Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [99,2,Mod(98,99)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(99, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("99.98");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.d (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: | \(0.790518980011\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 98.1 | ||
Root | \(0.517638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 99.98 |
Dual form | 99.2.d.a.98.2 |
$q$-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 \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73205 | −1.22474 | −0.612372 | − | 0.790569i | \(-0.709785\pi\) | ||||
−0.612372 | + | 0.790569i | \(0.709785\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | − | 1.41421i | − | 0.632456i | −0.948683 | − | 0.316228i | \(-0.897584\pi\) | ||
0.948683 | − | 0.316228i | \(-0.102416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.44949i | − | 0.925820i | −0.886405 | − | 0.462910i | \(-0.846805\pi\) | ||
0.886405 | − | 0.462910i | \(-0.153195\pi\) | |||||||
\(8\) | 1.73205 | 0.612372 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.44949i | 0.774597i | ||||||||
\(11\) | 1.73205 | − | 2.82843i | 0.522233 | − | 0.852803i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.89898i | − | 1.35873i | −0.733799 | − | 0.679366i | \(-0.762255\pi\) | ||
0.733799 | − | 0.679366i | \(-0.237745\pi\) | |||||||
\(14\) | 4.24264i | 1.13389i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.34847i | 1.68585i | 0.538028 | + | 0.842927i | \(0.319170\pi\) | ||||
−0.538028 | + | 0.842927i | \(0.680830\pi\) | |||||||
\(20\) | − | 1.41421i | − | 0.316228i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.00000 | + | 4.89898i | −0.639602 | + | 1.04447i | ||||
\(23\) | 2.82843i | 0.589768i | 0.955533 | + | 0.294884i | \(0.0952810\pi\) | ||||
−0.955533 | + | 0.294884i | \(0.904719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | 8.48528i | 1.66410i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 2.44949i | − | 0.462910i | ||||||
\(29\) | −6.92820 | −1.28654 | −0.643268 | − | 0.765641i | \(-0.722422\pi\) | ||||
−0.643268 | + | 0.765641i | \(0.722422\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 5.19615 | 0.918559 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.46410 | −0.585540 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.00000 | 1.31519 | 0.657596 | − | 0.753371i | \(-0.271573\pi\) | ||||
0.657596 | + | 0.753371i | \(0.271573\pi\) | |||||||
\(38\) | − | 12.7279i | − | 2.06474i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 2.44949i | − | 0.387298i | ||||||
\(41\) | 6.92820 | 1.08200 | 0.541002 | − | 0.841021i | \(-0.318045\pi\) | ||||
0.541002 | + | 0.841021i | \(0.318045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.44949i | − | 0.373544i | −0.982403 | − | 0.186772i | \(-0.940197\pi\) | ||
0.982403 | − | 0.186772i | \(-0.0598025\pi\) | |||||||
\(44\) | 1.73205 | − | 2.82843i | 0.261116 | − | 0.426401i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 4.89898i | − | 0.722315i | ||||||
\(47\) | 2.82843i | 0.412568i | 0.978492 | + | 0.206284i | \(0.0661372\pi\) | ||||
−0.978492 | + | 0.206284i | \(0.933863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −5.19615 | −0.734847 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 4.89898i | − | 0.679366i | ||||||
\(53\) | − | 9.89949i | − | 1.35980i | −0.733305 | − | 0.679900i | \(-0.762023\pi\) | ||
0.733305 | − | 0.679900i | \(-0.237977\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | − | 2.44949i | −0.539360 | − | 0.330289i | ||||
\(56\) | − | 4.24264i | − | 0.566947i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 12.0000 | 1.57568 | ||||||||
\(59\) | 11.3137i | 1.47292i | 0.676481 | + | 0.736460i | \(0.263504\pi\) | ||||
−0.676481 | + | 0.736460i | \(0.736496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.89898i | 0.627250i | 0.949547 | + | 0.313625i | \(0.101543\pi\) | ||||
−0.949547 | + | 0.313625i | \(0.898457\pi\) | |||||||
\(62\) | 6.92820 | 0.879883 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.92820 | −0.859338 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.00000 | 0.717137 | ||||||||
\(71\) | 2.82843i | 0.335673i | 0.985815 | + | 0.167836i | \(0.0536780\pi\) | ||||
−0.985815 | + | 0.167836i | \(0.946322\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | −13.8564 | −1.61077 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.34847i | 0.842927i | ||||||||
\(77\) | −6.92820 | − | 4.24264i | −0.789542 | − | 0.483494i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.2474i | 1.37795i | 0.724787 | + | 0.688973i | \(0.241938\pi\) | ||||
−0.724787 | + | 0.688973i | \(0.758062\pi\) | |||||||
\(80\) | 7.07107i | 0.790569i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −12.0000 | −1.32518 | ||||||||
\(83\) | 13.8564 | 1.52094 | 0.760469 | − | 0.649374i | \(-0.224969\pi\) | ||||
0.760469 | + | 0.649374i | \(0.224969\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.24264i | 0.457496i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.00000 | − | 4.89898i | 0.319801 | − | 0.522233i | ||||
\(89\) | 7.07107i | 0.749532i | 0.927119 | + | 0.374766i | \(0.122277\pi\) | ||||
−0.927119 | + | 0.374766i | \(0.877723\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.0000 | −1.25794 | ||||||||
\(92\) | 2.82843i | 0.294884i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 4.89898i | − | 0.505291i | ||||||
\(95\) | 10.3923 | 1.06623 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | −1.73205 | −0.174964 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.00000 | 0.300000 | ||||||||
\(101\) | 13.8564 | 1.37876 | 0.689382 | − | 0.724398i | \(-0.257882\pi\) | ||||
0.689382 | + | 0.724398i | \(0.257882\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | − | 8.48528i | − | 0.832050i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 17.1464i | 1.66541i | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 14.6969i | − | 1.40771i | −0.710343 | − | 0.703856i | \(-0.751460\pi\) | ||
0.710343 | − | 0.703856i | \(-0.248540\pi\) | |||||||
\(110\) | 6.92820 | + | 4.24264i | 0.660578 | + | 0.404520i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12.2474i | 1.15728i | ||||||||
\(113\) | − | 1.41421i | − | 0.133038i | −0.997785 | − | 0.0665190i | \(-0.978811\pi\) | ||
0.997785 | − | 0.0665190i | \(-0.0211893\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | 0.373002 | ||||||||
\(116\) | −6.92820 | −0.643268 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 19.5959i | − | 1.80395i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | − | 9.79796i | −0.454545 | − | 0.890724i | ||||
\(122\) | − | 8.48528i | − | 0.768221i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.00000 | −0.359211 | ||||||||
\(125\) | − | 11.3137i | − | 1.01193i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.34847i | 0.652071i | 0.945357 | + | 0.326036i | \(0.105713\pi\) | ||||
−0.945357 | + | 0.326036i | \(0.894287\pi\) | |||||||
\(128\) | −12.1244 | −1.07165 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 12.0000 | 1.05247 | ||||||||
\(131\) | −3.46410 | −0.302660 | −0.151330 | − | 0.988483i | \(-0.548356\pi\) | ||||
−0.151330 | + | 0.988483i | \(0.548356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.0000 | 1.56080 | ||||||||
\(134\) | 6.92820 | 0.598506 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.5563i | 1.32907i | 0.747258 | + | 0.664534i | \(0.231370\pi\) | ||||
−0.747258 | + | 0.664534i | \(0.768630\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.44949i | 0.207763i | 0.994590 | + | 0.103882i | \(0.0331263\pi\) | ||||
−0.994590 | + | 0.103882i | \(0.966874\pi\) | |||||||
\(140\) | −3.46410 | −0.292770 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 4.89898i | − | 0.411113i | ||||||
\(143\) | −13.8564 | − | 8.48528i | −1.15873 | − | 0.709575i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.79796i | 0.813676i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.00000 | 0.657596 | ||||||||
\(149\) | −13.8564 | −1.13516 | −0.567581 | − | 0.823318i | \(-0.692120\pi\) | ||||
−0.567581 | + | 0.823318i | \(0.692120\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.44949i | − | 0.199337i | −0.995021 | − | 0.0996683i | \(-0.968222\pi\) | ||
0.995021 | − | 0.0996683i | \(-0.0317782\pi\) | |||||||
\(152\) | 12.7279i | 1.03237i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.0000 | + | 7.34847i | 0.966988 | + | 0.592157i | ||||
\(155\) | 5.65685i | 0.454369i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | − | 21.2132i | − | 1.68763i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 7.34847i | − | 0.580948i | ||||||
\(161\) | 6.92820 | 0.546019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.00000 | 0.626608 | 0.313304 | − | 0.949653i | \(-0.398564\pi\) | ||||
0.313304 | + | 0.949653i | \(0.398564\pi\) | |||||||
\(164\) | 6.92820 | 0.541002 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −24.0000 | −1.86276 | ||||||||
\(167\) | −3.46410 | −0.268060 | −0.134030 | − | 0.990977i | \(-0.542792\pi\) | ||||
−0.134030 | + | 0.990977i | \(0.542792\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 2.44949i | − | 0.186772i | ||||||
\(173\) | −6.92820 | −0.526742 | −0.263371 | − | 0.964695i | \(-0.584834\pi\) | ||||
−0.263371 | + | 0.964695i | \(0.584834\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 7.34847i | − | 0.555492i | ||||||
\(176\) | −8.66025 | + | 14.1421i | −0.652791 | + | 1.06600i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 12.2474i | − | 0.917985i | ||||||
\(179\) | − | 22.6274i | − | 1.69125i | −0.533775 | − | 0.845626i | \(-0.679227\pi\) | ||
0.533775 | − | 0.845626i | \(-0.320773\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.00000 | 0.594635 | 0.297318 | − | 0.954779i | \(-0.403908\pi\) | ||||
0.297318 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(182\) | 20.7846 | 1.54066 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.89898i | 0.361158i | ||||||||
\(185\) | − | 11.3137i | − | 0.831800i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.82843i | 0.206284i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −18.0000 | −1.30586 | ||||||||
\(191\) | 2.82843i | 0.204658i | 0.994751 | + | 0.102329i | \(0.0326294\pi\) | ||||
−0.994751 | + | 0.102329i | \(0.967371\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.79796i | 0.705273i | 0.935760 | + | 0.352636i | \(0.114715\pi\) | ||||
−0.935760 | + | 0.352636i | \(0.885285\pi\) | |||||||
\(194\) | 17.3205 | 1.24354 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 5.19615 | 0.367423 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −24.0000 | −1.68863 | ||||||||
\(203\) | 16.9706i | 1.19110i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 9.79796i | − | 0.684319i | ||||||
\(206\) | 6.92820 | 0.482711 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 24.4949i | 1.69842i | ||||||||
\(209\) | 20.7846 | + | 12.7279i | 1.43770 | + | 0.880409i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 12.2474i | − | 0.843149i | −0.906794 | − | 0.421575i | \(-0.861478\pi\) | ||
0.906794 | − | 0.421575i | \(-0.138522\pi\) | |||||||
\(212\) | − | 9.89949i | − | 0.679900i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.46410 | −0.236250 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.79796i | 0.665129i | ||||||||
\(218\) | 25.4558i | 1.72409i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.00000 | − | 2.44949i | −0.269680 | − | 0.165145i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | − | 12.7279i | − | 0.850420i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.44949i | 0.162938i | ||||||||
\(227\) | −27.7128 | −1.83936 | −0.919682 | − | 0.392664i | \(-0.871554\pi\) | ||||
−0.919682 | + | 0.392664i | \(0.871554\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | −6.92820 | −0.456832 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.0000 | −0.787839 | ||||||||
\(233\) | −20.7846 | −1.36165 | −0.680823 | − | 0.732448i | \(-0.738378\pi\) | ||||
−0.680823 | + | 0.732448i | \(0.738378\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000 | 0.260931 | ||||||||
\(236\) | 11.3137i | 0.736460i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.3205 | 1.12037 | 0.560185 | − | 0.828367i | \(-0.310730\pi\) | ||||
0.560185 | + | 0.828367i | \(0.310730\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.5959i | 1.26228i | 0.775667 | + | 0.631142i | \(0.217413\pi\) | ||||
−0.775667 | + | 0.631142i | \(0.782587\pi\) | |||||||
\(242\) | 8.66025 | + | 16.9706i | 0.556702 | + | 1.09091i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.89898i | 0.313625i | ||||||||
\(245\) | − | 1.41421i | − | 0.0903508i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 36.0000 | 2.29063 | ||||||||
\(248\) | −6.92820 | −0.439941 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 19.5959i | 1.23935i | ||||||||
\(251\) | − | 5.65685i | − | 0.357057i | −0.983935 | − | 0.178529i | \(-0.942866\pi\) | ||
0.983935 | − | 0.178529i | \(-0.0571337\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000 | + | 4.89898i | 0.502956 | + | 0.307996i | ||||
\(254\) | − | 12.7279i | − | 0.798621i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | − | 9.89949i | − | 0.617514i | −0.951141 | − | 0.308757i | \(-0.900087\pi\) | ||
0.951141 | − | 0.308757i | \(-0.0999129\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 19.5959i | − | 1.21763i | ||||||
\(260\) | −6.92820 | −0.429669 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.00000 | 0.370681 | ||||||||
\(263\) | 3.46410 | 0.213606 | 0.106803 | − | 0.994280i | \(-0.465939\pi\) | ||||
0.106803 | + | 0.994280i | \(0.465939\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.0000 | −0.860013 | ||||||||
\(266\) | −31.1769 | −1.91158 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.00000 | −0.244339 | ||||||||
\(269\) | 15.5563i | 0.948487i | 0.880394 | + | 0.474244i | \(0.157278\pi\) | ||||
−0.880394 | + | 0.474244i | \(0.842722\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7.34847i | − | 0.446388i | −0.974774 | − | 0.223194i | \(-0.928352\pi\) | ||
0.974774 | − | 0.223194i | \(-0.0716483\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 26.9444i | − | 1.62777i | ||||||
\(275\) | 5.19615 | − | 8.48528i | 0.313340 | − | 0.511682i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 24.4949i | − | 1.47176i | −0.677114 | − | 0.735878i | \(-0.736770\pi\) | ||
0.677114 | − | 0.735878i | \(-0.263230\pi\) | |||||||
\(278\) | − | 4.24264i | − | 0.254457i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.00000 | −0.358569 | ||||||||
\(281\) | 13.8564 | 0.826604 | 0.413302 | − | 0.910594i | \(-0.364375\pi\) | ||||
0.413302 | + | 0.910594i | \(0.364375\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.44949i | 0.145607i | 0.997346 | + | 0.0728035i | \(0.0231946\pi\) | ||||
−0.997346 | + | 0.0728035i | \(0.976805\pi\) | |||||||
\(284\) | 2.82843i | 0.167836i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 24.0000 | + | 14.6969i | 1.41915 | + | 0.869048i | ||||
\(287\) | − | 16.9706i | − | 1.00174i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | − | 16.9706i | − | 0.996546i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.92820 | 0.404750 | 0.202375 | − | 0.979308i | \(-0.435134\pi\) | ||||
0.202375 | + | 0.979308i | \(0.435134\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.0000 | 0.931556 | ||||||||
\(296\) | 13.8564 | 0.805387 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 24.0000 | 1.39028 | ||||||||
\(299\) | 13.8564 | 0.801337 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.00000 | −0.345834 | ||||||||
\(302\) | 4.24264i | 0.244137i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 36.7423i | − | 2.10732i | ||||||
\(305\) | 6.92820 | 0.396708 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.34847i | 0.419399i | 0.977766 | + | 0.209700i | \(0.0672486\pi\) | ||||
−0.977766 | + | 0.209700i | \(0.932751\pi\) | |||||||
\(308\) | −6.92820 | − | 4.24264i | −0.394771 | − | 0.241747i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 9.79796i | − | 0.556487i | ||||||
\(311\) | − | 14.1421i | − | 0.801927i | −0.916094 | − | 0.400963i | \(-0.868675\pi\) | ||
0.916094 | − | 0.400963i | \(-0.131325\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.0000 | −0.904373 | −0.452187 | − | 0.891923i | \(-0.649356\pi\) | ||||
−0.452187 | + | 0.891923i | \(0.649356\pi\) | |||||||
\(314\) | −24.2487 | −1.36843 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.2474i | 0.688973i | ||||||||
\(317\) | − | 18.3848i | − | 1.03259i | −0.856410 | − | 0.516296i | \(-0.827310\pi\) | ||
0.856410 | − | 0.516296i | \(-0.172690\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.0000 | + | 19.5959i | −0.671871 | + | 1.09716i | ||||
\(320\) | − | 1.41421i | − | 0.0790569i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.0000 | −0.668734 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 14.6969i | − | 0.815239i | ||||||
\(326\) | −13.8564 | −0.767435 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 12.0000 | 0.662589 | ||||||||
\(329\) | 6.92820 | 0.381964 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | 13.8564 | 0.760469 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.00000 | 0.328305 | ||||||||
\(335\) | 5.65685i | 0.309067i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.79796i | 0.533729i | 0.963734 | + | 0.266864i | \(0.0859876\pi\) | ||||
−0.963734 | + | 0.266864i | \(0.914012\pi\) | |||||||
\(338\) | 19.0526 | 1.03632 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.92820 | + | 11.3137i | −0.375183 | + | 0.612672i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.5959i | − | 1.05808i | ||||||
\(344\) | − | 4.24264i | − | 0.228748i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.0000 | 0.645124 | ||||||||
\(347\) | −13.8564 | −0.743851 | −0.371925 | − | 0.928263i | \(-0.621302\pi\) | ||||
−0.371925 | + | 0.928263i | \(0.621302\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.89898i | 0.262236i | 0.991367 | + | 0.131118i | \(0.0418567\pi\) | ||||
−0.991367 | + | 0.131118i | \(0.958143\pi\) | |||||||
\(350\) | 12.7279i | 0.680336i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.00000 | − | 14.6969i | 0.479702 | − | 0.783349i | ||||
\(353\) | 32.5269i | 1.73123i | 0.500708 | + | 0.865616i | \(0.333073\pi\) | ||||
−0.500708 | + | 0.865616i | \(0.666927\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.00000 | 0.212298 | ||||||||
\(356\) | 7.07107i | 0.374766i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 39.1918i | 2.07135i | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −35.0000 | −1.84211 | ||||||||
\(362\) | −13.8564 | −0.728277 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.0000 | −0.628971 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000 | 0.417597 | 0.208798 | − | 0.977959i | \(-0.433045\pi\) | ||||
0.208798 | + | 0.977959i | \(0.433045\pi\) | |||||||
\(368\) | − | 14.1421i | − | 0.737210i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 19.5959i | 1.01874i | ||||||||
\(371\) | −24.2487 | −1.25893 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.4949i | 1.26830i | 0.773211 | + | 0.634149i | \(0.218649\pi\) | ||||
−0.773211 | + | 0.634149i | \(0.781351\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.89898i | 0.252646i | ||||||||
\(377\) | 33.9411i | 1.74806i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.0000 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | 10.3923 | 0.533114 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 4.89898i | − | 0.250654i | ||||||
\(383\) | 36.7696i | 1.87884i | 0.342773 | + | 0.939418i | \(0.388634\pi\) | ||||
−0.342773 | + | 0.939418i | \(0.611366\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.00000 | + | 9.79796i | −0.305788 | + | 0.499350i | ||||
\(386\) | − | 16.9706i | − | 0.863779i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.0000 | −0.507673 | ||||||||
\(389\) | − | 9.89949i | − | 0.501924i | −0.967997 | − | 0.250962i | \(-0.919253\pi\) | ||
0.967997 | − | 0.250962i | \(-0.0807470\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 1.73205 | 0.0874818 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17.3205 | 0.871489 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.00000 | 0.401508 | 0.200754 | − | 0.979642i | \(-0.435661\pi\) | ||||
0.200754 | + | 0.979642i | \(0.435661\pi\) | |||||||
\(398\) | −13.8564 | −0.694559 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −15.0000 | −0.750000 | ||||||||
\(401\) | − | 1.41421i | − | 0.0706225i | −0.999376 | − | 0.0353112i | \(-0.988758\pi\) | ||
0.999376 | − | 0.0353112i | \(-0.0112422\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.5959i | 0.976142i | ||||||||
\(404\) | 13.8564 | 0.689382 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 29.3939i | − | 1.45879i | ||||||
\(407\) | 13.8564 | − | 22.6274i | 0.686837 | − | 1.12160i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 39.1918i | 1.93791i | 0.247234 | + | 0.968956i | \(0.420478\pi\) | ||||
−0.247234 | + | 0.968956i | \(0.579522\pi\) | |||||||
\(410\) | 16.9706i | 0.838116i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.00000 | −0.197066 | ||||||||
\(413\) | 27.7128 | 1.36366 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 19.5959i | − | 0.961926i | ||||||
\(416\) | − | 25.4558i | − | 1.24808i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −36.0000 | − | 22.0454i | −1.76082 | − | 1.07828i | ||||
\(419\) | 11.3137i | 0.552711i | 0.961056 | + | 0.276355i | \(0.0891267\pi\) | ||||
−0.961056 | + | 0.276355i | \(0.910873\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.00000 | 0.389896 | 0.194948 | − | 0.980814i | \(-0.437546\pi\) | ||||
0.194948 | + | 0.980814i | \(0.437546\pi\) | |||||||
\(422\) | 21.2132i | 1.03264i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 17.1464i | − | 0.832704i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.0000 | 0.580721 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.00000 | 0.289346 | ||||||||
\(431\) | −10.3923 | −0.500580 | −0.250290 | − | 0.968171i | \(-0.580526\pi\) | ||||
−0.250290 | + | 0.968171i | \(0.580526\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.0000 | −0.768911 | −0.384455 | − | 0.923144i | \(-0.625611\pi\) | ||||
−0.384455 | + | 0.923144i | \(0.625611\pi\) | |||||||
\(434\) | − | 16.9706i | − | 0.814613i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 14.6969i | − | 0.703856i | ||||||
\(437\) | −20.7846 | −0.994263 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.44949i | − | 0.116908i | −0.998290 | − | 0.0584539i | \(-0.981383\pi\) | ||
0.998290 | − | 0.0584539i | \(-0.0186171\pi\) | |||||||
\(440\) | −6.92820 | − | 4.24264i | −0.330289 | − | 0.202260i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 22.6274i | − | 1.07506i | −0.843244 | − | 0.537531i | \(-0.819357\pi\) | ||
0.843244 | − | 0.537531i | \(-0.180643\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.0000 | 0.474045 | ||||||||
\(446\) | 27.7128 | 1.31224 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 2.44949i | − | 0.115728i | ||||||
\(449\) | − | 9.89949i | − | 0.467186i | −0.972334 | − | 0.233593i | \(-0.924952\pi\) | ||
0.972334 | − | 0.233593i | \(-0.0750483\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000 | − | 19.5959i | 0.565058 | − | 0.922736i | ||||
\(452\) | − | 1.41421i | − | 0.0665190i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 48.0000 | 2.25275 | ||||||||
\(455\) | 16.9706i | 0.795592i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 9.79796i | − | 0.458329i | −0.973388 | − | 0.229165i | \(-0.926401\pi\) | ||
0.973388 | − | 0.229165i | \(-0.0735994\pi\) | |||||||
\(458\) | 17.3205 | 0.809334 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.00000 | 0.186501 | ||||||||
\(461\) | −6.92820 | −0.322679 | −0.161339 | − | 0.986899i | \(-0.551581\pi\) | ||||
−0.161339 | + | 0.986899i | \(0.551581\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.0000 | −1.30127 | −0.650635 | − | 0.759390i | \(-0.725497\pi\) | ||||
−0.650635 | + | 0.759390i | \(0.725497\pi\) | |||||||
\(464\) | 34.6410 | 1.60817 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 36.0000 | 1.66767 | ||||||||
\(467\) | − | 22.6274i | − | 1.04707i | −0.852004 | − | 0.523536i | \(-0.824613\pi\) | ||
0.852004 | − | 0.523536i | \(-0.175387\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.79796i | 0.452428i | ||||||||
\(470\) | −6.92820 | −0.319574 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 19.5959i | 0.901975i | ||||||||
\(473\) | −6.92820 | − | 4.24264i | −0.318559 | − | 0.195077i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.0454i | 1.01151i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −30.0000 | −1.37217 | ||||||||
\(479\) | −38.1051 | −1.74107 | −0.870534 | − | 0.492109i | \(-0.836226\pi\) | ||||
−0.870534 | + | 0.492109i | \(0.836226\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 39.1918i | − | 1.78699i | ||||||
\(482\) | − | 33.9411i | − | 1.54598i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.00000 | − | 9.79796i | −0.227273 | − | 0.445362i | ||||
\(485\) | 14.1421i | 0.642161i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.00000 | 0.362515 | 0.181257 | − | 0.983436i | \(-0.441983\pi\) | ||||
0.181257 | + | 0.983436i | \(0.441983\pi\) | |||||||
\(488\) | 8.48528i | 0.384111i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.44949i | 0.110657i | ||||||||
\(491\) | 27.7128 | 1.25066 | 0.625331 | − | 0.780360i | \(-0.284964\pi\) | ||||
0.625331 | + | 0.780360i | \(0.284964\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −62.3538 | −2.80543 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.0000 | 0.898027 | ||||||||
\(497\) | 6.92820 | 0.310772 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.0000 | 1.43252 | 0.716258 | − | 0.697835i | \(-0.245853\pi\) | ||||
0.716258 | + | 0.697835i | \(0.245853\pi\) | |||||||
\(500\) | − | 11.3137i | − | 0.505964i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.79796i | 0.437304i | ||||||||
\(503\) | −31.1769 | −1.39011 | −0.695055 | − | 0.718957i | \(-0.744620\pi\) | ||||
−0.695055 | + | 0.718957i | \(0.744620\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 19.5959i | − | 0.872007i | ||||||
\(506\) | −13.8564 | − | 8.48528i | −0.615992 | − | 0.377217i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.34847i | 0.326036i | ||||||||
\(509\) | 15.5563i | 0.689523i | 0.938690 | + | 0.344762i | \(0.112040\pi\) | ||||
−0.938690 | + | 0.344762i | \(0.887960\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −8.66025 | −0.382733 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 17.1464i | 0.756297i | ||||||||
\(515\) | 5.65685i | 0.249271i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.00000 | + | 4.89898i | 0.351840 | + | 0.215457i | ||||
\(518\) | 33.9411i | 1.49129i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.0000 | −0.526235 | ||||||||
\(521\) | 15.5563i | 0.681536i | 0.940147 | + | 0.340768i | \(0.110687\pi\) | ||||
−0.940147 | + | 0.340768i | \(0.889313\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.0454i | 0.963978i | 0.876177 | + | 0.481989i | \(0.160086\pi\) | ||||
−0.876177 | + | 0.481989i | \(0.839914\pi\) | |||||||
\(524\) | −3.46410 | −0.151330 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.00000 | −0.261612 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000 | 0.652174 | ||||||||
\(530\) | 24.2487 | 1.05330 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 18.0000 | 0.780399 | ||||||||
\(533\) | − | 33.9411i | − | 1.47015i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.92820 | −0.299253 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 26.9444i | − | 1.16166i | ||||||
\(539\) | 1.73205 | − | 2.82843i | 0.0746047 | − | 0.121829i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.6969i | 0.631871i | 0.948781 | + | 0.315935i | \(0.102318\pi\) | ||||
−0.948781 | + | 0.315935i | \(0.897682\pi\) | |||||||
\(542\) | 12.7279i | 0.546711i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20.7846 | −0.890315 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 31.8434i | − | 1.36152i | −0.732505 | − | 0.680762i | \(-0.761649\pi\) | ||
0.732505 | − | 0.680762i | \(-0.238351\pi\) | |||||||
\(548\) | 15.5563i | 0.664534i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9.00000 | + | 14.6969i | −0.383761 | + | 0.626680i | ||||
\(551\) | − | 50.9117i | − | 2.16891i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.0000 | 1.27573 | ||||||||
\(554\) | 42.4264i | 1.80253i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.44949i | 0.103882i | ||||||||
\(557\) | 20.7846 | 0.880672 | 0.440336 | − | 0.897833i | \(-0.354859\pi\) | ||||
0.440336 | + | 0.897833i | \(0.354859\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.0000 | −0.507546 | ||||||||
\(560\) | 17.3205 | 0.731925 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −24.0000 | −1.01238 | ||||||||
\(563\) | 17.3205 | 0.729972 | 0.364986 | − | 0.931013i | \(-0.381074\pi\) | ||||
0.364986 | + | 0.931013i | \(0.381074\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.00000 | −0.0841406 | ||||||||
\(566\) | − | 4.24264i | − | 0.178331i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.89898i | 0.205557i | ||||||||
\(569\) | 13.8564 | 0.580891 | 0.290445 | − | 0.956892i | \(-0.406197\pi\) | ||||
0.290445 | + | 0.956892i | \(0.406197\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.44949i | 0.102508i | 0.998686 | + | 0.0512540i | \(0.0163218\pi\) | ||||
−0.998686 | + | 0.0512540i | \(0.983678\pi\) | |||||||
\(572\) | −13.8564 | − | 8.48528i | −0.579365 | − | 0.354787i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 29.3939i | 1.22688i | ||||||||
\(575\) | 8.48528i | 0.353861i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.0000 | −0.416305 | −0.208153 | − | 0.978096i | \(-0.566745\pi\) | ||||
−0.208153 | + | 0.978096i | \(0.566745\pi\) | |||||||
\(578\) | 29.4449 | 1.22474 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.79796i | 0.406838i | ||||||||
\(581\) | − | 33.9411i | − | 1.40812i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −28.0000 | − | 17.1464i | −1.15964 | − | 0.710132i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.0000 | −0.495715 | ||||||||
\(587\) | 28.2843i | 1.16742i | 0.811963 | + | 0.583708i | \(0.198399\pi\) | ||||
−0.811963 | + | 0.583708i | \(0.801601\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 29.3939i | − | 1.21115i | ||||||
\(590\) | −27.7128 | −1.14092 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −40.0000 | −1.64399 | ||||||||
\(593\) | 41.5692 | 1.70704 | 0.853522 | − | 0.521057i | \(-0.174462\pi\) | ||||
0.853522 | + | 0.521057i | \(0.174462\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13.8564 | −0.567581 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −24.0000 | −0.981433 | ||||||||
\(599\) | 2.82843i | 0.115566i | 0.998329 | + | 0.0577832i | \(0.0184032\pi\) | ||||
−0.998329 | + | 0.0577832i | \(0.981597\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.5959i | 0.799334i | 0.916660 | + | 0.399667i | \(0.130874\pi\) | ||||
−0.916660 | + | 0.399667i | \(0.869126\pi\) | |||||||
\(602\) | 10.3923 | 0.423559 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 2.44949i | − | 0.0996683i | ||||||
\(605\) | −13.8564 | + | 7.07107i | −0.563343 | + | 0.287480i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 12.2474i | − | 0.497109i | −0.968618 | − | 0.248554i | \(-0.920045\pi\) | ||
0.968618 | − | 0.248554i | \(-0.0799554\pi\) | |||||||
\(608\) | 38.1838i | 1.54856i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.0000 | −0.485866 | ||||||||
\(611\) | 13.8564 | 0.560570 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 14.6969i | − | 0.593604i | −0.954939 | − | 0.296802i | \(-0.904080\pi\) | ||
0.954939 | − | 0.296802i | \(-0.0959201\pi\) | |||||||
\(614\) | − | 12.7279i | − | 0.513657i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.0000 | − | 7.34847i | −0.483494 | − | 0.296078i | ||||
\(617\) | − | 26.8701i | − | 1.08175i | −0.841104 | − | 0.540874i | \(-0.818094\pi\) | ||
0.841104 | − | 0.540874i | \(-0.181906\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.0000 | −1.12542 | −0.562708 | − | 0.826656i | \(-0.690240\pi\) | ||||
−0.562708 | + | 0.826656i | \(0.690240\pi\) | |||||||
\(620\) | 5.65685i | 0.227185i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.4949i | 0.982156i | ||||||||
\(623\) | 17.3205 | 0.693932 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 27.7128 | 1.10763 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.0000 | 0.558661 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.0000 | 1.75161 | 0.875806 | − | 0.482663i | \(-0.160330\pi\) | ||||
0.875806 | + | 0.482663i | \(0.160330\pi\) | |||||||
\(632\) | 21.2132i | 0.843816i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 31.8434i | 1.26466i | ||||||||
\(635\) | 10.3923 | 0.412406 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4.89898i | − | 0.194105i | ||||||
\(638\) | 20.7846 | − | 33.9411i | 0.822871 | − | 1.34374i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 17.1464i | 0.677772i | ||||||||
\(641\) | 32.5269i | 1.28474i | 0.766396 | + | 0.642368i | \(0.222048\pi\) | ||||
−0.766396 | + | 0.642368i | \(0.777952\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.0000 | −1.10421 | −0.552106 | − | 0.833774i | \(-0.686176\pi\) | ||||
−0.552106 | + | 0.833774i | \(0.686176\pi\) | |||||||
\(644\) | 6.92820 | 0.273009 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.7990i | 0.778379i | 0.921158 | + | 0.389189i | \(0.127245\pi\) | ||||
−0.921158 | + | 0.389189i | \(0.872755\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.0000 | + | 19.5959i | 1.25611 | + | 0.769207i | ||||
\(650\) | 25.4558i | 0.998460i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.00000 | 0.313304 | ||||||||
\(653\) | − | 26.8701i | − | 1.05151i | −0.850637 | − | 0.525753i | \(-0.823784\pi\) | ||
0.850637 | − | 0.525753i | \(-0.176216\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.89898i | 0.191419i | ||||||||
\(656\) | −34.6410 | −1.35250 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.0000 | −0.467809 | ||||||||
\(659\) | −38.1051 | −1.48436 | −0.742182 | − | 0.670198i | \(-0.766209\pi\) | ||||
−0.742182 | + | 0.670198i | \(0.766209\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.0000 | −0.855701 | −0.427850 | − | 0.903850i | \(-0.640729\pi\) | ||||
−0.427850 | + | 0.903850i | \(0.640729\pi\) | |||||||
\(662\) | −13.8564 | −0.538545 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 24.0000 | 0.931381 | ||||||||
\(665\) | − | 25.4558i | − | 0.987135i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 19.5959i | − | 0.758757i | ||||||
\(668\) | −3.46410 | −0.134030 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 9.79796i | − | 0.378528i | ||||||
\(671\) | 13.8564 | + | 8.48528i | 0.534921 | + | 0.327571i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 39.1918i | − | 1.51073i | −0.655302 | − | 0.755367i | \(-0.727459\pi\) | ||
0.655302 | − | 0.755367i | \(-0.272541\pi\) | |||||||
\(674\) | − | 16.9706i | − | 0.653682i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.0000 | −0.423077 | ||||||||
\(677\) | −27.7128 | −1.06509 | −0.532545 | − | 0.846402i | \(-0.678764\pi\) | ||||
−0.532545 | + | 0.846402i | \(0.678764\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.4949i | 0.940028i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.0000 | − | 19.5959i | 0.459504 | − | 0.750366i | ||||
\(683\) | 28.2843i | 1.08227i | 0.840937 | + | 0.541134i | \(0.182005\pi\) | ||||
−0.840937 | + | 0.541134i | \(0.817995\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.0000 | 0.840577 | ||||||||
\(686\) | 33.9411i | 1.29588i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 12.2474i | 0.466930i | ||||||||
\(689\) | −48.4974 | −1.84760 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.0000 | 1.67384 | 0.836919 | − | 0.547326i | \(-0.184354\pi\) | ||||
0.836919 | + | 0.547326i | \(0.184354\pi\) | |||||||
\(692\) | −6.92820 | −0.263371 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.0000 | 0.911028 | ||||||||
\(695\) | 3.46410 | 0.131401 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | − | 8.48528i | − | 0.321173i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − | 7.34847i | − | 0.277746i | ||||||
\(701\) | −20.7846 | −0.785024 | −0.392512 | − | 0.919747i | \(-0.628394\pi\) | ||||
−0.392512 | + | 0.919747i | \(0.628394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 58.7878i | 2.21722i | ||||||||
\(704\) | 1.73205 | − | 2.82843i | 0.0652791 | − | 0.106600i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 56.3383i | − | 2.12032i | ||||||
\(707\) | − | 33.9411i | − | 1.27649i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.0000 | −0.375558 | −0.187779 | − | 0.982211i | \(-0.560129\pi\) | ||||
−0.187779 | + | 0.982211i | \(0.560129\pi\) | |||||||
\(710\) | −6.92820 | −0.260011 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.2474i | 0.458993i | ||||||||
\(713\) | − | 11.3137i | − | 0.423702i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0000 | + | 19.5959i | −0.448775 | + | 0.732846i | ||||
\(716\) | − | 22.6274i | − | 0.845626i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.82843i | 0.105483i | 0.998608 | + | 0.0527413i | \(0.0167959\pi\) | ||||
−0.998608 | + | 0.0527413i | \(0.983204\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.79796i | 0.364895i | ||||||||
\(722\) | 60.6218 | 2.25611 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.00000 | 0.297318 | ||||||||
\(725\) | −20.7846 | −0.771921 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.00000 | 0.296704 | 0.148352 | − | 0.988935i | \(-0.452603\pi\) | ||||
0.148352 | + | 0.988935i | \(0.452603\pi\) | |||||||
\(728\) | −20.7846 | −0.770329 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 34.2929i | − | 1.26664i | −0.773892 | − | 0.633318i | \(-0.781693\pi\) | ||
0.773892 | − | 0.633318i | \(-0.218307\pi\) | |||||||
\(734\) | −13.8564 | −0.511449 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 14.6969i | 0.541736i | ||||||||
\(737\) | −6.92820 | + | 11.3137i | −0.255204 | + | 0.416746i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 7.34847i | − | 0.270318i | −0.990824 | − | 0.135159i | \(-0.956846\pi\) | ||
0.990824 | − | 0.135159i | \(-0.0431545\pi\) | |||||||
\(740\) | − | 11.3137i | − | 0.415900i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 42.0000 | 1.54187 | ||||||||
\(743\) | 27.7128 | 1.01668 | 0.508342 | − | 0.861155i | \(-0.330258\pi\) | ||||
0.508342 | + | 0.861155i | \(0.330258\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.5959i | 0.717939i | ||||||||
\(746\) | − | 42.4264i | − | 1.55334i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.00000 | −0.145962 | −0.0729810 | − | 0.997333i | \(-0.523251\pi\) | ||||
−0.0729810 | + | 0.997333i | \(0.523251\pi\) | |||||||
\(752\) | − | 14.1421i | − | 0.515711i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 58.7878i | − | 2.14092i | ||||||
\(755\) | −3.46410 | −0.126072 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.00000 | 0.290765 | 0.145382 | − | 0.989376i | \(-0.453559\pi\) | ||||
0.145382 | + | 0.989376i | \(0.453559\pi\) | |||||||
\(758\) | 27.7128 | 1.00657 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 18.0000 | 0.652929 | ||||||||
\(761\) | −13.8564 | −0.502294 | −0.251147 | − | 0.967949i | \(-0.580808\pi\) | ||||
−0.251147 | + | 0.967949i | \(0.580808\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −36.0000 | −1.30329 | ||||||||
\(764\) | 2.82843i | 0.102329i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 63.6867i | − | 2.30110i | ||||||
\(767\) | 55.4256 | 2.00130 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 19.5959i | − | 0.706647i | −0.935501 | − | 0.353323i | \(-0.885052\pi\) | ||
0.935501 | − | 0.353323i | \(-0.114948\pi\) | |||||||
\(770\) | 10.3923 | − | 16.9706i | 0.374513 | − | 0.611577i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.79796i | 0.352636i | ||||||||
\(773\) | 32.5269i | 1.16991i | 0.811065 | + | 0.584956i | \(0.198888\pi\) | ||||
−0.811065 | + | 0.584956i | \(0.801112\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.0000 | −0.431053 | ||||||||
\(776\) | −17.3205 | −0.621770 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.1464i | 0.614729i | ||||||||
\(779\) | 50.9117i | 1.82410i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | + | 4.89898i | 0.286263 | + | 0.175299i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.00000 | −0.178571 | ||||||||
\(785\) | − | 19.7990i | − | 0.706656i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 12.2474i | − | 0.436574i | −0.975885 | − | 0.218287i | \(-0.929953\pi\) | ||
0.975885 | − | 0.218287i | \(-0.0700470\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −30.0000 | −1.06735 | ||||||||
\(791\) | −3.46410 | −0.123169 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.0000 | 0.852265 | ||||||||
\(794\) | −13.8564 | −0.491745 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.00000 | 0.283552 | ||||||||
\(797\) | − | 26.8701i | − | 0.951786i | −0.879503 | − | 0.475893i | \(-0.842125\pi\) | ||
0.879503 | − | 0.475893i | \(-0.157875\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 15.5885 | 0.551135 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.44949i | 0.0864945i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 9.79796i | − | 0.345333i | ||||||
\(806\) | − | 33.9411i | − | 1.19553i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 24.0000 | 0.844317 | ||||||||
\(809\) | 20.7846 | 0.730748 | 0.365374 | − | 0.930861i | \(-0.380941\pi\) | ||||
0.365374 | + | 0.930861i | \(0.380941\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.0454i | 0.774119i | 0.922055 | + | 0.387059i | \(0.126509\pi\) | ||||
−0.922055 | + | 0.387059i | \(0.873491\pi\) | |||||||
\(812\) | 16.9706i | 0.595550i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −24.0000 | + | 39.1918i | −0.841200 | + | 1.37367i | ||||
\(815\) | − | 11.3137i | − | 0.396302i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.0000 | 0.629740 | ||||||||
\(818\) | − | 67.8823i | − | 2.37345i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 9.79796i | − | 0.342160i | ||||||
\(821\) | 13.8564 | 0.483592 | 0.241796 | − | 0.970327i | \(-0.422264\pi\) | ||||
0.241796 | + | 0.970327i | \(0.422264\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.00000 | 0.278862 | 0.139431 | − | 0.990232i | \(-0.455473\pi\) | ||||
0.139431 | + | 0.990232i | \(0.455473\pi\) | |||||||
\(824\) | −6.92820 | −0.241355 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −48.0000 | −1.67013 | ||||||||
\(827\) | −41.5692 | −1.44550 | −0.722752 | − | 0.691108i | \(-0.757123\pi\) | ||||
−0.722752 | + | 0.691108i | \(0.757123\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.0000 | −1.59765 | −0.798823 | − | 0.601566i | \(-0.794544\pi\) | ||||
−0.798823 | + | 0.601566i | \(0.794544\pi\) | |||||||
\(830\) | 33.9411i | 1.17811i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 4.89898i | − | 0.169842i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.89898i | 0.169536i | ||||||||
\(836\) | 20.7846 | + | 12.7279i | 0.718851 | + | 0.440204i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 19.5959i | − | 0.676930i | ||||||
\(839\) | 19.7990i | 0.683537i | 0.939784 | + | 0.341769i | \(0.111026\pi\) | ||||
−0.939784 | + | 0.341769i | \(0.888974\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.0000 | 0.655172 | ||||||||
\(842\) | −13.8564 | −0.477523 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 12.2474i | − | 0.421575i | ||||||
\(845\) | 15.5563i | 0.535155i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.0000 | + | 12.2474i | −0.824650 | + | 0.420827i | ||||
\(848\) | 49.4975i | 1.69975i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.6274i | 0.775658i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.2929i | 1.17417i | 0.809527 | + | 0.587083i | \(0.199724\pi\) | ||||
−0.809527 | + | 0.587083i | \(0.800276\pi\) | |||||||
\(854\) | −20.7846 | −0.711235 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.6410 | 1.18331 | 0.591657 | − | 0.806190i | \(-0.298474\pi\) | ||||
0.591657 | + | 0.806190i | \(0.298474\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.0000 | −1.36478 | −0.682391 | − | 0.730987i | \(-0.739060\pi\) | ||||
−0.682391 | + | 0.730987i | \(0.739060\pi\) | |||||||
\(860\) | −3.46410 | −0.118125 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.0000 | 0.613082 | ||||||||
\(863\) | 19.7990i | 0.673965i | 0.941511 | + | 0.336983i | \(0.109406\pi\) | ||||
−0.941511 | + | 0.336983i | \(0.890594\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.79796i | 0.333141i | ||||||||
\(866\) | 27.7128 | 0.941720 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.79796i | 0.332564i | ||||||||
\(869\) | 34.6410 | + | 21.2132i | 1.17512 | + | 0.719609i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.5959i | 0.663982i | ||||||||
\(872\) | − | 25.4558i | − | 0.862044i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 36.0000 | 1.21772 | ||||||||
\(875\) | −27.7128 | −0.936864 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 53.8888i | 1.81969i | 0.414943 | + | 0.909847i | \(0.363801\pi\) | ||||
−0.414943 | + | 0.909847i | \(0.636199\pi\) | |||||||
\(878\) | 4.24264i | 0.143182i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 20.0000 | + | 12.2474i | 0.674200 | + | 0.412861i | ||||
\(881\) | − | 9.89949i | − | 0.333522i | −0.985997 | − | 0.166761i | \(-0.946669\pi\) | ||
0.985997 | − | 0.166761i | \(-0.0533309\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.0000 | −0.942275 | −0.471138 | − | 0.882060i | \(-0.656156\pi\) | ||||
−0.471138 | + | 0.882060i | \(0.656156\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 39.1918i | 1.31668i | ||||||||
\(887\) | −55.4256 | −1.86101 | −0.930505 | − | 0.366279i | \(-0.880632\pi\) | ||||
−0.930505 | + | 0.366279i | \(0.880632\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0000 | 0.603701 | ||||||||
\(890\) | −17.3205 | −0.580585 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16.0000 | −0.535720 | ||||||||
\(893\) | −20.7846 | −0.695530 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.0000 | −1.06964 | ||||||||
\(896\) | 29.6985i | 0.992157i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.1464i | 0.572184i | ||||||||
\(899\) | 27.7128 | 0.924274 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −20.7846 | + | 33.9411i | −0.692052 | + | 1.13012i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 2.44949i | − | 0.0814688i | ||||||
\(905\) | − | 11.3137i | − | 0.376080i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −52.0000 | −1.72663 | −0.863316 | − | 0.504664i | \(-0.831616\pi\) | ||||
−0.863316 | + | 0.504664i | \(0.831616\pi\) | |||||||
\(908\) | −27.7128 | −0.919682 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | − | 29.3939i | − | 0.974398i | ||||||
\(911\) | 53.7401i | 1.78049i | 0.455483 | + | 0.890245i | \(0.349467\pi\) | ||||
−0.455483 | + | 0.890245i | \(0.650533\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.0000 | − | 39.1918i | 0.794284 | − | 1.29706i | ||||
\(914\) | 16.9706i | 0.561336i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.0000 | −0.330409 | ||||||||
\(917\) | 8.48528i | 0.280209i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 36.7423i | − | 1.21202i | −0.795458 | − | 0.606009i | \(-0.792770\pi\) | ||
0.795458 | − | 0.606009i | \(-0.207230\pi\) | |||||||
\(920\) | 6.92820 | 0.228416 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.0000 | 0.395199 | ||||||||
\(923\) | 13.8564 | 0.456089 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.0000 | 0.789115 | ||||||||
\(926\) | 48.4974 | 1.59372 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −36.0000 | −1.18176 | ||||||||
\(929\) | − | 9.89949i | − | 0.324792i | −0.986726 | − | 0.162396i | \(-0.948078\pi\) | ||
0.986726 | − | 0.162396i | \(-0.0519222\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.34847i | 0.240836i | ||||||||
\(932\) | −20.7846 | −0.680823 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 39.1918i | 1.28240i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 29.3939i | − | 0.960256i | −0.877198 | − | 0.480128i | \(-0.840590\pi\) | ||
0.877198 | − | 0.480128i | \(-0.159410\pi\) | |||||||
\(938\) | − | 16.9706i | − | 0.554109i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.00000 | 0.130466 | ||||||||
\(941\) | 27.7128 | 0.903412 | 0.451706 | − | 0.892167i | \(-0.350816\pi\) | ||||
0.451706 | + | 0.892167i | \(0.350816\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.5959i | 0.638131i | ||||||||
\(944\) | − | 56.5685i | − | 1.84115i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.0000 | + | 7.34847i | 0.390154 | + | 0.238919i | ||||
\(947\) | − | 22.6274i | − | 0.735292i | −0.929966 | − | 0.367646i | \(-0.880164\pi\) | ||
0.929966 | − | 0.367646i | \(-0.119836\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | − | 38.1838i | − | 1.23884i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.7846 | −0.673280 | −0.336640 | − | 0.941634i | \(-0.609290\pi\) | ||||
−0.336640 | + | 0.941634i | \(0.609290\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.00000 | 0.129437 | ||||||||
\(956\) | 17.3205 | 0.560185 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 66.0000 | 2.13236 | ||||||||
\(959\) | 38.1051 | 1.23048 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 67.8823i | 2.18861i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 19.5959i | 0.631142i | ||||||||
\(965\) | 13.8564 | 0.446054 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 41.6413i | − | 1.33909i | −0.742769 | − | 0.669547i | \(-0.766488\pi\) | ||
0.742769 | − | 0.669547i | \(-0.233512\pi\) | |||||||
\(968\) | −8.66025 | − | 16.9706i | −0.278351 | − | 0.545455i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 24.4949i | − | 0.786484i | ||||||
\(971\) | − | 56.5685i | − | 1.81537i | −0.419651 | − | 0.907685i | \(-0.637848\pi\) | ||
0.419651 | − | 0.907685i | \(-0.362152\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.00000 | 0.192351 | ||||||||
\(974\) | −13.8564 | −0.443988 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 24.4949i | − | 0.784063i | ||||||
\(977\) | − | 35.3553i | − | 1.13112i | −0.824708 | − | 0.565559i | \(-0.808661\pi\) | ||
0.824708 | − | 0.565559i | \(-0.191339\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.0000 | + | 12.2474i | 0.639203 | + | 0.391430i | ||||
\(980\) | − | 1.41421i | − | 0.0451754i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −48.0000 | −1.53174 | ||||||||
\(983\) | − | 48.0833i | − | 1.53362i | −0.641875 | − | 0.766809i | \(-0.721843\pi\) | ||
0.641875 | − | 0.766809i | \(-0.278157\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 36.0000 | 1.14531 | ||||||||
\(989\) | 6.92820 | 0.220304 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.0000 | −1.65183 | −0.825917 | − | 0.563791i | \(-0.809342\pi\) | ||||
−0.825917 | + | 0.563791i | \(0.809342\pi\) | |||||||
\(992\) | −20.7846 | −0.659912 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.0000 | −0.380617 | ||||||||
\(995\) | − | 11.3137i | − | 0.358669i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 24.4949i | − | 0.775761i | −0.921710 | − | 0.387881i | \(-0.873207\pi\) | ||
0.921710 | − | 0.387881i | \(-0.126793\pi\) | |||||||
\(998\) | −55.4256 | −1.75447 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))