Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,7,Mod(22,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.22");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.8737317698\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.12 | ||
Character | \(\chi\) | \(=\) | 69.22 |
Dual form | 69.7.d.a.22.11 |
$q$-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 \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(47\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.69366 | −0.461708 | −0.230854 | − | 0.972988i | \(-0.574152\pi\) | ||||
−0.230854 | + | 0.972988i | \(0.574152\pi\) | |||||||
\(3\) | 15.5885 | 0.577350 | ||||||||
\(4\) | −50.3569 | −0.786826 | ||||||||
\(5\) | 218.943i | 1.75155i | 0.482723 | + | 0.875773i | \(0.339648\pi\) | ||||
−0.482723 | + | 0.875773i | \(0.660352\pi\) | |||||||
\(6\) | −57.5785 | −0.266567 | ||||||||
\(7\) | 261.444i | 0.762227i | 0.924528 | + | 0.381113i | \(0.124459\pi\) | ||||
−0.924528 | + | 0.381113i | \(0.875541\pi\) | |||||||
\(8\) | 422.396 | 0.824991 | ||||||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | − | 808.702i | − | 0.808702i | ||||||
\(11\) | − | 1771.61i | − | 1.33104i | −0.746380 | − | 0.665520i | \(-0.768210\pi\) | ||
0.746380 | − | 0.665520i | \(-0.231790\pi\) | |||||||
\(12\) | −784.986 | −0.454274 | ||||||||
\(13\) | −2889.11 | −1.31503 | −0.657513 | − | 0.753444i | \(-0.728391\pi\) | ||||
−0.657513 | + | 0.753444i | \(0.728391\pi\) | |||||||
\(14\) | − | 965.685i | − | 0.351926i | ||||||
\(15\) | 3412.99i | 1.01126i | ||||||||
\(16\) | 1662.65 | 0.405921 | ||||||||
\(17\) | 559.041i | 0.113788i | 0.998380 | + | 0.0568940i | \(0.0181197\pi\) | ||||
−0.998380 | + | 0.0568940i | \(0.981880\pi\) | |||||||
\(18\) | −897.560 | −0.153903 | ||||||||
\(19\) | 1593.98i | 0.232392i | 0.993226 | + | 0.116196i | \(0.0370701\pi\) | ||||
−0.993226 | + | 0.116196i | \(0.962930\pi\) | |||||||
\(20\) | − | 11025.3i | − | 1.37816i | ||||||
\(21\) | 4075.50i | 0.440072i | ||||||||
\(22\) | 6543.74i | 0.614552i | ||||||||
\(23\) | −11698.6 | + | 3343.37i | −0.961504 | + | 0.274790i | ||||
\(24\) | 6584.50 | 0.476309 | ||||||||
\(25\) | −32311.1 | −2.06791 | ||||||||
\(26\) | 10671.4 | 0.607157 | ||||||||
\(27\) | 3788.00 | 0.192450 | ||||||||
\(28\) | − | 13165.5i | − | 0.599740i | ||||||
\(29\) | −19917.0 | −0.816640 | −0.408320 | − | 0.912839i | \(-0.633885\pi\) | ||||
−0.408320 | + | 0.912839i | \(0.633885\pi\) | |||||||
\(30\) | − | 12606.4i | − | 0.466904i | ||||||
\(31\) | 14468.1 | 0.485652 | 0.242826 | − | 0.970070i | \(-0.421926\pi\) | ||||
0.242826 | + | 0.970070i | \(0.421926\pi\) | |||||||
\(32\) | −33174.6 | −1.01241 | ||||||||
\(33\) | − | 27616.7i | − | 0.768476i | ||||||
\(34\) | − | 2064.91i | − | 0.0525368i | ||||||
\(35\) | −57241.3 | −1.33507 | ||||||||
\(36\) | −12236.7 | −0.262275 | ||||||||
\(37\) | − | 63378.4i | − | 1.25123i | −0.780133 | − | 0.625613i | \(-0.784849\pi\) | ||
0.780133 | − | 0.625613i | \(-0.215151\pi\) | |||||||
\(38\) | − | 5887.61i | − | 0.107297i | ||||||
\(39\) | −45036.8 | −0.759230 | ||||||||
\(40\) | 92480.7i | 1.44501i | ||||||||
\(41\) | 4348.78 | 0.0630981 | 0.0315491 | − | 0.999502i | \(-0.489956\pi\) | ||||
0.0315491 | + | 0.999502i | \(0.489956\pi\) | |||||||
\(42\) | − | 15053.5i | − | 0.203185i | ||||||
\(43\) | − | 26412.8i | − | 0.332207i | −0.986108 | − | 0.166104i | \(-0.946881\pi\) | ||
0.986108 | − | 0.166104i | \(-0.0531186\pi\) | |||||||
\(44\) | 89212.9i | 1.04730i | ||||||||
\(45\) | 53203.2i | 0.583849i | ||||||||
\(46\) | 43210.8 | − | 12349.3i | 0.443934 | − | 0.126873i | ||||
\(47\) | −155401. | −1.49679 | −0.748394 | − | 0.663254i | \(-0.769175\pi\) | ||||
−0.748394 | + | 0.663254i | \(0.769175\pi\) | |||||||
\(48\) | 25918.2 | 0.234359 | ||||||||
\(49\) | 49296.2 | 0.419011 | ||||||||
\(50\) | 119346. | 0.954772 | ||||||||
\(51\) | 8714.59i | 0.0656956i | ||||||||
\(52\) | 145487. | 1.03470 | ||||||||
\(53\) | − | 119055.i | − | 0.799690i | −0.916583 | − | 0.399845i | \(-0.869064\pi\) | ||
0.916583 | − | 0.399845i | \(-0.130936\pi\) | |||||||
\(54\) | −13991.6 | −0.0888557 | ||||||||
\(55\) | 387883. | 2.33138 | ||||||||
\(56\) | 110433.i | 0.628830i | ||||||||
\(57\) | 24847.6i | 0.134172i | ||||||||
\(58\) | 73566.8 | 0.377049 | ||||||||
\(59\) | 235457. | 1.14645 | 0.573226 | − | 0.819398i | \(-0.305692\pi\) | ||||
0.573226 | + | 0.819398i | \(0.305692\pi\) | |||||||
\(60\) | − | 171867.i | − | 0.795682i | ||||||
\(61\) | 210647.i | 0.928036i | 0.885826 | + | 0.464018i | \(0.153593\pi\) | ||||
−0.885826 | + | 0.464018i | \(0.846407\pi\) | |||||||
\(62\) | −53440.1 | −0.224229 | ||||||||
\(63\) | 63530.8i | 0.254076i | ||||||||
\(64\) | 16126.0 | 0.0615157 | ||||||||
\(65\) | − | 632551.i | − | 2.30333i | ||||||
\(66\) | 102007.i | 0.354811i | ||||||||
\(67\) | 494703.i | 1.64483i | 0.568891 | + | 0.822413i | \(0.307373\pi\) | ||||
−0.568891 | + | 0.822413i | \(0.692627\pi\) | |||||||
\(68\) | − | 28151.5i | − | 0.0895314i | ||||||
\(69\) | −182363. | + | 52118.0i | −0.555125 | + | 0.158650i | ||||
\(70\) | 211430. | 0.616414 | ||||||||
\(71\) | −508838. | −1.42169 | −0.710844 | − | 0.703350i | \(-0.751687\pi\) | ||||
−0.710844 | + | 0.703350i | \(0.751687\pi\) | |||||||
\(72\) | 102642. | 0.274997 | ||||||||
\(73\) | −39370.7 | −0.101206 | −0.0506028 | − | 0.998719i | \(-0.516114\pi\) | ||||
−0.0506028 | + | 0.998719i | \(0.516114\pi\) | |||||||
\(74\) | 234098.i | 0.577701i | ||||||||
\(75\) | −503681. | −1.19391 | ||||||||
\(76\) | − | 80267.6i | − | 0.182852i | ||||||
\(77\) | 463177. | 1.01455 | ||||||||
\(78\) | 166351. | 0.350542 | ||||||||
\(79\) | 150541.i | 0.305333i | 0.988278 | + | 0.152667i | \(0.0487861\pi\) | ||||
−0.988278 | + | 0.152667i | \(0.951214\pi\) | |||||||
\(80\) | 364027.i | 0.710989i | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | −16062.9 | −0.0291329 | ||||||||
\(83\) | − | 226820.i | − | 0.396686i | −0.980133 | − | 0.198343i | \(-0.936444\pi\) | ||
0.980133 | − | 0.198343i | \(-0.0635560\pi\) | |||||||
\(84\) | − | 205230.i | − | 0.346260i | ||||||
\(85\) | −122398. | −0.199305 | ||||||||
\(86\) | 97560.0i | 0.153383i | ||||||||
\(87\) | −310476. | −0.471488 | ||||||||
\(88\) | − | 748322.i | − | 1.09810i | ||||||
\(89\) | 576409.i | 0.817637i | 0.912616 | + | 0.408819i | \(0.134059\pi\) | ||||
−0.912616 | + | 0.408819i | \(0.865941\pi\) | |||||||
\(90\) | − | 196515.i | − | 0.269567i | ||||||
\(91\) | − | 755340.i | − | 1.00235i | ||||||
\(92\) | 589106. | − | 168362.i | 0.756536 | − | 0.216212i | ||||
\(93\) | 225535. | 0.280391 | ||||||||
\(94\) | 573999. | 0.691079 | ||||||||
\(95\) | −348990. | −0.407045 | ||||||||
\(96\) | −517141. | −0.584514 | ||||||||
\(97\) | − | 973550.i | − | 1.06670i | −0.845894 | − | 0.533351i | \(-0.820932\pi\) | ||
0.845894 | − | 0.533351i | \(-0.179068\pi\) | |||||||
\(98\) | −182083. | −0.193460 | ||||||||
\(99\) | − | 430502.i | − | 0.443680i | ||||||
\(100\) | 1.62709e6 | 1.62709 | ||||||||
\(101\) | −1.22771e6 | −1.19160 | −0.595801 | − | 0.803132i | \(-0.703165\pi\) | ||||
−0.595801 | + | 0.803132i | \(0.703165\pi\) | |||||||
\(102\) | − | 32188.7i | − | 0.0303322i | ||||||
\(103\) | 1.71152e6i | 1.56628i | 0.621842 | + | 0.783142i | \(0.286384\pi\) | ||||
−0.621842 | + | 0.783142i | \(0.713616\pi\) | |||||||
\(104\) | −1.22035e6 | −1.08488 | ||||||||
\(105\) | −892304. | −0.770806 | ||||||||
\(106\) | 439751.i | 0.369223i | ||||||||
\(107\) | 2.25275e6i | 1.83891i | 0.393190 | + | 0.919457i | \(0.371371\pi\) | ||||
−0.393190 | + | 0.919457i | \(0.628629\pi\) | |||||||
\(108\) | −190752. | −0.151425 | ||||||||
\(109\) | 1.94287e6i | 1.50025i | 0.661293 | + | 0.750127i | \(0.270008\pi\) | ||||
−0.661293 | + | 0.750127i | \(0.729992\pi\) | |||||||
\(110\) | −1.43271e6 | −1.07642 | ||||||||
\(111\) | − | 987971.i | − | 0.722396i | ||||||
\(112\) | 434690.i | 0.309404i | ||||||||
\(113\) | − | 2.07914e6i | − | 1.44095i | −0.693481 | − | 0.720475i | \(-0.743924\pi\) | ||
0.693481 | − | 0.720475i | \(-0.256076\pi\) | |||||||
\(114\) | − | 91778.7i | − | 0.0619480i | ||||||
\(115\) | −732009. | − | 2.56133e6i | −0.481308 | − | 1.68412i | ||||
\(116\) | 1.00296e6 | 0.642554 | ||||||||
\(117\) | −702054. | −0.438342 | ||||||||
\(118\) | −869699. | −0.529325 | ||||||||
\(119\) | −146158. | −0.0867323 | ||||||||
\(120\) | 1.44163e6i | 0.834277i | ||||||||
\(121\) | −1.36706e6 | −0.771668 | ||||||||
\(122\) | − | 778057.i | − | 0.428481i | ||||||
\(123\) | 67790.8 | 0.0364297 | ||||||||
\(124\) | −728566. | −0.382124 | ||||||||
\(125\) | − | 3.65332e6i | − | 1.87050i | ||||||
\(126\) | − | 234661.i | − | 0.117309i | ||||||
\(127\) | 3.21735e6 | 1.57068 | 0.785339 | − | 0.619066i | \(-0.212489\pi\) | ||||
0.785339 | + | 0.619066i | \(0.212489\pi\) | |||||||
\(128\) | 2.06361e6 | 0.984006 | ||||||||
\(129\) | − | 411735.i | − | 0.191800i | ||||||
\(130\) | 2.33643e6i | 1.06346i | ||||||||
\(131\) | −1.76389e6 | −0.784618 | −0.392309 | − | 0.919834i | \(-0.628324\pi\) | ||||
−0.392309 | + | 0.919834i | \(0.628324\pi\) | |||||||
\(132\) | 1.39069e6i | 0.604657i | ||||||||
\(133\) | −416735. | −0.177135 | ||||||||
\(134\) | − | 1.82727e6i | − | 0.759429i | ||||||
\(135\) | 829356.i | 0.337085i | ||||||||
\(136\) | 236136.i | 0.0938742i | ||||||||
\(137\) | − | 2.12948e6i | − | 0.828154i | −0.910242 | − | 0.414077i | \(-0.864104\pi\) | ||
0.910242 | − | 0.414077i | \(-0.135896\pi\) | |||||||
\(138\) | 673589. | − | 192506.i | 0.256305 | − | 0.0732500i | ||||
\(139\) | 132686. | 0.0494060 | 0.0247030 | − | 0.999695i | \(-0.492136\pi\) | ||||
0.0247030 | + | 0.999695i | \(0.492136\pi\) | |||||||
\(140\) | 2.88249e6 | 1.05047 | ||||||||
\(141\) | −2.42246e6 | −0.864171 | ||||||||
\(142\) | 1.87947e6 | 0.656404 | ||||||||
\(143\) | 5.11839e6i | 1.75035i | ||||||||
\(144\) | 404025. | 0.135307 | ||||||||
\(145\) | − | 4.36070e6i | − | 1.43038i | ||||||
\(146\) | 145422. | 0.0467274 | ||||||||
\(147\) | 768451. | 0.241916 | ||||||||
\(148\) | 3.19154e6i | 0.984498i | ||||||||
\(149\) | 5.17537e6i | 1.56453i | 0.622949 | + | 0.782263i | \(0.285935\pi\) | ||||
−0.622949 | + | 0.782263i | \(0.714065\pi\) | |||||||
\(150\) | 1.86043e6 | 0.551238 | ||||||||
\(151\) | 1.40318e6 | 0.407550 | 0.203775 | − | 0.979018i | \(-0.434679\pi\) | ||||
0.203775 | + | 0.979018i | \(0.434679\pi\) | |||||||
\(152\) | 673288.i | 0.191721i | ||||||||
\(153\) | 135847.i | 0.0379294i | ||||||||
\(154\) | −1.71082e6 | −0.468428 | ||||||||
\(155\) | 3.16768e6i | 0.850642i | ||||||||
\(156\) | 2.26791e6 | 0.597382 | ||||||||
\(157\) | 4.35430e6i | 1.12517i | 0.826739 | + | 0.562586i | \(0.190194\pi\) | ||||
−0.826739 | + | 0.562586i | \(0.809806\pi\) | |||||||
\(158\) | − | 556048.i | − | 0.140975i | ||||||
\(159\) | − | 1.85589e6i | − | 0.461701i | ||||||
\(160\) | − | 7.26335e6i | − | 1.77328i | ||||||
\(161\) | −874104. | − | 3.05853e6i | −0.209452 | − | 0.732884i | ||||
\(162\) | −218107. | −0.0513009 | ||||||||
\(163\) | −6.04372e6 | −1.39554 | −0.697769 | − | 0.716323i | \(-0.745824\pi\) | ||||
−0.697769 | + | 0.716323i | \(0.745824\pi\) | |||||||
\(164\) | −218991. | −0.0496472 | ||||||||
\(165\) | 6.04650e6 | 1.34602 | ||||||||
\(166\) | 837796.i | 0.183153i | ||||||||
\(167\) | 5.03976e6 | 1.08208 | 0.541041 | − | 0.840996i | \(-0.318030\pi\) | ||||
0.541041 | + | 0.840996i | \(0.318030\pi\) | |||||||
\(168\) | 1.72147e6i | 0.363055i | ||||||||
\(169\) | 3.52015e6 | 0.729291 | ||||||||
\(170\) | 452098. | 0.0920207 | ||||||||
\(171\) | 387336.i | 0.0774640i | ||||||||
\(172\) | 1.33007e6i | 0.261389i | ||||||||
\(173\) | −2.13405e6 | −0.412161 | −0.206080 | − | 0.978535i | \(-0.566071\pi\) | ||||
−0.206080 | + | 0.978535i | \(0.566071\pi\) | |||||||
\(174\) | 1.14679e6 | 0.217689 | ||||||||
\(175\) | − | 8.44755e6i | − | 1.57622i | ||||||
\(176\) | − | 2.94558e6i | − | 0.540297i | ||||||
\(177\) | 3.67041e6 | 0.661904 | ||||||||
\(178\) | − | 2.12906e6i | − | 0.377509i | ||||||
\(179\) | −5.58887e6 | −0.974463 | −0.487231 | − | 0.873273i | \(-0.661993\pi\) | ||||
−0.487231 | + | 0.873273i | \(0.661993\pi\) | |||||||
\(180\) | − | 2.67915e6i | − | 0.459387i | ||||||
\(181\) | 4.82682e6i | 0.814001i | 0.913428 | + | 0.407001i | \(0.133425\pi\) | ||||
−0.913428 | + | 0.407001i | \(0.866575\pi\) | |||||||
\(182\) | 2.78997e6i | 0.462791i | ||||||||
\(183\) | 3.28365e6i | 0.535802i | ||||||||
\(184\) | −4.94145e6 | + | 1.41223e6i | −0.793233 | + | 0.226699i | ||||
\(185\) | 1.38763e7 | 2.19158 | ||||||||
\(186\) | −833049. | −0.129459 | ||||||||
\(187\) | 990405. | 0.151457 | ||||||||
\(188\) | 7.82551e6 | 1.17771 | ||||||||
\(189\) | 990348.i | 0.146691i | ||||||||
\(190\) | 1.28905e6 | 0.187936 | ||||||||
\(191\) | 7.07156e6i | 1.01488i | 0.861687 | + | 0.507440i | \(0.169408\pi\) | ||||
−0.861687 | + | 0.507440i | \(0.830592\pi\) | |||||||
\(192\) | 251379. | 0.0355161 | ||||||||
\(193\) | −1.35096e7 | −1.87919 | −0.939597 | − | 0.342284i | \(-0.888800\pi\) | ||||
−0.939597 | + | 0.342284i | \(0.888800\pi\) | |||||||
\(194\) | 3.59597e6i | 0.492505i | ||||||||
\(195\) | − | 9.86050e6i | − | 1.32983i | ||||||
\(196\) | −2.48240e6 | −0.329688 | ||||||||
\(197\) | −6.44400e6 | −0.842862 | −0.421431 | − | 0.906860i | \(-0.638472\pi\) | ||||
−0.421431 | + | 0.906860i | \(0.638472\pi\) | |||||||
\(198\) | 1.59013e6i | 0.204851i | ||||||||
\(199\) | 1.20114e6i | 0.152417i | 0.997092 | + | 0.0762084i | \(0.0242814\pi\) | ||||
−0.997092 | + | 0.0762084i | \(0.975719\pi\) | |||||||
\(200\) | −1.36481e7 | −1.70601 | ||||||||
\(201\) | 7.71166e6i | 0.949641i | ||||||||
\(202\) | 4.53474e6 | 0.550172 | ||||||||
\(203\) | − | 5.20719e6i | − | 0.622465i | ||||||
\(204\) | − | 438839.i | − | 0.0516910i | ||||||
\(205\) | 952137.i | 0.110519i | ||||||||
\(206\) | − | 6.32178e6i | − | 0.723166i | ||||||
\(207\) | −2.84277e6 | + | 812439.i | −0.320501 | + | 0.0915967i | ||||
\(208\) | −4.80359e6 | −0.533796 | ||||||||
\(209\) | 2.82391e6 | 0.309323 | ||||||||
\(210\) | 3.29587e6 | 0.355887 | ||||||||
\(211\) | 5.47137e6 | 0.582437 | 0.291218 | − | 0.956657i | \(-0.405939\pi\) | ||||
0.291218 | + | 0.956657i | \(0.405939\pi\) | |||||||
\(212\) | 5.99526e6i | 0.629217i | ||||||||
\(213\) | −7.93199e6 | −0.820812 | ||||||||
\(214\) | − | 8.32089e6i | − | 0.849041i | ||||||
\(215\) | 5.78290e6 | 0.581876 | ||||||||
\(216\) | 1.60003e6 | 0.158770 | ||||||||
\(217\) | 3.78258e6i | 0.370177i | ||||||||
\(218\) | − | 7.17632e6i | − | 0.692679i | ||||||
\(219\) | −613728. | −0.0584311 | ||||||||
\(220\) | −1.95326e7 | −1.83439 | ||||||||
\(221\) | − | 1.61513e6i | − | 0.149634i | ||||||
\(222\) | 3.64923e6i | 0.333536i | ||||||||
\(223\) | −1.00870e7 | −0.909590 | −0.454795 | − | 0.890596i | \(-0.650287\pi\) | ||||
−0.454795 | + | 0.890596i | \(0.650287\pi\) | |||||||
\(224\) | − | 8.67329e6i | − | 0.771684i | ||||||
\(225\) | −7.85161e6 | −0.689304 | ||||||||
\(226\) | 7.67965e6i | 0.665298i | ||||||||
\(227\) | − | 1.98153e7i | − | 1.69404i | −0.531560 | − | 0.847021i | \(-0.678394\pi\) | ||
0.531560 | − | 0.847021i | \(-0.321606\pi\) | |||||||
\(228\) | − | 1.25125e6i | − | 0.105570i | ||||||
\(229\) | 7.97432e6i | 0.664029i | 0.943274 | + | 0.332015i | \(0.107728\pi\) | ||||
−0.943274 | + | 0.332015i | \(0.892272\pi\) | |||||||
\(230\) | 2.70379e6 | + | 9.46070e6i | 0.222223 | + | 0.777571i | ||||
\(231\) | 7.22022e6 | 0.585753 | ||||||||
\(232\) | −8.41287e6 | −0.673721 | ||||||||
\(233\) | 5.30042e6 | 0.419028 | 0.209514 | − | 0.977806i | \(-0.432812\pi\) | ||||
0.209514 | + | 0.977806i | \(0.432812\pi\) | |||||||
\(234\) | 2.59315e6 | 0.202386 | ||||||||
\(235\) | − | 3.40240e7i | − | 2.62169i | ||||||
\(236\) | −1.18569e7 | −0.902058 | ||||||||
\(237\) | 2.34670e6i | 0.176284i | ||||||||
\(238\) | 539857. | 0.0400450 | ||||||||
\(239\) | −6.35315e6 | −0.465366 | −0.232683 | − | 0.972553i | \(-0.574751\pi\) | ||||
−0.232683 | + | 0.972553i | \(0.574751\pi\) | |||||||
\(240\) | 5.67461e6i | 0.410490i | ||||||||
\(241\) | 9.34983e6i | 0.667964i | 0.942580 | + | 0.333982i | \(0.108392\pi\) | ||||
−0.942580 | + | 0.333982i | \(0.891608\pi\) | |||||||
\(242\) | 5.04945e6 | 0.356285 | ||||||||
\(243\) | 920483. | 0.0641500 | ||||||||
\(244\) | − | 1.06075e7i | − | 0.730203i | ||||||
\(245\) | 1.07931e7i | 0.733916i | ||||||||
\(246\) | −250396. | −0.0168199 | ||||||||
\(247\) | − | 4.60517e6i | − | 0.305601i | ||||||
\(248\) | 6.11125e6 | 0.400659 | ||||||||
\(249\) | − | 3.53577e6i | − | 0.229027i | ||||||
\(250\) | 1.34941e7i | 0.863624i | ||||||||
\(251\) | − | 2.94710e6i | − | 0.186369i | −0.995649 | − | 0.0931847i | \(-0.970295\pi\) | ||
0.995649 | − | 0.0931847i | \(-0.0297047\pi\) | |||||||
\(252\) | − | 3.19921e6i | − | 0.199913i | ||||||
\(253\) | 5.92317e6 | + | 2.07254e7i | 0.365757 | + | 1.27980i | ||||
\(254\) | −1.18838e7 | −0.725194 | ||||||||
\(255\) | −1.90800e6 | −0.115069 | ||||||||
\(256\) | −8.65434e6 | −0.515839 | ||||||||
\(257\) | 593358. | 0.0349556 | 0.0174778 | − | 0.999847i | \(-0.494436\pi\) | ||||
0.0174778 | + | 0.999847i | \(0.494436\pi\) | |||||||
\(258\) | 1.52081e6i | 0.0885555i | ||||||||
\(259\) | 1.65699e7 | 0.953718 | ||||||||
\(260\) | 3.18533e7i | 1.81232i | ||||||||
\(261\) | −4.83984e6 | −0.272213 | ||||||||
\(262\) | 6.51522e6 | 0.362264 | ||||||||
\(263\) | − | 8.55513e6i | − | 0.470283i | −0.971961 | − | 0.235142i | \(-0.924445\pi\) | ||
0.971961 | − | 0.235142i | \(-0.0755554\pi\) | |||||||
\(264\) | − | 1.16652e7i | − | 0.633986i | ||||||
\(265\) | 2.60664e7 | 1.40069 | ||||||||
\(266\) | 1.53928e6 | 0.0817847 | ||||||||
\(267\) | 8.98532e6i | 0.472063i | ||||||||
\(268\) | − | 2.49117e7i | − | 1.29419i | ||||||
\(269\) | 2.39465e7 | 1.23023 | 0.615114 | − | 0.788439i | \(-0.289110\pi\) | ||||
0.615114 | + | 0.788439i | \(0.289110\pi\) | |||||||
\(270\) | − | 3.06336e6i | − | 0.155635i | ||||||
\(271\) | −8.20740e6 | −0.412380 | −0.206190 | − | 0.978512i | \(-0.566106\pi\) | ||||
−0.206190 | + | 0.978512i | \(0.566106\pi\) | |||||||
\(272\) | 929491.i | 0.0461890i | ||||||||
\(273\) | − | 1.17746e7i | − | 0.578705i | ||||||
\(274\) | 7.86557e6i | 0.382365i | ||||||||
\(275\) | 5.72429e7i | 2.75248i | ||||||||
\(276\) | 9.18325e6 | − | 2.62450e6i | 0.436787 | − | 0.124830i | ||||
\(277\) | 2.22467e7 | 1.04671 | 0.523356 | − | 0.852114i | \(-0.324680\pi\) | ||||
0.523356 | + | 0.852114i | \(0.324680\pi\) | |||||||
\(278\) | −490096. | −0.0228111 | ||||||||
\(279\) | 3.51574e6 | 0.161884 | ||||||||
\(280\) | −2.41785e7 | −1.10143 | ||||||||
\(281\) | − | 7.91487e6i | − | 0.356718i | −0.983965 | − | 0.178359i | \(-0.942921\pi\) | ||
0.983965 | − | 0.178359i | \(-0.0570788\pi\) | |||||||
\(282\) | 8.94776e6 | 0.398994 | ||||||||
\(283\) | − | 1.78585e6i | − | 0.0787928i | −0.999224 | − | 0.0393964i | \(-0.987456\pi\) | ||
0.999224 | − | 0.0393964i | \(-0.0125435\pi\) | |||||||
\(284\) | 2.56235e7 | 1.11862 | ||||||||
\(285\) | −5.44022e6 | −0.235008 | ||||||||
\(286\) | − | 1.89056e7i | − | 0.808151i | ||||||
\(287\) | 1.13696e6i | 0.0480951i | ||||||||
\(288\) | −8.06143e6 | −0.337469 | ||||||||
\(289\) | 2.38250e7 | 0.987052 | ||||||||
\(290\) | 1.61070e7i | 0.660419i | ||||||||
\(291\) | − | 1.51761e7i | − | 0.615861i | ||||||
\(292\) | 1.98258e6 | 0.0796312 | ||||||||
\(293\) | − | 4.56796e7i | − | 1.81602i | −0.418953 | − | 0.908008i | \(-0.637603\pi\) | ||
0.418953 | − | 0.908008i | \(-0.362397\pi\) | |||||||
\(294\) | −2.83840e6 | −0.111694 | ||||||||
\(295\) | 5.15517e7i | 2.00806i | ||||||||
\(296\) | − | 2.67708e7i | − | 1.03225i | ||||||
\(297\) | − | 6.71087e6i | − | 0.256159i | ||||||
\(298\) | − | 1.91161e7i | − | 0.722354i | ||||||
\(299\) | 3.37986e7 | − | 9.65937e6i | 1.26440 | − | 0.361356i | ||||
\(300\) | 2.53638e7 | 0.939400 | ||||||||
\(301\) | 6.90546e6 | 0.253217 | ||||||||
\(302\) | −5.18286e6 | −0.188169 | ||||||||
\(303\) | −1.91381e7 | −0.687972 | ||||||||
\(304\) | 2.65023e6i | 0.0943328i | ||||||||
\(305\) | −4.61196e7 | −1.62550 | ||||||||
\(306\) | − | 501773.i | − | 0.0175123i | ||||||
\(307\) | 5.19187e7 | 1.79436 | 0.897178 | − | 0.441670i | \(-0.145614\pi\) | ||||
0.897178 | + | 0.441670i | \(0.145614\pi\) | |||||||
\(308\) | −2.33242e7 | −0.798278 | ||||||||
\(309\) | 2.66800e7i | 0.904295i | ||||||||
\(310\) | − | 1.17004e7i | − | 0.392748i | ||||||
\(311\) | −3.85711e7 | −1.28227 | −0.641137 | − | 0.767426i | \(-0.721537\pi\) | ||||
−0.641137 | + | 0.767426i | \(0.721537\pi\) | |||||||
\(312\) | −1.90233e7 | −0.626358 | ||||||||
\(313\) | 5.22230e7i | 1.70306i | 0.524309 | + | 0.851528i | \(0.324324\pi\) | ||||
−0.524309 | + | 0.851528i | \(0.675676\pi\) | |||||||
\(314\) | − | 1.60833e7i | − | 0.519501i | ||||||
\(315\) | −1.39096e7 | −0.445025 | ||||||||
\(316\) | − | 7.58078e6i | − | 0.240244i | ||||||
\(317\) | 4.17049e7 | 1.30921 | 0.654605 | − | 0.755972i | \(-0.272835\pi\) | ||||
0.654605 | + | 0.755972i | \(0.272835\pi\) | |||||||
\(318\) | 6.85504e6i | 0.213171i | ||||||||
\(319\) | 3.52853e7i | 1.08698i | ||||||||
\(320\) | 3.53067e6i | 0.107747i | ||||||||
\(321\) | 3.51169e7i | 1.06170i | ||||||||
\(322\) | 3.22864e6 | + | 1.12972e7i | 0.0967058 | + | 0.338378i | ||||
\(323\) | −891098. | −0.0264434 | ||||||||
\(324\) | −2.97352e6 | −0.0874251 | ||||||||
\(325\) | 9.33505e7 | 2.71936 | ||||||||
\(326\) | 2.23235e7 | 0.644330 | ||||||||
\(327\) | 3.02864e7i | 0.866173i | ||||||||
\(328\) | 1.83691e6 | 0.0520554 | ||||||||
\(329\) | − | 4.06286e7i | − | 1.14089i | ||||||
\(330\) | −2.23337e7 | −0.621469 | ||||||||
\(331\) | −4.94227e7 | −1.36283 | −0.681417 | − | 0.731896i | \(-0.738636\pi\) | ||||
−0.681417 | + | 0.731896i | \(0.738636\pi\) | |||||||
\(332\) | 1.14219e7i | 0.312123i | ||||||||
\(333\) | − | 1.54010e7i | − | 0.417076i | ||||||
\(334\) | −1.86152e7 | −0.499606 | ||||||||
\(335\) | −1.08312e8 | −2.88099 | ||||||||
\(336\) | 6.77615e6i | 0.178634i | ||||||||
\(337\) | − | 7.33390e7i | − | 1.91622i | −0.286402 | − | 0.958110i | \(-0.592459\pi\) | ||
0.286402 | − | 0.958110i | \(-0.407541\pi\) | |||||||
\(338\) | −1.30022e7 | −0.336719 | ||||||||
\(339\) | − | 3.24106e7i | − | 0.831933i | ||||||
\(340\) | 6.16359e6 | 0.156818 | ||||||||
\(341\) | − | 2.56318e7i | − | 0.646423i | ||||||
\(342\) | − | 1.43069e6i | − | 0.0357657i | ||||||
\(343\) | 4.36468e7i | 1.08161i | ||||||||
\(344\) | − | 1.11567e7i | − | 0.274068i | ||||||
\(345\) | −1.14109e7 | − | 3.99272e7i | −0.277883 | − | 0.972326i | ||||
\(346\) | 7.88246e6 | 0.190298 | ||||||||
\(347\) | −7.00163e7 | −1.67576 | −0.837878 | − | 0.545857i | \(-0.816204\pi\) | ||||
−0.837878 | + | 0.545857i | \(0.816204\pi\) | |||||||
\(348\) | 1.56346e7 | 0.370979 | ||||||||
\(349\) | −4.25755e6 | −0.100157 | −0.0500787 | − | 0.998745i | \(-0.515947\pi\) | ||||
−0.0500787 | + | 0.998745i | \(0.515947\pi\) | |||||||
\(350\) | 3.12024e7i | 0.727752i | ||||||||
\(351\) | −1.09439e7 | −0.253077 | ||||||||
\(352\) | 5.87726e7i | 1.34756i | ||||||||
\(353\) | −2.44696e7 | −0.556292 | −0.278146 | − | 0.960539i | \(-0.589720\pi\) | ||||
−0.278146 | + | 0.960539i | \(0.589720\pi\) | |||||||
\(354\) | −1.35573e7 | −0.305606 | ||||||||
\(355\) | − | 1.11407e8i | − | 2.49015i | ||||||
\(356\) | − | 2.90261e7i | − | 0.643338i | ||||||
\(357\) | −2.27837e6 | −0.0500749 | ||||||||
\(358\) | 2.06434e7 | 0.449917 | ||||||||
\(359\) | 4.27662e7i | 0.924310i | 0.886799 | + | 0.462155i | \(0.152924\pi\) | ||||
−0.886799 | + | 0.462155i | \(0.847076\pi\) | |||||||
\(360\) | 2.24728e7i | 0.481670i | ||||||||
\(361\) | 4.45051e7 | 0.945994 | ||||||||
\(362\) | − | 1.78286e7i | − | 0.375831i | ||||||
\(363\) | −2.13103e7 | −0.445523 | ||||||||
\(364\) | 3.80365e7i | 0.788673i | ||||||||
\(365\) | − | 8.61995e6i | − | 0.177266i | ||||||
\(366\) | − | 1.21287e7i | − | 0.247384i | ||||||
\(367\) | − | 3.81457e7i | − | 0.771699i | −0.922562 | − | 0.385849i | \(-0.873908\pi\) | ||
0.922562 | − | 0.385849i | \(-0.126092\pi\) | |||||||
\(368\) | −1.94507e7 | + | 5.55887e6i | −0.390295 | + | 0.111543i | ||||
\(369\) | 1.05675e6 | 0.0210327 | ||||||||
\(370\) | −5.12543e7 | −1.01187 | ||||||||
\(371\) | 3.11263e7 | 0.609545 | ||||||||
\(372\) | −1.13572e7 | −0.220619 | ||||||||
\(373\) | − | 8.90738e7i | − | 1.71642i | −0.513299 | − | 0.858210i | \(-0.671577\pi\) | ||
0.513299 | − | 0.858210i | \(-0.328423\pi\) | |||||||
\(374\) | −3.65822e6 | −0.0699286 | ||||||||
\(375\) | − | 5.69496e7i | − | 1.07993i | ||||||
\(376\) | −6.56407e7 | −1.23484 | ||||||||
\(377\) | 5.75425e7 | 1.07390 | ||||||||
\(378\) | − | 3.65801e6i | − | 0.0677282i | ||||||
\(379\) | 6.77299e7i | 1.24412i | 0.782969 | + | 0.622061i | \(0.213704\pi\) | ||||
−0.782969 | + | 0.622061i | \(0.786296\pi\) | |||||||
\(380\) | 1.75741e7 | 0.320274 | ||||||||
\(381\) | 5.01535e7 | 0.906831 | ||||||||
\(382\) | − | 2.61199e7i | − | 0.468578i | ||||||
\(383\) | 2.59319e7i | 0.461570i | 0.973005 | + | 0.230785i | \(0.0741294\pi\) | ||||
−0.973005 | + | 0.230785i | \(0.925871\pi\) | |||||||
\(384\) | 3.21685e7 | 0.568116 | ||||||||
\(385\) | 1.01410e8i | 1.77704i | ||||||||
\(386\) | 4.99000e7 | 0.867638 | ||||||||
\(387\) | − | 6.41831e6i | − | 0.110736i | ||||||
\(388\) | 4.90249e7i | 0.839309i | ||||||||
\(389\) | 3.18918e7i | 0.541788i | 0.962609 | + | 0.270894i | \(0.0873193\pi\) | ||||
−0.962609 | + | 0.270894i | \(0.912681\pi\) | |||||||
\(390\) | 3.64213e7i | 0.613991i | ||||||||
\(391\) | −1.86908e6 | − | 6.54001e6i | −0.0312678 | − | 0.109408i | ||||
\(392\) | 2.08225e7 | 0.345680 | ||||||||
\(393\) | −2.74964e7 | −0.452999 | ||||||||
\(394\) | 2.38019e7 | 0.389156 | ||||||||
\(395\) | −3.29600e7 | −0.534805 | ||||||||
\(396\) | 2.16787e7i | 0.349099i | ||||||||
\(397\) | −6.02801e7 | −0.963391 | −0.481696 | − | 0.876339i | \(-0.659979\pi\) | ||||
−0.481696 | + | 0.876339i | \(0.659979\pi\) | |||||||
\(398\) | − | 4.43659e6i | − | 0.0703720i | ||||||
\(399\) | −6.49626e6 | −0.102269 | ||||||||
\(400\) | −5.37222e7 | −0.839410 | ||||||||
\(401\) | 8.25668e7i | 1.28048i | 0.768176 | + | 0.640239i | \(0.221165\pi\) | ||||
−0.768176 | + | 0.640239i | \(0.778835\pi\) | |||||||
\(402\) | − | 2.84842e7i | − | 0.438457i | ||||||
\(403\) | −4.17998e7 | −0.638645 | ||||||||
\(404\) | 6.18236e7 | 0.937583 | ||||||||
\(405\) | 1.29284e7i | 0.194616i | ||||||||
\(406\) | 1.92336e7i | 0.287397i | ||||||||
\(407\) | −1.12282e8 | −1.66543 | ||||||||
\(408\) | 3.68100e6i | 0.0541983i | ||||||||
\(409\) | 1.28874e8 | 1.88363 | 0.941816 | − | 0.336129i | \(-0.109118\pi\) | ||||
0.941816 | + | 0.336129i | \(0.109118\pi\) | |||||||
\(410\) | − | 3.51687e6i | − | 0.0510276i | ||||||
\(411\) | − | 3.31953e7i | − | 0.478135i | ||||||
\(412\) | − | 8.61869e7i | − | 1.23239i | ||||||
\(413\) | 6.15588e7i | 0.873856i | ||||||||
\(414\) | 1.05002e7 | − | 3.00088e6i | 0.147978 | − | 0.0422909i | ||||
\(415\) | 4.96607e7 | 0.694814 | ||||||||
\(416\) | 9.58451e7 | 1.33134 | ||||||||
\(417\) | 2.06837e6 | 0.0285246 | ||||||||
\(418\) | −1.04306e7 | −0.142817 | ||||||||
\(419\) | − | 3.80324e7i | − | 0.517025i | −0.966008 | − | 0.258513i | \(-0.916768\pi\) | ||
0.966008 | − | 0.258513i | \(-0.0832323\pi\) | |||||||
\(420\) | 4.49336e7 | 0.606490 | ||||||||
\(421\) | − | 2.33866e7i | − | 0.313416i | −0.987645 | − | 0.156708i | \(-0.949912\pi\) | ||
0.987645 | − | 0.156708i | \(-0.0500882\pi\) | |||||||
\(422\) | −2.02094e7 | −0.268916 | ||||||||
\(423\) | −3.77624e7 | −0.498929 | ||||||||
\(424\) | − | 5.02885e7i | − | 0.659738i | ||||||
\(425\) | − | 1.80633e7i | − | 0.235304i | ||||||
\(426\) | 2.92981e7 | 0.378975 | ||||||||
\(427\) | −5.50722e7 | −0.707374 | ||||||||
\(428\) | − | 1.13441e8i | − | 1.44691i | ||||||
\(429\) | 7.97878e7i | 1.01057i | ||||||||
\(430\) | −2.13601e7 | −0.268657 | ||||||||
\(431\) | 3.70034e7i | 0.462179i | 0.972932 | + | 0.231090i | \(0.0742290\pi\) | ||||
−0.972932 | + | 0.231090i | \(0.925771\pi\) | |||||||
\(432\) | 6.29812e6 | 0.0781195 | ||||||||
\(433\) | − | 1.05066e8i | − | 1.29419i | −0.762408 | − | 0.647096i | \(-0.775983\pi\) | ||
0.762408 | − | 0.647096i | \(-0.224017\pi\) | |||||||
\(434\) | − | 1.39716e7i | − | 0.170914i | ||||||
\(435\) | − | 6.79766e7i | − | 0.825832i | ||||||
\(436\) | − | 9.78370e7i | − | 1.18044i | ||||||
\(437\) | −5.32925e6 | − | 1.86473e7i | −0.0638590 | − | 0.223446i | ||||
\(438\) | 2.26691e6 | 0.0269781 | ||||||||
\(439\) | −4.23482e7 | −0.500543 | −0.250271 | − | 0.968176i | \(-0.580520\pi\) | ||||
−0.250271 | + | 0.968176i | \(0.580520\pi\) | |||||||
\(440\) | 1.63840e8 | 1.92337 | ||||||||
\(441\) | 1.19790e7 | 0.139670 | ||||||||
\(442\) | 5.96575e6i | 0.0690873i | ||||||||
\(443\) | −7.62775e7 | −0.877375 | −0.438688 | − | 0.898640i | \(-0.644557\pi\) | ||||
−0.438688 | + | 0.898640i | \(0.644557\pi\) | |||||||
\(444\) | 4.97511e7i | 0.568400i | ||||||||
\(445\) | −1.26201e8 | −1.43213 | ||||||||
\(446\) | 3.72578e7 | 0.419965 | ||||||||
\(447\) | 8.06760e7i | 0.903279i | ||||||||
\(448\) | 4.21603e6i | 0.0468889i | ||||||||
\(449\) | −2.09418e7 | −0.231353 | −0.115676 | − | 0.993287i | \(-0.536904\pi\) | ||||
−0.115676 | + | 0.993287i | \(0.536904\pi\) | |||||||
\(450\) | 2.90012e7 | 0.318257 | ||||||||
\(451\) | − | 7.70437e6i | − | 0.0839861i | ||||||
\(452\) | 1.04699e8i | 1.13378i | ||||||||
\(453\) | 2.18734e7 | 0.235299 | ||||||||
\(454\) | 7.31912e7i | 0.782152i | ||||||||
\(455\) | 1.65377e8 | 1.75566 | ||||||||
\(456\) | 1.04955e7i | 0.110690i | ||||||||
\(457\) | 1.44360e8i | 1.51251i | 0.654274 | + | 0.756257i | \(0.272974\pi\) | ||||
−0.654274 | + | 0.756257i | \(0.727026\pi\) | |||||||
\(458\) | − | 2.94544e7i | − | 0.306587i | ||||||
\(459\) | 2.11764e6i | 0.0218985i | ||||||||
\(460\) | 3.68617e7 | + | 1.28981e8i | 0.378705 | + | 1.32511i | ||||
\(461\) | 5.85463e7 | 0.597581 | 0.298790 | − | 0.954319i | \(-0.403417\pi\) | ||||
0.298790 | + | 0.954319i | \(0.403417\pi\) | |||||||
\(462\) | −2.66691e7 | −0.270447 | ||||||||
\(463\) | −3.56162e7 | −0.358843 | −0.179422 | − | 0.983772i | \(-0.557423\pi\) | ||||
−0.179422 | + | 0.983772i | \(0.557423\pi\) | |||||||
\(464\) | −3.31151e7 | −0.331492 | ||||||||
\(465\) | 4.93793e7i | 0.491118i | ||||||||
\(466\) | −1.95780e7 | −0.193468 | ||||||||
\(467\) | − | 9.94961e7i | − | 0.976912i | −0.872589 | − | 0.488456i | \(-0.837560\pi\) | ||
0.872589 | − | 0.488456i | \(-0.162440\pi\) | |||||||
\(468\) | 3.53532e7 | 0.344899 | ||||||||
\(469\) | −1.29337e8 | −1.25373 | ||||||||
\(470\) | 1.25673e8i | 1.21046i | ||||||||
\(471\) | 6.78768e7i | 0.649619i | ||||||||
\(472\) | 9.94560e7 | 0.945813 | ||||||||
\(473\) | −4.67933e7 | −0.442181 | ||||||||
\(474\) | − | 8.66793e6i | − | 0.0813918i | ||||||
\(475\) | − | 5.15032e7i | − | 0.480566i | ||||||
\(476\) | 7.36004e6 | 0.0682432 | ||||||||
\(477\) | − | 2.89305e7i | − | 0.266563i | ||||||
\(478\) | 2.34664e7 | 0.214863 | ||||||||
\(479\) | − | 1.73205e8i | − | 1.57599i | −0.615679 | − | 0.787997i | \(-0.711118\pi\) | ||
0.615679 | − | 0.787997i | \(-0.288882\pi\) | |||||||
\(480\) | − | 1.13224e8i | − | 1.02380i | ||||||
\(481\) | 1.83107e8i | 1.64539i | ||||||||
\(482\) | − | 3.45351e7i | − | 0.308404i | ||||||
\(483\) | −1.36259e7 | − | 4.76778e7i | −0.120927 | − | 0.423131i | ||||
\(484\) | 6.88407e7 | 0.607168 | ||||||||
\(485\) | 2.13152e8 | 1.86838 | ||||||||
\(486\) | −3.39995e6 | −0.0296186 | ||||||||
\(487\) | 4.78345e7 | 0.414147 | 0.207073 | − | 0.978325i | \(-0.433606\pi\) | ||||
0.207073 | + | 0.978325i | \(0.433606\pi\) | |||||||
\(488\) | 8.89762e7i | 0.765622i | ||||||||
\(489\) | −9.42123e7 | −0.805714 | ||||||||
\(490\) | − | 3.98659e7i | − | 0.338855i | ||||||
\(491\) | 1.10447e8 | 0.933059 | 0.466530 | − | 0.884506i | \(-0.345504\pi\) | ||||
0.466530 | + | 0.884506i | \(0.345504\pi\) | |||||||
\(492\) | −3.41373e6 | −0.0286638 | ||||||||
\(493\) | − | 1.11344e7i | − | 0.0929240i | ||||||
\(494\) | 1.70099e7i | 0.141098i | ||||||||
\(495\) | 9.42556e7 | 0.777126 | ||||||||
\(496\) | 2.40554e7 | 0.197136 | ||||||||
\(497\) | − | 1.33032e8i | − | 1.08365i | ||||||
\(498\) | 1.30600e7i | 0.105743i | ||||||||
\(499\) | 3.75153e7 | 0.301930 | 0.150965 | − | 0.988539i | \(-0.451762\pi\) | ||||
0.150965 | + | 0.988539i | \(0.451762\pi\) | |||||||
\(500\) | 1.83970e8i | 1.47176i | ||||||||
\(501\) | 7.85621e7 | 0.624741 | ||||||||
\(502\) | 1.08856e7i | 0.0860482i | ||||||||
\(503\) | 101609.i | 0.000798411i | 1.00000 | 0.000399205i | \(0.000127071\pi\) | |||||
−1.00000 | 0.000399205i | \(0.999873\pi\) | ||||||||
\(504\) | 2.68351e7i | 0.209610i | ||||||||
\(505\) | − | 2.68799e8i | − | 2.08715i | ||||||
\(506\) | −2.18782e7 | − | 7.65528e7i | −0.168873 | − | 0.590894i | ||||
\(507\) | 5.48737e7 | 0.421056 | ||||||||
\(508\) | −1.62016e8 | −1.23585 | ||||||||
\(509\) | 9.08093e7 | 0.688616 | 0.344308 | − | 0.938857i | \(-0.388114\pi\) | ||||
0.344308 | + | 0.938857i | \(0.388114\pi\) | |||||||
\(510\) | 7.04751e6 | 0.0531282 | ||||||||
\(511\) | − | 1.02932e7i | − | 0.0771416i | ||||||
\(512\) | −1.00105e8 | −0.745839 | ||||||||
\(513\) | 6.03797e6i | 0.0447238i | ||||||||
\(514\) | −2.19166e6 | −0.0161393 | ||||||||
\(515\) | −3.74726e8 | −2.74342 | ||||||||
\(516\) | 2.07337e7i | 0.150913i | ||||||||
\(517\) | 2.75311e8i | 1.99228i | ||||||||
\(518\) | −6.12036e7 | −0.440339 | ||||||||
\(519\) | −3.32666e7 | −0.237961 | ||||||||
\(520\) | − | 2.67187e8i | − | 1.90022i | ||||||
\(521\) | 1.52672e8i | 1.07956i | 0.841806 | + | 0.539779i | \(0.181492\pi\) | ||||
−0.841806 | + | 0.539779i | \(0.818508\pi\) | |||||||
\(522\) | 1.78767e7 | 0.125683 | ||||||||
\(523\) | − | 1.29320e8i | − | 0.903982i | −0.892023 | − | 0.451991i | \(-0.850714\pi\) | ||
0.892023 | − | 0.451991i | \(-0.149286\pi\) | |||||||
\(524\) | 8.88241e7 | 0.617358 | ||||||||
\(525\) | − | 1.31684e8i | − | 0.910030i | ||||||
\(526\) | 3.15998e7i | 0.217133i | ||||||||
\(527\) | 8.08824e6i | 0.0552614i | ||||||||
\(528\) | − | 4.59170e7i | − | 0.311941i | ||||||
\(529\) | 1.25680e8 | − | 7.82257e7i | 0.848981 | − | 0.528424i | ||||
\(530\) | −9.62805e7 | −0.646711 | ||||||||
\(531\) | 5.72161e7 | 0.382150 | ||||||||
\(532\) | 2.09855e7 | 0.139375 | ||||||||
\(533\) | −1.25641e7 | −0.0829756 | ||||||||
\(534\) | − | 3.31888e7i | − | 0.217955i | ||||||
\(535\) | −4.93224e8 | −3.22094 | ||||||||
\(536\) | 2.08960e8i | 1.35697i | ||||||||
\(537\) | −8.71219e7 | −0.562606 | ||||||||
\(538\) | −8.84503e7 | −0.568005 | ||||||||
\(539\) | − | 8.73338e7i | − | 0.557720i | ||||||
\(540\) | − | 4.17638e7i | − | 0.265227i | ||||||
\(541\) | 3.69700e7 | 0.233484 | 0.116742 | − | 0.993162i | \(-0.462755\pi\) | ||||
0.116742 | + | 0.993162i | \(0.462755\pi\) | |||||||
\(542\) | 3.03153e7 | 0.190399 | ||||||||
\(543\) | 7.52426e7i | 0.469964i | ||||||||
\(544\) | − | 1.85460e7i | − | 0.115200i | ||||||
\(545\) | −4.25379e8 | −2.62777 | ||||||||
\(546\) | 4.34913e7i | 0.267193i | ||||||||
\(547\) | −1.45850e8 | −0.891140 | −0.445570 | − | 0.895247i | \(-0.646999\pi\) | ||||
−0.445570 | + | 0.895247i | \(0.646999\pi\) | |||||||
\(548\) | 1.07234e8i | 0.651613i | ||||||||
\(549\) | 5.11871e7i | 0.309345i | ||||||||
\(550\) | − | 2.11436e8i | − | 1.27084i | ||||||
\(551\) | − | 3.17473e7i | − | 0.189781i | ||||||
\(552\) | −7.70295e7 | + | 2.20144e7i | −0.457973 | + | 0.130885i | ||||
\(553\) | −3.93580e7 | −0.232733 | ||||||||
\(554\) | −8.21719e7 | −0.483275 | ||||||||
\(555\) | 2.16310e8 | 1.26531 | ||||||||
\(556\) | −6.68164e6 | −0.0388739 | ||||||||
\(557\) | 1.78399e8i | 1.03235i | 0.856483 | + | 0.516175i | \(0.172645\pi\) | ||||
−0.856483 | + | 0.516175i | \(0.827355\pi\) | |||||||
\(558\) | −1.29860e7 | −0.0747431 | ||||||||
\(559\) | 7.63095e7i | 0.436861i | ||||||||
\(560\) | −9.51725e7 | −0.541935 | ||||||||
\(561\) | 1.54389e7 | 0.0874435 | ||||||||
\(562\) | 2.92349e7i | 0.164699i | ||||||||
\(563\) | − | 1.68361e8i | − | 0.943442i | −0.881748 | − | 0.471721i | \(-0.843633\pi\) | ||
0.881748 | − | 0.471721i | \(-0.156367\pi\) | |||||||
\(564\) | 1.21988e8 | 0.679952 | ||||||||
\(565\) | 4.55214e8 | 2.52389 | ||||||||
\(566\) | 6.59634e6i | 0.0363792i | ||||||||
\(567\) | 1.54380e7i | 0.0846918i | ||||||||
\(568\) | −2.14931e8 | −1.17288 | ||||||||
\(569\) | 1.19163e8i | 0.646852i | 0.946253 | + | 0.323426i | \(0.104835\pi\) | ||||
−0.946253 | + | 0.323426i | \(0.895165\pi\) | |||||||
\(570\) | 2.00943e7 | 0.108505 | ||||||||
\(571\) | 2.59509e7i | 0.139394i | 0.997568 | + | 0.0696970i | \(0.0222032\pi\) | ||||
−0.997568 | + | 0.0696970i | \(0.977797\pi\) | |||||||
\(572\) | − | 2.57746e8i | − | 1.37722i | ||||||
\(573\) | 1.10235e8i | 0.585942i | ||||||||
\(574\) | − | 4.19956e6i | − | 0.0222059i | ||||||
\(575\) | 3.77996e8 | − | 1.08028e8i | 1.98831 | − | 0.568242i | ||||
\(576\) | 3.91861e6 | 0.0205052 | ||||||||
\(577\) | 8.32275e7 | 0.433251 | 0.216625 | − | 0.976255i | \(-0.430495\pi\) | ||||
0.216625 | + | 0.976255i | \(0.430495\pi\) | |||||||
\(578\) | −8.80017e7 | −0.455730 | ||||||||
\(579\) | −2.10594e8 | −1.08495 | ||||||||
\(580\) | 2.19591e8i | 1.12546i | ||||||||
\(581\) | 5.93007e7 | 0.302365 | ||||||||
\(582\) | 5.60556e7i | 0.284348i | ||||||||
\(583\) | −2.10920e8 | −1.06442 | ||||||||
\(584\) | −1.66300e7 | −0.0834937 | ||||||||
\(585\) | − | 1.53710e8i | − | 0.767776i | ||||||
\(586\) | 1.68725e8i | 0.838468i | ||||||||
\(587\) | −6.50290e6 | −0.0321509 | −0.0160754 | − | 0.999871i | \(-0.505117\pi\) | ||||
−0.0160754 | + | 0.999871i | \(0.505117\pi\) | |||||||
\(588\) | −3.86968e7 | −0.190346 | ||||||||
\(589\) | 2.30617e7i | 0.112862i | ||||||||
\(590\) | − | 1.90415e8i | − | 0.927138i | ||||||
\(591\) | −1.00452e8 | −0.486627 | ||||||||
\(592\) | − | 1.05376e8i | − | 0.507899i | ||||||
\(593\) | 7.43776e7 | 0.356680 | 0.178340 | − | 0.983969i | \(-0.442927\pi\) | ||||
0.178340 | + | 0.983969i | \(0.442927\pi\) | |||||||
\(594\) | 2.47877e7i | 0.118270i | ||||||||
\(595\) | − | 3.20002e7i | − | 0.151916i | ||||||
\(596\) | − | 2.60615e8i | − | 1.23101i | ||||||
\(597\) | 1.87238e7i | 0.0879978i | ||||||||
\(598\) | −1.24841e8 | + | 3.56784e7i | −0.583784 | + | 0.166841i | ||||
\(599\) | 1.01274e8 | 0.471213 | 0.235606 | − | 0.971849i | \(-0.424292\pi\) | ||||
0.235606 | + | 0.971849i | \(0.424292\pi\) | |||||||
\(600\) | −2.12753e8 | −0.984966 | ||||||||
\(601\) | 2.15901e8 | 0.994561 | 0.497281 | − | 0.867590i | \(-0.334332\pi\) | ||||
0.497281 | + | 0.867590i | \(0.334332\pi\) | |||||||
\(602\) | −2.55064e7 | −0.116912 | ||||||||
\(603\) | 1.20213e8i | 0.548275i | ||||||||
\(604\) | −7.06595e7 | −0.320671 | ||||||||
\(605\) | − | 2.99308e8i | − | 1.35161i | ||||||
\(606\) | 7.06896e7 | 0.317642 | ||||||||
\(607\) | 3.76162e8 | 1.68193 | 0.840966 | − | 0.541088i | \(-0.181987\pi\) | ||||
0.840966 | + | 0.541088i | \(0.181987\pi\) | |||||||
\(608\) | − | 5.28795e7i | − | 0.235275i | ||||||
\(609\) | − | 8.11720e7i | − | 0.359380i | ||||||
\(610\) | 1.70350e8 | 0.750505 | ||||||||
\(611\) | 4.48971e8 | 1.96831 | ||||||||
\(612\) | − | 6.84083e6i | − | 0.0298438i | ||||||
\(613\) | 2.12207e8i | 0.921250i | 0.887595 | + | 0.460625i | \(0.152375\pi\) | ||||
−0.887595 | + | 0.460625i | \(0.847625\pi\) | |||||||
\(614\) | −1.91770e8 | −0.828468 | ||||||||
\(615\) | 1.48423e7i | 0.0638083i | ||||||||
\(616\) | 1.95644e8 | 0.836998 | ||||||||
\(617\) | 2.28882e8i | 0.974443i | 0.873278 | + | 0.487222i | \(0.161990\pi\) | ||||
−0.873278 | + | 0.487222i | \(0.838010\pi\) | |||||||
\(618\) | − | 9.85468e7i | − | 0.417520i | ||||||
\(619\) | 2.46253e8i | 1.03827i | 0.854693 | + | 0.519133i | \(0.173745\pi\) | ||||
−0.854693 | + | 0.519133i | \(0.826255\pi\) | |||||||
\(620\) | − | 1.59515e8i | − | 0.669307i | ||||||
\(621\) | −4.43143e7 | + | 1.26647e7i | −0.185042 | + | 0.0528834i | ||||
\(622\) | 1.42469e8 | 0.592036 | ||||||||
\(623\) | −1.50698e8 | −0.623225 | ||||||||
\(624\) | −7.48805e7 | −0.308187 | ||||||||
\(625\) | 2.95008e8 | 1.20835 | ||||||||
\(626\) | − | 1.92894e8i | − | 0.786314i | ||||||
\(627\) | 4.40204e7 | 0.178588 | ||||||||
\(628\) | − | 2.19269e8i | − | 0.885315i | ||||||
\(629\) | 3.54311e7 | 0.142375 | ||||||||
\(630\) | 5.13775e7 | 0.205471 | ||||||||
\(631\) | − | 7.39331e7i | − | 0.294273i | −0.989116 | − | 0.147137i | \(-0.952994\pi\) | ||
0.989116 | − | 0.147137i | \(-0.0470057\pi\) | |||||||
\(632\) | 6.35879e7i | 0.251897i | ||||||||
\(633\) | 8.52903e7 | 0.336270 | ||||||||
\(634\) | −1.54044e8 | −0.604472 | ||||||||
\(635\) | 7.04417e8i | 2.75111i | ||||||||
\(636\) | 9.34569e7i | 0.363279i | ||||||||
\(637\) | −1.42422e8 | −0.551010 | ||||||||
\(638\) | − | 1.30332e8i | − | 0.501868i | ||||||
\(639\) | −1.23648e8 | −0.473896 | ||||||||
\(640\) | 4.51814e8i | 1.72353i | ||||||||
\(641\) | 4.71156e8i | 1.78892i | 0.447149 | + | 0.894460i | \(0.352439\pi\) | ||||
−0.447149 | + | 0.894460i | \(0.647561\pi\) | |||||||
\(642\) | − | 1.29710e8i | − | 0.490194i | ||||||
\(643\) | 4.36101e8i | 1.64042i | 0.572065 | + | 0.820208i | \(0.306143\pi\) | ||||
−0.572065 | + | 0.820208i | \(0.693857\pi\) | |||||||
\(644\) | 4.40171e7 | + | 1.54018e8i | 0.164803 | + | 0.576652i | ||||
\(645\) | 9.01466e7 | 0.335946 | ||||||||
\(646\) | 3.29141e6 | 0.0122091 | ||||||||
\(647\) | 2.21024e8 | 0.816067 | 0.408034 | − | 0.912967i | \(-0.366215\pi\) | ||||
0.408034 | + | 0.912967i | \(0.366215\pi\) | |||||||
\(648\) | 2.49420e7 | 0.0916657 | ||||||||
\(649\) | − | 4.17139e8i | − | 1.52597i | ||||||
\(650\) | −3.44805e8 | −1.25555 | ||||||||
\(651\) | 5.89647e7i | 0.213722i | ||||||||
\(652\) | 3.04343e8 | 1.09805 | ||||||||
\(653\) | −1.19383e8 | −0.428749 | −0.214374 | − | 0.976752i | \(-0.568771\pi\) | ||||
−0.214374 | + | 0.976752i | \(0.568771\pi\) | |||||||
\(654\) | − | 1.11868e8i | − | 0.399919i | ||||||
\(655\) | − | 3.86192e8i | − | 1.37429i | ||||||
\(656\) | 7.23052e6 | 0.0256129 | ||||||||
\(657\) | −9.56708e6 | −0.0337352 | ||||||||
\(658\) | 1.50068e8i | 0.526758i | ||||||||
\(659\) | − | 3.11263e8i | − | 1.08760i | −0.839213 | − | 0.543802i | \(-0.816984\pi\) | ||
0.839213 | − | 0.543802i | \(-0.183016\pi\) | |||||||
\(660\) | −3.04483e8 | −1.05908 | ||||||||
\(661\) | − | 1.51166e8i | − | 0.523421i | −0.965146 | − | 0.261710i | \(-0.915714\pi\) | ||
0.965146 | − | 0.261710i | \(-0.0842865\pi\) | |||||||
\(662\) | 1.82551e8 | 0.629231 | ||||||||
\(663\) | − | 2.51774e7i | − | 0.0863913i | ||||||
\(664\) | − | 9.58078e7i | − | 0.327263i | ||||||
\(665\) | − | 9.12413e7i | − | 0.310261i | ||||||
\(666\) | 5.68859e7i | 0.192567i | ||||||||
\(667\) | 2.33002e8 | − | 6.65901e7i | 0.785203 | − | 0.224405i | ||||
\(668\) | −2.53787e8 | −0.851411 | ||||||||
\(669\) | −1.57240e8 | −0.525152 | ||||||||
\(670\) | 4.00067e8 | 1.33017 | ||||||||
\(671\) | 3.73184e8 | 1.23525 | ||||||||
\(672\) | − | 1.35203e8i | − | 0.445532i | ||||||
\(673\) | 4.67833e6 | 0.0153478 | 0.00767389 | − | 0.999971i | \(-0.497557\pi\) | ||||
0.00767389 | + | 0.999971i | \(0.497557\pi\) | |||||||
\(674\) | 2.70889e8i | 0.884733i | ||||||||
\(675\) | −1.22394e8 | −0.397970 | ||||||||
\(676\) | −1.77264e8 | −0.573825 | ||||||||
\(677\) | − | 1.72661e8i | − | 0.556454i | −0.960515 | − | 0.278227i | \(-0.910253\pi\) | ||
0.960515 | − | 0.278227i | \(-0.0897468\pi\) | |||||||
\(678\) | 1.19714e8i | 0.384110i | ||||||||
\(679\) | 2.54529e8 | 0.813069 | ||||||||
\(680\) | −5.17005e7 | −0.164425 | ||||||||
\(681\) | − | 3.08891e8i | − | 0.978056i | ||||||
\(682\) | 9.46753e7i | 0.298458i | ||||||||
\(683\) | −4.96528e8 | −1.55841 | −0.779205 | − | 0.626769i | \(-0.784377\pi\) | ||||
−0.779205 | + | 0.626769i | \(0.784377\pi\) | |||||||
\(684\) | − | 1.95050e7i | − | 0.0609507i | ||||||
\(685\) | 4.66235e8 | 1.45055 | ||||||||
\(686\) | − | 1.61216e8i | − | 0.499387i | ||||||
\(687\) | 1.24307e8i | 0.383377i | ||||||||
\(688\) | − | 4.39153e7i | − | 0.134850i | ||||||
\(689\) | 3.43964e8i | 1.05161i | ||||||||
\(690\) | 4.21480e7 | + | 1.47478e8i | 0.128301 | + | 0.448931i | ||||
\(691\) | 3.22850e8 | 0.978512 | 0.489256 | − | 0.872140i | \(-0.337268\pi\) | ||||
0.489256 | + | 0.872140i | \(0.337268\pi\) | |||||||
\(692\) | 1.07464e8 | 0.324299 | ||||||||
\(693\) | 1.12552e8 | 0.338185 | ||||||||
\(694\) | 2.58617e8 | 0.773710 | ||||||||
\(695\) | 2.90506e7i | 0.0865369i | ||||||||
\(696\) | −1.31144e8 | −0.388973 | ||||||||
\(697\) | 2.43115e6i | 0.00717981i | ||||||||
\(698\) | 1.57259e7 | 0.0462435 | ||||||||
\(699\) | 8.26254e7 | 0.241926 | ||||||||
\(700\) | 4.25392e8i | 1.24021i | ||||||||
\(701\) | − | 7.25912e7i | − | 0.210732i | −0.994434 | − | 0.105366i | \(-0.966399\pi\) | ||
0.994434 | − | 0.105366i | \(-0.0336014\pi\) | |||||||
\(702\) | 4.04232e7 | 0.116847 | ||||||||
\(703\) | 1.01024e8 | 0.290775 | ||||||||
\(704\) | − | 2.85690e7i | − | 0.0818798i | ||||||
\(705\) | − | 5.30382e8i | − | 1.51364i | ||||||
\(706\) | 9.03824e7 | 0.256844 | ||||||||
\(707\) | − | 3.20977e8i | − | 0.908271i | ||||||
\(708\) | −1.84830e8 | −0.520803 | ||||||||
\(709\) | − | 3.61431e8i | − | 1.01411i | −0.861912 | − | 0.507057i | \(-0.830733\pi\) | ||
0.861912 | − | 0.507057i | \(-0.169267\pi\) | |||||||
\(710\) | 4.11498e8i | 1.14972i | ||||||||
\(711\) | 3.65815e7i | 0.101778i | ||||||||
\(712\) | 2.43473e8i | 0.674544i | ||||||||
\(713\) | −1.69256e8 | + | 4.83721e7i | −0.466957 | + | 0.133452i | ||||
\(714\) | 8.41554e6 | 0.0231200 | ||||||||
\(715\) | −1.12064e9 | −3.06582 | ||||||||
\(716\) | 2.81438e8 | 0.766733 | ||||||||
\(717\) | −9.90357e7 | −0.268679 | ||||||||
\(718\) | − | 1.57964e8i | − | 0.426761i | ||||||
\(719\) | −3.68121e8 | −0.990384 | −0.495192 | − | 0.868784i | \(-0.664902\pi\) | ||||
−0.495192 | + | 0.868784i | \(0.664902\pi\) | |||||||
\(720\) | 8.84585e7i | 0.236996i | ||||||||
\(721\) | −4.47467e8 | −1.19386 | ||||||||
\(722\) | −1.64387e8 | −0.436773 | ||||||||
\(723\) | 1.45749e8i | 0.385649i | ||||||||
\(724\) | − | 2.43063e8i | − | 0.640478i | ||||||
\(725\) | 6.43542e8 | 1.68874 | ||||||||
\(726\) | 7.87131e7 | 0.205701 | ||||||||
\(727\) | 4.93322e8i | 1.28389i | 0.766751 | + | 0.641944i | \(0.221872\pi\) | ||||
−0.766751 | + | 0.641944i | \(0.778128\pi\) | |||||||
\(728\) | − | 3.19052e8i | − | 0.826928i | ||||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | 3.18392e7i | 0.0818452i | ||||||||
\(731\) | 1.47658e7 | 0.0378012 | ||||||||
\(732\) | − | 1.65355e8i | − | 0.421583i | ||||||
\(733\) | − | 6.84962e8i | − | 1.73922i | −0.493738 | − | 0.869611i | \(-0.664370\pi\) | ||
0.493738 | − | 0.869611i | \(-0.335630\pi\) | |||||||
\(734\) | 1.40897e8i | 0.356299i | ||||||||
\(735\) | 1.68247e8i | 0.423727i | ||||||||
\(736\) | 3.88097e8 | − | 1.10915e8i | 0.973435 | − | 0.278200i | ||||
\(737\) | 8.76423e8 | 2.18933 | ||||||||
\(738\) | −3.90329e6 | −0.00971096 | ||||||||
\(739\) | −2.60679e8 | −0.645911 | −0.322956 | − | 0.946414i | \(-0.604676\pi\) | ||||
−0.322956 | + | 0.946414i | \(0.604676\pi\) | |||||||
\(740\) | −6.98766e8 | −1.72439 | ||||||||
\(741\) | − | 7.17875e7i | − | 0.176439i | ||||||
\(742\) | −1.14970e8 | −0.281432 | ||||||||
\(743\) | − | 6.77473e7i | − | 0.165168i | −0.996584 | − | 0.0825839i | \(-0.973683\pi\) | ||
0.996584 | − | 0.0825839i | \(-0.0263172\pi\) | |||||||
\(744\) | 9.52649e7 | 0.231320 | ||||||||
\(745\) | −1.13311e9 | −2.74034 | ||||||||
\(746\) | 3.29008e8i | 0.792484i | ||||||||
\(747\) | − | 5.51173e7i | − | 0.132229i | ||||||
\(748\) | −4.98737e7 | −0.119170 | ||||||||
\(749\) | −5.88967e8 | −1.40167 | ||||||||
\(750\) | 2.10353e8i | 0.498613i | ||||||||
\(751\) | − | 1.58709e8i | − | 0.374698i | −0.982293 | − | 0.187349i | \(-0.940010\pi\) | ||
0.982293 | − | 0.187349i | \(-0.0599896\pi\) | |||||||
\(752\) | −2.58378e8 | −0.607578 | ||||||||
\(753\) | − | 4.59408e7i | − | 0.107600i | ||||||
\(754\) | −2.12543e8 | −0.495829 | ||||||||
\(755\) | 3.07216e8i | 0.713843i | ||||||||
\(756\) | − | 4.98708e7i | − | 0.115420i | ||||||
\(757\) | 4.53416e8i | 1.04522i | 0.852571 | + | 0.522612i | \(0.175042\pi\) | ||||
−0.852571 | + | 0.522612i | \(0.824958\pi\) | |||||||
\(758\) | − | 2.50171e8i | − | 0.574421i | ||||||
\(759\) | 9.23330e7 | + | 3.23078e8i | 0.211170 | + | 0.738893i | ||||
\(760\) | −1.47412e8 | −0.335809 | ||||||||
\(761\) | 1.89469e8 | 0.429917 | 0.214958 | − | 0.976623i | \(-0.431038\pi\) | ||||
0.214958 | + | 0.976623i | \(0.431038\pi\) | |||||||
\(762\) | −1.85250e8 | −0.418691 | ||||||||
\(763\) | −5.07952e8 | −1.14353 | ||||||||
\(764\) | − | 3.56101e8i | − | 0.798534i | ||||||
\(765\) | −2.97428e7 | −0.0664350 | ||||||||
\(766\) | − | 9.57836e7i | − | 0.213110i | ||||||
\(767\) | −6.80261e8 | −1.50761 | ||||||||
\(768\) | −1.34908e8 | −0.297820 | ||||||||
\(769\) | 4.26727e8i | 0.938363i | 0.883102 | + | 0.469182i | \(0.155451\pi\) | ||||
−0.883102 | + | 0.469182i | \(0.844549\pi\) | |||||||
\(770\) | − | 3.74573e8i | − | 0.820472i | ||||||
\(771\) | 9.24953e6 | 0.0201816 | ||||||||
\(772\) | 6.80303e8 | 1.47860 | ||||||||
\(773\) | − | 3.03849e8i | − | 0.657839i | −0.944358 | − | 0.328919i | \(-0.893316\pi\) | ||
0.944358 | − | 0.328919i | \(-0.106684\pi\) | |||||||
\(774\) | 2.37071e7i | 0.0511276i | ||||||||
\(775\) | −4.67480e8 | −1.00429 | ||||||||
\(776\) | − | 4.11223e8i | − | 0.880020i | ||||||
\(777\) | 2.58299e8 | 0.550630 | ||||||||
\(778\) | − | 1.17797e8i | − | 0.250148i | ||||||
\(779\) | 6.93186e6i | 0.0146635i | ||||||||
\(780\) | 4.96544e8i | 1.04634i | ||||||||
\(781\) | 9.01464e8i | 1.89232i | ||||||||
\(782\) | 6.90376e6 | + | 2.41566e7i | 0.0144366 | + | 0.0505144i | ||||
\(783\) | −7.54457e7 | −0.157163 | ||||||||
\(784\) | 8.19624e7 | 0.170085 | ||||||||
\(785\) | −9.53344e8 | −1.97079 | ||||||||
\(786\) | 1.01562e8 | 0.209153 | ||||||||
\(787\) | − | 2.54470e8i | − | 0.522050i | −0.965332 | − | 0.261025i | \(-0.915940\pi\) | ||
0.965332 | − | 0.261025i | \(-0.0840604\pi\) | |||||||
\(788\) | 3.24499e8 | 0.663186 | ||||||||
\(789\) | − | 1.33361e8i | − | 0.271518i | ||||||
\(790\) | 1.21743e8 | 0.246924 | ||||||||
\(791\) | 5.43579e8 | 1.09833 | ||||||||
\(792\) | − | 1.81842e8i | − | 0.366032i | ||||||
\(793\) | − | 6.08581e8i | − | 1.22039i | ||||||
\(794\) | 2.22654e8 | 0.444805 | ||||||||
\(795\) | 4.06335e8 | 0.808691 | ||||||||
\(796\) | − | 6.04854e7i | − | 0.119925i | ||||||
\(797\) | − | 1.67207e8i | − | 0.330277i | −0.986270 | − | 0.165139i | \(-0.947193\pi\) | ||
0.986270 | − | 0.165139i | \(-0.0528071\pi\) | |||||||
\(798\) | 2.39950e7 | 0.0472184 | ||||||||
\(799\) | − | 8.68755e7i | − | 0.170317i | ||||||
\(800\) | 1.07191e9 | 2.09357 | ||||||||
\(801\) | 1.40067e8i | 0.272546i | ||||||||
\(802\) | − | 3.04974e8i | − | 0.591207i | ||||||
\(803\) | 6.97497e7i | 0.134709i | ||||||||
\(804\) | − | 3.88335e8i | − | 0.747202i | ||||||
\(805\) | 6.69645e8 | − | 1.91379e8i | 1.28368 | − | 0.366865i | ||||
\(806\) | 1.54394e8 | 0.294867 | ||||||||
\(807\) | 3.73289e8 | 0.710272 | ||||||||
\(808\) | −5.18579e8 | −0.983061 | ||||||||
\(809\) | 3.49295e8 | 0.659700 | 0.329850 | − | 0.944033i | \(-0.393002\pi\) | ||||
0.329850 | + | 0.944033i | \(0.393002\pi\) | |||||||
\(810\) | − | 4.77531e7i | − | 0.0898558i | ||||||
\(811\) | −1.94555e8 | −0.364737 | −0.182369 | − | 0.983230i | \(-0.558376\pi\) | ||||
−0.182369 | + | 0.983230i | \(0.558376\pi\) | |||||||
\(812\) | 2.62218e8i | 0.489772i | ||||||||
\(813\) | −1.27941e8 | −0.238088 | ||||||||
\(814\) | 4.14732e8 | 0.768943 | ||||||||
\(815\) | − | 1.32323e9i | − | 2.44435i | ||||||
\(816\) | 1.44893e7i | 0.0266672i | ||||||||
\(817\) | 4.21014e7 | 0.0772023 | ||||||||
\(818\) | −4.76018e8 | −0.869687 | ||||||||
\(819\) | − | 1.83548e8i | − | 0.334116i | ||||||
\(820\) | − | 4.79466e7i | − | 0.0869594i | ||||||
\(821\) | −5.79161e8 | −1.04657 | −0.523287 | − | 0.852157i | \(-0.675294\pi\) | ||||
−0.523287 | + | 0.852157i | \(0.675294\pi\) | |||||||
\(822\) | 1.22612e8i | 0.220759i | ||||||||
\(823\) | 7.10616e8 | 1.27478 | 0.637390 | − | 0.770541i | \(-0.280014\pi\) | ||||
0.637390 | + | 0.770541i | \(0.280014\pi\) | |||||||
\(824\) | 7.22939e8i | 1.29217i | ||||||||
\(825\) | 8.92328e8i | 1.58914i | ||||||||
\(826\) | − | 2.27377e8i | − | 0.403466i | ||||||
\(827\) | 8.70562e7i | 0.153916i | 0.997034 | + | 0.0769579i | \(0.0245207\pi\) | ||||
−0.997034 | + | 0.0769579i | \(0.975479\pi\) | |||||||
\(828\) | 1.43153e8 | − | 4.09119e7i | 0.252179 | − | 0.0720707i | ||||
\(829\) | −3.58917e8 | −0.629985 | −0.314993 | − | 0.949094i | \(-0.602002\pi\) | ||||
−0.314993 | + | 0.949094i | \(0.602002\pi\) | |||||||
\(830\) | −1.83430e8 | −0.320801 | ||||||||
\(831\) | 3.46792e8 | 0.604319 | ||||||||
\(832\) | −4.65897e7 | −0.0808946 | ||||||||
\(833\) | 2.75586e7i | 0.0476784i | ||||||||
\(834\) | −7.63985e6 | −0.0131700 | ||||||||
\(835\) | 1.10342e9i | 1.89532i | ||||||||
\(836\) | −1.42203e8 | −0.243383 | ||||||||
\(837\) | 5.48050e7 | 0.0934638 | ||||||||
\(838\) | 1.40479e8i | 0.238714i | ||||||||
\(839\) | 5.88198e8i | 0.995950i | 0.867191 | + | 0.497975i | \(0.165923\pi\) | ||||
−0.867191 | + | 0.497975i | \(0.834077\pi\) | |||||||
\(840\) | −3.76905e8 | −0.635908 | ||||||||
\(841\) | −1.98135e8 | −0.333098 | ||||||||
\(842\) | 8.63823e7i | 0.144707i | ||||||||
\(843\) | − | 1.23381e8i | − | 0.205951i | ||||||
\(844\) | −2.75521e8 | −0.458277 | ||||||||
\(845\) | 7.70713e8i | 1.27739i | ||||||||
\(846\) | 1.39482e8 | 0.230360 | ||||||||
\(847\) | − | 3.57408e8i | − | 0.588186i | ||||||
\(848\) | − | 1.97948e8i | − | 0.324611i | ||||||
\(849\) | − | 2.78387e7i | − | 0.0454910i | ||||||
\(850\) | 6.67195e7i | 0.108642i | ||||||||
\(851\) | 2.11898e8 | + | 7.41440e8i | 0.343825 | + | 1.20306i | ||||
\(852\) | 3.99430e8 | 0.645836 | ||||||||
\(853\) | −4.28088e8 | −0.689740 | −0.344870 | − | 0.938650i | \(-0.612077\pi\) | ||||
−0.344870 | + | 0.938650i | \(0.612077\pi\) | |||||||
\(854\) | 2.03418e8 | 0.326600 | ||||||||
\(855\) | −8.48046e7 | −0.135682 | ||||||||
\(856\) | 9.51551e8i | 1.51709i | ||||||||
\(857\) | 2.10898e8 | 0.335066 | 0.167533 | − | 0.985867i | \(-0.446420\pi\) | ||||
0.167533 | + | 0.985867i | \(0.446420\pi\) | |||||||
\(858\) | − | 2.94709e8i | − | 0.466586i | ||||||
\(859\) | 2.05527e7 | 0.0324257 | 0.0162128 | − | 0.999869i | \(-0.494839\pi\) | ||||
0.0162128 | + | 0.999869i | \(0.494839\pi\) | |||||||
\(860\) | −2.91209e8 | −0.457835 | ||||||||
\(861\) | 1.77235e7i | 0.0277677i | ||||||||
\(862\) | − | 1.36678e8i | − | 0.213392i | ||||||
\(863\) | 6.24282e8 | 0.971289 | 0.485644 | − | 0.874156i | \(-0.338585\pi\) | ||||
0.485644 | + | 0.874156i | \(0.338585\pi\) | |||||||
\(864\) | −1.25665e8 | −0.194838 | ||||||||
\(865\) | − | 4.67236e8i | − | 0.721918i | ||||||
\(866\) | 3.88079e8i | 0.597539i | ||||||||
\(867\) | 3.71396e8 | 0.569875 | ||||||||
\(868\) | − | 1.90479e8i | − | 0.291265i | ||||||
\(869\) | 2.66701e8 | 0.406411 | ||||||||
\(870\) | 2.51083e8i | 0.381293i | ||||||||
\(871\) | − | 1.42925e9i | − | 2.16299i | ||||||
\(872\) | 8.20661e8i | 1.23770i | ||||||||
\(873\) | − | 2.36573e8i | − | 0.355567i | ||||||
\(874\) | 1.96845e7 | + | 6.88769e7i | 0.0294842 | + | 0.103167i | ||||
\(875\) | 9.55137e8 | 1.42574 | ||||||||
\(876\) | 3.09054e7 | 0.0459751 | ||||||||
\(877\) | 1.30626e8 | 0.193656 | 0.0968281 | − | 0.995301i | \(-0.469130\pi\) | ||||
0.0968281 | + | 0.995301i | \(0.469130\pi\) | |||||||
\(878\) | 1.56420e8 | 0.231104 | ||||||||
\(879\) | − | 7.12075e8i | − | 1.04848i | ||||||
\(880\) | 6.44915e8 | 0.946355 | ||||||||
\(881\) | − | 5.42231e8i | − | 0.792970i | −0.918041 | − | 0.396485i | \(-0.870230\pi\) | ||
0.918041 | − | 0.396485i | \(-0.129770\pi\) | |||||||
\(882\) | −4.42463e7 | −0.0644868 | ||||||||
\(883\) | −9.62220e8 | −1.39763 | −0.698815 | − | 0.715302i | \(-0.746289\pi\) | ||||
−0.698815 | + | 0.715302i | \(0.746289\pi\) | |||||||
\(884\) | 8.13329e7i | 0.117736i | ||||||||
\(885\) | 8.03612e8i | 1.15936i | ||||||||
\(886\) | 2.81743e8 | 0.405091 | ||||||||
\(887\) | −2.90513e8 | −0.416288 | −0.208144 | − | 0.978098i | \(-0.566742\pi\) | ||||
−0.208144 | + | 0.978098i | \(0.566742\pi\) | |||||||
\(888\) | − | 4.17315e8i | − | 0.595971i | ||||||
\(889\) | 8.41156e8i | 1.19721i | ||||||||
\(890\) | 4.66143e8 | 0.661225 | ||||||||
\(891\) | − | 1.04612e8i | − | 0.147893i | ||||||
\(892\) | 5.07947e8 | 0.715689 | ||||||||
\(893\) | − | 2.47705e8i | − | 0.347841i | ||||||
\(894\) | − | 2.97990e8i | − | 0.417051i | ||||||
\(895\) | − | 1.22365e9i | − | 1.70682i | ||||||
\(896\) | 5.39518e8i | 0.750036i | ||||||||
\(897\) | 5.26868e8 | − | 1.50575e8i | 0.730003 | − | 0.208629i | ||||
\(898\) | 7.73518e7 | 0.106817 | ||||||||
\(899\) | −2.88161e8 | −0.396603 | ||||||||
\(900\) | 3.95382e8 | 0.542363 | ||||||||
\(901\) | 6.65569e7 | 0.0909952 | ||||||||
\(902\) | 2.84573e7i | 0.0387770i | ||||||||
\(903\) | 1.07645e8 | 0.146195 | ||||||||
\(904\) | − | 8.78220e8i | − | 1.18877i | ||||||
\(905\) | −1.05680e9 | −1.42576 | ||||||||
\(906\) | −8.07928e7 | −0.108640 | ||||||||
\(907\) | − | 2.33369e8i | − | 0.312768i | −0.987696 | − | 0.156384i | \(-0.950016\pi\) | ||
0.987696 | − | 0.156384i | \(-0.0499837\pi\) | |||||||
\(908\) | 9.97839e8i | 1.33292i | ||||||||
\(909\) | −2.98333e8 | −0.397201 | ||||||||
\(910\) | −6.10845e8 | −0.810600 | ||||||||
\(911\) | − | 1.10739e8i | − | 0.146469i | −0.997315 | − | 0.0732347i | \(-0.976668\pi\) | ||
0.997315 | − | 0.0732347i | \(-0.0233322\pi\) | |||||||
\(912\) | 4.13130e7i | 0.0544630i | ||||||||
\(913\) | −4.01838e8 | −0.528005 | ||||||||
\(914\) | − | 5.33219e8i | − | 0.698340i | ||||||
\(915\) | −7.18934e8 | −0.938481 | ||||||||
\(916\) | − | 4.01562e8i | − | 0.522475i | ||||||
\(917\) | − | 4.61158e8i | − | 0.598056i | ||||||
\(918\) | − | 7.82186e6i | − | 0.0101107i | ||||||
\(919\) | − | 7.56808e8i | − | 0.975077i | −0.873101 | − | 0.487539i | \(-0.837895\pi\) | ||
0.873101 | − | 0.487539i | \(-0.162105\pi\) | |||||||
\(920\) | −3.09197e8 | − | 1.08190e9i | −0.397075 | − | 1.38938i | ||||
\(921\) | 8.09332e8 | 1.03597 | ||||||||
\(922\) | −2.16250e8 | −0.275908 | ||||||||
\(923\) | 1.47009e9 | 1.86955 | ||||||||
\(924\) | −3.63588e8 | −0.460886 | ||||||||
\(925\) | 2.04783e9i | 2.58743i | ||||||||
\(926\) | 1.31554e8 | 0.165681 | ||||||||
\(927\) | 4.15900e8i | 0.522095i | ||||||||
\(928\) | 6.60740e8 | 0.826773 | ||||||||
\(929\) | −3.59892e7 | −0.0448874 | −0.0224437 | − | 0.999748i | \(-0.507145\pi\) | ||||
−0.0224437 | + | 0.999748i | \(0.507145\pi\) | |||||||
\(930\) | − | 1.82391e8i | − | 0.226753i | ||||||
\(931\) | 7.85769e7i | 0.0973747i | ||||||||
\(932\) | −2.66913e8 | −0.329702 | ||||||||
\(933\) | −6.01264e8 | −0.740322 | ||||||||
\(934\) | 3.67505e8i | 0.451048i | ||||||||
\(935\) | 2.16842e8i | 0.265283i | ||||||||
\(936\) | −2.96544e8 | −0.361628 | ||||||||
\(937\) | 4.13887e8i | 0.503110i | 0.967843 | + | 0.251555i | \(0.0809419\pi\) | ||||
−0.967843 | + | 0.251555i | \(0.919058\pi\) | |||||||
\(938\) | 4.77727e8 | 0.578857 | ||||||||
\(939\) | 8.14076e8i | 0.983260i | ||||||||
\(940\) | 1.71334e9i | 2.06282i | ||||||||
\(941\) | − | 1.03553e9i | − | 1.24278i | −0.783500 | − | 0.621391i | \(-0.786568\pi\) | ||
0.783500 | − | 0.621391i | \(-0.213432\pi\) | |||||||
\(942\) | − | 2.50714e8i | − | 0.299934i | ||||||
\(943\) | −5.08748e7 | + | 1.45396e7i | −0.0606691 | + | 0.0173387i | ||||
\(944\) | 3.91483e8 | 0.465369 | ||||||||
\(945\) | −2.16830e8 | −0.256935 | ||||||||
\(946\) | 1.72839e8 | 0.204158 | ||||||||
\(947\) | 1.48320e8 | 0.174643 | 0.0873214 | − | 0.996180i | \(-0.472169\pi\) | ||||
0.0873214 | + | 0.996180i | \(0.472169\pi\) | |||||||
\(948\) | − | 1.18173e8i | − | 0.138705i | ||||||
\(949\) | 1.13746e8 | 0.133088 | ||||||||
\(950\) | 1.90235e8i | 0.221881i | ||||||||
\(951\) | 6.50115e8 | 0.755872 | ||||||||
\(952\) | −6.17364e7 | −0.0715534 | ||||||||
\(953\) | 9.98605e8i | 1.15376i | 0.816829 | + | 0.576879i | \(0.195730\pi\) | ||||
−0.816829 | + | 0.576879i | \(0.804270\pi\) | |||||||
\(954\) | 1.06859e8i | 0.123074i | ||||||||
\(955\) | −1.54827e9 | −1.77761 | ||||||||
\(956\) | 3.19924e8 | 0.366162 | ||||||||
\(957\) | 5.50044e8i | 0.627569i | ||||||||
\(958\) | 6.39762e8i | 0.727649i | ||||||||
\(959\) | 5.56738e8 | 0.631241 | ||||||||
\(960\) | 5.50377e7i | 0.0622080i | ||||||||
\(961\) | −6.78179e8 | −0.764142 | ||||||||
\(962\) | − | 6.76336e8i | − | 0.759692i | ||||||
\(963\) | 5.47418e8i | 0.612971i | ||||||||
\(964\) | − | 4.70828e8i | − | 0.525571i | ||||||
\(965\) | − | 2.95784e9i | − | 3.29149i | ||||||
\(966\) | 5.03296e7 | + | 1.76106e8i | 0.0558331 | + | 0.195363i | ||||
\(967\) | −1.25410e9 | −1.38692 | −0.693462 | − | 0.720493i | \(-0.743915\pi\) | ||||
−0.693462 | + | 0.720493i | \(0.743915\pi\) | |||||||
\(968\) | −5.77439e8 | −0.636619 | ||||||||
\(969\) | −1.38908e7 | −0.0152671 | ||||||||
\(970\) | −7.87312e8 | −0.862644 | ||||||||
\(971\) | 2.21220e8i | 0.241639i | 0.992675 | + | 0.120819i | \(0.0385522\pi\) | ||||
−0.992675 | + | 0.120819i | \(0.961448\pi\) | |||||||
\(972\) | −4.63526e7 | −0.0504749 | ||||||||
\(973\) | 3.46899e7i | 0.0376586i | ||||||||
\(974\) | −1.76684e8 | −0.191215 | ||||||||
\(975\) | 1.45519e9 | 1.57002 | ||||||||
\(976\) | 3.50232e8i | 0.376709i | ||||||||
\(977\) | 8.32816e8i | 0.893029i | 0.894776 | + | 0.446514i | \(0.147335\pi\) | ||||
−0.894776 | + | 0.446514i | \(0.852665\pi\) | |||||||
\(978\) | 3.47988e8 | 0.372004 | ||||||||
\(979\) | 1.02117e9 | 1.08831 | ||||||||
\(980\) | − | 5.43505e8i | − | 0.577464i | ||||||
\(981\) | 4.72118e8i | 0.500085i | ||||||||
\(982\) | −4.07954e8 | −0.430801 | ||||||||
\(983\) | 7.30746e8i | 0.769319i | 0.923059 | + | 0.384659i | \(0.125681\pi\) | ||||
−0.923059 | + | 0.384659i | \(0.874319\pi\) | |||||||
\(984\) | 2.86346e7 | 0.0300542 | ||||||||
\(985\) | − | 1.41087e9i | − | 1.47631i | ||||||
\(986\) | 4.11269e7i | 0.0429037i | ||||||||
\(987\) | − | 6.33337e8i | − | 0.658694i | ||||||
\(988\) | 2.31902e8i | 0.240455i | ||||||||
\(989\) | 8.83078e7 | + | 3.08993e8i | 0.0912873 | + | 0.319419i | ||||
\(990\) | −3.48148e8 | −0.358805 | ||||||||
\(991\) | 7.30256e7 | 0.0750333 | 0.0375167 | − | 0.999296i | \(-0.488055\pi\) | ||||
0.0375167 | + | 0.999296i | \(0.488055\pi\) | |||||||
\(992\) | −4.79972e8 | −0.491678 | ||||||||
\(993\) | −7.70424e8 | −0.786832 | ||||||||
\(994\) | 4.91377e8i | 0.500329i | ||||||||
\(995\) | −2.62980e8 | −0.266965 | ||||||||
\(996\) | 1.78050e8i | 0.180204i | ||||||||
\(997\) | 1.36699e8 | 0.137937 | 0.0689685 | − | 0.997619i | \(-0.478029\pi\) | ||||
0.0689685 | + | 0.997619i | \(0.478029\pi\) | |||||||
\(998\) | −1.38569e8 | −0.139404 | ||||||||
\(999\) | − | 2.40077e8i | − | 0.240799i |
(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 | 69.7.d.a.22.12 | yes | 24 | |
3.2 | odd | 2 | 207.7.d.e.91.13 | 24 | |||
23.22 | odd | 2 | inner | 69.7.d.a.22.11 | ✓ | 24 | |
69.68 | even | 2 | 207.7.d.e.91.14 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.7.d.a.22.11 | ✓ | 24 | 23.22 | odd | 2 | inner | |
69.7.d.a.22.12 | yes | 24 | 1.1 | even | 1 | trivial | |
207.7.d.e.91.13 | 24 | 3.2 | odd | 2 | |||
207.7.d.e.91.14 | 24 | 69.68 | even | 2 |