Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(293,1764)]
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, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.293");
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.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: | \(14.0856109166\) |
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 | 293.5 | ||
Root | \(1.68042 - 0.419752i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.293 |
Dual form | 1764.2.x.b.1469.5 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.240682 | + | 1.71525i | 0.138958 | + | 0.990298i | ||||
\(4\) | 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 | ||||||||
\(9\) | −2.88414 | + | 0.825658i | −0.961381 | + | 0.275219i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.09466 | − | 2.36406i | 1.23459 | − | 0.712790i | 0.266605 | − | 0.963806i | \(-0.414098\pi\) |
0.967983 | + | 0.251016i | \(0.0807648\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.54045 | + | 2.04408i | 0.981945 | + | 0.566926i | 0.902857 | − | 0.429942i | \(-0.141466\pi\) |
0.0790880 | + | 0.996868i | \(0.474799\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.76900 | + | 1.92801i | 1.23135 | + | 0.497809i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.67056 | −0.405169 | −0.202585 | − | 0.979265i | \(-0.564934\pi\) | ||||
−0.202585 | + | 0.979265i | \(0.564934\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.91183i | − | 1.12685i | −0.826167 | − | 0.563426i | \(-0.809483\pi\) | ||
0.826167 | − | 0.563426i | \(-0.190517\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.25297 | − | 2.45545i | −0.886805 | − | 0.511997i | −0.0139086 | − | 0.999903i | \(-0.504427\pi\) |
−0.872896 | + | 0.487906i | \(0.837761\pi\) | |||||||
\(24\) | 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 | −0.477687 | − | 0.878530i | \(-0.658525\pi\) |
0.521986 | + | 0.852954i | \(0.325191\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.38847 | + | 0.801636i | 0.249377 | + | 0.143978i | 0.619479 | − | 0.785013i | \(-0.287344\pi\) |
−0.370102 | + | 0.928991i | \(0.620677\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.04045 | + | 6.45438i | 0.877430 | + | 1.12356i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.39362 | 0.557907 | 0.278954 | − | 0.960305i | \(-0.410012\pi\) | ||||
0.278954 | + | 0.960305i | \(0.410012\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.65398 | + | 6.56472i | −0.424977 | + | 1.05120i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.55632 | − | 6.15972i | 0.555404 | − | 0.961987i | −0.442468 | − | 0.896784i | \(-0.645897\pi\) |
0.997872 | − | 0.0652031i | \(-0.0207695\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.22930 | + | 9.05742i | 0.797461 | + | 1.38124i | 0.921265 | + | 0.388936i | \(0.127157\pi\) |
−0.123804 | + | 0.992307i | \(0.539509\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.15919 | + | 8.64404i | −0.321874 | + | 1.28858i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.49885 | − | 9.52430i | −0.802090 | − | 1.38926i | −0.918238 | − | 0.396029i | \(-0.870388\pi\) |
0.116148 | − | 0.993232i | \(-0.462945\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.402073 | − | 2.86541i | −0.0563014 | − | 0.401238i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.816814i | 0.112198i | 0.998425 | + | 0.0560990i | \(0.0178662\pi\) | ||||
−0.998425 | + | 0.0560990i | \(0.982134\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 14.0419i | − | 1.89341i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.42500 | − | 1.18219i | 1.11592 | − | 0.156585i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.37428 | − | 2.38032i | 0.178916 | − | 0.309891i | −0.762594 | − | 0.646878i | \(-0.776074\pi\) |
0.941509 | + | 0.336986i | \(0.109408\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.23807 | − | 3.60155i | 0.798703 | − | 0.461131i | −0.0443147 | − | 0.999018i | \(-0.514110\pi\) |
0.843017 | + | 0.537886i | \(0.180777\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.5147 | − | 6.07067i | 1.30419 | − | 0.752974i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.80513 | + | 10.0548i | −0.709210 | + | 1.22839i | 0.255941 | + | 0.966692i | \(0.417615\pi\) |
−0.965151 | + | 0.261695i | \(0.915719\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.18809 | − | 7.88587i | 0.383801 | − | 0.949347i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.4406i | − | 1.23907i | −0.784968 | − | 0.619537i | \(-0.787320\pi\) | ||
0.784968 | − | 0.619537i | \(-0.212680\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 15.7608i | − | 1.84467i | −0.386395 | − | 0.922334i | \(-0.626280\pi\) | ||
0.386395 | − | 0.922334i | \(-0.373720\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.21495 | − | 4.07254i | 0.602171 | − | 0.470257i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.15163 | + | 10.6549i | 0.692112 | + | 1.19877i | 0.971145 | + | 0.238492i | \(0.0766530\pi\) |
−0.279032 | + | 0.960282i | \(0.590014\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.63658 | − | 4.76264i | 0.848509 | − | 0.529182i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.03981 | + | 6.99715i | 0.443426 | + | 0.768037i | 0.997941 | − | 0.0641368i | \(-0.0204294\pi\) |
−0.554515 | + | 0.832174i | \(0.687096\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.48067 | + | 4.29665i | −0.269067 | + | 0.466037i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.293659 | + | 0.376035i | 0.0314835 | + | 0.0403151i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.21744 | 0.977047 | 0.488523 | − | 0.872551i | \(-0.337536\pi\) | ||||
0.488523 | + | 0.872551i | \(0.337536\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.04082 | + | 2.57452i | −0.107928 | + | 0.266965i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.6332 | − | 7.29377i | −1.29614 | − | 0.748325i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.00772 | + | 4.04591i | −0.711527 | + | 0.410800i | −0.811626 | − | 0.584177i | \(-0.801417\pi\) |
0.100099 | + | 0.994977i | \(0.468084\pi\) | |||||||
\(98\) | 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 | 0.169355 | − | 0.985555i | \(-0.445832\pi\) |
−0.768838 | + | 0.639443i | \(0.779165\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.1588i | 1.36878i | 0.729117 | + | 0.684389i | \(0.239931\pi\) | ||||
−0.729117 | + | 0.684389i | \(0.760069\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.64405 | 0.540602 | 0.270301 | − | 0.962776i | \(-0.412877\pi\) | ||||
0.270301 | + | 0.962776i | \(0.412877\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.816783 | + | 5.82089i | 0.0775256 | + | 0.552495i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.6411 | + | 6.72099i | 1.09510 | + | 0.632258i | 0.934930 | − | 0.354831i | \(-0.115462\pi\) |
0.160172 | + | 0.987089i | \(0.448795\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.6308 | + | 7.29239i | −1.17783 | + | 0.680019i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.8989 | − | 2.97222i | −1.10005 | − | 0.274782i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.67752 | − | 9.83375i | 0.516138 | − | 0.893977i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.4214 | + | 4.61743i | 1.02983 | + | 0.416340i | ||||
\(124\) | 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 | ||||||||
\(129\) | −14.2771 | + | 11.1495i | −1.25703 | + | 0.981659i | ||||
\(130\) | 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 | ||||||||
\(135\) | −15.3464 | − | 1.62309i | −1.32080 | − | 0.139693i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.79449 | − | 4.50015i | 0.665928 | − | 0.384474i | −0.128604 | − | 0.991696i | \(-0.541050\pi\) |
0.794532 | + | 0.607222i | \(0.207716\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.54902 | − | 0.894326i | −0.131386 | − | 0.0758557i | 0.432866 | − | 0.901458i | \(-0.357502\pi\) |
−0.564252 | + | 0.825602i | \(0.690836\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.0130 | − | 11.7242i | 1.26433 | − | 0.987357i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.3293 | 1.61640 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 0.818088i | − | 0.0679385i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.1779 | + | 6.45358i | 0.915732 | + | 0.528698i | 0.882271 | − | 0.470742i | \(-0.156014\pi\) |
0.0334609 | + | 0.999440i | \(0.489347\pi\) | |||||||
\(150\) | 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 | ||||||||
\(157\) | −14.8720 | − | 8.58638i | −1.18692 | − | 0.685268i | −0.229314 | − | 0.973353i | \(-0.573648\pi\) |
−0.957605 | + | 0.288085i | \(0.906981\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.40104 | + | 0.196592i | −0.111109 | + | 0.0155908i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.06214 | −0.396497 | −0.198249 | − | 0.980152i | \(-0.563525\pi\) | ||||
−0.198249 | + | 0.980152i | \(0.563525\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 24.0854 | − | 3.37964i | 1.87504 | − | 0.263104i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.79673 | − | 10.0402i | 0.448564 | − | 0.776936i | −0.549729 | − | 0.835343i | \(-0.685269\pi\) |
0.998293 | + | 0.0584072i | \(0.0186022\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.85653 | + | 3.21561i | 0.142810 | + | 0.247354i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.05549 | + | 14.1664i | 0.310131 | + | 1.08333i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.13346 | + | 5.42730i | 0.238232 | + | 0.412630i | 0.960207 | − | 0.279289i | \(-0.0900987\pi\) |
−0.721975 | + | 0.691919i | \(0.756765\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.41360 | + | 1.78433i | 0.331747 | + | 0.134118i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 14.7418i | − | 1.10185i | −0.834554 | − | 0.550927i | \(-0.814274\pi\) | ||
0.834554 | − | 0.550927i | \(-0.185726\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.0833642i | 0.00619641i | 0.999995 | + | 0.00309821i | \(0.000986191\pi\) | ||||
−0.999995 | + | 0.00309821i | \(0.999014\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.67894 | + | 9.83300i | 0.567643 | + | 0.726876i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.03932 | − | 8.72835i | 0.370498 | − | 0.641721i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.84036 | + | 3.94929i | −0.500217 | + | 0.288800i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.3672 | + | 7.71754i | −0.967214 | + | 0.558421i | −0.898386 | − | 0.439207i | \(-0.855259\pi\) |
−0.0688282 | + | 0.997629i | \(0.521926\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.7779 | + | 18.6678i | −0.775808 | + | 1.34374i | 0.158532 | + | 0.987354i | \(0.449324\pi\) |
−0.934339 | + | 0.356385i | \(0.884009\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.9434 | + | 16.5742i | 0.926896 | + | 1.18691i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 9.88306i | − | 0.704139i | −0.935974 | − | 0.352069i | \(-0.885478\pi\) | ||
0.935974 | − | 0.352069i | \(-0.114522\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.5612i | 0.748660i | 0.927295 | + | 0.374330i | \(0.122127\pi\) | ||||
−0.927295 | + | 0.374330i | \(0.877873\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.6436 | − | 7.53723i | −1.31502 | − | 0.531635i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.5618 | − | 18.2936i | −0.737670 | − | 1.27768i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.2935 | + | 3.57038i | 0.993469 | + | 0.248158i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.6118 | − | 20.1123i | −0.803208 | − | 1.39120i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.08453 | − | 10.5387i | 0.418876 | − | 0.725514i | −0.576951 | − | 0.816779i | \(-0.695758\pi\) |
0.995827 | + | 0.0912645i | \(0.0290909\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 17.9082 | − | 2.51287i | 1.22705 | − | 0.172179i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 31.0608 | 2.11833 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 27.0337 | − | 3.79335i | 1.82677 | − | 0.256331i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.91452 | − | 3.41475i | −0.397854 | − | 0.229701i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.714485 | + | 0.412508i | −0.0478455 | + | 0.0276236i | −0.523732 | − | 0.851883i | \(-0.675461\pi\) |
0.475886 | + | 0.879507i | \(0.342127\pi\) | |||||||
\(224\) | 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 | 0.852247 | − | 0.523139i | \(-0.175239\pi\) |
−0.0269285 | + | 0.999637i | \(0.508573\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.7748i | 0.967927i | 0.875088 | + | 0.483964i | \(0.160803\pi\) | ||||
−0.875088 | + | 0.483964i | \(0.839197\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −32.6619 | −2.13063 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.7953 | + | 13.1160i | −1.09097 | + | 0.851976i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.5339 | − | 13.0100i | −1.45760 | − | 0.841545i | −0.458707 | − | 0.888588i | \(-0.651687\pi\) |
−0.998893 | + | 0.0470423i | \(0.985020\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.66295 | − | 0.960105i | 0.107120 | − | 0.0618458i | −0.445483 | − | 0.895290i | \(-0.646968\pi\) |
0.552603 | + | 0.833445i | \(0.313635\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.0071 | + | 11.9523i | 0.641955 | + | 0.766743i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.0402 | − | 17.3901i | 0.638841 | − | 1.10651i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.0295 | + | 8.61336i | −0.698968 | + | 0.545849i | ||||
\(250\) | 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 | ||||||||
\(255\) | −7.96687 | − | 3.22084i | −0.498905 | − | 0.201697i | ||||
\(256\) | 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 | ||||||||
\(261\) | −0.574314 | + | 0.594202i | −0.0355491 | + | 0.0367802i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.11010 | + | 3.52767i | −0.376765 | + | 0.217525i | −0.676410 | − | 0.736525i | \(-0.736465\pi\) |
0.299645 | + | 0.954051i | \(0.403132\pi\) | |||||||
\(264\) | 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 | ||||||||
\(269\) | 29.7795 | 1.81569 | 0.907844 | − | 0.419308i | \(-0.137727\pi\) | ||||
0.907844 | + | 0.419308i | \(0.137727\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2.78816i | − | 0.169369i | −0.996408 | − | 0.0846843i | \(-0.973012\pi\) | ||
0.996408 | − | 0.0846843i | \(-0.0269882\pi\) | |||||||
\(272\) | 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 | −0.613383 | − | 0.789785i | \(-0.710192\pi\) |
0.377283 | + | 0.926098i | \(0.376859\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.6685 | − | 10.2009i | −1.05029 | − | 0.606383i | −0.127556 | − | 0.991831i | \(-0.540713\pi\) |
−0.922729 | + | 0.385449i | \(0.874047\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.47004 | − | 23.4245i | 0.560957 | − | 1.38755i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.2092 | −0.835838 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.62637 | − | 11.0462i | −0.505687 | − | 0.647540i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.41037 | + | 11.1031i | −0.374498 | + | 0.648649i | −0.990252 | − | 0.139289i | \(-0.955518\pi\) |
0.615754 | + | 0.787939i | \(0.288852\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.08144 | − | 7.06926i | −0.237631 | − | 0.411589i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −19.8665 | − | 14.4537i | −1.15277 | − | 0.838686i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.0383 | − | 17.3868i | −0.580529 | − | 1.00551i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.97524 | + | 7.79002i | −0.573062 | + | 0.447525i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 21.3923i | − | 1.22492i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.93411i | 0.110386i | 0.998476 | + | 0.0551928i | \(0.0175773\pi\) | ||||
−0.998476 | + | 0.0551928i | \(0.982423\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.56073 | − | 11.2812i | 0.259451 | − | 0.641762i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.04458 | − | 1.80926i | 0.0592326 | − | 0.102594i | −0.834889 | − | 0.550419i | \(-0.814468\pi\) |
0.894121 | + | 0.447825i | \(0.147801\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.4066 | + | 11.2044i | −1.09692 | + | 0.633309i | −0.935411 | − | 0.353562i | \(-0.884970\pi\) |
−0.161512 | + | 0.986871i | \(0.551637\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.01788 | − | 1.74237i | 0.169501 | − | 0.0978614i | −0.412850 | − | 0.910799i | \(-0.635466\pi\) |
0.582350 | + | 0.812938i | \(0.302133\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.651207 | − | 1.12792i | 0.0364606 | − | 0.0631516i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.2858 | + | 3.40776i | −1.35550 | + | 0.190203i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.20549i | 0.456565i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 15.6175i | − | 0.866304i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.35842 | + | 9.68095i | 0.0751209 | + | 0.535358i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.28857 | + | 3.96392i | 0.125791 | + | 0.217877i | 0.922042 | − | 0.387090i | \(-0.126520\pi\) |
−0.796251 | + | 0.604967i | \(0.793186\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.78768 | + | 2.80197i | −0.536362 | + | 0.153547i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.2405 | + | 29.8615i | 0.941951 | + | 1.63151i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.7062 | + | 25.4720i | −0.801100 | + | 1.38755i | 0.117793 | + | 0.993038i | \(0.462418\pi\) |
−0.918893 | + | 0.394508i | \(0.870915\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.72636 | + | 21.5850i | −0.473951 | + | 1.17234i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.58045 | 0.410504 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15.5483 | − | 19.9098i | −0.837090 | − | 1.07191i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.0245 | − | 9.82911i | −0.913924 | − | 0.527654i | −0.0322323 | − | 0.999480i | \(-0.510262\pi\) |
−0.881692 | + | 0.471826i | \(0.843595\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.47286 | − | 4.89181i | 0.453542 | − | 0.261852i | −0.255783 | − | 0.966734i | \(-0.582333\pi\) |
0.709325 | + | 0.704882i | \(0.249000\pi\) | |||||||
\(350\) | 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 | ||||||||
\(359\) | 9.35147i | 0.493552i | 0.969073 | + | 0.246776i | \(0.0793712\pi\) | ||||
−0.969073 | + | 0.246776i | \(0.920629\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.12609 | −0.269794 | ||||||||
\(362\) | 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 | 0.0842608 | − | 0.996444i | \(-0.473147\pi\) |
0.905076 | + | 0.425250i | \(0.139814\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.17111 | + | 20.7018i | −0.269197 | + | 1.07769i | ||||
\(370\) | 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 | ||||||||
\(375\) | 0.843330 | + | 6.01009i | 0.0435494 | + | 0.310360i | ||||
\(376\) | 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 | ||||||||
\(381\) | −3.07424 | − | 21.9089i | −0.157498 | − | 1.12243i | ||||
\(382\) | 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 | ||||||||
\(387\) | −22.5604 | − | 21.8053i | −1.14681 | − | 1.10842i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.51109 | − | 4.91388i | 0.431529 | − | 0.249144i | −0.268469 | − | 0.963288i | \(-0.586518\pi\) |
0.699998 | + | 0.714145i | \(0.253184\pi\) | |||||||
\(390\) | 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 | ||||||||
\(395\) | 36.5392 | 1.83849 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.25762i | 0.263873i | 0.991258 | + | 0.131936i | \(0.0421194\pi\) | ||||
−0.991258 | + | 0.131936i | \(0.957881\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.7847 | − | 8.53594i | −0.738312 | − | 0.426265i | 0.0831432 | − | 0.996538i | \(-0.473504\pi\) |
−0.821455 | + | 0.570273i | \(0.806837\pi\) | |||||||
\(402\) | 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 | ||||||||
\(409\) | −16.9484 | − | 9.78516i | −0.838044 | − | 0.483845i | 0.0185546 | − | 0.999828i | \(-0.494094\pi\) |
−0.856599 | + | 0.515983i | \(0.827427\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.59486 | + | 12.2864i | 0.473280 | + | 0.606042i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.9955 | 1.17789 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.16117 | − | 2.87220i | 0.0568627 | − | 0.140652i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.3073 | + | 17.8529i | −0.503547 | + | 0.872169i | 0.496445 | + | 0.868068i | \(0.334639\pi\) |
−0.999992 | + | 0.00410056i | \(0.998695\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.704748 | + | 1.22066i | 0.0343473 | + | 0.0594913i | 0.882688 | − | 0.469959i | \(-0.155731\pi\) |
−0.848341 | + | 0.529451i | \(0.822398\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 23.7233 | + | 22.9293i | 1.15347 | + | 1.11486i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.19091 | + | 5.52682i | 0.154782 | + | 0.268090i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.65221 | + | 33.1545i | 0.224611 | + | 1.60071i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.4714i | 0.648894i | 0.945904 | + | 0.324447i | \(0.105178\pi\) | ||||
−0.945904 | + | 0.324447i | \(0.894822\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.9356i | 0.621646i | 0.950468 | + | 0.310823i | \(0.100605\pi\) | ||||
−0.950468 | + | 0.310823i | \(0.899395\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.40322 | − | 0.196899i | 0.0672794 | − | 0.00944059i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.0608 | + | 20.8899i | −0.576944 | + | 0.999297i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.75023 | + | 5.05195i | −0.417626 | + | 0.241116i | −0.694061 | − | 0.719916i | \(-0.744180\pi\) |
0.276435 | + | 0.961033i | \(0.410847\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.1220 | − | 14.5042i | 1.19358 | − | 0.689115i | 0.234466 | − | 0.972124i | \(-0.424666\pi\) |
0.959117 | + | 0.283009i | \(0.0913326\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.6873 | − | 23.7072i | 0.648842 | − | 1.12383i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.37916 | + | 20.7262i | −0.396321 | + | 0.980314i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 7.94881i | − | 0.375127i | −0.982252 | − | 0.187564i | \(-0.939941\pi\) | ||
0.982252 | − | 0.187564i | \(-0.0600591\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 33.6293i | − | 1.58354i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.7017 | + | 13.8239i | −0.831700 | + | 0.649504i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.98084 | + | 12.0912i | 0.326550 | + | 0.565601i | 0.981825 | − | 0.189789i | \(-0.0607805\pi\) |
−0.655275 | + | 0.755391i | \(0.727447\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.52549 | + | 7.93230i | 0.164556 | + | 0.370248i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.4030 | + | 28.4108i | 0.763964 | + | 1.32322i | 0.940793 | + | 0.338983i | \(0.110083\pi\) |
−0.176829 | + | 0.984242i | \(0.556584\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.8812 | + | 24.0429i | −0.645112 | + | 1.11737i | 0.339163 | + | 0.940727i | \(0.389856\pi\) |
−0.984276 | + | 0.176640i | \(0.943477\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.07607 | + | 6.49999i | 0.235397 | + | 0.301430i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.8621 | −1.05793 | −0.528966 | − | 0.848643i | \(-0.677420\pi\) | ||||
−0.528966 | + | 0.848643i | \(0.677420\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.1483 | − | 27.5758i | 0.513688 | − | 1.27063i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 42.8245 | + | 24.7247i | 1.96907 | + | 1.13684i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.2502 | + | 9.38204i | −0.745609 | + | 0.430478i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.674409 | − | 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 | ||||||||
\(485\) | 24.0317i | 1.09122i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.3930 | −0.470952 | −0.235476 | − | 0.971880i | \(-0.575665\pi\) | ||||
−0.235476 | + | 0.971880i | \(0.575665\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.21837 | − | 8.68282i | −0.0550964 | − | 0.392651i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.93014 | − | 1.69172i | −0.132235 | − | 0.0763462i | 0.432423 | − | 0.901671i | \(-0.357659\pi\) |
−0.564658 | + | 0.825325i | \(0.690992\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.398522 | + | 0.230087i | −0.0179485 | + | 0.0103626i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.5938 | + | 40.4989i | 0.521104 | + | 1.82029i | ||||
\(496\) | 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 | ||||||||
\(501\) | 18.6166 | + | 7.52632i | 0.831730 | + | 0.336251i | ||||
\(502\) | 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 | ||||||||
\(507\) | −5.06873 | + | 3.95835i | −0.225110 | + | 0.175797i | ||||
\(508\) | 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 | ||||||||
\(513\) | −23.3228 | + | 10.3658i | −1.02973 | + | 0.457660i | ||||
\(514\) | 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 | ||||||||
\(521\) | −15.5024 | −0.679175 | −0.339587 | − | 0.940575i | \(-0.610287\pi\) | ||||
−0.339587 | + | 0.940575i | \(0.610287\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.8079i | 0.472595i | 0.971681 | + | 0.236298i | \(0.0759340\pi\) | ||||
−0.971681 | + | 0.236298i | \(0.924066\pi\) | |||||||
\(524\) | 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 | ||||||||
\(535\) | 36.4162 | + | 21.0249i | 1.57441 | + | 0.908986i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.2858 | − | 3.54808i | 1.09116 | − | 0.153111i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.5871 | 0.756130 | 0.378065 | − | 0.925779i | \(-0.376590\pi\) | ||||
0.378065 | + | 0.925779i | \(0.376590\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.142990 | + | 0.0200643i | −0.00613630 | + | 0.000861040i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.38108 | − | 14.5165i | 0.359006 | − | 0.621817i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.72451 | − | 9.91513i | −0.244762 | − | 0.423940i | 0.717303 | − | 0.696762i | \(-0.245377\pi\) |
−0.962065 | + | 0.272821i | \(0.912043\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.0178 | + | 15.5379i | −0.640946 | + | 0.663141i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.676511 | − | 1.17175i | −0.0288203 | − | 0.0499183i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 16.1842 | + | 6.54291i | 0.686979 | + | 0.277731i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 38.0080i | − | 1.61045i | −0.592968 | − | 0.805226i | \(-0.702044\pi\) | ||
0.592968 | − | 0.805226i | \(-0.297956\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 42.7565i | 1.80841i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.42035 | − | 10.7824i | −0.355508 | − | 0.455233i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.88438 | + | 15.3882i | −0.374432 | + | 0.648535i | −0.990242 | − | 0.139360i | \(-0.955496\pi\) |
0.615810 | + | 0.787895i | \(0.288829\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 34.5727 | − | 19.9605i | 1.45448 | − | 0.839746i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.7404 | − | 19.4801i | 1.41447 | − | 0.816646i | 0.418667 | − | 0.908140i | \(-0.362497\pi\) |
0.995806 | + | 0.0914936i | \(0.0291641\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.45245 | + | 14.6401i | −0.353724 | + | 0.612668i | −0.986899 | − | 0.161341i | \(-0.948418\pi\) |
0.633175 | + | 0.774009i | \(0.281752\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.4547 | − | 21.0705i | −0.687406 | − | 0.880233i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.7605i | 0.782368i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 47.2653i | 1.96768i | 0.179050 | + | 0.983840i | \(0.442698\pi\) | ||||
−0.179050 | + | 0.983840i | \(0.557302\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −34.6139 | − | 13.9937i | −1.43851 | − | 0.581558i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.93099 | + | 3.34458i | 0.0799736 | + | 0.138518i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −25.3136 | + | 26.1903i | −1.04659 | + | 1.08283i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.6343 | − | 20.1513i | −0.480200 | − | 0.831731i | 0.519542 | − | 0.854445i | \(-0.326103\pi\) |
−0.999742 | + | 0.0227138i | \(0.992769\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.93750 | − | 6.81995i | 0.162242 | − | 0.281011i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.9519 | − | 2.37867i | 0.697307 | − | 0.0978456i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −37.1924 | −1.52731 | −0.763654 | − | 0.645626i | \(-0.776596\pi\) | ||||
−0.763654 | + | 0.645626i | \(0.776596\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.1150 | + | 2.54188i | −0.741397 | + | 0.104032i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.9591 | − | 16.1422i | −1.14238 | − | 0.659552i | −0.195359 | − | 0.980732i | \(-0.562587\pi\) |
−0.947018 | + | 0.321180i | \(0.895921\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.7559 | − | 8.51933i | 0.601906 | − | 0.347511i | −0.167885 | − | 0.985807i | \(-0.553694\pi\) |
0.769791 | + | 0.638296i | \(0.220360\pi\) | |||||||
\(602\) | 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 | 0.661478 | − | 0.749965i | \(-0.269930\pi\) |
−0.318749 | + | 0.947839i | \(0.603263\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 44.9604i | − | 1.81890i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.7266 | 0.554414 | 0.277207 | − | 0.960810i | \(-0.410591\pi\) | ||||
0.277207 | + | 0.960810i | \(0.410591\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 28.8361 | − | 22.5191i | 1.16278 | − | 0.908058i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.84301 | − | 1.64141i | −0.114455 | − | 0.0660807i | 0.441680 | − | 0.897173i | \(-0.354383\pi\) |
−0.556135 | + | 0.831092i | \(0.687716\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.9907 | + | 8.65490i | −0.602528 | + | 0.347870i | −0.770036 | − | 0.638001i | \(-0.779762\pi\) |
0.167507 | + | 0.985871i | \(0.446428\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.68388 | + | 25.3763i | −0.107701 | + | 1.01831i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.7536 | − | 25.5539i | 0.590142 | − | 1.02216i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 31.7028 | − | 24.7579i | 1.26609 | − | 0.988733i | ||||
\(628\) | 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 | ||||||||
\(633\) | 19.5409 | + | 7.89999i | 0.776682 | + | 0.313996i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.9672 | + | 32.8522i | −0.752691 | + | 1.30370i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.62038 | + | 30.1123i | 0.341017 | + | 1.19122i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.9788 | − | 10.3801i | 0.710120 | − | 0.409988i | −0.100986 | − | 0.994888i | \(-0.532200\pi\) |
0.811105 | + | 0.584900i | \(0.198866\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.2553 | + | 9.96236i | 0.680483 | + | 0.392877i | 0.800037 | − | 0.599950i | \(-0.204813\pi\) |
−0.119554 | + | 0.992828i | \(0.538146\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.47577 | + | 53.2769i | 0.294358 | + | 2.09778i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.5340 | −1.16110 | −0.580551 | − | 0.814224i | \(-0.697163\pi\) | ||||
−0.580551 | + | 0.814224i | \(0.697163\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 12.9955i | − | 0.510118i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.7914 | − | 7.96249i | −0.539701 | − | 0.311596i | 0.205257 | − | 0.978708i | \(-0.434197\pi\) |
−0.744958 | + | 0.667112i | \(0.767530\pi\) | |||||||
\(654\) | 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 | −0.444414 | − | 0.895821i | \(-0.646588\pi\) |
0.553597 | + | 0.832785i | \(0.313255\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.71194 | − | 4.45249i | −0.299960 | − | 0.173182i | 0.342465 | − | 0.939531i | \(-0.388738\pi\) |
−0.642425 | + | 0.766349i | \(0.722072\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.43362 | − | 10.9667i | 0.172188 | − | 0.425913i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.35277 | −0.0523793 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.879517 | − | 1.12624i | −0.0340041 | − | 0.0435428i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.0285 | − | 29.4943i | 0.657379 | − | 1.13861i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.2311 | − | 22.9169i | −0.510021 | − | 0.883382i | −0.999933 | − | 0.0116101i | \(-0.996304\pi\) |
0.489912 | − | 0.871772i | \(-0.337029\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11.6782 | + | 16.0516i | −0.449492 | + | 0.617825i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.46424 | + | 7.73229i | 0.171575 | + | 0.297176i | 0.938971 | − | 0.343997i | \(-0.111781\pi\) |
−0.767396 | + | 0.641174i | \(0.778448\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.455341 | − | 0.355592i | 0.0174487 | − | 0.0136263i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.8628i | 1.44878i | 0.689390 | + | 0.724390i | \(0.257879\pi\) | ||||
−0.689390 | + | 0.724390i | \(0.742121\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 26.7298i | − | 1.02129i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.36221 | + | 23.1578i | −0.357191 | + | 0.883525i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.66963 | + | 2.89189i | −0.0636080 | + | 0.110172i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.94211 | − | 2.85333i | 0.188007 | − | 0.108546i | −0.403042 | − | 0.915181i | \(-0.632047\pi\) |
0.591049 | + | 0.806636i | \(0.298714\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.60039 | + | 2.65604i | −0.174503 | + | 0.100749i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.94103 | + | 10.2902i | −0.225032 | + | 0.389768i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25.3424 | + | 3.55602i | −0.958537 | + | 0.134501i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.19949i | 0.309690i | 0.987939 | + | 0.154845i | \(0.0494879\pi\) | ||||
−0.987939 | + | 0.154845i | \(0.950512\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 16.6689i | − | 0.628679i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.86112 | − | 56.0232i | −0.296067 | − | 2.10995i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.0757 | − | 17.4517i | −0.378402 | − | 0.655412i | 0.612428 | − | 0.790527i | \(-0.290193\pi\) |
−0.990830 | + | 0.135115i | \(0.956860\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −26.5395 | − | 25.6512i | −0.995309 | − | 0.961996i | ||||
\(712\) | 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 | ||||||||
\(717\) | 16.8918 | − | 41.7825i | 0.630836 | − | 1.56040i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 51.1991 | 1.90940 | 0.954702 | − | 0.297563i | \(-0.0961739\pi\) | ||||
0.954702 | + | 0.297563i | \(0.0961739\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.04706 | + | 2.62129i | 0.0761309 | + | 0.0974868i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.911330 | − | 0.526157i | −0.0338460 | − | 0.0195410i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.7848 | + | 7.95865i | −0.511249 | + | 0.295170i | −0.733347 | − | 0.679854i | \(-0.762043\pi\) |
0.222098 | + | 0.975024i | \(0.428710\pi\) | |||||||
\(728\) | 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 | 0.566282 | − | 0.824212i | \(-0.308381\pi\) |
−0.430647 | + | 0.902520i | \(0.641715\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 54.8946i | 2.02207i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.3669 | 1.04349 | 0.521747 | − | 0.853100i | \(-0.325280\pi\) | ||||
0.521747 | + | 0.853100i | \(0.325280\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 32.2448 | + | 13.0359i | 1.18454 | + | 0.478886i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.8850 | + | 12.6353i | 0.802884 | + | 0.463545i | 0.844479 | − | 0.535589i | \(-0.179910\pi\) |
−0.0415945 | + | 0.999135i | \(0.513244\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 33.1971 | − | 19.1664i | 1.21625 | − | 0.702201i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17.4286 | − | 16.8453i | −0.637681 | − | 0.616337i | ||||
\(748\) | 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 | ||||||||
\(753\) | −2.40120 | − | 17.1124i | −0.0875045 | − | 0.623610i | ||||
\(754\) | 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 | ||||||||
\(759\) | −5.58847 | − | 39.8268i | −0.202848 | − | 1.44562i | ||||
\(760\) | 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 | ||||||||
\(765\) | 3.60705 | − | 14.4404i | 0.130413 | − | 0.522092i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.73114 | − | 5.61827i | 0.351371 | − | 0.202864i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.2182 | + | 11.6730i | 0.729086 | + | 0.420938i | 0.818088 | − | 0.575094i | \(-0.195034\pi\) |
−0.0890020 | + | 0.996031i | \(0.528368\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.0985 | − | 9.74253i | −0.867887 | − | 0.350869i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34.4402 | 1.23873 | 0.619364 | − | 0.785104i | \(-0.287391\pi\) | ||||
0.619364 | + | 0.785104i | \(0.287391\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 6.12479i | − | 0.220009i | ||||||
\(776\) | 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 | ||||||||
\(787\) | 7.19975 | + | 4.15678i | 0.256643 | + | 0.148173i | 0.622802 | − | 0.782379i | \(-0.285994\pi\) |
−0.366159 | + | 0.930552i | \(0.619327\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.52142 | − | 9.63129i | −0.267769 | − | 0.342883i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.4474 | 1.04571 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.57482 | + | 3.89538i | −0.0558532 | + | 0.138155i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.426036 | − | 0.737916i | 0.0150910 | − | 0.0261383i | −0.858381 | − | 0.513012i | \(-0.828530\pi\) |
0.873472 | + | 0.486874i | \(0.161863\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.18614 | + | 15.9109i | 0.324982 | + | 0.562886i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −26.5844 | + | 7.61045i | −0.939314 | + | 0.268902i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −37.2595 | − | 64.5354i | −1.31486 | − | 2.27740i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.16739 | + | 51.0792i | 0.252304 | + | 1.79807i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.4400i | 1.28116i | 0.767891 | + | 0.640581i | \(0.221306\pi\) | ||||
−0.767891 | + | 0.640581i | \(0.778694\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.08986i | − | 0.0382702i | −0.999817 | − | 0.0191351i | \(-0.993909\pi\) | ||
0.999817 | − | 0.0191351i | \(-0.00609126\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.78238 | − | 0.671060i | 0.167725 | − | 0.0235351i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.51697 | + | 13.0198i | −0.263308 | + | 0.456063i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 44.4885 | − | 25.6855i | 1.55646 | − | 0.898620i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.9748 | − | 12.1098i | 0.732025 | − | 0.422635i | −0.0871374 | − | 0.996196i | \(-0.527772\pi\) |
0.819163 | + | 0.573561i | \(0.194439\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.85592 | + | 4.94660i | −0.0995512 | + | 0.172428i | −0.911499 | − | 0.411302i | \(-0.865074\pi\) |
0.811948 | + | 0.583730i | \(0.198407\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.7258 | − | 29.0041i | 0.408239 | − | 1.00979i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.4579i | 1.26777i | 0.773429 | + | 0.633883i | \(0.218540\pi\) | ||||
−0.773429 | + | 0.633883i | \(0.781460\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.575352i | 0.0199828i | 0.999950 | + | 0.00999140i | \(0.00318041\pi\) | ||||
−0.999950 | + | 0.00999140i | \(0.996820\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.5402 | − | 14.4787i | 0.643151 | − | 0.502260i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.2156 | − | 29.8183i | −0.595770 | − | 1.03190i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.876213 | − | 8.28464i | 0.0302864 | − | 0.286359i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.9341 | − | 41.4550i | −0.826295 | − | 1.43119i | −0.900925 | − | 0.433974i | \(-0.857111\pi\) |
0.0746300 | − | 0.997211i | \(-0.476222\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4621 | + | 25.0490i | −0.498692 | + | 0.863759i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.87193 | − | 6.23859i | −0.167798 | − | 0.214868i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.0274 | 0.379352 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.2446 | − | 32.7611i | 0.454554 | − | 1.12436i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.4329 | − | 8.33286i | −0.494755 | − | 0.285647i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.5393 | − | 23.4054i | 1.38804 | − | 0.801385i | 0.394945 | − | 0.918705i | \(-0.370764\pi\) |
0.993094 | + | 0.117320i | \(0.0374303\pi\) | |||||||
\(854\) | 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 | 0.417975 | − | 0.908459i | \(-0.362740\pi\) |
−0.577761 | + | 0.816206i | \(0.696073\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.0383i | 1.39696i | 0.715630 | + | 0.698480i | \(0.246140\pi\) | ||||
−0.715630 | + | 0.698480i | \(0.753860\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.6120 | 0.632826 | ||||||||
\(866\) | 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 | ||||||||
\(873\) | 16.8707 | − | 17.4550i | 0.570988 | − | 0.590762i | ||||
\(874\) | 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 | ||||||||
\(879\) | −20.5874 | − | 8.32305i | −0.694396 | − | 0.280730i | ||||
\(880\) | 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 | ||||||||
\(885\) | 11.1432 | − | 8.70213i | 0.374575 | − | 0.292519i | ||||
\(886\) | 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 | ||||||||
\(891\) | 20.0101 | − | 37.5547i | 0.670363 | − | 1.25813i | ||||
\(892\) | 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 | ||||||||
\(899\) | 0.441640 | 0.0147295 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.36453i | − | 0.0454592i | ||||||
\(902\) | 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 | 0.366713 | − | 0.930334i | \(-0.380483\pi\) |
0.989050 | + | 0.147584i | \(0.0471496\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33.0833 | + | 19.1007i | 1.09490 | + | 0.632140i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 36.6931 | − | 5.14875i | 1.21304 | − | 0.170212i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.6325 | −0.977486 | −0.488743 | − | 0.872428i | \(-0.662544\pi\) | ||||
−0.488743 | + | 0.872428i | \(0.662544\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.31748 | + | 0.465506i | −0.109315 | + | 0.0153389i | ||||
\(922\) | 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 | ||||||||
\(927\) | 20.4476 | + | 5.10761i | 0.671589 | + | 0.167756i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.6186 | + | 28.7842i | 0.545238 | + | 0.944380i | 0.998592 | + | 0.0530496i | \(0.0168941\pi\) |
−0.453354 | + | 0.891331i | \(0.649773\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.35474 | + | 1.35625i | 0.109829 | + | 0.0444017i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 23.4578i | 0.767152i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 23.8190i | − | 0.778134i | −0.921209 | − | 0.389067i | \(-0.872797\pi\) | ||
0.921209 | − | 0.389067i | \(-0.127203\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.8891 | − | 30.5903i | −0.779591 | − | 0.998278i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.1201 | + | 46.9734i | −0.884091 | + | 1.53129i | −0.0373389 | + | 0.999303i | \(0.511888\pi\) |
−0.846752 | + | 0.531988i | \(0.821445\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.2498 | + | 17.4647i | −0.985069 | + | 0.568730i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.2427 | + | 10.5324i | −0.592807 | + | 0.342257i | −0.766207 | − | 0.642594i | \(-0.777858\pi\) |
0.173399 | + | 0.984852i | \(0.444525\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.2164 | − | 55.8005i | 1.04579 | − | 1.81136i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.71495 | + | 4.75705i | 0.120465 | + | 0.154258i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.50028i | 0.145778i | 0.997340 | + | 0.0728892i | \(0.0232219\pi\) | ||||
−0.997340 | + | 0.0728892i | \(0.976778\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 45.8403i | 1.48336i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.09140 | + | 0.845510i | 0.0676054 | + | 0.0273314i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.2148 | − | 24.6207i | −0.458541 | − | 0.794216i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.6903 | − | 40.8359i | −0.376715 | − | 1.31592i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32.0090 | + | 55.4411i | 1.03040 | + | 1.78471i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.8811 | + | 18.8466i | −0.349912 | + | 0.606065i | −0.986233 | − | 0.165359i | \(-0.947122\pi\) |
0.636322 | + | 0.771424i | \(0.280455\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.0744 | + | 1.97491i | −0.452136 | + | 0.0634434i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.0443 | 1.50972 | 0.754862 | − | 0.655884i | \(-0.227704\pi\) | ||||
0.754862 | + | 0.655884i | \(0.227704\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 26.7879 | − | 3.75886i | 0.857899 | − | 0.120380i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.7766 | + | 12.5727i | 0.696695 | + | 0.402237i | 0.806115 | − | 0.591758i | \(-0.201566\pi\) |
−0.109420 | + | 0.993996i | \(0.534899\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 37.7423 | − | 21.7905i | 1.20625 | − | 0.696429i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −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 | ||||||||
\(989\) | − | 51.3612i | − | 1.63319i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.6554 | 0.592608 | 0.296304 | − | 0.955094i | \(-0.404246\pi\) | ||||
0.296304 | + | 0.955094i | \(0.404246\pi\) | |||||||
\(992\) | 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 | −0.720220 | − | 0.693746i | \(-0.755959\pi\) |
0.240691 | + | 0.970602i | \(0.422626\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.16179 | − | 16.1139i | −0.226589 | − | 0.509822i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))