Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [539,2,Mod(148,539)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(539, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("539.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 539 = 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 539.f (of order \(5\), 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: | \(4.30393666895\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.159390625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 246.1 | ||
Root | \(-0.762262 - 2.34600i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 539.246 |
Dual form | 539.2.f.d.344.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(442\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.99563 | − | 1.44991i | −1.41112 | − | 1.02524i | −0.993158 | − | 0.116777i | \(-0.962744\pi\) |
−0.417964 | − | 0.908464i | \(-0.637256\pi\) | |||||||
\(3\) | 0.500000 | − | 1.53884i | 0.288675 | − | 0.888451i | −0.696598 | − | 0.717462i | \(-0.745304\pi\) |
0.985273 | − | 0.170989i | \(-0.0546962\pi\) | |||||||
\(4\) | 1.26226 | + | 3.88484i | 0.631131 | + | 1.94242i | ||||
\(5\) | −2.80464 | + | 2.03769i | −1.25428 | + | 0.911284i | −0.998462 | − | 0.0554418i | \(-0.982343\pi\) |
−0.255813 | + | 0.966726i | \(0.582343\pi\) | |||||||
\(6\) | −3.22899 | + | 2.34600i | −1.31823 | + | 0.957751i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.58914 | − | 4.89086i | 0.561845 | − | 1.72918i | ||||
\(9\) | 0.309017 | + | 0.224514i | 0.103006 | + | 0.0748380i | ||||
\(10\) | 8.55150 | 2.70422 | ||||||||
\(11\) | 2.91998 | − | 1.57281i | 0.880406 | − | 0.474220i | ||||
\(12\) | 6.60929 | 1.90794 | ||||||||
\(13\) | −0.528896 | − | 0.384266i | −0.146689 | − | 0.106576i | 0.512020 | − | 0.858973i | \(-0.328897\pi\) |
−0.658709 | + | 0.752397i | \(0.728897\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.73337 | + | 5.33475i | 0.447553 | + | 1.37743i | ||||
\(16\) | −3.65334 | + | 2.65431i | −0.913336 | + | 0.663577i | ||||
\(17\) | −0.919977 | + | 0.668402i | −0.223127 | + | 0.162111i | −0.693733 | − | 0.720232i | \(-0.744035\pi\) |
0.470606 | + | 0.882343i | \(0.344035\pi\) | |||||||
\(18\) | −0.291158 | − | 0.896093i | −0.0686266 | − | 0.211211i | ||||
\(19\) | 1.87759 | − | 5.77864i | 0.430750 | − | 1.32571i | −0.466630 | − | 0.884452i | \(-0.654532\pi\) |
0.897380 | − | 0.441259i | \(-0.145468\pi\) | |||||||
\(20\) | −11.4563 | − | 8.32350i | −2.56171 | − | 1.86119i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.10762 | − | 1.09495i | −1.72855 | − | 0.233445i | ||||
\(23\) | −6.66708 | −1.39018 | −0.695091 | − | 0.718921i | \(-0.744636\pi\) | ||||
−0.695091 | + | 0.718921i | \(0.744636\pi\) | |||||||
\(24\) | −6.73170 | − | 4.89086i | −1.37410 | − | 0.998343i | ||||
\(25\) | 2.16875 | − | 6.67473i | 0.433750 | − | 1.33495i | ||||
\(26\) | 0.498330 | + | 1.53370i | 0.0977306 | + | 0.300784i | ||||
\(27\) | 4.42705 | − | 3.21644i | 0.851986 | − | 0.619004i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.41331 | − | 4.34973i | −0.262445 | − | 0.807724i | −0.992271 | − | 0.124090i | \(-0.960399\pi\) |
0.729826 | − | 0.683633i | \(-0.239601\pi\) | |||||||
\(30\) | 4.27575 | − | 13.1594i | 0.780641 | − | 2.40257i | ||||
\(31\) | 2.26226 | + | 1.64363i | 0.406314 | + | 0.295205i | 0.772108 | − | 0.635491i | \(-0.219202\pi\) |
−0.365794 | + | 0.930696i | \(0.619202\pi\) | |||||||
\(32\) | 0.854102 | 0.150985 | ||||||||
\(33\) | −0.960319 | − | 5.27979i | −0.167170 | − | 0.919093i | ||||
\(34\) | 2.80505 | 0.481063 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.482141 | + | 1.48388i | −0.0803569 | + | 0.247313i | ||||
\(37\) | −0.135893 | − | 0.418235i | −0.0223406 | − | 0.0687574i | 0.939265 | − | 0.343194i | \(-0.111509\pi\) |
−0.961605 | + | 0.274436i | \(0.911509\pi\) | |||||||
\(38\) | −12.1255 | + | 8.80968i | −1.96701 | + | 1.42912i | ||||
\(39\) | −0.855772 | + | 0.621755i | −0.137033 | + | 0.0995604i | ||||
\(40\) | 5.50911 | + | 16.9553i | 0.871068 | + | 2.68087i | ||||
\(41\) | 1.82417 | − | 5.61423i | 0.284888 | − | 0.876795i | −0.701544 | − | 0.712626i | \(-0.747506\pi\) |
0.986432 | − | 0.164169i | \(-0.0524943\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.70820 | 1.32799 | 0.663994 | − | 0.747738i | \(-0.268860\pi\) | ||||
0.663994 | + | 0.747738i | \(0.268860\pi\) | |||||||
\(44\) | 9.79590 | + | 9.35835i | 1.47679 | + | 1.41082i | ||||
\(45\) | −1.32417 | −0.197396 | ||||||||
\(46\) | 13.3050 | + | 9.66666i | 1.96172 | + | 1.42527i | ||||
\(47\) | 0.186864 | − | 0.575107i | 0.0272569 | − | 0.0838880i | −0.936503 | − | 0.350660i | \(-0.885957\pi\) |
0.963760 | + | 0.266772i | \(0.0859572\pi\) | |||||||
\(48\) | 2.25789 | + | 6.94907i | 0.325898 | + | 1.00301i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −14.0058 | + | 10.1758i | −1.98072 | + | 1.43907i | ||||
\(51\) | 0.568577 | + | 1.74990i | 0.0796167 | + | 0.245035i | ||||
\(52\) | 0.825206 | − | 2.53972i | 0.114435 | − | 0.352196i | ||||
\(53\) | −7.94654 | − | 5.77350i | −1.09154 | − | 0.793051i | −0.111883 | − | 0.993721i | \(-0.535688\pi\) |
−0.979659 | + | 0.200670i | \(0.935688\pi\) | |||||||
\(54\) | −13.4983 | −1.83688 | ||||||||
\(55\) | −4.98459 | + | 10.3612i | −0.672122 | + | 1.39710i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.95362 | − | 5.77864i | −1.05348 | − | 0.765400i | ||||
\(58\) | −3.48626 | + | 10.7296i | −0.457768 | + | 1.40887i | ||||
\(59\) | −0.523492 | − | 1.61114i | −0.0681529 | − | 0.209753i | 0.911180 | − | 0.412009i | \(-0.135173\pi\) |
−0.979333 | + | 0.202256i | \(0.935173\pi\) | |||||||
\(60\) | −18.5367 | + | 13.4677i | −2.39308 | + | 1.73867i | ||||
\(61\) | 5.54839 | − | 4.03114i | 0.710398 | − | 0.516134i | −0.172904 | − | 0.984939i | \(-0.555315\pi\) |
0.883302 | + | 0.468804i | \(0.155315\pi\) | |||||||
\(62\) | −2.13152 | − | 6.56015i | −0.270703 | − | 0.833139i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.60222 | + | 4.07025i | 0.700277 | + | 0.508781i | ||||
\(65\) | 2.26638 | 0.281110 | ||||||||
\(66\) | −5.73877 | + | 11.9289i | −0.706394 | + | 1.46834i | ||||
\(67\) | −6.17828 | −0.754797 | −0.377398 | − | 0.926051i | \(-0.623181\pi\) | ||||
−0.377398 | + | 0.926051i | \(0.623181\pi\) | |||||||
\(68\) | −3.75789 | − | 2.73027i | −0.455711 | − | 0.331093i | ||||
\(69\) | −3.33354 | + | 10.2596i | −0.401311 | + | 1.23511i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.38234 | − | 3.18395i | 0.520088 | − | 0.377866i | −0.296549 | − | 0.955018i | \(-0.595836\pi\) |
0.816637 | + | 0.577152i | \(0.195836\pi\) | |||||||
\(72\) | 1.58914 | − | 1.15458i | 0.187282 | − | 0.136068i | ||||
\(73\) | −2.07103 | − | 6.37396i | −0.242395 | − | 0.746016i | −0.996054 | − | 0.0887500i | \(-0.971713\pi\) |
0.753659 | − | 0.657266i | \(-0.228287\pi\) | |||||||
\(74\) | −0.335211 | + | 1.03167i | −0.0389675 | + | 0.119930i | ||||
\(75\) | −9.18698 | − | 6.67473i | −1.06082 | − | 0.770732i | ||||
\(76\) | 24.8191 | 2.84695 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.60929 | 0.295444 | ||||||||
\(79\) | −2.14693 | − | 1.55984i | −0.241549 | − | 0.175495i | 0.460424 | − | 0.887699i | \(-0.347697\pi\) |
−0.701973 | + | 0.712204i | \(0.747697\pi\) | |||||||
\(80\) | 4.83766 | − | 14.8888i | 0.540867 | − | 1.66462i | ||||
\(81\) | −2.38197 | − | 7.33094i | −0.264663 | − | 0.814549i | ||||
\(82\) | −11.7805 | + | 8.55903i | −1.30094 | + | 0.945187i | ||||
\(83\) | 5.41765 | − | 3.93615i | 0.594664 | − | 0.432049i | −0.249317 | − | 0.968422i | \(-0.580206\pi\) |
0.843981 | + | 0.536373i | \(0.180206\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.21821 | − | 3.74926i | 0.132133 | − | 0.406665i | ||||
\(86\) | −17.3783 | − | 12.6261i | −1.87395 | − | 1.36151i | ||||
\(87\) | −7.40020 | −0.793384 | ||||||||
\(88\) | −3.05216 | − | 16.7806i | −0.325361 | − | 1.78882i | ||||
\(89\) | 0.698213 | 0.0740105 | 0.0370052 | − | 0.999315i | \(-0.488218\pi\) | ||||
0.0370052 | + | 0.999315i | \(0.488218\pi\) | |||||||
\(90\) | 2.64256 | + | 1.91993i | 0.278550 | + | 0.202378i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.41560 | − | 25.9006i | −0.877387 | − | 2.70032i | ||||
\(93\) | 3.66042 | − | 2.65945i | 0.379568 | − | 0.275772i | ||||
\(94\) | −1.20676 | + | 0.876765i | −0.124468 | + | 0.0904314i | ||||
\(95\) | 6.50911 | + | 20.0330i | 0.667821 | + | 2.05534i | ||||
\(96\) | 0.427051 | − | 1.31433i | 0.0435857 | − | 0.134143i | ||||
\(97\) | −12.0209 | − | 8.73372i | −1.22054 | − | 0.886775i | −0.224396 | − | 0.974498i | \(-0.572041\pi\) |
−0.996145 | + | 0.0877234i | \(0.972041\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.25544 | + | 0.169550i | 0.126177 | + | 0.0170404i | ||||
\(100\) | 28.6678 | 2.86678 | ||||||||
\(101\) | 6.97340 | + | 5.06647i | 0.693879 | + | 0.504133i | 0.877933 | − | 0.478784i | \(-0.158922\pi\) |
−0.184054 | + | 0.982916i | \(0.558922\pi\) | |||||||
\(102\) | 1.40253 | − | 4.31653i | 0.138871 | − | 0.427401i | ||||
\(103\) | 0.288300 | + | 0.887296i | 0.0284070 | + | 0.0874279i | 0.964255 | − | 0.264976i | \(-0.0853642\pi\) |
−0.935848 | + | 0.352404i | \(0.885364\pi\) | |||||||
\(104\) | −2.71988 | + | 1.97611i | −0.266706 | + | 0.193773i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.48729 | + | 23.0435i | 0.727230 | + | 2.23818i | ||||
\(107\) | 2.04635 | − | 6.29801i | 0.197828 | − | 0.608851i | −0.802104 | − | 0.597184i | \(-0.796286\pi\) |
0.999932 | − | 0.0116671i | \(-0.00371383\pi\) | |||||||
\(108\) | 18.0835 | + | 13.1384i | 1.74008 | + | 1.26424i | ||||
\(109\) | −4.12507 | −0.395110 | −0.197555 | − | 0.980292i | \(-0.563300\pi\) | ||||
−0.197555 | + | 0.980292i | \(0.563300\pi\) | |||||||
\(110\) | 24.9702 | − | 13.4499i | 2.38081 | − | 1.28240i | ||||
\(111\) | −0.711544 | −0.0675368 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.81749 | + | 17.9044i | −0.547264 | + | 1.68430i | 0.168282 | + | 0.985739i | \(0.446178\pi\) |
−0.715546 | + | 0.698566i | \(0.753822\pi\) | |||||||
\(114\) | 7.49396 | + | 23.0640i | 0.701873 | + | 2.16014i | ||||
\(115\) | 18.6988 | − | 13.5855i | 1.74367 | − | 1.26685i | ||||
\(116\) | 15.1140 | − | 10.9810i | 1.40330 | − | 1.01956i | ||||
\(117\) | −0.0771649 | − | 0.237489i | −0.00713390 | − | 0.0219559i | ||||
\(118\) | −1.29131 | + | 3.97426i | −0.118875 | + | 0.365860i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 28.8461 | 2.63328 | ||||||||
\(121\) | 6.05253 | − | 9.18514i | 0.550230 | − | 0.835013i | ||||
\(122\) | −16.9173 | −1.53162 | ||||||||
\(123\) | −7.72732 | − | 5.61423i | −0.696749 | − | 0.506218i | ||||
\(124\) | −3.52968 | + | 10.8632i | −0.316974 | + | 0.975546i | ||||
\(125\) | 2.16209 | + | 6.65422i | 0.193383 | + | 0.595171i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.44491 | − | 4.68250i | 0.571893 | − | 0.415505i | −0.263899 | − | 0.964550i | \(-0.585009\pi\) |
0.835792 | + | 0.549045i | \(0.185009\pi\) | |||||||
\(128\) | −5.80631 | − | 17.8700i | −0.513211 | − | 1.57950i | ||||
\(129\) | 4.35410 | − | 13.4005i | 0.383357 | − | 1.17985i | ||||
\(130\) | −4.52285 | − | 3.28605i | −0.396681 | − | 0.288205i | ||||
\(131\) | 4.80505 | 0.419819 | 0.209910 | − | 0.977721i | \(-0.432683\pi\) | ||||
0.209910 | + | 0.977721i | \(0.432683\pi\) | |||||||
\(132\) | 19.2990 | − | 10.3952i | 1.67976 | − | 0.904783i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 12.3295 | + | 8.95793i | 1.06511 | + | 0.773848i | ||||
\(135\) | −5.86218 | + | 18.0419i | −0.504537 | + | 1.55280i | ||||
\(136\) | 1.80709 | + | 5.56166i | 0.154957 | + | 0.476909i | ||||
\(137\) | 17.6995 | − | 12.8594i | 1.51217 | − | 1.09865i | 0.546962 | − | 0.837157i | \(-0.315784\pi\) |
0.965204 | − | 0.261496i | \(-0.0842160\pi\) | |||||||
\(138\) | 21.5280 | − | 15.6410i | 1.83258 | − | 1.33145i | ||||
\(139\) | 6.12278 | + | 18.8440i | 0.519327 | + | 1.59832i | 0.775268 | + | 0.631632i | \(0.217615\pi\) |
−0.255941 | + | 0.966692i | \(0.582385\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.791567 | − | 0.575107i | −0.0666620 | − | 0.0484328i | ||||
\(142\) | −13.3620 | −1.12131 | ||||||||
\(143\) | −2.14874 | − | 0.290193i | −0.179687 | − | 0.0242671i | ||||
\(144\) | −1.72487 | −0.143740 | ||||||||
\(145\) | 12.8272 | + | 9.31954i | 1.06524 | + | 0.773946i | ||||
\(146\) | −5.10867 | + | 15.7229i | −0.422796 | + | 1.30123i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.45325 | − | 1.05584i | 0.119456 | − | 0.0867899i | ||||
\(149\) | −2.55820 | + | 1.85864i | −0.209576 | + | 0.152266i | −0.687622 | − | 0.726069i | \(-0.741345\pi\) |
0.478046 | + | 0.878335i | \(0.341345\pi\) | |||||||
\(150\) | 8.65604 | + | 26.6406i | 0.706763 | + | 2.17519i | ||||
\(151\) | 2.75892 | − | 8.49109i | 0.224518 | − | 0.690995i | −0.773822 | − | 0.633403i | \(-0.781658\pi\) |
0.998340 | − | 0.0575923i | \(-0.0183423\pi\) | |||||||
\(152\) | −25.2788 | − | 18.3661i | −2.05038 | − | 1.48969i | ||||
\(153\) | −0.434354 | −0.0351155 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.69406 | −0.778645 | ||||||||
\(156\) | −3.49563 | − | 2.53972i | −0.279874 | − | 0.203341i | ||||
\(157\) | −0.352179 | + | 1.08390i | −0.0281070 | + | 0.0865044i | −0.964126 | − | 0.265445i | \(-0.914481\pi\) |
0.936019 | + | 0.351949i | \(0.114481\pi\) | |||||||
\(158\) | 2.02285 | + | 6.22570i | 0.160930 | + | 0.495290i | ||||
\(159\) | −12.8578 | + | 9.34172i | −1.01969 | + | 0.740847i | ||||
\(160\) | −2.39545 | + | 1.74040i | −0.189377 | + | 0.137591i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5.87567 | + | 18.0835i | −0.461636 | + | 1.42077i | ||||
\(163\) | 4.09951 | + | 2.97847i | 0.321099 | + | 0.233292i | 0.736644 | − | 0.676281i | \(-0.236409\pi\) |
−0.415545 | + | 0.909572i | \(0.636409\pi\) | |||||||
\(164\) | 24.1130 | 1.88291 | ||||||||
\(165\) | 13.4519 | + | 12.8511i | 1.04723 | + | 1.00046i | ||||
\(166\) | −16.5187 | −1.28210 | ||||||||
\(167\) | −15.9432 | − | 11.5834i | −1.23372 | − | 0.896351i | −0.236558 | − | 0.971617i | \(-0.576019\pi\) |
−0.997164 | + | 0.0752658i | \(0.976019\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.88515 | − | 11.9573i | −0.298858 | − | 0.919789i | ||||
\(170\) | −7.86718 | + | 5.71584i | −0.603385 | + | 0.438385i | ||||
\(171\) | 1.87759 | − | 1.36415i | 0.143583 | − | 0.104319i | ||||
\(172\) | 10.9920 | + | 33.8300i | 0.838135 | + | 2.57951i | ||||
\(173\) | 4.44824 | − | 13.6903i | 0.338193 | − | 1.04085i | −0.626935 | − | 0.779072i | \(-0.715691\pi\) |
0.965128 | − | 0.261779i | \(-0.0843093\pi\) | |||||||
\(174\) | 14.7680 | + | 10.7296i | 1.11956 | + | 0.813409i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.49295 | + | 13.4965i | −0.489424 | + | 1.01734i | ||||
\(177\) | −2.74104 | −0.206029 | ||||||||
\(178\) | −1.39337 | − | 1.01235i | −0.104438 | − | 0.0758785i | ||||
\(179\) | −1.44132 | + | 4.43592i | −0.107729 | + | 0.331556i | −0.990361 | − | 0.138508i | \(-0.955769\pi\) |
0.882632 | + | 0.470064i | \(0.155769\pi\) | |||||||
\(180\) | −1.67145 | − | 5.14421i | −0.124583 | − | 0.383427i | ||||
\(181\) | 8.01578 | − | 5.82381i | 0.595808 | − | 0.432880i | −0.248580 | − | 0.968611i | \(-0.579964\pi\) |
0.844389 | + | 0.535731i | \(0.179964\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.42909 | − | 10.5537i | −0.253486 | − | 0.780149i | ||||
\(184\) | −10.5949 | + | 32.6078i | −0.781067 | + | 2.40388i | ||||
\(185\) | 1.23337 | + | 0.896093i | 0.0906789 | + | 0.0658821i | ||||
\(186\) | −11.1608 | −0.818349 | ||||||||
\(187\) | −1.63504 | + | 3.39867i | −0.119566 | + | 0.248535i | ||||
\(188\) | 2.47007 | 0.180148 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16.0562 | − | 49.4160i | 1.16484 | − | 3.58502i | ||||
\(191\) | 3.07254 | + | 9.45631i | 0.222321 | + | 0.684234i | 0.998552 | + | 0.0537861i | \(0.0171289\pi\) |
−0.776231 | + | 0.630448i | \(0.782871\pi\) | |||||||
\(192\) | 9.06458 | − | 6.58580i | 0.654179 | − | 0.475289i | ||||
\(193\) | −2.99874 | + | 2.17871i | −0.215854 | + | 0.156827i | −0.690458 | − | 0.723372i | \(-0.742591\pi\) |
0.474604 | + | 0.880199i | \(0.342591\pi\) | |||||||
\(194\) | 11.3262 | + | 34.8585i | 0.813175 | + | 2.50269i | ||||
\(195\) | 1.13319 | − | 3.48760i | 0.0811495 | − | 0.249752i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.91982 | 0.421770 | 0.210885 | − | 0.977511i | \(-0.432365\pi\) | ||||
0.210885 | + | 0.977511i | \(0.432365\pi\) | |||||||
\(198\) | −2.25956 | − | 2.15863i | −0.160580 | − | 0.153407i | ||||
\(199\) | −11.4842 | −0.814095 | −0.407047 | − | 0.913407i | \(-0.633442\pi\) | ||||
−0.407047 | + | 0.913407i | \(0.633442\pi\) | |||||||
\(200\) | −29.1988 | − | 21.2141i | −2.06466 | − | 1.50007i | ||||
\(201\) | −3.08914 | + | 9.50739i | −0.217891 | + | 0.670599i | ||||
\(202\) | −6.57039 | − | 20.2216i | −0.462291 | − | 1.42279i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.08039 | + | 4.41766i | −0.425713 | + | 0.309298i | ||||
\(205\) | 6.32392 | + | 19.4630i | 0.441682 | + | 1.35936i | ||||
\(206\) | 0.711159 | − | 2.18872i | 0.0495488 | − | 0.152495i | ||||
\(207\) | −2.06024 | − | 1.49685i | −0.143197 | − | 0.104038i | ||||
\(208\) | 2.95220 | 0.204698 | ||||||||
\(209\) | −3.60618 | − | 19.8266i | −0.249445 | − | 1.37143i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.05857 | − | 5.12835i | −0.485932 | − | 0.353050i | 0.317686 | − | 0.948196i | \(-0.397094\pi\) |
−0.803618 | + | 0.595146i | \(0.797094\pi\) | |||||||
\(212\) | 12.3985 | − | 38.1587i | 0.851534 | − | 2.62075i | ||||
\(213\) | −2.70843 | − | 8.33570i | −0.185579 | − | 0.571153i | ||||
\(214\) | −13.2153 | + | 9.60146i | −0.903378 | + | 0.656342i | ||||
\(215\) | −24.4234 | + | 17.7447i | −1.66566 | + | 1.21018i | ||||
\(216\) | −8.69598 | − | 26.7635i | −0.591686 | − | 1.82102i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.23210 | + | 5.98097i | 0.557548 | + | 0.405083i | ||||
\(219\) | −10.8440 | −0.732772 | ||||||||
\(220\) | −46.5435 | − | 6.28581i | −3.13796 | − | 0.423789i | ||||
\(221\) | 0.743416 | 0.0500076 | ||||||||
\(222\) | 1.41998 | + | 1.03167i | 0.0953026 | + | 0.0692414i | ||||
\(223\) | −3.19302 | + | 9.82712i | −0.213821 | + | 0.658072i | 0.785415 | + | 0.618970i | \(0.212450\pi\) |
−0.999235 | + | 0.0391023i | \(0.987550\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.16875 | − | 1.57569i | 0.144583 | − | 0.105046i | ||||
\(226\) | 37.5693 | − | 27.2957i | 2.49907 | − | 1.81568i | ||||
\(227\) | 4.10033 | + | 12.6195i | 0.272149 | + | 0.837587i | 0.989960 | + | 0.141349i | \(0.0451441\pi\) |
−0.717811 | + | 0.696238i | \(0.754856\pi\) | |||||||
\(228\) | 12.4096 | − | 38.1927i | 0.821843 | − | 2.52937i | ||||
\(229\) | −2.01949 | − | 1.46725i | −0.133452 | − | 0.0969583i | 0.519057 | − | 0.854740i | \(-0.326283\pi\) |
−0.652508 | + | 0.757781i | \(0.726283\pi\) | |||||||
\(230\) | −57.0135 | −3.75936 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −23.5199 | −1.54415 | ||||||||
\(233\) | 7.76971 | + | 5.64502i | 0.509010 | + | 0.369818i | 0.812448 | − | 0.583034i | \(-0.198134\pi\) |
−0.303438 | + | 0.952851i | \(0.598134\pi\) | |||||||
\(234\) | −0.190345 | + | 0.585822i | −0.0124433 | + | 0.0382964i | ||||
\(235\) | 0.647806 | + | 1.99374i | 0.0422582 | + | 0.130057i | ||||
\(236\) | 5.59825 | − | 4.06737i | 0.364415 | − | 0.264763i | ||||
\(237\) | −3.47381 | + | 2.52387i | −0.225648 | + | 0.163943i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.71914 | − | 5.29098i | 0.111202 | − | 0.342245i | −0.879934 | − | 0.475096i | \(-0.842413\pi\) |
0.991136 | + | 0.132851i | \(0.0424132\pi\) | |||||||
\(240\) | −20.4927 | − | 14.8888i | −1.32280 | − | 0.961067i | ||||
\(241\) | −15.0208 | −0.967572 | −0.483786 | − | 0.875186i | \(-0.660739\pi\) | ||||
−0.483786 | + | 0.875186i | \(0.660739\pi\) | |||||||
\(242\) | −25.3962 | + | 9.55452i | −1.63253 | + | 0.614188i | ||||
\(243\) | 3.94427 | 0.253025 | ||||||||
\(244\) | 22.6639 | + | 16.4663i | 1.45090 | + | 1.05414i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.28074 | + | 22.4078i | 0.464203 | + | 1.42867i | ||||
\(247\) | −3.21358 | + | 2.33481i | −0.204475 | + | 0.148560i | ||||
\(248\) | 11.6338 | − | 8.45246i | 0.738748 | − | 0.536732i | ||||
\(249\) | −3.34829 | − | 10.3050i | −0.212189 | − | 0.653051i | ||||
\(250\) | 5.33329 | − | 16.4142i | 0.337307 | − | 1.03812i | ||||
\(251\) | 22.3394 | + | 16.2305i | 1.41005 | + | 1.02446i | 0.993315 | + | 0.115436i | \(0.0368266\pi\) |
0.416738 | + | 0.909027i | \(0.363173\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.4677 | + | 10.4861i | −1.22393 | + | 0.659253i | ||||
\(254\) | −19.6508 | −1.23300 | ||||||||
\(255\) | −5.16042 | − | 3.74926i | −0.323158 | − | 0.234788i | ||||
\(256\) | −10.0429 | + | 30.9089i | −0.627682 | + | 1.93181i | ||||
\(257\) | 8.79709 | + | 27.0747i | 0.548747 | + | 1.68887i | 0.711909 | + | 0.702271i | \(0.247831\pi\) |
−0.163162 | + | 0.986599i | \(0.552169\pi\) | |||||||
\(258\) | −28.1187 | + | 20.4295i | −1.75060 | + | 1.27188i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.86077 | + | 8.80454i | 0.177417 | + | 0.546034i | ||||
\(261\) | 0.539837 | − | 1.66145i | 0.0334151 | − | 0.102841i | ||||
\(262\) | −9.58910 | − | 6.96689i | −0.592417 | − | 0.430416i | ||||
\(263\) | 14.1803 | 0.874397 | 0.437199 | − | 0.899365i | \(-0.355971\pi\) | ||||
0.437199 | + | 0.899365i | \(0.355971\pi\) | |||||||
\(264\) | −27.3488 | − | 3.69352i | −1.68320 | − | 0.227321i | ||||
\(265\) | 34.0519 | 2.09179 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.349107 | − | 1.07444i | 0.0213650 | − | 0.0657546i | ||||
\(268\) | −7.79860 | − | 24.0016i | −0.476375 | − | 1.46613i | ||||
\(269\) | −19.5731 | + | 14.2207i | −1.19339 | + | 0.867050i | −0.993619 | − | 0.112792i | \(-0.964021\pi\) |
−0.199774 | + | 0.979842i | \(0.564021\pi\) | |||||||
\(270\) | 37.8579 | − | 27.5054i | 2.30396 | − | 1.67392i | ||||
\(271\) | −2.30210 | − | 7.08513i | −0.139843 | − | 0.430391i | 0.856469 | − | 0.516198i | \(-0.172653\pi\) |
−0.996312 | + | 0.0858070i | \(0.972653\pi\) | |||||||
\(272\) | 1.58684 | − | 4.88381i | 0.0962166 | − | 0.296124i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −53.9665 | −3.26024 | ||||||||
\(275\) | −4.16539 | − | 22.9011i | −0.251182 | − | 1.38099i | ||||
\(276\) | −44.0647 | −2.65238 | ||||||||
\(277\) | 15.5242 | + | 11.2790i | 0.932761 | + | 0.677690i | 0.946667 | − | 0.322213i | \(-0.104427\pi\) |
−0.0139064 | + | 0.999903i | \(0.504427\pi\) | |||||||
\(278\) | 15.1032 | − | 46.4830i | 0.905833 | − | 2.78787i | ||||
\(279\) | 0.330060 | + | 1.01582i | 0.0197602 | + | 0.0608155i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.53764 | − | 1.11716i | 0.0917279 | − | 0.0666442i | −0.540976 | − | 0.841038i | \(-0.681945\pi\) |
0.632704 | + | 0.774394i | \(0.281945\pi\) | |||||||
\(282\) | 0.745821 | + | 2.29540i | 0.0444130 | + | 0.136689i | ||||
\(283\) | −2.24092 | + | 6.89685i | −0.133209 | + | 0.409975i | −0.995307 | − | 0.0967663i | \(-0.969150\pi\) |
0.862098 | + | 0.506741i | \(0.169150\pi\) | |||||||
\(284\) | 17.9008 | + | 13.0057i | 1.06222 | + | 0.771747i | ||||
\(285\) | 34.0822 | 2.01885 | ||||||||
\(286\) | 3.86734 | + | 3.69460i | 0.228680 | + | 0.218466i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.263932 | + | 0.191758i | 0.0155523 | + | 0.0112994i | ||||
\(289\) | −4.85369 | + | 14.9381i | −0.285511 | + | 0.878714i | ||||
\(290\) | −12.0859 | − | 37.1967i | −0.709710 | − | 2.18426i | ||||
\(291\) | −19.4503 | + | 14.1315i | −1.14020 | + | 0.828400i | ||||
\(292\) | 22.1477 | − | 16.0912i | 1.29609 | − | 0.941668i | ||||
\(293\) | 1.01078 | + | 3.11088i | 0.0590507 | + | 0.181739i | 0.976231 | − | 0.216734i | \(-0.0695403\pi\) |
−0.917180 | + | 0.398473i | \(0.869540\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.75122 | + | 3.45197i | 0.276627 | + | 0.200981i | ||||
\(296\) | −2.26148 | −0.131446 | ||||||||
\(297\) | 7.86803 | − | 16.3548i | 0.456550 | − | 0.949005i | ||||
\(298\) | 7.80008 | 0.451846 | ||||||||
\(299\) | 3.52619 | + | 2.56193i | 0.203925 | + | 0.148160i | ||||
\(300\) | 14.3339 | − | 44.1152i | 0.827569 | − | 2.54699i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −17.8171 | + | 12.9449i | −1.02526 | + | 0.744894i | ||||
\(303\) | 11.2832 | − | 8.19772i | 0.648203 | − | 0.470947i | ||||
\(304\) | 8.47880 | + | 26.0951i | 0.486293 | + | 1.49665i | ||||
\(305\) | −7.34703 | + | 22.6118i | −0.420690 | + | 1.29475i | ||||
\(306\) | 0.866809 | + | 0.629774i | 0.0495522 | + | 0.0360018i | ||||
\(307\) | −31.6121 | −1.80420 | −0.902099 | − | 0.431530i | \(-0.857974\pi\) | ||||
−0.902099 | + | 0.431530i | \(0.857974\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.50956 | 0.0858758 | ||||||||
\(310\) | 19.3457 | + | 14.0555i | 1.09876 | + | 0.798298i | ||||
\(311\) | 2.79298 | − | 8.59592i | 0.158376 | − | 0.487430i | −0.840112 | − | 0.542414i | \(-0.817511\pi\) |
0.998487 | + | 0.0549835i | \(0.0175106\pi\) | |||||||
\(312\) | 1.68098 | + | 5.17352i | 0.0951666 | + | 0.292893i | ||||
\(313\) | 11.7300 | − | 8.52232i | 0.663017 | − | 0.481710i | −0.204664 | − | 0.978832i | \(-0.565610\pi\) |
0.867680 | + | 0.497122i | \(0.165610\pi\) | |||||||
\(314\) | 2.27437 | − | 1.65243i | 0.128350 | − | 0.0932518i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.34973 | − | 10.3094i | 0.188437 | − | 0.579950i | ||||
\(317\) | 14.9000 | + | 10.8255i | 0.836865 | + | 0.608018i | 0.921493 | − | 0.388394i | \(-0.126970\pi\) |
−0.0846278 | + | 0.996413i | \(0.526970\pi\) | |||||||
\(318\) | 39.2040 | 2.19845 | ||||||||
\(319\) | −10.9681 | − | 10.4782i | −0.614098 | − | 0.586668i | ||||
\(320\) | −24.0061 | −1.34198 | ||||||||
\(321\) | −8.66846 | − | 6.29801i | −0.483826 | − | 0.351520i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.13511 | + | 6.57120i | 0.118801 | + | 0.365632i | ||||
\(324\) | 25.4729 | − | 18.5071i | 1.41516 | − | 1.02817i | ||||
\(325\) | −3.71191 | + | 2.69686i | −0.205900 | + | 0.149595i | ||||
\(326\) | −3.86259 | − | 11.8878i | −0.213929 | − | 0.658407i | ||||
\(327\) | −2.06253 | + | 6.34783i | −0.114058 | + | 0.351036i | ||||
\(328\) | −24.5596 | − | 17.8436i | −1.35608 | − | 0.985246i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −8.21217 | − | 45.1501i | −0.452065 | − | 2.48543i | ||||
\(331\) | −6.47653 | −0.355982 | −0.177991 | − | 0.984032i | \(-0.556960\pi\) | ||||
−0.177991 | + | 0.984032i | \(0.556960\pi\) | |||||||
\(332\) | 22.1298 | + | 16.0782i | 1.21453 | + | 0.882409i | ||||
\(333\) | 0.0519064 | − | 0.159752i | 0.00284445 | − | 0.00875433i | ||||
\(334\) | 15.0218 | + | 46.2324i | 0.821957 | + | 2.52972i | ||||
\(335\) | 17.3279 | − | 12.5894i | 0.946723 | − | 0.687834i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.93346 | + | 5.95059i | 0.105322 | + | 0.324149i | 0.989806 | − | 0.142422i | \(-0.0454891\pi\) |
−0.884484 | + | 0.466571i | \(0.845489\pi\) | |||||||
\(338\) | −9.58362 | + | 29.4954i | −0.521280 | + | 1.60434i | ||||
\(339\) | 24.6433 | + | 17.9044i | 1.33844 | + | 0.972434i | ||||
\(340\) | 16.1030 | 0.873308 | ||||||||
\(341\) | 9.19087 | + | 1.24125i | 0.497714 | + | 0.0672174i | ||||
\(342\) | −5.72487 | −0.309566 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 13.8385 | − | 42.5906i | 0.746124 | − | 2.29633i | ||||
\(345\) | −11.5565 | − | 35.5672i | −0.622181 | − | 1.91488i | ||||
\(346\) | −28.7266 | + | 20.8711i | −1.54435 | + | 1.12204i | ||||
\(347\) | −18.3773 | + | 13.3519i | −0.986547 | + | 0.716768i | −0.959162 | − | 0.282857i | \(-0.908718\pi\) |
−0.0273845 | + | 0.999625i | \(0.508718\pi\) | |||||||
\(348\) | −9.34099 | − | 28.7486i | −0.500729 | − | 1.54109i | ||||
\(349\) | −9.17597 | + | 28.2407i | −0.491178 | + | 1.51169i | 0.331651 | + | 0.943402i | \(0.392394\pi\) |
−0.822829 | + | 0.568289i | \(0.807606\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.57742 | −0.190948 | ||||||||
\(352\) | 2.49396 | − | 1.34334i | 0.132928 | − | 0.0716003i | ||||
\(353\) | 6.82506 | 0.363262 | 0.181631 | − | 0.983367i | \(-0.441862\pi\) | ||||
0.181631 | + | 0.983367i | \(0.441862\pi\) | |||||||
\(354\) | 5.47010 | + | 3.97426i | 0.290732 | + | 0.211229i | ||||
\(355\) | −5.80297 | + | 17.8597i | −0.307990 | + | 0.947896i | ||||
\(356\) | 0.881328 | + | 2.71245i | 0.0467103 | + | 0.143760i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.30801 | − | 6.76266i | 0.491944 | − | 0.357418i | ||||
\(359\) | −2.24337 | − | 6.90439i | −0.118401 | − | 0.364400i | 0.874241 | − | 0.485493i | \(-0.161360\pi\) |
−0.992641 | + | 0.121094i | \(0.961360\pi\) | |||||||
\(360\) | −2.10429 | + | 6.47635i | −0.110906 | + | 0.341334i | ||||
\(361\) | −14.4960 | − | 10.5320i | −0.762947 | − | 0.554314i | ||||
\(362\) | −24.4405 | −1.28456 | ||||||||
\(363\) | −11.1082 | − | 13.9065i | −0.583030 | − | 0.729900i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.7967 | + | 13.6566i | 0.983863 | + | 0.714818i | ||||
\(366\) | −8.45865 | + | 26.0330i | −0.442141 | + | 1.36077i | ||||
\(367\) | 11.2286 | + | 34.5582i | 0.586130 | + | 1.80392i | 0.594686 | + | 0.803958i | \(0.297277\pi\) |
−0.00855584 | + | 0.999963i | \(0.502723\pi\) | |||||||
\(368\) | 24.3571 | − | 17.6965i | 1.26970 | − | 0.922494i | ||||
\(369\) | 1.82417 | − | 1.32534i | 0.0949627 | − | 0.0689944i | ||||
\(370\) | −1.16209 | − | 3.57654i | −0.0604140 | − | 0.185935i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 14.9519 | + | 10.8632i | 0.775222 | + | 0.563232i | ||||
\(373\) | −14.2913 | −0.739977 | −0.369989 | − | 0.929036i | \(-0.620638\pi\) | ||||
−0.369989 | + | 0.929036i | \(0.620638\pi\) | |||||||
\(374\) | 8.19069 | − | 4.41182i | 0.423531 | − | 0.228130i | ||||
\(375\) | 11.3208 | 0.584605 | ||||||||
\(376\) | −2.51582 | − | 1.82785i | −0.129743 | − | 0.0942641i | ||||
\(377\) | −0.923955 | + | 2.84364i | −0.0475861 | + | 0.146455i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.05917 | − | 1.49608i | 0.105773 | − | 0.0768482i | −0.533642 | − | 0.845711i | \(-0.679177\pi\) |
0.639414 | + | 0.768862i | \(0.279177\pi\) | |||||||
\(380\) | −69.6088 | + | 50.5738i | −3.57086 | + | 2.59438i | ||||
\(381\) | −3.98317 | − | 12.2589i | −0.204064 | − | 0.628045i | ||||
\(382\) | 7.57913 | − | 23.3262i | 0.387782 | − | 1.19347i | ||||
\(383\) | −18.7180 | − | 13.5994i | −0.956444 | − | 0.694897i | −0.00412192 | − | 0.999992i | \(-0.501312\pi\) |
−0.952322 | + | 0.305094i | \(0.901312\pi\) | |||||||
\(384\) | −30.4023 | −1.55146 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.14330 | 0.465382 | ||||||||
\(387\) | 2.69098 | + | 1.95511i | 0.136790 | + | 0.0993840i | ||||
\(388\) | 18.7556 | − | 57.7237i | 0.952169 | − | 2.93048i | ||||
\(389\) | 9.35130 | + | 28.7804i | 0.474130 | + | 1.45922i | 0.847128 | + | 0.531390i | \(0.178330\pi\) |
−0.372998 | + | 0.927832i | \(0.621670\pi\) | |||||||
\(390\) | −7.31813 | + | 5.31693i | −0.370568 | + | 0.269233i | ||||
\(391\) | 6.13356 | − | 4.45629i | 0.310188 | − | 0.225364i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.40253 | − | 7.39422i | 0.121191 | − | 0.372989i | ||||
\(394\) | −11.8138 | − | 8.58320i | −0.595169 | − | 0.432415i | ||||
\(395\) | 9.19985 | 0.462894 | ||||||||
\(396\) | 0.926019 | + | 5.09121i | 0.0465342 | + | 0.255843i | ||||
\(397\) | 22.6740 | 1.13798 | 0.568989 | − | 0.822345i | \(-0.307335\pi\) | ||||
0.568989 | + | 0.822345i | \(0.307335\pi\) | |||||||
\(398\) | 22.9182 | + | 16.6511i | 1.14879 | + | 0.834643i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.79361 | + | 30.1416i | 0.489680 | + | 1.50708i | ||||
\(401\) | 13.1211 | − | 9.53304i | 0.655237 | − | 0.476057i | −0.209814 | − | 0.977741i | \(-0.567286\pi\) |
0.865051 | + | 0.501684i | \(0.167286\pi\) | |||||||
\(402\) | 19.9496 | − | 14.4942i | 0.994996 | − | 0.722907i | ||||
\(403\) | −0.564911 | − | 1.73862i | −0.0281402 | − | 0.0866068i | ||||
\(404\) | −10.8802 | + | 33.4858i | −0.541309 | + | 1.66598i | ||||
\(405\) | 21.6188 | + | 15.7070i | 1.07425 | + | 0.780485i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.05461 | − | 1.00750i | −0.0522750 | − | 0.0499401i | ||||
\(408\) | 9.46207 | 0.468442 | ||||||||
\(409\) | −28.3653 | − | 20.6086i | −1.40257 | − | 1.01903i | −0.994351 | − | 0.106146i | \(-0.966149\pi\) |
−0.408222 | − | 0.912883i | \(-0.633851\pi\) | |||||||
\(410\) | 15.5994 | − | 48.0101i | 0.770400 | − | 2.37105i | ||||
\(411\) | −10.9389 | − | 33.6664i | −0.539575 | − | 1.66064i | ||||
\(412\) | −3.08310 | + | 2.24000i | −0.151893 | + | 0.110357i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.94118 | + | 5.97432i | 0.0954036 | + | 0.293622i | ||||
\(415\) | −7.17390 | + | 22.0790i | −0.352153 | + | 1.08382i | ||||
\(416\) | −0.451731 | − | 0.328202i | −0.0221479 | − | 0.0160914i | ||||
\(417\) | 32.0593 | 1.56995 | ||||||||
\(418\) | −21.5502 | + | 44.7951i | −1.05405 | + | 2.19100i | ||||
\(419\) | −28.2633 | −1.38075 | −0.690376 | − | 0.723451i | \(-0.742555\pi\) | ||||
−0.690376 | + | 0.723451i | \(0.742555\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.26279 | + | 13.1195i | −0.207756 | + | 0.639406i | 0.791833 | + | 0.610737i | \(0.209127\pi\) |
−0.999589 | + | 0.0286688i | \(0.990873\pi\) | |||||||
\(422\) | 6.65064 | + | 20.4686i | 0.323748 | + | 0.996394i | ||||
\(423\) | 0.186864 | − | 0.135764i | 0.00908562 | − | 0.00660109i | ||||
\(424\) | −40.8656 | + | 29.6906i | −1.98461 | + | 1.44190i | ||||
\(425\) | 2.46621 | + | 7.59020i | 0.119629 | + | 0.368179i | ||||
\(426\) | −6.68098 | + | 20.5619i | −0.323694 | + | 0.996229i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 27.0498 | 1.30750 | ||||||||
\(429\) | −1.52093 | + | 3.16148i | −0.0734313 | + | 0.152638i | ||||
\(430\) | 74.4682 | 3.59117 | ||||||||
\(431\) | −22.7900 | − | 16.5579i | −1.09776 | − | 0.797568i | −0.117065 | − | 0.993124i | \(-0.537349\pi\) |
−0.980692 | + | 0.195557i | \(0.937349\pi\) | |||||||
\(432\) | −7.63611 | + | 23.5015i | −0.367392 | + | 1.13072i | ||||
\(433\) | −4.38165 | − | 13.4853i | −0.210569 | − | 0.648064i | −0.999439 | − | 0.0335038i | \(-0.989333\pi\) |
0.788870 | − | 0.614560i | \(-0.210667\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 20.7549 | − | 15.0793i | 0.995122 | − | 0.722999i | ||||
\(436\) | −5.20692 | − | 16.0252i | −0.249366 | − | 0.767470i | ||||
\(437\) | −12.5181 | + | 38.5267i | −0.598821 | + | 1.84298i | ||||
\(438\) | 21.6407 | + | 15.7229i | 1.03403 | + | 0.751267i | ||||
\(439\) | −28.0185 | −1.33725 | −0.668625 | − | 0.743599i | \(-0.733117\pi\) | ||||
−0.668625 | + | 0.743599i | \(0.733117\pi\) | |||||||
\(440\) | 42.7540 | + | 40.8443i | 2.03822 | + | 1.94718i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.48358 | − | 1.07789i | −0.0705668 | − | 0.0512698i | ||||
\(443\) | 5.35743 | − | 16.4885i | 0.254539 | − | 0.783391i | −0.739381 | − | 0.673287i | \(-0.764882\pi\) |
0.993920 | − | 0.110103i | \(-0.0351182\pi\) | |||||||
\(444\) | −0.898155 | − | 2.76424i | −0.0426245 | − | 0.131185i | ||||
\(445\) | −1.95824 | + | 1.42274i | −0.0928295 | + | 0.0674446i | ||||
\(446\) | 20.6205 | − | 14.9817i | 0.976409 | − | 0.709403i | ||||
\(447\) | 1.58106 | + | 4.86599i | 0.0747813 | + | 0.230153i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.8834 | + | 17.3523i | 1.12713 | + | 0.818906i | 0.985274 | − | 0.170982i | \(-0.0546940\pi\) |
0.141853 | + | 0.989888i | \(0.454694\pi\) | |||||||
\(450\) | −6.61263 | −0.311722 | ||||||||
\(451\) | −3.50358 | − | 19.2625i | −0.164977 | − | 0.907036i | ||||
\(452\) | −76.8990 | −3.61702 | ||||||||
\(453\) | −11.6870 | − | 8.49109i | −0.549102 | − | 0.398946i | ||||
\(454\) | 10.1144 | − | 31.1290i | 0.474693 | − | 1.46096i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −40.9019 | + | 29.7170i | −1.91541 | + | 1.39163i | ||||
\(457\) | −7.84524 | + | 5.69990i | −0.366985 | + | 0.266630i | −0.755960 | − | 0.654618i | \(-0.772829\pi\) |
0.388975 | + | 0.921248i | \(0.372829\pi\) | |||||||
\(458\) | 1.90278 | + | 5.85615i | 0.0889110 | + | 0.273640i | ||||
\(459\) | −1.92291 | + | 5.91810i | −0.0897537 | + | 0.276233i | ||||
\(460\) | 76.3802 | + | 55.4935i | 3.56125 | + | 2.58740i | ||||
\(461\) | 19.2216 | 0.895240 | 0.447620 | − | 0.894224i | \(-0.352272\pi\) | ||||
0.447620 | + | 0.894224i | \(0.352272\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.5327 | 0.954235 | 0.477117 | − | 0.878840i | \(-0.341682\pi\) | ||||
0.477117 | + | 0.878840i | \(0.341682\pi\) | |||||||
\(464\) | 16.7088 | + | 12.1397i | 0.775688 | + | 0.563570i | ||||
\(465\) | −4.84703 | + | 14.9176i | −0.224776 | + | 0.691788i | ||||
\(466\) | −7.32068 | − | 22.5307i | −0.339124 | − | 1.04372i | ||||
\(467\) | 27.2408 | − | 19.7916i | 1.26055 | − | 0.915845i | 0.261768 | − | 0.965131i | \(-0.415695\pi\) |
0.998785 | + | 0.0492858i | \(0.0156945\pi\) | |||||||
\(468\) | 0.825206 | − | 0.599547i | 0.0381452 | − | 0.0277141i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.59796 | − | 4.91803i | 0.0737086 | − | 0.226852i | ||||
\(471\) | 1.49186 | + | 1.08390i | 0.0687411 | + | 0.0499433i | ||||
\(472\) | −8.71178 | −0.400992 | ||||||||
\(473\) | 25.4278 | − | 13.6964i | 1.16917 | − | 0.629759i | ||||
\(474\) | 10.5918 | 0.486498 | ||||||||
\(475\) | −34.4988 | − | 25.0649i | −1.58292 | − | 1.15006i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.15938 | − | 3.56822i | −0.0530846 | − | 0.163378i | ||||
\(478\) | −11.1022 | + | 8.06623i | −0.507804 | + | 0.368941i | ||||
\(479\) | 11.4644 | − | 8.32937i | 0.523822 | − | 0.380579i | −0.294220 | − | 0.955738i | \(-0.595060\pi\) |
0.818042 | + | 0.575159i | \(0.195060\pi\) | |||||||
\(480\) | 1.48047 | + | 4.55642i | 0.0675740 | + | 0.207971i | ||||
\(481\) | −0.0888401 | + | 0.273422i | −0.00405076 | + | 0.0124670i | ||||
\(482\) | 29.9758 | + | 21.7787i | 1.36536 | + | 0.991993i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 43.3227 | + | 11.9191i | 1.96921 | + | 0.541776i | ||||
\(485\) | 51.5111 | 2.33900 | ||||||||
\(486\) | −7.87130 | − | 5.71883i | −0.357049 | − | 0.259412i | ||||
\(487\) | 8.57259 | − | 26.3837i | 0.388461 | − | 1.19556i | −0.545477 | − | 0.838126i | \(-0.683652\pi\) |
0.933938 | − | 0.357434i | \(-0.116348\pi\) | |||||||
\(488\) | −10.8986 | − | 33.5424i | −0.493356 | − | 1.51839i | ||||
\(489\) | 6.63315 | − | 4.81927i | 0.299962 | − | 0.217935i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.06393 | − | 3.27444i | −0.0480145 | − | 0.147774i | 0.924175 | − | 0.381970i | \(-0.124754\pi\) |
−0.972189 | + | 0.234196i | \(0.924754\pi\) | |||||||
\(492\) | 12.0565 | − | 37.1061i | 0.543549 | − | 1.67287i | ||||
\(493\) | 4.20758 | + | 3.05699i | 0.189500 | + | 0.137680i | ||||
\(494\) | 9.79837 | 0.440850 | ||||||||
\(495\) | −3.86656 | + | 2.08268i | −0.173789 | + | 0.0936093i | ||||
\(496\) | −12.6275 | −0.566992 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −8.25933 | + | 25.4196i | −0.370109 | + | 1.13908i | ||||
\(499\) | −0.800117 | − | 2.46251i | −0.0358181 | − | 0.110237i | 0.931549 | − | 0.363616i | \(-0.118458\pi\) |
−0.967367 | + | 0.253379i | \(0.918458\pi\) | |||||||
\(500\) | −23.1215 | + | 16.7987i | −1.03402 | + | 0.751262i | ||||
\(501\) | −25.7966 | + | 18.7424i | −1.15251 | + | 0.837347i | ||||
\(502\) | −21.0484 | − | 64.7803i | −0.939435 | − | 2.89129i | ||||
\(503\) | 7.07731 | − | 21.7817i | 0.315561 | − | 0.971198i | −0.659961 | − | 0.751300i | \(-0.729427\pi\) |
0.975523 | − | 0.219899i | \(-0.0705727\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.8818 | −1.32972 | ||||||||
\(506\) | 54.0542 | + | 7.30014i | 2.40300 | + | 0.324531i | ||||
\(507\) | −20.3429 | −0.903460 | ||||||||
\(508\) | 26.3259 | + | 19.1269i | 1.16803 | + | 0.848620i | ||||
\(509\) | 7.44685 | − | 22.9191i | 0.330076 | − | 1.01587i | −0.639021 | − | 0.769189i | \(-0.720660\pi\) |
0.969097 | − | 0.246680i | \(-0.0793397\pi\) | |||||||
\(510\) | 4.86218 | + | 14.9643i | 0.215301 | + | 0.662629i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 34.4547 | − | 25.0328i | 1.52270 | − | 1.10631i | ||||
\(513\) | −10.2744 | − | 31.6215i | −0.453628 | − | 1.39612i | ||||
\(514\) | 21.7001 | − | 66.7859i | 0.957149 | − | 2.94580i | ||||
\(515\) | −2.61662 | − | 1.90108i | −0.115302 | − | 0.0837717i | ||||
\(516\) | 57.5550 | 2.53372 | ||||||||
\(517\) | −0.358897 | − | 1.97320i | −0.0157843 | − | 0.0867813i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.8430 | − | 13.6903i | −0.827117 | − | 0.600936i | ||||
\(520\) | 3.60159 | − | 11.0846i | 0.157940 | − | 0.486090i | ||||
\(521\) | 10.3538 | + | 31.8658i | 0.453610 | + | 1.39607i | 0.872760 | + | 0.488150i | \(0.162328\pi\) |
−0.419150 | + | 0.907917i | \(0.637672\pi\) | |||||||
\(522\) | −3.48626 | + | 2.53292i | −0.152589 | + | 0.110863i | ||||
\(523\) | −25.2068 | + | 18.3138i | −1.10222 | + | 0.800808i | −0.981421 | − | 0.191869i | \(-0.938545\pi\) |
−0.120798 | + | 0.992677i | \(0.538545\pi\) | |||||||
\(524\) | 6.06524 | + | 18.6669i | 0.264961 | + | 0.815466i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.2987 | − | 20.5602i | −1.23388 | − | 0.896467i | ||||
\(527\) | −3.17983 | −0.138516 | ||||||||
\(528\) | 17.5226 | + | 16.7399i | 0.762572 | + | 0.728510i | ||||
\(529\) | 21.4500 | 0.932608 | ||||||||
\(530\) | −67.9548 | − | 49.3721i | −2.95177 | − | 2.14459i | ||||
\(531\) | 0.199956 | − | 0.615402i | 0.00867736 | − | 0.0267062i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.12215 | + | 2.26838i | −0.135235 | + | 0.0982543i | ||||
\(534\) | −2.25453 | + | 1.63801i | −0.0975629 | + | 0.0708836i | ||||
\(535\) | 7.09413 | + | 21.8335i | 0.306706 | + | 0.943944i | ||||
\(536\) | −9.81813 | + | 30.2171i | −0.424079 | + | 1.30518i | ||||
\(537\) | 6.10552 | + | 4.43592i | 0.263473 | + | 0.191424i | ||||
\(538\) | 59.6793 | 2.57296 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −77.4898 | −3.33463 | ||||||||
\(541\) | −18.2896 | − | 13.2881i | −0.786330 | − | 0.571302i | 0.120542 | − | 0.992708i | \(-0.461537\pi\) |
−0.906872 | + | 0.421406i | \(0.861537\pi\) | |||||||
\(542\) | −5.67866 | + | 17.4771i | −0.243919 | + | 0.750707i | ||||
\(543\) | −4.95402 | − | 15.2469i | −0.212598 | − | 0.654308i | ||||
\(544\) | −0.785754 | + | 0.570884i | −0.0336889 | + | 0.0244764i | ||||
\(545\) | 11.5694 | − | 8.40563i | 0.495577 | − | 0.360058i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.48072 | + | 26.1010i | −0.362610 | + | 1.11600i | 0.588855 | + | 0.808239i | \(0.299579\pi\) |
−0.951464 | + | 0.307759i | \(0.900421\pi\) | |||||||
\(548\) | 72.2981 | + | 52.5277i | 3.08842 | + | 2.24387i | ||||
\(549\) | 2.61959 | 0.111801 | ||||||||
\(550\) | −24.8919 | + | 51.7415i | −1.06140 | + | 2.20627i | ||||
\(551\) | −27.7891 | −1.18386 | ||||||||
\(552\) | 44.8808 | + | 32.6078i | 1.91025 | + | 1.38788i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −14.6271 | − | 45.0174i | −0.621444 | − | 1.91261i | ||||
\(555\) | 1.99563 | − | 1.44991i | 0.0847097 | − | 0.0615452i | ||||
\(556\) | −65.4773 | + | 47.5721i | −2.77686 | + | 2.01750i | ||||
\(557\) | −9.34788 | − | 28.7698i | −0.396082 | − | 1.21902i | −0.928115 | − | 0.372293i | \(-0.878572\pi\) |
0.532033 | − | 0.846724i | \(-0.321428\pi\) | |||||||
\(558\) | 0.814168 | − | 2.50575i | 0.0344665 | − | 0.106077i | ||||
\(559\) | −4.60574 | − | 3.34626i | −0.194802 | − | 0.141532i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.41249 | + | 4.21540i | 0.186296 | + | 0.177974i | ||||
\(562\) | −4.68834 | −0.197766 | ||||||||
\(563\) | 6.03716 | + | 4.38625i | 0.254436 | + | 0.184858i | 0.707690 | − | 0.706523i | \(-0.249737\pi\) |
−0.453255 | + | 0.891381i | \(0.649737\pi\) | |||||||
\(564\) | 1.23504 | − | 3.80105i | 0.0520044 | − | 0.160053i | ||||
\(565\) | −20.1677 | − | 62.0698i | −0.848461 | − | 2.61129i | ||||
\(566\) | 14.4718 | − | 10.5144i | 0.608297 | − | 0.441954i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.60815 | − | 26.4932i | −0.361190 | − | 1.11163i | ||||
\(569\) | 11.0159 | − | 33.9036i | 0.461812 | − | 1.42131i | −0.401136 | − | 0.916019i | \(-0.631384\pi\) |
0.862948 | − | 0.505293i | \(-0.168616\pi\) | |||||||
\(570\) | −68.0153 | − | 49.4160i | −2.84885 | − | 2.06981i | ||||
\(571\) | 25.8902 | 1.08347 | 0.541737 | − | 0.840548i | \(-0.317767\pi\) | ||||
0.541737 | + | 0.840548i | \(0.317767\pi\) | |||||||
\(572\) | −1.58492 | − | 8.71382i | −0.0662689 | − | 0.364343i | ||||
\(573\) | 16.0880 | 0.672087 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.4592 | + | 44.5010i | −0.602992 | + | 1.85582i | ||||
\(576\) | 0.817352 | + | 2.51555i | 0.0340563 | + | 0.104815i | ||||
\(577\) | 6.60467 | − | 4.79857i | 0.274956 | − | 0.199767i | −0.441758 | − | 0.897134i | \(-0.645645\pi\) |
0.716714 | + | 0.697367i | \(0.245645\pi\) | |||||||
\(578\) | 31.3451 | − | 22.7735i | 1.30378 | − | 0.947254i | ||||
\(579\) | 1.85332 | + | 5.70394i | 0.0770215 | + | 0.237048i | ||||
\(580\) | −20.0136 | + | 61.5955i | −0.831020 | + | 2.55762i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 59.3048 | 2.45826 | ||||||||
\(583\) | −32.2843 | − | 4.36008i | −1.33708 | − | 0.180576i | ||||
\(584\) | −34.4653 | −1.42619 | ||||||||
\(585\) | 0.700350 | + | 0.508834i | 0.0289559 | + | 0.0210377i | ||||
\(586\) | 2.49333 | − | 7.67370i | 0.102999 | − | 0.316997i | ||||
\(587\) | 3.85140 | + | 11.8534i | 0.158964 | + | 0.489242i | 0.998541 | − | 0.0539994i | \(-0.0171969\pi\) |
−0.839577 | + | 0.543241i | \(0.817197\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.7456 | − | 9.98673i | 0.566376 | − | 0.411496i | ||||
\(590\) | −4.47664 | − | 13.7777i | −0.184300 | − | 0.567218i | ||||
\(591\) | 2.95991 | − | 9.10967i | 0.121754 | − | 0.374722i | ||||
\(592\) | 1.60659 | + | 1.16725i | 0.0660304 | + | 0.0479739i | ||||
\(593\) | 23.6707 | 0.972037 | 0.486019 | − | 0.873948i | \(-0.338449\pi\) | ||||
0.486019 | + | 0.873948i | \(0.338449\pi\) | |||||||
\(594\) | −39.4147 | + | 21.2303i | −1.61720 | + | 0.871088i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.4497 | − | 7.59212i | −0.428034 | − | 0.310985i | ||||
\(597\) | −5.74211 | + | 17.6724i | −0.235009 | + | 0.723283i | ||||
\(598\) | −3.32241 | − | 10.2253i | −0.135863 | − | 0.418144i | ||||
\(599\) | −31.5362 | + | 22.9124i | −1.28853 | + | 0.936175i | −0.999775 | − | 0.0212271i | \(-0.993243\pi\) |
−0.288759 | + | 0.957402i | \(0.593243\pi\) | |||||||
\(600\) | −47.2446 | + | 34.3252i | −1.92875 | + | 1.40132i | ||||
\(601\) | −9.44078 | − | 29.0557i | −0.385097 | − | 1.18521i | −0.936410 | − | 0.350909i | \(-0.885873\pi\) |
0.551312 | − | 0.834299i | \(-0.314127\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.90919 | − | 1.38711i | −0.0777483 | − | 0.0564875i | ||||
\(604\) | 36.4690 | 1.48390 | ||||||||
\(605\) | 1.74132 | + | 38.0943i | 0.0707946 | + | 1.54875i | ||||
\(606\) | −34.4030 | −1.39753 | ||||||||
\(607\) | 30.4330 | + | 22.1109i | 1.23524 | + | 0.897454i | 0.997272 | − | 0.0738195i | \(-0.0235189\pi\) |
0.237967 | + | 0.971273i | \(0.423519\pi\) | |||||||
\(608\) | 1.60366 | − | 4.93555i | 0.0650369 | − | 0.200163i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 47.4470 | − | 34.4723i | 1.92107 | − | 1.39574i | ||||
\(611\) | −0.319825 | + | 0.232367i | −0.0129387 | + | 0.00940055i | ||||
\(612\) | −0.548269 | − | 1.68740i | −0.0221625 | − | 0.0682090i | ||||
\(613\) | 5.44711 | − | 16.7645i | 0.220007 | − | 0.677111i | −0.778754 | − | 0.627330i | \(-0.784148\pi\) |
0.998760 | − | 0.0497807i | \(-0.0158522\pi\) | |||||||
\(614\) | 63.0860 | + | 45.8346i | 2.54594 | + | 1.84974i | ||||
\(615\) | 33.1125 | 1.33522 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −44.4849 | −1.79089 | −0.895447 | − | 0.445168i | \(-0.853144\pi\) | ||||
−0.895447 | + | 0.445168i | \(0.853144\pi\) | |||||||
\(618\) | −3.01252 | − | 2.18872i | −0.121181 | − | 0.0880433i | ||||
\(619\) | 1.91722 | − | 5.90058i | 0.0770594 | − | 0.237164i | −0.905105 | − | 0.425188i | \(-0.860208\pi\) |
0.982165 | + | 0.188023i | \(0.0602081\pi\) | |||||||
\(620\) | −12.2364 | − | 37.6599i | −0.491427 | − | 1.51246i | ||||
\(621\) | −29.5155 | + | 21.4443i | −1.18442 | + | 0.860529i | ||||
\(622\) | −18.0371 | + | 13.1047i | −0.723220 | + | 0.525450i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.47610 | − | 4.54297i | 0.0590913 | − | 0.181864i | ||||
\(625\) | 8.76619 | + | 6.36901i | 0.350647 | + | 0.254760i | ||||
\(626\) | −35.7652 | −1.42947 | ||||||||
\(627\) | −32.3131 | − | 4.36396i | −1.29046 | − | 0.174280i | ||||
\(628\) | −4.65531 | −0.185767 | ||||||||
\(629\) | 0.404567 | + | 0.293935i | 0.0161312 | + | 0.0117200i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.8457 | + | 42.6128i | 0.551190 | + | 1.69639i | 0.705799 | + | 0.708412i | \(0.250588\pi\) |
−0.154609 | + | 0.987976i | \(0.549412\pi\) | |||||||
\(632\) | −11.0407 | + | 8.02155i | −0.439176 | + | 0.319080i | ||||
\(633\) | −11.4210 | + | 8.29785i | −0.453944 | + | 0.329810i | ||||
\(634\) | −14.0389 | − | 43.2072i | −0.557554 | − | 1.71598i | ||||
\(635\) | −8.53418 | + | 26.2655i | −0.338669 | + | 1.04231i | ||||
\(636\) | −52.5210 | − | 38.1587i | −2.08259 | − | 1.51309i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.69585 | + | 36.8134i | 0.265091 | + | 1.45746i | ||||
\(639\) | 2.06906 | 0.0818507 | ||||||||
\(640\) | 52.6982 | + | 38.2875i | 2.08308 | + | 1.51345i | ||||
\(641\) | −3.17534 | + | 9.77271i | −0.125419 | + | 0.385999i | −0.993977 | − | 0.109588i | \(-0.965047\pi\) |
0.868559 | + | 0.495587i | \(0.165047\pi\) | |||||||
\(642\) | 8.16749 | + | 25.1370i | 0.322345 | + | 0.992076i | ||||
\(643\) | −13.3039 | + | 9.66588i | −0.524656 | + | 0.381185i | −0.818355 | − | 0.574713i | \(-0.805114\pi\) |
0.293699 | + | 0.955898i | \(0.405114\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.0945 | + | 46.4561i | 0.594346 | + | 1.82921i | ||||
\(646\) | 5.26675 | − | 16.2094i | 0.207218 | − | 0.637750i | ||||
\(647\) | −21.8181 | − | 15.8518i | −0.857758 | − | 0.623197i | 0.0695163 | − | 0.997581i | \(-0.477854\pi\) |
−0.927274 | + | 0.374383i | \(0.877854\pi\) | |||||||
\(648\) | −39.6399 | −1.55720 | ||||||||
\(649\) | −4.06261 | − | 3.88115i | −0.159471 | − | 0.152348i | ||||
\(650\) | 11.3178 | 0.443921 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.39623 | + | 19.6856i | −0.250496 | + | 0.770947i | ||||
\(653\) | 2.19588 | + | 6.75823i | 0.0859315 | + | 0.264470i | 0.984784 | − | 0.173780i | \(-0.0555983\pi\) |
−0.898853 | + | 0.438250i | \(0.855598\pi\) | |||||||
\(654\) | 13.3198 | − | 9.67742i | 0.520846 | − | 0.378417i | ||||
\(655\) | −13.4765 | + | 9.79123i | −0.526569 | + | 0.382575i | ||||
\(656\) | 8.23757 | + | 25.3526i | 0.321623 | + | 0.989854i | ||||
\(657\) | 0.791062 | − | 2.43464i | 0.0308623 | − | 0.0949843i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32.6279 | −1.27100 | −0.635502 | − | 0.772099i | \(-0.719207\pi\) | ||||
−0.635502 | + | 0.772099i | \(0.719207\pi\) | |||||||
\(660\) | −32.9446 | + | 68.4801i | −1.28237 | + | 2.66559i | ||||
\(661\) | 33.8165 | 1.31531 | 0.657654 | − | 0.753320i | \(-0.271549\pi\) | ||||
0.657654 | + | 0.753320i | \(0.271549\pi\) | |||||||
\(662\) | 12.9247 | + | 9.39038i | 0.502334 | + | 0.364967i | ||||
\(663\) | 0.371708 | − | 1.14400i | 0.0144359 | − | 0.0444293i | ||||
\(664\) | −10.6418 | − | 32.7520i | −0.412981 | − | 1.27103i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.335211 | + | 0.243545i | −0.0129892 | + | 0.00943718i | ||||
\(667\) | 9.42266 | + | 29.0000i | 0.364847 | + | 1.12288i | ||||
\(668\) | 24.8752 | − | 76.5581i | 0.962452 | − | 2.96212i | ||||
\(669\) | 13.5259 | + | 9.82712i | 0.522940 | + | 0.379938i | ||||
\(670\) | −52.8335 | −2.04114 | ||||||||
\(671\) | 9.86094 | − | 20.4974i | 0.380677 | − | 0.791293i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.2138 | − | 13.9596i | −0.740638 | − | 0.538105i | 0.152273 | − | 0.988338i | \(-0.451341\pi\) |
−0.892911 | + | 0.450234i | \(0.851341\pi\) | |||||||
\(674\) | 4.76934 | − | 14.6785i | 0.183708 | − | 0.565395i | ||||
\(675\) | −11.8677 | − | 36.5250i | −0.456788 | − | 1.40585i | ||||
\(676\) | 41.5480 | − | 30.1864i | 1.59800 | − | 1.16102i | ||||
\(677\) | −36.9164 | + | 26.8213i | −1.41881 | + | 1.03083i | −0.426845 | + | 0.904325i | \(0.640375\pi\) |
−0.991966 | + | 0.126502i | \(0.959625\pi\) | |||||||
\(678\) | −23.2191 | − | 71.4611i | −0.891724 | − | 2.74445i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −16.4012 | − | 11.9162i | −0.628958 | − | 0.456965i | ||||
\(681\) | 21.4696 | 0.822717 | ||||||||
\(682\) | −16.5419 | − | 15.8030i | −0.633421 | − | 0.605128i | ||||
\(683\) | −28.8727 | −1.10478 | −0.552392 | − | 0.833585i | \(-0.686285\pi\) | ||||
−0.552392 | + | 0.833585i | \(0.686285\pi\) | |||||||
\(684\) | 7.66953 | + | 5.57224i | 0.293252 | + | 0.213060i | ||||
\(685\) | −23.4372 | + | 72.1322i | −0.895488 | + | 2.75603i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.26760 | + | 2.37405i | −0.124667 | + | 0.0905758i | ||||
\(688\) | −31.8141 | + | 23.1143i | −1.21290 | + | 0.881223i | ||||
\(689\) | 1.98434 | + | 6.10716i | 0.0755973 | + | 0.232664i | ||||
\(690\) | −28.5068 | + | 87.7348i | −1.08523 | + | 3.34001i | ||||
\(691\) | −21.8948 | − | 15.9075i | −0.832918 | − | 0.605150i | 0.0874654 | − | 0.996168i | \(-0.472123\pi\) |
−0.920383 | + | 0.391017i | \(0.872123\pi\) | |||||||
\(692\) | 58.7994 | 2.23522 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 56.0334 | 2.12700 | ||||||||
\(695\) | −55.5705 | − | 40.3743i | −2.10791 | − | 1.53148i | ||||
\(696\) | −11.7599 | + | 36.1933i | −0.445759 | + | 1.37191i | ||||
\(697\) | 2.07437 | + | 6.38424i | 0.0785722 | + | 0.241820i | ||||
\(698\) | 59.2583 | − | 43.0537i | 2.24296 | − | 1.62961i | ||||
\(699\) | 12.5716 | − | 9.13384i | 0.475503 | − | 0.345473i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.9020 | − | 36.6305i | 0.449531 | − | 1.38352i | −0.427905 | − | 0.903823i | \(-0.640748\pi\) |
0.877437 | − | 0.479692i | \(-0.159252\pi\) | |||||||
\(702\) | 7.13919 | + | 5.18693i | 0.269452 | + | 0.195768i | ||||
\(703\) | −2.67198 | −0.100776 | ||||||||
\(704\) | 22.7601 | + | 3.07380i | 0.857802 | + | 0.115848i | ||||
\(705\) | 3.39196 | 0.127748 | ||||||||
\(706\) | −13.6203 | − | 9.89572i | −0.512606 | − | 0.372430i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.45991 | − | 10.6485i | −0.130031 | − | 0.400195i | ||||
\(709\) | 1.53280 | − | 1.11364i | 0.0575654 | − | 0.0418237i | −0.558630 | − | 0.829417i | \(-0.688673\pi\) |
0.616196 | + | 0.787593i | \(0.288673\pi\) | |||||||
\(710\) | 37.4755 | − | 27.2276i | 1.40643 | − | 1.02183i | ||||
\(711\) | −0.313233 | − | 0.964032i | −0.0117472 | − | 0.0361540i | ||||
\(712\) | 1.10956 | − | 3.41487i | 0.0415824 | − | 0.127978i | ||||
\(713\) | −15.0827 | − | 10.9582i | −0.564851 | − | 0.410388i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.61778 | − | 3.56459i | 0.247491 | − | 0.133308i | ||||
\(716\) | −19.0522 | −0.712013 | ||||||||
\(717\) | −7.28241 | − | 5.29098i | −0.271967 | − | 0.197595i | ||||
\(718\) | −5.53379 | + | 17.0313i | −0.206519 | + | 0.635601i | ||||
\(719\) | −4.50461 | − | 13.8638i | −0.167994 | − | 0.517031i | 0.831251 | − | 0.555898i | \(-0.187625\pi\) |
−0.999244 | + | 0.0388664i | \(0.987625\pi\) | |||||||
\(720\) | 4.83766 | − | 3.51477i | 0.180289 | − | 0.130988i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13.6582 | + | 42.0357i | 0.508307 | + | 1.56441i | ||||
\(723\) | −7.51038 | + | 23.1146i | −0.279314 | + | 0.859640i | ||||
\(724\) | 32.7426 | + | 23.7889i | 1.21687 | + | 0.884107i | ||||
\(725\) | −32.0984 | −1.19210 | ||||||||
\(726\) | 2.00478 | + | 43.8580i | 0.0744044 | + | 1.62772i | ||||
\(727\) | −4.04780 | −0.150125 | −0.0750623 | − | 0.997179i | \(-0.523916\pi\) | ||||
−0.0750623 | + | 0.997179i | \(0.523916\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.11803 | − | 28.0624i | 0.337705 | − | 1.03935i | ||||
\(730\) | −17.7104 | − | 54.5069i | −0.655490 | − | 2.01739i | ||||
\(731\) | −8.01135 | + | 5.82058i | −0.296310 | + | 0.215282i | ||||
\(732\) | 36.6709 | − | 26.6430i | 1.35540 | − | 0.984752i | ||||
\(733\) | 7.26226 | + | 22.3509i | 0.268238 | + | 0.825551i | 0.990930 | + | 0.134381i | \(0.0429045\pi\) |
−0.722692 | + | 0.691170i | \(0.757095\pi\) | |||||||
\(734\) | 27.6980 | − | 85.2457i | 1.02235 | − | 3.14648i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.69437 | −0.209897 | ||||||||
\(737\) | −18.0404 | + | 9.71726i | −0.664527 | + | 0.357940i | ||||
\(738\) | −5.56199 | −0.204740 | ||||||||
\(739\) | 26.4376 | + | 19.2080i | 0.972522 | + | 0.706578i | 0.956025 | − | 0.293286i | \(-0.0947487\pi\) |
0.0164968 | + | 0.999864i | \(0.494749\pi\) | |||||||
\(740\) | −1.92435 | + | 5.92254i | −0.0707405 | + | 0.217717i | ||||
\(741\) | 1.98610 | + | 6.11260i | 0.0729614 | + | 0.224552i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.6479 | − | 10.6423i | 0.537379 | − | 0.390429i | −0.285731 | − | 0.958310i | \(-0.592237\pi\) |
0.823111 | + | 0.567881i | \(0.192237\pi\) | |||||||
\(744\) | −7.19009 | − | 22.1288i | −0.263602 | − | 0.811282i | ||||
\(745\) | 3.38750 | − | 10.4257i | 0.124108 | − | 0.381967i | ||||
\(746\) | 28.5202 | + | 20.7211i | 1.04420 | + | 0.758655i | ||||
\(747\) | 2.55787 | 0.0935874 | ||||||||
\(748\) | −15.2671 | − | 2.06186i | −0.558222 | − | 0.0753892i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −22.5922 | − | 16.4142i | −0.824949 | − | 0.599361i | ||||
\(751\) | 2.82552 | − | 8.69605i | 0.103105 | − | 0.317323i | −0.886176 | − | 0.463348i | \(-0.846648\pi\) |
0.989281 | + | 0.146025i | \(0.0466479\pi\) | |||||||
\(752\) | 0.843835 | + | 2.59706i | 0.0307715 | + | 0.0947049i | ||||
\(753\) | 36.1460 | − | 26.2616i | 1.31723 | − | 0.957025i | ||||
\(754\) | 5.96689 | − | 4.33520i | 0.217301 | − | 0.157879i | ||||
\(755\) | 9.56444 | + | 29.4363i | 0.348086 | + | 1.07130i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.3077 | − | 27.8322i | −1.39232 | − | 1.01158i | −0.995607 | − | 0.0936338i | \(-0.970152\pi\) |
−0.396710 | − | 0.917944i | \(-0.629848\pi\) | |||||||
\(758\) | −6.27851 | −0.228046 | ||||||||
\(759\) | 6.40253 | + | 35.2008i | 0.232397 | + | 1.27771i | ||||
\(760\) | 108.323 | 3.92927 | ||||||||
\(761\) | 2.78972 | + | 2.02685i | 0.101127 | + | 0.0734732i | 0.637200 | − | 0.770699i | \(-0.280093\pi\) |
−0.536073 | + | 0.844172i | \(0.680093\pi\) | |||||||
\(762\) | −9.82542 | + | 30.2395i | −0.355937 | + | 1.09546i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −32.8579 | + | 23.8727i | −1.18876 | + | 0.863683i | ||||
\(765\) | 1.21821 | − | 0.885081i | 0.0440444 | − | 0.0320002i | ||||
\(766\) | 17.6362 | + | 54.2787i | 0.637223 | + | 1.96117i | ||||
\(767\) | −0.342234 | + | 1.05329i | −0.0123573 | + | 0.0380320i | ||||
\(768\) | 42.5424 | + | 30.9089i | 1.53512 | + | 1.11533i | ||||
\(769\) | −34.9787 | −1.26137 | −0.630683 | − | 0.776041i | \(-0.717225\pi\) | ||||
−0.630683 | + | 0.776041i | \(0.717225\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 46.0622 | 1.65889 | ||||||||
\(772\) | −12.2491 | − | 8.89953i | −0.440856 | − | 0.320301i | ||||
\(773\) | −7.84266 | + | 24.1372i | −0.282081 | + | 0.868155i | 0.705178 | + | 0.709031i | \(0.250867\pi\) |
−0.987258 | + | 0.159125i | \(0.949133\pi\) | |||||||
\(774\) | −2.53546 | − | 7.80336i | −0.0911354 | − | 0.280486i | ||||
\(775\) | 15.8771 | − | 11.5354i | 0.570321 | − | 0.414363i | ||||
\(776\) | −61.8183 | + | 44.9137i | −2.21915 | + | 1.61231i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.0672 | − | 70.9934i | 0.826998 | − | 2.54524i | ||||
\(779\) | −29.0176 | − | 21.0825i | −1.03966 | − | 0.755358i | ||||
\(780\) | 14.9792 | 0.536340 | ||||||||
\(781\) | 7.78856 | − | 16.1897i | 0.278697 | − | 0.579312i | ||||
\(782\) | −18.7015 | −0.668765 | ||||||||
\(783\) | −20.2474 | − | 14.7106i | −0.723584 | − | 0.525715i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.22091 | − | 3.75758i | −0.0435762 | − | 0.134114i | ||||
\(786\) | −15.5155 | + | 11.2727i | −0.553419 | + | 0.402083i | ||||
\(787\) | 24.0725 | − | 17.4897i | 0.858090 | − | 0.623439i | −0.0692745 | − | 0.997598i | \(-0.522068\pi\) |
0.927365 | + | 0.374159i | \(0.122068\pi\) | |||||||
\(788\) | 7.47236 | + | 22.9976i | 0.266192 | + | 0.819255i | ||||
\(789\) | 7.09017 | − | 21.8213i | 0.252417 | − | 0.776859i | ||||
\(790\) | −18.3595 | − | 13.3389i | −0.653201 | − | 0.474578i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.82432 | − | 5.87075i | 0.100358 | − | 0.208608i | ||||
\(793\) | −4.48355 | −0.159215 | ||||||||
\(794\) | −45.2490 | − | 32.8753i | −1.60583 | − | 1.16670i | ||||
\(795\) | 17.0259 | − | 52.4004i | 0.603847 | − | 1.85845i | ||||
\(796\) | −14.4961 | − | 44.6144i | −0.513800 | − | 1.58132i | ||||
\(797\) | −5.05094 | + | 3.66972i | −0.178913 | + | 0.129988i | −0.673638 | − | 0.739062i | \(-0.735269\pi\) |
0.494724 | + | 0.869050i | \(0.335269\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.212493 | + | 0.653985i | 0.00751745 | + | 0.0231363i | ||||
\(800\) | 1.85234 | − | 5.70090i | 0.0654899 | − | 0.201557i | ||||
\(801\) | 0.215760 | + | 0.156759i | 0.00762350 | + | 0.00553879i | ||||
\(802\) | −40.0069 | −1.41269 | ||||||||
\(803\) | −16.0724 | − | 15.3545i | −0.567182 | − | 0.541848i | ||||
\(804\) | −40.8340 | −1.44010 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.39349 | + | 4.28871i | −0.0490834 | + | 0.151063i | ||||
\(807\) | 12.0968 | + | 37.2302i | 0.425829 | + | 1.31057i | ||||
\(808\) | 35.8611 | − | 26.0546i | 1.26159 | − | 0.916598i | ||||
\(809\) | −31.7022 | + | 23.0330i | −1.11459 | + | 0.809796i | −0.983380 | − | 0.181559i | \(-0.941886\pi\) |
−0.131209 | + | 0.991355i | \(0.541886\pi\) | |||||||
\(810\) | −20.3694 | − | 62.6905i | −0.715707 | − | 2.20272i | ||||
\(811\) | 3.82591 | − | 11.7749i | 0.134346 | − | 0.413474i | −0.861142 | − | 0.508365i | \(-0.830250\pi\) |
0.995488 | + | 0.0948906i | \(0.0302501\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.0539 | −0.422750 | ||||||||
\(814\) | 0.643819 | + | 3.53969i | 0.0225659 | + | 0.124066i | ||||
\(815\) | −17.5669 | −0.615341 | ||||||||
\(816\) | −6.72198 | − | 4.88381i | −0.235316 | − | 0.170967i | ||||
\(817\) | 16.3505 | − | 50.3216i | 0.572031 | − | 1.76053i | ||||
\(818\) | 26.7260 | + | 82.2541i | 0.934452 | + | 2.87595i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −67.6284 | + | 49.1349i | −2.36168 | + | 1.71586i | ||||
\(821\) | 14.7397 | + | 45.3642i | 0.514420 | + | 1.58322i | 0.784335 | + | 0.620337i | \(0.213004\pi\) |
−0.269916 | + | 0.962884i | \(0.586996\pi\) | |||||||
\(822\) | −26.9833 | + | 83.0459i | −0.941149 | + | 2.89656i | ||||
\(823\) | 11.7475 | + | 8.53507i | 0.409493 | + | 0.297514i | 0.773396 | − | 0.633923i | \(-0.218556\pi\) |
−0.363904 | + | 0.931437i | \(0.618556\pi\) | |||||||
\(824\) | 4.79779 | 0.167139 | ||||||||
\(825\) | −37.3239 | − | 5.04068i | −1.29945 | − | 0.175494i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.0287 | + | 18.1844i | 0.870335 | + | 0.632335i | 0.930677 | − | 0.365843i | \(-0.119219\pi\) |
−0.0603420 | + | 0.998178i | \(0.519219\pi\) | |||||||
\(828\) | 3.21448 | − | 9.89314i | 0.111711 | − | 0.343810i | ||||
\(829\) | −0.0265154 | − | 0.0816061i | −0.000920918 | − | 0.00283430i | 0.950595 | − | 0.310434i | \(-0.100474\pi\) |
−0.951516 | + | 0.307600i | \(0.900474\pi\) | |||||||
\(830\) | 46.3290 | − | 33.6600i | 1.60810 | − | 1.16835i | ||||
\(831\) | 25.1187 | − | 18.2498i | 0.871359 | − | 0.633080i | ||||
\(832\) | −1.39893 | − | 4.30548i | −0.0484993 | − | 0.149266i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −63.9784 | − | 46.4830i | −2.21539 | − | 1.60958i | ||||
\(835\) | 68.3185 | 2.36426 | ||||||||
\(836\) | 72.4713 | − | 39.0358i | 2.50647 | − | 1.35008i | ||||
\(837\) | 15.3018 | 0.528907 | ||||||||
\(838\) | 56.4030 | + | 40.9792i | 1.94841 | + | 1.41560i | ||||
\(839\) | −3.30355 | + | 10.1673i | −0.114051 | + | 0.351014i | −0.991748 | − | 0.128203i | \(-0.959079\pi\) |
0.877697 | + | 0.479217i | \(0.159079\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.53883 | − | 4.75074i | 0.225477 | − | 0.163819i | ||||
\(842\) | 27.5290 | − | 20.0010i | 0.948713 | − | 0.689281i | ||||
\(843\) | −0.950314 | − | 2.92477i | −0.0327306 | − | 0.100734i | ||||
\(844\) | 11.0131 | − | 33.8948i | 0.379086 | − | 1.16671i | ||||
\(845\) | 35.2617 | + | 25.6191i | 1.21304 | + | 0.881325i | ||||
\(846\) | −0.569756 | −0.0195886 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 44.3561 | 1.52319 | ||||||||
\(849\) | 9.49270 | + | 6.89685i | 0.325789 | + | 0.236699i | ||||
\(850\) | 6.08347 | − | 18.7230i | 0.208661 | − | 0.642193i | ||||
\(851\) | 0.906008 | + | 2.78841i | 0.0310576 | + | 0.0955854i | ||||
\(852\) | 28.9641 | − | 21.0437i | 0.992295 | − | 0.720944i | ||||
\(853\) | 17.1514 | − | 12.4612i | 0.587252 | − | 0.426664i | −0.254079 | − | 0.967183i | \(-0.581772\pi\) |
0.841331 | + | 0.540520i | \(0.181772\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.48626 | + | 7.65192i | −0.0850283 | + | 0.261690i | ||||
\(856\) | −27.5508 | − | 20.0168i | −0.941666 | − | 0.684160i | ||||
\(857\) | 9.45359 | 0.322929 | 0.161464 | − | 0.986879i | \(-0.448378\pi\) | ||||
0.161464 | + | 0.986879i | \(0.448378\pi\) | |||||||
\(858\) | 7.61907 | − | 4.10392i | 0.260111 | − | 0.140106i | ||||
\(859\) | 38.8261 | 1.32473 | 0.662365 | − | 0.749181i | \(-0.269553\pi\) | ||||
0.662365 | + | 0.749181i | \(0.269553\pi\) | |||||||
\(860\) | −99.7640 | − | 72.4828i | −3.40192 | − | 2.47164i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21.4730 | + | 66.0869i | 0.731372 | + | 2.25093i | ||||
\(863\) | 30.4228 | − | 22.1034i | 1.03560 | − | 0.752410i | 0.0661810 | − | 0.997808i | \(-0.478919\pi\) |
0.969423 | + | 0.245398i | \(0.0789185\pi\) | |||||||
\(864\) | 3.78115 | − | 2.74717i | 0.128637 | − | 0.0934606i | ||||
\(865\) | 15.4208 | + | 47.4605i | 0.524324 | + | 1.61370i | ||||
\(866\) | −10.8084 | + | 33.2647i | −0.367283 | + | 1.13038i | ||||
\(867\) | 20.5606 | + | 14.9381i | 0.698274 | + | 0.507326i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.72231 | − | 1.17797i | −0.295884 | − | 0.0399599i | ||||
\(870\) | −63.2828 | −2.14549 | ||||||||
\(871\) | 3.26767 | + | 2.37410i | 0.110721 | + | 0.0804433i | ||||
\(872\) | −6.55530 | + | 20.1752i | −0.221991 | + | 0.683217i | ||||
\(873\) | −1.75383 | − | 5.39773i | −0.0593582 | − | 0.182686i | ||||
\(874\) | 80.8416 | − | 58.7348i | 2.73451 | − | 1.98674i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −13.6880 | − | 42.1274i | −0.462475 | − | 1.42335i | ||||
\(877\) | 6.80103 | − | 20.9314i | 0.229654 | − | 0.706804i | −0.768131 | − | 0.640293i | \(-0.778813\pi\) |
0.997786 | − | 0.0665113i | \(-0.0211869\pi\) | |||||||
\(878\) | 55.9145 | + | 40.6243i | 1.88702 | + | 1.37100i | ||||
\(879\) | 5.29254 | 0.178513 | ||||||||
\(880\) | −9.29140 | − | 51.0836i | −0.313213 | − | 1.72203i | ||||
\(881\) | 6.92969 | 0.233467 | 0.116734 | − | 0.993163i | \(-0.462758\pi\) | ||||
0.116734 | + | 0.993163i | \(0.462758\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.0834 | − | 40.2666i | 0.440292 | − | 1.35508i | −0.447274 | − | 0.894397i | \(-0.647605\pi\) |
0.887566 | − | 0.460681i | \(-0.152395\pi\) | |||||||
\(884\) | 0.938386 | + | 2.88806i | 0.0315613 | + | 0.0971358i | ||||
\(885\) | 7.68764 | − | 5.58540i | 0.258417 | − | 0.187751i | ||||
\(886\) | −34.5982 | + | 25.1371i | −1.16235 | + | 0.844496i | ||||
\(887\) | −2.48959 | − | 7.66216i | −0.0835921 | − | 0.257270i | 0.900521 | − | 0.434812i | \(-0.143185\pi\) |
−0.984113 | + | 0.177542i | \(0.943185\pi\) | |||||||
\(888\) | −1.13074 | + | 3.48006i | −0.0379452 | + | 0.116783i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.97077 | 0.200141 | ||||||||
\(891\) | −18.4855 | − | 17.6598i | −0.619286 | − | 0.591625i | ||||
\(892\) | −42.2072 | −1.41320 | ||||||||
\(893\) | −2.97248 | − | 2.15964i | −0.0994703 | − | 0.0722694i | ||||
\(894\) | 3.90004 | − | 12.0031i | 0.130437 | − | 0.401443i | ||||
\(895\) | −4.99666 | − | 15.3781i | −0.167020 | − | 0.514034i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.70550 | − | 4.14529i | 0.190501 | − | 0.138407i | ||||
\(898\) | −22.5031 | − | 69.2575i | −0.750939 | − | 2.31115i | ||||
\(899\) | 3.95206 | − | 12.1632i | 0.131808 | − | 0.405665i | ||||
\(900\) | 8.85884 | + | 6.43633i | 0.295295 | + | 0.214544i | ||||
\(901\) | 11.1697 | 0.372115 | ||||||||
\(902\) | −20.9370 | + | 43.5207i | −0.697127 | + | 1.44908i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 78.3232 | + | 56.9051i | 2.60499 | + | 1.89264i | ||||
\(905\) | −10.6143 | + | 32.6674i | −0.352831 | + | 1.08590i | ||||
\(906\) | 11.0116 | + | 33.8901i | 0.365835 | + | 1.12592i | ||||
\(907\) | −2.34153 | + | 1.70122i | −0.0777492 | + | 0.0564881i | −0.625981 | − | 0.779838i | \(-0.715301\pi\) |
0.548232 | + | 0.836327i | \(0.315301\pi\) | |||||||
\(908\) | −43.8492 | + | 31.8583i | −1.45519 | + | 1.05725i | ||||
\(909\) | 1.01740 | + | 3.13125i | 0.0337452 | + | 0.103857i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.3826 | + | 11.9026i | 0.542779 | + | 0.394352i | 0.825116 | − | 0.564963i | \(-0.191110\pi\) |
−0.282337 | + | 0.959315i | \(0.591110\pi\) | |||||||
\(912\) | 44.3956 | 1.47008 | ||||||||
\(913\) | 9.62858 | − | 20.0144i | 0.318659 | − | 0.662380i | ||||
\(914\) | 23.9205 | 0.791220 | ||||||||
\(915\) | 31.1225 | + | 22.6118i | 1.02888 | + | 0.747524i | ||||
\(916\) | 3.15089 | − | 9.69745i | 0.104108 | − | 0.320413i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 12.4181 | − | 9.02229i | 0.409859 | − | 0.297780i | ||||
\(919\) | −15.1498 | + | 11.0069i | −0.499744 | + | 0.363085i | −0.808919 | − | 0.587920i | \(-0.799947\pi\) |
0.309175 | + | 0.951005i | \(0.399947\pi\) | |||||||
\(920\) | −36.7297 | − | 113.042i | −1.21094 | − | 3.72690i | ||||
\(921\) | −15.8060 | + | 48.6460i | −0.520827 | + | 1.60294i | ||||
\(922\) | −38.3592 | − | 27.8696i | −1.26329 | − | 0.917836i | ||||
\(923\) | −3.54128 | −0.116563 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.08632 | −0.101478 | ||||||||
\(926\) | −40.9756 | − | 29.7705i | −1.34654 | − | 0.978320i | ||||
\(927\) | −0.110121 | + | 0.338917i | −0.00361684 | + | 0.0111315i | ||||
\(928\) | −1.20711 | − | 3.71511i | −0.0396254 | − | 0.121954i | ||||
\(929\) | −36.6243 | + | 26.6091i | −1.20160 | + | 0.873016i | −0.994441 | − | 0.105291i | \(-0.966423\pi\) |
−0.207162 | + | 0.978307i | \(0.566423\pi\) | |||||||
\(930\) | 31.3020 | − | 22.7423i | 1.02643 | − | 0.745748i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −12.1226 | + | 37.3096i | −0.397090 | + | 1.22212i | ||||
\(933\) | −11.8313 | − | 8.59592i | −0.387338 | − | 0.281418i | ||||
\(934\) | −83.0584 | −2.71775 | ||||||||
\(935\) | −2.33974 | − | 12.8638i | −0.0765177 | − | 0.420690i | ||||
\(936\) | −1.28415 | −0.0419738 | ||||||||
\(937\) | 23.8336 | + | 17.3161i | 0.778609 | + | 0.565692i | 0.904561 | − | 0.426344i | \(-0.140199\pi\) |
−0.125952 | + | 0.992036i | \(0.540199\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.24952 | − | 22.3117i | −0.236579 | − | 0.728115i | ||||
\(940\) | −6.92767 | + | 5.03325i | −0.225956 | + | 0.164167i | ||||
\(941\) | 47.1128 | − | 34.2294i | 1.53583 | − | 1.11585i | 0.582950 | − | 0.812508i | \(-0.301898\pi\) |
0.952882 | − | 0.303340i | \(-0.0981017\pi\) | |||||||
\(942\) | −1.40564 | − | 4.32611i | −0.0457982 | − | 0.140952i | ||||
\(943\) | −12.1619 | + | 37.4305i | −0.396046 | + | 1.21891i | ||||
\(944\) | 6.18897 | + | 4.49655i | 0.201434 | + | 0.146350i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −70.6028 | − | 9.53508i | −2.29550 | − | 0.310012i | ||||
\(947\) | 45.3642 | 1.47414 | 0.737069 | − | 0.675818i | \(-0.236209\pi\) | ||||
0.737069 | + | 0.675818i | \(0.236209\pi\) | |||||||
\(948\) | −14.1897 | − | 10.3094i | −0.460859 | − | 0.334834i | ||||
\(949\) | −1.35394 | + | 4.16699i | −0.0439506 | + | 0.135266i | ||||
\(950\) | 32.5051 | + | 100.040i | 1.05460 | + | 3.24574i | ||||
\(951\) | 24.1087 | − | 17.5160i | 0.781777 | − | 0.567994i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.7740 | − | 39.3143i | −0.413790 | − | 1.27352i | −0.913328 | − | 0.407224i | \(-0.866497\pi\) |
0.499538 | − | 0.866292i | \(-0.333503\pi\) | |||||||
\(954\) | −2.85989 | + | 8.80184i | −0.0925924 | + | 0.284970i | ||||
\(955\) | −27.8864 | − | 20.2607i | −0.902384 | − | 0.655620i | ||||
\(956\) | 22.7247 | 0.734968 | ||||||||
\(957\) | −21.6084 | + | 11.6391i | −0.698500 | + | 0.376239i | ||||
\(958\) | −34.9555 | −1.12936 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −12.0031 | + | 36.9417i | −0.387398 | + | 1.19229i | ||||
\(961\) | −7.16322 | − | 22.0461i | −0.231071 | − | 0.711165i | ||||
\(962\) | 0.573728 | − | 0.416838i | 0.0184977 | − | 0.0134394i | ||||
\(963\) | 2.04635 | − | 1.48676i | 0.0659426 | − | 0.0479101i | ||||
\(964\) | −18.9601 | − | 58.3533i | −0.610665 | − | 1.87943i | ||||
\(965\) | 3.97085 | − | 12.2210i | 0.127826 | − | 0.393409i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.52818 | −0.209932 | −0.104966 | − | 0.994476i | \(-0.533473\pi\) | ||||
−0.104966 | + | 0.994476i | \(0.533473\pi\) | |||||||
\(968\) | −35.3050 | − | 44.1986i | −1.13475 | − | 1.42060i | ||||
\(969\) | 11.1796 | 0.359140 | ||||||||
\(970\) | −102.797 | − | 74.6864i | −3.30061 | − | 2.39803i | ||||
\(971\) | −8.91783 | + | 27.4462i | −0.286187 | + | 0.880792i | 0.699854 | + | 0.714286i | \(0.253248\pi\) |
−0.986040 | + | 0.166506i | \(0.946752\pi\) | |||||||
\(972\) | 4.97870 | + | 15.3229i | 0.159692 | + | 0.491482i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −55.3617 | + | 40.2226i | −1.77390 | + | 1.28882i | ||||
\(975\) | 2.29409 | + | 7.06048i | 0.0734697 | + | 0.226116i | ||||
\(976\) | −9.57027 | + | 29.4543i | −0.306337 | + | 0.942808i | ||||
\(977\) | 7.26864 | + | 5.28097i | 0.232544 | + | 0.168953i | 0.697955 | − | 0.716141i | \(-0.254093\pi\) |
−0.465411 | + | 0.885095i | \(0.654093\pi\) | |||||||
\(978\) | −20.2248 | −0.646718 | ||||||||
\(979\) | 2.03877 | − | 1.09816i | 0.0651593 | − | 0.0350973i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.27472 | − | 0.926136i | −0.0406986 | − | 0.0295692i | ||||
\(982\) | −2.62443 | + | 8.07717i | −0.0837490 | + | 0.257753i | ||||
\(983\) | −11.3971 | − | 35.0768i | −0.363512 | − | 1.11877i | −0.950908 | − | 0.309475i | \(-0.899847\pi\) |
0.587396 | − | 0.809300i | \(-0.300153\pi\) | |||||||
\(984\) | −39.7382 | + | 28.8715i | −1.26681 | + | 0.920390i | ||||
\(985\) | −16.6030 | + | 12.0628i | −0.529015 | + | 0.384352i | ||||
\(986\) | −3.96441 | − | 12.2012i | −0.126253 | − | 0.388566i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13.1267 | − | 9.53713i | −0.417617 | − | 0.303417i | ||||
\(989\) | −58.0583 | −1.84615 | ||||||||
\(990\) | 10.7359 | + | 1.44991i | 0.341209 | + | 0.0460811i | ||||
\(991\) | −2.98352 | −0.0947746 | −0.0473873 | − | 0.998877i | \(-0.515089\pi\) | ||||
−0.0473873 | + | 0.998877i | \(0.515089\pi\) | |||||||
\(992\) | 1.93220 | + | 1.40383i | 0.0613475 | + | 0.0445716i | ||||
\(993\) | −3.23826 | + | 9.96635i | −0.102763 | + | 0.316273i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32.2092 | − | 23.4013i | 1.02110 | − | 0.741872i | ||||
\(996\) | 35.8068 | − | 26.0152i | 1.13458 | − | 0.824322i | ||||
\(997\) | −19.4234 | − | 59.7790i | −0.615144 | − | 1.89322i | −0.399437 | − | 0.916760i | \(-0.630795\pi\) |
−0.215707 | − | 0.976458i | \(-0.569205\pi\) | |||||||
\(998\) | −1.97367 | + | 6.07434i | −0.0624755 | + | 0.192280i | ||||
\(999\) | −1.94683 | − | 1.41446i | −0.0615951 | − | 0.0447514i |
(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 | 539.2.f.d.246.1 | 8 | ||
7.2 | even | 3 | 539.2.q.b.312.1 | 16 | |||
7.3 | odd | 6 | 539.2.q.c.422.2 | 16 | |||
7.4 | even | 3 | 539.2.q.b.422.2 | 16 | |||
7.5 | odd | 6 | 539.2.q.c.312.1 | 16 | |||
7.6 | odd | 2 | 77.2.f.a.15.1 | ✓ | 8 | ||
11.3 | even | 5 | inner | 539.2.f.d.344.1 | 8 | ||
11.5 | even | 5 | 5929.2.a.bi.1.4 | 4 | |||
11.6 | odd | 10 | 5929.2.a.bb.1.1 | 4 | |||
21.20 | even | 2 | 693.2.m.g.631.2 | 8 | |||
77.3 | odd | 30 | 539.2.q.c.520.1 | 16 | |||
77.6 | even | 10 | 847.2.a.k.1.1 | 4 | |||
77.13 | even | 10 | 847.2.f.s.148.1 | 8 | |||
77.20 | odd | 10 | 847.2.f.p.148.2 | 8 | |||
77.25 | even | 15 | 539.2.q.b.520.1 | 16 | |||
77.27 | odd | 10 | 847.2.a.l.1.4 | 4 | |||
77.41 | even | 10 | 847.2.f.q.729.2 | 8 | |||
77.47 | odd | 30 | 539.2.q.c.410.2 | 16 | |||
77.48 | odd | 10 | 847.2.f.p.372.2 | 8 | |||
77.58 | even | 15 | 539.2.q.b.410.2 | 16 | |||
77.62 | even | 10 | 847.2.f.s.372.1 | 8 | |||
77.69 | odd | 10 | 77.2.f.a.36.1 | yes | 8 | ||
77.76 | even | 2 | 847.2.f.q.323.2 | 8 | |||
231.83 | odd | 10 | 7623.2.a.co.1.4 | 4 | |||
231.104 | even | 10 | 7623.2.a.ch.1.1 | 4 | |||
231.146 | even | 10 | 693.2.m.g.190.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.a.15.1 | ✓ | 8 | 7.6 | odd | 2 | ||
77.2.f.a.36.1 | yes | 8 | 77.69 | odd | 10 | ||
539.2.f.d.246.1 | 8 | 1.1 | even | 1 | trivial | ||
539.2.f.d.344.1 | 8 | 11.3 | even | 5 | inner | ||
539.2.q.b.312.1 | 16 | 7.2 | even | 3 | |||
539.2.q.b.410.2 | 16 | 77.58 | even | 15 | |||
539.2.q.b.422.2 | 16 | 7.4 | even | 3 | |||
539.2.q.b.520.1 | 16 | 77.25 | even | 15 | |||
539.2.q.c.312.1 | 16 | 7.5 | odd | 6 | |||
539.2.q.c.410.2 | 16 | 77.47 | odd | 30 | |||
539.2.q.c.422.2 | 16 | 7.3 | odd | 6 | |||
539.2.q.c.520.1 | 16 | 77.3 | odd | 30 | |||
693.2.m.g.190.2 | 8 | 231.146 | even | 10 | |||
693.2.m.g.631.2 | 8 | 21.20 | even | 2 | |||
847.2.a.k.1.1 | 4 | 77.6 | even | 10 | |||
847.2.a.l.1.4 | 4 | 77.27 | odd | 10 | |||
847.2.f.p.148.2 | 8 | 77.20 | odd | 10 | |||
847.2.f.p.372.2 | 8 | 77.48 | odd | 10 | |||
847.2.f.q.323.2 | 8 | 77.76 | even | 2 | |||
847.2.f.q.729.2 | 8 | 77.41 | even | 10 | |||
847.2.f.s.148.1 | 8 | 77.13 | even | 10 | |||
847.2.f.s.372.1 | 8 | 77.62 | even | 10 | |||
5929.2.a.bb.1.1 | 4 | 11.6 | odd | 10 | |||
5929.2.a.bi.1.4 | 4 | 11.5 | even | 5 | |||
7623.2.a.ch.1.1 | 4 | 231.104 | even | 10 | |||
7623.2.a.co.1.4 | 4 | 231.83 | odd | 10 |