Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,2,Mod(173,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.173");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.bm (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.01223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} - 156 x^{7} + 558 x^{6} - 837 x^{5} + 1782 x^{4} - 4131 x^{3} + 3645 x^{2} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 185.1 | ||
Root | \(1.68042 + 0.419752i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.185 |
Dual form | 252.2.bm.a.173.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.60579 | − | 0.649187i | −0.927102 | − | 0.374808i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.96988 | −1.32817 | −0.664085 | − | 0.747657i | \(-0.731179\pi\) | ||||
−0.664085 | + | 0.747657i | \(0.731179\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.38485 | + | 1.14563i | 0.901390 | + | 0.433009i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.15711 | + | 2.08491i | 0.719038 | + | 0.694971i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.72811i | 1.42558i | 0.701378 | + | 0.712790i | \(0.252569\pi\) | ||||
−0.701378 | + | 0.712790i | \(0.747431\pi\) | |||||||
\(12\) | 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 | ||||||||
\(17\) | 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 | −0.901024 | − | 0.433768i | \(-0.857184\pi\) |
−0.0748577 | + | 0.997194i | \(0.523850\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.08584 | − | 3.38786i | −0.673385 | − | 0.739292i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.91090i | 1.02399i | 0.858987 | + | 0.511997i | \(0.171094\pi\) | ||||
−0.858987 | + | 0.511997i | \(0.828906\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.82018 | 0.764036 | ||||||||
\(26\) | 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 | \(-0.712656\pi\) |
0.370102 | + | 0.928991i | \(0.379323\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.06943 | − | 7.59235i | 0.534319 | − | 1.32166i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.08273 | − | 3.40239i | −1.19720 | − | 0.575109i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.69681 | − | 2.93896i | −0.278954 | − | 0.483162i | 0.692171 | − | 0.721733i | \(-0.256654\pi\) |
−0.971125 | + | 0.238571i | \(0.923321\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.35823 | − | 5.58078i | −0.697875 | − | 0.893639i | ||||
\(40\) | 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 | ||||||||
\(45\) | −6.40637 | − | 6.19194i | −0.955005 | − | 0.923040i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.49885 | + | 9.52430i | −0.802090 | + | 1.38926i | 0.116148 | + | 0.993232i | \(0.462945\pi\) |
−0.918238 | + | 0.396029i | \(0.870388\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.37505 | + | 5.46433i | 0.625007 | + | 0.780619i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.28049 | + | 1.78091i | −0.319332 | + | 0.249378i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.707381 | − | 0.408407i | −0.0971663 | − | 0.0560990i | 0.450629 | − | 0.892711i | \(-0.351200\pi\) |
−0.547796 | + | 0.836612i | \(0.684533\pi\) | |||||||
\(54\) | 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 | 0.941509 | − | 0.336986i | \(-0.109408\pi\) |
−0.762594 | + | 0.646878i | \(0.776074\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.23807 | − | 3.60155i | −0.798703 | − | 0.461131i | 0.0443147 | − | 0.999018i | \(-0.485890\pi\) |
−0.843017 | + | 0.537886i | \(0.819223\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.75585 | + | 7.44347i | 0.347205 | + | 0.937789i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.5147 | − | 6.07067i | −1.30419 | − | 0.752974i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.80513 | − | 10.0548i | −0.709210 | − | 1.22839i | −0.965151 | − | 0.261695i | \(-0.915719\pi\) |
0.255941 | − | 0.966692i | \(-0.417615\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 13.6493 | + | 7.88042i | 1.59753 | + | 0.922334i | 0.991962 | + | 0.126539i | \(0.0403870\pi\) |
0.605567 | + | 0.795794i | \(0.292946\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.13440 | − | 2.48001i | −0.708340 | − | 0.286367i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.41668 | + | 11.2759i | −0.617288 | + | 1.28500i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.15163 | − | 10.6549i | 0.692112 | − | 1.19877i | −0.279032 | − | 0.960282i | \(-0.590014\pi\) |
0.971145 | − | 0.238492i | \(-0.0766530\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.306275 | + | 8.99479i | 0.0340305 | + | 0.999421i | ||||
\(82\) | 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 | ||||||||
\(87\) | −0.472485 | + | 0.0662987i | −0.0506557 | + | 0.00710797i | ||||
\(88\) | 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 | ||||||||
\(91\) | 6.10169 | + | 8.93089i | 0.639631 | + | 0.936212i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.75001 | − | 0.385879i | 0.285163 | − | 0.0400138i | ||||
\(94\) | 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 | ||||||||
\(101\) | −7.30730 | −0.727103 | −0.363552 | − | 0.931574i | \(-0.618436\pi\) | ||||
−0.363552 | + | 0.931574i | \(0.618436\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.02530i | 0.692224i | 0.938193 | + | 0.346112i | \(0.112498\pi\) | ||||
−0.938193 | + | 0.346112i | \(0.887502\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.16457 | + | 10.0615i | 0.894371 | + | 0.981905i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.2618 | − | 7.07938i | 1.18540 | − | 0.684389i | 0.228140 | − | 0.973628i | \(-0.426735\pi\) |
0.957257 | + | 0.289239i | \(0.0934022\pi\) | |||||||
\(108\) | 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 | 0.934930 | − | 0.354831i | \(-0.115462\pi\) |
0.160172 | + | 0.987089i | \(0.448795\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 14.5848i | − | 1.36004i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.37542 | + | 11.7908i | 0.312058 | + | 1.09006i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.64945 | − | 2.49335i | 0.334545 | − | 0.228565i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.3550 | −1.03228 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.70951 | + | 7.58250i | −0.875477 | + | 0.683691i | ||||
\(124\) | 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 | ||||||||
\(129\) | −2.51720 | − | 17.9391i | −0.221627 | − | 1.57945i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.4178 | 1.17232 | 0.586159 | − | 0.810196i | \(-0.300639\pi\) | ||||
0.586159 | + | 0.810196i | \(0.300639\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.9582 | + | 0.983737i | −1.12362 | + | 0.0853008i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.26754 | + | 14.1019i | 0.539424 | + | 1.21370i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.00030i | 0.768948i | 0.923136 | + | 0.384474i | \(0.125617\pi\) | ||||
−0.923136 | + | 0.384474i | \(0.874383\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.54902 | − | 0.894326i | −0.131386 | − | 0.0758557i | 0.432866 | − | 0.901458i | \(-0.357502\pi\) |
−0.564252 | + | 0.825602i | \(0.690836\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.0130 | − | 11.7242i | 1.26433 | − | 0.987357i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.66464 | + | 16.7397i | −0.808198 | + | 1.39984i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.708485 | + | 0.409044i | −0.0588365 | + | 0.0339693i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.47803 | − | 11.6148i | −0.286863 | − | 0.957972i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 12.9072i | − | 1.05740i | −0.848810 | − | 0.528698i | \(-0.822680\pi\) | ||
0.848810 | − | 0.528698i | \(-0.177320\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.9673 | −1.05526 | −0.527631 | − | 0.849473i | \(-0.676920\pi\) | ||||
−0.527631 | + | 0.849473i | \(0.676920\pi\) | |||||||
\(152\) | 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 | \(-0.426352\pi\) |
0.957605 | + | 0.288085i | \(0.0930185\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.870773 | + | 1.11504i | 0.0690568 | + | 0.0884282i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.62609 | + | 11.7118i | −0.443398 | + | 0.923017i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.53107 | + | 4.38394i | 0.198249 | + | 0.343377i | 0.947961 | − | 0.318387i | \(-0.103141\pi\) |
−0.749712 | + | 0.661764i | \(0.769808\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.11583 | + | 22.5484i | −0.709666 | + | 1.75539i | ||||
\(166\) | 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 | ||||||||
\(171\) | −14.2962 | − | 3.57105i | −1.09326 | − | 0.273085i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.13346 | − | 5.42730i | 0.238232 | − | 0.412630i | −0.721975 | − | 0.691919i | \(-0.756765\pi\) |
0.960207 | + | 0.279289i | \(0.0900987\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.11057 | + | 4.37653i | 0.688694 | + | 0.330834i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.661528 | − | 4.71446i | −0.0497235 | − | 0.354360i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.7668 | + | 7.37089i | 0.954233 | + | 0.550927i | 0.894393 | − | 0.447281i | \(-0.147608\pi\) |
0.0598395 | + | 0.998208i | \(0.480941\pi\) | |||||||
\(180\) | 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 | ||||||||
\(189\) | 0.406887 | − | 13.7417i | 0.0295967 | − | 0.999562i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.3672 | + | 7.71754i | 0.967214 | + | 0.558421i | 0.898386 | − | 0.439207i | \(-0.144741\pi\) |
0.0688282 | + | 0.997629i | \(0.478074\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.7779 | − | 18.6678i | −0.775808 | − | 1.34374i | −0.934339 | − | 0.356385i | \(-0.884009\pi\) |
0.158532 | − | 0.987354i | \(-0.449324\pi\) | |||||||
\(194\) | 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 | ||||||||
\(199\) | −9.14623 | − | 5.28058i | −0.648359 | − | 0.374330i | 0.139468 | − | 0.990227i | \(-0.455461\pi\) |
−0.787827 | + | 0.615896i | \(0.788794\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.79438 | + | 19.9145i | 0.197100 | + | 1.40466i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.726712 | − | 0.0551692i | 0.0510052 | − | 0.00387212i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.5618 | + | 18.2936i | −0.737670 | + | 1.27768i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.2388 | + | 10.5934i | −0.711646 | + | 0.736290i | ||||
\(208\) | 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 | ||||||||
\(213\) | −6.77791 | + | 16.7654i | −0.464415 | + | 1.14875i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.5304 | − | 26.8994i | −1.05916 | − | 1.83453i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.22969 | + | 0.321102i | −0.287130 | + | 0.0217978i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.8020 | − | 21.5152i | −1.13537 | − | 1.45386i | ||||
\(220\) | 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 | ||||||||
\(227\) | 0.333557 | 0.0221390 | 0.0110695 | − | 0.999939i | \(-0.496476\pi\) | ||||
0.0110695 | + | 0.999939i | \(0.496476\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 14.4214i | − | 0.952996i | −0.879176 | − | 0.476498i | \(-0.841906\pi\) | ||
0.879176 | − | 0.476498i | \(-0.158094\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.0182 | − | 14.5902i | 1.05392 | − | 0.959964i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.7953 | − | 7.38739i | 0.838250 | − | 0.483964i | −0.0184192 | − | 0.999830i | \(-0.505863\pi\) |
0.856669 | + | 0.515867i | \(0.172530\pi\) | |||||||
\(234\) | 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 | −0.458707 | − | 0.888588i | \(-0.651687\pi\) |
−0.998893 | + | 0.0470423i | \(0.985020\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.92021i | 0.123692i | 0.998086 | + | 0.0618458i | \(0.0196987\pi\) | ||||
−0.998086 | + | 0.0618458i | \(0.980301\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.34748 | − | 14.6426i | 0.343041 | − | 0.939320i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.9934 | − | 16.2284i | −0.830116 | − | 1.03680i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.0804 | −1.27768 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.94462 | − | 13.8585i | −0.123235 | − | 0.878249i | ||||
\(250\) | 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 | ||||||||
\(255\) | 6.77277 | − | 5.28909i | 0.424127 | − | 0.331216i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.0073 | 0.936129 | 0.468064 | − | 0.883694i | \(-0.344952\pi\) | ||||
0.468064 | + | 0.883694i | \(0.344952\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.679670 | − | 8.95291i | −0.0422327 | − | 0.556306i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.801751 | + | 0.200269i | 0.0496271 | + | 0.0123964i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 7.05534i | − | 0.435051i | −0.976055 | − | 0.217525i | \(-0.930202\pi\) | ||
0.976055 | − | 0.217525i | \(-0.0697985\pi\) | |||||||
\(264\) | 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 | −0.571543 | − | 0.820572i | \(-0.693655\pi\) |
0.424865 | + | 0.905257i | \(0.360321\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.00021 | − | 18.3023i | −0.242104 | − | 1.10770i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 18.0622i | 1.08919i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.5815 | 0.816032 | 0.408016 | − | 0.912975i | \(-0.366221\pi\) | ||||
0.408016 | + | 0.912975i | \(0.366221\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −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 | \(-0.459287\pi\) |
0.922729 | + | 0.385449i | \(0.125953\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −25.0212 | + | 3.51096i | −1.48213 | + | 0.207971i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.5381 | − | 10.6158i | 0.917184 | − | 0.626631i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.10462 | + | 12.3056i | 0.417919 | + | 0.723857i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.8795 | − | 1.94756i | 0.813629 | − | 0.114168i | ||||
\(292\) | 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 | ||||||||
\(297\) | 22.4505 | − | 9.97806i | 1.30271 | − | 0.578986i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.0383 | + | 17.3868i | −0.580529 | + | 1.00551i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.09464 | + | 27.5915i | 0.120733 | + | 1.59035i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.7340 | + | 4.74380i | 0.674099 | + | 0.272524i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 18.5263 | + | 10.6962i | 1.06081 | + | 0.612461i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.93411i | 0.110386i | 0.998476 | + | 0.0551928i | \(0.0175773\pi\) | ||||
−0.998476 | + | 0.0551928i | \(0.982423\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.56073 | − | 11.2812i | 0.259451 | − | 0.641762i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.04458 | + | 1.80926i | 0.0592326 | + | 0.102594i | 0.894121 | − | 0.447825i | \(-0.147801\pi\) |
−0.834889 | + | 0.550419i | \(0.814468\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.4066 | + | 11.2044i | 1.09692 | + | 0.633309i | 0.935411 | − | 0.353562i | \(-0.115030\pi\) |
0.161512 | + | 0.986871i | \(0.448363\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.18455 | − | 22.1062i | −0.461147 | − | 1.24554i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.01788 | − | 1.74237i | −0.169501 | − | 0.0978614i | 0.412850 | − | 0.910799i | \(-0.364534\pi\) |
−0.582350 | + | 0.812938i | \(0.697867\pi\) | |||||||
\(318\) | 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 | ||||||||
\(325\) | 13.5252 | + | 7.80876i | 0.750241 | + | 0.433152i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.70473 | − | 6.01690i | 0.426073 | − | 0.332735i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.0253 | + | 16.4144i | −1.32456 | + | 0.904954i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.28857 | − | 3.96392i | 0.125791 | − | 0.217877i | −0.796251 | − | 0.604967i | \(-0.793186\pi\) |
0.922042 | + | 0.387090i | \(0.126520\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.46727 | − | 9.87737i | 0.135205 | − | 0.541276i | ||||
\(334\) | 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 | ||||||||
\(339\) | −14.3300 | − | 18.3497i | −0.778297 | − | 0.996621i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.79023 | − | 6.56486i | −0.205252 | − | 0.355507i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.17373 | + | 18.0438i | 0.225360 | + | 0.974276i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.46825 | + | 23.4201i | −0.509753 | + | 1.26089i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.0245 | − | 9.82911i | 0.913924 | − | 0.527654i | 0.0322323 | − | 0.999480i | \(-0.489738\pi\) |
0.881692 | + | 0.471826i | \(0.156405\pi\) | |||||||
\(348\) | 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 | ||||||||
\(353\) | 25.0645 | 1.33405 | 0.667023 | − | 0.745037i | \(-0.267568\pi\) | ||||
0.667023 | + | 0.745037i | \(0.267568\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 31.0074i | 1.64570i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.47890 | + | 1.63461i | −0.395825 | + | 0.0865130i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.09861 | − | 4.67574i | 0.427428 | − | 0.246776i | −0.270822 | − | 0.962629i | \(-0.587296\pi\) |
0.698251 | + | 0.715853i | \(0.253962\pi\) | |||||||
\(360\) | 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 | ||||||||
\(367\) | 21.8850i | 1.14239i | 0.820815 | + | 0.571194i | \(0.193520\pi\) | ||||
−0.820815 | + | 0.571194i | \(0.806480\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 20.5139 | − | 5.87261i | 1.06791 | − | 0.305716i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.21912 | − | 1.78439i | −0.0632934 | − | 0.0926409i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.61644 | 0.239030 | 0.119515 | − | 0.992832i | \(-0.461866\pi\) | ||||
0.119515 | + | 0.992832i | \(0.461866\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.62655 | − | 2.27470i | −0.290554 | − | 0.117465i | ||||
\(376\) | 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 | ||||||||
\(381\) | 20.5108 | + | 8.29209i | 1.05080 | + | 0.424817i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.9977 | −1.12403 | −0.562015 | − | 0.827127i | \(-0.689974\pi\) | ||||
−0.562015 | + | 0.827127i | \(0.689974\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.0869 | − | 33.4879i | 0.819864 | − | 1.70670i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.60373 | + | 30.4405i | −0.386519 | + | 1.54738i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.82776i | 0.498287i | 0.968467 | + | 0.249144i | \(0.0801491\pi\) | ||||
−0.968467 | + | 0.249144i | \(0.919851\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.10481 | + | 4.10197i | 0.359306 | + | 0.207445i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −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 | −0.381369 | − | 0.924423i | \(-0.624547\pi\) |
0.609889 | + | 0.792487i | \(0.291214\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 21.4468 | + | 6.83262i | 1.07368 | + | 0.342059i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.0719i | 0.852529i | 0.904598 | + | 0.426265i | \(0.140171\pi\) | ||||
−0.904598 | + | 0.426265i | \(0.859829\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.55444 | −0.326500 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.909599 | − | 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 | \(-0.505906\pi\) |
0.856599 | + | 0.515983i | \(0.172573\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.84288 | − | 14.4526i | 0.288208 | − | 0.712893i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.550478 | + | 7.25114i | 0.0270873 | + | 0.356805i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.9977 | − | 20.7807i | −0.588946 | − | 1.02008i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.90681 | + | 2.44170i | 0.0933769 | + | 0.119571i | ||||
\(418\) | 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 | ||||||||
\(423\) | −31.7190 | + | 9.08035i | −1.54223 | + | 0.441502i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.19091 | − | 5.52682i | 0.154782 | − | 0.268090i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.7508 | − | 15.7357i | −0.520268 | − | 0.761504i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 26.3865 | − | 20.6062i | 1.27395 | − | 0.994876i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.6666 | − | 6.73569i | −0.561959 | − | 0.324447i | 0.191973 | − | 0.981400i | \(-0.438512\pi\) |
−0.753931 | + | 0.656953i | \(0.771845\pi\) | |||||||
\(432\) | 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 | \(-0.255820\pi\) |
−0.276435 | + | 0.961033i | \(0.589153\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.95519 | + | 20.9088i | −0.0931041 | + | 0.995656i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.1220 | − | 14.5042i | −1.19358 | − | 0.689115i | −0.234466 | − | 0.972124i | \(-0.575334\pi\) |
−0.959117 | + | 0.283009i | \(0.908667\pi\) | |||||||
\(444\) | 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 | ||||||||
\(451\) | 29.1239 | + | 16.8147i | 1.37139 | + | 0.791772i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.8227 | + | 8.41819i | 0.978337 | + | 0.395521i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.1213 | − | 26.5237i | −0.849539 | − | 1.24345i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.98084 | − | 12.0912i | 0.326550 | − | 0.565601i | −0.655275 | − | 0.755391i | \(-0.727447\pi\) |
0.981825 | + | 0.189789i | \(0.0607805\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.63231 | − | 0.912985i | −0.402922 | − | 0.0426145i | ||||
\(460\) | 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 | ||||||||
\(465\) | −8.16719 | + | 1.14601i | −0.378744 | + | 0.0531451i | ||||
\(466\) | 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 | ||||||||
\(469\) | −2.32529 | − | 30.6297i | −0.107372 | − | 1.41435i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −29.4555 | + | 4.13318i | −1.35724 | + | 0.190447i | ||||
\(472\) | 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 | ||||||||
\(479\) | 2.42425 | 0.110767 | 0.0553834 | − | 0.998465i | \(-0.482362\pi\) | ||||
0.0553834 | + | 0.998465i | \(0.482362\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 13.8737i | − | 0.632584i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.6374 | − | 15.1543i | 0.757030 | − | 0.689542i | ||||
\(484\) | 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 | 0.432423 | − | 0.901671i | \(-0.357659\pi\) |
−0.564658 | + | 0.825325i | \(0.690992\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 0.460174i | − | 0.0207252i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 29.2762 | − | 30.2900i | 1.31587 | − | 1.36143i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.9611 | − | 24.8993i | 0.536530 | − | 1.11689i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.5603 | 1.77096 | 0.885481 | − | 0.464676i | \(-0.153829\pi\) | ||||
0.885481 | + | 0.464676i | \(0.153829\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.8263 | + | 12.3593i | −0.707067 | + | 0.552174i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.5476 | −0.648645 | −0.324323 | − | 0.945947i | \(-0.605136\pi\) | ||||
−0.324323 | + | 0.945947i | \(0.605136\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.7018 | 0.965717 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.893668 | − | 6.36882i | −0.0396892 | − | 0.282849i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.3916 | 0.903841 | 0.451921 | − | 0.892058i | \(-0.350739\pi\) | ||||
0.451921 | + | 0.892058i | \(0.350739\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.5235 | + | 34.4307i | 1.04062 | + | 1.52313i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.6385 | + | 15.0153i | 0.911210 | + | 0.662941i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 20.8643i | − | 0.919391i | ||||||
\(516\) | 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 | −0.281201 | − | 0.959649i | \(-0.590733\pi\) |
0.690480 | + | 0.723351i | \(0.257399\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11.7885 | − | 12.9422i | −0.514491 | − | 0.564846i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.67836i | 0.116671i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.11695 | −0.0485631 | ||||||||
\(530\) | 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 | ||||||||
\(537\) | −15.7156 | − | 20.1241i | −0.678180 | − | 0.868419i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.8360 | + | 20.6857i | −1.11283 | + | 0.890997i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.79357 | − | 15.2309i | −0.378065 | − | 0.654828i | 0.612716 | − | 0.790303i | \(-0.290077\pi\) |
−0.990781 | + | 0.135476i | \(0.956744\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.0541189 | − | 0.133865i | 0.00232247 | − | 0.00574471i | ||||
\(544\) | 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 | ||||||||
\(549\) | −5.94730 | − | 20.7748i | −0.253824 | − | 0.886646i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.676511 | + | 1.17175i | −0.0288203 | + | 0.0499183i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.8774 | − | 18.3629i | 1.14294 | − | 0.780871i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.42575 | − | 17.2873i | −0.102967 | − | 0.733807i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 32.9159 | + | 19.0040i | 1.39469 | + | 0.805226i | 0.993830 | − | 0.110912i | \(-0.0353771\pi\) |
0.400863 | + | 0.916138i | \(0.368710\pi\) | |||||||
\(558\) | 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 | 0.615810 | − | 0.787895i | \(-0.288829\pi\) |
−0.990242 | + | 0.139360i | \(0.955496\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.5727 | − | 19.9605i | −1.45448 | − | 0.839746i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.57431 | + | 21.8021i | −0.402083 | + | 0.915603i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −33.7404 | − | 19.4801i | −1.41447 | − | 0.816646i | −0.418667 | − | 0.908140i | \(-0.637503\pi\) |
−0.995806 | + | 0.0914936i | \(0.970836\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.45245 | − | 14.6401i | −0.353724 | − | 0.612668i | 0.633175 | − | 0.774009i | \(-0.281752\pi\) |
−0.986899 | + | 0.161341i | \(0.948418\pi\) | |||||||
\(572\) | 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 | \(-0.890636\pi\) |
−0.762506 | − | 0.646982i | \(-0.776031\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.18808 | + | 36.9734i | 0.215609 | + | 1.53656i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.61818 | + | 21.3153i | 0.0671333 | + | 0.884308i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.93099 | − | 3.34458i | 0.0799736 | − | 0.138518i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.0246 | − | 35.0174i | −0.414466 | − | 1.44779i | ||||
\(586\) | 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 | ||||||||
\(591\) | −6.41595 | + | 15.8701i | −0.263917 | + | 0.652809i | ||||
\(592\) | 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 | ||||||||
\(595\) | −10.8384 | + | 7.40494i | −0.444332 | + | 0.303573i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.2588 | + | 14.4171i | 0.460793 | + | 0.590053i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.9591 | − | 16.1422i | 1.14238 | − | 0.659552i | 0.195359 | − | 0.980732i | \(-0.437413\pi\) |
0.947018 | + | 0.321180i | \(0.104079\pi\) | |||||||
\(600\) | 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 | ||||||||
\(605\) | 33.7231 | 1.37104 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 9.75021i | − | 0.395749i | −0.980227 | − | 0.197874i | \(-0.936596\pi\) | ||
0.980227 | − | 0.197874i | \(-0.0634038\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.20276 | − | 0.383182i | −0.0487383 | − | 0.0155273i | ||||
\(610\) | 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 | 0.441680 | − | 0.897173i | \(-0.354383\pi\) |
−0.556135 | + | 0.831092i | \(0.687716\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 17.3098i | − | 0.695740i | −0.937543 | − | 0.347870i | \(-0.886905\pi\) | ||
0.937543 | − | 0.347870i | \(-0.113095\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 23.3184 | − | 10.3638i | 0.935736 | − | 0.415886i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.84606 | − | 24.3171i | −0.0739608 | − | 0.974243i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.5071 | −1.18028 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.58952 | + | 39.8344i | 0.223224 | + | 1.59083i | ||||
\(628\) | 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 | ||||||||
\(633\) | −16.6120 | + | 12.9729i | −0.660270 | + | 0.515628i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 37.9344 | 1.50538 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.32011 | + | 28.2892i | 0.171169 | + | 1.12086i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 21.7678 | − | 22.5216i | 0.861120 | − | 0.890941i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.7601i | 0.819976i | 0.912091 | + | 0.409988i | \(0.134467\pi\) | ||||
−0.912091 | + | 0.409988i | \(0.865533\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.2553 | + | 9.96236i | 0.680483 | + | 0.392877i | 0.800037 | − | 0.599950i | \(-0.204813\pi\) |
−0.119554 | + | 0.992828i | \(0.538146\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.47577 | + | 53.2769i | 0.294358 | + | 2.09778i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 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 | ||||||||
\(651\) | 7.00044 | + | 2.23024i | 0.274369 | + | 0.0874099i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.9250i | 0.623193i | 0.950215 | + | 0.311596i | \(0.100864\pi\) | ||||
−0.950215 | + | 0.311596i | \(0.899136\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −39.8493 | −1.55704 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 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 | \(-0.611262\pi\) |
0.642425 | + | 0.766349i | \(0.277928\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.7143 | + | 1.64374i | −0.454945 | + | 0.0638375i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 38.4843 | − | 2.92158i | 1.49236 | − | 0.113294i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.676383 | + | 1.17153i | 0.0261896 | + | 0.0453618i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.41511 | − | 0.198567i | 0.0547112 | − | 0.00767703i | ||||
\(670\) | 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 | ||||||||
\(675\) | −8.06199 | − | 18.1394i | −0.310306 | − | 0.698184i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.46424 | − | 7.73229i | 0.171575 | − | 0.297176i | −0.767396 | − | 0.641174i | \(-0.778448\pi\) |
0.938971 | + | 0.343997i | \(0.111781\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21.3475 | + | 1.62062i | −0.819243 | + | 0.0621938i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.535622 | − | 0.216541i | −0.0205251 | − | 0.00829786i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.7902 | − | 18.9314i | −1.25468 | − | 0.724390i | −0.282645 | − | 0.959225i | \(-0.591212\pi\) |
−0.972035 | + | 0.234834i | \(0.924545\pi\) | |||||||
\(684\) | 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 | \(-0.367953\pi\) |
−0.591049 | + | 0.806636i | \(0.701286\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −35.1936 | + | 13.0300i | −1.33689 | + | 0.494968i | ||||
\(694\) | 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 | ||||||||
\(703\) | 14.4357 | + | 8.33444i | 0.544452 | + | 0.314339i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −44.5869 | + | 34.8195i | −1.67924 | + | 1.31138i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.4268 | − | 8.37148i | −0.655403 | − | 0.314842i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.0757 | + | 17.4517i | −0.378402 | + | 0.655412i | −0.990830 | − | 0.135115i | \(-0.956860\pi\) |
0.612428 | + | 0.790527i | \(0.290193\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 35.4844 | − | 10.1583i | 1.33077 | − | 0.380965i | ||||
\(712\) | 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 | ||||||||
\(717\) | 27.7388 | + | 35.5200i | 1.03593 | + | 1.32652i | ||||
\(718\) | 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 | ||||||||
\(721\) | −8.04842 | + | 16.7543i | −0.299739 | + | 0.623963i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.24657 | − | 3.08345i | 0.0463606 | − | 0.114675i | ||||
\(724\) | 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 | ||||||||
\(731\) | 17.4717 | 0.646213 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 4.24025i | − | 0.156617i | −0.996929 | − | 0.0783086i | \(-0.975048\pi\) | ||
0.996929 | − | 0.0783086i | \(-0.0249519\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.3293 | + | 34.4945i | 0.381003 | + | 1.27235i | ||||
\(736\) | 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 | 0.844479 | − | 0.535589i | \(-0.179910\pi\) |
−0.0415945 | + | 0.999135i | \(0.513244\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 38.3327i | 1.40440i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.87413 | + | 23.5163i | −0.214923 | + | 0.860416i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 37.3531 | − | 2.83570i | 1.36485 | − | 0.103614i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.5460 | 1.73498 | 0.867490 | − | 0.497455i | \(-0.165732\pi\) | ||||
0.867490 | + | 0.497455i | \(0.165732\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.0204 | + | 6.47670i | 0.583814 | + | 0.236024i | ||||
\(754\) | 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 | ||||||||
\(759\) | 37.2853 | + | 15.0737i | 1.35337 | + | 0.547139i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.24283 | −0.298802 | −0.149401 | − | 0.988777i | \(-0.547735\pi\) | ||||
−0.149401 | + | 0.988777i | \(0.547735\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.3299 | + | 8.42390i | −0.446371 | + | 0.304966i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.3092 | + | 4.09638i | −0.517352 | + | 0.148105i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.2365i | 0.405728i | ||||||||
\(768\) | 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 | ||||||||
\(773\) | −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 | ||||||||
\(777\) | −4.72070 | + | 14.8177i | −0.169354 | + | 0.531582i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34.9361i | 1.25171i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49.3644 | 1.76640 | ||||||||
\(782\) | 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 | \(-0.714006\pi\) |
0.366159 | + | 0.930552i | \(0.380673\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.58023 | + | 11.3294i | −0.163061 | + | 0.403337i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.0625 | + | 29.3650i | 0.713341 | + | 1.04410i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.7237 | − | 25.5022i | −0.522854 | − | 0.905610i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.58609 | − | 3.31153i | −0.0917191 | − | 0.117448i | ||||
\(796\) | 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 | ||||||||
\(801\) | 6.70136 | − | 26.8280i | 0.236781 | − | 0.947921i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −37.2595 | + | 64.5354i | −1.31486 | + | 2.27740i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.7088 | − | 34.7826i | 0.588908 | − | 1.22592i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 40.6522 | − | 31.7467i | 1.43102 | − | 1.11754i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31.5580 | − | 18.2200i | −1.10952 | − | 0.640581i | −0.170814 | − | 0.985303i | \(-0.554640\pi\) |
−0.938705 | + | 0.344722i | \(0.887973\pi\) | |||||||
\(810\) | 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 | ||||||||
\(819\) | −5.45810 | + | 31.9864i | −0.190721 | + | 1.11770i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.9748 | − | 12.1098i | −0.732025 | − | 0.422635i | 0.0871374 | − | 0.996196i | \(-0.472228\pi\) |
−0.819163 | + | 0.573561i | \(0.805561\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.85592 | − | 4.94660i | −0.0995512 | − | 0.172428i | 0.811948 | − | 0.583730i | \(-0.198407\pi\) |
−0.911499 | + | 0.411302i | \(0.865074\pi\) | |||||||
\(824\) | 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 | ||||||||
\(829\) | −0.498269 | − | 0.287676i | −0.0173056 | − | 0.00999140i | 0.491322 | − | 0.870978i | \(-0.336514\pi\) |
−0.508628 | + | 0.860986i | \(0.669847\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.8090 | − | 8.81692i | −0.756545 | − | 0.305856i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.5599 | − | 1.76534i | 0.400526 | − | 0.0611653i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.2156 | + | 29.8183i | −0.595770 | + | 1.03190i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.73660 | + | 4.90114i | 0.232851 | + | 0.169408i | ||||
\(838\) | 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 | ||||||||
\(843\) | 7.83874 | − | 1.09993i | 0.269981 | − | 0.0378835i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.51368 | − | 9.54997i | −0.189676 | − | 0.328529i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.0801 | − | 13.0087i | −0.930483 | − | 0.446985i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −34.9943 | + | 4.91036i | −1.20100 | + | 0.168523i | ||||
\(850\) | 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 | ||||||||
\(857\) | 9.56441 | 0.326714 | 0.163357 | − | 0.986567i | \(-0.447768\pi\) | ||||
0.163357 | + | 0.986567i | \(0.447768\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.40759i | 0.184505i | 0.995736 | + | 0.0922523i | \(0.0294066\pi\) | ||||
−0.995736 | + | 0.0922523i | \(0.970593\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −31.8425 | + | 6.95961i | −1.08519 | + | 0.237183i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35.5402 | − | 20.5191i | 1.20980 | − | 0.698480i | 0.247086 | − | 0.968994i | \(-0.420527\pi\) |
0.962716 | + | 0.270514i | \(0.0871936\pi\) | |||||||
\(864\) | 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 | ||||||||
\(871\) | − | 47.4646i | − | 1.60828i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −23.5518 | − | 5.88301i | −0.797109 | − | 0.199110i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.35633 | + | 4.01421i | 0.282496 | + | 0.135705i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.6502 | −0.494701 | −0.247351 | − | 0.968926i | \(-0.579560\pi\) | ||||
−0.247351 | + | 0.968926i | \(0.579560\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17.5017 | − | 13.6677i | 0.590317 | − | 0.460999i | ||||
\(880\) | 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 | ||||||||
\(885\) | 1.96466 | + | 14.0014i | 0.0660413 | + | 0.470651i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.6844 | −0.895973 | −0.447987 | − | 0.894040i | \(-0.647859\pi\) | ||||
−0.447987 | + | 0.894040i | \(0.647859\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.4618 | − | 14.6332i | −1.02166 | − | 0.490783i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −42.5284 | + | 1.44810i | −1.42475 | + | 0.0485132i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 54.0189i | − | 1.80767i | ||||||
\(894\) | 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 | ||||||||
\(903\) | 14.5485 | − | 45.6659i | 0.484143 | − | 1.51967i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 0.247582i | − | 0.00822989i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.9442 | −0.529419 | −0.264710 | − | 0.964328i | \(-0.585276\pi\) | ||||
−0.264710 | + | 0.964328i | \(0.585276\pi\) | |||||||
\(908\) | 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 | ||||||||
\(915\) | −22.8055 | − | 29.2028i | −0.753927 | − | 0.965415i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 31.9995 | + | 15.3719i | 1.05672 | + | 0.507624i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.8163 | + | 25.6625i | 0.488743 | + | 0.846528i | 0.999916 | − | 0.0129500i | \(-0.00412223\pi\) |
−0.511173 | + | 0.859478i | \(0.670789\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.25560 | − | 3.10578i | 0.0413734 | − | 0.102339i | ||||
\(922\) | 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 | ||||||||
\(927\) | −14.6471 | + | 15.1544i | −0.481075 | + | 0.497735i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.6186 | − | 28.7842i | 0.545238 | − | 0.944380i | −0.453354 | − | 0.891331i | \(-0.649773\pi\) |
0.998592 | − | 0.0530496i | \(-0.0168941\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.0304 | − | 12.4993i | −1.04975 | − | 0.409647i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.502822 | − | 3.58342i | −0.0164617 | − | 0.117316i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.3151 | − | 11.7289i | −0.664373 | − | 0.383576i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 23.8190i | − | 0.778134i | −0.921209 | − | 0.389067i | \(-0.872797\pi\) | ||
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 | −0.846752 | − | 0.531988i | \(-0.821445\pi\) |
−0.0373389 | − | 0.999303i | \(-0.511888\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.2498 | + | 17.4647i | 0.985069 | + | 0.568730i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.20841 | + | 40.8112i | −0.0393095 | + | 1.32759i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.2427 | + | 10.5324i | 0.592807 | + | 0.342257i | 0.766207 | − | 0.642594i | \(-0.222142\pi\) |
−0.173399 | + | 0.984852i | \(0.555475\pi\) | |||||||
\(948\) | 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 | ||||||||
\(955\) | −39.6989 | − | 22.9201i | −1.28462 | − | 0.741679i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.313468 | − | 2.23396i | −0.0101330 | − | 0.0722137i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.3110 | + | 21.4644i | −0.332961 | + | 0.693122i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.2148 | + | 24.6207i | −0.458541 | + | 0.794216i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 41.2101 | + | 10.2939i | 1.32798 | + | 0.331715i | ||||
\(964\) | 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 | ||||||||
\(969\) | 5.32689 | − | 13.1763i | 0.171124 | − | 0.423283i | ||||
\(970\) | 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 | ||||||||
\(973\) | −2.66961 | − | 3.90744i | −0.0855838 | − | 0.125267i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16.6492 | − | 21.3196i | −0.533202 | − | 0.682773i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.7766 | + | 12.5727i | −0.696695 | + | 0.402237i | −0.806115 | − | 0.591758i | \(-0.798434\pi\) |
0.109420 | + | 0.993996i | \(0.465101\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | −36.2142 | −1.15505 | −0.577527 | − | 0.816372i | \(-0.695982\pi\) | ||||
−0.577527 | + | 0.816372i | \(0.695982\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.3515i | 0.935216i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 49.2356 | − | 10.7611i | 1.56719 | − | 0.342530i | ||||
\(988\) | 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 | ||||||||
\(997\) | − | 17.4836i | − | 0.553712i | −0.960911 | − | 0.276856i | \(-0.910708\pi\) | ||
0.960911 | − | 0.276856i | \(-0.0892925\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.3742 | + | 14.2592i | −0.328224 | + | 0.451143i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))