Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [77,2,Mod(76,77)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(77, 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("77.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 77 = 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 77.b (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: | \(0.614848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 76.3 | ||
Root | \(1.58114 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 77.76 |
Dual form | 77.2.b.b.76.2 |
$q$-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 \(\left(\mathbb{Z}/77\mathbb{Z}\right)^\times\).
\(n\) | \(45\) | \(57\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | − | 2.23607i | − | 1.29099i | −0.763763 | − | 0.645497i | \(-0.776650\pi\) | ||
0.763763 | − | 0.645497i | \(-0.223350\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 3.16228 | 1.29099 | ||||||||
\(7\) | 1.58114 | − | 2.12132i | 0.597614 | − | 0.801784i | ||||
\(8\) | 2.82843i | 1.00000i | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | −3.16228 | −1.00000 | ||||||||
\(11\) | −3.00000 | − | 1.41421i | −0.904534 | − | 0.426401i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.32456 | −1.75412 | −0.877058 | − | 0.480384i | \(-0.840497\pi\) | ||||
−0.877058 | + | 0.480384i | \(0.840497\pi\) | |||||||
\(14\) | 3.00000 | + | 2.23607i | 0.801784 | + | 0.597614i | ||||
\(15\) | 5.00000 | 1.29099 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | − | 2.82843i | − | 0.666667i | ||||||
\(19\) | 3.16228 | 0.725476 | 0.362738 | − | 0.931891i | \(-0.381842\pi\) | ||||
0.362738 | + | 0.931891i | \(0.381842\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.74342 | − | 3.53553i | −1.03510 | − | 0.771517i | ||||
\(22\) | 2.00000 | − | 4.24264i | 0.426401 | − | 0.904534i | ||||
\(23\) | −3.00000 | −0.625543 | −0.312772 | − | 0.949828i | \(-0.601257\pi\) | ||||
−0.312772 | + | 0.949828i | \(0.601257\pi\) | |||||||
\(24\) | 6.32456 | 1.29099 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 8.94427i | − | 1.75412i | ||||||
\(27\) | − | 2.23607i | − | 0.430331i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.41421i | 0.262613i | 0.991342 | + | 0.131306i | \(0.0419172\pi\) | ||||
−0.991342 | + | 0.131306i | \(0.958083\pi\) | |||||||
\(30\) | 7.07107i | 1.29099i | ||||||||
\(31\) | 6.70820i | 1.20483i | 0.798183 | + | 0.602414i | \(0.205795\pi\) | ||||
−0.798183 | + | 0.602414i | \(0.794205\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.16228 | + | 6.70820i | −0.550482 | + | 1.16775i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.74342 | + | 3.53553i | 0.801784 | + | 0.597614i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.164399 | −0.0821995 | − | 0.996616i | \(-0.526194\pi\) | ||||
−0.0821995 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(38\) | 4.47214i | 0.725476i | ||||||||
\(39\) | 14.1421i | 2.26455i | ||||||||
\(40\) | −6.32456 | −1.00000 | ||||||||
\(41\) | 9.48683 | 1.48159 | 0.740797 | − | 0.671729i | \(-0.234448\pi\) | ||||
0.740797 | + | 0.671729i | \(0.234448\pi\) | |||||||
\(42\) | 5.00000 | − | 6.70820i | 0.771517 | − | 1.03510i | ||||
\(43\) | − | 4.24264i | − | 0.646997i | −0.946229 | − | 0.323498i | \(-0.895141\pi\) | ||
0.946229 | − | 0.323498i | \(-0.104859\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 4.47214i | − | 0.666667i | ||||||
\(46\) | − | 4.24264i | − | 0.625543i | ||||||
\(47\) | − | 4.47214i | − | 0.652328i | −0.945313 | − | 0.326164i | \(-0.894244\pi\) | ||
0.945313 | − | 0.326164i | \(-0.105756\pi\) | |||||||
\(48\) | 8.94427i | 1.29099i | ||||||||
\(49\) | −2.00000 | − | 6.70820i | −0.285714 | − | 0.958315i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 3.16228 | 0.430331 | ||||||||
\(55\) | 3.16228 | − | 6.70820i | 0.426401 | − | 0.904534i | ||||
\(56\) | 6.00000 | + | 4.47214i | 0.801784 | + | 0.597614i | ||||
\(57\) | − | 7.07107i | − | 0.936586i | ||||||
\(58\) | −2.00000 | −0.262613 | ||||||||
\(59\) | 2.23607i | 0.291111i | 0.989350 | + | 0.145556i | \(0.0464970\pi\) | ||||
−0.989350 | + | 0.145556i | \(0.953503\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.16228 | 0.404888 | 0.202444 | − | 0.979294i | \(-0.435112\pi\) | ||||
0.202444 | + | 0.979294i | \(0.435112\pi\) | |||||||
\(62\) | −9.48683 | −1.20483 | ||||||||
\(63\) | −3.16228 | + | 4.24264i | −0.398410 | + | 0.534522i | ||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | − | 14.1421i | − | 1.75412i | ||||||
\(66\) | −9.48683 | − | 4.47214i | −1.16775 | − | 0.550482i | ||||
\(67\) | 11.0000 | 1.34386 | 0.671932 | − | 0.740613i | \(-0.265465\pi\) | ||||
0.671932 | + | 0.740613i | \(0.265465\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.70820i | 0.807573i | ||||||||
\(70\) | −5.00000 | + | 6.70820i | −0.597614 | + | 0.801784i | ||||
\(71\) | 9.00000 | 1.06810 | 0.534052 | − | 0.845452i | \(-0.320669\pi\) | ||||
0.534052 | + | 0.845452i | \(0.320669\pi\) | |||||||
\(72\) | − | 5.65685i | − | 0.666667i | ||||||
\(73\) | 3.16228 | 0.370117 | 0.185058 | − | 0.982728i | \(-0.440753\pi\) | ||||
0.185058 | + | 0.982728i | \(0.440753\pi\) | |||||||
\(74\) | − | 1.41421i | − | 0.164399i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.74342 | + | 4.12789i | −0.882444 | + | 0.470417i | ||||
\(78\) | −20.0000 | −2.26455 | ||||||||
\(79\) | 8.48528i | 0.954669i | 0.878722 | + | 0.477334i | \(0.158397\pi\) | ||||
−0.878722 | + | 0.477334i | \(0.841603\pi\) | |||||||
\(80\) | − | 8.94427i | − | 1.00000i | ||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 13.4164i | 1.48159i | ||||||||
\(83\) | −9.48683 | −1.04132 | −0.520658 | − | 0.853766i | \(-0.674313\pi\) | ||||
−0.520658 | + | 0.853766i | \(0.674313\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.00000 | 0.646997 | ||||||||
\(87\) | 3.16228 | 0.339032 | ||||||||
\(88\) | 4.00000 | − | 8.48528i | 0.426401 | − | 0.904534i | ||||
\(89\) | 2.23607i | 0.237023i | 0.992953 | + | 0.118511i | \(0.0378122\pi\) | ||||
−0.992953 | + | 0.118511i | \(0.962188\pi\) | |||||||
\(90\) | 6.32456 | 0.666667 | ||||||||
\(91\) | −10.0000 | + | 13.4164i | −1.04828 | + | 1.40642i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.0000 | 1.55543 | ||||||||
\(94\) | 6.32456 | 0.652328 | ||||||||
\(95\) | 7.07107i | 0.725476i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.70820i | − | 0.681115i | −0.940224 | − | 0.340557i | \(-0.889384\pi\) | ||
0.940224 | − | 0.340557i | \(-0.110616\pi\) | |||||||
\(98\) | 9.48683 | − | 2.82843i | 0.958315 | − | 0.285714i | ||||
\(99\) | 6.00000 | + | 2.82843i | 0.603023 | + | 0.284268i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.48683 | −0.943975 | −0.471988 | − | 0.881605i | \(-0.656463\pi\) | ||||
−0.471988 | + | 0.881605i | \(0.656463\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 13.4164i | − | 1.32196i | −0.750404 | − | 0.660979i | \(-0.770141\pi\) | ||
0.750404 | − | 0.660979i | \(-0.229859\pi\) | |||||||
\(104\) | − | 17.8885i | − | 1.75412i | ||||||
\(105\) | 7.90569 | − | 10.6066i | 0.771517 | − | 1.03510i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 2.82843i | − | 0.273434i | −0.990610 | − | 0.136717i | \(-0.956345\pi\) | ||
0.990610 | − | 0.136717i | \(-0.0436552\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.7279i | 1.21911i | 0.792742 | + | 0.609557i | \(0.208653\pi\) | ||||
−0.792742 | + | 0.609557i | \(0.791347\pi\) | |||||||
\(110\) | 9.48683 | + | 4.47214i | 0.904534 | + | 0.426401i | ||||
\(111\) | 2.23607i | 0.212238i | ||||||||
\(112\) | −6.32456 | + | 8.48528i | −0.597614 | + | 0.801784i | ||||
\(113\) | −3.00000 | −0.282216 | −0.141108 | − | 0.989994i | \(-0.545067\pi\) | ||||
−0.141108 | + | 0.989994i | \(0.545067\pi\) | |||||||
\(114\) | 10.0000 | 0.936586 | ||||||||
\(115\) | − | 6.70820i | − | 0.625543i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.6491 | 1.16941 | ||||||||
\(118\) | −3.16228 | −0.291111 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 14.1421i | 1.29099i | ||||||||
\(121\) | 7.00000 | + | 8.48528i | 0.636364 | + | 0.771389i | ||||
\(122\) | 4.47214i | 0.404888i | ||||||||
\(123\) | − | 21.2132i | − | 1.91273i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803i | 1.00000i | ||||||||
\(126\) | −6.00000 | − | 4.47214i | −0.534522 | − | 0.398410i | ||||
\(127\) | 12.7279i | 1.12942i | 0.825289 | + | 0.564710i | \(0.191012\pi\) | ||||
−0.825289 | + | 0.564710i | \(0.808988\pi\) | |||||||
\(128\) | − | 11.3137i | − | 1.00000i | ||||||
\(129\) | −9.48683 | −0.835269 | ||||||||
\(130\) | 20.0000 | 1.75412 | ||||||||
\(131\) | −18.9737 | −1.65774 | −0.828868 | − | 0.559444i | \(-0.811015\pi\) | ||||
−0.828868 | + | 0.559444i | \(0.811015\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.00000 | − | 6.70820i | 0.433555 | − | 0.581675i | ||||
\(134\) | 15.5563i | 1.34386i | ||||||||
\(135\) | 5.00000 | 0.430331 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.0000 | −1.28154 | −0.640768 | − | 0.767734i | \(-0.721384\pi\) | ||||
−0.640768 | + | 0.767734i | \(0.721384\pi\) | |||||||
\(138\) | −9.48683 | −0.807573 | ||||||||
\(139\) | 12.6491 | 1.07288 | 0.536442 | − | 0.843937i | \(-0.319768\pi\) | ||||
0.536442 | + | 0.843937i | \(0.319768\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.0000 | −0.842152 | ||||||||
\(142\) | 12.7279i | 1.06810i | ||||||||
\(143\) | 18.9737 | + | 8.94427i | 1.58666 | + | 0.747958i | ||||
\(144\) | 8.00000 | 0.666667 | ||||||||
\(145\) | −3.16228 | −0.262613 | ||||||||
\(146\) | 4.47214i | 0.370117i | ||||||||
\(147\) | −15.0000 | + | 4.47214i | −1.23718 | + | 0.368856i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 19.7990i | − | 1.62200i | −0.585049 | − | 0.810998i | \(-0.698925\pi\) | ||
0.585049 | − | 0.810998i | \(-0.301075\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 16.9706i | − | 1.38104i | −0.723311 | − | 0.690522i | \(-0.757381\pi\) | ||
0.723311 | − | 0.690522i | \(-0.242619\pi\) | |||||||
\(152\) | 8.94427i | 0.725476i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.83772 | − | 10.9508i | −0.470417 | − | 0.882444i | ||||
\(155\) | −15.0000 | −1.20483 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.70820i | 0.535373i | 0.963506 | + | 0.267686i | \(0.0862591\pi\) | ||||
−0.963506 | + | 0.267686i | \(0.913741\pi\) | |||||||
\(158\) | −12.0000 | −0.954669 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.74342 | + | 6.36396i | −0.373834 | + | 0.501550i | ||||
\(162\) | − | 15.5563i | − | 1.22222i | ||||||
\(163\) | −10.0000 | −0.783260 | −0.391630 | − | 0.920123i | \(-0.628089\pi\) | ||||
−0.391630 | + | 0.920123i | \(0.628089\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −15.0000 | − | 7.07107i | −1.16775 | − | 0.550482i | ||||
\(166\) | − | 13.4164i | − | 1.04132i | ||||||
\(167\) | 9.48683 | 0.734113 | 0.367057 | − | 0.930199i | \(-0.380366\pi\) | ||||
0.367057 | + | 0.930199i | \(0.380366\pi\) | |||||||
\(168\) | 10.0000 | − | 13.4164i | 0.771517 | − | 1.03510i | ||||
\(169\) | 27.0000 | 2.07692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.32456 | −0.483651 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.48683 | −0.721271 | −0.360635 | − | 0.932707i | \(-0.617440\pi\) | ||||
−0.360635 | + | 0.932707i | \(0.617440\pi\) | |||||||
\(174\) | 4.47214i | 0.339032i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 12.0000 | + | 5.65685i | 0.904534 | + | 0.426401i | ||||
\(177\) | 5.00000 | 0.375823 | ||||||||
\(178\) | −3.16228 | −0.237023 | ||||||||
\(179\) | 9.00000 | 0.672692 | 0.336346 | − | 0.941739i | \(-0.390809\pi\) | ||||
0.336346 | + | 0.941739i | \(0.390809\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.1246i | 1.49585i | 0.663783 | + | 0.747925i | \(0.268950\pi\) | ||||
−0.663783 | + | 0.747925i | \(0.731050\pi\) | |||||||
\(182\) | −18.9737 | − | 14.1421i | −1.40642 | − | 1.04828i | ||||
\(183\) | − | 7.07107i | − | 0.522708i | ||||||
\(184\) | − | 8.48528i | − | 0.625543i | ||||||
\(185\) | − | 2.23607i | − | 0.164399i | ||||||
\(186\) | 21.2132i | 1.55543i | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.74342 | − | 3.53553i | −0.345033 | − | 0.257172i | ||||
\(190\) | −10.0000 | −0.725476 | ||||||||
\(191\) | 3.00000 | 0.217072 | 0.108536 | − | 0.994092i | \(-0.465384\pi\) | ||||
0.108536 | + | 0.994092i | \(0.465384\pi\) | |||||||
\(192\) | 17.8885i | 1.29099i | ||||||||
\(193\) | 4.24264i | 0.305392i | 0.988273 | + | 0.152696i | \(0.0487955\pi\) | ||||
−0.988273 | + | 0.152696i | \(0.951204\pi\) | |||||||
\(194\) | 9.48683 | 0.681115 | ||||||||
\(195\) | −31.6228 | −2.26455 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.65685i | 0.403034i | 0.979485 | + | 0.201517i | \(0.0645872\pi\) | ||||
−0.979485 | + | 0.201517i | \(0.935413\pi\) | |||||||
\(198\) | −4.00000 | + | 8.48528i | −0.284268 | + | 0.603023i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 24.5967i | − | 1.73492i | ||||||
\(202\) | − | 13.4164i | − | 0.943975i | ||||||
\(203\) | 3.00000 | + | 2.23607i | 0.210559 | + | 0.156941i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.2132i | 1.48159i | ||||||||
\(206\) | 18.9737 | 1.32196 | ||||||||
\(207\) | 6.00000 | 0.417029 | ||||||||
\(208\) | 25.2982 | 1.75412 | ||||||||
\(209\) | −9.48683 | − | 4.47214i | −0.656218 | − | 0.309344i | ||||
\(210\) | 15.0000 | + | 11.1803i | 1.03510 | + | 0.771517i | ||||
\(211\) | − | 21.2132i | − | 1.46038i | −0.683246 | − | 0.730189i | \(-0.739432\pi\) | ||
0.683246 | − | 0.730189i | \(-0.260568\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 20.1246i | − | 1.37892i | ||||||
\(214\) | 4.00000 | 0.273434 | ||||||||
\(215\) | 9.48683 | 0.646997 | ||||||||
\(216\) | 6.32456 | 0.430331 | ||||||||
\(217\) | 14.2302 | + | 10.6066i | 0.966012 | + | 0.720023i | ||||
\(218\) | −18.0000 | −1.21911 | ||||||||
\(219\) | − | 7.07107i | − | 0.477818i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.16228 | −0.212238 | ||||||||
\(223\) | − | 6.70820i | − | 0.449215i | −0.974449 | − | 0.224607i | \(-0.927890\pi\) | ||
0.974449 | − | 0.224607i | \(-0.0721099\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 4.24264i | − | 0.282216i | ||||||
\(227\) | −9.48683 | −0.629663 | −0.314832 | − | 0.949148i | \(-0.601948\pi\) | ||||
−0.314832 | + | 0.949148i | \(0.601948\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.70820i | 0.443291i | 0.975127 | + | 0.221645i | \(0.0711427\pi\) | ||||
−0.975127 | + | 0.221645i | \(0.928857\pi\) | |||||||
\(230\) | 9.48683 | 0.625543 | ||||||||
\(231\) | 9.23025 | + | 17.3148i | 0.607306 | + | 1.13923i | ||||
\(232\) | −4.00000 | −0.262613 | ||||||||
\(233\) | 18.3848i | 1.20443i | 0.798335 | + | 0.602213i | \(0.205714\pi\) | ||||
−0.798335 | + | 0.602213i | \(0.794286\pi\) | |||||||
\(234\) | 17.8885i | 1.16941i | ||||||||
\(235\) | 10.0000 | 0.652328 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.9737 | 1.23247 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 7.07107i | − | 0.457389i | −0.973498 | − | 0.228695i | \(-0.926554\pi\) | ||
0.973498 | − | 0.228695i | \(-0.0734457\pi\) | |||||||
\(240\) | −20.0000 | −1.29099 | ||||||||
\(241\) | 12.6491 | 0.814801 | 0.407400 | − | 0.913250i | \(-0.366435\pi\) | ||||
0.407400 | + | 0.913250i | \(0.366435\pi\) | |||||||
\(242\) | −12.0000 | + | 9.89949i | −0.771389 | + | 0.636364i | ||||
\(243\) | 17.8885i | 1.14755i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.0000 | − | 4.47214i | 0.958315 | − | 0.285714i | ||||
\(246\) | 30.0000 | 1.91273 | ||||||||
\(247\) | −20.0000 | −1.27257 | ||||||||
\(248\) | −18.9737 | −1.20483 | ||||||||
\(249\) | 21.2132i | 1.34433i | ||||||||
\(250\) | −15.8114 | −1.00000 | ||||||||
\(251\) | − | 11.1803i | − | 0.705697i | −0.935681 | − | 0.352848i | \(-0.885213\pi\) | ||
0.935681 | − | 0.352848i | \(-0.114787\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.00000 | + | 4.24264i | 0.565825 | + | 0.266733i | ||||
\(254\) | −18.0000 | −1.12942 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.3607i | 1.39482i | 0.716672 | + | 0.697410i | \(0.245665\pi\) | ||||
−0.716672 | + | 0.697410i | \(0.754335\pi\) | |||||||
\(258\) | − | 13.4164i | − | 0.835269i | ||||||
\(259\) | −1.58114 | + | 2.12132i | −0.0982472 | + | 0.131812i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 2.82843i | − | 0.175075i | ||||||
\(262\) | − | 26.8328i | − | 1.65774i | ||||||
\(263\) | − | 11.3137i | − | 0.697633i | −0.937191 | − | 0.348817i | \(-0.886584\pi\) | ||
0.937191 | − | 0.348817i | \(-0.113416\pi\) | |||||||
\(264\) | −18.9737 | − | 8.94427i | −1.16775 | − | 0.550482i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 9.48683 | + | 7.07107i | 0.581675 | + | 0.433555i | ||||
\(267\) | 5.00000 | 0.305995 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 17.8885i | − | 1.09068i | −0.838214 | − | 0.545342i | \(-0.816400\pi\) | ||
0.838214 | − | 0.545342i | \(-0.183600\pi\) | |||||||
\(270\) | 7.07107i | 0.430331i | ||||||||
\(271\) | −25.2982 | −1.53676 | −0.768379 | − | 0.639995i | \(-0.778936\pi\) | ||||
−0.768379 | + | 0.639995i | \(0.778936\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 30.0000 | + | 22.3607i | 1.81568 | + | 1.35333i | ||||
\(274\) | − | 21.2132i | − | 1.28154i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 4.24264i | − | 0.254916i | −0.991844 | − | 0.127458i | \(-0.959318\pi\) | ||
0.991844 | − | 0.127458i | \(-0.0406817\pi\) | |||||||
\(278\) | 17.8885i | 1.07288i | ||||||||
\(279\) | − | 13.4164i | − | 0.803219i | ||||||
\(280\) | −10.0000 | + | 13.4164i | −0.597614 | + | 0.801784i | ||||
\(281\) | − | 24.0416i | − | 1.43420i | −0.696969 | − | 0.717102i | \(-0.745468\pi\) | ||
0.696969 | − | 0.717102i | \(-0.254532\pi\) | |||||||
\(282\) | − | 14.1421i | − | 0.842152i | ||||||
\(283\) | −6.32456 | −0.375956 | −0.187978 | − | 0.982173i | \(-0.560193\pi\) | ||||
−0.187978 | + | 0.982173i | \(0.560193\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.8114 | 0.936586 | ||||||||
\(286\) | −12.6491 | + | 26.8328i | −0.747958 | + | 1.58666i | ||||
\(287\) | 15.0000 | − | 20.1246i | 0.885422 | − | 1.18792i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | − | 4.47214i | − | 0.262613i | ||||||
\(291\) | −15.0000 | −0.879316 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.48683 | 0.554227 | 0.277113 | − | 0.960837i | \(-0.410622\pi\) | ||||
0.277113 | + | 0.960837i | \(0.410622\pi\) | |||||||
\(294\) | −6.32456 | − | 21.2132i | −0.368856 | − | 1.23718i | ||||
\(295\) | −5.00000 | −0.291111 | ||||||||
\(296\) | − | 2.82843i | − | 0.164399i | ||||||
\(297\) | −3.16228 | + | 6.70820i | −0.183494 | + | 0.389249i | ||||
\(298\) | 28.0000 | 1.62200 | ||||||||
\(299\) | 18.9737 | 1.09728 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.00000 | − | 6.70820i | −0.518751 | − | 0.386654i | ||||
\(302\) | 24.0000 | 1.38104 | ||||||||
\(303\) | 21.2132i | 1.21867i | ||||||||
\(304\) | −12.6491 | −0.725476 | ||||||||
\(305\) | 7.07107i | 0.404888i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.32456 | −0.360961 | −0.180481 | − | 0.983579i | \(-0.557765\pi\) | ||||
−0.180481 | + | 0.983579i | \(0.557765\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −30.0000 | −1.70664 | ||||||||
\(310\) | − | 21.2132i | − | 1.20483i | ||||||
\(311\) | − | 4.47214i | − | 0.253592i | −0.991929 | − | 0.126796i | \(-0.959531\pi\) | ||
0.991929 | − | 0.126796i | \(-0.0404693\pi\) | |||||||
\(312\) | −40.0000 | −2.26455 | ||||||||
\(313\) | − | 6.70820i | − | 0.379170i | −0.981864 | − | 0.189585i | \(-0.939286\pi\) | ||
0.981864 | − | 0.189585i | \(-0.0607143\pi\) | |||||||
\(314\) | −9.48683 | −0.535373 | ||||||||
\(315\) | −9.48683 | − | 7.07107i | −0.534522 | − | 0.398410i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.0000 | 1.17948 | 0.589739 | − | 0.807594i | \(-0.299231\pi\) | ||||
0.589739 | + | 0.807594i | \(0.299231\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.00000 | − | 4.24264i | 0.111979 | − | 0.237542i | ||||
\(320\) | − | 17.8885i | − | 1.00000i | ||||||
\(321\) | −6.32456 | −0.353002 | ||||||||
\(322\) | −9.00000 | − | 6.70820i | −0.501550 | − | 0.373834i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 14.1421i | − | 0.783260i | ||||||
\(327\) | 28.4605 | 1.57387 | ||||||||
\(328\) | 26.8328i | 1.48159i | ||||||||
\(329\) | −9.48683 | − | 7.07107i | −0.523026 | − | 0.389841i | ||||
\(330\) | 10.0000 | − | 21.2132i | 0.550482 | − | 1.16775i | ||||
\(331\) | −19.0000 | −1.04433 | −0.522167 | − | 0.852843i | \(-0.674876\pi\) | ||||
−0.522167 | + | 0.852843i | \(0.674876\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.00000 | 0.109599 | ||||||||
\(334\) | 13.4164i | 0.734113i | ||||||||
\(335\) | 24.5967i | 1.34386i | ||||||||
\(336\) | 18.9737 | + | 14.1421i | 1.03510 | + | 0.771517i | ||||
\(337\) | 16.9706i | 0.924445i | 0.886764 | + | 0.462223i | \(0.152948\pi\) | ||||
−0.886764 | + | 0.462223i | \(0.847052\pi\) | |||||||
\(338\) | 38.1838i | 2.07692i | ||||||||
\(339\) | 6.70820i | 0.364340i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.48683 | − | 20.1246i | 0.513741 | − | 1.08981i | ||||
\(342\) | − | 8.94427i | − | 0.483651i | ||||||
\(343\) | −17.3925 | − | 6.36396i | −0.939108 | − | 0.343622i | ||||
\(344\) | 12.0000 | 0.646997 | ||||||||
\(345\) | −15.0000 | −0.807573 | ||||||||
\(346\) | − | 13.4164i | − | 0.721271i | ||||||
\(347\) | 1.41421i | 0.0759190i | 0.999279 | + | 0.0379595i | \(0.0120858\pi\) | ||||
−0.999279 | + | 0.0379595i | \(0.987914\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.6491 | 0.677091 | 0.338546 | − | 0.940950i | \(-0.390065\pi\) | ||||
0.338546 | + | 0.940950i | \(0.390065\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.1421i | 0.754851i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.6525i | 0.833097i | 0.909113 | + | 0.416549i | \(0.136760\pi\) | ||||
−0.909113 | + | 0.416549i | \(0.863240\pi\) | |||||||
\(354\) | 7.07107i | 0.375823i | ||||||||
\(355\) | 20.1246i | 1.06810i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.7279i | 0.672692i | ||||||||
\(359\) | 5.65685i | 0.298557i | 0.988795 | + | 0.149279i | \(0.0476951\pi\) | ||||
−0.988795 | + | 0.149279i | \(0.952305\pi\) | |||||||
\(360\) | 12.6491 | 0.666667 | ||||||||
\(361\) | −9.00000 | −0.473684 | ||||||||
\(362\) | −28.4605 | −1.49585 | ||||||||
\(363\) | 18.9737 | − | 15.6525i | 0.995859 | − | 0.821542i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.07107i | 0.370117i | ||||||||
\(366\) | 10.0000 | 0.522708 | ||||||||
\(367\) | 33.5410i | 1.75083i | 0.483375 | + | 0.875413i | \(0.339411\pi\) | ||||
−0.483375 | + | 0.875413i | \(0.660589\pi\) | |||||||
\(368\) | 12.0000 | 0.625543 | ||||||||
\(369\) | −18.9737 | −0.987730 | ||||||||
\(370\) | 3.16228 | 0.164399 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.24264i | 0.219676i | 0.993950 | + | 0.109838i | \(0.0350331\pi\) | ||||
−0.993950 | + | 0.109838i | \(0.964967\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 25.0000 | 1.29099 | ||||||||
\(376\) | 12.6491 | 0.652328 | ||||||||
\(377\) | − | 8.94427i | − | 0.460653i | ||||||
\(378\) | 5.00000 | − | 6.70820i | 0.257172 | − | 0.345033i | ||||
\(379\) | 17.0000 | 0.873231 | 0.436616 | − | 0.899648i | \(-0.356177\pi\) | ||||
0.436616 | + | 0.899648i | \(0.356177\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 28.4605 | 1.45808 | ||||||||
\(382\) | 4.24264i | 0.217072i | ||||||||
\(383\) | − | 24.5967i | − | 1.25684i | −0.777876 | − | 0.628418i | \(-0.783703\pi\) | ||
0.777876 | − | 0.628418i | \(-0.216297\pi\) | |||||||
\(384\) | −25.2982 | −1.29099 | ||||||||
\(385\) | −9.23025 | − | 17.3148i | −0.470417 | − | 0.882444i | ||||
\(386\) | −6.00000 | −0.305392 | ||||||||
\(387\) | 8.48528i | 0.431331i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.00000 | 0.152106 | 0.0760530 | − | 0.997104i | \(-0.475768\pi\) | ||||
0.0760530 | + | 0.997104i | \(0.475768\pi\) | |||||||
\(390\) | − | 44.7214i | − | 2.26455i | ||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 18.9737 | − | 5.65685i | 0.958315 | − | 0.285714i | ||||
\(393\) | 42.4264i | 2.14013i | ||||||||
\(394\) | −8.00000 | −0.403034 | ||||||||
\(395\) | −18.9737 | −0.954669 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.0000 | − | 11.1803i | −0.750939 | − | 0.559717i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.0000 | 1.19850 | 0.599251 | − | 0.800561i | \(-0.295465\pi\) | ||||
0.599251 | + | 0.800561i | \(0.295465\pi\) | |||||||
\(402\) | 34.7851 | 1.73492 | ||||||||
\(403\) | − | 42.4264i | − | 2.11341i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 24.5967i | − | 1.22222i | ||||||
\(406\) | −3.16228 | + | 4.24264i | −0.156941 | + | 0.210559i | ||||
\(407\) | 3.00000 | + | 1.41421i | 0.148704 | + | 0.0701000i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.6491 | 0.625458 | 0.312729 | − | 0.949842i | \(-0.398757\pi\) | ||||
0.312729 | + | 0.949842i | \(0.398757\pi\) | |||||||
\(410\) | −30.0000 | −1.48159 | ||||||||
\(411\) | 33.5410i | 1.65446i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.74342 | + | 3.53553i | 0.233408 | + | 0.173972i | ||||
\(414\) | 8.48528i | 0.417029i | ||||||||
\(415\) | − | 21.2132i | − | 1.04132i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 28.2843i | − | 1.38509i | ||||||
\(418\) | 6.32456 | − | 13.4164i | 0.309344 | − | 0.656218i | ||||
\(419\) | 22.3607i | 1.09239i | 0.837658 | + | 0.546195i | \(0.183924\pi\) | ||||
−0.837658 | + | 0.546195i | \(0.816076\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.00000 | −0.194948 | −0.0974740 | − | 0.995238i | \(-0.531076\pi\) | ||||
−0.0974740 | + | 0.995238i | \(0.531076\pi\) | |||||||
\(422\) | 30.0000 | 1.46038 | ||||||||
\(423\) | 8.94427i | 0.434885i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 28.4605 | 1.37892 | ||||||||
\(427\) | 5.00000 | − | 6.70820i | 0.241967 | − | 0.324633i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 20.0000 | − | 42.4264i | 0.965609 | − | 2.04837i | ||||
\(430\) | 13.4164i | 0.646997i | ||||||||
\(431\) | 35.3553i | 1.70301i | 0.524349 | + | 0.851503i | \(0.324309\pi\) | ||||
−0.524349 | + | 0.851503i | \(0.675691\pi\) | |||||||
\(432\) | 8.94427i | 0.430331i | ||||||||
\(433\) | − | 20.1246i | − | 0.967127i | −0.875309 | − | 0.483564i | \(-0.839342\pi\) | ||
0.875309 | − | 0.483564i | \(-0.160658\pi\) | |||||||
\(434\) | −15.0000 | + | 20.1246i | −0.720023 | + | 0.966012i | ||||
\(435\) | 7.07107i | 0.339032i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.48683 | −0.453817 | ||||||||
\(438\) | 10.0000 | 0.477818 | ||||||||
\(439\) | −15.8114 | −0.754636 | −0.377318 | − | 0.926084i | \(-0.623154\pi\) | ||||
−0.377318 | + | 0.926084i | \(0.623154\pi\) | |||||||
\(440\) | 18.9737 | + | 8.94427i | 0.904534 | + | 0.426401i | ||||
\(441\) | 4.00000 | + | 13.4164i | 0.190476 | + | 0.638877i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.0000 | −0.712672 | −0.356336 | − | 0.934358i | \(-0.615974\pi\) | ||||
−0.356336 | + | 0.934358i | \(0.615974\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.00000 | −0.237023 | ||||||||
\(446\) | 9.48683 | 0.449215 | ||||||||
\(447\) | −44.2719 | −2.09399 | ||||||||
\(448\) | −12.6491 | + | 16.9706i | −0.597614 | + | 0.801784i | ||||
\(449\) | −27.0000 | −1.27421 | −0.637104 | − | 0.770778i | \(-0.719868\pi\) | ||||
−0.637104 | + | 0.770778i | \(0.719868\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.4605 | − | 13.4164i | −1.34015 | − | 0.631754i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −37.9473 | −1.78292 | ||||||||
\(454\) | − | 13.4164i | − | 0.629663i | ||||||
\(455\) | −30.0000 | − | 22.3607i | −1.40642 | − | 1.04828i | ||||
\(456\) | 20.0000 | 0.936586 | ||||||||
\(457\) | 8.48528i | 0.396925i | 0.980109 | + | 0.198462i | \(0.0635948\pi\) | ||||
−0.980109 | + | 0.198462i | \(0.936405\pi\) | |||||||
\(458\) | −9.48683 | −0.443291 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.48683 | −0.441846 | −0.220923 | − | 0.975291i | \(-0.570907\pi\) | ||||
−0.220923 | + | 0.975291i | \(0.570907\pi\) | |||||||
\(462\) | −24.4868 | + | 13.0535i | −1.13923 | + | 0.607306i | ||||
\(463\) | −25.0000 | −1.16185 | −0.580924 | − | 0.813958i | \(-0.697309\pi\) | ||||
−0.580924 | + | 0.813958i | \(0.697309\pi\) | |||||||
\(464\) | − | 5.65685i | − | 0.262613i | ||||||
\(465\) | 33.5410i | 1.55543i | ||||||||
\(466\) | −26.0000 | −1.20443 | ||||||||
\(467\) | − | 11.1803i | − | 0.517364i | −0.965962 | − | 0.258682i | \(-0.916712\pi\) | ||
0.965962 | − | 0.258682i | \(-0.0832882\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.3925 | − | 23.3345i | 0.803112 | − | 1.07749i | ||||
\(470\) | 14.1421i | 0.652328i | ||||||||
\(471\) | 15.0000 | 0.691164 | ||||||||
\(472\) | −6.32456 | −0.291111 | ||||||||
\(473\) | −6.00000 | + | 12.7279i | −0.275880 | + | 0.585230i | ||||
\(474\) | 26.8328i | 1.23247i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.0000 | 0.457389 | ||||||||
\(479\) | 18.9737 | 0.866929 | 0.433464 | − | 0.901171i | \(-0.357291\pi\) | ||||
0.433464 | + | 0.901171i | \(0.357291\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.32456 | 0.288375 | ||||||||
\(482\) | 17.8885i | 0.814801i | ||||||||
\(483\) | 14.2302 | + | 10.6066i | 0.647499 | + | 0.482617i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.0000 | 0.681115 | ||||||||
\(486\) | −25.2982 | −1.14755 | ||||||||
\(487\) | 29.0000 | 1.31412 | 0.657058 | − | 0.753840i | \(-0.271801\pi\) | ||||
0.657058 | + | 0.753840i | \(0.271801\pi\) | |||||||
\(488\) | 8.94427i | 0.404888i | ||||||||
\(489\) | 22.3607i | 1.01118i | ||||||||
\(490\) | 6.32456 | + | 21.2132i | 0.285714 | + | 0.958315i | ||||
\(491\) | − | 32.5269i | − | 1.46792i | −0.679193 | − | 0.733959i | \(-0.737670\pi\) | ||
0.679193 | − | 0.733959i | \(-0.262330\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | − | 28.2843i | − | 1.27257i | ||||||
\(495\) | −6.32456 | + | 13.4164i | −0.284268 | + | 0.603023i | ||||
\(496\) | − | 26.8328i | − | 1.20483i | ||||||
\(497\) | 14.2302 | − | 19.0919i | 0.638314 | − | 0.856388i | ||||
\(498\) | −30.0000 | −1.34433 | ||||||||
\(499\) | −16.0000 | −0.716258 | −0.358129 | − | 0.933672i | \(-0.616585\pi\) | ||||
−0.358129 | + | 0.933672i | \(0.616585\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 21.2132i | − | 0.947736i | ||||||
\(502\) | 15.8114 | 0.705697 | ||||||||
\(503\) | 28.4605 | 1.26899 | 0.634495 | − | 0.772927i | \(-0.281208\pi\) | ||||
0.634495 | + | 0.772927i | \(0.281208\pi\) | |||||||
\(504\) | −12.0000 | − | 8.94427i | −0.534522 | − | 0.398410i | ||||
\(505\) | − | 21.2132i | − | 0.943975i | ||||||
\(506\) | −6.00000 | + | 12.7279i | −0.266733 | + | 0.565825i | ||||
\(507\) | − | 60.3738i | − | 2.68130i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.6525i | 0.693784i | 0.937905 | + | 0.346892i | \(0.112763\pi\) | ||||
−0.937905 | + | 0.346892i | \(0.887237\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.00000 | − | 6.70820i | 0.221187 | − | 0.296753i | ||||
\(512\) | − | 22.6274i | − | 1.00000i | ||||||
\(513\) | − | 7.07107i | − | 0.312195i | ||||||
\(514\) | −31.6228 | −1.39482 | ||||||||
\(515\) | 30.0000 | 1.32196 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.32456 | + | 13.4164i | −0.278154 | + | 0.590053i | ||||
\(518\) | −3.00000 | − | 2.23607i | −0.131812 | − | 0.0982472i | ||||
\(519\) | 21.2132i | 0.931156i | ||||||||
\(520\) | 40.0000 | 1.75412 | ||||||||
\(521\) | − | 11.1803i | − | 0.489820i | −0.969546 | − | 0.244910i | \(-0.921242\pi\) | ||
0.969546 | − | 0.244910i | \(-0.0787583\pi\) | |||||||
\(522\) | 4.00000 | 0.175075 | ||||||||
\(523\) | 31.6228 | 1.38277 | 0.691384 | − | 0.722488i | \(-0.257001\pi\) | ||||
0.691384 | + | 0.722488i | \(0.257001\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.0000 | 0.697633 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 12.6491 | − | 26.8328i | 0.550482 | − | 1.16775i | ||||
\(529\) | −14.0000 | −0.608696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 4.47214i | − | 0.194074i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −60.0000 | −2.59889 | ||||||||
\(534\) | 7.07107i | 0.305995i | ||||||||
\(535\) | 6.32456 | 0.273434 | ||||||||
\(536\) | 31.1127i | 1.34386i | ||||||||
\(537\) | − | 20.1246i | − | 0.868441i | ||||||
\(538\) | 25.2982 | 1.09068 | ||||||||
\(539\) | −3.48683 | + | 22.9530i | −0.150189 | + | 0.988657i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 25.4558i | − | 1.09443i | −0.836991 | − | 0.547216i | \(-0.815688\pi\) | ||
0.836991 | − | 0.547216i | \(-0.184312\pi\) | |||||||
\(542\) | − | 35.7771i | − | 1.53676i | ||||||
\(543\) | 45.0000 | 1.93113 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −28.4605 | −1.21911 | ||||||||
\(546\) | −31.6228 | + | 42.4264i | −1.35333 | + | 1.81568i | ||||
\(547\) | 8.48528i | 0.362804i | 0.983409 | + | 0.181402i | \(0.0580636\pi\) | ||||
−0.983409 | + | 0.181402i | \(0.941936\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.32456 | −0.269925 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.47214i | 0.190519i | ||||||||
\(552\) | −18.9737 | −0.807573 | ||||||||
\(553\) | 18.0000 | + | 13.4164i | 0.765438 | + | 0.570524i | ||||
\(554\) | 6.00000 | 0.254916 | ||||||||
\(555\) | −5.00000 | −0.212238 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.6274i | 0.958754i | 0.877609 | + | 0.479377i | \(0.159137\pi\) | ||||
−0.877609 | + | 0.479377i | \(0.840863\pi\) | |||||||
\(558\) | 18.9737 | 0.803219 | ||||||||
\(559\) | 26.8328i | 1.13491i | ||||||||
\(560\) | −18.9737 | − | 14.1421i | −0.801784 | − | 0.597614i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 34.0000 | 1.43420 | ||||||||
\(563\) | 37.9473 | 1.59929 | 0.799645 | − | 0.600473i | \(-0.205021\pi\) | ||||
0.799645 | + | 0.600473i | \(0.205021\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 6.70820i | − | 0.282216i | ||||||
\(566\) | − | 8.94427i | − | 0.375956i | ||||||
\(567\) | −17.3925 | + | 23.3345i | −0.730417 | + | 0.979958i | ||||
\(568\) | 25.4558i | 1.06810i | ||||||||
\(569\) | − | 15.5563i | − | 0.652156i | −0.945343 | − | 0.326078i | \(-0.894273\pi\) | ||
0.945343 | − | 0.326078i | \(-0.105727\pi\) | |||||||
\(570\) | 22.3607i | 0.936586i | ||||||||
\(571\) | 16.9706i | 0.710196i | 0.934829 | + | 0.355098i | \(0.115552\pi\) | ||||
−0.934829 | + | 0.355098i | \(0.884448\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 6.70820i | − | 0.280239i | ||||||
\(574\) | 28.4605 | + | 21.2132i | 1.18792 | + | 0.885422i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 16.0000 | 0.666667 | ||||||||
\(577\) | − | 20.1246i | − | 0.837799i | −0.908033 | − | 0.418899i | \(-0.862416\pi\) | ||
0.908033 | − | 0.418899i | \(-0.137584\pi\) | |||||||
\(578\) | − | 24.0416i | − | 1.00000i | ||||||
\(579\) | 9.48683 | 0.394259 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.0000 | + | 20.1246i | −0.622305 | + | 0.834910i | ||||
\(582\) | − | 21.2132i | − | 0.879316i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 8.94427i | 0.370117i | ||||||||
\(585\) | 28.2843i | 1.16941i | ||||||||
\(586\) | 13.4164i | 0.554227i | ||||||||
\(587\) | − | 4.47214i | − | 0.184585i | −0.995732 | − | 0.0922924i | \(-0.970581\pi\) | ||
0.995732 | − | 0.0922924i | \(-0.0294195\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.2132i | 0.874075i | ||||||||
\(590\) | − | 7.07107i | − | 0.291111i | ||||||
\(591\) | 12.6491 | 0.520315 | ||||||||
\(592\) | 4.00000 | 0.164399 | ||||||||
\(593\) | 28.4605 | 1.16873 | 0.584366 | − | 0.811490i | \(-0.301343\pi\) | ||||
0.584366 | + | 0.811490i | \(0.301343\pi\) | |||||||
\(594\) | −9.48683 | − | 4.47214i | −0.389249 | − | 0.183494i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 26.8328i | 1.09728i | ||||||||
\(599\) | −12.0000 | −0.490307 | −0.245153 | − | 0.969484i | \(-0.578838\pi\) | ||||
−0.245153 | + | 0.969484i | \(0.578838\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.8114 | −0.644960 | −0.322480 | − | 0.946576i | \(-0.604517\pi\) | ||||
−0.322480 | + | 0.946576i | \(0.604517\pi\) | |||||||
\(602\) | 9.48683 | − | 12.7279i | 0.386654 | − | 0.518751i | ||||
\(603\) | −22.0000 | −0.895909 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −18.9737 | + | 15.6525i | −0.771389 | + | 0.636364i | ||||
\(606\) | −30.0000 | −1.21867 | ||||||||
\(607\) | −6.32456 | −0.256706 | −0.128353 | − | 0.991729i | \(-0.540969\pi\) | ||||
−0.128353 | + | 0.991729i | \(0.540969\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.00000 | − | 6.70820i | 0.202610 | − | 0.271830i | ||||
\(610\) | −10.0000 | −0.404888 | ||||||||
\(611\) | 28.2843i | 1.14426i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.4558i | 1.02815i | 0.857745 | + | 0.514076i | \(0.171865\pi\) | ||||
−0.857745 | + | 0.514076i | \(0.828135\pi\) | |||||||
\(614\) | − | 8.94427i | − | 0.360961i | ||||||
\(615\) | 47.4342 | 1.91273 | ||||||||
\(616\) | −11.6754 | − | 21.9017i | −0.470417 | − | 0.882444i | ||||
\(617\) | 24.0000 | 0.966204 | 0.483102 | − | 0.875564i | \(-0.339510\pi\) | ||||
0.483102 | + | 0.875564i | \(0.339510\pi\) | |||||||
\(618\) | − | 42.4264i | − | 1.70664i | ||||||
\(619\) | − | 46.9574i | − | 1.88738i | −0.330833 | − | 0.943689i | \(-0.607330\pi\) | ||
0.330833 | − | 0.943689i | \(-0.392670\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.70820i | 0.269191i | ||||||||
\(622\) | 6.32456 | 0.253592 | ||||||||
\(623\) | 4.74342 | + | 3.53553i | 0.190041 | + | 0.141648i | ||||
\(624\) | − | 56.5685i | − | 2.26455i | ||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 9.48683 | 0.379170 | ||||||||
\(627\) | −10.0000 | + | 21.2132i | −0.399362 | + | 0.847174i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 10.0000 | − | 13.4164i | 0.398410 | − | 0.534522i | ||||
\(631\) | 11.0000 | 0.437903 | 0.218952 | − | 0.975736i | \(-0.429736\pi\) | ||||
0.218952 | + | 0.975736i | \(0.429736\pi\) | |||||||
\(632\) | −24.0000 | −0.954669 | ||||||||
\(633\) | −47.4342 | −1.88534 | ||||||||
\(634\) | 29.6985i | 1.17948i | ||||||||
\(635\) | −28.4605 | −1.12942 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.6491 | + | 42.4264i | 0.501176 | + | 1.68100i | ||||
\(638\) | 6.00000 | + | 2.82843i | 0.237542 | + | 0.111979i | ||||
\(639\) | −18.0000 | −0.712069 | ||||||||
\(640\) | 25.2982 | 1.00000 | ||||||||
\(641\) | 21.0000 | 0.829450 | 0.414725 | − | 0.909947i | \(-0.363878\pi\) | ||||
0.414725 | + | 0.909947i | \(0.363878\pi\) | |||||||
\(642\) | − | 8.94427i | − | 0.353002i | ||||||
\(643\) | 6.70820i | 0.264546i | 0.991213 | + | 0.132273i | \(0.0422275\pi\) | ||||
−0.991213 | + | 0.132273i | \(0.957772\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 21.2132i | − | 0.835269i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.0689i | 1.14282i | 0.820666 | + | 0.571408i | \(0.193603\pi\) | ||||
−0.820666 | + | 0.571408i | \(0.806397\pi\) | |||||||
\(648\) | − | 31.1127i | − | 1.22222i | ||||||
\(649\) | 3.16228 | − | 6.70820i | 0.124130 | − | 0.263320i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 23.7171 | − | 31.8198i | 0.929546 | − | 1.24712i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.0000 | 0.586995 | 0.293498 | − | 0.955960i | \(-0.405181\pi\) | ||||
0.293498 | + | 0.955960i | \(0.405181\pi\) | |||||||
\(654\) | 40.2492i | 1.57387i | ||||||||
\(655\) | − | 42.4264i | − | 1.65774i | ||||||
\(656\) | −37.9473 | −1.48159 | ||||||||
\(657\) | −6.32456 | −0.246744 | ||||||||
\(658\) | 10.0000 | − | 13.4164i | 0.389841 | − | 0.523026i | ||||
\(659\) | 14.1421i | 0.550899i | 0.961315 | + | 0.275450i | \(0.0888267\pi\) | ||||
−0.961315 | + | 0.275450i | \(0.911173\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.9574i | 1.82643i | 0.407476 | + | 0.913216i | \(0.366409\pi\) | ||||
−0.407476 | + | 0.913216i | \(0.633591\pi\) | |||||||
\(662\) | − | 26.8701i | − | 1.04433i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 26.8328i | − | 1.04132i | ||||||
\(665\) | 15.0000 | + | 11.1803i | 0.581675 | + | 0.433555i | ||||
\(666\) | 2.82843i | 0.109599i | ||||||||
\(667\) | − | 4.24264i | − | 0.164276i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.0000 | −0.579934 | ||||||||
\(670\) | −34.7851 | −1.34386 | ||||||||
\(671\) | −9.48683 | − | 4.47214i | −0.366235 | − | 0.172645i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 29.6985i | − | 1.14479i | −0.819977 | − | 0.572396i | \(-0.806014\pi\) | ||
0.819977 | − | 0.572396i | \(-0.193986\pi\) | |||||||
\(674\) | −24.0000 | −0.924445 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.9473 | −1.45843 | −0.729217 | − | 0.684282i | \(-0.760116\pi\) | ||||
−0.729217 | + | 0.684282i | \(0.760116\pi\) | |||||||
\(678\) | −9.48683 | −0.364340 | ||||||||
\(679\) | −14.2302 | − | 10.6066i | −0.546107 | − | 0.407044i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.2132i | 0.812892i | ||||||||
\(682\) | 28.4605 | + | 13.4164i | 1.08981 | + | 0.513741i | ||||
\(683\) | 18.0000 | 0.688751 | 0.344375 | − | 0.938832i | \(-0.388091\pi\) | ||||
0.344375 | + | 0.938832i | \(0.388091\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 33.5410i | − | 1.28154i | ||||||
\(686\) | 9.00000 | − | 24.5967i | 0.343622 | − | 0.939108i | ||||
\(687\) | 15.0000 | 0.572286 | ||||||||
\(688\) | 16.9706i | 0.646997i | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | − | 21.2132i | − | 0.807573i | ||||||
\(691\) | − | 6.70820i | − | 0.255192i | −0.991826 | − | 0.127596i | \(-0.959274\pi\) | ||
0.991826 | − | 0.127596i | \(-0.0407261\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.4868 | − | 8.25579i | 0.588296 | − | 0.313611i | ||||
\(694\) | −2.00000 | −0.0759190 | ||||||||
\(695\) | 28.2843i | 1.07288i | ||||||||
\(696\) | 8.94427i | 0.339032i | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 17.8885i | 0.677091i | ||||||||
\(699\) | 41.1096 | 1.55491 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 7.07107i | − | 0.267071i | −0.991044 | − | 0.133535i | \(-0.957367\pi\) | ||
0.991044 | − | 0.133535i | \(-0.0426329\pi\) | |||||||
\(702\) | −20.0000 | −0.754851 | ||||||||
\(703\) | −3.16228 | −0.119268 | ||||||||
\(704\) | 24.0000 | + | 11.3137i | 0.904534 | + | 0.426401i | ||||
\(705\) | − | 22.3607i | − | 0.842152i | ||||||
\(706\) | −22.1359 | −0.833097 | ||||||||
\(707\) | −15.0000 | + | 20.1246i | −0.564133 | + | 0.756864i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.0000 | 1.53979 | 0.769894 | − | 0.638172i | \(-0.220309\pi\) | ||||
0.769894 | + | 0.638172i | \(0.220309\pi\) | |||||||
\(710\) | −28.4605 | −1.06810 | ||||||||
\(711\) | − | 16.9706i | − | 0.636446i | ||||||
\(712\) | −6.32456 | −0.237023 | ||||||||
\(713\) | − | 20.1246i | − | 0.753673i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20.0000 | + | 42.4264i | −0.747958 | + | 1.58666i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.8114 | −0.590487 | ||||||||
\(718\) | −8.00000 | −0.298557 | ||||||||
\(719\) | − | 51.4296i | − | 1.91800i | −0.283408 | − | 0.959000i | \(-0.591465\pi\) | ||
0.283408 | − | 0.959000i | \(-0.408535\pi\) | |||||||
\(720\) | 17.8885i | 0.666667i | ||||||||
\(721\) | −28.4605 | − | 21.2132i | −1.05992 | − | 0.790021i | ||||
\(722\) | − | 12.7279i | − | 0.473684i | ||||||
\(723\) | − | 28.2843i | − | 1.05190i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 22.1359 | + | 26.8328i | 0.821542 | + | 0.995859i | ||||
\(727\) | 33.5410i | 1.24397i | 0.783030 | + | 0.621984i | \(0.213673\pi\) | ||||
−0.783030 | + | 0.621984i | \(0.786327\pi\) | |||||||
\(728\) | −37.9473 | − | 28.2843i | −1.40642 | − | 1.04828i | ||||
\(729\) | 7.00000 | 0.259259 | ||||||||
\(730\) | −10.0000 | −0.370117 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.6491 | 0.467206 | 0.233603 | − | 0.972332i | \(-0.424948\pi\) | ||||
0.233603 | + | 0.972332i | \(0.424948\pi\) | |||||||
\(734\) | −47.4342 | −1.75083 | ||||||||
\(735\) | −10.0000 | − | 33.5410i | −0.368856 | − | 1.23718i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −33.0000 | − | 15.5563i | −1.21557 | − | 0.573025i | ||||
\(738\) | − | 26.8328i | − | 0.987730i | ||||||
\(739\) | 50.9117i | 1.87282i | 0.350912 | + | 0.936408i | \(0.385872\pi\) | ||||
−0.350912 | + | 0.936408i | \(0.614128\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 44.7214i | 1.64288i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 19.7990i | − | 0.726354i | −0.931720 | − | 0.363177i | \(-0.881692\pi\) | ||
0.931720 | − | 0.363177i | \(-0.118308\pi\) | |||||||
\(744\) | 42.4264i | 1.55543i | ||||||||
\(745\) | 44.2719 | 1.62200 | ||||||||
\(746\) | −6.00000 | −0.219676 | ||||||||
\(747\) | 18.9737 | 0.694210 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.00000 | − | 4.47214i | −0.219235 | − | 0.163408i | ||||
\(750\) | 35.3553i | 1.29099i | ||||||||
\(751\) | −7.00000 | −0.255434 | −0.127717 | − | 0.991811i | \(-0.540765\pi\) | ||||
−0.127717 | + | 0.991811i | \(0.540765\pi\) | |||||||
\(752\) | 17.8885i | 0.652328i | ||||||||
\(753\) | −25.0000 | −0.911051 | ||||||||
\(754\) | 12.6491 | 0.460653 | ||||||||
\(755\) | 37.9473 | 1.38104 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.0000 | 1.59921 | 0.799604 | − | 0.600528i | \(-0.205043\pi\) | ||||
0.799604 | + | 0.600528i | \(0.205043\pi\) | |||||||
\(758\) | 24.0416i | 0.873231i | ||||||||
\(759\) | 9.48683 | − | 20.1246i | 0.344350 | − | 0.730477i | ||||
\(760\) | −20.0000 | −0.725476 | ||||||||
\(761\) | 37.9473 | 1.37559 | 0.687795 | − | 0.725905i | \(-0.258579\pi\) | ||||
0.687795 | + | 0.725905i | \(0.258579\pi\) | |||||||
\(762\) | 40.2492i | 1.45808i | ||||||||
\(763\) | 27.0000 | + | 20.1246i | 0.977466 | + | 0.728560i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34.7851 | 1.25684 | ||||||||
\(767\) | − | 14.1421i | − | 0.510643i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.32456 | −0.228069 | −0.114035 | − | 0.993477i | \(-0.536377\pi\) | ||||
−0.114035 | + | 0.993477i | \(0.536377\pi\) | |||||||
\(770\) | 24.4868 | − | 13.0535i | 0.882444 | − | 0.470417i | ||||
\(771\) | 50.0000 | 1.80071 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.94427i | 0.321703i | 0.986979 | + | 0.160852i | \(0.0514240\pi\) | ||||
−0.986979 | + | 0.160852i | \(0.948576\pi\) | |||||||
\(774\) | −12.0000 | −0.431331 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 18.9737 | 0.681115 | ||||||||
\(777\) | 4.74342 | + | 3.53553i | 0.170169 | + | 0.126837i | ||||
\(778\) | 4.24264i | 0.152106i | ||||||||
\(779\) | 30.0000 | 1.07486 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.0000 | − | 12.7279i | −0.966136 | − | 0.455441i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.16228 | 0.113011 | ||||||||
\(784\) | 8.00000 | + | 26.8328i | 0.285714 | + | 0.958315i | ||||
\(785\) | −15.0000 | −0.535373 | ||||||||
\(786\) | −60.0000 | −2.14013 | ||||||||
\(787\) | 22.1359 | 0.789061 | 0.394531 | − | 0.918883i | \(-0.370907\pi\) | ||||
0.394531 | + | 0.918883i | \(0.370907\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.2982 | −0.900641 | ||||||||
\(790\) | − | 26.8328i | − | 0.954669i | ||||||
\(791\) | −4.74342 | + | 6.36396i | −0.168656 | + | 0.226276i | ||||
\(792\) | −8.00000 | + | 16.9706i | −0.284268 | + | 0.603023i | ||||
\(793\) | −20.0000 | −0.710221 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 38.0132i | − | 1.34650i | −0.739417 | − | 0.673248i | \(-0.764899\pi\) | ||
0.739417 | − | 0.673248i | \(-0.235101\pi\) | |||||||
\(798\) | 15.8114 | − | 21.2132i | 0.559717 | − | 0.750939i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 4.47214i | − | 0.158015i | ||||||
\(802\) | 33.9411i | 1.19850i | ||||||||
\(803\) | −9.48683 | − | 4.47214i | −0.334783 | − | 0.157818i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.2302 | − | 10.6066i | −0.501550 | − | 0.373834i | ||||
\(806\) | 60.0000 | 2.11341 | ||||||||
\(807\) | −40.0000 | −1.40807 | ||||||||
\(808\) | − | 26.8328i | − | 0.943975i | ||||||
\(809\) | − | 41.0122i | − | 1.44191i | −0.692981 | − | 0.720956i | \(-0.743703\pi\) | ||
0.692981 | − | 0.720956i | \(-0.256297\pi\) | |||||||
\(810\) | 34.7851 | 1.22222 | ||||||||
\(811\) | −25.2982 | −0.888341 | −0.444170 | − | 0.895942i | \(-0.646502\pi\) | ||||
−0.444170 | + | 0.895942i | \(0.646502\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 56.5685i | 1.98395i | ||||||||
\(814\) | −2.00000 | + | 4.24264i | −0.0701000 | + | 0.148704i | ||||
\(815\) | − | 22.3607i | − | 0.783260i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 13.4164i | − | 0.469381i | ||||||
\(818\) | 17.8885i | 0.625458i | ||||||||
\(819\) | 20.0000 | − | 26.8328i | 0.698857 | − | 0.937614i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.1421i | 0.493564i | 0.969071 | + | 0.246782i | \(0.0793731\pi\) | ||||
−0.969071 | + | 0.246782i | \(0.920627\pi\) | |||||||
\(822\) | −47.4342 | −1.65446 | ||||||||
\(823\) | −43.0000 | −1.49889 | −0.749443 | − | 0.662069i | \(-0.769679\pi\) | ||||
−0.749443 | + | 0.662069i | \(0.769679\pi\) | |||||||
\(824\) | 37.9473 | 1.32196 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.00000 | + | 6.70820i | −0.173972 | + | 0.233408i | ||||
\(827\) | 22.6274i | 0.786832i | 0.919360 | + | 0.393416i | \(0.128707\pi\) | ||||
−0.919360 | + | 0.393416i | \(0.871293\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 20.1246i | − | 0.698957i | −0.936944 | − | 0.349478i | \(-0.886359\pi\) | ||
0.936944 | − | 0.349478i | \(-0.113641\pi\) | |||||||
\(830\) | 30.0000 | 1.04132 | ||||||||
\(831\) | −9.48683 | −0.329095 | ||||||||
\(832\) | 50.5964 | 1.75412 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 40.0000 | 1.38509 | ||||||||
\(835\) | 21.2132i | 0.734113i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.0000 | 0.518476 | ||||||||
\(838\) | −31.6228 | −1.09239 | ||||||||
\(839\) | 15.6525i | 0.540383i | 0.962807 | + | 0.270192i | \(0.0870871\pi\) | ||||
−0.962807 | + | 0.270192i | \(0.912913\pi\) | |||||||
\(840\) | 30.0000 | + | 22.3607i | 1.03510 | + | 0.771517i | ||||
\(841\) | 27.0000 | 0.931034 | ||||||||
\(842\) | − | 5.65685i | − | 0.194948i | ||||||
\(843\) | −53.7587 | −1.85155 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 60.3738i | 2.07692i | ||||||||
\(846\) | −12.6491 | −0.434885 | ||||||||
\(847\) | 29.0680 | − | 1.43283i | 0.998787 | − | 0.0492328i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.1421i | 0.485357i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.00000 | 0.102839 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.2982 | −0.866195 | −0.433097 | − | 0.901347i | \(-0.642579\pi\) | ||||
−0.433097 | + | 0.901347i | \(0.642579\pi\) | |||||||
\(854\) | 9.48683 | + | 7.07107i | 0.324633 | + | 0.241967i | ||||
\(855\) | − | 14.1421i | − | 0.483651i | ||||||
\(856\) | 8.00000 | 0.273434 | ||||||||
\(857\) | 18.9737 | 0.648128 | 0.324064 | − | 0.946035i | \(-0.394951\pi\) | ||||
0.324064 | + | 0.946035i | \(0.394951\pi\) | |||||||
\(858\) | 60.0000 | + | 28.2843i | 2.04837 | + | 0.965609i | ||||
\(859\) | 6.70820i | 0.228881i | 0.993430 | + | 0.114440i | \(0.0365075\pi\) | ||||
−0.993430 | + | 0.114440i | \(0.963492\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −45.0000 | − | 33.5410i | −1.53360 | − | 1.14307i | ||||
\(862\) | −50.0000 | −1.70301 | ||||||||
\(863\) | 18.0000 | 0.612727 | 0.306364 | − | 0.951915i | \(-0.400888\pi\) | ||||
0.306364 | + | 0.951915i | \(0.400888\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 21.2132i | − | 0.721271i | ||||||
\(866\) | 28.4605 | 0.967127 | ||||||||
\(867\) | 38.0132i | 1.29099i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.0000 | − | 25.4558i | 0.407072 | − | 0.863530i | ||||
\(870\) | −10.0000 | −0.339032 | ||||||||
\(871\) | −69.5701 | −2.35729 | ||||||||
\(872\) | −36.0000 | −1.21911 | ||||||||
\(873\) | 13.4164i | 0.454077i | ||||||||
\(874\) | − | 13.4164i | − | 0.453817i | ||||||
\(875\) | 23.7171 | + | 17.6777i | 0.801784 | + | 0.597614i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.24264i | 0.143264i | 0.997431 | + | 0.0716319i | \(0.0228207\pi\) | ||||
−0.997431 | + | 0.0716319i | \(0.977179\pi\) | |||||||
\(878\) | − | 22.3607i | − | 0.754636i | ||||||
\(879\) | − | 21.2132i | − | 0.715504i | ||||||
\(880\) | −12.6491 | + | 26.8328i | −0.426401 | + | 0.904534i | ||||
\(881\) | − | 51.4296i | − | 1.73271i | −0.499432 | − | 0.866353i | \(-0.666458\pi\) | ||
0.499432 | − | 0.866353i | \(-0.333542\pi\) | |||||||
\(882\) | −18.9737 | + | 5.65685i | −0.638877 | + | 0.190476i | ||||
\(883\) | 8.00000 | 0.269221 | 0.134611 | − | 0.990899i | \(-0.457022\pi\) | ||||
0.134611 | + | 0.990899i | \(0.457022\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.1803i | 0.375823i | ||||||||
\(886\) | − | 21.2132i | − | 0.712672i | ||||||
\(887\) | −18.9737 | −0.637073 | −0.318537 | − | 0.947911i | \(-0.603191\pi\) | ||||
−0.318537 | + | 0.947911i | \(0.603191\pi\) | |||||||
\(888\) | −6.32456 | −0.212238 | ||||||||
\(889\) | 27.0000 | + | 20.1246i | 0.905551 | + | 0.674958i | ||||
\(890\) | − | 7.07107i | − | 0.237023i | ||||||
\(891\) | 33.0000 | + | 15.5563i | 1.10554 | + | 0.521157i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 14.1421i | − | 0.473249i | ||||||
\(894\) | − | 62.6099i | − | 2.09399i | ||||||
\(895\) | 20.1246i | 0.672692i | ||||||||
\(896\) | −24.0000 | − | 17.8885i | −0.801784 | − | 0.597614i | ||||
\(897\) | − | 42.4264i | − | 1.41658i | ||||||
\(898\) | − | 38.1838i | − | 1.27421i | ||||||
\(899\) | −9.48683 | −0.316404 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 18.9737 | − | 40.2492i | 0.631754 | − | 1.34015i | ||||
\(903\) | −15.0000 | + | 20.1246i | −0.499169 | + | 0.669705i | ||||
\(904\) | − | 8.48528i | − | 0.282216i | ||||||
\(905\) | −45.0000 | −1.49585 | ||||||||
\(906\) | − | 53.6656i | − | 1.78292i | ||||||
\(907\) | −10.0000 | −0.332045 | −0.166022 | − | 0.986122i | \(-0.553092\pi\) | ||||
−0.166022 | + | 0.986122i | \(0.553092\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.9737 | 0.629317 | ||||||||
\(910\) | 31.6228 | − | 42.4264i | 1.04828 | − | 1.40642i | ||||
\(911\) | −6.00000 | −0.198789 | −0.0993944 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993944 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(912\) | 28.2843i | 0.936586i | ||||||||
\(913\) | 28.4605 | + | 13.4164i | 0.941905 | + | 0.444018i | ||||
\(914\) | −12.0000 | −0.396925 | ||||||||
\(915\) | 15.8114 | 0.522708 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −30.0000 | + | 40.2492i | −0.990687 | + | 1.32915i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 12.7279i | − | 0.419855i | −0.977717 | − | 0.209928i | \(-0.932677\pi\) | ||
0.977717 | − | 0.209928i | \(-0.0673229\pi\) | |||||||
\(920\) | 18.9737 | 0.625543 | ||||||||
\(921\) | 14.1421i | 0.465999i | ||||||||
\(922\) | − | 13.4164i | − | 0.441846i | ||||||
\(923\) | −56.9210 | −1.87358 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 35.3553i | − | 1.16185i | ||||||
\(927\) | 26.8328i | 0.881305i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.7771i | 1.17381i | 0.809656 | + | 0.586904i | \(0.199653\pi\) | ||||
−0.809656 | + | 0.586904i | \(0.800347\pi\) | |||||||
\(930\) | −47.4342 | −1.55543 | ||||||||
\(931\) | −6.32456 | − | 21.2132i | −0.207279 | − | 0.695235i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.0000 | −0.327385 | ||||||||
\(934\) | 15.8114 | 0.517364 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 35.7771i | 1.16941i | ||||||||
\(937\) | 50.5964 | 1.65291 | 0.826457 | − | 0.563000i | \(-0.190353\pi\) | ||||
0.826457 | + | 0.563000i | \(0.190353\pi\) | |||||||
\(938\) | 33.0000 | + | 24.5967i | 1.07749 | + | 0.803112i | ||||
\(939\) | −15.0000 | −0.489506 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.9473 | 1.23705 | 0.618524 | − | 0.785766i | \(-0.287731\pi\) | ||||
0.618524 | + | 0.785766i | \(0.287731\pi\) | |||||||
\(942\) | 21.2132i | 0.691164i | ||||||||
\(943\) | −28.4605 | −0.926801 | ||||||||
\(944\) | − | 8.94427i | − | 0.291111i | ||||||
\(945\) | 7.90569 | − | 10.6066i | 0.257172 | − | 0.345033i | ||||
\(946\) | −18.0000 | − | 8.48528i | −0.585230 | − | 0.275880i | ||||
\(947\) | −15.0000 | −0.487435 | −0.243717 | − | 0.969846i | \(-0.578367\pi\) | ||||
−0.243717 | + | 0.969846i | \(0.578367\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.0000 | −0.649227 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 46.9574i | − | 1.52270i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.89949i | 0.320676i | 0.987062 | + | 0.160338i | \(0.0512584\pi\) | ||||
−0.987062 | + | 0.160338i | \(0.948742\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.70820i | 0.217072i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.48683 | − | 4.47214i | −0.306666 | − | 0.144564i | ||||
\(958\) | 26.8328i | 0.866929i | ||||||||
\(959\) | −23.7171 | + | 31.8198i | −0.765865 | + | 1.02752i | ||||
\(960\) | −40.0000 | −1.29099 | ||||||||
\(961\) | −14.0000 | −0.451613 | ||||||||
\(962\) | 8.94427i | 0.288375i | ||||||||
\(963\) | 5.65685i | 0.182290i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.48683 | −0.305392 | ||||||||
\(966\) | −15.0000 | + | 20.1246i | −0.482617 | + | 0.647499i | ||||
\(967\) | − | 46.6690i | − | 1.50078i | −0.660998 | − | 0.750388i | \(-0.729867\pi\) | ||
0.660998 | − | 0.750388i | \(-0.270133\pi\) | |||||||
\(968\) | −24.0000 | + | 19.7990i | −0.771389 | + | 0.636364i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 21.2132i | 0.681115i | ||||||||
\(971\) | 29.0689i | 0.932865i | 0.884557 | + | 0.466432i | \(0.154461\pi\) | ||||
−0.884557 | + | 0.466432i | \(0.845539\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.0000 | − | 26.8328i | 0.641171 | − | 0.860221i | ||||
\(974\) | 41.0122i | 1.31412i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.6491 | −0.404888 | ||||||||
\(977\) | −21.0000 | −0.671850 | −0.335925 | − | 0.941889i | \(-0.609049\pi\) | ||||
−0.335925 | + | 0.941889i | \(0.609049\pi\) | |||||||
\(978\) | −31.6228 | −1.01118 | ||||||||
\(979\) | 3.16228 | − | 6.70820i | 0.101067 | − | 0.214395i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 25.4558i | − | 0.812743i | ||||||
\(982\) | 46.0000 | 1.46792 | ||||||||
\(983\) | 29.0689i | 0.927153i | 0.886057 | + | 0.463577i | \(0.153434\pi\) | ||||
−0.886057 | + | 0.463577i | \(0.846566\pi\) | |||||||
\(984\) | 60.0000 | 1.91273 | ||||||||
\(985\) | −12.6491 | −0.403034 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15.8114 | + | 21.2132i | −0.503282 | + | 0.675224i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.7279i | 0.404724i | ||||||||
\(990\) | −18.9737 | − | 8.94427i | −0.603023 | − | 0.284268i | ||||
\(991\) | −46.0000 | −1.46124 | −0.730619 | − | 0.682785i | \(-0.760768\pi\) | ||||
−0.730619 | + | 0.682785i | \(0.760768\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 42.4853i | 1.34823i | ||||||||
\(994\) | 27.0000 | + | 20.1246i | 0.856388 | + | 0.638314i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −53.7587 | −1.70256 | −0.851278 | − | 0.524715i | \(-0.824172\pi\) | ||||
−0.851278 | + | 0.524715i | \(0.824172\pi\) | |||||||
\(998\) | − | 22.6274i | − | 0.716258i | ||||||
\(999\) | 2.23607i | 0.0707461i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))