Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(17,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.df (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1601.7 | ||
Root | \(1.68042 + 0.419752i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.1601 |
Dual form | 3024.2.df.d.17.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.96988 | 1.32817 | 0.664085 | − | 0.747657i | \(-0.268821\pi\) | ||||
0.664085 | + | 0.747657i | \(0.268821\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.38485 | + | 1.14563i | −0.901390 | + | 0.433009i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.72811i | − | 1.42558i | −0.701378 | − | 0.712790i | \(-0.747431\pi\) | ||
0.701378 | − | 0.712790i | \(-0.252569\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.54045 | − | 2.04408i | 0.981945 | − | 0.566926i | 0.0790880 | − | 0.996868i | \(-0.474799\pi\) |
0.902857 | + | 0.429942i | \(0.141466\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.835278 | − | 1.44674i | −0.202585 | − | 0.350887i | 0.746776 | − | 0.665076i | \(-0.231601\pi\) |
−0.949360 | + | 0.314189i | \(0.898267\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.25377 | + | 2.45592i | 0.975882 | + | 0.563426i | 0.901024 | − | 0.433768i | \(-0.142816\pi\) |
0.0748577 | + | 0.997194i | \(0.476150\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 4.91090i | − | 1.02399i | −0.858987 | − | 0.511997i | \(-0.828906\pi\) | ||
0.858987 | − | 0.511997i | \(-0.171094\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.82018 | 0.764036 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.238557 | − | 0.137731i | −0.0442989 | − | 0.0255760i | 0.477687 | − | 0.878530i | \(-0.341475\pi\) |
−0.521986 | + | 0.852954i | \(0.674809\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.38847 | + | 0.801636i | 0.249377 | + | 0.143978i | 0.619479 | − | 0.785013i | \(-0.287344\pi\) |
−0.370102 | + | 0.928991i | \(0.620677\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.08273 | + | 3.40239i | −1.19720 | + | 0.575109i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.69681 | + | 2.93896i | −0.278954 | + | 0.483162i | −0.971125 | − | 0.238571i | \(-0.923321\pi\) |
0.692171 | + | 0.721733i | \(0.256654\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.55632 | − | 6.15972i | −0.555404 | − | 0.961987i | −0.997872 | − | 0.0652031i | \(-0.979230\pi\) |
0.442468 | − | 0.896784i | \(-0.354103\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.22930 | + | 9.05742i | −0.797461 | + | 1.38124i | 0.123804 | + | 0.992307i | \(0.460491\pi\) |
−0.921265 | + | 0.388936i | \(0.872843\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.49885 | − | 9.52430i | −0.802090 | − | 1.38926i | −0.918238 | − | 0.396029i | \(-0.870388\pi\) |
0.116148 | − | 0.993232i | \(-0.462945\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.37505 | − | 5.46433i | 0.625007 | − | 0.780619i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.707381 | − | 0.408407i | 0.0971663 | − | 0.0560990i | −0.450629 | − | 0.892711i | \(-0.648800\pi\) |
0.547796 | + | 0.836612i | \(0.315467\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 14.0419i | − | 1.89341i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.37428 | − | 2.38032i | 0.178916 | − | 0.309891i | −0.762594 | − | 0.646878i | \(-0.776074\pi\) |
0.941509 | + | 0.336986i | \(0.109408\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.23807 | + | 3.60155i | −0.798703 | + | 0.461131i | −0.843017 | − | 0.537886i | \(-0.819223\pi\) |
0.0443147 | + | 0.999018i | \(0.485890\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.5147 | − | 6.07067i | 1.30419 | − | 0.752974i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.80513 | − | 10.0548i | 0.709210 | − | 1.22839i | −0.255941 | − | 0.966692i | \(-0.582385\pi\) |
0.965151 | − | 0.261695i | \(-0.0842814\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.4406i | 1.23907i | 0.784968 | + | 0.619537i | \(0.212680\pi\) | ||||
−0.784968 | + | 0.619537i | \(0.787320\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.6493 | − | 7.88042i | 1.59753 | − | 0.922334i | 0.605567 | − | 0.795794i | \(-0.292946\pi\) |
0.991962 | − | 0.126539i | \(-0.0403870\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.41668 | + | 11.2759i | 0.617288 | + | 1.28500i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.15163 | − | 10.6549i | −0.692112 | − | 1.19877i | −0.971145 | − | 0.238492i | \(-0.923347\pi\) |
0.279032 | − | 0.960282i | \(-0.409986\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.03981 | − | 6.99715i | 0.443426 | − | 0.768037i | −0.554515 | − | 0.832174i | \(-0.687096\pi\) |
0.997941 | + | 0.0641368i | \(0.0204294\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.48067 | − | 4.29665i | −0.269067 | − | 0.466037i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.60872 | − | 7.98254i | 0.488523 | − | 0.846147i | −0.511390 | − | 0.859349i | \(-0.670869\pi\) |
0.999913 | + | 0.0132019i | \(0.00420240\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.10169 | + | 8.93089i | −0.639631 | + | 0.936212i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.6332 | + | 7.29377i | 1.29614 | + | 0.748325i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.00772 | − | 4.04591i | −0.711527 | − | 0.410800i | 0.100099 | − | 0.994977i | \(-0.468084\pi\) |
−0.811626 | + | 0.584177i | \(0.801417\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.30730 | 0.727103 | 0.363552 | − | 0.931574i | \(-0.381564\pi\) | ||||
0.363552 | + | 0.931574i | \(0.381564\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.02530i | 0.692224i | 0.938193 | + | 0.346112i | \(0.112498\pi\) | ||||
−0.938193 | + | 0.346112i | \(0.887502\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.2618 | + | 7.07938i | 1.18540 | + | 0.684389i | 0.957257 | − | 0.289239i | \(-0.0934022\pi\) |
0.228140 | + | 0.973628i | \(0.426735\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.82203 | − | 4.88789i | −0.270301 | − | 0.468175i | 0.698638 | − | 0.715476i | \(-0.253790\pi\) |
−0.968939 | + | 0.247300i | \(0.920457\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.6411 | + | 6.72099i | −1.09510 | + | 0.632258i | −0.934930 | − | 0.354831i | \(-0.884538\pi\) |
−0.160172 | + | 0.987089i | \(0.551205\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 14.5848i | − | 1.36004i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.64945 | + | 2.49335i | 0.334545 | + | 0.228565i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.3550 | −1.03228 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.50392 | −0.313400 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.7730 | 1.13342 | 0.566712 | − | 0.823916i | \(-0.308215\pi\) | ||||
0.566712 | + | 0.823916i | \(0.308215\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.4178 | 1.17232 | 0.586159 | − | 0.810196i | \(-0.300639\pi\) | ||||
0.586159 | + | 0.810196i | \(0.300639\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.9582 | − | 0.983737i | −1.12362 | − | 0.0853008i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.00030i | 0.768948i | 0.923136 | + | 0.384474i | \(0.125617\pi\) | ||||
−0.923136 | + | 0.384474i | \(0.874383\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.54902 | − | 0.894326i | 0.131386 | − | 0.0758557i | −0.432866 | − | 0.901458i | \(-0.642498\pi\) |
0.564252 | + | 0.825602i | \(0.309164\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.66464 | − | 16.7397i | −0.808198 | − | 1.39984i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.708485 | − | 0.409044i | −0.0588365 | − | 0.0339693i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 12.9072i | − | 1.05740i | −0.848810 | − | 0.528698i | \(-0.822680\pi\) | ||
0.848810 | − | 0.528698i | \(-0.177320\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.9673 | 1.05526 | 0.527631 | − | 0.849473i | \(-0.323080\pi\) | ||||
0.527631 | + | 0.849473i | \(0.323080\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.12360 | + | 2.38076i | 0.331216 | + | 0.191227i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8720 | + | 8.58638i | 1.18692 | + | 0.685268i | 0.957605 | − | 0.288085i | \(-0.0930185\pi\) |
0.229314 | + | 0.973353i | \(0.426352\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.62609 | + | 11.7118i | 0.443398 | + | 0.923017i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.53107 | + | 4.38394i | −0.198249 | + | 0.343377i | −0.947961 | − | 0.318387i | \(-0.896859\pi\) |
0.749712 | + | 0.661764i | \(0.230192\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.79673 | + | 10.0402i | 0.448564 | + | 0.776936i | 0.998293 | − | 0.0584072i | \(-0.0186022\pi\) |
−0.549729 | + | 0.835343i | \(0.685269\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.85653 | − | 3.21561i | 0.142810 | − | 0.247354i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.13346 | − | 5.42730i | −0.238232 | − | 0.412630i | 0.721975 | − | 0.691919i | \(-0.243235\pi\) |
−0.960207 | + | 0.279289i | \(0.909901\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.11057 | + | 4.37653i | −0.688694 | + | 0.330834i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.7668 | − | 7.37089i | 0.954233 | − | 0.550927i | 0.0598395 | − | 0.998208i | \(-0.480941\pi\) |
0.894393 | + | 0.447281i | \(0.147608\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.0833642i | − | 0.00619641i | −0.999995 | − | 0.00309821i | \(-0.999014\pi\) | ||
0.999995 | − | 0.00309821i | \(-0.000986191\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.03932 | + | 8.72835i | −0.370498 | + | 0.641721i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.84036 | + | 3.94929i | −0.500217 | + | 0.288800i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.3672 | − | 7.71754i | 0.967214 | − | 0.558421i | 0.0688282 | − | 0.997629i | \(-0.478074\pi\) |
0.898386 | + | 0.439207i | \(0.144741\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.7779 | + | 18.6678i | −0.775808 | + | 1.34374i | 0.158532 | + | 0.987354i | \(0.449324\pi\) |
−0.934339 | + | 0.356385i | \(0.884009\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 9.88306i | − | 0.704139i | −0.935974 | − | 0.352069i | \(-0.885478\pi\) | ||
0.935974 | − | 0.352069i | \(-0.114522\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.14623 | − | 5.28058i | 0.648359 | − | 0.374330i | −0.139468 | − | 0.990227i | \(-0.544539\pi\) |
0.787827 | + | 0.615896i | \(0.211206\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.726712 | + | 0.0551692i | 0.0510052 | + | 0.00387212i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.5618 | − | 18.2936i | −0.737670 | − | 1.27768i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.6118 | − | 20.1123i | 0.803208 | − | 1.39120i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.08453 | − | 10.5387i | −0.418876 | − | 0.725514i | 0.576951 | − | 0.816779i | \(-0.304242\pi\) |
−0.995827 | + | 0.0912645i | \(0.970909\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.5304 | + | 26.8994i | −1.05916 | + | 1.83453i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.22969 | − | 0.321102i | −0.287130 | − | 0.0217978i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.91452 | − | 3.41475i | −0.397854 | − | 0.229701i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.714485 | + | 0.412508i | 0.0478455 | + | 0.0276236i | 0.523732 | − | 0.851883i | \(-0.324539\pi\) |
−0.475886 | + | 0.879507i | \(0.657873\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.333557 | 0.0221390 | 0.0110695 | − | 0.999939i | \(-0.496476\pi\) | ||||
0.0110695 | + | 0.999939i | \(0.496476\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.4214i | 0.952996i | 0.879176 | + | 0.476498i | \(0.158094\pi\) | ||||
−0.879176 | + | 0.476498i | \(0.841906\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.7953 | − | 7.38739i | −0.838250 | − | 0.483964i | 0.0184192 | − | 0.999830i | \(-0.494137\pi\) |
−0.856669 | + | 0.515867i | \(0.827470\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.3309 | − | 28.2860i | −1.06531 | − | 1.84518i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.5339 | + | 13.0100i | −1.45760 | + | 0.841545i | −0.998893 | − | 0.0470423i | \(-0.985020\pi\) |
−0.458707 | + | 0.888588i | \(0.651687\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 1.92021i | − | 0.123692i | −0.998086 | − | 0.0618458i | \(-0.980301\pi\) | ||
0.998086 | − | 0.0618458i | \(-0.0196987\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.9934 | − | 16.2284i | 0.830116 | − | 1.03680i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.0804 | 1.27768 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.97663 | −0.629719 | −0.314860 | − | 0.949138i | \(-0.601957\pi\) | ||||
−0.314860 | + | 0.949138i | \(0.601957\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −23.2193 | −1.45978 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.0073 | −0.936129 | −0.468064 | − | 0.883694i | \(-0.655048\pi\) | ||||
−0.468064 | + | 0.883694i | \(0.655048\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.679670 | − | 8.95291i | 0.0422327 | − | 0.556306i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.05534i | 0.435051i | 0.976055 | + | 0.217525i | \(0.0697985\pi\) | ||||
−0.976055 | + | 0.217525i | \(0.930202\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.10084 | − | 1.21292i | 0.129053 | − | 0.0745090i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.8898 | + | 25.7898i | 0.907844 | + | 1.57243i | 0.817053 | + | 0.576562i | \(0.195606\pi\) |
0.0907911 | + | 0.995870i | \(0.471060\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.41462 | + | 1.39408i | 0.146677 | + | 0.0846843i | 0.571543 | − | 0.820572i | \(-0.306345\pi\) |
−0.424865 | + | 0.905257i | \(0.639679\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 18.0622i | − | 1.08919i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.5815 | 0.816032 | 0.408016 | − | 0.912975i | \(-0.366221\pi\) | ||||
0.408016 | + | 0.912975i | \(0.366221\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.95777 | + | 2.28502i | 0.236101 | + | 0.136313i | 0.613383 | − | 0.789785i | \(-0.289808\pi\) |
−0.377283 | + | 0.926098i | \(0.623141\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.6685 | − | 10.2009i | −1.05029 | − | 0.606383i | −0.127556 | − | 0.991831i | \(-0.540713\pi\) |
−0.922729 | + | 0.385449i | \(0.874047\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.5381 | + | 10.6158i | 0.917184 | + | 0.626631i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.10462 | − | 12.3056i | 0.417919 | − | 0.723857i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.41037 | + | 11.1031i | 0.374498 | + | 0.648649i | 0.990252 | − | 0.139289i | \(-0.0444818\pi\) |
−0.615754 | + | 0.787939i | \(0.711148\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.08144 | − | 7.06926i | 0.237631 | − | 0.411589i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.0383 | − | 17.3868i | −0.580529 | − | 1.00551i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.09464 | − | 27.5915i | 0.120733 | − | 1.59035i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.5263 | + | 10.6962i | −1.06081 | + | 0.612461i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.93411i | 0.110386i | 0.998476 | + | 0.0551928i | \(0.0175773\pi\) | ||||
−0.998476 | + | 0.0551928i | \(0.982423\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.04458 | − | 1.80926i | 0.0592326 | − | 0.102594i | −0.834889 | − | 0.550419i | \(-0.814468\pi\) |
0.894121 | + | 0.447825i | \(0.147801\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.4066 | − | 11.2044i | 1.09692 | − | 0.633309i | 0.161512 | − | 0.986871i | \(-0.448363\pi\) |
0.935411 | + | 0.353562i | \(0.115030\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.01788 | − | 1.74237i | 0.169501 | − | 0.0978614i | −0.412850 | − | 0.910799i | \(-0.635466\pi\) |
0.582350 | + | 0.812938i | \(0.302133\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.651207 | + | 1.12792i | −0.0364606 | + | 0.0631516i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 8.20549i | − | 0.456565i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.5252 | − | 7.80876i | 0.750241 | − | 0.433152i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.0253 | + | 16.4144i | 1.32456 | + | 0.904954i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.28857 | − | 3.96392i | −0.125791 | − | 0.217877i | 0.796251 | − | 0.604967i | \(-0.206814\pi\) |
−0.922042 | + | 0.387090i | \(0.873480\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.2405 | − | 29.8615i | 0.941951 | − | 1.63151i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.7062 | − | 25.4720i | −0.801100 | − | 1.38755i | −0.918893 | − | 0.394508i | \(-0.870915\pi\) |
0.117793 | − | 0.993038i | \(-0.462418\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.79023 | − | 6.56486i | 0.205252 | − | 0.355507i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.17373 | + | 18.0438i | −0.225360 | + | 0.974276i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.0245 | + | 9.82911i | 0.913924 | + | 0.527654i | 0.881692 | − | 0.471826i | \(-0.156405\pi\) |
0.0322323 | + | 0.999480i | \(0.489738\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.47286 | + | 4.89181i | 0.453542 | + | 0.261852i | 0.709325 | − | 0.704882i | \(-0.249000\pi\) |
−0.255783 | + | 0.966734i | \(0.582333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.0645 | −1.33405 | −0.667023 | − | 0.745037i | \(-0.732432\pi\) | ||||
−0.667023 | + | 0.745037i | \(0.732432\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 31.0074i | 1.64570i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.09861 | + | 4.67574i | 0.427428 | + | 0.246776i | 0.698251 | − | 0.715853i | \(-0.253962\pi\) |
−0.270822 | + | 0.962629i | \(0.587296\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.56305 | + | 4.43933i | 0.134897 | + | 0.233649i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 40.5367 | − | 23.4039i | 2.12179 | − | 1.22502i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.8850i | 1.14239i | 0.820815 | + | 0.571194i | \(0.193520\pi\) | ||||
−0.820815 | + | 0.571194i | \(0.806480\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.21912 | + | 1.78439i | −0.0632934 | + | 0.0926409i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.61644 | 0.239030 | 0.119515 | − | 0.992832i | \(-0.461866\pi\) | ||||
0.119515 | + | 0.992832i | \(0.461866\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.12613 | −0.0579988 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.22396 | 0.319703 | 0.159852 | − | 0.987141i | \(-0.448898\pi\) | ||||
0.159852 | + | 0.987141i | \(0.448898\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.9977 | −1.12403 | −0.562015 | − | 0.827127i | \(-0.689974\pi\) | ||||
−0.562015 | + | 0.827127i | \(0.689974\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.0869 | + | 33.4879i | 0.819864 | + | 1.70670i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.82776i | 0.498287i | 0.968467 | + | 0.249144i | \(0.0801491\pi\) | ||||
−0.968467 | + | 0.249144i | \(0.919851\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.10481 | + | 4.10197i | −0.359306 | + | 0.207445i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.2696 | − | 31.6439i | −0.919243 | − | 1.59218i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.55324 | + | 2.62881i | 0.228520 | + | 0.131936i | 0.609889 | − | 0.792487i | \(-0.291214\pi\) |
−0.381369 | + | 0.924423i | \(0.624547\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.0719i | 0.852529i | 0.904598 | + | 0.426265i | \(0.140171\pi\) | ||||
−0.904598 | + | 0.426265i | \(0.859829\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.55444 | 0.326500 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.8957 | + | 8.02270i | 0.688786 | + | 0.397671i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.9484 | + | 9.78516i | 0.838044 | + | 0.483845i | 0.856599 | − | 0.515983i | \(-0.172573\pi\) |
−0.0185546 | + | 0.999828i | \(0.505906\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.550478 | + | 7.25114i | −0.0270873 | + | 0.356805i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.9977 | − | 20.7807i | 0.588946 | − | 1.02008i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.3073 | − | 17.8529i | −0.503547 | − | 0.872169i | −0.999992 | − | 0.00410056i | \(-0.998695\pi\) |
0.496445 | − | 0.868068i | \(-0.334639\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.704748 | − | 1.22066i | 0.0343473 | − | 0.0594913i | −0.848341 | − | 0.529451i | \(-0.822398\pi\) |
0.882688 | + | 0.469959i | \(0.155731\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.19091 | − | 5.52682i | −0.154782 | − | 0.268090i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.7508 | − | 15.7357i | 0.520268 | − | 0.761504i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.6666 | + | 6.73569i | −0.561959 | + | 0.324447i | −0.753931 | − | 0.656953i | \(-0.771845\pi\) |
0.191973 | + | 0.981400i | \(0.438512\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 12.9356i | − | 0.621646i | −0.950468 | − | 0.310823i | \(-0.899395\pi\) | ||
0.950468 | − | 0.310823i | \(-0.100605\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.0608 | − | 20.8899i | 0.576944 | − | 0.999297i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.75023 | + | 5.05195i | −0.417626 | + | 0.241116i | −0.694061 | − | 0.719916i | \(-0.744180\pi\) |
0.276435 | + | 0.961033i | \(0.410847\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.1220 | + | 14.5042i | −1.19358 | + | 0.689115i | −0.959117 | − | 0.283009i | \(-0.908667\pi\) |
−0.234466 | + | 0.972124i | \(0.575334\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.6873 | − | 23.7072i | 0.648842 | − | 1.12383i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 7.94881i | − | 0.375127i | −0.982252 | − | 0.187564i | \(-0.939941\pi\) | ||
0.982252 | − | 0.187564i | \(-0.0600591\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.1239 | + | 16.8147i | −1.37139 | + | 0.791772i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.1213 | + | 26.5237i | −0.849539 | + | 1.24345i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.98084 | + | 12.0912i | 0.326550 | + | 0.565601i | 0.981825 | − | 0.189789i | \(-0.0607805\pi\) |
−0.655275 | + | 0.755391i | \(0.727447\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.4030 | + | 28.4108i | −0.763964 | + | 1.32322i | 0.176829 | + | 0.984242i | \(0.443416\pi\) |
−0.940793 | + | 0.338983i | \(0.889917\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.8812 | + | 24.0429i | 0.645112 | + | 1.11737i | 0.984276 | + | 0.176640i | \(0.0565227\pi\) |
−0.339163 | + | 0.940727i | \(0.610144\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.4311 | − | 19.7992i | 0.528966 | − | 0.916196i | −0.470463 | − | 0.882420i | \(-0.655913\pi\) |
0.999429 | − | 0.0337767i | \(-0.0107535\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.32529 | + | 30.6297i | −0.107372 | + | 1.41435i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 42.8245 | + | 24.7247i | 1.96907 | + | 1.13684i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.2502 | + | 9.38204i | 0.745609 | + | 0.430478i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.42425 | 0.110767 | 0.0553834 | − | 0.998465i | \(-0.482362\pi\) | ||||
0.0553834 | + | 0.998465i | \(0.482362\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.8737i | 0.632584i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.8121 | − | 12.0159i | −0.945028 | − | 0.545612i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.19651 | − | 9.00061i | −0.235476 | − | 0.407857i | 0.723935 | − | 0.689868i | \(-0.242332\pi\) |
−0.959411 | + | 0.282012i | \(0.908998\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.93014 | + | 1.69172i | −0.132235 | + | 0.0763462i | −0.564658 | − | 0.825325i | \(-0.690992\pi\) |
0.432423 | + | 0.901671i | \(0.357659\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.460174i | 0.0207252i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.9611 | − | 24.8993i | −0.536530 | − | 1.11689i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −39.5603 | −1.77096 | −0.885481 | − | 0.464676i | \(-0.846171\pi\) | ||||
−0.885481 | + | 0.464676i | \(0.846171\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.5476 | −0.648645 | −0.324323 | − | 0.945947i | \(-0.605136\pi\) | ||||
−0.324323 | + | 0.945947i | \(0.605136\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.7018 | 0.965717 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.3916 | −0.903841 | −0.451921 | − | 0.892058i | \(-0.649261\pi\) | ||||
−0.451921 | + | 0.892058i | \(0.649261\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.5235 | + | 34.4307i | −1.04062 | + | 1.52313i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.8643i | 0.919391i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −45.0319 | + | 25.9992i | −1.98050 | + | 1.14344i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.75122 | − | 13.4255i | −0.339587 | − | 0.588182i | 0.644768 | − | 0.764379i | \(-0.276954\pi\) |
−0.984355 | + | 0.176196i | \(0.943621\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.35989 | − | 5.40394i | −0.409280 | − | 0.236298i | 0.281201 | − | 0.959649i | \(-0.409267\pi\) |
−0.690480 | + | 0.723351i | \(0.742601\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 2.67836i | − | 0.116671i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.11695 | −0.0485631 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −25.1819 | − | 14.5388i | −1.09075 | − | 0.629745i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 36.4162 | + | 21.0249i | 1.57441 | + | 0.908986i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.8360 | − | 20.6857i | −1.11283 | − | 0.890997i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.79357 | + | 15.2309i | −0.378065 | + | 0.654828i | −0.990781 | − | 0.135476i | \(-0.956744\pi\) |
0.612716 | + | 0.790303i | \(0.290077\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.38108 | − | 14.5165i | −0.359006 | − | 0.621817i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.72451 | − | 9.91513i | 0.244762 | − | 0.423940i | −0.717303 | − | 0.696762i | \(-0.754623\pi\) |
0.962065 | + | 0.272821i | \(0.0879568\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.676511 | − | 1.17175i | −0.0288203 | − | 0.0499183i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.8774 | + | 18.3629i | 1.14294 | + | 0.780871i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.9159 | + | 19.0040i | −1.39469 | + | 0.805226i | −0.993830 | − | 0.110912i | \(-0.964623\pi\) |
−0.400863 | + | 0.916138i | \(0.631290\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 42.7565i | 1.80841i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.88438 | + | 15.3882i | −0.374432 | + | 0.648535i | −0.990242 | − | 0.139360i | \(-0.955496\pi\) |
0.615810 | + | 0.787895i | \(0.288829\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.5727 | + | 19.9605i | −1.45448 | + | 0.839746i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.7404 | − | 19.4801i | 1.41447 | − | 0.816646i | 0.418667 | − | 0.908140i | \(-0.362497\pi\) |
0.995806 | + | 0.0914936i | \(0.0291641\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.45245 | − | 14.6401i | 0.353724 | − | 0.612668i | −0.633175 | − | 0.774009i | \(-0.718248\pi\) |
0.986899 | + | 0.161341i | \(0.0515818\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 18.7605i | − | 0.782368i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −40.9329 | + | 23.6326i | −1.70406 | + | 0.983840i | −0.762506 | + | 0.646982i | \(0.776031\pi\) |
−0.941555 | + | 0.336858i | \(0.890636\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.61818 | + | 21.3153i | −0.0671333 | + | 0.884308i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.93099 | − | 3.34458i | −0.0799736 | − | 0.138518i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.6343 | + | 20.1513i | −0.480200 | + | 0.831731i | −0.999742 | − | 0.0227138i | \(-0.992769\pi\) |
0.519542 | + | 0.854445i | \(0.326103\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.93750 | + | 6.81995i | 0.162242 | + | 0.281011i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.5962 | + | 32.2095i | −0.763654 | + | 1.32269i | 0.177302 | + | 0.984157i | \(0.443263\pi\) |
−0.940955 | + | 0.338530i | \(0.890070\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.8384 | + | 7.40494i | 0.444332 | + | 0.303573i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.9591 | + | 16.1422i | 1.14238 | + | 0.659552i | 0.947018 | − | 0.321180i | \(-0.104079\pi\) |
0.195359 | + | 0.980732i | \(0.437413\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.7559 | + | 8.51933i | 0.601906 | + | 0.347511i | 0.769791 | − | 0.638296i | \(-0.220360\pi\) |
−0.167885 | + | 0.985807i | \(0.553694\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −33.7231 | −1.37104 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 9.75021i | − | 0.395749i | −0.980227 | − | 0.197874i | \(-0.936596\pi\) | ||
0.980227 | − | 0.197874i | \(-0.0634038\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −38.9369 | − | 22.4802i | −1.57522 | − | 0.909452i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.86332 | − | 11.8876i | −0.277207 | − | 0.480136i | 0.693483 | − | 0.720473i | \(-0.256075\pi\) |
−0.970690 | + | 0.240337i | \(0.922742\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.84301 | − | 1.64141i | 0.114455 | − | 0.0660807i | −0.441680 | − | 0.897173i | \(-0.645617\pi\) |
0.556135 | + | 0.831092i | \(0.312284\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 17.3098i | − | 0.695740i | −0.937543 | − | 0.347870i | \(-0.886905\pi\) | ||
0.937543 | − | 0.347870i | \(-0.113095\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.84606 | + | 24.3171i | −0.0739608 | + | 0.974243i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.5071 | −1.18028 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.66923 | 0.226047 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.27821 | 0.249932 | 0.124966 | − | 0.992161i | \(-0.460118\pi\) | ||||
0.124966 | + | 0.992161i | \(0.460118\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 37.9344 | 1.50538 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.32011 | − | 28.2892i | 0.171169 | − | 1.12086i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.7601i | 0.819976i | 0.912091 | + | 0.409988i | \(0.134467\pi\) | ||||
−0.912091 | + | 0.409988i | \(0.865533\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.2553 | + | 9.96236i | −0.680483 | + | 0.392877i | −0.800037 | − | 0.599950i | \(-0.795187\pi\) |
0.119554 | + | 0.992828i | \(0.461854\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.7670 | + | 25.5772i | 0.580551 | + | 1.00554i | 0.995414 | + | 0.0956605i | \(0.0304963\pi\) |
−0.414863 | + | 0.909884i | \(0.636170\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.2544 | − | 6.49774i | −0.441775 | − | 0.255059i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.9250i | 0.623193i | 0.950215 | + | 0.311596i | \(0.100864\pi\) | ||||
−0.950215 | + | 0.311596i | \(0.899136\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 39.8493 | 1.55704 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.80283 | + | 1.61822i | 0.109183 | + | 0.0630368i | 0.553597 | − | 0.832785i | \(-0.313255\pi\) |
−0.444414 | + | 0.895821i | \(0.646588\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.71194 | + | 4.45249i | 0.299960 | + | 0.173182i | 0.642425 | − | 0.766349i | \(-0.277928\pi\) |
−0.342465 | + | 0.939531i | \(0.611262\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −38.4843 | − | 2.92158i | −1.49236 | − | 0.113294i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.676383 | + | 1.17153i | −0.0261896 | + | 0.0453618i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.0285 | + | 29.4943i | 0.657379 | + | 1.13861i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.2311 | + | 22.9169i | −0.510021 | + | 0.883382i | 0.489912 | + | 0.871772i | \(0.337029\pi\) |
−0.999933 | + | 0.0116101i | \(0.996304\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.46424 | − | 7.73229i | −0.171575 | − | 0.297176i | 0.767396 | − | 0.641174i | \(-0.221552\pi\) |
−0.938971 | + | 0.343997i | \(0.888219\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.3475 | + | 1.62062i | 0.819243 | + | 0.0621938i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.7902 | + | 18.9314i | −1.25468 | + | 0.724390i | −0.972035 | − | 0.234834i | \(-0.924545\pi\) |
−0.282645 | + | 0.959225i | \(0.591212\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.7298i | 1.02129i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.66963 | − | 2.89189i | 0.0636080 | − | 0.110172i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.94211 | − | 2.85333i | 0.188007 | − | 0.108546i | −0.403042 | − | 0.915181i | \(-0.632047\pi\) |
0.591049 | + | 0.806636i | \(0.298714\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.60039 | − | 2.65604i | 0.174503 | − | 0.100749i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.94103 | + | 10.2902i | −0.225032 | + | 0.389768i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.19949i | 0.309690i | 0.987939 | + | 0.154845i | \(0.0494879\pi\) | ||||
−0.987939 | + | 0.154845i | \(0.950512\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.4357 | + | 8.33444i | −0.544452 | + | 0.314339i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.4268 | + | 8.37148i | −0.655403 | + | 0.314842i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.0757 | − | 17.4517i | −0.378402 | − | 0.655412i | 0.612428 | − | 0.790527i | \(-0.290193\pi\) |
−0.990830 | + | 0.135115i | \(0.956860\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.93676 | − | 6.81866i | 0.147433 | − | 0.255361i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28.7028 | − | 49.7147i | −1.07342 | − | 1.85923i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.5996 | + | 44.3397i | −0.954702 | + | 1.65359i | −0.219654 | + | 0.975578i | \(0.570493\pi\) |
−0.735048 | + | 0.678015i | \(0.762841\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.04842 | − | 16.7543i | −0.299739 | − | 0.623963i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.911330 | − | 0.526157i | −0.0338460 | − | 0.0195410i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.7848 | + | 7.95865i | 0.511249 | + | 0.295170i | 0.733347 | − | 0.679854i | \(-0.237957\pi\) |
−0.222098 | + | 0.975024i | \(0.571290\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.4717 | 0.646213 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.24025i | 0.156617i | 0.996929 | + | 0.0783086i | \(0.0249519\pi\) | ||||
−0.996929 | + | 0.0783086i | \(0.975048\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −47.5401 | − | 27.4473i | −1.75116 | − | 1.01103i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.1835 | + | 24.5665i | 0.521747 | + | 0.903693i | 0.999680 | + | 0.0252966i | \(0.00805300\pi\) |
−0.477933 | + | 0.878397i | \(0.658614\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.8850 | − | 12.6353i | 0.802884 | − | 0.463545i | −0.0415945 | − | 0.999135i | \(-0.513244\pi\) |
0.844479 | + | 0.535589i | \(0.179910\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 38.3327i | − | 1.40440i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −37.3531 | − | 2.83570i | −1.36485 | − | 0.103614i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −47.5460 | −1.73498 | −0.867490 | − | 0.497455i | \(-0.834268\pi\) | ||||
−0.867490 | + | 0.497455i | \(0.834268\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 38.5113 | 1.40157 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.3922 | 1.35904 | 0.679521 | − | 0.733656i | \(-0.262188\pi\) | ||||
0.679521 | + | 0.733656i | \(0.262188\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.24283 | 0.298802 | 0.149401 | − | 0.988777i | \(-0.452265\pi\) | ||||
0.149401 | + | 0.988777i | \(0.452265\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.3299 | + | 8.42390i | 0.446371 | + | 0.304966i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 11.2365i | − | 0.405728i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.2182 | − | 11.6730i | 0.729086 | − | 0.420938i | −0.0890020 | − | 0.996031i | \(-0.528368\pi\) |
0.818088 | + | 0.575094i | \(0.195034\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.2201 | + | 29.8261i | 0.619364 | + | 1.07277i | 0.989602 | + | 0.143833i | \(0.0459428\pi\) |
−0.370238 | + | 0.928937i | \(0.620724\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.30422 | + | 3.06240i | 0.190533 | + | 0.110004i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 34.9361i | − | 1.25171i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49.3644 | 1.76640 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 44.1682 | + | 25.5005i | 1.57643 | + | 0.910152i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.19975 | + | 4.15678i | 0.256643 | + | 0.148173i | 0.622802 | − | 0.782379i | \(-0.285994\pi\) |
−0.366159 | + | 0.930552i | \(0.619327\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.0625 | − | 29.3650i | 0.713341 | − | 1.04410i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.7237 | + | 25.5022i | −0.522854 | + | 0.905610i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.426036 | − | 0.737916i | −0.0150910 | − | 0.0261383i | 0.858381 | − | 0.513012i | \(-0.171470\pi\) |
−0.873472 | + | 0.486874i | \(0.838137\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.18614 | + | 15.9109i | −0.324982 | + | 0.562886i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −37.2595 | − | 64.5354i | −1.31486 | − | 2.27740i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.7088 | + | 34.7826i | 0.588908 | + | 1.22592i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.5580 | − | 18.2200i | 1.10952 | − | 0.640581i | 0.170814 | − | 0.985303i | \(-0.445360\pi\) |
0.938705 | + | 0.344722i | \(0.112027\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.08986i | − | 0.0382702i | −0.999817 | − | 0.0191351i | \(-0.993909\pi\) | ||
0.999817 | − | 0.0191351i | \(-0.00609126\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.51697 | + | 13.0198i | −0.263308 | + | 0.456063i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −44.4885 | + | 25.6855i | −1.55646 | + | 0.898620i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.9748 | − | 12.1098i | 0.732025 | − | 0.422635i | −0.0871374 | − | 0.996196i | \(-0.527772\pi\) |
0.819163 | + | 0.573561i | \(0.194439\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.85592 | − | 4.94660i | 0.0995512 | − | 0.172428i | −0.811948 | − | 0.583730i | \(-0.801593\pi\) |
0.911499 | + | 0.411302i | \(0.134926\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 36.4579i | − | 1.26777i | −0.773429 | − | 0.633883i | \(-0.781460\pi\) | ||
0.773429 | − | 0.633883i | \(-0.218540\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.498269 | + | 0.287676i | −0.0173056 | + | 0.00999140i | −0.508628 | − | 0.860986i | \(-0.669847\pi\) |
0.491322 | + | 0.870978i | \(0.336514\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.5599 | − | 1.76534i | −0.400526 | − | 0.0611653i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.2156 | + | 29.8183i | 0.595770 | + | 1.03190i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.9341 | + | 41.4550i | −0.826295 | + | 1.43119i | 0.0746300 | + | 0.997211i | \(0.476222\pi\) |
−0.900925 | + | 0.433974i | \(0.857111\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4621 | − | 25.0490i | −0.498692 | − | 0.863759i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.51368 | − | 9.54997i | 0.189676 | − | 0.328529i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.0801 | − | 13.0087i | 0.930483 | − | 0.446985i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.4329 | + | 8.33286i | 0.494755 | + | 0.285647i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.5393 | + | 23.4054i | 1.38804 | + | 0.801385i | 0.993094 | − | 0.117320i | \(-0.0374303\pi\) |
0.394945 | + | 0.918705i | \(0.370764\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.56441 | −0.326714 | −0.163357 | − | 0.986567i | \(-0.552232\pi\) | ||||
−0.163357 | + | 0.986567i | \(0.552232\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.40759i | 0.184505i | 0.995736 | + | 0.0922523i | \(0.0294066\pi\) | ||||
−0.995736 | + | 0.0922523i | \(0.970593\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35.5402 | + | 20.5191i | 1.20980 | + | 0.698480i | 0.962716 | − | 0.270514i | \(-0.0871936\pi\) |
0.247086 | + | 0.968994i | \(0.420527\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.30598 | − | 16.1184i | −0.316413 | − | 0.548043i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −50.3777 | + | 29.0856i | −1.70895 | + | 0.986661i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 47.4646i | − | 1.60828i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.35633 | − | 4.01421i | 0.282496 | − | 0.135705i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.6502 | −0.494701 | −0.247351 | − | 0.968926i | \(-0.579560\pi\) | ||||
−0.247351 | + | 0.968926i | \(0.579560\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.8295 | 1.51034 | 0.755172 | − | 0.655527i | \(-0.227553\pi\) | ||||
0.755172 | + | 0.655527i | \(0.227553\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.8527 | −1.13923 | −0.569617 | − | 0.821910i | \(-0.692909\pi\) | ||||
−0.569617 | + | 0.821910i | \(0.692909\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.6844 | −0.895973 | −0.447987 | − | 0.894040i | \(-0.647859\pi\) | ||||
−0.447987 | + | 0.894040i | \(0.647859\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.4618 | + | 14.6332i | −1.02166 | + | 0.490783i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 54.0189i | − | 1.80767i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37.9157 | − | 21.8907i | 1.26738 | − | 0.731724i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.220820 | − | 0.382472i | −0.00736476 | − | 0.0127561i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.18172 | − | 0.682266i | −0.0393688 | − | 0.0227296i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 0.247582i | − | 0.00822989i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.9442 | 0.529419 | 0.264710 | − | 0.964328i | \(-0.414724\pi\) | ||||
0.264710 | + | 0.964328i | \(0.414724\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.9207 | + | 23.6256i | 1.35576 | + | 0.782750i | 0.989050 | − | 0.147584i | \(-0.0471496\pi\) |
0.366713 | + | 0.930334i | \(0.380483\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.0833 | − | 19.1007i | −1.09490 | − | 0.632140i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −31.9995 | + | 15.3719i | −1.05672 | + | 0.507624i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.8163 | + | 25.6625i | −0.488743 | + | 0.846528i | −0.999916 | − | 0.0129500i | \(-0.995878\pi\) |
0.511173 | + | 0.859478i | \(0.329211\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.3415 | + | 36.9645i | 0.702463 | + | 1.21670i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.48212 | + | 11.2274i | −0.213131 | + | 0.369153i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.6186 | − | 28.7842i | −0.545238 | − | 0.944380i | −0.998592 | − | 0.0530496i | \(-0.983106\pi\) |
0.453354 | − | 0.891331i | \(-0.350227\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.0304 | − | 12.4993i | 1.04975 | − | 0.409647i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.3151 | + | 11.7289i | −0.664373 | + | 0.383576i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.8190i | 0.778134i | 0.921209 | + | 0.389067i | \(0.127203\pi\) | ||||
−0.921209 | + | 0.389067i | \(0.872797\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.1201 | − | 46.9734i | 0.884091 | − | 1.53129i | 0.0373389 | − | 0.999303i | \(-0.488112\pi\) |
0.846752 | − | 0.531988i | \(-0.178555\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.2498 | + | 17.4647i | −0.985069 | + | 0.568730i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.2427 | − | 10.5324i | 0.592807 | − | 0.342257i | −0.173399 | − | 0.984852i | \(-0.555475\pi\) |
0.766207 | + | 0.642594i | \(0.222142\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.2164 | − | 55.8005i | 1.04579 | − | 1.81136i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.50028i | 0.145778i | 0.997340 | + | 0.0728892i | \(0.0232219\pi\) | ||||
−0.997340 | + | 0.0728892i | \(0.976778\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 39.6989 | − | 22.9201i | 1.28462 | − | 0.741679i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.3110 | − | 21.4644i | −0.332961 | − | 0.693122i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.2148 | − | 24.6207i | −0.458541 | − | 0.794216i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −32.0090 | + | 55.4411i | −1.03040 | + | 1.78471i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.8811 | + | 18.8466i | 0.349912 | + | 0.606065i | 0.986233 | − | 0.165359i | \(-0.0528783\pi\) |
−0.636322 | + | 0.771424i | \(0.719545\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.5222 | + | 40.7416i | −0.754862 | + | 1.30746i | 0.190581 | + | 0.981671i | \(0.438963\pi\) |
−0.945443 | + | 0.325788i | \(0.894371\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.66961 | + | 3.90744i | −0.0855838 | + | 0.125267i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.7766 | + | 12.5727i | 0.696695 | + | 0.402237i | 0.806115 | − | 0.591758i | \(-0.201566\pi\) |
−0.109420 | + | 0.993996i | \(0.534899\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −37.7423 | − | 21.7905i | −1.20625 | − | 0.696429i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36.2142 | −1.15505 | −0.577527 | − | 0.816372i | \(-0.695982\pi\) | ||||
−0.577527 | + | 0.816372i | \(0.695982\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 29.3515i | − | 0.935216i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 44.4801 | + | 25.6806i | 1.41438 | + | 0.816595i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.32769 | + | 16.1560i | 0.296304 | + | 0.513213i | 0.975287 | − | 0.220940i | \(-0.0709126\pi\) |
−0.678984 | + | 0.734153i | \(0.737579\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27.1632 | − | 15.6827i | 0.861131 | − | 0.497174i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.4836i | 0.553712i | 0.960911 | + | 0.276856i | \(0.0892925\pi\) | ||||
−0.960911 | + | 0.276856i | \(0.910708\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))