Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,2,Mod(289,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.55521286468\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 289.6 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.289 |
Dual form | 320.2.f.b.289.5 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.44949 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.41421 | + | 1.73205i | −0.632456 | + | 0.774597i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.41421i | 0.534522i | 0.963624 | + | 0.267261i | \(0.0861187\pi\) | ||||
−0.963624 | + | 0.267261i | \(0.913881\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000i | 0.603023i | 0.953463 | + | 0.301511i | \(0.0974911\pi\) | ||||
−0.953463 | + | 0.301511i | \(0.902509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.65685 | 1.56893 | 0.784465 | − | 0.620174i | \(-0.212938\pi\) | ||||
0.784465 | + | 0.620174i | \(0.212938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.46410 | + | 4.24264i | −0.894427 | + | 1.09545i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.89898i | − | 1.18818i | −0.804400 | − | 0.594089i | \(-0.797513\pi\) | ||
0.804400 | − | 0.594089i | \(-0.202487\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.00000i | 1.37649i | 0.725476 | + | 0.688247i | \(0.241620\pi\) | ||||
−0.725476 | + | 0.688247i | \(0.758380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.46410i | 0.755929i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 7.07107i | − | 1.47442i | −0.675664 | − | 0.737210i | \(-0.736143\pi\) | ||
0.675664 | − | 0.737210i | \(-0.263857\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | − | 4.89898i | −0.200000 | − | 0.979796i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.92820i | − | 1.28654i | −0.765641 | − | 0.643268i | \(-0.777578\pi\) | ||
0.765641 | − | 0.643268i | \(-0.222422\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.92820 | −1.24434 | −0.622171 | − | 0.782881i | \(-0.713749\pi\) | ||||
−0.622171 | + | 0.782881i | \(0.713749\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.89898i | 0.852803i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.44949 | − | 2.00000i | −0.414039 | − | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.82843 | −0.464991 | −0.232495 | − | 0.972598i | \(-0.574689\pi\) | ||||
−0.232495 | + | 0.972598i | \(0.574689\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.8564 | 2.21880 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.00000 | −0.624695 | −0.312348 | − | 0.949968i | \(-0.601115\pi\) | ||||
−0.312348 | + | 0.949968i | \(0.601115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.44949 | 0.373544 | 0.186772 | − | 0.982403i | \(-0.440197\pi\) | ||||
0.186772 | + | 0.982403i | \(0.440197\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.24264 | + | 5.19615i | −0.632456 | + | 0.774597i | ||||
\(46\) | 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 | ||||||||
\(51\) | − | 12.0000i | − | 1.68034i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.46410 | − | 2.82843i | −0.467099 | − | 0.381385i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.6969i | 1.94666i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 2.00000i | − | 0.260378i | −0.991489 | − | 0.130189i | \(-0.958442\pi\) | ||
0.991489 | − | 0.130189i | \(-0.0415584\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.46410i | 0.443533i | 0.975100 | + | 0.221766i | \(0.0711822\pi\) | ||||
−0.975100 | + | 0.221766i | \(0.928818\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.24264i | 0.534522i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.00000 | + | 9.79796i | −0.992278 | + | 1.21529i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.44949 | −0.299253 | −0.149626 | − | 0.988743i | \(-0.547807\pi\) | ||||
−0.149626 | + | 0.988743i | \(0.547807\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 17.3205i | − | 2.08514i | ||||||
\(70\) | 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 | ||||||||
\(75\) | −2.44949 | − | 12.0000i | −0.282843 | − | 1.38564i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.82843 | −0.322329 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.92820 | 0.779484 | 0.389742 | − | 0.920924i | \(-0.372564\pi\) | ||||
0.389742 | + | 0.920924i | \(0.372564\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.2474 | −1.34433 | −0.672166 | − | 0.740400i | \(-0.734636\pi\) | ||||
−0.672166 | + | 0.740400i | \(0.734636\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.48528 | + | 6.92820i | 0.920358 | + | 0.751469i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 16.9706i | − | 1.81944i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.00000i | 0.838628i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −16.9706 | −1.75977 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.3923 | − | 8.48528i | −1.06623 | − | 0.870572i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 14.6969i | − | 1.49225i | −0.665807 | − | 0.746124i | \(-0.731913\pi\) | ||
0.665807 | − | 0.746124i | \(-0.268087\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.00000i | 0.603023i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 6.92820i | − | 0.689382i | −0.938716 | − | 0.344691i | \(-0.887984\pi\) | ||
0.938716 | − | 0.344691i | \(-0.112016\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.89949i | 0.975426i | 0.873004 | + | 0.487713i | \(0.162169\pi\) | ||||
−0.873004 | + | 0.487713i | \(0.837831\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.00000 | − | 4.89898i | −0.585540 | − | 0.478091i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.44949 | −0.236801 | −0.118401 | − | 0.992966i | \(-0.537777\pi\) | ||||
−0.118401 | + | 0.992966i | \(0.537777\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.46410i | − | 0.331801i | −0.986143 | − | 0.165900i | \(-0.946947\pi\) | ||
0.986143 | − | 0.165900i | \(-0.0530530\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.92820 | −0.657596 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.2474 | + | 10.0000i | 1.14208 | + | 0.932505i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.9706 | 1.56893 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.92820 | 0.635107 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.79796 | −0.883452 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.89949 | + | 5.19615i | 0.885438 | + | 0.464758i | ||||
\(126\) | 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 | ||||||||
\(131\) | − | 10.0000i | − | 0.873704i | −0.899533 | − | 0.436852i | \(-0.856093\pi\) | ||
0.899533 | − | 0.436852i | \(-0.143907\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.48528 | −0.735767 | ||||||||
\(134\) | 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 | ||||||||
\(139\) | 10.0000i | 0.848189i | 0.905618 | + | 0.424094i | \(0.139408\pi\) | ||||
−0.905618 | + | 0.424094i | \(0.860592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.3923i | 0.875190i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.3137i | 0.946100i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.0000 | + | 9.79796i | 0.996546 | + | 0.813676i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.2474 | 1.01015 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.3923i | 0.851371i | 0.904871 | + | 0.425685i | \(0.139967\pi\) | ||||
−0.904871 | + | 0.425685i | \(0.860033\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | 9.79796 | − | 12.0000i | 0.786991 | − | 0.963863i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.82843 | 0.225733 | 0.112867 | − | 0.993610i | \(-0.463997\pi\) | ||||
0.112867 | + | 0.993610i | \(0.463997\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.0000 | 0.788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.0454 | 1.72673 | 0.863365 | − | 0.504580i | \(-0.168353\pi\) | ||||
0.863365 | + | 0.504580i | \(0.168353\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.48528 | − | 6.92820i | −0.660578 | − | 0.539360i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.89949i | 0.766046i | 0.923739 | + | 0.383023i | \(0.125117\pi\) | ||||
−0.923739 | + | 0.383023i | \(0.874883\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.0000 | 1.46154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.0000i | 1.37649i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.48528 | 0.645124 | 0.322562 | − | 0.946548i | \(-0.395456\pi\) | ||||
0.322562 | + | 0.946548i | \(0.395456\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.92820 | − | 1.41421i | 0.523723 | − | 0.106904i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 4.89898i | − | 0.368230i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.00000i | 0.149487i | 0.997203 | + | 0.0747435i | \(0.0238138\pi\) | ||||
−0.997203 | + | 0.0747435i | \(0.976186\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.7846i | 1.54491i | 0.635071 | + | 0.772454i | \(0.280971\pi\) | ||||
−0.635071 | + | 0.772454i | \(0.719029\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.48528i | 0.627250i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.00000 | − | 4.89898i | 0.294086 | − | 0.360180i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.79796 | 0.716498 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.8564 | 1.00261 | 0.501307 | − | 0.865269i | \(-0.332853\pi\) | ||||
0.501307 | + | 0.865269i | \(0.332853\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4.89898i | − | 0.352636i | −0.984333 | − | 0.176318i | \(-0.943581\pi\) | ||
0.984333 | − | 0.176318i | \(-0.0564187\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −19.5959 | + | 24.0000i | −1.40329 | + | 1.71868i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.6274 | −1.61214 | −0.806068 | − | 0.591822i | \(-0.798409\pi\) | ||||
−0.806068 | + | 0.591822i | \(0.798409\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | 9.79796 | 0.687682 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.65685 | − | 6.92820i | 0.395092 | − | 0.483887i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 21.2132i | − | 1.47442i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.0000 | −0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 10.0000i | − | 0.688428i | −0.938891 | − | 0.344214i | \(-0.888145\pi\) | ||
0.938891 | − | 0.344214i | \(-0.111855\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.9706 | 1.16280 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.46410 | + | 4.24264i | −0.236250 | + | 0.289346i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 9.79796i | − | 0.665129i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 12.0000i | − | 0.810885i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 27.7128i | − | 1.86417i | ||||||
\(222\) | 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 | ||||||||
\(227\) | −17.1464 | −1.13805 | −0.569024 | − | 0.822321i | \(-0.692679\pi\) | ||||
−0.569024 | + | 0.822321i | \(0.692679\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.92820i | 0.457829i | 0.973447 | + | 0.228914i | \(0.0735176\pi\) | ||||
−0.973447 | + | 0.228914i | \(0.926482\pi\) | |||||||
\(230\) | 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 | ||||||||
\(235\) | −7.34847 | − | 6.00000i | −0.479361 | − | 0.391397i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.9706 | 1.10236 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.92820 | −0.448148 | −0.224074 | − | 0.974572i | \(-0.571936\pi\) | ||||
−0.224074 | + | 0.974572i | \(0.571936\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.0454 | −1.41421 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.07107 | + | 8.66025i | −0.451754 | + | 0.553283i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 33.9411i | 2.15962i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −30.0000 | −1.90117 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.0000i | 1.64111i | 0.571571 | + | 0.820553i | \(0.306334\pi\) | ||||
−0.571571 | + | 0.820553i | \(0.693666\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.1421 | 0.889108 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 20.7846 | + | 16.9706i | 1.30158 | + | 1.06274i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.79796i | 0.611180i | 0.952163 | + | 0.305590i | \(0.0988537\pi\) | ||||
−0.952163 | + | 0.305590i | \(0.901146\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 4.00000i | − | 0.248548i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 20.7846i | − | 1.28654i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 26.8701i | − | 1.65688i | −0.560079 | − | 0.828439i | \(-0.689229\pi\) | ||
0.560079 | − | 0.828439i | \(-0.310771\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.89898 | −0.299813 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.3205i | 1.05605i | 0.849229 | + | 0.528025i | \(0.177067\pi\) | ||||
−0.849229 | + | 0.528025i | \(0.822933\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.7846 | 1.26258 | 0.631288 | − | 0.775549i | \(-0.282527\pi\) | ||||
0.631288 | + | 0.775549i | \(0.282527\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 19.5959i | 1.18600i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.79796 | − | 2.00000i | 0.590839 | − | 0.120605i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.1421 | −0.849719 | −0.424859 | − | 0.905259i | \(-0.639676\pi\) | ||||
−0.424859 | + | 0.905259i | \(0.639676\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −20.7846 | −1.24434 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.00000 | 0.477240 | 0.238620 | − | 0.971113i | \(-0.423305\pi\) | ||||
0.238620 | + | 0.971113i | \(0.423305\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.44949 | −0.145607 | −0.0728035 | − | 0.997346i | \(-0.523195\pi\) | ||||
−0.0728035 | + | 0.997346i | \(0.523195\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −25.4558 | − | 20.7846i | −1.50787 | − | 1.23117i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 5.65685i | − | 0.333914i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 36.0000i | − | 2.11036i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.82843 | −0.165238 | −0.0826192 | − | 0.996581i | \(-0.526329\pi\) | ||||
−0.0826192 | + | 0.996581i | \(0.526329\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.46410 | + | 2.82843i | 0.201688 | + | 0.164677i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 40.0000i | − | 2.31326i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.46410i | 0.199667i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 16.9706i | − | 0.974933i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.00000 | − | 4.89898i | −0.343559 | − | 0.280515i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.44949 | −0.139800 | −0.0698999 | − | 0.997554i | \(-0.522268\pi\) | ||||
−0.0698999 | + | 0.997554i | \(0.522268\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 24.2487i | 1.37946i | ||||||||
\(310\) | 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 | ||||||||
\(315\) | −7.34847 | − | 6.00000i | −0.414039 | − | 0.338062i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.6274 | −1.27088 | −0.635441 | − | 0.772149i | \(-0.719182\pi\) | ||||
−0.635441 | + | 0.772149i | \(0.719182\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.8564 | 0.775810 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.00000 | −0.334887 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.3939 | 1.63552 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.65685 | − | 27.7128i | −0.313786 | − | 1.53723i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 8.48528i | − | 0.469237i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.00000 | −0.330791 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.00000i | 0.329790i | 0.986311 | + | 0.164895i | \(0.0527285\pi\) | ||||
−0.986311 | + | 0.164895i | \(0.947272\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.48528 | −0.464991 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.46410 | − | 4.24264i | 0.189264 | − | 0.231800i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.5959i | 1.06746i | 0.845656 | + | 0.533729i | \(0.179210\pi\) | ||||
−0.845656 | + | 0.533729i | \(0.820790\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 13.8564i | − | 0.750366i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706i | 0.916324i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 30.0000 | + | 24.4949i | 1.61515 | + | 1.31876i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.1464 | −0.920468 | −0.460234 | − | 0.887798i | \(-0.652235\pi\) | ||||
−0.460234 | + | 0.887798i | \(0.652235\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.92820i | 0.370858i | 0.982658 | + | 0.185429i | \(0.0593675\pi\) | ||||
−0.982658 | + | 0.185429i | \(0.940632\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 9.79796i | − | 0.521493i | −0.965407 | − | 0.260746i | \(-0.916031\pi\) | ||
0.965407 | − | 0.260746i | \(-0.0839686\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.79796 | + | 12.0000i | −0.520022 | + | 0.636894i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.9706 | 0.898177 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 17.1464 | 0.899954 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.48528 | + | 6.92820i | 0.444140 | + | 0.362639i | ||||
\(366\) | 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 | ||||||||
\(373\) | 19.7990 | 1.02515 | 0.512576 | − | 0.858642i | \(-0.328691\pi\) | ||||
0.512576 | + | 0.858642i | \(0.328691\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24.2487 | + | 12.7279i | 1.25220 | + | 0.657267i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 39.1918i | − | 2.01848i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 14.0000i | − | 0.719132i | −0.933120 | − | 0.359566i | \(-0.882925\pi\) | ||
0.933120 | − | 0.359566i | \(-0.117075\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.3205i | 0.887357i | ||||||||
\(382\) | 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 | ||||||||
\(387\) | 7.34847 | 0.373544 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3.46410i | − | 0.175637i | −0.996136 | − | 0.0878185i | \(-0.972010\pi\) | ||
0.996136 | − | 0.0878185i | \(-0.0279895\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −34.6410 | −1.75187 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 24.4949i | − | 1.23560i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.79796 | + | 12.0000i | −0.492989 | + | 0.603786i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.3137 | −0.567819 | −0.283909 | − | 0.958851i | \(-0.591631\pi\) | ||||
−0.283909 | + | 0.958851i | \(0.591631\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | −39.1918 | −1.95228 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.7279 | − | 15.5885i | 0.632456 | − | 0.774597i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5.65685i | − | 0.280400i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.0000 | −0.988936 | −0.494468 | − | 0.869196i | \(-0.664637\pi\) | ||||
−0.494468 | + | 0.869196i | \(0.664637\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.0000i | 1.18383i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.82843 | 0.139178 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.3205 | − | 21.2132i | 0.850230 | − | 1.04132i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 24.4949i | 1.19952i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.0000i | 1.27018i | 0.772437 | + | 0.635092i | \(0.219038\pi\) | ||||
−0.772437 | + | 0.635092i | \(0.780962\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 3.46410i | − | 0.168830i | −0.996431 | − | 0.0844150i | \(-0.973098\pi\) | ||
0.996431 | − | 0.0844150i | \(-0.0269021\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.7279i | 0.618853i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −24.0000 | + | 4.89898i | −1.16417 | + | 0.237635i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.89898 | −0.237078 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 27.7128i | 1.33799i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.92820 | 0.333720 | 0.166860 | − | 0.985981i | \(-0.446637\pi\) | ||||
0.166860 | + | 0.985981i | \(0.446637\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 34.2929i | − | 1.64801i | −0.566583 | − | 0.824005i | \(-0.691735\pi\) | ||
0.566583 | − | 0.824005i | \(-0.308265\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 29.3939 | + | 24.0000i | 1.40933 | + | 1.15071i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 42.4264 | 2.02953 | ||||||||
\(438\) | 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 | ||||||||
\(443\) | −22.0454 | −1.04741 | −0.523704 | − | 0.851900i | \(-0.675450\pi\) | ||||
−0.523704 | + | 0.851900i | \(0.675450\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.82843 | − | 3.46410i | 0.134080 | − | 0.164214i | ||||
\(446\) | 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 | ||||||||
\(451\) | − | 8.00000i | − | 0.376705i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −33.9411 | −1.59469 | ||||||||
\(454\) | 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 | ||||||||
\(461\) | − | 20.7846i | − | 0.968036i | −0.875058 | − | 0.484018i | \(-0.839177\pi\) | ||
0.875058 | − | 0.484018i | \(-0.160823\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | 31.8434 | 1.47354 | 0.736768 | − | 0.676146i | \(-0.236351\pi\) | ||||
0.736768 | + | 0.676146i | \(0.236351\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 3.46410i | − | 0.159957i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.92820 | 0.319235 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.89898i | 0.225255i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 29.3939 | − | 6.00000i | 1.34868 | − | 0.275299i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −41.5692 | −1.89935 | −0.949673 | − | 0.313243i | \(-0.898585\pi\) | ||||
−0.949673 | + | 0.313243i | \(0.898585\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.0000 | −0.729537 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.4949 | 1.11456 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25.4558 | + | 20.7846i | 1.15589 | + | 0.943781i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 26.8701i | − | 1.21760i | −0.793324 | − | 0.608799i | \(-0.791651\pi\) | ||
0.793324 | − | 0.608799i | \(-0.208349\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 54.0000 | 2.44196 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.0000i | 1.71492i | 0.514554 | + | 0.857458i | \(0.327958\pi\) | ||||
−0.514554 | + | 0.857458i | \(0.672042\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.9411 | −1.52863 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.3923 | − | 8.48528i | −0.467099 | − | 0.381385i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.79796i | 0.439499i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 6.00000i | − | 0.268597i | −0.990941 | − | 0.134298i | \(-0.957122\pi\) | ||
0.990941 | − | 0.134298i | \(-0.0428781\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.2487i | 1.08335i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.2132i | 0.945850i | 0.881103 | + | 0.472925i | \(0.156802\pi\) | ||||
−0.881103 | + | 0.472925i | \(0.843198\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0000 | + | 9.79796i | 0.533993 | + | 0.436003i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 46.5403 | 2.06693 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.7846i | 0.921262i | 0.887592 | + | 0.460631i | \(0.152377\pi\) | ||||
−0.887592 | + | 0.460631i | \(0.847623\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.92820 | 0.306486 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.1464 | − | 14.0000i | −0.755562 | − | 0.616914i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.48528 | −0.373182 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.7846 | 0.912343 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.0000 | 1.48957 | 0.744784 | − | 0.667306i | \(-0.232553\pi\) | ||||
0.744784 | + | 0.667306i | \(0.232553\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.44949 | −0.107109 | −0.0535544 | − | 0.998565i | \(-0.517055\pi\) | ||||
−0.0535544 | + | 0.998565i | \(0.517055\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16.9706 | − | 3.46410i | 0.740656 | − | 0.151186i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 33.9411i | 1.47850i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −27.0000 | −1.17391 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 6.00000i | − | 0.260378i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.6274 | −0.980102 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.46410 | − | 4.24264i | 0.149766 | − | 0.183425i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.89898i | 0.211407i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.0000i | 0.430730i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.92820i | 0.297867i | 0.988847 | + | 0.148933i | \(0.0475840\pi\) | ||||
−0.988847 | + | 0.148933i | \(0.952416\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 50.9117i | 2.18483i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.00000 | + | 4.89898i | 0.257012 | + | 0.209849i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.9444 | −1.15206 | −0.576029 | − | 0.817429i | \(-0.695399\pi\) | ||||
−0.576029 | + | 0.817429i | \(0.695399\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.3923i | 0.443533i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 41.5692 | 1.77091 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.79796i | 0.416652i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.79796 | − | 12.0000i | 0.415900 | − | 0.509372i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.4558 | 1.07860 | 0.539299 | − | 0.842114i | \(-0.318689\pi\) | ||||
0.539299 | + | 0.842114i | \(0.318689\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.8564 | 0.586064 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0000 | 1.01328 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.34847 | −0.309701 | −0.154851 | − | 0.987938i | \(-0.549490\pi\) | ||||
−0.154851 | + | 0.987938i | \(0.549490\pi\) | |||||||
\(564\) | 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 | \(-0.699656\pi\) | ||||
−0.586911 | + | 0.809652i | \(0.699656\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 30.0000i | − | 1.25546i | −0.778431 | − | 0.627730i | \(-0.783984\pi\) | ||
0.778431 | − | 0.627730i | \(-0.216016\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 33.9411 | 1.41791 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −34.6410 | + | 7.07107i | −1.44463 | + | 0.294884i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.3939i | 1.22368i | 0.790980 | + | 0.611842i | \(0.209571\pi\) | ||||
−0.790980 | + | 0.611842i | \(0.790429\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 12.0000i | − | 0.498703i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 17.3205i | − | 0.718576i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −24.0000 | + | 29.3939i | −0.992278 | + | 1.21529i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.2474 | 0.505506 | 0.252753 | − | 0.967531i | \(-0.418664\pi\) | ||||
0.252753 | + | 0.967531i | \(0.418664\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 41.5692i | − | 1.71283i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −55.4256 | −2.27991 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 29.3939i | − | 1.20706i | −0.797340 | − | 0.603531i | \(-0.793760\pi\) | ||
0.797340 | − | 0.603531i | \(-0.206240\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.79796 | + | 12.0000i | −0.401677 | + | 0.491952i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −50.9117 | −2.08368 | ||||||||
\(598\) | 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 | \(-0.662817\pi\) | ||||
−0.489490 | + | 0.872009i | \(0.662817\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.34847 | −0.299253 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.89949 | + | 12.1244i | −0.402472 | + | 0.492925i | ||||
\(606\) | 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 | ||||||||
\(611\) | 24.0000i | 0.970936i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.65685 | 0.228478 | 0.114239 | − | 0.993453i | \(-0.463557\pi\) | ||||
0.114239 | + | 0.993453i | \(0.463557\pi\) | |||||||
\(614\) | 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 | ||||||||
\(619\) | 14.0000i | 0.562708i | 0.959604 | + | 0.281354i | \(0.0907834\pi\) | ||||
−0.959604 | + | 0.281354i | \(0.909217\pi\) | |||||||
\(620\) | 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 | ||||||||
\(627\) | −29.3939 | −1.17388 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.8564i | 0.552491i | ||||||||
\(630\) | 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 | ||||||||
\(635\) | −12.2474 | − | 10.0000i | −0.486025 | − | 0.396838i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.2843 | 1.12066 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | −2.44949 | −0.0965984 | −0.0482992 | − | 0.998833i | \(-0.515380\pi\) | ||||
−0.0482992 | + | 0.998833i | \(0.515380\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.48528 | + | 10.3923i | −0.334108 | + | 0.409197i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 4.24264i | − | 0.166795i | −0.996516 | − | 0.0833977i | \(-0.973423\pi\) | ||
0.996516 | − | 0.0833977i | \(-0.0265772\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.00000 | 0.157014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 24.0000i | − | 0.940634i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.65685 | 0.221370 | 0.110685 | − | 0.993856i | \(-0.464696\pi\) | ||||
0.110685 | + | 0.993856i | \(0.464696\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.3205 | + | 14.1421i | 0.676768 | + | 0.552579i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 14.6969i | − | 0.573382i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.00000i | 0.0779089i | 0.999241 | + | 0.0389545i | \(0.0124027\pi\) | ||||
−0.999241 | + | 0.0389545i | \(0.987597\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 10.3923i | − | 0.404214i | −0.979363 | − | 0.202107i | \(-0.935221\pi\) | ||
0.979363 | − | 0.202107i | \(-0.0647788\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 67.8823i | − | 2.63633i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.0000 | − | 14.6969i | 0.465340 | − | 0.569923i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −48.9898 | −1.89689 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 65.8179i | − | 2.54467i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.92820 | −0.267460 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.4949i | 0.944209i | 0.881543 | + | 0.472104i | \(0.156505\pi\) | ||||
−0.881543 | + | 0.472104i | \(0.843495\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.65685 | 0.217411 | 0.108705 | − | 0.994074i | \(-0.465330\pi\) | ||||
0.108705 | + | 0.994074i | \(0.465330\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.7846 | 0.797640 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −42.0000 | −1.60944 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.44949 | 0.0937271 | 0.0468636 | − | 0.998901i | \(-0.485077\pi\) | ||||
0.0468636 | + | 0.998901i | \(0.485077\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.9706 | − | 13.8564i | −0.648412 | − | 0.529426i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.9706i | 0.647467i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 42.0000i | − | 1.59776i | −0.601494 | − | 0.798878i | \(-0.705427\pi\) | ||
0.601494 | − | 0.798878i | \(-0.294573\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.48528 | −0.322329 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.3205 | − | 14.1421i | −0.657004 | − | 0.536442i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.5959i | 0.742248i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 36.0000i | 1.36165i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 3.46410i | − | 0.130837i | −0.997858 | − | 0.0654187i | \(-0.979162\pi\) | ||
0.997858 | − | 0.0654187i | \(-0.0208383\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 16.9706i | − | 0.640057i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −18.0000 | − | 14.6969i | −0.677919 | − | 0.553519i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.79796 | 0.368490 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 34.6410i | − | 1.30097i | −0.759519 | − | 0.650485i | \(-0.774566\pi\) | ||
0.759519 | − | 0.650485i | \(-0.225434\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.7846 | 0.779484 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 48.9898i | 1.83468i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.5959 | − | 16.0000i | −0.732846 | − | 0.598366i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.9706 | −0.633777 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.92820 | 0.258378 | 0.129189 | − | 0.991620i | \(-0.458763\pi\) | ||||
0.129189 | + | 0.991620i | \(0.458763\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.0000 | −0.521387 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −33.9411 | + | 6.92820i | −1.26054 | + | 0.257307i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.3848i | 0.681854i | 0.940090 | + | 0.340927i | \(0.110741\pi\) | ||||
−0.940090 | + | 0.340927i | \(0.889259\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 12.0000i | − | 0.443836i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.7990 | −0.731292 | −0.365646 | − | 0.930754i | \(-0.619152\pi\) | ||||
−0.365646 | + | 0.930754i | \(0.619152\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −17.3205 | + | 21.2132i | −0.638877 | + | 0.782461i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 4.89898i | − | 0.180456i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 30.0000i | − | 1.10357i | −0.833987 | − | 0.551784i | \(-0.813947\pi\) | ||
0.833987 | − | 0.551784i | \(-0.186053\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 83.1384i | 3.05417i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 4.24264i | − | 0.155647i | −0.996967 | − | 0.0778237i | \(-0.975203\pi\) | ||
0.996967 | − | 0.0778237i | \(-0.0247971\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.0000 | − | 14.6969i | −0.659469 | − | 0.538454i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −36.7423 | −1.34433 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 3.46410i | − | 0.126576i | ||||||
\(750\) | 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 | ||||||||
\(755\) | 19.5959 | − | 24.0000i | 0.713168 | − | 0.873449i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.82843 | 0.102801 | 0.0514005 | − | 0.998678i | \(-0.483632\pi\) | ||||
0.0514005 | + | 0.998678i | \(0.483632\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 34.6410 | 1.25739 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.0000 | 1.37750 | 0.688749 | − | 0.724999i | \(-0.258160\pi\) | ||||
0.688749 | + | 0.724999i | \(0.258160\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.89898 | 0.177355 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 25.4558 | + | 20.7846i | 0.920358 | + | 0.751469i | ||||
\(766\) | 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 | ||||||||
\(771\) | 24.0000i | 0.864339i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 45.2548 | 1.62770 | 0.813852 | − | 0.581073i | \(-0.197367\pi\) | ||||
0.813852 | + | 0.581073i | \(0.197367\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.92820 | + | 33.9411i | 0.248868 | + | 1.21920i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 9.79796i | − | 0.351500i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 24.0000i | − | 0.859889i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8564i | 0.495821i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.00000 | + | 4.89898i | −0.142766 | + | 0.174852i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.5403 | 1.65898 | 0.829491 | − | 0.558520i | \(-0.188630\pi\) | ||||
0.829491 | + | 0.558520i | \(0.188630\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 65.8179i | − | 2.34318i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.5959i | 0.695871i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.9411 | −1.20226 | −0.601128 | − | 0.799153i | \(-0.705282\pi\) | ||||
−0.601128 | + | 0.799153i | \(0.705282\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.7846 | 0.735307 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.00000 | −0.212000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.79796 | 0.345762 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.1421 | + | 17.3205i | −0.498445 | + | 0.610468i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 42.4264i | 1.49348i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 50.0000 | 1.75791 | 0.878953 | − | 0.476908i | \(-0.158243\pi\) | ||||
0.878953 | + | 0.476908i | \(0.158243\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 22.0000i | − | 0.772524i | −0.922389 | − | 0.386262i | \(-0.873766\pi\) | ||
0.922389 | − | 0.386262i | \(-0.126234\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 50.9117 | 1.78555 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −31.1769 | + | 38.1838i | −1.09208 | + | 1.33752i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.6969i | 0.514181i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 24.0000i | 0.838628i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 51.9615i | − | 1.81347i | −0.421701 | − | 0.906735i | \(-0.638567\pi\) | ||
0.421701 | − | 0.906735i | \(-0.361433\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 35.3553i | − | 1.23241i | −0.787586 | − | 0.616205i | \(-0.788669\pi\) | ||
0.787586 | − | 0.616205i | \(-0.211331\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 24.0000 | − | 4.89898i | 0.835573 | − | 0.170561i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.8434 | 1.10730 | 0.553651 | − | 0.832749i | \(-0.313234\pi\) | ||||
0.553651 | + | 0.832749i | \(0.313234\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.0333i | 1.56407i | 0.623233 | + | 0.782036i | \(0.285819\pi\) | ||||
−0.623233 | + | 0.782036i | \(0.714181\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −34.6410 | −1.20168 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 24.4949i | − | 0.848698i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.1464 | − | 14.0000i | −0.593377 | − | 0.484490i | ||||
\(836\) | 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 | ||||||||
\(843\) | 19.5959 | 0.674919 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −26.8701 | + | 32.9090i | −0.924358 | + | 1.13210i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.89949i | 0.340151i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.00000 | −0.205919 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.0000i | 0.685591i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.65685 | 0.193687 | 0.0968435 | − | 0.995300i | \(-0.469125\pi\) | ||||
0.0968435 | + | 0.995300i | \(0.469125\pi\) | |||||||
\(854\) | 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 | ||||||||
\(859\) | 22.0000i | 0.750630i | 0.926897 | + | 0.375315i | \(0.122466\pi\) | ||||
−0.926897 | + | 0.375315i | \(0.877534\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 13.8564i | − | 0.472225i | ||||||
\(862\) | 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 | ||||||||
\(867\) | −17.1464 | −0.582323 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.8564i | 0.470046i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.8564 | −0.469506 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 44.0908i | − | 1.49225i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.34847 | + | 14.0000i | −0.248424 | + | 0.473286i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.7696 | −1.24162 | −0.620810 | − | 0.783961i | \(-0.713196\pi\) | ||||
−0.620810 | + | 0.783961i | \(0.713196\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 12.2474 | 0.412159 | 0.206080 | − | 0.978535i | \(-0.433929\pi\) | ||||
0.206080 | + | 0.978535i | \(0.433929\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.48528 | + | 6.92820i | 0.285230 | + | 0.232889i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 49.4975i | − | 1.66196i | −0.556300 | − | 0.830981i | \(-0.687780\pi\) | ||
0.556300 | − | 0.830981i | \(-0.312220\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.0000 | −0.335389 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 18.0000i | − | 0.603023i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25.4558 | −0.851847 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.46410 | − | 2.82843i | −0.115792 | − | 0.0945439i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 97.9796i | − | 3.27144i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 48.0000i | 1.60089i | ||||||||
\(900\) | 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 | ||||||||
\(907\) | 26.9444 | 0.894674 | 0.447337 | − | 0.894366i | \(-0.352373\pi\) | ||||
0.447337 | + | 0.894366i | \(0.352373\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 20.7846i | − | 0.689382i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.4974 | 1.60679 | 0.803396 | − | 0.595446i | \(-0.203024\pi\) | ||||
0.803396 | + | 0.595446i | \(0.203024\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 24.4949i | − | 0.810663i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.6969 | − | 12.0000i | −0.485866 | − | 0.396708i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.1421 | 0.467014 | ||||||||
\(918\) | 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 | ||||||||
\(923\) | 39.1918 | 1.29001 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.82843 | + | 13.8564i | 0.0929981 | + | 0.455596i | ||||
\(926\) | 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 | ||||||||
\(931\) | 30.0000i | 0.983210i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 67.8823 | 2.22237 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | 72.0000i | 2.34963i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.6410i | 1.12926i | 0.825342 | + | 0.564632i | \(0.190982\pi\) | ||||
−0.825342 | + | 0.564632i | \(0.809018\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.2843i | 0.921063i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.6413 | −1.35316 | −0.676581 | − | 0.736369i | \(-0.736539\pi\) | ||||
−0.676581 | + | 0.736369i | \(0.736539\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 27.7128i | − | 0.899596i | ||||||
\(950\) | 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 | ||||||||
\(955\) | −19.5959 | + | 24.0000i | −0.634109 | + | 0.776622i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 33.9411 | 1.09716 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.8564 | −0.447447 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.0000 | 0.548387 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.34847 | −0.236801 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.48528 | + | 6.92820i | 0.273151 | + | 0.223027i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.5563i | 0.500258i | 0.968212 | + | 0.250129i | \(0.0804731\pi\) | ||||
−0.968212 | + | 0.250129i | \(0.919527\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 72.0000 | 2.31297 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.0000i | 0.706014i | 0.935621 | + | 0.353007i | \(0.114841\pi\) | ||||
−0.935621 | + | 0.353007i | \(0.885159\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.1421 | −0.453376 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13.8564 | − | 67.8823i | −0.443760 | − | 2.17397i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.89898i | 0.156732i | 0.996925 | + | 0.0783661i | \(0.0249703\pi\) | ||||
−0.996925 | + | 0.0783661i | \(0.975030\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 4.00000i | − | 0.127841i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 10.3923i | − | 0.331801i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 46.6690i | 1.48851i | 0.667895 | + | 0.744256i | \(0.267196\pi\) | ||||
−0.667895 | + | 0.744256i | \(0.732804\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 32.0000 | − | 39.1918i | 1.01960 | − | 1.24876i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.6969 | −0.467809 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 17.3205i | − | 0.550760i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.7128 | −0.880327 | −0.440163 | − | 0.897918i | \(-0.645079\pi\) | ||||
−0.440163 | + | 0.897918i | \(0.645079\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.6969i | 0.466393i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 29.3939 | − | 36.0000i | 0.931849 | − | 1.14128i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 56.5685 | 1.79154 | 0.895772 | − | 0.444514i | \(-0.146624\pi\) | ||||
0.895772 | + | 0.444514i | \(0.146624\pi\) | |||||||
\(998\) | 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 \(a_p\))