0.243554i | ||||
\(599\) | −1.67564e19 | − | 1.67564e19i | −0.605610 | − | 0.605610i | 0.336185 | − | 0.941796i | \(-0.390863\pi\) |
−0.941796 | + | 0.336185i | \(0.890863\pi\) | |||||||
\(600\) | −2.29815e19 | −0.820955 | ||||||||
\(601\) | −4.15842e18 | − | 4.15842e18i | −0.146827 | − | 0.146827i | 0.629872 | − | 0.776699i | \(-0.283107\pi\) |
−0.776699 | + | 0.629872i | \(0.783107\pi\) | |||||||
\(602\) | − | 5.68070e18i | − | 0.198256i | ||||||
\(603\) | 1.57935e19 | 0.544825 | ||||||||
\(604\) | −2.14640e19 | −0.731902 | ||||||||
\(605\) | −1.23703e19 | −0.416957 | ||||||||
\(606\) | −6.38295e18 | + | 6.38295e18i | −0.212673 | + | 0.212673i | ||||
\(607\) | 1.75765e19 | − | 1.75765e19i | 0.578910 | − | 0.578910i | −0.355693 | − | 0.934603i | \(-0.615755\pi\) |
0.934603 | + | 0.355693i | \(0.115755\pi\) | |||||||
\(608\) | − | 1.98377e19i | − | 0.645902i | ||||||
\(609\) | 9.47780e18 | + | 7.12044e18i | 0.305061 | + | 0.229185i | ||||
\(610\) | −2.30795e19 | −0.734376 | ||||||||
\(611\) | 8.18832e18 | + | 8.18832e18i | 0.257577 | + | 0.257577i | ||||
\(612\) | 7.82016e19 | + | 7.82016e19i | 2.43196 | + | 2.43196i | ||||
\(613\) | − | 6.28825e19i | − | 1.93333i | −0.256041 | − | 0.966666i | \(-0.582418\pi\) | ||
0.256041 | − | 0.966666i | \(-0.417582\pi\) | |||||||
\(614\) | 1.69439e19i | 0.515033i | ||||||||
\(615\) | − | 5.45402e19i | − | 1.63905i | ||||||
\(616\) | −4.07509e18 | −0.121080 | ||||||||
\(617\) | −4.42237e19 | + | 4.42237e19i | −1.29915 | + | 1.29915i | −0.370194 | + | 0.928955i | \(0.620709\pi\) |
−0.928955 | + | 0.370194i | \(0.879291\pi\) | |||||||
\(618\) | 3.70757e19i | 1.07689i | ||||||||
\(619\) | −4.00346e18 | + | 4.00346e18i | −0.114974 | + | 0.114974i | −0.762253 | − | 0.647279i | \(-0.775907\pi\) |
0.647279 | + | 0.762253i | \(0.275907\pi\) | |||||||
\(620\) | 1.08188e19 | + | 1.08188e19i | 0.307210 | + | 0.307210i | ||||
\(621\) | −5.78316e19 | + | 5.78316e19i | −1.62377 | + | 1.62377i | ||||
\(622\) | − | 8.38763e17i | − | 0.0232866i | ||||||
\(623\) | 2.49265e18 | + | 2.49265e18i | 0.0684298 | + | 0.0684298i | ||||
\(624\) | −8.89121e18 | + | 8.89121e18i | −0.241362 | + | 0.241362i | ||||
\(625\) | −1.11006e19 | −0.297980 | ||||||||
\(626\) | 9.74393e18 | + | 9.74393e18i | 0.258651 | + | 0.258651i | ||||
\(627\) | 2.05783e19 | − | 2.05783e19i | 0.540177 | − | 0.540177i | ||||
\(628\) | 1.56180e19 | + | 1.56180e19i | 0.405423 | + | 0.405423i | ||||
\(629\) | 2.01115e19 | 0.516285 | ||||||||
\(630\) | −5.56131e18 | − | 5.56131e18i | −0.141187 | − | 0.141187i | ||||
\(631\) | − | 1.75309e19i | − | 0.440148i | −0.975483 | − | 0.220074i | \(-0.929370\pi\) | ||
0.975483 | − | 0.220074i | \(-0.0706298\pi\) | |||||||
\(632\) | −1.72585e19 | −0.428532 | ||||||||
\(633\) | 9.23346e17 | 0.0226745 | ||||||||
\(634\) | −6.73653e18 | −0.163611 | ||||||||
\(635\) | −1.22173e19 | + | 1.22173e19i | −0.293466 | + | 0.293466i | ||||
\(636\) | 5.05738e18 | − | 5.05738e18i | 0.120151 | − | 0.120151i | ||||
\(637\) | 3.31913e19i | 0.779916i | ||||||||
\(638\) | −2.10847e18 | − | 1.48458e19i | −0.0490029 | − | 0.345031i | ||||
\(639\) | 2.19697e19 | 0.505031 | ||||||||
\(640\) | −1.93407e19 | − | 1.93407e19i | −0.439758 | − | 0.439758i | ||||
\(641\) | −1.54209e17 | − | 1.54209e17i | −0.00346819 | − | 0.00346819i | 0.705371 | − | 0.708839i | \(-0.250781\pi\) |
−0.708839 | + | 0.705371i | \(0.750781\pi\) | |||||||
\(642\) | 5.76216e19i | 1.28186i | ||||||||
\(643\) | − | 2.64698e19i | − | 0.582471i | −0.956651 | − | 0.291235i | \(-0.905934\pi\) | ||
0.956651 | − | 0.291235i | \(-0.0940663\pi\) | |||||||
\(644\) | − | 5.26077e18i | − | 0.114511i | ||||||
\(645\) | 1.15653e20 | 2.49022 | ||||||||
\(646\) | −2.09922e19 | + | 2.09922e19i | −0.447126 | + | 0.447126i | ||||
\(647\) | 1.17468e19i | 0.247508i | 0.992313 | + | 0.123754i | \(0.0394934\pi\) | ||||
−0.992313 | + | 0.123754i | \(0.960507\pi\) | |||||||
\(648\) | 9.08017e19 | − | 9.08017e19i | 1.89264 | − | 1.89264i | ||||
\(649\) | 1.95703e19 | + | 1.95703e19i | 0.403538 | + | 0.403538i | ||||
\(650\) | −7.17689e18 | + | 7.17689e18i | −0.146400 | + | 0.146400i | ||||
\(651\) | − | 1.58964e19i | − | 0.320798i | ||||||
\(652\) | 1.03033e18 | + | 1.03033e18i | 0.0205705 | + | 0.0205705i | ||||
\(653\) | 5.41769e19 | − | 5.41769e19i | 1.07009 | − | 1.07009i | 0.0727437 | − | 0.997351i | \(-0.476824\pi\) |
0.997351 | − | 0.0727437i | \(-0.0231755\pi\) | |||||||
\(654\) | −8.54993e17 | −0.0167078 | ||||||||
\(655\) | −2.50474e19 | − | 2.50474e19i | −0.484255 | − | 0.484255i | ||||
\(656\) | −9.91523e18 | + | 9.91523e18i | −0.189660 | + | 0.189660i | ||||
\(657\) | −4.55468e19 | − | 4.55468e19i | −0.861986 | − | 0.861986i | ||||
\(658\) | 2.59484e18 | 0.0485880 | ||||||||
\(659\) | 1.16257e19 | + | 1.16257e19i | 0.215388 | + | 0.215388i | 0.806552 | − | 0.591163i | \(-0.201331\pi\) |
−0.591163 | + | 0.806552i | \(0.701331\pi\) | |||||||
\(660\) | − | 3.45510e19i | − | 0.633364i | ||||||
\(661\) | −1.00629e20 | −1.82521 | −0.912606 | − | 0.408841i | \(-0.865933\pi\) | ||||
−0.912606 | + | 0.408841i | \(0.865933\pi\) | |||||||
\(662\) | 2.31255e19 | 0.415035 | ||||||||
\(663\) | 1.63424e20 | 2.90216 | ||||||||
\(664\) | 4.77695e19 | − | 4.77695e19i | 0.839409 | − | 0.839409i | ||||
\(665\) | −3.72091e18 | + | 3.72091e18i | −0.0646991 | + | 0.0646991i | ||||
\(666\) | − | 2.15254e19i | − | 0.370366i | ||||||
\(667\) | 4.60198e19 | − | 6.53596e18i | 0.783545 | − | 0.111283i | ||||
\(668\) | −7.89258e19 | −1.32979 | ||||||||
\(669\) | 8.65310e19 | + | 8.65310e19i | 1.44274 | + | 1.44274i | ||||
\(670\) | 3.55911e18 | + | 3.55911e18i | 0.0587244 | + | 0.0587244i | ||||
\(671\) | 7.55996e19i | 1.23442i | ||||||||
\(672\) | 2.44701e19i | 0.395412i | ||||||||
\(673\) | − | 4.79193e19i | − | 0.766310i | −0.923684 | − | 0.383155i | \(-0.874837\pi\) | ||
0.923684 | − | 0.383155i | \(-0.125163\pi\) | |||||||
\(674\) | −3.92333e19 | −0.620920 | ||||||||
\(675\) | −6.23156e19 | + | 6.23156e19i | −0.976047 | + | 0.976047i | ||||
\(676\) | − | 1.55825e19i | − | 0.241551i | ||||||
\(677\) | −3.63672e19 | + | 3.63672e19i | −0.557943 | + | 0.557943i | −0.928721 | − | 0.370779i | \(-0.879091\pi\) |
0.370779 | + | 0.928721i | \(0.379091\pi\) | |||||||
\(678\) | 4.41573e19 | + | 4.41573e19i | 0.670494 | + | 0.670494i | ||||
\(679\) | 6.76956e18 | − | 6.76956e18i | 0.101735 | − | 0.101735i | ||||
\(680\) | 8.46329e19i | 1.25886i | ||||||||
\(681\) | −1.69190e19 | − | 1.69190e19i | −0.249083 | − | 0.249083i | ||||
\(682\) | −1.42180e19 | + | 1.42180e19i | −0.207180 | + | 0.207180i | ||||
\(683\) | 5.50209e19 | 0.793565 | 0.396783 | − | 0.917913i | \(-0.370127\pi\) | ||||
0.396783 | + | 0.917913i | \(0.370127\pi\) | |||||||
\(684\) | −5.60009e19 | − | 5.60009e19i | −0.799470 | − | 0.799470i | ||||
\(685\) | −4.50117e19 | + | 4.50117e19i | −0.636051 | + | 0.636051i | ||||
\(686\) | 1.07436e19 | + | 1.07436e19i | 0.150273 | + | 0.150273i | ||||
\(687\) | −2.14754e20 | −2.97334 | ||||||||
\(688\) | −2.10253e19 | − | 2.10253e19i | −0.288152 | − | 0.288152i | ||||
\(689\) | − | 7.58478e18i | − | 0.102898i | ||||||
\(690\) | −4.29707e19 | −0.577071 | ||||||||
\(691\) | 1.00668e20 | 1.33828 | 0.669140 | − | 0.743136i | \(-0.266662\pi\) | ||||
0.669140 | + | 0.743136i | \(0.266662\pi\) | |||||||
\(692\) | 2.11954e19 | 0.278932 | ||||||||
\(693\) | −1.82167e19 | + | 1.82167e19i | −0.237321 | + | 0.237321i | ||||
\(694\) | −2.04383e19 | + | 2.04383e19i | −0.263590 | + | 0.263590i | ||||
\(695\) | 2.97083e19i | 0.379302i | ||||||||
\(696\) | −1.35176e20 | + | 1.91984e19i | −1.70858 | + | 0.242661i | ||||
\(697\) | 1.82246e20 | 2.28049 | ||||||||
\(698\) | 3.27256e19 | + | 3.27256e19i | 0.405415 | + | 0.405415i | ||||
\(699\) | −1.92313e20 | − | 1.92313e20i | −2.35867 | − | 2.35867i | ||||
\(700\) | − | 5.66867e18i | − | 0.0688328i | ||||||
\(701\) | − | 2.31238e19i | − | 0.277992i | −0.990293 | − | 0.138996i | \(-0.955612\pi\) | ||
0.990293 | − | 0.138996i | \(-0.0443875\pi\) | |||||||
\(702\) | − | 1.06098e20i | − | 1.26284i | ||||||
\(703\) | −1.44020e19 | −0.169721 | ||||||||
\(704\) | 1.30851e19 | − | 1.30851e19i | 0.152675 | − | 0.152675i | ||||
\(705\) | 5.28279e19i | 0.610295i | ||||||||
\(706\) | 2.97450e19 | − | 2.97450e19i | 0.340236 | − | 0.340236i | ||||
\(707\) | −3.78054e18 | − | 3.78054e18i | −0.0428172 | − | 0.0428172i | ||||
\(708\) | 7.42105e19 | − | 7.42105e19i | 0.832210 | − | 0.832210i | ||||
\(709\) | − | 1.19336e20i | − | 1.32510i | −0.749017 | − | 0.662551i | \(-0.769474\pi\) | ||
0.749017 | − | 0.662551i | \(-0.230526\pi\) | |||||||
\(710\) | 4.95094e18 | + | 4.95094e18i | 0.0544351 | + | 0.0544351i | ||||
\(711\) | −7.71500e19 | + | 7.71500e19i | −0.839941 | + | 0.839941i | ||||
\(712\) | −4.06004e19 | −0.437694 | ||||||||
\(713\) | −4.40739e19 | − | 4.40739e19i | −0.470495 | − | 0.470495i | ||||
\(714\) | 2.58941e19 | − | 2.58941e19i | 0.273724 | − | 0.273724i | ||||
\(715\) | −2.59089e19 | − | 2.59089e19i | −0.271210 | − | 0.271210i | ||||
\(716\) | −9.27394e19 | −0.961331 | ||||||||
\(717\) | 1.24809e19 | + | 1.24809e19i | 0.128118 | + | 0.128118i | ||||
\(718\) | 9.52629e19i | 0.968395i | ||||||||
\(719\) | 1.14477e20 | 1.15244 | 0.576219 | − | 0.817296i | \(-0.304528\pi\) | ||||
0.576219 | + | 0.817296i | \(0.304528\pi\) | |||||||
\(720\) | −4.11667e19 | −0.410411 | ||||||||
\(721\) | −2.19595e19 | −0.216808 | ||||||||
\(722\) | −2.36644e19 | + | 2.36644e19i | −0.231385 | + | 0.231385i | ||||
\(723\) | −1.91409e20 | + | 1.91409e20i | −1.85350 | + | 1.85350i | ||||
\(724\) | − | 3.30584e19i | − | 0.317038i | ||||||
\(725\) | 4.95880e19 | − | 7.04273e18i | 0.470989 | − | 0.0668921i | ||||
\(726\) | −6.16466e19 | −0.579900 | ||||||||
\(727\) | 4.05188e19 | + | 4.05188e19i | 0.377499 | + | 0.377499i | 0.870199 | − | 0.492700i | \(-0.163990\pi\) |
−0.492700 | + | 0.870199i | \(0.663990\pi\) | |||||||
\(728\) | 1.15876e19 | + | 1.15876e19i | 0.106924 | + | 0.106924i | ||||
\(729\) | − | 2.14308e20i | − | 1.95860i | ||||||
\(730\) | − | 2.05282e19i | − | 0.185820i | ||||||
\(731\) | 3.86453e20i | 3.46478i | ||||||||
\(732\) | 2.86674e20 | 2.54572 | ||||||||
\(733\) | 4.67208e19 | − | 4.67208e19i | 0.410944 | − | 0.410944i | −0.471124 | − | 0.882067i | \(-0.656151\pi\) |
0.882067 | + | 0.471124i | \(0.156151\pi\) | |||||||
\(734\) | − | 1.16141e20i | − | 1.01185i | ||||||
\(735\) | −1.07069e20 | + | 1.07069e20i | −0.923956 | + | 0.923956i | ||||
\(736\) | 6.78450e19 | + | 6.78450e19i | 0.579927 | + | 0.579927i | ||||
\(737\) | 1.16583e19 | − | 1.16583e19i | 0.0987102 | − | 0.0987102i | ||||
\(738\) | − | 1.95058e20i | − | 1.63595i | ||||||
\(739\) | −1.12681e20 | − | 1.12681e20i | −0.936139 | − | 0.936139i | 0.0619409 | − | 0.998080i | \(-0.480271\pi\) |
−0.998080 | + | 0.0619409i | \(0.980271\pi\) | |||||||
\(740\) | −1.20905e19 | + | 1.20905e19i | −0.0995000 | + | 0.0995000i | ||||
\(741\) | −1.17029e20 | −0.954042 | ||||||||
\(742\) | −1.20179e18 | − | 1.20179e18i | −0.00970512 | − | 0.00970512i | ||||
\(743\) | 1.86280e19 | − | 1.86280e19i | 0.149020 | − | 0.149020i | −0.628660 | − | 0.777680i | \(-0.716396\pi\) |
0.777680 | + | 0.628660i | \(0.216396\pi\) | |||||||
\(744\) | 1.29461e20 | + | 1.29461e20i | 1.02595 | + | 1.02595i | ||||
\(745\) | 1.36795e20 | 1.07393 | ||||||||
\(746\) | −5.34144e19 | − | 5.34144e19i | −0.415419 | − | 0.415419i | ||||
\(747\) | − | 4.27084e20i | − | 3.29055i | ||||||
\(748\) | 1.15452e20 | 0.881233 | ||||||||
\(749\) | −3.41286e19 | −0.258075 | ||||||||
\(750\) | −1.43635e20 | −1.07605 | ||||||||
\(751\) | 1.30339e20 | − | 1.30339e20i | 0.967375 | − | 0.967375i | −0.0321094 | − | 0.999484i | \(-0.510223\pi\) |
0.999484 | + | 0.0321094i | \(0.0102225\pi\) | |||||||
\(752\) | 9.60393e18 | − | 9.60393e18i | 0.0706194 | − | 0.0706194i | ||||
\(753\) | − | 6.34725e19i | − | 0.462403i | ||||||
\(754\) | −3.62187e19 | + | 4.82096e19i | −0.261417 | + | 0.347964i | ||||
\(755\) | −1.03841e20 | −0.742572 | ||||||||
\(756\) | 4.19010e19 | + | 4.19010e19i | 0.296874 | + | 0.296874i | ||||
\(757\) | 1.07890e20 | + | 1.07890e20i | 0.757374 | + | 0.757374i | 0.975844 | − | 0.218469i | \(-0.0701064\pi\) |
−0.218469 | + | 0.975844i | \(0.570106\pi\) | |||||||
\(758\) | 1.06515e20i | 0.740841i | ||||||||
\(759\) | 1.40755e20i | 0.970003i | ||||||||
\(760\) | − | 6.06064e19i | − | 0.413831i | ||||||
\(761\) | 5.41190e19 | 0.366149 | 0.183074 | − | 0.983099i | \(-0.441395\pi\) | ||||
0.183074 | + | 0.983099i | \(0.441395\pi\) | |||||||
\(762\) | −6.08842e19 | + | 6.08842e19i | −0.408150 | + | 0.408150i | ||||
\(763\) | − | 5.06402e17i | − | 0.00336375i | ||||||
\(764\) | 1.33138e19 | − | 1.33138e19i | 0.0876292 | − | 0.0876292i | ||||
\(765\) | 3.78331e20 | + | 3.78331e20i | 2.46741 | + | 2.46741i | ||||
\(766\) | −2.90905e19 | + | 2.90905e19i | −0.187996 | + | 0.187996i | ||||
\(767\) | − | 1.11297e20i | − | 0.712714i | ||||||
\(768\) | −1.65910e20 | − | 1.65910e20i | −1.05280 | − | 1.05280i | ||||
\(769\) | −1.07417e20 | + | 1.07417e20i | −0.675440 | + | 0.675440i | −0.958965 | − | 0.283525i | \(-0.908496\pi\) |
0.283525 | + | 0.958965i | \(0.408496\pi\) | |||||||
\(770\) | −8.21038e18 | −0.0511598 | ||||||||
\(771\) | −2.53969e20 | − | 2.53969e20i | −1.56820 | − | 1.56820i | ||||
\(772\) | −6.78429e19 | + | 6.78429e19i | −0.415129 | + | 0.415129i | ||||
\(773\) | 6.75970e19 | + | 6.75970e19i | 0.409894 | + | 0.409894i | 0.881701 | − | 0.471808i | \(-0.156398\pi\) |
−0.471808 | + | 0.881701i | \(0.656398\pi\) | |||||||
\(774\) | 4.13622e20 | 2.48552 | ||||||||
\(775\) | −4.74912e19 | − | 4.74912e19i | −0.282814 | − | 0.282814i | ||||
\(776\) | 1.10263e20i | 0.650724i | ||||||||
\(777\) | 1.77650e19 | 0.103901 | ||||||||
\(778\) | 5.83806e19 | 0.338385 | ||||||||
\(779\) | −1.30508e20 | −0.749678 | ||||||||
\(780\) | −9.82465e19 | + | 9.82465e19i | −0.559313 | + | 0.559313i | ||||
\(781\) | 1.62174e19 | − | 1.62174e19i | 0.0915004 | − | 0.0915004i | ||||
\(782\) | − | 1.43587e20i | − | 0.802909i | ||||||
\(783\) | −3.14481e20 | + | 4.18596e20i | −1.74286 | + | 2.31986i | ||||
\(784\) | 3.89294e19 | 0.213828 | ||||||||
\(785\) | 7.55583e19 | + | 7.55583e19i | 0.411334 | + | 0.411334i | ||||
\(786\) | −1.24823e20 | − | 1.24823e20i | −0.673496 | − | 0.673496i | ||||
\(787\) | − | 2.28850e20i | − | 1.22385i | −0.790916 | − | 0.611925i | \(-0.790395\pi\) | ||
0.790916 | − | 0.611925i | \(-0.209605\pi\) | |||||||
\(788\) | 2.63936e20i | 1.39899i | ||||||||
\(789\) | 5.89393e20i | 3.09646i | ||||||||
\(790\) | −3.47720e19 | −0.181067 | ||||||||
\(791\) | −2.61539e19 | + | 2.61539e19i | −0.134990 | + | 0.134990i | ||||
\(792\) | − | 2.96714e20i | − | 1.51797i | ||||||
\(793\) | 2.14969e20 | − | 2.14969e20i | 1.09009 | − | 1.09009i | ||||
\(794\) | 1.14985e20 | + | 1.14985e20i | 0.577959 | + | 0.577959i | ||||
\(795\) | 2.44671e19 | − | 2.44671e19i | 0.121902 | − | 0.121902i | ||||
\(796\) | − | 1.96229e20i | − | 0.969109i | ||||||
\(797\) | 2.42410e19 | + | 2.42410e19i | 0.118670 | + | 0.118670i | 0.763948 | − | 0.645278i | \(-0.223258\pi\) |
−0.645278 | + | 0.763948i | \(0.723258\pi\) | |||||||
\(798\) | −1.85430e19 | + | 1.85430e19i | −0.0899829 | + | 0.0899829i | ||||
\(799\) | −1.76524e20 | −0.849136 | ||||||||
\(800\) | 7.31055e19 | + | 7.31055e19i | 0.348594 | + | 0.348594i | ||||
\(801\) | −1.81494e20 | + | 1.81494e20i | −0.857897 | + | 0.857897i | ||||
\(802\) | −7.55311e19 | − | 7.55311e19i | −0.353920 | − | 0.353920i | ||||
\(803\) | −6.72425e19 | −0.312346 | ||||||||
\(804\) | −4.42082e19 | − | 4.42082e19i | −0.203568 | − | 0.203568i | ||||
\(805\) | − | 2.54511e19i | − | 0.116181i | ||||||
\(806\) | 8.08584e19 | 0.365915 | ||||||||
\(807\) | 6.27275e20 | 2.81412 | ||||||||
\(808\) | 6.15776e19 | 0.273869 | ||||||||
\(809\) | 6.55444e19 | − | 6.55444e19i | 0.288999 | − | 0.288999i | −0.547686 | − | 0.836684i | \(-0.684491\pi\) |
0.836684 | + | 0.547686i | \(0.184491\pi\) | |||||||
\(810\) | 1.82945e20 | − | 1.82945e20i | 0.799697 | − | 0.799697i | ||||
\(811\) | 1.33538e19i | 0.0578705i | 0.999581 | + | 0.0289353i | \(0.00921167\pi\) | ||||
−0.999581 | + | 0.0289353i | \(0.990788\pi\) | |||||||
\(812\) | −4.73552e18 | − | 3.33429e19i | −0.0203459 | − | 0.143256i | ||||
\(813\) | 3.47709e20 | 1.48109 | ||||||||
\(814\) | −1.58894e19 | − | 1.58894e19i | −0.0671021 | − | 0.0671021i | ||||
\(815\) | 4.98464e18 | + | 4.98464e18i | 0.0208704 | + | 0.0208704i | ||||
\(816\) | − | 1.91677e20i | − | 0.795681i | ||||||
\(817\) | − | 2.76742e20i | − | 1.13899i | ||||||
\(818\) | 5.92379e19i | 0.241728i | ||||||||
\(819\) | 1.03599e20 | 0.419149 | ||||||||
\(820\) | −1.09562e20 | + | 1.09562e20i | −0.439503 | + | 0.439503i | ||||
\(821\) | − | 2.44658e20i | − | 0.973099i | −0.873653 | − | 0.486549i | \(-0.838255\pi\) | ||
0.873653 | − | 0.486549i | \(-0.161745\pi\) | |||||||
\(822\) | −2.24314e20 | + | 2.24314e20i | −0.884613 | + | 0.884613i | ||||
\(823\) | 1.16674e20 | + | 1.16674e20i | 0.456219 | + | 0.456219i | 0.897412 | − | 0.441193i | \(-0.145445\pi\) |
−0.441193 | + | 0.897412i | \(0.645445\pi\) | |||||||
\(824\) | 1.78838e20 | − | 1.78838e20i | 0.693378 | − | 0.693378i | ||||
\(825\) | 1.51669e20i | 0.583068i | ||||||||
\(826\) | −1.76347e19 | − | 1.76347e19i | −0.0672214 | − | 0.0672214i | ||||
\(827\) | −2.50337e20 | + | 2.50337e20i | −0.946209 | + | 0.946209i | −0.998625 | − | 0.0524161i | \(-0.983308\pi\) |
0.0524161 | + | 0.998625i | \(0.483308\pi\) | |||||||
\(828\) | 3.83046e20 | 1.43562 | ||||||||
\(829\) | 8.18348e19 | + | 8.18348e19i | 0.304128 | + | 0.304128i | 0.842627 | − | 0.538498i | \(-0.181008\pi\) |
−0.538498 | + | 0.842627i | \(0.681008\pi\) | |||||||
\(830\) | 9.62447e19 | − | 9.62447e19i | 0.354675 | − | 0.354675i | ||||
\(831\) | −1.64880e20 | − | 1.64880e20i | −0.602505 | − | 0.602505i | ||||
\(832\) | −7.44155e19 | −0.269650 | ||||||||
\(833\) | −3.57770e20 | − | 3.57770e20i | −1.28555 | − | 1.28555i | ||||
\(834\) | 1.48050e20i | 0.527529i | ||||||||
\(835\) | −3.81835e20 | −1.34918 | ||||||||
\(836\) | −8.26763e19 | −0.289692 | ||||||||
\(837\) | 7.02079e20 | 2.43954 | ||||||||
\(838\) | 1.37832e20 | − | 1.37832e20i | 0.474942 | − | 0.474942i | ||||
\(839\) | −2.46308e20 | + | 2.46308e20i | −0.841677 | + | 0.841677i | −0.989077 | − | 0.147400i | \(-0.952910\pi\) |
0.147400 | + | 0.989077i | \(0.452910\pi\) | |||||||
\(840\) | 7.47587e19i | 0.253342i | ||||||||
\(841\) | 2.85791e20 | − | 8.28501e19i | 0.960456 | − | 0.278433i | ||||
\(842\) | 9.97773e19 | 0.332542 | ||||||||
\(843\) | 2.44307e20 | + | 2.44307e20i | 0.807501 | + | 0.807501i | ||||
\(844\) | −1.85484e18 | − | 1.85484e18i | −0.00608008 | − | 0.00608008i | ||||
\(845\) | − | 7.53862e19i | − | 0.245073i | ||||||
\(846\) | 1.88934e20i | 0.609142i | ||||||||
\(847\) | − | 3.65126e19i | − | 0.116750i | ||||||
\(848\) | −8.89606e18 | −0.0282115 | ||||||||
\(849\) | −3.56644e18 | + | 3.56644e18i | −0.0112171 | + | 0.0112171i | ||||
\(850\) | − | 1.54720e20i | − | 0.482629i | ||||||
\(851\) | 4.92549e19 | − | 4.92549e19i | 0.152385 | − | 0.152385i | ||||
\(852\) | −6.14962e19 | − | 6.14962e19i | −0.188700 | − | 0.188700i | ||||
\(853\) | −2.30765e20 | + | 2.30765e20i | −0.702306 | + | 0.702306i | −0.964905 | − | 0.262599i | \(-0.915420\pi\) |
0.262599 | + | 0.964905i | \(0.415420\pi\) | |||||||
\(854\) | − | 6.81225e19i | − | 0.205630i | ||||||
\(855\) | −2.70926e20 | − | 2.70926e20i | −0.811126 | − | 0.811126i | ||||
\(856\) | 2.77944e20 | − | 2.77944e20i | 0.825355 | − | 0.825355i | ||||
\(857\) | −3.12364e20 | −0.920016 | −0.460008 | − | 0.887915i | \(-0.652153\pi\) | ||||
−0.460008 | + | 0.887915i | \(0.652153\pi\) | |||||||
\(858\) | −1.29116e20 | − | 1.29116e20i | −0.377197 | − | 0.377197i | ||||
\(859\) | 4.37711e19 | − | 4.37711e19i | 0.126834 | − | 0.126834i | −0.640840 | − | 0.767674i | \(-0.721414\pi\) |
0.767674 | + | 0.640840i | \(0.221414\pi\) | |||||||
\(860\) | −2.32326e20 | − | 2.32326e20i | −0.667742 | − | 0.667742i | ||||
\(861\) | 1.60983e20 | 0.458943 | ||||||||
\(862\) | −1.91032e20 | − | 1.91032e20i | −0.540201 | − | 0.540201i | ||||
\(863\) | − | 6.20342e20i | − | 1.74002i | −0.493030 | − | 0.870012i | \(-0.664111\pi\) | ||
0.493030 | − | 0.870012i | \(-0.335889\pi\) | |||||||
\(864\) | −1.08074e21 | −3.00695 | ||||||||
\(865\) | 1.02541e20 | 0.282999 | ||||||||
\(866\) | 2.97954e20 | 0.815687 | ||||||||
\(867\) | −1.27151e21 | + | 1.27151e21i | −3.45293 | + | 3.45293i | ||||
\(868\) | −3.19331e19 | + | 3.19331e19i | −0.0860206 | + | 0.0860206i | ||||
\(869\) | 1.13900e20i | 0.304357i | ||||||||
\(870\) | −2.72350e20 | + | 3.86804e19i | −0.721925 | + | 0.102531i | ||||
\(871\) | −6.63010e19 | −0.174338 | ||||||||
\(872\) | 4.12415e18 | + | 4.12415e18i | 0.0107577 | + | 0.0107577i | ||||
\(873\) | 4.92903e20 | + | 4.92903e20i | 1.27545 | + | 1.27545i | ||||
\(874\) | 1.02824e20i | 0.263945i | ||||||||
\(875\) | − | 8.50733e19i | − | 0.216639i | ||||||
\(876\) | 2.54984e20i | 0.644145i | ||||||||
\(877\) | −2.88814e19 | −0.0723804 | −0.0361902 | − | 0.999345i | \(-0.511522\pi\) | ||||
−0.0361902 | + | 0.999345i | \(0.511522\pi\) | |||||||
\(878\) | −1.49358e20 | + | 1.49358e20i | −0.371335 | + | 0.371335i | ||||
\(879\) | 1.39012e20i | 0.342871i | ||||||||
\(880\) | −3.03880e19 | + | 3.03880e19i | −0.0743574 | + | 0.0743574i | ||||
\(881\) | 6.81011e19 | + | 6.81011e19i | 0.165319 | + | 0.165319i | 0.784918 | − | 0.619599i | \(-0.212705\pi\) |
−0.619599 | + | 0.784918i | \(0.712705\pi\) | |||||||
\(882\) | −3.82922e20 | + | 3.82922e20i | −0.922210 | + | 0.922210i | ||||
\(883\) | 5.73939e19i | 0.137133i | 0.997647 | + | 0.0685663i | \(0.0218425\pi\) | ||||
−0.997647 | + | 0.0685663i | \(0.978158\pi\) | |||||||
\(884\) | −3.28290e20 | − | 3.28290e20i | −0.778202 | − | 0.778202i | ||||
\(885\) | 3.59023e20 | − | 3.59023e20i | 0.844343 | − | 0.844343i | ||||
\(886\) | −2.94734e20 | −0.687693 | ||||||||
\(887\) | 1.49366e20 | + | 1.49366e20i | 0.345770 | + | 0.345770i | 0.858531 | − | 0.512761i | \(-0.171377\pi\) |
−0.512761 | + | 0.858531i | \(0.671377\pi\) | |||||||
\(888\) | −1.44679e20 | + | 1.44679e20i | −0.332288 | + | 0.332288i | ||||
\(889\) | −3.60610e19 | − | 3.60610e19i | −0.0821723 | − | 0.0821723i | ||||
\(890\) | −8.18006e19 | −0.184938 | ||||||||
\(891\) | −5.99257e20 | − | 5.99257e20i | −1.34422 | − | 1.34422i | ||||
\(892\) | − | 3.47651e20i | − | 0.773730i | ||||||
\(893\) | 1.26411e20 | 0.279141 | ||||||||
\(894\) | 6.81711e20 | 1.49361 | ||||||||
\(895\) | −4.48663e20 | −0.975347 | ||||||||
\(896\) | 5.70869e19 | − | 5.70869e19i | 0.123135 | − | 0.123135i | ||||
\(897\) | 4.00241e20 | − | 4.00241e20i | 0.856592 | − | 0.856592i | ||||
\(898\) | 3.75485e19i | 0.0797367i | ||||||||
\(899\) | −3.19015e20 | − | 2.39668e20i | −0.672192 | − | 0.505002i | ||||
\(900\) | 4.12746e20 | 0.862949 | ||||||||
\(901\) | 8.17566e19 | + | 8.17566e19i | 0.169609 | + | 0.169609i | ||||
\(902\) | −1.43986e20 | − | 1.43986e20i | −0.296398 | − | 0.296398i | ||||
\(903\) | 3.41365e20i | 0.697276i | ||||||||
\(904\) | − | 4.25995e20i | − | 0.863426i | ||||||
\(905\) | − | 1.59933e20i | − | 0.321660i | ||||||
\(906\) | −5.17485e20 | −1.03276 | ||||||||
\(907\) | −4.47350e20 | + | 4.47350e20i | −0.885924 | + | 0.885924i | −0.994129 | − | 0.108205i | \(-0.965490\pi\) |
0.108205 | + | 0.994129i | \(0.465490\pi\) | |||||||
\(908\) | 6.79744e19i | 0.133581i | ||||||||
\(909\) | 2.75268e20 | − | 2.75268e20i | 0.536795 | − | 0.536795i | ||||
\(910\) | 2.33464e19 | + | 2.33464e19i | 0.0451783 | + | 0.0451783i | ||||
\(911\) | 1.97182e19 | − | 1.97182e19i | 0.0378651 | − | 0.0378651i | −0.687921 | − | 0.725786i | \(-0.741476\pi\) |
0.725786 | + | 0.687921i | \(0.241476\pi\) | |||||||
\(912\) | 1.37262e20i | 0.261569i | ||||||||
\(913\) | −3.15260e20 | − | 3.15260e20i | −0.596175 | − | 0.596175i | ||||
\(914\) | 3.79818e20 | − | 3.79818e20i | 0.712775 | − | 0.712775i | ||||
\(915\) | 1.38690e21 | 2.58284 | ||||||||
\(916\) | 4.31403e20 | + | 4.31403e20i | 0.797287 | + | 0.797287i | ||||
\(917\) | 7.39309e19 | − | 7.39309e19i | 0.135594 | − | 0.135594i | ||||
\(918\) | 1.14364e21 | + | 1.14364e21i | 2.08156 | + | 2.08156i | ||||
\(919\) | −2.41948e20 | −0.437031 | −0.218516 | − | 0.975833i | \(-0.570122\pi\) | ||||
−0.218516 | + | 0.975833i | \(0.570122\pi\) | |||||||
\(920\) | 2.07274e20 | + | 2.07274e20i | 0.371561 | + | 0.371561i | ||||
\(921\) | − | 1.01819e21i | − | 1.81140i | ||||||
\(922\) | −4.36092e20 | −0.769948 | ||||||||
\(923\) | −9.22287e19 | −0.161605 | ||||||||
\(924\) | 1.01982e20 | 0.177346 | ||||||||
\(925\) | 5.30739e19 | − | 5.30739e19i | 0.0915986 | − | 0.0915986i | ||||
\(926\) | 3.33766e20 | − | 3.33766e20i | 0.571697 | − | 0.571697i | ||||
\(927\) | − | 1.59891e21i | − | 2.71810i | ||||||
\(928\) | 4.91075e20 | + | 3.68933e20i | 0.828537 | + | 0.622460i | ||||
\(929\) | 4.43872e19 | 0.0743272 | 0.0371636 | − | 0.999309i | \(-0.488168\pi\) | ||||
0.0371636 | + | 0.999309i | \(0.488168\pi\) | |||||||
\(930\) | 2.60834e20 | + | 2.60834e20i | 0.433494 | + | 0.433494i | ||||
\(931\) | 2.56202e20 | + | 2.56202e20i | 0.422605 | + | 0.422605i | ||||
\(932\) | 7.72645e20i | 1.26494i | ||||||||
\(933\) | 5.04030e19i | 0.0819002i | ||||||||
\(934\) | 4.58602e20i | 0.739618i | ||||||||
\(935\) | 5.58545e20 | 0.894081 | ||||||||
\(936\) | −8.43712e20 | + | 8.43712e20i | −1.34049 | + | 1.34049i | ||||
\(937\) | 1.04484e20i | 0.164768i | 0.996601 | + | 0.0823840i | \(0.0262534\pi\) | ||||
−0.996601 | + | 0.0823840i | \(0.973747\pi\) | |||||||
\(938\) | −1.05052e19 | + | 1.05052e19i | −0.0164432 | + | 0.0164432i | ||||
\(939\) | −5.85533e20 | − | 5.85533e20i | −0.909687 | − | 0.909687i | ||||
\(940\) | 1.06122e20 | − | 1.06122e20i | 0.163648 | − | 0.163648i | ||||
\(941\) | 4.89866e20i | 0.749808i | 0.927064 | + | 0.374904i | \(0.122324\pi\) | ||||
−0.927064 | + | 0.374904i | \(0.877676\pi\) | |||||||
\(942\) | 3.76541e20 | + | 3.76541e20i | 0.572079 | + | 0.572079i | ||||
\(943\) | 4.46337e20 | − | 4.46337e20i | 0.673103 | − | 0.673103i | ||||
\(944\) | −1.30538e20 | −0.195404 | ||||||||
\(945\) | 2.02712e20 | + | 2.02712e20i | 0.301202 | + | 0.301202i | ||||
\(946\) | 3.05323e20 | − | 3.05323e20i | 0.450320 | − | 0.450320i | ||||
\(947\) | 6.25580e20 | + | 6.25580e20i | 0.915868 | + | 0.915868i | 0.996726 | − | 0.0808579i | \(-0.0257660\pi\) |
−0.0808579 | + | 0.996726i | \(0.525766\pi\) | |||||||
\(948\) | 4.31907e20 | 0.627671 | ||||||||
\(949\) | 1.91205e20 | + | 1.91205e20i | 0.275827 | + | 0.275827i | ||||
\(950\) | 1.10796e20i | 0.158657i | ||||||||
\(951\) | 4.04812e20 | 0.575427 | ||||||||
\(952\) | −2.49806e20 | −0.352488 | ||||||||
\(953\) | −1.10866e21 | −1.55291 | −0.776456 | − | 0.630172i | \(-0.782985\pi\) | ||||
−0.776456 | + | 0.630172i | \(0.782985\pi\) | |||||||
\(954\) | 8.75043e19 | − | 8.75043e19i | 0.121672 | − | 0.121672i | ||||
\(955\) | 6.44108e19 | − | 6.44108e19i | 0.0889068 | − | 0.0889068i | ||||
\(956\) | − | 5.01437e19i | − | 0.0687086i | ||||||
\(957\) | 1.26702e20 | + | 8.92112e20i | 0.172346 | + | 1.21349i | ||||
\(958\) | 9.42666e19 | 0.127292 | ||||||||
\(959\) | −1.32858e20 | − | 1.32858e20i | −0.178098 | − | 0.178098i | ||||
\(960\) | −2.40050e20 | − | 2.40050e20i | −0.319451 | − | 0.319451i | ||||
\(961\) | − | 2.21883e20i | − | 0.293131i | ||||||
\(962\) | 9.03634e19i | 0.118513i | ||||||||
\(963\) | − | 2.48496e21i | − | 3.23546i | ||||||
\(964\) | 7.69012e20 | 0.994017 | ||||||||
\(965\) | −3.28217e20 | + | 3.28217e20i | −0.421181 | + | 0.421181i | ||||
\(966\) | − | 1.26834e20i | − | 0.161583i | ||||||
\(967\) | −6.35002e20 | + | 6.35002e20i | −0.803137 | + | 0.803137i | −0.983585 | − | 0.180447i | \(-0.942245\pi\) |
0.180447 | + | 0.983585i | \(0.442245\pi\) | |||||||
\(968\) | 2.97359e20 | + | 2.97359e20i | 0.373382 | + | 0.373382i | ||||
\(969\) | 1.26146e21 | − | 1.26146e21i | 1.57256 | − | 1.57256i | ||||
\(970\) | 2.22155e20i | 0.274950i | ||||||||
\(971\) | −7.19881e20 | − | 7.19881e20i | −0.884557 | − | 0.884557i | 0.109437 | − | 0.993994i | \(-0.465095\pi\) |
−0.993994 | + | 0.109437i | \(0.965095\pi\) | |||||||
\(972\) | −1.07210e21 | + | 1.07210e21i | −1.30789 | + | 1.30789i | ||||
\(973\) | −8.76883e19 | −0.106207 | ||||||||
\(974\) | −6.60887e19 | − | 6.60887e19i | −0.0794721 | − | 0.0794721i | ||||
\(975\) | 4.31274e20 | − | 4.31274e20i | 0.514898 | − | 0.514898i | ||||
\(976\) | −2.52133e20 | − | 2.52133e20i | −0.298869 | − | 0.298869i | ||||
\(977\) | −4.90519e20 | −0.577290 | −0.288645 | − | 0.957436i | \(-0.593205\pi\) | ||||
−0.288645 | + | 0.957436i | \(0.593205\pi\) | |||||||
\(978\) | 2.48407e19 | + | 2.48407e19i | 0.0290263 | + | 0.0290263i | ||||
\(979\) | 2.67947e20i | 0.310864i | ||||||||
\(980\) | 4.30164e20 | 0.495509 | ||||||||
\(981\) | 3.68720e19 | 0.0421710 | ||||||||
\(982\) | −3.08543e20 | −0.350376 | ||||||||
\(983\) | −3.40382e20 | + | 3.40382e20i | −0.383789 | + | 0.383789i | −0.872465 | − | 0.488676i | \(-0.837480\pi\) |
0.488676 | + | 0.872465i | \(0.337480\pi\) | |||||||
\(984\) | −1.31105e21 | + | 1.31105e21i | −1.46775 | + | 1.46775i | ||||
\(985\) | 1.27689e21i | 1.41939i | ||||||||
\(986\) | −1.29251e20 | − | 9.10056e20i | −0.142657 | − | 1.00445i | ||||
\(987\) | −1.55929e20 | −0.170886 | ||||||||
\(988\) | 2.35092e20 | + | 2.35092e20i | 0.255822 | + | 0.255822i | ||||
\(989\) | 9.46459e20 | + | 9.46459e20i | 1.02265 | + | 1.02265i | ||||
\(990\) | − | 5.97812e20i | − | 0.641384i | ||||||
\(991\) | 9.41171e20i | 1.00266i | 0.865257 | + | 0.501329i | \(0.167155\pi\) | ||||
−0.865257 | + | 0.501329i | \(0.832845\pi\) | |||||||
\(992\) | − | 8.23643e20i | − | 0.871279i | ||||||
\(993\) | −1.38966e21 | −1.45970 | ||||||||
\(994\) | −1.46134e19 | + | 1.46134e19i | −0.0152422 | + | 0.0152422i | ||||
\(995\) | − | 9.49337e20i | − | 0.983238i | ||||||
\(996\) | −1.19547e21 | + | 1.19547e21i | −1.22948 | + | 1.22948i | ||||
\(997\) | 1.04466e21 | + | 1.04466e21i | 1.06687 | + | 1.06687i | 0.997598 | + | 0.0692675i | \(0.0220662\pi\) |
0.0692675 | + | 0.997598i | \(0.477934\pi\) | |||||||
\(998\) | 5.72746e20 | − | 5.72746e20i | 0.580829 | − | 0.580829i | ||||
\(999\) | 7.84610e20i | 0.790124i |
(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 | 29.15.c.a.12.15 | ✓ | 68 | |
29.17 | odd | 4 | inner | 29.15.c.a.17.15 | yes | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.15.c.a.12.15 | ✓ | 68 | 1.1 | even | 1 | trivial | |
29.15.c.a.17.15 | yes | 68 | 29.17 | odd | 4 | inner |