Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,2,Mod(769,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.769");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.c (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: | \(10.2208514587\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 320) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.1 | ||
Root | \(-1.93185i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.769 |
Dual form | 1280.2.c.h.769.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.44949i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.73205 | + | 1.41421i | −0.774597 | + | 0.632456i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.41421i | − | 0.534522i | −0.963624 | − | 0.267261i | \(-0.913881\pi\) | ||
0.963624 | − | 0.267261i | \(-0.0861187\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.65685i | 1.56893i | 0.620174 | + | 0.784465i | \(0.287062\pi\) | ||||
−0.620174 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.46410 | + | 4.24264i | 0.894427 | + | 1.09545i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.89898i | 1.18818i | 0.804400 | + | 0.594089i | \(0.202487\pi\) | ||||
−0.804400 | + | 0.594089i | \(0.797513\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.00000 | −1.37649 | −0.688247 | − | 0.725476i | \(-0.741620\pi\) | ||||
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.46410 | −0.755929 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.07107i | 1.47442i | 0.675664 | + | 0.737210i | \(0.263857\pi\) | ||||
−0.675664 | + | 0.737210i | \(0.736143\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | − | 4.89898i | 0.200000 | − | 0.979796i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.92820 | −1.28654 | −0.643268 | − | 0.765641i | \(-0.722422\pi\) | ||||
−0.643268 | + | 0.765641i | \(0.722422\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.92820 | 1.24434 | 0.622171 | − | 0.782881i | \(-0.286251\pi\) | ||||
0.622171 | + | 0.782881i | \(0.286251\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 4.89898i | − | 0.852803i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000 | + | 2.44949i | 0.338062 | + | 0.414039i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.82843i | 0.464991i | 0.972598 | + | 0.232495i | \(0.0746890\pi\) | ||||
−0.972598 | + | 0.232495i | \(0.925311\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.8564 | 2.21880 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.00000 | 0.624695 | 0.312348 | − | 0.949968i | \(-0.398885\pi\) | ||||
0.312348 | + | 0.949968i | \(0.398885\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.44949i | 0.373544i | 0.982403 | + | 0.186772i | \(0.0598025\pi\) | ||||
−0.982403 | + | 0.186772i | \(0.940197\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.19615 | − | 4.24264i | 0.774597 | − | 0.632456i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.24264i | 0.618853i | 0.950923 | + | 0.309426i | \(0.100137\pi\) | ||||
−0.950923 | + | 0.309426i | \(0.899863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.0000 | 1.68034 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.46410 | + | 2.82843i | −0.467099 | + | 0.381385i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.6969i | 1.94666i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00000 | −0.260378 | −0.130189 | − | 0.991489i | \(-0.541558\pi\) | ||||
−0.130189 | + | 0.991489i | \(0.541558\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.46410 | 0.443533 | 0.221766 | − | 0.975100i | \(-0.428818\pi\) | ||||
0.221766 | + | 0.975100i | \(0.428818\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.24264i | 0.534522i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.00000 | − | 9.79796i | −0.992278 | − | 1.21529i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.44949i | 0.299253i | 0.988743 | + | 0.149626i | \(0.0478071\pi\) | ||||
−0.988743 | + | 0.149626i | \(0.952193\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.3205 | 2.08514 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.92820 | 0.822226 | 0.411113 | − | 0.911584i | \(-0.365140\pi\) | ||||
0.411113 | + | 0.911584i | \(0.365140\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.89898i | − | 0.573382i | −0.958023 | − | 0.286691i | \(-0.907445\pi\) | ||
0.958023 | − | 0.286691i | \(-0.0925553\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.0000 | − | 2.44949i | −1.38564 | − | 0.282843i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.82843i | − | 0.322329i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.92820 | −0.779484 | −0.389742 | − | 0.920924i | \(-0.627436\pi\) | ||||
−0.389742 | + | 0.920924i | \(0.627436\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.2474i | 1.34433i | 0.740400 | + | 0.672166i | \(0.234636\pi\) | ||||
−0.740400 | + | 0.672166i | \(0.765364\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.92820 | − | 8.48528i | −0.751469 | − | 0.920358i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 16.9706i | 1.81944i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.00000 | 0.838628 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 16.9706i | − | 1.75977i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.3923 | − | 8.48528i | 1.06623 | − | 0.870572i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.6969i | 1.49225i | 0.665807 | + | 0.746124i | \(0.268087\pi\) | ||||
−0.665807 | + | 0.746124i | \(0.731913\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.92820 | 0.689382 | 0.344691 | − | 0.938716i | \(-0.387984\pi\) | ||||
0.344691 | + | 0.938716i | \(0.387984\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.89949i | − | 0.975426i | −0.873004 | − | 0.487713i | \(-0.837831\pi\) | ||
0.873004 | − | 0.487713i | \(-0.162169\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.00000 | − | 4.89898i | 0.585540 | − | 0.478091i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 2.44949i | − | 0.236801i | −0.992966 | − | 0.118401i | \(-0.962223\pi\) | ||
0.992966 | − | 0.118401i | \(-0.0377767\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.46410 | −0.331801 | −0.165900 | − | 0.986143i | \(-0.553053\pi\) | ||||
−0.165900 | + | 0.986143i | \(0.553053\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.92820 | 0.657596 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.0000 | − | 12.2474i | −0.932505 | − | 1.14208i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 16.9706i | − | 1.56893i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.92820 | 0.635107 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 9.79796i | − | 0.883452i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.19615 | + | 9.89949i | 0.464758 | + | 0.885438i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.07107i | 0.627456i | 0.949513 | + | 0.313728i | \(0.101578\pi\) | ||||
−0.949513 | + | 0.313728i | \(0.898422\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.00000 | 0.528271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0000 | 0.873704 | 0.436852 | − | 0.899533i | \(-0.356093\pi\) | ||||
0.436852 | + | 0.899533i | \(0.356093\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.48528i | 0.735767i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.79796i | 0.837096i | 0.908195 | + | 0.418548i | \(0.137461\pi\) | ||||
−0.908195 | + | 0.418548i | \(0.862539\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0000 | 0.848189 | 0.424094 | − | 0.905618i | \(-0.360592\pi\) | ||||
0.424094 | + | 0.905618i | \(0.360592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.3923 | 0.875190 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.3137i | 0.946100i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.0000 | − | 9.79796i | 0.996546 | − | 0.813676i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 12.2474i | − | 1.01015i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.3923 | −0.851371 | −0.425685 | − | 0.904871i | \(-0.639967\pi\) | ||||
−0.425685 | + | 0.904871i | \(0.639967\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.8564 | −1.12762 | −0.563809 | − | 0.825905i | \(-0.690665\pi\) | ||||
−0.563809 | + | 0.825905i | \(0.690665\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 14.6969i | − | 1.18818i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.0000 | + | 9.79796i | −0.963863 | + | 0.786991i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.82843i | 0.225733i | 0.993610 | + | 0.112867i | \(0.0360032\pi\) | ||||
−0.993610 | + | 0.112867i | \(0.963997\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.0000 | 0.788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 22.0454i | − | 1.72673i | −0.504580 | − | 0.863365i | \(-0.668353\pi\) | ||
0.504580 | − | 0.863365i | \(-0.331647\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.92820 | + | 8.48528i | 0.539360 | + | 0.660578i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 9.89949i | − | 0.766046i | −0.923739 | − | 0.383023i | \(-0.874883\pi\) | ||
0.923739 | − | 0.383023i | \(-0.125117\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −19.0000 | −1.46154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.0000 | 1.37649 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.48528i | 0.645124i | 0.946548 | + | 0.322562i | \(0.104544\pi\) | ||||
−0.946548 | + | 0.322562i | \(0.895456\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.92820 | − | 1.41421i | −0.523723 | − | 0.106904i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.89898i | 0.368230i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.00000 | −0.149487 | −0.0747435 | − | 0.997203i | \(-0.523814\pi\) | ||||
−0.0747435 | + | 0.997203i | \(0.523814\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.7846 | −1.54491 | −0.772454 | − | 0.635071i | \(-0.780971\pi\) | ||||
−0.772454 | + | 0.635071i | \(0.780971\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 8.48528i | − | 0.627250i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00000 | − | 4.89898i | −0.294086 | − | 0.360180i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.79796i | 0.716498i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.8564 | −1.00261 | −0.501307 | − | 0.865269i | \(-0.667147\pi\) | ||||
−0.501307 | + | 0.865269i | \(0.667147\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.89898i | 0.352636i | 0.984333 | + | 0.176318i | \(0.0564187\pi\) | ||||
−0.984333 | + | 0.176318i | \(0.943581\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −24.0000 | + | 19.5959i | −1.71868 | + | 1.40329i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.6274i | 1.61214i | 0.591822 | + | 0.806068i | \(0.298409\pi\) | ||||
−0.591822 | + | 0.806068i | \(0.701591\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.7846 | −1.47338 | −0.736691 | − | 0.676230i | \(-0.763613\pi\) | ||||
−0.736691 | + | 0.676230i | \(0.763613\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.00000 | 0.423207 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.79796i | 0.687682i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.92820 | + | 5.65685i | −0.483887 | + | 0.395092i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 21.2132i | − | 1.47442i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.0000 | −0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0000 | 0.688428 | 0.344214 | − | 0.938891i | \(-0.388145\pi\) | ||||
0.344214 | + | 0.938891i | \(0.388145\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 16.9706i | − | 1.16280i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.46410 | − | 4.24264i | −0.236250 | − | 0.289346i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 9.79796i | − | 0.665129i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.0000 | −0.810885 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −27.7128 | −1.86417 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 26.8701i | − | 1.79935i | −0.436558 | − | 0.899676i | \(-0.643803\pi\) | ||
0.436558 | − | 0.899676i | \(-0.356197\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | + | 14.6969i | −0.200000 | + | 0.979796i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.1464i | 1.13805i | 0.822321 | + | 0.569024i | \(0.192679\pi\) | ||||
−0.822321 | + | 0.569024i | \(0.807321\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.92820 | −0.457829 | −0.228914 | − | 0.973447i | \(-0.573518\pi\) | ||||
−0.228914 | + | 0.973447i | \(0.573518\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.92820 | −0.455842 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.6969i | 0.962828i | 0.876493 | + | 0.481414i | \(0.159877\pi\) | ||||
−0.876493 | + | 0.481414i | \(0.840123\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00000 | − | 7.34847i | −0.391397 | − | 0.479361i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.9706i | 1.10236i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.92820 | 0.448148 | 0.224074 | − | 0.974572i | \(-0.428064\pi\) | ||||
0.224074 | + | 0.974572i | \(0.428064\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.0454i | 1.41421i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.66025 | + | 7.07107i | −0.553283 | + | 0.451754i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 33.9411i | − | 2.15962i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 30.0000 | 1.90117 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.0000 | 1.64111 | 0.820553 | − | 0.571571i | \(-0.193666\pi\) | ||||
0.820553 | + | 0.571571i | \(0.193666\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.1421i | 0.889108i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −20.7846 | + | 16.9706i | −1.30158 | + | 1.06274i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 9.79796i | − | 0.611180i | −0.952163 | − | 0.305590i | \(-0.901146\pi\) | ||
0.952163 | − | 0.305590i | \(-0.0988537\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.7846 | 1.28654 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.8701i | 1.65688i | 0.560079 | + | 0.828439i | \(0.310771\pi\) | ||||
−0.560079 | + | 0.828439i | \(0.689229\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 4.89898i | − | 0.299813i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.3205 | 1.05605 | 0.528025 | − | 0.849229i | \(-0.322933\pi\) | ||||
0.528025 | + | 0.849229i | \(0.322933\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.7846 | −1.26258 | −0.631288 | − | 0.775549i | \(-0.717473\pi\) | ||||
−0.631288 | + | 0.775549i | \(0.717473\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 19.5959i | − | 1.18600i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.00000 | − | 9.79796i | 0.120605 | − | 0.590839i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.1421i | 0.849719i | 0.905259 | + | 0.424859i | \(0.139676\pi\) | ||||
−0.905259 | + | 0.424859i | \(0.860324\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −20.7846 | −1.24434 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.00000 | −0.477240 | −0.238620 | − | 0.971113i | \(-0.576695\pi\) | ||||
−0.238620 | + | 0.971113i | \(0.576695\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.44949i | − | 0.145607i | −0.997346 | − | 0.0728035i | \(-0.976805\pi\) | ||
0.997346 | − | 0.0728035i | \(-0.0231946\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −20.7846 | − | 25.4558i | −1.23117 | − | 1.50787i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 5.65685i | − | 0.333914i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 36.0000 | 2.11036 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.82843i | 0.165238i | 0.996581 | + | 0.0826192i | \(0.0263285\pi\) | ||||
−0.996581 | + | 0.0826192i | \(0.973671\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.46410 | − | 2.82843i | 0.201688 | − | 0.164677i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −40.0000 | −2.31326 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.46410 | 0.199667 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 16.9706i | − | 0.974933i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.00000 | + | 4.89898i | −0.343559 | + | 0.280515i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.44949i | 0.139800i | 0.997554 | + | 0.0698999i | \(0.0222680\pi\) | ||||
−0.997554 | + | 0.0698999i | \(0.977732\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −24.2487 | −1.37946 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.7128 | 1.57145 | 0.785725 | − | 0.618576i | \(-0.212290\pi\) | ||||
0.785725 | + | 0.618576i | \(0.212290\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.3939i | 1.66144i | 0.556690 | + | 0.830720i | \(0.312071\pi\) | ||||
−0.556690 | + | 0.830720i | \(0.687929\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.00000 | − | 7.34847i | −0.338062 | − | 0.414039i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 22.6274i | − | 1.27088i | −0.772149 | − | 0.635441i | \(-0.780818\pi\) | ||
0.772149 | − | 0.635441i | \(-0.219182\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.8564 | −0.775810 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.00000 | −0.334887 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 29.3939i | − | 1.63552i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 27.7128 | + | 5.65685i | 1.53723 | + | 0.313786i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.48528i | 0.469237i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.00000 | 0.330791 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.00000 | 0.329790 | 0.164895 | − | 0.986311i | \(-0.447272\pi\) | ||||
0.164895 | + | 0.986311i | \(0.447272\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 8.48528i | − | 0.464991i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.46410 | − | 4.24264i | −0.189264 | − | 0.231800i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 19.5959i | − | 1.06746i | −0.845656 | − | 0.533729i | \(-0.820790\pi\) | ||
0.845656 | − | 0.533729i | \(-0.179210\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.8564 | 0.750366 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.9706i | − | 0.916324i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −30.0000 | + | 24.4949i | −1.61515 | + | 1.31876i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 17.1464i | − | 0.920468i | −0.887798 | − | 0.460234i | \(-0.847765\pi\) | ||
0.887798 | − | 0.460234i | \(-0.152235\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.92820 | 0.370858 | 0.185429 | − | 0.982658i | \(-0.440632\pi\) | ||||
0.185429 | + | 0.982658i | \(0.440632\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.79796i | 0.521493i | 0.965407 | + | 0.260746i | \(0.0839686\pi\) | ||||
−0.965407 | + | 0.260746i | \(0.916031\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.0000 | + | 9.79796i | −0.636894 | + | 0.520022i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 16.9706i | − | 0.898177i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.7128 | −1.46263 | −0.731313 | − | 0.682042i | \(-0.761092\pi\) | ||||
−0.731313 | + | 0.682042i | \(0.761092\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.1464i | 0.899954i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.92820 | + | 8.48528i | 0.362639 | + | 0.444140i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 9.89949i | − | 0.516749i | −0.966045 | − | 0.258375i | \(-0.916813\pi\) | ||
0.966045 | − | 0.258375i | \(-0.0831869\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.0000 | −0.624695 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 19.7990i | − | 1.02515i | −0.858642 | − | 0.512576i | \(-0.828691\pi\) | ||
0.858642 | − | 0.512576i | \(-0.171309\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24.2487 | − | 12.7279i | 1.25220 | − | 0.657267i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 39.1918i | − | 2.01848i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.0000 | −0.719132 | −0.359566 | − | 0.933120i | \(-0.617075\pi\) | ||||
−0.359566 | + | 0.933120i | \(0.617075\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.3205 | 0.887357 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.7279i | 0.650366i | 0.945651 | + | 0.325183i | \(0.105426\pi\) | ||||
−0.945651 | + | 0.325183i | \(0.894574\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | + | 4.89898i | 0.203859 | + | 0.249675i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 7.34847i | − | 0.373544i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.46410 | 0.175637 | 0.0878185 | − | 0.996136i | \(-0.472010\pi\) | ||||
0.0878185 | + | 0.996136i | \(0.472010\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −34.6410 | −1.75187 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 24.4949i | − | 1.23560i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.0000 | − | 9.79796i | 0.603786 | − | 0.492989i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 11.3137i | − | 0.567819i | −0.958851 | − | 0.283909i | \(-0.908369\pi\) | ||
0.958851 | − | 0.283909i | \(-0.0916315\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 20.7846 | 1.04053 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.0000 | 1.09863 | 0.549314 | − | 0.835616i | \(-0.314889\pi\) | ||||
0.549314 | + | 0.835616i | \(0.314889\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 39.1918i | 1.95228i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.5885 | − | 12.7279i | 0.774597 | − | 0.632456i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.65685i | 0.280400i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.0000 | 0.988936 | 0.494468 | − | 0.869196i | \(-0.335363\pi\) | ||||
0.494468 | + | 0.869196i | \(0.335363\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.0000 | 1.18383 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.82843i | 0.139178i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.3205 | − | 21.2132i | −0.850230 | − | 1.04132i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 24.4949i | − | 1.19952i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.0000 | −1.27018 | −0.635092 | − | 0.772437i | \(-0.719038\pi\) | ||||
−0.635092 | + | 0.772437i | \(0.719038\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.46410 | 0.168830 | 0.0844150 | − | 0.996431i | \(-0.473098\pi\) | ||||
0.0844150 | + | 0.996431i | \(0.473098\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 12.7279i | − | 0.618853i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24.0000 | + | 4.89898i | 1.16417 | + | 0.237635i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 4.89898i | − | 0.237078i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 27.7128 | 1.33799 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.92820 | −0.333720 | −0.166860 | − | 0.985981i | \(-0.553363\pi\) | ||||
−0.166860 | + | 0.985981i | \(0.553363\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.2929i | 1.64801i | 0.566583 | + | 0.824005i | \(0.308265\pi\) | ||||
−0.566583 | + | 0.824005i | \(0.691735\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −24.0000 | − | 29.3939i | −1.15071 | − | 1.40933i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 42.4264i | − | 2.02953i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.0000 | −0.714286 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 22.0454i | − | 1.04741i | −0.851900 | − | 0.523704i | \(-0.824550\pi\) | ||
0.851900 | − | 0.523704i | \(-0.175450\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.46410 | + | 2.82843i | −0.164214 | + | 0.134080i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 25.4558i | 1.20402i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.0000 | 0.755087 | 0.377543 | − | 0.925992i | \(-0.376769\pi\) | ||||
0.377543 | + | 0.925992i | \(0.376769\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.00000 | 0.376705 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 33.9411i | 1.59469i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.8564 | + | 11.3137i | −0.649598 | + | 0.530395i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 19.5959i | − | 0.916658i | −0.888783 | − | 0.458329i | \(-0.848448\pi\) | ||
0.888783 | − | 0.458329i | \(-0.151552\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.7846 | −0.968036 | −0.484018 | − | 0.875058i | \(-0.660823\pi\) | ||||
−0.484018 | + | 0.875058i | \(0.660823\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.41421i | − | 0.0657241i | −0.999460 | − | 0.0328620i | \(-0.989538\pi\) | ||
0.999460 | − | 0.0328620i | \(-0.0104622\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 24.0000 | + | 29.3939i | 1.11297 | + | 1.36311i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 31.8434i | − | 1.47354i | −0.676146 | − | 0.736768i | \(-0.736351\pi\) | ||
0.676146 | − | 0.736768i | \(-0.263649\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.46410 | 0.159957 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.92820 | 0.319235 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.89898i | 0.225255i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.00000 | + | 29.3939i | −0.275299 | + | 1.34868i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 41.5692 | 1.89935 | 0.949673 | − | 0.313243i | \(-0.101415\pi\) | ||||
0.949673 | + | 0.313243i | \(0.101415\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.0000 | −0.729537 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 24.4949i | − | 1.11456i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.7846 | − | 25.4558i | −0.943781 | − | 1.15589i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.8701i | 1.21760i | 0.793324 | + | 0.608799i | \(0.208349\pi\) | ||||
−0.793324 | + | 0.608799i | \(0.791651\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −54.0000 | −2.44196 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.0000 | 1.71492 | 0.857458 | − | 0.514554i | \(-0.172042\pi\) | ||||
0.857458 | + | 0.514554i | \(0.172042\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 33.9411i | − | 1.52863i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.3923 | − | 8.48528i | 0.467099 | − | 0.381385i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 9.79796i | − | 0.439499i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.00000 | 0.268597 | 0.134298 | − | 0.990941i | \(-0.457122\pi\) | ||||
0.134298 | + | 0.990941i | \(0.457122\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.2487 | −1.08335 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 21.2132i | − | 0.945850i | −0.881103 | − | 0.472925i | \(-0.843198\pi\) | ||
0.881103 | − | 0.472925i | \(-0.156802\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | + | 9.79796i | −0.533993 | + | 0.436003i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 46.5403i | 2.06693i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.7846 | 0.921262 | 0.460631 | − | 0.887592i | \(-0.347623\pi\) | ||||
0.460631 | + | 0.887592i | \(0.347623\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.92820 | −0.306486 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.0000 | + | 17.1464i | 0.616914 | + | 0.755562i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.48528i | 0.373182i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.7846 | 0.912343 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.0000 | −1.48957 | −0.744784 | − | 0.667306i | \(-0.767447\pi\) | ||||
−0.744784 | + | 0.667306i | \(0.767447\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.44949i | − | 0.107109i | −0.998565 | − | 0.0535544i | \(-0.982945\pi\) | ||
0.998565 | − | 0.0535544i | \(-0.0170550\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.46410 | + | 16.9706i | −0.151186 | + | 0.740656i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 33.9411i | 1.47850i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −27.0000 | −1.17391 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.00000 | 0.260378 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.6274i | 0.980102i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.46410 | + | 4.24264i | 0.149766 | + | 0.183425i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.89898i | 0.211407i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.0000 | 0.430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.92820 | 0.297867 | 0.148933 | − | 0.988847i | \(-0.452416\pi\) | ||||
0.148933 | + | 0.988847i | \(0.452416\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 50.9117i | 2.18483i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.00000 | − | 4.89898i | 0.257012 | − | 0.209849i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.9444i | 1.15206i | 0.817429 | + | 0.576029i | \(0.195399\pi\) | ||||
−0.817429 | + | 0.576029i | \(0.804601\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.3923 | −0.443533 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 41.5692 | 1.77091 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.79796i | 0.416652i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.0000 | + | 9.79796i | −0.509372 | + | 0.415900i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.4558i | 1.07860i | 0.842114 | + | 0.539299i | \(0.181311\pi\) | ||||
−0.842114 | + | 0.539299i | \(0.818689\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.8564 | −0.586064 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0000 | 1.01328 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.34847i | 0.309701i | 0.987938 | + | 0.154851i | \(0.0494896\pi\) | ||||
−0.987938 | + | 0.154851i | \(0.950510\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.7279i | 0.534522i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.0000 | 1.17382 | 0.586911 | − | 0.809652i | \(-0.300344\pi\) | ||||
0.586911 | + | 0.809652i | \(0.300344\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.0000 | −1.25546 | −0.627730 | − | 0.778431i | \(-0.716016\pi\) | ||||
−0.627730 | + | 0.778431i | \(0.716016\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 33.9411i | 1.41791i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34.6410 | + | 7.07107i | 1.44463 | + | 0.294884i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 29.3939i | − | 1.22368i | −0.790980 | − | 0.611842i | \(-0.790429\pi\) | ||
0.790980 | − | 0.611842i | \(-0.209571\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.0000 | 0.498703 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.3205 | 0.718576 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 24.0000 | + | 29.3939i | 0.992278 | + | 1.21529i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.2474i | 0.505506i | 0.967531 | + | 0.252753i | \(0.0813361\pi\) | ||||
−0.967531 | + | 0.252753i | \(0.918664\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −41.5692 | −1.71283 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 55.4256 | 2.27991 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.3939i | 1.20706i | 0.797340 | + | 0.603531i | \(0.206240\pi\) | ||||
−0.797340 | + | 0.603531i | \(0.793760\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0000 | + | 9.79796i | −0.491952 | + | 0.401677i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 50.9117i | 2.08368i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.7846 | 0.849236 | 0.424618 | − | 0.905373i | \(-0.360408\pi\) | ||||
0.424618 | + | 0.905373i | \(0.360408\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.0000 | 0.978980 | 0.489490 | − | 0.872009i | \(-0.337183\pi\) | ||||
0.489490 | + | 0.872009i | \(0.337183\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 7.34847i | − | 0.299253i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.1244 | − | 9.89949i | 0.492925 | − | 0.402472i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 41.0122i | − | 1.66463i | −0.554300 | − | 0.832317i | \(-0.687014\pi\) | ||
0.554300 | − | 0.832317i | \(-0.312986\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 24.0000 | 0.972529 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.0000 | −0.970936 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 5.65685i | − | 0.228478i | −0.993453 | − | 0.114239i | \(-0.963557\pi\) | ||
0.993453 | − | 0.114239i | \(-0.0364430\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.8564 | + | 16.9706i | 0.558744 | + | 0.684319i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 24.4949i | − | 0.986127i | −0.869993 | − | 0.493064i | \(-0.835877\pi\) | ||
0.869993 | − | 0.493064i | \(-0.164123\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.0000 | 0.562708 | 0.281354 | − | 0.959604i | \(-0.409217\pi\) | ||||
0.281354 | + | 0.959604i | \(0.409217\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 2.82843i | − | 0.113319i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.0000 | − | 9.79796i | −0.920000 | − | 0.391918i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 29.3939i | 1.17388i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.8564 | −0.552491 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.8564 | −0.551615 | −0.275807 | − | 0.961213i | \(-0.588945\pi\) | ||||
−0.275807 | + | 0.961213i | \(0.588945\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 24.4949i | − | 0.973585i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.0000 | − | 12.2474i | −0.396838 | − | 0.486025i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.2843i | 1.12066i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −20.7846 | −0.822226 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.0000 | −1.57991 | −0.789953 | − | 0.613168i | \(-0.789895\pi\) | ||||
−0.789953 | + | 0.613168i | \(0.789895\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.44949i | 0.0965984i | 0.998833 | + | 0.0482992i | \(0.0153801\pi\) | ||||
−0.998833 | + | 0.0482992i | \(0.984620\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.3923 | + | 8.48528i | −0.409197 | + | 0.334108i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.24264i | 0.166795i | 0.996516 | + | 0.0833977i | \(0.0265772\pi\) | ||||
−0.996516 | + | 0.0833977i | \(0.973423\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.00000 | −0.157014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.0000 | −0.940634 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.65685i | 0.221370i | 0.993856 | + | 0.110685i | \(0.0353044\pi\) | ||||
−0.993856 | + | 0.110685i | \(0.964696\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.3205 | + | 14.1421i | −0.676768 | + | 0.552579i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.6969i | 0.573382i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.00000 | −0.0779089 | −0.0389545 | − | 0.999241i | \(-0.512403\pi\) | ||||
−0.0389545 | + | 0.999241i | \(0.512403\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.3923 | 0.404214 | 0.202107 | − | 0.979363i | \(-0.435221\pi\) | ||||
0.202107 | + | 0.979363i | \(0.435221\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 67.8823i | 2.63633i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.0000 | − | 14.6969i | −0.465340 | − | 0.569923i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 48.9898i | − | 1.89689i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −65.8179 | −2.54467 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.92820 | 0.267460 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 24.4949i | − | 0.944209i | −0.881543 | − | 0.472104i | \(-0.843495\pi\) | ||
0.881543 | − | 0.472104i | \(-0.156505\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 5.65685i | − | 0.217411i | −0.994074 | − | 0.108705i | \(-0.965330\pi\) | ||
0.994074 | − | 0.108705i | \(-0.0346705\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.7846 | 0.797640 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 42.0000 | 1.60944 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.44949i | 0.0937271i | 0.998901 | + | 0.0468636i | \(0.0149226\pi\) | ||||
−0.998901 | + | 0.0468636i | \(0.985077\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.8564 | − | 16.9706i | −0.529426 | − | 0.648412i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.9706i | 0.647467i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.0000 | 1.59776 | 0.798878 | − | 0.601494i | \(-0.205427\pi\) | ||||
0.798878 | + | 0.601494i | \(0.205427\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.48528i | 0.322329i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.3205 | + | 14.1421i | −0.657004 | + | 0.536442i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.5959i | 0.742248i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 36.0000 | 1.36165 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.46410 | −0.130837 | −0.0654187 | − | 0.997858i | \(-0.520838\pi\) | ||||
−0.0654187 | + | 0.997858i | \(0.520838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 16.9706i | − | 0.640057i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −18.0000 | + | 14.6969i | −0.677919 | + | 0.553519i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 9.79796i | − | 0.368490i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.6410 | 1.30097 | 0.650485 | − | 0.759519i | \(-0.274566\pi\) | ||||
0.650485 | + | 0.759519i | \(0.274566\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.7846 | 0.779484 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 48.9898i | 1.83468i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.0000 | − | 19.5959i | −0.598366 | − | 0.732846i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 16.9706i | − | 0.633777i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.92820 | −0.258378 | −0.129189 | − | 0.991620i | \(-0.541237\pi\) | ||||
−0.129189 | + | 0.991620i | \(0.541237\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.0000 | −0.521387 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.92820 | + | 33.9411i | −0.257307 | + | 1.26054i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 18.3848i | − | 0.681854i | −0.940090 | − | 0.340927i | \(-0.889259\pi\) | ||
0.940090 | − | 0.340927i | \(-0.110741\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0000 | −0.443836 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 19.7990i | − | 0.731292i | −0.930754 | − | 0.365646i | \(-0.880848\pi\) | ||
0.930754 | − | 0.365646i | \(-0.119152\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.3205 | + | 21.2132i | 0.638877 | + | 0.782461i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.89898i | 0.180456i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.0000 | 1.10357 | 0.551784 | − | 0.833987i | \(-0.313947\pi\) | ||||
0.551784 | + | 0.833987i | \(0.313947\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −83.1384 | −3.05417 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.24264i | 0.155647i | 0.996967 | + | 0.0778237i | \(0.0247971\pi\) | ||||
−0.996967 | + | 0.0778237i | \(0.975203\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.0000 | − | 14.6969i | 0.659469 | − | 0.538454i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 36.7423i | − | 1.34433i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.46410 | −0.126576 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 63.6867i | − | 2.32087i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.0000 | − | 19.5959i | 0.873449 | − | 0.713168i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2.82843i | − | 0.102801i | −0.998678 | − | 0.0514005i | \(-0.983632\pi\) | ||
0.998678 | − | 0.0514005i | \(-0.0163685\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 34.6410 | 1.25739 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.0000 | −1.37750 | −0.688749 | − | 0.724999i | \(-0.741840\pi\) | ||||
−0.688749 | + | 0.724999i | \(0.741840\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.89898i | 0.177355i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 20.7846 | + | 25.4558i | 0.751469 | + | 0.920358i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 11.3137i | − | 0.408514i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.0000 | 1.51456 | 0.757279 | − | 0.653091i | \(-0.226528\pi\) | ||||
0.757279 | + | 0.653091i | \(0.226528\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.0000 | −0.864339 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 45.2548i | − | 1.62770i | −0.581073 | − | 0.813852i | \(-0.697367\pi\) | ||
0.581073 | − | 0.813852i | \(-0.302633\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.92820 | − | 33.9411i | 0.248868 | − | 1.21920i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 9.79796i | − | 0.351500i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.0000 | −0.859889 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8564 | 0.495821 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.00000 | − | 4.89898i | −0.142766 | − | 0.174852i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 46.5403i | − | 1.65898i | −0.558520 | − | 0.829491i | \(-0.688630\pi\) | ||
0.558520 | − | 0.829491i | \(-0.311370\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 65.8179 | 2.34318 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.5959i | 0.695871i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 33.9411i | − | 1.20226i | −0.799153 | − | 0.601128i | \(-0.794718\pi\) | ||
0.799153 | − | 0.601128i | \(-0.205282\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.7846 | −0.735307 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.00000 | −0.212000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 9.79796i | − | 0.345762i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.3205 | + | 14.1421i | −0.610468 | + | 0.498445i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 42.4264i | − | 1.49348i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −50.0000 | −1.75791 | −0.878953 | − | 0.476908i | \(-0.841757\pi\) | ||||
−0.878953 | + | 0.476908i | \(0.841757\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.0000 | −0.772524 | −0.386262 | − | 0.922389i | \(-0.626234\pi\) | ||||
−0.386262 | + | 0.922389i | \(0.626234\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 50.9117i | 1.78555i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 31.1769 | + | 38.1838i | 1.09208 | + | 1.33752i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 14.6969i | − | 0.514181i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −24.0000 | −0.838628 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 51.9615 | 1.81347 | 0.906735 | − | 0.421701i | \(-0.138567\pi\) | ||||
0.906735 | + | 0.421701i | \(0.138567\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.3553i | 1.23241i | 0.787586 | + | 0.616205i | \(0.211331\pi\) | ||||
−0.787586 | + | 0.616205i | \(0.788669\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −24.0000 | − | 4.89898i | −0.835573 | − | 0.170561i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.8434i | 1.10730i | 0.832749 | + | 0.553651i | \(0.186766\pi\) | ||||
−0.832749 | + | 0.553651i | \(0.813234\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.0333 | 1.56407 | 0.782036 | − | 0.623233i | \(-0.214181\pi\) | ||||
0.782036 | + | 0.623233i | \(0.214181\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 34.6410 | 1.20168 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.4949i | 0.848698i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.0000 | + | 17.1464i | 0.484490 | + | 0.593377i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 41.5692 | 1.43513 | 0.717564 | − | 0.696492i | \(-0.245257\pi\) | ||||
0.717564 | + | 0.696492i | \(0.245257\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.0000 | 0.655172 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.5959i | 0.674919i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 32.9090 | − | 26.8701i | 1.13210 | − | 0.924358i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.89949i | 0.340151i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.00000 | −0.205919 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.0000 | −0.685591 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 5.65685i | − | 0.193687i | −0.995300 | − | 0.0968435i | \(-0.969125\pi\) | ||
0.995300 | − | 0.0968435i | \(-0.0308746\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −31.1769 | + | 25.4558i | −1.06623 | + | 0.870572i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.1918i | 1.33877i | 0.742917 | + | 0.669384i | \(0.233442\pi\) | ||||
−0.742917 | + | 0.669384i | \(0.766558\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.0000 | 0.750630 | 0.375315 | − | 0.926897i | \(-0.377534\pi\) | ||||
0.375315 | + | 0.926897i | \(0.377534\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.8564 | −0.472225 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 24.0416i | − | 0.818387i | −0.912448 | − | 0.409193i | \(-0.865810\pi\) | ||
0.912448 | − | 0.409193i | \(-0.134190\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.0000 | − | 14.6969i | −0.408012 | − | 0.499711i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.1464i | 0.582323i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.8564 | −0.470046 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.8564 | −0.469506 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 44.0908i | − | 1.49225i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14.0000 | − | 7.34847i | 0.473286 | − | 0.248424i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 36.7696i | − | 1.24162i | −0.783961 | − | 0.620810i | \(-0.786804\pi\) | ||
0.783961 | − | 0.620810i | \(-0.213196\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.92820 | 0.233682 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 52.0000 | 1.75192 | 0.875962 | − | 0.482380i | \(-0.160227\pi\) | ||||
0.875962 | + | 0.482380i | \(0.160227\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 12.2474i | − | 0.412159i | −0.978535 | − | 0.206080i | \(-0.933929\pi\) | ||
0.978535 | − | 0.206080i | \(-0.0660706\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.92820 | − | 8.48528i | −0.232889 | − | 0.285230i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 49.4975i | 1.66196i | 0.556300 | + | 0.830981i | \(0.312220\pi\) | ||||
−0.556300 | + | 0.830981i | \(0.687780\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.0000 | 0.335389 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.0000 | −0.603023 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 25.4558i | − | 0.851847i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.46410 | − | 2.82843i | 0.115792 | − | 0.0945439i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 97.9796i | 3.27144i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −48.0000 | −1.60089 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 8.48528i | − | 0.282372i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36.0000 | − | 29.3939i | 1.19668 | − | 0.977086i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.9444i | 0.894674i | 0.894366 | + | 0.447337i | \(0.147627\pi\) | ||||
−0.894366 | + | 0.447337i | \(0.852373\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −20.7846 | −0.689382 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.4974 | −1.60679 | −0.803396 | − | 0.595446i | \(-0.796976\pi\) | ||||
−0.803396 | + | 0.595446i | \(0.796976\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.4949i | 0.810663i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.0000 | + | 14.6969i | 0.396708 | + | 0.485866i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 14.1421i | − | 0.467014i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.92820 | −0.228540 | −0.114270 | − | 0.993450i | \(-0.536453\pi\) | ||||
−0.114270 | + | 0.993450i | \(0.536453\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.00000 | 0.197707 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 39.1918i | 1.29001i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.8564 | + | 2.82843i | 0.455596 | + | 0.0929981i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 29.6985i | 0.975426i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.00000 | −0.262471 | −0.131236 | − | 0.991351i | \(-0.541894\pi\) | ||||
−0.131236 | + | 0.991351i | \(0.541894\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.0000 | −0.983210 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 67.8823i | − | 2.22237i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.8564 | − | 16.9706i | −0.453153 | − | 0.554997i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.4949i | 0.800213i | 0.916469 | + | 0.400107i | \(0.131027\pi\) | ||||
−0.916469 | + | 0.400107i | \(0.868973\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 72.0000 | 2.34963 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.6410 | 1.12926 | 0.564632 | − | 0.825342i | \(-0.309018\pi\) | ||||
0.564632 | + | 0.825342i | \(0.309018\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.2843i | 0.921063i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.6413i | 1.35316i | 0.736369 | + | 0.676581i | \(0.236539\pi\) | ||||
−0.736369 | + | 0.676581i | \(0.763461\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.7128 | 0.899596 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −55.4256 | −1.79730 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 39.1918i | − | 1.26955i | −0.772698 | − | 0.634774i | \(-0.781093\pi\) | ||
0.772698 | − | 0.634774i | \(-0.218907\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.0000 | − | 19.5959i | 0.776622 | − | 0.634109i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 33.9411i | 1.09716i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.8564 | 0.447447 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.0000 | 0.548387 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.34847i | 0.236801i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.92820 | − | 8.48528i | −0.223027 | − | 0.273151i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 15.5563i | − | 0.500258i | −0.968212 | − | 0.250129i | \(-0.919527\pi\) | ||
0.968212 | − | 0.250129i | \(-0.0804731\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −72.0000 | −2.31297 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.0000 | 0.706014 | 0.353007 | − | 0.935621i | \(-0.385159\pi\) | ||||
0.353007 | + | 0.935621i | \(0.385159\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 14.1421i | − | 0.453376i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.8564 | − | 67.8823i | 0.443760 | − | 2.17397i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 4.89898i | − | 0.156732i | −0.996925 | − | 0.0783661i | \(-0.975030\pi\) | ||
0.996925 | − | 0.0783661i | \(-0.0249703\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.00000 | 0.127841 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.3923 | 0.331801 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 46.6690i | − | 1.48851i | −0.667895 | − | 0.744256i | \(-0.732804\pi\) | ||
0.667895 | − | 0.744256i | \(-0.267196\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −32.0000 | − | 39.1918i | −1.01960 | − | 1.24876i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 14.6969i | − | 0.467809i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.3205 | −0.550760 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.7128 | 0.880327 | 0.440163 | − | 0.897918i | \(-0.354921\pi\) | ||||
0.440163 | + | 0.897918i | \(0.354921\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 14.6969i | − | 0.466393i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 36.0000 | − | 29.3939i | 1.14128 | − | 0.931849i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 56.5685i | − | 1.79154i | −0.444514 | − | 0.895772i | \(-0.646624\pi\) | ||
0.444514 | − | 0.895772i | \(-0.353376\pi\) | |||||||
\(998\) | 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 \(a_p\))