Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,6,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, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.129");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
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: | \(41.0582578721\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 4) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.129 |
Dual form | 256.6.b.g.129.1 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 12.0000i | 0.769800i | 0.922958 | + | 0.384900i | \(0.125764\pi\) | ||||
−0.922958 | + | 0.384900i | \(0.874236\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 54.0000i | 0.965981i | 0.875625 | + | 0.482991i | \(0.160450\pi\) | ||||
−0.875625 | + | 0.482991i | \(0.839550\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 88.0000 | 0.678793 | 0.339397 | − | 0.940643i | \(-0.389777\pi\) | ||||
0.339397 | + | 0.940643i | \(0.389777\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 99.0000 | 0.407407 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 540.000i | 1.34559i | 0.739830 | + | 0.672794i | \(0.234906\pi\) | ||||
−0.739830 | + | 0.672794i | \(0.765094\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 418.000i | 0.685990i | 0.939337 | + | 0.342995i | \(0.111441\pi\) | ||||
−0.939337 | + | 0.342995i | \(0.888559\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −648.000 | −0.743613 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 594.000 | 0.498499 | 0.249249 | − | 0.968439i | \(-0.419816\pi\) | ||||
0.249249 | + | 0.968439i | \(0.419816\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 836.000i | − 0.531279i | −0.964072 | − | 0.265639i | \(-0.914417\pi\) | ||||
0.964072 | − | 0.265639i | \(-0.0855830\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1056.00i | 0.522535i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4104.00 | 1.61766 | 0.808831 | − | 0.588041i | \(-0.200101\pi\) | ||||
0.808831 | + | 0.588041i | \(0.200101\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 209.000 | 0.0668800 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4104.00i | 1.08342i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 594.000i | 0.131157i | 0.997847 | + | 0.0655785i | \(0.0208893\pi\) | ||||
−0.997847 | + | 0.0655785i | \(0.979111\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4256.00 | 0.795422 | 0.397711 | − | 0.917511i | \(-0.369805\pi\) | ||||
0.397711 | + | 0.917511i | \(0.369805\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6480.00 | −1.03583 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4752.00i | 0.655702i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 298.000i | − 0.0357859i | −0.999840 | − | 0.0178930i | \(-0.994304\pi\) | ||||
0.999840 | − | 0.0178930i | \(-0.00569581\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5016.00 | −0.528075 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −17226.0 | −1.60039 | −0.800193 | − | 0.599742i | \(-0.795270\pi\) | ||||
−0.800193 | + | 0.599742i | \(0.795270\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 12100.0i | − 0.997963i | −0.866613 | − | 0.498981i | \(-0.833708\pi\) | ||||
0.866613 | − | 0.498981i | \(-0.166292\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5346.00i | 0.393548i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1296.00 | −0.0855777 | −0.0427888 | − | 0.999084i | \(-0.513624\pi\) | ||||
−0.0427888 | + | 0.999084i | \(0.513624\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9063.00 | −0.539240 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7128.00i | 0.383745i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 19494.0i | 0.953260i | 0.879104 | + | 0.476630i | \(0.158142\pi\) | ||||
−0.879104 | + | 0.476630i | \(0.841858\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −29160.0 | −1.29981 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10032.0 | 0.408978 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 7668.00i | − 0.286782i | −0.989666 | − | 0.143391i | \(-0.954199\pi\) | ||||
0.989666 | − | 0.143391i | \(-0.0458007\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 34738.0i | 1.19531i | 0.801754 | + | 0.597655i | \(0.203901\pi\) | ||||
−0.801754 | + | 0.597655i | \(0.796099\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8712.00 | 0.276545 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −22572.0 | −0.662654 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 21812.0i | − 0.593620i | −0.954937 | − | 0.296810i | \(-0.904077\pi\) | ||||
0.954937 | − | 0.296810i | \(-0.0959228\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 49248.0i | 1.24528i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 46872.0 | 1.10349 | 0.551744 | − | 0.834014i | \(-0.313963\pi\) | ||||
0.551744 | + | 0.834014i | \(0.313963\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −67562.0 | −1.48387 | −0.741934 | − | 0.670473i | \(-0.766091\pi\) | ||||
−0.741934 | + | 0.670473i | \(0.766091\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2508.00i | 0.0514842i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 47520.0i | 0.913376i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −76912.0 | −1.38652 | −0.693260 | − | 0.720687i | \(-0.743826\pi\) | ||||
−0.693260 | + | 0.720687i | \(0.743826\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −25191.0 | −0.426612 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 67716.0i | − 1.07894i | −0.842006 | − | 0.539468i | \(-0.818625\pi\) | ||||
0.842006 | − | 0.539468i | \(-0.181375\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 32076.0i | 0.481541i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7128.00 | −0.100965 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −29754.0 | −0.398172 | −0.199086 | − | 0.979982i | \(-0.563797\pi\) | ||||
−0.199086 | + | 0.979982i | \(0.563797\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 36784.0i | 0.465646i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 51072.0i | 0.612316i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 45144.0 | 0.513205 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −122398. | −1.32082 | −0.660412 | − | 0.750903i | \(-0.729618\pi\) | ||||
−0.660412 | + | 0.750903i | \(0.729618\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 53460.0i | 0.548202i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11286.0i | 0.110087i | 0.998484 | + | 0.0550436i | \(0.0175298\pi\) | ||||
−0.998484 | + | 0.0550436i | \(0.982470\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 27256.0 | 0.253145 | 0.126572 | − | 0.991957i | \(-0.459602\pi\) | ||||
0.126572 | + | 0.991957i | \(0.459602\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −57024.0 | −0.504759 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 122364.i | 1.03322i | 0.856220 | + | 0.516612i | \(0.172807\pi\) | ||||
−0.856220 | + | 0.516612i | \(0.827193\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 99902.0i | − 0.805393i | −0.915334 | − | 0.402697i | \(-0.868073\pi\) | ||||
0.915334 | − | 0.402697i | \(-0.131927\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3576.00 | 0.0275480 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −29646.0 | −0.218409 | −0.109204 | − | 0.994019i | \(-0.534830\pi\) | ||||
−0.109204 | + | 0.994019i | \(0.534830\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 221616.i | 1.56263i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 41382.0i | 0.279477i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 52272.0 | 0.338378 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −130549. | −0.810607 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 206712.i | − 1.23198i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 180036.i | 1.03059i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 336512. | 1.85136 | 0.925681 | − | 0.378305i | \(-0.123493\pi\) | ||||
0.925681 | + | 0.378305i | \(0.123493\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 145200. | 0.768232 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 100980.i | − 0.514111i | −0.966397 | − | 0.257056i | \(-0.917248\pi\) | ||||
0.966397 | − | 0.257056i | \(-0.0827524\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 73568.0i | − 0.360628i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −221616. | −1.04657 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 317142. | 1.44362 | 0.721809 | − | 0.692092i | \(-0.243311\pi\) | ||||
0.721809 | + | 0.692092i | \(0.243311\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 148324.i | − 0.651140i | −0.945518 | − | 0.325570i | \(-0.894444\pi\) | ||||
0.945518 | − | 0.325570i | \(-0.105556\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 15552.0i | − 0.0658777i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −225720. | −0.923060 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −32076.0 | −0.126695 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 108756.i | − 0.415107i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 196614.i | 0.725519i | 0.931883 | + | 0.362759i | \(0.118165\pi\) | ||||
−0.931883 | + | 0.362759i | \(0.881835\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −74360.0 | −0.265398 | −0.132699 | − | 0.991156i | \(-0.542364\pi\) | ||||
−0.132699 | + | 0.991156i | \(0.542364\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 58806.0 | 0.203092 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 229824.i | 0.768362i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 120878.i | − 0.391380i | −0.980666 | − | 0.195690i | \(-0.937305\pi\) | ||||
0.980666 | − | 0.195690i | \(-0.0626946\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −233928. | −0.733820 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 361152. | 1.09806 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 111340.i | 0.328233i | 0.986441 | + | 0.164116i | \(0.0524773\pi\) | ||||
−0.986441 | + | 0.164116i | \(0.947523\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 349920.i | − 1.00060i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 491832. | 1.36466 | 0.682332 | − | 0.731043i | \(-0.260966\pi\) | ||||
0.682332 | + | 0.731043i | \(0.260966\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 196569. | 0.529417 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 82764.0i | − 0.216447i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 707454.i | − 1.79714i | −0.438826 | − | 0.898572i | \(-0.644605\pi\) | ||||
0.438826 | − | 0.898572i | \(-0.355395\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18392.0 | 0.0453977 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 92016.0 | 0.220765 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 493668.i | − 1.15160i | −0.817590 | − | 0.575801i | \(-0.804690\pi\) | ||||
0.817590 | − | 0.575801i | \(-0.195310\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 559450.i | − 1.26930i | −0.772799 | − | 0.634651i | \(-0.781144\pi\) | ||||
0.772799 | − | 0.634651i | \(-0.218856\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −416856. | −0.920149 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16092.0 | 0.0345685 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 320760.i | 0.670774i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 361152.i | 0.735420i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −724032. | −1.43607 | −0.718033 | − | 0.696009i | \(-0.754957\pi\) | ||||
−0.718033 | + | 0.696009i | \(0.754957\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7106.00 | 0.0137319 | 0.00686597 | − | 0.999976i | \(-0.497814\pi\) | ||||
0.00686597 | + | 0.999976i | \(0.497814\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 270864.i | − 0.510111i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 530442.i | − 0.973806i | −0.873456 | − | 0.486903i | \(-0.838127\pi\) | ||||
0.873456 | − | 0.486903i | \(-0.161873\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −56168.0 | −0.100544 | −0.0502720 | − | 0.998736i | \(-0.516009\pi\) | ||||
−0.0502720 | + | 0.998736i | \(0.516009\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 261744. | 0.456969 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 52272.0i | 0.0890285i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 930204.i | − 1.54594i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 406296. | 0.659047 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 451440. | 0.714882 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 339196.i | 0.524499i | 0.965000 | + | 0.262249i | \(0.0844643\pi\) | ||||
−0.965000 | + | 0.262249i | \(0.915536\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 562464.i | 0.849465i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 653400. | 0.964013 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 374528. | 0.539927 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 810744.i | − 1.14228i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 248292.i | 0.341965i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 779360. | 1.04948 | 0.524742 | − | 0.851261i | \(-0.324162\pi\) | ||||
0.524742 | + | 0.851261i | \(0.324162\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 20691.0 | 0.0272474 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 744876.i | 0.959443i | 0.877421 | + | 0.479722i | \(0.159262\pi\) | ||||
−0.877421 | + | 0.479722i | \(0.840738\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 272746.i | − 0.343692i | −0.985124 | − | 0.171846i | \(-0.945027\pi\) | ||||
0.985124 | − | 0.171846i | \(-0.0549732\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −570240. | −0.703117 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 153846. | 0.185651 | 0.0928253 | − | 0.995682i | \(-0.470410\pi\) | ||||
0.0928253 | + | 0.995682i | \(0.470410\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 69984.0i | − 0.0826664i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 922944.i | − 1.06734i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.15474e6 | 1.30764 | 0.653820 | − | 0.756650i | \(-0.273166\pi\) | ||||
0.653820 | + | 0.756650i | \(0.273166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 657074. | 0.728738 | 0.364369 | − | 0.931255i | \(-0.381285\pi\) | ||||
0.364369 | + | 0.931255i | \(0.381285\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 694980.i | 0.755017i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 489402.i | − 0.520895i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 349448. | 0.364452 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 812592. | 0.830566 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.34190e6i | 1.34442i | 0.740359 | + | 0.672211i | \(0.234655\pi\) | ||||
−0.740359 | + | 0.672211i | \(0.765345\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.21616e6i | 2.17671i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −384912. | −0.370690 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 132354. | 0.124998 | 0.0624992 | − | 0.998045i | \(-0.480093\pi\) | ||||
0.0624992 | + | 0.998045i | \(0.480093\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 26224.0i | − 0.0242912i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 58806.0i | 0.0534343i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −943272. | −0.840906 | −0.420453 | − | 0.907314i | \(-0.638129\pi\) | ||||
−0.420453 | + | 0.907314i | \(0.638129\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.05268e6 | −0.920831 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 357048.i | − 0.306513i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 967518.i | − 0.815227i | −0.913155 | − | 0.407613i | \(-0.866361\pi\) | ||||
0.913155 | − | 0.407613i | \(-0.133639\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −518320. | −0.428721 | −0.214360 | − | 0.976755i | \(-0.568767\pi\) | ||||
−0.214360 | + | 0.976755i | \(0.568767\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −441408. | −0.358454 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 112860.i | 0.0899929i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.22273e6i | 1.74055i | 0.492566 | + | 0.870275i | \(0.336059\pi\) | ||||
−0.492566 | + | 0.870275i | \(0.663941\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 421344. | 0.324061 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 196614. | 0.148542 | 0.0742709 | − | 0.997238i | \(-0.476337\pi\) | ||||
0.0742709 | + | 0.997238i | \(0.476337\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1.55228e6i | − 1.15213i | −0.817403 | − | 0.576067i | \(-0.804587\pi\) | ||||
0.817403 | − | 0.576067i | \(-0.195413\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 541728.i | 0.395066i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.51589e6 | −1.08633 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.06702e6 | −0.751499 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 1.46878e6i | − 1.01677i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 1.07217e6i | − 0.729616i | −0.931083 | − | 0.364808i | \(-0.881135\pi\) | ||||
0.931083 | − | 0.364808i | \(-0.118865\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 414072. | 0.277026 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.21616e6 | −1.45784 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.71547e6i | 1.10970i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.06480e6i | − 0.677410i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −135432. | −0.0847451 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.87585e6 | −1.15465 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.58589e6i | − 0.960346i | −0.877174 | − | 0.480173i | \(-0.840574\pi\) | ||||
0.877174 | − | 0.480173i | \(-0.159426\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 327072.i | 0.194871i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 730728. | 0.428405 | 0.214203 | − | 0.976789i | \(-0.431285\pi\) | ||||
0.214203 | + | 0.976789i | \(0.431285\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −584858. | −0.337435 | −0.168717 | − | 0.985664i | \(-0.553962\pi\) | ||||
−0.168717 | + | 0.985664i | \(0.553962\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 470448.i | 0.267138i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.48287e6i | 1.38773i | 0.720105 | + | 0.693865i | \(0.244094\pi\) | ||||
−0.720105 | + | 0.693865i | \(0.755906\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −320760. | −0.176483 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.46837e6 | −0.795376 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 496584.i | − 0.264842i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 87362.0i | 0.0458790i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.19882e6 | 0.619992 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −114048. | −0.0580895 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 377948.i | 0.189610i | 0.995496 | + | 0.0948052i | \(0.0302228\pi\) | ||||
−0.995496 | + | 0.0948052i | \(0.969777\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 29502.0i | − 0.0145794i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.17785e6 | 0.573426 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 639122. | 0.306555 | 0.153278 | − | 0.988183i | \(-0.451017\pi\) | ||||
0.153278 | + | 0.988183i | \(0.451017\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 355752.i | − 0.168131i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.29824e6i | 1.07031i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.27656e6 | −1.04483 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.65939e6 | −1.20291 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 2.90466e6i | − 1.29501i | −0.762063 | − | 0.647503i | \(-0.775813\pi\) | ||||
0.762063 | − | 0.647503i | \(-0.224187\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.99157e6i | 1.75420i | 0.480304 | + | 0.877102i | \(0.340526\pi\) | ||||
−0.480304 | + | 0.877102i | \(0.659474\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.71547e6 | −0.743217 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.42922e6 | 0.610466 | 0.305233 | − | 0.952278i | \(-0.401266\pi\) | ||||
0.305233 | + | 0.952278i | \(0.401266\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.53109e6i | 1.06595i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 627264.i | 0.260483i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.16186e6 | −0.475794 | −0.237897 | − | 0.971290i | \(-0.576458\pi\) | ||||
−0.237897 | + | 0.971290i | \(0.576458\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.77720e6 | 0.717743 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1.56659e6i | − 0.624005i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 3.64835e6i | − 1.43339i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.08923e6 | −0.422139 | −0.211069 | − | 0.977471i | \(-0.567695\pi\) | ||||
−0.211069 | + | 0.977471i | \(0.567695\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.70537e6 | −0.652009 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.71547e6i | 0.647066i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.50577e6i | 1.30470i | 0.757918 | + | 0.652350i | \(0.226217\pi\) | ||||
−0.757918 | + | 0.652350i | \(0.773783\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.16043e6 | −0.793346 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −248292. | −0.0899724 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.04385e6i | 1.44610i | 0.690798 | + | 0.723048i | \(0.257260\pi\) | ||||
−0.690798 | + | 0.723048i | \(0.742740\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.03814e6i | 1.42518i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.18746e6 | 1.80700 | 0.903499 | − | 0.428591i | \(-0.140990\pi\) | ||||
0.903499 | + | 0.428591i | \(0.140990\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.56608e6 | −0.882304 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1.19790e6i | − 0.406577i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 950346.i | − 0.318425i | −0.987244 | − | 0.159213i | \(-0.949104\pi\) | ||||
0.987244 | − | 0.159213i | \(-0.0508956\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.43778e6 | 0.806403 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.21176e6 | 0.395763 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 4.15325e6i | − 1.33935i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 520738.i | 0.165822i | 0.996557 | + | 0.0829112i | \(0.0264218\pi\) | ||||
−0.996557 | + | 0.0829112i | \(0.973578\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 882816. | 0.277612 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 764370. | 0.237379 | 0.118690 | − | 0.992931i | \(-0.462131\pi\) | ||||
0.118690 | + | 0.992931i | \(0.462131\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.77901e6i | 0.545651i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 1.36031e6i | − 0.412099i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 160920. | 0.0481531 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.64051e6 | −0.780511 | −0.390255 | − | 0.920707i | \(-0.627613\pi\) | ||||
−0.390255 | + | 0.920707i | \(0.627613\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.80570e6i | 1.11130i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 674784.i | − 0.194666i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.65666e6 | 1.04223 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.77989e6 | 0.501248 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.98020e6i | 1.38584i | 0.721016 | + | 0.692918i | \(0.243675\pi\) | ||||
−0.721016 | + | 0.692918i | \(0.756325\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 237994.i | − 0.0654426i | −0.999465 | − | 0.0327213i | \(-0.989583\pi\) | ||||
0.999465 | − | 0.0327213i | \(-0.0104174\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −128304. | −0.0348650 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 124146. | 0.0333396 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.05694e6i | 0.811368i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 2.70864e6i | − 0.710572i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.88238e6 | −1.00671 | −0.503356 | − | 0.864079i | \(-0.667902\pi\) | ||||
−0.503356 | + | 0.864079i | \(0.667902\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −66958.0 | −0.0171626 | −0.00858129 | − | 0.999963i | \(-0.502732\pi\) | ||||
−0.00858129 | + | 0.999963i | \(0.502732\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 384912.i | − 0.0975300i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3.43094e6i | − 0.859429i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.50135e6 | 1.61006 | 0.805031 | − | 0.593233i | \(-0.202149\pi\) | ||||
0.805031 | + | 0.593233i | \(0.202149\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −897237. | −0.219690 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 4.60760e6i | − 1.11549i | −0.830012 | − | 0.557745i | \(-0.811667\pi\) | ||||
0.830012 | − | 0.557745i | \(-0.188333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1.60672e6i | − 0.384626i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.35937e6 | −0.558505 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.77671e6 | 0.884092 | 0.442046 | − | 0.896992i | \(-0.354253\pi\) | ||||
0.442046 | + | 0.896992i | \(0.354253\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 9.30204e6i | − 2.15346i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 892320.i | − 0.204303i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.98634e6 | −0.449805 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.18069e6 | 0.712412 | 0.356206 | − | 0.934407i | \(-0.384070\pi\) | ||||
0.356206 | + | 0.934407i | \(0.384070\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.43778e6i | 0.540085i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 6.68547e6i | − 1.46514i | −0.680691 | − | 0.732571i | \(-0.738320\pi\) | ||||
0.680691 | − | 0.732571i | \(-0.261680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.35122e6 | −0.943318 | −0.471659 | − | 0.881781i | \(-0.656345\pi\) | ||||
−0.471659 | + | 0.881781i | \(0.656345\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.75789e6 | −0.591486 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 7.07994e6i | − 1.50223i | −0.660170 | − | 0.751117i | \(-0.729516\pi\) | ||||
0.660170 | − | 0.751117i | \(-0.270484\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 1.91946e6i | − 0.402945i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.45054e6 | 0.301284 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.53400e6 | 1.34285 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 174724.i | − 0.0355319i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.92991e6i | 0.388365i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.22186e6 | 0.641604 | 0.320802 | − | 0.947146i | \(-0.396048\pi\) | ||||
0.320802 | + | 0.947146i | \(0.396048\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 124564. | 0.0245488 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.33382e6i | 0.845286i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 6.60949e6i | − 1.27589i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.29710e6 | −0.438891 | −0.219446 | − | 0.975625i | \(-0.570425\pi\) | ||||
−0.219446 | + | 0.975625i | \(0.570425\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.33608e6 | −0.252674 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.82150e6i | 0.528173i | 0.964499 | + | 0.264087i | \(0.0850705\pi\) | ||||
−0.964499 | + | 0.264087i | \(0.914930\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 352836.i | 0.0653816i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.88684e6 | −0.529553 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.12474e6 | 0.749040 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.13628e6i | 0.743634i | 0.928306 | + | 0.371817i | \(0.121265\pi\) | ||||
−0.928306 | + | 0.371817i | \(0.878735\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.90198e6i | 1.05052i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.33263e6 | −1.46846 | −0.734230 | − | 0.678901i | \(-0.762457\pi\) | ||||
−0.734230 | + | 0.678901i | \(0.762457\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −609444. | −0.106342 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.35883e6i | 0.407546i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 4.34101e6i | − 0.742670i | −0.928499 | − | 0.371335i | \(-0.878900\pi\) | ||||
0.928499 | − | 0.371335i | \(-0.121100\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.94546e6 | −1.00724 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.43094e6 | 0.575599 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.47182e6i | 0.244533i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 699840.i | − 0.115152i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.48945e6 | 1.38344 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.74185e6 | 1.08814 | 0.544070 | − | 0.839040i | \(-0.316883\pi\) | ||||
0.544070 | + | 0.839040i | \(0.316883\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 7.72196e6i | − 1.23445i | −0.786787 | − | 0.617224i | \(-0.788257\pi\) | ||||
0.786787 | − | 0.617224i | \(-0.211743\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 220704.i | 0.0349472i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.52806e6 | 0.396517 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.04065e7 | 1.61683 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 759132.i | − 0.116837i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 7.20047e6i | − 1.09785i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.60766e6 | −0.998075 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.92402e6 | 0.886504 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 4.89402e6i | − 0.725594i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 682066.i | 0.100192i | 0.998744 | + | 0.0500960i | \(0.0159527\pi\) | ||||
−0.998744 | + | 0.0500960i | \(0.984047\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.71340e6 | 0.977109 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.39471e6 | 0.777995 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 2.15772e6i | − 0.308337i | −0.988045 | − | 0.154169i | \(-0.950730\pi\) | ||||
0.988045 | − | 0.154169i | \(-0.0492699\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.43906e6i | 0.486978i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 496584. | 0.0696809 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.76826e6 | −0.941161 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 193104.i | 0.0266109i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.67597e6i | 0.365463i | 0.983163 | + | 0.182731i | \(0.0584939\pi\) | ||||
−0.983163 | + | 0.182731i | \(0.941506\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.05780e6 | 0.684592 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.84912e6 | −0.516362 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.55331e6i | 0.472457i | 0.971698 | + | 0.236228i | \(0.0759113\pi\) | ||||
−0.971698 | + | 0.236228i | \(0.924089\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 1.60088e6i | − 0.210979i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.21681e6 | −0.289581 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.29225e7 | 1.67327 | 0.836633 | − | 0.547764i | \(-0.184521\pi\) | ||||
0.836633 | + | 0.547764i | \(0.184521\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 6.08357e6i | − 0.780851i | −0.920634 | − | 0.390426i | \(-0.872328\pi\) | ||||
0.920634 | − | 0.390426i | \(-0.127672\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 8.68838e6i | − 1.10548i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 857736. | 0.108189 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.58241e7 | −1.97869 | −0.989347 | − | 0.145579i | \(-0.953495\pi\) | ||||
−0.989347 | + | 0.145579i | \(0.953495\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 85272.0i | 0.0105709i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 5.95901e6i | − 0.732375i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.05268e7 | −1.28269 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.23463e6 | −0.269970 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.60220e6i | 0.551278i | 0.961261 | + | 0.275639i | \(0.0888894\pi\) | ||||
−0.961261 | + | 0.275639i | \(0.911111\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 3.55802e6i | − 0.422590i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.36530e6 | 0.749636 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.61122e6 | 1.00561 | 0.502803 | − | 0.864401i | \(-0.332302\pi\) | ||||
0.502803 | + | 0.864401i | \(0.332302\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.82269e6i | 0.326867i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 674016.i | − 0.0773988i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.98228e6 | 0.908992 | 0.454496 | − | 0.890749i | \(-0.349819\pi\) | ||||
0.454496 | + | 0.890749i | \(0.349819\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.01740e7 | −1.14896 | −0.574481 | − | 0.818518i | \(-0.694796\pi\) | ||||
−0.574481 | + | 0.818518i | \(0.694796\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 2.15939e6i | − 0.241845i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 7.04965e6i | − 0.783031i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.95843e6 | −1.09703 | −0.548516 | − | 0.836140i | \(-0.684807\pi\) | ||||
−0.548516 | + | 0.836140i | \(0.684807\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −627264. | −0.0685342 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 541728.i | − 0.0587054i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.19586e6i | 0.450993i | 0.974244 | + | 0.225497i | \(0.0724005\pi\) | ||||
−0.974244 | + | 0.225497i | \(0.927600\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.11624e7 | 1.19007 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.12551e6 | −0.965038 | −0.482519 | − | 0.875885i | \(-0.660278\pi\) | ||||
−0.482519 | + | 0.875885i | \(0.660278\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.45734e6i | 0.677372i | 0.940900 | + | 0.338686i | \(0.109982\pi\) | ||||
−0.940900 | + | 0.338686i | \(0.890018\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.68428e7i | 1.75261i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.61835e6 | −0.270276 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.06882e6 | −0.928647 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.41728e6i | 0.550316i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 177012.i | − 0.0178392i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.40514e7 | 1.40490 | 0.702450 | − | 0.711733i | \(-0.252090\pi\) | ||||
0.702450 | + | 0.711733i | \(0.252090\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.07035e6 | −0.403759 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.81716e7i | 1.78838i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3.78833e6i | − 0.369913i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.64033e6 | 0.449569 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.47168e6 | 0.814375 | 0.407188 | − | 0.913345i | \(-0.366510\pi\) | ||||
0.407188 | + | 0.913345i | \(0.366510\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 488564.i | − 0.0466009i | −0.999729 | − | 0.0233004i | \(-0.992583\pi\) | ||||
0.999729 | − | 0.0233004i | \(-0.00741743\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.84080e6i | 0.742098i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.48119e6 | −0.233023 | −0.116512 | − | 0.993189i | \(-0.537171\pi\) | ||||
−0.116512 | + | 0.993189i | \(0.537171\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.14072e6 | 0.385891 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.49434e6i | 0.415636i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.29130e6i | 0.485601i | 0.970076 | + | 0.242800i | \(0.0780660\pi\) | ||||
−0.970076 | + | 0.242800i | \(0.921934\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.45292e6 | 0.496622 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.68864e6 | −0.604539 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 4.72468e6i | − 0.423798i | −0.977292 | − | 0.211899i | \(-0.932035\pi\) | ||||
0.977292 | − | 0.211899i | \(-0.0679647\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 6.17420e6i | − 0.549639i | −0.961496 | − | 0.274819i | \(-0.911382\pi\) | ||||
0.961496 | − | 0.274819i | \(-0.0886180\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.97950e6 | −0.263245 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.97267e6 | 0.348360 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.43778e6i | 0.212168i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.35232e6i | 0.807893i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.87585e7 | −1.60839 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.40925e6 | −0.800787 | −0.400394 | − | 0.916343i | \(-0.631127\pi\) | ||||
−0.400394 | + | 0.916343i | \(0.631127\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 857736.i | 0.0724593i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.50086e7i | 1.25854i | 0.777185 | + | 0.629272i | \(0.216647\pi\) | ||||
−0.777185 | + | 0.629272i | \(0.783353\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.07710e7 | −0.896567 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.93851e6 | −0.738580 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.29707e7i | − 1.06393i | −0.846768 | − | 0.531963i | \(-0.821455\pi\) | ||||
0.846768 | − | 0.531963i | \(-0.178545\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.71257e7i | 1.39451i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.27295e6 | 0.264574 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.14849e6 | −0.653927 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 2.26556e7i | − 1.80501i | −0.430677 | − | 0.902506i | \(-0.641725\pi\) | ||||
0.430677 | − | 0.902506i | \(-0.358275\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.70448e6i | 0.372116i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.00950e6 | 0.628989 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.02322e7 | −0.797791 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.84615e6i | 0.142914i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 1.90169e7i | − 1.46166i | −0.682562 | − | 0.730828i | \(-0.739134\pi\) | ||||
0.682562 | − | 0.730828i | \(-0.260866\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −249128. | −0.0190123 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 839808. | 0.0636366 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 993168.i | 0.0747264i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.51311e7i | 1.13046i | 0.824933 | + | 0.565231i | \(0.191213\pi\) | ||||
−0.824933 | + | 0.565231i | \(0.808787\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.61429e6 | −0.564879 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.74666e7 | 1.28672 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1.21889e7i | − 0.891659i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.38568e7i | 1.00662i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.50323e7 | −1.08443 | −0.542217 | − | 0.840238i | \(-0.682415\pi\) | ||||
−0.542217 | + | 0.840238i | \(0.682415\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.39853e6 | 0.171833 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.88489e6i | 0.560983i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 124146.i | 0.00877178i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.41230e6 | 0.520136 | 0.260068 | − | 0.965590i | \(-0.416255\pi\) | ||||
0.260068 | + | 0.965590i | \(0.416255\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.44612e7 | −1.00782 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 7.18740e6i | − 0.497483i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.77928e6i | 0.191061i | 0.995426 | + | 0.0955306i | \(0.0304548\pi\) | ||||
−0.995426 | + | 0.0955306i | \(0.969545\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.87282e6 | 0.400985 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.17785e7 | 0.798768 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.21046e7i | 0.815342i | 0.913129 | + | 0.407671i | \(0.133659\pi\) | ||||
−0.913129 | + | 0.407671i | \(0.866341\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.19338e6i | 0.280555i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.46926e6 | −0.297005 | −0.148502 | − | 0.988912i | \(-0.547445\pi\) | ||||
−0.148502 | + | 0.988912i | \(0.547445\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.06172e7 | −0.700838 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 6.70388e6i | − 0.439567i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.07680e7i | 0.701345i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.88463e7 | 1.86634 | 0.933168 | − | 0.359442i | \(-0.117033\pi\) | ||||
0.933168 | + | 0.359442i | \(0.117033\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.61028e7 | −1.03494 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 4.01544e6i | − 0.256369i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.60868e6i | 0.609430i | 0.952444 | + | 0.304715i | \(0.0985612\pi\) | ||||
−0.952444 | + | 0.304715i | \(0.901439\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.65939e7 | −1.67563 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.54588e6 | −0.284549 | −0.142274 | − | 0.989827i | \(-0.545442\pi\) | ||||
−0.142274 | + | 0.989827i | \(0.545442\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 8.79138e6i | − 0.546696i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.17552e6i | 0.196183i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.20522e6 | 0.196730 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.15923e7 | −1.31669 | −0.658345 | − | 0.752716i | \(-0.728743\pi\) | ||||
−0.658345 | + | 0.752716i | \(0.728743\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.58825e6i | 0.0962238i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.48400e7i | − 0.893276i | −0.894715 | − | 0.446638i | \(-0.852621\pi\) | ||||
0.894715 | − | 0.446638i | \(-0.147379\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 889504. | 0.0531978 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 314688. | 0.0186994 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.44009e7i | 0.850251i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.53109e7i | 1.48484i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.43778e6 | −0.142098 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.52741e6 | 0.378065 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.48785e7i | 1.43182i | 0.698194 | + | 0.715909i | \(0.253987\pi\) | ||||
−0.698194 | + | 0.715909i | \(0.746013\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 1.13193e7i | − 0.647330i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.60885e6 | −0.148254 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.45205e7 | −0.819970 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 1.26321e7i | − 0.708856i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 3.16080e7i | − 1.76259i | −0.472568 | − | 0.881294i | \(-0.656673\pi\) | ||||
0.472568 | − | 0.881294i | \(-0.343327\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −769824. | −0.0426604 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.94565e6 | −0.162218 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 3.64835e7i | − 1.99668i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.95022e7i | 1.06070i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.16102e7 | 0.627562 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.10009e6 | 0.166534 | 0.0832669 | − | 0.996527i | \(-0.473465\pi\) | ||||
0.0832669 | + | 0.996527i | \(0.473465\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.87180e6i | 0.0999328i | 0.998751 | + | 0.0499664i | \(0.0159114\pi\) | ||||
−0.998751 | + | 0.0499664i | \(0.984089\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 6.21984e6i | − 0.330030i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.01236e6 | −0.317067 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.01156e7 | −0.530196 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.64162e6i | 0.189707i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 2.00184e7i | − 1.03650i | −0.855228 | − | 0.518252i | \(-0.826583\pi\) | ||||
0.855228 | − | 0.518252i | \(-0.173417\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.53118e7 | −0.787999 | −0.394000 | − | 0.919111i | \(-0.628909\pi\) | ||||
−0.394000 | + | 0.919111i | \(0.628909\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.35432e6 | −0.0692766 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.59310e6i | 0.487748i | 0.969807 | + | 0.243874i | \(0.0784183\pi\) | ||||
−0.969807 | + | 0.243874i | \(0.921582\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 2.52209e7i | − 1.27460i | −0.770615 | − | 0.637302i | \(-0.780051\pi\) | ||||
0.770615 | − | 0.637302i | \(-0.219949\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.66727e7 | −1.33988 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.38342e6 | −0.268810 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.65589e7i | 1.31824i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.74666e7i | 0.861778i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.77623e7 | 0.871154 | 0.435577 | − | 0.900151i | \(-0.356544\pi\) | ||||
0.435577 | + | 0.900151i | \(0.356544\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.01583e7 | 0.982798 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.35937e6i | 0.114348i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.06147e7i | 0.511407i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.14883e7 | −0.550234 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.86273e7 | 0.886913 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1.22299e6i | − 0.0578895i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 486970.i | − 0.0229155i | −0.999934 | − | 0.0114578i | \(-0.996353\pi\) | ||||
0.999934 | − | 0.0114578i | \(-0.00364720\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.46926e6 | 0.209084 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.92634e6 | 0.0895945 | 0.0447972 | − | 0.998996i | \(-0.485736\pi\) | ||||
0.0447972 | + | 0.998996i | \(0.485736\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.23538e7i | 1.03364i | 0.856094 | + | 0.516820i | \(0.172884\pi\) | ||||
−0.856094 | + | 0.516820i | \(0.827116\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 1.81907e7i | − 0.836258i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.85838e7 | 0.849390 | 0.424695 | − | 0.905337i | \(-0.360381\pi\) | ||||
0.424695 | + | 0.905337i | \(0.360381\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.82025e7 | 1.73601 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 1.28043e7i | − 0.578504i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 4.15325e7i | − 1.86569i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.11742e6 | 0.407217 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.21174e7 | −0.538114 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.58432e7i | 0.699555i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.91048e7i | 1.27781i | 0.769286 | + | 0.638905i | \(0.220612\pi\) | ||||
−0.769286 | + | 0.638905i | \(0.779388\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.28660e7 | 0.561659 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.14696e6 | −0.136600 | −0.0683001 | − | 0.997665i | \(-0.521758\pi\) | ||||
−0.0683001 | + | 0.997665i | \(0.521758\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1.59995e7i | − 0.690566i | −0.938499 | − | 0.345283i | \(-0.887783\pi\) | ||||
0.938499 | − | 0.345283i | \(-0.112217\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.96886e6i | 0.213255i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.45874e7 | 1.47608 | 0.738039 | − | 0.674758i | \(-0.235752\pi\) | ||||
0.738039 | + | 0.674758i | \(0.235752\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.96131e7 | 1.25669 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 1.36031e7i | − 0.574044i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.08346e6i | 0.0454656i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.66581e7 | 1.11243 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.05857e7 | −0.854248 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.52806e6i | 0.104325i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.15794e7i | 0.475199i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.27776e7 | 0.521471 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.02103e7 | 1.22612 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.74396e7i | 0.703914i | 0.936016 | + | 0.351957i | \(0.114484\pi\) | ||||
−0.936016 | + | 0.351957i | \(0.885516\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.11731e6i | 0.0448503i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.59589e6 | −0.103631 | −0.0518155 | − | 0.998657i | \(-0.516501\pi\) | ||||
−0.0518155 | + | 0.998657i | \(0.516501\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.65666e7 | 1.45180 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 2.25102e7i | − 0.888847i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 8.88624e6i | − 0.348975i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.76411e7 | 0.689028 | 0.344514 | − | 0.938781i | \(-0.388044\pi\) | ||||
0.344514 | + | 0.938781i | \(0.388044\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.90307e7 | 0.739275 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.95925e7i | 0.756982i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 62282.0i | − 0.00239336i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.69834e6 | 0.103133 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.96785e7 | 1.50840 | 0.754199 | − | 0.656646i | \(-0.228025\pi\) | ||||
0.754199 | + | 0.656646i | \(0.228025\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.57667e6i | 0.286486i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.76874e6i | 0.329787i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.73210e7 | −0.647955 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.93413e7 | −1.46386 | −0.731930 | − | 0.681380i | \(-0.761380\pi\) | ||||
−0.731930 | + | 0.681380i | \(0.761380\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 7.01830e6i | − 0.259757i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 4.62506e7i | − 1.70272i | −0.524581 | − | 0.851361i | \(-0.675778\pi\) | ||||
0.524581 | − | 0.851361i | \(-0.324222\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.06955e7 | −2.58888 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.95022e7 | −0.710402 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.79025e7i | 1.37339i | 0.726947 | + | 0.686693i | \(0.240938\pi\) | ||||
−0.726947 | + | 0.686693i | \(0.759062\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 2.82409e7i | − 1.01792i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.97944e7 | −1.06828 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.66462e7 | 0.950394 | 0.475197 | − | 0.879879i | \(-0.342377\pi\) | ||||
0.475197 | + | 0.879879i | \(0.342377\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 3.90977e7i | − 1.38721i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 3.84912e6i | − 0.135857i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.79085e7 | 0.979918 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.05156e7 | −0.367304 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.21140e7i | 0.420943i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 383724.i | 0.0132648i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.09790e7 | −1.40927 | −0.704637 | − | 0.709568i | \(-0.748890\pi\) | ||||
−0.704637 | + | 0.709568i | \(0.748890\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.95901e6 | 0.203875 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 2.72034e7i | − 0.925922i | −0.886379 | − | 0.462961i | \(-0.846787\pi\) | ||||
0.886379 | − | 0.462961i | \(-0.153213\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1.30525e7i | − 0.441990i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.04834e6 | −0.0353177 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.53555e7 | 0.849839 | 0.424919 | − | 0.905231i | \(-0.360302\pi\) | ||||
0.424919 | + | 0.905231i | \(0.360302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1.60672e7i | − 0.535775i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 9.89030e6i | − 0.328123i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.19139e7 | −0.393252 | −0.196626 | − | 0.980479i | \(-0.562998\pi\) | ||||
−0.196626 | + | 0.980479i | \(0.562998\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.86439e7 | 0.940678 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1.36858e6i | − 0.0447173i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 4.96584e7i | − 1.61437i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.91931e7 | 0.944268 | 0.472134 | − | 0.881527i | \(-0.343484\pi\) | ||||
0.472134 | + | 0.881527i | \(0.343484\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.53538e6 | −0.145962 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 3.03307e6i | − 0.0971237i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.73001e7i | − 0.551201i | −0.961272 | − | 0.275601i | \(-0.911123\pi\) | ||||
0.961272 | − | 0.275601i | \(-0.0888767\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.22299e6 | 0.0387713 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))