Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(125,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.125");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.x (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: | \(6.03669039281\) |
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: | \( x^{16} - 3x^{14} - 9x^{12} - 9x^{10} + 225x^{8} - 81x^{6} - 729x^{4} - 2187x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
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 | 629.2 | ||
Root | \(-1.69483 - 0.357142i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.629 |
Dual form | 756.2.x.a.125.2 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.21244 | − | 2.10001i | −0.542220 | − | 0.939152i | −0.998776 | − | 0.0494574i | \(-0.984251\pi\) |
0.456557 | − | 0.889694i | \(-0.349083\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.05649 | − | 2.42566i | 0.399316 | − | 0.916813i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.09680 | − | 1.21059i | −0.632209 | − | 0.365006i | 0.149398 | − | 0.988777i | \(-0.452267\pi\) |
−0.781607 | + | 0.623771i | \(0.785600\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.73574 | + | 2.73418i | −1.31346 | + | 0.758325i | −0.982667 | − | 0.185380i | \(-0.940648\pi\) |
−0.330790 | + | 0.943704i | \(0.607315\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.58069 | −0.625909 | −0.312954 | − | 0.949768i | \(-0.601319\pi\) | ||||
−0.312954 | + | 0.949768i | \(0.601319\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.402708i | − | 0.0923876i | −0.998932 | − | 0.0461938i | \(-0.985291\pi\) | ||
0.998932 | − | 0.0461938i | \(-0.0147092\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.06895 | + | 1.77186i | −0.639920 | + | 0.369458i | −0.784584 | − | 0.620023i | \(-0.787123\pi\) |
0.144664 | + | 0.989481i | \(0.453790\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.440020 | + | 0.762137i | −0.0880040 | + | 0.152427i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.31784 | + | 3.64761i | 1.17319 | + | 0.677343i | 0.954430 | − | 0.298435i | \(-0.0964645\pi\) |
0.218763 | + | 0.975778i | \(0.429798\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.63732 | + | 2.10001i | −0.653282 | + | 0.377172i | −0.789712 | − | 0.613477i | \(-0.789770\pi\) |
0.136431 | + | 0.990650i | \(0.456437\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.37484 | + | 0.722330i | −1.07754 | + | 0.122096i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.19360 | −0.525025 | −0.262513 | − | 0.964929i | \(-0.584551\pi\) | ||||
−0.262513 | + | 0.964929i | \(0.584551\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.03924 | − | 6.99618i | −0.630824 | − | 1.09262i | −0.987384 | − | 0.158346i | \(-0.949384\pi\) |
0.356560 | − | 0.934273i | \(-0.383950\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.22573 | + | 7.31918i | −0.644418 | + | 1.11616i | 0.340018 | + | 0.940419i | \(0.389567\pi\) |
−0.984436 | + | 0.175745i | \(0.943766\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.25769 | − | 3.91043i | 0.329317 | − | 0.570395i | −0.653059 | − | 0.757307i | \(-0.726515\pi\) |
0.982377 | + | 0.186912i | \(0.0598480\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.76766 | − | 5.12537i | −0.681094 | − | 0.732196i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 14.0288i | − | 1.92701i | −0.267690 | − | 0.963505i | \(-0.586260\pi\) | ||
0.267690 | − | 0.963505i | \(-0.413740\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.87106i | 0.791654i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.0779043 | + | 0.134934i | 0.0101423 | + | 0.0175669i | 0.871052 | − | 0.491191i | \(-0.163438\pi\) |
−0.860910 | + | 0.508758i | \(0.830105\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.2288 | − | 5.90561i | −1.30967 | − | 0.756136i | −0.327626 | − | 0.944808i | \(-0.606248\pi\) |
−0.982040 | + | 0.188672i | \(0.939582\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.4836 | + | 6.63005i | 1.42436 | + | 0.822357i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.53682 | + | 4.39390i | 0.309922 | + | 0.536801i | 0.978345 | − | 0.206981i | \(-0.0663637\pi\) |
−0.668423 | + | 0.743781i | \(0.733030\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.73987i | − | 1.03723i | −0.855007 | − | 0.518616i | \(-0.826448\pi\) | ||
0.855007 | − | 0.518616i | \(-0.173552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.80274i | − | 1.03028i | −0.857105 | − | 0.515141i | \(-0.827739\pi\) | ||
0.857105 | − | 0.515141i | \(-0.172261\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.15173 | + | 3.80715i | −0.587094 | + | 0.433865i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.66575 | − | 9.81337i | 0.637447 | − | 1.10409i | −0.348544 | − | 0.937292i | \(-0.613324\pi\) |
0.985991 | − | 0.166798i | \(-0.0533427\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.50937 | + | 13.0066i | −0.824260 | + | 1.42766i | 0.0782227 | + | 0.996936i | \(0.475075\pi\) |
−0.902483 | + | 0.430725i | \(0.858258\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.12893 | + | 5.41946i | 0.339380 | + | 0.587823i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.6668 | 1.66068 | 0.830338 | − | 0.557260i | \(-0.188148\pi\) | ||||
0.830338 | + | 0.557260i | \(0.188148\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.62893 | + | 14.3759i | 0.170758 | + | 1.50701i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.845690 | + | 0.488259i | −0.0867660 | + | 0.0500944i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.97713 | + | 2.87355i | 0.505351 | + | 0.291765i | 0.730921 | − | 0.682462i | \(-0.239091\pi\) |
−0.225569 | + | 0.974227i | \(0.572424\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.83838 | − | 8.38031i | 0.481436 | − | 0.833872i | −0.518337 | − | 0.855177i | \(-0.673449\pi\) |
0.999773 | + | 0.0213045i | \(0.00678194\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.6863 | − | 9.63382i | 1.64415 | − | 0.949249i | 0.664811 | − | 0.747012i | \(-0.268512\pi\) |
0.979337 | − | 0.202237i | \(-0.0648212\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.09086i | 0.105458i | 0.998609 | + | 0.0527288i | \(0.0167919\pi\) | ||||
−0.998609 | + | 0.0527288i | \(0.983208\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.31356 | 0.221599 | 0.110800 | − | 0.993843i | \(-0.464659\pi\) | ||||
0.110800 | + | 0.993843i | \(0.464659\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.8868 | + | 8.01754i | −1.30636 | + | 0.754227i | −0.981487 | − | 0.191531i | \(-0.938655\pi\) |
−0.324872 | + | 0.945758i | \(0.605321\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.44183 | + | 4.29654i | 0.693954 | + | 0.400655i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.72647 | + | 6.25987i | −0.249935 | + | 0.573842i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.56895 | − | 4.44955i | −0.233541 | − | 0.404505i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.99041 | −0.893569 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.06425 | −0.271909 | −0.135954 | − | 0.990715i | \(-0.543410\pi\) | ||||
−0.135954 | + | 0.990715i | \(0.543410\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.73151 | + | 9.92727i | 0.500765 | + | 0.867350i | 1.00000 | 0.000883062i | \(0.000281087\pi\) | |
−0.499235 | + | 0.866467i | \(0.666386\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.976833 | − | 0.425457i | −0.0847022 | − | 0.0368918i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.71002 | − | 0.987278i | −0.146096 | − | 0.0843488i | 0.425170 | − | 0.905114i | \(-0.360214\pi\) |
−0.571266 | + | 0.820765i | \(0.693548\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.37804 | − | 3.10501i | 0.456159 | − | 0.263364i | −0.254269 | − | 0.967134i | \(-0.581835\pi\) |
0.710428 | + | 0.703770i | \(0.248501\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.2399 | 1.10717 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 17.6900i | − | 1.46907i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.5389 | + | 6.08462i | −0.863378 | + | 0.498472i | −0.865142 | − | 0.501527i | \(-0.832772\pi\) |
0.00176397 | + | 0.999998i | \(0.499439\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.31784 | + | 9.21076i | −0.432759 | + | 0.749561i | −0.997110 | − | 0.0759740i | \(-0.975793\pi\) |
0.564350 | + | 0.825535i | \(0.309127\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.82006 | + | 5.09226i | 0.708444 | + | 0.409021i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.06154 | − | 1.76758i | 0.244337 | − | 0.141068i | −0.372831 | − | 0.927899i | \(-0.621613\pi\) |
0.617169 | + | 0.786831i | \(0.288280\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.05561 | + | 9.31618i | 0.0831939 | + | 0.734218i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.33150 | 0.495921 | 0.247961 | − | 0.968770i | \(-0.420240\pi\) | ||||
0.247961 | + | 0.968770i | \(0.420240\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.39779 | + | 14.5454i | 0.649840 | + | 1.12556i | 0.983161 | + | 0.182743i | \(0.0584976\pi\) |
−0.333320 | + | 0.942814i | \(0.608169\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.45146 | − | 14.6384i | 0.650112 | − | 1.12603i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.30850 | − | 14.3907i | 0.631684 | − | 1.09411i | −0.355524 | − | 0.934667i | \(-0.615697\pi\) |
0.987207 | − | 0.159441i | \(-0.0509692\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.38381 | + | 1.87253i | 0.104606 | + | 0.141550i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.5587i | 1.08817i | 0.839030 | + | 0.544086i | \(0.183123\pi\) | ||||
−0.839030 | + | 0.544086i | \(0.816877\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.02355i | 0.299068i | 0.988757 | + | 0.149534i | \(0.0477774\pi\) | ||||
−0.988757 | + | 0.149534i | \(0.952223\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.87205 | + | 6.70659i | 0.284679 | + | 0.493078i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.41119 | + | 3.12415i | 0.395705 | + | 0.228461i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.28998 | − | 4.20887i | −0.527485 | − | 0.304543i | 0.212507 | − | 0.977160i | \(-0.431837\pi\) |
−0.739992 | + | 0.672616i | \(0.765171\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.31784 | + | 7.47871i | 0.310805 | + | 0.538330i | 0.978537 | − | 0.206072i | \(-0.0660681\pi\) |
−0.667732 | + | 0.744402i | \(0.732735\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 23.3303i | − | 1.66221i | −0.556112 | − | 0.831107i | \(-0.687708\pi\) | ||
0.556112 | − | 0.831107i | \(-0.312292\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 14.1383i | − | 1.00223i | −0.865379 | − | 0.501117i | \(-0.832923\pi\) | ||
0.865379 | − | 0.501117i | \(-0.167077\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.5226 | − | 11.4713i | 1.08947 | − | 0.805125i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.79468 | + | 16.9649i | −0.684090 | + | 1.18488i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.487514 | + | 0.844399i | −0.0337221 | + | 0.0584083i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.75786 | − | 11.7050i | −0.465230 | − | 0.805802i | 0.533982 | − | 0.845496i | \(-0.320695\pi\) |
−0.999212 | + | 0.0396938i | \(0.987362\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.4938 | 1.39766 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.25111 | + | 11.0415i | 0.0849310 | + | 0.749548i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.2215 | − | 7.05606i | 0.822104 | − | 0.474642i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.4054 | + | 7.73961i | 0.897692 | + | 0.518283i | 0.876451 | − | 0.481492i | \(-0.159905\pi\) |
0.0212411 | + | 0.999774i | \(0.493238\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.50835 | + | 13.0048i | −0.498347 | + | 0.863162i | −0.999998 | − | 0.00190793i | \(-0.999393\pi\) |
0.501651 | + | 0.865070i | \(0.332726\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.9685 | − | 9.79677i | 1.12131 | − | 0.647389i | 0.179575 | − | 0.983744i | \(-0.442528\pi\) |
0.941735 | + | 0.336355i | \(0.109194\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 19.5471i | − | 1.28057i | −0.768136 | − | 0.640287i | \(-0.778815\pi\) | ||
0.768136 | − | 0.640287i | \(-0.221185\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.9492 | −0.714249 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.36210 | + | 4.25051i | −0.476215 | + | 0.274943i | −0.718838 | − | 0.695178i | \(-0.755326\pi\) |
0.242623 | + | 0.970121i | \(0.421992\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.21480 | + | 4.16547i | 0.464746 | + | 0.268321i | 0.714038 | − | 0.700107i | \(-0.246864\pi\) |
−0.249292 | + | 0.968428i | \(0.580198\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.98283 | + | 16.2263i | −0.318341 | + | 1.03666i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.10108 | + | 1.90712i | 0.0700598 | + | 0.121347i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.5763 | −0.856928 | −0.428464 | − | 0.903559i | \(-0.640945\pi\) | ||||
−0.428464 | + | 0.903559i | \(0.640945\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.57997 | 0.539418 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.99030 | − | 5.17935i | −0.186530 | − | 0.323079i | 0.757561 | − | 0.652764i | \(-0.226391\pi\) |
−0.944091 | + | 0.329685i | \(0.893057\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.37401 | + | 7.74660i | −0.209651 | + | 0.481350i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.91506 | + | 1.68301i | 0.179750 | + | 0.103779i | 0.587175 | − | 0.809460i | \(-0.300240\pi\) |
−0.407425 | + | 0.913239i | \(0.633573\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −29.4607 | + | 17.0091i | −1.80976 | + | 1.04486i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.2822 | 0.748862 | 0.374431 | − | 0.927255i | \(-0.377838\pi\) | ||||
0.374431 | + | 0.927255i | \(0.377838\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 29.4244i | − | 1.78741i | −0.448659 | − | 0.893703i | \(-0.648098\pi\) | ||
0.448659 | − | 0.893703i | \(-0.351902\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.84527 | − | 1.06537i | 0.111274 | − | 0.0642440i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.60108 | − | 7.96930i | 0.276452 | − | 0.478829i | −0.694049 | − | 0.719928i | \(-0.744175\pi\) |
0.970500 | + | 0.241100i | \(0.0775080\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.05254 | − | 0.607682i | −0.0627891 | − | 0.0362513i | 0.468277 | − | 0.883582i | \(-0.344875\pi\) |
−0.531066 | + | 0.847331i | \(0.678208\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.5776 | + | 6.10696i | −0.628771 | + | 0.363021i | −0.780276 | − | 0.625435i | \(-0.784921\pi\) |
0.151505 | + | 0.988457i | \(0.451588\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.2378 | + | 2.40644i | −1.25363 | + | 0.142048i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.3400 | −0.608238 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.15082 | − | 5.45739i | −0.184073 | − | 0.318824i | 0.759191 | − | 0.650868i | \(-0.225595\pi\) |
−0.943264 | + | 0.332044i | \(0.892262\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.188909 | − | 0.327199i | 0.0109987 | − | 0.0190503i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.68915 | − | 16.7821i | 0.560338 | − | 0.970534i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.2894 | + | 17.9828i | 0.765988 | + | 1.03651i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 28.6408i | 1.63997i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.7264i | 1.63950i | 0.572721 | + | 0.819750i | \(0.305888\pi\) | ||||
−0.572721 | + | 0.819750i | \(0.694112\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.86623 | − | 15.3568i | −0.502758 | − | 0.870802i | −0.999995 | − | 0.00318766i | \(-0.998985\pi\) |
0.497237 | − | 0.867615i | \(-0.334348\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.4526 | − | 13.5404i | −1.32562 | − | 0.765348i | −0.341003 | − | 0.940062i | \(-0.610767\pi\) |
−0.984619 | + | 0.174714i | \(0.944100\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.65389 | + | 2.68692i | 0.261388 | + | 0.150913i | 0.624968 | − | 0.780651i | \(-0.285112\pi\) |
−0.363579 | + | 0.931563i | \(0.618445\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.83150 | − | 15.2966i | −0.494469 | − | 0.856446i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.03926i | 0.0578262i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4.81237i | − | 0.266942i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.10015 | − | 9.60771i | −0.391444 | − | 0.529690i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.72104 | − | 6.44502i | 0.204527 | − | 0.354250i | −0.745455 | − | 0.666556i | \(-0.767768\pi\) |
0.949982 | + | 0.312305i | \(0.101101\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.15149 | − | 10.6547i | 0.336092 | − | 0.582128i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.31784 | − | 9.21076i | −0.289681 | − | 0.501742i | 0.684053 | − | 0.729433i | \(-0.260216\pi\) |
−0.973734 | + | 0.227690i | \(0.926883\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.1690 | 0.550681 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.4694 | + | 6.14981i | −0.943259 | + | 0.332058i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.63842 | − | 0.945944i | 0.0879552 | − | 0.0507809i | −0.455377 | − | 0.890299i | \(-0.650496\pi\) |
0.543332 | + | 0.839518i | \(0.317162\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.1105 | − | 9.30140i | −0.862375 | − | 0.497892i | 0.00243201 | − | 0.999997i | \(-0.499226\pi\) |
−0.864807 | + | 0.502105i | \(0.832559\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.94505 | − | 3.36893i | 0.103525 | − | 0.179310i | −0.809610 | − | 0.586968i | \(-0.800321\pi\) |
0.913134 | + | 0.407659i | \(0.133655\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.3538 | + | 10.5966i | −0.974118 | + | 0.562407i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.62553i | 0.455238i | 0.973750 | + | 0.227619i | \(0.0730940\pi\) | ||||
−0.973750 | + | 0.227619i | \(0.926906\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.8378 | 0.991465 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.4858 | + | 10.6728i | −0.967592 | + | 0.558639i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.8701 | − | 9.16260i | −0.828412 | − | 0.478284i | 0.0248966 | − | 0.999690i | \(-0.492074\pi\) |
−0.853309 | + | 0.521406i | \(0.825408\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −34.0292 | − | 14.8213i | −1.76671 | − | 0.769486i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.84791 | + | 6.66478i | 0.199237 | + | 0.345089i | 0.948281 | − | 0.317431i | \(-0.102820\pi\) |
−0.749044 | + | 0.662520i | \(0.769487\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −39.8928 | −2.05458 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.52510 | −0.386539 | −0.193269 | − | 0.981146i | \(-0.561909\pi\) | ||||
−0.193269 | + | 0.981146i | \(0.561909\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.70467 | + | 2.95258i | 0.0871047 | + | 0.150870i | 0.906286 | − | 0.422665i | \(-0.138905\pi\) |
−0.819181 | + | 0.573534i | \(0.805572\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.2412 | + | 6.20272i | 0.725799 | + | 0.316120i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.33425 | − | 4.81178i | −0.422563 | − | 0.243967i | 0.273610 | − | 0.961841i | \(-0.411782\pi\) |
−0.696173 | + | 0.717874i | \(0.745116\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.92000 | − | 4.57261i | 0.400532 | − | 0.231247i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −27.4775 | −1.38254 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.4807i | 1.17846i | 0.807964 | + | 0.589232i | \(0.200570\pi\) | ||||
−0.807964 | + | 0.589232i | \(0.799430\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.2019 | − | 12.8183i | 1.10871 | − | 0.640113i | 0.170214 | − | 0.985407i | \(-0.445554\pi\) |
0.938495 | + | 0.345294i | \(0.112221\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.4836 | − | 19.8902i | 0.572038 | − | 0.990799i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.69635 | + | 3.86614i | 0.331926 | + | 0.191637i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.3646 | − | 7.71603i | 0.660835 | − | 0.381533i | −0.131760 | − | 0.991282i | \(-0.542063\pi\) |
0.792595 | + | 0.609748i | \(0.208730\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.409610 | − | 0.0464127i | 0.0201556 | − | 0.00228382i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 36.4186 | 1.78772 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.10643 | − | 12.3087i | −0.347172 | − | 0.601319i | 0.638574 | − | 0.769560i | \(-0.279525\pi\) |
−0.985746 | + | 0.168241i | \(0.946191\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.849964 | + | 1.47218i | −0.0414247 | + | 0.0717497i | −0.885994 | − | 0.463696i | \(-0.846523\pi\) |
0.844570 | + | 0.535446i | \(0.179856\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.13555 | − | 1.96684i | 0.0550825 | − | 0.0954057i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −25.1317 | + | 18.5724i | −1.21621 | + | 0.898782i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.6628i | 1.57331i | 0.617392 | + | 0.786656i | \(0.288189\pi\) | ||||
−0.617392 | + | 0.786656i | \(0.711811\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.6919i | 0.657992i | 0.944331 | + | 0.328996i | \(0.106710\pi\) | ||||
−0.944331 | + | 0.328996i | \(0.893290\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.713542 | + | 1.23589i | 0.0341333 | + | 0.0591207i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.64139 | − | 4.41176i | −0.364704 | − | 0.210562i | 0.306438 | − | 0.951890i | \(-0.400863\pi\) |
−0.671142 | + | 0.741329i | \(0.734196\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.3562 | − | 12.3300i | −1.01466 | − | 0.585816i | −0.102109 | − | 0.994773i | \(-0.532559\pi\) |
−0.912554 | + | 0.408957i | \(0.865893\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.9950 | − | 32.9004i | −0.900451 | − | 1.55963i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.61306i | 0.217704i | 0.994058 | + | 0.108852i | \(0.0347174\pi\) | ||||
−0.994058 | + | 0.108852i | \(0.965283\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.5595i | 0.921019i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 28.2146 | − | 20.8507i | 1.32272 | − | 0.977496i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.85935 | + | 6.68460i | −0.180533 | + | 0.312692i | −0.942062 | − | 0.335438i | \(-0.891116\pi\) |
0.761529 | + | 0.648131i | \(0.224449\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.28621 | + | 16.0842i | −0.432502 | + | 0.749115i | −0.997088 | − | 0.0762589i | \(-0.975702\pi\) |
0.564586 | + | 0.825374i | \(0.309036\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7046 | + | 30.6653i | 0.822804 | + | 1.42514i | 0.903586 | + | 0.428406i | \(0.140925\pi\) |
−0.0807828 | + | 0.996732i | \(0.525742\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.8433 | −0.733141 | −0.366571 | − | 0.930390i | \(-0.619468\pi\) | ||||
−0.366571 | + | 0.930390i | \(0.619468\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.3382 | − | 1.51135i | 0.615903 | − | 0.0697877i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.7210 | − | 10.2312i | 0.814814 | − | 0.470433i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.306919 | + | 0.177200i | 0.0140824 | + | 0.00813048i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.2512 | − | 22.9518i | 0.605465 | − | 1.04870i | −0.386513 | − | 0.922284i | \(-0.626321\pi\) |
0.991978 | − | 0.126412i | \(-0.0403461\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.1241 | − | 8.73188i | 0.689598 | − | 0.398139i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 13.9360i | − | 0.632802i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.00939 | −0.317626 | −0.158813 | − | 0.987309i | \(-0.550767\pi\) | ||||
−0.158813 | + | 0.987309i | \(0.550767\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.4508 | − | 9.49785i | 0.742413 | − | 0.428632i | −0.0805333 | − | 0.996752i | \(-0.525662\pi\) |
0.822946 | + | 0.568120i | \(0.192329\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.3044 | − | 9.41333i | −0.734312 | − | 0.423955i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −21.2000 | − | 9.23359i | −0.950948 | − | 0.414183i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.628929 | − | 1.08934i | −0.0281547 | − | 0.0487654i | 0.851605 | − | 0.524184i | \(-0.175630\pi\) |
−0.879759 | + | 0.475419i | \(0.842296\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.9507 | 1.69214 | 0.846070 | − | 0.533072i | \(-0.178963\pi\) | ||||
0.846070 | + | 0.533072i | \(0.178963\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.4650 | −1.04418 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.90471 | − | 5.03110i | −0.128749 | − | 0.223000i | 0.794443 | − | 0.607338i | \(-0.207763\pi\) |
−0.923192 | + | 0.384339i | \(0.874429\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.3524 | − | 9.30001i | −0.944577 | − | 0.411408i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −40.4622 | − | 23.3609i | −1.78298 | − | 1.02940i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.46784 | + | 5.46626i | −0.416395 | + | 0.240406i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.6999 | 0.600203 | 0.300102 | − | 0.953907i | \(-0.402979\pi\) | ||||
0.300102 | + | 0.953907i | \(0.402979\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 24.4881i | − | 1.07079i | −0.844602 | − | 0.535394i | \(-0.820163\pi\) | ||
0.844602 | − | 0.535394i | \(-0.179837\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.38679 | − | 5.41946i | 0.408895 | − | 0.236076i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.22104 | + | 9.04310i | −0.227002 | + | 0.393178i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 38.2576 | + | 22.0880i | 1.65712 | + | 0.956739i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.29082 | − | 1.32261i | 0.0990408 | − | 0.0571812i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.79211 | + | 16.5186i | 0.163338 | + | 0.711505i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.1608 | −1.59767 | −0.798833 | − | 0.601552i | \(-0.794549\pi\) | ||||
−0.798833 | + | 0.601552i | \(0.794549\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.80506 | − | 4.85850i | −0.120155 | − | 0.208115i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.31826 | + | 5.74739i | −0.141878 | + | 0.245741i | −0.928204 | − | 0.372072i | \(-0.878648\pi\) |
0.786326 | + | 0.617812i | \(0.211981\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.46892 | − | 2.54424i | 0.0625781 | − | 0.108388i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.8181 | − | 24.1109i | −0.757702 | − | 1.02530i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.6188i | 1.04313i | 0.853211 | + | 0.521565i | \(0.174652\pi\) | ||||
−0.853211 | + | 0.521565i | \(0.825348\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 46.2156i | − | 1.95471i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.28555 | − | 10.8869i | −0.264904 | − | 0.458828i | 0.702634 | − | 0.711551i | \(-0.252007\pi\) |
−0.967539 | + | 0.252724i | \(0.918674\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.6738 | + | 19.4416i | 1.41667 | + | 0.817913i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.8872 | + | 7.44043i | 0.540260 | + | 0.311919i | 0.745184 | − | 0.666859i | \(-0.232362\pi\) |
−0.204924 | + | 0.978778i | \(0.565695\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.45573 | + | 14.6458i | 0.353861 | + | 0.612906i | 0.986922 | − | 0.161196i | \(-0.0515351\pi\) |
−0.633061 | + | 0.774102i | \(0.718202\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 3.11861i | − | 0.130055i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.9013i | 0.870133i | 0.900398 | + | 0.435067i | \(0.143275\pi\) | ||||
−0.900398 | + | 0.435067i | \(0.856725\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23.6160 | + | 31.9565i | 0.979759 | + | 1.32578i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.9832 | + | 29.4157i | −0.703371 | + | 1.21827i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.8542 | + | 25.7283i | −0.613100 | + | 1.06192i | 0.377615 | + | 0.925963i | \(0.376744\pi\) |
−0.990715 | + | 0.135957i | \(0.956589\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.845690 | + | 1.46478i | 0.0348461 | + | 0.0603551i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.7921 | −0.484241 | −0.242121 | − | 0.970246i | \(-0.577843\pi\) | ||||
−0.242121 | + | 0.970246i | \(0.577843\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.4515 | − | 1.86411i | 0.674444 | − | 0.0764210i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.7991 | − | 16.0498i | 1.13584 | − | 0.655778i | 0.190443 | − | 0.981698i | \(-0.439008\pi\) |
0.945397 | + | 0.325921i | \(0.105674\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.1636 | + | 9.33208i | 0.659329 | + | 0.380664i | 0.792021 | − | 0.610494i | \(-0.209029\pi\) |
−0.132692 | + | 0.991157i | \(0.542362\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.22939 | + | 10.7896i | −0.253261 | + | 0.438661i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.0104 | + | 6.93419i | −0.487486 | + | 0.281450i | −0.723531 | − | 0.690292i | \(-0.757482\pi\) |
0.236045 | + | 0.971742i | \(0.424149\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.6917i | 0.998918i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.9021 | −0.844227 | −0.422114 | − | 0.906543i | \(-0.638712\pi\) | ||||
−0.422114 | + | 0.906543i | \(0.638712\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.2904 | + | 8.82792i | −0.615569 | + | 0.355399i | −0.775142 | − | 0.631787i | \(-0.782322\pi\) |
0.159573 | + | 0.987186i | \(0.448988\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.78789 | − | 2.76429i | −0.192441 | − | 0.111106i | 0.400684 | − | 0.916216i | \(-0.368773\pi\) |
−0.593125 | + | 0.805110i | \(0.702106\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.5518 | − | 38.0023i | 0.663134 | − | 1.52253i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.3129 | + | 24.7906i | 0.572515 | + | 0.991624i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.24169 | 0.328618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.3544 | 0.969533 | 0.484766 | − | 0.874644i | \(-0.338905\pi\) | ||||
0.484766 | + | 0.874644i | \(0.338905\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.71522 | + | 6.43496i | 0.147434 | + | 0.255363i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 36.5920 | + | 11.2368i | 1.44983 | + | 0.445218i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.3174 | − | 14.6170i | −0.999978 | − | 0.577337i | −0.0917361 | − | 0.995783i | \(-0.529242\pi\) |
−0.908242 | + | 0.418446i | \(0.862575\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.6535 | − | 20.0072i | 1.36660 | − | 0.789008i | 0.376109 | − | 0.926575i | \(-0.377262\pi\) |
0.990492 | + | 0.137567i | \(0.0439284\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.56553 | −0.297432 | −0.148716 | − | 0.988880i | \(-0.547514\pi\) | ||||
−0.148716 | + | 0.988880i | \(0.547514\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 0.377240i | − | 0.0148080i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −33.9375 | + | 19.5938i | −1.32808 | + | 0.766766i | −0.985002 | − | 0.172542i | \(-0.944802\pi\) |
−0.343076 | + | 0.939308i | \(0.611469\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.8982 | − | 24.0724i | 0.543049 | − | 0.940588i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.8594 | + | 13.1979i | 0.890474 | + | 0.514115i | 0.874098 | − | 0.485751i | \(-0.161454\pi\) |
0.0163765 | + | 0.999866i | \(0.494787\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.3501 | − | 15.7906i | 1.06380 | − | 0.614184i | 0.137317 | − | 0.990527i | \(-0.456152\pi\) |
0.926480 | + | 0.376343i | \(0.122819\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.290888 | + | 2.56720i | 0.0112802 | + | 0.0995517i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.8522 | −1.00100 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.2985 | + | 24.7658i | 0.551989 | + | 0.956073i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.21676 | + | 12.4998i | −0.278186 | + | 0.481832i | −0.970934 | − | 0.239348i | \(-0.923066\pi\) |
0.692748 | + | 0.721180i | \(0.256400\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.2099 | + | 29.8084i | −0.661430 | + | 1.14563i | 0.318809 | + | 0.947819i | \(0.396717\pi\) |
−0.980240 | + | 0.197812i | \(0.936616\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.2285 | − | 9.03696i | 0.469289 | − | 0.346807i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 19.0172i | − | 0.727674i | −0.931463 | − | 0.363837i | \(-0.881467\pi\) | ||
0.931463 | − | 0.363837i | \(-0.118533\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.78806i | 0.182942i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 38.3574 | + | 66.4369i | 1.46130 | + | 2.53104i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.7795 | + | 9.68764i | 0.638321 | + | 0.368535i | 0.783968 | − | 0.620802i | \(-0.213193\pi\) |
−0.145646 | + | 0.989337i | \(0.546526\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.0411 | − | 7.52928i | −0.494677 | − | 0.285602i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.4240 | + | 18.0549i | 0.394838 | + | 0.683880i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 23.0297i | − | 0.869819i | −0.900474 | − | 0.434910i | \(-0.856780\pi\) | ||
0.900474 | − | 0.434910i | \(-0.143220\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.28609i | 0.0485058i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.2161 | − | 20.5900i | −0.572260 | − | 0.774366i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.4119 | − | 35.3544i | 0.766585 | − | 1.32776i | −0.172820 | − | 0.984953i | \(-0.555288\pi\) |
0.939405 | − | 0.342810i | \(-0.111379\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.44183 | − | 12.8896i | 0.278699 | − | 0.482720i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.0525 | − | 27.8038i | −0.600331 | − | 1.03980i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 42.3156 | 1.57811 | 0.789054 | − | 0.614324i | \(-0.210571\pi\) | ||||
0.789054 | + | 0.614324i | \(0.210571\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.73950 | − | 50.6533i | −0.213750 | − | 1.88643i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.55995 | + | 3.21004i | −0.206491 | + | 0.119218i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.58754 | − | 2.64862i | −0.170142 | − | 0.0982318i | 0.412511 | − | 0.910953i | \(-0.364652\pi\) |
−0.582653 | + | 0.812721i | \(0.697985\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.9053 | − | 18.8885i | 0.403347 | − | 0.698617i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.1513 | + | 9.32497i | −0.596563 | + | 0.344426i | −0.767688 | − | 0.640824i | \(-0.778593\pi\) |
0.171125 | + | 0.985249i | \(0.445260\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 12.2842i | − | 0.452494i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 41.1837 | 1.51497 | 0.757483 | − | 0.652855i | \(-0.226429\pi\) | ||||
0.757483 | + | 0.652855i | \(0.226429\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.5831 | + | 11.8837i | −0.755122 | + | 0.435970i | −0.827542 | − | 0.561404i | \(-0.810261\pi\) |
0.0724196 | + | 0.997374i | \(0.476928\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.5555 | + | 14.7545i | 0.936281 | + | 0.540562i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.64606 | + | 1.15249i | 0.0966850 | + | 0.0421109i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.06151 | − | 15.6950i | −0.330659 | − | 0.572718i | 0.651982 | − | 0.758234i | \(-0.273938\pi\) |
−0.982641 | + | 0.185516i | \(0.940604\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.7902 | 0.938603 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.1059 | 1.34864 | 0.674319 | − | 0.738440i | \(-0.264437\pi\) | ||||
0.674319 | + | 0.738440i | \(0.264437\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.90537 | + | 10.2284i | 0.214070 | + | 0.370779i | 0.952984 | − | 0.303020i | \(-0.0979948\pi\) |
−0.738915 | + | 0.673799i | \(0.764661\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.44426 | − | 5.61192i | 0.0884880 | − | 0.203165i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.737868 | − | 0.426009i | −0.0266429 | − | 0.0153823i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.14015 | − | 1.81297i | 0.113237 | − | 0.0653773i | −0.442312 | − | 0.896861i | \(-0.645842\pi\) |
0.555549 | + | 0.831484i | \(0.312508\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.1111 | 0.435605 | 0.217802 | − | 0.975993i | \(-0.430111\pi\) | ||||
0.217802 | + | 0.975993i | \(0.430111\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.69618i | − | 0.132771i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.81742 | + | 1.62664i | −0.100944 | + | 0.0582803i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.5804 | + | 18.3258i | −0.378596 | + | 0.655748i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.42386 | − | 4.28617i | −0.264969 | − | 0.152980i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.5995 | + | 10.1611i | −0.627354 | + | 0.362203i | −0.779727 | − | 0.626120i | \(-0.784642\pi\) |
0.152372 | + | 0.988323i | \(0.451309\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.77657 | + | 42.1551i | 0.169835 | + | 1.49886i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 64.5880 | 2.29359 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.8973 | − | 29.2669i | −0.598532 | − | 1.03669i | −0.993038 | − | 0.117795i | \(-0.962418\pi\) |
0.394506 | − | 0.918893i | \(-0.370916\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.82639 | + | 10.0916i | −0.206123 | + | 0.357015i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.6565 | + | 18.4576i | −0.376060 | + | 0.651354i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.2842 | − | 13.5121i | 0.644433 | − | 0.476239i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 4.84175i | − | 0.170227i | −0.996371 | − | 0.0851134i | \(-0.972875\pi\) | ||
0.996371 | − | 0.0851134i | \(-0.0271253\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.493486i | 0.0173286i | 0.999962 | + | 0.00866432i | \(0.00275797\pi\) | ||||
−0.999962 | + | 0.00866432i | \(0.997242\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.67656 | − | 13.2962i | −0.268898 | − | 0.465745i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.94749 | + | 1.70174i | 0.103120 | + | 0.0595362i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.6931 | + | 15.4113i | 0.931595 | + | 0.537857i | 0.887316 | − | 0.461163i | \(-0.152568\pi\) |
0.0442792 | + | 0.999019i | \(0.485901\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.94249 | + | 13.7568i | 0.276858 | + | 0.479532i | 0.970602 | − | 0.240690i | \(-0.0773736\pi\) |
−0.693744 | + | 0.720221i | \(0.744040\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 35.6756i | − | 1.24056i | −0.784379 | − | 0.620282i | \(-0.787018\pi\) | ||
0.784379 | − | 0.620282i | \(-0.212982\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 3.32551i | − | 0.115500i | −0.998331 | − | 0.0577498i | \(-0.981607\pi\) | ||
0.998331 | − | 0.0577498i | \(-0.0183926\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.3038 | + | 13.2270i | 0.426303 | + | 0.458288i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.3636 | − | 35.2708i | 0.704712 | − | 1.22060i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.9689 | − | 36.3192i | 0.723926 | − | 1.25388i | −0.235488 | − | 0.971877i | \(-0.575669\pi\) |
0.959414 | − | 0.282000i | \(-0.0909978\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.1100 | + | 20.9752i | 0.417588 | + | 0.723283i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −40.9875 | −1.41001 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.5072 | + | 1.53049i | −0.464112 | + | 0.0525883i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.80100 | − | 5.65861i | 0.335974 | − | 0.193975i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.5330 | − | 7.23594i | −0.429122 | − | 0.247754i | 0.269851 | − | 0.962902i | \(-0.413026\pi\) |
−0.698973 | + | 0.715149i | \(0.746359\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.7329 | + | 41.1065i | −0.810699 | + | 1.40417i | 0.101676 | + | 0.994818i | \(0.467579\pi\) |
−0.912375 | + | 0.409355i | \(0.865754\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.20316 | + | 3.00405i | −0.177530 | + | 0.102497i | −0.586131 | − | 0.810216i | \(-0.699350\pi\) |
0.408602 | + | 0.912713i | \(0.366016\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.2998i | 1.06546i | 0.846286 | + | 0.532729i | \(0.178834\pi\) | ||||
−0.846286 | + | 0.532729i | \(0.821166\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −40.2942 | −1.37004 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.7599 | + | 13.7178i | −0.806000 | + | 0.465344i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.0274 | − | 13.8722i | −0.814139 | − | 0.470043i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.5548 | + | 24.2333i | −0.356816 | + | 0.819236i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.6882 | − | 35.8330i | −0.698591 | − | 1.21000i | −0.968955 | − | 0.247237i | \(-0.920477\pi\) |
0.270364 | − | 0.962758i | \(-0.412856\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.7350 | 1.33870 | 0.669352 | − | 0.742945i | \(-0.266572\pi\) | ||||
0.669352 | + | 0.742945i | \(0.266572\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.1324 | −1.61978 | −0.809892 | − | 0.586579i | \(-0.800474\pi\) | ||||
−0.809892 | + | 0.586579i | \(0.800474\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.0561 | − | 24.3459i | −0.471958 | − | 0.817456i | 0.527527 | − | 0.849538i | \(-0.323119\pi\) |
−0.999485 | + | 0.0320827i | \(0.989786\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.23735 | + | 7.43284i | −0.108577 | + | 0.249289i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.57476 | − | 0.909189i | −0.0526974 | − | 0.0304248i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.5735 | − | 17.6516i | 1.02196 | − | 0.590028i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.6400 | −1.02190 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.2041i | 1.20613i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.44949 | − | 4.87831i | 0.280870 | − | 0.162161i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.7430 | + | 51.5163i | −0.987599 | + | 1.71057i | −0.357836 | + | 0.933784i | \(0.616485\pi\) |
−0.629763 | + | 0.776788i | \(0.716848\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.4502 | − | 14.6937i | −0.843204 | − | 0.486824i | 0.0151480 | − | 0.999885i | \(-0.495178\pi\) |
−0.858352 | + | 0.513061i | \(0.828511\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.4913 | − | 18.1815i | 1.04221 | − | 0.601721i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 30.1355 | − | 3.41464i | 0.995161 | − | 0.112761i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.5987 | −1.37222 | −0.686108 | − | 0.727500i | \(-0.740682\pi\) | ||||
−0.686108 | + | 0.727500i | \(0.740682\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 23.8964 | + | 41.3897i | 0.786558 | + | 1.36236i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.40525 | − | 2.43396i | 0.0462043 | − | 0.0800282i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.21614 | − | 2.10641i | 0.0399002 | − | 0.0691092i | −0.845386 | − | 0.534156i | \(-0.820629\pi\) |
0.885286 | + | 0.465047i | \(0.153963\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.06403 | + | 1.91997i | −0.0676458 | + | 0.0629246i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 15.1514i | − | 0.495503i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.29837i | 0.238427i | 0.992869 | + | 0.119214i | \(0.0380374\pi\) | ||||
−0.992869 | + | 0.119214i | \(0.961963\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.2367 | − | 36.7831i | −0.692298 | − | 1.19910i | −0.971083 | − | 0.238742i | \(-0.923265\pi\) |
0.278785 | − | 0.960354i | \(-0.410068\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.7925 | + | 14.3139i | 0.807354 | + | 0.466126i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.3119 | + | 27.3155i | 1.53743 | + | 0.887636i | 0.998988 | + | 0.0449739i | \(0.0143205\pi\) |
0.538443 | + | 0.842662i | \(0.319013\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0683 | + | 41.6874i | 0.781288 | + | 1.35323i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 17.1877i | − | 0.556764i | −0.960470 | − | 0.278382i | \(-0.910202\pi\) | ||
0.960470 | − | 0.278382i | \(-0.0897981\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.4120i | 0.660518i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.20142 | + | 3.10487i | −0.135671 | + | 0.100261i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.67994 | + | 11.5700i | −0.215482 | + | 0.373226i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.4702 | − | 18.1350i | 0.337049 | − | 0.583786i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.1546 | − | 19.3203i | −0.358706 | − | 0.621298i | 0.629039 | − | 0.777374i | \(-0.283449\pi\) |
−0.987745 | + | 0.156076i | \(0.950115\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −54.2481 | −1.74091 | −0.870453 | − | 0.492252i | \(-0.836174\pi\) | ||||
−0.870453 | + | 0.492252i | \(0.836174\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.84986 | − | 16.3257i | −0.0593037 | − | 0.523378i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 35.6936 | − | 20.6077i | 1.14194 | − | 0.659299i | 0.195029 | − | 0.980797i | \(-0.437520\pi\) |
0.946910 | + | 0.321498i | \(0.104186\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.8501 | − | 18.9660i | −1.04989 | − | 0.606157i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.21969 | + | 15.9690i | −0.294062 | + | 0.509331i | −0.974766 | − | 0.223228i | \(-0.928341\pi\) |
0.680704 | + | 0.732559i | \(0.261674\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −48.9938 | + | 28.2866i | −1.56107 | + | 0.901285i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 29.9496i | − | 0.952341i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.72231 | −0.118243 | −0.0591216 | − | 0.998251i | \(-0.518830\pi\) | ||||
−0.0591216 | + | 0.998251i | \(0.518830\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29.6904 | + | 17.1418i | −0.941250 | + | 0.543431i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.411648 | − | 0.237665i | −0.0130370 | − | 0.00752693i | 0.493467 | − | 0.869764i | \(-0.335729\pi\) |
−0.506504 | + | 0.862237i | \(0.669063\pi\) | |||||||
\(998\) | 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 \(a_p\))