Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(509,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.509");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.w (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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1109.6 | ||
Root | \(1.68042 - 0.419752i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1109 |
Dual form | 1764.2.w.b.509.6 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.36511 | + | 1.06606i | 0.788145 | + | 0.615490i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.48494 | − | 2.57199i | 0.664085 | − | 1.15023i | −0.315447 | − | 0.948943i | \(-0.602155\pi\) |
0.979532 | − | 0.201286i | \(-0.0645121\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.727031 | + | 2.91057i | 0.242344 | + | 0.970190i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.09466 | + | 2.36406i | −1.23459 | + | 0.712790i | −0.967983 | − | 0.251016i | \(-0.919235\pi\) |
−0.266605 | + | 0.963806i | \(0.585902\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.54045 | − | 2.04408i | 0.981945 | − | 0.566926i | 0.0790880 | − | 0.996868i | \(-0.474799\pi\) |
0.902857 | + | 0.429942i | \(0.141466\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.76900 | − | 1.92801i | 1.23135 | − | 0.497809i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.835278 | − | 1.44674i | 0.202585 | − | 0.350887i | −0.746776 | − | 0.665076i | \(-0.768399\pi\) |
0.949360 | + | 0.314189i | \(0.101733\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.25377 | − | 2.45592i | 0.975882 | − | 0.563426i | 0.0748577 | − | 0.997194i | \(-0.476150\pi\) |
0.901024 | + | 0.433768i | \(0.142816\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.25297 | + | 2.45545i | 0.886805 | + | 0.511997i | 0.872896 | − | 0.487906i | \(-0.162239\pi\) |
0.0139086 | + | 0.999903i | \(0.495573\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.91009 | − | 3.30837i | −0.382018 | − | 0.661675i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.11037 | + | 4.74830i | −0.406141 | + | 0.913811i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.238557 | + | 0.137731i | 0.0442989 | + | 0.0255760i | 0.521986 | − | 0.852954i | \(-0.325191\pi\) |
−0.477687 | + | 0.878530i | \(0.658525\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.60327i | 0.287956i | 0.989581 | + | 0.143978i | \(0.0459895\pi\) | ||||
−0.989581 | + | 0.143978i | \(0.954011\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.10988 | − | 1.13797i | −1.41175 | − | 0.198095i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.69681 | − | 2.93896i | −0.278954 | − | 0.483162i | 0.692171 | − | 0.721733i | \(-0.256654\pi\) |
−0.971125 | + | 0.238571i | \(0.923321\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.01221 | + | 0.983947i | 1.12285 | + | 0.157558i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.55632 | + | 6.15972i | 0.555404 | + | 0.961987i | 0.997872 | + | 0.0652031i | \(0.0207695\pi\) |
−0.442468 | + | 0.896784i | \(0.645897\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.22930 | − | 9.05742i | 0.797461 | − | 1.38124i | −0.123804 | − | 0.992307i | \(-0.539509\pi\) |
0.921265 | − | 0.388936i | \(-0.127157\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.56556 | + | 2.45211i | 1.27688 | + | 0.365538i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.9977 | 1.60418 | 0.802090 | − | 0.597203i | \(-0.203721\pi\) | ||||
0.802090 | + | 0.597203i | \(0.203721\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.68256 | − | 1.08450i | 0.375633 | − | 0.151861i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.707381 | + | 0.408407i | 0.0971663 | + | 0.0560990i | 0.547796 | − | 0.836612i | \(-0.315467\pi\) |
−0.450629 | + | 0.892711i | \(0.648800\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.0419i | 1.89341i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.42500 | + | 1.18219i | 1.11592 | + | 0.156585i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.74856 | −0.357832 | −0.178916 | − | 0.983864i | \(-0.557259\pi\) | ||||
−0.178916 | + | 0.983864i | \(0.557259\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 7.20310i | − | 0.922262i | −0.887332 | − | 0.461131i | \(-0.847444\pi\) | ||
0.887332 | − | 0.461131i | \(-0.152556\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 12.1413i | − | 1.50595i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.6103 | 1.41842 | 0.709210 | − | 0.704998i | \(-0.249052\pi\) | ||||
0.709210 | + | 0.704998i | \(0.249052\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.18809 | + | 7.88587i | 0.383801 | + | 0.949347i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.4406i | 1.23907i | 0.784968 | + | 0.619537i | \(0.212680\pi\) | ||||
−0.784968 | + | 0.619537i | \(0.787320\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.6493 | − | 7.88042i | −1.59753 | − | 0.922334i | −0.991962 | − | 0.126539i | \(-0.959613\pi\) |
−0.605567 | − | 0.795794i | \(-0.707054\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.919449 | − | 6.55255i | 0.106169 | − | 0.756624i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.3033 | −1.38422 | −0.692112 | − | 0.721790i | \(-0.743320\pi\) | ||||
−0.692112 | + | 0.721790i | \(0.743320\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.94285 | + | 4.23215i | −0.882539 | + | 0.470239i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.03981 | − | 6.99715i | 0.443426 | − | 0.768037i | −0.554515 | − | 0.832174i | \(-0.687096\pi\) |
0.997941 | + | 0.0641368i | \(0.0204294\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.48067 | − | 4.29665i | −0.269067 | − | 0.466037i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.178826 | + | 0.442333i | 0.0191722 | + | 0.0474231i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.60872 | − | 7.98254i | −0.488523 | − | 0.846147i | 0.511390 | − | 0.859349i | \(-0.329131\pi\) |
−0.999913 | + | 0.0132019i | \(0.995798\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.70919 | + | 2.18864i | −0.177234 | + | 0.226951i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 14.5875i | − | 1.49665i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.00772 | − | 4.04591i | −0.711527 | − | 0.410800i | 0.100099 | − | 0.994977i | \(-0.468084\pi\) |
−0.811626 | + | 0.584177i | \(0.801417\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.85770 | − | 10.1991i | −0.990736 | − | 1.02505i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.65365 | + | 6.32831i | 0.363552 | + | 0.629690i | 0.988543 | − | 0.150942i | \(-0.0482307\pi\) |
−0.624991 | + | 0.780632i | \(0.714897\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.08409 | + | 3.51265i | 0.599483 | + | 0.346112i | 0.768838 | − | 0.639443i | \(-0.220835\pi\) |
−0.169355 | + | 0.985555i | \(0.554168\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.2618 | + | 7.07938i | −1.18540 | + | 0.684389i | −0.957257 | − | 0.289239i | \(-0.906598\pi\) |
−0.228140 | + | 0.973628i | \(0.573265\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.82203 | + | 4.88789i | −0.270301 | + | 0.468175i | −0.968939 | − | 0.247300i | \(-0.920457\pi\) |
0.698638 | + | 0.715476i | \(0.253790\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.816783 | − | 5.82089i | 0.0775256 | − | 0.552495i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.6411 | − | 6.72099i | 1.09510 | − | 0.632258i | 0.160172 | − | 0.987089i | \(-0.448795\pi\) |
0.934930 | + | 0.354831i | \(0.115462\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.6308 | − | 7.29239i | 1.17783 | − | 0.680019i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.52346 | + | 8.81863i | 0.787994 | + | 0.815282i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.67752 | − | 9.83375i | 0.516138 | − | 0.893977i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.71188 | + | 12.1999i | −0.154355 | + | 1.10003i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.50392 | 0.313400 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.7730 | −1.13342 | −0.566712 | − | 0.823916i | \(-0.691785\pi\) | ||||
−0.566712 | + | 0.823916i | \(0.691785\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.7943 | − | 6.78959i | 1.47866 | − | 0.597790i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.70890 | + | 11.6202i | −0.586159 | + | 1.01526i | 0.408570 | + | 0.912727i | \(0.366027\pi\) |
−0.994730 | + | 0.102531i | \(0.967306\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.07881 | + | 12.4788i | 0.781379 | + | 1.07400i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.79449 | + | 4.50015i | −0.665928 | + | 0.384474i | −0.794532 | − | 0.607222i | \(-0.792284\pi\) |
0.128604 | + | 0.991696i | \(0.458950\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.54902 | + | 0.894326i | −0.131386 | + | 0.0758557i | −0.564252 | − | 0.825602i | \(-0.690836\pi\) |
0.432866 | + | 0.901458i | \(0.357502\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.0130 | + | 11.7242i | 1.26433 | + | 0.987357i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.66464 | + | 16.7397i | −0.808198 | + | 1.39984i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.708485 | − | 0.409044i | 0.0588365 | − | 0.0339693i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.1779 | − | 6.45358i | −0.915732 | − | 0.528698i | −0.0334609 | − | 0.999440i | \(-0.510653\pi\) |
−0.882271 | + | 0.470742i | \(0.843986\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.48364 | + | 11.2300i | 0.527631 | + | 0.913884i | 0.999481 | + | 0.0322054i | \(0.0102531\pi\) |
−0.471850 | + | 0.881679i | \(0.656414\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.81812 | + | 1.37931i | 0.389522 | + | 0.111510i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.12360 | + | 2.38076i | 0.331216 | + | 0.191227i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 17.1728i | − | 1.37054i | −0.728291 | − | 0.685268i | \(-0.759685\pi\) | ||
0.728291 | − | 0.685268i | \(-0.240315\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.530265 | + | 1.31163i | 0.0420527 | + | 0.104019i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.53107 | + | 4.38394i | 0.198249 | + | 0.343377i | 0.947961 | − | 0.318387i | \(-0.103141\pi\) |
−0.749712 | + | 0.661764i | \(0.769808\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.9695 | + | 19.1687i | −1.16538 | + | 1.49228i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.79673 | + | 10.0402i | 0.448564 | + | 0.776936i | 0.998293 | − | 0.0584072i | \(-0.0186022\pi\) |
−0.549729 | + | 0.835343i | \(0.685269\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.85653 | − | 3.21561i | 0.142810 | − | 0.247354i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.2407 | + | 10.5954i | 0.783129 | + | 0.810249i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.26691 | −0.476464 | −0.238232 | − | 0.971208i | \(-0.576568\pi\) | ||||
−0.238232 | + | 0.971208i | \(0.576568\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.75207 | − | 2.93013i | −0.282023 | − | 0.220242i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.7668 | − | 7.37089i | −0.954233 | − | 0.550927i | −0.0598395 | − | 0.998208i | \(-0.519059\pi\) |
−0.894393 | + | 0.447281i | \(0.852392\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.0833642i | − | 0.00619641i | −0.999995 | − | 0.00309821i | \(-0.999014\pi\) | ||
0.999995 | − | 0.00309821i | \(-0.000986191\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.67894 | − | 9.83300i | 0.567643 | − | 0.726876i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.0786 | −0.740996 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.89857i | 0.577601i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.4351i | 1.11684i | 0.829558 | + | 0.558421i | \(0.188593\pi\) | ||||
−0.829558 | + | 0.558421i | \(0.811407\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.5557 | 1.55162 | 0.775808 | − | 0.630969i | \(-0.217343\pi\) | ||||
0.775808 | + | 0.630969i | \(0.217343\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.9434 | − | 16.5742i | 0.926896 | − | 1.18691i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.88306i | 0.704139i | 0.935974 | + | 0.352069i | \(0.114522\pi\) | ||||
−0.935974 | + | 0.352069i | \(0.885478\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.14623 | + | 5.28058i | 0.648359 | + | 0.374330i | 0.787827 | − | 0.615896i | \(-0.211206\pi\) |
−0.139468 | + | 0.990227i | \(0.544539\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.8492 | + | 12.3772i | 1.11792 | + | 0.873023i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.1237 | 1.47534 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.05473 | + | 14.1637i | −0.281823 | + | 0.984449i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.6118 | + | 20.1123i | −0.803208 | + | 1.39120i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.08453 | + | 10.5387i | 0.418876 | + | 0.725514i | 0.995827 | − | 0.0912645i | \(-0.0290909\pi\) |
−0.576951 | + | 0.816779i | \(0.695758\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.1303 | + | 14.2526i | −0.762638 | + | 0.976569i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.5304 | − | 26.8994i | −1.05916 | − | 1.83453i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.2317 | − | 25.3086i | −0.691396 | − | 1.71020i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 6.82950i | − | 0.459402i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.714485 | − | 0.412508i | −0.0478455 | − | 0.0276236i | 0.475886 | − | 0.879507i | \(-0.342127\pi\) |
−0.523732 | + | 0.851883i | \(0.675461\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.24056 | − | 7.96475i | 0.549371 | − | 0.530983i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.166778 | − | 0.288869i | −0.0110695 | − | 0.0191729i | 0.860438 | − | 0.509556i | \(-0.170190\pi\) |
−0.871507 | + | 0.490383i | \(0.836857\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.4893 | − | 7.21072i | −0.825319 | − | 0.476498i | 0.0269285 | − | 0.999637i | \(-0.491427\pi\) |
−0.852247 | + | 0.523139i | \(0.824761\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.7953 | + | 7.38739i | −0.838250 | + | 0.483964i | −0.856669 | − | 0.515867i | \(-0.827470\pi\) |
0.0184192 | + | 0.999830i | \(0.494137\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.3309 | − | 28.2860i | 1.06531 | − | 1.84518i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.7953 | − | 13.1160i | −1.09097 | − | 0.851976i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.5339 | + | 13.0100i | −1.45760 | + | 0.841545i | −0.998893 | − | 0.0470423i | \(-0.985020\pi\) |
−0.458707 | + | 0.888588i | \(0.651687\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.66295 | + | 0.960105i | −0.107120 | + | 0.0618458i | −0.552603 | − | 0.833445i | \(-0.686365\pi\) |
0.445483 | + | 0.895290i | \(0.353032\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.3546 | − | 2.69022i | −0.984996 | − | 0.172578i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.0402 | − | 17.3901i | 0.638841 | − | 1.10651i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.9742 | − | 5.24518i | 0.822203 | − | 0.332400i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.97663 | −0.629719 | −0.314860 | − | 0.949138i | \(-0.601957\pi\) | ||||
−0.314860 | + | 0.949138i | \(0.601957\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −23.2193 | −1.45978 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.19411 | − | 8.50994i | 0.0747779 | − | 0.532913i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.50364 | + | 12.9967i | −0.468064 | + | 0.810711i | −0.999334 | − | 0.0364915i | \(-0.988382\pi\) |
0.531270 | + | 0.847203i | \(0.321715\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.227437 | + | 0.794471i | −0.0140780 | + | 0.0491765i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.11010 | − | 3.52767i | 0.376765 | − | 0.217525i | −0.299645 | − | 0.954051i | \(-0.596868\pi\) |
0.676410 | + | 0.736525i | \(0.263535\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.10084 | − | 1.21292i | 0.129053 | − | 0.0745090i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.21847 | − | 15.8102i | 0.135768 | − | 0.967568i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.8898 | + | 25.7898i | −0.907844 | + | 1.57243i | −0.0907911 | + | 0.995870i | \(0.528940\pi\) |
−0.817053 | + | 0.576562i | \(0.804394\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.41462 | − | 1.39408i | 0.146677 | − | 0.0846843i | −0.424865 | − | 0.905257i | \(-0.639679\pi\) |
0.571543 | + | 0.820572i | \(0.306345\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.6424 | + | 9.03112i | 0.943270 | + | 0.544597i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.79074 | − | 11.7619i | −0.408016 | − | 0.706705i | 0.586651 | − | 0.809840i | \(-0.300446\pi\) |
−0.994667 | + | 0.103135i | \(0.967113\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.66644 | + | 1.16563i | −0.279372 | + | 0.0697844i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.95777 | − | 2.28502i | −0.236101 | − | 0.136313i | 0.377283 | − | 0.926098i | \(-0.376859\pi\) |
−0.613383 | + | 0.789785i | \(0.710192\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 20.4019i | − | 1.21277i | −0.795173 | − | 0.606383i | \(-0.792620\pi\) | ||
0.795173 | − | 0.606383i | \(-0.207380\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.5512 | − | 19.9136i | 0.921174 | − | 1.17958i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.10462 | + | 12.3056i | 0.417919 | + | 0.723857i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.25310 | − | 12.9938i | −0.307942 | − | 0.761707i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.41037 | − | 11.1031i | −0.374498 | − | 0.648649i | 0.615754 | − | 0.787939i | \(-0.288852\pi\) |
−0.990252 | + | 0.139289i | \(0.955518\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.08144 | + | 7.06926i | −0.237631 | + | 0.411589i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.58399 | − | 24.4317i | −0.149938 | − | 1.41767i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.0766 | 1.16106 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.75874 | + | 12.5338i | −0.101037 | + | 0.720049i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.5263 | − | 10.6962i | −1.06081 | − | 0.612461i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.93411i | − | 0.110386i | −0.998476 | − | 0.0551928i | \(-0.982423\pi\) | ||
0.998476 | − | 0.0551928i | \(-0.0175773\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.56073 | + | 11.2812i | 0.259451 | + | 0.641762i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.08916 | −0.118465 | −0.0592326 | − | 0.998244i | \(-0.518865\pi\) | ||||
−0.0592326 | + | 0.998244i | \(0.518865\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.4088i | 1.26662i | 0.773899 | + | 0.633309i | \(0.218304\pi\) | ||||
−0.773899 | + | 0.633309i | \(0.781696\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 3.48474i | − | 0.195723i | −0.995200 | − | 0.0978614i | \(-0.968800\pi\) | ||
0.995200 | − | 0.0978614i | \(-0.0312002\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.30241 | −0.0729212 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.2858 | − | 3.40776i | −1.35550 | − | 0.190203i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 8.20549i | − | 0.456565i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.5252 | − | 7.80876i | −0.750241 | − | 0.433152i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.06316 | + | 3.66405i | −0.501194 | + | 0.202622i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.57715 | −0.251583 | −0.125791 | − | 0.992057i | \(-0.540147\pi\) | ||||
−0.125791 | + | 0.992057i | \(0.540147\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.32042 | − | 7.07540i | 0.401156 | − | 0.387729i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.2405 | − | 29.8615i | 0.941951 | − | 1.63151i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.7062 | − | 25.4720i | −0.801100 | − | 1.38755i | −0.918893 | − | 0.394508i | \(-0.870915\pi\) |
0.117793 | − | 0.993038i | \(-0.462418\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23.0563 | + | 3.23524i | 1.25225 | + | 0.175714i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.79023 | − | 6.56486i | −0.205252 | − | 0.355507i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 25.0165 | + | 3.51030i | 1.34684 | + | 0.188988i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 19.6582i | − | 1.05531i | −0.849459 | − | 0.527654i | \(-0.823072\pi\) | ||
0.849459 | − | 0.527654i | \(-0.176928\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.47286 | + | 4.89181i | 0.453542 | + | 0.261852i | 0.709325 | − | 0.704882i | \(-0.249000\pi\) |
−0.255783 | + | 0.966734i | \(0.582333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.23424 | + | 21.1249i | 0.119255 | + | 1.12756i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.5322 | − | 21.7065i | −0.667023 | − | 1.15532i | −0.978733 | − | 0.205141i | \(-0.934235\pi\) |
0.311709 | − | 0.950178i | \(-0.399099\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.8532 | + | 15.5037i | 1.42522 | + | 0.822850i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.09861 | + | 4.67574i | −0.427428 | + | 0.246776i | −0.698251 | − | 0.715853i | \(-0.746038\pi\) |
0.270822 | + | 0.962629i | \(0.412704\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.56305 | − | 4.43933i | 0.134897 | − | 0.233649i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.2338 | − | 7.37154i | 0.957026 | − | 0.386906i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −40.5367 | + | 23.4039i | −2.12179 | + | 1.22502i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.9530 | + | 10.9425i | −0.989337 | + | 0.571194i | −0.905076 | − | 0.425250i | \(-0.860186\pi\) |
−0.0842608 | + | 0.996444i | \(0.526853\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −15.3428 | + | 14.8292i | −0.798712 | + | 0.771979i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.30822 | + | 3.99795i | −0.119515 | + | 0.207006i | −0.919576 | − | 0.392913i | \(-0.871467\pi\) |
0.800061 | + | 0.599919i | \(0.204801\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.78322 | + | 3.73539i | 0.247005 | + | 0.192895i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.12613 | 0.0579988 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.22396 | −0.319703 | −0.159852 | − | 0.987141i | \(-0.551102\pi\) | ||||
−0.159852 | + | 0.987141i | \(0.551102\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.4366 | − | 13.6168i | −0.893303 | − | 0.697612i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.9989 | − | 19.0506i | 0.562015 | − | 0.973439i | −0.435305 | − | 0.900283i | \(-0.643360\pi\) |
0.997321 | − | 0.0731560i | \(-0.0233071\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 30.1641 | + | 8.63523i | 1.53333 | + | 0.438954i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.51109 | + | 4.91388i | −0.431529 | + | 0.249144i | −0.699998 | − | 0.714145i | \(-0.746816\pi\) |
0.268469 | + | 0.963288i | \(0.413482\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.10481 | − | 4.10197i | 0.359306 | − | 0.207445i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.5462 | + | 8.71066i | −1.08686 | + | 0.439395i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.2696 | + | 31.6439i | −0.919243 | + | 1.59218i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.55324 | + | 2.62881i | −0.228520 | + | 0.131936i | −0.609889 | − | 0.792487i | \(-0.708786\pi\) |
0.381369 | + | 0.924423i | \(0.375453\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.7847 | + | 8.53594i | 0.738312 | + | 0.426265i | 0.821455 | − | 0.570273i | \(-0.193163\pi\) |
−0.0831432 | + | 0.996538i | \(0.526496\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.27722 | + | 5.67631i | 0.163250 | + | 0.282757i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.909599 | + | 26.7134i | −0.0451983 | + | 1.32740i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.8957 | + | 8.02270i | 0.688786 | + | 0.397671i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 19.5703i | − | 0.967690i | −0.875154 | − | 0.483845i | \(-0.839240\pi\) | ||
0.875154 | − | 0.483845i | \(-0.160760\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.4377 | − | 2.16621i | −0.761488 | − | 0.106851i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.9977 | − | 20.7807i | −0.588946 | − | 1.02008i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.06798 | − | 0.430496i | −0.150240 | − | 0.0210815i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.3073 | − | 17.8529i | −0.503547 | − | 0.872169i | −0.999992 | − | 0.00410056i | \(-0.998695\pi\) |
0.496445 | − | 0.868068i | \(-0.334639\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.704748 | − | 1.22066i | 0.0343473 | − | 0.0594913i | −0.848341 | − | 0.529451i | \(-0.822398\pi\) |
0.882688 | + | 0.469959i | \(0.155731\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.99568 | + | 32.0096i | 0.388763 | + | 1.55636i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.38182 | −0.309564 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −31.0387 | + | 12.5483i | −1.49856 | + | 0.605838i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.6666 | + | 6.73569i | 0.561959 | + | 0.324447i | 0.753931 | − | 0.656953i | \(-0.228155\pi\) |
−0.191973 | + | 0.981400i | \(0.561488\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 12.9356i | − | 0.621646i | −0.950468 | − | 0.310823i | \(-0.899395\pi\) | ||
0.950468 | − | 0.310823i | \(-0.100605\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.40322 | + | 0.196899i | 0.0672794 | + | 0.00944059i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24.1215 | 1.15389 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.1039i | 0.482233i | 0.970496 | + | 0.241116i | \(0.0775135\pi\) | ||||
−0.970496 | + | 0.241116i | \(0.922486\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 29.0084i | − | 1.37823i | −0.724652 | − | 0.689115i | \(-0.757999\pi\) | ||
0.724652 | − | 0.689115i | \(-0.242001\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −27.3747 | −1.29768 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.37916 | − | 20.7262i | −0.396321 | − | 0.980314i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.94881i | 0.375127i | 0.982252 | + | 0.187564i | \(0.0600591\pi\) | ||||
−0.982252 | + | 0.187564i | \(0.939941\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.1239 | − | 16.8147i | −1.37139 | − | 0.791772i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.12099 | + | 22.2421i | −0.146637 | + | 1.04502i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.9617 | −0.653100 | −0.326550 | − | 0.945180i | \(-0.605886\pi\) | ||||
−0.326550 | + | 0.945180i | \(0.605886\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.10682 | + | 7.01931i | 0.238366 | + | 0.327633i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.4030 | − | 28.4108i | 0.763964 | − | 1.32322i | −0.176829 | − | 0.984242i | \(-0.556584\pi\) |
0.940793 | − | 0.338983i | \(-0.110083\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.8812 | − | 24.0429i | −0.645112 | − | 1.11737i | −0.984276 | − | 0.176640i | \(-0.943477\pi\) |
0.339163 | − | 0.940727i | \(-0.389856\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.09112 | + | 7.64600i | 0.143347 | + | 0.354575i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.4311 | + | 19.7992i | 0.528966 | + | 0.916196i | 0.999429 | + | 0.0337767i | \(0.0107535\pi\) |
−0.470463 | + | 0.882420i | \(0.655913\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.3072 | − | 23.4426i | 0.843551 | − | 1.08018i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 49.4494i | 2.27369i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.2502 | − | 9.38204i | −0.745609 | − | 0.430478i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.674409 | + | 2.35581i | −0.0308791 | + | 0.107865i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.21212 | − | 2.09946i | −0.0553834 | − | 0.0959269i | 0.837004 | − | 0.547196i | \(-0.184305\pi\) |
−0.892388 | + | 0.451269i | \(0.850971\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0149 | − | 6.93683i | −0.547834 | − | 0.316292i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.8121 | + | 12.0159i | −0.945028 | + | 0.545612i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.19651 | − | 9.00061i | 0.235476 | − | 0.407857i | −0.723935 | − | 0.689868i | \(-0.757668\pi\) |
0.959411 | + | 0.282012i | \(0.0910017\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.21837 | + | 8.68282i | −0.0550964 | + | 0.392651i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.93014 | + | 1.69172i | −0.132235 | + | 0.0763462i | −0.564658 | − | 0.825325i | \(-0.690992\pi\) |
0.432423 | + | 0.901671i | \(0.357659\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.398522 | − | 0.230087i | 0.0179485 | − | 0.0103626i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −40.8700 | + | 10.2089i | −1.83697 | + | 0.458856i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.7801 | + | 34.2602i | −0.885481 | + | 1.53370i | −0.0403188 | + | 0.999187i | \(0.512837\pi\) |
−0.845162 | + | 0.534511i | \(0.820496\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.79034 | + | 19.8856i | −0.124663 | + | 0.888425i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.5476 | −0.648645 | −0.324323 | − | 0.945947i | \(-0.605136\pi\) | ||||
−0.324323 | + | 0.945947i | \(0.605136\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.7018 | 0.965717 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.96240 | − | 2.41047i | 0.264799 | − | 0.107053i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.1958 | + | 17.6596i | −0.451921 | + | 0.782750i | −0.998505 | − | 0.0546542i | \(-0.982594\pi\) |
0.546585 | + | 0.837404i | \(0.315928\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.68439 | + | 25.3811i | 0.118519 | + | 1.12060i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.0690 | − | 10.4322i | 0.796216 | − | 0.459696i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −45.0319 | + | 25.9992i | −1.98050 | + | 1.14344i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.55500 | − | 6.68091i | −0.375523 | − | 0.293259i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.75122 | − | 13.4255i | 0.339587 | − | 0.588182i | −0.644768 | − | 0.764379i | \(-0.723046\pi\) |
0.984355 | + | 0.176196i | \(0.0563793\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.35989 | + | 5.40394i | −0.409280 | + | 0.236298i | −0.690480 | − | 0.723351i | \(-0.742601\pi\) |
0.281201 | + | 0.959649i | \(0.409267\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.31952 | + | 1.33918i | 0.101040 | + | 0.0583355i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.558476 | + | 0.967309i | 0.0242816 | + | 0.0420569i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.99829 | − | 7.99987i | −0.0867183 | − | 0.347165i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.1819 | + | 14.5388i | 1.09075 | + | 0.629745i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 42.0498i | 1.81797i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.57017 | − | 23.6722i | −0.412983 | − | 1.02153i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.79357 | − | 15.2309i | −0.378065 | − | 0.654828i | 0.612716 | − | 0.790303i | \(-0.290077\pi\) |
−0.990781 | + | 0.135476i | \(0.956744\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.0888713 | − | 0.113801i | 0.00381383 | − | 0.00488367i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.38108 | + | 14.5165i | 0.359006 | + | 0.621817i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.72451 | + | 9.91513i | −0.244762 | + | 0.423940i | −0.962065 | − | 0.272821i | \(-0.912043\pi\) |
0.717303 | + | 0.696762i | \(0.245377\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20.9651 | − | 5.23688i | 0.894770 | − | 0.223504i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.35302 | 0.0576407 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.7584 | − | 10.7444i | −0.584012 | − | 0.456076i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.9159 | − | 19.0040i | −1.39469 | − | 0.805226i | −0.400863 | − | 0.916138i | \(-0.631290\pi\) |
−0.993830 | + | 0.110912i | \(0.964623\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 42.7565i | − | 1.80841i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.42035 | + | 10.7824i | −0.355508 | + | 0.455233i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.7688 | 0.748864 | 0.374432 | − | 0.927254i | \(-0.377838\pi\) | ||||
0.374432 | + | 0.927254i | \(0.377838\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 39.9211i | − | 1.67949i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 38.9601i | − | 1.63329i | −0.577139 | − | 0.816646i | \(-0.695831\pi\) | ||
0.577139 | − | 0.816646i | \(-0.304169\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.9049 | 0.707448 | 0.353724 | − | 0.935350i | \(-0.384915\pi\) | ||||
0.353724 | + | 0.935350i | \(0.384915\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.4547 | + | 21.0705i | −0.687406 | + | 0.880233i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 18.7605i | − | 0.782368i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.9329 | + | 23.6326i | 1.70406 | + | 0.983840i | 0.941555 | + | 0.336858i | \(0.109364\pi\) |
0.762506 | + | 0.646982i | \(0.223969\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 29.4259 | + | 22.9797i | 1.22290 | + | 0.955004i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.86199 | −0.159947 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 35.3383 | − | 8.82714i | 1.46106 | − | 0.364957i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.6343 | + | 20.1513i | −0.480200 | + | 0.831731i | −0.999742 | − | 0.0227138i | \(-0.992769\pi\) |
0.519542 | + | 0.854445i | \(0.326103\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.93750 | + | 6.81995i | 0.162242 | + | 0.281011i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.5359 | + | 13.4914i | −0.433391 | + | 0.554963i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.5962 | + | 32.2095i | 0.763654 | + | 1.32269i | 0.940955 | + | 0.338530i | \(0.109930\pi\) |
−0.177302 | + | 0.984157i | \(0.556737\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.85616 | + | 16.9590i | 0.280604 | + | 0.694085i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 32.2844i | − | 1.31910i | −0.751659 | − | 0.659552i | \(-0.770746\pi\) | ||
0.751659 | − | 0.659552i | \(-0.229254\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.7559 | + | 8.51933i | 0.601906 | + | 0.347511i | 0.769791 | − | 0.638296i | \(-0.220360\pi\) |
−0.167885 | + | 0.985807i | \(0.553694\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.44102 | + | 33.7925i | 0.343745 | + | 1.37614i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.8615 | − | 29.2051i | −0.685519 | − | 1.18735i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.44393 | − | 4.87510i | −0.342728 | − | 0.197874i | 0.318749 | − | 0.947839i | \(-0.396737\pi\) |
−0.661478 | + | 0.749965i | \(0.730070\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 38.9369 | − | 22.4802i | 1.57522 | − | 0.909452i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.86332 | + | 11.8876i | −0.277207 | + | 0.480136i | −0.970690 | − | 0.240337i | \(-0.922742\pi\) |
0.693483 | + | 0.720473i | \(0.256075\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 28.8361 | + | 22.5191i | 1.16278 | + | 0.908058i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.84301 | + | 1.64141i | −0.114455 | + | 0.0660807i | −0.556135 | − | 0.831092i | \(-0.687716\pi\) |
0.441680 | + | 0.897173i | \(0.354383\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.9907 | − | 8.65490i | 0.602528 | − | 0.347870i | −0.167507 | − | 0.985871i | \(-0.553572\pi\) |
0.770036 | + | 0.638001i | \(0.220238\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.6345 | + | 15.0124i | −0.828036 | + | 0.602429i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.7536 | − | 25.5539i | 0.590142 | − | 1.02216i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −37.2923 | + | 15.0765i | −1.48931 | + | 0.602098i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.66923 | −0.226047 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.27821 | −0.249932 | −0.124966 | − | 0.992161i | \(-0.539882\pi\) | ||||
−0.124966 | + | 0.992161i | \(0.539882\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.92887 | + | 20.8729i | −0.116412 | + | 0.829624i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.9672 | + | 32.8522i | −0.752691 | + | 1.30370i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −30.3882 | + | 7.59066i | −1.20214 | + | 0.300282i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.9788 | + | 10.3801i | −0.710120 | + | 0.409988i | −0.811105 | − | 0.584900i | \(-0.801134\pi\) |
0.100986 | + | 0.994888i | \(0.467800\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.2553 | − | 9.96236i | 0.680483 | − | 0.392877i | −0.119554 | − | 0.992828i | \(-0.538146\pi\) |
0.800037 | + | 0.599950i | \(0.204813\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.47577 | − | 53.2769i | 0.294358 | − | 2.09778i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.7670 | − | 25.5772i | 0.580551 | − | 1.00554i | −0.414863 | − | 0.909884i | \(-0.636170\pi\) |
0.995414 | − | 0.0956605i | \(-0.0304963\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.2544 | − | 6.49774i | 0.441775 | − | 0.255059i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.7914 | + | 7.96249i | 0.539701 | + | 0.311596i | 0.744958 | − | 0.667112i | \(-0.232470\pi\) |
−0.205257 | + | 0.978708i | \(0.565803\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.9246 | + | 34.5105i | 0.778520 | + | 1.34844i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.0131 | − | 45.4565i | 0.507688 | − | 1.77343i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.80283 | + | 1.61822i | 0.109183 | + | 0.0630368i | 0.553597 | − | 0.832785i | \(-0.313255\pi\) |
−0.444414 | + | 0.895821i | \(0.646588\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 8.90498i | − | 0.346364i | −0.984890 | − | 0.173182i | \(-0.944595\pi\) | ||
0.984890 | − | 0.173182i | \(-0.0554048\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.28066 | − | 9.32299i | 0.282757 | − | 0.362075i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.676383 | + | 1.17153i | 0.0261896 | + | 0.0453618i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.535590 | − | 1.32480i | −0.0207071 | − | 0.0512198i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.0285 | + | 29.4943i | 0.657379 | + | 1.13861i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.2311 | + | 22.9169i | −0.510021 | + | 0.883382i | 0.489912 | + | 0.871772i | \(0.337029\pi\) |
−0.999933 | + | 0.0116101i | \(0.996304\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 19.7401 | − | 2.08779i | 0.759799 | − | 0.0803590i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.92848 | −0.343149 | −0.171575 | − | 0.985171i | \(-0.554886\pi\) | ||||
−0.171575 | + | 0.985171i | \(0.554886\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0802812 | − | 0.572132i | 0.00307638 | − | 0.0219242i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.7902 | + | 18.9314i | 1.25468 | + | 0.724390i | 0.972035 | − | 0.234834i | \(-0.0754547\pi\) |
0.282645 | + | 0.959225i | \(0.408788\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.7298i | 1.02129i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.36221 | − | 23.1578i | −0.357191 | − | 0.883525i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.33927 | 0.127216 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 5.70665i | − | 0.217091i | −0.994091 | − | 0.108546i | \(-0.965381\pi\) | ||
0.994091 | − | 0.108546i | \(-0.0346194\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.31208i | 0.201499i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.8821 | 0.450065 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25.3424 | − | 3.55602i | −0.958537 | − | 0.134501i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 8.19949i | − | 0.309690i | −0.987939 | − | 0.154845i | \(-0.950512\pi\) | ||
0.987939 | − | 0.154845i | \(-0.0494879\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.4357 | − | 8.33444i | −0.544452 | − | 0.314339i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 52.4480 | − | 21.2036i | 1.97531 | − | 0.798576i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.1515 | 0.756805 | 0.378402 | − | 0.925641i | \(-0.376474\pi\) | ||||
0.378402 | + | 0.925641i | \(0.376474\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.94485 | − | 35.8095i | −0.335458 | − | 1.34296i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.93676 | + | 6.81866i | −0.147433 | + | 0.255361i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28.7028 | + | 49.7147i | 1.07342 | + | 1.85923i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −44.6306 | − | 6.26254i | −1.66676 | − | 0.233879i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.5996 | − | 44.3397i | −0.954702 | − | 1.65359i | −0.735048 | − | 0.678015i | \(-0.762841\pi\) |
−0.219654 | − | 0.975578i | \(-0.570493\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.29363 | − | 0.462160i | −0.122492 | − | 0.0171879i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1.05231i | − | 0.0390820i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.7848 | − | 7.95865i | −0.511249 | − | 0.295170i | 0.222098 | − | 0.975024i | \(-0.428710\pi\) |
−0.733347 | + | 0.679854i | \(0.762043\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.0927 | − | 20.0413i | −0.670099 | − | 0.742271i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.73584 | − | 15.1309i | −0.323107 | − | 0.559637i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.67216 | − | 2.12012i | −0.135634 | − | 0.0783086i | 0.430647 | − | 0.902520i | \(-0.358285\pi\) |
−0.566282 | + | 0.824212i | \(0.691619\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −47.5401 | + | 27.4473i | −1.75116 | + | 1.01103i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.1835 | + | 24.5665i | −0.521747 | + | 0.903693i | 0.477933 | + | 0.878397i | \(0.341386\pi\) |
−0.999680 | + | 0.0252966i | \(0.991947\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 32.2448 | − | 13.0359i | 1.18454 | − | 0.478886i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.8850 | − | 12.6353i | 0.802884 | − | 0.463545i | −0.0415945 | − | 0.999135i | \(-0.513244\pi\) |
0.844479 | + | 0.535589i | \(0.179910\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33.1971 | + | 19.1664i | −1.21625 | + | 0.702201i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 23.3028 | + | 6.67100i | 0.852604 | + | 0.244079i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.7730 | + | 41.1761i | −0.867490 | + | 1.50254i | −0.00293597 | + | 0.999996i | \(0.500935\pi\) |
−0.864554 | + | 0.502540i | \(0.832399\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.6192 | − | 10.6357i | −0.496310 | − | 0.387586i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 38.5113 | 1.40157 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.3922 | 1.35904 | 0.679521 | − | 0.733656i | \(-0.262188\pi\) | ||||
0.679521 | + | 0.733656i | \(0.262188\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −31.6968 | − | 24.7532i | −1.15052 | − | 0.898483i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.12142 | − | 7.13850i | 0.149401 | − | 0.258770i | −0.781605 | − | 0.623774i | \(-0.785599\pi\) |
0.931006 | + | 0.365003i | \(0.118932\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.7022 | − | 10.3440i | 0.386938 | − | 0.373987i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.73114 | + | 5.61827i | −0.351371 | + | 0.202864i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.2182 | − | 11.6730i | 0.729086 | − | 0.420938i | −0.0890020 | − | 0.996031i | \(-0.528368\pi\) |
0.818088 | + | 0.575094i | \(0.195034\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.0985 | + | 9.74253i | −0.867887 | + | 0.350869i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.2201 | + | 29.8261i | −0.619364 | + | 1.07277i | 0.370238 | + | 0.928937i | \(0.379276\pi\) |
−0.989602 | + | 0.143833i | \(0.954057\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.30422 | − | 3.06240i | 0.190533 | − | 0.110004i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.2555 | + | 17.4680i | 1.08402 | + | 0.625857i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.6822 | − | 42.7508i | −0.883199 | − | 1.52975i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.15743 | + | 0.842076i | −0.0413632 | + | 0.0300933i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −44.1682 | − | 25.5005i | −1.57643 | − | 0.910152i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.31355i | 0.296346i | 0.988961 | + | 0.148173i | \(0.0473393\pi\) | ||||
−0.988961 | + | 0.148173i | \(0.952661\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.1016 | + | 1.69809i | 0.430830 | + | 0.0604537i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.7237 | − | 25.5022i | −0.522854 | − | 0.905610i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.16091 | + | 0.583856i | 0.147572 | + | 0.0207072i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.426036 | + | 0.737916i | 0.0150910 | + | 0.0261383i | 0.873472 | − | 0.486874i | \(-0.161863\pi\) |
−0.858381 | + | 0.513012i | \(0.828530\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.18614 | − | 15.9109i | 0.324982 | − | 0.562886i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19.8831 | − | 19.2176i | 0.702533 | − | 0.679019i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 74.5190 | 2.62972 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −47.8196 | + | 19.3325i | −1.68333 | + | 0.680535i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.5580 | + | 18.2200i | 1.10952 | + | 0.640581i | 0.938705 | − | 0.344722i | \(-0.112027\pi\) |
0.170814 | + | 0.985303i | \(0.445360\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.08986i | 0.0382702i | 0.999817 | + | 0.0191351i | \(0.00609126\pi\) | ||||
−0.999817 | + | 0.0191351i | \(0.993909\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.78238 | + | 0.671060i | 0.167725 | + | 0.0235351i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.0339 | 0.526616 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 51.3709i | − | 1.79724i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 24.2196i | − | 0.845270i | −0.906300 | − | 0.422635i | \(-0.861105\pi\) | ||
0.906300 | − | 0.422635i | \(-0.138895\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.71185 | 0.199102 | 0.0995512 | − | 0.995032i | \(-0.468259\pi\) | ||||
0.0995512 | + | 0.995032i | \(0.468259\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.7258 | + | 29.0041i | 0.408239 | + | 1.00979i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 36.4579i | − | 1.26777i | −0.773429 | − | 0.633883i | \(-0.781460\pi\) | ||
0.773429 | − | 0.633883i | \(-0.218540\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.498269 | + | 0.287676i | 0.0173056 | + | 0.00999140i | 0.508628 | − | 0.860986i | \(-0.330153\pi\) |
−0.491322 | + | 0.870978i | \(0.663486\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.26882 | − | 23.2956i | 0.113394 | − | 0.808115i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 34.4312 | 1.19154 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.61282 | − | 3.38350i | −0.263137 | − | 0.116951i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.9341 | + | 41.4550i | −0.826295 | + | 1.43119i | 0.0746300 | + | 0.997211i | \(0.476222\pi\) |
−0.900925 | + | 0.433974i | \(0.857111\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4621 | − | 25.0490i | −0.498692 | − | 0.863759i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.96681 | − | 7.33851i | −0.102182 | − | 0.252752i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.51368 | − | 9.54997i | −0.189676 | − | 0.328529i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21.7496 | − | 27.8507i | 0.746445 | − | 0.955835i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 16.6657i | − | 0.571294i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.5393 | + | 23.4054i | 1.38804 | + | 0.801385i | 0.993094 | − | 0.117320i | \(-0.0374303\pi\) |
0.394945 | + | 0.918705i | \(0.370764\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 42.4581 | − | 10.6056i | 1.45204 | − | 0.362704i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.78220 | − | 8.28302i | −0.163357 | − | 0.282943i | 0.772714 | − | 0.634755i | \(-0.218899\pi\) |
−0.936071 | + | 0.351812i | \(0.885566\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.68311 | + | 2.70379i | 0.159786 | + | 0.0922523i | 0.577761 | − | 0.816206i | \(-0.303927\pi\) |
−0.417975 | + | 0.908459i | \(0.637260\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.5402 | + | 20.5191i | −1.20980 | + | 0.698480i | −0.962716 | − | 0.270514i | \(-0.912806\pi\) |
−0.247086 | + | 0.968994i | \(0.579473\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.30598 | + | 16.1184i | −0.316413 | + | 0.548043i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.41991 | + | 24.3724i | −0.116146 | + | 0.827729i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 50.3777 | − | 29.0856i | 1.70895 | − | 0.986661i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 41.1056 | − | 23.7323i | 1.39281 | − | 0.804139i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.68108 | − | 23.3380i | 0.226120 | − | 0.789871i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.32509 | − | 12.6874i | 0.247351 | − | 0.428424i | −0.715439 | − | 0.698675i | \(-0.753773\pi\) |
0.962790 | + | 0.270251i | \(0.0871067\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.08572 | − | 21.9907i | 0.104079 | − | 0.741729i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.8295 | −1.51034 | −0.755172 | − | 0.655527i | \(-0.772447\pi\) | ||||
−0.755172 | + | 0.655527i | \(0.772447\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.8527 | 1.13923 | 0.569617 | − | 0.821910i | \(-0.307091\pi\) | ||||
0.569617 | + | 0.821910i | \(0.307091\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.1079 | + | 5.29924i | −0.440616 | + | 0.178132i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.3422 | − | 23.1093i | 0.447987 | − | 0.775936i | −0.550268 | − | 0.834988i | \(-0.685475\pi\) |
0.998255 | + | 0.0590523i | \(0.0188079\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 22.5183 | − | 36.1066i | 0.754390 | − | 1.20962i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 46.7817 | − | 27.0094i | 1.56549 | − | 0.903837i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −37.9157 | + | 21.8907i | −1.26738 | + | 0.731724i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 27.4066 | + | 21.4028i | 0.915081 | + | 0.714619i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.220820 | + | 0.382472i | −0.00736476 | + | 0.0127561i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.18172 | − | 0.682266i | 0.0393688 | − | 0.0227296i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.214412 | − | 0.123791i | −0.00712729 | − | 0.00411494i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.97211 | + | 13.8081i | 0.264710 | + | 0.458490i | 0.967487 | − | 0.252919i | \(-0.0813906\pi\) |
−0.702778 | + | 0.711409i | \(0.748057\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.7627 | + | 15.2351i | −0.522815 | + | 0.505316i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.9207 | + | 23.6256i | 1.35576 | + | 0.782750i | 0.989050 | − | 0.147584i | \(-0.0471496\pi\) |
0.366713 | + | 0.930334i | \(0.380483\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.2013i | 1.26428i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.8876 | − | 34.3516i | −0.459110 | − | 1.13563i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.8163 | + | 25.6625i | 0.488743 | + | 0.846528i | 0.999916 | − | 0.0129500i | \(-0.00412223\pi\) |
−0.511173 | + | 0.859478i | \(0.670789\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.06188 | − | 2.64027i | 0.0679413 | − | 0.0869998i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.3415 | + | 36.9645i | 0.702463 | + | 1.21670i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.48212 | + | 11.2274i | −0.213131 | + | 0.369153i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.80050 | + | 20.2620i | −0.190513 | + | 0.665491i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.2372 | −1.09048 | −0.545238 | − | 0.838281i | \(-0.683561\pi\) | ||||
−0.545238 | + | 0.838281i | \(0.683561\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.85192 | − | 2.22717i | −0.0933677 | − | 0.0729142i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.3151 | + | 11.7289i | 0.664373 | + | 0.383576i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.8190i | 0.778134i | 0.921209 | + | 0.389067i | \(0.127203\pi\) | ||||
−0.921209 | + | 0.389067i | \(0.872797\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.8891 | + | 30.5903i | −0.779591 | + | 0.998278i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 54.2403 | 1.76818 | 0.884091 | − | 0.467315i | \(-0.154779\pi\) | ||||
0.884091 | + | 0.467315i | \(0.154779\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.9295i | 1.13746i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.0648i | 0.684515i | 0.939606 | + | 0.342257i | \(0.111191\pi\) | ||||
−0.939606 | + | 0.342257i | \(0.888809\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −64.4329 | −2.09158 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.71495 | − | 4.75705i | 0.120465 | − | 0.154258i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 4.50028i | − | 0.145778i | −0.997340 | − | 0.0728892i | \(-0.976778\pi\) | ||
0.997340 | − | 0.0728892i | \(-0.0232219\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 39.6989 | + | 22.9201i | 1.28462 | + | 0.741679i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.77793 | − | 1.38845i | −0.0574724 | − | 0.0448823i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.4295 | 0.917081 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −29.5198 | − | 30.5420i | −0.951262 | − | 0.984204i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32.0090 | − | 55.4411i | 1.03040 | − | 1.78471i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.8811 | − | 18.8466i | −0.349912 | − | 0.606065i | 0.636322 | − | 0.771424i | \(-0.280455\pi\) |
−0.986233 | + | 0.165359i | \(0.947122\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.74754 | − | 11.2014i | 0.281012 | − | 0.359840i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.5222 | − | 40.7416i | −0.754862 | − | 1.30746i | −0.945443 | − | 0.325788i | \(-0.894371\pi\) |
0.190581 | − | 0.981671i | \(-0.438963\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.1387 | − | 25.0784i | −0.324698 | − | 0.803153i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.1455i | 0.804475i | 0.915535 | + | 0.402237i | \(0.131767\pi\) | ||||
−0.915535 | + | 0.402237i | \(0.868233\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 37.7423 | + | 21.7905i | 1.20625 | + | 0.696429i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.2783 | − | 4.66006i | −0.519725 | − | 0.148784i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.1071 | + | 31.3624i | 0.577527 | + | 1.00031i | 0.995762 | + | 0.0919674i | \(0.0293156\pi\) |
−0.418235 | + | 0.908339i | \(0.637351\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.4191 | + | 14.6757i | 0.809921 | + | 0.467608i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 44.4801 | − | 25.6806i | 1.41438 | − | 0.816595i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.32769 | + | 16.1560i | −0.296304 | + | 0.513213i | −0.975287 | − | 0.220940i | \(-0.929087\pi\) |
0.678984 | + | 0.734153i | \(0.262421\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.24829 | − | 4.87951i | −0.198284 | − | 0.154847i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27.1632 | − | 15.6827i | 0.861131 | − | 0.497174i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.1413 | − | 8.74181i | 0.479528 | − | 0.276856i | −0.240691 | − | 0.970602i | \(-0.577374\pi\) |
0.720220 | + | 0.693746i | \(0.244041\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 17.5359 | − | 1.85466i | 0.554813 | − | 0.0586790i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))