Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,8,Mod(129,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.129");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(79.9705665239\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.50765497344.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 101x^{4} + 2512x^{2} + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | no (minimal twist has level 128) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.4 | ||
Root | \(-0.119748i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.129 |
Dual form | 256.8.b.l.129.3 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.95798i | 0.0632515i | 0.999500 | + | 0.0316258i | \(0.0100685\pi\) | ||||
−0.999500 | + | 0.0316258i | \(0.989932\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 362.486i | − 1.29687i | −0.761271 | − | 0.648434i | \(-0.775424\pi\) | ||||
0.761271 | − | 0.648434i | \(-0.224576\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −715.055 | −0.787946 | −0.393973 | − | 0.919122i | \(-0.628900\pi\) | ||||
−0.393973 | + | 0.919122i | \(0.628900\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2178.25 | 0.995999 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7298.99i | 1.65344i | 0.562614 | + | 0.826720i | \(0.309796\pi\) | ||||
−0.562614 | + | 0.826720i | \(0.690204\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 10398.4i | − 1.31270i | −0.754457 | − | 0.656349i | \(-0.772100\pi\) | ||||
0.754457 | − | 0.656349i | \(-0.227900\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1072.23 | 0.0820289 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −11225.0 | −0.554137 | −0.277068 | − | 0.960850i | \(-0.589363\pi\) | ||||
−0.277068 | + | 0.960850i | \(0.589363\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26695.5i | 0.892895i | 0.894810 | + | 0.446447i | \(0.147311\pi\) | ||||
−0.894810 | + | 0.446447i | \(0.852689\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 2115.12i | − 0.0498388i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −23531.8 | −0.403280 | −0.201640 | − | 0.979460i | \(-0.564627\pi\) | ||||
−0.201640 | + | 0.979460i | \(0.564627\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −53270.9 | −0.681867 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 12912.3i | 0.126250i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 44148.6i | 0.336143i | 0.985775 | + | 0.168071i | \(0.0537539\pi\) | ||||
−0.985775 | + | 0.168071i | \(0.946246\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −311489. | −1.87792 | −0.938960 | − | 0.344025i | \(-0.888209\pi\) | ||||
−0.938960 | + | 0.344025i | \(0.888209\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −21590.3 | −0.104583 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 259197.i | 1.02186i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 139795.i | 0.453716i | 0.973928 | + | 0.226858i | \(0.0728454\pi\) | ||||
−0.973928 | + | 0.226858i | \(0.927155\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 30758.3 | 0.0830302 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 753482. | 1.70738 | 0.853688 | − | 0.520785i | \(-0.174361\pi\) | ||||
0.853688 | + | 0.520785i | \(0.174361\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 125011.i | − 0.239777i | −0.992787 | − | 0.119889i | \(-0.961746\pi\) | ||||
0.992787 | − | 0.119889i | \(-0.0382537\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 789585.i | − 1.29168i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 798879. | 1.12238 | 0.561188 | − | 0.827688i | \(-0.310344\pi\) | ||||
0.561188 | + | 0.827688i | \(0.310344\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −312239. | −0.379141 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 33203.5i | − 0.0350500i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.14579e6i | 1.05716i | 0.848884 | + | 0.528580i | \(0.177275\pi\) | ||||
−0.848884 | + | 0.528580i | \(0.822725\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.64578e6 | 2.14429 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −78964.7 | −0.0564769 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 2.01433e6i | − 1.27687i | −0.769674 | − | 0.638437i | \(-0.779581\pi\) | ||||
0.769674 | − | 0.638437i | \(-0.220419\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5678.84i | 0.00320336i | 0.999999 | + | 0.00160168i | \(0.000509831\pi\) | ||||
−0.999999 | + | 0.00160168i | \(0.999490\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.55757e6 | −0.784794 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.76927e6 | −1.70240 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.80769e6i | 1.54668i | 0.633993 | + | 0.773339i | \(0.281415\pi\) | ||||
−0.633993 | + | 0.773339i | \(0.718585\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 69606.5i | − 0.0255081i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.78448e6 | 0.923293 | 0.461647 | − | 0.887064i | \(-0.347259\pi\) | ||||
0.461647 | + | 0.887064i | \(0.347259\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.85336e6 | 0.557609 | 0.278805 | − | 0.960348i | \(-0.410062\pi\) | ||||
0.278805 | + | 0.960348i | \(0.410062\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 157574.i | − 0.0431291i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 5.21918e6i | − 1.30282i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.26678e6 | −0.517267 | −0.258633 | − | 0.965976i | \(-0.583272\pi\) | ||||
−0.258633 | + | 0.965976i | \(0.583272\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.72564e6 | 0.988014 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.79311e6i | 0.536186i | 0.963393 | + | 0.268093i | \(0.0863934\pi\) | ||||
−0.963393 | + | 0.268093i | \(0.913607\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.06892e6i | 0.718642i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −130591. | −0.0212615 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.86158e6 | 0.881353 | 0.440676 | − | 0.897666i | \(-0.354739\pi\) | ||||
0.440676 | + | 0.897666i | \(0.354739\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.43544e6i | 1.03434i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 921379.i | − 0.118781i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.67673e6 | 1.15797 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.46999e7 | −1.63536 | −0.817682 | − | 0.575670i | \(-0.804741\pi\) | ||||
−0.817682 | + | 0.575670i | \(0.804741\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.58990e7i | 1.64682i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.80039e6i | 0.753340i | 0.926347 | + | 0.376670i | \(0.122931\pi\) | ||||
−0.926347 | + | 0.376670i | \(0.877069\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.20366e7 | 1.08536 | 0.542678 | − | 0.839941i | \(-0.317410\pi\) | ||||
0.542678 | + | 0.839941i | \(0.317410\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −766701. | −0.0646343 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.89549e7i | 1.49582i | 0.663802 | + | 0.747908i | \(0.268942\pi\) | ||||
−0.663802 | + | 0.747908i | \(0.731058\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.75553e7i | 1.29842i | 0.760608 | + | 0.649212i | \(0.224901\pi\) | ||||
−0.760608 | + | 0.649212i | \(0.775099\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −413510. | −0.0286982 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.26566e7 | 1.47713 | 0.738566 | − | 0.674181i | \(-0.235503\pi\) | ||||
0.738566 | + | 0.674181i | \(0.235503\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.52993e6i | 0.523001i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 2.26503e7i | − 1.30745i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.02653e6 | 0.436630 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.37881e7 | −1.73386 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.22878e6i | 0.107994i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 9.00926e6i | − 0.412576i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.34969e7 | 1.88428 | 0.942140 | − | 0.335220i | \(-0.108810\pi\) | ||||
0.942140 | + | 0.335220i | \(0.108810\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 369779. | 0.0151663 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 2.44242e7i | − 0.949230i | −0.880194 | − | 0.474615i | \(-0.842587\pi\) | ||||
0.880194 | − | 0.474615i | \(-0.157413\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1.90887e7i | − 0.703553i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.68053e6 | 0.163730 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.33908e7 | 0.777184 | 0.388592 | − | 0.921410i | \(-0.372962\pi\) | ||||
0.388592 | + | 0.921410i | \(0.372962\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.57032e6i | 0.270673i | 0.990800 | + | 0.135337i | \(0.0432116\pi\) | ||||
−0.990800 | + | 0.135337i | \(0.956788\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.36307e6i | 0.0709920i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.58979e7 | 2.17047 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.60032e7 | 0.435933 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 923596.i | − 0.0239812i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 837746.i | − 0.0207472i | −0.999946 | − | 0.0103736i | \(-0.996698\pi\) | ||||
0.999946 | − | 0.0103736i | \(-0.00330209\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.95926e7 | 0.935825 | 0.467912 | − | 0.883775i | \(-0.345006\pi\) | ||||
0.467912 | + | 0.883775i | \(0.345006\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.44510e7 | −0.551920 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.12910e8i | 2.43542i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.58442e7i | 0.739213i | 0.929188 | + | 0.369607i | \(0.120508\pi\) | ||||
−0.929188 | + | 0.369607i | \(0.879492\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.38923e6 | −0.0668669 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.68265e7 | 0.317763 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.00430e7i | 0.362498i | 0.983437 | + | 0.181249i | \(0.0580139\pi\) | ||||
−0.983437 | + | 0.181249i | \(0.941986\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.82617e6i | 0.135630i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.04947e7 | −0.672807 | −0.336403 | − | 0.941718i | \(-0.609211\pi\) | ||||
−0.336403 | + | 0.941718i | \(0.609211\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.53784e7 | −0.723178 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.81494e7i | 0.889322i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.72293e7i | 0.840345i | 0.907444 | + | 0.420172i | \(0.138030\pi\) | ||||
−0.907444 | + | 0.420172i | \(0.861970\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.80916e7 | 0.537275 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.95834e6 | 0.0807643 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.52231e8i | 1.98389i | 0.126660 | + | 0.991946i | \(0.459574\pi\) | ||||
−0.126660 | + | 0.991946i | \(0.540426\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 2.20505e7i | − 0.276403i | −0.990404 | − | 0.138201i | \(-0.955868\pi\) | ||||
0.990404 | − | 0.138201i | \(-0.0441321\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16797.9 | −0.000202617 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.06735e7 | 0.588410 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 8.19315e7i | − 0.916231i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 9.23303e6i | − 0.0994782i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.06826e8 | −1.10933 | −0.554666 | − | 0.832073i | \(-0.687154\pi\) | ||||
−0.554666 | + | 0.832073i | \(0.687154\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.77720e7 | 0.678577 | 0.339289 | − | 0.940682i | \(-0.389814\pi\) | ||||
0.339289 | + | 0.940682i | \(0.389814\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 1.11494e7i | − 0.107679i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.58559e6i | 0.0427330i | 0.999772 | + | 0.0213665i | \(0.00680168\pi\) | ||||
−0.999772 | + | 0.0213665i | \(0.993198\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.30771e7 | 0.837254 | 0.418627 | − | 0.908158i | \(-0.362512\pi\) | ||||
0.418627 | + | 0.908158i | \(0.362512\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.12631e7 | −0.0978297 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 3.15687e7i | − 0.264862i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 2.73126e8i | − 2.21424i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.12581e7 | −0.401667 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.94850e8 | −1.47635 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1.64300e8i | − 1.20407i | −0.798472 | − | 0.602033i | \(-0.794358\pi\) | ||||
0.798472 | − | 0.602033i | \(-0.205642\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.23643e6i | 0.0583997i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.53146e7 | −0.310959 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.22732e8 | 1.47970 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.48220e6i | 0.0352696i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.16723e8i | 0.727414i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.50678e8 | 0.909880 | 0.454940 | − | 0.890522i | \(-0.349661\pi\) | ||||
0.454940 | + | 0.890522i | \(0.349661\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.16037e8 | −0.679139 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.08452e8i | 0.615384i | 0.951486 | + | 0.307692i | \(0.0995567\pi\) | ||||
−0.951486 | + | 0.307692i | \(0.900443\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.21842e8i | 1.22073i | 0.792120 | + | 0.610366i | \(0.208978\pi\) | ||||
−0.792120 | + | 0.610366i | \(0.791022\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.54382e7 | 0.0824054 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.54008e8 | −0.797620 | −0.398810 | − | 0.917034i | \(-0.630577\pi\) | ||||
−0.398810 | + | 0.917034i | \(0.630577\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 2.89582e8i | − 1.45557i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 6.70509e6i | − 0.0327179i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.75515e8 | −1.77924 | −0.889620 | − | 0.456701i | \(-0.849031\pi\) | ||||
−0.889620 | + | 0.456701i | \(0.849031\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.33310e8 | −1.07368 | −0.536839 | − | 0.843684i | \(-0.680382\pi\) | ||||
−0.536839 | + | 0.843684i | \(0.680382\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.22176e7i | 0.188743i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.13182e8i | 0.491696i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.77591e8 | 1.17210 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.26197e6 | −0.0339145 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 3.97050e8i | − 1.58485i | −0.609972 | − | 0.792423i | \(-0.708819\pi\) | ||||
0.609972 | − | 0.792423i | \(-0.291181\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1.71758e8i | − 0.666800i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.20358e7 | −0.0454552 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.13203e8 | 1.88592 | 0.942960 | − | 0.332907i | \(-0.108029\pi\) | ||||
0.942960 | + | 0.332907i | \(0.108029\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 9.99609e7i | − 0.357504i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.61666e7i | 0.334798i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.43951e6 | 0.0252173 | 0.0126087 | − | 0.999921i | \(-0.495986\pi\) | ||||
0.0126087 | + | 0.999921i | \(0.495986\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.15333e8 | 1.37100 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.73384e7i | 0.0557469i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.30769e7i | 0.291547i | 0.989318 | + | 0.145774i | \(0.0465671\pi\) | ||||
−0.989318 | + | 0.145774i | \(0.953433\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.06914e8 | −0.631534 | −0.315767 | − | 0.948837i | \(-0.602262\pi\) | ||||
−0.315767 | + | 0.948837i | \(0.602262\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.19939e7 | −0.0654233 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 3.88824e8i | − 1.12743i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 5.45157e8i | − 1.54114i | −0.637354 | − | 0.770571i | \(-0.719971\pi\) | ||||
0.637354 | − | 0.770571i | \(-0.280029\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.78502e8 | −1.87041 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.34356e8 | −0.361230 | −0.180615 | − | 0.983554i | \(-0.557809\pi\) | ||||
−0.180615 | + | 0.983554i | \(0.557809\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2.03505e8i | − 0.533731i | −0.963734 | − | 0.266865i | \(-0.914012\pi\) | ||||
0.963734 | − | 0.266865i | \(-0.0859879\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.86236e7i | 0.0732431i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.38781e8 | −1.34532 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.84337e8 | −0.692933 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 4.34821e7i | − 0.103439i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.57765e8i | 0.366415i | 0.983074 | + | 0.183207i | \(0.0586480\pi\) | ||||
−0.983074 | + | 0.183207i | \(0.941352\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.30165e8 | −1.65594 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.42469e7 | −0.208747 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.44693e8i | 0.529386i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.93896e7i | 0.188931i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.30734e7 | −0.0476499 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.05850e6 | 0.00415433 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 3.79087e8i | − 0.747747i | −0.927480 | − | 0.373873i | \(-0.878029\pi\) | ||||
0.927480 | − | 0.373873i | \(-0.121971\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.56039e7i | 0.0686504i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.18149e8 | −1.16528 | −0.582642 | − | 0.812729i | \(-0.697981\pi\) | ||||
−0.582642 | + | 0.812729i | \(0.697981\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.64450e8 | −0.856119 | −0.428060 | − | 0.903751i | \(-0.640803\pi\) | ||||
−0.428060 | + | 0.903751i | \(0.640803\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.64597e8i | 1.01777i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.44567e8i | − 0.254895i | −0.991845 | − | 0.127447i | \(-0.959322\pi\) | ||||
0.991845 | − | 0.127447i | \(-0.0406784\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.22240e8 | −0.555792 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.60682e7 | −0.0946127 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2.99658e8i | − 0.494785i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.53932e8i | 0.895086i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.19283e7 | −0.0821273 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.71243e8 | −0.884372 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 4.95770e8i | − 0.751418i | −0.926738 | − | 0.375709i | \(-0.877399\pi\) | ||||
0.926738 | − | 0.375709i | \(-0.122601\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.04508e8i | 0.451901i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.38023e9 | 2.00584 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.05972e9 | 1.50830 | 0.754148 | − | 0.656705i | \(-0.228050\pi\) | ||||
0.754148 | + | 0.656705i | \(0.228050\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.70177e7i | 0.0934308i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 2.27356e9i | − 3.10503i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.12147e8 | 1.08669 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.52314e7 | −0.0330806 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 3.45456e8i | − 0.443853i | −0.975063 | − | 0.221927i | \(-0.928765\pi\) | ||||
0.975063 | − | 0.221927i | \(-0.0712345\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.46126e9i | 1.84009i | 0.391811 | + | 0.920046i | \(0.371849\pi\) | ||||
−0.391811 | + | 0.920046i | \(0.628151\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.34268e8 | 0.165728 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.48645e7 | −0.0542864 | −0.0271432 | − | 0.999632i | \(-0.508641\pi\) | ||||
−0.0271432 | + | 0.999632i | \(0.508641\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 1.00933e9i | − 1.19739i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.37423e7i | 0.0276175i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.28983e8 | −0.375269 | −0.187634 | − | 0.982239i | \(-0.560082\pi\) | ||||
−0.187634 | + | 0.982239i | \(0.560082\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.81223e8 | 0.202739 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 9.99445e7i | − 0.109670i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 6.71817e8i | − 0.723146i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.26178e8 | −0.661251 | −0.330626 | − | 0.943762i | \(-0.607260\pi\) | ||||
−0.330626 | + | 0.943762i | \(0.607260\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.64127e9 | 1.70055 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 8.19305e8i | − 0.832985i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.10119e9i | 1.09870i | 0.835591 | + | 0.549352i | \(0.185125\pi\) | ||||
−0.835591 | + | 0.549352i | \(0.814875\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.66492e7 | 0.0260961 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.59075e8 | 0.441254 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.96469e8i | 0.279732i | 0.990170 | + | 0.139866i | \(0.0446672\pi\) | ||||
−0.990170 | + | 0.139866i | \(0.955333\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.28663e8i | 0.119184i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.05233e8 | 0.641412 | 0.320706 | − | 0.947179i | \(-0.396080\pi\) | ||||
0.320706 | + | 0.947179i | \(0.396080\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.89188e9 | −1.68959 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 2.72305e8i | − 0.238818i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.28994e9i | 1.11108i | 0.831491 | + | 0.555539i | \(0.187488\pi\) | ||||
−0.831491 | + | 0.555539i | \(0.812512\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.64145e8 | 0.223472 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.22464e7 | 0.0600402 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.21675e8i | 0.670827i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 1.73147e9i | − 1.38883i | −0.719576 | − | 0.694414i | \(-0.755664\pi\) | ||||
0.719576 | − | 0.694414i | \(-0.244336\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.64641e7 | 0.0445008 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.16737e8 | −0.555079 | −0.277539 | − | 0.960714i | \(-0.589519\pi\) | ||||
−0.277539 | + | 0.960714i | \(0.589519\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.23899e9i | 2.46514i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 1.71298e9i | − 1.28132i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.02036e9 | −0.750192 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.14164e8 | −0.443867 | −0.221934 | − | 0.975062i | \(-0.571237\pi\) | ||||
−0.221934 | + | 0.975062i | \(0.571237\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.91896e7i | 0.0491580i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.44036e9i | 1.00611i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.01246e9 | 0.695362 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.53508e7 | −0.0171205 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.45049e8i | 0.295569i | 0.989020 | + | 0.147785i | \(0.0472142\pi\) | ||||
−0.989020 | + | 0.147785i | \(0.952786\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.16226e9i | 1.41228i | 0.708072 | + | 0.706140i | \(0.249565\pi\) | ||||
−0.708072 | + | 0.706140i | \(0.750435\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.74016e9 | 1.11789 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.97968e8 | 0.377848 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 4.06069e6i | − 0.00252407i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.24504e8i | 0.137285i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.00597e9 | −0.605221 | −0.302611 | − | 0.953114i | \(-0.597858\pi\) | ||||
−0.302611 | + | 0.953114i | \(0.597858\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.27827e9 | −0.756684 | −0.378342 | − | 0.925666i | \(-0.623506\pi\) | ||||
−0.378342 | + | 0.925666i | \(0.623506\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.73372e7i | 0.0275734i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 6.28192e8i | − 0.360087i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.69631e9 | 1.52105 | 0.760526 | − | 0.649307i | \(-0.224941\pi\) | ||||
0.760526 | + | 0.649307i | \(0.224941\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.80134e8 | −0.377624 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.14940e9i | 1.17464i | 0.809355 | + | 0.587319i | \(0.199817\pi\) | ||||
−0.809355 | + | 0.587319i | \(0.800183\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 2.12474e9i | − 1.14300i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.47804e6 | 0.00131229 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.72637e8 | 0.142142 | 0.0710710 | − | 0.997471i | \(-0.477358\pi\) | ||||
0.0710710 | + | 0.997471i | \(0.477358\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.49966e9i | 2.82304i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.17114e8i | 0.0591923i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.69524e9 | 1.34140 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.75201e9 | 1.34879 | 0.674393 | − | 0.738372i | \(-0.264405\pi\) | ||||
0.674393 | + | 0.738372i | \(0.264405\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 1.44941e8i | − 0.0699597i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 2.98450e9i | − 1.41879i | −0.704810 | − | 0.709396i | \(-0.748968\pi\) | ||||
0.704810 | − | 0.709396i | \(-0.251032\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.35761e9 | −1.10392 | −0.551961 | − | 0.833870i | \(-0.686120\pi\) | ||||
−0.551961 | + | 0.833870i | \(0.686120\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.33987e8 | −0.154044 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.25311e9i | 0.569353i | 0.958624 | + | 0.284677i | \(0.0918862\pi\) | ||||
−0.958624 | + | 0.284677i | \(0.908114\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 2.72271e9i | − 1.21870i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.06026e8 | −0.0467564 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.12452e8 | 0.396457 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1.42209e9i | − 0.608836i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.49582e9i | 1.05293i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.16863e8 | 0.381180 | 0.190590 | − | 0.981670i | \(-0.438960\pi\) | ||||
0.190590 | + | 0.981670i | \(0.438960\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.45364e9 | 0.595593 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.97725e7i | 0.0200990i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.32852e9i | 2.12085i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.04379e8 | 0.0409507 | 0.0204754 | − | 0.999790i | \(-0.493482\pi\) | ||||
0.0204754 | + | 0.999790i | \(0.493482\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.92867e7 | −0.0229285 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.13088e9i | 0.431152i | 0.976487 | + | 0.215576i | \(0.0691629\pi\) | ||||
−0.976487 | + | 0.215576i | \(0.930837\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4.95570e8i | − 0.186269i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.76317e9 | 2.13572 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.99106e9 | −0.727505 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.91325e8i | 0.104960i | 0.998622 | + | 0.0524802i | \(0.0167126\pi\) | ||||
−0.998622 | + | 0.0524802i | \(0.983287\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 1.19782e8i | − 0.0425560i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.54979e7 | 0.0124370 | 0.00621848 | − | 0.999981i | \(-0.498021\pi\) | ||||
0.00621848 | + | 0.999981i | \(0.498021\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.82753e9 | 0.976983 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 1.34228e8i | − 0.0457421i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.24184e8i | 0.176186i | 0.996112 | + | 0.0880929i | \(0.0280773\pi\) | ||||
−0.996112 | + | 0.0880929i | \(0.971923\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.32526e9 | −0.439366 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.44701e8 | −0.112728 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 4.36308e9i | − 1.40756i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.83101e9i | 1.85578i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.69283e8 | −0.0531531 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.69562e9 | −1.76445 | −0.882224 | − | 0.470830i | \(-0.843954\pi\) | ||||
−0.882224 | + | 0.470830i | \(0.843954\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.65242e9i | 0.505086i | 0.967586 | + | 0.252543i | \(0.0812669\pi\) | ||||
−0.967586 | + | 0.252543i | \(0.918733\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.12674e8i | 0.0339834i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.49648e9 | 1.04062 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.85108e9 | −0.837365 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 4.38771e9i | − 1.27177i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 7.83501e9i | − 2.24127i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.87088e9 | 1.93988 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.50297e8 | −0.125484 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 2.27903e9i | − 0.626887i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 9.74487e8i | − 0.264598i | −0.991210 | − | 0.132299i | \(-0.957764\pi\) | ||||
0.991210 | − | 0.132299i | \(-0.0422358\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.52248e7 | 0.0174829 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.36356e9 | 1.68388 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.69600e9i | 1.48804i | 0.668158 | + | 0.744020i | \(0.267083\pi\) | ||||
−0.668158 | + | 0.744020i | \(0.732917\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.23699e7i | 0.00319054i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.17857e9 | −0.300140 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.62087e9 | 0.407578 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.49891e8i | 0.0372178i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.93761e9i | 1.45586i | 0.685653 | + | 0.727929i | \(0.259517\pi\) | ||||
−0.685653 | + | 0.727929i | \(0.740483\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.29991e9 | −0.314755 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.42352e8 | 0.0579530 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.27832e9i | 0.301898i | 0.988542 | + | 0.150949i | \(0.0482329\pi\) | ||||
−0.988542 | + | 0.150949i | \(0.951767\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 8.21268e9i | − 1.91565i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.37909e9 | −0.778502 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.00139e8 | 0.204841 | 0.102420 | − | 0.994741i | \(-0.467341\pi\) | ||||
0.102420 | + | 0.994741i | \(0.467341\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.35919e9i | 0.979894i | 0.871752 | + | 0.489947i | \(0.162984\pi\) | ||||
−0.871752 | + | 0.489947i | \(0.837016\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 3.15990e8i | − 0.0701669i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.25356e9 | 0.274984 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.38461e8 | 0.116691 | 0.0583457 | − | 0.998296i | \(-0.481417\pi\) | ||||
0.0583457 | + | 0.998296i | \(0.481417\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.00468e8i | 0.0429210i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 1.99723e9i | − 0.422485i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.36313e9 | −1.74795 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.21042e9 | −1.69559 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.48508e8i | 0.152744i | 0.997079 | + | 0.0763718i | \(0.0243336\pi\) | ||||
−0.997079 | + | 0.0763718i | \(0.975666\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 8.31536e9i | − 1.67679i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.35641e7 | −0.00270292 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.19788e9 | 1.22054 | 0.610269 | − | 0.792194i | \(-0.291061\pi\) | ||||
0.610269 | + | 0.792194i | \(0.291061\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 2.90950e9i | − 0.566251i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.75320e8i | 0.0529576i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.22711e9 | −1.56406 | −0.782030 | − | 0.623241i | \(-0.785816\pi\) | ||||
−0.782030 | + | 0.623241i | \(0.785816\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.54211e9 | −0.289772 | −0.144886 | − | 0.989448i | \(-0.546281\pi\) | ||||
−0.144886 | + | 0.989448i | \(0.546281\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.29410e9i | 1.54049i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.22477e10i | 2.24859i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.19592e9 | −0.942979 | −0.471490 | − | 0.881872i | \(-0.656283\pi\) | ||||
−0.471490 | + | 0.881872i | \(0.656283\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.33795e7 | 0.0167529 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 8.30707e9i | − 1.47334i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.51568e9i | 1.66851i | 0.551380 | + | 0.834254i | \(0.314101\pi\) | ||||
−0.551380 | + | 0.834254i | \(0.685899\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.07902e8 | 0.140054 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.68458e9 | −0.288731 | −0.144365 | − | 0.989524i | \(-0.546114\pi\) | ||||
−0.144365 | + | 0.989524i | \(0.546114\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 1.82919e9i | − 0.309985i | −0.987916 | − | 0.154993i | \(-0.950465\pi\) | ||||
0.987916 | − | 0.154993i | \(-0.0495354\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 3.03850e8i | − 0.0509141i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.19136e9 | −0.694458 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.42752e9 | −1.21692 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 5.76363e8i | − 0.0933812i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 1.56920e9i | − 0.251421i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.37467e9 | −1.16853 | −0.584265 | − | 0.811563i | \(-0.698617\pi\) | ||||
−0.584265 | + | 0.811563i | \(0.698617\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.85997e8 | 0.0761589 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.57670e10i | − 2.44366i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.24679e9i | 0.497698i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.06529e9 | 0.919599 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.89218e8 | −0.118357 | −0.0591785 | − | 0.998247i | \(-0.518848\pi\) | ||||
−0.0591785 | + | 0.998247i | \(0.518848\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 7.69347e9i | − 1.14126i | −0.821208 | − | 0.570629i | \(-0.806700\pi\) | ||||
0.821208 | − | 0.570629i | \(-0.193300\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 1.34040e8i | − 0.0196686i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.01740e9 | −0.292837 | −0.146419 | − | 0.989223i | \(-0.546775\pi\) | ||||
−0.146419 | + | 0.989223i | \(0.546775\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.47026e10 | 2.11124 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.58837e8i | 0.0935933i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 2.41614e9i | − 0.339567i | −0.985481 | − | 0.169784i | \(-0.945693\pi\) | ||||
0.985481 | − | 0.169784i | \(-0.0543069\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.85343e9 | −1.23103 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.03708e9 | 0.555378 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 6.27602e9i | − 0.854251i | −0.904192 | − | 0.427126i | \(-0.859526\pi\) | ||||
0.904192 | − | 0.427126i | \(-0.140474\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 2.24996e9i | − 0.303018i | −0.988456 | − | 0.151509i | \(-0.951587\pi\) | ||||
0.988456 | − | 0.151509i | \(-0.0484133\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.45263e8 | −0.0460101 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.91940e9 | −0.912415 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1.03889e9i | − 0.135560i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.45704e8i | 0.0575513i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.14498e7 | −0.00529656 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.16874e9 | −0.400714 | −0.200357 | − | 0.979723i | \(-0.564210\pi\) | ||||
−0.200357 | + | 0.979723i | \(0.564210\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 6.87851e8i | − 0.0860857i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.37662e9i | 0.294373i | 0.989109 | + | 0.147187i | \(0.0470218\pi\) | ||||
−0.989109 | + | 0.147187i | \(0.952978\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.05113e10 | 1.28858 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.20798e8 | −0.0389240 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 5.19062e9i | − 0.623371i | −0.950185 | − | 0.311685i | \(-0.899107\pi\) | ||||
0.950185 | − | 0.311685i | \(-0.100893\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 8.47884e9i | − 1.00790i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.56205e8 | −0.0772131 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.19144e10 | 1.38773 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.24469e10i | 1.43512i | 0.696496 | + | 0.717560i | \(0.254741\pi\) | ||||
−0.696496 | + | 0.717560i | \(0.745259\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1.13687e10i | − 1.29761i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.10662e9 | 0.351027 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.45786e9 | −0.946119 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 4.55551e8i | − 0.0504507i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.62046e8i | 0.0616253i | 0.999525 | + | 0.0308126i | \(0.00980952\pi\) | ||||
−0.999525 | + | 0.0308126i | \(0.990190\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.73188e9 | −0.405121 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.56579e8 | 0.0920673 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 5.57771e9i | − 0.593592i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.37748e10i | 1.45152i | 0.687949 | + | 0.725759i | \(0.258511\pi\) | ||||
−0.687949 | + | 0.725759i | \(0.741489\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.93762e9 | −0.515197 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.32989e9 | 0.757328 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 2.75119e10i | − 2.81481i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1.11077e9i | − 0.112540i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.36301e10 | −1.36757 | −0.683785 | − | 0.729684i | \(-0.739667\pi\) | ||||
−0.683785 | + | 0.729684i | \(0.739667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.60681e9 | −0.855203 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 6.90128e8i | − 0.0679118i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 2.35183e9i | − 0.229205i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.17899e10 | 1.13799 | 0.568995 | − | 0.822341i | \(-0.307333\pi\) | ||||
0.568995 | + | 0.822341i | \(0.307333\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.02101e10 | 0.976075 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.40325e9i | 0.132869i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 9.79375e9i | − 0.918513i | −0.888304 | − | 0.459256i | \(-0.848116\pi\) | ||||
0.888304 | − | 0.459256i | \(-0.151884\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.34790e8 | −0.0311005 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.77923e10 | −2.55734 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.85928e9i | 0.625206i | 0.949884 | + | 0.312603i | \(0.101201\pi\) | ||||
−0.949884 | + | 0.312603i | \(0.898799\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.21107e8i | 0.0741372i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.71545e10 | −1.53433 | −0.767164 | − | 0.641451i | \(-0.778333\pi\) | ||||
−0.767164 | + | 0.641451i | \(0.778333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.03671e8 | −0.0269064 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.08410e9i | 0.534040i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1.35538e10i | − 1.17862i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.15572e10 | 0.995665 | 0.497832 | − | 0.867273i | \(-0.334130\pi\) | ||||
0.497832 | + | 0.867273i | \(0.334130\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.17447e9 | 0.100244 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 1.43517e10i | − 1.21364i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.28367e10i | 1.07552i | 0.843099 | + | 0.537758i | \(0.180729\pi\) | ||||
−0.843099 | + | 0.537758i | \(0.819271\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.08057e8 | 0.0421761 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.25308e9 | 0.761097 | 0.380549 | − | 0.924761i | \(-0.375735\pi\) | ||||
0.380549 | + | 0.924761i | \(0.375735\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.25530e10i | − 1.02309i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.86312e9i | 0.715767i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.09458e10 | −1.67615 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.83050e9 | −0.700234 | −0.350117 | − | 0.936706i | \(-0.613858\pi\) | ||||
−0.350117 | + | 0.936706i | \(0.613858\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.51804e9i | 0.119287i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.19769e10i | 0.932645i | 0.884615 | + | 0.466323i | \(0.154421\pi\) | ||||
−0.884615 | + | 0.466323i | \(0.845579\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.65933e10 | 1.28049 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.95682e8 | 0.0226127 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.01146e10i | 1.52451i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.03239e10i | 1.52661i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.70061e8 | −0.0424380 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.29930e10 | 0.958662 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.01486e10i | 0.742155i | 0.928602 | + | 0.371077i | \(0.121012\pi\) | ||||
−0.928602 | + | 0.371077i | \(0.878988\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.20059e7i | 0.00159503i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.62007e10 | −1.16390 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.90509e7 | 0.00420505 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.22855e9i | 0.0867176i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 2.13861e10i | − 1.49633i | −0.663512 | − | 0.748166i | \(-0.730935\pi\) | ||||
0.663512 | − | 0.748166i | \(-0.269065\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.96745e9 | −0.621950 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.27680e10 | 0.877827 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.35277e10i | 0.921973i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 6.09937e9i | − 0.412097i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.75320e8 | −0.0184408 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.11340e10 | −0.739318 | −0.369659 | − | 0.929168i | \(-0.620525\pi\) | ||||
−0.369659 | + | 0.929168i | \(0.620525\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.29809e9i | 0.414606i | 0.978277 | + | 0.207303i | \(0.0664686\pi\) | ||||
−0.978277 | + | 0.207303i | \(0.933531\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 6.12047e8i | − 0.0399455i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.26528e9 | 0.470112 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.33722e9 | 0.214096 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.61962e10i | 1.03020i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1.63187e10i | − 1.02916i | −0.857442 | − | 0.514581i | \(-0.827948\pi\) | ||||
0.857442 | − | 0.514581i | \(-0.172052\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.61829e9 | 0.538917 | 0.269458 | − | 0.963012i | \(-0.413155\pi\) | ||||
0.269458 | + | 0.963012i | \(0.413155\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.15013e9 | 0.0713114 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.60314e9i | 0.467437i | 0.972304 | + | 0.233719i | \(0.0750895\pi\) | ||||
−0.972304 | + | 0.233719i | \(0.924911\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.02101e9i | 0.306091i | 0.988219 | + | 0.153045i | \(0.0489081\pi\) | ||||
−0.988219 | + | 0.153045i | \(0.951092\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.61256e9 | 0.0974796 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.50489e9 | 0.210096 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.46787e10i | 0.872542i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 4.02205e9i | − 0.237087i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.34694e10 | −0.787376 | −0.393688 | − | 0.919244i | \(-0.628801\pi\) | ||||
−0.393688 | + | 0.919244i | \(0.628801\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.53008e10 | 0.887008 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 3.97421e8i | − 0.0228483i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.64490e10i | 0.937867i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.41604e10 | 1.36619 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.01963e8 | 0.0337593 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 3.28961e9i | − 0.182975i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.08663e10i | 0.599461i | 0.954024 | + | 0.299731i | \(0.0968968\pi\) | ||||
−0.954024 | + | 0.299731i | \(0.903103\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.10783e10 | 1.15333 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.18222e9 | 0.281244 | 0.140622 | − | 0.990063i | \(-0.455090\pi\) | ||||
0.140622 | + | 0.990063i | \(0.455090\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.90203e9i | 0.371536i | 0.982594 | + | 0.185768i | \(0.0594773\pi\) | ||||
−0.982594 | + | 0.185768i | \(0.940523\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 1.59370e9i | − 0.0850935i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.60877e10 | 0.852033 | 0.426017 | − | 0.904715i | \(-0.359916\pi\) | ||||
0.426017 | + | 0.904715i | \(0.359916\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.07448e10 | 1.08982 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 8.41064e8i | − 0.0438290i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.65452e10i | − 0.855270i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.95939e10 | 2.03032 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.20201e10 | −1.62882 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.44212e9i | 0.325088i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1.08720e10i | − 0.544266i | −0.962260 | − | 0.272133i | \(-0.912271\pi\) | ||||
0.962260 | − | 0.272133i | \(-0.0877291\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.66664e8 | −0.0231763 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.06281e10 | −1.01635 | −0.508176 | − | 0.861253i | \(-0.669680\pi\) | ||||
−0.508176 | + | 0.861253i | \(0.669680\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 3.77865e10i | − 1.84703i | −0.383562 | − | 0.923515i | \(-0.625303\pi\) | ||||
0.383562 | − | 0.923515i | \(-0.374697\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 2.15981e9i | − 0.104741i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.65710e9 | −0.224070 | −0.112035 | − | 0.993704i | \(-0.535737\pi\) | ||||
−0.112035 | + | 0.993704i | \(0.535737\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.11027e10 | −1.48471 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.44924e10i | 1.63362i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.13265e10i | 1.00216i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.51816e10 | 2.57285 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.23797e8 | −0.0334844 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1.37518e10i | − 0.631249i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1.28616e10i | − 0.585811i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.64413e8 | −0.0119502 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.99298e9 | −0.358458 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.02909e10i | 0.902975i | 0.892277 | + | 0.451488i | \(0.149106\pi\) | ||||
−0.892277 | + | 0.451488i | \(0.850894\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.69912e10i | 0.750327i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.59071e10 | 0.697069 | 0.348535 | − | 0.937296i | \(-0.386679\pi\) | ||||
0.348535 | + | 0.937296i | \(0.386679\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.03869e10 | −0.886551 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.08900e6i | 0 0.000262768i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.74647e10i | 0.747942i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.82106e10 | −0.773963 | −0.386981 | − | 0.922088i | \(-0.626482\pi\) | ||||
−0.386981 | + | 0.922088i | \(0.626482\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.12133e9 | 0.0472961 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 2.89541e10i | − 1.21201i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 7.44698e9i | − 0.309374i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.62187e10 | 1.08101 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.72491e9 | 0.397952 | 0.198976 | − | 0.980004i | \(-0.436238\pi\) | ||||
0.198976 | + | 0.980004i | \(0.436238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 8.33536e9i | − 0.338533i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 1.82847e9i | − 0.0737060i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.96990e10 | −1.18823 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.22623e10 | 1.28117 | 0.640585 | − | 0.767887i | \(-0.278692\pi\) | ||||
0.640585 | + | 0.767887i | \(0.278692\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 1.37384e9i | − 0.0541508i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 2.31558e9i | − 0.0905933i | −0.998974 | − | 0.0452966i | \(-0.985577\pi\) | ||||
0.998974 | − | 0.0452966i | \(-0.0144233\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.77307e10 | −0.688551 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.34684e9 | −0.129010 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.20741e10i | 0.844612i | 0.906453 | + | 0.422306i | \(0.138779\pi\) | ||||
−0.906453 | + | 0.422306i | \(0.861221\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 1.92720e10i | − 0.731973i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.27626e8 | 0.0161225 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.01706e9 | −0.0380647 | −0.0190323 | − | 0.999819i | \(-0.506059\pi\) | ||||
−0.0190323 | + | 0.999819i | \(0.506059\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.87230e10i | 1.43866i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 9.53180e8i | − 0.0351547i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.67257e10 | −0.612379 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.95130e10 | 2.52659 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.12885e10i | 1.48983i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 2.45664e10i | − 0.880026i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.62288e10 | 1.28843 | 0.644216 | − | 0.764844i | \(-0.277184\pi\) | ||||
0.644216 | + | 0.764844i | \(0.277184\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.86382e8 | 0.0312959 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.55229e9i | 0.194628i | 0.995254 | + | 0.0973139i | \(0.0310251\pi\) | ||||
−0.995254 | + | 0.0973139i | \(0.968975\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 6.12825e9i | − 0.213276i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.63852e9 | −0.0566156 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.96135e10 | 0.672861 | 0.336430 | − | 0.941708i | \(-0.390780\pi\) | ||||
0.336430 | + | 0.941708i | \(0.390780\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.27836e10i | 1.45726i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.82399e10i | 1.29323i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.57104e10 | 0.863319 | 0.431659 | − | 0.902037i | \(-0.357928\pi\) | ||||
0.431659 | + | 0.902037i | \(0.357928\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.66221e9 | 0.0554190 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1.68973e9i | − 0.0559379i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.94172e9i | 0.0966974i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.56956e9 | 0.0838688 | 0.0419344 | − | 0.999120i | \(-0.486648\pi\) | ||||
0.0419344 | + | 0.999120i | \(0.486648\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.46648e9 | 0.0475284 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 3.37391e10i | − 1.08581i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 5.32099e10i | − 1.70043i | −0.526433 | − | 0.850216i | \(-0.676471\pi\) | ||||
0.526433 | − | 0.850216i | \(-0.323529\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.80507e9 | −0.0572816 |
(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 | 256.8.b.l.129.4 | 6 | ||
4.3 | odd | 2 | 256.8.b.k.129.3 | 6 | |||
8.3 | odd | 2 | 256.8.b.k.129.4 | 6 | |||
8.5 | even | 2 | inner | 256.8.b.l.129.3 | 6 | ||
16.3 | odd | 4 | 128.8.a.c.1.2 | yes | 3 | ||
16.5 | even | 4 | 128.8.a.d.1.2 | yes | 3 | ||
16.11 | odd | 4 | 128.8.a.b.1.2 | yes | 3 | ||
16.13 | even | 4 | 128.8.a.a.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
128.8.a.a.1.2 | ✓ | 3 | 16.13 | even | 4 | ||
128.8.a.b.1.2 | yes | 3 | 16.11 | odd | 4 | ||
128.8.a.c.1.2 | yes | 3 | 16.3 | odd | 4 | ||
128.8.a.d.1.2 | yes | 3 | 16.5 | even | 4 | ||
256.8.b.k.129.3 | 6 | 4.3 | odd | 2 | |||
256.8.b.k.129.4 | 6 | 8.3 | odd | 2 | |||
256.8.b.l.129.3 | 6 | 8.5 | even | 2 | inner | ||
256.8.b.l.129.4 | 6 | 1.1 | even | 1 | trivial |