Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,9,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
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("43.42");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.5172802326\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.27 | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.9.b.b.42.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 31.0929i | 1.94331i | 0.236407 | + | 0.971654i | \(0.424030\pi\) | ||||
−0.236407 | + | 0.971654i | \(0.575970\pi\) | |||||||
\(3\) | − | 76.9602i | − | 0.950126i | −0.879952 | − | 0.475063i | \(-0.842425\pi\) | ||
0.879952 | − | 0.475063i | \(-0.157575\pi\) | |||||||
\(4\) | −710.770 | −2.77645 | ||||||||
\(5\) | 309.101i | 0.494561i | 0.968944 | + | 0.247280i | \(0.0795369\pi\) | ||||
−0.968944 | + | 0.247280i | \(0.920463\pi\) | |||||||
\(6\) | 2392.92 | 1.84639 | ||||||||
\(7\) | − | 1604.82i | − | 0.668397i | −0.942503 | − | 0.334199i | \(-0.891534\pi\) | ||
0.942503 | − | 0.334199i | \(-0.108466\pi\) | |||||||
\(8\) | − | 14140.1i | − | 3.45218i | ||||||
\(9\) | 638.125 | 0.0972603 | ||||||||
\(10\) | −9610.84 | −0.961084 | ||||||||
\(11\) | −7356.08 | −0.502430 | −0.251215 | − | 0.967931i | \(-0.580830\pi\) | ||||
−0.251215 | + | 0.967931i | \(0.580830\pi\) | |||||||
\(12\) | 54701.0i | 2.63797i | ||||||||
\(13\) | 42183.4 | 1.47696 | 0.738480 | − | 0.674275i | \(-0.235544\pi\) | ||||
0.738480 | + | 0.674275i | \(0.235544\pi\) | |||||||
\(14\) | 49898.6 | 1.29890 | ||||||||
\(15\) | 23788.4 | 0.469895 | ||||||||
\(16\) | 257701. | 3.93221 | ||||||||
\(17\) | −57088.6 | −0.683524 | −0.341762 | − | 0.939787i | \(-0.611024\pi\) | ||||
−0.341762 | + | 0.939787i | \(0.611024\pi\) | |||||||
\(18\) | 19841.2i | 0.189007i | ||||||||
\(19\) | 127050.i | 0.974901i | 0.873151 | + | 0.487450i | \(0.162073\pi\) | ||||
−0.873151 | + | 0.487450i | \(0.837927\pi\) | |||||||
\(20\) | − | 219700.i | − | 1.37312i | ||||||
\(21\) | −123507. | −0.635062 | ||||||||
\(22\) | − | 228722.i | − | 0.976377i | ||||||
\(23\) | 287238. | 1.02643 | 0.513217 | − | 0.858259i | \(-0.328454\pi\) | ||||
0.513217 | + | 0.858259i | \(0.328454\pi\) | |||||||
\(24\) | −1.08823e6 | −3.28001 | ||||||||
\(25\) | 295082. | 0.755410 | ||||||||
\(26\) | 1.31161e6i | 2.87019i | ||||||||
\(27\) | − | 554046.i | − | 1.04254i | ||||||
\(28\) | 1.14066e6i | 1.85577i | ||||||||
\(29\) | − | 292238.i | − | 0.413186i | −0.978427 | − | 0.206593i | \(-0.933762\pi\) | ||
0.978427 | − | 0.206593i | \(-0.0662375\pi\) | |||||||
\(30\) | 739653.i | 0.913151i | ||||||||
\(31\) | −478095. | −0.517687 | −0.258844 | − | 0.965919i | \(-0.583341\pi\) | ||||
−0.258844 | + | 0.965919i | \(0.583341\pi\) | |||||||
\(32\) | 4.39281e6i | 4.18931i | ||||||||
\(33\) | 566125.i | 0.477372i | ||||||||
\(34\) | − | 1.77505e6i | − | 1.32830i | ||||||
\(35\) | 496051. | 0.330563 | ||||||||
\(36\) | −453560. | −0.270038 | ||||||||
\(37\) | − | 1.22416e6i | − | 0.653180i | −0.945166 | − | 0.326590i | \(-0.894100\pi\) | ||
0.945166 | − | 0.326590i | \(-0.105900\pi\) | |||||||
\(38\) | −3.95036e6 | −1.89453 | ||||||||
\(39\) | − | 3.24645e6i | − | 1.40330i | ||||||
\(40\) | 4.37073e6 | 1.70732 | ||||||||
\(41\) | 5.52026e6 | 1.95355 | 0.976775 | − | 0.214270i | \(-0.0687371\pi\) | ||||
0.976775 | + | 0.214270i | \(0.0687371\pi\) | |||||||
\(42\) | − | 3.84021e6i | − | 1.23412i | ||||||
\(43\) | 1.30315e6 | − | 3.16070e6i | 0.381172 | − | 0.924504i | ||||
\(44\) | 5.22848e6 | 1.39497 | ||||||||
\(45\) | 197245.i | 0.0481011i | ||||||||
\(46\) | 8.93108e6i | 1.99468i | ||||||||
\(47\) | −1.51306e6 | −0.310073 | −0.155036 | − | 0.987909i | \(-0.549549\pi\) | ||||
−0.155036 | + | 0.987909i | \(0.549549\pi\) | |||||||
\(48\) | − | 1.98328e7i | − | 3.73610i | ||||||
\(49\) | 3.18935e6 | 0.553245 | ||||||||
\(50\) | 9.17496e6i | 1.46799i | ||||||||
\(51\) | 4.39355e6i | 0.649434i | ||||||||
\(52\) | −2.99827e7 | −4.10070 | ||||||||
\(53\) | 7.83616e6 | 0.993116 | 0.496558 | − | 0.868004i | \(-0.334597\pi\) | ||||
0.496558 | + | 0.868004i | \(0.334597\pi\) | |||||||
\(54\) | 1.72269e7 | 2.02597 | ||||||||
\(55\) | − | 2.27377e6i | − | 0.248482i | ||||||
\(56\) | −2.26924e7 | −2.30743 | ||||||||
\(57\) | 9.77780e6 | 0.926279 | ||||||||
\(58\) | 9.08655e6 | 0.802947 | ||||||||
\(59\) | 1.53013e7 | 1.26276 | 0.631378 | − | 0.775475i | \(-0.282489\pi\) | ||||
0.631378 | + | 0.775475i | \(0.282489\pi\) | |||||||
\(60\) | −1.69081e7 | −1.30464 | ||||||||
\(61\) | − | 3.41732e6i | − | 0.246812i | −0.992356 | − | 0.123406i | \(-0.960618\pi\) | ||
0.992356 | − | 0.123406i | \(-0.0393817\pi\) | |||||||
\(62\) | − | 1.48654e7i | − | 1.00603i | ||||||
\(63\) | − | 1.02408e6i | − | 0.0650085i | ||||||
\(64\) | −7.06139e7 | −4.20892 | ||||||||
\(65\) | 1.30389e7i | 0.730447i | ||||||||
\(66\) | −1.76025e7 | −0.927681 | ||||||||
\(67\) | −3.26404e7 | −1.61978 | −0.809892 | − | 0.586580i | \(-0.800474\pi\) | ||||
−0.809892 | + | 0.586580i | \(0.800474\pi\) | |||||||
\(68\) | 4.05769e7 | 1.89777 | ||||||||
\(69\) | − | 2.21059e7i | − | 0.975242i | ||||||
\(70\) | 1.54237e7i | 0.642386i | ||||||||
\(71\) | 4.27345e7i | 1.68169i | 0.541279 | + | 0.840843i | \(0.317940\pi\) | ||||
−0.541279 | + | 0.840843i | \(0.682060\pi\) | |||||||
\(72\) | − | 9.02318e6i | − | 0.335761i | ||||||
\(73\) | − | 5.32427e7i | − | 1.87486i | −0.348175 | − | 0.937430i | \(-0.613198\pi\) | ||
0.348175 | − | 0.937430i | \(-0.386802\pi\) | |||||||
\(74\) | 3.80629e7 | 1.26933 | ||||||||
\(75\) | − | 2.27096e7i | − | 0.717734i | ||||||
\(76\) | − | 9.03034e7i | − | 2.70676i | ||||||
\(77\) | 1.18052e7i | 0.335823i | ||||||||
\(78\) | 1.00942e8 | 2.72704 | ||||||||
\(79\) | 4.22399e7 | 1.08446 | 0.542231 | − | 0.840230i | \(-0.317580\pi\) | ||||
0.542231 | + | 0.840230i | \(0.317580\pi\) | |||||||
\(80\) | 7.96556e7i | 1.94472i | ||||||||
\(81\) | −3.84528e7 | −0.893280 | ||||||||
\(82\) | 1.71641e8i | 3.79635i | ||||||||
\(83\) | −4.72358e7 | −0.995311 | −0.497656 | − | 0.867375i | \(-0.665806\pi\) | ||||
−0.497656 | + | 0.867375i | \(0.665806\pi\) | |||||||
\(84\) | 8.77854e7 | 1.76322 | ||||||||
\(85\) | − | 1.76461e7i | − | 0.338044i | ||||||
\(86\) | 9.82753e7 | + | 4.05188e7i | 1.79660 | + | 0.740735i | ||||
\(87\) | −2.24907e7 | −0.392578 | ||||||||
\(88\) | 1.04016e8i | 1.73448i | ||||||||
\(89\) | − | 7.79613e7i | − | 1.24256i | −0.783587 | − | 0.621282i | \(-0.786612\pi\) | ||
0.783587 | − | 0.621282i | \(-0.213388\pi\) | |||||||
\(90\) | −6.13292e6 | −0.0934754 | ||||||||
\(91\) | − | 6.76969e7i | − | 0.987196i | ||||||
\(92\) | −2.04161e8 | −2.84984 | ||||||||
\(93\) | 3.67943e7i | 0.491868i | ||||||||
\(94\) | − | 4.70453e7i | − | 0.602567i | ||||||
\(95\) | −3.92712e7 | −0.482148 | ||||||||
\(96\) | 3.38072e8 | 3.98038 | ||||||||
\(97\) | 5.35770e7 | 0.605190 | 0.302595 | − | 0.953119i | \(-0.402147\pi\) | ||||
0.302595 | + | 0.953119i | \(0.402147\pi\) | |||||||
\(98\) | 9.91662e7i | 1.07513i | ||||||||
\(99\) | −4.69410e6 | −0.0488665 | ||||||||
\(100\) | −2.09735e8 | −2.09735 | ||||||||
\(101\) | 4.84542e7 | 0.465635 | 0.232818 | − | 0.972520i | \(-0.425205\pi\) | ||||
0.232818 | + | 0.972520i | \(0.425205\pi\) | |||||||
\(102\) | −1.36608e8 | −1.26205 | ||||||||
\(103\) | −1.76149e8 | −1.56506 | −0.782531 | − | 0.622612i | \(-0.786072\pi\) | ||||
−0.782531 | + | 0.622612i | \(0.786072\pi\) | |||||||
\(104\) | − | 5.96480e8i | − | 5.09874i | ||||||
\(105\) | − | 3.81762e7i | − | 0.314077i | ||||||
\(106\) | 2.43649e8i | 1.92993i | ||||||||
\(107\) | −4.01578e7 | −0.306362 | −0.153181 | − | 0.988198i | \(-0.548952\pi\) | ||||
−0.153181 | + | 0.988198i | \(0.548952\pi\) | |||||||
\(108\) | 3.93800e8i | 2.89455i | ||||||||
\(109\) | 4.85598e7 | 0.344010 | 0.172005 | − | 0.985096i | \(-0.444976\pi\) | ||||
0.172005 | + | 0.985096i | \(0.444976\pi\) | |||||||
\(110\) | 7.06981e7 | 0.482878 | ||||||||
\(111\) | −9.42120e7 | −0.620603 | ||||||||
\(112\) | − | 4.13565e8i | − | 2.62828i | ||||||
\(113\) | 7.49574e7i | 0.459728i | 0.973223 | + | 0.229864i | \(0.0738281\pi\) | ||||
−0.973223 | + | 0.229864i | \(0.926172\pi\) | |||||||
\(114\) | 3.04020e8i | 1.80005i | ||||||||
\(115\) | 8.87855e7i | 0.507634i | ||||||||
\(116\) | 2.07714e8i | 1.14719i | ||||||||
\(117\) | 2.69183e7 | 0.143650 | ||||||||
\(118\) | 4.75762e8i | 2.45393i | ||||||||
\(119\) | 9.16170e7i | 0.456865i | ||||||||
\(120\) | − | 3.36372e8i | − | 1.62216i | ||||||
\(121\) | −1.60247e8 | −0.747564 | ||||||||
\(122\) | 1.06254e8 | 0.479632 | ||||||||
\(123\) | − | 4.24841e8i | − | 1.85612i | ||||||
\(124\) | 3.39816e8 | 1.43733 | ||||||||
\(125\) | 2.11952e8i | 0.868157i | ||||||||
\(126\) | 3.18416e7 | 0.126332 | ||||||||
\(127\) | −7.98391e7 | −0.306903 | −0.153451 | − | 0.988156i | \(-0.549039\pi\) | ||||
−0.153451 | + | 0.988156i | \(0.549039\pi\) | |||||||
\(128\) | − | 1.07103e9i | − | 3.98991i | ||||||
\(129\) | −2.43248e8 | − | 1.00291e8i | −0.878395 | − | 0.362162i | ||||
\(130\) | −4.05418e8 | −1.41948 | ||||||||
\(131\) | 1.37065e8i | 0.465415i | 0.972547 | + | 0.232707i | \(0.0747584\pi\) | ||||
−0.972547 | + | 0.232707i | \(0.925242\pi\) | |||||||
\(132\) | − | 4.02385e8i | − | 1.32540i | ||||||
\(133\) | 2.03893e8 | 0.651621 | ||||||||
\(134\) | − | 1.01489e9i | − | 3.14774i | ||||||
\(135\) | 1.71256e8 | 0.515597 | ||||||||
\(136\) | 8.07241e8i | 2.35965i | ||||||||
\(137\) | − | 3.72743e8i | − | 1.05810i | −0.848590 | − | 0.529051i | \(-0.822548\pi\) | ||
0.848590 | − | 0.529051i | \(-0.177452\pi\) | |||||||
\(138\) | 6.87338e8 | 1.89520 | ||||||||
\(139\) | −1.21246e8 | −0.324794 | −0.162397 | − | 0.986726i | \(-0.551922\pi\) | ||||
−0.162397 | + | 0.986726i | \(0.551922\pi\) | |||||||
\(140\) | −3.52579e8 | −0.917791 | ||||||||
\(141\) | 1.16445e8i | 0.294608i | ||||||||
\(142\) | −1.32874e9 | −3.26803 | ||||||||
\(143\) | −3.10305e8 | −0.742069 | ||||||||
\(144\) | 1.64446e8 | 0.382448 | ||||||||
\(145\) | 9.03310e7 | 0.204345 | ||||||||
\(146\) | 1.65547e9 | 3.64343 | ||||||||
\(147\) | − | 2.45453e8i | − | 0.525653i | ||||||
\(148\) | 8.70100e8i | 1.81352i | ||||||||
\(149\) | − | 5.70992e8i | − | 1.15847i | −0.815160 | − | 0.579235i | \(-0.803351\pi\) | ||
0.815160 | − | 0.579235i | \(-0.196649\pi\) | |||||||
\(150\) | 7.06107e8 | 1.39478 | ||||||||
\(151\) | 5.19180e8i | 0.998644i | 0.866417 | + | 0.499322i | \(0.166417\pi\) | ||||
−0.866417 | + | 0.499322i | \(0.833583\pi\) | |||||||
\(152\) | 1.79651e9 | 3.36554 | ||||||||
\(153\) | −3.64297e7 | −0.0664797 | ||||||||
\(154\) | −3.67058e8 | −0.652607 | ||||||||
\(155\) | − | 1.47779e8i | − | 0.256028i | ||||||
\(156\) | 2.30748e9i | 3.89618i | ||||||||
\(157\) | 7.05045e8i | 1.16043i | 0.814464 | + | 0.580214i | \(0.197031\pi\) | ||||
−0.814464 | + | 0.580214i | \(0.802969\pi\) | |||||||
\(158\) | 1.31336e9i | 2.10744i | ||||||||
\(159\) | − | 6.03073e8i | − | 0.943585i | ||||||
\(160\) | −1.35782e9 | −2.07187 | ||||||||
\(161\) | − | 4.60966e8i | − | 0.686066i | ||||||
\(162\) | − | 1.19561e9i | − | 1.73592i | ||||||
\(163\) | − | 2.10320e8i | − | 0.297940i | −0.988842 | − | 0.148970i | \(-0.952404\pi\) | ||
0.988842 | − | 0.148970i | \(-0.0475958\pi\) | |||||||
\(164\) | −3.92364e9 | −5.42393 | ||||||||
\(165\) | −1.74990e8 | −0.236090 | ||||||||
\(166\) | − | 1.46870e9i | − | 1.93420i | ||||||
\(167\) | 1.19295e8 | 0.153375 | 0.0766877 | − | 0.997055i | \(-0.475566\pi\) | ||||
0.0766877 | + | 0.997055i | \(0.475566\pi\) | |||||||
\(168\) | 1.74641e9i | 2.19235i | ||||||||
\(169\) | 9.63713e8 | 1.18141 | ||||||||
\(170\) | 5.48670e8 | 0.656924 | ||||||||
\(171\) | 8.10738e7i | 0.0948192i | ||||||||
\(172\) | −9.26242e8 | + | 2.24653e9i | −1.05830 | + | 2.56684i | ||||
\(173\) | 1.83412e8 | 0.204759 | 0.102380 | − | 0.994745i | \(-0.467354\pi\) | ||||
0.102380 | + | 0.994745i | \(0.467354\pi\) | |||||||
\(174\) | − | 6.99303e8i | − | 0.762901i | ||||||
\(175\) | − | 4.73554e8i | − | 0.504914i | ||||||
\(176\) | −1.89567e9 | −1.97566 | ||||||||
\(177\) | − | 1.17759e9i | − | 1.19978i | ||||||
\(178\) | 2.42404e9 | 2.41469 | ||||||||
\(179\) | 1.83639e9i | 1.78876i | 0.447304 | + | 0.894382i | \(0.352384\pi\) | ||||
−0.447304 | + | 0.894382i | \(0.647616\pi\) | |||||||
\(180\) | − | 1.40196e8i | − | 0.133550i | ||||||
\(181\) | 7.96225e8 | 0.741859 | 0.370930 | − | 0.928661i | \(-0.379039\pi\) | ||||
0.370930 | + | 0.928661i | \(0.379039\pi\) | |||||||
\(182\) | 2.10490e9 | 1.91843 | ||||||||
\(183\) | −2.62998e8 | −0.234502 | ||||||||
\(184\) | − | 4.06159e9i | − | 3.54344i | ||||||
\(185\) | 3.78390e8 | 0.323037 | ||||||||
\(186\) | −1.14404e9 | −0.955852 | ||||||||
\(187\) | 4.19948e8 | 0.343423 | ||||||||
\(188\) | 1.07544e9 | 0.860900 | ||||||||
\(189\) | −8.89145e8 | −0.696828 | ||||||||
\(190\) | − | 1.22106e9i | − | 0.936962i | ||||||
\(191\) | 1.27800e9i | 0.960279i | 0.877192 | + | 0.480140i | \(0.159414\pi\) | ||||
−0.877192 | + | 0.480140i | \(0.840586\pi\) | |||||||
\(192\) | 5.43446e9i | 3.99900i | ||||||||
\(193\) | −2.03388e8 | −0.146587 | −0.0732937 | − | 0.997310i | \(-0.523351\pi\) | ||||
−0.0732937 | + | 0.997310i | \(0.523351\pi\) | |||||||
\(194\) | 1.66587e9i | 1.17607i | ||||||||
\(195\) | 1.00348e9 | 0.694016 | ||||||||
\(196\) | −2.26689e9 | −1.53606 | ||||||||
\(197\) | 1.84082e9 | 1.22221 | 0.611107 | − | 0.791548i | \(-0.290725\pi\) | ||||
0.611107 | + | 0.791548i | \(0.290725\pi\) | |||||||
\(198\) | − | 1.45953e8i | − | 0.0949627i | ||||||
\(199\) | − | 3.93508e8i | − | 0.250923i | −0.992098 | − | 0.125462i | \(-0.959959\pi\) | ||
0.992098 | − | 0.125462i | \(-0.0400412\pi\) | |||||||
\(200\) | − | 4.17250e9i | − | 2.60781i | ||||||
\(201\) | 2.51202e9i | 1.53900i | ||||||||
\(202\) | 1.50658e9i | 0.904873i | ||||||||
\(203\) | −4.68990e8 | −0.276172 | ||||||||
\(204\) | − | 3.12281e9i | − | 1.80312i | ||||||
\(205\) | 1.70632e9i | 0.966149i | ||||||||
\(206\) | − | 5.47699e9i | − | 3.04140i | ||||||
\(207\) | 1.83294e8 | 0.0998313 | ||||||||
\(208\) | 1.08707e10 | 5.80772 | ||||||||
\(209\) | − | 9.34590e8i | − | 0.489820i | ||||||
\(210\) | 1.18701e9 | 0.610348 | ||||||||
\(211\) | − | 3.33053e9i | − | 1.68029i | −0.542362 | − | 0.840145i | \(-0.682470\pi\) | ||
0.542362 | − | 0.840145i | \(-0.317530\pi\) | |||||||
\(212\) | −5.56971e9 | −2.75733 | ||||||||
\(213\) | 3.28885e9 | 1.59781 | ||||||||
\(214\) | − | 1.24862e9i | − | 0.595355i | ||||||
\(215\) | 9.76973e8 | + | 4.02805e8i | 0.457224 | + | 0.188513i | ||||
\(216\) | −7.83429e9 | −3.59903 | ||||||||
\(217\) | 7.67258e8i | 0.346021i | ||||||||
\(218\) | 1.50987e9i | 0.668517i | ||||||||
\(219\) | −4.09757e9 | −1.78135 | ||||||||
\(220\) | 1.61613e9i | 0.689898i | ||||||||
\(221\) | −2.40819e9 | −1.00954 | ||||||||
\(222\) | − | 2.92933e9i | − | 1.20602i | ||||||
\(223\) | − | 2.90423e9i | − | 1.17439i | −0.809446 | − | 0.587195i | \(-0.800232\pi\) | ||
0.809446 | − | 0.587195i | \(-0.199768\pi\) | |||||||
\(224\) | 7.04968e9 | 2.80013 | ||||||||
\(225\) | 1.88299e8 | 0.0734714 | ||||||||
\(226\) | −2.33065e9 | −0.893393 | ||||||||
\(227\) | 2.65538e9i | 1.00005i | 0.866010 | + | 0.500027i | \(0.166677\pi\) | ||||
−0.866010 | + | 0.500027i | \(0.833323\pi\) | |||||||
\(228\) | −6.94977e9 | −2.57176 | ||||||||
\(229\) | −6.07345e8 | −0.220848 | −0.110424 | − | 0.993885i | \(-0.535221\pi\) | ||||
−0.110424 | + | 0.993885i | \(0.535221\pi\) | |||||||
\(230\) | −2.76060e9 | −0.986490 | ||||||||
\(231\) | 9.08531e8 | 0.319074 | ||||||||
\(232\) | −4.13229e9 | −1.42639 | ||||||||
\(233\) | 9.56751e8i | 0.324620i | 0.986740 | + | 0.162310i | \(0.0518944\pi\) | ||||
−0.986740 | + | 0.162310i | \(0.948106\pi\) | |||||||
\(234\) | 8.36969e8i | 0.279155i | ||||||||
\(235\) | − | 4.67686e8i | − | 0.153350i | ||||||
\(236\) | −1.08757e10 | −3.50598 | ||||||||
\(237\) | − | 3.25079e9i | − | 1.03037i | ||||||
\(238\) | −2.84864e9 | −0.887830 | ||||||||
\(239\) | 1.06815e8 | 0.0327373 | 0.0163686 | − | 0.999866i | \(-0.494789\pi\) | ||||
0.0163686 | + | 0.999866i | \(0.494789\pi\) | |||||||
\(240\) | 6.13032e9 | 1.84773 | ||||||||
\(241\) | 5.00348e9i | 1.48321i | 0.670835 | + | 0.741607i | \(0.265936\pi\) | ||||
−0.670835 | + | 0.741607i | \(0.734064\pi\) | |||||||
\(242\) | − | 4.98255e9i | − | 1.45275i | ||||||
\(243\) | − | 6.75763e8i | − | 0.193807i | ||||||
\(244\) | 2.42893e9i | 0.685260i | ||||||||
\(245\) | 9.85829e8i | 0.273613i | ||||||||
\(246\) | 1.32095e10 | 3.60701 | ||||||||
\(247\) | 5.35941e9i | 1.43989i | ||||||||
\(248\) | 6.76034e9i | 1.78715i | ||||||||
\(249\) | 3.63528e9i | 0.945671i | ||||||||
\(250\) | −6.59022e9 | −1.68710 | ||||||||
\(251\) | 6.27266e9 | 1.58036 | 0.790182 | − | 0.612872i | \(-0.209986\pi\) | ||||
0.790182 | + | 0.612872i | \(0.209986\pi\) | |||||||
\(252\) | 7.27884e8i | 0.180493i | ||||||||
\(253\) | −2.11295e9 | −0.515712 | ||||||||
\(254\) | − | 2.48243e9i | − | 0.596407i | ||||||
\(255\) | −1.35805e9 | −0.321185 | ||||||||
\(256\) | 1.52244e10 | 3.54471 | ||||||||
\(257\) | 3.46689e9i | 0.794708i | 0.917665 | + | 0.397354i | \(0.130072\pi\) | ||||
−0.917665 | + | 0.397354i | \(0.869928\pi\) | |||||||
\(258\) | 3.11834e9 | − | 7.56329e9i | 0.703792 | − | 1.70699i | ||||
\(259\) | −1.96457e9 | −0.436584 | ||||||||
\(260\) | − | 9.26768e9i | − | 2.02805i | ||||||
\(261\) | − | 1.86485e8i | − | 0.0401866i | ||||||
\(262\) | −4.26174e9 | −0.904444 | ||||||||
\(263\) | 1.63128e9i | 0.340961i | 0.985361 | + | 0.170480i | \(0.0545319\pi\) | ||||
−0.985361 | + | 0.170480i | \(0.945468\pi\) | |||||||
\(264\) | 8.00510e9 | 1.64798 | ||||||||
\(265\) | 2.42216e9i | 0.491156i | ||||||||
\(266\) | 6.33962e9i | 1.26630i | ||||||||
\(267\) | −5.99992e9 | −1.18059 | ||||||||
\(268\) | 2.31999e10 | 4.49724 | ||||||||
\(269\) | 3.80777e8 | 0.0727212 | 0.0363606 | − | 0.999339i | \(-0.488424\pi\) | ||||
0.0363606 | + | 0.999339i | \(0.488424\pi\) | |||||||
\(270\) | 5.32485e9i | 1.00196i | ||||||||
\(271\) | −4.98415e9 | −0.924089 | −0.462045 | − | 0.886857i | \(-0.652884\pi\) | ||||
−0.462045 | + | 0.886857i | \(0.652884\pi\) | |||||||
\(272\) | −1.47118e10 | −2.68776 | ||||||||
\(273\) | −5.20997e9 | −0.937961 | ||||||||
\(274\) | 1.15897e10 | 2.05622 | ||||||||
\(275\) | −2.17065e9 | −0.379541 | ||||||||
\(276\) | 1.57122e10i | 2.70771i | ||||||||
\(277\) | − | 1.03473e10i | − | 1.75755i | −0.477233 | − | 0.878777i | \(-0.658360\pi\) | ||
0.477233 | − | 0.878777i | \(-0.341640\pi\) | |||||||
\(278\) | − | 3.76989e9i | − | 0.631174i | ||||||
\(279\) | −3.05084e8 | −0.0503504 | ||||||||
\(280\) | − | 7.01424e9i | − | 1.14116i | ||||||
\(281\) | 5.27555e9 | 0.846140 | 0.423070 | − | 0.906097i | \(-0.360952\pi\) | ||||
0.423070 | + | 0.906097i | \(0.360952\pi\) | |||||||
\(282\) | −3.62062e9 | −0.572515 | ||||||||
\(283\) | 6.87347e9 | 1.07159 | 0.535797 | − | 0.844347i | \(-0.320011\pi\) | ||||
0.535797 | + | 0.844347i | \(0.320011\pi\) | |||||||
\(284\) | − | 3.03744e10i | − | 4.66911i | ||||||
\(285\) | 3.02232e9i | 0.458101i | ||||||||
\(286\) | − | 9.64829e9i | − | 1.44207i | ||||||
\(287\) | − | 8.85904e9i | − | 1.30575i | ||||||
\(288\) | 2.80316e9i | 0.407454i | ||||||||
\(289\) | −3.71665e9 | −0.532795 | ||||||||
\(290\) | 2.80866e9i | 0.397106i | ||||||||
\(291\) | − | 4.12330e9i | − | 0.575007i | ||||||
\(292\) | 3.78433e10i | 5.20545i | ||||||||
\(293\) | −1.19152e10 | −1.61671 | −0.808355 | − | 0.588696i | \(-0.799642\pi\) | ||||
−0.808355 | + | 0.588696i | \(0.799642\pi\) | |||||||
\(294\) | 7.63185e9 | 1.02151 | ||||||||
\(295\) | 4.72963e9i | 0.624510i | ||||||||
\(296\) | −1.73099e10 | −2.25490 | ||||||||
\(297\) | 4.07561e9i | 0.523801i | ||||||||
\(298\) | 1.77538e10 | 2.25127 | ||||||||
\(299\) | 1.21167e10 | 1.51600 | ||||||||
\(300\) | 1.61413e10i | 1.99275i | ||||||||
\(301\) | −5.07235e9 | − | 2.09133e9i | −0.617936 | − | 0.254775i | ||||
\(302\) | −1.61428e10 | −1.94067 | ||||||||
\(303\) | − | 3.72904e9i | − | 0.442412i | ||||||
\(304\) | 3.27410e10i | 3.83352i | ||||||||
\(305\) | 1.05629e9 | 0.122064 | ||||||||
\(306\) | − | 1.13270e9i | − | 0.129191i | ||||||
\(307\) | 6.03350e9 | 0.679229 | 0.339614 | − | 0.940565i | \(-0.389703\pi\) | ||||
0.339614 | + | 0.940565i | \(0.389703\pi\) | |||||||
\(308\) | − | 8.39079e9i | − | 0.932395i | ||||||
\(309\) | 1.35565e10i | 1.48701i | ||||||||
\(310\) | 4.59490e9 | 0.497541 | ||||||||
\(311\) | −1.24617e10 | −1.33209 | −0.666046 | − | 0.745911i | \(-0.732015\pi\) | ||||
−0.666046 | + | 0.745911i | \(0.732015\pi\) | |||||||
\(312\) | −4.59052e10 | −4.84444 | ||||||||
\(313\) | − | 6.35655e9i | − | 0.662283i | −0.943581 | − | 0.331142i | \(-0.892566\pi\) | ||
0.943581 | − | 0.331142i | \(-0.107434\pi\) | |||||||
\(314\) | −2.19219e10 | −2.25507 | ||||||||
\(315\) | 3.16543e8 | 0.0321507 | ||||||||
\(316\) | −3.00228e10 | −3.01095 | ||||||||
\(317\) | 1.40297e10 | 1.38935 | 0.694676 | − | 0.719323i | \(-0.255548\pi\) | ||||
0.694676 | + | 0.719323i | \(0.255548\pi\) | |||||||
\(318\) | 1.87513e10 | 1.83368 | ||||||||
\(319\) | 2.14973e9i | 0.207597i | ||||||||
\(320\) | − | 2.18268e10i | − | 2.08157i | ||||||
\(321\) | 3.09055e9i | 0.291082i | ||||||||
\(322\) | 1.43328e10 | 1.33324 | ||||||||
\(323\) | − | 7.25311e9i | − | 0.666368i | ||||||
\(324\) | 2.73311e10 | 2.48014 | ||||||||
\(325\) | 1.24476e10 | 1.11571 | ||||||||
\(326\) | 6.53945e9 | 0.578990 | ||||||||
\(327\) | − | 3.73717e9i | − | 0.326853i | ||||||
\(328\) | − | 7.80573e10i | − | 6.74401i | ||||||
\(329\) | 2.42819e9i | 0.207252i | ||||||||
\(330\) | − | 5.44094e9i | − | 0.458795i | ||||||
\(331\) | − | 1.45095e10i | − | 1.20876i | −0.796696 | − | 0.604380i | \(-0.793421\pi\) | ||
0.796696 | − | 0.604380i | \(-0.206579\pi\) | |||||||
\(332\) | 3.35738e10 | 2.76343 | ||||||||
\(333\) | − | 7.81170e8i | − | 0.0635285i | ||||||
\(334\) | 3.70923e9i | 0.298056i | ||||||||
\(335\) | − | 1.00892e10i | − | 0.801081i | ||||||
\(336\) | −3.18280e10 | −2.49720 | ||||||||
\(337\) | −1.52910e10 | −1.18554 | −0.592772 | − | 0.805370i | \(-0.701966\pi\) | ||||
−0.592772 | + | 0.805370i | \(0.701966\pi\) | |||||||
\(338\) | 2.99647e10i | 2.29584i | ||||||||
\(339\) | 5.76874e9 | 0.436800 | ||||||||
\(340\) | 1.25423e10i | 0.938562i | ||||||||
\(341\) | 3.51691e9 | 0.260102 | ||||||||
\(342\) | −2.52082e9 | −0.184263 | ||||||||
\(343\) | − | 1.43698e10i | − | 1.03818i | ||||||
\(344\) | −4.46927e10 | − | 1.84268e10i | −3.19156 | − | 1.31588i | ||||
\(345\) | 6.83295e9 | 0.482317 | ||||||||
\(346\) | 5.70282e9i | 0.397910i | ||||||||
\(347\) | 3.46237e8i | 0.0238812i | 0.999929 | + | 0.0119406i | \(0.00380090\pi\) | ||||
−0.999929 | + | 0.0119406i | \(0.996199\pi\) | |||||||
\(348\) | 1.59857e10 | 1.08997 | ||||||||
\(349\) | 2.52716e10i | 1.70346i | 0.523983 | + | 0.851729i | \(0.324446\pi\) | ||||
−0.523983 | + | 0.851729i | \(0.675554\pi\) | |||||||
\(350\) | 1.47242e10 | 0.981203 | ||||||||
\(351\) | − | 2.33716e10i | − | 1.53978i | ||||||
\(352\) | − | 3.23139e10i | − | 2.10484i | ||||||
\(353\) | 2.62821e9 | 0.169263 | 0.0846315 | − | 0.996412i | \(-0.473029\pi\) | ||||
0.0846315 | + | 0.996412i | \(0.473029\pi\) | |||||||
\(354\) | 3.66147e10 | 2.33154 | ||||||||
\(355\) | −1.32092e10 | −0.831696 | ||||||||
\(356\) | 5.54126e10i | 3.44991i | ||||||||
\(357\) | 7.05087e9 | 0.434080 | ||||||||
\(358\) | −5.70988e10 | −3.47612 | ||||||||
\(359\) | 2.51278e10 | 1.51278 | 0.756392 | − | 0.654119i | \(-0.226960\pi\) | ||||
0.756392 | + | 0.654119i | \(0.226960\pi\) | |||||||
\(360\) | 2.78907e9 | 0.166054 | ||||||||
\(361\) | 8.41845e8 | 0.0495682 | ||||||||
\(362\) | 2.47570e10i | 1.44166i | ||||||||
\(363\) | 1.23326e10i | 0.710280i | ||||||||
\(364\) | 4.81170e10i | 2.74090i | ||||||||
\(365\) | 1.64574e10 | 0.927232 | ||||||||
\(366\) | − | 8.17736e9i | − | 0.455710i | ||||||
\(367\) | 9.39858e9 | 0.518081 | 0.259041 | − | 0.965866i | \(-0.416594\pi\) | ||||
0.259041 | + | 0.965866i | \(0.416594\pi\) | |||||||
\(368\) | 7.40217e10 | 4.03616 | ||||||||
\(369\) | 3.52262e9 | 0.190003 | ||||||||
\(370\) | 1.17653e10i | 0.627761i | ||||||||
\(371\) | − | 1.25756e10i | − | 0.663796i | ||||||
\(372\) | − | 2.61523e10i | − | 1.36565i | ||||||
\(373\) | − | 5.81508e9i | − | 0.300414i | −0.988655 | − | 0.150207i | \(-0.952006\pi\) | ||
0.988655 | − | 0.150207i | \(-0.0479940\pi\) | |||||||
\(374\) | 1.30574e10i | 0.667377i | ||||||||
\(375\) | 1.63119e10 | 0.824859 | ||||||||
\(376\) | 2.13948e10i | 1.07043i | ||||||||
\(377\) | − | 1.23276e10i | − | 0.610258i | ||||||
\(378\) | − | 2.76461e10i | − | 1.35415i | ||||||
\(379\) | −2.73939e10 | −1.32769 | −0.663845 | − | 0.747871i | \(-0.731076\pi\) | ||||
−0.663845 | + | 0.747871i | \(0.731076\pi\) | |||||||
\(380\) | 2.79128e10 | 1.33866 | ||||||||
\(381\) | 6.14444e9i | 0.291596i | ||||||||
\(382\) | −3.97368e10 | −1.86612 | ||||||||
\(383\) | − | 1.63024e9i | − | 0.0757627i | −0.999282 | − | 0.0378813i | \(-0.987939\pi\) | ||
0.999282 | − | 0.0378813i | \(-0.0120609\pi\) | |||||||
\(384\) | −8.24270e10 | −3.79092 | ||||||||
\(385\) | −3.64899e9 | −0.166085 | ||||||||
\(386\) | − | 6.32393e9i | − | 0.284864i | ||||||
\(387\) | 8.31574e8 | − | 2.01692e9i | 0.0370729 | − | 0.0899176i | ||||
\(388\) | −3.80810e10 | −1.68028 | ||||||||
\(389\) | − | 5.91193e9i | − | 0.258185i | −0.991633 | − | 0.129092i | \(-0.958794\pi\) | ||
0.991633 | − | 0.129092i | \(-0.0412064\pi\) | |||||||
\(390\) | 3.12011e10i | 1.34869i | ||||||||
\(391\) | −1.63980e10 | −0.701592 | ||||||||
\(392\) | − | 4.50978e10i | − | 1.90990i | ||||||
\(393\) | 1.05485e10 | 0.442202 | ||||||||
\(394\) | 5.72366e10i | 2.37514i | ||||||||
\(395\) | 1.30564e10i | 0.536332i | ||||||||
\(396\) | 3.33643e9 | 0.135675 | ||||||||
\(397\) | −2.24349e10 | −0.903154 | −0.451577 | − | 0.892232i | \(-0.649138\pi\) | ||||
−0.451577 | + | 0.892232i | \(0.649138\pi\) | |||||||
\(398\) | 1.22353e10 | 0.487622 | ||||||||
\(399\) | − | 1.56916e10i | − | 0.619122i | ||||||
\(400\) | 7.60430e10 | 2.97043 | ||||||||
\(401\) | −1.52627e10 | −0.590272 | −0.295136 | − | 0.955455i | \(-0.595365\pi\) | ||||
−0.295136 | + | 0.955455i | \(0.595365\pi\) | |||||||
\(402\) | −7.81059e10 | −2.99075 | ||||||||
\(403\) | −2.01677e10 | −0.764603 | ||||||||
\(404\) | −3.44398e10 | −1.29281 | ||||||||
\(405\) | − | 1.18858e10i | − | 0.441781i | ||||||
\(406\) | − | 1.45823e10i | − | 0.536688i | ||||||
\(407\) | 9.00505e9i | 0.328177i | ||||||||
\(408\) | 6.21255e10 | 2.24197 | ||||||||
\(409\) | − | 7.64531e9i | − | 0.273213i | −0.990625 | − | 0.136607i | \(-0.956380\pi\) | ||
0.990625 | − | 0.136607i | \(-0.0436196\pi\) | |||||||
\(410\) | −5.30544e10 | −1.87753 | ||||||||
\(411\) | −2.86864e10 | −1.00533 | ||||||||
\(412\) | 1.25202e11 | 4.34531 | ||||||||
\(413\) | − | 2.45558e10i | − | 0.844023i | ||||||
\(414\) | 5.69915e9i | 0.194003i | ||||||||
\(415\) | − | 1.46006e10i | − | 0.492242i | ||||||
\(416\) | 1.85304e11i | 6.18745i | ||||||||
\(417\) | 9.33111e9i | 0.308595i | ||||||||
\(418\) | 2.90592e10 | 0.951870 | ||||||||
\(419\) | − | 2.18738e10i | − | 0.709689i | −0.934925 | − | 0.354844i | \(-0.884534\pi\) | ||
0.934925 | − | 0.354844i | \(-0.115466\pi\) | |||||||
\(420\) | 2.71345e10i | 0.872017i | ||||||||
\(421\) | 1.91405e10i | 0.609291i | 0.952466 | + | 0.304645i | \(0.0985380\pi\) | ||||
−0.952466 | + | 0.304645i | \(0.901462\pi\) | |||||||
\(422\) | 1.03556e11 | 3.26532 | ||||||||
\(423\) | −9.65519e8 | −0.0301578 | ||||||||
\(424\) | − | 1.10804e11i | − | 3.42842i | ||||||
\(425\) | −1.68458e10 | −0.516340 | ||||||||
\(426\) | 1.02260e11i | 3.10504i | ||||||||
\(427\) | −5.48419e9 | −0.164968 | ||||||||
\(428\) | 2.85430e10 | 0.850597 | ||||||||
\(429\) | 2.38811e10i | 0.705059i | ||||||||
\(430\) | −1.25244e10 | + | 3.03769e10i | −0.366339 | + | 0.888526i | ||||
\(431\) | 1.65854e10 | 0.480636 | 0.240318 | − | 0.970694i | \(-0.422748\pi\) | ||||
0.240318 | + | 0.970694i | \(0.422748\pi\) | |||||||
\(432\) | − | 1.42778e11i | − | 4.09947i | ||||||
\(433\) | 2.27110e8i | 0.00646078i | 0.999995 | + | 0.00323039i | \(0.00102827\pi\) | ||||
−0.999995 | + | 0.00323039i | \(0.998972\pi\) | |||||||
\(434\) | −2.38563e10 | −0.672425 | ||||||||
\(435\) | − | 6.95190e9i | − | 0.194154i | ||||||
\(436\) | −3.45148e10 | −0.955125 | ||||||||
\(437\) | 3.64937e10i | 1.00067i | ||||||||
\(438\) | − | 1.27405e11i | − | 3.46172i | ||||||
\(439\) | −3.63557e10 | −0.978846 | −0.489423 | − | 0.872046i | \(-0.662793\pi\) | ||||
−0.489423 | + | 0.872046i | \(0.662793\pi\) | |||||||
\(440\) | −3.21514e10 | −0.857807 | ||||||||
\(441\) | 2.03520e9 | 0.0538088 | ||||||||
\(442\) | − | 7.48778e10i | − | 1.96184i | ||||||
\(443\) | −5.00268e10 | −1.29894 | −0.649468 | − | 0.760389i | \(-0.725008\pi\) | ||||
−0.649468 | + | 0.760389i | \(0.725008\pi\) | |||||||
\(444\) | 6.69631e10 | 1.72307 | ||||||||
\(445\) | 2.40979e10 | 0.614524 | ||||||||
\(446\) | 9.03012e10 | 2.28220 | ||||||||
\(447\) | −4.39437e10 | −1.10069 | ||||||||
\(448\) | 1.13323e11i | 2.81323i | ||||||||
\(449\) | 6.46660e10i | 1.59108i | 0.605904 | + | 0.795538i | \(0.292812\pi\) | ||||
−0.605904 | + | 0.795538i | \(0.707188\pi\) | |||||||
\(450\) | 5.85477e9i | 0.142778i | ||||||||
\(451\) | −4.06075e10 | −0.981522 | ||||||||
\(452\) | − | 5.32775e10i | − | 1.27641i | ||||||
\(453\) | 3.99562e10 | 0.948837 | ||||||||
\(454\) | −8.25636e10 | −1.94341 | ||||||||
\(455\) | 2.09252e10 | 0.488228 | ||||||||
\(456\) | − | 1.38260e11i | − | 3.19769i | ||||||
\(457\) | 7.15621e10i | 1.64066i | 0.571891 | + | 0.820330i | \(0.306210\pi\) | ||||
−0.571891 | + | 0.820330i | \(0.693790\pi\) | |||||||
\(458\) | − | 1.88841e10i | − | 0.429176i | ||||||
\(459\) | 3.16297e10i | 0.712598i | ||||||||
\(460\) | − | 6.31061e10i | − | 1.40942i | ||||||
\(461\) | −9.56302e9 | −0.211734 | −0.105867 | − | 0.994380i | \(-0.533762\pi\) | ||||
−0.105867 | + | 0.994380i | \(0.533762\pi\) | |||||||
\(462\) | 2.82489e10i | 0.620059i | ||||||||
\(463\) | − | 1.69947e10i | − | 0.369819i | −0.982756 | − | 0.184909i | \(-0.940801\pi\) | ||
0.982756 | − | 0.184909i | \(-0.0591991\pi\) | |||||||
\(464\) | − | 7.53102e10i | − | 1.62473i | ||||||
\(465\) | −1.13731e10 | −0.243259 | ||||||||
\(466\) | −2.97482e10 | −0.630837 | ||||||||
\(467\) | − | 4.90505e10i | − | 1.03128i | −0.856806 | − | 0.515640i | \(-0.827554\pi\) | ||
0.856806 | − | 0.515640i | \(-0.172446\pi\) | |||||||
\(468\) | −1.91327e10 | −0.398835 | ||||||||
\(469\) | 5.23821e10i | 1.08266i | ||||||||
\(470\) | 1.45417e10 | 0.298006 | ||||||||
\(471\) | 5.42604e10 | 1.10255 | ||||||||
\(472\) | − | 2.16362e11i | − | 4.35927i | ||||||
\(473\) | −9.58609e9 | + | 2.32503e10i | −0.191512 | + | 0.464499i | ||||
\(474\) | 1.01077e11 | 2.00234 | ||||||||
\(475\) | 3.74902e10i | 0.736449i | ||||||||
\(476\) | − | 6.51187e10i | − | 1.26846i | ||||||
\(477\) | 5.00045e9 | 0.0965908 | ||||||||
\(478\) | 3.32121e9i | 0.0636186i | ||||||||
\(479\) | 3.24807e10 | 0.616997 | 0.308499 | − | 0.951225i | \(-0.400174\pi\) | ||||
0.308499 | + | 0.951225i | \(0.400174\pi\) | |||||||
\(480\) | 1.04498e11i | 1.96854i | ||||||||
\(481\) | − | 5.16395e10i | − | 0.964721i | ||||||
\(482\) | −1.55573e11 | −2.88234 | ||||||||
\(483\) | −3.54761e10 | −0.651849 | ||||||||
\(484\) | 1.13899e11 | 2.07557 | ||||||||
\(485\) | 1.65607e10i | 0.299303i | ||||||||
\(486\) | 2.10115e10 | 0.376627 | ||||||||
\(487\) | 6.76777e10 | 1.20318 | 0.601589 | − | 0.798806i | \(-0.294535\pi\) | ||||
0.601589 | + | 0.798806i | \(0.294535\pi\) | |||||||
\(488\) | −4.83214e10 | −0.852040 | ||||||||
\(489\) | −1.61862e10 | −0.283081 | ||||||||
\(490\) | −3.06523e10 | −0.531715 | ||||||||
\(491\) | − | 5.31270e10i | − | 0.914091i | −0.889443 | − | 0.457046i | \(-0.848908\pi\) | ||
0.889443 | − | 0.457046i | \(-0.151092\pi\) | |||||||
\(492\) | 3.01964e11i | 5.15341i | ||||||||
\(493\) | 1.66835e10i | 0.282422i | ||||||||
\(494\) | −1.66640e11 | −2.79815 | ||||||||
\(495\) | − | 1.45095e9i | − | 0.0241675i | ||||||
\(496\) | −1.23206e11 | −2.03566 | ||||||||
\(497\) | 6.85812e10 | 1.12403 | ||||||||
\(498\) | −1.13031e11 | −1.83773 | ||||||||
\(499\) | 8.54031e10i | 1.37744i | 0.725029 | + | 0.688718i | \(0.241826\pi\) | ||||
−0.725029 | + | 0.688718i | \(0.758174\pi\) | |||||||
\(500\) | − | 1.50649e11i | − | 2.41039i | ||||||
\(501\) | − | 9.18096e9i | − | 0.145726i | ||||||
\(502\) | 1.95036e11i | 3.07113i | ||||||||
\(503\) | 3.93175e10i | 0.614206i | 0.951676 | + | 0.307103i | \(0.0993596\pi\) | ||||
−0.951676 | + | 0.307103i | \(0.900640\pi\) | |||||||
\(504\) | −1.44806e10 | −0.224421 | ||||||||
\(505\) | 1.49772e10i | 0.230285i | ||||||||
\(506\) | − | 6.56978e10i | − | 1.00219i | ||||||
\(507\) | − | 7.41675e10i | − | 1.12249i | ||||||
\(508\) | 5.67473e10 | 0.852100 | ||||||||
\(509\) | 4.01712e10 | 0.598471 | 0.299236 | − | 0.954179i | \(-0.403268\pi\) | ||||
0.299236 | + | 0.954179i | \(0.403268\pi\) | |||||||
\(510\) | − | 4.22257e10i | − | 0.624161i | ||||||
\(511\) | −8.54451e10 | −1.25315 | ||||||||
\(512\) | 1.99187e11i | 2.89855i | ||||||||
\(513\) | 7.03916e10 | 1.01637 | ||||||||
\(514\) | −1.07796e11 | −1.54436 | ||||||||
\(515\) | − | 5.44478e10i | − | 0.774018i | ||||||
\(516\) | 1.72893e11 | + | 7.12838e10i | 2.43882 | + | 1.00552i | ||||
\(517\) | 1.11302e10 | 0.155790 | ||||||||
\(518\) | − | 6.10841e10i | − | 0.848417i | ||||||
\(519\) | − | 1.41154e10i | − | 0.194547i | ||||||
\(520\) | 1.84372e11 | 2.52164 | ||||||||
\(521\) | − | 2.34037e10i | − | 0.317639i | −0.987308 | − | 0.158819i | \(-0.949231\pi\) | ||
0.987308 | − | 0.158819i | \(-0.0507687\pi\) | |||||||
\(522\) | 5.79835e9 | 0.0780949 | ||||||||
\(523\) | 1.53893e9i | 0.0205689i | 0.999947 | + | 0.0102844i | \(0.00327370\pi\) | ||||
−0.999947 | + | 0.0102844i | \(0.996726\pi\) | |||||||
\(524\) | − | 9.74214e10i | − | 1.29220i | ||||||
\(525\) | −3.64448e10 | −0.479732 | ||||||||
\(526\) | −5.07211e10 | −0.662592 | ||||||||
\(527\) | 2.72938e10 | 0.353852 | ||||||||
\(528\) | 1.45891e11i | 1.87713i | ||||||||
\(529\) | 4.19490e9 | 0.0535673 | ||||||||
\(530\) | −7.53121e10 | −0.954468 | ||||||||
\(531\) | 9.76413e9 | 0.122816 | ||||||||
\(532\) | −1.44921e11 | −1.80919 | ||||||||
\(533\) | 2.32864e11 | 2.88531 | ||||||||
\(534\) | − | 1.86555e11i | − | 2.29426i | ||||||
\(535\) | − | 1.24128e10i | − | 0.151515i | ||||||
\(536\) | 4.61541e11i | 5.59179i | ||||||||
\(537\) | 1.41329e11 | 1.69955 | ||||||||
\(538\) | 1.18395e10i | 0.141320i | ||||||||
\(539\) | −2.34611e10 | −0.277967 | ||||||||
\(540\) | −1.21724e11 | −1.43153 | ||||||||
\(541\) | −2.14855e10 | −0.250816 | −0.125408 | − | 0.992105i | \(-0.540024\pi\) | ||||
−0.125408 | + | 0.992105i | \(0.540024\pi\) | |||||||
\(542\) | − | 1.54972e11i | − | 1.79579i | ||||||
\(543\) | − | 6.12776e10i | − | 0.704860i | ||||||
\(544\) | − | 2.50780e11i | − | 2.86350i | ||||||
\(545\) | 1.50099e10i | 0.170134i | ||||||||
\(546\) | − | 1.61993e11i | − | 1.82275i | ||||||
\(547\) | −7.55950e10 | −0.844391 | −0.422196 | − | 0.906505i | \(-0.638741\pi\) | ||||
−0.422196 | + | 0.906505i | \(0.638741\pi\) | |||||||
\(548\) | 2.64935e11i | 2.93777i | ||||||||
\(549\) | − | 2.18068e9i | − | 0.0240050i | ||||||
\(550\) | − | 6.74917e10i | − | 0.737564i | ||||||
\(551\) | 3.71289e10 | 0.402815 | ||||||||
\(552\) | −3.12581e11 | −3.36671 | ||||||||
\(553\) | − | 6.77874e10i | − | 0.724851i | ||||||
\(554\) | 3.21728e11 | 3.41547 | ||||||||
\(555\) | − | 2.91210e10i | − | 0.306926i | ||||||
\(556\) | 8.61780e10 | 0.901773 | ||||||||
\(557\) | −1.76314e11 | −1.83175 | −0.915877 | − | 0.401459i | \(-0.868503\pi\) | ||||
−0.915877 | + | 0.401459i | \(0.868503\pi\) | |||||||
\(558\) | − | 9.48597e9i | − | 0.0978464i | ||||||
\(559\) | 5.49715e10 | − | 1.33329e11i | 0.562976 | − | 1.36546i | ||||
\(560\) | 1.27833e11 | 1.29984 | ||||||||
\(561\) | − | 3.23193e10i | − | 0.326295i | ||||||
\(562\) | 1.64032e11i | 1.64431i | ||||||||
\(563\) | 4.11955e9 | 0.0410031 | 0.0205015 | − | 0.999790i | \(-0.493474\pi\) | ||||
0.0205015 | + | 0.999790i | \(0.493474\pi\) | |||||||
\(564\) | − | 8.27657e10i | − | 0.817964i | ||||||
\(565\) | −2.31694e10 | −0.227364 | ||||||||
\(566\) | 2.13716e11i | 2.08244i | ||||||||
\(567\) | 6.17099e10i | 0.597066i | ||||||||
\(568\) | 6.04271e11 | 5.80549 | ||||||||
\(569\) | −5.45267e10 | −0.520188 | −0.260094 | − | 0.965583i | \(-0.583754\pi\) | ||||
−0.260094 | + | 0.965583i | \(0.583754\pi\) | |||||||
\(570\) | −9.39729e10 | −0.890232 | ||||||||
\(571\) | 1.57005e11i | 1.47697i | 0.674272 | + | 0.738483i | \(0.264457\pi\) | ||||
−0.674272 | + | 0.738483i | \(0.735543\pi\) | |||||||
\(572\) | 2.20555e11 | 2.06032 | ||||||||
\(573\) | 9.83552e10 | 0.912387 | ||||||||
\(574\) | 2.75453e11 | 2.53747 | ||||||||
\(575\) | 8.47588e10 | 0.775378 | ||||||||
\(576\) | −4.50605e10 | −0.409361 | ||||||||
\(577\) | 1.19552e11i | 1.07858i | 0.842120 | + | 0.539291i | \(0.181308\pi\) | ||||
−0.842120 | + | 0.539291i | \(0.818692\pi\) | |||||||
\(578\) | − | 1.15562e11i | − | 1.03539i | ||||||
\(579\) | 1.56528e10i | 0.139276i | ||||||||
\(580\) | −6.42046e10 | −0.567354 | ||||||||
\(581\) | 7.58050e10i | 0.665263i | ||||||||
\(582\) | 1.28205e11 | 1.11742 | ||||||||
\(583\) | −5.76434e10 | −0.498971 | ||||||||
\(584\) | −7.52860e11 | −6.47236 | ||||||||
\(585\) | 8.32046e9i | 0.0710435i | ||||||||
\(586\) | − | 3.70480e11i | − | 3.14177i | ||||||
\(587\) | 9.65927e10i | 0.813564i | 0.913525 | + | 0.406782i | \(0.133349\pi\) | ||||
−0.913525 | + | 0.406782i | \(0.866651\pi\) | |||||||
\(588\) | 1.74461e11i | 1.45945i | ||||||||
\(589\) | − | 6.07420e10i | − | 0.504694i | ||||||
\(590\) | −1.47058e11 | −1.21362 | ||||||||
\(591\) | − | 1.41670e11i | − | 1.16126i | ||||||
\(592\) | − | 3.15469e11i | − | 2.56844i | ||||||
\(593\) | 1.38229e11i | 1.11784i | 0.829222 | + | 0.558920i | \(0.188784\pi\) | ||||
−0.829222 | + | 0.558920i | \(0.811216\pi\) | |||||||
\(594\) | −1.26723e11 | −1.01791 | ||||||||
\(595\) | −2.83189e10 | −0.225948 | ||||||||
\(596\) | 4.05844e11i | 3.21643i | ||||||||
\(597\) | −3.02845e10 | −0.238409 | ||||||||
\(598\) | 3.76744e11i | 2.94606i | ||||||||
\(599\) | 7.61743e10 | 0.591700 | 0.295850 | − | 0.955234i | \(-0.404397\pi\) | ||||
0.295850 | + | 0.955234i | \(0.404397\pi\) | |||||||
\(600\) | −3.21117e11 | −2.47775 | ||||||||
\(601\) | 1.66678e11i | 1.27756i | 0.769391 | + | 0.638778i | \(0.220560\pi\) | ||||
−0.769391 | + | 0.638778i | \(0.779440\pi\) | |||||||
\(602\) | 6.50255e10 | − | 1.57714e11i | 0.495106 | − | 1.20084i | ||||
\(603\) | −2.08287e10 | −0.157541 | ||||||||
\(604\) | − | 3.69018e11i | − | 2.77268i | ||||||
\(605\) | − | 4.95324e10i | − | 0.369716i | ||||||
\(606\) | 1.15947e11 | 0.859743 | ||||||||
\(607\) | − | 7.27298e10i | − | 0.535745i | −0.963454 | − | 0.267872i | \(-0.913679\pi\) | ||
0.963454 | − | 0.267872i | \(-0.0863205\pi\) | |||||||
\(608\) | −5.58107e11 | −4.08417 | ||||||||
\(609\) | 3.60936e10i | 0.262398i | ||||||||
\(610\) | 3.28433e10i | 0.237207i | ||||||||
\(611\) | −6.38259e10 | −0.457965 | ||||||||
\(612\) | 2.58931e10 | 0.184577 | ||||||||
\(613\) | −1.54770e11 | −1.09608 | −0.548042 | − | 0.836451i | \(-0.684627\pi\) | ||||
−0.548042 | + | 0.836451i | \(0.684627\pi\) | |||||||
\(614\) | 1.87599e11i | 1.31995i | ||||||||
\(615\) | 1.31318e11 | 0.917963 | ||||||||
\(616\) | 1.66927e11 | 1.15932 | ||||||||
\(617\) | 9.53827e10 | 0.658156 | 0.329078 | − | 0.944303i | \(-0.393262\pi\) | ||||
0.329078 | + | 0.944303i | \(0.393262\pi\) | |||||||
\(618\) | −4.21510e11 | −2.88971 | ||||||||
\(619\) | −6.89842e9 | −0.0469880 | −0.0234940 | − | 0.999724i | \(-0.507479\pi\) | ||||
−0.0234940 | + | 0.999724i | \(0.507479\pi\) | |||||||
\(620\) | 1.05037e11i | 0.710848i | ||||||||
\(621\) | − | 1.59143e11i | − | 1.07009i | ||||||
\(622\) | − | 3.87469e11i | − | 2.58867i | ||||||
\(623\) | −1.25114e11 | −0.830527 | ||||||||
\(624\) | − | 8.36614e11i | − | 5.51806i | ||||||
\(625\) | 4.97518e10 | 0.326053 | ||||||||
\(626\) | 1.97644e11 | 1.28702 | ||||||||
\(627\) | −7.19263e10 | −0.465390 | ||||||||
\(628\) | − | 5.01125e11i | − | 3.22187i | ||||||
\(629\) | 6.98858e10i | 0.446464i | ||||||||
\(630\) | 9.84224e9i | 0.0624787i | ||||||||
\(631\) | 7.55488e10i | 0.476552i | 0.971198 | + | 0.238276i | \(0.0765823\pi\) | ||||
−0.971198 | + | 0.238276i | \(0.923418\pi\) | |||||||
\(632\) | − | 5.97278e11i | − | 3.74376i | ||||||
\(633\) | −2.56319e11 | −1.59649 | ||||||||
\(634\) | 4.36225e11i | 2.69994i | ||||||||
\(635\) | − | 2.46783e10i | − | 0.151782i | ||||||
\(636\) | 4.28646e11i | 2.61981i | ||||||||
\(637\) | 1.34538e11 | 0.817121 | ||||||||
\(638\) | −6.68414e10 | −0.403425 | ||||||||
\(639\) | 2.72699e10i | 0.163561i | ||||||||
\(640\) | 3.31057e11 | 1.97325 | ||||||||
\(641\) | − | 6.44169e10i | − | 0.381564i | −0.981632 | − | 0.190782i | \(-0.938898\pi\) | ||
0.981632 | − | 0.190782i | \(-0.0611024\pi\) | |||||||
\(642\) | −9.60943e10 | −0.565663 | ||||||||
\(643\) | −8.74404e10 | −0.511527 | −0.255763 | − | 0.966739i | \(-0.582327\pi\) | ||||
−0.255763 | + | 0.966739i | \(0.582327\pi\) | |||||||
\(644\) | 3.27641e11i | 1.90483i | ||||||||
\(645\) | 3.10000e10 | − | 7.51880e10i | 0.179111 | − | 0.434420i | ||||
\(646\) | 2.25520e11 | 1.29496 | ||||||||
\(647\) | − | 2.45475e11i | − | 1.40085i | −0.713728 | − | 0.700423i | \(-0.752995\pi\) | ||
0.713728 | − | 0.700423i | \(-0.247005\pi\) | |||||||
\(648\) | 5.43728e11i | 3.08377i | ||||||||
\(649\) | −1.12557e11 | −0.634447 | ||||||||
\(650\) | 3.87031e11i | 2.16817i | ||||||||
\(651\) | 5.90483e10 | 0.328763 | ||||||||
\(652\) | 1.49489e11i | 0.827215i | ||||||||
\(653\) | − | 2.93482e10i | − | 0.161410i | −0.996738 | − | 0.0807048i | \(-0.974283\pi\) | ||
0.996738 | − | 0.0807048i | \(-0.0257171\pi\) | |||||||
\(654\) | 1.16200e11 | 0.635175 | ||||||||
\(655\) | −4.23667e10 | −0.230176 | ||||||||
\(656\) | 1.42258e12 | 7.68177 | ||||||||
\(657\) | − | 3.39755e10i | − | 0.182349i | ||||||
\(658\) | −7.54994e10 | −0.402754 | ||||||||
\(659\) | −2.33390e11 | −1.23749 | −0.618744 | − | 0.785593i | \(-0.712358\pi\) | ||||
−0.618744 | + | 0.785593i | \(0.712358\pi\) | |||||||
\(660\) | 1.24378e11 | 0.655490 | ||||||||
\(661\) | −2.66026e11 | −1.39353 | −0.696767 | − | 0.717297i | \(-0.745379\pi\) | ||||
−0.696767 | + | 0.717297i | \(0.745379\pi\) | |||||||
\(662\) | 4.51143e11 | 2.34900 | ||||||||
\(663\) | 1.85335e11i | 0.959188i | ||||||||
\(664\) | 6.67921e11i | 3.43600i | ||||||||
\(665\) | 6.30233e10i | 0.322266i | ||||||||
\(666\) | 2.42889e10 | 0.123455 | ||||||||
\(667\) | − | 8.39421e10i | − | 0.424108i | ||||||
\(668\) | −8.47913e10 | −0.425839 | ||||||||
\(669\) | −2.23511e11 | −1.11582 | ||||||||
\(670\) | 3.13702e11 | 1.55675 | ||||||||
\(671\) | 2.51381e10i | 0.124006i | ||||||||
\(672\) | − | 5.42545e11i | − | 2.66047i | ||||||
\(673\) | − | 2.88073e11i | − | 1.40424i | −0.712058 | − | 0.702121i | \(-0.752237\pi\) | ||
0.712058 | − | 0.702121i | \(-0.247763\pi\) | |||||||
\(674\) | − | 4.75443e11i | − | 2.30388i | ||||||
\(675\) | − | 1.63489e11i | − | 0.787541i | ||||||
\(676\) | −6.84978e11 | −3.28012 | ||||||||
\(677\) | 2.49369e11i | 1.18710i | 0.804796 | + | 0.593551i | \(0.202275\pi\) | ||||
−0.804796 | + | 0.593551i | \(0.797725\pi\) | |||||||
\(678\) | 1.79367e11i | 0.848836i | ||||||||
\(679\) | − | 8.59816e10i | − | 0.404507i | ||||||
\(680\) | −2.49519e11 | −1.16699 | ||||||||
\(681\) | 2.04359e11 | 0.950178 | ||||||||
\(682\) | 1.09351e11i | 0.505458i | ||||||||
\(683\) | −7.43209e10 | −0.341530 | −0.170765 | − | 0.985312i | \(-0.554624\pi\) | ||||
−0.170765 | + | 0.985312i | \(0.554624\pi\) | |||||||
\(684\) | − | 5.76249e10i | − | 0.263260i | ||||||
\(685\) | 1.15215e11 | 0.523296 | ||||||||
\(686\) | 4.46800e11 | 2.01751 | ||||||||
\(687\) | 4.67414e10i | 0.209834i | ||||||||
\(688\) | 3.35824e11 | − | 8.14515e11i | 1.49885 | − | 3.63534i | ||||
\(689\) | 3.30556e11 | 1.46679 | ||||||||
\(690\) | 2.12457e11i | 0.937290i | ||||||||
\(691\) | − | 1.05148e11i | − | 0.461200i | −0.973049 | − | 0.230600i | \(-0.925931\pi\) | ||
0.973049 | − | 0.230600i | \(-0.0740689\pi\) | |||||||
\(692\) | −1.30364e11 | −0.568503 | ||||||||
\(693\) | 7.53319e9i | 0.0326622i | ||||||||
\(694\) | −1.07655e10 | −0.0464085 | ||||||||
\(695\) | − | 3.74772e10i | − | 0.160630i | ||||||
\(696\) | 3.18022e11i | 1.35525i | ||||||||
\(697\) | −3.15144e11 | −1.33530 | ||||||||
\(698\) | −7.85769e11 | −3.31034 | ||||||||
\(699\) | 7.36318e10 | 0.308430 | ||||||||
\(700\) | 3.36588e11i | 1.40187i | ||||||||
\(701\) | −3.01602e11 | −1.24900 | −0.624501 | − | 0.781024i | \(-0.714697\pi\) | ||||
−0.624501 | + | 0.781024i | \(0.714697\pi\) | |||||||
\(702\) | 7.26691e11 | 2.99227 | ||||||||
\(703\) | 1.55530e11 | 0.636786 | ||||||||
\(704\) | 5.19442e11 | 2.11469 | ||||||||
\(705\) | −3.59932e10 | −0.145702 | ||||||||
\(706\) | 8.17189e10i | 0.328930i | ||||||||
\(707\) | − | 7.77603e10i | − | 0.311229i | ||||||
\(708\) | 8.36996e11i | 3.33112i | ||||||||
\(709\) | −3.95499e11 | −1.56516 | −0.782582 | − | 0.622547i | \(-0.786098\pi\) | ||||
−0.782582 | + | 0.622547i | \(0.786098\pi\) | |||||||
\(710\) | − | 4.10714e11i | − | 1.61624i | ||||||
\(711\) | 2.69543e10 | 0.105475 | ||||||||
\(712\) | −1.10238e12 | −4.28956 | ||||||||
\(713\) | −1.37327e11 | −0.531372 | ||||||||
\(714\) | 2.19232e11i | 0.843551i | ||||||||
\(715\) | − | 9.59154e10i | − | 0.366998i | ||||||
\(716\) | − | 1.30525e12i | − | 4.96641i | ||||||
\(717\) | − | 8.22054e9i | − | 0.0311045i | ||||||
\(718\) | 7.81297e11i | 2.93981i | ||||||||
\(719\) | 3.76466e11 | 1.40867 | 0.704337 | − | 0.709866i | \(-0.251244\pi\) | ||||
0.704337 | + | 0.709866i | \(0.251244\pi\) | |||||||
\(720\) | 5.08302e10i | 0.189144i | ||||||||
\(721\) | 2.82688e11i | 1.04608i | ||||||||
\(722\) | 2.61754e10i | 0.0963263i | ||||||||
\(723\) | 3.85069e11 | 1.40924 | ||||||||
\(724\) | −5.65933e11 | −2.05973 | ||||||||
\(725\) | − | 8.62342e10i | − | 0.312124i | ||||||
\(726\) | −3.83458e11 | −1.38029 | ||||||||
\(727\) | − | 1.34308e11i | − | 0.480800i | −0.970674 | − | 0.240400i | \(-0.922721\pi\) | ||
0.970674 | − | 0.240400i | \(-0.0772785\pi\) | |||||||
\(728\) | −9.57244e11 | −3.40798 | ||||||||
\(729\) | −3.04296e11 | −1.07742 | ||||||||
\(730\) | 5.11707e11i | 1.80190i | ||||||||
\(731\) | −7.43951e10 | + | 1.80440e11i | −0.260540 | + | 0.631921i | ||||
\(732\) | 1.86931e11 | 0.651084 | ||||||||
\(733\) | 1.41612e10i | 0.0490550i | 0.999699 | + | 0.0245275i | \(0.00780813\pi\) | ||||
−0.999699 | + | 0.0245275i | \(0.992192\pi\) | |||||||
\(734\) | 2.92229e11i | 1.00679i | ||||||||
\(735\) | 7.58696e10 | 0.259967 | ||||||||
\(736\) | 1.26178e12i | 4.30006i | ||||||||
\(737\) | 2.40106e11 | 0.813828 | ||||||||
\(738\) | 1.09529e11i | 0.369234i | ||||||||
\(739\) | 1.01671e11i | 0.340893i | 0.985367 | + | 0.170447i | \(0.0545210\pi\) | ||||
−0.985367 | + | 0.170447i | \(0.945479\pi\) | |||||||
\(740\) | −2.68948e11 | −0.896896 | ||||||||
\(741\) | 4.12461e11 | 1.36808 | ||||||||
\(742\) | 3.91014e11 | 1.28996 | ||||||||
\(743\) | − | 7.42954e10i | − | 0.243785i | −0.992543 | − | 0.121892i | \(-0.961104\pi\) | ||
0.992543 | − | 0.121892i | \(-0.0388963\pi\) | |||||||
\(744\) | 5.20277e11 | 1.69802 | ||||||||
\(745\) | 1.76494e11 | 0.572934 | ||||||||
\(746\) | 1.80808e11 | 0.583797 | ||||||||
\(747\) | −3.01423e10 | −0.0968043 | ||||||||
\(748\) | −2.98487e11 | −0.953496 | ||||||||
\(749\) | 6.44461e10i | 0.204771i | ||||||||
\(750\) | 5.07185e11i | 1.60295i | ||||||||
\(751\) | − | 3.61993e10i | − | 0.113799i | −0.998380 | − | 0.0568997i | \(-0.981878\pi\) | ||
0.998380 | − | 0.0568997i | \(-0.0181215\pi\) | |||||||
\(752\) | −3.89917e11 | −1.21927 | ||||||||
\(753\) | − | 4.82746e11i | − | 1.50155i | ||||||
\(754\) | 3.83302e11 | 1.18592 | ||||||||
\(755\) | −1.60479e11 | −0.493890 | ||||||||
\(756\) | 6.31978e11 | 1.93471 | ||||||||
\(757\) | − | 1.37097e11i | − | 0.417489i | −0.977970 | − | 0.208744i | \(-0.933062\pi\) | ||
0.977970 | − | 0.208744i | \(-0.0669377\pi\) | |||||||
\(758\) | − | 8.51755e11i | − | 2.58011i | ||||||
\(759\) | 1.62613e11i | 0.489991i | ||||||||
\(760\) | 5.55301e11i | 1.66446i | ||||||||
\(761\) | − | 3.33327e10i | − | 0.0993876i | −0.998764 | − | 0.0496938i | \(-0.984175\pi\) | ||
0.998764 | − | 0.0496938i | \(-0.0158245\pi\) | |||||||
\(762\) | −1.91049e11 | −0.566662 | ||||||||
\(763\) | − | 7.79298e10i | − | 0.229935i | ||||||
\(764\) | − | 9.08365e11i | − | 2.66617i | ||||||
\(765\) | − | 1.12604e10i | − | 0.0328783i | ||||||
\(766\) | 5.06888e10 | 0.147230 | ||||||||
\(767\) | 6.45461e11 | 1.86504 | ||||||||
\(768\) | − | 1.17167e12i | − | 3.36792i | ||||||
\(769\) | −2.60316e11 | −0.744381 | −0.372190 | − | 0.928156i | \(-0.621393\pi\) | ||||
−0.372190 | + | 0.928156i | \(0.621393\pi\) | |||||||
\(770\) | − | 1.13458e11i | − | 0.322754i | ||||||
\(771\) | 2.66813e11 | 0.755073 | ||||||||
\(772\) | 1.44562e11 | 0.406992 | ||||||||
\(773\) | − | 4.75435e11i | − | 1.33160i | −0.746131 | − | 0.665799i | \(-0.768091\pi\) | ||
0.746131 | − | 0.665799i | \(-0.231909\pi\) | |||||||
\(774\) | 6.27119e10 | + | 2.58561e10i | 0.174738 | + | 0.0720442i | ||||
\(775\) | −1.41077e11 | −0.391066 | ||||||||
\(776\) | − | 7.57587e11i | − | 2.08923i | ||||||
\(777\) | 1.51193e11i | 0.414810i | ||||||||
\(778\) | 1.83819e11 | 0.501733 | ||||||||
\(779\) | 7.01350e11i | 1.90452i | ||||||||
\(780\) | −7.13243e11 | −1.92690 | ||||||||
\(781\) | − | 3.14358e11i | − | 0.844929i | ||||||
\(782\) | − | 5.09863e11i | − | 1.36341i | ||||||
\(783\) | −1.61914e11 | −0.430761 | ||||||||
\(784\) | 8.21899e11 | 2.17548 | ||||||||
\(785\) | −2.17930e11 | −0.573903 | ||||||||
\(786\) | 3.27984e11i | 0.859336i | ||||||||
\(787\) | 1.32872e11 | 0.346365 | 0.173182 | − | 0.984890i | \(-0.444595\pi\) | ||||
0.173182 | + | 0.984890i | \(0.444595\pi\) | |||||||
\(788\) | −1.30840e12 | −3.39341 | ||||||||
\(789\) | 1.25543e11 | 0.323956 | ||||||||
\(790\) | −4.05961e11 | −1.04226 | ||||||||
\(791\) | 1.20293e11 | 0.307281 | ||||||||
\(792\) | 6.63752e10i | 0.168696i | ||||||||
\(793\) | − | 1.44154e11i | − | 0.364531i | ||||||
\(794\) | − | 6.97566e11i | − | 1.75511i | ||||||
\(795\) | 1.86410e11 | 0.466660 | ||||||||
\(796\) | 2.79694e11i | 0.696676i | ||||||||
\(797\) | −2.24404e10 | −0.0556157 | −0.0278079 | − | 0.999613i | \(-0.508853\pi\) | ||||
−0.0278079 | + | 0.999613i | \(0.508853\pi\) | |||||||
\(798\) | 4.87899e11 | 1.20315 | ||||||||
\(799\) | 8.63782e10 | 0.211942 | ||||||||
\(800\) | 1.29624e12i | 3.16465i | ||||||||
\(801\) | − | 4.97490e10i | − | 0.120852i | ||||||
\(802\) | − | 4.74561e11i | − | 1.14708i | ||||||
\(803\) | 3.91658e11i | 0.941986i | ||||||||
\(804\) | − | 1.78547e12i | − | 4.27295i | ||||||
\(805\) | 1.42485e11 | 0.339301 | ||||||||
\(806\) | − | 6.27073e11i | − | 1.48586i | ||||||
\(807\) | − | 2.93047e10i | − | 0.0690943i | ||||||
\(808\) | − | 6.85149e11i | − | 1.60746i | ||||||
\(809\) | 5.81192e11 | 1.35683 | 0.678415 | − | 0.734679i | \(-0.262667\pi\) | ||||
0.678415 | + | 0.734679i | \(0.262667\pi\) | |||||||
\(810\) | 3.69564e11 | 0.858517 | ||||||||
\(811\) | 1.37076e11i | 0.316867i | 0.987370 | + | 0.158434i | \(0.0506444\pi\) | ||||
−0.987370 | + | 0.158434i | \(0.949356\pi\) | |||||||
\(812\) | 3.33345e11 | 0.766777 | ||||||||
\(813\) | 3.83581e11i | 0.878001i | ||||||||
\(814\) | −2.79993e11 | −0.637750 | ||||||||
\(815\) | 6.50099e10 | 0.147350 | ||||||||
\(816\) | 1.13222e12i | 2.55371i | ||||||||
\(817\) | 4.01567e11 | + | 1.65566e11i | 0.901300 | + | 0.371605i | ||||
\(818\) | 2.37715e11 | 0.530938 | ||||||||
\(819\) | − | 4.31991e10i | − | 0.0960150i | ||||||
\(820\) | − | 1.21280e12i | − | 2.68246i | ||||||
\(821\) | −1.00200e11 | −0.220544 | −0.110272 | − | 0.993901i | \(-0.535172\pi\) | ||||
−0.110272 | + | 0.993901i | \(0.535172\pi\) | |||||||
\(822\) | − | 8.91945e11i | − | 1.95367i | ||||||
\(823\) | 5.38250e11 | 1.17323 | 0.586617 | − | 0.809865i | \(-0.300460\pi\) | ||||
0.586617 | + | 0.809865i | \(0.300460\pi\) | |||||||
\(824\) | 2.49077e12i | 5.40288i | ||||||||
\(825\) | 1.67053e11i | 0.360611i | ||||||||
\(826\) | 7.63513e11 | 1.64020 | ||||||||
\(827\) | −7.72181e11 | −1.65081 | −0.825405 | − | 0.564541i | \(-0.809053\pi\) | ||||
−0.825405 | + | 0.564541i | \(0.809053\pi\) | |||||||
\(828\) | −1.30280e11 | −0.277176 | ||||||||
\(829\) | − | 4.98666e11i | − | 1.05582i | −0.849299 | − | 0.527912i | \(-0.822975\pi\) | ||
0.849299 | − | 0.527912i | \(-0.177025\pi\) | |||||||
\(830\) | 4.53976e11 | 0.956578 | ||||||||
\(831\) | −7.96332e11 | −1.66990 | ||||||||
\(832\) | −2.97874e12 | −6.21640 | ||||||||
\(833\) | −1.82075e11 | −0.378156 | ||||||||
\(834\) | −2.90131e11 | −0.599695 | ||||||||
\(835\) | 3.68741e10i | 0.0758535i | ||||||||
\(836\) | 6.64279e11i | 1.35996i | ||||||||
\(837\) | 2.64887e11i | 0.539708i | ||||||||
\(838\) | 6.80120e11 | 1.37914 | ||||||||
\(839\) | 4.50167e10i | 0.0908503i | 0.998968 | + | 0.0454251i | \(0.0144642\pi\) | ||||
−0.998968 | + | 0.0454251i | \(0.985536\pi\) | |||||||
\(840\) | −5.39817e11 | −1.08425 | ||||||||
\(841\) | 4.14843e11 | 0.829278 | ||||||||
\(842\) | −5.95134e11 | −1.18404 | ||||||||
\(843\) | − | 4.06007e11i | − | 0.803940i | ||||||
\(844\) | 2.36725e12i | 4.66524i | ||||||||
\(845\) | 2.97884e11i | 0.584279i | ||||||||
\(846\) | − | 3.00208e10i | − | 0.0586058i | ||||||
\(847\) | 2.57168e11i | 0.499670i | ||||||||
\(848\) | 2.01939e12 | 3.90514 | ||||||||
\(849\) | − | 5.28983e11i | − | 1.01815i | ||||||
\(850\) | − | 5.23786e11i | − | 1.00341i | ||||||
\(851\) | − | 3.51627e11i | − | 0.670446i | ||||||
\(852\) | −2.33762e12 | −4.43624 | ||||||||
\(853\) | 6.35607e10 | 0.120058 | 0.0600292 | − | 0.998197i | \(-0.480881\pi\) | ||||
0.0600292 | + | 0.998197i | \(0.480881\pi\) | |||||||
\(854\) | − | 1.70519e11i | − | 0.320584i | ||||||
\(855\) | −2.50600e10 | −0.0468939 | ||||||||
\(856\) | 5.67837e11i | 1.05762i | ||||||||
\(857\) | −3.04132e11 | −0.563818 | −0.281909 | − | 0.959441i | \(-0.590968\pi\) | ||||
−0.281909 | + | 0.959441i | \(0.590968\pi\) | |||||||
\(858\) | −7.42534e11 | −1.37015 | ||||||||
\(859\) | − | 8.70514e10i | − | 0.159883i | −0.996800 | − | 0.0799417i | \(-0.974527\pi\) | ||
0.996800 | − | 0.0799417i | \(-0.0254734\pi\) | |||||||
\(860\) | −6.94403e11 | − | 2.86302e11i | −1.26946 | − | 0.523396i | ||||
\(861\) | −6.81794e11 | −1.24062 | ||||||||
\(862\) | 5.15688e11i | 0.934024i | ||||||||
\(863\) | 6.30779e11i | 1.13719i | 0.822617 | + | 0.568596i | \(0.192513\pi\) | ||||
−0.822617 | + | 0.568596i | \(0.807487\pi\) | |||||||
\(864\) | 2.43382e12 | 4.36751 | ||||||||
\(865\) | 5.66928e10i | 0.101266i | ||||||||
\(866\) | −7.06152e9 | −0.0125553 | ||||||||
\(867\) | 2.86034e11i | 0.506223i | ||||||||
\(868\) | − | 5.45344e11i | − | 0.960708i | ||||||
\(869\) | −3.10720e11 | −0.544866 | ||||||||
\(870\) | 2.16155e11 | 0.377301 | ||||||||
\(871\) | −1.37689e12 | −2.39235 | ||||||||
\(872\) | − | 6.86642e11i | − | 1.18758i | ||||||
\(873\) | 3.41888e10 | 0.0588610 | ||||||||
\(874\) | −1.13469e12 | −1.94461 | ||||||||
\(875\) | 3.40146e11 | 0.580274 | ||||||||
\(876\) | 2.91243e12 | 4.94583 | ||||||||
\(877\) | 7.43976e11 | 1.25765 | 0.628826 | − | 0.777546i | \(-0.283536\pi\) | ||||
0.628826 | + | 0.777546i | \(0.283536\pi\) | |||||||
\(878\) | − | 1.13041e12i | − | 1.90220i | ||||||
\(879\) | 9.16999e11i | 1.53608i | ||||||||
\(880\) | − | 5.85953e11i | − | 0.977085i | ||||||
\(881\) | 2.51985e11 | 0.418283 | 0.209142 | − | 0.977885i | \(-0.432933\pi\) | ||||
0.209142 | + | 0.977885i | \(0.432933\pi\) | |||||||
\(882\) | 6.32804e10i | 0.104567i | ||||||||
\(883\) | 7.60754e11 | 1.25142 | 0.625708 | − | 0.780058i | \(-0.284810\pi\) | ||||
0.625708 | + | 0.780058i | \(0.284810\pi\) | |||||||
\(884\) | 1.71167e12 | 2.80293 | ||||||||
\(885\) | 3.63994e11 | 0.593363 | ||||||||
\(886\) | − | 1.55548e12i | − | 2.52423i | ||||||
\(887\) | 6.24953e11i | 1.00961i | 0.863234 | + | 0.504804i | \(0.168435\pi\) | ||||
−0.863234 | + | 0.504804i | \(0.831565\pi\) | |||||||
\(888\) | 1.33217e12i | 2.14244i | ||||||||
\(889\) | 1.28128e11i | 0.205133i | ||||||||
\(890\) | 7.49273e11i | 1.19421i | ||||||||
\(891\) | 2.82862e11 | 0.448811 | ||||||||
\(892\) | 2.06424e12i | 3.26063i | ||||||||
\(893\) | − | 1.92234e11i | − | 0.302290i | ||||||
\(894\) | − | 1.36634e12i | − | 2.13899i | ||||||
\(895\) | −5.67629e11 | −0.884653 | ||||||||
\(896\) | −1.71882e12 | −2.66684 | ||||||||
\(897\) | − | 9.32504e11i | − | 1.44039i | ||||||
\(898\) | −2.01066e12 | −3.09195 | ||||||||
\(899\) | 1.39718e11i | 0.213901i | ||||||||
\(900\) | −1.33837e11 | −0.203989 | ||||||||
\(901\) | −4.47355e11 | −0.678818 | ||||||||
\(902\) | − | 1.26261e12i | − | 1.90740i | ||||||
\(903\) | −1.60949e11 | + | 3.90369e11i | −0.242068 | + | 0.587117i | ||||
\(904\) | 1.05991e12 | 1.58707 | ||||||||
\(905\) | 2.46114e11i | 0.366894i | ||||||||
\(906\) | 1.24236e12i | 1.84388i | ||||||||
\(907\) | 9.82966e10 | 0.145248 | 0.0726238 | − | 0.997359i | \(-0.476863\pi\) | ||||
0.0726238 | + | 0.997359i | \(0.476863\pi\) | |||||||
\(908\) | − | 1.88737e12i | − | 2.77660i | ||||||
\(909\) | 3.09198e10 | 0.0452878 | ||||||||
\(910\) | 6.50624e11i | 0.948778i | ||||||||
\(911\) | − | 1.06133e11i | − | 0.154092i | −0.997028 | − | 0.0770458i | \(-0.975451\pi\) | ||
0.997028 | − | 0.0770458i | \(-0.0245488\pi\) | |||||||
\(912\) | 2.51975e12 | 3.64232 | ||||||||
\(913\) | 3.47470e11 | 0.500074 | ||||||||
\(914\) | −2.22508e12 | −3.18831 | ||||||||
\(915\) | − | 8.12927e10i | − | 0.115976i | ||||||
\(916\) | 4.31683e11 | 0.613173 | ||||||||
\(917\) | 2.19964e11 | 0.311082 | ||||||||
\(918\) | −9.83461e11 | −1.38480 | ||||||||
\(919\) | −4.81945e11 | −0.675671 | −0.337836 | − | 0.941205i | \(-0.609695\pi\) | ||||
−0.337836 | + | 0.941205i | \(0.609695\pi\) | |||||||
\(920\) | 1.25544e12 | 1.75245 | ||||||||
\(921\) | − | 4.64340e11i | − | 0.645353i | ||||||
\(922\) | − | 2.97342e11i | − | 0.411465i | ||||||
\(923\) | 1.80269e12i | 2.48378i | ||||||||
\(924\) | −6.45757e11 | −0.885892 | ||||||||
\(925\) | − | 3.61229e11i | − | 0.493418i | ||||||
\(926\) | 5.28414e11 | 0.718671 | ||||||||
\(927\) | −1.12405e11 | −0.152218 | ||||||||
\(928\) | 1.28375e12 | 1.73096 | ||||||||
\(929\) | 8.60540e11i | 1.15534i | 0.816272 | + | 0.577668i | \(0.196037\pi\) | ||||
−0.816272 | + | 0.577668i | \(0.803963\pi\) | |||||||
\(930\) | − | 3.53624e11i | − | 0.472727i | ||||||
\(931\) | 4.05207e11i | 0.539359i | ||||||||
\(932\) | − | 6.80030e11i | − | 0.901290i | ||||||
\(933\) | 9.59052e11i | 1.26566i | ||||||||
\(934\) | 1.52513e12 | 2.00409 | ||||||||
\(935\) | 1.29806e11i | 0.169844i | ||||||||
\(936\) | − | 3.80629e11i | − | 0.495905i | ||||||
\(937\) | 4.51510e11i | 0.585745i | 0.956151 | + | 0.292873i | \(0.0946112\pi\) | ||||
−0.956151 | + | 0.292873i | \(0.905389\pi\) | |||||||
\(938\) | −1.62871e12 | −2.10394 | ||||||||
\(939\) | −4.89201e11 | −0.629253 | ||||||||
\(940\) | 3.32418e11i | 0.425768i | ||||||||
\(941\) | −1.02846e11 | −0.131168 | −0.0655840 | − | 0.997847i | \(-0.520891\pi\) | ||||
−0.0655840 | + | 0.997847i | \(0.520891\pi\) | |||||||
\(942\) | 1.68712e12i | 2.14260i | ||||||||
\(943\) | 1.58563e12 | 2.00519 | ||||||||
\(944\) | 3.94316e12 | 4.96543 | ||||||||
\(945\) | − | 2.74835e11i | − | 0.344624i | ||||||
\(946\) | −7.22921e11 | − | 2.98060e11i | −0.902664 | − | 0.372168i | ||||
\(947\) | −7.66897e11 | −0.953536 | −0.476768 | − | 0.879029i | \(-0.658192\pi\) | ||||
−0.476768 | + | 0.879029i | \(0.658192\pi\) | |||||||
\(948\) | 2.31056e12i | 2.86078i | ||||||||
\(949\) | − | 2.24596e12i | − | 2.76909i | ||||||
\(950\) | −1.16568e12 | −1.43115 | ||||||||
\(951\) | − | 1.07973e12i | − | 1.32006i | ||||||
\(952\) | 1.29548e12 | 1.57718 | ||||||||
\(953\) | − | 1.03653e12i | − | 1.25663i | −0.777958 | − | 0.628317i | \(-0.783744\pi\) | ||
0.777958 | − | 0.628317i | \(-0.216256\pi\) | |||||||
\(954\) | 1.55479e11i | 0.187706i | ||||||||
\(955\) | −3.95031e11 | −0.474917 | ||||||||
\(956\) | −7.59213e10 | −0.0908933 | ||||||||
\(957\) | 1.65444e11 | 0.197243 | ||||||||
\(958\) | 1.00992e12i | 1.19902i | ||||||||
\(959\) | −5.98187e11 | −0.707233 | ||||||||
\(960\) | −1.67980e12 | −1.97775 | ||||||||
\(961\) | −6.24316e11 | −0.732000 | ||||||||
\(962\) | 1.60562e12 | 1.87475 | ||||||||
\(963\) | −2.56257e10 | −0.0297968 | ||||||||
\(964\) | − | 3.55632e12i | − | 4.11806i | ||||||
\(965\) | − | 6.28674e10i | − | 0.0724963i | ||||||
\(966\) | − | 1.10306e12i | − | 1.26674i | ||||||
\(967\) | 3.67231e11 | 0.419984 | 0.209992 | − | 0.977703i | \(-0.432656\pi\) | ||||
0.209992 | + | 0.977703i | \(0.432656\pi\) | |||||||
\(968\) | 2.26592e12i | 2.58073i | ||||||||
\(969\) | −5.58201e11 | −0.633134 | ||||||||
\(970\) | −5.14920e11 | −0.581638 | ||||||||
\(971\) | 1.05490e12 | 1.18668 | 0.593341 | − | 0.804951i | \(-0.297809\pi\) | ||||
0.593341 | + | 0.804951i | \(0.297809\pi\) | |||||||
\(972\) | 4.80312e11i | 0.538095i | ||||||||
\(973\) | 1.94578e11i | 0.217091i | ||||||||
\(974\) | 2.10430e12i | 2.33815i | ||||||||
\(975\) | − | 9.57968e11i | − | 1.06006i | ||||||
\(976\) | − | 8.80648e11i | − | 0.970516i | ||||||
\(977\) | −3.10125e11 | −0.340376 | −0.170188 | − | 0.985412i | \(-0.554438\pi\) | ||||
−0.170188 | + | 0.985412i | \(0.554438\pi\) | |||||||
\(978\) | − | 5.03278e11i | − | 0.550113i | ||||||
\(979\) | 5.73489e11i | 0.624302i | ||||||||
\(980\) | − | 7.00698e11i | − | 0.759673i | ||||||
\(981\) | 3.09872e10 | 0.0334585 | ||||||||
\(982\) | 1.65187e12 | 1.77636 | ||||||||
\(983\) | 5.39951e11i | 0.578282i | 0.957286 | + | 0.289141i | \(0.0933697\pi\) | ||||
−0.957286 | + | 0.289141i | \(0.906630\pi\) | |||||||
\(984\) | −6.00731e12 | −6.40766 | ||||||||
\(985\) | 5.68999e11i | 0.604459i | ||||||||
\(986\) | −5.18738e11 | −0.548833 | ||||||||
\(987\) | 1.86874e11 | 0.196915 | ||||||||
\(988\) | − | 3.80931e12i | − | 3.99778i | ||||||
\(989\) | 3.74315e11 | − | 9.07873e11i | 0.391248 | − | 0.948943i | ||||
\(990\) | 4.51142e10 | 0.0469648 | ||||||||
\(991\) | − | 1.96408e11i | − | 0.203641i | −0.994803 | − | 0.101821i | \(-0.967533\pi\) | ||
0.994803 | − | 0.101821i | \(-0.0324667\pi\) | |||||||
\(992\) | − | 2.10018e12i | − | 2.16875i | ||||||
\(993\) | −1.11665e12 | −1.14848 | ||||||||
\(994\) | 2.13239e12i | 2.18434i | ||||||||
\(995\) | 1.21634e11 | 0.124097 | ||||||||
\(996\) | − | 2.58385e12i | − | 2.62561i | ||||||
\(997\) | − | 1.02710e12i | − | 1.03952i | −0.854313 | − | 0.519758i | \(-0.826022\pi\) | ||
0.854313 | − | 0.519758i | \(-0.173978\pi\) | |||||||
\(998\) | −2.65543e12 | −2.67678 | ||||||||
\(999\) | −6.78244e11 | −0.680964 |
(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 | 43.9.b.b.42.27 | yes | 28 | |
43.42 | odd | 2 | inner | 43.9.b.b.42.2 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.9.b.b.42.2 | ✓ | 28 | 43.42 | odd | 2 | inner | |
43.9.b.b.42.27 | yes | 28 | 1.1 | even | 1 | trivial |