Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [81,9,Mod(26,81)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(81, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("81.26");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 81.d (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.9976674150\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 53.6 | ||
Character | \(\chi\) | \(=\) | 81.53 |
Dual form | 81.9.d.g.26.6 |
$q$-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 \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.67350 | + | 5.00765i | −0.542094 | + | 0.312978i | −0.745927 | − | 0.666028i | \(-0.767993\pi\) |
0.203833 | + | 0.979006i | \(0.434660\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −77.8470 | + | 134.835i | −0.304090 | + | 0.526699i | ||||
\(5\) | −514.754 | − | 297.193i | −0.823606 | − | 0.475509i | 0.0280522 | − | 0.999606i | \(-0.491070\pi\) |
−0.851658 | + | 0.524097i | \(0.824403\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2204.76 | − | 3818.75i | −0.918265 | − | 1.59048i | −0.802049 | − | 0.597258i | \(-0.796257\pi\) |
−0.116217 | − | 0.993224i | \(-0.537077\pi\) | |||||||
\(8\) | − | 4123.23i | − | 1.00665i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5952.96 | 0.595296 | ||||||||
\(11\) | 3013.23 | − | 1739.69i | 0.205808 | − | 0.118823i | −0.393554 | − | 0.919302i | \(-0.628755\pi\) |
0.599362 | + | 0.800478i | \(0.295421\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9131.48 | − | 15816.2i | 0.319718 | − | 0.553768i | −0.660711 | − | 0.750641i | \(-0.729745\pi\) |
0.980429 | + | 0.196872i | \(0.0630784\pi\) | |||||||
\(14\) | 38245.9 | + | 22081.3i | 0.995572 | + | 0.574794i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 718.880 | + | 1245.14i | 0.0109692 | + | 0.0189993i | ||||
\(17\) | 86637.8i | 1.03732i | 0.854981 | + | 0.518659i | \(0.173568\pi\) | ||||
−0.854981 | + | 0.518659i | \(0.826432\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 76109.5 | 0.584016 | 0.292008 | − | 0.956416i | \(-0.405677\pi\) | ||||
0.292008 | + | 0.956416i | \(0.405677\pi\) | |||||||
\(20\) | 80144.1 | − | 46271.2i | 0.500900 | − | 0.289195i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −17423.5 | + | 30178.4i | −0.0743780 | + | 0.128826i | ||||
\(23\) | −453885. | − | 262051.i | −1.62194 | − | 0.936427i | −0.986401 | − | 0.164357i | \(-0.947445\pi\) |
−0.635538 | − | 0.772070i | \(-0.719222\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −18664.8 | − | 32328.3i | −0.0477818 | − | 0.0827605i | ||||
\(26\) | 182909.i | 0.400259i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 686534. | 1.11694 | ||||||||
\(29\) | −671532. | + | 387709.i | −0.949455 | + | 0.548168i | −0.892912 | − | 0.450232i | \(-0.851341\pi\) |
−0.0565435 | + | 0.998400i | \(0.518008\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 462712. | − | 801441.i | 0.501031 | − | 0.867811i | −0.498969 | − | 0.866620i | \(-0.666288\pi\) |
0.999999 | − | 0.00119055i | \(-0.000378963\pi\) | |||||||
\(32\) | 901661. | + | 520574.i | 0.859891 | + | 0.496458i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −433851. | − | 751453.i | −0.324657 | − | 0.562323i | ||||
\(35\) | 2.62095e6i | 1.74658i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 237767. | 0.126866 | 0.0634329 | − | 0.997986i | \(-0.479795\pi\) | ||||
0.0634329 | + | 0.997986i | \(0.479795\pi\) | |||||||
\(38\) | −660136. | + | 381130.i | −0.316591 | + | 0.182784i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.22540e6 | + | 2.12245e6i | −0.478671 | + | 0.829083i | ||||
\(41\) | −446772. | − | 257944.i | −0.158107 | − | 0.0912829i | 0.418859 | − | 0.908051i | \(-0.362430\pi\) |
−0.576966 | + | 0.816768i | \(0.695763\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.97918e6 | − | 3.42804e6i | −0.578910 | − | 1.00270i | −0.995605 | − | 0.0936549i | \(-0.970145\pi\) |
0.416695 | − | 0.909046i | \(-0.363188\pi\) | |||||||
\(44\) | 541718.i | 0.144532i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.24903e6 | 1.17232 | ||||||||
\(47\) | −4.61257e6 | + | 2.66307e6i | −0.945260 | + | 0.545746i | −0.891605 | − | 0.452813i | \(-0.850420\pi\) |
−0.0536550 | + | 0.998560i | \(0.517087\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.83949e6 | + | 1.18463e7i | −1.18642 | + | 2.05494i | ||||
\(50\) | 323777. | + | 186933.i | 0.0518044 | + | 0.0299093i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.42172e6 | + | 2.46248e6i | 0.194446 | + | 0.336791i | ||||
\(53\) | 1.30260e7i | 1.65085i | 0.564514 | + | 0.825424i | \(0.309064\pi\) | ||||
−0.564514 | + | 0.825424i | \(0.690936\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.06810e6 | −0.226006 | ||||||||
\(56\) | −1.57456e7 | + | 9.09072e6i | −1.60106 | + | 0.924371i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.88302e6 | − | 6.72559e6i | 0.343129 | − | 0.594317i | ||||
\(59\) | 1.08626e7 | + | 6.27153e6i | 0.896450 | + | 0.517566i | 0.876047 | − | 0.482226i | \(-0.160172\pi\) |
0.0204032 | + | 0.999792i | \(0.493505\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.94218e6 | − | 1.02922e7i | −0.429167 | − | 0.743340i | 0.567632 | − | 0.823282i | \(-0.307860\pi\) |
−0.996799 | + | 0.0799427i | \(0.974526\pi\) | |||||||
\(62\) | 9.26840e6i | 0.627246i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.07955e7 | −0.643460 | ||||||||
\(65\) | −9.40093e6 | + | 5.42763e6i | −0.526644 | + | 0.304058i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.76578e6 | + | 1.17187e7i | −0.335752 | + | 0.581540i | −0.983629 | − | 0.180205i | \(-0.942324\pi\) |
0.647877 | + | 0.761745i | \(0.275657\pi\) | |||||||
\(68\) | −1.16818e7 | − | 6.74449e6i | −0.546354 | − | 0.315438i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.31248e7 | − | 2.27328e7i | −0.546639 | − | 0.946807i | ||||
\(71\) | − | 133345.i | − | 0.00524738i | −0.999997 | − | 0.00262369i | \(-0.999165\pi\) | ||
0.999997 | − | 0.00262369i | \(-0.000835147\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.24749e7 | 1.84782 | 0.923910 | − | 0.382609i | \(-0.124974\pi\) | ||||
0.923910 | + | 0.382609i | \(0.124974\pi\) | |||||||
\(74\) | −2.06227e6 | + | 1.19065e6i | −0.0687731 | + | 0.0397062i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.92489e6 | + | 1.02622e7i | −0.177593 | + | 0.307600i | ||||
\(77\) | −1.32869e7 | − | 7.67118e6i | −0.377972 | − | 0.218222i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.39249e7 | + | 4.14392e7i | 0.614246 | + | 1.06391i | 0.990516 | + | 0.137395i | \(0.0438731\pi\) |
−0.376270 | + | 0.926510i | \(0.622794\pi\) | |||||||
\(80\) | − | 854585.i | − | 0.0208639i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.16676e6 | 0.114278 | ||||||||
\(83\) | 5.06857e7 | − | 2.92634e7i | 1.06800 | − | 0.616612i | 0.140369 | − | 0.990099i | \(-0.455171\pi\) |
0.927635 | + | 0.373487i | \(0.121838\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.57482e7 | − | 4.45971e7i | 0.493254 | − | 0.854341i | ||||
\(86\) | 3.43328e7 | + | 1.98220e7i | 0.627647 | + | 0.362372i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.17315e6 | − | 1.24243e7i | −0.119613 | − | 0.207176i | ||||
\(89\) | 4.62606e7i | 0.737312i | 0.929566 | + | 0.368656i | \(0.120182\pi\) | ||||
−0.929566 | + | 0.368656i | \(0.879818\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.05307e7 | −1.17435 | ||||||||
\(92\) | 7.06671e7 | − | 4.07997e7i | 0.986430 | − | 0.569515i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.66714e7 | − | 4.61962e7i | 0.341613 | − | 0.591691i | ||||
\(95\) | −3.91777e7 | − | 2.26192e7i | −0.480999 | − | 0.277705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.41196e7 | + | 7.64173e7i | 0.498361 | + | 0.863187i | 0.999998 | − | 0.00189124i | \(-0.000602002\pi\) |
−0.501637 | + | 0.865078i | \(0.667269\pi\) | |||||||
\(98\) | − | 1.36999e8i | − | 1.48530i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.81198e6 | 0.0581198 | ||||||||
\(101\) | −4.97112e7 | + | 2.87007e7i | −0.477714 | + | 0.275809i | −0.719464 | − | 0.694530i | \(-0.755612\pi\) |
0.241749 | + | 0.970339i | \(0.422279\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.94562e7 | − | 6.83401e7i | 0.350563 | − | 0.607193i | −0.635785 | − | 0.771866i | \(-0.719324\pi\) |
0.986348 | + | 0.164673i | \(0.0526569\pi\) | |||||||
\(104\) | −6.52138e7 | − | 3.76512e7i | −0.557450 | − | 0.321844i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.52295e7 | − | 1.12981e8i | −0.516679 | − | 0.894914i | ||||
\(107\) | − | 2.50821e8i | − | 1.91350i | −0.290907 | − | 0.956751i | \(-0.593957\pi\) | ||
0.290907 | − | 0.956751i | \(-0.406043\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.76440e7 | −0.550050 | −0.275025 | − | 0.961437i | \(-0.588686\pi\) | ||||
−0.275025 | + | 0.961437i | \(0.588686\pi\) | |||||||
\(110\) | 1.79376e7 | − | 1.03563e7i | 0.122516 | − | 0.0707349i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.16991e6 | − | 5.49044e6i | 0.0201453 | − | 0.0348927i | ||||
\(113\) | 5.33353e7 | + | 3.07931e7i | 0.327115 | + | 0.188860i | 0.654560 | − | 0.756010i | \(-0.272854\pi\) |
−0.327444 | + | 0.944870i | \(0.606187\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.55759e8 | + | 2.69783e8i | 0.890559 | + | 1.54249i | ||||
\(116\) | − | 1.20728e8i | − | 0.666769i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.25622e8 | −0.647946 | ||||||||
\(119\) | 3.30848e8 | − | 1.91015e8i | 1.64983 | − | 0.952533i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.01126e8 | + | 1.75156e8i | −0.471762 | + | 0.817116i | ||||
\(122\) | 1.03079e8 | + | 5.95127e7i | 0.465298 | + | 0.268640i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.20415e7 | + | 1.24780e8i | 0.304717 | + | 0.527785i | ||||
\(125\) | 2.54370e8i | 1.04190i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.58325e8 | −1.37741 | −0.688703 | − | 0.725044i | \(-0.741819\pi\) | ||||
−0.688703 | + | 0.725044i | \(0.741819\pi\) | |||||||
\(128\) | −1.37191e8 | + | 7.92071e7i | −0.511075 | + | 0.295069i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.43593e7 | − | 9.41530e7i | 0.190327 | − | 0.329656i | ||||
\(131\) | 1.62075e8 | + | 9.35739e7i | 0.550339 | + | 0.317738i | 0.749259 | − | 0.662277i | \(-0.230410\pi\) |
−0.198920 | + | 0.980016i | \(0.563743\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.67803e8 | − | 2.90643e8i | −0.536281 | − | 0.928867i | ||||
\(134\) | − | 1.35523e8i | − | 0.420332i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.57228e8 | 1.04421 | ||||||||
\(137\) | 1.30060e8 | − | 7.50900e7i | 0.369199 | − | 0.213157i | −0.303909 | − | 0.952701i | \(-0.598292\pi\) |
0.673108 | + | 0.739544i | \(0.264959\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.49820e7 | + | 1.12552e8i | −0.174074 | + | 0.301505i | −0.939840 | − | 0.341614i | \(-0.889027\pi\) |
0.765766 | + | 0.643119i | \(0.222360\pi\) | |||||||
\(140\) | −3.53396e8 | − | 2.04033e8i | −0.919919 | − | 0.531115i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 667743. | + | 1.15656e6i | 0.00164231 | + | 0.00284457i | ||||
\(143\) | − | 6.35437e7i | − | 0.151960i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.60898e8 | 1.04264 | ||||||||
\(146\) | −4.55140e8 | + | 2.62775e8i | −1.00169 | + | 0.578327i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.85094e7 | + | 3.20593e7i | −0.0385786 | + | 0.0668200i | ||||
\(149\) | 1.30697e8 | + | 7.54578e7i | 0.265167 | + | 0.153094i | 0.626689 | − | 0.779269i | \(-0.284410\pi\) |
−0.361522 | + | 0.932363i | \(0.617743\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.56221e7 | − | 1.48302e8i | −0.164694 | − | 0.285258i | 0.771853 | − | 0.635802i | \(-0.219330\pi\) |
−0.936547 | + | 0.350543i | \(0.885997\pi\) | |||||||
\(152\) | − | 3.13817e8i | − | 0.587899i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.53658e8 | 0.273195 | ||||||||
\(155\) | −4.76366e8 | + | 2.75030e8i | −0.825304 | + | 0.476490i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.60934e8 | − | 6.25156e8i | 0.594059 | − | 1.02894i | −0.399620 | − | 0.916681i | \(-0.630858\pi\) |
0.993679 | − | 0.112259i | \(-0.0358087\pi\) | |||||||
\(158\) | −4.15026e8 | − | 2.39615e8i | −0.665958 | − | 0.384491i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.09422e8 | − | 5.35935e8i | −0.472141 | − | 0.817772i | ||||
\(161\) | 2.31103e9i | 3.43955i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.90963e8 | −0.270520 | −0.135260 | − | 0.990810i | \(-0.543187\pi\) | ||||
−0.135260 | + | 0.990810i | \(0.543187\pi\) | |||||||
\(164\) | 6.95596e7 | − | 4.01603e7i | 0.0961572 | − | 0.0555164i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.93081e8 | + | 5.07632e8i | −0.385972 | + | 0.668523i | ||||
\(167\) | 4.84429e8 | + | 2.79685e8i | 0.622822 | + | 0.359586i | 0.777967 | − | 0.628305i | \(-0.216251\pi\) |
−0.155145 | + | 0.987892i | \(0.549584\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.41098e8 | + | 4.17593e8i | 0.295560 | + | 0.511926i | ||||
\(170\) | 5.15751e8i | 0.617510i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.16292e8 | 0.704162 | ||||||||
\(173\) | −5.25797e8 | + | 3.03569e8i | −0.586994 | + | 0.338901i | −0.763908 | − | 0.645325i | \(-0.776722\pi\) |
0.176914 | + | 0.984226i | \(0.443389\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.23024e7 | + | 1.42552e8i | −0.0877527 | + | 0.151992i | ||||
\(176\) | 4.33230e6 | + | 2.50125e6i | 0.00451510 | + | 0.00260680i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.31657e8 | − | 4.01241e8i | −0.230762 | − | 0.399692i | ||||
\(179\) | 4.18834e8i | 0.407971i | 0.978974 | + | 0.203986i | \(0.0653896\pi\) | ||||
−0.978974 | + | 0.203986i | \(0.934610\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.10216e9 | 1.02690 | 0.513451 | − | 0.858119i | \(-0.328367\pi\) | ||||
0.513451 | + | 0.858119i | \(0.328367\pi\) | |||||||
\(182\) | 6.98483e8 | − | 4.03269e8i | 0.636605 | − | 0.367544i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.08050e9 | + | 1.87147e9i | −0.942653 | + | 1.63272i | ||||
\(185\) | −1.22391e8 | − | 7.06627e7i | −0.104487 | − | 0.0603258i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.50723e8 | + | 2.61060e8i | 0.123257 | + | 0.213488i | ||||
\(188\) | − | 8.29247e8i | − | 0.663823i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.53077e8 | 0.347662 | ||||||||
\(191\) | −1.54781e9 | + | 8.93626e8i | −1.16301 | + | 0.671463i | −0.952023 | − | 0.306026i | \(-0.901001\pi\) |
−0.210985 | + | 0.977489i | \(0.567667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.58643e8 | − | 6.21188e8i | 0.258484 | − | 0.447707i | −0.707352 | − | 0.706861i | \(-0.750110\pi\) |
0.965836 | + | 0.259154i | \(0.0834438\pi\) | |||||||
\(194\) | −7.65342e8 | − | 4.41870e8i | −0.540317 | − | 0.311952i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.06487e9 | − | 1.84440e9i | −0.721558 | − | 1.24977i | ||||
\(197\) | − | 1.81939e9i | − | 1.20798i | −0.796992 | − | 0.603990i | \(-0.793577\pi\) | ||
0.796992 | − | 0.603990i | \(-0.206423\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.90300e9 | −1.21346 | −0.606730 | − | 0.794908i | \(-0.707519\pi\) | ||||
−0.606730 | + | 0.794908i | \(0.707519\pi\) | |||||||
\(200\) | −1.33297e8 | + | 7.69592e7i | −0.0833108 | + | 0.0480995i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.87446e8 | − | 4.97872e8i | 0.172644 | − | 0.299028i | ||||
\(203\) | 2.96113e9 | + | 1.70961e9i | 1.74370 | + | 1.00673i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.53318e8 | + | 2.65555e8i | 0.0868118 | + | 0.150362i | ||||
\(206\) | 7.90331e8i | 0.438874i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.62577e7 | 0.0140283 | ||||||||
\(209\) | 2.29335e8 | − | 1.32407e8i | 0.120195 | − | 0.0693946i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.99513e7 | + | 1.38480e8i | −0.0403363 | + | 0.0698645i | −0.885489 | − | 0.464661i | \(-0.846176\pi\) |
0.845152 | + | 0.534525i | \(0.179510\pi\) | |||||||
\(212\) | −1.75636e9 | − | 1.01403e9i | −0.869499 | − | 0.502006i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.25602e9 | + | 2.17550e9i | 0.598884 | + | 1.03730i | ||||
\(215\) | 2.35279e9i | 1.10111i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.08067e9 | −1.84032 | ||||||||
\(218\) | 6.73445e8 | − | 3.88814e8i | 0.298179 | − | 0.172153i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.60995e8 | − | 2.78851e8i | 0.0687261 | − | 0.119037i | ||||
\(221\) | 1.37028e9 | + | 7.91131e8i | 0.574434 | + | 0.331649i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.06593e8 | + | 5.31035e8i | 0.123977 | + | 0.214735i | 0.921333 | − | 0.388775i | \(-0.127102\pi\) |
−0.797355 | + | 0.603510i | \(0.793768\pi\) | |||||||
\(224\) | − | 4.59096e9i | − | 1.82352i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.16805e8 | −0.236436 | ||||||||
\(227\) | 2.56740e9 | − | 1.48229e9i | 0.966919 | − | 0.558251i | 0.0686235 | − | 0.997643i | \(-0.478139\pi\) |
0.898296 | + | 0.439392i | \(0.144806\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.89482e9 | − | 3.28193e9i | 0.689013 | − | 1.19340i | −0.283145 | − | 0.959077i | \(-0.591378\pi\) |
0.972158 | − | 0.234328i | \(-0.0752889\pi\) | |||||||
\(230\) | −2.70196e9 | − | 1.55998e9i | −0.965533 | − | 0.557451i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.59862e9 | + | 2.76888e9i | 0.551813 | + | 0.955768i | ||||
\(233\) | − | 3.76374e9i | − | 1.27701i | −0.769616 | − | 0.638507i | \(-0.779552\pi\) | ||
0.769616 | − | 0.638507i | \(-0.220448\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.16578e9 | 1.03803 | ||||||||
\(236\) | −1.69124e9 | + | 9.76439e8i | −0.545202 | + | 0.314773i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.91307e9 | + | 3.31354e9i | −0.596243 | + | 1.03272i | ||||
\(239\) | −4.58786e8 | − | 2.64880e8i | −0.140611 | − | 0.0811816i | 0.428044 | − | 0.903758i | \(-0.359203\pi\) |
−0.568655 | + | 0.822576i | \(0.692536\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.19453e8 | + | 7.26513e8i | 0.124341 | + | 0.215365i | 0.921475 | − | 0.388437i | \(-0.126985\pi\) |
−0.797134 | + | 0.603802i | \(0.793652\pi\) | |||||||
\(242\) | − | 2.02562e9i | − | 0.590604i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.85032e9 | 0.522021 | ||||||||
\(245\) | 7.04131e9 | − | 4.06530e9i | 1.95429 | − | 1.12831i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.94992e8 | − | 1.20376e9i | 0.186721 | − | 0.323409i | ||||
\(248\) | −3.30453e9 | − | 1.90787e9i | −0.873581 | − | 0.504362i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.27380e9 | − | 2.20628e9i | −0.326092 | − | 0.564808i | ||||
\(251\) | 2.40283e9i | 0.605380i | 0.953089 | + | 0.302690i | \(0.0978847\pi\) | ||||
−0.953089 | + | 0.302690i | \(0.902115\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.82355e9 | −0.445076 | ||||||||
\(254\) | 3.10793e9 | − | 1.79436e9i | 0.746683 | − | 0.431097i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.17510e9 | − | 3.76739e9i | 0.506431 | − | 0.877164i | ||||
\(257\) | 4.15154e9 | + | 2.39689e9i | 0.951648 | + | 0.549434i | 0.893592 | − | 0.448879i | \(-0.148177\pi\) |
0.0580555 | + | 0.998313i | \(0.481510\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.24218e8 | − | 9.07972e8i | −0.116496 | − | 0.201778i | ||||
\(260\) | − | 1.69010e9i | − | 0.369844i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.87434e9 | −0.397780 | ||||||||
\(263\) | −1.94790e9 | + | 1.12462e9i | −0.407139 | + | 0.235062i | −0.689560 | − | 0.724229i | \(-0.742196\pi\) |
0.282421 | + | 0.959291i | \(0.408863\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.87123e9 | − | 6.70517e9i | 0.784993 | − | 1.35965i | ||||
\(266\) | 2.91088e9 | + | 1.68059e9i | 0.581429 | + | 0.335688i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.05339e9 | − | 1.82453e9i | −0.204197 | − | 0.353680i | ||||
\(269\) | 2.01512e9i | 0.384851i | 0.981312 | + | 0.192425i | \(0.0616353\pi\) | ||||
−0.981312 | + | 0.192425i | \(0.938365\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.85840e9 | −1.08618 | −0.543090 | − | 0.839675i | \(-0.682746\pi\) | ||||
−0.543090 | + | 0.839675i | \(0.682746\pi\) | |||||||
\(272\) | −1.07876e8 | + | 6.22821e7i | −0.0197083 | + | 0.0113786i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.52049e8 | + | 1.30259e9i | −0.133427 | + | 0.231102i | ||||
\(275\) | −1.12482e8 | − | 6.49417e7i | −0.0196677 | − | 0.0113552i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.40794e9 | + | 5.90273e9i | 0.578859 | + | 1.00261i | 0.995611 | + | 0.0935933i | \(0.0298353\pi\) |
−0.416751 | + | 0.909021i | \(0.636831\pi\) | |||||||
\(278\) | − | 1.30163e9i | − | 0.217925i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.08068e10 | 1.75819 | ||||||||
\(281\) | −1.79419e9 | + | 1.03588e9i | −0.287768 | + | 0.166143i | −0.636935 | − | 0.770918i | \(-0.719798\pi\) |
0.349167 | + | 0.937061i | \(0.386465\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.80878e8 | + | 8.32906e8i | −0.0749704 | + | 0.129852i | −0.901073 | − | 0.433667i | \(-0.857220\pi\) |
0.826103 | + | 0.563519i | \(0.190553\pi\) | |||||||
\(284\) | 1.79795e7 | + | 1.03805e7i | 0.00276379 | + | 0.00159567i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.18204e8 | + | 5.51146e8i | 0.0475600 | + | 0.0823764i | ||||
\(287\) | 2.27481e9i | 0.335288i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.30347e8 | −0.0760272 | ||||||||
\(290\) | −3.99760e9 | + | 2.30801e9i | −0.565207 | + | 0.326322i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.08501e9 | + | 7.07544e9i | −0.561903 | + | 0.973245i | ||||
\(293\) | −1.05291e10 | − | 6.07899e9i | −1.42864 | − | 0.824823i | −0.431623 | − | 0.902054i | \(-0.642059\pi\) |
−0.997013 | + | 0.0772309i | \(0.975392\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.72771e9 | − | 6.45659e9i | −0.492215 | − | 0.852541i | ||||
\(296\) | − | 9.80369e8i | − | 0.127709i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.51146e9 | −0.191660 | ||||||||
\(299\) | −8.28928e9 | + | 4.78582e9i | −1.03713 | + | 0.598786i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.72720e9 | + | 1.51160e10i | −1.06319 | + | 1.84149i | ||||
\(302\) | 1.48529e9 | + | 8.57530e8i | 0.178559 | + | 0.103091i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.47136e7 | + | 9.47667e7i | 0.00640620 | + | 0.0110959i | ||||
\(305\) | 7.06391e9i | 0.816292i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.91035e9 | 0.552788 | 0.276394 | − | 0.961044i | \(-0.410860\pi\) | ||||
0.276394 | + | 0.961044i | \(0.410860\pi\) | |||||||
\(308\) | 2.06868e9 | − | 1.19436e9i | 0.229875 | − | 0.132718i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.75451e9 | − | 4.77094e9i | 0.298261 | − | 0.516604i | ||||
\(311\) | 2.32924e9 | + | 1.34479e9i | 0.248984 | + | 0.143751i | 0.619299 | − | 0.785155i | \(-0.287417\pi\) |
−0.370315 | + | 0.928906i | \(0.620750\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.56653e9 | + | 4.44536e9i | 0.267405 | + | 0.463158i | 0.968191 | − | 0.250213i | \(-0.0805007\pi\) |
−0.700786 | + | 0.713371i | \(0.747167\pi\) | |||||||
\(314\) | 7.22972e9i | 0.743709i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.44993e9 | −0.747144 | ||||||||
\(317\) | −1.33196e10 | + | 7.69006e9i | −1.31903 | + | 0.761540i | −0.983572 | − | 0.180516i | \(-0.942223\pi\) |
−0.335455 | + | 0.942056i | \(0.608890\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.34899e9 | + | 2.33651e9i | −0.130270 | + | 0.225634i | ||||
\(320\) | 5.55701e9 | + | 3.20834e9i | 0.529958 | + | 0.305971i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.15728e10 | − | 2.00447e10i | −1.07650 | − | 1.86456i | ||||
\(323\) | 6.59396e9i | 0.605810i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.81747e8 | −0.0611068 | ||||||||
\(326\) | 1.65632e9 | − | 9.56278e8i | 0.146647 | − | 0.0846669i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.06356e9 | + | 1.84214e9i | −0.0918899 | + | 0.159158i | ||||
\(329\) | 2.03392e10 | + | 1.17428e10i | 1.73600 | + | 1.00228i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.70488e9 | + | 6.41704e9i | 0.308647 | + | 0.534593i | 0.978067 | − | 0.208292i | \(-0.0667904\pi\) |
−0.669419 | + | 0.742885i | \(0.733457\pi\) | |||||||
\(332\) | 9.11226e9i | 0.750022i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.60225e9 | −0.450170 | ||||||||
\(335\) | 6.96542e9 | − | 4.02149e9i | 0.553055 | − | 0.319306i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.35250e9 | + | 4.07466e9i | −0.182394 | + | 0.315916i | −0.942695 | − | 0.333655i | \(-0.891718\pi\) |
0.760301 | + | 0.649571i | \(0.225051\pi\) | |||||||
\(338\) | −4.18232e9 | − | 2.41466e9i | −0.320443 | − | 0.185008i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.00883e9 | + | 6.94350e9i | 0.299987 | + | 0.519593i | ||||
\(341\) | − | 3.21990e9i | − | 0.238136i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.48977e10 | 2.52127 | ||||||||
\(344\) | −1.41346e10 | + | 8.16061e9i | −1.00937 | + | 0.582759i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.04033e9 | − | 5.26601e9i | 0.212137 | − | 0.367432i | ||||
\(347\) | −4.21934e9 | − | 2.43604e9i | −0.291023 | − | 0.168022i | 0.347380 | − | 0.937724i | \(-0.387071\pi\) |
−0.638403 | + | 0.769702i | \(0.720405\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.18998e10 | − | 2.06110e10i | −0.802117 | − | 1.38931i | −0.918221 | − | 0.396070i | \(-0.870374\pi\) |
0.116104 | − | 0.993237i | \(-0.462959\pi\) | |||||||
\(350\) | − | 1.64857e9i | − | 0.109859i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.62255e9 | 0.235963 | ||||||||
\(353\) | −6.84869e9 | + | 3.95409e9i | −0.441071 | + | 0.254652i | −0.704052 | − | 0.710149i | \(-0.748628\pi\) |
0.262981 | + | 0.964801i | \(0.415294\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.96291e7 | + | 6.86397e7i | −0.00249518 | + | 0.00432177i | ||||
\(356\) | −6.23754e9 | − | 3.60125e9i | −0.388341 | − | 0.224209i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.09737e9 | − | 3.63275e9i | −0.127686 | − | 0.221158i | ||||
\(359\) | − | 7.90247e9i | − | 0.475757i | −0.971295 | − | 0.237879i | \(-0.923548\pi\) | ||
0.971295 | − | 0.237879i | \(-0.0764520\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.11909e10 | −0.658926 | ||||||||
\(362\) | −9.55954e9 | + | 5.51920e9i | −0.556676 | + | 0.321397i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.26907e9 | − | 1.08583e10i | 0.357106 | − | 0.618526i | ||||
\(365\) | −2.70116e10 | − | 1.55952e10i | −1.52188 | − | 0.878656i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.94556e9 | + | 1.20301e10i | 0.382863 | + | 0.663137i | 0.991470 | − | 0.130334i | \(-0.0416049\pi\) |
−0.608608 | + | 0.793471i | \(0.708272\pi\) | |||||||
\(368\) | − | 7.53531e8i | − | 0.0410875i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.41542e9 | 0.0755226 | ||||||||
\(371\) | 4.97429e10 | − | 2.87191e10i | 2.62564 | − | 1.51592i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.08855e10 | + | 1.88542e10i | −0.562356 | + | 0.974029i | 0.434934 | + | 0.900462i | \(0.356772\pi\) |
−0.997290 | + | 0.0735671i | \(0.976562\pi\) | |||||||
\(374\) | −2.61459e9 | − | 1.50953e9i | −0.133634 | − | 0.0771536i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.09805e10 | + | 1.90187e10i | 0.549375 | + | 0.951546i | ||||
\(377\) | 1.41614e10i | 0.701038i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.86928e10 | −0.905975 | −0.452988 | − | 0.891517i | \(-0.649642\pi\) | ||||
−0.452988 | + | 0.891517i | \(0.649642\pi\) | |||||||
\(380\) | 6.09973e9 | − | 3.52168e9i | 0.292534 | − | 0.168894i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.94992e9 | − | 1.55017e10i | 0.420306 | − | 0.727992i | ||||
\(383\) | −1.29018e10 | − | 7.44885e9i | −0.599590 | − | 0.346174i | 0.169290 | − | 0.985566i | \(-0.445852\pi\) |
−0.768880 | + | 0.639393i | \(0.779186\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.55965e9 | + | 7.89754e9i | 0.207533 | + | 0.359459i | ||||
\(386\) | 7.18383e9i | 0.323599i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.37383e10 | −0.606186 | ||||||||
\(389\) | −1.45384e10 | + | 8.39374e9i | −0.634918 | + | 0.366570i | −0.782654 | − | 0.622457i | \(-0.786135\pi\) |
0.147736 | + | 0.989027i | \(0.452801\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.27035e10 | − | 3.93236e10i | 0.971372 | − | 1.68246i | ||||
\(392\) | 4.88453e10 | + | 2.82008e10i | 2.06861 | + | 1.19431i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.11084e9 | + | 1.57804e10i | 0.378071 | + | 0.654838i | ||||
\(395\) | − | 2.84413e10i | − | 1.16832i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.63950e10 | 1.46514 | 0.732570 | − | 0.680692i | \(-0.238321\pi\) | ||||
0.732570 | + | 0.680692i | \(0.238321\pi\) | |||||||
\(398\) | 1.65056e10 | − | 9.52953e9i | 0.657809 | − | 0.379786i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.68354e7 | − | 4.64803e7i | 0.00104826 | − | 0.00181564i | ||||
\(401\) | −2.67932e9 | − | 1.54691e9i | −0.103621 | − | 0.0598255i | 0.447294 | − | 0.894387i | \(-0.352388\pi\) |
−0.550915 | + | 0.834561i | \(0.685721\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.45049e9 | − | 1.46367e10i | −0.320377 | − | 0.554910i | ||||
\(404\) | − | 8.93706e9i | − | 0.335482i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.42444e10 | −1.26033 | ||||||||
\(407\) | 7.16446e8 | − | 4.13640e8i | 0.0261099 | − | 0.0150746i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.89420e9 | − | 5.01291e9i | 0.103427 | − | 0.179142i | −0.809667 | − | 0.586889i | \(-0.800352\pi\) |
0.913095 | + | 0.407748i | \(0.133686\pi\) | |||||||
\(410\) | −2.65961e9 | − | 1.53553e9i | −0.0941202 | − | 0.0543403i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.14309e9 | + | 1.06401e10i | 0.213205 | + | 0.369282i | ||||
\(413\) | − | 5.53087e10i | − | 1.90105i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.47875e10 | −1.17282 | ||||||||
\(416\) | 1.64670e10 | − | 9.50722e9i | 0.549846 | − | 0.317454i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.32609e9 | + | 2.29686e9i | −0.0434379 | + | 0.0752367i | ||||
\(419\) | −2.09245e10 | − | 1.20808e10i | −0.678889 | − | 0.391957i | 0.120547 | − | 0.992708i | \(-0.461535\pi\) |
−0.799436 | + | 0.600751i | \(0.794868\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.83472e9 | − | 1.01060e10i | −0.185734 | − | 0.321701i | 0.758090 | − | 0.652150i | \(-0.226133\pi\) |
−0.943824 | + | 0.330450i | \(0.892800\pi\) | |||||||
\(422\) | − | 1.60147e9i | − | 0.0504975i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.37092e10 | 1.66182 | ||||||||
\(425\) | 2.80085e9 | − | 1.61707e9i | 0.0858489 | − | 0.0495649i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.62021e10 | + | 4.53834e10i | −0.788179 | + | 1.36517i | ||||
\(428\) | 3.38194e10 | + | 1.95257e10i | 1.00784 | + | 0.581876i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.17820e10 | − | 2.04069e10i | −0.344622 | − | 0.596904i | ||||
\(431\) | − | 6.44251e10i | − | 1.86701i | −0.358568 | − | 0.933504i | \(-0.616735\pi\) | ||
0.358568 | − | 0.933504i | \(-0.383265\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.35776e10 | −1.52416 | −0.762082 | − | 0.647480i | \(-0.775823\pi\) | ||||
−0.762082 | + | 0.647480i | \(0.775823\pi\) | |||||||
\(434\) | 3.53937e10 | − | 2.04346e10i | 0.997624 | − | 0.575978i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.04435e9 | − | 1.04691e10i | 0.167265 | − | 0.289711i | ||||
\(437\) | −3.45450e10 | − | 1.99445e10i | −0.947238 | − | 0.546888i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.13976e9 | + | 3.70617e9i | 0.0576111 | + | 0.0997854i | 0.893393 | − | 0.449277i | \(-0.148318\pi\) |
−0.835781 | + | 0.549062i | \(0.814985\pi\) | |||||||
\(440\) | 8.52725e9i | 0.227509i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.58468e10 | −0.415196 | ||||||||
\(443\) | −1.04572e10 | + | 6.03744e9i | −0.271518 | + | 0.156761i | −0.629577 | − | 0.776938i | \(-0.716772\pi\) |
0.358059 | + | 0.933699i | \(0.383439\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.37483e10 | − | 2.38128e10i | 0.350599 | − | 0.607255i | ||||
\(446\) | −5.31847e9 | − | 3.07062e9i | −0.134415 | − | 0.0776044i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.38014e10 | + | 4.12252e10i | 0.590867 | + | 1.02341i | ||||
\(449\) | 3.17911e10i | 0.782205i | 0.920347 | + | 0.391103i | \(0.127906\pi\) | ||||
−0.920347 | + | 0.391103i | \(0.872094\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.79497e9 | −0.0433861 | ||||||||
\(452\) | −8.30398e9 | + | 4.79431e9i | −0.198945 | + | 0.114861i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.48456e10 | + | 2.57133e10i | −0.349440 | + | 0.605249i | ||||
\(455\) | 4.14535e10 | + | 2.39332e10i | 0.967198 | + | 0.558412i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.15200e9 | + | 7.19148e9i | 0.0951903 | + | 0.164874i | 0.909688 | − | 0.415292i | \(-0.136321\pi\) |
−0.814498 | + | 0.580167i | \(0.802987\pi\) | |||||||
\(458\) | 3.79544e10i | 0.862583i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.85016e10 | −1.08324 | ||||||||
\(461\) | −2.76292e10 | + | 1.59518e10i | −0.611738 | + | 0.353187i | −0.773645 | − | 0.633619i | \(-0.781569\pi\) |
0.161908 | + | 0.986806i | \(0.448235\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.37770e10 | + | 2.38625e10i | −0.299800 | + | 0.519269i | −0.976090 | − | 0.217366i | \(-0.930253\pi\) |
0.676290 | + | 0.736636i | \(0.263587\pi\) | |||||||
\(464\) | −9.65501e8 | − | 5.57432e8i | −0.0208296 | − | 0.0120260i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.88475e10 | + | 3.26448e10i | 0.399677 | + | 0.692261i | ||||
\(467\) | 2.60699e10i | 0.548114i | 0.961713 | + | 0.274057i | \(0.0883658\pi\) | ||||
−0.961713 | + | 0.274057i | \(0.911634\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.96675e10 | 1.23324 | ||||||||
\(470\) | −2.74584e10 | + | 1.58531e10i | −0.562709 | + | 0.324880i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.58590e10 | − | 4.47891e10i | 0.521007 | − | 0.902411i | ||||
\(473\) | −1.19274e10 | − | 6.88631e9i | −0.238288 | − | 0.137576i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.42057e9 | − | 2.46049e9i | −0.0279053 | − | 0.0483334i | ||||
\(476\) | 5.94798e10i | 1.15862i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.30570e9 | 0.101632 | ||||||||
\(479\) | 1.92371e9 | − | 1.11066e9i | 0.0365425 | − | 0.0210978i | −0.481617 | − | 0.876382i | \(-0.659951\pi\) |
0.518160 | + | 0.855284i | \(0.326617\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.17116e9 | − | 3.76056e9i | 0.0405613 | − | 0.0702542i | ||||
\(482\) | −7.27624e9 | − | 4.20094e9i | −0.134809 | − | 0.0778321i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.57448e10 | − | 2.72707e10i | −0.286916 | − | 0.496953i | ||||
\(485\) | − | 5.24482e10i | − | 0.947902i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.62519e10 | 1.53339 | 0.766696 | − | 0.642011i | \(-0.221900\pi\) | ||||
0.766696 | + | 0.642011i | \(0.221900\pi\) | |||||||
\(488\) | −4.24370e10 | + | 2.45010e10i | −0.748282 | + | 0.432021i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.07152e10 | + | 7.05208e10i | −0.706272 | + | 1.22330i | ||||
\(491\) | 3.81434e9 | + | 2.20221e9i | 0.0656286 | + | 0.0378907i | 0.532455 | − | 0.846458i | \(-0.321269\pi\) |
−0.466827 | + | 0.884349i | \(0.654603\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.35902e10 | − | 5.81800e10i | −0.568624 | − | 0.984886i | ||||
\(494\) | 1.39211e10i | 0.233758i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.33054e9 | 0.0219837 | ||||||||
\(497\) | −5.09210e8 | + | 2.93992e8i | −0.00834586 | + | 0.00481848i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.38520e10 | − | 2.39924e10i | 0.223414 | − | 0.386965i | −0.732428 | − | 0.680844i | \(-0.761613\pi\) |
0.955843 | + | 0.293879i | \(0.0949464\pi\) | |||||||
\(500\) | −3.42980e10 | − | 1.98020e10i | −0.548768 | − | 0.316831i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.20325e10 | − | 2.08409e10i | −0.189471 | − | 0.328173i | ||||
\(503\) | 2.37306e10i | 0.370712i | 0.982671 | + | 0.185356i | \(0.0593438\pi\) | ||||
−0.982671 | + | 0.185356i | \(0.940656\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.41187e10 | 0.524598 | ||||||||
\(506\) | 1.58165e10 | − | 9.13167e9i | 0.241273 | − | 0.139299i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.78945e10 | − | 4.83147e10i | 0.418855 | − | 0.725478i | ||||
\(509\) | −3.31689e10 | − | 1.91501e10i | −0.494152 | − | 0.285299i | 0.232143 | − | 0.972682i | \(-0.425426\pi\) |
−0.726295 | + | 0.687383i | \(0.758759\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.15694e11 | − | 2.00388e11i | −1.69679 | − | 2.93893i | ||||
\(512\) | 3.01455e9i | 0.0438674i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.80111e10 | −0.687843 | ||||||||
\(515\) | −4.06205e10 | + | 2.34522e10i | −0.577452 | + | 0.333392i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.26582e9 | + | 1.60489e10i | −0.129695 | + | 0.224638i | ||||
\(518\) | 9.09360e9 | + | 5.25019e9i | 0.126304 | + | 0.0729216i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.23794e10 | + | 3.87622e10i | 0.306080 | + | 0.530146i | ||||
\(521\) | 1.29094e11i | 1.75208i | 0.482238 | + | 0.876040i | \(0.339824\pi\) | ||||
−0.482238 | + | 0.876040i | \(0.660176\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.37220e11 | 1.83405 | 0.917024 | − | 0.398831i | \(-0.130584\pi\) | ||||
0.917024 | + | 0.398831i | \(0.130584\pi\) | |||||||
\(524\) | −2.52341e10 | + | 1.45689e10i | −0.334705 | + | 0.193242i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.12634e10 | − | 1.95087e10i | 0.147138 | − | 0.254851i | ||||
\(527\) | 6.94351e10 | + | 4.00884e10i | 0.900195 | + | 0.519728i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.81855e10 | + | 1.70062e11i | 1.25379 | + | 2.17163i | ||||
\(530\) | 7.75431e10i | 0.982742i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.22518e10 | 0.652311 | ||||||||
\(533\) | −8.15937e9 | + | 4.71081e9i | −0.101099 | + | 0.0583696i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.45424e10 | + | 1.29111e11i | −0.909888 | + | 1.57597i | ||||
\(536\) | 4.83188e10 | + | 2.78969e10i | 0.585406 | + | 0.337984i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.00910e10 | − | 1.74782e10i | −0.120450 | − | 0.208625i | ||||
\(539\) | 4.75944e10i | 0.563898i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.71547e10 | −0.900686 | −0.450343 | − | 0.892856i | \(-0.648698\pi\) | ||||
−0.450343 | + | 0.892856i | \(0.648698\pi\) | |||||||
\(542\) | 5.08128e10 | − | 2.93368e10i | 0.588811 | − | 0.339950i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.51014e10 | + | 7.81179e10i | −0.514985 | + | 0.891980i | ||||
\(545\) | 3.99676e10 | + | 2.30753e10i | 0.453025 | + | 0.261554i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.66534e10 | + | 4.61651e10i | 0.297717 | + | 0.515661i | 0.975613 | − | 0.219497i | \(-0.0704415\pi\) |
−0.677896 | + | 0.735157i | \(0.737108\pi\) | |||||||
\(548\) | 2.33821e10i | 0.259276i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.30082e9 | 0.0142157 | ||||||||
\(551\) | −5.11099e10 | + | 2.95083e10i | −0.554497 | + | 0.320139i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.05497e11 | − | 1.82727e11i | 1.12808 | − | 1.95390i | ||||
\(554\) | −5.91175e10 | − | 3.41315e10i | −0.627592 | − | 0.362340i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.01173e10 | − | 1.75237e10i | −0.105868 | − | 0.183369i | ||||
\(557\) | − | 1.56229e11i | − | 1.62309i | −0.584291 | − | 0.811544i | \(-0.698627\pi\) | ||
0.584291 | − | 0.811544i | \(-0.301373\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.22912e10 | −0.740352 | ||||||||
\(560\) | −3.26344e9 | + | 1.88415e9i | −0.0331836 | + | 0.0191586i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.03746e10 | − | 1.79693e10i | 0.103998 | − | 0.180130i | ||||
\(563\) | −4.20078e10 | − | 2.42532e10i | −0.418116 | − | 0.241399i | 0.276155 | − | 0.961113i | \(-0.410940\pi\) |
−0.694271 | + | 0.719714i | \(0.744273\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.83030e10 | − | 3.17018e10i | −0.179609 | − | 0.311093i | ||||
\(566\) | − | 9.63228e9i | − | 0.0938563i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.49811e8 | −0.00528227 | ||||||||
\(569\) | −4.20475e10 | + | 2.42762e10i | −0.401136 | + | 0.231596i | −0.686974 | − | 0.726682i | \(-0.741061\pi\) |
0.285838 | + | 0.958278i | \(0.407728\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.27408e10 | + | 1.43311e11i | −0.778351 | + | 1.34814i | 0.154541 | + | 0.987986i | \(0.450610\pi\) |
−0.932892 | + | 0.360156i | \(0.882723\pi\) | |||||||
\(572\) | 8.56791e9 | + | 4.94668e9i | 0.0800370 | + | 0.0462094i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.13914e10 | − | 1.97306e10i | −0.104938 | − | 0.181757i | ||||
\(575\) | 1.95644e10i | 0.178977i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.25738e11 | −1.13439 | −0.567194 | − | 0.823584i | \(-0.691971\pi\) | ||||
−0.567194 | + | 0.823584i | \(0.691971\pi\) | |||||||
\(578\) | 4.59997e9 | − | 2.65579e9i | 0.0412139 | − | 0.0237948i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.58795e10 | + | 6.21451e10i | −0.317055 | + | 0.549155i | ||||
\(581\) | −2.23499e11 | − | 1.29037e11i | −1.96142 | − | 1.13243i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.26612e10 | + | 3.92503e10i | 0.196159 | + | 0.339757i | ||||
\(584\) | − | 2.16366e11i | − | 1.86011i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.21766e11 | 1.03261 | ||||||||
\(587\) | 5.90985e10 | − | 3.41205e10i | 0.497765 | − | 0.287385i | −0.230025 | − | 0.973185i | \(-0.573881\pi\) |
0.727790 | + | 0.685800i | \(0.240548\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.52168e10 | − | 6.09973e10i | 0.292610 | − | 0.506815i | ||||
\(590\) | 6.46646e10 | + | 3.73341e10i | 0.533653 | + | 0.308105i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.70926e8 | + | 2.96052e8i | 0.00139162 | + | 0.00241036i | ||||
\(593\) | − | 2.22279e10i | − | 0.179755i | −0.995953 | − | 0.0898774i | \(-0.971352\pi\) | ||
0.995953 | − | 0.0898774i | \(-0.0286475\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.27074e11 | −1.81175 | ||||||||
\(596\) | −2.03487e10 | + | 1.17483e10i | −0.161269 | + | 0.0931088i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.79314e10 | − | 8.30195e10i | 0.374813 | − | 0.649196i | ||||
\(599\) | 1.84741e11 | + | 1.06660e11i | 1.43501 | + | 0.828503i | 0.997497 | − | 0.0707089i | \(-0.0225261\pi\) |
0.437513 | + | 0.899212i | \(0.355859\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.74980e10 | − | 3.03074e10i | −0.134119 | − | 0.232301i | 0.791142 | − | 0.611633i | \(-0.209487\pi\) |
−0.925261 | + | 0.379332i | \(0.876154\pi\) | |||||||
\(602\) | − | 1.74811e11i | − | 1.33101i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.66617e10 | 0.200327 | ||||||||
\(605\) | 1.04110e11 | − | 6.01082e10i | 0.777093 | − | 0.448655i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.53846e10 | − | 9.59289e10i | 0.407975 | − | 0.706634i | −0.586687 | − | 0.809814i | \(-0.699568\pi\) |
0.994663 | + | 0.103179i | \(0.0329015\pi\) | |||||||
\(608\) | 6.86250e10 | + | 3.96207e10i | 0.502190 | + | 0.289939i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.53736e10 | − | 6.12688e10i | −0.255481 | − | 0.442507i | ||||
\(611\) | 9.72710e10i | 0.697940i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.84434e10 | −0.343078 | −0.171539 | − | 0.985177i | \(-0.554874\pi\) | ||||
−0.171539 | + | 0.985177i | \(0.554874\pi\) | |||||||
\(614\) | −4.25899e10 | + | 2.45893e10i | −0.299663 | + | 0.173011i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.16301e10 | + | 5.47849e10i | −0.219673 | + | 0.380485i | ||||
\(617\) | 6.64633e10 | + | 3.83726e10i | 0.458607 | + | 0.264777i | 0.711459 | − | 0.702728i | \(-0.248035\pi\) |
−0.252851 | + | 0.967505i | \(0.581368\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.05958e11 | + | 1.83524e11i | 0.721721 | + | 1.25006i | 0.960310 | + | 0.278936i | \(0.0899818\pi\) |
−0.238589 | + | 0.971121i | \(0.576685\pi\) | |||||||
\(620\) | − | 8.56410e10i | − | 0.579582i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.69368e10 | −0.179964 | ||||||||
\(623\) | 1.76658e11 | − | 1.01993e11i | 1.17268 | − | 0.677048i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.83063e10 | − | 1.18310e11i | 0.447652 | − | 0.775356i | ||||
\(626\) | −4.45216e10 | − | 2.57045e10i | −0.289917 | − | 0.167383i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.61953e10 | + | 9.73330e10i | 0.361294 | + | 0.625780i | ||||
\(629\) | 2.05996e10i | 0.131600i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.44761e10 | −0.0913130 | −0.0456565 | − | 0.998957i | \(-0.514538\pi\) | ||||
−0.0456565 | + | 0.998957i | \(0.514538\pi\) | |||||||
\(632\) | 1.70864e11 | − | 9.86481e10i | 1.07098 | − | 0.618330i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.70182e10 | − | 1.33400e11i | 0.476691 | − | 0.825652i | ||||
\(635\) | 1.84449e11 | + | 1.06492e11i | 1.13444 | + | 0.654969i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.24909e11 | + | 2.16349e11i | 0.758642 | + | 1.31401i | ||||
\(638\) | − | 2.70210e10i | − | 0.163087i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.41593e10 | 0.561233 | ||||||||
\(641\) | 2.06878e10 | − | 1.19441e10i | 0.122541 | − | 0.0707494i | −0.437476 | − | 0.899230i | \(-0.644128\pi\) |
0.560018 | + | 0.828481i | \(0.310794\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.57675e10 | + | 1.31233e11i | −0.443240 | + | 0.767714i | −0.997928 | − | 0.0643445i | \(-0.979504\pi\) |
0.554688 | + | 0.832059i | \(0.312838\pi\) | |||||||
\(644\) | −3.11607e11 | − | 1.79907e11i | −1.81161 | − | 1.04593i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.30202e10 | − | 5.71927e10i | −0.189605 | − | 0.328406i | ||||
\(647\) | − | 1.51614e11i | − | 0.865208i | −0.901584 | − | 0.432604i | \(-0.857595\pi\) | ||
0.901584 | − | 0.432604i | \(-0.142405\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.36420e10 | 0.245995 | ||||||||
\(650\) | 5.91313e9 | − | 3.41395e9i | 0.0331256 | − | 0.0191251i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.48659e10 | − | 2.57485e10i | 0.0822624 | − | 0.142483i | ||||
\(653\) | −1.58425e11 | − | 9.14665e10i | −0.871305 | − | 0.503048i | −0.00352329 | − | 0.999994i | \(-0.501122\pi\) |
−0.867782 | + | 0.496946i | \(0.834455\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.56191e10 | − | 9.63351e10i | −0.302175 | − | 0.523383i | ||||
\(656\) | − | 7.41722e8i | − | 0.00400521i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.35216e11 | −1.25477 | ||||||||
\(659\) | 2.57869e11 | − | 1.48881e11i | 1.36728 | − | 0.789398i | 0.376698 | − | 0.926336i | \(-0.377059\pi\) |
0.990580 | + | 0.136938i | \(0.0437260\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.59595e10 | + | 9.69247e10i | −0.293135 | + | 0.507725i | −0.974549 | − | 0.224173i | \(-0.928032\pi\) |
0.681414 | + | 0.731898i | \(0.261365\pi\) | |||||||
\(662\) | −6.42686e10 | − | 3.71055e10i | −0.334631 | − | 0.193199i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.20660e11 | − | 2.08989e11i | −0.620712 | − | 1.07511i | ||||
\(665\) | 1.99480e11i | 1.02003i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.06397e11 | 2.05328 | ||||||||
\(668\) | −7.54226e10 | + | 4.35452e10i | −0.378787 | + | 0.218693i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.02764e10 | + | 6.97607e10i | −0.199872 | + | 0.346188i | ||||
\(671\) | −3.58103e10 | − | 2.06751e10i | −0.176652 | − | 0.101990i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.33548e10 | + | 4.04517e10i | 0.113845 | + | 0.197186i | 0.917318 | − | 0.398156i | \(-0.130350\pi\) |
−0.803472 | + | 0.595342i | \(0.797016\pi\) | |||||||
\(674\) | − | 4.71220e10i | − | 0.228341i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.50749e10 | −0.359507 | ||||||||
\(677\) | −1.48801e11 | + | 8.59105e10i | −0.708357 | + | 0.408970i | −0.810452 | − | 0.585804i | \(-0.800779\pi\) |
0.102095 | + | 0.994775i | \(0.467445\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.94546e11 | − | 3.36963e11i | 0.915256 | − | 1.58527i | ||||
\(680\) | −1.83884e11 | − | 1.06166e11i | −0.860022 | − | 0.496534i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.61241e10 | + | 2.79278e10i | 0.0745313 | + | 0.129092i | ||||
\(683\) | − | 6.74141e10i | − | 0.309790i | −0.987931 | − | 0.154895i | \(-0.950496\pi\) | ||
0.987931 | − | 0.154895i | \(-0.0495040\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.92650e10 | −0.405433 | ||||||||
\(686\) | −3.02685e11 | + | 1.74755e11i | −1.36677 | + | 0.789103i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.84558e9 | − | 4.92869e9i | 0.0127004 | − | 0.0219977i | ||||
\(689\) | 2.06021e11 | + | 1.18946e11i | 0.914187 | + | 0.527806i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.43078e10 | − | 5.94228e10i | −0.150481 | − | 0.260640i | 0.780924 | − | 0.624626i | \(-0.214749\pi\) |
−0.931404 | + | 0.363987i | \(0.881415\pi\) | |||||||
\(692\) | − | 9.45277e10i | − | 0.412225i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.87953e10 | 0.210349 | ||||||||
\(695\) | 6.68995e10 | − | 3.86244e10i | 0.286737 | − | 0.165548i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.23477e10 | − | 3.87073e10i | 0.0946894 | − | 0.164007i | ||||
\(698\) | 2.06426e11 | + | 1.19180e11i | 0.869644 | + | 0.502089i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.28140e10 | − | 2.21945e10i | −0.0533694 | − | 0.0924385i | ||||
\(701\) | 3.47803e11i | 1.44033i | 0.693804 | + | 0.720164i | \(0.255934\pi\) | ||||
−0.693804 | + | 0.720164i | \(0.744066\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.80963e10 | 0.0740916 | ||||||||
\(704\) | −3.25292e10 | + | 1.87808e10i | −0.132429 | + | 0.0764580i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.96014e10 | − | 6.85916e10i | 0.159401 | − | 0.276091i | ||||
\(707\) | 2.19202e11 | + | 1.26556e11i | 0.877337 | + | 0.506531i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.32405e11 | + | 2.29332e11i | 0.523986 | + | 0.907570i | 0.999610 | + | 0.0279213i | \(0.00888879\pi\) |
−0.475624 | + | 0.879648i | \(0.657778\pi\) | |||||||
\(710\) | − | 7.93795e8i | − | 0.00312374i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.90743e11 | 0.742215 | ||||||||
\(713\) | −4.20036e11 | + | 2.42508e11i | −1.62528 | + | 0.938357i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.88848e10 | + | 3.27094e10i | −0.0722583 | + | 0.125155i | ||||
\(716\) | −5.64734e10 | − | 3.26049e10i | −0.214878 | − | 0.124060i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.95728e10 | + | 6.85421e10i | 0.148901 | + | 0.257905i | ||||
\(719\) | 2.48269e11i | 0.928981i | 0.885578 | + | 0.464491i | \(0.153763\pi\) | ||||
−0.885578 | + | 0.464491i | \(0.846237\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.47965e11 | −1.28764 | ||||||||
\(722\) | 9.70643e10 | − | 5.60401e10i | 0.357199 | − | 0.206229i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.57995e10 | + | 1.48609e11i | −0.312270 | + | 0.540868i | ||||
\(725\) | 2.50679e10 | + | 1.44730e10i | 0.0907333 | + | 0.0523849i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.47750e11 | − | 2.55911e11i | −0.528921 | − | 0.916117i | −0.999431 | − | 0.0337230i | \(-0.989264\pi\) |
0.470511 | − | 0.882394i | \(-0.344070\pi\) | |||||||
\(728\) | 3.32047e11i | 1.18215i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.12380e11 | 1.10000 | ||||||||
\(731\) | 2.96997e11 | − | 1.71472e11i | 1.04012 | − | 0.600513i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.13954e11 | + | 3.70578e11i | −0.741146 | + | 1.28370i | 0.210828 | + | 0.977523i | \(0.432384\pi\) |
−0.951974 | + | 0.306179i | \(0.900949\pi\) | |||||||
\(734\) | −1.20485e11 | − | 6.95618e10i | −0.415095 | − | 0.239655i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.72834e11 | − | 4.72562e11i | −0.929794 | − | 1.61045i | ||||
\(737\) | 4.70814e10i | 0.159580i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.19830e10 | −0.0401781 | −0.0200890 | − | 0.999798i | \(-0.506395\pi\) | ||||
−0.0200890 | + | 0.999798i | \(0.506395\pi\) | |||||||
\(740\) | 1.90556e10 | − | 1.10018e10i | 0.0635471 | − | 0.0366889i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.87630e11 | + | 4.98190e11i | −0.948896 | + | 1.64354i | ||||
\(743\) | 2.40378e11 | + | 1.38782e11i | 0.788749 | + | 0.455384i | 0.839522 | − | 0.543326i | \(-0.182835\pi\) |
−0.0507731 | + | 0.998710i | \(0.516169\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.48511e10 | − | 7.76844e10i | −0.145595 | − | 0.252179i | ||||
\(746\) | − | 2.18042e11i | − | 0.704020i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.69332e10 | −0.149925 | ||||||||
\(749\) | −9.57823e11 | + | 5.52999e11i | −3.04339 | + | 1.75710i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.24572e9 | + | 1.25499e10i | −0.0227783 | + | 0.0394532i | −0.877190 | − | 0.480144i | \(-0.840585\pi\) |
0.854412 | + | 0.519597i | \(0.173918\pi\) | |||||||
\(752\) | −6.63176e9 | − | 3.82885e9i | −0.0207376 | − | 0.0119728i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.09154e10 | − | 1.22829e11i | −0.219409 | − | 0.380028i | ||||
\(755\) | 1.01785e11i | 0.313254i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.94269e11 | 0.591590 | 0.295795 | − | 0.955251i | \(-0.404415\pi\) | ||||
0.295795 | + | 0.955251i | \(0.404415\pi\) | |||||||
\(758\) | 1.62132e11 | − | 9.36067e10i | 0.491123 | − | 0.283550i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9.32644e10 | + | 1.61539e11i | −0.279551 | + | 0.484197i | ||||
\(761\) | −3.88024e11 | − | 2.24026e11i | −1.15696 | − | 0.667974i | −0.206390 | − | 0.978470i | \(-0.566172\pi\) |
−0.950575 | + | 0.310496i | \(0.899505\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.71186e11 | + | 2.96503e11i | 0.505092 | + | 0.874845i | ||||
\(764\) | − | 2.78264e11i | − | 0.816740i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.49205e11 | 0.433379 | ||||||||
\(767\) | 1.98383e11 | − | 1.14537e11i | 0.573223 | − | 0.330950i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.13694e11 | + | 1.96924e11i | −0.325113 | + | 0.563111i | −0.981535 | − | 0.191282i | \(-0.938736\pi\) |
0.656423 | + | 0.754393i | \(0.272069\pi\) | |||||||
\(770\) | −7.90961e10 | − | 4.56662e10i | −0.225005 | − | 0.129907i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.58386e10 | + | 9.67152e10i | 0.157205 | + | 0.272286i | ||||
\(773\) | 3.48003e11i | 0.974686i | 0.873211 | + | 0.487343i | \(0.162034\pi\) | ||||
−0.873211 | + | 0.487343i | \(0.837966\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.45457e10 | −0.0957605 | ||||||||
\(776\) | 3.15087e11 | − | 1.81915e11i | 0.868926 | − | 0.501675i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.40657e10 | − | 1.45606e11i | 0.229457 | − | 0.397431i | ||||
\(779\) | −3.40036e10 | − | 1.96320e10i | −0.0923368 | − | 0.0533107i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.31978e8 | − | 4.01798e8i | −0.000623509 | − | 0.00107995i | ||||
\(782\) | 4.54764e11i | 1.21607i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.96671e10 | −0.0520566 | ||||||||
\(785\) | −3.71585e11 | + | 2.14534e11i | −0.978541 | + | 0.564961i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.27120e11 | + | 2.20178e11i | −0.331370 | + | 0.573950i | −0.982781 | − | 0.184775i | \(-0.940844\pi\) |
0.651411 | + | 0.758725i | \(0.274178\pi\) | |||||||
\(788\) | 2.45317e11 | + | 1.41634e11i | 0.636242 | + | 0.367334i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.42424e11 | + | 2.46686e11i | 0.365658 | + | 0.633338i | ||||
\(791\) | − | 2.71565e11i | − | 0.693695i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.17044e11 | −0.548851 | ||||||||
\(794\) | −3.15672e11 | + | 1.82253e11i | −0.794243 | + | 0.458557i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.48143e11 | − | 2.56590e11i | 0.369001 | − | 0.639128i | ||||
\(797\) | 4.79540e11 | + | 2.76863e11i | 1.18848 | + | 0.686169i | 0.957961 | − | 0.286898i | \(-0.0926242\pi\) |
0.230519 | + | 0.973068i | \(0.425958\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.30722e11 | − | 3.99623e11i | −0.566112 | − | 0.980535i | ||||
\(800\) | − | 3.88656e10i | − | 0.0948866i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.09854e10 | 0.0748962 | ||||||||
\(803\) | 1.58119e11 | − | 9.12899e10i | 0.380296 | − | 0.219564i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.86823e11 | − | 1.18961e12i | 1.63554 | − | 2.83284i | ||||
\(806\) | 1.46591e11 | + | 8.46342e10i | 0.347349 | + | 0.200542i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.18340e11 | + | 2.04971e11i | 0.277642 | + | 0.480891i | ||||
\(809\) | − | 1.00027e11i | − | 0.233519i | −0.993160 | − | 0.116759i | \(-0.962749\pi\) | ||
0.993160 | − | 0.116759i | \(-0.0372506\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.06002e10 | 0.209433 | 0.104717 | − | 0.994502i | \(-0.466606\pi\) | ||||
0.104717 | + | 0.994502i | \(0.466606\pi\) | |||||||
\(812\) | −4.61029e11 | + | 2.66175e11i | −1.06048 | + | 0.612271i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.14273e9 | + | 7.17542e9i | −0.00943602 | + | 0.0163437i | ||||
\(815\) | 9.82992e10 | + | 5.67531e10i | 0.222802 | + | 0.128635i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.50634e11 | − | 2.60906e11i | −0.338092 | − | 0.585593i | ||||
\(818\) | 5.79726e10i | 0.129482i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.77415e10 | −0.105594 | ||||||||
\(821\) | 5.36582e11 | − | 3.09796e11i | 1.18104 | − | 0.681871i | 0.224782 | − | 0.974409i | \(-0.427833\pi\) |
0.956254 | + | 0.292538i | \(0.0944997\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.81861e10 | + | 3.14993e10i | −0.0396407 | + | 0.0686597i | −0.885165 | − | 0.465277i | \(-0.845955\pi\) |
0.845524 | + | 0.533937i | \(0.179288\pi\) | |||||||
\(824\) | −2.81782e11 | − | 1.62687e11i | −0.611231 | − | 0.352894i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.76967e11 | + | 4.79720e11i | 0.594987 | + | 1.03055i | ||||
\(827\) | − | 6.85214e10i | − | 0.146489i | −0.997314 | − | 0.0732444i | \(-0.976665\pi\) | ||
0.997314 | − | 0.0732444i | \(-0.0233353\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.13133e11 | −1.29819 | −0.649093 | − | 0.760709i | \(-0.724851\pi\) | ||||
−0.649093 | + | 0.760709i | \(0.724851\pi\) | |||||||
\(830\) | 3.01730e11 | − | 1.74204e11i | 0.635778 | − | 0.367067i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −9.85786e10 | + | 1.70743e11i | −0.205726 | + | 0.356328i | ||||
\(833\) | −1.02634e12 | − | 5.92558e11i | −2.13163 | − | 1.23070i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.66241e11 | − | 2.87938e11i | −0.341973 | − | 0.592315i | ||||
\(836\) | 4.12299e10i | 0.0844087i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.41985e11 | 0.490695 | ||||||||
\(839\) | 3.19993e11 | − | 1.84748e11i | 0.645792 | − | 0.372848i | −0.141050 | − | 0.990002i | \(-0.545048\pi\) |
0.786842 | + | 0.617154i | \(0.211715\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.05133e10 | − | 8.74916e10i | 0.100977 | − | 0.174897i | ||||
\(842\) | 1.01215e11 | + | 5.84364e10i | 0.201370 | + | 0.116261i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.24479e10 | − | 2.15605e10i | −0.0245317 | − | 0.0424901i | ||||
\(845\) | − | 2.86610e11i | − | 0.562167i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.91836e11 | 1.73281 | ||||||||
\(848\) | −1.62191e10 | + | 9.36411e9i | −0.0313649 | + | 0.0181085i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.61955e10 | + | 2.80514e10i | −0.0310254 | + | 0.0537376i | ||||
\(851\) | −1.07919e11 | − | 6.23069e10i | −0.205768 | − | 0.118800i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.02690e11 | − | 1.77864e11i | −0.193969 | − | 0.335963i | 0.752593 | − | 0.658486i | \(-0.228803\pi\) |
−0.946562 | + | 0.322522i | \(0.895469\pi\) | |||||||
\(854\) | − | 5.24844e11i | − | 0.986730i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.03419e12 | −1.92623 | ||||||||
\(857\) | 4.89607e11 | − | 2.82675e11i | 0.907662 | − | 0.524039i | 0.0279838 | − | 0.999608i | \(-0.491091\pi\) |
0.879678 | + | 0.475570i | \(0.157758\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.17033e10 | + | 5.49116e10i | −0.0582279 | + | 0.100854i | −0.893670 | − | 0.448725i | \(-0.851878\pi\) |
0.835442 | + | 0.549579i | \(0.185212\pi\) | |||||||
\(860\) | −3.17239e11 | − | 1.83158e11i | −0.579952 | − | 0.334836i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.22618e11 | + | 5.58791e11i | 0.584332 | + | 1.01209i | ||||
\(863\) | − | 7.20037e11i | − | 1.29811i | −0.760742 | − | 0.649055i | \(-0.775165\pi\) | ||
0.760742 | − | 0.649055i | \(-0.224835\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.60875e11 | 0.644602 | ||||||||
\(866\) | 4.64705e11 | − | 2.68298e11i | 0.826240 | − | 0.477030i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.17668e11 | − | 5.50217e11i | 0.559621 | − | 0.969293i | ||||
\(869\) | 1.44183e11 | + | 8.32439e10i | 0.252833 | + | 0.145973i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.23563e11 | + | 2.14018e11i | 0.214692 | + | 0.371858i | ||||
\(872\) | 3.20145e11i | 0.553707i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.99501e11 | 0.684655 | ||||||||
\(875\) | 9.71377e11 | − | 5.60825e11i | 1.65713 | − | 0.956742i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.43477e11 | + | 4.21715e11i | −0.411586 | + | 0.712887i | −0.995063 | − | 0.0992421i | \(-0.968358\pi\) |
0.583478 | + | 0.812129i | \(0.301692\pi\) | |||||||
\(878\) | −3.71184e10 | − | 2.14303e10i | −0.0624612 | − | 0.0360620i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.48671e9 | − | 2.57506e9i | −0.00247911 | − | 0.00429395i | ||||
\(881\) | − | 1.10625e12i | − | 1.83633i | −0.396196 | − | 0.918166i | \(-0.629670\pi\) | ||
0.396196 | − | 0.918166i | \(-0.370330\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.45262e10 | 0.122593 | 0.0612966 | − | 0.998120i | \(-0.480476\pi\) | ||||
0.0612966 | + | 0.998120i | \(0.480476\pi\) | |||||||
\(884\) | −2.13344e11 | + | 1.23174e11i | −0.349359 | + | 0.201702i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.04667e10 | − | 1.04731e11i | 0.0981254 | − | 0.169958i | ||||
\(887\) | 1.00427e12 | + | 5.79818e11i | 1.62240 | + | 0.936692i | 0.986276 | + | 0.165105i | \(0.0527962\pi\) |
0.636123 | + | 0.771588i | \(0.280537\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.90018e11 | + | 1.36835e12i | 1.26482 | + | 2.19074i | ||||
\(890\) | 2.75387e11i | 0.438919i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.54693e10 | −0.150801 | ||||||||
\(893\) | −3.51060e11 | + | 2.02685e11i | −0.552047 | + | 0.318724i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.24475e11 | − | 2.15596e11i | 0.193994 | − | 0.336008i | ||||
\(896\) | 6.04944e11 | + | 3.49265e11i | 0.938606 | + | 0.541904i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.59199e11 | − | 2.75740e11i | −0.244813 | − | 0.424028i | ||||
\(899\) | 7.17591e11i | 1.09860i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.12854e12 | −1.71245 | ||||||||
\(902\) | 1.55686e10 | − | 8.98856e9i | 0.0235193 | − | 0.0135789i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.26967e11 | − | 2.19914e11i | 0.190116 | − | 0.329290i | ||||
\(905\) | −5.67339e11 | − | 3.27553e11i | −0.845762 | − | 0.488301i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.30868e11 | − | 1.09270e12i | −0.932201 | − | 1.61462i | −0.779551 | − | 0.626339i | \(-0.784553\pi\) |
−0.152650 | − | 0.988280i | \(-0.548781\pi\) | |||||||
\(908\) | 4.61567e11i | 0.679034i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.79396e11 | −0.699083 | ||||||||
\(911\) | −6.43775e11 | + | 3.71684e11i | −0.934675 | + | 0.539635i | −0.888287 | − | 0.459289i | \(-0.848104\pi\) |
−0.0463878 | + | 0.998924i | \(0.514771\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.01818e11 | − | 1.76355e11i | 0.146536 | − | 0.253807i | ||||
\(914\) | −7.20248e10 | − | 4.15835e10i | −0.103204 | − | 0.0595849i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.95013e11 | + | 5.10977e11i | 0.419043 | + | 0.725804i | ||||
\(917\) | − | 8.25230e11i | − | 1.16707i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.99130e10 | −0.126055 | −0.0630276 | − | 0.998012i | \(-0.520076\pi\) | ||||
−0.0630276 | + | 0.998012i | \(0.520076\pi\) | |||||||
\(920\) | 1.11238e12 | − | 6.42232e11i | 1.55275 | − | 0.896481i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.59761e11 | − | 2.76715e11i | 0.221079 | − | 0.382921i | ||||
\(923\) | −2.10900e9 | − | 1.21763e9i | −0.00290583 | − | 0.00167768i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.43786e9 | − | 7.68660e9i | −0.00606187 | − | 0.0104995i | ||||
\(926\) | − | 2.75962e11i | − | 0.375323i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.07325e11 | −1.08857 | ||||||||
\(929\) | −7.43680e11 | + | 4.29364e11i | −0.998442 | + | 0.576451i | −0.907787 | − | 0.419431i | \(-0.862230\pi\) |
−0.0906554 | + | 0.995882i | \(0.528896\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.20550e11 | + | 9.01620e11i | −0.692890 | + | 1.20012i | ||||
\(932\) | 5.07483e11 | + | 2.92995e11i | 0.672602 | + | 0.388327i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.30549e11 | − | 2.26117e11i | −0.171548 | − | 0.297129i | ||||
\(935\) | − | 1.79175e11i | − | 0.234440i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.25416e11 | 0.162702 | 0.0813512 | − | 0.996685i | \(-0.474076\pi\) | ||||
0.0813512 | + | 0.996685i | \(0.474076\pi\) | |||||||
\(938\) | −5.17526e11 | + | 2.98794e11i | −0.668530 | + | 0.385976i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.46447e11 | + | 4.26858e11i | −0.315654 | + | 0.546729i | ||||
\(941\) | −8.77244e11 | − | 5.06477e11i | −1.11882 | − | 0.645954i | −0.177724 | − | 0.984080i | \(-0.556873\pi\) |
−0.941101 | + | 0.338127i | \(0.890207\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.35189e11 | + | 2.34154e11i | 0.170960 | + | 0.296111i | ||||
\(944\) | 1.80339e10i | 0.0227092i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.37937e11 | 0.172233 | ||||||||
\(947\) | −2.58946e11 | + | 1.49503e11i | −0.321966 | + | 0.185887i | −0.652269 | − | 0.757988i | \(-0.726183\pi\) |
0.330303 | + | 0.943875i | \(0.392849\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.79173e11 | − | 8.29952e11i | 0.590782 | − | 1.02326i | ||||
\(950\) | 2.46425e10 | + | 1.42274e10i | 0.0302546 | + | 0.0174675i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.87600e11 | − | 1.36416e12i | −0.958866 | − | 1.66080i | ||||
\(953\) | − | 9.57954e11i | − | 1.16138i | −0.814126 | − | 0.580688i | \(-0.802783\pi\) | ||
0.814126 | − | 0.580688i | \(-0.197217\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.06232e12 | 1.27715 | ||||||||
\(956\) | 7.14301e10 | − | 4.12402e10i | 0.0855165 | − | 0.0493730i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.11235e10 | + | 1.92665e10i | −0.0132063 | + | 0.0228740i | ||||
\(959\) | −5.73500e11 | − | 3.31110e11i | −0.678045 | − | 0.391470i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.75995e9 | − | 3.04832e9i | −0.00206351 | − | 0.00357410i | ||||
\(962\) | 4.34896e10i | 0.0507792i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.30612e11 | −0.151243 | ||||||||
\(965\) | −3.69226e11 | + | 2.13173e11i | −0.425778 | + | 0.245823i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.92952e11 | + | 1.02702e12i | −0.678131 | + | 1.17456i | 0.297412 | + | 0.954749i | \(0.403876\pi\) |
−0.975543 | + | 0.219808i | \(0.929457\pi\) | |||||||
\(968\) | 7.22210e11 | + | 4.16968e11i | 0.822549 | + | 0.474899i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.62642e11 | + | 4.54909e11i | 0.296672 | + | 0.513851i | ||||
\(971\) | − | 5.47759e10i | − | 0.0616187i | −0.999525 | − | 0.0308093i | \(-0.990192\pi\) | ||
0.999525 | − | 0.0308093i | \(-0.00980847\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.73077e11 | 0.639384 | ||||||||
\(974\) | −7.48106e11 | + | 4.31919e11i | −0.831242 | + | 0.479918i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.54343e9 | − | 1.47977e10i | 0.00941527 | − | 0.0163077i | ||||
\(977\) | −8.01165e11 | − | 4.62553e11i | −0.879313 | − | 0.507672i | −0.00888112 | − | 0.999961i | \(-0.502827\pi\) |
−0.870432 | + | 0.492289i | \(0.836160\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.04791e10 | + | 1.39394e11i | 0.0876097 | + | 0.151744i | ||||
\(980\) | 1.26589e12i | 1.37243i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.41116e10 | −0.0474358 | ||||||||
\(983\) | −5.00770e11 | + | 2.89120e11i | −0.536321 | + | 0.309645i | −0.743586 | − | 0.668640i | \(-0.766877\pi\) |
0.207266 | + | 0.978285i | \(0.433543\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.40709e11 | + | 9.36536e11i | −0.574406 | + | 0.994900i | ||||
\(986\) | 5.82690e11 | + | 3.36416e11i | 0.616495 | + | 0.355934i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.08206e11 | + | 1.87418e11i | 0.113560 | + | 0.196691i | ||||
\(989\) | 2.07458e12i | 2.16843i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.41284e11 | −0.146487 | −0.0732435 | − | 0.997314i | \(-0.523335\pi\) | ||||
−0.0732435 | + | 0.997314i | \(0.523335\pi\) | |||||||
\(992\) | 8.34419e11 | − | 4.81752e11i | 0.861664 | − | 0.497482i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.94442e9 | − | 5.09988e9i | 0.00301616 | − | 0.00522414i | ||||
\(995\) | 9.79575e11 | + | 5.65558e11i | 0.999414 | + | 0.577012i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.20994e11 | + | 1.07559e12i | 0.628502 | + | 1.08860i | 0.987852 | + | 0.155395i | \(0.0496649\pi\) |
−0.359351 | + | 0.933203i | \(0.617002\pi\) | |||||||
\(998\) | 2.77464e11i | 0.279695i | ||||||||
\(999\) | 0 | 0 |
(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 | 81.9.d.g.53.6 | 32 | ||
3.2 | odd | 2 | inner | 81.9.d.g.53.11 | 32 | ||
9.2 | odd | 6 | inner | 81.9.d.g.26.6 | 32 | ||
9.4 | even | 3 | 81.9.b.b.80.6 | ✓ | 16 | ||
9.5 | odd | 6 | 81.9.b.b.80.11 | yes | 16 | ||
9.7 | even | 3 | inner | 81.9.d.g.26.11 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
81.9.b.b.80.6 | ✓ | 16 | 9.4 | even | 3 | ||
81.9.b.b.80.11 | yes | 16 | 9.5 | odd | 6 | ||
81.9.d.g.26.6 | 32 | 9.2 | odd | 6 | inner | ||
81.9.d.g.26.11 | 32 | 9.7 | even | 3 | inner | ||
81.9.d.g.53.6 | 32 | 1.1 | even | 1 | trivial | ||
81.9.d.g.53.11 | 32 | 3.2 | odd | 2 | inner |