Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,8,Mod(193,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.193");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(119.955849786\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 449x^{6} + 50632x^{4} + 69129x^{2} + 18225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.8 | ||
Root | \(-15.2503i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.8.d.d.193.1 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 27.0000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 522.419i | 1.86906i | 0.355880 | + | 0.934532i | \(0.384181\pi\) | ||||
−0.355880 | + | 0.934532i | \(0.615819\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1309.01 | 1.44245 | 0.721226 | − | 0.692700i | \(-0.243579\pi\) | ||||
0.721226 | + | 0.692700i | \(0.243579\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −729.000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2794.57i | − 0.633054i | −0.948584 | − | 0.316527i | \(-0.897483\pi\) | ||||
0.948584 | − | 0.316527i | \(-0.102517\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 7351.17i | − 0.928015i | −0.885831 | − | 0.464007i | \(-0.846411\pi\) | ||||
0.885831 | − | 0.464007i | \(-0.153589\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −14105.3 | −1.07910 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5644.22 | 0.278633 | 0.139316 | − | 0.990248i | \(-0.455509\pi\) | ||||
0.139316 | + | 0.990248i | \(0.455509\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 20285.7i | 0.678504i | 0.940695 | + | 0.339252i | \(0.110174\pi\) | ||||
−0.940695 | + | 0.339252i | \(0.889826\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 35343.4i | 0.832800i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 79560.7 | 1.36349 | 0.681744 | − | 0.731591i | \(-0.261222\pi\) | ||||
0.681744 | + | 0.731591i | \(0.261222\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −194797. | −2.49340 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 19683.0i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 140530.i | 1.06998i | 0.844859 | + | 0.534989i | \(0.179684\pi\) | ||||
−0.844859 | + | 0.534989i | \(0.820316\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 321339. | 1.93730 | 0.968652 | − | 0.248423i | \(-0.0799123\pi\) | ||||
0.968652 | + | 0.248423i | \(0.0799123\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 75453.4 | 0.365494 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 683854.i | 2.69603i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 504903.i | 1.63871i | 0.573288 | + | 0.819354i | \(0.305668\pi\) | ||||
−0.573288 | + | 0.819354i | \(0.694332\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 198482. | 0.535790 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 262029. | 0.593753 | 0.296876 | − | 0.954916i | \(-0.404055\pi\) | ||||
0.296876 | + | 0.954916i | \(0.404055\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 503139.i | 0.965046i | 0.875883 | + | 0.482523i | \(0.160280\pi\) | ||||
−0.875883 | + | 0.482523i | \(0.839720\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 380844.i | − 0.623021i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −107852. | −0.151525 | −0.0757625 | − | 0.997126i | \(-0.524139\pi\) | ||||
−0.0757625 | + | 0.997126i | \(0.524139\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 889976. | 1.08067 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 152394.i | 0.160869i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 1.13491e6i | − 1.04712i | −0.851989 | − | 0.523560i | \(-0.824603\pi\) | ||||
0.851989 | − | 0.523560i | \(-0.175397\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.45994e6 | 1.18322 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −547714. | −0.391735 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 1.80023e6i | − 1.14116i | −0.821242 | − | 0.570579i | \(-0.806719\pi\) | ||||
0.821242 | − | 0.570579i | \(-0.193281\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00077e6i | 0.564518i | 0.959338 | + | 0.282259i | \(0.0910838\pi\) | ||||
−0.959338 | + | 0.282259i | \(0.908916\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −954271. | −0.480817 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.84039e6 | 1.73452 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.70272e6i | 1.91024i | 0.296222 | + | 0.955119i | \(0.404273\pi\) | ||||
−0.296222 | + | 0.955119i | \(0.595727\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.14814e6i | 0.787210i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.38848e6 | −1.45516 | −0.727579 | − | 0.686024i | \(-0.759354\pi\) | ||||
−0.727579 | + | 0.686024i | \(0.759354\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.51938e6 | −0.457127 | −0.228563 | − | 0.973529i | \(-0.573403\pi\) | ||||
−0.228563 | + | 0.973529i | \(0.573403\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 5.25951e6i | − 1.43956i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 3.65813e6i | − 0.913149i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 144735. | 0.0330278 | 0.0165139 | − | 0.999864i | \(-0.494743\pi\) | ||||
0.0165139 | + | 0.999864i | \(0.494743\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1.45912e6i | − 0.280102i | −0.990144 | − | 0.140051i | \(-0.955273\pi\) | ||||
0.990144 | − | 0.140051i | \(-0.0447267\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.94865e6i | 0.520783i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.79430e6 | −0.617753 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.58397e6 | 1.29069 | 0.645346 | − | 0.763890i | \(-0.276713\pi\) | ||||
0.645346 | + | 0.763890i | \(0.276713\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 9.62279e6i | − 1.33862i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.67616e6i | 1.11850i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.05976e7 | −1.26817 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.08726e6 | −0.899705 | −0.449853 | − | 0.893103i | \(-0.648524\pi\) | ||||
−0.449853 | + | 0.893103i | \(0.648524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.03724e6i | 0.211018i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.92632e6i | 0.379193i | 0.981862 | + | 0.189597i | \(0.0607180\pi\) | ||||
−0.981862 | + | 0.189597i | \(0.939282\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.56910e6 | −0.862861 | −0.431430 | − | 0.902146i | \(-0.641991\pi\) | ||||
−0.431430 | + | 0.902146i | \(0.641991\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.84641e7 | −1.55656 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 282494.i | − 0.0222928i | −0.999938 | − | 0.0111464i | \(-0.996452\pi\) | ||||
0.999938 | − | 0.0111464i | \(-0.00354809\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.12690e6i | 0.453156i | 0.973993 | + | 0.226578i | \(0.0727539\pi\) | ||||
−0.973993 | + | 0.226578i | \(0.927246\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.36324e7 | −0.946108 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.76431e6 | −0.180224 | −0.0901118 | − | 0.995932i | \(-0.528722\pi\) | ||||
−0.0901118 | + | 0.995932i | \(0.528722\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.15640e7i | 2.54844i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.35901e6i | 0.309338i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.38836e6 | 0.401915 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.16776e7 | 0.599243 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.07478e6i | 0.342803i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 6.09515e7i | − 2.79126i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.26911e7 | 0.982976 | 0.491488 | − | 0.870884i | \(-0.336453\pi\) | ||||
0.491488 | + | 0.870884i | \(0.336453\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.35847e7 | −0.557170 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 2.52080e6i | − 0.0979690i | −0.998800 | − | 0.0489845i | \(-0.984401\pi\) | ||||
0.998800 | − | 0.0489845i | \(-0.0155985\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.65543e7i | 0.978710i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.02828e7 | 0.359701 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.09088e7 | 1.69149 | 0.845747 | − | 0.533584i | \(-0.179155\pi\) | ||||
0.845747 | + | 0.533584i | \(0.179155\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.49354e7i | 1.73500i | 0.497434 | + | 0.867502i | \(0.334276\pi\) | ||||
−0.497434 | + | 0.867502i | \(0.665724\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 2.91200e6i | − 0.0874830i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.05434e7 | −0.587483 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.34154e7 | −1.99986 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.40293e7i | 0.623923i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 7.39556e7i | − 1.83155i | −0.401690 | − | 0.915776i | \(-0.631577\pi\) | ||||
0.401690 | − | 0.915776i | \(-0.368423\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.70345e7 | −0.402634 | −0.201317 | − | 0.979526i | \(-0.564522\pi\) | ||||
−0.201317 | + | 0.979526i | \(0.564522\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.11463e6 | −0.0928776 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.67874e8i | 3.62094i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 4.59236e7i | − 0.947080i | −0.880772 | − | 0.473540i | \(-0.842976\pi\) | ||||
0.880772 | − | 0.473540i | \(-0.157024\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.06426e7 | 0.604556 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.04146e8 | 1.96676 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 6.55609e7i | − 1.18574i | −0.805299 | − | 0.592868i | \(-0.797995\pi\) | ||||
0.805299 | − | 0.592868i | \(-0.202005\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.94183e7i | 0.683131i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.06517e6 | −0.0343121 | −0.0171561 | − | 0.999853i | \(-0.505461\pi\) | ||||
−0.0171561 | + | 0.999853i | \(0.505461\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.70875e6 | 0.138788 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 1.47883e7i | − 0.226168i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.19310e7i | 1.05622i | 0.849176 | + | 0.528111i | \(0.177099\pi\) | ||||
−0.849176 | + | 0.528111i | \(0.822901\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.54992e8 | −3.59661 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.86062e7 | 0.658848 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 6.97037e7i | − 0.908386i | −0.890903 | − | 0.454193i | \(-0.849928\pi\) | ||||
0.890903 | − | 0.454193i | \(-0.150072\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.59928e7i | 0.701870i | 0.936400 | + | 0.350935i | \(0.114136\pi\) | ||||
−0.936400 | + | 0.350935i | \(0.885864\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.70207e7 | −0.325925 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.63771e8 | −3.06285 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1.57732e7i | − 0.176390i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 2.57653e7i | − 0.277600i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.89901e7 | −1.02796 | −0.513979 | − | 0.857803i | \(-0.671829\pi\) | ||||
−0.513979 | + | 0.857803i | \(0.671829\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.30846e7 | −0.631645 | −0.315822 | − | 0.948818i | \(-0.602280\pi\) | ||||
−0.315822 | + | 0.948818i | \(0.602280\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.03691e8i | 1.00142i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.83443e7i | 0.543709i | 0.962338 | + | 0.271855i | \(0.0876370\pi\) | ||||
−0.962338 | + | 0.271855i | \(0.912363\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.34085e8 | −1.20613 | −0.603067 | − | 0.797691i | \(-0.706055\pi\) | ||||
−0.603067 | + | 0.797691i | \(0.706055\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.26974e8 | −1.10288 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.83955e8i | 1.54339i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.36889e8i | 1.10976i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.79997e7 | −0.454496 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.66898e7 | 0.429530 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.48026e7i | 0.474902i | 0.971400 | + | 0.237451i | \(0.0763118\pi\) | ||||
−0.971400 | + | 0.237451i | \(0.923688\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.18489e8i | − 0.840135i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.62849e8 | −1.80373 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.20637e8 | 2.79447 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 4.10233e7i | − 0.263922i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 4.14916e7i | − 0.258576i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.00971e6 | −0.0483671 | −0.0241835 | − | 0.999708i | \(-0.507699\pi\) | ||||
−0.0241835 | + | 0.999708i | \(0.507699\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.42007e8 | 0.831133 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.80971e7i | 0.386401i | 0.981159 | + | 0.193200i | \(0.0618867\pi\) | ||||
−0.981159 | + | 0.193200i | \(0.938113\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 1.20257e8i | − 0.661740i | −0.943676 | − | 0.330870i | \(-0.892658\pi\) | ||||
0.943676 | − | 0.330870i | \(-0.107342\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.87696e7 | 0.527207 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.83662e7 | −0.354075 | −0.177038 | − | 0.984204i | \(-0.556651\pi\) | ||||
−0.177038 | + | 0.984204i | \(0.556651\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 5.63438e7i | − 0.283210i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.90785e6i | 0.0190686i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.05674e8 | −1.44832 | −0.724162 | − | 0.689630i | \(-0.757773\pi\) | ||||
−0.724162 | + | 0.689630i | \(0.757773\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.58964e7 | −0.119174 | −0.0595869 | − | 0.998223i | \(-0.518978\pi\) | ||||
−0.0595869 | + | 0.998223i | \(0.518978\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.43489e7i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.64940e8i | 2.01983i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.49124e8 | 0.629662 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.93961e7 | 0.161717 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 4.32650e7i | − 0.172694i | −0.996265 | − | 0.0863472i | \(-0.972481\pi\) | ||||
0.996265 | − | 0.0863472i | \(-0.0275194\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2.22338e8i | − 0.863161i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.96135e7 | −0.300674 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.33105e8 | −0.489133 | −0.244567 | − | 0.969632i | \(-0.578646\pi\) | ||||
−0.244567 | + | 0.969632i | \(0.578646\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.60925e8i | 2.36376i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 1.02446e8i | − 0.356660i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.73164e8 | 1.94283 | 0.971413 | − | 0.237394i | \(-0.0762934\pi\) | ||||
0.971413 | + | 0.237394i | \(0.0762934\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.92900e8 | 1.95714 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.31767e8i | 0.745182i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.24355e8i | 1.32922i | 0.747191 | + | 0.664609i | \(0.231402\pi\) | ||||
−0.747191 | + | 0.664609i | \(0.768598\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.45956e8 | −1.66635 | −0.833173 | − | 0.553013i | \(-0.813478\pi\) | ||||
−0.833173 | + | 0.553013i | \(0.813478\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.59815e8 | 0.772851 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.44373e8i | 1.57845i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 4.35552e8i | − 1.23129i | −0.788023 | − | 0.615645i | \(-0.788895\pi\) | ||||
0.788023 | − | 0.615645i | \(-0.211105\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.34256e8 | −0.645768 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.75803e8 | −1.27925 | −0.639625 | − | 0.768687i | \(-0.720910\pi\) | ||||
−0.639625 | + | 0.768687i | \(0.720910\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.81622e8i | 1.26315i | 0.775316 | + | 0.631573i | \(0.217591\pi\) | ||||
−0.775316 | + | 0.631573i | \(0.782409\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 2.86136e8i | − 0.732177i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.42999e8 | 0.856459 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.78481e8 | −0.922364 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 2.18356e8i | − 0.519445i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 5.88523e8i | − 1.36687i | −0.730012 | − | 0.683435i | \(-0.760485\pi\) | ||||
0.730012 | − | 0.683435i | \(-0.239515\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.40475e8 | 2.13290 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.50055e7 | −0.121831 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 5.84864e8i | − 1.26534i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.58616e8i | 1.39203i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.06011e8 | −0.218927 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.22819e8 | −1.05512 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.44023e8i | 0.875834i | 0.899016 | + | 0.437917i | \(0.144284\pi\) | ||||
−0.899016 | + | 0.437917i | \(0.855716\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 2.58366e8i | − 0.498173i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.57481e8 | −0.296871 | −0.148435 | − | 0.988922i | \(-0.547424\pi\) | ||||
−0.148435 | + | 0.988922i | \(0.547424\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.55060e8 | 0.285821 | 0.142911 | − | 0.989736i | \(-0.454354\pi\) | ||||
0.142911 | + | 0.989736i | \(0.454354\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 4.98530e8i | − 0.898678i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.90492e8i | 0.512185i | 0.966652 | + | 0.256092i | \(0.0824352\pi\) | ||||
−0.966652 | + | 0.256092i | \(0.917565\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.92720e8 | 0.677354 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.62733e6 | 0.0128708 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.14497e8i | 0.189054i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.43198e9i | 2.31391i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.65426e8 | −0.261630 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.41179e8 | −0.218568 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 4.85485e8i | − 0.735831i | −0.929859 | − | 0.367915i | \(-0.880072\pi\) | ||||
0.929859 | − | 0.367915i | \(-0.119928\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 3.68074e8i | − 0.546236i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.45679e9 | −3.57036 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.59275e8 | −0.369026 | −0.184513 | − | 0.982830i | \(-0.559071\pi\) | ||||
−0.184513 | + | 0.982830i | \(0.559071\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 7.46363e7i | − 0.104052i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 8.98005e8i | − 1.22642i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.69613e7 | 0.116358 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.12223e9 | −1.47134 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 8.57834e8i | − 1.10217i | −0.834448 | − | 0.551087i | \(-0.814213\pi\) | ||||
0.834448 | − | 0.551087i | \(-0.185787\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 1.37991e7i | − 0.0173765i | −0.999962 | − | 0.00868827i | \(-0.997234\pi\) | ||||
0.999962 | − | 0.00868827i | \(-0.00276560\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.44693e8 | −0.178597 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.74329e8 | −0.210940 | −0.105470 | − | 0.994422i | \(-0.533635\pi\) | ||||
−0.105470 | + | 0.994422i | \(0.533635\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 2.29263e9i | − 2.71978i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.99486e8i | 0.232045i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.45142e9 | 1.65563 | 0.827813 | − | 0.561004i | \(-0.189585\pi\) | ||||
0.827813 | + | 0.561004i | \(0.189585\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.82362e8 | 0.539632 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.15294e8i | 0.345973i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 7.93753e8i | − 0.854399i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.49474e8 | −1.00266 | −0.501328 | − | 0.865257i | \(-0.667155\pi\) | ||||
−0.501328 | + | 0.865257i | \(0.667155\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.91019e8 | −0.197918 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 1.48562e9i | − 1.51042i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 6.16143e8i | − 0.614753i | −0.951588 | − | 0.307377i | \(-0.900549\pi\) | ||||
0.951588 | − | 0.307377i | \(-0.0994511\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.64569e9 | 1.61153 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.03306e9 | 0.992956 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.44694e8i | 0.230880i | 0.993314 | + | 0.115440i | \(0.0368278\pi\) | ||||
−0.993314 | + | 0.115440i | \(0.963172\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.12660e8i | 0.567521i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.25530e9 | 1.14170 | 0.570848 | − | 0.821056i | \(-0.306615\pi\) | ||||
0.570848 | + | 0.821056i | \(0.306615\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.91108e9 | 1.70673 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 3.66788e8i | − 0.321682i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 9.17850e8i | − 0.790584i | −0.918556 | − | 0.395292i | \(-0.870643\pi\) | ||||
0.918556 | − | 0.395292i | \(-0.129357\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.49058e8 | 0.379912 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.80616e7 | 0.0565625 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.56124e7i | 0.0617310i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 2.91845e8i | − 0.234091i | −0.993127 | − | 0.117046i | \(-0.962658\pi\) | ||||
0.993127 | − | 0.117046i | \(-0.0373424\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.16966e8 | −0.565058 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.30913e9 | 1.78831 | 0.894157 | − | 0.447754i | \(-0.147776\pi\) | ||||
0.894157 | + | 0.447754i | \(0.147776\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 2.36222e9i | − 1.79785i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.77635e8i | 0.207674i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.41099e9 | 1.03739 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.85520e9 | −1.34078 | −0.670392 | − | 0.742007i | \(-0.733874\pi\) | ||||
−0.670392 | + | 0.742007i | \(0.733874\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.37454e9i | 0.976585i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 2.35653e9i | − 1.64607i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.62270e8 | 0.523528 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.48326e9 | −1.00170 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.05244e9i | 1.36308i | 0.731782 | + | 0.681539i | \(0.238689\pi\) | ||||
−0.731782 | + | 0.681539i | \(0.761311\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.56223e9i | 1.02037i | 0.860065 | + | 0.510184i | \(0.170423\pi\) | ||||
−0.860065 | + | 0.510184i | \(0.829577\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.86239e7 | 0.0505083 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.09947e9 | −0.694743 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.31002e9i | 0.814290i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 5.54671e8i | − 0.339184i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.14071e9 | 0.686283 | 0.343141 | − | 0.939284i | \(-0.388509\pi\) | ||||
0.343141 | + | 0.939284i | \(0.388509\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.21428e9 | 0.718802 | 0.359401 | − | 0.933183i | \(-0.382981\pi\) | ||||
0.359401 | + | 0.933183i | \(0.382981\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 1.98222e9i | − 1.15462i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.61395e9i | 0.925132i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.88103e9 | 1.62526 | 0.812630 | − | 0.582781i | \(-0.198035\pi\) | ||||
0.812630 | + | 0.582781i | \(0.198035\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.48792e8 | −0.360222 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.98450e8i | 0.163102i | 0.996669 | + | 0.0815508i | \(0.0259873\pi\) | ||||
−0.996669 | + | 0.0815508i | \(0.974013\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.48443e9i | 2.41239i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.99680e9 | 1.05745 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.76245e7 | −0.0352567 | −0.0176284 | − | 0.999845i | \(-0.505612\pi\) | ||||
−0.0176284 | + | 0.999845i | \(0.505612\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 7.32258e8i | − 0.375877i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 4.59932e8i | − 0.232461i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.02713e9 | 2.50196 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.61798e9 | 1.28310 | 0.641548 | − | 0.767083i | \(-0.278293\pi\) | ||||
0.641548 | + | 0.767083i | \(0.278293\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 1.11095e8i | − 0.0536229i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 2.33589e9i | − 1.11045i | −0.831700 | − | 0.555225i | \(-0.812632\pi\) | ||||
0.831700 | − | 0.555225i | \(-0.187368\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.00500e9 | −1.40706 | −0.703528 | − | 0.710667i | \(-0.748393\pi\) | ||||
−0.703528 | + | 0.710667i | \(0.748393\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.53259e9 | −2.09055 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 1.57079e9i | − 0.713690i | −0.934164 | − | 0.356845i | \(-0.883852\pi\) | ||||
0.934164 | − | 0.356845i | \(-0.116148\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.15593e9i | 2.75543i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.23994e9 | 0.546797 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.40606e9 | 0.610926 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 3.95159e9i | − 1.69178i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.27351e8i | 0.349040i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.47580e9 | −0.613556 | −0.306778 | − | 0.951781i | \(-0.599251\pi\) | ||||
−0.306778 | + | 0.951781i | \(0.599251\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.71163e9 | 1.52075 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.81194e9i | 1.13551i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 4.22494e9i | − 1.68161i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.56484e9 | 1.39859 | 0.699293 | − | 0.714836i | \(-0.253498\pi\) | ||||
0.699293 | + | 0.714836i | \(0.253498\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.77014e9 | 0.684585 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 1.80845e9i | − 0.689480i | −0.938698 | − | 0.344740i | \(-0.887967\pi\) | ||||
0.938698 | − | 0.344740i | \(-0.112033\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.93180e8i | 0.298131i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.06429e9 | −0.394406 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.74458e9 | −2.09899 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.73339e9i | 1.34509i | 0.740055 | + | 0.672546i | \(0.234799\pi\) | ||||
−0.740055 | + | 0.672546i | \(0.765201\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 5.57595e7i | − 0.0198101i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.16793e8 | −0.110991 | −0.0554955 | − | 0.998459i | \(-0.517674\pi\) | ||||
−0.0554955 | + | 0.998459i | \(0.517674\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.05118e9 | −0.708736 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.35136e8i | 0.0801294i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.48810e9i | 1.50852i | 0.656578 | + | 0.754258i | \(0.272003\pi\) | ||||
−0.656578 | + | 0.754258i | \(0.727997\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.98889e9 | −0.659383 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.99284e8 | 0.130578 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 4.99908e9i | − 1.61274i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.01399e8i | 0.0959235i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.94214e9 | −0.609810 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.33409e9 | 1.34266 | 0.671329 | − | 0.741159i | \(-0.265724\pi\) | ||||
0.671329 | + | 0.741159i | \(0.265724\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 5.74767e9i | − 1.75686i | −0.477875 | − | 0.878428i | \(-0.658593\pi\) | ||||
0.477875 | − | 0.878428i | \(-0.341407\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 6.88478e9i | − 2.07650i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.81371e9 | 0.539796 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.92508e9 | 0.859097 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.31237e9i | 0.380386i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.92622e9i | − 0.551011i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.47580e8 | 0.0416667 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.88200e9 | 0.524457 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 2.48710e9i | − 0.684120i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 4.47248e9i | − 1.21439i | −0.794553 | − | 0.607195i | \(-0.792295\pi\) | ||||
0.794553 | − | 0.607195i | \(-0.207705\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.51180e9 | −0.405225 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.20081e9 | −0.846978 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.14796e8i | 0.212860i | 0.994320 | + | 0.106430i | \(0.0339420\pi\) | ||||
−0.994320 | + | 0.106430i | \(0.966058\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 7.29558e8i | − 0.188173i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.85075e9 | −0.725985 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.89460e8 | 0.0476410 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 7.12181e9i | − 1.76834i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 5.85518e8i | − 0.143565i | −0.997420 | − | 0.0717823i | \(-0.977131\pi\) | ||||
0.997420 | − | 0.0717823i | \(-0.0228687\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.69866e9 | 0.895578 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.25875e8 | 0.101839 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.19201e9i | 0.990018i | 0.868888 | + | 0.495009i | \(0.164835\pi\) | ||||
−0.868888 | + | 0.495009i | \(0.835165\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 1.44413e9i | − 0.336849i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.95664e8 | 0.160272 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.74762e9 | −1.76309 | −0.881547 | − | 0.472096i | \(-0.843497\pi\) | ||||
−0.881547 | + | 0.472096i | \(0.843497\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.48502e9i | 1.00818i | 0.863651 | + | 0.504090i | \(0.168172\pi\) | ||||
−0.863651 | + | 0.504090i | \(0.831828\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 2.67273e9i | − 0.593492i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.54982e10 | −3.39972 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.51505e9 | 1.41190 | 0.705948 | − | 0.708264i | \(-0.250521\pi\) | ||||
0.705948 | + | 0.708264i | \(0.250521\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 1.70328e9i | − 0.364680i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 1.91000e9i | − 0.404034i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.17159e9 | −0.662884 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.79965e9 | −0.578173 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.46081e9i | 0.298099i | 0.988830 | + | 0.149050i | \(0.0476214\pi\) | ||||
−0.988830 | + | 0.149050i | \(0.952379\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.51859e9i | 1.31447i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.57530e9 | −0.313911 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.59477e9 | −1.29870 | −0.649349 | − | 0.760490i | \(-0.724959\pi\) | ||||
−0.649349 | + | 0.760490i | \(0.724959\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.85982e9i | 0.751204i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 3.62030e9i | − 0.696362i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.13100e9 | −0.215015 | −0.107508 | − | 0.994204i | \(-0.534287\pi\) | ||||
−0.107508 | + | 0.994204i | \(0.534287\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.83427e9 | 1.47210 | 0.736051 | − | 0.676926i | \(-0.236688\pi\) | ||||
0.736051 | + | 0.676926i | \(0.236688\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 3.42829e9i | − 0.636746i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.10058e9i | 1.12002i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.94589e9 | −0.353149 | −0.176575 | − | 0.984287i | \(-0.556502\pi\) | ||||
−0.176575 | + | 0.984287i | \(0.556502\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.96680e9 | −0.891078 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.92836e8i | 0.140617i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.86592e9i | 1.37923i | 0.724174 | + | 0.689617i | \(0.242221\pi\) | ||||
−0.724174 | + | 0.689617i | \(0.757779\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.69600e9 | −0.640721 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.05302e9 | −1.20886 | −0.604432 | − | 0.796657i | \(-0.706600\pi\) | ||||
−0.604432 | + | 0.796657i | \(0.706600\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.09288e9i | 0.863070i | 0.902096 | + | 0.431535i | \(0.142028\pi\) | ||||
−0.902096 | + | 0.431535i | \(0.857972\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 1.56599e9i | − 0.262403i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.12365e10 | 1.86176 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.66237e10 | 2.72363 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.53063e9i | 0.247989i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.84978e9i | 0.456598i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.95936e9 | 1.10272 | 0.551362 | − | 0.834266i | \(-0.314108\pi\) | ||||
0.551362 | + | 0.834266i | \(0.314108\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.74967e9 | −0.274185 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.18543e10i | 1.83724i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 6.54237e9i | − 1.00288i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.19920e9 | 0.485052 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.26493e9 | −0.639601 | −0.319801 | − | 0.947485i | \(-0.603616\pi\) | ||||
−0.319801 | + | 0.947485i | \(0.603616\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.80345e9i | 1.15757i | 0.815479 | + | 0.578787i | \(0.196474\pi\) | ||||
−0.815479 | + | 0.578787i | \(0.803526\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 7.09693e9i | − 1.04139i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.27680e9 | 0.620803 | 0.310401 | − | 0.950606i | \(-0.399537\pi\) | ||||
0.310401 | + | 0.950606i | \(0.399537\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.03087e9 | −0.722415 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.13572e10i | 1.61339i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 4.79185e9i | − 0.673452i | −0.941603 | − | 0.336726i | \(-0.890680\pi\) | ||||
0.941603 | − | 0.336726i | \(-0.109320\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.31691e9 | 0.183110 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.10763e9 | 0.152376 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 4.04254e9i | − 0.550244i | −0.961409 | − | 0.275122i | \(-0.911282\pi\) | ||||
0.961409 | − | 0.275122i | \(-0.0887183\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 4.02211e8i | − 0.0541688i | −0.999633 | − | 0.0270844i | \(-0.991378\pi\) | ||||
0.999633 | − | 0.0270844i | \(-0.00862228\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.12027e9 | 0.149289 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.38725e10 | −1.82927 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.11806e10i | 1.45890i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 2.16262e8i | − 0.0279247i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.79671e9 | 0.357370 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.17076e9 | 0.527427 | 0.263713 | − | 0.964601i | \(-0.415053\pi\) | ||||
0.263713 | + | 0.964601i | \(0.415053\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.83418e9i | 0.479855i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.81235e8i | 0.0967657i | 0.998829 | + | 0.0483828i | \(0.0154068\pi\) | ||||
−0.998829 | + | 0.0483828i | \(0.984593\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.05863e10 | −1.29778 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.83862e9 | −0.223089 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.16917e10i | 1.40412i | 0.712117 | + | 0.702061i | \(0.247737\pi\) | ||||
−0.712117 | + | 0.702061i | \(0.752263\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.65957e10i | 3.16151i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.24695e9 | 0.382056 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.34294e9 | −0.971744 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 2.33629e9i | − 0.269373i | −0.990888 | − | 0.134687i | \(-0.956997\pi\) | ||||
0.990888 | − | 0.134687i | \(-0.0430028\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.66678e9i | 0.304383i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.86993e10 | −3.24283 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.47895e9 | 0.165439 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 1.84589e9i | − 0.204426i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.38336e10i | 1.51678i | 0.651801 | + | 0.758390i | \(0.274014\pi\) | ||||
−0.651801 | + | 0.758390i | \(0.725986\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.02423e10 | −1.11187 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.52128e9 | 0.163511 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.13961e9i | 0.546968i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.96747e8i | 0.0523448i | 0.999657 | + | 0.0261724i | \(0.00833188\pi\) | ||||
−0.999657 | + | 0.0261724i | \(0.991668\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.05512e8 | −0.0110093 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.55660e10 | 2.64149 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1.07322e10i | − 1.09804i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 8.25320e9i | − 0.836191i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.84708e9 | −0.285660 | −0.142830 | − | 0.989747i | \(-0.545620\pi\) | ||||
−0.142830 | + | 0.989747i | \(0.545620\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.25261e10 | −1.24463 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 6.99204e8i | − 0.0688050i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 2.73747e10i | − 2.66788i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.04361e8 | −0.0872914 | −0.0436457 | − | 0.999047i | \(-0.513897\pi\) | ||||
−0.0436457 | + | 0.999047i | \(0.513897\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.87420e8 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.83982e9i | 0.268894i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.59471e10i | − 1.49561i | −0.663921 | − | 0.747803i | \(-0.731109\pi\) | ||||
0.663921 | − | 0.747803i | \(-0.268891\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.25534e10 | −1.16615 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.31421e10 | 1.20928 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1.23619e9i | − 0.112675i | −0.998412 | − | 0.0563376i | \(-0.982058\pi\) | ||||
0.998412 | − | 0.0563376i | \(-0.0179423\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.02634e9i | 0.363536i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.28465e10 | 1.14901 | 0.574505 | − | 0.818501i | \(-0.305194\pi\) | ||||
0.574505 | + | 0.818501i | \(0.305194\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.86358e10 | 3.42329 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.06370e9i | 0.0933673i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 3.69788e8i | − 0.0321563i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.66117e9 | 0.573866 | 0.286933 | − | 0.957951i | \(-0.407364\pi\) | ||||
0.286933 | + | 0.957951i | \(0.407364\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.16815e9 | 0.0997052 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 8.89916e9i | − 0.752549i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.22593e10i | 1.02714i | 0.858049 | + | 0.513569i | \(0.171677\pi\) | ||||
−0.858049 | + | 0.513569i | \(0.828323\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.00312e9 | 0.498346 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.82752e8 | −0.0397080 | −0.0198540 | − | 0.999803i | \(-0.506320\pi\) | ||||
−0.0198540 | + | 0.999803i | \(0.506320\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.02020e9i | 0.653656i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 2.14956e9i | − 0.173594i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.32338e10 | −1.05901 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.09177e10 | −0.865745 | −0.432872 | − | 0.901455i | \(-0.642500\pi\) | ||||
−0.432872 | + | 0.901455i | \(0.642500\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 3.59383e9i | − 0.282401i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.93076e10i | − 1.50349i | −0.659453 | − | 0.751746i | \(-0.729212\pi\) | ||||
0.659453 | − | 0.751746i | \(-0.270788\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.25958e10 | −4.83047 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.78450e10 | −1.36472 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.31544e9i | 0.402864i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.22639e10i | 0.921193i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.76605e9 | 0.205918 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.39913e10 | 1.77015 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 2.09108e10i | − 1.52918i | −0.644517 | − | 0.764590i | \(-0.722942\pi\) | ||||
0.644517 | − | 0.764590i | \(-0.277058\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.54754e10i | 1.12169i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.61852e9 | −0.259964 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.35680e9 | 0.523881 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.60083e10i | 1.12995i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 9.05983e9i | − 0.633893i | −0.948443 | − | 0.316946i | \(-0.897342\pi\) | ||||
0.948443 | − | 0.316946i | \(-0.102658\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.08738e8 | −0.0422199 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.25771e9 | −0.430231 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.24601e9i | 0.289386i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.44079e10i | 3.67601i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.14576e10 | −0.767424 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.28791e10 | −1.51921 | −0.759606 | − | 0.650384i | \(-0.774608\pi\) | ||||
−0.759606 | + | 0.650384i | \(0.774608\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 5.84918e9i | − 0.385054i | −0.981292 | − | 0.192527i | \(-0.938332\pi\) | ||||
0.981292 | − | 0.192527i | \(-0.0616683\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 1.47408e10i | − 0.962065i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.42503e10 | 2.21622 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.02065e10 | −0.654788 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.01502e9i | 0.446206i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1.60574e10i | − 1.01268i | −0.862333 | − | 0.506342i | \(-0.830997\pi\) | ||||
0.862333 | − | 0.506342i | \(-0.169003\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.90253e8 | 0.0118969 | 0.00594844 | − | 0.999982i | \(-0.498107\pi\) | ||||
0.00594844 | + | 0.999982i | \(0.498107\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.46981e10 | −0.911321 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1.27195e10i | − 0.781989i | −0.920393 | − | 0.390994i | \(-0.872131\pi\) | ||||
0.920393 | − | 0.390994i | \(-0.127869\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.37231e9i | 0.327506i | 0.986501 | + | 0.163753i | \(0.0523601\pi\) | ||||
−0.986501 | + | 0.163753i | \(0.947640\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.17599e10 | 0.710886 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.02322e9 | 0.301109 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 1.07888e9i | − 0.0641316i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 6.32492e9i | − 0.372834i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.73272e10 | −1.01289 | −0.506445 | − | 0.862272i | \(-0.669041\pi\) | ||||
−0.506445 | + | 0.862272i | \(0.669041\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.49873e9 | −0.144855 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 1.28467e10i | − 0.738575i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.54962e9i | 0.259404i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.52861e10 | 0.864379 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.30038e10 | −0.729278 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.01704e10i | 2.23436i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 2.20248e10i | − 1.21504i | −0.794305 | − | 0.607520i | \(-0.792165\pi\) | ||||
0.794305 | − | 0.607520i | \(-0.207835\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.72568e9 | 0.422723 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.96218e9 | 0.160760 | 0.0803800 | − | 0.996764i | \(-0.474387\pi\) | ||||
0.0803800 | + | 0.996764i | \(0.474387\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.47029e9i | 0.186806i | 0.995628 | + | 0.0934028i | \(0.0297744\pi\) | ||||
−0.995628 | + | 0.0934028i | \(0.970226\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.26099e9i | 0.494477i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.13684e9 | 0.483903 | 0.241951 | − | 0.970288i | \(-0.422213\pi\) | ||||
0.241951 | + | 0.970288i | \(0.422213\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.75781e10 | −1.97414 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 1.02190e10i | − 0.532527i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 4.04472e8i | − 0.0209083i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.45705e10 | 1.77273 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.89561e9 | 0.299902 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 7.97864e10i | − 4.02625i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.62260e9i | 0.231413i | 0.993283 | + | 0.115706i | \(0.0369132\pi\) | ||||
−0.993283 | + | 0.115706i | \(0.963087\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.58901e10 | 0.789163 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.53164e9 | 0.420356 | 0.210178 | − | 0.977663i | \(-0.432596\pi\) | ||||
0.210178 | + | 0.977663i | \(0.432596\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.09924e10i | 1.02612i | 0.858352 | + | 0.513061i | \(0.171489\pi\) | ||||
−0.858352 | + | 0.513061i | \(0.828511\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.53928e10i | 1.23143i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.79154e10 | −0.861973 | −0.430986 | − | 0.902358i | \(-0.641834\pi\) | ||||
−0.430986 | + | 0.902358i | \(0.641834\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.97030e10 | 1.41790 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 1.48515e9i | − 0.0703393i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 2.18785e9i | − 0.102810i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.64146e10 | 1.69783 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.57913e10 | 0.730542 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.51577e10i | 2.07287i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 6.40569e9i | − 0.291762i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.77826e10 | −0.803691 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.92517e10 | −1.31184 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.75245e10i | 1.22488i | 0.790516 | + | 0.612441i | \(0.209812\pi\) | ||||
−0.790516 | + | 0.612441i | \(0.790188\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 2.86229e9i | − 0.126398i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.40208e10 | −0.614409 | −0.307204 | − | 0.951644i | \(-0.599393\pi\) | ||||
−0.307204 | + | 0.951644i | \(0.599393\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.07760e9 | −0.177320 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 1.41161e10i | − 0.609174i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 3.29976e9i | − 0.141316i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.39157e10 | 1.44144 | 0.720721 | − | 0.693226i | \(-0.243811\pi\) | ||||
0.720721 | + | 0.693226i | \(0.243811\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.19886e10 | −0.505663 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.22605e10i | 1.35041i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 9.83534e10i | − 4.08595i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.97587e9 | 0.287620 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.41796e9 | −0.385391 | −0.192696 | − | 0.981259i | \(-0.561723\pi\) | ||||
−0.192696 | + | 0.981259i | \(0.561723\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.80538e10i | 0.733237i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 4.25199e9i | − 0.171398i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.24020e9 | 0.329683 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.54198e10 | −1.00945 | −0.504723 | − | 0.863281i | \(-0.668405\pi\) | ||||
−0.504723 | + | 0.863281i | \(0.668405\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.18662e9i | 0.165019i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.70006e9i | 0.340376i | 0.985412 | + | 0.170188i | \(0.0544375\pi\) | ||||
−0.985412 | + | 0.170188i | \(0.945563\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.08472e10 | 0.809574 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.34603e10 | 0.518852 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 2.27301e10i | − 0.869716i | −0.900499 | − | 0.434858i | \(-0.856799\pi\) | ||||
0.900499 | − | 0.434858i | \(-0.143201\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.11692e10i | 0.424220i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.84328e9 | −0.295710 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.29285e10 | 1.23238 | 0.616192 | − | 0.787596i | \(-0.288674\pi\) | ||||
0.616192 | + | 0.787596i | \(0.288674\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 5.17143e10i | − 1.92132i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.06034e10i | 0.391071i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.66403e10 | 2.43990 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.57462e10 | 2.75314 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.05938e8i | 0.00743095i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 3.29566e10i | − 1.18058i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.34709e10 | 0.479074 | 0.239537 | − | 0.970887i | \(-0.423004\pi\) | ||||
0.239537 | + | 0.970887i | \(0.423004\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.09142e9 | −0.109150 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 3.31485e10i | − 1.16198i | −0.813912 | − | 0.580988i | \(-0.802666\pi\) | ||||
0.813912 | − | 0.580988i | \(-0.197334\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.19112e10i | 2.50266i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.86636e10 | −1.33594 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.46700e10 | 0.846326 | 0.423163 | − | 0.906053i | \(-0.360920\pi\) | ||||
0.423163 | + | 0.906053i | \(0.360920\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 2.39885e10i | − 0.817078i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 4.46651e9i | − 0.151052i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.13043e9 | 0.239430 | 0.119715 | − | 0.992808i | \(-0.461802\pi\) | ||||
0.119715 | + | 0.992808i | \(0.461802\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.04802e10 | −1.01623 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 3.81184e9i | − 0.126190i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.00301e10i | 1.31583i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.96102e10 | 1.29285 | 0.646426 | − | 0.762976i | \(-0.276263\pi\) | ||||
0.646426 | + | 0.762976i | \(0.276263\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.31081e10 | 0.424832 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 7.00487e10i | − 2.25434i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 4.99492e9i | − 0.159623i | −0.996810 | − | 0.0798116i | \(-0.974568\pi\) | ||||
0.996810 | − | 0.0798116i | \(-0.0254319\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.93800e9 | 0.315369 |
(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 | 384.8.d.d.193.8 | yes | 8 | |
4.3 | odd | 2 | 384.8.d.c.193.4 | ✓ | 8 | ||
8.3 | odd | 2 | 384.8.d.c.193.5 | yes | 8 | ||
8.5 | even | 2 | inner | 384.8.d.d.193.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.8.d.c.193.4 | ✓ | 8 | 4.3 | odd | 2 | ||
384.8.d.c.193.5 | yes | 8 | 8.3 | odd | 2 | ||
384.8.d.d.193.1 | yes | 8 | 8.5 | even | 2 | inner | |
384.8.d.d.193.8 | yes | 8 | 1.1 | even | 1 | trivial |