Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3240,2,Mod(1081,3240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3240, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3240.1081");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3240.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.8715302549\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2161.1 | ||
Root | \(-1.18614 + 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3240.2161 |
Dual form | 3240.2.q.bd.1081.1 |
$q$-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 \(\left(\mathbb{Z}/3240\mathbb{Z}\right)^\times\).
\(n\) | \(1297\) | \(1621\) | \(2431\) | \(3161\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.68614 | + | 2.92048i | −0.637301 | + | 1.10384i | 0.348721 | + | 0.937226i | \(0.386616\pi\) |
−0.986023 | + | 0.166612i | \(0.946717\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.18614 | − | 2.05446i | 0.357635 | − | 0.619442i | −0.629930 | − | 0.776652i | \(-0.716917\pi\) |
0.987565 | + | 0.157210i | \(0.0502499\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.68614 | + | 2.92048i | 0.467651 | + | 0.809996i | 0.999317 | − | 0.0369586i | \(-0.0117670\pi\) |
−0.531666 | + | 0.846954i | \(0.678434\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.74456 | 1.63580 | 0.817898 | − | 0.575363i | \(-0.195139\pi\) | ||||
0.817898 | + | 0.575363i | \(0.195139\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | 0.114708 | − | 0.993399i | \(-0.463407\pi\) | ||||
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.68614 | + | 4.65253i | 0.560099 | + | 0.970120i | 0.997487 | + | 0.0708472i | \(0.0225703\pi\) |
−0.437388 | + | 0.899273i | \(0.644096\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.18614 | − | 2.05446i | 0.220261 | − | 0.381503i | −0.734626 | − | 0.678472i | \(-0.762642\pi\) |
0.954887 | + | 0.296969i | \(0.0959758\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.55842 | − | 9.62747i | −0.998322 | − | 1.72914i | −0.549309 | − | 0.835619i | \(-0.685109\pi\) |
−0.449013 | − | 0.893525i | \(-0.648224\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.37228 | −0.570020 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.127719 | + | 0.221215i | 0.0199463 | + | 0.0345480i | 0.875826 | − | 0.482627i | \(-0.160317\pi\) |
−0.855880 | + | 0.517175i | \(0.826984\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.37228 | − | 4.10891i | 0.361770 | − | 0.626603i | −0.626483 | − | 0.779435i | \(-0.715506\pi\) |
0.988252 | + | 0.152832i | \(0.0488394\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.68614 | + | 8.11663i | −0.683544 | + | 1.18393i | 0.290348 | + | 0.956921i | \(0.406229\pi\) |
−0.973892 | + | 0.227012i | \(0.927104\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.18614 | − | 3.78651i | −0.312306 | − | 0.540930i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.1168 | −1.38966 | −0.694828 | − | 0.719176i | \(-0.744519\pi\) | ||||
−0.694828 | + | 0.719176i | \(0.744519\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.37228 | 0.319878 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.50000 | + | 4.33013i | 0.325472 | + | 0.563735i | 0.981608 | − | 0.190909i | \(-0.0611434\pi\) |
−0.656136 | + | 0.754643i | \(0.727810\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.37228 | + | 11.0371i | −0.815887 | + | 1.41316i | 0.0928022 | + | 0.995685i | \(0.470418\pi\) |
−0.908689 | + | 0.417473i | \(0.862916\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.68614 | + | 2.92048i | −0.209140 | + | 0.362241i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.372281 | + | 0.644810i | 0.0454814 | + | 0.0787761i | 0.887870 | − | 0.460095i | \(-0.152184\pi\) |
−0.842389 | + | 0.538871i | \(0.818851\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.37228 | 0.518894 | 0.259447 | − | 0.965757i | \(-0.416460\pi\) | ||||
0.259447 | + | 0.965757i | \(0.416460\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.7446 | 1.72572 | 0.862860 | − | 0.505443i | \(-0.168671\pi\) | ||||
0.862860 | + | 0.505443i | \(0.168671\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00000 | + | 6.92820i | 0.455842 | + | 0.789542i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.37228 | − | 2.37686i | 0.154394 | − | 0.267418i | −0.778444 | − | 0.627714i | \(-0.783991\pi\) |
0.932838 | + | 0.360296i | \(0.117324\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.00000 | + | 8.66025i | −0.548821 | + | 0.950586i | 0.449534 | + | 0.893263i | \(0.351590\pi\) |
−0.998356 | + | 0.0573233i | \(0.981743\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.37228 | + | 5.84096i | 0.365775 | + | 0.633541i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.37228 | 0.463461 | 0.231730 | − | 0.972780i | \(-0.425561\pi\) | ||||
0.231730 | + | 0.972780i | \(0.425561\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.3723 | −1.19214 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.500000 | + | 0.866025i | 0.0512989 | + | 0.0888523i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.37228 | − | 4.10891i | 0.240869 | − | 0.417197i | −0.720093 | − | 0.693877i | \(-0.755901\pi\) |
0.960962 | + | 0.276680i | \(0.0892344\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.93070 | + | 13.7364i | −0.789134 | + | 1.36682i | 0.137363 | + | 0.990521i | \(0.456137\pi\) |
−0.926498 | + | 0.376300i | \(0.877196\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.0584220 | + | 0.101190i | 0.00575649 | + | 0.00997053i | 0.868889 | − | 0.495006i | \(-0.164834\pi\) |
−0.863133 | + | 0.504977i | \(0.831501\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.00000 | 0.580042 | 0.290021 | − | 0.957020i | \(-0.406338\pi\) | ||||
0.290021 | + | 0.957020i | \(0.406338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.883156 | 0.0845910 | 0.0422955 | − | 0.999105i | \(-0.486533\pi\) | ||||
0.0422955 | + | 0.999105i | \(0.486533\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.37228 | + | 12.7692i | 0.693526 | + | 1.20122i | 0.970675 | + | 0.240395i | \(0.0772770\pi\) |
−0.277149 | + | 0.960827i | \(0.589390\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.68614 | + | 4.65253i | −0.250484 | + | 0.433851i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.3723 | + | 19.6974i | −1.04250 | + | 1.80565i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.68614 | + | 4.65253i | 0.244195 | + | 0.422957i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.8614 | −1.14127 | −0.570633 | − | 0.821205i | \(-0.693302\pi\) | ||||
−0.570633 | + | 0.821205i | \(0.693302\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.12772 | + | 5.41737i | 0.273270 | + | 0.473318i | 0.969697 | − | 0.244310i | \(-0.0785614\pi\) |
−0.696427 | + | 0.717627i | \(0.745228\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.68614 | + | 2.92048i | −0.146207 | + | 0.253238i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.62772 | + | 4.55134i | −0.224501 | + | 0.388847i | −0.956170 | − | 0.292813i | \(-0.905409\pi\) |
0.731669 | + | 0.681661i | \(0.238742\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.50000 | − | 12.9904i | −0.636142 | − | 1.10183i | −0.986272 | − | 0.165129i | \(-0.947196\pi\) |
0.350130 | − | 0.936701i | \(-0.386137\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.00000 | 0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.37228 | 0.197007 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.74456 | + | 16.8781i | 0.798306 | + | 1.38271i | 0.920719 | + | 0.390227i | \(0.127603\pi\) |
−0.122413 | + | 0.992479i | \(0.539063\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.1861 | + | 21.1070i | −0.991694 | + | 1.71766i | −0.384460 | + | 0.923142i | \(0.625612\pi\) |
−0.607234 | + | 0.794523i | \(0.707721\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.55842 | − | 9.62747i | 0.446463 | − | 0.773297i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.4307 | − | 19.7986i | −0.912269 | − | 1.58010i | −0.810851 | − | 0.585253i | \(-0.800995\pi\) |
−0.101419 | − | 0.994844i | \(-0.532338\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −18.1168 | −1.42781 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.48913 | 0.743246 | 0.371623 | − | 0.928384i | \(-0.378801\pi\) | ||||
0.371623 | + | 0.928384i | \(0.378801\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.00000 | − | 10.3923i | −0.464294 | − | 0.804181i | 0.534875 | − | 0.844931i | \(-0.320359\pi\) |
−0.999169 | + | 0.0407502i | \(0.987025\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.813859 | − | 1.40965i | 0.0626046 | − | 0.108434i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.43070 | − | 12.8704i | 0.564946 | − | 0.978515i | −0.432109 | − | 0.901821i | \(-0.642230\pi\) |
0.997055 | − | 0.0766935i | \(-0.0244363\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.68614 | − | 2.92048i | −0.127460 | − | 0.220768i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.25544 | 0.318066 | 0.159033 | − | 0.987273i | \(-0.449162\pi\) | ||||
0.159033 | + | 0.987273i | \(0.449162\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.8614 | −1.03031 | −0.515155 | − | 0.857097i | \(-0.672266\pi\) | ||||
−0.515155 | + | 0.857097i | \(0.672266\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.00000 | + | 5.19615i | 0.220564 | + | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.00000 | − | 13.8564i | 0.585018 | − | 1.01328i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.81386 | + | 4.87375i | −0.203604 | + | 0.352652i | −0.949687 | − | 0.313201i | \(-0.898599\pi\) |
0.746083 | + | 0.665853i | \(0.231932\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.372281 | − | 0.644810i | −0.0267974 | − | 0.0464145i | 0.852316 | − | 0.523028i | \(-0.175198\pi\) |
−0.879113 | + | 0.476613i | \(0.841864\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.627719 | 0.0447231 | 0.0223616 | − | 0.999750i | \(-0.492882\pi\) | ||||
0.0223616 | + | 0.999750i | \(0.492882\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.4891 | 0.956219 | 0.478109 | − | 0.878300i | \(-0.341322\pi\) | ||||
0.478109 | + | 0.878300i | \(0.341322\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.00000 | + | 6.92820i | 0.280745 | + | 0.486265i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.127719 | + | 0.221215i | −0.00892026 | + | 0.0154503i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.18614 | − | 2.05446i | 0.0820471 | − | 0.142110i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.50000 | − | 14.7224i | −0.585164 | − | 1.01353i | −0.994855 | − | 0.101310i | \(-0.967697\pi\) |
0.409691 | − | 0.912224i | \(-0.365637\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.74456 | 0.323576 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 37.4891 | 2.54493 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.3723 | + | 19.6974i | 0.764982 | + | 1.32499i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.7446 | + | 22.0742i | −0.853439 | + | 1.47820i | 0.0246466 | + | 0.999696i | \(0.492154\pi\) |
−0.878086 | + | 0.478504i | \(0.841179\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.74456 | + | 15.1460i | −0.580397 | + | 1.00528i | 0.415035 | + | 0.909805i | \(0.363769\pi\) |
−0.995432 | + | 0.0954717i | \(0.969564\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.37228 | + | 14.5012i | 0.553256 | + | 0.958267i | 0.998037 | + | 0.0626280i | \(0.0199482\pi\) |
−0.444781 | + | 0.895639i | \(0.646718\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.2337 | 0.932480 | 0.466240 | − | 0.884658i | \(-0.345608\pi\) | ||||
0.466240 | + | 0.884658i | \(0.345608\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.37228 | −0.611380 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.1168 | − | 17.5229i | −0.654404 | − | 1.13346i | −0.982043 | − | 0.188658i | \(-0.939586\pi\) |
0.327639 | − | 0.944803i | \(-0.393747\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.30298 | − | 9.18504i | 0.341595 | − | 0.591660i | −0.643134 | − | 0.765754i | \(-0.722366\pi\) |
0.984729 | + | 0.174093i | \(0.0556995\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.18614 | − | 3.78651i | 0.139667 | − | 0.241911i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.68614 | + | 2.92048i | 0.107287 | + | 0.185826i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.8614 | 0.811805 | 0.405902 | − | 0.913916i | \(-0.366957\pi\) | ||||
0.405902 | + | 0.913916i | \(0.366957\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.7446 | 0.801244 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.255437 | + | 0.442430i | 0.0159337 | + | 0.0275981i | 0.873882 | − | 0.486137i | \(-0.161595\pi\) |
−0.857949 | + | 0.513736i | \(0.828261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.1168 | + | 17.5229i | −0.628630 | + | 1.08882i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.05842 | − | 3.56529i | 0.126928 | − | 0.219845i | −0.795557 | − | 0.605879i | \(-0.792822\pi\) |
0.922485 | + | 0.386033i | \(0.126155\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.05842 | − | 8.76144i | −0.310736 | − | 0.538211i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.11684 | 0.311979 | 0.155990 | − | 0.987759i | \(-0.450143\pi\) | ||||
0.155990 | + | 0.987759i | \(0.450143\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.25544 | −0.562228 | −0.281114 | − | 0.959674i | \(-0.590704\pi\) | ||||
−0.281114 | + | 0.959674i | \(0.590704\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.18614 | + | 2.05446i | 0.0715270 | + | 0.123888i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.0584220 | + | 0.101190i | −0.00351024 | + | 0.00607991i | −0.867775 | − | 0.496957i | \(-0.834451\pi\) |
0.864265 | + | 0.503037i | \(0.167784\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.68614 | − | 15.0448i | 0.518172 | − | 0.897500i | −0.481605 | − | 0.876388i | \(-0.659946\pi\) |
0.999777 | − | 0.0211116i | \(-0.00672052\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.37228 | − | 14.5012i | −0.497680 | − | 0.862008i | 0.502316 | − | 0.864684i | \(-0.332481\pi\) |
−0.999996 | + | 0.00267630i | \(0.999148\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.861407 | −0.0508472 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.4891 | 1.67583 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.43070 | − | 12.8704i | −0.434106 | − | 0.751894i | 0.563116 | − | 0.826378i | \(-0.309602\pi\) |
−0.997222 | + | 0.0744837i | \(0.976269\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.50000 | + | 4.33013i | −0.145556 | + | 0.252110i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.05842 | + | 15.6896i | −0.523862 | + | 0.907356i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000 | + | 13.8564i | 0.461112 | + | 0.798670i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.7446 | −0.729752 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.744563 | 0.0424944 | 0.0212472 | − | 0.999774i | \(-0.493236\pi\) | ||||
0.0212472 | + | 0.999774i | \(0.493236\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.93070 | + | 15.4684i | 0.506414 | + | 0.877134i | 0.999972 | + | 0.00742183i | \(0.00236246\pi\) |
−0.493559 | + | 0.869712i | \(0.664304\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.00000 | − | 3.46410i | 0.113047 | − | 0.195803i | −0.803951 | − | 0.594696i | \(-0.797272\pi\) |
0.916997 | + | 0.398894i | \(0.130606\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.31386 | + | 9.20387i | −0.298456 | + | 0.516941i | −0.975783 | − | 0.218741i | \(-0.929805\pi\) |
0.677327 | + | 0.735682i | \(0.263138\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.81386 | − | 4.87375i | −0.157546 | − | 0.272877i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.74456 | 0.375278 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.37228 | −0.187061 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.8030 | − | 27.3716i | −0.871247 | − | 1.50904i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.81386 | + | 11.8020i | −0.374524 | + | 0.648694i | −0.990256 | − | 0.139262i | \(-0.955527\pi\) |
0.615732 | + | 0.787956i | \(0.288860\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.372281 | + | 0.644810i | −0.0203399 | + | 0.0352297i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.37228 | + | 9.30506i | 0.292647 | + | 0.506879i | 0.974435 | − | 0.224671i | \(-0.0721306\pi\) |
−0.681788 | + | 0.731550i | \(0.738797\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.3723 | −1.42814 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.86141 | −0.478471 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.11684 | + | 3.66648i | 0.113638 | + | 0.196827i | 0.917235 | − | 0.398348i | \(-0.130416\pi\) |
−0.803596 | + | 0.595175i | \(0.797083\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.81386 | − | 16.9981i | 0.525324 | − | 0.909888i | −0.474241 | − | 0.880395i | \(-0.657278\pi\) |
0.999565 | − | 0.0294926i | \(-0.00938915\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.4891 | + | 18.1677i | −0.558280 | + | 0.966969i | 0.439360 | + | 0.898311i | \(0.355205\pi\) |
−0.997640 | + | 0.0686581i | \(0.978128\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.18614 | + | 3.78651i | 0.116028 | + | 0.200967i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.3723 | 0.864096 | 0.432048 | − | 0.901851i | \(-0.357791\pi\) | ||||
0.432048 | + | 0.901851i | \(0.357791\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.37228 | + | 12.7692i | 0.385883 | + | 0.668369i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.1168 | − | 26.1831i | 0.789093 | − | 1.36675i | −0.137430 | − | 0.990511i | \(-0.543884\pi\) |
0.926523 | − | 0.376237i | \(-0.122782\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.0584 | − | 29.5461i | 0.885629 | − | 1.53395i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.37228 | + | 9.30506i | 0.278166 | + | 0.481798i | 0.970929 | − | 0.239368i | \(-0.0769401\pi\) |
−0.692763 | + | 0.721165i | \(0.743607\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.00000 | 0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.3505 | −1.35354 | −0.676768 | − | 0.736196i | \(-0.736620\pi\) | ||||
−0.676768 | + | 0.736196i | \(0.736620\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.68614 | − | 16.7769i | −0.494939 | − | 0.857259i | 0.505044 | − | 0.863093i | \(-0.331476\pi\) |
−0.999983 | + | 0.00583450i | \(0.998143\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.00000 | + | 6.92820i | −0.203859 | + | 0.353094i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.3723 | − | 17.9653i | 0.525896 | − | 0.910878i | −0.473649 | − | 0.880713i | \(-0.657064\pi\) |
0.999545 | − | 0.0301643i | \(-0.00960306\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.1168 | + | 31.3793i | 0.916208 | + | 1.58692i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.74456 | 0.138094 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.0000 | 1.70641 | 0.853206 | − | 0.521575i | \(-0.174655\pi\) | ||||
0.853206 | + | 0.521575i | \(0.174655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.1753 | + | 31.4805i | 0.907629 | + | 1.57206i | 0.817348 | + | 0.576144i | \(0.195443\pi\) |
0.0902813 | + | 0.995916i | \(0.471223\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.7446 | − | 32.4665i | 0.933733 | − | 1.61727i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.11684 | − | 12.3267i | 0.352769 | − | 0.611014i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.6861 | + | 18.5089i | 0.528396 | + | 0.915208i | 0.999452 | + | 0.0331049i | \(0.0105396\pi\) |
−0.471056 | + | 0.882103i | \(0.656127\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.8614 | −0.829696 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.0000 | −0.490881 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.4891 | + | 30.2921i | 0.854400 | + | 1.47986i | 0.877201 | + | 0.480124i | \(0.159408\pi\) |
−0.0228011 | + | 0.999740i | \(0.507258\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.1861 | + | 24.5711i | −0.691390 | + | 1.19752i | 0.279992 | + | 0.960002i | \(0.409668\pi\) |
−0.971382 | + | 0.237521i | \(0.923665\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.37228 | + | 5.84096i | −0.163580 | + | 0.283328i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.4891 | − | 37.2203i | −1.03993 | − | 1.80121i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.62772 | −0.463751 | −0.231875 | − | 0.972745i | \(-0.574486\pi\) | ||||
−0.231875 | + | 0.972745i | \(0.574486\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −41.2119 | −1.98052 | −0.990260 | − | 0.139233i | \(-0.955536\pi\) | ||||
−0.990260 | + | 0.139233i | \(0.955536\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.68614 | + | 4.65253i | 0.128496 | + | 0.222561i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0475 | − | 27.7952i | 0.765908 | − | 1.32659i | −0.173858 | − | 0.984771i | \(-0.555623\pi\) |
0.939765 | − | 0.341820i | \(-0.111043\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.4891 | + | 25.0959i | −0.688399 | + | 1.19234i | 0.283956 | + | 0.958837i | \(0.408353\pi\) |
−0.972356 | + | 0.233505i | \(0.924980\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.18614 | + | 3.78651i | 0.103633 | + | 0.179498i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.7228 | −1.63867 | −0.819335 | − | 0.573314i | \(-0.805657\pi\) | ||||
−0.819335 | + | 0.573314i | \(0.805657\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.605969 | 0.0285340 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.68614 | − | 9.84868i | −0.266570 | − | 0.461713i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.88316 | − | 4.99377i | 0.134868 | − | 0.233599i | −0.790679 | − | 0.612231i | \(-0.790272\pi\) |
0.925547 | + | 0.378632i | \(0.123606\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.5584 | − | 26.9480i | 0.724628 | − | 1.25509i | −0.234499 | − | 0.972116i | \(-0.575345\pi\) |
0.959127 | − | 0.282976i | \(-0.0913217\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.43070 | − | 5.94215i | −0.159438 | − | 0.276155i | 0.775228 | − | 0.631682i | \(-0.217635\pi\) |
−0.934666 | + | 0.355526i | \(0.884302\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.2337 | −0.751205 | −0.375603 | − | 0.926781i | \(-0.622564\pi\) | ||||
−0.375603 | + | 0.926781i | \(0.622564\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.51087 | −0.115941 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.62772 | − | 9.74749i | −0.258763 | − | 0.448190i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.500000 | + | 0.866025i | −0.0229416 | + | 0.0397360i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.44158 | + | 5.96099i | −0.157250 | + | 0.272364i | −0.933876 | − | 0.357597i | \(-0.883596\pi\) |
0.776626 | + | 0.629962i | \(0.216929\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.1168 | + | 17.5229i | 0.461288 | + | 0.798975i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.74456 | 0.215439 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.6060 | 0.888431 | 0.444216 | − | 0.895920i | \(-0.353482\pi\) | ||||
0.444216 | + | 0.895920i | \(0.353482\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.9891 | − | 22.4978i | −0.586191 | − | 1.01531i | −0.994726 | − | 0.102570i | \(-0.967293\pi\) |
0.408535 | − | 0.912743i | \(-0.366040\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.00000 | − | 13.8564i | 0.360302 | − | 0.624061i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.37228 | + | 12.7692i | −0.330692 | + | 0.572775i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.87228 | − | 17.0993i | −0.441944 | − | 0.765469i | 0.555890 | − | 0.831256i | \(-0.312378\pi\) |
−0.997834 | + | 0.0657866i | \(0.979044\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.9783 | −0.489496 | −0.244748 | − | 0.969587i | \(-0.578705\pi\) | ||||
−0.244748 | + | 0.969587i | \(0.578705\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.8614 | −0.705823 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.0000 | − | 32.9090i | −0.842160 | − | 1.45866i | −0.888065 | − | 0.459718i | \(-0.847950\pi\) |
0.0459045 | − | 0.998946i | \(-0.485383\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.8614 | + | 43.0612i | −1.09980 | + | 1.90492i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.0584220 | + | 0.101190i | −0.00257438 | + | 0.00445896i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.1168 | + | 19.2549i | 0.488918 | + | 0.846831i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.116844 | 0.00511903 | 0.00255951 | − | 0.999997i | \(-0.499185\pi\) | ||||
0.00255951 | + | 0.999997i | \(0.499185\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −40.2337 | −1.75930 | −0.879648 | − | 0.475625i | \(-0.842222\pi\) | ||||
−0.879648 | + | 0.475625i | \(0.842222\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −37.4891 | − | 64.9331i | −1.63305 | − | 2.82853i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.93070 | + | 5.07613i | −0.127422 | + | 0.220701i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.430703 | + | 0.746000i | −0.0186558 | + | 0.0323128i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.00000 | + | 5.19615i | 0.129701 | + | 0.224649i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.3723 | −0.446766 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.3505 | 0.573984 | 0.286992 | − | 0.957933i | \(-0.407345\pi\) | ||||
0.286992 | + | 0.957933i | \(0.407345\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.441578 | + | 0.764836i | 0.0189151 | + | 0.0327620i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0000 | − | 34.6410i | 0.855138 | − | 1.48114i | −0.0213785 | − | 0.999771i | \(-0.506805\pi\) |
0.876517 | − | 0.481371i | \(-0.159861\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.18614 | − | 2.05446i | 0.0505313 | − | 0.0875228i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.62772 | + | 8.01544i | 0.196791 | + | 0.340851i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.6060 | 1.33919 | 0.669594 | − | 0.742727i | \(-0.266468\pi\) | ||||
0.669594 | + | 0.742727i | \(0.266468\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.11684 | − | 8.86263i | −0.215649 | − | 0.373515i | 0.737824 | − | 0.674993i | \(-0.235853\pi\) |
−0.953473 | + | 0.301478i | \(0.902520\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.37228 | + | 12.7692i | −0.310154 | + | 0.537203i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.38316 | − | 7.59185i | 0.183751 | − | 0.318267i | −0.759404 | − | 0.650620i | \(-0.774509\pi\) |
0.943155 | + | 0.332353i | \(0.107843\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.55842 | + | 2.69927i | 0.0652179 | + | 0.112961i | 0.896791 | − | 0.442455i | \(-0.145892\pi\) |
−0.831573 | + | 0.555416i | \(0.812559\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.37228 | −0.224040 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.48913 | −0.395037 | −0.197519 | − | 0.980299i | \(-0.563288\pi\) | ||||
−0.197519 | + | 0.980299i | \(0.563288\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.8614 | − | 29.2048i | −0.699529 | − | 1.21162i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.0000 | + | 20.7846i | −0.496989 | + | 0.860811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.0000 | − | 25.9808i | 0.619116 | − | 1.07234i | −0.370531 | − | 0.928820i | \(-0.620824\pi\) |
0.989647 | − | 0.143521i | \(-0.0458424\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.55842 | − | 9.62747i | −0.229031 | − | 0.396693i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.9783 | 1.18999 | 0.594997 | − | 0.803728i | \(-0.297153\pi\) | ||||
0.594997 | + | 0.803728i | \(0.297153\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.7446 | −0.932436 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.67527 | + | 13.2940i | 0.313603 | + | 0.543176i | 0.979140 | − | 0.203189i | \(-0.0651306\pi\) |
−0.665537 | + | 0.746365i | \(0.731797\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.50000 | + | 11.2583i | −0.265141 | + | 0.459237i | −0.967600 | − | 0.252486i | \(-0.918752\pi\) |
0.702460 | + | 0.711723i | \(0.252085\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.68614 | + | 4.65253i | −0.109207 | + | 0.189152i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.3723 | + | 38.7499i | 0.908063 | + | 1.57281i | 0.816752 | + | 0.576989i | \(0.195772\pi\) |
0.0913107 | + | 0.995822i | \(0.470894\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −31.6060 | −1.27864 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.3505 | 0.741171 | 0.370586 | − | 0.928798i | \(-0.379157\pi\) | ||||
0.370586 | + | 0.928798i | \(0.379157\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.86141 | + | 11.8843i | 0.276230 | + | 0.478444i | 0.970445 | − | 0.241324i | \(-0.0775816\pi\) |
−0.694215 | + | 0.719768i | \(0.744248\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.3139 | − | 28.2564i | 0.655709 | − | 1.13572i | −0.326006 | − | 0.945368i | \(-0.605703\pi\) |
0.981715 | − | 0.190354i | \(-0.0609637\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.37228 | + | 12.7692i | −0.295364 | + | 0.511586i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 40.4674 | 1.61354 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.3723 | −1.68681 | −0.843407 | − | 0.537275i | \(-0.819454\pi\) | ||||
−0.843407 | + | 0.537275i | \(0.819454\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.43070 | − | 11.1383i | −0.255195 | − | 0.442010i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.37228 | − | 12.7692i | 0.292100 | − | 0.505933i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.3030 | − | 36.8979i | 0.841417 | − | 1.45738i | −0.0472793 | − | 0.998882i | \(-0.515055\pi\) |
0.888697 | − | 0.458496i | \(-0.151612\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.3723 | − | 28.3576i | −0.645660 | − | 1.11832i | −0.984149 | − | 0.177345i | \(-0.943249\pi\) |
0.338489 | − | 0.940970i | \(-0.390084\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.7228 | 1.24715 | 0.623576 | − | 0.781763i | \(-0.285679\pi\) | ||||
0.623576 | + | 0.781763i | \(0.285679\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.8614 | 0.465601 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.62772 | − | 11.4795i | −0.259363 | − | 0.449229i | 0.706709 | − | 0.707505i | \(-0.250179\pi\) |
−0.966071 | + | 0.258275i | \(0.916846\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.12772 | + | 5.41737i | −0.122210 | + | 0.211674i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.2921 | − | 33.4149i | 0.751514 | − | 1.30166i | −0.195575 | − | 0.980689i | \(-0.562657\pi\) |
0.947089 | − | 0.320972i | \(-0.104009\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.04755 | − | 15.6708i | −0.351909 | − | 0.609524i | 0.634675 | − | 0.772779i | \(-0.281134\pi\) |
−0.986584 | + | 0.163255i | \(0.947801\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.37228 | −0.130771 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.7446 | 0.493471 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.1168 | + | 26.1831i | 0.583579 | + | 1.01079i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.7446 | − | 20.3422i | 0.452720 | − | 0.784133i | −0.545834 | − | 0.837893i | \(-0.683787\pi\) |
0.998554 | + | 0.0537598i | \(0.0171205\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.94158 | + | 3.36291i | −0.0746209 | + | 0.129247i | −0.900921 | − | 0.433982i | \(-0.857108\pi\) |
0.826300 | + | 0.563230i | \(0.190441\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.00000 | + | 13.8564i | 0.307012 | + | 0.531760i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.76631 | −0.144114 | −0.0720570 | − | 0.997401i | \(-0.522956\pi\) | ||||
−0.0720570 | + | 0.997401i | \(0.522956\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.25544 | −0.200800 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17.0584 | − | 29.5461i | −0.649874 | − | 1.12561i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.17527 | − | 8.96382i | 0.196876 | − | 0.341000i | −0.750638 | − | 0.660714i | \(-0.770254\pi\) |
0.947514 | + | 0.319714i | \(0.103587\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.50000 | − | 12.9904i | 0.284491 | − | 0.492753i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.861407 | + | 1.49200i | 0.0326281 | + | 0.0565135i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.11684 | −0.344338 | −0.172169 | − | 0.985067i | \(-0.555078\pi\) | ||||
−0.172169 | + | 0.985067i | \(0.555078\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.00000 | 0.226294 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −26.7446 | − | 46.3229i | −1.00583 | − | 1.74215i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.2337 | − | 43.7060i | 0.947671 | − | 1.64141i | 0.197358 | − | 0.980331i | \(-0.436764\pi\) |
0.750313 | − | 0.661083i | \(-0.229903\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29.8614 | − | 51.7215i | 1.11832 | − | 1.93698i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | + | 6.92820i | 0.149592 | + | 0.259100i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 50.6060 | 1.88728 | 0.943642 | − | 0.330968i | \(-0.107375\pi\) | ||||
0.943642 | + | 0.330968i | \(0.107375\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.394031 | −0.0146745 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.18614 | + | 2.05446i | 0.0440522 | + | 0.0763006i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.9416 | − | 25.8796i | 0.554152 | − | 0.959820i | −0.443816 | − | 0.896118i | \(-0.646376\pi\) |
0.997969 | − | 0.0637025i | \(-0.0202909\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.0000 | − | 27.7128i | 0.591781 | − | 1.02500i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.48913 | − | 14.7036i | −0.313553 | − | 0.543090i | 0.665576 | − | 0.746330i | \(-0.268186\pi\) |
−0.979129 | + | 0.203240i | \(0.934853\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.76631 | 0.0650629 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.8614 | 0.583471 | 0.291736 | − | 0.956499i | \(-0.405767\pi\) | ||||
0.291736 | + | 0.956499i | \(0.405767\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.25544 | − | 5.63858i | −0.119430 | − | 0.206860i | 0.800112 | − | 0.599851i | \(-0.204774\pi\) |
−0.919542 | + | 0.392992i | \(0.871440\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.74456 | + | 16.8781i | −0.357013 | + | 0.618365i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.1168 | + | 17.5229i | −0.369661 | + | 0.640272i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.88316 | + | 3.26172i | 0.0687173 | + | 0.119022i | 0.898337 | − | 0.439307i | \(-0.144776\pi\) |
−0.829620 | + | 0.558329i | \(0.811443\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.3723 | −0.886998 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.88316 | 0.359209 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.61684 | + | 14.9248i | 0.312360 | + | 0.541024i | 0.978873 | − | 0.204470i | \(-0.0655470\pi\) |
−0.666513 | + | 0.745494i | \(0.732214\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.48913 | + | 2.57924i | −0.0539100 | + | 0.0933748i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.43070 | + | 14.6024i | −0.304415 | + | 0.527262i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.67527 | − | 16.7581i | −0.348899 | − | 0.604311i | 0.637155 | − | 0.770736i | \(-0.280111\pi\) |
−0.986054 | + | 0.166425i | \(0.946778\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.0000 | −0.647415 | −0.323708 | − | 0.946157i | \(-0.604929\pi\) | ||||
−0.323708 | + | 0.946157i | \(0.604929\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.1168 | 0.399329 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.127719 | + | 0.221215i | 0.00457600 | + | 0.00792586i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.18614 | − | 8.98266i | 0.185575 | − | 0.321425i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.4307 | − | 19.7986i | 0.407979 | − | 0.706641i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.8614 | + | 36.1330i | 0.743629 | + | 1.28800i | 0.950833 | + | 0.309705i | \(0.100230\pi\) |
−0.207204 | + | 0.978298i | \(0.566436\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −49.7228 | −1.76794 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −42.9783 | −1.52620 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.1168 | − | 17.5229i | −0.358357 | − | 0.620693i | 0.629330 | − | 0.777139i | \(-0.283330\pi\) |
−0.987687 | + | 0.156446i | \(0.949996\pi\) | |||||||
\(798\) | 0 |