Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(107,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([3, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.q (of order \(12\), degree \(4\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 107.6 | ||
Character | \(\chi\) | \(=\) | 950.107 |
Dual form | 950.2.q.e.293.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.965926 | + | 0.258819i | 0.683013 | + | 0.183013i | ||||
\(3\) | 0.431989 | − | 1.61221i | 0.249409 | − | 0.930808i | −0.721707 | − | 0.692199i | \(-0.756642\pi\) |
0.971116 | − | 0.238609i | \(-0.0766914\pi\) | |||||||
\(4\) | 0.866025 | + | 0.500000i | 0.433013 | + | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.834540 | − | 1.44546i | 0.340699 | − | 0.590109i | ||||
\(7\) | −2.81008 | − | 2.81008i | −1.06211 | − | 1.06211i | −0.997939 | − | 0.0641702i | \(-0.979560\pi\) |
−0.0641702 | − | 0.997939i | \(-0.520440\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 0.185481 | + | 0.107087i | 0.0618270 | + | 0.0356958i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.57889 | −1.68210 | −0.841049 | − | 0.540959i | \(-0.818061\pi\) | ||||
−0.841049 | + | 0.540959i | \(0.818061\pi\) | |||||||
\(12\) | 1.18022 | − | 1.18022i | 0.340699 | − | 0.340699i | ||||
\(13\) | 3.10465 | − | 0.831890i | 0.861076 | − | 0.230725i | 0.198851 | − | 0.980030i | \(-0.436279\pi\) |
0.662225 | + | 0.749305i | \(0.269612\pi\) | |||||||
\(14\) | −1.98702 | − | 3.44163i | −0.531055 | − | 0.919814i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 1.06453 | − | 3.97289i | 0.258187 | − | 0.963566i | −0.708103 | − | 0.706109i | \(-0.750449\pi\) |
0.966290 | − | 0.257457i | \(-0.0828846\pi\) | |||||||
\(18\) | 0.151445 | + | 0.151445i | 0.0356958 | + | 0.0356958i | ||||
\(19\) | −0.254973 | − | 4.35144i | −0.0584949 | − | 0.998288i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.74435 | + | 3.31650i | −1.25352 | + | 0.723720i | ||||
\(22\) | −5.38879 | − | 1.44392i | −1.14889 | − | 0.307845i | ||||
\(23\) | −1.02856 | − | 3.83864i | −0.214469 | − | 0.800411i | −0.986353 | − | 0.164647i | \(-0.947352\pi\) |
0.771883 | − | 0.635764i | \(-0.219315\pi\) | |||||||
\(24\) | 1.44546 | − | 0.834540i | 0.295054 | − | 0.170350i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.21417 | 0.630352 | ||||||||
\(27\) | 3.79342 | − | 3.79342i | 0.730045 | − | 0.730045i | ||||
\(28\) | −1.02856 | − | 3.83864i | −0.194379 | − | 0.725434i | ||||
\(29\) | 2.09440 | − | 3.62760i | 0.388920 | − | 0.673629i | −0.603385 | − | 0.797450i | \(-0.706182\pi\) |
0.992305 | + | 0.123821i | \(0.0395150\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.573172i | 0.102945i | 0.998674 | + | 0.0514724i | \(0.0163914\pi\) | ||||
−0.998674 | + | 0.0514724i | \(0.983609\pi\) | |||||||
\(32\) | 0.258819 | + | 0.965926i | 0.0457532 | + | 0.170753i | ||||
\(33\) | −2.41002 | + | 8.99432i | −0.419531 | + | 1.56571i | ||||
\(34\) | 2.05652 | − | 3.56199i | 0.352690 | − | 0.610877i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.107087 | + | 0.185481i | 0.0178479 | + | 0.0309135i | ||||
\(37\) | −7.24641 | + | 7.24641i | −1.19130 | + | 1.19130i | −0.214600 | + | 0.976702i | \(0.568845\pi\) |
−0.976702 | + | 0.214600i | \(0.931155\pi\) | |||||||
\(38\) | 0.879949 | − | 4.26916i | 0.142747 | − | 0.692548i | ||||
\(39\) | − | 5.36471i | − | 0.859041i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.12760 | + | 2.96042i | −0.800797 | + | 0.462340i | −0.843750 | − | 0.536737i | \(-0.819657\pi\) |
0.0429529 | + | 0.999077i | \(0.486323\pi\) | |||||||
\(42\) | −6.40699 | + | 1.71675i | −0.988620 | + | 0.264900i | ||||
\(43\) | −5.37742 | − | 1.44088i | −0.820049 | − | 0.219731i | −0.175681 | − | 0.984447i | \(-0.556213\pi\) |
−0.644368 | + | 0.764716i | \(0.722879\pi\) | |||||||
\(44\) | −4.83146 | − | 2.78944i | −0.728370 | − | 0.420524i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 3.97405i | − | 0.585941i | ||||||
\(47\) | 11.7844 | − | 3.15762i | 1.71893 | − | 0.460587i | 0.741346 | − | 0.671123i | \(-0.234188\pi\) |
0.977586 | + | 0.210536i | \(0.0675209\pi\) | |||||||
\(48\) | 1.61221 | − | 0.431989i | 0.232702 | − | 0.0623523i | ||||
\(49\) | 8.79306i | 1.25615i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.94525 | − | 3.43249i | −0.832501 | − | 0.480645i | ||||
\(52\) | 3.10465 | + | 0.831890i | 0.430538 | + | 0.115362i | ||||
\(53\) | 3.66382 | − | 0.981717i | 0.503264 | − | 0.134849i | 0.00174955 | − | 0.999998i | \(-0.499443\pi\) |
0.501514 | + | 0.865149i | \(0.332776\pi\) | |||||||
\(54\) | 4.64598 | − | 2.68236i | 0.632237 | − | 0.365022i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 3.97405i | − | 0.531055i | ||||||
\(57\) | −7.12556 | − | 1.46870i | −0.943803 | − | 0.194535i | ||||
\(58\) | 2.96192 | − | 2.96192i | 0.388920 | − | 0.388920i | ||||
\(59\) | 3.75696 | + | 6.50724i | 0.489114 | + | 0.847170i | 0.999922 | − | 0.0125249i | \(-0.00398690\pi\) |
−0.510808 | + | 0.859695i | \(0.670654\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.06199 | + | 1.83942i | −0.135974 | + | 0.235514i | −0.925969 | − | 0.377599i | \(-0.876750\pi\) |
0.789995 | + | 0.613113i | \(0.210083\pi\) | |||||||
\(62\) | −0.148348 | + | 0.553641i | −0.0188402 | + | 0.0703125i | ||||
\(63\) | −0.220292 | − | 0.822140i | −0.0277541 | − | 0.103580i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.65580 | + | 8.06409i | −0.573090 | + | 0.992620i | ||||
\(67\) | 3.07561 | + | 11.4783i | 0.375746 | + | 1.40230i | 0.852252 | + | 0.523132i | \(0.175236\pi\) |
−0.476506 | + | 0.879171i | \(0.658097\pi\) | |||||||
\(68\) | 2.90835 | − | 2.90835i | 0.352690 | − | 0.352690i | ||||
\(69\) | −6.63300 | −0.798520 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.56561 | + | 2.63596i | −0.541838 | + | 0.312830i | −0.745824 | − | 0.666143i | \(-0.767944\pi\) |
0.203985 | + | 0.978974i | \(0.434611\pi\) | |||||||
\(72\) | 0.0554326 | + | 0.206877i | 0.00653279 | + | 0.0243807i | ||||
\(73\) | 13.0991 | + | 3.50990i | 1.53314 | + | 0.410802i | 0.924041 | − | 0.382295i | \(-0.124866\pi\) |
0.609095 | + | 0.793097i | \(0.291533\pi\) | |||||||
\(74\) | −8.87500 | + | 5.12398i | −1.03170 | + | 0.595651i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.95490 | − | 3.89594i | 0.224243 | − | 0.446895i | ||||
\(77\) | 15.6771 | + | 15.6771i | 1.78657 | + | 1.78657i | ||||
\(78\) | 1.38849 | − | 5.18191i | 0.157216 | − | 0.586736i | ||||
\(79\) | 2.48836 | + | 4.30996i | 0.279962 | + | 0.484908i | 0.971375 | − | 0.237551i | \(-0.0763448\pi\) |
−0.691413 | + | 0.722460i | \(0.743012\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.15580 | − | 7.19806i | −0.461756 | − | 0.799784i | ||||
\(82\) | −5.71910 | + | 1.53243i | −0.631569 | + | 0.169228i | ||||
\(83\) | 7.30376 | − | 7.30376i | 0.801692 | − | 0.801692i | −0.181668 | − | 0.983360i | \(-0.558150\pi\) |
0.983360 | + | 0.181668i | \(0.0581496\pi\) | |||||||
\(84\) | −6.63300 | −0.723720 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.82126 | − | 2.78356i | −0.519890 | − | 0.300159i | ||||
\(87\) | −4.94369 | − | 4.94369i | −0.530019 | − | 0.530019i | ||||
\(88\) | −3.94487 | − | 3.94487i | −0.420524 | − | 0.420524i | ||||
\(89\) | 7.08207 | − | 12.2665i | 0.750698 | − | 1.30025i | −0.196787 | − | 0.980446i | \(-0.563051\pi\) |
0.947485 | − | 0.319801i | \(-0.103616\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.0620 | − | 6.38664i | −1.15961 | − | 0.669502i | ||||
\(92\) | 1.02856 | − | 3.83864i | 0.107235 | − | 0.400205i | ||||
\(93\) | 0.924071 | + | 0.247604i | 0.0958217 | + | 0.0256754i | ||||
\(94\) | 12.2001 | 1.25835 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.66908 | 0.170350 | ||||||||
\(97\) | 2.31297 | + | 0.619757i | 0.234846 | + | 0.0629268i | 0.374323 | − | 0.927299i | \(-0.377875\pi\) |
−0.139476 | + | 0.990225i | \(0.544542\pi\) | |||||||
\(98\) | −2.27581 | + | 8.49345i | −0.229892 | + | 0.857968i | ||||
\(99\) | −1.03478 | − | 0.597429i | −0.103999 | − | 0.0600439i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.240729 | + | 0.416955i | −0.0239534 | + | 0.0414886i | −0.877754 | − | 0.479112i | \(-0.840959\pi\) |
0.853800 | + | 0.520601i | \(0.174292\pi\) | |||||||
\(102\) | −4.85427 | − | 4.85427i | −0.480645 | − | 0.480645i | ||||
\(103\) | −9.90973 | − | 9.90973i | −0.976435 | − | 0.976435i | 0.0232940 | − | 0.999729i | \(-0.492585\pi\) |
−0.999729 | + | 0.0232940i | \(0.992585\pi\) | |||||||
\(104\) | 2.78356 | + | 1.60709i | 0.272950 | + | 0.157588i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.79306 | 0.368415 | ||||||||
\(107\) | 1.75977 | − | 1.75977i | 0.170124 | − | 0.170124i | −0.616910 | − | 0.787034i | \(-0.711616\pi\) |
0.787034 | + | 0.616910i | \(0.211616\pi\) | |||||||
\(108\) | 5.18191 | − | 1.38849i | 0.498630 | − | 0.133607i | ||||
\(109\) | 1.33809 | + | 2.31764i | 0.128166 | + | 0.221990i | 0.922966 | − | 0.384881i | \(-0.125758\pi\) |
−0.794800 | + | 0.606871i | \(0.792424\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.55233 | + | 14.8131i | 0.811752 | + | 1.40599i | ||||
\(112\) | 1.02856 | − | 3.83864i | 0.0971897 | − | 0.362717i | ||||
\(113\) | 6.56319 | + | 6.56319i | 0.617413 | + | 0.617413i | 0.944867 | − | 0.327454i | \(-0.106191\pi\) |
−0.327454 | + | 0.944867i | \(0.606191\pi\) | |||||||
\(114\) | −6.50263 | − | 3.26289i | −0.609027 | − | 0.305598i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.62760 | − | 2.09440i | 0.336814 | − | 0.194460i | ||||
\(117\) | 0.664939 | + | 0.178170i | 0.0614737 | + | 0.0164718i | ||||
\(118\) | 1.94474 | + | 7.25788i | 0.179028 | + | 0.668142i | ||||
\(119\) | −14.1555 | + | 8.17270i | −1.29764 | + | 0.749190i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.1240 | 1.82945 | ||||||||
\(122\) | −1.50188 | + | 1.50188i | −0.135974 | + | 0.135974i | ||||
\(123\) | 2.55774 | + | 9.54562i | 0.230624 | + | 0.860700i | ||||
\(124\) | −0.286586 | + | 0.496381i | −0.0257362 | + | 0.0445764i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 0.851142i | − | 0.0758257i | ||||||
\(127\) | −3.35965 | − | 12.5384i | −0.298121 | − | 1.11260i | −0.938707 | − | 0.344715i | \(-0.887975\pi\) |
0.640587 | − | 0.767886i | \(-0.278691\pi\) | |||||||
\(128\) | −0.258819 | + | 0.965926i | −0.0228766 | + | 0.0853766i | ||||
\(129\) | −4.64598 | + | 8.04707i | −0.409055 | + | 0.708505i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.86636 | + | 8.42878i | 0.425176 | + | 0.736426i | 0.996437 | − | 0.0843425i | \(-0.0268790\pi\) |
−0.571261 | + | 0.820768i | \(0.693546\pi\) | |||||||
\(132\) | −6.58430 | + | 6.58430i | −0.573090 | + | 0.573090i | ||||
\(133\) | −11.5114 | + | 12.9444i | −0.998163 | + | 1.12242i | ||||
\(134\) | 11.8833i | 1.02656i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.56199 | − | 2.05652i | 0.305438 | − | 0.176345i | ||||
\(137\) | 0.761069 | − | 0.203928i | 0.0650225 | − | 0.0174227i | −0.226161 | − | 0.974090i | \(-0.572618\pi\) |
0.291184 | + | 0.956667i | \(0.405951\pi\) | |||||||
\(138\) | −6.40699 | − | 1.71675i | −0.545399 | − | 0.146139i | ||||
\(139\) | −12.5016 | − | 7.21779i | −1.06037 | − | 0.612205i | −0.134836 | − | 0.990868i | \(-0.543051\pi\) |
−0.925535 | + | 0.378663i | \(0.876384\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 20.3630i | − | 1.71487i | ||||||
\(142\) | −5.09228 | + | 1.36447i | −0.427334 | + | 0.114504i | ||||
\(143\) | −17.3205 | + | 4.64102i | −1.44841 | + | 0.388101i | ||||
\(144\) | 0.214175i | 0.0178479i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 11.7443 | + | 6.78060i | 0.971969 | + | 0.561167i | ||||
\(147\) | 14.1762 | + | 3.79851i | 1.16924 | + | 0.313296i | ||||
\(148\) | −9.89878 | + | 2.65237i | −0.813674 | + | 0.218023i | ||||
\(149\) | 10.9655 | − | 6.33092i | 0.898327 | − | 0.518649i | 0.0216699 | − | 0.999765i | \(-0.493102\pi\) |
0.876657 | + | 0.481116i | \(0.159768\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.7958i | 1.20407i | 0.798470 | + | 0.602034i | \(0.205643\pi\) | ||||
−0.798470 | + | 0.602034i | \(0.794357\pi\) | |||||||
\(152\) | 2.89664 | − | 3.25722i | 0.234948 | − | 0.264196i | ||||
\(153\) | 0.622897 | − | 0.622897i | 0.0503582 | − | 0.0503582i | ||||
\(154\) | 11.0854 | + | 19.2004i | 0.893286 | + | 1.54722i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.68236 | − | 4.64598i | 0.214760 | − | 0.371976i | ||||
\(157\) | 1.64480 | − | 6.13849i | 0.131270 | − | 0.489905i | −0.868716 | − | 0.495311i | \(-0.835054\pi\) |
0.999985 | + | 0.00540611i | \(0.00172083\pi\) | |||||||
\(158\) | 1.28807 | + | 4.80713i | 0.102473 | + | 0.382435i | ||||
\(159\) | − | 6.33092i | − | 0.502075i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.89653 | + | 13.6772i | −0.622334 | + | 1.07791i | ||||
\(162\) | −2.15120 | − | 8.02839i | −0.169014 | − | 0.630770i | ||||
\(163\) | 13.5793 | − | 13.5793i | 1.06362 | − | 1.06362i | 0.0657815 | − | 0.997834i | \(-0.479046\pi\) |
0.997834 | − | 0.0657815i | \(-0.0209540\pi\) | |||||||
\(164\) | −5.92084 | −0.462340 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.94525 | − | 5.16454i | 0.694286 | − | 0.400846i | ||||
\(167\) | 0.667465 | + | 2.49101i | 0.0516500 | + | 0.192760i | 0.986930 | − | 0.161147i | \(-0.0515194\pi\) |
−0.935280 | + | 0.353908i | \(0.884853\pi\) | |||||||
\(168\) | −6.40699 | − | 1.71675i | −0.494310 | − | 0.132450i | ||||
\(169\) | −2.31149 | + | 1.33454i | −0.177807 | + | 0.102657i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.418692 | − | 0.834413i | 0.0320181 | − | 0.0638092i | ||||
\(172\) | −3.93654 | − | 3.93654i | −0.300159 | − | 0.300159i | ||||
\(173\) | −0.524511 | + | 1.95750i | −0.0398778 | + | 0.148826i | −0.982994 | − | 0.183637i | \(-0.941213\pi\) |
0.943116 | + | 0.332463i | \(0.107880\pi\) | |||||||
\(174\) | −3.49571 | − | 6.05475i | −0.265009 | − | 0.459010i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.78944 | − | 4.83146i | −0.210262 | − | 0.364185i | ||||
\(177\) | 12.1140 | − | 3.24593i | 0.910542 | − | 0.243979i | ||||
\(178\) | 10.0156 | − | 10.0156i | 0.750698 | − | 0.750698i | ||||
\(179\) | 21.3656 | 1.59694 | 0.798471 | − | 0.602034i | \(-0.205643\pi\) | ||||
0.798471 | + | 0.602034i | \(0.205643\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.74435 | + | 1.58445i | 0.203986 | + | 0.117771i | 0.598513 | − | 0.801113i | \(-0.295758\pi\) |
−0.394527 | + | 0.918884i | \(0.629092\pi\) | |||||||
\(182\) | −9.03208 | − | 9.03208i | −0.669502 | − | 0.669502i | ||||
\(183\) | 2.50676 | + | 2.50676i | 0.185305 | + | 0.185305i | ||||
\(184\) | 1.98702 | − | 3.44163i | 0.146485 | − | 0.253720i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.828500 | + | 0.478335i | 0.0607485 | + | 0.0350732i | ||||
\(187\) | −5.93890 | + | 22.1643i | −0.434295 | + | 1.62081i | ||||
\(188\) | 11.7844 | + | 3.15762i | 0.859466 | + | 0.230293i | ||||
\(189\) | −21.3196 | −1.55077 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.4130 | 1.33232 | 0.666158 | − | 0.745810i | \(-0.267938\pi\) | ||||
0.666158 | + | 0.745810i | \(0.267938\pi\) | |||||||
\(192\) | 1.61221 | + | 0.431989i | 0.116351 | + | 0.0311762i | ||||
\(193\) | 2.21163 | − | 8.25393i | 0.159197 | − | 0.594131i | −0.839512 | − | 0.543340i | \(-0.817159\pi\) |
0.998709 | − | 0.0507904i | \(-0.0161740\pi\) | |||||||
\(194\) | 2.07375 | + | 1.19728i | 0.148886 | + | 0.0859596i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.39653 | + | 7.61502i | −0.314038 | + | 0.543930i | ||||
\(197\) | −6.38603 | − | 6.38603i | −0.454986 | − | 0.454986i | 0.442019 | − | 0.897005i | \(-0.354262\pi\) |
−0.897005 | + | 0.442019i | \(0.854262\pi\) | |||||||
\(198\) | −0.844892 | − | 0.844892i | −0.0600439 | − | 0.0600439i | ||||
\(199\) | 12.7686 | + | 7.37195i | 0.905141 | + | 0.522584i | 0.878865 | − | 0.477071i | \(-0.158302\pi\) |
0.0262767 | + | 0.999655i | \(0.491635\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.8341 | 1.39899 | ||||||||
\(202\) | −0.340442 | + | 0.340442i | −0.0239534 | + | 0.0239534i | ||||
\(203\) | −16.0793 | + | 4.30842i | −1.12854 | + | 0.302392i | ||||
\(204\) | −3.43249 | − | 5.94525i | −0.240322 | − | 0.416250i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.00724 | − | 12.1369i | −0.488217 | − | 0.845617i | ||||
\(207\) | 0.220292 | − | 0.822140i | 0.0153113 | − | 0.0571427i | ||||
\(208\) | 2.27276 | + | 2.27276i | 0.157588 | + | 0.157588i | ||||
\(209\) | 1.42247 | + | 24.2762i | 0.0983942 | + | 1.67922i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.0878 | + | 9.86563i | −1.17637 | + | 0.679178i | −0.955172 | − | 0.296051i | \(-0.904330\pi\) |
−0.221198 | + | 0.975229i | \(0.570997\pi\) | |||||||
\(212\) | 3.66382 | + | 0.981717i | 0.251632 | + | 0.0674246i | ||||
\(213\) | 2.27741 | + | 8.49941i | 0.156046 | + | 0.582370i | ||||
\(214\) | 2.15527 | − | 1.24435i | 0.147331 | − | 0.0850619i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.36471 | 0.365022 | ||||||||
\(217\) | 1.61066 | − | 1.61066i | 0.109339 | − | 0.109339i | ||||
\(218\) | 0.692648 | + | 2.58500i | 0.0469120 | + | 0.175078i | ||||
\(219\) | 11.3174 | − | 19.6022i | 0.764756 | − | 1.32460i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 13.2200i | − | 0.889274i | ||||||
\(222\) | 4.42701 | + | 16.5218i | 0.297122 | + | 1.10887i | ||||
\(223\) | −3.96208 | + | 14.7867i | −0.265321 | + | 0.990190i | 0.696733 | + | 0.717330i | \(0.254636\pi\) |
−0.962054 | + | 0.272860i | \(0.912030\pi\) | |||||||
\(224\) | 1.98702 | − | 3.44163i | 0.132764 | − | 0.229953i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.64088 | + | 8.03824i | 0.308707 | + | 0.534696i | ||||
\(227\) | −14.0408 | + | 14.0408i | −0.931921 | + | 0.931921i | −0.997826 | − | 0.0659048i | \(-0.979007\pi\) |
0.0659048 | + | 0.997826i | \(0.479007\pi\) | |||||||
\(228\) | −5.43656 | − | 4.83471i | −0.360045 | − | 0.320187i | ||||
\(229\) | 15.1988i | 1.00437i | 0.864762 | + | 0.502183i | \(0.167469\pi\) | ||||
−0.864762 | + | 0.502183i | \(0.832531\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 32.0471 | − | 18.5024i | 2.10854 | − | 1.21737i | ||||
\(232\) | 4.04606 | − | 1.08414i | 0.265637 | − | 0.0711773i | ||||
\(233\) | −7.75045 | − | 2.07673i | −0.507749 | − | 0.136051i | −0.00415495 | − | 0.999991i | \(-0.501323\pi\) |
−0.503594 | + | 0.863940i | \(0.667989\pi\) | |||||||
\(234\) | 0.596168 | + | 0.344198i | 0.0389727 | + | 0.0225009i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.51391i | 0.489114i | ||||||||
\(237\) | 8.02349 | − | 2.14989i | 0.521181 | − | 0.139650i | ||||
\(238\) | −15.7884 | + | 4.23050i | −1.02341 | + | 0.274223i | ||||
\(239\) | 14.6498i | 0.947614i | 0.880629 | + | 0.473807i | \(0.157121\pi\) | ||||
−0.880629 | + | 0.473807i | \(0.842879\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.2118 | + | 7.05046i | 0.786628 | + | 0.454160i | 0.838774 | − | 0.544479i | \(-0.183273\pi\) |
−0.0521460 | + | 0.998639i | \(0.516606\pi\) | |||||||
\(242\) | 19.4383 | + | 5.20847i | 1.24954 | + | 0.334813i | ||||
\(243\) | 2.14572 | − | 0.574944i | 0.137648 | − | 0.0368827i | ||||
\(244\) | −1.83942 | + | 1.06199i | −0.117757 | + | 0.0679870i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.88236i | 0.630076i | ||||||||
\(247\) | −4.41152 | − | 13.2976i | −0.280698 | − | 0.846106i | ||||
\(248\) | −0.405294 | + | 0.405294i | −0.0257362 | + | 0.0257362i | ||||
\(249\) | −8.62003 | − | 14.9303i | −0.546272 | − | 0.946171i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.77617 | − | 13.4687i | 0.490827 | − | 0.850138i | −0.509117 | − | 0.860697i | \(-0.670028\pi\) |
0.999944 | + | 0.0105596i | \(0.00336127\pi\) | |||||||
\(252\) | 0.220292 | − | 0.822140i | 0.0138771 | − | 0.0517899i | ||||
\(253\) | 5.73822 | + | 21.4153i | 0.360759 | + | 1.34637i | ||||
\(254\) | − | 12.9807i | − | 0.814481i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −1.21532 | − | 4.53563i | −0.0758095 | − | 0.282925i | 0.917606 | − | 0.397491i | \(-0.130119\pi\) |
−0.993416 | + | 0.114566i | \(0.963452\pi\) | |||||||
\(258\) | −6.57040 | + | 6.57040i | −0.409055 | + | 0.409055i | ||||
\(259\) | 40.7259 | 2.53059 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.776942 | − | 0.448567i | 0.0480915 | − | 0.0277656i | ||||
\(262\) | 2.51901 | + | 9.40108i | 0.155625 | + | 0.580801i | ||||
\(263\) | −19.8765 | − | 5.32590i | −1.22564 | − | 0.328409i | −0.412759 | − | 0.910840i | \(-0.635435\pi\) |
−0.812880 | + | 0.582431i | \(0.802102\pi\) | |||||||
\(264\) | −8.06409 | + | 4.65580i | −0.496310 | + | 0.286545i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −14.4694 | + | 9.52393i | −0.887175 | + | 0.583950i | ||||
\(267\) | −16.7168 | − | 16.7168i | −1.02305 | − | 1.02305i | ||||
\(268\) | −3.07561 | + | 11.4783i | −0.187873 | + | 0.701151i | ||||
\(269\) | −4.61436 | − | 7.99231i | −0.281343 | − | 0.487300i | 0.690373 | − | 0.723454i | \(-0.257446\pi\) |
−0.971716 | + | 0.236154i | \(0.924113\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.5036 | − | 21.6569i | −0.759541 | − | 1.31556i | −0.943085 | − | 0.332552i | \(-0.892090\pi\) |
0.183544 | − | 0.983011i | \(-0.441243\pi\) | |||||||
\(272\) | 3.97289 | − | 1.06453i | 0.240892 | − | 0.0645467i | ||||
\(273\) | −15.0753 | + | 15.0753i | −0.912396 | + | 0.912396i | ||||
\(274\) | 0.787917 | 0.0475998 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.74435 | − | 3.31650i | −0.345769 | − | 0.199630i | ||||
\(277\) | −11.1332 | − | 11.1332i | −0.668927 | − | 0.668927i | 0.288541 | − | 0.957468i | \(-0.406830\pi\) |
−0.957468 | + | 0.288541i | \(0.906830\pi\) | |||||||
\(278\) | −10.2075 | − | 10.2075i | −0.612205 | − | 0.612205i | ||||
\(279\) | −0.0613795 | + | 0.106312i | −0.00367470 | + | 0.00636476i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.0185 | − | 9.24831i | −0.955586 | − | 0.551708i | −0.0607743 | − | 0.998152i | \(-0.519357\pi\) |
−0.894812 | + | 0.446444i | \(0.852690\pi\) | |||||||
\(282\) | 5.27032 | − | 19.6691i | 0.313843 | − | 1.17128i | ||||
\(283\) | −14.8499 | − | 3.97901i | −0.882733 | − | 0.236528i | −0.211147 | − | 0.977454i | \(-0.567720\pi\) |
−0.671586 | + | 0.740927i | \(0.734387\pi\) | |||||||
\(284\) | −5.27191 | −0.312830 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −17.9315 | −1.06031 | ||||||||
\(287\) | 22.7280 | + | 6.08994i | 1.34159 | + | 0.359478i | ||||
\(288\) | −0.0554326 | + | 0.206877i | −0.00326640 | + | 0.0121904i | ||||
\(289\) | 0.0718408 | + | 0.0414773i | 0.00422593 | + | 0.00243984i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.99835 | − | 3.46125i | 0.117146 | − | 0.202902i | ||||
\(292\) | 9.58922 | + | 9.58922i | 0.561167 | + | 0.561167i | ||||
\(293\) | 1.79454 | + | 1.79454i | 0.104838 | + | 0.104838i | 0.757580 | − | 0.652742i | \(-0.226381\pi\) |
−0.652742 | + | 0.757580i | \(0.726381\pi\) | |||||||
\(294\) | 12.7101 | + | 7.33816i | 0.741266 | + | 0.427970i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −10.2480 | −0.595651 | ||||||||
\(297\) | −21.1631 | + | 21.1631i | −1.22801 | + | 1.22801i | ||||
\(298\) | 12.2304 | − | 3.27713i | 0.708488 | − | 0.189839i | ||||
\(299\) | −6.38664 | − | 11.0620i | −0.369349 | − | 0.639731i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.0620 | + | 19.1599i | 0.637603 | + | 1.10436i | ||||
\(302\) | −3.82945 | + | 14.2917i | −0.220360 | + | 0.822394i | ||||
\(303\) | 0.568225 | + | 0.568225i | 0.0326437 | + | 0.0326437i | ||||
\(304\) | 3.64097 | − | 2.39653i | 0.208824 | − | 0.137450i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.762890 | − | 0.440454i | 0.0436115 | − | 0.0251791i | ||||
\(307\) | 5.53039 | + | 1.48186i | 0.315636 | + | 0.0845744i | 0.413159 | − | 0.910659i | \(-0.364425\pi\) |
−0.0975232 | + | 0.995233i | \(0.531092\pi\) | |||||||
\(308\) | 5.73822 | + | 21.4153i | 0.326965 | + | 1.22025i | ||||
\(309\) | −20.2574 | + | 11.6956i | −1.15240 | + | 0.665341i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.7931 | −0.895542 | −0.447771 | − | 0.894148i | \(-0.647782\pi\) | ||||
−0.447771 | + | 0.894148i | \(0.647782\pi\) | |||||||
\(312\) | 3.79342 | − | 3.79342i | 0.214760 | − | 0.214760i | ||||
\(313\) | 1.68078 | + | 6.27274i | 0.0950030 | + | 0.354556i | 0.997020 | − | 0.0771446i | \(-0.0245803\pi\) |
−0.902017 | + | 0.431701i | \(0.857914\pi\) | |||||||
\(314\) | 3.17752 | − | 5.50362i | 0.179318 | − | 0.310587i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.97671i | 0.279962i | ||||||||
\(317\) | 1.59960 | + | 5.96979i | 0.0898425 | + | 0.335297i | 0.996187 | − | 0.0872424i | \(-0.0278055\pi\) |
−0.906345 | + | 0.422539i | \(0.861139\pi\) | |||||||
\(318\) | 1.63856 | − | 6.11520i | 0.0918860 | − | 0.342923i | ||||
\(319\) | −11.6844 | + | 20.2380i | −0.654201 | + | 1.13311i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.07691 | − | 3.59732i | −0.115922 | − | 0.200783i | ||||
\(322\) | −11.1674 | + | 11.1674i | −0.622334 | + | 0.622334i | ||||
\(323\) | −17.5592 | − | 3.61926i | −0.977019 | − | 0.201381i | ||||
\(324\) | − | 8.31160i | − | 0.461756i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.6312 | − | 9.60204i | 0.921118 | − | 0.531808i | ||||
\(327\) | 4.31456 | − | 1.15608i | 0.238596 | − | 0.0639316i | ||||
\(328\) | −5.71910 | − | 1.53243i | −0.315784 | − | 0.0846141i | ||||
\(329\) | −41.9882 | − | 24.2419i | −2.31489 | − | 1.33650i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.4402i | 1.61818i | 0.587686 | + | 0.809089i | \(0.300039\pi\) | ||||
−0.587686 | + | 0.809089i | \(0.699961\pi\) | |||||||
\(332\) | 9.97713 | − | 2.67336i | 0.547566 | − | 0.146720i | ||||
\(333\) | −2.12007 | + | 0.568071i | −0.116179 | + | 0.0311301i | ||||
\(334\) | 2.57889i | 0.141110i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.74435 | − | 3.31650i | −0.313380 | − | 0.180930i | ||||
\(337\) | −31.0900 | − | 8.33054i | −1.69358 | − | 0.453793i | −0.722270 | − | 0.691611i | \(-0.756901\pi\) |
−0.971310 | + | 0.237818i | \(0.923568\pi\) | |||||||
\(338\) | −2.57813 | + | 0.690809i | −0.140232 | + | 0.0375750i | ||||
\(339\) | 13.4165 | − | 7.74599i | 0.728682 | − | 0.420705i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 3.19766i | − | 0.173163i | ||||||
\(342\) | 0.620387 | − | 0.697616i | 0.0335467 | − | 0.0377227i | ||||
\(343\) | 5.03864 | − | 5.03864i | 0.272061 | − | 0.272061i | ||||
\(344\) | −2.78356 | − | 4.82126i | −0.150079 | − | 0.259945i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.01328 | + | 1.75505i | −0.0544741 | + | 0.0943519i | ||||
\(347\) | 5.54741 | − | 20.7032i | 0.297801 | − | 1.11141i | −0.641167 | − | 0.767401i | \(-0.721549\pi\) |
0.938968 | − | 0.344005i | \(-0.111784\pi\) | |||||||
\(348\) | −1.80951 | − | 6.75320i | −0.0970002 | − | 0.362010i | ||||
\(349\) | 18.2359i | 0.976145i | 0.872803 | + | 0.488072i | \(0.162300\pi\) | ||||
−0.872803 | + | 0.488072i | \(0.837700\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.62156 | − | 14.9330i | 0.460185 | − | 0.797064i | ||||
\(352\) | −1.44392 | − | 5.38879i | −0.0769613 | − | 0.287224i | ||||
\(353\) | 14.6042 | − | 14.6042i | 0.777303 | − | 0.777303i | −0.202068 | − | 0.979371i | \(-0.564766\pi\) |
0.979371 | + | 0.202068i | \(0.0647662\pi\) | |||||||
\(354\) | 12.5413 | 0.666563 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.2665 | − | 7.08207i | 0.650124 | − | 0.375349i | ||||
\(357\) | 7.06104 | + | 26.3522i | 0.373710 | + | 1.39470i | ||||
\(358\) | 20.6376 | + | 5.52983i | 1.09073 | + | 0.292261i | ||||
\(359\) | 12.8174 | − | 7.40015i | 0.676478 | − | 0.390565i | −0.122049 | − | 0.992524i | \(-0.538946\pi\) |
0.798527 | + | 0.601959i | \(0.205613\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8700 | + | 2.21900i | −0.993157 | + | 0.116790i | ||||
\(362\) | 2.24075 | + | 2.24075i | 0.117771 | + | 0.117771i | ||||
\(363\) | 8.69335 | − | 32.4440i | 0.456282 | − | 1.70287i | ||||
\(364\) | −6.38664 | − | 11.0620i | −0.334751 | − | 0.579806i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.77255 | + | 3.07014i | 0.0926526 | + | 0.160479i | ||||
\(367\) | −21.3376 | + | 5.71739i | −1.11381 | + | 0.298446i | −0.768378 | − | 0.639997i | \(-0.778936\pi\) |
−0.345436 | + | 0.938442i | \(0.612269\pi\) | |||||||
\(368\) | 2.81008 | − | 2.81008i | 0.146485 | − | 0.146485i | ||||
\(369\) | −1.26810 | −0.0660145 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.0543 | − | 7.53691i | −0.677746 | − | 0.391297i | ||||
\(372\) | 0.676467 | + | 0.676467i | 0.0350732 | + | 0.0350732i | ||||
\(373\) | 3.26677 | + | 3.26677i | 0.169147 | + | 0.169147i | 0.786604 | − | 0.617457i | \(-0.211837\pi\) |
−0.617457 | + | 0.786604i | \(0.711837\pi\) | |||||||
\(374\) | −11.4731 | + | 19.8719i | −0.593259 | + | 1.02755i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.5656 | + | 6.10006i | 0.544880 | + | 0.314586i | ||||
\(377\) | 3.48461 | − | 13.0048i | 0.179467 | − | 0.669779i | ||||
\(378\) | −20.5932 | − | 5.51793i | −1.05920 | − | 0.283811i | ||||
\(379\) | 24.1730 | 1.24168 | 0.620841 | − | 0.783937i | \(-0.286791\pi\) | ||||
0.620841 | + | 0.783937i | \(0.286791\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.6658 | −1.10997 | ||||||||
\(382\) | 17.7856 | + | 4.76563i | 0.909989 | + | 0.243831i | ||||
\(383\) | 6.80409 | − | 25.3932i | 0.347673 | − | 1.29753i | −0.541786 | − | 0.840517i | \(-0.682252\pi\) |
0.889458 | − | 0.457016i | \(-0.151082\pi\) | |||||||
\(384\) | 1.44546 | + | 0.834540i | 0.0737636 | + | 0.0425874i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.27255 | − | 7.40027i | 0.217467 | − | 0.376664i | ||||
\(387\) | −0.843109 | − | 0.843109i | −0.0428577 | − | 0.0428577i | ||||
\(388\) | 1.69321 | + | 1.69321i | 0.0859596 | + | 0.0859596i | ||||
\(389\) | −28.8228 | − | 16.6409i | −1.46138 | − | 0.843726i | −0.462301 | − | 0.886723i | \(-0.652976\pi\) |
−0.999075 | + | 0.0429969i | \(0.986309\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.3454 | −0.826622 | ||||||||
\(392\) | −6.21763 | + | 6.21763i | −0.314038 | + | 0.314038i | ||||
\(393\) | 15.6912 | − | 4.20443i | 0.791514 | − | 0.212085i | ||||
\(394\) | −4.51561 | − | 7.82126i | −0.227493 | − | 0.394030i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.597429 | − | 1.03478i | −0.0300219 | − | 0.0519995i | ||||
\(397\) | −4.90913 | + | 18.3211i | −0.246382 | + | 0.919510i | 0.726302 | + | 0.687376i | \(0.241237\pi\) |
−0.972684 | + | 0.232134i | \(0.925429\pi\) | |||||||
\(398\) | 10.4255 | + | 10.4255i | 0.522584 | + | 0.522584i | ||||
\(399\) | 15.8962 | + | 24.1505i | 0.795805 | + | 1.20904i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.4303 | − | 14.6822i | 1.26993 | − | 0.733194i | 0.294955 | − | 0.955511i | \(-0.404695\pi\) |
0.974974 | + | 0.222317i | \(0.0713619\pi\) | |||||||
\(402\) | 19.1583 | + | 5.13344i | 0.955527 | + | 0.256033i | ||||
\(403\) | 0.476816 | + | 1.77950i | 0.0237519 | + | 0.0886432i | ||||
\(404\) | −0.416955 | + | 0.240729i | −0.0207443 | + | 0.0119767i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16.6465 | −0.826150 | ||||||||
\(407\) | 40.4269 | − | 40.4269i | 2.00389 | − | 2.00389i | ||||
\(408\) | −1.77679 | − | 6.63106i | −0.0879641 | − | 0.328286i | ||||
\(409\) | −1.12100 | + | 1.94163i | −0.0554298 | + | 0.0960073i | −0.892409 | − | 0.451228i | \(-0.850986\pi\) |
0.836979 | + | 0.547235i | \(0.184320\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 1.31510i | − | 0.0648689i | ||||||
\(412\) | −3.62721 | − | 13.5369i | −0.178700 | − | 0.666917i | ||||
\(413\) | 7.72850 | − | 28.8432i | 0.380295 | − | 1.41928i | ||||
\(414\) | 0.425571 | − | 0.737110i | 0.0209157 | − | 0.0362270i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.60709 | + | 2.78356i | 0.0787939 | + | 0.136475i | ||||
\(417\) | −17.0371 | + | 17.0371i | −0.834312 | + | 0.834312i | ||||
\(418\) | −4.90914 | + | 23.8171i | −0.240114 | + | 1.16493i | ||||
\(419\) | 39.9653i | 1.95243i | 0.216797 | + | 0.976217i | \(0.430439\pi\) | ||||
−0.216797 | + | 0.976217i | \(0.569561\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.8606 | + | 8.57980i | −0.724264 | + | 0.418154i | −0.816320 | − | 0.577600i | \(-0.803989\pi\) |
0.0920564 | + | 0.995754i | \(0.470656\pi\) | |||||||
\(422\) | −19.0589 | + | 5.10683i | −0.927774 | + | 0.248596i | ||||
\(423\) | 2.52393 | + | 0.676284i | 0.122717 | + | 0.0328820i | ||||
\(424\) | 3.28489 | + | 1.89653i | 0.159528 | + | 0.0921037i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.79924i | 0.426325i | ||||||||
\(427\) | 8.15320 | − | 2.18464i | 0.394561 | − | 0.105722i | ||||
\(428\) | 2.40390 | − | 0.644122i | 0.116197 | − | 0.0311348i | ||||
\(429\) | 29.9291i | 1.44499i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.9452 | + | 10.3607i | 0.864392 | + | 0.499057i | 0.865481 | − | 0.500942i | \(-0.167013\pi\) |
−0.00108855 | + | 0.999999i | \(0.500346\pi\) | |||||||
\(432\) | 5.18191 | + | 1.38849i | 0.249315 | + | 0.0668037i | ||||
\(433\) | 36.2323 | − | 9.70841i | 1.74121 | − | 0.466556i | 0.758496 | − | 0.651678i | \(-0.225934\pi\) |
0.982716 | + | 0.185121i | \(0.0592678\pi\) | |||||||
\(434\) | 1.97264 | − | 1.13891i | 0.0946899 | − | 0.0546693i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.67618i | 0.128166i | ||||||||
\(437\) | −16.4413 | + | 5.45446i | −0.786495 | + | 0.260922i | ||||
\(438\) | 16.0052 | − | 16.0052i | 0.764756 | − | 0.764756i | ||||
\(439\) | −8.85200 | − | 15.3321i | −0.422483 | − | 0.731762i | 0.573699 | − | 0.819066i | \(-0.305508\pi\) |
−0.996182 | + | 0.0873044i | \(0.972175\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.941627 | + | 1.63095i | −0.0448394 | + | 0.0776641i | ||||
\(442\) | 3.42159 | − | 12.7695i | 0.162748 | − | 0.607385i | ||||
\(443\) | −1.58801 | − | 5.92652i | −0.0754485 | − | 0.281578i | 0.917886 | − | 0.396844i | \(-0.129895\pi\) |
−0.993335 | + | 0.115266i | \(0.963228\pi\) | |||||||
\(444\) | 17.1047i | 0.811752i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.65416 | + | 13.2574i | −0.362435 | + | 0.627755i | ||||
\(447\) | −5.46978 | − | 20.4135i | −0.258712 | − | 0.965526i | ||||
\(448\) | 2.81008 | − | 2.81008i | 0.132764 | − | 0.132764i | ||||
\(449\) | 10.8678 | 0.512883 | 0.256441 | − | 0.966560i | \(-0.417450\pi\) | ||||
0.256441 | + | 0.966560i | \(0.417450\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.6063 | − | 16.5159i | 1.34702 | − | 0.777702i | ||||
\(452\) | 2.40230 | + | 8.96549i | 0.112994 | + | 0.421701i | ||||
\(453\) | 23.8540 | + | 6.39165i | 1.12076 | + | 0.300306i | ||||
\(454\) | −17.1964 | + | 9.92835i | −0.807067 | + | 0.465961i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.00000 | − | 6.07706i | −0.187317 | − | 0.284584i | ||||
\(457\) | −7.87309 | − | 7.87309i | −0.368288 | − | 0.368288i | 0.498565 | − | 0.866852i | \(-0.333861\pi\) |
−0.866852 | + | 0.498565i | \(0.833861\pi\) | |||||||
\(458\) | −3.93374 | + | 14.6809i | −0.183812 | + | 0.685994i | ||||
\(459\) | −11.0326 | − | 19.1091i | −0.514959 | − | 0.891935i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.3941 | + | 30.1275i | 0.810124 | + | 1.40318i | 0.912776 | + | 0.408459i | \(0.133934\pi\) |
−0.102652 | + | 0.994717i | \(0.532733\pi\) | |||||||
\(462\) | 35.7439 | − | 9.57754i | 1.66295 | − | 0.445587i | ||||
\(463\) | 13.5882 | − | 13.5882i | 0.631497 | − | 0.631497i | −0.316946 | − | 0.948443i | \(-0.602658\pi\) |
0.948443 | + | 0.316946i | \(0.102658\pi\) | |||||||
\(464\) | 4.18879 | 0.194460 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.94886 | − | 4.01193i | −0.321900 | − | 0.185849i | ||||
\(467\) | −24.3519 | − | 24.3519i | −1.12687 | − | 1.12687i | −0.990683 | − | 0.136189i | \(-0.956514\pi\) |
−0.136189 | − | 0.990683i | \(-0.543486\pi\) | |||||||
\(468\) | 0.486769 | + | 0.486769i | 0.0225009 | + | 0.0225009i | ||||
\(469\) | 23.6123 | − | 40.8977i | 1.09032 | − | 1.88848i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.18597 | − | 5.30353i | −0.423267 | − | 0.244374i | ||||
\(472\) | −1.94474 | + | 7.25788i | −0.0895141 | + | 0.334071i | ||||
\(473\) | 30.0000 | + | 8.03848i | 1.37940 | + | 0.369610i | ||||
\(474\) | 8.30652 | 0.381531 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −16.3454 | −0.749190 | ||||||||
\(477\) | 0.784698 | + | 0.210259i | 0.0359289 | + | 0.00962711i | ||||
\(478\) | −3.79164 | + | 14.1506i | −0.173425 | + | 0.647233i | ||||
\(479\) | −29.0760 | − | 16.7870i | −1.32852 | − | 0.767019i | −0.343445 | − | 0.939173i | \(-0.611594\pi\) |
−0.985070 | + | 0.172154i | \(0.944927\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.4694 | + | 28.5258i | −0.750939 | + | 1.30066i | ||||
\(482\) | 9.97086 | + | 9.97086i | 0.454160 | + | 0.454160i | ||||
\(483\) | 18.6392 | + | 18.6392i | 0.848115 | + | 0.848115i | ||||
\(484\) | 17.4279 | + | 10.0620i | 0.792176 | + | 0.457363i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.22141 | 0.100765 | ||||||||
\(487\) | −23.7780 | + | 23.7780i | −1.07748 | + | 1.07748i | −0.0807490 | + | 0.996734i | \(0.525731\pi\) |
−0.996734 | + | 0.0807490i | \(0.974269\pi\) | |||||||
\(488\) | −2.05161 | + | 0.549727i | −0.0928720 | + | 0.0248850i | ||||
\(489\) | −16.0266 | − | 27.7588i | −0.724746 | − | 1.25530i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.0205143 | − | 0.0355318i | −0.000925798 | − | 0.00160353i | 0.865562 | − | 0.500802i | \(-0.166961\pi\) |
−0.866488 | + | 0.499198i | \(0.833628\pi\) | |||||||
\(492\) | −2.55774 | + | 9.54562i | −0.115312 | + | 0.430350i | ||||
\(493\) | −12.1825 | − | 12.1825i | −0.548672 | − | 0.548672i | ||||
\(494\) | −0.819529 | − | 13.9863i | −0.0368724 | − | 0.629272i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.496381 | + | 0.286586i | −0.0222882 | + | 0.0128681i | ||||
\(497\) | 20.2370 | + | 5.42248i | 0.907751 | + | 0.243231i | ||||
\(498\) | −4.46205 | − | 16.6526i | −0.199949 | − | 0.746221i | ||||
\(499\) | 17.8866 | − | 10.3269i | 0.800716 | − | 0.462293i | −0.0430056 | − | 0.999075i | \(-0.513693\pi\) |
0.843721 | + | 0.536781i | \(0.180360\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.30437 | 0.192305 | ||||||||
\(502\) | 10.9972 | − | 10.9972i | 0.490827 | − | 0.490827i | ||||
\(503\) | −3.22065 | − | 12.0196i | −0.143602 | − | 0.535928i | −0.999814 | − | 0.0193038i | \(-0.993855\pi\) |
0.856212 | − | 0.516624i | \(-0.172812\pi\) | |||||||
\(504\) | 0.425571 | − | 0.737110i | 0.0189564 | − | 0.0328335i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 22.1708i | 0.985611i | ||||||||
\(507\) | 1.15301 | + | 4.30311i | 0.0512072 | + | 0.191108i | ||||
\(508\) | 3.35965 | − | 12.5384i | 0.149060 | − | 0.556301i | ||||
\(509\) | 8.59703 | − | 14.8905i | 0.381057 | − | 0.660009i | −0.610157 | − | 0.792281i | \(-0.708894\pi\) |
0.991214 | + | 0.132271i | \(0.0422270\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −26.9464 | − | 46.6726i | −1.19204 | − | 2.06467i | ||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −17.4741 | − | 15.5396i | −0.771499 | − | 0.686091i | ||||
\(514\) | − | 4.69563i | − | 0.207116i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −8.04707 | + | 4.64598i | −0.354252 | + | 0.204528i | ||||
\(517\) | −65.7439 | + | 17.6160i | −2.89141 | + | 0.774752i | ||||
\(518\) | 39.3382 | + | 10.5406i | 1.72842 | + | 0.463129i | ||||
\(519\) | 2.92931 | + | 1.69124i | 0.128583 | + | 0.0742372i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7.98939i | − | 0.350022i | −0.984567 | − | 0.175011i | \(-0.944004\pi\) | ||
0.984567 | − | 0.175011i | \(-0.0559961\pi\) | |||||||
\(522\) | 0.866566 | − | 0.232196i | 0.0379286 | − | 0.0101629i | ||||
\(523\) | 14.7144 | − | 3.94272i | 0.643417 | − | 0.172403i | 0.0776662 | − | 0.996979i | \(-0.475253\pi\) |
0.565751 | + | 0.824576i | \(0.308586\pi\) | |||||||
\(524\) | 9.73272i | 0.425176i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.8208 | − | 10.2889i | −0.777024 | − | 0.448615i | ||||
\(527\) | 2.27715 | + | 0.610159i | 0.0991940 | + | 0.0265790i | ||||
\(528\) | −8.99432 | + | 2.41002i | −0.391427 | + | 0.104883i | ||||
\(529\) | 6.24139 | − | 3.60347i | 0.271365 | − | 0.156673i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.60929i | 0.0698373i | ||||||||
\(532\) | −16.4413 | + | 5.45446i | −0.712822 | + | 0.236481i | ||||
\(533\) | −13.4567 | + | 13.4567i | −0.582874 | + | 0.582874i | ||||
\(534\) | −11.8205 | − | 20.4738i | −0.511525 | − | 0.885987i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.94163 | + | 10.2912i | −0.256639 | + | 0.444512i | ||||
\(537\) | 9.22972 | − | 34.4458i | 0.398292 | − | 1.48645i | ||||
\(538\) | −2.38857 | − | 8.91427i | −0.102979 | − | 0.384321i | ||||
\(539\) | − | 49.0555i | − | 2.11297i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.38687 | − | 4.13418i | 0.102620 | − | 0.177742i | −0.810144 | − | 0.586232i | \(-0.800611\pi\) |
0.912763 | + | 0.408489i | \(0.133944\pi\) | |||||||
\(542\) | −6.47235 | − | 24.1551i | −0.278011 | − | 1.03755i | ||||
\(543\) | 3.73999 | − | 3.73999i | 0.160498 | − | 0.160498i | ||||
\(544\) | 4.11303 | 0.176345 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −18.4633 | + | 10.6598i | −0.790158 | + | 0.456198i | ||||
\(547\) | −1.13342 | − | 4.22997i | −0.0484614 | − | 0.180860i | 0.937453 | − | 0.348113i | \(-0.113177\pi\) |
−0.985914 | + | 0.167252i | \(0.946511\pi\) | |||||||
\(548\) | 0.761069 | + | 0.203928i | 0.0325113 | + | 0.00871137i | ||||
\(549\) | −0.393958 | + | 0.227452i | −0.0168137 | + | 0.00970742i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.3193 | − | 8.18869i | −0.695225 | − | 0.348850i | ||||
\(552\) | −4.69024 | − | 4.69024i | −0.199630 | − | 0.199630i | ||||
\(553\) | 5.11884 | − | 19.1038i | 0.217675 | − | 0.812375i | ||||
\(554\) | −7.87234 | − | 13.6353i | −0.334464 | − | 0.579308i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.21779 | − | 12.5016i | −0.306103 | − | 0.530185i | ||||
\(557\) | 35.5939 | − | 9.53737i | 1.50816 | − | 0.404111i | 0.592339 | − | 0.805689i | \(-0.298205\pi\) |
0.915825 | + | 0.401578i | \(0.131538\pi\) | |||||||
\(558\) | −0.0868038 | + | 0.0868038i | −0.00367470 | + | 0.00367470i | ||||
\(559\) | −17.8937 | −0.756822 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 33.1679 | + | 19.1495i | 1.40035 | + | 0.808491i | ||||
\(562\) | −13.0791 | − | 13.0791i | −0.551708 | − | 0.551708i | ||||
\(563\) | 16.9569 | + | 16.9569i | 0.714648 | + | 0.714648i | 0.967504 | − | 0.252856i | \(-0.0813698\pi\) |
−0.252856 | + | 0.967504i | \(0.581370\pi\) | |||||||
\(564\) | 10.1815 | − | 17.6348i | 0.428718 | − | 0.742561i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13.3140 | − | 7.68686i | −0.559630 | − | 0.323103i | ||||
\(567\) | −8.54898 | + | 31.9052i | −0.359023 | + | 1.33989i | ||||
\(568\) | −5.09228 | − | 1.36447i | −0.213667 | − | 0.0572519i | ||||
\(569\) | 20.7088 | 0.868160 | 0.434080 | − | 0.900874i | \(-0.357073\pi\) | ||||
0.434080 | + | 0.900874i | \(0.357073\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.7544 | 1.87291 | 0.936457 | − | 0.350782i | \(-0.114084\pi\) | ||||
0.936457 | + | 0.350782i | \(0.114084\pi\) | |||||||
\(572\) | −17.3205 | − | 4.64102i | −0.724207 | − | 0.194051i | ||||
\(573\) | 7.95421 | − | 29.6855i | 0.332292 | − | 1.24013i | ||||
\(574\) | 20.3773 | + | 11.7649i | 0.850534 | + | 0.491056i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.107087 | + | 0.185481i | −0.00446198 | + | 0.00772837i | ||||
\(577\) | 0.691973 | + | 0.691973i | 0.0288072 | + | 0.0288072i | 0.721364 | − | 0.692556i | \(-0.243516\pi\) |
−0.692556 | + | 0.721364i | \(0.743516\pi\) | |||||||
\(578\) | 0.0586577 | + | 0.0586577i | 0.00243984 | + | 0.00243984i | ||||
\(579\) | −12.3516 | − | 7.13122i | −0.513316 | − | 0.296363i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −41.0483 | −1.70297 | ||||||||
\(582\) | 2.82610 | − | 2.82610i | 0.117146 | − | 0.117146i | ||||
\(583\) | −20.4400 | + | 5.47689i | −0.846539 | + | 0.226829i | ||||
\(584\) | 6.78060 | + | 11.7443i | 0.280583 | + | 0.485985i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.26893 | + | 2.19785i | 0.0524190 | + | 0.0907923i | ||||
\(587\) | −4.05541 | + | 15.1350i | −0.167385 | + | 0.624689i | 0.830339 | + | 0.557258i | \(0.188147\pi\) |
−0.997724 | + | 0.0674303i | \(0.978520\pi\) | |||||||
\(588\) | 10.3777 | + | 10.3777i | 0.427970 | + | 0.427970i | ||||
\(589\) | 2.49412 | − | 0.146144i | 0.102768 | − | 0.00602174i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.0543 | + | 7.53691i | −0.536982 | + | 0.310027i | ||||
\(592\) | −9.89878 | − | 2.65237i | −0.406837 | − | 0.109012i | ||||
\(593\) | −4.03459 | − | 15.0573i | −0.165681 | − | 0.618329i | −0.997952 | − | 0.0639609i | \(-0.979627\pi\) |
0.832272 | − | 0.554368i | \(-0.187040\pi\) | |||||||
\(594\) | −25.9194 | + | 14.9646i | −1.06349 | + | 0.614003i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.6618 | 0.518649 | ||||||||
\(597\) | 17.4010 | − | 17.4010i | 0.712176 | − | 0.712176i | ||||
\(598\) | −3.30597 | − | 12.3380i | −0.135191 | − | 0.504540i | ||||
\(599\) | −13.8776 | + | 24.0366i | −0.567022 | + | 0.982110i | 0.429837 | + | 0.902907i | \(0.358571\pi\) |
−0.996858 | + | 0.0792037i | \(0.974762\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.35237i | 0.218328i | 0.994024 | + | 0.109164i | \(0.0348173\pi\) | ||||
−0.994024 | + | 0.109164i | \(0.965183\pi\) | |||||||
\(602\) | 5.72611 | + | 21.3701i | 0.233379 | + | 0.870981i | ||||
\(603\) | −0.658719 | + | 2.45837i | −0.0268251 | + | 0.100113i | ||||
\(604\) | −7.39792 | + | 12.8136i | −0.301017 | + | 0.521377i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.401796 | + | 0.695931i | 0.0163218 | + | 0.0282703i | ||||
\(607\) | 18.0625 | − | 18.0625i | 0.733133 | − | 0.733133i | −0.238106 | − | 0.971239i | \(-0.576527\pi\) |
0.971239 | + | 0.238106i | \(0.0765265\pi\) | |||||||
\(608\) | 4.13717 | − | 1.37252i | 0.167784 | − | 0.0556630i | ||||
\(609\) | 27.7843i | 1.12588i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 33.9597 | − | 19.6067i | 1.37386 | − | 0.793200i | ||||
\(612\) | 0.850893 | − | 0.227996i | 0.0343953 | − | 0.00921619i | ||||
\(613\) | −13.0713 | − | 3.50245i | −0.527946 | − | 0.141463i | −0.0150066 | − | 0.999887i | \(-0.504777\pi\) |
−0.512940 | + | 0.858425i | \(0.671444\pi\) | |||||||
\(614\) | 4.95841 | + | 2.86274i | 0.200105 | + | 0.115531i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 22.1708i | 0.893286i | ||||||||
\(617\) | −7.91702 | + | 2.12136i | −0.318727 | + | 0.0854027i | −0.414636 | − | 0.909987i | \(-0.636091\pi\) |
0.0959086 | + | 0.995390i | \(0.469424\pi\) | |||||||
\(618\) | −22.5942 | + | 6.05411i | −0.908873 | + | 0.243532i | ||||
\(619\) | 25.0072i | 1.00513i | 0.864541 | + | 0.502563i | \(0.167609\pi\) | ||||
−0.864541 | + | 0.502563i | \(0.832391\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.4633 | − | 10.6598i | −0.740908 | − | 0.427764i | ||||
\(622\) | −15.2549 | − | 4.08755i | −0.611667 | − | 0.163896i | ||||
\(623\) | −54.3710 | + | 14.5687i | −2.17833 | + | 0.583681i | ||||
\(624\) | 4.64598 | − | 2.68236i | 0.185988 | − | 0.107380i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.49402i | 0.259553i | ||||||||
\(627\) | 39.7527 | + | 8.19374i | 1.58757 | + | 0.327226i | ||||
\(628\) | 4.49369 | − | 4.49369i | 0.179318 | − | 0.179318i | ||||
\(629\) | 21.0751 | + | 36.5032i | 0.840320 | + | 1.45548i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.1667 | + | 24.5374i | −0.563966 | + | 0.976817i | 0.433179 | + | 0.901308i | \(0.357392\pi\) |
−0.997145 | + | 0.0755096i | \(0.975942\pi\) | |||||||
\(632\) | −1.28807 | + | 4.80713i | −0.0512366 | + | 0.191218i | ||||
\(633\) | 8.52370 | + | 31.8109i | 0.338786 | + | 1.26437i | ||||
\(634\) | 6.18038i | 0.245454i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.16546 | − | 5.48274i | 0.125519 | − | 0.217405i | ||||
\(637\) | 7.31486 | + | 27.2994i | 0.289825 | + | 1.08164i | ||||
\(638\) | −16.5242 | + | 16.5242i | −0.654201 | + | 0.654201i | ||||
\(639\) | −1.12911 | −0.0446670 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.4996 | − | 11.8354i | 0.809684 | − | 0.467471i | −0.0371624 | − | 0.999309i | \(-0.511832\pi\) |
0.846846 | + | 0.531838i | \(0.178499\pi\) | |||||||
\(642\) | −1.07509 | − | 4.01229i | −0.0424304 | − | 0.158353i | ||||
\(643\) | −9.95594 | − | 2.66769i | −0.392624 | − | 0.105203i | 0.0571053 | − | 0.998368i | \(-0.481813\pi\) |
−0.449729 | + | 0.893165i | \(0.648480\pi\) | |||||||
\(644\) | −13.6772 | + | 7.89653i | −0.538957 | + | 0.311167i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.0241 | − | 8.04059i | −0.630461 | − | 0.316353i | ||||
\(647\) | 5.01831 | + | 5.01831i | 0.197290 | + | 0.197290i | 0.798837 | − | 0.601547i | \(-0.205449\pi\) |
−0.601547 | + | 0.798837i | \(0.705449\pi\) | |||||||
\(648\) | 2.15120 | − | 8.02839i | 0.0845072 | − | 0.315385i | ||||
\(649\) | −20.9596 | − | 36.3031i | −0.822737 | − | 1.42502i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.90092 | − | 3.29250i | −0.0745031 | − | 0.129043i | ||||
\(652\) | 18.5497 | − | 4.97038i | 0.726463 | − | 0.194655i | ||||
\(653\) | −12.6324 | + | 12.6324i | −0.494344 | + | 0.494344i | −0.909672 | − | 0.415328i | \(-0.863667\pi\) |
0.415328 | + | 0.909672i | \(0.363667\pi\) | |||||||
\(654\) | 4.46676 | 0.174664 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.12760 | − | 2.96042i | −0.200199 | − | 0.115585i | ||||
\(657\) | 2.05377 | + | 2.05377i | 0.0801252 | + | 0.0801252i | ||||
\(658\) | −34.2833 | − | 34.2833i | −1.33650 | − | 1.33650i | ||||
\(659\) | 4.34736 | − | 7.52985i | 0.169349 | − | 0.293321i | −0.768842 | − | 0.639439i | \(-0.779167\pi\) |
0.938191 | + | 0.346117i | \(0.112500\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.8131 | − | 18.3673i | −1.23739 | − | 0.714406i | −0.268828 | − | 0.963188i | \(-0.586636\pi\) |
−0.968559 | + | 0.248782i | \(0.919970\pi\) | |||||||
\(662\) | −7.61968 | + | 28.4370i | −0.296147 | + | 1.10524i | ||||
\(663\) | −21.3134 | − | 5.71090i | −0.827743 | − | 0.221793i | ||||
\(664\) | 10.3291 | 0.400846 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.19486 | −0.0850490 | ||||||||
\(667\) | −16.0793 | − | 4.30842i | −0.622591 | − | 0.166823i | ||||
\(668\) | −0.667465 | + | 2.49101i | −0.0258250 | + | 0.0963802i | ||||
\(669\) | 22.1276 | + | 12.7754i | 0.855503 | + | 0.493925i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.92473 | − | 10.2619i | 0.228722 | − | 0.396158i | ||||
\(672\) | −4.69024 | − | 4.69024i | −0.180930 | − | 0.180930i | ||||
\(673\) | −2.45665 | − | 2.45665i | −0.0946967 | − | 0.0946967i | 0.658171 | − | 0.752868i | \(-0.271330\pi\) |
−0.752868 | + | 0.658171i | \(0.771330\pi\) | |||||||
\(674\) | −27.8745 | − | 16.0934i | −1.07369 | − | 0.619893i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.66908 | −0.102657 | ||||||||
\(677\) | −17.3822 | + | 17.3822i | −0.668053 | + | 0.668053i | −0.957265 | − | 0.289212i | \(-0.906607\pi\) |
0.289212 | + | 0.957265i | \(0.406607\pi\) | |||||||
\(678\) | 14.9641 | − | 4.00962i | 0.574693 | − | 0.153989i | ||||
\(679\) | −4.75805 | − | 8.24118i | −0.182597 | − | 0.316267i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.5712 | + | 28.7022i | 0.635010 | + | 1.09987i | ||||
\(682\) | 0.827616 | − | 3.08870i | 0.0316910 | − | 0.118273i | ||||
\(683\) | 24.5836 | + | 24.5836i | 0.940667 | + | 0.940667i | 0.998336 | − | 0.0576691i | \(-0.0183669\pi\) |
−0.0576691 | + | 0.998336i | \(0.518367\pi\) | |||||||
\(684\) | 0.779804 | − | 0.513277i | 0.0298166 | − | 0.0196256i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.17105 | − | 3.56286i | 0.235612 | − | 0.136031i | ||||
\(687\) | 24.5036 | + | 6.56572i | 0.934871 | + | 0.250498i | ||||
\(688\) | −1.44088 | − | 5.37742i | −0.0549329 | − | 0.205012i | ||||
\(689\) | 10.5582 | − | 6.09578i | 0.402236 | − | 0.232231i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.0377 | 0.572062 | 0.286031 | − | 0.958220i | \(-0.407664\pi\) | ||||
0.286031 | + | 0.958220i | \(0.407664\pi\) | |||||||
\(692\) | −1.43299 | + | 1.43299i | −0.0544741 | + | 0.0544741i | ||||
\(693\) | 1.22898 | + | 4.58663i | 0.0466852 | + | 0.174232i | ||||
\(694\) | 10.7168 | − | 18.5620i | 0.406803 | − | 0.704604i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 6.99143i | − | 0.265009i | ||||||
\(697\) | 6.30293 | + | 23.5228i | 0.238740 | + | 0.890991i | ||||
\(698\) | −4.71979 | + | 17.6145i | −0.178647 | + | 0.666719i | ||||
\(699\) | −6.69623 | + | 11.5982i | −0.253275 | + | 0.438684i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.5314 | − | 44.2216i | −0.964307 | − | 1.67023i | −0.711467 | − | 0.702720i | \(-0.751969\pi\) |
−0.252840 | − | 0.967508i | \(-0.581365\pi\) | |||||||
\(702\) | 12.1927 | − | 12.1927i | 0.460185 | − | 0.460185i | ||||
\(703\) | 33.3799 | + | 29.6846i | 1.25895 | + | 1.11958i | ||||
\(704\) | − | 5.57889i | − | 0.210262i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.8864 | − | 10.3267i | 0.673164 | − | 0.388652i | ||||
\(707\) | 1.84814 | − | 0.495208i | 0.0695066 | − | 0.0186242i | ||||
\(708\) | 12.1140 | + | 3.24593i | 0.455271 | + | 0.121990i | ||||
\(709\) | −21.2658 | − | 12.2778i | −0.798654 | − | 0.461103i | 0.0443465 | − | 0.999016i | \(-0.485879\pi\) |
−0.843000 | + | 0.537913i | \(0.819213\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.06589i | 0.0399739i | ||||||||
\(712\) | 13.6815 | − | 3.66595i | 0.512736 | − | 0.137387i | ||||
\(713\) | 2.20020 | − | 0.589541i | 0.0823981 | − | 0.0220785i | ||||
\(714\) | 27.2818i | 1.02099i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18.5032 | + | 10.6828i | 0.691496 | + | 0.399235i | ||||
\(717\) | 23.6184 | + | 6.32854i | 0.882047 | + | 0.236344i | ||||
\(718\) | 14.2960 | − | 3.83060i | 0.533522 | − | 0.142957i | ||||
\(719\) | 20.5077 | − | 11.8401i | 0.764808 | − | 0.441562i | −0.0662111 | − | 0.997806i | \(-0.521091\pi\) |
0.831020 | + | 0.556243i | \(0.187758\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 55.6942i | 2.07416i | ||||||||
\(722\) | −18.8013 | − | 2.74052i | −0.699713 | − | 0.101992i | ||||
\(723\) | 16.6421 | − | 16.6421i | 0.618928 | − | 0.618928i | ||||
\(724\) | 1.58445 | + | 2.74435i | 0.0588856 | + | 0.101993i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 16.7943 | − | 29.0885i | 0.623293 | − | 1.07958i | ||||
\(727\) | −0.315088 | + | 1.17593i | −0.0116860 | + | 0.0436127i | −0.971523 | − | 0.236947i | \(-0.923853\pi\) |
0.959837 | + | 0.280559i | \(0.0905200\pi\) | |||||||
\(728\) | −3.30597 | − | 12.3380i | −0.122527 | − | 0.457278i | ||||
\(729\) | − | 28.6425i | − | 1.06083i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.4489 | + | 19.8300i | −0.423452 | + | 0.733440i | ||||
\(732\) | 0.917538 | + | 3.42430i | 0.0339132 | + | 0.126566i | ||||
\(733\) | −28.3801 | + | 28.3801i | −1.04824 | + | 1.04824i | −0.0494669 | + | 0.998776i | \(0.515752\pi\) |
−0.998776 | + | 0.0494669i | \(0.984248\pi\) | |||||||
\(734\) | −22.0903 | −0.815368 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.44163 | − | 1.98702i | 0.126860 | − | 0.0732427i | ||||
\(737\) | −17.1585 | − | 64.0364i | −0.632041 | − | 2.35881i | ||||
\(738\) | −1.22489 | − | 0.328208i | −0.0450887 | − | 0.0120815i | ||||
\(739\) | −27.8620 | + | 16.0861i | −1.02492 | + | 0.591738i | −0.915525 | − | 0.402261i | \(-0.868225\pi\) |
−0.109395 | + | 0.993998i | \(0.534891\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23.3442 | + | 1.36786i | −0.857571 | + | 0.0502496i | ||||
\(742\) | −10.6588 | − | 10.6588i | −0.391297 | − | 0.391297i | ||||
\(743\) | 0.571198 | − | 2.13174i | 0.0209552 | − | 0.0782059i | −0.954656 | − | 0.297710i | \(-0.903777\pi\) |
0.975612 | + | 0.219504i | \(0.0704439\pi\) | |||||||
\(744\) | 0.478335 | + | 0.828500i | 0.0175366 | + | 0.0303743i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.30996 | + | 4.00096i | 0.0845736 | + | 0.146486i | ||||
\(747\) | 2.13685 | − | 0.572567i | 0.0781833 | − | 0.0209491i | ||||
\(748\) | −16.2254 | + | 16.2254i | −0.593259 | + | 0.593259i | ||||
\(749\) | −9.89020 | −0.361380 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.4090 | − | 16.9793i | −1.07315 | − | 0.619584i | −0.144110 | − | 0.989562i | \(-0.546032\pi\) |
−0.929041 | + | 0.369978i | \(0.879365\pi\) | |||||||
\(752\) | 8.62678 | + | 8.62678i | 0.314586 | + | 0.314586i | ||||
\(753\) | −18.3551 | − | 18.3551i | −0.668898 | − | 0.668898i | ||||
\(754\) | 6.73176 | − | 11.6597i | 0.245156 | − | 0.424623i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −18.4633 | − | 10.6598i | −0.671505 | − | 0.387694i | ||||
\(757\) | −12.0906 | + | 45.1229i | −0.439442 | + | 1.64002i | 0.290765 | + | 0.956795i | \(0.406090\pi\) |
−0.730207 | + | 0.683226i | \(0.760576\pi\) | |||||||
\(758\) | 23.3493 | + | 6.25642i | 0.848084 | + | 0.227243i | ||||
\(759\) | 37.0048 | 1.34319 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.34210 | 0.121151 | 0.0605756 | − | 0.998164i | \(-0.480706\pi\) | ||||
0.0605756 | + | 0.998164i | \(0.480706\pi\) | |||||||
\(762\) | −20.9275 | − | 5.60752i | −0.758125 | − | 0.203139i | ||||
\(763\) | 2.75262 | − | 10.2729i | 0.0996514 | − | 0.371904i | ||||
\(764\) | 15.9461 | + | 9.20649i | 0.576910 | + | 0.333079i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.1445 | − | 22.7669i | 0.474930 | − | 0.822603i | ||||
\(767\) | 17.0774 | + | 17.0774i | 0.616627 | + | 0.616627i | ||||
\(768\) | 1.18022 | + | 1.18022i | 0.0425874 | + | 0.0425874i | ||||
\(769\) | 29.7858 | + | 17.1968i | 1.07410 | + | 0.620134i | 0.929300 | − | 0.369327i | \(-0.120412\pi\) |
0.144803 | + | 0.989460i | \(0.453745\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.83738 | −0.282256 | ||||||||
\(772\) | 6.04230 | − | 6.04230i | 0.217467 | − | 0.217467i | ||||
\(773\) | −6.93953 | + | 1.85944i | −0.249597 | + | 0.0668794i | −0.381448 | − | 0.924390i | \(-0.624575\pi\) |
0.131851 | + | 0.991270i | \(0.457908\pi\) | |||||||
\(774\) | −0.596168 | − | 1.03259i | −0.0214288 | − | 0.0371158i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.19728 | + | 2.07375i | 0.0429798 | + | 0.0744432i | ||||
\(777\) | 17.5932 | − | 65.6586i | 0.631151 | − | 2.35549i | ||||
\(778\) | −23.5338 | − | 23.5338i | −0.843726 | − | 0.843726i | ||||
\(779\) | 14.1895 | + | 21.5576i | 0.508391 | + | 0.772381i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.4710 | − | 14.7057i | 0.911425 | − | 0.526211i | ||||
\(782\) | −15.7884 | − | 4.23050i | −0.564593 | − | 0.151282i | ||||
\(783\) | −5.81610 | − | 21.7060i | −0.207850 | − | 0.775708i | ||||
\(784\) | −7.61502 | + | 4.39653i | −0.271965 | + | 0.157019i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 16.2447 | 0.579428 | ||||||||
\(787\) | 14.6739 | − | 14.6739i | 0.523068 | − | 0.523068i | −0.395429 | − | 0.918497i | \(-0.629404\pi\) |
0.918497 | + | 0.395429i | \(0.129404\pi\) | |||||||
\(788\) | −2.33745 | − | 8.72348i | −0.0832682 | − | 0.310761i | ||||
\(789\) | −17.1729 | + | 29.7443i | −0.611372 | + | 1.05893i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 36.8862i | − | 1.31152i | ||||||
\(792\) | −0.309252 | − | 1.15414i | −0.0109888 | − | 0.0410107i | ||||
\(793\) | −1.76692 | + | 6.59423i | −0.0627452 | + | 0.234168i | ||||
\(794\) | −9.48370 | + | 16.4263i | −0.336564 | + | 0.582946i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.37195 | + | 12.7686i | 0.261292 | + | 0.452571i | ||||
\(797\) | −14.1820 | + | 14.1820i | −0.502353 | + | 0.502353i | −0.912168 | − | 0.409816i | \(-0.865593\pi\) |
0.409816 | + | 0.912168i | \(0.365593\pi\) | |||||||
\(798\) | 9.10393 | + | 27.4419i | 0.322275 | + | 0.971432i | ||||
\(799\) | − | 50.1795i | − | 1.77522i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.62718 | − | 1.51680i | 0.0928268 | − | 0.0535936i | ||||
\(802\) | 28.3638 | − | 7.60007i | 1.00156 | − | 0.268368i | ||||
\(803\) | −73.0785 | − | 19.5813i | −2.57888 | − | 0.691010i | ||||
\(804\) | 17.1768 | + | 9.91705i | 0.605780 | + | 0.349747i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.84227i | 0.0648914i | ||||||||
\(807\) | −14.8786 | + | 3.98671i | −0.523752 | + | 0.140339i | ||||
\(808\) | −0.465053 | + | 0.124611i | −0.0163605 | + | 0.00438378i | ||||
\(809\) | − | 31.2471i | − | 1.09859i | −0.835629 | − | 0.549294i | \(-0.814897\pi\) | ||
0.835629 | − | 0.549294i | \(-0.185103\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.51809 | − | 5.49527i | −0.334225 | − | 0.192965i | 0.323490 | − | 0.946232i | \(-0.395144\pi\) |
−0.657716 | + | 0.753266i | \(0.728477\pi\) | |||||||
\(812\) | −16.0793 | − | 4.30842i | −0.564271 | − | 0.151196i | ||||
\(813\) | −40.3168 | + | 10.8029i | −1.41397 | + | 0.378873i | ||||
\(814\) | 49.5126 | − | 28.5861i | 1.73542 | − | 1.00194i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 6.86498i | − | 0.240322i | ||||||
\(817\) | −4.89878 | + | 23.7669i | −0.171386 | + | 0.831498i | ||||
\(818\) | −1.58533 | + | 1.58533i | −0.0554298 | + | 0.0554298i | ||||
\(819\) | −1.36786 | − | 2.36920i | −0.0477969 | − | 0.0827866i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.6836 | + | 32.3609i | −0.652061 | + | 1.12940i | 0.330562 | + | 0.943784i | \(0.392762\pi\) |
−0.982622 | + | 0.185618i | \(0.940571\pi\) | |||||||
\(822\) | 0.340372 | − | 1.27028i | 0.0118718 | − | 0.0443063i | ||||
\(823\) | 12.0787 | + | 45.0785i | 0.421039 | + | 1.57134i | 0.772424 | + | 0.635107i | \(0.219044\pi\) |
−0.351386 | + | 0.936231i | \(0.614289\pi\) | |||||||
\(824\) | − | 14.0145i | − | 0.488217i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.9303 | − | 25.8601i | 0.519492 | − | 0.899787i | ||||
\(827\) | −3.29047 | − | 12.2802i | −0.114421 | − | 0.427024i | 0.884822 | − | 0.465929i | \(-0.154280\pi\) |
−0.999243 | + | 0.0389046i | \(0.987613\pi\) | |||||||
\(828\) | 0.601848 | − | 0.601848i | 0.0209157 | − | 0.0209157i | ||||
\(829\) | −47.6024 | −1.65330 | −0.826650 | − | 0.562716i | \(-0.809756\pi\) | ||||
−0.826650 | + | 0.562716i | \(0.809756\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.7584 | + | 13.1396i | −0.789479 | + | 0.455806i | ||||
\(832\) | 0.831890 | + | 3.10465i | 0.0288406 | + | 0.107635i | ||||
\(833\) | 34.9338 | + | 9.36049i | 1.21039 | + | 0.324322i | ||||
\(834\) | −20.8661 | + | 12.0471i | −0.722535 | + | 0.417156i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10.9062 | + | 21.7350i | −0.377198 | + | 0.751721i | ||||
\(837\) | 2.17428 | + | 2.17428i | 0.0751543 | + | 0.0751543i | ||||
\(838\) | −10.3438 | + | 38.6035i | −0.357320 | + | 1.33354i | ||||
\(839\) | 13.6456 | + | 23.6348i | 0.471098 | + | 0.815965i | 0.999453 | − | 0.0330579i | \(-0.0105246\pi\) |
−0.528356 | + | 0.849023i | \(0.677191\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.72700 | + | 9.91946i | 0.197483 | + | 0.342050i | ||||
\(842\) | −16.5749 | + | 4.44123i | −0.571209 | + | 0.153055i | ||||
\(843\) | −21.8300 | + | 21.8300i | −0.751866 | + | 0.751866i | ||||
\(844\) | −19.7313 | −0.679178 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.26289 | + | 1.30648i | 0.0777997 | + | 0.0449177i | ||||
\(847\) | −56.5499 | − | 56.5499i | −1.94308 | − | 1.94308i | ||||
\(848\) | 2.68210 | + | 2.68210i | 0.0921037 | + | 0.0921037i | ||||
\(849\) | −12.8300 | + | 22.2222i | −0.440323 | + | 0.762663i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.2697 | + | 20.3630i | 1.20903 | + | 0.698033i | ||||
\(852\) | −2.27741 | + | 8.49941i | −0.0780228 | + | 0.291185i | ||||
\(853\) | −3.69985 | − | 0.991372i | −0.126680 | − | 0.0339439i | 0.194922 | − | 0.980819i | \(-0.437555\pi\) |
−0.321602 | + | 0.946875i | \(0.604221\pi\) | |||||||
\(854\) | 8.44081 | 0.288839 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.48870 | 0.0850619 | ||||||||
\(857\) | −10.8647 | − | 2.91119i | −0.371131 | − | 0.0994443i | 0.0684325 | − | 0.997656i | \(-0.478200\pi\) |
−0.439564 | + | 0.898211i | \(0.644867\pi\) | |||||||
\(858\) | −7.74623 | + | 28.9093i | −0.264452 | + | 0.986948i | ||||
\(859\) | 34.1982 | + | 19.7443i | 1.16683 | + | 0.673668i | 0.952931 | − | 0.303188i | \(-0.0980509\pi\) |
0.213897 | + | 0.976856i | \(0.431384\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.6365 | − | 34.0114i | 0.669210 | − | 1.15911i | ||||
\(862\) | 14.6522 | + | 14.6522i | 0.499057 | + | 0.499057i | ||||
\(863\) | 18.3050 | + | 18.3050i | 0.623110 | + | 0.623110i | 0.946325 | − | 0.323215i | \(-0.104764\pi\) |
−0.323215 | + | 0.946325i | \(0.604764\pi\) | |||||||
\(864\) | 4.64598 | + | 2.68236i | 0.158059 | + | 0.0912556i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 37.5104 | 1.27466 | ||||||||
\(867\) | 0.0979044 | − | 0.0979044i | 0.00332501 | − | 0.00332501i | ||||
\(868\) | 2.20020 | − | 0.589541i | 0.0746796 | − | 0.0200103i | ||||
\(869\) | −13.8823 | − | 24.0448i | −0.470923 | − | 0.815663i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.0974 | + | 33.0777i | 0.647092 | + | 1.12080i | ||||
\(872\) | −0.692648 | + | 2.58500i | −0.0234560 | + | 0.0875390i | ||||
\(873\) | 0.362643 | + | 0.362643i | 0.0122736 | + | 0.0122736i | ||||
\(874\) | −17.2928 | + | 1.01328i | −0.584938 | + | 0.0342746i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 19.6022 | − | 11.3174i | 0.662298 | − | 0.382378i | ||||
\(877\) | 37.2238 | + | 9.97410i | 1.25696 | + | 0.336801i | 0.825021 | − | 0.565102i | \(-0.191163\pi\) |
0.431939 | + | 0.901903i | \(0.357830\pi\) | |||||||
\(878\) | −4.58213 | − | 17.1008i | −0.154640 | − | 0.577123i | ||||
\(879\) | 3.66839 | − | 2.11794i | 0.123732 | − | 0.0714365i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.5894 | 0.491530 | 0.245765 | − | 0.969329i | \(-0.420961\pi\) | ||||
0.245765 | + | 0.969329i | \(0.420961\pi\) | |||||||
\(882\) | −1.33166 | + | 1.33166i | −0.0448394 | + | 0.0448394i | ||||
\(883\) | 10.1631 | + | 37.9291i | 0.342015 | + | 1.27642i | 0.896061 | + | 0.443931i | \(0.146417\pi\) |
−0.554046 | + | 0.832486i | \(0.686917\pi\) | |||||||
\(884\) | 6.61000 | − | 11.4489i | 0.222319 | − | 0.385067i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 6.13559i | − | 0.206129i | ||||||
\(887\) | 7.97545 | + | 29.7648i | 0.267789 | + | 0.999404i | 0.960521 | + | 0.278208i | \(0.0897405\pi\) |
−0.692731 | + | 0.721196i | \(0.743593\pi\) | |||||||
\(888\) | −4.42701 | + | 16.5218i | −0.148561 | + | 0.554437i | ||||
\(889\) | −25.7929 | + | 44.6747i | −0.865067 | + | 1.49834i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.1848 | + | 40.1572i | 0.776718 | + | 1.34532i | ||||
\(892\) | −10.8246 | + | 10.8246i | −0.362435 | + | 0.362435i | ||||
\(893\) | −16.7449 | − | 50.4740i | −0.560347 | − | 1.68905i | ||||
\(894\) | − | 21.1336i | − | 0.706814i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.44163 | − | 1.98702i | 0.114977 | − | 0.0663818i | ||||
\(897\) | −20.5932 | + | 5.51793i | −0.687586 | + | 0.184238i | ||||
\(898\) | 10.4975 | + | 2.81279i | 0.350305 | + | 0.0938640i | ||||
\(899\) | 2.07924 | + | 1.20045i | 0.0693465 | + | 0.0400372i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 15.6010i | − | 0.519744i | ||||||
\(902\) | 31.9062 | − | 8.54924i | 1.06236 | − | 0.284659i | ||||
\(903\) | 35.6684 | − | 9.55733i | 1.18697 | − | 0.318048i | ||||
\(904\) | 9.28176i | 0.308707i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 21.3869 | + | 12.3477i | 0.710531 | + | 0.410225i | ||||
\(907\) | 50.1145 | + | 13.4281i | 1.66402 | + | 0.445874i | 0.963490 | − | 0.267744i | \(-0.0862782\pi\) |
0.700535 | + | 0.713618i | \(0.252945\pi\) | |||||||
\(908\) | −19.1801 | + | 5.13929i | −0.636514 | + | 0.170553i | ||||
\(909\) | −0.0893013 | + | 0.0515582i | −0.00296194 | + | 0.00171008i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 25.5121i | − | 0.845254i | −0.906304 | − | 0.422627i | \(-0.861108\pi\) | ||
0.906304 | − | 0.422627i | \(-0.138892\pi\) | |||||||
\(912\) | −2.29084 | − | 6.90527i | −0.0758574 | − | 0.228656i | ||||
\(913\) | −40.7469 | + | 40.7469i | −1.34852 | + | 1.34852i | ||||
\(914\) | −5.56711 | − | 9.64252i | −0.184144 | − | 0.318946i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.59940 | + | 13.1625i | −0.251091 | + | 0.434903i | ||||
\(917\) | 10.0107 | − | 37.3604i | 0.330582 | − | 1.23375i | ||||
\(918\) | −5.71090 | − | 21.3134i | −0.188488 | − | 0.703447i | ||||
\(919\) | 10.8124i | 0.356667i | 0.983970 | + | 0.178334i | \(0.0570707\pi\) | ||||
−0.983970 | + | 0.178334i | \(0.942929\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.77814 | − | 8.27598i | 0.157445 | − | 0.272703i | ||||
\(922\) | 9.00385 | + | 33.6028i | 0.296526 | + | 1.10665i | ||||
\(923\) | −11.9818 | + | 11.9818i | −0.394386 | + | 0.394386i | ||||
\(924\) | 37.0048 | 1.21737 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 16.6421 | − | 9.60831i | 0.546893 | − | 0.315749i | ||||
\(927\) | −0.776858 | − | 2.89927i | −0.0255154 | − | 0.0952247i | ||||
\(928\) | 4.04606 | + | 1.08414i | 0.132819 | + | 0.0355886i | ||||
\(929\) | 22.5585 | − | 13.0241i | 0.740119 | − | 0.427308i | −0.0819935 | − | 0.996633i | \(-0.526129\pi\) |
0.822113 | + | 0.569325i | \(0.192795\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 38.2624 | − | 2.24200i | 1.25400 | − | 0.0734785i | ||||
\(932\) | −5.67372 | − | 5.67372i | −0.185849 | − | 0.185849i | ||||
\(933\) | −6.82244 | + | 25.4617i | −0.223357 | + | 0.833578i | ||||
\(934\) | −17.2194 | − | 29.8249i | −0.563436 | − | 0.975900i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.344198 | + | 0.596168i | 0.0112505 | + | 0.0194864i | ||||
\(937\) | 15.7972 | − | 4.23284i | 0.516071 | − | 0.138281i | 0.00862262 | − | 0.999963i | \(-0.497255\pi\) |
0.507449 | + | 0.861682i | \(0.330589\pi\) | |||||||
\(938\) | 33.3929 | − | 33.3929i | 1.09032 | − | 1.09032i | ||||
\(939\) | 10.8390 | 0.353718 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.0769 | + | 18.5196i | 1.04568 | + | 0.603722i | 0.921436 | − | 0.388530i | \(-0.127017\pi\) |
0.124241 | + | 0.992252i | \(0.460350\pi\) | |||||||
\(942\) | −7.50032 | − | 7.50032i | −0.244374 | − | 0.244374i | ||||
\(943\) | 16.6380 | + | 16.6380i | 0.541809 | + | 0.541809i | ||||
\(944\) | −3.75696 | + | 6.50724i | −0.122278 | + | 0.211793i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 26.8973 | + | 15.5292i | 0.874506 | + | 0.504896i | ||||
\(947\) | −5.14037 | + | 19.1841i | −0.167039 | + | 0.623400i | 0.830732 | + | 0.556673i | \(0.187922\pi\) |
−0.997771 | + | 0.0667269i | \(0.978744\pi\) | |||||||
\(948\) | 8.02349 | + | 2.14989i | 0.260591 | + | 0.0698251i | ||||
\(949\) | 43.5881 | 1.41493 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.3155 | 0.334505 | ||||||||
\(952\) | −15.7884 | − | 4.23050i | −0.511706 | − | 0.137111i | ||||
\(953\) | 10.8760 | − | 40.5899i | 0.352309 | − | 1.31483i | −0.531529 | − | 0.847040i | \(-0.678382\pi\) |
0.883837 | − | 0.467794i | \(-0.154951\pi\) | |||||||
\(954\) | 0.703541 | + | 0.406190i | 0.0227780 | + | 0.0131509i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.32488 | + | 12.6871i | −0.236904 | + | 0.410329i | ||||
\(957\) | 27.5803 | + | 27.5803i | 0.891543 | + | 0.891543i | ||||
\(958\) | −23.7404 | − | 23.7404i | −0.767019 | − | 0.767019i | ||||
\(959\) | −2.71172 | − | 1.56561i | −0.0875659 | − | 0.0505562i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.6715 | 0.989402 | ||||||||
\(962\) | −23.2912 | + | 23.2912i | −0.750939 | + | 0.750939i | ||||
\(963\) | 0.514854 | − | 0.137955i | 0.0165909 | − | 0.00444553i | ||||
\(964\) | 7.05046 | + | 12.2118i | 0.227080 | + | 0.393314i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 13.1799 | + | 22.8283i | 0.424057 | + | 0.734489i | ||||
\(967\) | 12.2226 | − | 45.6155i | 0.393053 | − | 1.46690i | −0.432017 | − | 0.901865i | \(-0.642198\pi\) |
0.825070 | − | 0.565030i | \(-0.191135\pi\) | |||||||
\(968\) | 14.2298 | + | 14.2298i | 0.457363 | + | 0.457363i | ||||
\(969\) | −13.4204 | + | 26.7455i | −0.431125 | + | 0.859191i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.9303 | + | 17.2803i | −0.960510 | + | 0.554551i | −0.896330 | − | 0.443388i | \(-0.853776\pi\) |
−0.0641799 | + | 0.997938i | \(0.520443\pi\) | |||||||
\(972\) | 2.14572 | + | 0.574944i | 0.0688240 | + | 0.0184413i | ||||
\(973\) | 14.8479 | + | 55.4130i | 0.476001 | + | 1.77646i | ||||
\(974\) | −29.1220 | + | 16.8136i | −0.933128 | + | 0.538742i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.12398 | −0.0679870 | ||||||||
\(977\) | −25.5697 | + | 25.5697i | −0.818048 | + | 0.818048i | −0.985825 | − | 0.167777i | \(-0.946341\pi\) |
0.167777 | + | 0.985825i | \(0.446341\pi\) | |||||||
\(978\) | −8.29596 | − | 30.9609i | −0.265276 | − | 0.990022i | ||||
\(979\) | −39.5101 | + | 68.4335i | −1.26275 | + | 2.18714i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.573172i | 0.0183000i | ||||||||
\(982\) | −0.0106190 | − | 0.0396306i | −0.000338866 | − | 0.00126466i | ||||
\(983\) | 10.0139 | − | 37.3724i | 0.319394 | − | 1.19200i | −0.600434 | − | 0.799674i | \(-0.705005\pi\) |
0.919828 | − | 0.392321i | \(-0.128328\pi\) | |||||||
\(984\) | −4.94118 | + | 8.55837i | −0.157519 | + | 0.272831i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −8.61432 | − | 14.9204i | −0.274336 | − | 0.475164i | ||||
\(987\) | −57.2215 | + | 57.2215i | −1.82138 | + | 1.82138i | ||||
\(988\) | 2.82831 | − | 13.7218i | 0.0899805 | − | 0.436549i | ||||
\(989\) | 22.1240i | 0.703502i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.31720 | + | 3.64723i | −0.200672 | + | 0.115858i | −0.596969 | − | 0.802264i | \(-0.703628\pi\) |
0.396297 | + | 0.918122i | \(0.370295\pi\) | |||||||
\(992\) | −0.553641 | + | 0.148348i | −0.0175781 | + | 0.00471005i | ||||
\(993\) | 47.4636 | + | 12.7178i | 1.50621 | + | 0.403589i | ||||
\(994\) | 18.1440 | + | 10.4754i | 0.575491 | + | 0.332260i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 17.2401i | − | 0.546272i | ||||||
\(997\) | 32.0072 | − | 8.57629i | 1.01368 | − | 0.271614i | 0.286512 | − | 0.958077i | \(-0.407504\pi\) |
0.727165 | + | 0.686463i | \(0.240838\pi\) | |||||||
\(998\) | 19.9499 | − | 5.34557i | 0.631505 | − | 0.169211i | ||||
\(999\) | 54.9774i | 1.73941i |
(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 | 950.2.q.e.107.6 | yes | 24 | |
5.2 | odd | 4 | inner | 950.2.q.e.943.1 | yes | 24 | |
5.3 | odd | 4 | inner | 950.2.q.e.943.6 | yes | 24 | |
5.4 | even | 2 | inner | 950.2.q.e.107.1 | ✓ | 24 | |
19.8 | odd | 6 | inner | 950.2.q.e.407.6 | yes | 24 | |
95.8 | even | 12 | inner | 950.2.q.e.293.6 | yes | 24 | |
95.27 | even | 12 | inner | 950.2.q.e.293.1 | yes | 24 | |
95.84 | odd | 6 | inner | 950.2.q.e.407.1 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.q.e.107.1 | ✓ | 24 | 5.4 | even | 2 | inner | |
950.2.q.e.107.6 | yes | 24 | 1.1 | even | 1 | trivial | |
950.2.q.e.293.1 | yes | 24 | 95.27 | even | 12 | inner | |
950.2.q.e.293.6 | yes | 24 | 95.8 | even | 12 | inner | |
950.2.q.e.407.1 | yes | 24 | 95.84 | odd | 6 | inner | |
950.2.q.e.407.6 | yes | 24 | 19.8 | odd | 6 | inner | |
950.2.q.e.943.1 | yes | 24 | 5.2 | odd | 4 | inner | |
950.2.q.e.943.6 | yes | 24 | 5.3 | odd | 4 | inner |