Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [729,2,Mod(28,729)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(729, base_ring=CyclotomicField(54))
chi = DirichletCharacter(H, H._module([44]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("729.28");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 729.g (of order \(27\), degree \(18\), 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: | \(5.82109430735\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{27})\) |
Twist minimal: | no (minimal twist has level 81) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{27}]$ |
Embedding invariants
Embedding label | 703.2 | ||
Character | \(\chi\) | \(=\) | 729.703 |
Dual form | 729.2.g.b.28.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{5}{27}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.76769 | − | 1.16263i | −1.24994 | − | 0.822101i | −0.260284 | − | 0.965532i | \(-0.583816\pi\) |
−0.989660 | + | 0.143431i | \(0.954186\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.980860 | + | 2.27389i | 0.490430 | + | 1.13694i | ||||
\(5\) | 2.67150 | + | 2.83162i | 1.19473 | + | 1.26634i | 0.955371 | + | 0.295408i | \(0.0954557\pi\) |
0.239359 | + | 0.970931i | \(0.423063\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.31264 | − | 0.387192i | 1.25206 | − | 0.146345i | 0.535901 | − | 0.844281i | \(-0.319972\pi\) |
0.716160 | + | 0.697936i | \(0.245898\pi\) | |||||||
\(8\) | 0.175036 | − | 0.992677i | 0.0618845 | − | 0.350964i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.43025 | − | 8.11138i | −0.452286 | − | 2.56504i | ||||
\(11\) | 0.217034 | + | 0.724944i | 0.0654382 | + | 0.218579i | 0.984454 | − | 0.175641i | \(-0.0561999\pi\) |
−0.919016 | + | 0.394220i | \(0.871015\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.144562 | − | 2.48203i | −0.0400942 | − | 0.688390i | −0.957143 | − | 0.289615i | \(-0.906473\pi\) |
0.917049 | − | 0.398775i | \(-0.130564\pi\) | |||||||
\(14\) | −6.30588 | − | 3.16693i | −1.68532 | − | 0.846398i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.93533 | − | 2.05133i | 0.483831 | − | 0.512831i | ||||
\(17\) | 0.700932 | + | 0.255119i | 0.170001 | + | 0.0618753i | 0.425619 | − | 0.904903i | \(-0.360057\pi\) |
−0.255617 | + | 0.966778i | \(0.582279\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.21736 | − | 1.53499i | 0.967530 | − | 0.352152i | 0.190550 | − | 0.981678i | \(-0.438973\pi\) |
0.776980 | + | 0.629526i | \(0.216751\pi\) | |||||||
\(20\) | −3.81843 | + | 8.85211i | −0.853827 | + | 1.97939i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.459191 | − | 1.53380i | 0.0978998 | − | 0.327008i | ||||
\(23\) | −2.27126 | − | 0.265472i | −0.473590 | − | 0.0553547i | −0.124049 | − | 0.992276i | \(-0.539588\pi\) |
−0.349540 | + | 0.936921i | \(0.613662\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.590459 | + | 10.1378i | −0.118092 | + | 2.02756i | ||||
\(26\) | −2.63013 | + | 4.55552i | −0.515811 | + | 0.893410i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.12967 | + | 7.15280i | 0.780435 | + | 1.35175i | ||||
\(29\) | −0.414639 | + | 0.208240i | −0.0769966 | + | 0.0386691i | −0.486881 | − | 0.873468i | \(-0.661865\pi\) |
0.409884 | + | 0.912138i | \(0.365569\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.35407 | + | 3.16206i | −0.422803 | + | 0.567923i | −0.961580 | − | 0.274526i | \(-0.911479\pi\) |
0.538777 | + | 0.842449i | \(0.318887\pi\) | |||||||
\(32\) | −7.76762 | + | 1.84096i | −1.37313 | + | 0.325439i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.942422 | − | 1.26589i | −0.161624 | − | 0.217099i | ||||
\(35\) | 9.94610 | + | 8.34577i | 1.68120 | + | 1.41069i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.64375 | + | 3.05747i | −0.599029 | + | 0.502645i | −0.891134 | − | 0.453741i | \(-0.850089\pi\) |
0.292104 | + | 0.956387i | \(0.405645\pi\) | |||||||
\(38\) | −9.23961 | − | 2.18983i | −1.49886 | − | 0.355237i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.27849 | − | 2.15630i | 0.518375 | − | 0.340941i | ||||
\(41\) | 4.08763 | − | 2.68847i | 0.638380 | − | 0.419869i | −0.188636 | − | 0.982047i | \(-0.560407\pi\) |
0.827016 | + | 0.562178i | \(0.190036\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.78094 | + | 1.37011i | 0.881585 | + | 0.208939i | 0.646388 | − | 0.763009i | \(-0.276279\pi\) |
0.235196 | + | 0.971948i | \(0.424427\pi\) | |||||||
\(44\) | −1.43556 | + | 1.20458i | −0.216419 | + | 0.181597i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.70623 | + | 3.10990i | 0.546454 | + | 0.458529i | ||||
\(47\) | 6.42922 | + | 8.63594i | 0.937798 | + | 1.25968i | 0.965590 | + | 0.260067i | \(0.0837448\pi\) |
−0.0277927 | + | 0.999614i | \(0.508848\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.01237 | − | 0.950949i | 0.573195 | − | 0.135850i | ||||
\(50\) | 12.8302 | − | 17.2340i | 1.81447 | − | 2.43725i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.50206 | − | 2.76324i | 0.762998 | − | 0.383192i | ||||
\(53\) | −5.75294 | − | 9.96438i | −0.790227 | − | 1.36871i | −0.925826 | − | 0.377949i | \(-0.876629\pi\) |
0.135600 | − | 0.990764i | \(-0.456704\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.47296 | + | 2.55124i | −0.198614 | + | 0.344010i | ||||
\(56\) | 0.195474 | − | 3.35616i | 0.0261213 | − | 0.448485i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.975058 | + | 0.113968i | 0.128031 | + | 0.0149647i | ||||
\(59\) | −1.19000 | + | 3.97488i | −0.154925 | + | 0.517485i | −0.999849 | − | 0.0174017i | \(-0.994461\pi\) |
0.844924 | + | 0.534887i | \(0.179646\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.105839 | − | 0.245363i | 0.0135513 | − | 0.0314155i | −0.911306 | − | 0.411730i | \(-0.864925\pi\) |
0.924857 | + | 0.380314i | \(0.124184\pi\) | |||||||
\(62\) | 7.83755 | − | 2.85264i | 0.995370 | − | 0.362285i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 10.5709 | + | 3.84748i | 1.32136 | + | 0.480935i | ||||
\(65\) | 6.64196 | − | 7.04007i | 0.823834 | − | 0.873213i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.71358 | − | 0.860594i | −0.209348 | − | 0.105138i | 0.341036 | − | 0.940050i | \(-0.389222\pi\) |
−0.550384 | + | 0.834912i | \(0.685519\pi\) | |||||||
\(68\) | 0.107405 | + | 1.84408i | 0.0130248 | + | 0.223627i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.87859 | − | 26.3163i | −0.941671 | − | 3.14540i | ||||
\(71\) | −1.17278 | − | 6.65118i | −0.139184 | − | 0.789350i | −0.971855 | − | 0.235582i | \(-0.924300\pi\) |
0.832671 | − | 0.553768i | \(-0.186811\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.37723 | − | 7.81064i | 0.161192 | − | 0.914167i | −0.791712 | − | 0.610895i | \(-0.790810\pi\) |
0.952904 | − | 0.303272i | \(-0.0980791\pi\) | |||||||
\(74\) | 9.99572 | − | 1.16833i | 1.16198 | − | 0.135816i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.62705 | + | 8.08420i | 0.874883 | + | 0.927322i | ||||
\(77\) | 0.999649 | + | 2.31745i | 0.113921 | + | 0.264098i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.60662 | − | 2.37211i | −0.405777 | − | 0.266884i | 0.330172 | − | 0.943921i | \(-0.392893\pi\) |
−0.735949 | + | 0.677037i | \(0.763264\pi\) | |||||||
\(80\) | 10.9788 | 1.22747 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.3513 | −1.14311 | ||||||||
\(83\) | −2.12790 | − | 1.39954i | −0.233567 | − | 0.153620i | 0.427331 | − | 0.904095i | \(-0.359454\pi\) |
−0.660898 | + | 0.750476i | \(0.729824\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.15014 | + | 2.66632i | 0.124750 | + | 0.289203i | ||||
\(86\) | −8.62597 | − | 9.14299i | −0.930162 | − | 0.985914i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.757624 | − | 0.0885535i | 0.0807630 | − | 0.00943984i | ||||
\(89\) | 0.935549 | − | 5.30576i | 0.0991680 | − | 0.562410i | −0.894222 | − | 0.447623i | \(-0.852271\pi\) |
0.993390 | − | 0.114786i | \(-0.0366184\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.43990 | − | 8.16609i | −0.150943 | − | 0.856039i | ||||
\(92\) | −1.62413 | − | 5.42498i | −0.169327 | − | 0.565593i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.32448 | − | 22.7404i | −0.136610 | − | 2.34550i | ||||
\(95\) | 15.6132 | + | 7.84124i | 1.60188 | + | 0.804495i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.51132 | + | 6.90160i | −0.661125 | + | 0.700751i | −0.967986 | − | 0.251003i | \(-0.919240\pi\) |
0.306862 | + | 0.951754i | \(0.400721\pi\) | |||||||
\(98\) | −8.19821 | − | 2.98391i | −0.828145 | − | 0.301420i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −23.6314 | + | 8.60112i | −2.36314 | + | 0.860112i | ||||
\(101\) | 4.87482 | − | 11.3011i | 0.485063 | − | 1.12450i | −0.483413 | − | 0.875392i | \(-0.660603\pi\) |
0.968475 | − | 0.249109i | \(-0.0801377\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.78109 | + | 15.9700i | −0.471095 | + | 1.57357i | 0.311001 | + | 0.950410i | \(0.399336\pi\) |
−0.782096 | + | 0.623158i | \(0.785849\pi\) | |||||||
\(104\) | −2.48915 | − | 0.290940i | −0.244081 | − | 0.0285290i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.41546 | + | 24.3024i | −0.137481 | + | 2.36046i | ||||
\(107\) | −1.84694 | + | 3.19899i | −0.178550 | + | 0.309258i | −0.941384 | − | 0.337336i | \(-0.890474\pi\) |
0.762834 | + | 0.646595i | \(0.223807\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.66961 | + | 15.0162i | 0.830398 | + | 1.43829i | 0.897723 | + | 0.440561i | \(0.145220\pi\) |
−0.0673245 | + | 0.997731i | \(0.521446\pi\) | |||||||
\(110\) | 5.56988 | − | 2.79730i | 0.531067 | − | 0.266712i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.61678 | − | 7.54465i | 0.530736 | − | 0.712902i | ||||
\(113\) | 10.0311 | − | 2.37743i | 0.943651 | − | 0.223649i | 0.270135 | − | 0.962822i | \(-0.412932\pi\) |
0.673516 | + | 0.739173i | \(0.264783\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.31594 | − | 7.14055i | −0.495714 | − | 0.665859i | ||||
\(116\) | −0.880217 | − | 0.738590i | −0.0817261 | − | 0.0685764i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.72485 | − | 5.64282i | 0.619072 | − | 0.519464i | ||||
\(119\) | 2.42072 | + | 0.573721i | 0.221907 | + | 0.0525929i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.71193 | − | 5.72992i | 0.791993 | − | 0.520902i | ||||
\(122\) | −0.472356 | + | 0.310674i | −0.0427651 | + | 0.0281271i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.49919 | − | 2.25135i | −0.853052 | − | 0.202177i | ||||
\(125\) | −15.3730 | + | 12.8995i | −1.37500 | + | 1.15376i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.1217 | − | 8.49315i | −0.898159 | − | 0.753645i | 0.0716705 | − | 0.997428i | \(-0.477167\pi\) |
−0.969830 | + | 0.243783i | \(0.921611\pi\) | |||||||
\(128\) | −4.67882 | − | 6.28474i | −0.413553 | − | 0.555498i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −19.9259 | + | 4.72252i | −1.74762 | + | 0.414192i | ||||
\(131\) | −6.00822 | + | 8.07044i | −0.524940 | + | 0.705117i | −0.982959 | − | 0.183825i | \(-0.941152\pi\) |
0.458018 | + | 0.888943i | \(0.348559\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.3763 | − | 6.71782i | 1.15987 | − | 0.582509i | ||||
\(134\) | 2.02853 | + | 3.51352i | 0.175238 | + | 0.303522i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.375938 | − | 0.651145i | 0.0322365 | − | 0.0558352i | ||||
\(137\) | −0.550552 | + | 9.45261i | −0.0470368 | + | 0.807591i | 0.889481 | + | 0.456972i | \(0.151066\pi\) |
−0.936518 | + | 0.350619i | \(0.885971\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.4293 | + | 1.21902i | 0.884605 | + | 0.103396i | 0.546249 | − | 0.837623i | \(-0.316055\pi\) |
0.338356 | + | 0.941018i | \(0.390129\pi\) | |||||||
\(140\) | −9.22162 | + | 30.8024i | −0.779369 | + | 2.60327i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.65973 | + | 13.1207i | −0.474954 | + | 1.10107i | ||||
\(143\) | 1.76795 | − | 0.643483i | 0.147844 | − | 0.0538107i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.69736 | − | 0.617790i | −0.140958 | − | 0.0513047i | ||||
\(146\) | −11.5154 | + | 12.2056i | −0.953019 | + | 1.01014i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.5264 | − | 5.28654i | −0.865262 | − | 0.434551i | ||||
\(149\) | 0.722705 | + | 12.4084i | 0.0592063 | + | 1.01653i | 0.888838 | + | 0.458222i | \(0.151513\pi\) |
−0.829632 | + | 0.558311i | \(0.811449\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.22757 | + | 17.4613i | 0.425413 | + | 1.42098i | 0.855317 | + | 0.518105i | \(0.173362\pi\) |
−0.429904 | + | 0.902875i | \(0.641453\pi\) | |||||||
\(152\) | −0.785565 | − | 4.45516i | −0.0637177 | − | 0.361361i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.927258 | − | 5.25874i | 0.0747206 | − | 0.423761i | ||||
\(155\) | −15.2426 | + | 1.78161i | −1.22432 | + | 0.143102i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.0388 | − | 17.0001i | −1.28003 | − | 1.35675i | −0.902459 | − | 0.430775i | \(-0.858240\pi\) |
−0.377573 | − | 0.925980i | \(-0.623241\pi\) | |||||||
\(158\) | 3.61750 | + | 8.38631i | 0.287793 | + | 0.667179i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −25.9641 | − | 17.0768i | −2.05264 | − | 1.35004i | ||||
\(161\) | −7.62665 | −0.601064 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.7238 | 0.918278 | 0.459139 | − | 0.888364i | \(-0.348158\pi\) | ||||
0.459139 | + | 0.888364i | \(0.348158\pi\) | |||||||
\(164\) | 10.1227 | + | 6.65780i | 0.790449 | + | 0.519886i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.13432 | + | 4.94790i | 0.165655 | + | 0.384032i | ||||
\(167\) | −16.6160 | − | 17.6119i | −1.28579 | − | 1.36285i | −0.897314 | − | 0.441393i | \(-0.854484\pi\) |
−0.388472 | − | 0.921461i | \(-0.626997\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.77255 | − | 0.791597i | 0.520965 | − | 0.0608921i | ||||
\(170\) | 1.06685 | − | 6.05041i | 0.0818237 | − | 0.464045i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.55482 | + | 14.4891i | 0.194803 | + | 1.10478i | ||||
\(173\) | −4.44902 | − | 14.8608i | −0.338253 | − | 1.12984i | −0.942824 | − | 0.333292i | \(-0.891841\pi\) |
0.604571 | − | 0.796551i | \(-0.293345\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.96930 | + | 33.8115i | 0.148865 | + | 2.55591i | ||||
\(176\) | 1.90713 | + | 0.957795i | 0.143755 | + | 0.0721965i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.82238 | + | 8.29124i | −0.586312 | + | 0.621455i | ||||
\(179\) | −6.75474 | − | 2.45852i | −0.504873 | − | 0.183759i | 0.0770114 | − | 0.997030i | \(-0.475462\pi\) |
−0.581884 | + | 0.813271i | \(0.697684\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.27112 | − | 2.64647i | 0.540458 | − | 0.196711i | −0.0573439 | − | 0.998354i | \(-0.518263\pi\) |
0.597802 | + | 0.801644i | \(0.296041\pi\) | |||||||
\(182\) | −6.94882 | + | 16.1092i | −0.515081 | + | 1.19409i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.661079 | + | 2.20816i | −0.0487354 | + | 0.162787i | ||||
\(185\) | −18.3919 | − | 2.14970i | −1.35220 | − | 0.158049i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.0328205 | + | 0.563506i | −0.00240007 | + | 0.0412077i | ||||
\(188\) | −13.3310 | + | 23.0900i | −0.972264 | + | 1.68401i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −18.4828 | − | 32.0132i | −1.34089 | − | 2.32248i | ||||
\(191\) | 9.00617 | − | 4.52307i | 0.651664 | − | 0.327278i | −0.0920711 | − | 0.995752i | \(-0.529349\pi\) |
0.743735 | + | 0.668475i | \(0.233052\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.54993 | + | 12.8278i | −0.687419 | + | 0.923364i | −0.999645 | − | 0.0266441i | \(-0.991518\pi\) |
0.312226 | + | 0.950008i | \(0.398925\pi\) | |||||||
\(194\) | 19.5340 | − | 4.62964i | 1.40246 | − | 0.332389i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.09793 | + | 8.19094i | 0.435566 | + | 0.585067i | ||||
\(197\) | −8.40349 | − | 7.05136i | −0.598724 | − | 0.502389i | 0.292311 | − | 0.956323i | \(-0.405576\pi\) |
−0.891035 | + | 0.453934i | \(0.850020\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.68937 | − | 2.25665i | 0.190644 | − | 0.159970i | −0.542470 | − | 0.840075i | \(-0.682511\pi\) |
0.733114 | + | 0.680106i | \(0.238066\pi\) | |||||||
\(200\) | 9.96020 | + | 2.36061i | 0.704293 | + | 0.166920i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −21.7561 | + | 14.3092i | −1.53075 | + | 1.00679i | ||||
\(203\) | −1.29292 | + | 0.850369i | −0.0907454 | + | 0.0596842i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.5328 | + | 4.39236i | 1.29439 | + | 0.306776i | ||||
\(206\) | 27.0186 | − | 22.6713i | 1.88247 | − | 1.57958i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.37122 | − | 4.50698i | −0.372427 | − | 0.312503i | ||||
\(209\) | 2.02810 | + | 2.72421i | 0.140286 | + | 0.188437i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.47663 | + | 1.77199i | −0.514712 | + | 0.121989i | −0.479760 | − | 0.877400i | \(-0.659276\pi\) |
−0.0349525 | + | 0.999389i | \(0.511128\pi\) | |||||||
\(212\) | 17.0151 | − | 22.8552i | 1.16860 | − | 1.56970i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.98404 | − | 3.50752i | 0.477419 | − | 0.239769i | ||||
\(215\) | 11.5641 | + | 20.0297i | 0.788667 | + | 1.36601i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.57386 | + | 11.3863i | −0.446262 | + | 0.772949i | ||||
\(218\) | 2.13308 | − | 36.6235i | 0.144470 | − | 2.48046i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.24602 | − | 0.846938i | −0.488526 | − | 0.0571005i | ||||
\(221\) | 0.531883 | − | 1.77661i | 0.0357783 | − | 0.119508i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.29520 | − | 9.95739i | 0.287628 | − | 0.666796i | −0.711737 | − | 0.702447i | \(-0.752091\pi\) |
0.999364 | + | 0.0356504i | \(0.0113503\pi\) | |||||||
\(224\) | −25.0185 | + | 9.10600i | −1.67162 | + | 0.608420i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −20.4960 | − | 7.45993i | −1.36337 | − | 0.496227i | ||||
\(227\) | −7.45351 | + | 7.90026i | −0.494707 | + | 0.524358i | −0.925833 | − | 0.377933i | \(-0.876635\pi\) |
0.431126 | + | 0.902292i | \(0.358116\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.04594 | + | 1.02751i | 0.135199 | + | 0.0678997i | 0.515113 | − | 0.857122i | \(-0.327750\pi\) |
−0.379914 | + | 0.925022i | \(0.624046\pi\) | |||||||
\(230\) | 1.09513 | + | 18.8027i | 0.0722110 | + | 1.23981i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.134138 | + | 0.448052i | 0.00880659 | + | 0.0294161i | ||||
\(233\) | −3.09286 | − | 17.5405i | −0.202620 | − | 1.14912i | −0.901141 | − | 0.433526i | \(-0.857269\pi\) |
0.698521 | − | 0.715590i | \(-0.253842\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.27807 | + | 41.2760i | −0.474769 | + | 2.69255i | ||||
\(236\) | −10.2057 | + | 1.19287i | −0.664332 | + | 0.0776493i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.61205 | − | 3.82855i | −0.234135 | − | 0.248168i | ||||
\(239\) | 4.85842 | + | 11.2631i | 0.314265 | + | 0.728548i | 1.00000 | 0.000696435i | \(0.000221682\pi\) | |
−0.685735 | + | 0.727851i | \(0.740519\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.6206 | − | 9.61612i | −0.941795 | − | 0.619429i | −0.0169845 | − | 0.999856i | \(-0.505407\pi\) |
−0.924811 | + | 0.380427i | \(0.875777\pi\) | |||||||
\(242\) | −22.0617 | −1.41818 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.661742 | 0.0423637 | ||||||||
\(245\) | 13.4118 | + | 8.82105i | 0.856846 | + | 0.563556i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.41956 | − | 10.2457i | −0.281210 | − | 0.651918i | ||||
\(248\) | 2.72686 | + | 2.89030i | 0.173156 | + | 0.183534i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 42.1719 | − | 4.92919i | 2.66719 | − | 0.311749i | ||||
\(251\) | −3.26810 | + | 18.5343i | −0.206281 | + | 1.16988i | 0.689131 | + | 0.724637i | \(0.257992\pi\) |
−0.895412 | + | 0.445239i | \(0.853119\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.300488 | − | 1.70415i | −0.0188915 | − | 0.107139i | ||||
\(254\) | 8.01772 | + | 26.7810i | 0.503076 | + | 1.68039i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.344295 | − | 5.91131i | −0.0215184 | − | 0.369457i | ||||
\(257\) | −15.4090 | − | 7.73869i | −0.961187 | − | 0.482726i | −0.102222 | − | 0.994762i | \(-0.532595\pi\) |
−0.858964 | + | 0.512035i | \(0.828892\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.8866 | + | 11.5391i | −0.676462 | + | 0.717008i | ||||
\(260\) | 22.5232 | + | 8.19776i | 1.39683 | + | 0.508404i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 20.0036 | − | 7.28070i | 1.23582 | − | 0.449803i | ||||
\(263\) | 9.74813 | − | 22.5987i | 0.601095 | − | 1.39350i | −0.297502 | − | 0.954721i | \(-0.596154\pi\) |
0.898597 | − | 0.438774i | \(-0.144587\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.8464 | − | 42.9100i | 0.789148 | − | 2.63594i | ||||
\(266\) | −31.4554 | − | 3.67661i | −1.92865 | − | 0.225427i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.276110 | − | 4.74062i | 0.0168661 | − | 0.289580i | ||||
\(269\) | 5.32448 | − | 9.22227i | 0.324639 | − | 0.562292i | −0.656800 | − | 0.754065i | \(-0.728090\pi\) |
0.981439 | + | 0.191773i | \(0.0614238\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.35817 | + | 4.08447i | 0.143249 | + | 0.248114i | 0.928718 | − | 0.370786i | \(-0.120912\pi\) |
−0.785469 | + | 0.618900i | \(0.787578\pi\) | |||||||
\(272\) | 1.87986 | − | 0.944103i | 0.113983 | − | 0.0572447i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.9631 | − | 16.0692i | 0.722715 | − | 0.970775i | ||||
\(275\) | −7.47748 | + | 1.77220i | −0.450909 | + | 0.106867i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.94818 | − | 5.30333i | −0.237223 | − | 0.318646i | 0.667529 | − | 0.744583i | \(-0.267352\pi\) |
−0.904753 | + | 0.425937i | \(0.859944\pi\) | |||||||
\(278\) | −17.0186 | − | 14.2803i | −1.02071 | − | 0.856474i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 10.0256 | − | 8.41245i | 0.599142 | − | 0.502740i | ||||
\(281\) | 2.40945 | + | 0.571049i | 0.143736 | + | 0.0340659i | 0.301854 | − | 0.953354i | \(-0.402395\pi\) |
−0.158118 | + | 0.987420i | \(0.550543\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.774627 | + | 0.509480i | −0.0460468 | + | 0.0302855i | −0.572324 | − | 0.820028i | \(-0.693958\pi\) |
0.526277 | + | 0.850313i | \(0.323588\pi\) | |||||||
\(284\) | 13.9737 | − | 9.19066i | 0.829188 | − | 0.545365i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.87332 | − | 0.917994i | −0.229034 | − | 0.0542821i | ||||
\(287\) | 12.4999 | − | 10.4887i | 0.737845 | − | 0.619126i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.5965 | − | 10.5697i | −0.740973 | − | 0.621750i | ||||
\(290\) | 2.28215 | + | 3.06546i | 0.134012 | + | 0.180010i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 19.1114 | − | 4.52949i | 1.11841 | − | 0.265068i | ||||
\(293\) | −1.40037 | + | 1.88103i | −0.0818106 | + | 0.109891i | −0.841144 | − | 0.540811i | \(-0.818118\pi\) |
0.759334 | + | 0.650701i | \(0.225525\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.4344 | + | 7.24925i | −0.840405 | + | 0.422067i | ||||
\(296\) | 2.39729 | + | 4.15224i | 0.139340 | + | 0.241344i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.1488 | − | 22.7744i | 0.761688 | − | 1.31928i | ||||
\(299\) | −0.330572 | + | 5.67569i | −0.0191174 | + | 0.328234i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.6807 | + | 2.30034i | 1.13438 | + | 0.132589i | ||||
\(302\) | 11.0603 | − | 36.9438i | 0.636446 | − | 2.12588i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.01320 | − | 11.6219i | 0.287527 | − | 0.666562i | ||||
\(305\) | 0.977524 | − | 0.355790i | 0.0559729 | − | 0.0203725i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.3376 | + | 5.21846i | 0.818289 | + | 0.297833i | 0.717043 | − | 0.697028i | \(-0.245495\pi\) |
0.101246 | + | 0.994861i | \(0.467717\pi\) | |||||||
\(308\) | −4.28910 | + | 4.54618i | −0.244394 | + | 0.259043i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 29.0156 | + | 14.5722i | 1.64797 | + | 0.827644i | ||||
\(311\) | −0.973556 | − | 16.7153i | −0.0552053 | − | 0.947838i | −0.906249 | − | 0.422744i | \(-0.861067\pi\) |
0.851044 | − | 0.525094i | \(-0.175970\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.34214 | − | 31.2049i | −0.528049 | − | 1.76381i | −0.638178 | − | 0.769889i | \(-0.720312\pi\) |
0.110129 | − | 0.993917i | \(-0.464873\pi\) | |||||||
\(314\) | 8.58676 | + | 48.6979i | 0.484579 | + | 2.74818i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.85633 | − | 10.5278i | 0.104427 | − | 0.592234i | ||||
\(317\) | 21.5243 | − | 2.51583i | 1.20893 | − | 0.141303i | 0.512344 | − | 0.858780i | \(-0.328777\pi\) |
0.696582 | + | 0.717477i | \(0.254703\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.240953 | − | 0.255395i | −0.0134908 | − | 0.0142994i | ||||
\(320\) | 17.3454 | + | 40.2112i | 0.969639 | + | 2.24788i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 13.4815 | + | 8.86695i | 0.751297 | + | 0.494136i | ||||
\(323\) | 3.34769 | 0.186271 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.2476 | 1.40049 | ||||||||
\(326\) | −20.7240 | − | 13.6304i | −1.14780 | − | 0.754917i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.95331 | − | 4.52827i | −0.107853 | − | 0.250032i | ||||
\(329\) | 24.6415 | + | 26.1184i | 1.35853 | + | 1.43996i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.6512 | + | 2.76443i | −1.29999 | + | 0.151947i | −0.737775 | − | 0.675046i | \(-0.764124\pi\) |
−0.562212 | + | 0.826993i | \(0.690050\pi\) | |||||||
\(332\) | 1.09523 | − | 6.21136i | 0.0601086 | − | 0.340893i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.89581 | + | 50.4507i | 0.486757 | + | 2.76054i | ||||
\(335\) | −2.14096 | − | 7.15130i | −0.116973 | − | 0.390717i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.06959 | + | 18.3641i | 0.0582643 | + | 1.00036i | 0.893100 | + | 0.449859i | \(0.148526\pi\) |
−0.834835 | + | 0.550500i | \(0.814437\pi\) | |||||||
\(338\) | −12.8921 | − | 6.47465i | −0.701237 | − | 0.352174i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.93480 | + | 5.23058i | −0.267627 | + | 0.283668i | ||||
\(341\) | −2.80323 | − | 1.02029i | −0.151803 | − | 0.0552519i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.01506 | + | 3.28121i | −0.486767 | + | 0.177169i | ||||
\(344\) | 2.37194 | − | 5.49878i | 0.127887 | − | 0.296475i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.41304 | + | 31.4417i | −0.506048 | + | 1.69032i | ||||
\(347\) | −16.7968 | − | 1.96326i | −0.901698 | − | 0.105393i | −0.347405 | − | 0.937715i | \(-0.612937\pi\) |
−0.554293 | + | 0.832322i | \(0.687011\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.474881 | + | 8.15340i | −0.0254198 | + | 0.436441i | 0.961456 | + | 0.274959i | \(0.0886644\pi\) |
−0.986876 | + | 0.161482i | \(0.948373\pi\) | |||||||
\(350\) | 35.8291 | − | 62.0578i | 1.91514 | − | 3.31713i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.02043 | − | 5.23154i | −0.160989 | − | 0.278842i | ||||
\(353\) | −21.9963 | + | 11.0469i | −1.17074 | + | 0.587969i | −0.924479 | − | 0.381234i | \(-0.875499\pi\) |
−0.246264 | + | 0.969203i | \(0.579203\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.7005 | − | 21.0895i | 0.833298 | − | 1.11931i | ||||
\(356\) | 12.9824 | − | 3.07688i | 0.688064 | − | 0.163074i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.08193 | + | 12.1991i | 0.479995 | + | 0.644745i | ||||
\(359\) | 9.68682 | + | 8.12821i | 0.511251 | + | 0.428990i | 0.861569 | − | 0.507640i | \(-0.169482\pi\) |
−0.350318 | + | 0.936631i | \(0.613927\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.875105 | − | 0.734300i | 0.0460582 | − | 0.0386474i | ||||
\(362\) | −15.9299 | − | 3.77546i | −0.837258 | − | 0.198434i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 17.1564 | − | 11.2840i | 0.899242 | − | 0.591441i | ||||
\(365\) | 25.7960 | − | 16.9663i | 1.35023 | − | 0.888058i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.2113 | − | 2.42012i | −0.533025 | − | 0.126329i | −0.0447153 | − | 0.999000i | \(-0.514238\pi\) |
−0.488309 | + | 0.872671i | \(0.662386\pi\) | |||||||
\(368\) | −4.94019 | + | 4.14531i | −0.257525 | + | 0.216089i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 30.0118 | + | 25.1829i | 1.56024 | + | 1.30920i | ||||
\(371\) | −22.9156 | − | 30.7809i | −1.18972 | − | 1.59807i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.4784 | − | 2.72044i | 0.594330 | − | 0.140859i | 0.0775669 | − | 0.996987i | \(-0.475285\pi\) |
0.516763 | + | 0.856128i | \(0.327137\pi\) | |||||||
\(374\) | 0.713164 | − | 0.957945i | 0.0368768 | − | 0.0495342i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.69804 | − | 4.87054i | 0.500138 | − | 0.251179i | ||||
\(377\) | 0.576797 | + | 0.999042i | 0.0297066 | + | 0.0514533i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.06853 | + | 15.7072i | −0.465819 | + | 0.806823i | −0.999238 | − | 0.0390286i | \(-0.987574\pi\) |
0.533419 | + | 0.845851i | \(0.320907\pi\) | |||||||
\(380\) | −2.51576 | + | 43.1939i | −0.129056 | + | 2.21580i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −21.1787 | − | 2.47544i | −1.08360 | − | 0.126655i | ||||
\(383\) | 4.45051 | − | 14.8657i | 0.227410 | − | 0.759603i | −0.765780 | − | 0.643102i | \(-0.777647\pi\) |
0.993191 | − | 0.116501i | \(-0.0371678\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.89157 | + | 9.02168i | −0.198333 | + | 0.459787i | ||||
\(386\) | 31.7952 | − | 11.5725i | 1.61833 | − | 0.589025i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −22.0802 | − | 8.03653i | −1.12095 | − | 0.407993i | ||||
\(389\) | −10.5917 | + | 11.2265i | −0.537019 | + | 0.569207i | −0.937892 | − | 0.346927i | \(-0.887225\pi\) |
0.400873 | + | 0.916133i | \(0.368707\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.52427 | − | 0.765518i | −0.0770857 | − | 0.0387139i | ||||
\(392\) | −0.241677 | − | 4.14943i | −0.0122065 | − | 0.209578i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.65664 | + | 22.2347i | 0.335357 | + | 1.12017i | ||||
\(395\) | −2.91816 | − | 16.5497i | −0.146828 | − | 0.832705i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.354695 | − | 2.01157i | 0.0178016 | − | 0.100958i | −0.974612 | − | 0.223899i | \(-0.928121\pi\) |
0.992414 | + | 0.122941i | \(0.0392326\pi\) | |||||||
\(398\) | −7.37761 | + | 0.862319i | −0.369806 | + | 0.0432241i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.6532 | + | 20.8312i | 0.982659 | + | 1.04156i | ||||
\(401\) | −5.92303 | − | 13.7311i | −0.295782 | − | 0.685700i | 0.703916 | − | 0.710284i | \(-0.251433\pi\) |
−0.999698 | + | 0.0245834i | \(0.992174\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.18862 | + | 5.38574i | 0.407904 | + | 0.268283i | ||||
\(404\) | 30.4790 | 1.51639 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.27415 | 0.162493 | ||||||||
\(407\) | −3.00731 | − | 1.97794i | −0.149067 | − | 0.0980429i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.11470 | + | 9.53894i | 0.203459 | + | 0.471670i | 0.989143 | − | 0.146958i | \(-0.0469481\pi\) |
−0.785684 | + | 0.618628i | \(0.787689\pi\) | |||||||
\(410\) | −27.6536 | − | 29.3111i | −1.36571 | − | 1.44757i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −41.0035 | + | 4.79262i | −2.02010 | + | 0.236116i | ||||
\(413\) | −2.40300 | + | 13.6281i | −0.118244 | + | 0.670595i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.72170 | − | 9.76427i | −0.0845151 | − | 0.479309i | ||||
\(416\) | 5.69221 | + | 19.0133i | 0.279083 | + | 0.932203i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.417807 | − | 7.17347i | −0.0204356 | − | 0.350866i | ||||
\(419\) | −0.473719 | − | 0.237911i | −0.0231427 | − | 0.0116227i | 0.437190 | − | 0.899369i | \(-0.355974\pi\) |
−0.460333 | + | 0.887746i | \(0.652270\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0048 | − | 23.3237i | 1.07245 | − | 1.13673i | 0.0823146 | − | 0.996606i | \(-0.473769\pi\) |
0.990134 | − | 0.140123i | \(-0.0447497\pi\) | |||||||
\(422\) | 15.2765 | + | 5.56019i | 0.743649 | + | 0.270666i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.8984 | + | 3.96668i | −0.529272 | + | 0.192639i | ||||
\(425\) | −3.00021 | + | 6.95527i | −0.145532 | + | 0.337380i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.255605 | − | 0.853780i | 0.0123696 | − | 0.0413173i | ||||
\(428\) | −9.08574 | − | 1.06197i | −0.439176 | − | 0.0513323i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.84524 | − | 48.8510i | 0.137210 | − | 2.35580i | ||||
\(431\) | 2.69146 | − | 4.66175i | 0.129643 | − | 0.224549i | −0.793895 | − | 0.608055i | \(-0.791950\pi\) |
0.923538 | + | 0.383506i | \(0.125283\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.6465 | − | 28.8325i | −0.799978 | − | 1.38560i | −0.919630 | − | 0.392787i | \(-0.871511\pi\) |
0.119652 | − | 0.992816i | \(-0.461822\pi\) | |||||||
\(434\) | 24.8585 | − | 12.4844i | 1.19325 | − | 0.599270i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −25.6415 | + | 34.4425i | −1.22801 | + | 1.64950i | ||||
\(437\) | −9.98622 | + | 2.36678i | −0.477705 | + | 0.113218i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.1561 | − | 14.9852i | −0.532451 | − | 0.715206i | 0.451773 | − | 0.892133i | \(-0.350792\pi\) |
−0.984224 | + | 0.176927i | \(0.943384\pi\) | |||||||
\(440\) | 2.27474 | + | 1.90873i | 0.108444 | + | 0.0909953i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.00574 | + | 2.52212i | −0.142968 | + | 0.119965i | ||||
\(443\) | 18.3619 | + | 4.35184i | 0.872398 | + | 0.206762i | 0.642345 | − | 0.766416i | \(-0.277962\pi\) |
0.230053 | + | 0.973178i | \(0.426110\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.5232 | − | 11.5252i | 0.830681 | − | 0.546348i | ||||
\(446\) | −19.1693 | + | 12.6078i | −0.907693 | + | 0.596999i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 36.5072 | + | 8.65237i | 1.72480 | + | 0.408786i | ||||
\(449\) | 5.33643 | − | 4.47780i | 0.251842 | − | 0.211320i | −0.508123 | − | 0.861284i | \(-0.669661\pi\) |
0.759965 | + | 0.649964i | \(0.225216\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.83615 | + | 2.37981i | 0.133549 | + | 0.112061i | ||||
\(452\) | 15.2452 | + | 20.4778i | 0.717072 | + | 0.963195i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 22.3605 | − | 5.29954i | 1.04943 | − | 0.248720i | ||||
\(455\) | 19.2766 | − | 25.8929i | 0.903700 | − | 1.21388i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.5985 | − | 16.8738i | 1.57167 | − | 0.789324i | 0.572148 | − | 0.820150i | \(-0.306110\pi\) |
0.999525 | + | 0.0308265i | \(0.00981393\pi\) | |||||||
\(458\) | −2.42197 | − | 4.19498i | −0.113171 | − | 0.196018i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 11.0226 | − | 19.0917i | 0.513932 | − | 0.890157i | ||||
\(461\) | −1.60695 | + | 27.5903i | −0.0748432 | + | 1.28501i | 0.726652 | + | 0.687006i | \(0.241075\pi\) |
−0.801495 | + | 0.598002i | \(0.795962\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.4012 | − | 2.85209i | −1.13402 | − | 0.132548i | −0.471694 | − | 0.881763i | \(-0.656357\pi\) |
−0.662327 | + | 0.749215i | \(0.730431\pi\) | |||||||
\(464\) | −0.375295 | + | 1.25357i | −0.0174226 | + | 0.0581956i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.9258 | + | 34.6020i | −0.691426 | + | 1.60291i | ||||
\(467\) | 7.38677 | − | 2.68856i | 0.341819 | − | 0.124412i | −0.165406 | − | 0.986226i | \(-0.552893\pi\) |
0.507225 | + | 0.861814i | \(0.330671\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.00971 | − | 2.18735i | −0.277503 | − | 0.101003i | ||||
\(470\) | 60.8539 | − | 64.5014i | 2.80698 | − | 2.97523i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.73748 | + | 1.87703i | 0.172031 | + | 0.0863974i | ||||
\(473\) | 0.261409 | + | 4.48821i | 0.0120196 | + | 0.206368i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.0713 | + | 43.6611i | 0.599752 | + | 2.00331i | ||||
\(476\) | 1.06981 | + | 6.06719i | 0.0490346 | + | 0.278089i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.50659 | − | 25.5581i | 0.206127 | − | 1.16900i | ||||
\(479\) | −17.5918 | + | 2.05619i | −0.803791 | + | 0.0939497i | −0.508060 | − | 0.861322i | \(-0.669637\pi\) |
−0.295731 | + | 0.955271i | \(0.595563\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.11547 | + | 8.60190i | 0.370034 | + | 0.392213i | ||||
\(482\) | 14.6647 | + | 33.9966i | 0.667959 | + | 1.54850i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.5744 | + | 14.1897i | 0.980654 | + | 0.644987i | ||||
\(485\) | −36.9377 | −1.67725 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −42.1146 | −1.90840 | −0.954198 | − | 0.299175i | \(-0.903289\pi\) | ||||
−0.954198 | + | 0.299175i | \(0.903289\pi\) | |||||||
\(488\) | −0.225040 | − | 0.148011i | −0.0101871 | − | 0.00670016i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13.4522 | − | 31.1857i | −0.607709 | − | 1.40883i | ||||
\(491\) | −4.99416 | − | 5.29350i | −0.225383 | − | 0.238892i | 0.604808 | − | 0.796372i | \(-0.293250\pi\) |
−0.830191 | + | 0.557479i | \(0.811769\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.343760 | + | 0.0401798i | −0.0154822 | + | 0.00180961i | ||||
\(494\) | −4.09952 | + | 23.2495i | −0.184446 | + | 1.04604i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.93053 | + | 10.9486i | 0.0866833 | + | 0.491606i | ||||
\(497\) | −6.46030 | − | 21.5789i | −0.289784 | − | 0.967946i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.937877 | − | 16.1027i | −0.0419851 | − | 0.720857i | −0.951965 | − | 0.306205i | \(-0.900941\pi\) |
0.909980 | − | 0.414651i | \(-0.136096\pi\) | |||||||
\(500\) | −44.4107 | − | 22.3039i | −1.98611 | − | 0.997461i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 27.3255 | − | 28.9633i | 1.21960 | − | 1.29270i | ||||
\(503\) | −34.7114 | − | 12.6339i | −1.54771 | − | 0.563319i | −0.579827 | − | 0.814739i | \(-0.696880\pi\) |
−0.967878 | + | 0.251421i | \(0.919102\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 45.0235 | − | 16.3872i | 2.00352 | − | 0.729221i | ||||
\(506\) | −1.45012 | + | 3.36176i | −0.0644658 | + | 0.149449i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.38447 | − | 31.3463i | 0.416369 | − | 1.39077i | ||||
\(509\) | 11.6029 | + | 1.35619i | 0.514291 | + | 0.0601120i | 0.369280 | − | 0.929318i | \(-0.379604\pi\) |
0.145011 | + | 0.989430i | \(0.453678\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.53804 | − | 26.4071i | 0.0680389 | − | 1.16818i | ||||
\(512\) | −14.0992 | + | 24.4205i | −0.623101 | + | 1.07924i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.2411 | + | 31.5945i | 0.804580 | + | 1.39357i | ||||
\(515\) | −57.9936 | + | 29.1255i | −2.55550 | + | 1.28342i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.86521 | + | 6.53511i | −0.213972 | + | 0.287414i | ||||
\(518\) | 32.6599 | − | 7.74053i | 1.43499 | − | 0.340099i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.82593 | − | 7.82558i | −0.255484 | − | 0.343175i | ||||
\(521\) | 0.659940 | + | 0.553755i | 0.0289125 | + | 0.0242605i | 0.657129 | − | 0.753778i | \(-0.271771\pi\) |
−0.628217 | + | 0.778038i | \(0.716215\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.06895 | + | 5.09246i | −0.265377 | + | 0.222678i | −0.765760 | − | 0.643126i | \(-0.777637\pi\) |
0.500383 | + | 0.865804i | \(0.333192\pi\) | |||||||
\(524\) | −24.2445 | − | 5.74605i | −1.05913 | − | 0.251018i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −43.5055 | + | 28.6140i | −1.89693 | + | 1.24763i | ||||
\(527\) | −2.45674 | + | 1.61582i | −0.107017 | + | 0.0703864i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.2919 | − | 4.09826i | −0.751822 | − | 0.178185i | ||||
\(530\) | −72.5967 | + | 60.9158i | −3.15340 | + | 2.64601i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 28.3958 | + | 23.8269i | 1.23112 | + | 1.03303i | ||||
\(533\) | −7.26378 | − | 9.75694i | −0.314629 | − | 0.422620i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.9924 | + | 3.31627i | −0.604945 | + | 0.143375i | ||||
\(536\) | −1.15423 | + | 1.55040i | −0.0498552 | + | 0.0669671i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.1341 | + | 10.1117i | −0.868042 | + | 0.435947i | ||||
\(539\) | 1.56020 | + | 2.70235i | 0.0672028 | + | 0.116399i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.01461 | − | 10.4176i | 0.258588 | − | 0.447888i | −0.707276 | − | 0.706938i | \(-0.750076\pi\) |
0.965864 | + | 0.259050i | \(0.0834094\pi\) | |||||||
\(542\) | 0.580206 | − | 9.96175i | 0.0249220 | − | 0.427894i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.91424 | − | 0.691275i | −0.253571 | − | 0.0296382i | ||||
\(545\) | −19.3594 | + | 64.6648i | −0.829265 | + | 2.76994i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.52741 | + | 5.85920i | −0.108064 | + | 0.250521i | −0.963664 | − | 0.267116i | \(-0.913929\pi\) |
0.855600 | + | 0.517638i | \(0.173188\pi\) | |||||||
\(548\) | −22.0342 | + | 8.01980i | −0.941255 | + | 0.342589i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 15.2783 | + | 5.56083i | 0.651467 | + | 0.237115i | ||||
\(551\) | −1.42904 | + | 1.51469i | −0.0608791 | + | 0.0645280i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.8659 | − | 6.46151i | −0.547115 | − | 0.274771i | ||||
\(554\) | 0.813362 | + | 13.9649i | 0.0345565 | + | 0.593311i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.45782 | + | 24.9109i | 0.316282 | + | 1.05646i | ||||
\(557\) | 6.99671 | + | 39.6803i | 0.296460 | + | 1.68131i | 0.661207 | + | 0.750203i | \(0.270044\pi\) |
−0.364747 | + | 0.931107i | \(0.618844\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.56494 | − | 14.5465i | 0.108485 | − | 0.615251i | ||||
\(560\) | 36.3688 | − | 4.25091i | 1.53686 | − | 0.179634i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.59523 | − | 3.81072i | −0.151656 | − | 0.160746i | ||||
\(563\) | 0.628050 | + | 1.45598i | 0.0264692 | + | 0.0613624i | 0.930938 | − | 0.365177i | \(-0.118992\pi\) |
−0.904469 | + | 0.426540i | \(0.859732\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.5302 | + | 22.0531i | 1.41062 | + | 0.927782i | ||||
\(566\) | 1.96163 | 0.0824536 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.80775 | −0.285647 | ||||||||
\(569\) | 9.22728 | + | 6.06888i | 0.386828 | + | 0.254421i | 0.727996 | − | 0.685582i | \(-0.240452\pi\) |
−0.341168 | + | 0.940002i | \(0.610822\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.13218 | + | 7.26120i | 0.131078 | + | 0.303872i | 0.971097 | − | 0.238684i | \(-0.0767160\pi\) |
−0.840020 | + | 0.542556i | \(0.817457\pi\) | |||||||
\(572\) | 3.19733 | + | 3.38897i | 0.133687 | + | 0.141700i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −34.2903 | + | 4.00796i | −1.43125 | + | 0.167289i | ||||
\(575\) | 4.03238 | − | 22.8688i | 0.168162 | − | 0.953695i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.01656 | − | 45.4642i | −0.333734 | − | 1.89270i | −0.439392 | − | 0.898295i | \(-0.644806\pi\) |
0.105658 | − | 0.994402i | \(-0.466305\pi\) | |||||||
\(578\) | 9.97807 | + | 33.3291i | 0.415033 | + | 1.38631i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.260091 | − | 4.46558i | −0.0107997 | − | 0.185423i | ||||
\(581\) | −7.59086 | − | 3.81227i | −0.314922 | − | 0.158160i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.97503 | − | 6.33317i | 0.247461 | − | 0.262293i | ||||
\(584\) | −7.51238 | − | 2.73428i | −0.310865 | − | 0.113145i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.66235 | − | 1.69696i | 0.192600 | − | 0.0701007i | ||||
\(587\) | −14.5601 | + | 33.7540i | −0.600959 | + | 1.39318i | 0.297755 | + | 0.954642i | \(0.403762\pi\) |
−0.898713 | + | 0.438536i | \(0.855497\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.07421 | + | 16.9490i | −0.209079 | + | 0.698373i | ||||
\(590\) | 33.9437 | + | 3.96745i | 1.39744 | + | 0.163337i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.779979 | + | 13.3917i | −0.0320570 | + | 0.550397i | ||||
\(593\) | 7.17407 | − | 12.4258i | 0.294604 | − | 0.510268i | −0.680289 | − | 0.732944i | \(-0.738146\pi\) |
0.974893 | + | 0.222676i | \(0.0714791\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.84238 | + | 8.38725i | 0.198518 | + | 0.343844i | ||||
\(596\) | −27.5064 | + | 13.8142i | −1.12671 | + | 0.565853i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.18306 | − | 9.64853i | 0.293737 | − | 0.394558i | ||||
\(599\) | 12.6650 | − | 3.00166i | 0.517479 | − | 0.122645i | 0.0364259 | − | 0.999336i | \(-0.488403\pi\) |
0.481053 | + | 0.876692i | \(0.340255\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.76081 | − | 5.05165i | −0.153407 | − | 0.206061i | 0.718775 | − | 0.695242i | \(-0.244703\pi\) |
−0.872182 | + | 0.489181i | \(0.837296\pi\) | |||||||
\(602\) | −32.1148 | − | 26.9476i | −1.30890 | − | 1.09830i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −34.5775 | + | 29.0140i | −1.40694 | + | 1.18056i | ||||
\(605\) | 39.4989 | + | 9.36140i | 1.60586 | + | 0.380595i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.9863 | + | 7.22582i | −0.445921 | + | 0.293287i | −0.752542 | − | 0.658545i | \(-0.771172\pi\) |
0.306620 | + | 0.951832i | \(0.400802\pi\) | |||||||
\(608\) | −29.9330 | + | 19.6872i | −1.21394 | + | 0.798423i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.14161 | − | 0.507571i | −0.0867112 | − | 0.0205509i | ||||
\(611\) | 20.5052 | − | 17.2059i | 0.829552 | − | 0.696076i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.3321 | − | 23.7734i | −1.14432 | − | 0.960200i | −0.144750 | − | 0.989468i | \(-0.546238\pi\) |
−0.999572 | + | 0.0292684i | \(0.990682\pi\) | |||||||
\(614\) | −19.2773 | − | 25.8939i | −0.777967 | − | 1.04499i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.47545 | − | 0.586692i | 0.0997387 | − | 0.0236385i | ||||
\(617\) | −19.3944 | + | 26.0512i | −0.780789 | + | 1.04878i | 0.216579 | + | 0.976265i | \(0.430510\pi\) |
−0.997367 | + | 0.0725160i | \(0.976897\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −38.3557 | + | 19.2630i | −1.54165 | + | 0.774243i | −0.997885 | − | 0.0649972i | \(-0.979296\pi\) |
−0.543760 | + | 0.839241i | \(0.683000\pi\) | |||||||
\(620\) | −19.0021 | − | 32.9126i | −0.763142 | − | 1.32180i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −17.7127 | + | 30.6793i | −0.710215 | + | 1.23013i | ||||
\(623\) | 1.04479 | − | 17.9383i | 0.0418586 | − | 0.718684i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.1638 | − | 3.17499i | −1.08655 | − | 0.126999i | ||||
\(626\) | −19.7657 | + | 66.0220i | −0.789995 | + | 2.63877i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.9245 | − | 53.1451i | 0.914789 | − | 2.12072i | ||||
\(629\) | −3.33404 | + | 1.21349i | −0.132937 | + | 0.0483851i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.0635 | + | 4.75472i | 0.520049 | + | 0.189282i | 0.588690 | − | 0.808359i | \(-0.299644\pi\) |
−0.0686408 | + | 0.997641i | \(0.521866\pi\) | |||||||
\(632\) | −2.98603 | + | 3.16501i | −0.118778 | + | 0.125897i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −40.9732 | − | 20.5775i | −1.62725 | − | 0.817238i | ||||
\(635\) | −2.99082 | − | 51.3504i | −0.118687 | − | 2.03778i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.94031 | − | 9.82133i | −0.116499 | − | 0.389135i | ||||
\(638\) | 0.129000 | + | 0.731597i | 0.00510717 | + | 0.0289642i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.29656 | − | 30.0383i | 0.209365 | − | 1.18737i | ||||
\(641\) | −2.60191 | + | 0.304120i | −0.102769 | + | 0.0120120i | −0.167322 | − | 0.985902i | \(-0.553512\pi\) |
0.0645528 | + | 0.997914i | \(0.479438\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.0703439 | + | 0.0745602i | 0.00277409 | + | 0.00294037i | 0.728759 | − | 0.684770i | \(-0.240097\pi\) |
−0.725985 | + | 0.687710i | \(0.758616\pi\) | |||||||
\(644\) | −7.48068 | − | 17.3422i | −0.294780 | − | 0.683377i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.91768 | − | 3.89212i | −0.232828 | − | 0.153133i | ||||
\(647\) | 25.1564 | 0.988998 | 0.494499 | − | 0.869178i | \(-0.335351\pi\) | ||||
0.494499 | + | 0.869178i | \(0.335351\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.13983 | −0.123249 | ||||||||
\(650\) | −44.6299 | − | 29.3536i | −1.75053 | − | 1.15134i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.4994 | + | 26.6586i | 0.450351 | + | 1.04403i | ||||
\(653\) | −5.11903 | − | 5.42585i | −0.200323 | − | 0.212330i | 0.619423 | − | 0.785058i | \(-0.287367\pi\) |
−0.819746 | + | 0.572728i | \(0.805885\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −38.9034 | + | 4.54715i | −1.52008 | + | 0.177672i | ||||
\(656\) | 2.39595 | − | 13.5881i | 0.0935463 | − | 0.530527i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −13.1924 | − | 74.8181i | −0.514295 | − | 2.91671i | ||||
\(659\) | 4.66341 | + | 15.5769i | 0.181661 | + | 0.606789i | 0.999508 | + | 0.0313543i | \(0.00998201\pi\) |
−0.817848 | + | 0.575435i | \(0.804833\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.09720 | − | 18.8381i | −0.0426760 | − | 0.732718i | −0.949993 | − | 0.312271i | \(-0.898910\pi\) |
0.907317 | − | 0.420447i | \(-0.138127\pi\) | |||||||
\(662\) | 45.0219 | + | 22.6109i | 1.74983 | + | 0.878796i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.76175 | + | 1.86735i | −0.0683691 | + | 0.0724670i | ||||
\(665\) | 54.7570 | + | 19.9299i | 2.12339 | + | 0.772849i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.997034 | − | 0.362891i | 0.0386053 | − | 0.0140512i | ||||
\(668\) | 23.7496 | − | 55.0578i | 0.918901 | − | 2.13025i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.52974 | + | 15.1304i | −0.174999 | + | 0.584538i | ||||
\(671\) | 0.200845 | + | 0.0234754i | 0.00775354 | + | 0.000906259i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.475690 | − | 8.16727i | 0.0183365 | − | 0.314825i | −0.976651 | − | 0.214830i | \(-0.931080\pi\) |
0.994988 | − | 0.0999952i | \(-0.0318827\pi\) | |||||||
\(674\) | 19.4599 | − | 33.7056i | 0.749569 | − | 1.29829i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.44293 | + | 14.6236i | 0.324728 | + | 0.562445i | ||||
\(677\) | 20.6357 | − | 10.3637i | 0.793096 | − | 0.398308i | −0.00564403 | − | 0.999984i | \(-0.501797\pi\) |
0.798740 | + | 0.601676i | \(0.205500\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.8974 | + | 25.3837i | −0.725217 | + | 0.974136i | ||||
\(680\) | 2.84811 | − | 0.675015i | 0.109220 | − | 0.0258857i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.76902 | + | 5.06267i | 0.144323 | + | 0.193860i | ||||
\(683\) | 14.3566 | + | 12.0466i | 0.549340 | + | 0.460951i | 0.874717 | − | 0.484633i | \(-0.161047\pi\) |
−0.325378 | + | 0.945584i | \(0.605491\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28.2370 | + | 23.6937i | −1.07888 | + | 0.905289i | ||||
\(686\) | 19.7506 | + | 4.68099i | 0.754083 | + | 0.178721i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 13.9985 | − | 9.20698i | 0.533689 | − | 0.351013i | ||||
\(689\) | −23.9002 | + | 15.7194i | −0.910525 | + | 0.598862i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.47006 | − | 1.53343i | −0.246133 | − | 0.0583345i | 0.105698 | − | 0.994398i | \(-0.466292\pi\) |
−0.351830 | + | 0.936064i | \(0.614441\pi\) | |||||||
\(692\) | 29.4279 | − | 24.6929i | 1.11868 | − | 0.938684i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27.4089 | + | 22.9988i | 1.04043 | + | 0.873023i | ||||
\(695\) | 24.4102 | + | 32.7885i | 0.925931 | + | 1.24374i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.55103 | − | 0.841610i | 0.134505 | − | 0.0318782i | ||||
\(698\) | 10.3188 | − | 13.8605i | 0.390572 | − | 0.524630i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −74.9521 | + | 37.6423i | −2.83292 | + | 1.42275i | ||||
\(701\) | −12.1477 | − | 21.0405i | −0.458813 | − | 0.794687i | 0.540086 | − | 0.841610i | \(-0.318392\pi\) |
−0.998899 | + | 0.0469230i | \(0.985058\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.6738 | + | 18.4876i | −0.402571 | + | 0.697274i | ||||
\(704\) | −0.494971 | + | 8.49832i | −0.0186549 | + | 0.320292i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 51.7260 | + | 6.04590i | 1.94673 | + | 0.227540i | ||||
\(707\) | 11.7728 | − | 39.3240i | 0.442763 | − | 1.47893i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.8515 | − | 27.4749i | 0.445093 | − | 1.03184i | −0.537024 | − | 0.843567i | \(-0.680451\pi\) |
0.982117 | − | 0.188274i | \(-0.0602893\pi\) | |||||||
\(710\) | −52.2729 | + | 19.0258i | −1.96177 | + | 0.714024i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.10315 | − | 1.85740i | −0.191249 | − | 0.0696089i | ||||
\(713\) | 6.18613 | − | 6.55691i | 0.231672 | − | 0.245558i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.54519 | + | 3.28712i | 0.244776 | + | 0.122931i | ||||
\(716\) | −1.03504 | − | 17.7710i | −0.0386814 | − | 0.664134i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.67320 | − | 25.6303i | −0.286361 | − | 0.956514i | ||||
\(719\) | 2.12889 | + | 12.0735i | 0.0793943 | + | 0.450267i | 0.998426 | + | 0.0560838i | \(0.0178614\pi\) |
−0.919032 | + | 0.394183i | \(0.871027\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.65461 | + | 54.7540i | −0.359556 | + | 2.03915i | ||||
\(722\) | −2.40063 | + | 0.280593i | −0.0893422 | + | 0.0104426i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.1497 | + | 13.9379i | 0.488706 | + | 0.517998i | ||||
\(725\) | −1.86626 | − | 4.32649i | −0.0693113 | − | 0.160682i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.9555 | + | 26.9369i | 1.51896 | + | 0.999033i | 0.988483 | + | 0.151331i | \(0.0483560\pi\) |
0.530473 | + | 0.847702i | \(0.322014\pi\) | |||||||
\(728\) | −8.35832 | −0.309780 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −65.3249 | −2.41778 | ||||||||
\(731\) | 3.70251 | + | 2.43518i | 0.136942 | + | 0.0900683i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.00055 | − | 18.5474i | −0.295507 | − | 0.685063i | 0.704181 | − | 0.710020i | \(-0.251314\pi\) |
−0.999689 | + | 0.0249576i | \(0.992055\pi\) | |||||||
\(734\) | 15.2367 | + | 16.1499i | 0.562396 | + | 0.596104i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.1310 | − | 2.11921i | 0.668317 | − | 0.0781150i | ||||
\(737\) | 0.251977 | − | 1.42903i | 0.00928168 | − | 0.0526390i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.349401 | + | 1.98155i | 0.0128529 | + | 0.0728925i | 0.990560 | − | 0.137083i | \(-0.0437727\pi\) |
−0.977707 | + | 0.209975i | \(0.932662\pi\) | |||||||
\(740\) | −13.1517 | − | 43.9297i | −0.483465 | − | 1.61489i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.72082 | + | 81.0533i | 0.173307 | + | 2.97556i | ||||
\(743\) | −19.2775 | − | 9.68153i | −0.707223 | − | 0.355181i | 0.0585563 | − | 0.998284i | \(-0.481350\pi\) |
−0.765779 | + | 0.643103i | \(0.777647\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33.2051 | + | 35.1953i | −1.21654 | + | 1.28946i | ||||
\(746\) | −23.4531 | − | 8.53624i | −0.858680 | − | 0.312534i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.31354 | + | 0.478091i | −0.0480279 | + | 0.0174807i | ||||
\(749\) | −4.87962 | + | 11.3122i | −0.178298 | + | 0.413340i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.15221 | − | 13.8693i | 0.151516 | − | 0.506099i | −0.848206 | − | 0.529666i | \(-0.822317\pi\) |
0.999722 | + | 0.0235670i | \(0.00750231\pi\) | |||||||
\(752\) | 30.1577 | + | 3.52494i | 1.09974 | + | 0.128541i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.141915 | − | 2.43659i | 0.00516826 | − | 0.0887355i | ||||
\(755\) | −35.4783 | + | 61.4503i | −1.29119 | + | 2.23640i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.26451 | − | 9.11840i | −0.191342 | − | 0.331414i | 0.754353 | − | 0.656469i | \(-0.227951\pi\) |
−0.945695 | + | 0.325055i | \(0.894617\pi\) | |||||||
\(758\) | 34.2919 | − | 17.2220i | 1.24554 | − | 0.625533i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.5167 | − | 14.1264i | 0.381480 | − | 0.512417i | ||||
\(761\) | 41.1358 | − | 9.74936i | 1.49117 | − | 0.353414i | 0.597402 | − | 0.801942i | \(-0.296200\pi\) |
0.893769 | + | 0.448528i | \(0.148051\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.5335 | + | 46.3865i | 1.25020 | + | 1.67930i | ||||
\(764\) | 19.1188 | + | 16.0425i | 0.691693 | + | 0.580399i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.1504 | + | 21.1037i | −0.908721 | + | 0.762507i | ||||
\(767\) | 10.0378 | + | 2.37900i | 0.362443 | + | 0.0859006i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.53547 | − | 4.95616i | 0.271736 | − | 0.178724i | −0.406326 | − | 0.913728i | \(-0.633190\pi\) |
0.678062 | + | 0.735005i | \(0.262820\pi\) | |||||||
\(770\) | 17.3679 | − | 11.4231i | 0.625897 | − | 0.411659i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −38.5361 | − | 9.13322i | −1.38694 | − | 0.328712i | ||||
\(773\) | −0.551231 | + | 0.462537i | −0.0198264 | + | 0.0166363i | −0.652647 | − | 0.757662i | \(-0.726342\pi\) |
0.632821 | + | 0.774298i | \(0.281897\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −30.6663 | − | 25.7321i | −1.10157 | − | 0.924325i | ||||
\(776\) | 5.71134 | + | 7.67167i | 0.205025 | + | 0.275397i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.7750 | − | 7.53081i | 1.13919 | − | 0.269993i | ||||
\(779\) | 13.1122 | − | 17.6128i | 0.469794 | − | 0.631043i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.56720 | − | 2.29373i | 0.163427 | − | 0.0820763i | ||||
\(782\) | 1.80442 | + | 3.12535i | 0.0645261 | + | 0.111762i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.81453 | − | 10.0711i | 0.207662 | − | 0.359681i | ||||
\(785\) | 5.29033 | − | 90.8314i | 0.188820 | − | 3.24191i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.3231 | − | 1.79102i | −0.546210 | − | 0.0638428i | −0.161487 | − | 0.986875i | \(-0.551629\pi\) |
−0.384723 | + | 0.923032i | \(0.625703\pi\) | |||||||
\(788\) | 7.79138 | − | 26.0250i | 0.277556 | − | 0.927102i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −14.0827 | + | 32.6474i | −0.501041 | + | 1.16154i | ||||
\(791\) | 32.3091 | − | 11.7595i | 1.14878 | − | 0.418121i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.624297 | − | 0.227226i | −0.0221695 | − | 0.00806902i | ||||
\(794\) | −2.96570 | + | 3.14346i | −0.105249 | + | 0.111557i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.76927 | + | 3.90187i | 0.275374 | + | 0.138298i | ||||
\(797\) | 0.809987 | + | 13.9069i | 0.0286912 | + | 0.492609i | 0.981792 | + | 0.189957i | \(0.0608349\pi\) |
−0.953101 | + | 0.302652i | \(0.902128\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.30326 | + | 7.69342i | 0.0814835 | + | 0.272174i | ||||
\(800\) | −14.0768 | − | 79.8335i | −0.497690 | − | 2.82254i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.49411 | + | 31.1586i | −0.194004 | + | 1.10025i | ||||
\(803\) | 5.96118 | − | 0.696763i | 0.210366 | − | 0.0245882i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.3746 | − | 21.5958i | −0.718109 | − | 0.761152i | ||||
\(806\) | −8.21332 | − | 19.0406i | −0.289302 | − | 0.670677i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.3651 | − | 6.81721i | −0.364642 | − | 0.239829i | ||||
\(809\) | 40.8781 | 1.43720 | 0.718599 | − | 0.695424i | \(-0.244784\pi\) | ||||
0.718599 | + | 0.695424i | \(0.244784\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 51.1039 | 1.79450 | 0.897250 | − | 0.441524i | \(-0.145562\pi\) | ||||
0.897250 | + | 0.441524i | \(0.145562\pi\) | |||||||
\(812\) | −3.20182 | − | 2.10587i | −0.112362 | − | 0.0739016i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.01639 | + | 6.99277i | 0.105724 | + | 0.245096i | ||||
\(815\) | 31.3201 | + | 33.1973i | 1.09709 | + | 1.16285i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.4834 | − | 3.09547i | 0.926538 | − | 0.108297i | ||||
\(818\) | 3.81673 | − | 21.6457i | 0.133449 | − | 0.756825i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.19037 | + | 46.4499i | 0.286020 | + | 1.62210i | ||||
\(821\) | −13.9304 | − | 46.5308i | −0.486174 | − | 1.62393i | −0.751470 | − | 0.659768i | \(-0.770655\pi\) |
0.265296 | − | 0.964167i | \(-0.414530\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.57149 | − | 26.9814i | −0.0547787 | − | 0.940513i | −0.908002 | − | 0.418967i | \(-0.862392\pi\) |
0.853223 | − | 0.521546i | \(-0.174645\pi\) | |||||||
\(824\) | 15.0162 | + | 7.54139i | 0.523112 | + | 0.262717i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 20.0922 | − | 21.2964i | 0.699096 | − | 0.740998i | ||||
\(827\) | 14.9793 | + | 5.45201i | 0.520880 | + | 0.189585i | 0.589062 | − | 0.808088i | \(-0.299497\pi\) |
−0.0681816 | + | 0.997673i | \(0.521720\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.59698 | − | 0.581253i | 0.0554654 | − | 0.0201877i | −0.314138 | − | 0.949377i | \(-0.601716\pi\) |
0.369604 | + | 0.929189i | \(0.379493\pi\) | |||||||
\(830\) | −8.30876 | + | 19.2619i | −0.288401 | + | 0.668590i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.02140 | − | 26.7933i | 0.278092 | − | 0.928892i | ||||
\(833\) | 3.05500 | + | 0.357079i | 0.105850 | + | 0.0123720i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.48073 | − | 94.1005i | 0.189669 | − | 3.25648i | ||||
\(836\) | −4.20527 | + | 7.28373i | −0.145442 | + | 0.251913i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.560786 | + | 0.971310i | 0.0193720 | + | 0.0335534i | ||||
\(839\) | 41.4212 | − | 20.8025i | 1.43002 | − | 0.718183i | 0.445800 | − | 0.895132i | \(-0.352919\pi\) |
0.984220 | + | 0.176949i | \(0.0566229\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.1890 | + | 23.0889i | −0.592725 | + | 0.796168i | ||||
\(842\) | −66.0144 | + | 15.6457i | −2.27501 | + | 0.539187i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.3628 | − | 15.2629i | −0.391125 | − | 0.525372i | ||||
\(845\) | 20.3343 | + | 17.0625i | 0.699523 | + | 0.586969i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.6409 | − | 22.3544i | 0.915393 | − | 0.768106i | ||||
\(848\) | −31.5740 | − | 7.48317i | −1.08426 | − | 0.256973i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 13.3898 | − | 8.80663i | 0.459267 | − | 0.302065i | ||||
\(851\) | 9.08757 | − | 5.97699i | 0.311518 | − | 0.204889i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.5426 | − | 5.57970i | −0.806083 | − | 0.191045i | −0.193139 | − | 0.981171i | \(-0.561867\pi\) |
−0.612944 | + | 0.790126i | \(0.710015\pi\) | |||||||
\(854\) | −1.44446 | + | 1.21204i | −0.0494283 | + | 0.0414753i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.85228 | + | 2.39335i | 0.0974891 | + | 0.0818031i | ||||
\(857\) | 7.66072 | + | 10.2901i | 0.261685 | + | 0.351504i | 0.913475 | − | 0.406896i | \(-0.133389\pi\) |
−0.651789 | + | 0.758400i | \(0.725981\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.9669 | − | 4.73224i | 0.681262 | − | 0.161462i | 0.124607 | − | 0.992206i | \(-0.460233\pi\) |
0.556654 | + | 0.830744i | \(0.312085\pi\) | |||||||
\(860\) | −34.2024 | + | 45.9419i | −1.16629 | + | 1.56660i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.1775 | + | 5.11136i | −0.346649 | + | 0.174093i | ||||
\(863\) | −18.5110 | − | 32.0620i | −0.630121 | − | 1.09140i | −0.987527 | − | 0.157453i | \(-0.949672\pi\) |
0.357405 | − | 0.933949i | \(-0.383662\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.1945 | − | 52.2984i | 1.02664 | − | 1.77820i | ||||
\(866\) | −4.09570 | + | 70.3205i | −0.139178 | + | 2.38959i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −32.3391 | − | 3.77990i | −1.09766 | − | 0.128298i | ||||
\(869\) | 0.936890 | − | 3.12943i | 0.0317818 | − | 0.106159i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.88830 | + | 4.37757i | −0.0639826 | + | 0.148328i | ||||
\(872\) | 16.4237 | − | 5.97775i | 0.556178 | − | 0.202432i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 20.4042 | + | 7.42652i | 0.690182 | + | 0.251206i | ||||
\(875\) | −45.9306 | + | 48.6836i | −1.55274 | + | 1.64581i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.7549 | + | 19.4634i | 1.30866 | + | 0.657233i | 0.959996 | − | 0.280015i | \(-0.0903394\pi\) |
0.348663 | + | 0.937248i | \(0.386636\pi\) | |||||||
\(878\) | 2.29826 | + | 39.4596i | 0.0775625 | + | 1.33170i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.38277 | + | 7.95901i | 0.0803232 | + | 0.268298i | ||||
\(881\) | −1.78531 | − | 10.1250i | −0.0601486 | − | 0.341120i | 0.939851 | − | 0.341584i | \(-0.110963\pi\) |
−1.00000 | 0.000464198i | \(0.999852\pi\) | ||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.36337 | − | 7.73205i | 0.0458810 | − | 0.260204i | −0.953236 | − | 0.302228i | \(-0.902269\pi\) |
0.999117 | + | 0.0420240i | \(0.0133806\pi\) | |||||||
\(884\) | 4.56152 | − | 0.533166i | 0.153421 | − | 0.0179323i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27.3985 | − | 29.0407i | −0.920469 | − | 0.975640i | ||||
\(887\) | 13.8603 | + | 32.1317i | 0.465382 | + | 1.07888i | 0.975744 | + | 0.218917i | \(0.0702523\pi\) |
−0.510362 | + | 0.859960i | \(0.670488\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36.8182 | − | 24.2157i | −1.23484 | − | 0.812169i | ||||
\(890\) | −44.3751 | −1.48746 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 26.8550 | 0.899172 | ||||||||
\(893\) | 40.3705 | + | 26.5521i | 1.35095 | + | 0.888531i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.0837 | − | 25.6948i | −0.370486 | − | 0.858883i | ||||
\(896\) | −17.9327 | − | 19.0075i | −0.599088 | − | 0.634996i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −14.6391 | + | 1.71107i | −0.488515 | + | 0.0570992i | ||||
\(899\) | 0.317622 | − | 1.80133i | 0.0105933 | − | 0.0600776i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.49032 | − | 8.45204i | −0.0496498 | − | 0.281578i | ||||
\(902\) | −2.24659 | − | 7.50414i | −0.0748034 | − | 0.249861i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.604206 | − | 10.3738i | −0.0200956 | − | 0.345028i | ||||
\(905\) | 26.9186 | + | 13.5190i | 0.894804 | + | 0.449387i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.4760 | − | 36.5424i | 1.14476 | − | 1.21337i | 0.171124 | − | 0.985250i | \(-0.445260\pi\) |
0.973633 | − | 0.228122i | \(-0.0732584\pi\) | |||||||
\(908\) | −25.2752 | − | 9.19941i | −0.838786 | − | 0.305293i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −64.1788 | + | 23.3592i | −2.12751 | + | 0.774349i | ||||
\(911\) | 9.76794 | − | 22.6446i | 0.323626 | − | 0.750250i | −0.676281 | − | 0.736643i | \(-0.736410\pi\) |
0.999907 | − | 0.0136062i | \(-0.00433113\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.552762 | − | 1.84635i | 0.0182938 | − | 0.0611054i | ||||
\(914\) | −79.0097 | − | 9.23490i | −2.61341 | − | 0.305463i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.329662 | + | 5.66008i | −0.0108923 | + | 0.187014i | ||||
\(917\) | −16.7783 | + | 29.0608i | −0.554067 | + | 0.959672i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.12738 | − | 7.14883i | −0.136150 | − | 0.235818i | 0.789886 | − | 0.613253i | \(-0.210139\pi\) |
−0.926036 | + | 0.377435i | \(0.876806\pi\) | |||||||
\(920\) | −8.01873 | + | 4.02716i | −0.264370 | + | 0.132772i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 34.9178 | − | 46.9027i | 1.14996 | − | 1.54466i | ||||
\(923\) | −16.3389 | + | 3.87238i | −0.537800 | + | 0.127461i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.8445 | − | 38.7449i | −0.948403 | − | 1.27393i | ||||
\(926\) | 39.8178 | + | 33.4111i | 1.30849 | + | 1.09796i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.83740 | − | 2.38086i | 0.0931422 | − | 0.0781556i | ||||
\(929\) | 9.54344 | + | 2.26184i | 0.313110 | + | 0.0742085i | 0.384166 | − | 0.923264i | \(-0.374489\pi\) |
−0.0710563 | + | 0.997472i | \(0.522637\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.4619 | − | 10.1695i | 0.506744 | − | 0.333291i | ||||
\(932\) | 36.8515 | − | 24.2376i | 1.20711 | − | 0.793929i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −16.1833 | − | 3.83551i | −0.529534 | − | 0.125502i | ||||
\(935\) | −1.68332 | + | 1.41247i | −0.0550503 | + | 0.0461927i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.8490 | + | 28.4027i | 1.10580 | + | 0.927875i | 0.997801 | − | 0.0662763i | \(-0.0211119\pi\) |
0.107997 | + | 0.994151i | \(0.465556\pi\) | |||||||
\(938\) | 8.08021 | + | 10.8536i | 0.263828 | + | 0.354383i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −100.996 | + | 23.9365i | −3.29412 | + | 0.780721i | ||||
\(941\) | 6.35395 | − | 8.53483i | 0.207133 | − | 0.278228i | −0.686401 | − | 0.727223i | \(-0.740811\pi\) |
0.893534 | + | 0.448995i | \(0.148218\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.99777 | + | 5.02107i | −0.325572 | + | 0.163508i | ||||
\(944\) | 5.85073 | + | 10.1338i | 0.190425 | + | 0.329826i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.75603 | − | 8.23768i | 0.154632 | − | 0.267830i | ||||
\(947\) | −0.639255 | + | 10.9756i | −0.0207730 | + | 0.356659i | 0.971865 | + | 0.235539i | \(0.0756855\pi\) |
−0.992638 | + | 0.121120i | \(0.961352\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.5853 | − | 2.28919i | −0.635766 | − | 0.0743104i | ||||
\(950\) | 27.6556 | − | 92.3763i | 0.897267 | − | 2.99708i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.993232 | − | 2.30257i | 0.0321908 | − | 0.0746267i | ||||
\(953\) | −39.7723 | + | 14.4759i | −1.28835 | + | 0.468921i | −0.893185 | − | 0.449689i | \(-0.851535\pi\) |
−0.395165 | + | 0.918610i | \(0.629313\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36.8676 | + | 13.4187i | 1.19301 | + | 0.434219i | ||||
\(956\) | −20.8456 | + | 22.0950i | −0.674194 | + | 0.714604i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33.4874 | + | 16.8180i | 1.08193 | + | 0.543366i | ||||
\(959\) | 1.83620 | + | 31.5263i | 0.0592939 | + | 1.01804i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.43390 | + | 14.8103i | 0.143029 | + | 0.477751i | ||||
\(962\) | −4.34483 | − | 24.6407i | −0.140083 | − | 0.794449i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.52523 | − | 42.6777i | 0.242371 | − | 1.37456i | ||||
\(965\) | −61.8360 | + | 7.22759i | −1.99057 | + | 0.232664i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.70365 | + | 6.04552i | 0.183417 | + | 0.194411i | 0.812558 | − | 0.582881i | \(-0.198075\pi\) |
−0.629141 | + | 0.777291i | \(0.716593\pi\) | |||||||
\(968\) | −4.16306 | − | 9.65107i | −0.133806 | − | 0.310197i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 65.2943 | + | 42.9448i | 2.09647 | + | 1.37887i | ||||
\(971\) | 17.9539 | 0.576169 | 0.288084 | − | 0.957605i | \(-0.406982\pi\) | ||||
0.288084 | + | 0.957605i | \(0.406982\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.0207 | 1.12271 | ||||||||
\(974\) | 74.4455 | + | 48.9636i | 2.38539 | + | 1.56890i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.298486 | − | 0.691968i | −0.00955430 | − | 0.0221494i | ||||
\(977\) | −16.7513 | − | 17.7553i | −0.535922 | − | 0.568044i | 0.401669 | − | 0.915785i | \(-0.368430\pi\) |
−0.937591 | + | 0.347741i | \(0.886949\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.04943 | − | 0.473310i | 0.129420 | − | 0.0151271i | ||||
\(980\) | −6.90304 | + | 39.1491i | −0.220509 | + | 1.25057i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.67375 | + | 15.1636i | 0.0853228 | + | 0.483890i | ||||
\(983\) | 13.3688 | + | 44.6549i | 0.426399 | + | 1.42427i | 0.853986 | + | 0.520297i | \(0.174179\pi\) |
−0.427587 | + | 0.903974i | \(0.640636\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.48310 | − | 42.6332i | −0.0791182 | − | 1.35841i | ||||
\(986\) | 0.654375 | + | 0.328639i | 0.0208395 | + | 0.0104660i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.9626 | − | 20.0992i | 0.603281 | − | 0.639441i | ||||
\(989\) | −12.7663 | − | 4.64654i | −0.405944 | − | 0.147751i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55.3339 | + | 20.1399i | −1.75774 | + | 0.639765i | −0.999919 | − | 0.0126995i | \(-0.995958\pi\) |
−0.757820 | + | 0.652464i | \(0.773735\pi\) | |||||||
\(992\) | 12.4643 | − | 28.8954i | 0.395741 | − | 0.917430i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −13.6684 | + | 45.6557i | −0.433536 | + | 1.44811i | ||||
\(995\) | 13.5746 | + | 1.58665i | 0.430344 | + | 0.0503001i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.50559 | + | 60.1886i | −0.111023 | + | 1.90619i | 0.241517 | + | 0.970397i | \(0.422355\pi\) |
−0.352540 | + | 0.935797i | \(0.614682\pi\) | |||||||
\(998\) | −17.0636 | + | 29.5550i | −0.540138 | + | 0.935547i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 729.2.g.b.703.2 | 144 | ||
3.2 | odd | 2 | 729.2.g.c.703.7 | 144 | |||
9.2 | odd | 6 | 729.2.g.d.217.7 | 144 | |||
9.4 | even | 3 | 243.2.g.a.73.7 | 144 | |||
9.5 | odd | 6 | 81.2.g.a.25.2 | yes | 144 | ||
9.7 | even | 3 | 729.2.g.a.217.2 | 144 | |||
81.13 | even | 27 | 729.2.g.a.514.2 | 144 | |||
81.14 | odd | 54 | 729.2.g.c.28.7 | 144 | |||
81.38 | odd | 54 | 6561.2.a.c.1.12 | 72 | |||
81.40 | even | 27 | 243.2.g.a.10.7 | 144 | |||
81.41 | odd | 54 | 81.2.g.a.13.2 | ✓ | 144 | ||
81.43 | even | 27 | 6561.2.a.d.1.61 | 72 | |||
81.67 | even | 27 | inner | 729.2.g.b.28.2 | 144 | ||
81.68 | odd | 54 | 729.2.g.d.514.7 | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
81.2.g.a.13.2 | ✓ | 144 | 81.41 | odd | 54 | ||
81.2.g.a.25.2 | yes | 144 | 9.5 | odd | 6 | ||
243.2.g.a.10.7 | 144 | 81.40 | even | 27 | |||
243.2.g.a.73.7 | 144 | 9.4 | even | 3 | |||
729.2.g.a.217.2 | 144 | 9.7 | even | 3 | |||
729.2.g.a.514.2 | 144 | 81.13 | even | 27 | |||
729.2.g.b.28.2 | 144 | 81.67 | even | 27 | inner | ||
729.2.g.b.703.2 | 144 | 1.1 | even | 1 | trivial | ||
729.2.g.c.28.7 | 144 | 81.14 | odd | 54 | |||
729.2.g.c.703.7 | 144 | 3.2 | odd | 2 | |||
729.2.g.d.217.7 | 144 | 9.2 | odd | 6 | |||
729.2.g.d.514.7 | 144 | 81.68 | odd | 54 | |||
6561.2.a.c.1.12 | 72 | 81.38 | odd | 54 | |||
6561.2.a.d.1.61 | 72 | 81.43 | even | 27 |