Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(881,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.cc (of order \(6\), degree \(2\), 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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 881.2 | ||
Root | \(-0.474636 - 0.274031i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.881 |
Dual form | 3024.2.cc.a.2897.2 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.10552 | + | 1.91482i | −0.494405 | + | 0.856335i | −0.999979 | − | 0.00644798i | \(-0.997948\pi\) |
0.505574 | + | 0.862783i | \(0.331281\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.906161 | − | 2.48573i | 0.342497 | − | 0.939519i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.93818 | + | 1.69636i | −0.885894 | + | 0.511471i | −0.872597 | − | 0.488440i | \(-0.837566\pi\) |
−0.0132968 | + | 0.999912i | \(0.504233\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.56060 | − | 0.901012i | −0.432832 | − | 0.249896i | 0.267720 | − | 0.963497i | \(-0.413730\pi\) |
−0.700552 | + | 0.713601i | \(0.747063\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.96901 | 1.44770 | 0.723849 | − | 0.689959i | \(-0.242371\pi\) | ||||
0.723849 | + | 0.689959i | \(0.242371\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.64419i | 0.377202i | 0.982054 | + | 0.188601i | \(0.0603953\pi\) | ||||
−0.982054 | + | 0.188601i | \(0.939605\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.05563 | + | 1.18682i | 0.428629 | + | 0.247469i | 0.698762 | − | 0.715354i | \(-0.253734\pi\) |
−0.270133 | + | 0.962823i | \(0.587068\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0556321 | + | 0.0963576i | 0.0111264 | + | 0.0192715i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.44437 | + | 1.41126i | −0.453908 | + | 0.262064i | −0.709479 | − | 0.704726i | \(-0.751070\pi\) |
0.255571 | + | 0.966790i | \(0.417736\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.28558 | − | 5.36103i | −1.66774 | − | 0.962870i | −0.968853 | − | 0.247638i | \(-0.920346\pi\) |
−0.698887 | − | 0.715232i | \(-0.746321\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.75796 | + | 4.48318i | 0.635211 | + | 0.757795i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.69963 | 0.279417 | 0.139709 | − | 0.990193i | \(-0.455383\pi\) | ||||
0.139709 | + | 0.990193i | \(0.455383\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.455074 | − | 0.788211i | 0.0710706 | − | 0.123098i | −0.828300 | − | 0.560285i | \(-0.810692\pi\) |
0.899371 | + | 0.437187i | \(0.144025\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.96108 | + | 3.39669i | 0.299062 | + | 0.517990i | 0.975922 | − | 0.218122i | \(-0.0699931\pi\) |
−0.676860 | + | 0.736112i | \(0.736660\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.123005 | + | 0.213051i | 0.0179422 | + | 0.0310767i | 0.874857 | − | 0.484381i | \(-0.160955\pi\) |
−0.856915 | + | 0.515458i | \(0.827622\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.35774 | − | 4.50495i | −0.765392 | − | 0.643564i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.87589i | 1.08184i | 0.841075 | + | 0.540919i | \(0.181923\pi\) | ||||
−0.841075 | + | 0.540919i | \(0.818077\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 7.50146i | − | 1.01150i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.39093 | + | 9.33736i | −0.701839 | + | 1.21562i | 0.265981 | + | 0.963978i | \(0.414304\pi\) |
−0.967820 | + | 0.251643i | \(0.919029\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.22853 | − | 0.709292i | 0.157297 | − | 0.0908155i | −0.419285 | − | 0.907855i | \(-0.637719\pi\) |
0.576582 | + | 0.817039i | \(0.304386\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.45056 | − | 1.99218i | 0.427989 | − | 0.247100i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.99381 | + | 6.91748i | −0.487922 | + | 0.845105i | −0.999904 | − | 0.0138913i | \(-0.995578\pi\) |
0.511982 | + | 0.858996i | \(0.328911\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.1743i | 1.44482i | 0.691463 | + | 0.722412i | \(0.256966\pi\) | ||||
−0.691463 | + | 0.722412i | \(0.743034\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.426103i | 0.0498715i | 0.999689 | + | 0.0249358i | \(0.00793812\pi\) | ||||
−0.999689 | + | 0.0249358i | \(0.992062\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.55423 | + | 8.84070i | 0.177121 | + | 1.00749i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.49381 | − | 4.31941i | −0.280576 | − | 0.485971i | 0.690951 | − | 0.722902i | \(-0.257192\pi\) |
−0.971527 | + | 0.236930i | \(0.923859\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.28541 | − | 7.42254i | −0.470384 | − | 0.814730i | 0.529042 | − | 0.848596i | \(-0.322551\pi\) |
−0.999426 | + | 0.0338660i | \(0.989218\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.59888 | + | 11.4296i | −0.715750 | + | 1.23971i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.5358 | −1.11680 | −0.558399 | − | 0.829573i | \(-0.688584\pi\) | ||||
−0.558399 | + | 0.829573i | \(0.688584\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.65383 | + | 3.06277i | −0.383025 | + | 0.321065i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.14833 | − | 1.81769i | −0.323012 | − | 0.186491i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.30108 | + | 3.63793i | −0.639777 | + | 0.369376i | −0.784529 | − | 0.620092i | \(-0.787095\pi\) |
0.144751 | + | 0.989468i | \(0.453762\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.33405 | + | 4.04270i | 0.232247 | + | 0.402264i | 0.958469 | − | 0.285197i | \(-0.0920589\pi\) |
−0.726222 | + | 0.687460i | \(0.758726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.40462 | + | 3.12036i | 0.532533 | + | 0.307458i | 0.742047 | − | 0.670348i | \(-0.233855\pi\) |
−0.209515 | + | 0.977806i | \(0.567188\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.48939i | − | 0.143985i | −0.997405 | − | 0.0719925i | \(-0.977064\pi\) | ||
0.997405 | − | 0.0719925i | \(-0.0229358\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.38688 | −0.420187 | −0.210093 | − | 0.977681i | \(-0.567377\pi\) | ||||
−0.210093 | + | 0.977681i | \(0.567377\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.8764 | + | 8.58887i | 1.39945 | + | 0.807973i | 0.994335 | − | 0.106293i | \(-0.0338981\pi\) |
0.405115 | + | 0.914266i | \(0.367231\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.54510 | + | 2.62412i | −0.423833 | + | 0.244700i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.40888 | − | 14.8374i | 0.495831 | − | 1.36014i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.255260 | − | 0.442124i | 0.0232055 | − | 0.0401931i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.3013 | −1.01081 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.32141 | −0.560935 | −0.280467 | − | 0.959864i | \(-0.590489\pi\) | ||||
−0.280467 | + | 0.959864i | \(0.590489\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.51213 | + | 14.7434i | −0.743708 | + | 1.28814i | 0.207088 | + | 0.978322i | \(0.433601\pi\) |
−0.950796 | + | 0.309818i | \(0.899732\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.08701 | + | 1.48990i | 0.354389 | + | 0.129190i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.42580 | + | 3.13259i | −0.463557 | + | 0.267635i | −0.713539 | − | 0.700616i | \(-0.752909\pi\) |
0.249982 | + | 0.968251i | \(0.419575\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.65488 | − | 3.84220i | −0.564460 | − | 0.325891i | 0.190474 | − | 0.981692i | \(-0.438998\pi\) |
−0.754934 | + | 0.655801i | \(0.772331\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.11375 | 0.511258 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 6.24071i | − | 0.518263i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.3695 | − | 7.71887i | −1.09527 | − | 0.632355i | −0.160296 | − | 0.987069i | \(-0.551245\pi\) |
−0.934975 | + | 0.354714i | \(0.884578\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.84362 | + | 10.1215i | 0.475547 | + | 0.823672i | 0.999608 | − | 0.0280089i | \(-0.00891668\pi\) |
−0.524060 | + | 0.851681i | \(0.675583\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.5309 | − | 11.8535i | 1.64908 | − | 0.952096i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.93586 | − | 2.84972i | −0.393924 | − | 0.227432i | 0.289935 | − | 0.957046i | \(-0.406366\pi\) |
−0.683859 | + | 0.729614i | \(0.739700\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.81285 | − | 4.03430i | 0.379306 | − | 0.317948i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2101 | 0.799721 | 0.399860 | − | 0.916576i | \(-0.369059\pi\) | ||||
0.399860 | + | 0.916576i | \(0.369059\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.80661 | − | 3.12914i | 0.139800 | − | 0.242140i | −0.787621 | − | 0.616160i | \(-0.788688\pi\) |
0.927421 | + | 0.374020i | \(0.122021\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.87636 | − | 8.44610i | −0.375104 | − | 0.649700i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.03957 | − | 15.6570i | −0.687266 | − | 1.19038i | −0.972719 | − | 0.231987i | \(-0.925477\pi\) |
0.285453 | − | 0.958393i | \(-0.407856\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.289931 | − | 0.0509711i | 0.0219167 | − | 0.00385305i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.03194i | 0.376105i | 0.982159 | + | 0.188052i | \(0.0602175\pi\) | ||||
−0.982159 | + | 0.188052i | \(0.939783\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 13.5592i | − | 1.00785i | −0.863747 | − | 0.503925i | \(-0.831889\pi\) | ||
0.863747 | − | 0.503925i | \(-0.168111\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.87898 | + | 3.25449i | −0.138145 | + | 0.239275i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.5380 | + | 10.1256i | −1.28251 | + | 0.740455i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.86948 | + | 5.12080i | −0.641773 | + | 0.370528i | −0.785297 | − | 0.619119i | \(-0.787490\pi\) |
0.143524 | + | 0.989647i | \(0.454156\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.06615 | + | 13.9710i | −0.580614 | + | 1.00565i | 0.414792 | + | 0.909916i | \(0.363854\pi\) |
−0.995407 | + | 0.0957374i | \(0.969479\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3.86303i | − | 0.275230i | −0.990486 | − | 0.137615i | \(-0.956056\pi\) | ||
0.990486 | − | 0.137615i | \(-0.0439436\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.2034i | 1.07774i | 0.842388 | + | 0.538871i | \(0.181149\pi\) | ||||
−0.842388 | + | 0.538871i | \(0.818851\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.29302 | + | 7.35487i | 0.0907520 | + | 0.516211i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.00619 | + | 1.74277i | 0.0702753 | + | 0.121720i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.78913 | − | 4.83091i | −0.192928 | − | 0.334161i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.9523 | + | 20.7021i | −0.822833 | + | 1.42519i | 0.0807311 | + | 0.996736i | \(0.474274\pi\) |
−0.903564 | + | 0.428453i | \(0.859059\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.67208 | −0.591431 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.7403 | + | 18.2235i | −1.47583 | + | 1.23709i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.31522 | − | 5.37815i | −0.626610 | − | 0.361773i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.6198 | − | 9.59545i | 1.11294 | − | 0.642559i | 0.173354 | − | 0.984860i | \(-0.444539\pi\) |
0.939591 | + | 0.342300i | \(0.111206\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.33604 | + | 7.51024i | 0.287793 | + | 0.498472i | 0.973283 | − | 0.229610i | \(-0.0737451\pi\) |
−0.685490 | + | 0.728082i | \(0.740412\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.4437 | + | 7.18439i | 0.822304 | + | 0.474758i | 0.851211 | − | 0.524824i | \(-0.175869\pi\) |
−0.0289060 | + | 0.999582i | \(0.509202\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 29.7160i | 1.94676i | 0.229194 | + | 0.973381i | \(0.426391\pi\) | ||||
−0.229194 | + | 0.973381i | \(0.573609\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.543941 | −0.0354828 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.7101 | − | 7.91556i | −0.886836 | − | 0.512015i | −0.0139296 | − | 0.999903i | \(-0.504434\pi\) |
−0.872906 | + | 0.487888i | \(0.837767\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.34973 | + | 2.51132i | −0.280190 | + | 0.161768i | −0.633510 | − | 0.773735i | \(-0.718386\pi\) |
0.353319 | + | 0.935503i | \(0.385053\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.5493 | − | 5.27881i | 0.929521 | − | 0.337251i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.48143 | − | 2.56591i | 0.0942612 | − | 0.163265i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.29728 | −0.460600 | −0.230300 | − | 0.973120i | \(-0.573971\pi\) | ||||
−0.230300 | + | 0.973120i | \(0.573971\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.05308 | −0.506293 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.00397 | − | 6.93508i | 0.249761 | − | 0.432598i | −0.713699 | − | 0.700453i | \(-0.752981\pi\) |
0.963459 | + | 0.267855i | \(0.0863147\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.54014 | − | 4.22482i | 0.0956994 | − | 0.262518i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.6051 | + | 7.85489i | −0.838925 | + | 0.484353i | −0.856899 | − | 0.515485i | \(-0.827612\pi\) |
0.0179738 | + | 0.999838i | \(0.494278\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.0810 | − | 8.70699i | −0.926416 | − | 0.534866i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.4924 | −0.639731 | −0.319866 | − | 0.947463i | \(-0.603638\pi\) | ||||
−0.319866 | + | 0.947463i | \(0.603638\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 22.2537i | − | 1.35181i | −0.736987 | − | 0.675907i | \(-0.763752\pi\) | ||
0.736987 | − | 0.675907i | \(-0.236248\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.326914 | − | 0.188744i | −0.0197137 | − | 0.0113817i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.4251 | + | 19.7889i | 0.686468 | + | 1.18900i | 0.972973 | + | 0.230919i | \(0.0741733\pi\) |
−0.286505 | + | 0.958079i | \(0.592493\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.796041 | + | 0.459595i | −0.0474878 | + | 0.0274171i | −0.523556 | − | 0.851991i | \(-0.675395\pi\) |
0.476068 | + | 0.879408i | \(0.342062\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.1573 | + | 11.0605i | 1.13878 | + | 0.657477i | 0.946129 | − | 0.323790i | \(-0.104957\pi\) |
0.192654 | + | 0.981267i | \(0.438290\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.54691 | − | 1.84544i | −0.0913113 | − | 0.108933i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.6291 | 1.09583 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.6259 | + | 25.3328i | −0.854453 | + | 1.47996i | 0.0226986 | + | 0.999742i | \(0.492774\pi\) |
−0.877152 | + | 0.480214i | \(0.840559\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.9196 | − | 20.6454i | −0.693986 | − | 1.20202i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.13868 | − | 3.70430i | −0.123683 | − | 0.214225i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.2203 | − | 1.79677i | 0.589089 | − | 0.103564i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.13656i | 0.179599i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 14.8451i | − | 0.847254i | −0.905837 | − | 0.423627i | \(-0.860757\pi\) | ||
0.905837 | − | 0.423627i | \(-0.139243\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.69002 | − | 16.7836i | 0.549471 | − | 0.951711i | −0.448840 | − | 0.893612i | \(-0.648163\pi\) |
0.998311 | − | 0.0580991i | \(-0.0185040\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.6608 | − | 7.30974i | 0.715633 | − | 0.413171i | −0.0975102 | − | 0.995235i | \(-0.531088\pi\) |
0.813143 | + | 0.582064i | \(0.197755\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.7046 | − | 8.48973i | 0.825895 | − | 0.476831i | −0.0265499 | − | 0.999647i | \(-0.508452\pi\) |
0.852445 | + | 0.522817i | \(0.175119\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.78799 | − | 8.29305i | 0.268076 | − | 0.464321i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.81416i | 0.546074i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 0.200501i | − | 0.0111218i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.641051 | − | 0.112699i | 0.0353423 | − | 0.00621332i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.94801 | + | 17.2305i | 0.546792 | + | 0.947072i | 0.998492 | + | 0.0549016i | \(0.0174845\pi\) |
−0.451700 | + | 0.892170i | \(0.649182\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.83051 | − | 15.2949i | −0.482462 | − | 0.835649i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.490168 | − | 0.848996i | 0.0267012 | − | 0.0462478i | −0.852366 | − | 0.522946i | \(-0.824833\pi\) |
0.879067 | + | 0.476698i | \(0.158166\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 36.3769 | 1.96992 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.0531 | + | 9.23572i | −0.866785 | + | 0.498682i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.3702 | + | 10.6060i | 0.986162 | + | 0.569361i | 0.904125 | − | 0.427268i | \(-0.140524\pi\) |
0.0820373 | + | 0.996629i | \(0.473857\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.69945 | − | 5.02263i | 0.465671 | − | 0.268855i | −0.248755 | − | 0.968566i | \(-0.580021\pi\) |
0.714426 | + | 0.699711i | \(0.246688\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.37327 | − | 2.37858i | −0.0730920 | − | 0.126599i | 0.827163 | − | 0.561962i | \(-0.189953\pi\) |
−0.900255 | + | 0.435363i | \(0.856620\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.3116 | − | 13.4590i | −1.23725 | − | 0.714329i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.0013i | 0.527849i | 0.964543 | + | 0.263925i | \(0.0850170\pi\) | ||||
−0.964543 | + | 0.263925i | \(0.914983\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.2967 | 0.857719 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.815912 | − | 0.471067i | −0.0427068 | − | 0.0246568i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.03560 | − | 2.90731i | 0.262856 | − | 0.151760i | −0.362781 | − | 0.931875i | \(-0.618173\pi\) |
0.625637 | + | 0.780114i | \(0.284839\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.5774 | + | 7.13683i | 1.01641 | + | 0.370526i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.75959 | − | 13.4400i | 0.401776 | − | 0.695897i | −0.592164 | − | 0.805817i | \(-0.701726\pi\) |
0.993940 | + | 0.109920i | \(0.0350596\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.08623 | 0.261954 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.79714 | −0.143679 | −0.0718396 | − | 0.997416i | \(-0.522887\pi\) | ||||
−0.0718396 | + | 0.997416i | \(0.522887\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.74229 | + | 3.01773i | −0.0890268 | + | 0.154199i | −0.907100 | − | 0.420915i | \(-0.861709\pi\) |
0.818073 | + | 0.575114i | \(0.195042\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.6466 | − | 6.79753i | −0.950320 | − | 0.346434i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.37017 | − | 3.67782i | 0.322980 | − | 0.186473i | −0.329740 | − | 0.944072i | \(-0.606961\pi\) |
0.652720 | + | 0.757599i | \(0.273628\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.2701 | + | 7.08414i | 0.620525 | + | 0.358260i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.0279 | 0.554872 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 19.2838i | − | 0.967825i | −0.875116 | − | 0.483912i | \(-0.839215\pi\) | ||
0.875116 | − | 0.483912i | \(-0.160785\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.60576 | − | 5.54589i | −0.479689 | − | 0.276949i | 0.240598 | − | 0.970625i | \(-0.422656\pi\) |
−0.720287 | + | 0.693676i | \(0.755990\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.66071 | + | 16.7328i | 0.481234 | + | 0.833522i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.99381 | + | 2.88318i | −0.247534 | + | 0.142914i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.5597 | + | 10.1381i | 0.868274 | + | 0.501298i | 0.866774 | − | 0.498701i | \(-0.166189\pi\) |
0.00149954 | + | 0.999999i | \(0.499523\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.3252 | + | 21.8616i | 0.901722 | + | 1.07574i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.9505 | 0.930243 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.54936 | + | 9.61177i | −0.271104 | + | 0.469566i | −0.969145 | − | 0.246492i | \(-0.920722\pi\) |
0.698041 | + | 0.716058i | \(0.254055\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.59269 | + | 7.95478i | 0.223834 | + | 0.387692i | 0.955969 | − | 0.293467i | \(-0.0948092\pi\) |
−0.732135 | + | 0.681160i | \(0.761476\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.332068 | + | 0.575159i | 0.0161077 | + | 0.0278993i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.649865 | − | 3.69653i | −0.0314492 | − | 0.178888i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 15.1102i | − | 0.727833i | −0.931432 | − | 0.363916i | \(-0.881439\pi\) | ||
0.931432 | − | 0.363916i | \(-0.118561\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.33578i | 0.160307i | 0.996783 | + | 0.0801537i | \(0.0255411\pi\) | ||||
−0.996783 | + | 0.0801537i | \(0.974459\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.95135 | + | 3.37984i | −0.0933458 | + | 0.161680i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.91032 | + | 3.41233i | −0.282084 | + | 0.162861i | −0.634367 | − | 0.773032i | \(-0.718739\pi\) |
0.352282 | + | 0.935894i | \(0.385406\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.77747 | − | 5.64503i | 0.464542 | − | 0.268203i | −0.249410 | − | 0.968398i | \(-0.580237\pi\) |
0.713952 | + | 0.700195i | \(0.246903\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.6476 | − | 20.1743i | 0.552151 | − | 0.956354i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 24.8554i | − | 1.17300i | −0.809950 | − | 0.586498i | \(-0.800506\pi\) | ||
0.809950 | − | 0.586498i | \(-0.199494\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.08787i | 0.145402i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.82527 | − | 10.3824i | −0.0855700 | − | 0.486735i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.30470 | + | 10.9201i | 0.294922 | + | 0.510819i | 0.974967 | − | 0.222351i | \(-0.0713732\pi\) |
−0.680045 | + | 0.733170i | \(0.738040\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.4031 | − | 24.9470i | −0.670821 | − | 1.16190i | −0.977672 | − | 0.210138i | \(-0.932609\pi\) |
0.306851 | − | 0.951758i | \(-0.400725\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.5858 | − | 21.7993i | 0.584912 | − | 1.01310i | −0.409974 | − | 0.912097i | \(-0.634462\pi\) |
0.994886 | − | 0.101001i | \(-0.0322045\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.5951 | 1.18440 | 0.592199 | − | 0.805792i | \(-0.298260\pi\) | ||||
0.592199 | + | 0.805792i | \(0.298260\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.5760 | + | 16.1959i | 0.626881 | + | 0.747857i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.5240 | − | 6.65338i | −0.529874 | − | 0.305923i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.158430 | + | 0.0914695i | −0.00726926 | + | 0.00419691i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.267749 | − | 0.463755i | −0.0122338 | − | 0.0211895i | 0.859844 | − | 0.510557i | \(-0.170561\pi\) |
−0.872077 | + | 0.489368i | \(0.837228\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.65244 | − | 1.53138i | −0.120941 | − | 0.0698251i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 16.0873i | − | 0.730485i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.1323 | −1.54668 | −0.773341 | − | 0.633990i | \(-0.781416\pi\) | ||||
−0.773341 | + | 0.633990i | \(0.781416\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.86948 | + | 3.38874i | 0.264886 | + | 0.152932i | 0.626561 | − | 0.779372i | \(-0.284462\pi\) |
−0.361675 | + | 0.932304i | \(0.617795\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.5905 | + | 8.42380i | −0.657121 | + | 0.379389i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 30.2621 | + | 11.0319i | 1.35744 | + | 0.494847i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.30037 | − | 7.44846i | 0.192511 | − | 0.333439i | −0.753571 | − | 0.657367i | \(-0.771670\pi\) |
0.946082 | + | 0.323928i | \(0.105004\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.96518 | −0.132211 | −0.0661055 | − | 0.997813i | \(-0.521057\pi\) | ||||
−0.0661055 | + | 0.997813i | \(0.521057\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.3214 | −0.459297 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.04882 | − | 5.28072i | 0.135137 | − | 0.234064i | −0.790513 | − | 0.612445i | \(-0.790186\pi\) |
0.925650 | + | 0.378382i | \(0.123519\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.05918 | + | 0.386118i | 0.0468553 | + | 0.0170808i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.9499 | + | 6.89926i | −0.526574 | + | 0.304018i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.722823 | − | 0.417322i | −0.0317897 | − | 0.0183538i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.6929 | 1.43230 | 0.716150 | − | 0.697946i | \(-0.245903\pi\) | ||||
0.716150 | + | 0.697946i | \(0.245903\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.00252i | 0.0875643i | 0.999041 | + | 0.0437821i | \(0.0139407\pi\) | ||||
−0.999041 | + | 0.0437821i | \(0.986059\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −55.4257 | − | 32.0001i | −2.41438 | − | 1.39394i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.68292 | − | 15.0393i | −0.377518 | − | 0.653881i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.42037 | + | 0.820053i | −0.0615232 | + | 0.0355204i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.85192 | + | 1.64656i | 0.123299 | + | 0.0711870i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 23.3840 | + | 4.14769i | 1.00722 | + | 0.178654i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.4451 | −0.492061 | −0.246031 | − | 0.969262i | \(-0.579126\pi\) | ||||
−0.246031 | + | 0.969262i | \(0.579126\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.84980 | − | 8.40010i | 0.207743 | − | 0.359821i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.91961 | + | 6.78896i | 0.167590 | + | 0.290275i | 0.937572 | − | 0.347791i | \(-0.113068\pi\) |
−0.769982 | + | 0.638066i | \(0.779735\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.32037 | − | 4.01899i | −0.0988510 | − | 0.171215i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.9967 | + | 2.28487i | −0.552675 | + | 0.0971626i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 0.0134996i | − | 0.000571997i | −1.00000 | 0.000285998i | \(-0.999909\pi\) | |||
1.00000 | 0.000285998i | \(-9.10361e-5\pi\) | ||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7.06782i | − | 0.298937i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.54528 | + | 16.5329i | −0.402286 | + | 0.696779i | −0.994001 | − | 0.109368i | \(-0.965117\pi\) |
0.591716 | + | 0.806147i | \(0.298451\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.8923 | + | 18.9904i | −1.38379 | + | 0.798932i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −32.3406 | + | 18.6719i | −1.35579 | + | 0.782765i | −0.989053 | − | 0.147561i | \(-0.952858\pi\) |
−0.366735 | + | 0.930325i | \(0.619525\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.6421 | − | 39.2173i | 0.947544 | − | 1.64119i | 0.196968 | − | 0.980410i | \(-0.436890\pi\) |
0.750576 | − | 0.660784i | \(-0.229776\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.264101i | 0.0110138i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.0988i | 1.54444i | 0.635354 | + | 0.772221i | \(0.280854\pi\) | ||||
−0.635354 | + | 0.772221i | \(0.719146\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.3337 | + | 3.92636i | −0.926559 | + | 0.162893i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.3603 | − | 23.1408i | −0.553329 | − | 0.958393i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.0612 | − | 29.5509i | −0.704191 | − | 1.21969i | −0.966983 | − | 0.254842i | \(-0.917977\pi\) |
0.262792 | − | 0.964853i | \(-0.415357\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.81453 | − | 15.2672i | 0.363197 | − | 0.629075i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.6999 | −0.808980 | −0.404490 | − | 0.914542i | \(-0.632551\pi\) | ||||
−0.404490 | + | 0.914542i | \(0.632551\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.4313 | + | 26.7601i | 0.919594 | + | 1.09706i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.74033 | − | 5.62358i | −0.397979 | − | 0.229773i | 0.287632 | − | 0.957741i | \(-0.407132\pi\) |
−0.685612 | + | 0.727967i | \(0.740465\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.7646 | − | 17.1846i | 1.21412 | − | 0.700975i | 0.250469 | − | 0.968125i | \(-0.419415\pi\) |
0.963655 | + | 0.267150i | \(0.0860818\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.564393 | + | 0.977557i | 0.0229458 | + | 0.0397433i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.7888 | + | 19.5080i | 1.37145 | + | 0.791804i | 0.991110 | − | 0.133044i | \(-0.0424753\pi\) |
0.380335 | + | 0.924849i | \(0.375809\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 0.443317i | − | 0.0179347i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.1099 | −0.650672 | −0.325336 | − | 0.945598i | \(-0.605477\pi\) | ||||
−0.325336 | + | 0.945598i | \(0.605477\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.03569 | − | 4.06205i | −0.283246 | − | 0.163532i | 0.351646 | − | 0.936133i | \(-0.385622\pi\) |
−0.634892 | + | 0.772601i | \(0.718955\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.4018 | + | 18.7072i | −1.30234 | + | 0.751906i | −0.980805 | − | 0.194991i | \(-0.937532\pi\) |
−0.321535 | + | 0.946898i | \(0.604199\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.54718 | + | 26.1893i | −0.382499 | + | 1.04925i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.2156 | − | 21.1581i | 0.488626 | − | 0.846325i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.1451 | 0.404511 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.8268 | 0.789294 | 0.394647 | − | 0.918833i | \(-0.370867\pi\) | ||||
0.394647 | + | 0.918833i | \(0.370867\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.98848 | − | 12.1044i | 0.277329 | − | 0.480348i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.30227 | + | 11.8578i | 0.170462 | + | 0.469823i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.01849 | − | 4.62948i | 0.316711 | − | 0.182853i | −0.333214 | − | 0.942851i | \(-0.608133\pi\) |
0.649926 | + | 0.759998i | \(0.274800\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.3456 | − | 20.9841i | −1.43333 | − | 0.827534i | −0.435958 | − | 0.899967i | \(-0.643590\pi\) |
−0.997373 | + | 0.0724332i | \(0.976924\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.28587 | 0.247123 | 0.123561 | − | 0.992337i | \(-0.460568\pi\) | ||||
0.123561 | + | 0.992337i | \(0.460568\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 36.5798i | − | 1.43588i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.1668 | − | 11.6433i | −0.789189 | − | 0.455638i | 0.0504882 | − | 0.998725i | \(-0.483922\pi\) |
−0.839677 | + | 0.543086i | \(0.817256\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.8207 | − | 32.5985i | −0.735387 | − | 1.27373i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.8880 | − | 14.9464i | 1.00845 | − | 0.582230i | 0.0977141 | − | 0.995215i | \(-0.468847\pi\) |
0.910738 | + | 0.412984i | \(0.135514\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.6184 | + | 10.1720i | 0.685278 | + | 0.395645i | 0.801841 | − | 0.597538i | \(-0.203854\pi\) |
−0.116563 | + | 0.993183i | \(0.537188\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.37118 | + | 6.17878i | −0.285842 | + | 0.239603i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.69963 | −0.259411 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.40643 | + | 4.16805i | −0.0928990 | + | 0.160906i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.55996 | − | 14.8263i | −0.329962 | − | 0.571511i | 0.652542 | − | 0.757753i | \(-0.273703\pi\) |
−0.982504 | + | 0.186241i | \(0.940369\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.2078 | − | 24.6085i | −0.546048 | − | 0.945783i | −0.998540 | − | 0.0540148i | \(-0.982798\pi\) |
0.452492 | − | 0.891769i | \(-0.350535\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.33313 | + | 18.9593i | 0.127914 | + | 0.727593i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 20.9274i | − | 0.800764i | −0.916348 | − | 0.400382i | \(-0.868877\pi\) | ||
0.916348 | − | 0.400382i | \(-0.131123\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 13.8526i | − | 0.529281i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.09627 | − | 12.2911i | 0.270346 | − | 0.468254i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.7918 | − | 12.0041i | 0.790957 | − | 0.456659i | −0.0493424 | − | 0.998782i | \(-0.515713\pi\) |
0.840299 | + | 0.542123i | \(0.182379\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.7143 | − | 8.49529i | 0.558144 | − | 0.322245i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.71634 | − | 4.70484i | 0.102889 | − | 0.178208i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.0117i | 1.58676i | 0.608728 | + | 0.793379i | \(0.291680\pi\) | ||||
−0.608728 | + | 0.793379i | \(0.708320\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.79450i | 0.105397i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.1641 | − | 2.13850i | 0.457478 | − | 0.0804266i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.6094 | − | 32.2324i | −0.698891 | − | 1.21051i | −0.968851 | − | 0.247643i | \(-0.920344\pi\) |
0.269960 | − | 0.962871i | \(-0.412989\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.7252 | − | 22.0406i | −0.476561 | − | 0.825428i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.75890 | + | 11.7068i | −0.252769 | + | 0.437808i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.2978 | 0.682392 | 0.341196 | − | 0.939992i | \(-0.389168\pi\) | ||||
0.341196 | + | 0.939992i | \(0.389168\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.6538 | − | 10.6069i | 0.471253 | − | 0.395021i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.271971 | − | 0.157022i | −0.0101007 | − | 0.00583166i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.3214 | − | 16.3514i | 1.05038 | − | 0.606439i | 0.127626 | − | 0.991822i | \(-0.459264\pi\) |
0.922756 | + | 0.385384i | \(0.125931\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.7057 | + | 20.2749i | 0.432951 | + | 0.749893i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.431812 | + | 0.249307i | 0.0159494 | + | 0.00920836i | 0.507953 | − | 0.861385i | \(-0.330402\pi\) |
−0.492004 | + | 0.870593i | \(0.663736\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 27.0997i | − | 0.998231i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.7046 | 1.75484 | 0.877421 | − | 0.479722i | \(-0.159263\pi\) | ||||
0.877421 | + | 0.479722i | \(0.159263\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.20534 | + | 5.31470i | 0.337711 | + | 0.194978i | 0.659259 | − | 0.751916i | \(-0.270870\pi\) |
−0.321548 | + | 0.946893i | \(0.604203\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.5606 | − | 17.0668i | 1.08302 | − | 0.625279i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.70223 | − | 1.34963i | −0.135277 | − | 0.0493144i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.55927 | − | 16.5571i | 0.348823 | − | 0.604179i | −0.637218 | − | 0.770684i | \(-0.719915\pi\) |
0.986041 | + | 0.166505i | \(0.0532482\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.8411 | −0.940453 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.5388 | 1.03726 | 0.518631 | − | 0.854998i | \(-0.326442\pi\) | ||||
0.518631 | + | 0.854998i | \(0.326442\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.6650 | + | 37.5249i | −0.785355 | + | 1.36028i | 0.143431 | + | 0.989660i | \(0.454186\pi\) |
−0.928787 | + | 0.370615i | \(0.879147\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.97522 | + | 10.9046i | −0.143912 | + | 0.394773i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.8261 | − | 9.71458i | 0.607557 | − | 0.350773i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.75189 | + | 3.32086i | 0.207419 | + | 0.119753i | 0.600111 | − | 0.799917i | \(-0.295123\pi\) |
−0.392693 | + | 0.919670i | \(0.628456\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 44.4831 | 1.59995 | 0.799973 | − | 0.600036i | \(-0.204847\pi\) | ||||
0.799973 | + | 0.600036i | \(0.204847\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.19298i | − | 0.0428532i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.29596 | + | 0.748226i | 0.0464328 | + | 0.0268080i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.6520 | − | 35.7703i | −0.738986 | − | 1.27996i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.9134 | − | 6.30087i | 0.389517 | − | 0.224888i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.0399 | + | 10.9927i | 0.678700 | + | 0.391848i | 0.799365 | − | 0.600846i | \(-0.205169\pi\) |
−0.120665 | + | 0.992693i | \(0.538503\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.8300 | − | 29.1958i | 1.23841 | − | 1.03808i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.55632 | −0.0907776 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.71892 | − | 16.8337i | 0.344262 | − | 0.596279i | −0.640958 | − | 0.767576i | \(-0.721463\pi\) |
0.985219 | + | 0.171297i | \(0.0547959\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.734219 | + | 1.27171i | 0.0259748 | + | 0.0449897i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.722823 | − | 1.25197i | −0.0255079 | − | 0.0441809i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.40426 | + | 13.6758i | 0.0847390 | + | 0.482008i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 21.0058i | − | 0.738526i | −0.929325 | − | 0.369263i | \(-0.879610\pi\) | ||
0.929325 | − | 0.369263i | \(-0.120390\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.3291i | 1.31080i | 0.755281 | + | 0.655401i | \(0.227500\pi\) | ||||
−0.755281 | + | 0.655401i | \(0.772500\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.2876 | + | 19.5506i | −0.395386 | + | 0.684829i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.58478 | + | 3.22438i | −0.195387 | + | 0.112807i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.9017 | − | 6.29412i | 0.380473 | − | 0.219666i | −0.297551 | − | 0.954706i | \(-0.596170\pi\) |
0.678024 | + | 0.735040i | \(0.262837\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.4189 | + | 38.8307i | −0.781474 | + | 1.35355i | 0.149608 | + | 0.988745i | \(0.452199\pi\) |
−0.931083 | + | 0.364808i | \(0.881135\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 25.7293i | − | 0.894695i | −0.894360 | − | 0.447347i | \(-0.852369\pi\) | ||
0.894360 | − | 0.447347i | \(-0.147631\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.9628i | 0.589142i | 0.955630 | + | 0.294571i | \(0.0951767\pi\) | ||||
−0.955630 | + | 0.294571i | \(0.904823\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −31.9804 | − | 26.8901i | −1.10806 | − | 0.931686i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.99450 | + | 6.91867i | 0.138235 | + | 0.239431i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.3539 | − | 23.1296i | −0.461027 | − | 0.798522i | 0.537986 | − | 0.842954i | \(-0.319185\pi\) |
−0.999012 | + | 0.0444321i | \(0.985852\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.5167 | + | 18.2155i | −0.362645 | + | 0.628120i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.5637 | 0.741815 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.867695 | − | 1.03514i | −0.0298144 | − | 0.0355680i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.49381 | + | 2.01715i | 0.119766 | + | 0.0691471i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.6287 | − | 21.7249i | 1.28838 | − | 0.743848i | 0.310017 | − | 0.950731i | \(-0.399665\pi\) |
0.978366 | + | 0.206883i | \(0.0663319\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.83430 | + | 13.5694i | 0.267615 | + | 0.463522i | 0.968245 | − | 0.250002i | \(-0.0804312\pi\) |
−0.700631 | + | 0.713524i | \(0.747098\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.3578 | + | 10.0216i | 0.592242 | + | 0.341931i | 0.765984 | − | 0.642860i | \(-0.222252\pi\) |
−0.173742 | + | 0.984791i | \(0.555586\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.0219i | 1.36236i | 0.732115 | + | 0.681181i | \(0.238533\pi\) | ||||
−0.732115 | + | 0.681181i | \(0.761467\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39.9739 | 1.35915 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.6545 | + | 8.46079i | 0.497120 | + | 0.287013i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.4655 | − | 7.19694i | 0.422376 | − | 0.243859i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.2408 | + | 28.0919i | −0.346201 | + | 0.949680i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.6353 | + | 39.2054i | −0.764338 | + | 1.32387i | 0.176257 | + | 0.984344i | \(0.443601\pi\) |
−0.940596 | + | 0.339529i | \(0.889732\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.3385 | −1.52749 | −0.763746 | − | 0.645517i | \(-0.776642\pi\) | ||||
−0.763746 | + | 0.645517i | \(0.776642\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.5650 | −0.422845 | −0.211423 | − | 0.977395i | \(-0.567810\pi\) | ||||
−0.211423 | + | 0.977395i | \(0.567810\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.8620 | − | 30.9379i | 0.599748 | − | 1.03879i | −0.393110 | − | 0.919492i | \(-0.628601\pi\) |
0.992858 | − | 0.119303i | \(-0.0380659\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.72822 | + | 15.7133i | −0.192118 | + | 0.527009i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.350296 | + | 0.202243i | −0.0117222 | + | 0.00676782i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.63528 | − | 5.56293i | −0.322072 | − | 0.185948i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.2632 | 1.00933 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47.0113i | 1.56617i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.9635 | + | 14.9901i | 0.863058 | + | 0.498287i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.52104 | − | 7.83067i | −0.150119 | − | 0.260013i | 0.781152 | − | 0.624341i | \(-0.214632\pi\) |
−0.931271 | + | 0.364327i | \(0.881299\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.5171 | + | 20.5058i | −1.17673 | + | 0.679388i | −0.955257 | − | 0.295777i | \(-0.904421\pi\) |
−0.221478 | + | 0.975165i | \(0.571088\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.1826 | + | 14.5392i | 0.833421 | + | 0.481176i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28.9349 | + | 34.5188i | 0.955515 | + | 1.13991i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.2326 | −0.337541 | −0.168771 | − | 0.985655i | \(-0.553980\pi\) | ||||
−0.168771 | + | 0.985655i | \(0.553980\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.9692 | − | 18.9992i | 0.361055 | − | 0.625366i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.0945538 | + | 0.163772i | 0.00310891 | + | 0.00538479i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.8330 | + | 22.2273i | 0.421036 | + | 0.729255i | 0.996041 | − | 0.0888945i | \(-0.0283334\pi\) |
−0.575005 | + | 0.818150i | \(0.695000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.40697 | − | 8.80913i | 0.242754 | − | 0.288707i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 44.7763i | − | 1.46434i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 15.9276i | − | 0.520333i | −0.965564 | − | 0.260167i | \(-0.916223\pi\) | ||
0.965564 | − | 0.260167i | \(-0.0837775\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.6767 | + | 34.0810i | −0.641442 | + | 1.11101i | 0.343669 | + | 0.939091i | \(0.388330\pi\) |
−0.985111 | + | 0.171919i | \(0.945003\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.87093 | − | 1.08018i | 0.0609258 | − | 0.0351755i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.9086 | − | 16.6904i | 0.939403 | − | 0.542365i | 0.0496302 | − | 0.998768i | \(-0.484196\pi\) |
0.889773 | + | 0.456403i | \(0.150862\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.383923 | − | 0.664975i | 0.0124627 | − | 0.0215860i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 44.4622i | − | 1.44027i | −0.693832 | − | 0.720137i | \(-0.744079\pi\) | ||
0.693832 | − | 0.720137i | \(-0.255921\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 22.6447i | − | 0.732764i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.87013 | + | 16.3257i | 0.0926813 | + | 0.527185i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.9814 | + | 72.7138i | 1.35424 | + | 2.34561i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.8347 | − | 30.8905i | −0.574118 | − | 0.994401i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.0556 | − | 34.7372i | 0.644943 | − | 1.11707i | −0.339371 | − | 0.940652i | \(-0.610214\pi\) |
0.984315 | − | 0.176422i | \(-0.0564523\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −46.0026 | −1.47629 | −0.738147 | − | 0.674640i | \(-0.764299\pi\) | ||||
−0.738147 | + | 0.674640i | \(0.764299\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.5811 | + | 13.0606i | −0.499506 | + | 0.418704i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 46.8323 | + | 27.0386i | 1.49830 | + | 0.865042i | 0.999998 | − | 0.00196335i | \(-0.000624955\pi\) |
0.498299 | + | 0.867005i | \(0.333958\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.9562 | − | 17.8726i | 0.989365 | − | 0.571210i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.97890 | − | 12.0878i | −0.222592 | − | 0.385541i | 0.733002 | − | 0.680226i | \(-0.238119\pi\) |
−0.955594 | + | 0.294685i | \(0.904785\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.39703 | + | 4.27068i | 0.235689 | + | 0.136075i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.30979i | 0.296034i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.0297 | 1.17629 | 0.588144 | − | 0.808756i | \(-0.299859\pi\) | ||||
0.588144 | + | 0.808756i | \(0.299859\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29.1119 | − | 16.8077i | −0.922909 | − | 0.532841i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.4282 | + | 25.0733i | −1.37538 | + | 0.794079i | −0.991600 | − | 0.129344i | \(-0.958713\pi\) |
−0.383785 | + | 0.923422i | \(0.625380\pi\) | |||||||
\(998\) | 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 \(a_p\))