Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,27,Mod(2,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 27, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.2");
S:= CuspForms(chi, 27);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 27 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.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: | \(21.4146460365\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2.9 | ||
Character | \(\chi\) | \(=\) | 5.2 |
Dual form | 5.27.c.a.3.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6254.19 | + | 6254.19i | 0.763451 | + | 0.763451i | 0.976944 | − | 0.213493i | \(-0.0684842\pi\) |
−0.213493 | + | 0.976944i | \(0.568484\pi\) | |||||||
\(3\) | −748889. | + | 748889.i | −0.469723 | + | 0.469723i | −0.901825 | − | 0.432102i | \(-0.857772\pi\) |
0.432102 | + | 0.901825i | \(0.357772\pi\) | |||||||
\(4\) | 1.11210e7i | 0.165715i | ||||||||
\(5\) | 7.43869e8 | + | 9.67872e8i | 0.609377 | + | 0.792881i | ||||
\(6\) | −9.36739e9 | −0.717220 | ||||||||
\(7\) | 5.67260e10 | + | 5.67260e10i | 0.585474 | + | 0.585474i | 0.936402 | − | 0.350929i | \(-0.114134\pi\) |
−0.350929 | + | 0.936402i | \(0.614134\pi\) | |||||||
\(8\) | 3.50159e11 | − | 3.50159e11i | 0.636936 | − | 0.636936i | ||||
\(9\) | 1.42020e12i | 0.558722i | ||||||||
\(10\) | −1.40096e12 | + | 1.07056e13i | −0.140096 | + | 1.07056i | ||||
\(11\) | −7.24796e12 | −0.209948 | −0.104974 | − | 0.994475i | \(-0.533476\pi\) | ||||
−0.104974 | + | 0.994475i | \(0.533476\pi\) | |||||||
\(12\) | −8.32836e12 | − | 8.32836e12i | −0.0778401 | − | 0.0778401i | ||||
\(13\) | −3.18649e14 | + | 3.18649e14i | −1.05208 | + | 1.05208i | −0.0535145 | + | 0.998567i | \(0.517042\pi\) |
−0.998567 | + | 0.0535145i | \(0.982958\pi\) | |||||||
\(14\) | 7.09550e14i | 0.893961i | ||||||||
\(15\) | −1.28190e15 | − | 1.67754e14i | −0.658672 | − | 0.0861957i | ||||
\(16\) | 5.12624e15 | 1.13825 | ||||||||
\(17\) | −2.33224e15 | − | 2.33224e15i | −0.235471 | − | 0.235471i | 0.579501 | − | 0.814972i | \(-0.303248\pi\) |
−0.814972 | + | 0.579501i | \(0.803248\pi\) | |||||||
\(18\) | −8.88217e15 | + | 8.88217e15i | −0.426557 | + | 0.426557i | ||||
\(19\) | − | 5.21951e16i | − | 1.24117i | −0.784137 | − | 0.620587i | \(-0.786894\pi\) | ||
0.784137 | − | 0.620587i | \(-0.213106\pi\) | |||||||
\(20\) | −1.07637e16 | + | 8.27253e15i | −0.131392 | + | 0.100983i | ||||
\(21\) | −8.49629e16 | −0.550020 | ||||||||
\(22\) | −4.53301e16 | − | 4.53301e16i | −0.160285 | − | 0.160285i | ||||
\(23\) | −5.96659e17 | + | 5.96659e17i | −1.18376 | + | 1.18376i | −0.205000 | + | 0.978762i | \(0.565719\pi\) |
−0.978762 | + | 0.205000i | \(0.934281\pi\) | |||||||
\(24\) | 5.24461e17i | 0.598366i | ||||||||
\(25\) | −3.83435e17 | + | 1.43994e18i | −0.257319 | + | 0.966327i | ||||
\(26\) | −3.98579e18 | −1.60643 | ||||||||
\(27\) | −2.96715e18 | − | 2.96715e18i | −0.732167 | − | 0.732167i | ||||
\(28\) | −6.30847e17 | + | 6.30847e17i | −0.0970218 | + | 0.0970218i | ||||
\(29\) | 5.57295e18i | 0.543139i | 0.962419 | + | 0.271570i | \(0.0875427\pi\) | ||||
−0.962419 | + | 0.271570i | \(0.912457\pi\) | |||||||
\(30\) | −6.96811e18 | − | 9.06644e18i | −0.437058 | − | 0.568670i | ||||
\(31\) | 2.76741e18 | 0.113337 | 0.0566685 | − | 0.998393i | \(-0.481952\pi\) | ||||
0.0566685 | + | 0.998393i | \(0.481952\pi\) | |||||||
\(32\) | 8.56169e18 | + | 8.56169e18i | 0.232065 | + | 0.232065i | ||||
\(33\) | 5.42792e18 | − | 5.42792e18i | 0.0986171 | − | 0.0986171i | ||||
\(34\) | − | 2.91725e19i | − | 0.359541i | ||||||
\(35\) | −1.27068e19 | + | 9.71001e19i | −0.107436 | + | 0.820985i | ||||
\(36\) | −1.57939e19 | −0.0925886 | ||||||||
\(37\) | 1.45897e20 | + | 1.45897e20i | 0.598994 | + | 0.598994i | 0.940045 | − | 0.341051i | \(-0.110783\pi\) |
−0.341051 | + | 0.940045i | \(0.610783\pi\) | |||||||
\(38\) | 3.26438e20 | − | 3.26438e20i | 0.947576 | − | 0.947576i | ||||
\(39\) | − | 4.77266e20i | − | 0.988373i | ||||||
\(40\) | 5.99381e20 | + | 7.84367e19i | 0.893148 | + | 0.116880i | ||||
\(41\) | 7.08740e20 | 0.766120 | 0.383060 | − | 0.923723i | \(-0.374870\pi\) | ||||
0.383060 | + | 0.923723i | \(0.374870\pi\) | |||||||
\(42\) | −5.31374e20 | − | 5.31374e20i | −0.419914 | − | 0.419914i | ||||
\(43\) | −1.15322e20 | + | 1.15322e20i | −0.0671155 | + | 0.0671155i | −0.739868 | − | 0.672752i | \(-0.765112\pi\) |
0.672752 | + | 0.739868i | \(0.265112\pi\) | |||||||
\(44\) | − | 8.06042e19i | − | 0.0347915i | ||||||
\(45\) | −1.37457e21 | + | 1.05644e21i | −0.442999 | + | 0.340472i | ||||
\(46\) | −7.46324e21 | −1.80749 | ||||||||
\(47\) | 4.77547e21 | + | 4.77547e21i | 0.874469 | + | 0.874469i | 0.992956 | − | 0.118487i | \(-0.0378043\pi\) |
−0.118487 | + | 0.992956i | \(0.537804\pi\) | |||||||
\(48\) | −3.83899e21 | + | 3.83899e21i | −0.534663 | + | 0.534663i | ||||
\(49\) | − | 2.95181e21i | − | 0.314441i | ||||||
\(50\) | −1.14037e22 | + | 6.60758e21i | −0.934193 | + | 0.541293i | ||||
\(51\) | 3.49318e21 | 0.221212 | ||||||||
\(52\) | −3.54368e21 | − | 3.54368e21i | −0.174346 | − | 0.174346i | ||||
\(53\) | 8.79555e21 | − | 8.79555e21i | 0.337813 | − | 0.337813i | −0.517731 | − | 0.855544i | \(-0.673223\pi\) |
0.855544 | + | 0.517731i | \(0.173223\pi\) | |||||||
\(54\) | − | 3.71142e22i | − | 1.11795i | ||||||
\(55\) | −5.39153e21 | − | 7.01510e21i | −0.127937 | − | 0.166463i | ||||
\(56\) | 3.97262e22 | 0.745818 | ||||||||
\(57\) | 3.90883e22 | + | 3.90883e22i | 0.583008 | + | 0.583008i | ||||
\(58\) | −3.48543e22 | + | 3.48543e22i | −0.414660 | + | 0.414660i | ||||
\(59\) | − | 1.00850e22i | − | 0.0960731i | −0.998846 | − | 0.0480366i | \(-0.984704\pi\) | ||
0.998846 | − | 0.0480366i | \(-0.0152964\pi\) | |||||||
\(60\) | 1.86558e21 | − | 1.42560e22i | 0.0142839 | − | 0.109152i | ||||
\(61\) | 2.85427e23 | 1.76282 | 0.881408 | − | 0.472355i | \(-0.156596\pi\) | ||||
0.881408 | + | 0.472355i | \(0.156596\pi\) | |||||||
\(62\) | 1.73079e22 | + | 1.73079e22i | 0.0865272 | + | 0.0865272i | ||||
\(63\) | −8.05619e22 | + | 8.05619e22i | −0.327117 | + | 0.327117i | ||||
\(64\) | − | 2.36923e23i | − | 0.783913i | ||||||
\(65\) | −5.45445e23 | − | 7.13784e22i | −1.47529 | − | 0.193060i | ||||
\(66\) | 6.78945e22 | 0.150579 | ||||||||
\(67\) | 2.54963e23 | + | 2.54963e23i | 0.465055 | + | 0.465055i | 0.900308 | − | 0.435253i | \(-0.143341\pi\) |
−0.435253 | + | 0.900308i | \(0.643341\pi\) | |||||||
\(68\) | 2.59367e22 | − | 2.59367e22i | 0.0390210 | − | 0.0390210i | ||||
\(69\) | − | 8.93663e23i | − | 1.11208i | ||||||
\(70\) | −6.86753e23 | + | 5.27812e23i | −0.708804 | + | 0.544759i | ||||
\(71\) | −3.34850e23 | −0.287403 | −0.143702 | − | 0.989621i | \(-0.545901\pi\) | ||||
−0.143702 | + | 0.989621i | \(0.545901\pi\) | |||||||
\(72\) | 4.97294e23 | + | 4.97294e23i | 0.355870 | + | 0.355870i | ||||
\(73\) | −2.01383e24 | + | 2.01383e24i | −1.20455 | + | 1.20455i | −0.231783 | + | 0.972768i | \(0.574456\pi\) |
−0.972768 | + | 0.231783i | \(0.925544\pi\) | |||||||
\(74\) | 1.82493e24i | 0.914606i | ||||||||
\(75\) | −7.91204e23 | − | 1.36551e24i | −0.333037 | − | 0.574774i | ||||
\(76\) | 5.80459e23 | 0.205681 | ||||||||
\(77\) | −4.11148e23 | − | 4.11148e23i | −0.122919 | − | 0.122919i | ||||
\(78\) | 2.98491e24 | − | 2.98491e24i | 0.754574 | − | 0.754574i | ||||
\(79\) | − | 6.89052e24i | − | 1.47605i | −0.674775 | − | 0.738023i | \(-0.735760\pi\) | ||
0.674775 | − | 0.738023i | \(-0.264240\pi\) | |||||||
\(80\) | 3.81325e24 | + | 4.96154e24i | 0.693626 | + | 0.902499i | ||||
\(81\) | 8.34182e23 | 0.129109 | ||||||||
\(82\) | 4.43260e24 | + | 4.43260e24i | 0.584895 | + | 0.584895i | ||||
\(83\) | 8.09054e24 | − | 8.09054e24i | 0.911932 | − | 0.911932i | −0.0844922 | − | 0.996424i | \(-0.526927\pi\) |
0.996424 | + | 0.0844922i | \(0.0269268\pi\) | |||||||
\(84\) | − | 9.44869e23i | − | 0.0911466i | ||||||
\(85\) | 5.22429e23 | − | 3.99219e24i | 0.0432097 | − | 0.330191i | ||||
\(86\) | −1.44249e24 | −0.102479 | ||||||||
\(87\) | −4.17352e24 | − | 4.17352e24i | −0.255125 | − | 0.255125i | ||||
\(88\) | −2.53794e24 | + | 2.53794e24i | −0.133723 | + | 0.133723i | ||||
\(89\) | 3.36606e25i | 1.53127i | 0.643274 | + | 0.765636i | \(0.277576\pi\) | ||||
−0.643274 | + | 0.765636i | \(0.722424\pi\) | |||||||
\(90\) | −1.52040e25 | − | 1.98963e24i | −0.598142 | − | 0.0782746i | ||||
\(91\) | −3.61514e25 | −1.23193 | ||||||||
\(92\) | −6.63542e24 | − | 6.63542e24i | −0.196167 | − | 0.196167i | ||||
\(93\) | −2.07248e24 | + | 2.07248e24i | −0.0532369 | + | 0.0532369i | ||||
\(94\) | 5.97335e25i | 1.33523i | ||||||||
\(95\) | 5.05181e25 | − | 3.88263e25i | 0.984103 | − | 0.756343i | ||||
\(96\) | −1.28235e25 | −0.218012 | ||||||||
\(97\) | −5.11251e25 | − | 5.11251e25i | −0.759630 | − | 0.759630i | 0.216625 | − | 0.976255i | \(-0.430495\pi\) |
−0.976255 | + | 0.216625i | \(0.930495\pi\) | |||||||
\(98\) | 1.84612e25 | − | 1.84612e25i | 0.240061 | − | 0.240061i | ||||
\(99\) | − | 1.02935e25i | − | 0.117302i | ||||||
\(100\) | −1.60135e25 | − | 4.26416e24i | −0.160135 | − | 0.0426416i | ||||
\(101\) | −1.50967e25 | −0.132649 | −0.0663245 | − | 0.997798i | \(-0.521127\pi\) | ||||
−0.0663245 | + | 0.997798i | \(0.521127\pi\) | |||||||
\(102\) | 2.18470e25 | + | 2.18470e25i | 0.168884 | + | 0.168884i | ||||
\(103\) | 9.25640e25 | − | 9.25640e25i | 0.630316 | − | 0.630316i | −0.317831 | − | 0.948147i | \(-0.602955\pi\) |
0.948147 | + | 0.317831i | \(0.102955\pi\) | |||||||
\(104\) | 2.23156e26i | 1.34022i | ||||||||
\(105\) | −6.32013e25 | − | 8.22332e25i | −0.335170 | − | 0.436100i | ||||
\(106\) | 1.10018e26 | 0.515808 | ||||||||
\(107\) | 1.95019e26 | + | 1.95019e26i | 0.809259 | + | 0.809259i | 0.984522 | − | 0.175263i | \(-0.0560775\pi\) |
−0.175263 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(108\) | 3.29975e25 | − | 3.29975e25i | 0.121331 | − | 0.121331i | ||||
\(109\) | − | 2.92708e26i | − | 0.954750i | −0.878700 | − | 0.477375i | \(-0.841588\pi\) | ||
0.878700 | − | 0.477375i | \(-0.158412\pi\) | |||||||
\(110\) | 1.01541e25 | − | 7.75934e25i | 0.0294128 | − | 0.224760i | ||||
\(111\) | −2.18521e26 | −0.562722 | ||||||||
\(112\) | 2.90791e26 | + | 2.90791e26i | 0.666417 | + | 0.666417i | ||||
\(113\) | 5.51881e26 | − | 5.51881e26i | 1.12674 | − | 1.12674i | 0.136041 | − | 0.990703i | \(-0.456562\pi\) |
0.990703 | − | 0.136041i | \(-0.0434379\pi\) | |||||||
\(114\) | 4.88932e26i | 0.890195i | ||||||||
\(115\) | −1.02133e27 | − | 1.33653e26i | −1.65994 | − | 0.217224i | ||||
\(116\) | −6.19765e25 | −0.0900064 | ||||||||
\(117\) | −4.52544e26 | − | 4.52544e26i | −0.587821 | − | 0.587821i | ||||
\(118\) | 6.30738e25 | − | 6.30738e25i | 0.0733471 | − | 0.0733471i | ||||
\(119\) | − | 2.64597e26i | − | 0.275724i | ||||||
\(120\) | −5.07611e26 | + | 3.90130e26i | −0.474433 | + | 0.364631i | ||||
\(121\) | −1.13928e27 | −0.955922 | ||||||||
\(122\) | 1.78511e27 | + | 1.78511e27i | 1.34582 | + | 1.34582i | ||||
\(123\) | −5.30768e26 | + | 5.30768e26i | −0.359864 | + | 0.359864i | ||||
\(124\) | 3.07762e25i | 0.0187816i | ||||||||
\(125\) | −1.67890e27 | + | 7.00009e26i | −0.922986 | + | 0.384834i | ||||
\(126\) | −1.00770e27 | −0.499475 | ||||||||
\(127\) | 1.23338e27 | + | 1.23338e27i | 0.551633 | + | 0.551633i | 0.926912 | − | 0.375279i | \(-0.122453\pi\) |
−0.375279 | + | 0.926912i | \(0.622453\pi\) | |||||||
\(128\) | 2.05633e27 | − | 2.05633e27i | 0.830544 | − | 0.830544i | ||||
\(129\) | − | 1.72727e26i | − | 0.0630513i | ||||||
\(130\) | −2.96490e27 | − | 3.85773e27i | −0.978919 | − | 1.27370i | ||||
\(131\) | 5.33768e27 | 1.59524 | 0.797619 | − | 0.603162i | \(-0.206093\pi\) | ||||
0.797619 | + | 0.603162i | \(0.206093\pi\) | |||||||
\(132\) | 6.03636e25 | + | 6.03636e25i | 0.0163423 | + | 0.0163423i | ||||
\(133\) | 2.96082e27 | − | 2.96082e27i | 0.726675 | − | 0.726675i | ||||
\(134\) | 3.18917e27i | 0.710094i | ||||||||
\(135\) | 6.64650e26 | − | 5.07898e27i | 0.134355 | − | 1.02669i | ||||
\(136\) | −1.63331e27 | −0.299959 | ||||||||
\(137\) | 2.89434e27 | + | 2.89434e27i | 0.483261 | + | 0.483261i | 0.906172 | − | 0.422910i | \(-0.138991\pi\) |
−0.422910 | + | 0.906172i | \(0.638991\pi\) | |||||||
\(138\) | 5.58914e27 | − | 5.58914e27i | 0.849018 | − | 0.849018i | ||||
\(139\) | 1.18359e28i | 1.63685i | 0.574614 | + | 0.818425i | \(0.305152\pi\) | ||||
−0.574614 | + | 0.818425i | \(0.694848\pi\) | |||||||
\(140\) | −1.07985e27 | − | 1.41312e26i | −0.136050 | − | 0.0178038i | ||||
\(141\) | −7.15260e27 | −0.821515 | ||||||||
\(142\) | −2.09422e27 | − | 2.09422e27i | −0.219418 | − | 0.219418i | ||||
\(143\) | 2.30956e27 | − | 2.30956e27i | 0.220882 | − | 0.220882i | ||||
\(144\) | 7.28026e27i | 0.635967i | ||||||||
\(145\) | −5.39390e27 | + | 4.14554e27i | −0.430645 | + | 0.330977i | ||||
\(146\) | −2.51897e28 | −1.83923 | ||||||||
\(147\) | 2.21058e27 | + | 2.21058e27i | 0.147700 | + | 0.147700i | ||||
\(148\) | −1.62251e27 | + | 1.62251e27i | −0.0992624 | + | 0.0992624i | ||||
\(149\) | 1.17062e28i | 0.656135i | 0.944654 | + | 0.328067i | \(0.106397\pi\) | ||||
−0.944654 | + | 0.328067i | \(0.893603\pi\) | |||||||
\(150\) | 3.59179e27 | − | 1.34885e28i | 0.184554 | − | 0.693069i | ||||
\(151\) | 1.07463e28 | 0.506477 | 0.253238 | − | 0.967404i | \(-0.418504\pi\) | ||||
0.253238 | + | 0.967404i | \(0.418504\pi\) | |||||||
\(152\) | −1.82766e28 | − | 1.82766e28i | −0.790548 | − | 0.790548i | ||||
\(153\) | 3.31223e27 | − | 3.31223e27i | 0.131563 | − | 0.131563i | ||||
\(154\) | − | 5.14279e27i | − | 0.187685i | ||||||
\(155\) | 2.05859e27 | + | 2.67850e27i | 0.0690650 | + | 0.0898627i | ||||
\(156\) | 5.30765e27 | 0.163788 | ||||||||
\(157\) | 2.76978e28 | + | 2.76978e28i | 0.786592 | + | 0.786592i | 0.980934 | − | 0.194341i | \(-0.0622570\pi\) |
−0.194341 | + | 0.980934i | \(0.562257\pi\) | |||||||
\(158\) | 4.30946e28 | − | 4.30946e28i | 1.12689 | − | 1.12689i | ||||
\(159\) | 1.31738e28i | 0.317357i | ||||||||
\(160\) | −1.91785e27 | + | 1.46554e28i | −0.0425847 | + | 0.325415i | ||||
\(161\) | −6.76921e28 | −1.38612 | ||||||||
\(162\) | 5.21713e27 | + | 5.21713e27i | 0.0985682 | + | 0.0985682i | ||||
\(163\) | −3.27062e27 | + | 3.27062e27i | −0.0570415 | + | 0.0570415i | −0.735052 | − | 0.678011i | \(-0.762842\pi\) |
0.678011 | + | 0.735052i | \(0.262842\pi\) | |||||||
\(164\) | 7.88187e27i | 0.126958i | ||||||||
\(165\) | 9.29119e27 | + | 1.21587e27i | 0.138287 | + | 0.0180966i | ||||
\(166\) | 1.01200e29 | 1.39243 | ||||||||
\(167\) | 6.03005e27 | + | 6.03005e27i | 0.0767374 | + | 0.0767374i | 0.744434 | − | 0.667696i | \(-0.232720\pi\) |
−0.667696 | + | 0.744434i | \(0.732720\pi\) | |||||||
\(168\) | −2.97505e28 | + | 2.97505e28i | −0.350328 | + | 0.350328i | ||||
\(169\) | − | 1.11341e29i | − | 1.21375i | ||||||
\(170\) | 2.82353e28 | − | 2.17005e28i | 0.285073 | − | 0.219096i | ||||
\(171\) | 7.41272e28 | 0.693471 | ||||||||
\(172\) | −1.28249e27 | − | 1.28249e27i | −0.0111220 | − | 0.0111220i | ||||
\(173\) | −6.90284e28 | + | 6.90284e28i | −0.555173 | + | 0.555173i | −0.927929 | − | 0.372756i | \(-0.878413\pi\) |
0.372756 | + | 0.927929i | \(0.378413\pi\) | |||||||
\(174\) | − | 5.22040e28i | − | 0.389550i | ||||||
\(175\) | −1.03433e29 | + | 5.99312e28i | −0.716412 | + | 0.415105i | ||||
\(176\) | −3.71548e28 | −0.238974 | ||||||||
\(177\) | 7.55259e27 | + | 7.55259e27i | 0.0451277 | + | 0.0451277i | ||||
\(178\) | −2.10520e29 | + | 2.10520e29i | −1.16905 | + | 1.16905i | ||||
\(179\) | − | 3.22901e29i | − | 1.66717i | −0.552392 | − | 0.833584i | \(-0.686285\pi\) | ||
0.552392 | − | 0.833584i | \(-0.313715\pi\) | |||||||
\(180\) | −1.17486e28 | − | 1.52865e28i | −0.0564214 | − | 0.0734117i | ||||
\(181\) | 2.64516e29 | 1.18204 | 0.591018 | − | 0.806658i | \(-0.298726\pi\) | ||||
0.591018 | + | 0.806658i | \(0.298726\pi\) | |||||||
\(182\) | −2.26098e29 | − | 2.26098e29i | −0.940520 | − | 0.940520i | ||||
\(183\) | −2.13753e29 | + | 2.13753e29i | −0.828034 | + | 0.828034i | ||||
\(184\) | 4.17851e29i | 1.50796i | ||||||||
\(185\) | −3.26813e28 | + | 2.49737e29i | −0.109917 | + | 0.839944i | ||||
\(186\) | −2.59234e28 | −0.0812876 | ||||||||
\(187\) | 1.69040e28 | + | 1.69040e28i | 0.0494365 | + | 0.0494365i | ||||
\(188\) | −5.31078e28 | + | 5.31078e28i | −0.144913 | + | 0.144913i | ||||
\(189\) | − | 3.36628e29i | − | 0.857328i | ||||||
\(190\) | 5.58777e29 | + | 7.31231e28i | 1.32875 | + | 0.173883i | ||||
\(191\) | 3.07926e28 | 0.0683932 | 0.0341966 | − | 0.999415i | \(-0.489113\pi\) | ||||
0.0341966 | + | 0.999415i | \(0.489113\pi\) | |||||||
\(192\) | 1.77429e29 | + | 1.77429e29i | 0.368221 | + | 0.368221i | ||||
\(193\) | 4.02979e29 | − | 4.02979e29i | 0.781696 | − | 0.781696i | −0.198421 | − | 0.980117i | \(-0.563581\pi\) |
0.980117 | + | 0.198421i | \(0.0635813\pi\) | |||||||
\(194\) | − | 6.39493e29i | − | 1.15988i | ||||||
\(195\) | 4.61932e29 | − | 3.55023e29i | 0.783661 | − | 0.602292i | ||||
\(196\) | 3.28269e28 | 0.0521077 | ||||||||
\(197\) | −4.70545e29 | − | 4.70545e29i | −0.699101 | − | 0.699101i | 0.265115 | − | 0.964217i | \(-0.414590\pi\) |
−0.964217 | + | 0.265115i | \(0.914590\pi\) | |||||||
\(198\) | 6.43776e28 | − | 6.43776e28i | 0.0895545 | − | 0.0895545i | ||||
\(199\) | 2.75507e29i | 0.358958i | 0.983762 | + | 0.179479i | \(0.0574411\pi\) | ||||
−0.983762 | + | 0.179479i | \(0.942559\pi\) | |||||||
\(200\) | 3.69944e29 | + | 6.38471e29i | 0.451592 | + | 0.779384i | ||||
\(201\) | −3.81878e29 | −0.436894 | ||||||||
\(202\) | −9.44177e28 | − | 9.44177e28i | −0.101271 | − | 0.101271i | ||||
\(203\) | −3.16131e29 | + | 3.16131e29i | −0.317994 | + | 0.317994i | ||||
\(204\) | 3.88474e28i | 0.0366581i | ||||||||
\(205\) | 5.27210e29 | + | 6.85970e29i | 0.466856 | + | 0.607442i | ||||
\(206\) | 1.15783e30 | 0.962431 | ||||||||
\(207\) | −8.47372e29 | − | 8.47372e29i | −0.661393 | − | 0.661393i | ||||
\(208\) | −1.63347e30 | + | 1.63347e30i | −1.19754 | + | 1.19754i | ||||
\(209\) | 3.78308e29i | 0.260582i | ||||||||
\(210\) | 1.19030e29 | − | 9.09575e29i | 0.0770555 | − | 0.588827i | ||||
\(211\) | −2.20208e30 | −1.34017 | −0.670087 | − | 0.742282i | \(-0.733743\pi\) | ||||
−0.670087 | + | 0.742282i | \(0.733743\pi\) | |||||||
\(212\) | 9.78149e28 | + | 9.78149e28i | 0.0559807 | + | 0.0559807i | ||||
\(213\) | 2.50766e29 | − | 2.50766e29i | 0.135000 | − | 0.135000i | ||||
\(214\) | 2.43937e30i | 1.23566i | ||||||||
\(215\) | −1.97402e29 | − | 2.58325e28i | −0.0941132 | − | 0.0123159i | ||||
\(216\) | −2.07795e30 | −0.932686 | ||||||||
\(217\) | 1.56984e29 | + | 1.56984e29i | 0.0663558 | + | 0.0663558i | ||||
\(218\) | 1.83065e30 | − | 1.83065e30i | 0.728905 | − | 0.728905i | ||||
\(219\) | − | 3.01627e30i | − | 1.13161i | ||||||
\(220\) | 7.80145e28 | − | 5.99589e28i | 0.0275855 | − | 0.0212011i | ||||
\(221\) | 1.48633e30 | 0.495469 | ||||||||
\(222\) | −1.36667e30 | − | 1.36667e30i | −0.429611 | − | 0.429611i | ||||
\(223\) | 1.15101e30 | − | 1.15101e30i | 0.341284 | − | 0.341284i | −0.515566 | − | 0.856850i | \(-0.672418\pi\) |
0.856850 | + | 0.515566i | \(0.172418\pi\) | |||||||
\(224\) | 9.71341e29i | 0.271736i | ||||||||
\(225\) | −2.04499e30 | − | 5.44553e29i | −0.539907 | − | 0.143770i | ||||
\(226\) | 6.90313e30 | 1.72043 | ||||||||
\(227\) | 4.52492e30 | + | 4.52492e30i | 1.06482 | + | 1.06482i | 0.997748 | + | 0.0670680i | \(0.0213644\pi\) |
0.0670680 | + | 0.997748i | \(0.478636\pi\) | |||||||
\(228\) | −4.34700e29 | + | 4.34700e29i | −0.0966131 | + | 0.0966131i | ||||
\(229\) | 5.05515e30i | 1.06138i | 0.847565 | + | 0.530692i | \(0.178068\pi\) | ||||
−0.847565 | + | 0.530692i | \(0.821932\pi\) | |||||||
\(230\) | −5.55167e30 | − | 7.22346e30i | −1.10144 | − | 1.43312i | ||||
\(231\) | 6.15808e29 | 0.115475 | ||||||||
\(232\) | 1.95142e30 | + | 1.95142e30i | 0.345945 | + | 0.345945i | ||||
\(233\) | 3.06962e29 | − | 3.06962e29i | 0.0514585 | − | 0.0514585i | −0.680909 | − | 0.732368i | \(-0.738415\pi\) |
0.732368 | + | 0.680909i | \(0.238415\pi\) | |||||||
\(234\) | − | 5.66060e30i | − | 0.897545i | ||||||
\(235\) | −1.06972e30 | + | 8.17437e30i | −0.160468 | + | 1.22623i | ||||
\(236\) | 1.12155e29 | 0.0159208 | ||||||||
\(237\) | 5.16024e30 | + | 5.16024e30i | 0.693332 | + | 0.693332i | ||||
\(238\) | 1.65484e30 | − | 1.65484e30i | 0.210502 | − | 0.210502i | ||||
\(239\) | − | 6.86868e30i | − | 0.827371i | −0.910420 | − | 0.413686i | \(-0.864241\pi\) | ||
0.910420 | − | 0.413686i | \(-0.135759\pi\) | |||||||
\(240\) | −6.57135e30 | − | 8.59945e29i | −0.749736 | − | 0.0981125i | ||||
\(241\) | −8.79465e30 | −0.950598 | −0.475299 | − | 0.879824i | \(-0.657660\pi\) | ||||
−0.475299 | + | 0.879824i | \(0.657660\pi\) | |||||||
\(242\) | −7.12530e30 | − | 7.12530e30i | −0.729800 | − | 0.729800i | ||||
\(243\) | 6.91738e30 | − | 6.91738e30i | 0.671521 | − | 0.671521i | ||||
\(244\) | 3.17422e30i | 0.292125i | ||||||||
\(245\) | 2.85697e30 | − | 2.19576e30i | 0.249314 | − | 0.191613i | ||||
\(246\) | −6.63905e30 | −0.549477 | ||||||||
\(247\) | 1.66319e31 | + | 1.66319e31i | 1.30582 | + | 1.30582i | ||||
\(248\) | 9.69034e29 | − | 9.69034e29i | 0.0721884 | − | 0.0721884i | ||||
\(249\) | 1.21178e31i | 0.856710i | ||||||||
\(250\) | −1.48782e31 | − | 6.12218e30i | −0.998456 | − | 0.410852i | ||||
\(251\) | −2.09500e31 | −1.33483 | −0.667413 | − | 0.744687i | \(-0.732599\pi\) | ||||
−0.667413 | + | 0.744687i | \(0.732599\pi\) | |||||||
\(252\) | −8.95925e29 | − | 8.95925e29i | −0.0542082 | − | 0.0542082i | ||||
\(253\) | 4.32456e30 | − | 4.32456e30i | 0.248528 | − | 0.248528i | ||||
\(254\) | 1.54276e31i | 0.842289i | ||||||||
\(255\) | 2.59846e30 | + | 3.38095e30i | 0.134801 | + | 0.175394i | ||||
\(256\) | 9.82170e30 | 0.484247 | ||||||||
\(257\) | −2.49219e31 | − | 2.49219e31i | −1.16802 | − | 1.16802i | −0.982673 | − | 0.185346i | \(-0.940659\pi\) |
−0.185346 | − | 0.982673i | \(-0.559341\pi\) | |||||||
\(258\) | 1.08027e30 | − | 1.08027e30i | 0.0481366 | − | 0.0481366i | ||||
\(259\) | 1.65522e31i | 0.701391i | ||||||||
\(260\) | 7.93796e29 | − | 6.06587e30i | 0.0319930 | − | 0.244478i | ||||
\(261\) | −7.91468e30 | −0.303464 | ||||||||
\(262\) | 3.33829e31 | + | 3.33829e31i | 1.21789 | + | 1.21789i | ||||
\(263\) | 1.85981e31 | − | 1.85981e31i | 0.645718 | − | 0.645718i | −0.306237 | − | 0.951955i | \(-0.599070\pi\) |
0.951955 | + | 0.306237i | \(0.0990701\pi\) | |||||||
\(264\) | − | 3.80127e30i | − | 0.125626i | ||||||
\(265\) | 1.50557e31 | + | 1.97023e30i | 0.473701 | + | 0.0619899i | ||||
\(266\) | 3.70350e31 | 1.10956 | ||||||||
\(267\) | −2.52081e31 | − | 2.52081e31i | −0.719273 | − | 0.719273i | ||||
\(268\) | −2.83543e30 | + | 2.83543e30i | −0.0770667 | + | 0.0770667i | ||||
\(269\) | − | 2.38894e31i | − | 0.618623i | −0.950961 | − | 0.309311i | \(-0.899901\pi\) | ||
0.950961 | − | 0.309311i | \(-0.100099\pi\) | |||||||
\(270\) | 3.59218e31 | − | 2.76081e31i | 0.886398 | − | 0.681251i | ||||
\(271\) | 9.57627e30 | 0.225214 | 0.112607 | − | 0.993640i | \(-0.464080\pi\) | ||||
0.112607 | + | 0.993640i | \(0.464080\pi\) | |||||||
\(272\) | −1.19556e31 | − | 1.19556e31i | −0.268025 | − | 0.268025i | ||||
\(273\) | 2.70734e31 | − | 2.70734e31i | 0.578666 | − | 0.578666i | ||||
\(274\) | 3.62035e31i | 0.737893i | ||||||||
\(275\) | 2.77912e30 | − | 1.04366e31i | 0.0540235 | − | 0.202878i | ||||
\(276\) | 9.93838e30 | 0.184288 | ||||||||
\(277\) | −1.23203e31 | − | 1.23203e31i | −0.217964 | − | 0.217964i | 0.589676 | − | 0.807640i | \(-0.299255\pi\) |
−0.807640 | + | 0.589676i | \(0.799255\pi\) | |||||||
\(278\) | −7.40240e31 | + | 7.40240e31i | −1.24965 | + | 1.24965i | ||||
\(279\) | 3.93026e30i | 0.0633238i | ||||||||
\(280\) | 2.95511e31 | + | 3.84499e31i | 0.454485 | + | 0.591345i | ||||
\(281\) | −1.02452e32 | −1.50431 | −0.752156 | − | 0.658985i | \(-0.770986\pi\) | ||||
−0.752156 | + | 0.658985i | \(0.770986\pi\) | |||||||
\(282\) | −4.47337e31 | − | 4.47337e31i | −0.627187 | − | 0.627187i | ||||
\(283\) | −5.03276e31 | + | 5.03276e31i | −0.673880 | + | 0.673880i | −0.958608 | − | 0.284728i | \(-0.908097\pi\) |
0.284728 | + | 0.958608i | \(0.408097\pi\) | |||||||
\(284\) | − | 3.72385e30i | − | 0.0476271i | ||||||
\(285\) | −8.75591e30 | + | 6.69091e31i | −0.106984 | + | 0.817527i | ||||
\(286\) | 2.88888e31 | 0.337265 | ||||||||
\(287\) | 4.02040e31 | + | 4.02040e31i | 0.448543 | + | 0.448543i | ||||
\(288\) | −1.21593e31 | + | 1.21593e31i | −0.129660 | + | 0.129660i | ||||
\(289\) | − | 8.72220e31i | − | 0.889107i | ||||||
\(290\) | −5.96615e31 | − | 7.80747e30i | −0.581460 | − | 0.0760915i | ||||
\(291\) | 7.65741e31 | 0.713630 | ||||||||
\(292\) | −2.23957e31 | − | 2.23957e31i | −0.199612 | − | 0.199612i | ||||
\(293\) | −1.84989e31 | + | 1.84989e31i | −0.157713 | + | 0.157713i | −0.781552 | − | 0.623840i | \(-0.785572\pi\) |
0.623840 | + | 0.781552i | \(0.285572\pi\) | |||||||
\(294\) | 2.76508e31i | 0.225524i | ||||||||
\(295\) | 9.76103e30 | − | 7.50195e30i | 0.0761745 | − | 0.0585448i | ||||
\(296\) | 1.02174e32 | 0.763042 | ||||||||
\(297\) | 2.15058e31 | + | 2.15058e31i | 0.153717 | + | 0.153717i | ||||
\(298\) | −7.32126e31 | + | 7.32126e31i | −0.500927 | + | 0.500927i | ||||
\(299\) | − | 3.80250e32i | − | 2.49083i | ||||||
\(300\) | 1.51857e31 | − | 8.79894e30i | 0.0952487 | − | 0.0551892i | ||||
\(301\) | −1.30835e31 | −0.0785887 | ||||||||
\(302\) | 6.72095e31 | + | 6.72095e31i | 0.386670 | + | 0.386670i | ||||
\(303\) | 1.13058e31 | − | 1.13058e31i | 0.0623083 | − | 0.0623083i | ||||
\(304\) | − | 2.67564e32i | − | 1.41277i | ||||||
\(305\) | 2.12320e32 | + | 2.76257e32i | 1.07422 | + | 1.39770i | ||||
\(306\) | 4.14307e31 | 0.200883 | ||||||||
\(307\) | 1.16178e31 | + | 1.16178e31i | 0.0539912 | + | 0.0539912i | 0.733587 | − | 0.679596i | \(-0.237845\pi\) |
−0.679596 | + | 0.733587i | \(0.737845\pi\) | |||||||
\(308\) | 4.57235e30 | − | 4.57235e30i | 0.0203695 | − | 0.0203695i | ||||
\(309\) | 1.38640e32i | 0.592147i | ||||||||
\(310\) | −3.87703e30 | + | 2.96267e31i | −0.0158780 | + | 0.121333i | ||||
\(311\) | 2.03862e32 | 0.800667 | 0.400333 | − | 0.916370i | \(-0.368894\pi\) | ||||
0.400333 | + | 0.916370i | \(0.368894\pi\) | |||||||
\(312\) | −1.67119e32 | − | 1.67119e32i | −0.629530 | − | 0.629530i | ||||
\(313\) | −5.36965e31 | + | 5.36965e31i | −0.194030 | + | 0.194030i | −0.797435 | − | 0.603405i | \(-0.793810\pi\) |
0.603405 | + | 0.797435i | \(0.293810\pi\) | |||||||
\(314\) | 3.46455e32i | 1.20105i | ||||||||
\(315\) | −1.37901e32 | − | 1.80461e31i | −0.458702 | − | 0.0600270i | ||||
\(316\) | 7.66292e31 | 0.244603 | ||||||||
\(317\) | 1.09772e32 | + | 1.09772e32i | 0.336294 | + | 0.336294i | 0.854971 | − | 0.518676i | \(-0.173575\pi\) |
−0.518676 | + | 0.854971i | \(0.673575\pi\) | |||||||
\(318\) | −8.23914e31 | + | 8.23914e31i | −0.242287 | + | 0.242287i | ||||
\(319\) | − | 4.03925e31i | − | 0.114031i | ||||||
\(320\) | 2.29311e32 | − | 1.76240e32i | 0.621549 | − | 0.477699i | ||||
\(321\) | −2.92095e32 | −0.760254 | ||||||||
\(322\) | −4.23359e32 | − | 4.23359e32i | −1.05824 | − | 1.05824i | ||||
\(323\) | −1.21731e32 | + | 1.21731e32i | −0.292260 | + | 0.292260i | ||||
\(324\) | 9.27689e30i | 0.0213953i | ||||||||
\(325\) | −3.36654e32 | − | 5.81017e32i | −0.745934 | − | 1.28737i | ||||
\(326\) | −4.09101e31 | −0.0870967 | ||||||||
\(327\) | 2.19206e32 | + | 2.19206e32i | 0.448467 | + | 0.448467i | ||||
\(328\) | 2.48172e32 | − | 2.48172e32i | 0.487969 | − | 0.487969i | ||||
\(329\) | 5.41787e32i | 1.02396i | ||||||||
\(330\) | 5.05046e31 | + | 6.57132e31i | 0.0917592 | + | 0.119391i | ||||
\(331\) | −3.03702e32 | −0.530498 | −0.265249 | − | 0.964180i | \(-0.585454\pi\) | ||||
−0.265249 | + | 0.964180i | \(0.585454\pi\) | |||||||
\(332\) | 8.99745e31 | + | 8.99745e31i | 0.151121 | + | 0.151121i | ||||
\(333\) | −2.07202e32 | + | 2.07202e32i | −0.334671 | + | 0.334671i | ||||
\(334\) | 7.54262e31i | 0.117171i | ||||||||
\(335\) | −5.71125e31 | + | 4.36430e32i | −0.0853392 | + | 0.652127i | ||||
\(336\) | −4.35540e32 | −0.626063 | ||||||||
\(337\) | −1.46102e32 | − | 1.46102e32i | −0.202054 | − | 0.202054i | 0.598826 | − | 0.800879i | \(-0.295634\pi\) |
−0.800879 | + | 0.598826i | \(0.795634\pi\) | |||||||
\(338\) | 6.96351e32 | − | 6.96351e32i | 0.926640 | − | 0.926640i | ||||
\(339\) | 8.26595e32i | 1.05851i | ||||||||
\(340\) | 4.43969e31 | + | 5.80990e30i | 0.0547176 | + | 0.00716049i | ||||
\(341\) | −2.00581e31 | −0.0237948 | ||||||||
\(342\) | 4.63606e32 | + | 4.63606e32i | 0.529431 | + | 0.529431i | ||||
\(343\) | 6.99958e32 | − | 6.99958e32i | 0.769571 | − | 0.769571i | ||||
\(344\) | 8.07622e31i | 0.0854965i | ||||||||
\(345\) | 8.64951e32 | − | 6.64768e32i | 0.881746 | − | 0.677676i | ||||
\(346\) | −8.63434e32 | −0.847695 | ||||||||
\(347\) | −3.93314e31 | − | 3.93314e31i | −0.0371925 | − | 0.0371925i | 0.688266 | − | 0.725458i | \(-0.258372\pi\) |
−0.725458 | + | 0.688266i | \(0.758372\pi\) | |||||||
\(348\) | 4.64135e31 | − | 4.64135e31i | 0.0422780 | − | 0.0422780i | ||||
\(349\) | 1.91237e31i | 0.0167819i | 0.999965 | + | 0.00839095i | \(0.00267095\pi\) | ||||
−0.999965 | + | 0.00839095i | \(0.997329\pi\) | |||||||
\(350\) | −1.02171e33 | − | 2.72066e32i | −0.863858 | − | 0.230033i | ||||
\(351\) | 1.89096e33 | 1.54060 | ||||||||
\(352\) | −6.20548e31 | − | 6.20548e31i | −0.0487215 | − | 0.0487215i | ||||
\(353\) | 2.80382e31 | − | 2.80382e31i | 0.0212168 | − | 0.0212168i | −0.696419 | − | 0.717636i | \(-0.745224\pi\) |
0.717636 | + | 0.696419i | \(0.245224\pi\) | |||||||
\(354\) | 9.44706e31i | 0.0689056i | ||||||||
\(355\) | −2.49084e32 | − | 3.24092e32i | −0.175137 | − | 0.227876i | ||||
\(356\) | −3.74338e32 | −0.253755 | ||||||||
\(357\) | 1.98154e32 | + | 1.98154e32i | 0.129514 | + | 0.129514i | ||||
\(358\) | 2.01948e33 | − | 2.01948e33i | 1.27280 | − | 1.27280i | ||||
\(359\) | − | 6.07618e32i | − | 0.369320i | −0.982802 | − | 0.184660i | \(-0.940882\pi\) | ||
0.982802 | − | 0.184660i | \(-0.0591184\pi\) | |||||||
\(360\) | −1.11395e32 | + | 8.51239e32i | −0.0653033 | + | 0.499021i | ||||
\(361\) | −9.55873e32 | −0.540514 | ||||||||
\(362\) | 1.65434e33 | + | 1.65434e33i | 0.902427 | + | 0.902427i | ||||
\(363\) | 8.53198e32 | − | 8.53198e32i | 0.449018 | − | 0.449018i | ||||
\(364\) | − | 4.02038e32i | − | 0.204150i | ||||||
\(365\) | −3.44715e33 | − | 4.51104e32i | −1.68909 | − | 0.221039i | ||||
\(366\) | −2.67371e33 | −1.26433 | ||||||||
\(367\) | 1.04708e33 | + | 1.04708e33i | 0.477881 | + | 0.477881i | 0.904453 | − | 0.426572i | \(-0.140279\pi\) |
−0.426572 | + | 0.904453i | \(0.640279\pi\) | |||||||
\(368\) | −3.05862e33 | + | 3.05862e33i | −1.34742 | + | 1.34742i | ||||
\(369\) | 1.00655e33i | 0.428048i | ||||||||
\(370\) | −1.76630e33 | + | 1.35751e33i | −0.725173 | + | 0.557340i | ||||
\(371\) | 9.97872e32 | 0.395561 | ||||||||
\(372\) | −2.30480e31 | − | 2.30480e31i | −0.00882216 | − | 0.00882216i | ||||
\(373\) | −3.21980e33 | + | 3.21980e33i | −1.19018 | + | 1.19018i | −0.213168 | + | 0.977016i | \(0.568378\pi\) |
−0.977016 | + | 0.213168i | \(0.931622\pi\) | |||||||
\(374\) | 2.11441e32i | 0.0754847i | ||||||||
\(375\) | 7.33082e32 | − | 1.78154e33i | 0.252782 | − | 0.614312i | ||||
\(376\) | 3.34435e33 | 1.11396 | ||||||||
\(377\) | −1.77582e33 | − | 1.77582e33i | −0.571427 | − | 0.571427i | ||||
\(378\) | 2.10534e33 | − | 2.10534e33i | 0.654528 | − | 0.654528i | ||||
\(379\) | − | 3.87032e33i | − | 1.16262i | −0.813683 | − | 0.581309i | \(-0.802541\pi\) | ||
0.813683 | − | 0.581309i | \(-0.197459\pi\) | |||||||
\(380\) | 4.31785e32 | + | 5.61810e32i | 0.125337 | + | 0.163081i | ||||
\(381\) | −1.84734e33 | −0.518228 | ||||||||
\(382\) | 1.92583e32 | + | 1.92583e32i | 0.0522149 | + | 0.0522149i | ||||
\(383\) | 1.77337e33 | − | 1.77337e33i | 0.464745 | − | 0.464745i | −0.435462 | − | 0.900207i | \(-0.643415\pi\) |
0.900207 | + | 0.435462i | \(0.143415\pi\) | |||||||
\(384\) | 3.07992e33i | 0.780251i | ||||||||
\(385\) | 9.20983e31 | − | 7.03778e32i | 0.0225560 | − | 0.172364i | ||||
\(386\) | 5.04062e33 | 1.19357 | ||||||||
\(387\) | −1.63780e32 | − | 1.63780e32i | −0.0374989 | − | 0.0374989i | ||||
\(388\) | 5.68560e32 | − | 5.68560e32i | 0.125882 | − | 0.125882i | ||||
\(389\) | − | 1.05975e33i | − | 0.226912i | −0.993543 | − | 0.113456i | \(-0.963808\pi\) | ||
0.993543 | − | 0.113456i | \(-0.0361921\pi\) | |||||||
\(390\) | 5.10940e33 | + | 6.68630e32i | 1.05811 | + | 0.138467i | ||||
\(391\) | 2.78310e33 | 0.557482 | ||||||||
\(392\) | −1.03360e33 | − | 1.03360e33i | −0.200279 | − | 0.200279i | ||||
\(393\) | −3.99733e33 | + | 3.99733e33i | −0.749319 | + | 0.749319i | ||||
\(394\) | − | 5.88576e33i | − | 1.06746i | ||||||
\(395\) | 6.66914e33 | − | 5.12564e33i | 1.17033 | − | 0.899469i | ||||
\(396\) | 1.14474e32 | 0.0194387 | ||||||||
\(397\) | −1.34395e33 | − | 1.34395e33i | −0.220855 | − | 0.220855i | 0.588003 | − | 0.808858i | \(-0.299914\pi\) |
−0.808858 | + | 0.588003i | \(0.799914\pi\) | |||||||
\(398\) | −1.72308e33 | + | 1.72308e33i | −0.274047 | + | 0.274047i | ||||
\(399\) | 4.43465e33i | 0.682671i | ||||||||
\(400\) | −1.96558e33 | + | 7.38147e33i | −0.292894 | + | 1.09992i | ||||
\(401\) | −2.91176e33 | −0.420029 | −0.210014 | − | 0.977698i | \(-0.567351\pi\) | ||||
−0.210014 | + | 0.977698i | \(0.567351\pi\) | |||||||
\(402\) | −2.38834e33 | − | 2.38834e33i | −0.333547 | − | 0.333547i | ||||
\(403\) | −8.81834e32 | + | 8.81834e32i | −0.119240 | + | 0.119240i | ||||
\(404\) | − | 1.67890e32i | − | 0.0219820i | ||||||
\(405\) | 6.20522e32 | + | 8.07381e32i | 0.0786759 | + | 0.102368i | ||||
\(406\) | −3.95429e33 | −0.485545 | ||||||||
\(407\) | −1.05745e33 | − | 1.05745e33i | −0.125757 | − | 0.125757i | ||||
\(408\) | 1.22317e33 | − | 1.22317e33i | 0.140898 | − | 0.140898i | ||||
\(409\) | 7.07206e33i | 0.789120i | 0.918870 | + | 0.394560i | \(0.129103\pi\) | ||||
−0.918870 | + | 0.394560i | \(0.870897\pi\) | |||||||
\(410\) | −9.92916e32 | + | 7.58746e33i | −0.107330 | + | 0.820174i | ||||
\(411\) | −4.33508e33 | −0.453997 | ||||||||
\(412\) | 1.02940e33 | + | 1.02940e33i | 0.104453 | + | 0.104453i | ||||
\(413\) | 5.72084e32 | − | 5.72084e32i | 0.0562483 | − | 0.0562483i | ||||
\(414\) | − | 1.05993e34i | − | 1.00988i | ||||||
\(415\) | 1.38489e34 | + | 1.81231e33i | 1.27876 | + | 0.167343i | ||||
\(416\) | −5.45636e33 | −0.488303 | ||||||||
\(417\) | −8.86378e33 | − | 8.86378e33i | −0.768865 | − | 0.768865i | ||||
\(418\) | −2.36601e33 | + | 2.36601e33i | −0.198941 | + | 0.198941i | ||||
\(419\) | 1.36015e33i | 0.110867i | 0.998462 | + | 0.0554336i | \(0.0176541\pi\) | ||||
−0.998462 | + | 0.0554336i | \(0.982346\pi\) | |||||||
\(420\) | 9.14512e32 | − | 7.02858e32i | 0.0722684 | − | 0.0555427i | ||||
\(421\) | −2.23548e33 | −0.171279 | −0.0856394 | − | 0.996326i | \(-0.527293\pi\) | ||||
−0.0856394 | + | 0.996326i | \(0.527293\pi\) | |||||||
\(422\) | −1.37722e34 | − | 1.37722e34i | −1.02316 | − | 1.02316i | ||||
\(423\) | −6.78210e33 | + | 6.78210e33i | −0.488585 | + | 0.488585i | ||||
\(424\) | − | 6.15968e33i | − | 0.430331i | ||||||
\(425\) | 4.25254e33 | − | 2.46402e33i | 0.288133 | − | 0.166950i | ||||
\(426\) | 3.13667e33 | 0.206131 | ||||||||
\(427\) | 1.61911e34 | + | 1.61911e34i | 1.03208 | + | 1.03208i | ||||
\(428\) | −2.16880e33 | + | 2.16880e33i | −0.134106 | + | 0.134106i | ||||
\(429\) | 3.45921e33i | 0.207506i | ||||||||
\(430\) | −1.07303e33 | − | 1.39615e33i | −0.0624482 | − | 0.0812534i | ||||
\(431\) | 2.35758e34 | 1.33126 | 0.665630 | − | 0.746282i | \(-0.268163\pi\) | ||||
0.665630 | + | 0.746282i | \(0.268163\pi\) | |||||||
\(432\) | −1.52103e34 | − | 1.52103e34i | −0.833391 | − | 0.833391i | ||||
\(433\) | −2.10238e34 | + | 2.10238e34i | −1.11781 | + | 1.11781i | −0.125752 | + | 0.992062i | \(0.540134\pi\) |
−0.992062 | + | 0.125752i | \(0.959866\pi\) | |||||||
\(434\) | 1.96362e33i | 0.101319i | ||||||||
\(435\) | 9.34882e32 | − | 7.14399e33i | 0.0468162 | − | 0.357751i | ||||
\(436\) | 3.25519e33 | 0.158216 | ||||||||
\(437\) | 3.11427e34 | + | 3.11427e34i | 1.46925 | + | 1.46925i | ||||
\(438\) | 1.88643e34 | − | 1.88643e34i | 0.863928 | − | 0.863928i | ||||
\(439\) | − | 1.02267e34i | − | 0.454668i | −0.973817 | − | 0.227334i | \(-0.926999\pi\) | ||
0.973817 | − | 0.227334i | \(-0.0730010\pi\) | |||||||
\(440\) | −4.34429e33 | − | 5.68506e32i | −0.187514 | − | 0.0245386i | ||||
\(441\) | 4.19215e33 | 0.175685 | ||||||||
\(442\) | 9.29580e33 | + | 9.29580e33i | 0.378266 | + | 0.378266i | ||||
\(443\) | 1.68073e34 | − | 1.68073e34i | 0.664125 | − | 0.664125i | −0.292224 | − | 0.956350i | \(-0.594395\pi\) |
0.956350 | + | 0.292224i | \(0.0943954\pi\) | |||||||
\(444\) | − | 2.43016e33i | − | 0.0932515i | ||||||
\(445\) | −3.25792e34 | + | 2.50391e34i | −1.21412 | + | 0.933122i | ||||
\(446\) | 1.43973e34 | 0.521107 | ||||||||
\(447\) | −8.76662e33 | − | 8.76662e33i | −0.308201 | − | 0.308201i | ||||
\(448\) | 1.34397e34 | − | 1.34397e34i | 0.458960 | − | 0.458960i | ||||
\(449\) | − | 5.54257e34i | − | 1.83869i | −0.393450 | − | 0.919346i | \(-0.628719\pi\) | ||
0.393450 | − | 0.919346i | \(-0.371281\pi\) | |||||||
\(450\) | −9.38405e33 | − | 1.61955e34i | −0.302432 | − | 0.521954i | ||||
\(451\) | −5.13692e33 | −0.160845 | ||||||||
\(452\) | 6.13744e33 | + | 6.13744e33i | 0.186718 | + | 0.186718i | ||||
\(453\) | −8.04780e33 | + | 8.04780e33i | −0.237903 | + | 0.237903i | ||||
\(454\) | 5.65994e34i | 1.62587i | ||||||||
\(455\) | −2.68919e34 | − | 3.49899e34i | −0.750711 | − | 0.976775i | ||||
\(456\) | 2.73743e34 | 0.742677 | ||||||||
\(457\) | 4.18717e33 | + | 4.18717e33i | 0.110410 | + | 0.110410i | 0.760154 | − | 0.649743i | \(-0.225124\pi\) |
−0.649743 | + | 0.760154i | \(0.725124\pi\) | |||||||
\(458\) | −3.16159e34 | + | 3.16159e34i | −0.810315 | + | 0.810315i | ||||
\(459\) | 1.38402e34i | 0.344808i | ||||||||
\(460\) | 1.48635e33 | − | 1.13581e34i | 0.0359973 | − | 0.275077i | ||||
\(461\) | −8.17431e34 | −1.92459 | −0.962297 | − | 0.272002i | \(-0.912314\pi\) | ||||
−0.962297 | + | 0.272002i | \(0.912314\pi\) | |||||||
\(462\) | 3.85138e33 | + | 3.85138e33i | 0.0881598 | + | 0.0881598i | ||||
\(463\) | 3.24302e34 | − | 3.24302e34i | 0.721767 | − | 0.721767i | −0.247198 | − | 0.968965i | \(-0.579510\pi\) |
0.968965 | + | 0.247198i | \(0.0795097\pi\) | |||||||
\(464\) | 2.85683e34i | 0.618230i | ||||||||
\(465\) | −3.54756e33 | − | 4.64243e32i | −0.0746519 | − | 0.00976916i | ||||
\(466\) | 3.83960e33 | 0.0785721 | ||||||||
\(467\) | 1.00991e34 | + | 1.00991e34i | 0.200984 | + | 0.200984i | 0.800422 | − | 0.599437i | \(-0.204609\pi\) |
−0.599437 | + | 0.800422i | \(0.704609\pi\) | |||||||
\(468\) | 5.03272e33 | − | 5.03272e33i | 0.0974107 | − | 0.0974107i | ||||
\(469\) | 2.89260e34i | 0.544555i | ||||||||
\(470\) | −5.78143e34 | + | 4.44338e34i | −1.05868 | + | 0.813658i | ||||
\(471\) | −4.14852e34 | −0.738960 | ||||||||
\(472\) | −3.53137e33 | − | 3.53137e33i | −0.0611924 | − | 0.0611924i | ||||
\(473\) | 8.35850e32 | − | 8.35850e32i | 0.0140907 | − | 0.0140907i | ||||
\(474\) | 6.45462e34i | 1.05865i | ||||||||
\(475\) | 7.51577e34 | + | 2.00134e34i | 1.19938 | + | 0.319378i | ||||
\(476\) | 2.94257e33 | 0.0456916 | ||||||||
\(477\) | 1.24914e34 | + | 1.24914e34i | 0.188744 | + | 0.188744i | ||||
\(478\) | 4.29580e34 | − | 4.29580e34i | 0.631657 | − | 0.631657i | ||||
\(479\) | − | 8.73265e34i | − | 1.24964i | −0.780769 | − | 0.624819i | \(-0.785173\pi\) | ||
0.780769 | − | 0.624819i | \(-0.214827\pi\) | |||||||
\(480\) | −9.53902e33 | − | 1.24115e34i | −0.132852 | − | 0.172858i | ||||
\(481\) | −9.29797e34 | −1.26038 | ||||||||
\(482\) | −5.50034e34 | − | 5.50034e34i | −0.725735 | − | 0.725735i | ||||
\(483\) | 5.06939e34 | − | 5.06939e34i | 0.651093 | − | 0.651093i | ||||
\(484\) | − | 1.26699e34i | − | 0.158411i | ||||||
\(485\) | 1.14522e34 | − | 8.75130e34i | 0.139395 | − | 1.06520i | ||||
\(486\) | 8.65252e34 | 1.02535 | ||||||||
\(487\) | 1.04084e35 | + | 1.04084e35i | 1.20090 | + | 1.20090i | 0.973893 | + | 0.227009i | \(0.0728946\pi\) |
0.227009 | + | 0.973893i | \(0.427105\pi\) | |||||||
\(488\) | 9.99448e34 | − | 9.99448e34i | 1.12280 | − | 1.12280i | ||||
\(489\) | − | 4.89866e33i | − | 0.0535873i | ||||||
\(490\) | 3.16008e34 | + | 4.13536e33i | 0.336627 | + | 0.0440519i | ||||
\(491\) | 5.18891e33 | 0.0538290 | 0.0269145 | − | 0.999638i | \(-0.491432\pi\) | ||||
0.0269145 | + | 0.999638i | \(0.491432\pi\) | |||||||
\(492\) | −5.90265e33 | − | 5.90265e33i | −0.0596349 | − | 0.0596349i | ||||
\(493\) | 1.29974e34 | − | 1.29974e34i | 0.127893 | − | 0.127893i | ||||
\(494\) | 2.08039e35i | 1.99385i | ||||||||
\(495\) | 9.96281e33 | − | 7.65702e33i | 0.0930067 | − | 0.0714813i | ||||
\(496\) | 1.41864e34 | 0.129006 | ||||||||
\(497\) | −1.89947e34 | − | 1.89947e34i | −0.168267 | − | 0.168267i | ||||
\(498\) | −7.57873e34 | + | 7.57873e34i | −0.654056 | + | 0.654056i | ||||
\(499\) | − | 6.24363e34i | − | 0.524964i | −0.964937 | − | 0.262482i | \(-0.915459\pi\) | ||
0.964937 | − | 0.262482i | \(-0.0845411\pi\) | |||||||
\(500\) | −7.78477e33 | − | 1.86710e34i | −0.0637728 | − | 0.152953i | ||||
\(501\) | −9.03169e33 | −0.0720906 | ||||||||
\(502\) | −1.31025e35 | − | 1.31025e35i | −1.01908 | − | 1.01908i | ||||
\(503\) | −7.75841e34 | + | 7.75841e34i | −0.588016 | + | 0.588016i | −0.937094 | − | 0.349078i | \(-0.886495\pi\) |
0.349078 | + | 0.937094i | \(0.386495\pi\) | |||||||
\(504\) | 5.64190e34i | 0.416705i | ||||||||
\(505\) | −1.12300e34 | − | 1.46117e34i | −0.0808333 | − | 0.105175i | ||||
\(506\) | 5.40933e34 | 0.379478 | ||||||||
\(507\) | 8.33824e34 | + | 8.33824e34i | 0.570126 | + | 0.570126i | ||||
\(508\) | −1.37164e34 | + | 1.37164e34i | −0.0914138 | + | 0.0914138i | ||||
\(509\) | 1.41568e35i | 0.919672i | 0.888004 | + | 0.459836i | \(0.152092\pi\) | ||||
−0.888004 | + | 0.459836i | \(0.847908\pi\) | |||||||
\(510\) | −4.89379e33 | + | 3.73964e34i | −0.0309908 | + | 0.236819i | ||||
\(511\) | −2.28473e35 | −1.41047 | ||||||||
\(512\) | −7.65711e34 | − | 7.65711e34i | −0.460845 | − | 0.460845i | ||||
\(513\) | −1.54870e35 | + | 1.54870e35i | −0.908746 | + | 0.908746i | ||||
\(514\) | − | 3.11732e35i | − | 1.78345i | ||||||
\(515\) | 1.58446e35 | + | 2.07346e34i | 0.883866 | + | 0.115665i | ||||
\(516\) | 1.92089e33 | 0.0104486 | ||||||||
\(517\) | −3.46124e34 | − | 3.46124e34i | −0.183593 | − | 0.183593i | ||||
\(518\) | −1.03521e35 | + | 1.03521e35i | −0.535477 | + | 0.535477i | ||||
\(519\) | − | 1.03389e35i | − | 0.521555i | ||||||
\(520\) | −2.15986e35 | + | 1.65999e35i | −1.06263 | + | 0.816697i | ||||
\(521\) | 3.71768e35 | 1.78395 | 0.891973 | − | 0.452089i | \(-0.149321\pi\) | ||||
0.891973 | + | 0.452089i | \(0.149321\pi\) | |||||||
\(522\) | −4.94999e34 | − | 4.94999e34i | −0.231680 | − | 0.231680i | ||||
\(523\) | 2.40331e34 | − | 2.40331e34i | 0.109720 | − | 0.109720i | −0.650115 | − | 0.759836i | \(-0.725279\pi\) |
0.759836 | + | 0.650115i | \(0.225279\pi\) | |||||||
\(524\) | 5.93601e34i | 0.264355i | ||||||||
\(525\) | 3.25778e34 | − | 1.22341e35i | 0.141531 | − | 0.531499i | ||||
\(526\) | 2.32632e35 | 0.985948 | ||||||||
\(527\) | −6.45426e33 | − | 6.45426e33i | −0.0266875 | − | 0.0266875i | ||||
\(528\) | 2.78248e34 | − | 2.78248e34i | 0.112251 | − | 0.112251i | ||||
\(529\) | − | 4.57951e35i | − | 1.80258i | ||||||
\(530\) | 8.18390e34 | + | 1.06483e35i | 0.314321 | + | 0.408974i | ||||
\(531\) | 1.43227e34 | 0.0536781 | ||||||||
\(532\) | 3.29271e34 | + | 3.29271e34i | 0.120421 | + | 0.120421i | ||||
\(533\) | −2.25840e35 | + | 2.25840e35i | −0.806021 | + | 0.806021i | ||||
\(534\) | − | 3.15313e35i | − | 1.09826i | ||||||
\(535\) | −4.36848e34 | + | 3.33822e35i | −0.148502 | + | 1.13479i | ||||
\(536\) | 1.78555e35 | 0.592421 | ||||||||
\(537\) | 2.41817e35 | + | 2.41817e35i | 0.783107 | + | 0.783107i | ||||
\(538\) | 1.49409e35 | − | 1.49409e35i | 0.472288 | − | 0.472288i | ||||
\(539\) | 2.13946e34i | 0.0660162i | ||||||||
\(540\) | 5.64831e34 | + | 7.39154e33i | 0.170137 | + | 0.0222647i | ||||
\(541\) | −5.97797e35 | −1.75788 | −0.878940 | − | 0.476933i | \(-0.841749\pi\) | ||||
−0.878940 | + | 0.476933i | \(0.841749\pi\) | |||||||
\(542\) | 5.98918e34 | + | 5.98918e34i | 0.171940 | + | 0.171940i | ||||
\(543\) | −1.98093e35 | + | 1.98093e35i | −0.555229 | + | 0.555229i | ||||
\(544\) | − | 3.99358e34i | − | 0.109289i | ||||||
\(545\) | 2.83303e35 | − | 2.17736e35i | 0.757002 | − | 0.581803i | ||||
\(546\) | 3.38644e35 | 0.883567 | ||||||||
\(547\) | −9.83000e33 | − | 9.83000e33i | −0.0250448 | − | 0.0250448i | 0.694473 | − | 0.719518i | \(-0.255637\pi\) |
−0.719518 | + | 0.694473i | \(0.755637\pi\) | |||||||
\(548\) | −3.21878e34 | + | 3.21878e34i | −0.0800837 | + | 0.0800837i | ||||
\(549\) | 4.05362e35i | 0.984923i | ||||||||
\(550\) | 8.26538e34 | − | 4.78914e34i | 0.196132 | − | 0.113643i | ||||
\(551\) | 2.90881e35 | 0.674131 | ||||||||
\(552\) | −3.12924e35 | − | 3.12924e35i | −0.708323 | − | 0.708323i | ||||
\(553\) | 3.90871e35 | − | 3.90871e35i | 0.864186 | − | 0.864186i | ||||
\(554\) | − | 1.54107e35i | − | 0.332809i | ||||||
\(555\) | −1.62551e35 | − | 2.11500e35i | −0.342910 | − | 0.446171i | ||||
\(556\) | −1.31626e35 | −0.271251 | ||||||||
\(557\) | 1.31923e35 | + | 1.31923e35i | 0.265585 | + | 0.265585i | 0.827318 | − | 0.561734i | \(-0.189865\pi\) |
−0.561734 | + | 0.827318i | \(0.689865\pi\) | |||||||
\(558\) | −2.45806e34 | + | 2.45806e34i | −0.0483446 | + | 0.0483446i | ||||
\(559\) | − | 7.34946e34i | − | 0.141222i | ||||||
\(560\) | −6.51380e34 | + | 4.97758e35i | −0.122290 | + | 0.934489i | ||||
\(561\) | −2.53184e34 | −0.0464429 | ||||||||
\(562\) | −6.40754e35 | − | 6.40754e35i | −1.14847 | − | 1.14847i | ||||
\(563\) | −3.83699e35 | + | 3.83699e35i | −0.672020 | + | 0.672020i | −0.958181 | − | 0.286162i | \(-0.907621\pi\) |
0.286162 | + | 0.958181i | \(0.407621\pi\) | |||||||
\(564\) | − | 7.95437e34i | − | 0.136137i | ||||||
\(565\) | 9.44676e35 | + | 1.23623e35i | 1.57999 | + | 0.206761i | ||||
\(566\) | −6.29517e35 | −1.02895 | ||||||||
\(567\) | 4.73198e34 | + | 4.73198e34i | 0.0755897 | + | 0.0755897i | ||||
\(568\) | −1.17251e35 | + | 1.17251e35i | −0.183057 | + | 0.183057i | ||||
\(569\) | 3.21963e35i | 0.491300i | 0.969359 | + | 0.245650i | \(0.0790013\pi\) | ||||
−0.969359 | + | 0.245650i | \(0.920999\pi\) | |||||||
\(570\) | −4.73223e35 | + | 3.63701e35i | −0.705819 | + | 0.542465i | ||||
\(571\) | −1.04599e36 | −1.52496 | −0.762482 | − | 0.647009i | \(-0.776019\pi\) | ||||
−0.762482 | + | 0.647009i | \(0.776019\pi\) | |||||||
\(572\) | 2.56845e34 | + | 2.56845e34i | 0.0366035 | + | 0.0366035i | ||||
\(573\) | −2.30603e34 | + | 2.30603e34i | −0.0321258 | + | 0.0321258i | ||||
\(574\) | 5.02887e35i | 0.684882i | ||||||||
\(575\) | −6.30372e35 | − | 1.08793e36i | −0.839296 | − | 1.44850i | ||||
\(576\) | 3.36477e35 | 0.437989 | ||||||||
\(577\) | 1.77056e35 | + | 1.77056e35i | 0.225333 | + | 0.225333i | 0.810740 | − | 0.585407i | \(-0.199065\pi\) |
−0.585407 | + | 0.810740i | \(0.699065\pi\) | |||||||
\(578\) | 5.45503e35 | − | 5.45503e35i | 0.678790 | − | 0.678790i | ||||
\(579\) | 6.03574e35i | 0.734360i | ||||||||
\(580\) | −4.61024e34 | − | 5.99853e34i | −0.0548478 | − | 0.0713643i | ||||
\(581\) | 9.17888e35 | 1.06782 | ||||||||
\(582\) | 4.78909e35 | + | 4.78909e35i | 0.544822 | + | 0.544822i | ||||
\(583\) | −6.37498e34 | + | 6.37498e34i | −0.0709231 | + | 0.0709231i | ||||
\(584\) | 1.41032e36i | 1.53444i | ||||||||
\(585\) | 1.01371e35 | − | 7.74638e35i | 0.107867 | − | 0.824276i | ||||
\(586\) | −2.31391e35 | −0.240812 | ||||||||
\(587\) | −6.90189e35 | − | 6.90189e35i | −0.702542 | − | 0.702542i | 0.262413 | − | 0.964956i | \(-0.415482\pi\) |
−0.964956 | + | 0.262413i | \(0.915482\pi\) | |||||||
\(588\) | −2.45837e34 | + | 2.45837e34i | −0.0244761 | + | 0.0244761i | ||||
\(589\) | − | 1.44445e35i | − | 0.140671i | ||||||
\(590\) | 1.07966e35 | + | 1.41287e34i | 0.102852 | + | 0.0134594i | ||||
\(591\) | 7.04772e35 | 0.656767 | ||||||||
\(592\) | 7.47901e35 | + | 7.47901e35i | 0.681807 | + | 0.681807i | ||||
\(593\) | 7.31719e35 | − | 7.31719e35i | 0.652579 | − | 0.652579i | −0.301034 | − | 0.953613i | \(-0.597332\pi\) |
0.953613 | + | 0.301034i | \(0.0973319\pi\) | |||||||
\(594\) | 2.69002e35i | 0.234710i | ||||||||
\(595\) | 2.56096e35 | − | 1.96825e35i | 0.218616 | − | 0.168020i | ||||
\(596\) | −1.30184e35 | −0.108731 | ||||||||
\(597\) | −2.06325e35 | − | 2.06325e35i | −0.168610 | − | 0.168610i | ||||
\(598\) | 2.37816e36 | − | 2.37816e36i | 1.90163 | − | 1.90163i | ||||
\(599\) | − | 1.29851e36i | − | 1.01601i | −0.861355 | − | 0.508003i | \(-0.830384\pi\) | ||
0.861355 | − | 0.508003i | \(-0.169616\pi\) | |||||||
\(600\) | −7.55192e35 | − | 2.01097e35i | −0.578217 | − | 0.153971i | ||||
\(601\) | −4.40252e35 | −0.329863 | −0.164931 | − | 0.986305i | \(-0.552740\pi\) | ||||
−0.164931 | + | 0.986305i | \(0.552740\pi\) | |||||||
\(602\) | −8.18268e34 | − | 8.18268e34i | −0.0599986 | − | 0.0599986i | ||||
\(603\) | −3.62097e35 | + | 3.62097e35i | −0.259836 | + | 0.259836i | ||||
\(604\) | 1.19509e35i | 0.0839308i | ||||||||
\(605\) | −8.47478e35 | − | 1.10268e36i | −0.582517 | − | 0.757932i | ||||
\(606\) | 1.41417e35 | 0.0951386 | ||||||||
\(607\) | 1.86886e36 | + | 1.86886e36i | 1.23062 | + | 1.23062i | 0.963726 | + | 0.266893i | \(0.0859970\pi\) |
0.266893 | + | 0.963726i | \(0.414003\pi\) | |||||||
\(608\) | 4.46878e35 | − | 4.46878e35i | 0.288033 | − | 0.288033i | ||||
\(609\) | − | 4.73494e35i | − | 0.298738i | ||||||
\(610\) | −3.99871e35 | + | 3.05565e36i | −0.246963 | + | 1.88719i | ||||
\(611\) | −3.04340e36 | −1.84002 | ||||||||
\(612\) | 3.68352e34 | + | 3.68352e34i | 0.0218019 | + | 0.0218019i | ||||
\(613\) | −1.14582e36 | + | 1.14582e36i | −0.663942 | + | 0.663942i | −0.956307 | − | 0.292365i | \(-0.905558\pi\) |
0.292365 | + | 0.956307i | \(0.405558\pi\) | |||||||
\(614\) | 1.45319e35i | 0.0824393i | ||||||||
\(615\) | −9.08537e35 | − | 1.18894e35i | −0.504622 | − | 0.0660363i | ||||
\(616\) | −2.87934e35 | −0.156583 | ||||||||
\(617\) | 2.45170e35 | + | 2.45170e35i | 0.130545 | + | 0.130545i | 0.769360 | − | 0.638815i | \(-0.220575\pi\) |
−0.638815 | + | 0.769360i | \(0.720575\pi\) | |||||||
\(618\) | −8.67084e35 | + | 8.67084e35i | −0.452076 | + | 0.452076i | ||||
\(619\) | 7.48289e35i | 0.382024i | 0.981588 | + | 0.191012i | \(0.0611770\pi\) | ||||
−0.981588 | + | 0.191012i | \(0.938823\pi\) | |||||||
\(620\) | −2.97875e34 | + | 2.28935e34i | −0.0148916 | + | 0.0114451i | ||||
\(621\) | 3.54075e36 | 1.73342 | ||||||||
\(622\) | 1.27499e36 | + | 1.27499e36i | 0.611270 | + | 0.611270i | ||||
\(623\) | −1.90943e36 | + | 1.90943e36i | −0.896519 | + | 0.896519i | ||||
\(624\) | − | 2.44658e36i | − | 1.12502i | ||||||
\(625\) | −1.92640e36 | − | 1.10425e36i | −0.867574 | − | 0.497308i | ||||
\(626\) | −6.71656e35 | −0.296265 | ||||||||
\(627\) | −2.83311e35 | − | 2.83311e35i | −0.122401 | − | 0.122401i | ||||
\(628\) | −3.08026e35 | + | 3.08026e35i | −0.130350 | + | 0.130350i | ||||
\(629\) | − | 6.80531e35i | − | 0.282091i | ||||||
\(630\) | −7.49596e35 | − | 9.75324e35i | −0.304369 | − | 0.396024i | ||||
\(631\) | −1.97667e36 | −0.786237 | −0.393118 | − | 0.919488i | \(-0.628604\pi\) | ||||
−0.393118 | + | 0.919488i | \(0.628604\pi\) | |||||||
\(632\) | −2.41278e36 | − | 2.41278e36i | −0.940147 | − | 0.940147i | ||||
\(633\) | 1.64912e36 | − | 1.64912e36i | 0.629510 | − | 0.629510i | ||||
\(634\) | 1.37306e36i | 0.513488i | ||||||||
\(635\) | −2.76282e35 | + | 2.11123e36i | −0.101226 | + | 0.773531i | ||||
\(636\) | −1.46505e35 | −0.0525908 | ||||||||
\(637\) | 9.40593e35 | + | 9.40593e35i | 0.330818 | + | 0.330818i | ||||
\(638\) | 2.52623e35 | − | 2.52623e35i | 0.0870569 | − | 0.0870569i | ||||
\(639\) | − | 4.75552e35i | − | 0.160578i | ||||||
\(640\) | 3.51990e36 | + | 4.60624e35i | 1.16464 | + | 0.152408i | ||||
\(641\) | 5.06578e36 | 1.64245 | 0.821224 | − | 0.570606i | \(-0.193292\pi\) | ||||
0.821224 | + | 0.570606i | \(0.193292\pi\) | |||||||
\(642\) | −1.82682e36 | − | 1.82682e36i | −0.580417 | − | 0.580417i | ||||
\(643\) | 2.22275e36 | − | 2.22275e36i | 0.692067 | − | 0.692067i | −0.270619 | − | 0.962686i | \(-0.587228\pi\) |
0.962686 | + | 0.270619i | \(0.0872285\pi\) | |||||||
\(644\) | − | 7.52801e35i | − | 0.229701i | ||||||
\(645\) | 1.67178e35 | − | 1.28486e35i | 0.0499922 | − | 0.0384220i | ||||
\(646\) | −1.52266e36 | −0.446253 | ||||||||
\(647\) | 2.15344e36 | + | 2.15344e36i | 0.618552 | + | 0.618552i | 0.945160 | − | 0.326608i | \(-0.105906\pi\) |
−0.326608 | + | 0.945160i | \(0.605906\pi\) | |||||||
\(648\) | 2.92096e35 | − | 2.92096e35i | 0.0822339 | − | 0.0822339i | ||||
\(649\) | 7.30960e34i | 0.0201703i | ||||||||
\(650\) | 1.52829e36 | − | 5.73929e36i | 0.413364 | − | 1.55233i | ||||
\(651\) | −2.35127e35 | −0.0623376 | ||||||||
\(652\) | −3.63724e34 | − | 3.63724e34i | −0.00945263 | − | 0.00945263i | ||||
\(653\) | −2.03862e36 | + | 2.03862e36i | −0.519355 | + | 0.519355i | −0.917376 | − | 0.398021i | \(-0.869697\pi\) |
0.398021 | + | 0.917376i | \(0.369697\pi\) | |||||||
\(654\) | 2.74191e36i | 0.684766i | ||||||||
\(655\) | 3.97053e36 | + | 5.16619e36i | 0.972102 | + | 1.26483i | ||||
\(656\) | 3.63317e36 | 0.872039 | ||||||||
\(657\) | −2.86003e36 | − | 2.86003e36i | −0.673008 | − | 0.673008i | ||||
\(658\) | −3.38844e36 | + | 3.38844e36i | −0.781741 | + | 0.781741i | ||||
\(659\) | 3.21300e36i | 0.726775i | 0.931638 | + | 0.363388i | \(0.118380\pi\) | ||||
−0.931638 | + | 0.363388i | \(0.881620\pi\) | |||||||
\(660\) | −1.35216e34 | + | 1.03327e35i | −0.00299887 | + | 0.0229162i | ||||
\(661\) | 1.30866e36 | 0.284582 | 0.142291 | − | 0.989825i | \(-0.454553\pi\) | ||||
0.142291 | + | 0.989825i | \(0.454553\pi\) | |||||||
\(662\) | −1.89941e36 | − | 1.89941e36i | −0.405009 | − | 0.405009i | ||||
\(663\) | −1.11310e36 | + | 1.11310e36i | −0.232733 | + | 0.232733i | ||||
\(664\) | − | 5.66595e36i | − | 1.16168i | ||||||
\(665\) | 5.06815e36 | + | 6.63232e35i | 1.01899 | + | 0.133347i | ||||
\(666\) | −2.59176e36 | −0.511010 | ||||||||
\(667\) | −3.32515e36 | − | 3.32515e36i | −0.642948 | − | 0.642948i | ||||
\(668\) | −6.70599e34 | + | 6.70599e34i | −0.0127165 | + | 0.0127165i | ||||
\(669\) | 1.72396e36i | 0.320617i | ||||||||
\(670\) | −3.08671e36 | + | 2.37233e36i | −0.563019 | + | 0.432715i | ||||
\(671\) | −2.06876e36 | −0.370099 | ||||||||
\(672\) | −7.27427e35 | − | 7.27427e35i | −0.127641 | − | 0.127641i | ||||
\(673\) | −1.65247e36 | + | 1.65247e36i | −0.284406 | + | 0.284406i | −0.834863 | − | 0.550458i | \(-0.814453\pi\) |
0.550458 | + | 0.834863i | \(0.314453\pi\) | |||||||
\(674\) | − | 1.82750e36i | − | 0.308516i | ||||||
\(675\) | 5.41022e36 | − | 3.13480e36i | 0.895912 | − | 0.519112i | ||||
\(676\) | 1.23822e36 | 0.201137 | ||||||||
\(677\) | 1.23936e36 | + | 1.23936e36i | 0.197489 | + | 0.197489i | 0.798923 | − | 0.601433i | \(-0.205403\pi\) |
−0.601433 | + | 0.798923i | \(0.705403\pi\) | |||||||
\(678\) | −5.16968e36 | + | 5.16968e36i | −0.808124 | + | 0.808124i | ||||
\(679\) | − | 5.80025e36i | − | 0.889486i | ||||||
\(680\) | −1.21497e36 | − | 1.58083e36i | −0.182788 | − | 0.237832i | ||||
\(681\) | −6.77733e36 | −1.00034 | ||||||||
\(682\) | −1.25447e35 | − | 1.25447e35i | −0.0181662 | − | 0.0181662i | ||||
\(683\) | 2.28158e36 | − | 2.28158e36i | 0.324165 | − | 0.324165i | −0.526197 | − | 0.850363i | \(-0.676383\pi\) |
0.850363 | + | 0.526197i | \(0.176383\pi\) | |||||||
\(684\) | 8.24365e35i | 0.114919i | ||||||||
\(685\) | −6.48341e35 | + | 4.95436e36i | −0.0886801 | + | 0.677657i | ||||
\(686\) | 8.75534e36 | 1.17506 | ||||||||
\(687\) | −3.78575e36 | − | 3.78575e36i | −0.498556 | − | 0.498556i | ||||
\(688\) | −5.91169e35 | + | 5.91169e35i | −0.0763945 | + | 0.0763945i | ||||
\(689\) | 5.60539e36i | 0.710814i | ||||||||
\(690\) | 9.56716e36 | + | 1.25198e36i | 1.19054 | + | 0.155798i | ||||
\(691\) | −8.96721e36 | −1.09507 | −0.547536 | − | 0.836782i | \(-0.684434\pi\) | ||||
−0.547536 | + | 0.836782i | \(0.684434\pi\) | |||||||
\(692\) | −7.67661e35 | − | 7.67661e35i | −0.0920006 | − | 0.0920006i | ||||
\(693\) | 5.83910e35 | − | 5.83910e35i | 0.0686774 | − | 0.0686774i | ||||
\(694\) | − | 4.91972e35i | − | 0.0567894i | ||||||
\(695\) | −1.14556e37 | + | 8.80435e36i | −1.29783 | + | 0.997459i | ||||
\(696\) | −2.92279e36 | −0.324996 | ||||||||
\(697\) | −1.65295e36 | − | 1.65295e36i | −0.180399 | − | 0.180399i | ||||
\(698\) | −1.19603e35 | + | 1.19603e35i | −0.0128122 | + | 0.0128122i | ||||
\(699\) | 4.59761e35i | 0.0483425i | ||||||||
\(700\) | −6.66492e35 | − | 1.15027e36i | −0.0687892 | − | 0.118720i | ||||
\(701\) | 3.67140e36 | 0.371961 | 0.185980 | − | 0.982553i | \(-0.440454\pi\) | ||||
0.185980 | + | 0.982553i | \(0.440454\pi\) | |||||||
\(702\) | 1.18264e37 | + | 1.18264e37i | 1.17617 | + | 1.17617i | ||||
\(703\) | 7.61508e36 | − | 7.61508e36i | 0.743456 | − | 0.743456i | ||||
\(704\) | 1.71721e36i | 0.164581i | ||||||||
\(705\) | −5.32060e36 | − | 6.92280e36i | −0.500613 | − | 0.651363i | ||||
\(706\) | 3.50713e35 | 0.0323959 | ||||||||
\(707\) | −8.56375e35 | − | 8.56375e35i | −0.0776625 | − | 0.0776625i | ||||
\(708\) | −8.39919e34 | + | 8.39919e34i | −0.00747834 | + | 0.00747834i | ||||
\(709\) | − | 1.93132e37i | − | 1.68832i | −0.536093 | − | 0.844159i | \(-0.680100\pi\) | ||
0.536093 | − | 0.844159i | \(-0.319900\pi\) | |||||||
\(710\) | 4.69111e35 | − | 3.58475e36i | 0.0402640 | − | 0.307681i | ||||
\(711\) | 9.78589e36 | 0.824699 | ||||||||
\(712\) | 1.17866e37 | + | 1.17866e37i | 0.975322 | + | 0.975322i | ||||
\(713\) | −1.65120e36 | + | 1.65120e36i | −0.134164 | + | 0.134164i | ||||
\(714\) | 2.47858e36i | 0.197755i | ||||||||
\(715\) | 3.95336e36 | + | 5.17348e35i | 0.309733 | + | 0.0405326i | ||||
\(716\) | 3.59096e36 | 0.276275 | ||||||||
\(717\) | 5.14388e36 | + | 5.14388e36i | 0.388635 | + | 0.388635i | ||||
\(718\) | 3.80016e36 | − | 3.80016e36i | 0.281958 | − | 0.281958i | ||||
\(719\) | − | 1.43743e37i | − | 1.04739i | −0.851905 | − | 0.523697i | \(-0.824553\pi\) | ||
0.851905 | − | 0.523697i | \(-0.175447\pi\) | |||||||
\(720\) | −7.04636e36 | + | 5.41556e36i | −0.504246 | + | 0.387544i | ||||
\(721\) | 1.05016e37 | 0.738067 | ||||||||
\(722\) | −5.97821e36 | − | 5.97821e36i | −0.412656 | − | 0.412656i | ||||
\(723\) | 6.58622e36 | − | 6.58622e36i | 0.446517 | − | 0.446517i | ||||
\(724\) | 2.94167e36i | 0.195881i | ||||||||
\(725\) | −8.02471e36 | − | 2.13687e36i | −0.524850 | − | 0.139760i | ||||
\(726\) | 1.06721e37 | 0.685607 | ||||||||
\(727\) | −5.89050e36 | − | 5.89050e36i | −0.371710 | − | 0.371710i | 0.496390 | − | 0.868100i | \(-0.334659\pi\) |
−0.868100 | + | 0.496390i | \(0.834659\pi\) | |||||||
\(728\) | −1.26587e37 | + | 1.26587e37i | −0.784662 | + | 0.784662i | ||||
\(729\) | 1.24811e37i | 0.759966i | ||||||||
\(730\) | −1.87378e37 | − | 2.43804e37i | −1.12079 | − | 1.45829i | ||||
\(731\) | 5.37917e35 | 0.0316075 | ||||||||
\(732\) | −2.37714e36 | − | 2.37714e36i | −0.137218 | − | 0.137218i | ||||
\(733\) | 3.48486e36 | − | 3.48486e36i | 0.197621 | − | 0.197621i | −0.601358 | − | 0.798980i | \(-0.705373\pi\) |
0.798980 | + | 0.601358i | \(0.205373\pi\) | |||||||
\(734\) | 1.30972e37i | 0.729677i | ||||||||
\(735\) | −4.95177e35 | + | 3.78394e36i | −0.0271035 | + | 0.207114i | ||||
\(736\) | −1.02168e37 | −0.549420 | ||||||||
\(737\) | −1.84796e36 | − | 1.84796e36i | −0.0976372 | − | 0.0976372i | ||||
\(738\) | −6.29515e36 | + | 6.29515e36i | −0.326794 | + | 0.326794i | ||||
\(739\) | 2.97621e37i | 1.51805i | 0.651062 | + | 0.759025i | \(0.274324\pi\) | ||||
−0.651062 | + | 0.759025i | \(0.725676\pi\) | |||||||
\(740\) | −2.77731e36 | − | 3.63447e35i | −0.139191 | − | 0.0182150i | ||||
\(741\) | −2.49109e37 | −1.22674 | ||||||||
\(742\) | 6.24088e36 | + | 6.24088e36i | 0.301992 | + | 0.301992i | ||||
\(743\) | 9.12879e36 | − | 9.12879e36i | 0.434069 | − | 0.434069i | −0.455941 | − | 0.890010i | \(-0.650697\pi\) |
0.890010 | + | 0.455941i | \(0.150697\pi\) | |||||||
\(744\) | 1.45140e36i | 0.0678170i | ||||||||
\(745\) | −1.13301e37 | + | 8.70785e36i | −0.520237 | + | 0.399834i | ||||
\(746\) | −4.02745e37 | −1.81729 | ||||||||
\(747\) | 1.14901e37 | + | 1.14901e37i | 0.509516 | + | 0.509516i | ||||
\(748\) | −1.87988e35 | + | 1.87988e35i | −0.00819237 | + | 0.00819237i | ||||
\(749\) | 2.21253e37i | 0.947600i | ||||||||
\(750\) | 1.57269e37 | − | 6.55726e36i | 0.661984 | − | 0.276011i | ||||
\(751\) | −1.42103e37 | −0.587875 | −0.293938 | − | 0.955825i | \(-0.594966\pi\) | ||||
−0.293938 | + | 0.955825i | \(0.594966\pi\) | |||||||
\(752\) | 2.44802e37 | + | 2.44802e37i | 0.995367 | + | 0.995367i | ||||
\(753\) | 1.56892e37 | − | 1.56892e37i | 0.626998 | − | 0.626998i | ||||
\(754\) | − | 2.22126e37i | − | 0.872513i | ||||||
\(755\) | 7.99385e36 | + | 1.04011e37i | 0.308635 | + | 0.401575i | ||||
\(756\) | 3.74363e36 | 0.142072 | ||||||||
\(757\) | −3.00112e37 | − | 3.00112e37i | −1.11953 | − | 1.11953i | −0.991810 | − | 0.127722i | \(-0.959234\pi\) |
−0.127722 | − | 0.991810i | \(-0.540766\pi\) | |||||||
\(758\) | 2.42057e37 | − | 2.42057e37i | 0.887602 | − | 0.887602i | ||||
\(759\) | 6.47724e36i | 0.233478i | ||||||||
\(760\) | 4.09401e36 | − | 3.12848e37i | 0.145068 | − | 1.10855i | ||||
\(761\) | 1.34961e37 | 0.470120 | 0.235060 | − | 0.971981i | \(-0.424471\pi\) | ||||
0.235060 | + | 0.971981i | \(0.424471\pi\) | |||||||
\(762\) | −1.15536e37 | − | 1.15536e37i | −0.395642 | − | 0.395642i | ||||
\(763\) | 1.66041e37 | − | 1.66041e37i | 0.558981 | − | 0.558981i | ||||
\(764\) | 3.42443e35i | 0.0113338i | ||||||||
\(765\) | 5.66968e36 | + | 7.41950e35i | 0.184485 | + | 0.0241422i | ||||
\(766\) | 2.21820e37 | 0.709621 | ||||||||
\(767\) | 3.21359e36 | + | 3.21359e36i | 0.101077 | + | 0.101077i | ||||
\(768\) | −7.35536e36 | + | 7.35536e36i | −0.227462 | + | 0.227462i | ||||
\(769\) | 3.01328e37i | 0.916214i | 0.888897 | + | 0.458107i | \(0.151472\pi\) | ||||
−0.888897 | + | 0.458107i | \(0.848528\pi\) | |||||||
\(770\) | 4.97756e36 | − | 3.82556e36i | 0.148812 | − | 0.114371i | ||||
\(771\) | 3.73274e37 | 1.09729 | ||||||||
\(772\) | 4.48151e36 | + | 4.48151e36i | 0.129539 | + | 0.129539i | ||||
\(773\) | −6.65204e36 | + | 6.65204e36i | −0.189070 | + | 0.189070i | −0.795294 | − | 0.606224i | \(-0.792683\pi\) |
0.606224 | + | 0.795294i | \(0.292683\pi\) | |||||||
\(774\) | − | 2.04862e36i | − | 0.0572571i | ||||||
\(775\) | −1.06112e36 | + | 3.98490e36i | −0.0291638 | + | 0.109521i | ||||
\(776\) | −3.58039e37 | −0.967671 | ||||||||
\(777\) | −1.23958e37 | − | 1.23958e37i | −0.329459 | − | 0.329459i | ||||
\(778\) | 6.62786e36 | − | 6.62786e36i | 0.173236 | − | 0.173236i | ||||
\(779\) | − | 3.69928e37i | − | 0.950889i | ||||||
\(780\) | 3.94820e36 | + | 5.13713e36i | 0.0998088 | + | 0.129865i | ||||
\(781\) | 2.42698e36 | 0.0603396 | ||||||||
\(782\) | 1.74060e37 | + | 1.74060e37i | 0.425611 | + | 0.425611i | ||||
\(783\) | 1.65358e37 | − | 1.65358e37i | 0.397668 | − | 0.397668i | ||||
\(784\) | − | 1.51317e37i | − | 0.357914i | ||||||
\(785\) | −6.20439e36 | + | 4.74114e37i | −0.144342 | + | 1.10301i | ||||
\(786\) | −5.00001e37 | −1.14414 | ||||||||
\(787\) | 2.09349e36 | + | 2.09349e36i | 0.0471194 | + | 0.0471194i | 0.730274 | − | 0.683155i | \(-0.239392\pi\) |
−0.683155 | + | 0.730274i | \(0.739392\pi\) | |||||||
\(788\) | 5.23291e36 | − | 5.23291e36i | 0.115852 | − | 0.115852i | ||||
\(789\) | 2.78558e37i | 0.606616i | ||||||||
\(790\) | 7.37668e37 | + | 9.65333e36i | 1.58019 | + | 0.206788i | ||||
\(791\) | 6.26119e37 | 1.31936 | ||||||||
\(792\) | −3.60437e36 | − | 3.60437e36i | −0.0747140 | − | 0.0747140i | ||||
\(793\) | −9.09511e37 | + | 9.09511e37i | −1.85463 | + | 1.85463i | ||||
\(794\) | − | 1.68107e37i | − | 0.337224i | ||||||
\(795\) | −1.27505e37 | + | 9.79957e36i | −0.251626 | + | 0.193390i | ||||
\(796\) | −3.06390e36 | −0.0594847 | ||||||||
\(797\) | −3.27285e37 | − | 3.27285e37i | −0.625127 | − | 0.625127i | 0.321711 | − | 0.946838i | \(-0.395742\pi\) |
−0.946838 | + | 0.321711i | \(0.895742\pi\) | |||||||
\(798\) | −2.77351e37 | + | 2.77351e37i | −0.521186 | + | 0.521186i | ||||
\(799\) | − | 2.22751e37i | − | 0.411824i | ||||||
\(800\) | −1.56112e37 | + | 9.04546e36i | −0.283966 | + | 0.164536i | ||||
\(801\) | −4.78047e37 | −0.855555 | ||||||||
\(802\) | −1.82107e37 | − | 1.82107e37i | −0.320671 | − | 0.320671i | ||||
\(803\) | 1.45961e37 | − | 1.45961e37i | 0.252892 | − | 0.252892i | ||||
\(804\) | − | 4.24685e36i | − | 0.0723999i | ||||||
\(805\) | −5.03540e37 | − | 6.55173e37i | −0.844672 | − | 1.09903i | ||||
\(806\) | −1.10303e37 | −0.182067 | ||||||||
\(807\) | 1.78905e37 | + | 1.78905e37i | 0.290581 | + | 0.290581i | ||||
\(808\) | −5.28625e36 | + | 5.28625e36i | −0.0844889 | + | 0.0844889i | ||||
\(809\) | − | 3.80070e37i | − | 0.597769i | −0.954289 | − | 0.298884i | \(-0.903386\pi\) | ||
0.954289 | − | 0.298884i | \(-0.0966145\pi\) | |||||||
\(810\) | −1.16865e36 | + | 8.93038e36i | −0.0180876 | + | 0.138218i | ||||
\(811\) | 7.84596e37 | 1.19502 | 0.597510 | − | 0.801861i | \(-0.296157\pi\) | ||||
0.597510 | + | 0.801861i | \(0.296157\pi\) | |||||||
\(812\) | −3.51568e36 | − | 3.51568e36i | −0.0526964 | − | 0.0526964i | ||||
\(813\) | −7.17157e36 | + | 7.17157e36i | −0.105788 | + | 0.105788i | ||||
\(814\) | − | 1.32270e37i | − | 0.192019i | ||||||
\(815\) | −5.59844e36 | − | 7.32628e35i | −0.0799868 | − | 0.0104673i | ||||
\(816\) | 1.79069e37 | 0.251795 | ||||||||
\(817\) | 6.01925e36 | + | 6.01925e36i | 0.0833020 | + | 0.0833020i | ||||
\(818\) | −4.42300e37 | + | 4.42300e37i | −0.602455 | + | 0.602455i | ||||
\(819\) | − | 5.13420e37i | − | 0.688307i | ||||||
\(820\) | −7.62864e36 | + | 5.86307e36i | −0.100662 | + | 0.0773651i | ||||
\(821\) | 1.21357e38 | 1.57617 | 0.788087 | − | 0.615563i | \(-0.211072\pi\) | ||||
0.788087 | + | 0.615563i | \(0.211072\pi\) | |||||||
\(822\) | −2.71124e37 | − | 2.71124e37i | −0.346605 | − | 0.346605i | ||||
\(823\) | −7.77777e37 | + | 7.77777e37i | −0.978717 | + | 0.978717i | −0.999778 | − | 0.0210608i | \(-0.993296\pi\) |
0.0210608 | + | 0.999778i | \(0.493296\pi\) | |||||||
\(824\) | − | 6.48243e37i | − | 0.802942i | ||||||
\(825\) | 5.73462e36 | + | 9.89713e36i | 0.0699203 | + | 0.120672i | ||||
\(826\) | 7.15585e36 | 0.0858856 | ||||||||
\(827\) | 3.09291e36 | + | 3.09291e36i | 0.0365423 | + | 0.0365423i | 0.725142 | − | 0.688600i | \(-0.241774\pi\) |
−0.688600 | + | 0.725142i | \(0.741774\pi\) | |||||||
\(828\) | 9.42359e36 | − | 9.42359e36i | 0.109603 | − | 0.109603i | ||||
\(829\) | 8.86406e37i | 1.01490i | 0.861681 | + | 0.507451i | \(0.169412\pi\) | ||||
−0.861681 | + | 0.507451i | \(0.830588\pi\) | |||||||
\(830\) | 7.52792e37 | + | 9.79482e37i | 0.848516 | + | 1.10403i | ||||
\(831\) | 1.84531e37 | 0.204765 | ||||||||
\(832\) | 7.54954e37 | + | 7.54954e37i | 0.824740 | + | 0.824740i | ||||
\(833\) | −6.88433e36 | + | 6.88433e36i | −0.0740417 | + | 0.0740417i | ||||
\(834\) | − | 1.10872e38i | − | 1.17398i | ||||||
\(835\) | −1.35075e36 | + | 1.03219e37i | −0.0140816 | + | 0.107606i | ||||
\(836\) | −4.20714e36 | −0.0431823 | ||||||||
\(837\) | −8.21131e36 | − | 8.21131e36i | −0.0829816 | − | 0.0829816i | ||||
\(838\) | −8.50661e36 | + | 8.50661e36i | −0.0846417 | + | 0.0846417i | ||||
\(839\) | − | 1.48941e37i | − | 0.145918i | −0.997335 | − | 0.0729589i | \(-0.976756\pi\) | ||
0.997335 | − | 0.0729589i | \(-0.0232442\pi\) | |||||||
\(840\) | −5.09252e37 | − | 6.66422e36i | −0.491250 | − | 0.0642863i | ||||
\(841\) | 7.42227e37 | 0.705000 | ||||||||
\(842\) | −1.39811e37 | − | 1.39811e37i | −0.130763 | − | 0.130763i | ||||
\(843\) | 7.67252e37 | − | 7.67252e37i | 0.706609 | − | 0.706609i | ||||
\(844\) | − | 2.44892e37i | − | 0.222087i | ||||||
\(845\) | 1.07764e38 | − | 8.28234e37i | 0.962360 | − | 0.739632i | ||||
\(846\) | −8.48332e37 | −0.746021 | ||||||||
\(847\) | −6.46270e37 | − | 6.46270e37i | −0.559667 | − | 0.559667i | ||||
\(848\) | 4.50881e37 | − | 4.50881e37i | 0.384517 | − | 0.384517i | ||||
\(849\) | − | 7.53797e37i | − | 0.633074i | ||||||
\(850\) | 4.20066e37 | + | 1.11858e37i | 0.347434 | + | 0.0925166i | ||||
\(851\) | −1.74101e38 | −1.41813 | ||||||||
\(852\) | 2.78875e36 | + | 2.78875e36i | 0.0223715 | + | 0.0223715i | ||||
\(853\) | 2.75777e37 | − | 2.75777e37i | 0.217882 | − | 0.217882i | −0.589724 | − | 0.807605i | \(-0.700763\pi\) |
0.807605 | + | 0.589724i | \(0.200763\pi\) | |||||||
\(854\) | 2.02525e38i | 1.57589i | ||||||||
\(855\) | 5.51409e37 | + | 7.17456e37i | 0.422585 | + | 0.549840i | ||||
\(856\) | 1.36575e38 | 1.03089 | ||||||||
\(857\) | −1.41705e38 | − | 1.41705e38i | −1.05350 | − | 1.05350i | −0.998486 | − | 0.0550120i | \(-0.982480\pi\) |
−0.0550120 | − | 0.998486i | \(-0.517520\pi\) | |||||||
\(858\) | −2.16345e37 | + | 2.16345e37i | −0.158421 | + | 0.158421i | ||||
\(859\) | 7.78529e37i | 0.561518i | 0.959778 | + | 0.280759i | \(0.0905861\pi\) | ||||
−0.959778 | + | 0.280759i | \(0.909414\pi\) | |||||||
\(860\) | 2.87282e35 | − | 2.19529e36i | 0.00204093 | − | 0.0155960i | ||||
\(861\) | −6.02167e37 | −0.421382 | ||||||||
\(862\) | 1.47448e38 | + | 1.47448e38i | 1.01635 | + | 1.01635i | ||||
\(863\) | 6.25060e37 | − | 6.25060e37i | 0.424406 | − | 0.424406i | −0.462312 | − | 0.886717i | \(-0.652980\pi\) |
0.886717 | + | 0.462312i | \(0.152980\pi\) | |||||||
\(864\) | − | 5.08076e37i | − | 0.339821i | ||||||
\(865\) | −1.18159e38 | − | 1.54626e37i | −0.778496 | − | 0.101876i | ||||
\(866\) | −2.62974e38 | −1.70679 | ||||||||
\(867\) | 6.53196e37 | + | 6.53196e37i | 0.417634 | + | 0.417634i | ||||
\(868\) | −1.74581e36 | + | 1.74581e36i | −0.0109962 | + | 0.0109962i | ||||
\(869\) | 4.99422e37i | 0.309892i | ||||||||
\(870\) | 5.05268e37 | − | 3.88329e37i | 0.308867 | − | 0.237383i | ||||
\(871\) | −1.62487e38 | −0.978552 | ||||||||
\(872\) | −1.02494e38 | − | 1.02494e38i | −0.608114 | − | 0.608114i | ||||
\(873\) | 7.26077e37 | − | 7.26077e37i | 0.424421 | − | 0.424421i | ||||
\(874\) | 3.89544e38i | 2.24341i | ||||||||
\(875\) | −1.34946e38 | − | 5.55286e37i | −0.765694 | − | 0.315074i | ||||
\(876\) | 3.35438e37 | 0.187525 | ||||||||
\(877\) | 2.23939e37 | + | 2.23939e37i | 0.123349 | + | 0.123349i | 0.766087 | − | 0.642737i | \(-0.222201\pi\) |
−0.642737 | + | 0.766087i | \(0.722201\pi\) | |||||||
\(878\) | 6.39594e37 | − | 6.39594e37i | 0.347117 | − | 0.347117i | ||||
\(879\) | − | 2.77073e37i | − | 0.148163i | ||||||
\(880\) | −2.76383e37 | − | 3.59611e37i | −0.145625 | − | 0.189478i | ||||
\(881\) | −7.06238e37 | −0.366661 | −0.183330 | − | 0.983051i | \(-0.558688\pi\) | ||||
−0.183330 | + | 0.983051i | \(0.558688\pi\) | |||||||
\(882\) | 2.62185e37 | + | 2.62185e37i | 0.134127 | + | 0.134127i | ||||
\(883\) | −2.10427e38 | + | 2.10427e38i | −1.06075 | + | 1.06075i | −0.0627171 | + | 0.998031i | \(0.519977\pi\) |
−0.998031 | + | 0.0627171i | \(0.980023\pi\) | |||||||
\(884\) | 1.65294e37i | 0.0821066i | ||||||||
\(885\) | −1.69180e36 | + | 1.29281e37i | −0.00828108 | + | 0.0632807i | ||||
\(886\) | 2.10232e38 | 1.01405 | ||||||||
\(887\) | −6.34328e37 | − | 6.34328e37i | −0.301513 | − | 0.301513i | 0.540092 | − | 0.841606i | \(-0.318389\pi\) |
−0.841606 | + | 0.540092i | \(0.818389\pi\) | |||||||
\(888\) | −7.65170e37 | + | 7.65170e37i | −0.358418 | + | 0.358418i | ||||
\(889\) | 1.39930e38i | 0.645933i | ||||||||
\(890\) | −3.60356e38 | − | 4.71572e37i | −1.63931 | − | 0.214525i | ||||
\(891\) | −6.04612e36 | −0.0271061 | ||||||||
\(892\) | 1.28003e37 | + | 1.28003e37i | 0.0565559 | + | 0.0565559i | ||||
\(893\) | 2.49256e38 | − | 2.49256e38i | 1.08537 | − | 1.08537i | ||||
\(894\) | − | 1.09656e38i | − | 0.470593i | ||||||
\(895\) | 3.12526e38 | − | 2.40196e38i | 1.32187 | − | 1.01593i | ||||
\(896\) | 2.33294e38 | 0.972523 | ||||||||
\(897\) | 2.84765e38 | + | 2.84765e38i | 1.17000 | + | 1.17000i | ||||
\(898\) | 3.46643e38 | − | 3.46643e38i | 1.40375 | − | 1.40375i | ||||
\(899\) | 1.54226e37i | 0.0615578i | ||||||||
\(900\) | 6.05594e36 | − | 2.27423e37i | 0.0238248 | − | 0.0894708i | ||||
\(901\) | −4.10266e37 | −0.159090 | ||||||||
\(902\) | −3.21273e37 | − | 3.21273e37i | −0.122797 | − | 0.122797i | ||||
\(903\) | 9.79811e36 | − | 9.79811e36i | 0.0369149 | − | 0.0369149i | ||||
\(904\) | − | 3.86492e38i | − | 1.43533i | ||||||
\(905\) | 1.96765e38 | + | 2.56018e38i | 0.720306 | + | 0.937214i | ||||
\(906\) | −1.00665e38 | −0.363255 | ||||||||
\(907\) | −9.17296e37 | − | 9.17296e37i | −0.326298 | − | 0.326298i | 0.524879 | − | 0.851177i | \(-0.324111\pi\) |
−0.851177 | + | 0.524879i | \(0.824111\pi\) | |||||||
\(908\) | −5.03214e37 | + | 5.03214e37i | −0.176456 | + | 0.176456i | ||||
\(909\) | − | 2.14403e37i | − | 0.0741139i | ||||||
\(910\) | 5.06466e37 | − | 3.87020e38i | 0.172589 | − | 1.31885i | ||||
\(911\) | 1.33399e38 | 0.448138 | 0.224069 | − | 0.974573i | \(-0.428066\pi\) | ||||
0.224069 | + | 0.974573i | \(0.428066\pi\) | |||||||
\(912\) | 2.00376e38 | + | 2.00376e38i | 0.663610 | + | 0.663610i | ||||
\(913\) | −5.86399e37 | + | 5.86399e37i | −0.191458 | + | 0.191458i | ||||
\(914\) | 5.23747e37i | 0.168586i | ||||||||
\(915\) | −3.65890e38 | − | 4.78814e37i | −1.16112 | − | 0.151947i | ||||
\(916\) | −5.62181e37 | −0.175887 | ||||||||
\(917\) | 3.02785e38 | + | 3.02785e38i | 0.933970 | + | 0.933970i | ||||
\(918\) | −8.65591e37 | + | 8.65591e37i | −0.263244 | + | 0.263244i | ||||
\(919\) | 4.57388e38i | 1.37146i | 0.727855 | + | 0.685731i | \(0.240517\pi\) | ||||
−0.727855 | + | 0.685731i | \(0.759483\pi\) | |||||||
\(920\) | −4.04426e38 | + | 3.10826e38i | −1.19563 | + | 0.918917i | ||||
\(921\) | −1.74008e37 | −0.0507218 | ||||||||
\(922\) | −5.11237e38 | − | 5.11237e38i | −1.46933 | − | 1.46933i | ||||
\(923\) | 1.06700e38 | − | 1.06700e38i | 0.302372 | − | 0.302372i | ||||
\(924\) | 6.84837e36i | 0.0191360i | ||||||||
\(925\) | −2.66024e38 | + | 1.54140e38i | −0.732957 | + | 0.424691i | ||||
\(926\) | 4.05650e38 | 1.10207 | ||||||||
\(927\) | 1.31459e38 | + | 1.31459e38i | 0.352171 | + | 0.352171i | ||||
\(928\) | −4.77139e37 | + | 4.77139e37i | −0.126044 | + | 0.126044i | ||||
\(929\) | − | 3.44484e38i | − | 0.897357i | −0.893693 | − | 0.448678i | \(-0.851895\pi\) | ||
0.893693 | − | 0.448678i | \(-0.148105\pi\) | |||||||
\(930\) | −1.92836e37 | − | 2.50906e37i | −0.0495348 | − | 0.0644513i | ||||
\(931\) | −1.54070e38 | −0.390276 | ||||||||
\(932\) | 3.41371e36 | + | 3.41371e36i | 0.00852745 | + | 0.00852745i | ||||
\(933\) | −1.52670e38 | + | 1.52670e38i | −0.376091 | + | 0.376091i | ||||
\(934\) | 1.26323e38i | 0.306883i | ||||||||
\(935\) | −3.78654e36 | + | 2.89352e37i | −0.00907176 | + | 0.0693227i | ||||
\(936\) | −3.16925e38 | −0.748808 | ||||||||
\(937\) | 2.78324e38 | + | 2.78324e38i | 0.648539 | + | 0.648539i | 0.952640 | − | 0.304101i | \(-0.0983559\pi\) |
−0.304101 | + | 0.952640i | \(0.598356\pi\) | |||||||
\(938\) | −1.80909e38 | + | 1.80909e38i | −0.415741 | + | 0.415741i | ||||
\(939\) | − | 8.04255e37i | − | 0.182281i | ||||||
\(940\) | −9.09068e37 | − | 1.18963e37i | −0.203205 | − | 0.0265920i | ||||
\(941\) | −6.49529e37 | −0.143197 | −0.0715984 | − | 0.997434i | \(-0.522810\pi\) | ||||
−0.0715984 | + | 0.997434i | \(0.522810\pi\) | |||||||
\(942\) | −2.59456e38 | − | 2.59456e38i | −0.564160 | − | 0.564160i | ||||
\(943\) | −4.22876e38 | + | 4.22876e38i | −0.906904 | + | 0.906904i | ||||
\(944\) | − | 5.16984e37i | − | 0.109356i | ||||||
\(945\) | 3.25813e38 | − | 2.50407e38i | 0.679759 | − | 0.522436i | ||||
\(946\) | 1.04551e37 | 0.0215152 | ||||||||
\(947\) | 2.99649e38 | + | 2.99649e38i | 0.608224 | + | 0.608224i | 0.942482 | − | 0.334258i | \(-0.108486\pi\) |
−0.334258 | + | 0.942482i | \(0.608486\pi\) | |||||||
\(948\) | −5.73868e37 | + | 5.73868e37i | −0.114896 | + | 0.114896i | ||||
\(949\) | − | 1.28341e39i | − | 2.53457i | ||||||
\(950\) | 3.44883e38 | + | 5.95219e38i | 0.671838 | + | 1.15950i | ||||
\(951\) | −1.64413e38 | −0.315930 | ||||||||
\(952\) | −9.26510e37 | − | 9.26510e37i | −0.175618 | − | 0.175618i | ||||
\(953\) | 5.31170e38 | − | 5.31170e38i | 0.993175 | − | 0.993175i | −0.00680194 | − | 0.999977i | \(-0.502165\pi\) |
0.999977 | + | 0.00680194i | \(0.00216514\pi\) | |||||||
\(954\) | 1.56247e38i | 0.288193i | ||||||||
\(955\) | 2.29057e37 | + | 2.98033e37i | 0.0416772 | + | 0.0542276i | ||||
\(956\) | 7.63862e37 | 0.137108 | ||||||||
\(957\) | 3.02495e37 | + | 3.02495e37i | 0.0535628 | + | 0.0535628i | ||||
\(958\) | 5.46157e38 | − | 5.46157e38i | 0.954038 | − | 0.954038i | ||||
\(959\) | 3.28368e38i | 0.565874i | ||||||||
\(960\) | −3.97447e37 | + | 3.03713e38i | −0.0675699 | + | 0.516341i | ||||
\(961\) | −5.88558e38 | −0.987155 | ||||||||
\(962\) | −5.81513e38 | − | 5.81513e38i | −0.962240 | − | 0.962240i | ||||
\(963\) | −2.76965e38 | + | 2.76965e38i | −0.452150 | + | 0.452150i | ||||
\(964\) | − | 9.78048e37i | − | 0.157528i | ||||||
\(965\) | 6.89796e38 | + | 9.02687e37i | 1.09614 | + | 0.143444i | ||||
\(966\) | 6.34099e38 | 0.994155 | ||||||||
\(967\) | −3.92428e38 | − | 3.92428e38i | −0.607038 | − | 0.607038i | 0.335133 | − | 0.942171i | \(-0.391219\pi\) |
−0.942171 | + | 0.335133i | \(0.891219\pi\) | |||||||
\(968\) | −3.98931e38 | + | 3.98931e38i | −0.608861 | + | 0.608861i | ||||
\(969\) | − | 1.82327e38i | − | 0.274562i | ||||||
\(970\) | 6.18947e38 | − | 4.75699e38i | 0.919646 | − | 0.706805i | ||||
\(971\) | −1.64250e38 | −0.240799 | −0.120399 | − | 0.992726i | \(-0.538418\pi\) | ||||
−0.120399 | + | 0.992726i | \(0.538418\pi\) | |||||||
\(972\) | 7.69278e37 | + | 7.69278e37i | 0.111281 | + | 0.111281i | ||||
\(973\) | −6.71403e38 | + | 6.71403e38i | −0.958332 | + | 0.958332i | ||||
\(974\) | 1.30192e39i | 1.83366i | ||||||||
\(975\) | 6.87234e38 | + | 1.83001e38i | 0.955091 | + | 0.254327i | ||||
\(976\) | 1.46317e39 | 2.00653 | ||||||||
\(977\) | −2.49862e38 | − | 2.49862e38i | −0.338120 | − | 0.338120i | 0.517539 | − | 0.855659i | \(-0.326848\pi\) |
−0.855659 | + | 0.517539i | \(0.826848\pi\) | |||||||
\(978\) | 3.06371e37 | − | 3.06371e37i | 0.0409113 | − | 0.0409113i | ||||
\(979\) | − | 2.43971e38i | − | 0.321487i | ||||||
\(980\) | 2.44189e37 | + | 3.17723e37i | 0.0317532 | + | 0.0413151i | ||||
\(981\) | 4.15702e38 | 0.533439 | ||||||||
\(982\) | 3.24524e37 | + | 3.24524e37i | 0.0410958 | + | 0.0410958i | ||||
\(983\) | −2.89219e37 | + | 2.89219e37i | −0.0361435 | + | 0.0361435i | −0.724948 | − | 0.688804i | \(-0.758136\pi\) |
0.688804 | + | 0.724948i | \(0.258136\pi\) | |||||||
\(984\) | 3.71707e38i | 0.458420i | ||||||||
\(985\) | 1.05404e38 | − | 8.05451e38i | 0.128287 | − | 0.980320i | ||||
\(986\) | 1.62577e38 | 0.195281 | ||||||||
\(987\) | −4.05738e38 | − | 4.05738e38i | −0.480976 | − | 0.480976i | ||||
\(988\) | −1.84963e38 | + | 1.84963e38i | −0.216393 | + | 0.216393i | ||||
\(989\) | − | 1.37616e38i | − | 0.158898i | ||||||
\(990\) | 1.10198e38 | + | 1.44208e37i | 0.125579 | + | 0.0164336i | ||||
\(991\) | −1.36818e39 | −1.53881 | −0.769407 | − | 0.638758i | \(-0.779448\pi\) | ||||
−0.769407 | + | 0.638758i | \(0.779448\pi\) | |||||||
\(992\) | 2.36937e37 | + | 2.36937e37i | 0.0263016 | + | 0.0263016i | ||||
\(993\) | 2.27439e38 | − | 2.27439e38i | 0.249187 | − | 0.249187i | ||||
\(994\) | − | 2.37593e38i | − | 0.256927i | ||||||
\(995\) | −2.66656e38 | + | 2.04941e38i | −0.284610 | + | 0.218741i | ||||
\(996\) | −1.34762e38 | −0.141970 | ||||||||
\(997\) | 1.31247e38 | + | 1.31247e38i | 0.136475 | + | 0.136475i | 0.772044 | − | 0.635569i | \(-0.219234\pi\) |
−0.635569 | + | 0.772044i | \(0.719234\pi\) | |||||||
\(998\) | 3.90488e38 | − | 3.90488e38i | 0.400785 | − | 0.400785i | ||||
\(999\) | − | 8.65793e38i | − | 0.877127i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5.27.c.a.2.9 | ✓ | 24 | |
5.2 | odd | 4 | 25.27.c.b.18.4 | 24 | |||
5.3 | odd | 4 | inner | 5.27.c.a.3.9 | yes | 24 | |
5.4 | even | 2 | 25.27.c.b.7.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.27.c.a.2.9 | ✓ | 24 | 1.1 | even | 1 | trivial | |
5.27.c.a.3.9 | yes | 24 | 5.3 | odd | 4 | inner | |
25.27.c.b.7.4 | 24 | 5.4 | even | 2 | |||
25.27.c.b.18.4 | 24 | 5.2 | odd | 4 |