Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,4,Mod(1,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.a (trivial) |
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: | yes |
Analytic conductor: | \(8.49627504083\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 6) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 144.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.00000 | −0.536656 | −0.268328 | − | 0.963328i | \(-0.586471\pi\) | ||||
−0.268328 | + | 0.963328i | \(0.586471\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.0000 | 0.863919 | 0.431959 | − | 0.901893i | \(-0.357822\pi\) | ||||
0.431959 | + | 0.901893i | \(0.357822\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.0000 | 0.328921 | 0.164461 | − | 0.986384i | \(-0.447412\pi\) | ||||
0.164461 | + | 0.986384i | \(0.447412\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 38.0000 | 0.810716 | 0.405358 | − | 0.914158i | \(-0.367147\pi\) | ||||
0.405358 | + | 0.914158i | \(0.367147\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 126.000 | 1.79762 | 0.898808 | − | 0.438342i | \(-0.144434\pi\) | ||||
0.898808 | + | 0.438342i | \(0.144434\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −20.0000 | −0.241490 | −0.120745 | − | 0.992684i | \(-0.538528\pi\) | ||||
−0.120745 | + | 0.992684i | \(0.538528\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 168.000 | 1.52306 | 0.761531 | − | 0.648129i | \(-0.224448\pi\) | ||||
0.761531 | + | 0.648129i | \(0.224448\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −89.0000 | −0.712000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −30.0000 | −0.192099 | −0.0960493 | − | 0.995377i | \(-0.530621\pi\) | ||||
−0.0960493 | + | 0.995377i | \(0.530621\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 88.0000 | 0.509847 | 0.254924 | − | 0.966961i | \(-0.417950\pi\) | ||||
0.254924 | + | 0.966961i | \(0.417950\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −96.0000 | −0.463627 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 254.000 | 1.12858 | 0.564288 | − | 0.825578i | \(-0.309151\pi\) | ||||
0.564288 | + | 0.825578i | \(0.309151\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −42.0000 | −0.159983 | −0.0799914 | − | 0.996796i | \(-0.525489\pi\) | ||||
−0.0799914 | + | 0.996796i | \(0.525489\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 52.0000 | 0.184417 | 0.0922084 | − | 0.995740i | \(-0.470607\pi\) | ||||
0.0922084 | + | 0.995740i | \(0.470607\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −96.0000 | −0.297937 | −0.148969 | − | 0.988842i | \(-0.547595\pi\) | ||||
−0.148969 | + | 0.988842i | \(0.547595\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −87.0000 | −0.253644 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −198.000 | −0.513158 | −0.256579 | − | 0.966523i | \(-0.582595\pi\) | ||||
−0.256579 | + | 0.966523i | \(0.582595\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −72.0000 | −0.176518 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −660.000 | −1.45635 | −0.728175 | − | 0.685391i | \(-0.759631\pi\) | ||||
−0.728175 | + | 0.685391i | \(0.759631\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −538.000 | −1.12924 | −0.564622 | − | 0.825350i | \(-0.690978\pi\) | ||||
−0.564622 | + | 0.825350i | \(0.690978\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −228.000 | −0.435076 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −884.000 | −1.61191 | −0.805954 | − | 0.591979i | \(-0.798347\pi\) | ||||
−0.805954 | + | 0.591979i | \(0.798347\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 792.000 | 1.32385 | 0.661923 | − | 0.749572i | \(-0.269740\pi\) | ||||
0.661923 | + | 0.749572i | \(0.269740\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 218.000 | 0.349520 | 0.174760 | − | 0.984611i | \(-0.444085\pi\) | ||||
0.174760 | + | 0.984611i | \(0.444085\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 192.000 | 0.284161 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 520.000 | 0.740564 | 0.370282 | − | 0.928919i | \(-0.379261\pi\) | ||||
0.370282 | + | 0.928919i | \(0.379261\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −492.000 | −0.650651 | −0.325325 | − | 0.945602i | \(-0.605474\pi\) | ||||
−0.325325 | + | 0.945602i | \(0.605474\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −756.000 | −0.964703 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −810.000 | −0.964717 | −0.482359 | − | 0.875974i | \(-0.660220\pi\) | ||||
−0.482359 | + | 0.875974i | \(0.660220\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 608.000 | 0.700393 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 120.000 | 0.129597 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1154.00 | 1.20795 | 0.603974 | − | 0.797004i | \(-0.293583\pi\) | ||||
0.603974 | + | 0.797004i | \(0.293583\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 618.000 | 0.608845 | 0.304422 | − | 0.952537i | \(-0.401537\pi\) | ||||
0.304422 | + | 0.952537i | \(0.401537\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −128.000 | −0.122449 | −0.0612243 | − | 0.998124i | \(-0.519501\pi\) | ||||
−0.0612243 | + | 0.998124i | \(0.519501\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1476.00 | −1.33355 | −0.666777 | − | 0.745257i | \(-0.732327\pi\) | ||||
−0.666777 | + | 0.745257i | \(0.732327\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1190.00 | 1.04570 | 0.522850 | − | 0.852425i | \(-0.324869\pi\) | ||||
0.522850 | + | 0.852425i | \(0.324869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 462.000 | 0.384613 | 0.192307 | − | 0.981335i | \(-0.438403\pi\) | ||||
0.192307 | + | 0.981335i | \(0.438403\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1008.00 | −0.817361 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2016.00 | 1.55300 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1187.00 | −0.891811 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1284.00 | 0.918756 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2536.00 | 1.77192 | 0.885959 | − | 0.463763i | \(-0.153501\pi\) | ||||
0.885959 | + | 0.463763i | \(0.153501\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2292.00 | 1.52865 | 0.764324 | − | 0.644832i | \(-0.223073\pi\) | ||||
0.764324 | + | 0.644832i | \(0.223073\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −320.000 | −0.208628 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 726.000 | 0.452747 | 0.226374 | − | 0.974041i | \(-0.427313\pi\) | ||||
0.226374 | + | 0.974041i | \(0.427313\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −380.000 | −0.231879 | −0.115939 | − | 0.993256i | \(-0.536988\pi\) | ||||
−0.115939 | + | 0.993256i | \(0.536988\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 456.000 | 0.266662 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 180.000 | 0.103091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1590.00 | −0.874214 | −0.437107 | − | 0.899410i | \(-0.643997\pi\) | ||||
−0.437107 | + | 0.899410i | \(0.643997\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2432.00 | −1.31068 | −0.655342 | − | 0.755332i | \(-0.727476\pi\) | ||||
−0.655342 | + | 0.755332i | \(0.727476\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −528.000 | −0.273613 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 614.000 | 0.312118 | 0.156059 | − | 0.987748i | \(-0.450121\pi\) | ||||
0.156059 | + | 0.987748i | \(0.450121\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2688.00 | 1.31580 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1852.00 | 0.889938 | 0.444969 | − | 0.895546i | \(-0.353215\pi\) | ||||
0.444969 | + | 0.895546i | \(0.353215\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2136.00 | −0.989752 | −0.494876 | − | 0.868964i | \(-0.664787\pi\) | ||||
−0.494876 | + | 0.868964i | \(0.664787\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −753.000 | −0.342740 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1758.00 | −0.772591 | −0.386296 | − | 0.922375i | \(-0.626246\pi\) | ||||
−0.386296 | + | 0.922375i | \(0.626246\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1424.00 | −0.615110 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −540.000 | −0.225483 | −0.112742 | − | 0.993624i | \(-0.535963\pi\) | ||||
−0.112742 | + | 0.993624i | \(0.535963\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1982.00 | 0.813928 | 0.406964 | − | 0.913444i | \(-0.366588\pi\) | ||||
0.406964 | + | 0.913444i | \(0.366588\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1524.00 | −0.605658 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1512.00 | 0.591275 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2688.00 | −1.01831 | −0.509154 | − | 0.860675i | \(-0.670042\pi\) | ||||
−0.509154 | + | 0.860675i | \(0.670042\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2302.00 | −0.858557 | −0.429279 | − | 0.903172i | \(-0.641232\pi\) | ||||
−0.429279 | + | 0.903172i | \(0.641232\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4374.00 | −1.58190 | −0.790951 | − | 0.611880i | \(-0.790414\pi\) | ||||
−0.790951 | + | 0.611880i | \(0.790414\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1600.00 | 0.569955 | 0.284977 | − | 0.958534i | \(-0.408014\pi\) | ||||
0.284977 | + | 0.958534i | \(0.408014\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −480.000 | −0.165958 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 252.000 | 0.0858558 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −240.000 | −0.0794313 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3332.00 | −1.08713 | −0.543565 | − | 0.839367i | \(-0.682926\pi\) | ||||
−0.543565 | + | 0.839367i | \(0.682926\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −312.000 | −0.0989685 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1408.00 | 0.440467 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4788.00 | 1.45736 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2648.00 | −0.795171 | −0.397586 | − | 0.917565i | \(-0.630152\pi\) | ||||
−0.397586 | + | 0.917565i | \(0.630152\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2244.00 | 0.656121 | 0.328061 | − | 0.944657i | \(-0.393605\pi\) | ||||
0.328061 | + | 0.944657i | \(0.393605\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5650.00 | −1.63040 | −0.815202 | − | 0.579177i | \(-0.803374\pi\) | ||||
−0.815202 | + | 0.579177i | \(0.803374\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4698.00 | −1.32093 | −0.660464 | − | 0.750858i | \(-0.729640\pi\) | ||||
−0.660464 | + | 0.750858i | \(0.729640\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 576.000 | 0.159890 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1200.00 | −0.324776 | −0.162388 | − | 0.986727i | \(-0.551920\pi\) | ||||
−0.162388 | + | 0.986727i | \(0.551920\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −718.000 | −0.191911 | −0.0959553 | − | 0.995386i | \(-0.530591\pi\) | ||||
−0.0959553 | + | 0.995386i | \(0.530591\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 522.000 | 0.136120 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −760.000 | −0.195780 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6012.00 | 1.51185 | 0.755924 | − | 0.654659i | \(-0.227188\pi\) | ||||
0.755924 | + | 0.654659i | \(0.227188\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2016.00 | 0.500968 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2046.00 | 0.496599 | 0.248300 | − | 0.968683i | \(-0.420128\pi\) | ||||
0.248300 | + | 0.968683i | \(0.420128\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4064.00 | 0.974999 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6072.00 | −1.42363 | −0.711817 | − | 0.702365i | \(-0.752127\pi\) | ||||
−0.711817 | + | 0.702365i | \(0.752127\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1188.00 | 0.275390 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6930.00 | 1.57074 | 0.785371 | − | 0.619025i | \(-0.212472\pi\) | ||||
0.785371 | + | 0.619025i | \(0.212472\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1352.00 | −0.303056 | −0.151528 | − | 0.988453i | \(-0.548419\pi\) | ||||
−0.151528 | + | 0.988453i | \(0.548419\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1068.00 | −0.234192 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1186.00 | −0.257256 | −0.128628 | − | 0.991693i | \(-0.541057\pi\) | ||||
−0.128628 | + | 0.991693i | \(0.541057\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2442.00 | −0.518425 | −0.259213 | − | 0.965820i | \(-0.583463\pi\) | ||||
−0.259213 | + | 0.965820i | \(0.583463\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2828.00 | −0.594018 | −0.297009 | − | 0.954875i | \(-0.595989\pi\) | ||||
−0.297009 | + | 0.954875i | \(0.595989\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −672.000 | −0.138212 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10963.0 | 2.23143 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4758.00 | −0.948687 | −0.474344 | − | 0.880340i | \(-0.657315\pi\) | ||||
−0.474344 | + | 0.880340i | \(0.657315\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3960.00 | 0.781560 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6384.00 | 1.23477 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 832.000 | 0.159321 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3228.00 | 0.606016 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8476.00 | 1.57574 | 0.787868 | − | 0.615844i | \(-0.211185\pi\) | ||||
0.787868 | + | 0.615844i | \(0.211185\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4632.00 | 0.844555 | 0.422278 | − | 0.906467i | \(-0.361231\pi\) | ||||
0.422278 | + | 0.906467i | \(0.361231\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4822.00 | −0.870785 | −0.435392 | − | 0.900241i | \(-0.643390\pi\) | ||||
−0.435392 | + | 0.900241i | \(0.643390\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3426.00 | 0.607014 | 0.303507 | − | 0.952829i | \(-0.401842\pi\) | ||||
0.303507 | + | 0.952829i | \(0.401842\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −360.000 | −0.0631854 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2520.00 | −0.434107 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3382.00 | −0.577230 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1536.00 | −0.257393 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2788.00 | 0.462968 | 0.231484 | − | 0.972839i | \(-0.425642\pi\) | ||||
0.231484 | + | 0.972839i | \(0.425642\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5304.00 | 0.865040 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 434.000 | 0.0701528 | 0.0350764 | − | 0.999385i | \(-0.488833\pi\) | ||||
0.0350764 | + | 0.999385i | \(0.488833\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1056.00 | 0.167700 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6880.00 | −1.08305 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6684.00 | 1.03405 | 0.517026 | − | 0.855970i | \(-0.327039\pi\) | ||||
0.517026 | + | 0.855970i | \(0.327039\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2630.00 | 0.403383 | 0.201692 | − | 0.979449i | \(-0.435356\pi\) | ||||
0.201692 | + | 0.979449i | \(0.435356\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7422.00 | 1.11907 | 0.559537 | − | 0.828805i | \(-0.310979\pi\) | ||||
0.559537 | + | 0.828805i | \(0.310979\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4752.00 | −0.710451 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10440.0 | −1.53482 | −0.767412 | − | 0.641154i | \(-0.778456\pi\) | ||||
−0.767412 | + | 0.641154i | \(0.778456\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6459.00 | −0.941682 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1308.00 | −0.187572 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10424.0 | −1.48264 | −0.741319 | − | 0.671153i | \(-0.765800\pi\) | ||||
−0.741319 | + | 0.671153i | \(0.765800\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3168.00 | −0.443327 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3278.00 | 0.455036 | 0.227518 | − | 0.973774i | \(-0.426939\pi\) | ||||
0.227518 | + | 0.973774i | \(0.426939\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1140.00 | −0.155737 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6140.00 | −0.832165 | −0.416083 | − | 0.909327i | \(-0.636597\pi\) | ||||
−0.416083 | + | 0.909327i | \(0.636597\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3072.00 | −0.409848 | −0.204924 | − | 0.978778i | \(-0.565695\pi\) | ||||
−0.204924 | + | 0.978778i | \(0.565695\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1152.00 | −0.152497 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6150.00 | −0.801587 | −0.400794 | − | 0.916168i | \(-0.631266\pi\) | ||||
−0.400794 | + | 0.916168i | \(0.631266\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21168.0 | 2.73788 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3120.00 | −0.397428 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −106.000 | −0.0134005 | −0.00670024 | − | 0.999978i | \(-0.502133\pi\) | ||||
−0.00670024 | + | 0.999978i | \(0.502133\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1758.00 | 0.218929 | 0.109464 | − | 0.993991i | \(-0.465086\pi\) | ||||
0.109464 | + | 0.993991i | \(0.465086\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3344.00 | 0.413341 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3048.00 | 0.371213 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3670.00 | −0.443691 | −0.221846 | − | 0.975082i | \(-0.571208\pi\) | ||||
−0.221846 | + | 0.975082i | \(0.571208\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10560.0 | −1.25817 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2952.00 | 0.349176 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9660.00 | −1.12631 | −0.563153 | − | 0.826353i | \(-0.690412\pi\) | ||||
−0.563153 | + | 0.826353i | \(0.690412\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8462.00 | 0.979602 | 0.489801 | − | 0.871834i | \(-0.337069\pi\) | ||||
0.489801 | + | 0.871834i | \(0.337069\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11214.0 | −1.27990 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8608.00 | −0.975575 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9792.00 | 1.09435 | 0.547174 | − | 0.837019i | \(-0.315704\pi\) | ||||
0.547174 | + | 0.837019i | \(0.315704\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7342.00 | −0.814859 | −0.407430 | − | 0.913237i | \(-0.633575\pi\) | ||||
−0.407430 | + | 0.913237i | \(0.633575\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3360.00 | −0.367805 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10640.0 | −1.15676 | −0.578382 | − | 0.815766i | \(-0.696316\pi\) | ||||
−0.578382 | + | 0.815766i | \(0.696316\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17412.0 | −1.86742 | −0.933712 | − | 0.358024i | \(-0.883451\pi\) | ||||
−0.933712 | + | 0.358024i | \(0.883451\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4860.00 | 0.517722 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1710.00 | 0.179732 | 0.0898662 | − | 0.995954i | \(-0.471356\pi\) | ||||
0.0898662 | + | 0.995954i | \(0.471356\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −504.000 | −0.0526218 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3648.00 | −0.375870 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −646.000 | −0.0661239 | −0.0330619 | − | 0.999453i | \(-0.510526\pi\) | ||||
−0.0330619 | + | 0.999453i | \(0.510526\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6018.00 | 0.607996 | 0.303998 | − | 0.952673i | \(-0.401678\pi\) | ||||
0.303998 | + | 0.952673i | \(0.401678\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6712.00 | 0.673722 | 0.336861 | − | 0.941554i | \(-0.390635\pi\) | ||||
0.336861 | + | 0.941554i | \(0.390635\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5364.00 | 0.531512 | 0.265756 | − | 0.964040i | \(-0.414378\pi\) | ||||
0.265756 | + | 0.964040i | \(0.414378\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14144.0 | −1.39256 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 624.000 | 0.0606587 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1780.00 | 0.171941 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9840.00 | 0.938624 | 0.469312 | − | 0.883032i | \(-0.344502\pi\) | ||||
0.469312 | + | 0.883032i | \(0.344502\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9652.00 | 0.914955 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6924.00 | −0.648253 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1424.00 | −0.132500 | −0.0662501 | − | 0.997803i | \(-0.521104\pi\) | ||||
−0.0662501 | + | 0.997803i | \(0.521104\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4548.00 | −0.418021 | −0.209011 | − | 0.977913i | \(-0.567024\pi\) | ||||
−0.209011 | + | 0.977913i | \(0.567024\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3780.00 | −0.345320 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12672.0 | 1.14370 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6500.00 | −0.583126 | −0.291563 | − | 0.956552i | \(-0.594175\pi\) | ||||
−0.291563 | + | 0.956552i | \(0.594175\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12168.0 | 1.07862 | 0.539308 | − | 0.842108i | \(-0.318686\pi\) | ||||
0.539308 | + | 0.842108i | \(0.318686\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3708.00 | −0.326740 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21090.0 | 1.83654 | 0.918269 | − | 0.395957i | \(-0.129587\pi\) | ||||
0.918269 | + | 0.395957i | \(0.129587\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3488.00 | 0.301957 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 768.000 | 0.0657129 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1152.00 | −0.0979979 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5238.00 | 0.440462 | 0.220231 | − | 0.975448i | \(-0.429319\pi\) | ||||
0.220231 | + | 0.975448i | \(0.429319\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8588.00 | −0.718025 | −0.359012 | − | 0.933333i | \(-0.616886\pi\) | ||||
−0.359012 | + | 0.933333i | \(0.616886\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11088.0 | 0.916510 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16057.0 | 1.31972 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1596.00 | −0.129701 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8856.00 | 0.715660 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1044.00 | −0.0834291 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3062.00 | 0.243338 | 0.121669 | − | 0.992571i | \(-0.461175\pi\) | ||||
0.121669 | + | 0.992571i | \(0.461175\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7140.00 | −0.561182 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8476.00 | 0.662537 | 0.331268 | − | 0.943537i | \(-0.392523\pi\) | ||||
0.331268 | + | 0.943537i | \(0.392523\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 600.000 | 0.0463899 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8320.00 | 0.639787 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12546.0 | 0.954383 | 0.477191 | − | 0.878799i | \(-0.341655\pi\) | ||||
0.477191 | + | 0.878799i | \(0.341655\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1976.00 | 0.149510 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.0000 | −0.000898294 0 | −0.000449147 | − | 1.00000i | \(-0.500143\pi\) | ||||
−0.000449147 | 1.00000i | \(0.500143\pi\) | ||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2772.00 | −0.206405 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19290.0 | −1.42123 | −0.710614 | − | 0.703582i | \(-0.751583\pi\) | ||||
−0.710614 | + | 0.703582i | \(0.751583\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12148.0 | 0.890329 | 0.445165 | − | 0.895449i | \(-0.353145\pi\) | ||||
0.445165 | + | 0.895449i | \(0.353145\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14952.0 | −1.08442 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10366.0 | −0.747907 | −0.373953 | − | 0.927447i | \(-0.621998\pi\) | ||||
−0.373953 | + | 0.927447i | \(0.621998\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7872.00 | −0.562109 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2376.00 | −0.168789 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7644.00 | 0.537482 | 0.268741 | − | 0.963213i | \(-0.413393\pi\) | ||||
0.268741 | + | 0.963213i | \(0.413393\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1760.00 | −0.123123 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8658.00 | −0.599564 | −0.299782 | − | 0.954008i | \(-0.596914\pi\) | ||||
−0.299782 | + | 0.954008i | \(0.596914\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12096.0 | −0.833425 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25800.0 | 1.75987 | 0.879933 | − | 0.475098i | \(-0.157587\pi\) | ||||
0.879933 | + | 0.475098i | \(0.157587\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16202.0 | 1.09966 | 0.549828 | − | 0.835278i | \(-0.314693\pi\) | ||||
0.549828 | + | 0.835278i | \(0.314693\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7122.00 | 0.478596 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24136.0 | 1.61392 | 0.806960 | − | 0.590605i | \(-0.201111\pi\) | ||||
0.806960 | + | 0.590605i | \(0.201111\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3648.00 | −0.241542 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4642.00 | −0.305854 | −0.152927 | − | 0.988237i | \(-0.548870\pi\) | ||||
−0.152927 | + | 0.988237i | \(0.548870\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6726.00 | 0.438863 | 0.219432 | − | 0.975628i | \(-0.429580\pi\) | ||||
0.219432 | + | 0.975628i | \(0.429580\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21220.0 | 1.37787 | 0.688937 | − | 0.724821i | \(-0.258078\pi\) | ||||
0.688937 | + | 0.724821i | \(0.258078\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12960.0 | −0.833437 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3421.00 | 0.218944 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 32004.0 | 2.02875 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29792.0 | −1.87956 | −0.939779 | − | 0.341783i | \(-0.888969\pi\) | ||||
−0.939779 | + | 0.341783i | \(0.888969\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15216.0 | −0.950911 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3306.00 | −0.205633 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10158.0 | 0.625923 | 0.312962 | − | 0.949766i | \(-0.398679\pi\) | ||||
0.312962 | + | 0.949766i | \(0.398679\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29828.0 | −1.82940 | −0.914698 | − | 0.404138i | \(-0.867571\pi\) | ||||
−0.914698 | + | 0.404138i | \(0.867571\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1944.00 | 0.118124 | 0.0590622 | − | 0.998254i | \(-0.481189\pi\) | ||||
0.0590622 | + | 0.998254i | \(0.481189\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7920.00 | −0.479025 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26718.0 | −1.60116 | −0.800579 | − | 0.599227i | \(-0.795475\pi\) | ||||
−0.800579 | + | 0.599227i | \(0.795475\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13752.0 | −0.820359 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4260.00 | 0.251815 | 0.125907 | − | 0.992042i | \(-0.459816\pi\) | ||||
0.125907 | + | 0.992042i | \(0.459816\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22862.0 | 1.34528 | 0.672639 | − | 0.739971i | \(-0.265161\pi\) | ||||
0.672639 | + | 0.739971i | \(0.265161\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1920.00 | 0.111962 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5040.00 | −0.292578 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6456.00 | −0.371432 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32542.0 | −1.86390 | −0.931948 | − | 0.362592i | \(-0.881892\pi\) | ||||
−0.931948 | + | 0.362592i | \(0.881892\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14214.0 | −0.806925 | −0.403463 | − | 0.914996i | \(-0.632193\pi\) | ||||
−0.403463 | + | 0.914996i | \(0.632193\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18464.0 | 1.04357 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7092.00 | −0.397317 | −0.198659 | − | 0.980069i | \(-0.563659\pi\) | ||||
−0.198659 | + | 0.980069i | \(0.563659\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4356.00 | −0.242970 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7524.00 | −0.416026 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13228.0 | 0.728244 | 0.364122 | − | 0.931351i | \(-0.381369\pi\) | ||||
0.364122 | + | 0.931351i | \(0.381369\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2280.00 | 0.124439 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5292.00 | −0.287588 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28062.0 | −1.51196 | −0.755982 | − | 0.654592i | \(-0.772840\pi\) | ||||
−0.755982 | + | 0.654592i | \(0.772840\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5080.00 | −0.272540 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9888.00 | 0.525992 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27250.0 | −1.44343 | −0.721717 | − | 0.692188i | \(-0.756647\pi\) | ||||
−0.721717 | + | 0.692188i | \(0.756647\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14784.0 | 0.776529 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2736.00 | −0.143106 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14400.0 | −0.746912 | −0.373456 | − | 0.927648i | \(-0.621827\pi\) | ||||
−0.373456 | + | 0.927648i | \(0.621827\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2048.00 | −0.105786 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2670.00 | 0.136774 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17984.0 | −0.917455 | −0.458727 | − | 0.888577i | \(-0.651695\pi\) | ||||
−0.458727 | + | 0.888577i | \(0.651695\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6552.00 | 0.331511 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16598.0 | 0.836373 | 0.418186 | − | 0.908361i | \(-0.362666\pi\) | ||||
0.418186 | + | 0.908361i | \(0.362666\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10608.0 | −0.530191 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1460.00 | −0.0726752 | −0.0363376 | − | 0.999340i | \(-0.511569\pi\) | ||||
−0.0363376 | + | 0.999340i | \(0.511569\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30072.0 | −1.48484 | −0.742419 | − | 0.669936i | \(-0.766322\pi\) | ||||
−0.742419 | + | 0.669936i | \(0.766322\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9540.00 | 0.469152 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23616.0 | −1.15208 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18088.0 | 0.878882 | 0.439441 | − | 0.898271i | \(-0.355177\pi\) | ||||
0.439441 | + | 0.898271i | \(0.355177\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14592.0 | 0.703387 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24734.0 | 1.18755 | 0.593773 | − | 0.804633i | \(-0.297638\pi\) | ||||
0.593773 | + | 0.804633i | \(0.297638\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22278.0 | 1.06120 | 0.530602 | − | 0.847621i | \(-0.321966\pi\) | ||||
0.530602 | + | 0.847621i | \(0.321966\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19040.0 | 0.903400 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25080.0 | −1.18069 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16130.0 | 0.756388 | 0.378194 | − | 0.925726i | \(-0.376545\pi\) | ||||
0.378194 | + | 0.925726i | \(0.376545\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29718.0 | −1.38277 | −0.691386 | − | 0.722486i | \(-0.742999\pi\) | ||||
−0.691386 | + | 0.722486i | \(0.742999\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7832.00 | −0.363011 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 840.000 | 0.0386343 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9504.00 | 0.435442 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3684.00 | −0.167500 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9524.00 | −0.431377 | −0.215689 | − | 0.976462i | \(-0.569200\pi\) | ||||
−0.215689 | + | 0.976462i | \(0.569200\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7392.00 | 0.332275 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20444.0 | −0.915495 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33906.0 | 1.50692 | 0.753458 | − | 0.657496i | \(-0.228384\pi\) | ||||
0.753458 | + | 0.657496i | \(0.228384\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12096.0 | −0.535577 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2616.00 | 0.114965 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16128.0 | −0.706133 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 630.000 | 0.0273790 | 0.0136895 | − | 0.999906i | \(-0.495642\pi\) | ||||
0.0136895 | + | 0.999906i | \(0.495642\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20788.0 | 0.900081 | 0.450040 | − | 0.893008i | \(-0.351410\pi\) | ||||
0.450040 | + | 0.893008i | \(0.351410\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11112.0 | −0.477591 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1040.00 | −0.0445349 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 43098.0 | 1.83207 | 0.916036 | − | 0.401097i | \(-0.131371\pi\) | ||||
0.916036 | + | 0.401097i | \(0.131371\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14272.0 | 0.604484 | 0.302242 | − | 0.953231i | \(-0.402265\pi\) | ||||
0.302242 | + | 0.953231i | \(0.402265\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13644.0 | 0.573698 | 0.286849 | − | 0.957976i | \(-0.407392\pi\) | ||||
0.286849 | + | 0.957976i | \(0.407392\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2410.00 | −0.100968 | −0.0504842 | − | 0.998725i | \(-0.516076\pi\) | ||||
−0.0504842 | + | 0.998725i | \(0.516076\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10962.0 | −0.455955 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12816.0 | 0.531157 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23160.0 | 0.953006 | 0.476503 | − | 0.879173i | \(-0.341904\pi\) | ||||
0.476503 | + | 0.879173i | \(0.341904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23489.0 | −0.963098 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4518.00 | 0.183934 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18992.0 | −0.770452 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 42672.0 | 1.71889 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32078.0 | 1.28761 | 0.643804 | − | 0.765190i | \(-0.277355\pi\) | ||||
0.643804 | + | 0.765190i | \(0.277355\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14406.0 | 0.574212 | 0.287106 | − | 0.957899i | \(-0.407307\pi\) | ||||
0.287106 | + | 0.957899i | \(0.407307\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30620.0 | −1.21623 | −0.608115 | − | 0.793849i | \(-0.708074\pi\) | ||||
−0.608115 | + | 0.793849i | \(0.708074\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17568.0 | 0.692957 | 0.346478 | − | 0.938058i | \(-0.387377\pi\) | ||||
0.346478 | + | 0.938058i | \(0.387377\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10548.0 | 0.414616 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6240.00 | 0.243587 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33592.0 | −1.30680 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20544.0 | 0.793730 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21706.0 | −0.835758 | −0.417879 | − | 0.908503i | \(-0.637226\pi\) | ||||
−0.417879 | + | 0.908503i | \(0.637226\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14958.0 | 0.572018 | 0.286009 | − | 0.958227i | \(-0.407671\pi\) | ||||
0.286009 | + | 0.958227i | \(0.407671\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32812.0 | 1.25052 | 0.625261 | − | 0.780415i | \(-0.284992\pi\) | ||||
0.625261 | + | 0.780415i | \(0.284992\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38856.0 | −1.47086 | −0.735432 | − | 0.677598i | \(-0.763021\pi\) | ||||
−0.735432 | + | 0.677598i | \(0.763021\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 40576.0 | 1.53079 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1920.00 | 0.0719489 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3240.00 | 0.121007 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2640.00 | −0.0979410 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24948.0 | −0.922462 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11892.0 | −0.436799 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28276.0 | 1.03516 | 0.517579 | − | 0.855635i | \(-0.326833\pi\) | ||||
0.517579 | + | 0.855635i | \(0.326833\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8112.00 | 0.295019 | 0.147510 | − | 0.989061i | \(-0.452874\pi\) | ||||
0.147510 | + | 0.989061i | \(0.452874\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5904.00 | −0.214013 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36672.0 | 1.32063 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26080.0 | 0.936126 | 0.468063 | − | 0.883695i | \(-0.344952\pi\) | ||||
0.468063 | + | 0.883695i | \(0.344952\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30096.0 | 1.07326 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22606.0 | −0.803547 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −49170.0 | −1.73651 | −0.868254 | − | 0.496120i | \(-0.834757\pi\) | ||||
−0.868254 | + | 0.496120i | \(0.834757\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1740.00 | 0.0612526 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9072.00 | −0.317311 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48314.0 | 1.68447 | 0.842236 | − | 0.539110i | \(-0.181239\pi\) | ||||
0.842236 | + | 0.539110i | \(0.181239\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34782.0 | −1.20495 | −0.602477 | − | 0.798137i | \(-0.705819\pi\) | ||||
−0.602477 | + | 0.798137i | \(0.705819\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7056.00 | −0.243664 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25116.0 | −0.861838 | −0.430919 | − | 0.902391i | \(-0.641810\pi\) | ||||
−0.430919 | + | 0.902391i | \(0.641810\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8284.00 | 0.283361 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15462.0 | 0.525565 | 0.262782 | − | 0.964855i | \(-0.415360\pi\) | ||||
0.262782 | + | 0.964855i | \(0.415360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16128.0 | 0.546481 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11616.0 | 0.391137 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22047.0 | −0.740056 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13812.0 | 0.460750 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 736.000 | 0.0244759 | 0.0122379 | − | 0.999925i | \(-0.496104\pi\) | ||||
0.0122379 | + | 0.999925i | \(0.496104\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29268.0 | −0.967307 | −0.483653 | − | 0.875260i | \(-0.660690\pi\) | ||||
−0.483653 | + | 0.875260i | \(0.660690\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6080.00 | −0.200325 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16674.0 | −0.546007 | −0.273003 | − | 0.962013i | \(-0.588017\pi\) | ||||
−0.273003 | + | 0.962013i | \(0.588017\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9720.00 | −0.317316 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −31272.0 | −1.01467 | −0.507336 | − | 0.861749i | \(-0.669370\pi\) | ||||
−0.507336 | + | 0.861749i | \(0.669370\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26244.0 | 0.848937 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8736.00 | 0.280878 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15928.0 | 0.510565 | 0.255282 | − | 0.966867i | \(-0.417832\pi\) | ||||
0.255282 | + | 0.966867i | \(0.417832\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9600.00 | −0.305870 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42014.0 | 1.33460 | 0.667300 | − | 0.744789i | \(-0.267450\pi\) | ||||
0.667300 | + | 0.744789i | \(0.267450\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))