Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,2,Mod(41,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, 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("252.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.x (of order \(6\), degree \(2\), 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: | \(2.01223013094\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 41.2 | ||
Root | \(1.69483 - 0.357142i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.41 |
Dual form | 252.2.x.a.209.2 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.15671 | − | 1.28920i | −0.667826 | − | 0.744317i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.21244 | + | 2.10001i | −0.542220 | + | 0.939152i | 0.456557 | + | 0.889694i | \(0.349083\pi\) |
−0.998776 | + | 0.0494574i | \(0.984251\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.57244 | + | 2.12778i | 0.594326 | + | 0.804224i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.324049 | + | 2.98245i | −0.108016 | + | 0.994149i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.09680 | − | 1.21059i | 0.632209 | − | 0.365006i | −0.149398 | − | 0.988777i | \(-0.547733\pi\) |
0.781607 | + | 0.623771i | \(0.214400\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.73574 | + | 2.73418i | 1.31346 | + | 0.758325i | 0.982667 | − | 0.185380i | \(-0.0593516\pi\) |
0.330790 | + | 0.943704i | \(0.392685\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.10976 | − | 0.866025i | 1.06114 | − | 0.223607i | ||||
\(16\) | 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 | ||||||||
\(21\) | 0.924268 | − | 4.48840i | 0.201692 | − | 0.979449i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.06895 | + | 1.77186i | 0.639920 | + | 0.369458i | 0.784584 | − | 0.620023i | \(-0.212877\pi\) |
−0.144664 | + | 0.989481i | \(0.546210\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.440020 | − | 0.762137i | −0.0880040 | − | 0.152427i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.21979 | − | 3.03206i | 0.812098 | − | 0.583520i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.31784 | + | 3.64761i | −1.17319 | + | 0.677343i | −0.954430 | − | 0.298435i | \(-0.903535\pi\) |
−0.218763 | + | 0.975778i | \(0.570202\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.63732 | + | 2.10001i | 0.653282 | + | 0.377172i | 0.789712 | − | 0.613477i | \(-0.210230\pi\) |
−0.136431 | + | 0.990650i | \(0.543563\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.98607 | − | 1.30289i | −0.693887 | − | 0.226804i | ||||
\(34\) | 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 | ||||||||
\(39\) | −1.95298 | − | 9.26794i | −0.312727 | − | 1.48406i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.03924 | + | 6.99618i | −0.630824 | + | 1.09262i | 0.356560 | + | 0.934273i | \(0.383950\pi\) |
−0.987384 | + | 0.158346i | \(0.949384\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.22573 | − | 7.31918i | −0.644418 | − | 1.11616i | −0.984436 | − | 0.175745i | \(-0.943766\pi\) |
0.340018 | − | 0.940419i | \(-0.389567\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.87027 | − | 4.29654i | −0.875088 | − | 0.640491i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.25769 | + | 3.91043i | 0.329317 | + | 0.570395i | 0.982377 | − | 0.186912i | \(-0.0598480\pi\) |
−0.653059 | + | 0.757307i | \(0.726515\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.05488 | + | 6.69160i | −0.293554 | + | 0.955943i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.98510 | + | 3.32701i | 0.417998 | + | 0.465875i | ||||
\(52\) | 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 | ||||||||
\(57\) | −0.519169 | + | 0.465816i | −0.0687657 | + | 0.0616989i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.0779043 | − | 0.134934i | 0.0101423 | − | 0.0175669i | −0.860910 | − | 0.508758i | \(-0.830105\pi\) |
0.871052 | + | 0.491191i | \(0.163438\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.2288 | − | 5.90561i | 1.30967 | − | 0.756136i | 0.327626 | − | 0.944808i | \(-0.393752\pi\) |
0.982040 | + | 0.188672i | \(0.0604182\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.85553 | + | 4.00021i | −0.863716 | + | 0.503979i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.4836 | + | 6.63005i | −1.42436 | + | 0.822357i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.53682 | − | 4.39390i | 0.309922 | − | 0.536801i | −0.668423 | − | 0.743781i | \(-0.733030\pi\) |
0.978345 | + | 0.206981i | \(0.0663637\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.26561 | − | 6.00600i | −0.152361 | − | 0.723037i | ||||
\(70\) | 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 | ||||||||
\(75\) | −0.473569 | + | 1.44884i | −0.0546830 | + | 0.167298i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.87296 | + | 2.55795i | 0.669285 | + | 0.291506i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.66575 | + | 9.81337i | 0.637447 | + | 1.10409i | 0.985991 | + | 0.166798i | \(0.0533427\pi\) |
−0.348544 | + | 0.937292i | \(0.613324\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.78998 | − | 1.93292i | −0.976665 | − | 0.214769i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.50937 | − | 13.0066i | −0.824260 | − | 1.42766i | −0.902483 | − | 0.430725i | \(-0.858258\pi\) |
0.0782227 | − | 0.996936i | \(-0.475075\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.12893 | − | 5.41946i | 0.339380 | − | 0.587823i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.0104 | + | 3.92571i | 1.28765 | + | 0.420880i | ||||
\(88\) | 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 | ||||||||
\(93\) | −1.50000 | − | 7.11831i | −0.155543 | − | 0.738135i | ||||
\(94\) | 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 | \(-0.760909\pi\) |
0.225569 | + | 0.974227i | \(0.427576\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.93105 | + | 6.64589i | 0.294582 | + | 0.667937i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.83838 | + | 8.38031i | 0.481436 | + | 0.833872i | 0.999773 | − | 0.0213045i | \(-0.00678194\pi\) |
−0.518337 | + | 0.855177i | \(0.673449\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.6863 | − | 9.63382i | −1.64415 | − | 0.949249i | −0.979337 | − | 0.202237i | \(-0.935179\pi\) |
−0.664811 | − | 0.747012i | \(-0.731488\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.30505 | + | 7.38288i | 0.810490 | + | 0.720496i | ||||
\(106\) | 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 | ||||||||
\(111\) | 3.69407 | + | 4.11718i | 0.350626 | + | 0.390785i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.8868 | + | 8.01754i | 1.30636 | + | 0.754227i | 0.981487 | − | 0.191531i | \(-0.0613453\pi\) |
0.324872 | + | 0.945758i | \(0.394679\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.44183 | + | 4.29654i | −0.693954 | + | 0.400655i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.68915 | + | 13.2381i | −0.895763 | + | 1.22386i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.05797 | − | 5.49113i | −0.371994 | − | 0.503371i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.56895 | + | 4.44955i | −0.233541 | + | 0.404505i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.6917 | − | 2.88516i | 1.23454 | − | 0.260146i | ||||
\(124\) | 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 | ||||||||
\(129\) | −4.54791 | + | 13.9140i | −0.400421 | + | 1.22506i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.73151 | − | 9.92727i | 0.500765 | − | 0.867350i | −0.499235 | − | 0.866467i | \(-0.666386\pi\) |
1.00000 | 0.000883062i | \(-0.000281087\pi\) | ||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.856873 | − | 0.633234i | 0.0743003 | − | 0.0549083i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.25111 | + | 12.5378i | 0.107679 | + | 1.07908i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.71002 | − | 0.987278i | 0.146096 | − | 0.0843488i | −0.425170 | − | 0.905114i | \(-0.639786\pi\) |
0.571266 | + | 0.820765i | \(0.306452\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.37804 | − | 3.10501i | −0.456159 | − | 0.263364i | 0.254269 | − | 0.967134i | \(-0.418165\pi\) |
−0.710428 | + | 0.703770i | \(0.751499\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.42982 | − | 7.43383i | 0.204628 | − | 0.626041i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.2399 | 1.10717 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 17.6900i | − | 1.46907i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.0037 | − | 5.09110i | 0.907567 | − | 0.419906i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.5389 | + | 6.08462i | 0.863378 | + | 0.498472i | 0.865142 | − | 0.501527i | \(-0.167228\pi\) |
−0.00176397 | + | 0.999998i | \(0.500561\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.31784 | − | 9.21076i | −0.432759 | − | 0.749561i | 0.564350 | − | 0.825535i | \(-0.309127\pi\) |
−0.997110 | + | 0.0759740i | \(0.975793\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.836270 | − | 7.69677i | 0.0676084 | − | 0.622247i | ||||
\(154\) | 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 | \(-0.378387\pi\) |
−0.617169 | + | 0.786831i | \(0.711720\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.0859 | + | 16.2273i | −1.43431 | + | 1.28691i | ||||
\(160\) | 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 | ||||||||
\(165\) | 7.56895 | − | 6.79111i | 0.589242 | − | 0.528687i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.39779 | − | 14.5454i | 0.649840 | − | 1.12556i | −0.333320 | − | 0.942814i | \(-0.608169\pi\) |
0.983161 | − | 0.182743i | \(-0.0584976\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.45146 | + | 14.6384i | 0.650112 | + | 1.12603i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.20106 | + | 0.130497i | 0.0918470 | + | 0.00997937i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.30850 | + | 14.3907i | 0.631684 | + | 1.09411i | 0.987207 | + | 0.159441i | \(0.0509692\pi\) |
−0.355524 | + | 0.934667i | \(0.615697\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.929754 | − | 2.13468i | 0.0702828 | − | 0.161367i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.264069 | + | 0.0556457i | −0.0198487 | + | 0.00418259i | ||||
\(178\) | 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 | ||||||||
\(183\) | −19.4452 | − | 6.35587i | −1.43743 | − | 0.469839i | ||||
\(184\) | 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 | ||||||||
\(189\) | 13.0869 | + | 4.21104i | 0.951932 | + | 0.306308i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.28998 | − | 4.20887i | 0.527485 | − | 0.304543i | −0.212507 | − | 0.977160i | \(-0.568163\pi\) |
0.739992 | + | 0.672616i | \(0.234829\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.31784 | − | 7.47871i | 0.310805 | − | 0.538330i | −0.667732 | − | 0.744402i | \(-0.732735\pi\) |
0.978537 | + | 0.206072i | \(0.0660681\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 21.8306 | + | 7.13555i | 1.56332 | + | 0.510987i | ||||
\(196\) | 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 | ||||||||
\(201\) | −8.59896 | + | 1.81201i | −0.606524 | + | 0.127809i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.6957 | − | 7.70732i | −1.24199 | − | 0.540948i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.79468 | − | 16.9649i | −0.684090 | − | 1.18488i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.27896 | + | 8.57881i | −0.436418 | + | 0.596268i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.487514 | − | 0.844399i | −0.0337221 | − | 0.0584083i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.75786 | + | 11.7050i | −0.465230 | + | 0.805802i | −0.999212 | − | 0.0396938i | \(-0.987362\pi\) |
0.533982 | + | 0.845496i | \(0.320695\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.2674 | + | 10.1095i | −0.772029 | + | 0.692690i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.4938 | 1.39766 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.25111 | + | 11.0415i | 0.0849310 | + | 0.749548i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.3484 | + | 10.1822i | −0.766857 | + | 0.688050i | ||||
\(220\) | 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 | \(-0.840095\pi\) |
−0.0212411 | + | 0.999774i | \(0.506762\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.41562 | − | 1.06537i | 0.161041 | − | 0.0710245i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.50835 | − | 13.0048i | −0.498347 | − | 0.863162i | 0.501651 | − | 0.865070i | \(-0.332726\pi\) |
−0.999998 | + | 0.00190793i | \(0.999393\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.9685 | − | 9.79677i | −1.12131 | − | 0.647389i | −0.179575 | − | 0.983744i | \(-0.557472\pi\) |
−0.941735 | + | 0.336355i | \(0.890806\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.49560 | − | 10.5302i | −0.229994 | − | 0.692836i | ||||
\(232\) | 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 | ||||||||
\(237\) | 6.09772 | − | 18.6555i | 0.396090 | − | 1.21180i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.36210 | + | 4.25051i | 0.476215 | + | 0.274943i | 0.718838 | − | 0.695178i | \(-0.244674\pi\) |
−0.242623 | + | 0.970121i | \(0.578008\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.21480 | + | 4.16547i | −0.464746 | + | 0.268321i | −0.714038 | − | 0.700107i | \(-0.753136\pi\) |
0.249292 | + | 0.968428i | \(0.419802\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.67554 | + | 13.5678i | 0.492386 | + | 0.870377i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.5610 | − | 12.4284i | −0.738605 | − | 0.794022i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.10108 | − | 1.90712i | 0.0700598 | − | 0.121347i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.08191 | + | 24.7259i | −0.512170 | + | 1.56694i | ||||
\(250\) | 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 | ||||||||
\(255\) | −10.6060 | + | 2.23494i | −0.664174 | + | 0.139957i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.99030 | + | 5.17935i | −0.186530 | + | 0.323079i | −0.944091 | − | 0.329685i | \(-0.893057\pi\) |
0.757561 | + | 0.652764i | \(0.226391\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.02174 | − | 6.79528i | −0.312036 | − | 0.422238i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.83150 | − | 20.0246i | −0.546656 | − | 1.23949i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.91506 | + | 1.68301i | −0.179750 | + | 0.103779i | −0.587175 | − | 0.809460i | \(-0.699760\pi\) |
0.407425 | + | 0.913239i | \(0.366427\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 29.4607 | + | 17.0091i | 1.80976 | + | 1.04486i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.1219 | − | 20.1975i | −1.10904 | − | 1.23607i | ||||
\(268\) | 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 | ||||||||
\(273\) | 16.6492 | − | 18.7288i | 1.00765 | − | 1.13352i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.84527 | − | 1.06537i | −0.111274 | − | 0.0642440i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.60108 | + | 7.96930i | 0.276452 | + | 0.478829i | 0.970500 | − | 0.241100i | \(-0.0775080\pi\) |
−0.694049 | + | 0.719928i | \(0.744175\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.44183 | + | 10.1676i | −0.445531 | + | 0.608719i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.05254 | − | 0.607682i | 0.0627891 | − | 0.0362513i | −0.468277 | − | 0.883582i | \(-0.655125\pi\) |
0.531066 | + | 0.847331i | \(0.321792\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.5776 | + | 6.10696i | 0.628771 | + | 0.363021i | 0.780276 | − | 0.625435i | \(-0.215079\pi\) |
−0.151505 | + | 0.988457i | \(0.548412\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.348755 | − | 1.65503i | −0.0206585 | − | 0.0980357i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.2378 | + | 2.40644i | −1.25363 | + | 0.142048i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.3400 | −0.608238 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.46166 | + | 3.09264i | 0.554652 | + | 0.181294i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.15082 | + | 5.45739i | −0.184073 | + | 0.318824i | −0.943264 | − | 0.332044i | \(-0.892262\pi\) |
0.759191 | + | 0.650868i | \(0.225595\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.188909 | + | 0.327199i | 0.0109987 | + | 0.0190503i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.17748 | − | 11.4661i | 0.300428 | − | 0.665328i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.68915 | + | 16.7821i | 0.560338 | + | 0.970534i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.92889 | − | 20.5004i | 0.514652 | − | 1.18162i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.20727 | − | 15.9312i | 0.299150 | − | 0.915223i | ||||
\(304\) | 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 | ||||||||
\(309\) | 6.88128 | + | 32.6554i | 0.391462 | + | 1.85770i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.86623 | + | 15.3568i | −0.502758 | + | 0.870802i | 0.497237 | + | 0.867615i | \(0.334348\pi\) |
−0.999995 | + | 0.00318766i | \(0.998985\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.4526 | − | 13.5404i | 1.32562 | − | 0.765348i | 0.341003 | − | 0.940062i | \(-0.389233\pi\) |
0.984619 | + | 0.174714i | \(0.0559001\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0885507 | − | 19.2467i | −0.00498926 | − | 1.08443i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.65389 | + | 2.68692i | −0.261388 | + | 0.150913i | −0.624968 | − | 0.780651i | \(-0.714888\pi\) |
0.363579 | + | 0.931563i | \(0.381555\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.83150 | + | 15.2966i | −0.494469 | + | 0.856446i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.40633 | − | 1.26181i | 0.0784940 | − | 0.0704274i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.03926i | 0.0578262i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4.81237i | − | 0.266942i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.67612 | − | 2.98263i | −0.147990 | − | 0.164940i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.77045 | + | 10.9528i | −0.263003 | + | 0.603845i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.72104 | + | 6.44502i | 0.204527 | + | 0.354250i | 0.949982 | − | 0.312305i | \(-0.101101\pi\) |
−0.745455 | + | 0.666556i | \(0.767768\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.03488 | − | 9.52475i | 0.0567113 | − | 0.521953i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.15149 | + | 10.6547i | 0.336092 | + | 0.582128i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.31784 | + | 9.21076i | −0.289681 | + | 0.501742i | −0.973734 | − | 0.227690i | \(-0.926883\pi\) |
0.684053 | + | 0.729433i | \(0.260216\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.72679 | − | 27.1767i | −0.311037 | − | 1.47604i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.1690 | 0.550681 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.4694 | + | 6.14981i | −0.943259 | + | 0.332058i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 14.1471 | + | 4.62412i | 0.761655 | + | 0.248954i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.63842 | − | 0.945944i | −0.0879552 | − | 0.0507809i | 0.455377 | − | 0.890299i | \(-0.349504\pi\) |
−0.543332 | + | 0.839518i | \(0.682838\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.1105 | − | 9.30140i | 0.862375 | − | 0.497892i | −0.00243201 | − | 0.999997i | \(-0.500774\pi\) |
0.864807 | + | 0.502105i | \(0.167441\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 28.2740 | − | 2.82139i | 1.50915 | − | 0.150595i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.94505 | + | 3.36893i | 0.103525 | + | 0.179310i | 0.913134 | − | 0.407659i | \(-0.133655\pi\) |
−0.809610 | + | 0.586968i | \(0.800321\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.3538 | + | 10.5966i | 0.974118 | + | 0.562407i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.38525 | + | 11.5832i | −0.126241 | + | 0.613046i | ||||
\(358\) | 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 | ||||||||
\(363\) | 8.70786 | − | 1.83496i | 0.457044 | − | 0.0963103i | ||||
\(364\) | 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 | \(-0.507926\pi\) |
0.853309 | + | 0.521406i | \(0.174592\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −19.5568 | − | 14.3139i | −1.01809 | − | 0.745154i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 29.8503 | − | 22.0595i | 1.54975 | − | 1.14527i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.84791 | − | 6.66478i | 0.199237 | − | 0.345089i | −0.749044 | − | 0.662520i | \(-0.769487\pi\) |
0.948281 | + | 0.317431i | \(0.102820\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.5560 | + | 12.8796i | 0.596749 | + | 0.665099i | ||||
\(376\) | 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 | ||||||||
\(381\) | 3.54445 | + | 3.95042i | 0.181588 | + | 0.202386i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.70467 | − | 2.95258i | 0.0871047 | − | 0.150870i | −0.819181 | − | 0.573534i | \(-0.805572\pi\) |
0.906286 | + | 0.422665i | \(0.138905\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.4923 | + | 9.23189i | −0.636668 | + | 0.470501i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 23.1984 | − | 10.2312i | 1.17924 | − | 0.520083i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.33425 | − | 4.81178i | 0.422563 | − | 0.243967i | −0.273610 | − | 0.961841i | \(-0.588218\pi\) |
0.696173 | + | 0.717874i | \(0.254884\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.92000 | − | 4.57261i | −0.400532 | − | 0.231247i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.4279 | + | 4.09392i | −0.980007 | + | 0.206511i | ||||
\(394\) | 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 | ||||||||
\(399\) | −1.80752 | − | 0.372210i | −0.0904889 | − | 0.0186338i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.2019 | − | 12.8183i | −1.10871 | − | 0.640113i | −0.170214 | − | 0.985407i | \(-0.554446\pi\) |
−0.938495 | + | 0.345294i | \(0.887779\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.4836 | + | 19.8902i | 0.572038 | + | 0.990799i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.7165 | − | 16.1155i | 0.731267 | − | 0.800785i | ||||
\(406\) | 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 | \(-0.457937\pi\) |
−0.792595 | + | 0.609748i | \(0.791270\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.25078 | − | 1.06255i | −0.160349 | − | 0.0524118i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.409610 | − | 0.0464127i | 0.0201556 | − | 0.00228382i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 36.4186 | 1.78772 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.21786 | + | 10.5249i | 0.108609 | + | 0.515408i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.10643 | + | 12.3087i | −0.347172 | + | 0.601319i | −0.985746 | − | 0.168241i | \(-0.946191\pi\) |
0.638574 | + | 0.769560i | \(0.279525\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.849964 | − | 1.47218i | −0.0414247 | − | 0.0717497i | 0.844570 | − | 0.535446i | \(-0.179856\pi\) |
−0.885994 | + | 0.463696i | \(0.846523\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.3942 | + | 5.46626i | −0.602629 | + | 0.265779i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.13555 | + | 1.96684i | 0.0550825 | + | 0.0954057i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.6500 | + | 12.4784i | 1.38647 | + | 0.603874i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.3147 | − | 17.0688i | −0.739399 | − | 0.824088i | ||||
\(430\) | 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 | ||||||||
\(435\) | −22.8059 | + | 20.4622i | −1.09346 | + | 0.981087i | ||||
\(436\) | 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 | \(-0.599137\pi\) |
0.671142 | + | 0.741329i | \(0.265804\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.2915 | − | 8.29696i | −0.918641 | − | 0.395094i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.3562 | − | 12.3300i | 1.01466 | − | 0.585816i | 0.102109 | − | 0.994773i | \(-0.467441\pi\) |
0.912554 | + | 0.408957i | \(0.134107\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.9950 | + | 32.9004i | −0.900451 | + | 1.55963i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.34614 | − | 20.6248i | −0.205566 | − | 0.975520i | ||||
\(448\) | 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 | ||||||||
\(453\) | −5.72328 | + | 17.5099i | −0.268903 | + | 0.822687i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −32.1645 | − | 14.0092i | −1.50790 | − | 0.656760i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.85935 | − | 6.68460i | −0.180533 | − | 0.312692i | 0.761529 | − | 0.648131i | \(-0.224449\pi\) |
−0.942062 | + | 0.335438i | \(0.891116\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.8900 | + | 7.82480i | −0.508300 | + | 0.365231i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.28621 | − | 16.0842i | −0.432502 | − | 0.749115i | 0.564586 | − | 0.825374i | \(-0.309036\pi\) |
−0.997088 | + | 0.0762589i | \(0.975702\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7046 | − | 30.6653i | 0.822804 | − | 1.42514i | −0.0807828 | − | 0.996732i | \(-0.525742\pi\) |
0.903586 | − | 0.428406i | \(-0.140925\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.7672 | + | 5.48051i | 0.777559 | + | 0.254153i | ||||
\(466\) | 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 | ||||||||
\(471\) | 1.26255 | + | 5.99149i | 0.0581753 | + | 0.276073i | ||||
\(472\) | 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 | ||||||||
\(477\) | 41.8403 | + | 4.54603i | 1.91574 | + | 0.208149i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.2512 | + | 22.9518i | 0.605465 | + | 1.04870i | 0.991978 | + | 0.126412i | \(0.0403461\pi\) |
−0.386513 | + | 0.922284i | \(0.626321\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.1241 | − | 8.73188i | −0.689598 | − | 0.398139i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.7893 | − | 12.1370i | 0.490932 | − | 0.552252i | ||||
\(484\) | 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 | ||||||||
\(489\) | −7.32370 | − | 8.16254i | −0.331189 | − | 0.369123i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.4508 | − | 9.49785i | −0.742413 | − | 0.428632i | 0.0805333 | − | 0.996752i | \(-0.474338\pi\) |
−0.822946 | + | 0.568120i | \(0.807671\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.3044 | − | 9.41333i | 0.734312 | − | 0.423955i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −17.5101 | − | 1.90251i | −0.787022 | − | 0.0855116i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.5965 | − | 13.7429i | 0.834167 | − | 0.616454i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.628929 | + | 1.08934i | −0.0281547 | + | 0.0487654i | −0.879759 | − | 0.475419i | \(-0.842296\pi\) |
0.851605 | + | 0.524184i | \(0.175630\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −28.4657 | + | 5.99840i | −1.27175 | + | 0.267989i | ||||
\(502\) | 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 | ||||||||
\(507\) | 9.09582 | − | 27.8279i | 0.403960 | − | 1.23588i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.90471 | + | 5.03110i | −0.128749 | + | 0.223000i | −0.923192 | − | 0.384339i | \(-0.874429\pi\) |
0.794443 | + | 0.607338i | \(0.207763\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.7303 | − | 13.8418i | 0.828578 | − | 0.612323i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.22104 | − | 1.69934i | −0.0539100 | − | 0.0750278i | ||||
\(514\) | 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 | ||||||||
\(519\) | 8.94197 | − | 27.3572i | 0.392509 | − | 1.20085i | ||||
\(520\) | 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 | ||||||||
\(525\) | −3.82747 | + | 1.27057i | −0.167045 | + | 0.0554521i | ||||
\(526\) | 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 | ||||||||
\(531\) | 0.377189 | + | 0.276071i | 0.0163686 | + | 0.0119805i | ||||
\(532\) | 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 | ||||||||
\(537\) | 18.7691 | − | 16.8402i | 0.809945 | − | 0.726709i | ||||
\(538\) | 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 | ||||||||
\(543\) | 5.18714 | − | 4.65408i | 0.222602 | − | 0.199726i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.80506 | + | 4.85850i | −0.120155 | + | 0.208115i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.31826 | − | 5.74739i | −0.141878 | − | 0.245741i | 0.786326 | − | 0.617812i | \(-0.211981\pi\) |
−0.928204 | + | 0.372072i | \(0.878648\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.2985 | + | 32.4206i | 0.610247 | + | 1.38368i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.46892 | + | 2.54424i | 0.0625781 | + | 0.108388i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.9716 | + | 27.4864i | −0.509085 | + | 1.16884i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.1249 | + | 2.76574i | −0.557123 | + | 0.117399i | ||||
\(556\) | 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 | ||||||||
\(561\) | 10.2868 | + | 3.36235i | 0.434310 | + | 0.141958i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.28555 | + | 10.8869i | −0.264904 | + | 0.458828i | −0.967539 | − | 0.252724i | \(-0.918674\pi\) |
0.702634 | + | 0.711551i | \(0.252007\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33.6738 | + | 19.4416i | −1.41667 | + | 0.817913i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.70889 | − | 21.7425i | −0.407735 | − | 0.913100i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.8872 | + | 7.44043i | −0.540260 | + | 0.311919i | −0.745184 | − | 0.666859i | \(-0.767638\pi\) |
0.204924 | + | 0.978778i | \(0.434305\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.45573 | − | 14.6458i | 0.353861 | − | 0.612906i | −0.633061 | − | 0.774102i | \(-0.718202\pi\) |
0.986922 | + | 0.161196i | \(0.0515351\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.8585 | − | 4.52977i | −0.578945 | − | 0.189234i | ||||
\(574\) | 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 | ||||||||
\(579\) | −14.6360 | + | 3.08416i | −0.608252 | + | 0.128173i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.8672 | − | 36.4304i | 0.658281 | − | 1.51139i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.9832 | − | 29.4157i | −0.703371 | − | 1.21827i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −16.0525 | − | 36.3977i | −0.663691 | − | 1.50486i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.8542 | − | 25.7283i | −0.613100 | − | 1.06192i | −0.990715 | − | 0.135957i | \(-0.956589\pi\) |
0.377615 | − | 0.925963i | \(-0.376744\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.845690 | − | 1.46478i | 0.0348461 | − | 0.0603551i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.0773 | + | 26.9864i | −1.23721 | + | 1.11007i | ||||
\(592\) | 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 | ||||||||
\(597\) | −18.2270 | + | 16.3538i | −0.745980 | + | 0.669318i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.7991 | − | 16.0498i | −1.13584 | − | 0.655778i | −0.190443 | − | 0.981698i | \(-0.560992\pi\) |
−0.945397 | + | 0.325921i | \(0.894326\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.1636 | + | 9.33208i | −0.659329 | + | 0.380664i | −0.792021 | − | 0.610494i | \(-0.790971\pi\) |
0.132692 | + | 0.991157i | \(0.457638\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.2825 | + | 8.98978i | 0.500183 | + | 0.366092i | ||||
\(604\) | 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 | \(-0.242518\pi\) |
−0.236045 | + | 0.971742i | \(0.575851\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.5325 | + | 31.7283i | 0.426800 | + | 1.28570i | ||||
\(610\) | 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 | ||||||||
\(615\) | −10.5415 | + | 32.2507i | −0.425072 | + | 1.30047i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.2904 | + | 8.82792i | 0.615569 | + | 0.355399i | 0.775142 | − | 0.631787i | \(-0.217678\pi\) |
−0.159573 | + | 0.987186i | \(0.551012\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.78789 | − | 2.76429i | 0.192441 | − | 0.111106i | −0.400684 | − | 0.916216i | \(-0.631227\pi\) |
0.593125 | + | 0.805110i | \(0.297894\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.3227 | − | 1.82837i | 0.735264 | − | 0.0733701i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24.6350 | + | 33.3354i | 0.986982 | + | 1.33556i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.3129 | − | 24.7906i | 0.572515 | − | 0.991624i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.524684 | + | 1.60522i | −0.0209538 | + | 0.0641065i | ||||
\(628\) | 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 | ||||||||
\(633\) | 22.9068 | − | 4.82702i | 0.910465 | − | 0.191857i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.71522 | − | 6.43496i | 0.147434 | − | 0.255363i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −28.0274 | + | 26.0712i | −1.11048 | + | 1.03298i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 26.0662 | + | 2.83215i | 1.03116 | + | 0.112038i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.3174 | − | 14.6170i | 0.999978 | − | 0.577337i | 0.0917361 | − | 0.995783i | \(-0.470758\pi\) |
0.908242 | + | 0.418446i | \(0.137425\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.6535 | − | 20.0072i | −1.36660 | − | 0.789008i | −0.376109 | − | 0.926575i | \(-0.622738\pi\) |
−0.990492 | + | 0.137567i | \(0.956072\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −23.7053 | − | 26.4205i | −0.933396 | − | 1.04031i | ||||
\(646\) | 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 | ||||||||
\(651\) | 12.7875 | − | 14.3848i | 0.501183 | − | 0.563784i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.9375 | + | 19.5938i | 1.32808 | + | 0.766766i | 0.985002 | − | 0.172542i | \(-0.0551980\pi\) |
0.343076 | + | 0.939308i | \(0.388531\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.8982 | + | 24.0724i | 0.543049 | + | 0.940588i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 26.2537 | + | 2.85252i | 1.02425 | + | 0.111287i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.8594 | + | 13.1979i | −0.890474 | + | 0.514115i | −0.874098 | − | 0.485751i | \(-0.838546\pi\) |
−0.0163765 | + | 0.999866i | \(0.505213\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.3501 | − | 15.7906i | −1.06380 | − | 0.614184i | −0.137317 | − | 0.990527i | \(-0.543848\pi\) |
−0.926480 | + | 0.376343i | \(0.877181\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.04003 | + | 23.9177i | 0.195738 | + | 0.928885i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.290888 | + | 2.56720i | 0.0112802 | + | 0.0995517i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.8522 | −1.00100 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25.4840 | + | 8.32970i | 0.985269 | + | 0.322045i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.2985 | − | 24.7658i | 0.551989 | − | 0.956073i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.21676 | − | 12.4998i | −0.278186 | − | 0.481832i | 0.692748 | − | 0.721180i | \(-0.256400\pi\) |
−0.970934 | + | 0.239348i | \(0.923066\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.16764 | − | 1.88189i | −0.160412 | − | 0.0724340i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.2099 | − | 29.8084i | −0.661430 | − | 1.14563i | −0.980240 | − | 0.197812i | \(-0.936616\pi\) |
0.318809 | − | 0.947819i | \(-0.396717\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.9405 | − | 6.07175i | −0.534988 | − | 0.233013i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.08081 | + | 24.7226i | −0.309657 | + | 0.947370i | ||||
\(682\) | 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 | ||||||||
\(687\) | 6.99767 | + | 33.2077i | 0.266978 | + | 1.26695i | ||||
\(688\) | 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 | \(-0.786807\pi\) |
0.145646 | + | 0.989337i | \(0.453474\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.53208 | + | 16.6869i | −0.362094 | + | 0.633882i | ||||
\(694\) | 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 | ||||||||
\(699\) | −25.2001 | + | 22.6103i | −0.953154 | + | 0.855201i | ||||
\(700\) | 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 | ||||||||
\(705\) | 12.6651 | + | 14.1157i | 0.476995 | + | 0.531628i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.2234 | + | 23.4725i | −0.384490 | + | 0.882775i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.4119 | + | 35.3544i | 0.766585 | + | 1.32776i | 0.939405 | + | 0.342810i | \(0.111379\pi\) |
−0.172820 | + | 0.984953i | \(0.555288\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −31.1038 | + | 13.7178i | −1.16648 | + | 0.514457i | ||||
\(712\) | 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 | ||||||||
\(717\) | −3.03607 | − | 14.4078i | −0.113384 | − | 0.538069i | ||||
\(718\) | 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 | ||||||||
\(723\) | 13.7155 | + | 4.48306i | 0.510086 | + | 0.166727i | ||||
\(724\) | 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 | \(-0.635348\pi\) |
0.582653 | + | 0.812721i | \(0.302015\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.61321 | − | 25.5893i | 0.319008 | − | 0.947752i | ||||
\(730\) | 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 | \(-0.221407\pi\) |
−0.171125 | + | 0.985249i | \(0.554740\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.64995 | + | 29.2804i | −0.0977449 | + | 1.08002i | ||||
\(736\) | 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 | ||||||||
\(741\) | −3.73227 | + | 0.786480i | −0.137108 | + | 0.0288921i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.5831 | + | 11.8837i | 0.755122 | + | 0.435970i | 0.827542 | − | 0.561404i | \(-0.189739\pi\) |
−0.0724196 | + | 0.997374i | \(0.523072\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25.5555 | + | 14.7545i | −0.936281 | + | 0.540562i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 41.2249 | − | 18.1815i | 1.50834 | − | 0.665227i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.32111 | + | 1.71531i | −0.0848116 | + | 0.0626762i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.06151 | + | 15.6950i | −0.330659 | + | 0.572718i | −0.982641 | − | 0.185516i | \(-0.940604\pi\) |
0.651982 | + | 0.758234i | \(0.273938\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.7038 | + | 17.5025i | 0.572279 | + | 0.637826i | ||||
\(754\) | 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 | ||||||||
\(759\) | −9.92453 | − | 11.0613i | −0.360237 | − | 0.401498i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.90537 | − | 10.2284i | 0.214070 | − | 0.370779i | −0.738915 | − | 0.673799i | \(-0.764661\pi\) |
0.952984 | + | 0.303020i | \(0.0979948\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.63793 | + | 4.92275i | 0.131702 | + | 0.178215i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.1493 | + | 11.0880i | 0.547725 | + | 0.400889i | ||||
\(766\) | 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 | \(-0.354158\pi\) |
−0.555549 | + | 0.831484i | \(0.687492\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.1361 | − | 2.13592i | 0.365043 | − | 0.0769233i | ||||
\(772\) | 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 | ||||||||
\(777\) | −2.95174 | + | 14.3342i | −0.105893 | + | 0.514235i | ||||
\(778\) | 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 | ||||||||
\(783\) | −15.6002 | + | 34.5482i | −0.557505 | + | 1.23465i | ||||
\(784\) | 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 | \(-0.215358\pi\) |
−0.152372 | + | 0.988323i | \(0.548691\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.54160 | + | 1.81133i | 0.197286 | + | 0.0644850i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.77657 | + | 42.1551i | 0.169835 | + | 1.49886i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 64.5880 | 2.29359 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.1493 | − | 57.6552i | −0.430893 | − | 2.04482i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.8973 | + | 29.2669i | −0.598532 | + | 1.03669i | 0.394506 | + | 0.918893i | \(0.370916\pi\) |
−0.993038 | + | 0.117795i | \(0.962418\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.82639 | − | 10.0916i | −0.206123 | − | 0.357015i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.07681 | + | 46.7254i | −0.179380 | + | 1.65096i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.6565 | − | 18.4576i | −0.376060 | − | 0.651354i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.8439 | − | 9.07851i | −0.734651 | − | 0.319976i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.2070 | − | 15.8342i | −0.500109 | − | 0.557391i | ||||
\(808\) | 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 | ||||||||
\(813\) | −37.9338 | + | 34.0355i | −1.33040 | + | 1.19368i | ||||
\(814\) | 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 | ||||||||
\(819\) | −43.4033 | + | 0.199691i | −1.51663 | + | 0.00697777i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.6931 | + | 15.4113i | −0.931595 | + | 0.537857i | −0.887316 | − | 0.461163i | \(-0.847432\pi\) |
−0.0442792 | + | 0.999019i | \(0.514099\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.94249 | − | 13.7568i | 0.276858 | − | 0.479532i | −0.693744 | − | 0.720221i | \(-0.744040\pi\) |
0.970602 | + | 0.240690i | \(0.0773736\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.760974 | + | 3.61123i | 0.0264937 | + | 0.125727i | ||||
\(826\) | 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 | ||||||||
\(831\) | 4.95188 | − | 15.1498i | 0.171779 | − | 0.525542i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.30299 | − | 17.2689i | 0.183738 | − | 0.598333i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.3636 | + | 35.2708i | 0.704712 | + | 1.22060i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.7161 | − | 2.16699i | 0.750617 | − | 0.0749021i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.9689 | + | 36.3192i | 0.723926 | + | 1.25388i | 0.959414 | + | 0.282000i | \(0.0909978\pi\) |
−0.235488 | + | 0.971877i | \(0.575669\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.1100 | − | 20.9752i | 0.417588 | − | 0.723283i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.00090 | − | 0.654014i | −0.0689146 | − | 0.0225254i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −40.9875 | −1.41001 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.5072 | + | 1.53049i | −0.464112 | + | 0.0525883i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.36210 | − | 20.7005i | −0.149707 | − | 0.710441i | ||||
\(850\) | 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 | \(-0.586974\pi\) |
0.698973 | + | 0.715149i | \(0.253641\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.73025 | + | 2.36401i | −0.0591734 | + | 0.0808473i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.7329 | − | 41.1065i | −0.810699 | − | 1.40417i | −0.912375 | − | 0.409355i | \(-0.865754\pi\) |
0.101676 | − | 0.994818i | \(-0.467579\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.20316 | + | 3.00405i | 0.177530 | + | 0.102497i | 0.586131 | − | 0.810216i | \(-0.300650\pi\) |
−0.408602 | + | 0.912713i | \(0.633984\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.6683 | + | 24.5961i | 0.942933 | + | 0.838232i | ||||
\(862\) | 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 | ||||||||
\(867\) | 11.9604 | + | 13.3303i | 0.406197 | + | 0.452722i | ||||
\(868\) | 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 | ||||||||
\(873\) | −6.95737 | − | 15.7752i | −0.235471 | − | 0.533910i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.7093 | − | 21.2574i | −0.531071 | − | 0.718630i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.6882 | + | 35.8330i | −0.698591 | + | 1.21000i | 0.270364 | + | 0.962758i | \(0.412856\pi\) |
−0.968955 | + | 0.247237i | \(0.920477\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.6802 | − | 2.25058i | 0.360235 | − | 0.0759102i | ||||
\(880\) | 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 | ||||||||
\(885\) | 0.203311 | − | 0.622014i | 0.00683424 | − | 0.0209088i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.0561 | + | 24.3459i | −0.471958 | + | 0.817456i | −0.999485 | − | 0.0320827i | \(-0.989786\pi\) |
0.527527 | + | 0.849538i | \(0.323119\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.81835 | − | 6.52005i | −0.161602 | − | 0.218676i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.7708 | + | 6.58811i | −0.695849 | + | 0.220710i | ||||
\(892\) | 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 | ||||||||
\(897\) | 10.4279 | − | 31.9032i | 0.348177 | − | 1.06522i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.6400 | −1.02190 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.2041i | 1.20613i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −36.7571 | + | 12.2019i | −1.22320 | + | 0.406053i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.44949 | − | 4.87831i | −0.280870 | − | 0.162161i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.7430 | − | 51.5163i | −0.987599 | − | 1.71057i | −0.629763 | − | 0.776788i | \(-0.716848\pi\) |
−0.357836 | − | 0.933784i | \(-0.616485\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −26.5617 | + | 11.7146i | −0.880996 | + | 0.388548i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.4502 | − | 14.6937i | 0.843204 | − | 0.486824i | −0.0151480 | − | 0.999885i | \(-0.504822\pi\) |
0.858352 | + | 0.513061i | \(0.171489\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.4913 | − | 18.1815i | −1.04221 | − | 0.601721i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 36.9236 | − | 33.1291i | 1.22066 | − | 1.09521i | ||||
\(916\) | 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 | ||||||||
\(921\) | 37.0339 | − | 33.2280i | 1.22031 | − | 1.09490i | ||||
\(922\) | 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 | ||||||||
\(927\) | 34.1395 | − | 46.6441i | 1.12129 | − | 1.53199i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.21614 | + | 2.10641i | 0.0399002 | + | 0.0691092i | 0.885286 | − | 0.465047i | \(-0.153963\pi\) |
−0.845386 | + | 0.534156i | \(0.820629\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.69476 | + | 0.827515i | 0.0883172 | + | 0.0271207i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 30.0535 | − | 6.33300i | 0.983908 | − | 0.207333i | ||||
\(934\) | 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 | ||||||||
\(939\) | −44.5841 | − | 14.5728i | −1.45495 | − | 0.475564i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.2367 | + | 36.7831i | −0.692298 | + | 1.19910i | 0.278785 | + | 0.960354i | \(0.410068\pi\) |
−0.971083 | + | 0.238742i | \(0.923265\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.7925 | + | 14.3139i | −0.807354 | + | 0.466126i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −24.7103 | + | 22.3770i | −0.803826 | + | 0.727923i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −47.3119 | + | 27.3155i | −1.53743 | + | 0.887636i | −0.538443 | + | 0.842662i | \(0.680987\pi\) |
−0.998988 | + | 0.0449739i | \(0.985680\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0683 | − | 41.6874i | 0.781288 | − | 1.35323i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.84717 | + | 2.89178i | 0.286889 | + | 0.0937725i | ||||
\(952\) | 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 | ||||||||
\(957\) | 29.9358 | − | 6.30819i | 0.967687 | − | 0.203915i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.78960 | + | 2.08610i | 0.154664 | + | 0.0673637i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.67994 | − | 11.5700i | −0.215482 | − | 0.373226i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.25344 | − | 0.353493i | −0.104841 | − | 0.0113912i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.4702 | + | 18.1350i | 0.337049 | + | 0.583786i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.1546 | + | 19.3203i | −0.358706 | + | 0.621298i | −0.987745 | − | 0.156076i | \(-0.950115\pi\) |
0.629039 | + | 0.777374i | \(0.283449\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.33981 | − | 1.20213i | 0.0430410 | − | 0.0386179i | ||||
\(970\) | 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 | ||||||||
\(975\) | −6.20409 | + | 5.56652i | −0.198690 | + | 0.178271i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35.6936 | − | 20.6077i | −1.14194 | − | 0.659299i | −0.195029 | − | 0.980797i | \(-0.562480\pi\) |
−0.946910 | + | 0.321498i | \(0.895814\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.8501 | − | 18.9660i | 1.04989 | − | 0.606157i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.749708 | + | 6.90008i | −0.0239363 | + | 0.220303i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.21969 | − | 15.9690i | −0.294062 | − | 0.509331i | 0.680704 | − | 0.732559i | \(-0.261674\pi\) |
−0.974766 | + | 0.223228i | \(0.928341\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48.9938 | + | 28.2866i | 1.56107 | + | 0.901285i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 19.6383 | − | 6.51912i | 0.625093 | − | 0.207506i | ||||
\(988\) | 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 | ||||||||
\(993\) | 4.00474 | − | 12.2522i | 0.127087 | − | 0.388810i | ||||
\(994\) | 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 | \(-0.664271\pi\) |
0.506504 | + | 0.862237i | \(0.330937\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.4763 | + | 9.68320i | −0.426372 | + | 0.306363i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))