Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, 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("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.76332905120\) |
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 | 323.2 | ||
Root | \(-0.762262 - 2.34600i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.323 |
Dual form | 847.2.f.q.729.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 | \(0.0372561\pi\) |
0.417964 | + | 0.908464i | \(0.362744\pi\) | |||||||
\(3\) | −0.500000 | + | 1.53884i | −0.288675 | + | 0.888451i | 0.696598 | + | 0.717462i | \(0.254696\pi\) |
−0.985273 | + | 0.170989i | \(0.945304\pi\) | |||||||
\(4\) | 1.26226 | + | 3.88484i | 0.631131 | + | 1.94242i | ||||
\(5\) | 2.80464 | − | 2.03769i | 1.25428 | − | 0.911284i | 0.255813 | − | 0.966726i | \(-0.417657\pi\) |
0.998462 | + | 0.0554418i | \(0.0176567\pi\) | |||||||
\(6\) | −3.22899 | + | 2.34600i | −1.31823 | + | 0.957751i | ||||
\(7\) | 0.309017 | + | 0.951057i | 0.116797 | + | 0.359466i | ||||
\(8\) | −1.58914 | + | 4.89086i | −0.561845 | + | 1.72918i | ||||
\(9\) | 0.309017 | + | 0.224514i | 0.103006 | + | 0.0748380i | ||||
\(10\) | 8.55150 | 2.70422 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −6.60929 | −1.90794 | ||||||||
\(13\) | −0.528896 | − | 0.384266i | −0.146689 | − | 0.106576i | 0.512020 | − | 0.858973i | \(-0.328897\pi\) |
−0.658709 | + | 0.752397i | \(0.728897\pi\) | |||||||
\(14\) | −0.762262 | + | 2.34600i | −0.203723 | + | 0.626995i | ||||
\(15\) | 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 | ||||
\(21\) | −1.61803 | −0.353084 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −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 | ||||
\(28\) | −3.30464 | + | 2.40097i | −0.624519 | + | 0.453740i | ||||
\(29\) | 1.41331 | + | 4.34973i | 0.262445 | + | 0.807724i | 0.992271 | + | 0.124090i | \(0.0396013\pi\) |
−0.729826 | + | 0.683633i | \(0.760399\pi\) | |||||||
\(30\) | −4.27575 | + | 13.1594i | −0.780641 | + | 2.40257i | ||||
\(31\) | −2.26226 | − | 1.64363i | −0.406314 | − | 0.295205i | 0.365794 | − | 0.930696i | \(-0.380798\pi\) |
−0.772108 | + | 0.635491i | \(0.780798\pi\) | |||||||
\(32\) | −0.854102 | −0.150985 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.80505 | −0.481063 | ||||||||
\(35\) | 2.80464 | + | 2.03769i | 0.474072 | + | 0.344433i | ||||
\(36\) | −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 | \(-0.0524943\pi\) | |||||||
\(42\) | −3.22899 | − | 2.34600i | −0.498245 | − | 0.361996i | ||||
\(43\) | −8.70820 | −1.32799 | −0.663994 | − | 0.747738i | \(-0.731140\pi\) | ||||
−0.663994 | + | 0.747738i | \(0.731140\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.32417 | 0.197396 | ||||||||
\(46\) | −13.3050 | − | 9.66666i | −1.96172 | − | 1.42527i | ||||
\(47\) | −0.186864 | + | 0.575107i | −0.0272569 | + | 0.0838880i | −0.963760 | − | 0.266772i | \(-0.914043\pi\) |
0.936503 | + | 0.350660i | \(0.114043\pi\) | |||||||
\(48\) | −2.25789 | − | 6.94907i | −0.325898 | − | 1.00301i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 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 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.14256 | −0.687203 | ||||||||
\(57\) | 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 | 0.979333 | − | 0.202256i | \(-0.0648273\pi\) |
−0.911180 | + | 0.412009i | \(0.864827\pi\) | |||||||
\(60\) | −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 | ||||
\(63\) | −0.118034 | + | 0.363271i | −0.0148709 | + | 0.0457679i | ||||
\(64\) | 5.60222 | + | 4.07025i | 0.700277 | + | 0.508781i | ||||
\(65\) | −2.26638 | −0.281110 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −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 | ||||
\(70\) | 2.64256 | + | 8.13296i | 0.315846 | + | 0.972074i | ||||
\(71\) | 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 | 0.701973 | − | 0.712204i | \(-0.252303\pi\) |
−0.460424 | + | 0.887699i | \(0.652303\pi\) | |||||||
\(80\) | −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 | \(0.180206\pi\) | |||||||
\(84\) | −2.04238 | − | 6.28581i | −0.222842 | − | 0.685838i | ||||
\(85\) | −1.21821 | + | 3.74926i | −0.132133 | + | 0.406665i | ||||
\(86\) | −17.3783 | − | 12.6261i | −1.87395 | − | 1.36151i | ||||
\(87\) | −7.40020 | −0.793384 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.698213 | −0.0740105 | −0.0370052 | − | 0.999315i | \(-0.511782\pi\) | ||||
−0.0370052 | + | 0.999315i | \(0.511782\pi\) | |||||||
\(90\) | 2.64256 | + | 1.91993i | 0.278550 | + | 0.202378i | ||||
\(91\) | 0.202020 | − | 0.621755i | 0.0211775 | − | 0.0651776i | ||||
\(92\) | −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 | 0.996145 | − | 0.0877234i | \(-0.0279592\pi\) |
0.224396 | + | 0.974498i | \(0.427959\pi\) | |||||||
\(98\) | −2.46673 | −0.249178 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 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 | 0.935848 | − | 0.352404i | \(-0.114636\pi\) |
−0.964255 | + | 0.264976i | \(0.914636\pi\) | |||||||
\(104\) | 2.71988 | − | 1.97611i | 0.266706 | − | 0.193773i | ||||
\(105\) | −4.53801 | + | 3.29706i | −0.442865 | + | 0.321760i | ||||
\(106\) | −7.48729 | − | 23.0435i | −0.727230 | − | 2.23818i | ||||
\(107\) | −2.04635 | + | 6.29801i | −0.197828 | + | 0.608851i | 0.802104 | + | 0.597184i | \(0.203714\pi\) |
−0.999932 | + | 0.0116671i | \(0.996286\pi\) | |||||||
\(108\) | −18.0835 | − | 13.1384i | −1.74008 | − | 1.26424i | ||||
\(109\) | 4.12507 | 0.395110 | 0.197555 | − | 0.980292i | \(-0.436700\pi\) | ||||
0.197555 | + | 0.980292i | \(0.436700\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.711544 | 0.0675368 | ||||||||
\(112\) | −3.65334 | − | 2.65431i | −0.345208 | − | 0.250809i | ||||
\(113\) | −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 | ||||
\(119\) | −0.919977 | − | 0.668402i | −0.0843341 | − | 0.0612723i | ||||
\(120\) | −28.8461 | −2.63328 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 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 | ||||
\(126\) | −0.762262 | + | 0.553816i | −0.0679077 | + | 0.0493378i | ||||
\(127\) | −6.44491 | + | 4.68250i | −0.571893 | + | 0.415505i | −0.835792 | − | 0.549045i | \(-0.814991\pi\) |
0.263899 | + | 0.964550i | \(0.414991\pi\) | |||||||
\(128\) | 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 | \(0.432683\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.07602 | 0.526858 | ||||||||
\(134\) | −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 | \(0.582385\pi\) | |||||||
\(140\) | −4.37592 | + | 13.4677i | −0.369833 | + | 1.13823i | ||||
\(141\) | −0.791567 | − | 0.575107i | −0.0666620 | − | 0.0484328i | ||||
\(142\) | 13.3620 | 1.12131 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.72487 | −0.143740 | ||||||||
\(145\) | 12.8272 | + | 9.31954i | 1.06524 | + | 0.773946i | ||||
\(146\) | 5.10867 | − | 15.7229i | 0.422796 | − | 1.30123i | ||||
\(147\) | −0.500000 | − | 1.53884i | −0.0412393 | − | 0.126922i | ||||
\(148\) | 1.45325 | − | 1.05584i | 0.119456 | − | 0.0867899i | ||||
\(149\) | 2.55820 | − | 1.85864i | 0.209576 | − | 0.152266i | −0.478046 | − | 0.878335i | \(-0.658655\pi\) |
0.687622 | + | 0.726069i | \(0.258655\pi\) | |||||||
\(150\) | 8.65604 | + | 26.6406i | 0.706763 | + | 2.17519i | ||||
\(151\) | −2.75892 | + | 8.49109i | −0.224518 | + | 0.690995i | 0.773822 | + | 0.633403i | \(0.218342\pi\) |
−0.998340 | + | 0.0575923i | \(0.981658\pi\) | |||||||
\(152\) | 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 | −0.936019 | − | 0.351949i | \(-0.885519\pi\) |
0.964126 | + | 0.265445i | \(0.0855189\pi\) | |||||||
\(158\) | 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 | ||||
\(161\) | −2.06024 | − | 6.34077i | −0.162370 | − | 0.499723i | ||||
\(162\) | 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 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.5187 | 1.28210 | ||||||||
\(167\) | −15.9432 | − | 11.5834i | −1.23372 | − | 0.896351i | −0.236558 | − | 0.971617i | \(-0.576019\pi\) |
−0.997164 | + | 0.0752658i | \(0.976019\pi\) | |||||||
\(168\) | 2.57128 | − | 7.91358i | 0.198378 | − | 0.610546i | ||||
\(169\) | −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 | ||||
\(175\) | 7.01823 | 0.530528 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −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 | −0.844389 | − | 0.535731i | \(-0.820036\pi\) |
0.248580 | + | 0.968611i | \(0.420036\pi\) | |||||||
\(182\) | 1.30464 | − | 0.947880i | 0.0967067 | − | 0.0702615i | ||||
\(183\) | 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 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2.47007 | −0.180148 | ||||||||
\(189\) | −4.42705 | − | 3.21644i | −0.322021 | − | 0.233962i | ||||
\(190\) | 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 | −0.474604 | − | 0.880199i | \(-0.657409\pi\) |
0.690458 | + | 0.723372i | \(0.257409\pi\) | |||||||
\(194\) | 11.3262 | + | 34.8585i | 0.813175 | + | 2.50269i | ||||
\(195\) | 1.13319 | − | 3.48760i | 0.0811495 | − | 0.249752i | ||||
\(196\) | −3.30464 | − | 2.40097i | −0.236046 | − | 0.171498i | ||||
\(197\) | −5.91982 | −0.421770 | −0.210885 | − | 0.977511i | \(-0.567635\pi\) | ||||
−0.210885 | + | 0.977511i | \(0.567635\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.4842 | 0.814095 | 0.407047 | − | 0.913407i | \(-0.366558\pi\) | ||||
0.407047 | + | 0.913407i | \(0.366558\pi\) | |||||||
\(200\) | 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 | ||||
\(203\) | −3.70010 | + | 2.68828i | −0.259696 | + | 0.188680i | ||||
\(204\) | 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 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −13.8366 | −0.954817 | ||||||||
\(211\) | 7.05857 | + | 5.12835i | 0.485932 | + | 0.353050i | 0.803618 | − | 0.595146i | \(-0.202906\pi\) |
−0.317686 | + | 0.948196i | \(0.602906\pi\) | |||||||
\(212\) | 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 | ||||
\(217\) | 0.864107 | − | 2.65945i | 0.0586594 | − | 0.180535i | ||||
\(218\) | 8.23210 | + | 5.98097i | 0.557548 | + | 0.405083i | ||||
\(219\) | 10.8440 | 0.732772 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 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 | \(-0.787550\pi\) |
0.999235 | − | 0.0391023i | \(-0.0124498\pi\) | |||||||
\(224\) | −0.263932 | − | 0.812299i | −0.0176347 | − | 0.0542740i | ||||
\(225\) | 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 | 0.652508 | − | 0.757781i | \(-0.273717\pi\) |
−0.519057 | + | 0.854740i | \(0.673717\pi\) | |||||||
\(230\) | −57.0135 | −3.75936 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −23.5199 | −1.54415 | ||||||||
\(233\) | −7.76971 | − | 5.64502i | −0.509010 | − | 0.369818i | 0.303438 | − | 0.952851i | \(-0.401866\pi\) |
−0.812448 | + | 0.583034i | \(0.801866\pi\) | |||||||
\(234\) | 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 | ||||
\(238\) | −0.866809 | − | 2.66776i | −0.0561869 | − | 0.172925i | ||||
\(239\) | −1.71914 | + | 5.29098i | −0.111202 | + | 0.342245i | −0.991136 | − | 0.132851i | \(-0.957587\pi\) |
0.879934 | + | 0.475096i | \(0.157587\pi\) | |||||||
\(240\) | −20.4927 | − | 14.8888i | −1.32280 | − | 0.961067i | ||||
\(241\) | −15.0208 | −0.967572 | −0.483786 | − | 0.875186i | \(-0.660739\pi\) | ||||
−0.483786 | + | 0.875186i | \(0.660739\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.94427 | −0.253025 | ||||||||
\(244\) | 22.6639 | + | 16.4663i | 1.45090 | + | 1.05414i | ||||
\(245\) | −1.07128 | + | 3.29706i | −0.0684415 | + | 0.210641i | ||||
\(246\) | 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 | \(-0.963173\pi\) |
−0.416738 | − | 0.909027i | \(-0.636827\pi\) | |||||||
\(252\) | −1.56024 | −0.0982860 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −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 | \(-0.752169\pi\) |
0.163162 | − | 0.986599i | \(-0.447831\pi\) | |||||||
\(258\) | 28.1187 | − | 20.4295i | 1.75060 | − | 1.27188i | ||||
\(259\) | 0.355772 | − | 0.258483i | 0.0221066 | − | 0.0160614i | ||||
\(260\) | −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 | \(-0.644029\pi\) | ||||
−0.437199 | + | 0.899365i | \(0.644029\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −34.0519 | −2.09179 | ||||||||
\(266\) | 12.1255 | + | 8.80968i | 0.743461 | + | 0.540156i | ||||
\(267\) | 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 | 0.199774 | − | 0.979842i | \(-0.435979\pi\) |
0.993619 | + | 0.112792i | \(0.0359793\pi\) | |||||||
\(270\) | −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 | ||||
\(273\) | 0.855772 | + | 0.621755i | 0.0517937 | + | 0.0376303i | ||||
\(274\) | 53.9665 | 3.26024 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 44.0647 | 2.65238 | ||||||||
\(277\) | −15.5242 | − | 11.2790i | −0.932761 | − | 0.677690i | 0.0139064 | − | 0.999903i | \(-0.495573\pi\) |
−0.946667 | + | 0.322213i | \(0.895573\pi\) | |||||||
\(278\) | −15.1032 | + | 46.4830i | −0.905833 | + | 2.78787i | ||||
\(279\) | −0.330060 | − | 1.01582i | −0.0197602 | − | 0.0608155i | ||||
\(280\) | −14.4230 | + | 10.4790i | −0.861942 | + | 0.626238i | ||||
\(281\) | −1.53764 | + | 1.11716i | −0.0917279 | + | 0.0666442i | −0.632704 | − | 0.774394i | \(-0.718055\pi\) |
0.540976 | + | 0.841038i | \(0.318055\pi\) | |||||||
\(282\) | −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 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.90315 | 0.348452 | ||||||||
\(288\) | −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 | \(0.869540\pi\) | |||||||
\(294\) | 1.23337 | − | 3.79591i | 0.0719314 | − | 0.221382i | ||||
\(295\) | 4.75122 | + | 3.45197i | 0.276627 | + | 0.200981i | ||||
\(296\) | 2.26148 | 0.131446 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.80008 | 0.451846 | ||||||||
\(299\) | 3.52619 | + | 2.56193i | 0.203925 | + | 0.148160i | ||||
\(300\) | −14.3339 | + | 44.1152i | −0.827569 | + | 2.54699i | ||||
\(301\) | −2.69098 | − | 8.28199i | −0.155106 | − | 0.477366i | ||||
\(302\) | −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 | −0.998487 | − | 0.0549835i | \(-0.982489\pi\) |
0.840112 | + | 0.542414i | \(0.182489\pi\) | |||||||
\(312\) | 1.68098 | + | 5.17352i | 0.0951666 | + | 0.292893i | ||||
\(313\) | −11.7300 | + | 8.52232i | −0.663017 | + | 0.481710i | −0.867680 | − | 0.497122i | \(-0.834390\pi\) |
0.204664 | + | 0.978832i | \(0.434390\pi\) | |||||||
\(314\) | 2.27437 | − | 1.65243i | 0.128350 | − | 0.0932518i | ||||
\(315\) | 0.409192 | + | 1.25936i | 0.0230554 | + | 0.0709571i | ||||
\(316\) | −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 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 24.0061 | 1.34198 | ||||||||
\(321\) | −8.66846 | − | 6.29801i | −0.483826 | − | 0.351520i | ||||
\(322\) | 5.08206 | − | 15.6410i | 0.283212 | − | 0.871638i | ||||
\(323\) | 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 | ||||
\(329\) | −0.604703 | −0.0333384 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −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 | ||||
\(336\) | 5.91123 | − | 4.29476i | 0.322484 | − | 0.234298i | ||||
\(337\) | −1.93346 | − | 5.95059i | −0.105322 | − | 0.324149i | 0.884484 | − | 0.466571i | \(-0.154511\pi\) |
−0.989806 | + | 0.142422i | \(0.954511\pi\) | |||||||
\(338\) | 9.58362 | − | 29.4954i | 0.521280 | − | 1.60434i | ||||
\(339\) | −24.6433 | − | 17.9044i | −1.33844 | − | 0.972434i | ||||
\(340\) | −16.1030 | −0.873308 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 5.72487 | 0.309566 | ||||||||
\(343\) | −0.809017 | − | 0.587785i | −0.0436828 | − | 0.0317374i | ||||
\(344\) | 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 | 0.0273845 | − | 0.999625i | \(-0.491282\pi\) |
0.959162 | + | 0.282857i | \(0.0912822\pi\) | |||||||
\(348\) | −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 | \(0.807606\pi\) | |||||||
\(350\) | 14.0058 | + | 10.1758i | 0.748640 | + | 0.543919i | ||||
\(351\) | 3.57742 | 0.190948 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.82506 | −0.363262 | −0.181631 | − | 0.983367i | \(-0.558138\pi\) | ||||
−0.181631 | + | 0.983367i | \(0.558138\pi\) | |||||||
\(354\) | −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 | ||||
\(357\) | 1.48855 | − | 1.08150i | 0.0787826 | − | 0.0572389i | ||||
\(358\) | −9.30801 | + | 6.76266i | −0.491944 | + | 0.357418i | ||||
\(359\) | 2.24337 | + | 6.90439i | 0.118401 | + | 0.364400i | 0.992641 | − | 0.121094i | \(-0.0386401\pi\) |
−0.874241 | + | 0.485493i | \(0.838640\pi\) | |||||||
\(360\) | −2.10429 | + | 6.47635i | −0.110906 | + | 0.341334i | ||||
\(361\) | −14.4960 | − | 10.5320i | −0.762947 | − | 0.554314i | ||||
\(362\) | −24.4405 | −1.28456 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.67042 | 0.139968 | ||||||||
\(365\) | −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 | \(-0.702723\pi\) |
0.00855584 | − | 0.999963i | \(-0.497277\pi\) | |||||||
\(368\) | 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 | ||||
\(371\) | 3.03531 | − | 9.34172i | 0.157585 | − | 0.484998i | ||||
\(372\) | 14.9519 | + | 10.8632i | 0.775222 | + | 0.563232i | ||||
\(373\) | 14.2913 | 0.739977 | 0.369989 | − | 0.929036i | \(-0.379362\pi\) | ||||
0.369989 | + | 0.929036i | \(0.379362\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.3208 | 0.584605 | ||||||||
\(376\) | −2.51582 | − | 1.82785i | −0.129743 | − | 0.0942641i | ||||
\(377\) | 0.923955 | − | 2.84364i | 0.0475861 | − | 0.146455i | ||||
\(378\) | −4.17120 | − | 12.8376i | −0.214543 | − | 0.660297i | ||||
\(379\) | 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 | 0.952322 | − | 0.305094i | \(-0.0986879\pi\) |
0.00412192 | + | 0.999992i | \(0.498688\pi\) | |||||||
\(384\) | −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 | ||||
\(392\) | −1.58914 | − | 4.89086i | −0.0802636 | − | 0.247026i | ||||
\(393\) | −2.40253 | + | 7.39422i | −0.121191 | + | 0.372989i | ||||
\(394\) | −11.8138 | − | 8.58320i | −0.595169 | − | 0.432415i | ||||
\(395\) | 9.19985 | 0.462894 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.6740 | −1.13798 | −0.568989 | − | 0.822345i | \(-0.692665\pi\) | ||||
−0.568989 | + | 0.822345i | \(0.692665\pi\) | |||||||
\(398\) | 22.9182 | + | 16.6511i | 1.14879 | + | 0.834643i | ||||
\(399\) | −3.03801 | + | 9.35004i | −0.152091 | + | 0.468087i | ||||
\(400\) | 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 | ||||
\(406\) | −11.2818 | −0.559905 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 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 | ||||
\(413\) | −1.37052 | + | 0.995741i | −0.0674389 | + | 0.0489972i | ||||
\(414\) | −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 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.2633 | 1.38075 | 0.690376 | − | 0.723451i | \(-0.257445\pi\) | ||||
0.690376 | + | 0.723451i | \(0.257445\pi\) | |||||||
\(420\) | −18.5367 | − | 13.4677i | −0.904499 | − | 0.657157i | ||||
\(421\) | −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 | ||||
\(427\) | 5.54839 | + | 4.03114i | 0.268505 | + | 0.195080i | ||||
\(428\) | −27.0498 | −1.30750 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −74.4682 | −3.59117 | ||||||||
\(431\) | 22.7900 | + | 16.5579i | 1.09776 | + | 0.797568i | 0.980692 | − | 0.195557i | \(-0.0626514\pi\) |
0.117065 | + | 0.993124i | \(0.462651\pi\) | |||||||
\(432\) | 7.63611 | − | 23.5015i | 0.367392 | − | 1.13072i | ||||
\(433\) | 4.38165 | + | 13.4853i | 0.210569 | + | 0.648064i | 0.999439 | + | 0.0335038i | \(0.0106666\pi\) |
−0.788870 | + | 0.614560i | \(0.789333\pi\) | |||||||
\(434\) | 5.58039 | − | 4.05439i | 0.267867 | − | 0.194617i | ||||
\(435\) | −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 | \(0.733117\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.381966 | −0.0181889 | ||||||||
\(442\) | 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 | ||||
\(448\) | −2.13986 | + | 6.58580i | −0.101099 | + | 0.311150i | ||||
\(449\) | 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 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −76.8990 | −3.61702 | ||||||||
\(453\) | −11.6870 | − | 8.49109i | −0.549102 | − | 0.398946i | ||||
\(454\) | −10.1144 | + | 31.1290i | −0.474693 | + | 1.46096i | ||||
\(455\) | −0.700350 | − | 2.15546i | −0.0328329 | − | 0.101049i | ||||
\(456\) | −40.9019 | + | 29.7170i | −1.91541 | + | 1.39163i | ||||
\(457\) | 7.84524 | − | 5.69990i | 0.366985 | − | 0.266630i | −0.388975 | − | 0.921248i | \(-0.627171\pi\) |
0.755960 | + | 0.654618i | \(0.227171\pi\) | |||||||
\(458\) | 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 | −0.998785 | − | 0.0492858i | \(-0.984305\pi\) |
−0.261768 | + | 0.965131i | \(0.584305\pi\) | |||||||
\(468\) | 0.825206 | − | 0.599547i | 0.0381452 | − | 0.0277141i | ||||
\(469\) | −1.90919 | − | 5.87589i | −0.0881583 | − | 0.271323i | ||||
\(470\) | −1.59796 | + | 4.91803i | −0.0737086 | + | 0.226852i | ||||
\(471\) | 1.49186 | + | 1.08390i | 0.0687411 | + | 0.0499433i | ||||
\(472\) | −8.71178 | −0.400992 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −10.5918 | −0.486498 | ||||||||
\(475\) | −34.4988 | − | 25.0649i | −1.58292 | − | 1.15006i | ||||
\(476\) | 1.43539 | − | 4.41766i | 0.0657908 | − | 0.202483i | ||||
\(477\) | −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 | ||||
\(483\) | 10.7876 | 0.490851 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 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 | ||||
\(490\) | −6.91831 | + | 5.02644i | −0.312537 | + | 0.227072i | ||||
\(491\) | 1.06393 | + | 3.27444i | 0.0480145 | + | 0.147774i | 0.972189 | − | 0.234196i | \(-0.0752458\pi\) |
−0.924175 | + | 0.381970i | \(0.875246\pi\) | |||||||
\(492\) | −12.0565 | + | 37.1061i | −0.543549 | + | 1.67287i | ||||
\(493\) | −4.20758 | − | 3.05699i | −0.189500 | − | 0.137680i | ||||
\(494\) | −9.79837 | −0.440850 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.6275 | 0.566992 | ||||||||
\(497\) | 4.38234 | + | 3.18395i | 0.196575 | + | 0.142820i | ||||
\(498\) | −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 | \(-0.0705727\pi\) | |||||||
\(504\) | −1.58914 | − | 1.15458i | −0.0707858 | − | 0.0514289i | ||||
\(505\) | 29.8818 | 1.32972 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 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 | \(0.279340\pi\) |
−0.969097 | + | 0.246680i | \(0.920660\pi\) | |||||||
\(510\) | −4.86218 | − | 14.9643i | −0.215301 | − | 0.662629i | ||||
\(511\) | 5.42202 | − | 3.93933i | 0.239856 | − | 0.174266i | ||||
\(512\) | −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 | 0 | ||||||||
\(518\) | 1.08477 | 0.0476619 | ||||||||
\(519\) | 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 | \(-0.837672\pi\) |
0.419150 | − | 0.907917i | \(-0.362328\pi\) | |||||||
\(522\) | −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 | ||||
\(525\) | −3.50911 | + | 10.7999i | −0.153150 | + | 0.471348i | ||||
\(526\) | −28.2987 | − | 20.5602i | −1.23388 | − | 0.896467i | ||||
\(527\) | 3.17983 | 0.138516 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.4500 | 0.932608 | ||||||||
\(530\) | −67.9548 | − | 49.3721i | −2.95177 | − | 2.14459i | ||||
\(531\) | −0.199956 | + | 0.615402i | −0.00867736 | + | 0.0267062i | ||||
\(532\) | 7.66953 | + | 23.6044i | 0.332516 | + | 1.02338i | ||||
\(533\) | −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 | 0.906872 | − | 0.421406i | \(-0.138463\pi\) |
−0.120542 | + | 0.992708i | \(0.538463\pi\) | |||||||
\(542\) | 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 | ||||
\(546\) | 0.806315 | + | 2.48158i | 0.0345071 | + | 0.106202i | ||||
\(547\) | 8.48072 | − | 26.1010i | 0.362610 | − | 1.11600i | −0.588855 | − | 0.808239i | \(-0.700421\pi\) |
0.951464 | − | 0.307759i | \(-0.0995790\pi\) | |||||||
\(548\) | 72.2981 | + | 52.5277i | 3.08842 | + | 2.24387i | ||||
\(549\) | 2.61959 | 0.111801 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.7891 | 1.18386 | ||||||||
\(552\) | 44.8808 | + | 32.6078i | 1.91025 | + | 1.38788i | ||||
\(553\) | −0.820054 | + | 2.52387i | −0.0348723 | + | 0.107326i | ||||
\(554\) | −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 | \(0.121428\pi\) |
−0.532033 | + | 0.846724i | \(0.678572\pi\) | |||||||
\(558\) | 0.814168 | − | 2.50575i | 0.0344665 | − | 0.106077i | ||||
\(559\) | 4.60574 | + | 3.34626i | 0.194802 | + | 0.141532i | ||||
\(560\) | −15.6550 | −0.661544 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −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 | ||||
\(567\) | 6.23607 | − | 4.53077i | 0.261890 | − | 0.190274i | ||||
\(568\) | 8.60815 | + | 26.4932i | 0.361190 | + | 1.11163i | ||||
\(569\) | −11.0159 | + | 33.9036i | −0.461812 | + | 1.42131i | 0.401136 | + | 0.916019i | \(0.368616\pi\) |
−0.862948 | + | 0.505293i | \(0.831384\pi\) | |||||||
\(570\) | 68.0153 | + | 49.4160i | 2.84885 | + | 2.06981i | ||||
\(571\) | −25.8902 | −1.08347 | −0.541737 | − | 0.840548i | \(-0.682233\pi\) | ||||
−0.541737 | + | 0.840548i | \(0.682233\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.0880 | −0.672087 | ||||||||
\(574\) | 11.7805 | + | 8.55903i | 0.491708 | + | 0.357247i | ||||
\(575\) | −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 | −0.716714 | − | 0.697367i | \(-0.754355\pi\) |
0.441758 | + | 0.897134i | \(0.354355\pi\) | |||||||
\(578\) | −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 | ||||
\(581\) | 5.41765 | + | 3.93615i | 0.224762 | + | 0.163299i | ||||
\(582\) | −59.3048 | −2.45826 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 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 | 0.839577 | − | 0.543241i | \(-0.182803\pi\) |
−0.998541 | + | 0.0539994i | \(0.982803\pi\) | |||||||
\(588\) | 5.34703 | − | 3.88484i | 0.220508 | − | 0.160208i | ||||
\(589\) | −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 | \(0.338449\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.94221 | −0.161615 | ||||||||
\(596\) | 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 | \(-0.314127\pi\) | |||||||
\(602\) | 6.63793 | − | 20.4295i | 0.270542 | − | 0.832643i | ||||
\(603\) | −1.90919 | − | 1.38711i | −0.0777483 | − | 0.0564875i | ||||
\(604\) | −36.4690 | −1.48390 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −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 | ||||
\(609\) | −2.28679 | − | 7.03800i | −0.0926653 | − | 0.285194i | ||||
\(610\) | 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 | \(0.215852\pi\) |
−0.998760 | + | 0.0497807i | \(0.984148\pi\) | |||||||
\(614\) | −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 | −0.982165 | − | 0.188023i | \(-0.939792\pi\) |
0.905105 | + | 0.425188i | \(0.139792\pi\) | |||||||
\(620\) | −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 | ||||
\(623\) | −0.215760 | − | 0.664040i | −0.00864423 | − | 0.0266042i | ||||
\(624\) | −1.47610 | + | 4.54297i | −0.0590913 | + | 0.181864i | ||||
\(625\) | 8.76619 | + | 6.36901i | 0.350647 | + | 0.254760i | ||||
\(626\) | −35.7652 | −1.42947 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.65531 | 0.185767 | ||||||||
\(629\) | 0.404567 | + | 0.293935i | 0.0161312 | + | 0.0117200i | ||||
\(630\) | −1.00937 | + | 3.10651i | −0.0402142 | + | 0.123766i | ||||
\(631\) | 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 | ||||
\(637\) | 0.653752 | 0.0259026 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 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 | −0.293699 | − | 0.955898i | \(-0.594886\pi\) |
0.818355 | + | 0.574713i | \(0.194886\pi\) | |||||||
\(644\) | 22.0323 | − | 16.0074i | 0.868196 | − | 0.630781i | ||||
\(645\) | −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 | 0.927274 | − | 0.374383i | \(-0.122146\pi\) |
−0.0695163 | + | 0.997581i | \(0.522146\pi\) | |||||||
\(648\) | 39.6399 | 1.55720 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −11.3178 | −0.443921 | ||||||||
\(651\) | 3.66042 | + | 2.65945i | 0.143463 | + | 0.104232i | ||||
\(652\) | −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 | ||||
\(658\) | −1.20676 | − | 0.876765i | −0.0470445 | − | 0.0341798i | ||||
\(659\) | 32.6279 | 1.27100 | 0.635502 | − | 0.772099i | \(-0.280793\pi\) | ||||
0.635502 | + | 0.772099i | \(0.280793\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.8165 | −1.31531 | −0.657654 | − | 0.753320i | \(-0.728451\pi\) | ||||
−0.657654 | + | 0.753320i | \(0.728451\pi\) | |||||||
\(662\) | −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 | ||||
\(665\) | 17.0411 | − | 12.3811i | 0.660825 | − | 0.480117i | ||||
\(666\) | 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 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.38197 | 0.0533105 | ||||||||
\(673\) | 19.2138 | + | 13.9596i | 0.740638 | + | 0.538105i | 0.892911 | − | 0.450234i | \(-0.148659\pi\) |
−0.152273 | + | 0.988338i | \(0.548659\pi\) | |||||||
\(674\) | 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 | ||||
\(679\) | −4.59159 | + | 14.1315i | −0.176209 | + | 0.542315i | ||||
\(680\) | −16.4012 | − | 11.9162i | −0.628958 | − | 0.456965i | ||||
\(681\) | −21.4696 | −0.822717 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −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 | ||||
\(686\) | −0.762262 | − | 2.34600i | −0.0291033 | − | 0.0895707i | ||||
\(687\) | −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 | 0.920383 | − | 0.391017i | \(-0.127877\pi\) |
−0.0874654 | + | 0.996168i | \(0.527877\pi\) | |||||||
\(692\) | 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 | ||||
\(700\) | 8.85884 | + | 27.2647i | 0.334833 | + | 1.03051i | ||||
\(701\) | −11.9020 | + | 36.6305i | −0.449531 | + | 1.38352i | 0.427905 | + | 0.903823i | \(0.359252\pi\) |
−0.877437 | + | 0.479692i | \(0.840748\pi\) | |||||||
\(702\) | 7.13919 | + | 5.18693i | 0.269452 | + | 0.195768i | ||||
\(703\) | −2.67198 | −0.100776 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.39196 | −0.127748 | ||||||||
\(706\) | −13.6203 | − | 9.89572i | −0.512606 | − | 0.372430i | ||||
\(707\) | −2.66360 | + | 8.19772i | −0.100175 | + | 0.308307i | ||||
\(708\) | −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 | ||||
\(714\) | 4.53867 | 0.169856 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −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 | 0.999244 | − | 0.0388664i | \(-0.0123747\pi\) |
−0.831251 | + | 0.555898i | \(0.812375\pi\) | |||||||
\(720\) | −4.83766 | + | 3.51477i | −0.180289 | + | 0.130988i | ||||
\(721\) | 0.754779 | − | 0.548379i | 0.0281094 | − | 0.0204227i | ||||
\(722\) | −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 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.04780 | 0.150125 | 0.0750623 | − | 0.997179i | \(-0.476084\pi\) | ||||
0.0750623 | + | 0.997179i | \(0.476084\pi\) | |||||||
\(728\) | 2.71988 | + | 1.97611i | 0.100805 | + | 0.0732394i | ||||
\(729\) | 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 | ||||
\(735\) | −4.53801 | − | 3.29706i | −0.167387 | − | 0.121614i | ||||
\(736\) | 5.69437 | 0.209897 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 5.56199 | 0.204740 | ||||||||
\(739\) | −26.4376 | − | 19.2080i | −0.972522 | − | 0.706578i | −0.0164968 | − | 0.999864i | \(-0.505251\pi\) |
−0.956025 | + | 0.293286i | \(0.905251\pi\) | |||||||
\(740\) | 1.92435 | − | 5.92254i | 0.0707405 | − | 0.217717i | ||||
\(741\) | −1.98610 | − | 6.11260i | −0.0729614 | − | 0.224552i | ||||
\(742\) | 19.6020 | − | 14.2417i | 0.719612 | − | 0.522828i | ||||
\(743\) | −14.6479 | + | 10.6423i | −0.537379 | + | 0.390429i | −0.823111 | − | 0.567881i | \(-0.807763\pi\) |
0.285731 | + | 0.958310i | \(0.407763\pi\) | |||||||
\(744\) | 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 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.62212 | −0.241967 | ||||||||
\(750\) | 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 | ||||
\(756\) | 6.90727 | − | 21.2584i | 0.251215 | − | 0.773160i | ||||
\(757\) | −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 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 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 | ||||
\(763\) | 1.27472 | + | 3.92317i | 0.0461478 | + | 0.142028i | ||||
\(764\) | −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 | \(-0.749133\pi\) |
0.987258 | − | 0.159125i | \(-0.0508672\pi\) | |||||||
\(774\) | −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 | ||||
\(777\) | 0.219879 | + | 0.676718i | 0.00788812 | + | 0.0242771i | ||||
\(778\) | −23.0672 | + | 70.9934i | −0.826998 | + | 2.54524i | ||||
\(779\) | −29.0176 | − | 21.0825i | −1.03966 | − | 0.755358i | ||||
\(780\) | 14.9792 | 0.536340 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 18.7015 | 0.668765 | ||||||||
\(783\) | −20.2474 | − | 14.7106i | −0.723584 | − | 0.525715i | ||||
\(784\) | 1.39545 | − | 4.29476i | 0.0498376 | − | 0.153384i | ||||
\(785\) | −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 | ||||
\(791\) | −18.8258 | −0.669369 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −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 | −0.494724 | − | 0.869050i | \(-0.664731\pi\) |
0.673638 | + | 0.739062i | \(0.264731\pi\) | |||||||
\(798\) | −19.6194 | + | 14.2544i | −0.694521 | + | 0.504599i | ||||
\(799\) | −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 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 40.8340 | 1.44010 | ||||||||
\(805\) | −18.6988 | − | 13.5855i | −0.659046 | − | 0.478825i | ||||
\(806\) | −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 | 0.131209 | − | 0.991355i | \(-0.458114\pi\) |
0.983380 | + | 0.181559i | \(0.0581142\pi\) | |||||||
\(810\) | −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 | \(0.0302501\pi\) | |||||||
\(812\) | −15.1140 | − | 10.9810i | −0.530399 | − | 0.385357i | ||||
\(813\) | 12.0539 | 0.422750 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 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 | ||||
\(819\) | 0.202020 | − | 0.146776i | 0.00705916 | − | 0.00512878i | ||||
\(820\) | 67.6284 | − | 49.1349i | 2.36168 | − | 1.71586i | ||||
\(821\) | −14.7397 | − | 45.3642i | −0.514420 | − | 1.58322i | −0.784335 | − | 0.620337i | \(-0.786996\pi\) |
0.269916 | − | 0.962884i | \(-0.413004\pi\) | |||||||
\(822\) | −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 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.17878 | −0.145398 | ||||||||
\(827\) | −25.0287 | − | 18.1844i | −0.870335 | − | 0.632335i | 0.0603420 | − | 0.998178i | \(-0.480781\pi\) |
−0.930677 | + | 0.365843i | \(0.880781\pi\) | |||||||
\(828\) | 3.21448 | − | 9.89314i | 0.111711 | − | 0.343810i | ||||
\(829\) | 0.0265154 | + | 0.0816061i | 0.000920918 | + | 0.00283430i | 0.951516 | − | 0.307600i | \(-0.0995257\pi\) |
−0.950595 | + | 0.310434i | \(0.899526\pi\) | |||||||
\(830\) | 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 | ||||
\(833\) | 0.351400 | − | 1.08150i | 0.0121753 | − | 0.0374717i | ||||
\(834\) | −63.9784 | − | 46.4830i | −2.21539 | − | 1.60958i | ||||
\(835\) | −68.3185 | −2.36426 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.3018 | 0.528907 | ||||||||
\(838\) | 56.4030 | + | 40.9792i | 1.94841 | + | 1.41560i | ||||
\(839\) | 3.30355 | − | 10.1673i | 0.114051 | − | 0.351014i | −0.877697 | − | 0.479217i | \(-0.840921\pi\) |
0.991748 | + | 0.128203i | \(0.0409208\pi\) | |||||||
\(840\) | −8.91393 | − | 27.4343i | −0.307560 | − | 0.946572i | ||||
\(841\) | 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 | \(0.181772\pi\) | |||||||
\(854\) | 5.22773 | + | 16.0893i | 0.178889 | + | 0.550565i | ||||
\(855\) | 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 | \(0.448378\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.8261 | −1.32473 | −0.662365 | − | 0.749181i | \(-0.730447\pi\) | ||||
−0.662365 | + | 0.749181i | \(0.730447\pi\) | |||||||
\(860\) | −99.7640 | − | 72.4828i | −3.40192 | − | 2.47164i | ||||
\(861\) | −2.95158 | + | 9.08401i | −0.100589 | + | 0.309582i | ||||
\(862\) | 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 | ||||
\(868\) | 11.4223 | 0.387697 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −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 | ||||
\(875\) | 5.66042 | − | 4.11253i | 0.191357 | − | 0.139029i | ||||
\(876\) | 13.6880 | + | 42.1274i | 0.462475 | + | 1.42335i | ||||
\(877\) | −6.80103 | + | 20.9314i | −0.229654 | + | 0.706804i | 0.768131 | + | 0.640293i | \(0.221187\pi\) |
−0.997786 | + | 0.0665113i | \(0.978813\pi\) | |||||||
\(878\) | −55.9145 | − | 40.6243i | −1.88702 | − | 1.37100i | ||||
\(879\) | −5.29254 | −0.178513 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.92969 | −0.233467 | −0.116734 | − | 0.993163i | \(-0.537242\pi\) | ||||
−0.116734 | + | 0.993163i | \(0.537242\pi\) | |||||||
\(882\) | −0.762262 | − | 0.553816i | −0.0256667 | − | 0.0186479i | ||||
\(883\) | 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 | ||||
\(889\) | −6.44491 | − | 4.68250i | −0.216155 | − | 0.157046i | ||||
\(890\) | −5.97077 | −0.200141 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 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 | ||||
\(896\) | −15.2011 | + | 11.0443i | −0.507834 | + | 0.368963i | ||||
\(897\) | −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 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.0902 | 0.468891 | ||||||||
\(904\) | −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 | ||||
\(910\) | 1.72758 | − | 5.31693i | 0.0572686 | − | 0.176255i | ||||
\(911\) | 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 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 23.9205 | 0.791220 | ||||||||
\(915\) | 31.1225 | + | 22.6118i | 1.02888 | + | 0.747524i | ||||
\(916\) | −3.15089 | + | 9.69745i | −0.104108 | + | 0.320413i | ||||
\(917\) | 1.48484 | + | 4.56988i | 0.0490338 | + | 0.150911i | ||||
\(918\) | 12.4181 | − | 9.02229i | 0.409859 | − | 0.297780i | ||||
\(919\) | 15.1498 | − | 11.0069i | 0.499744 | − | 0.363085i | −0.309175 | − | 0.951005i | \(-0.600053\pi\) |
0.808919 | + | 0.587920i | \(0.200053\pi\) | |||||||
\(920\) | −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 | 0.207162 | − | 0.978307i | \(-0.433577\pi\) |
0.994441 | + | 0.105291i | \(0.0335774\pi\) | |||||||
\(930\) | 31.3020 | − | 22.7423i | 1.02643 | − | 0.745748i | ||||
\(931\) | 1.87759 | + | 5.77864i | 0.0615357 | + | 0.189387i | ||||
\(932\) | 12.1226 | − | 37.3096i | 0.397090 | − | 1.22212i | ||||
\(933\) | −11.8313 | − | 8.59592i | −0.387338 | − | 0.281418i | ||||
\(934\) | −83.0584 | −2.71775 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.28415 | 0.0419738 | ||||||||
\(937\) | 23.8336 | + | 17.3161i | 0.778609 | + | 0.565692i | 0.904561 | − | 0.426344i | \(-0.140199\pi\) |
−0.125952 | + | 0.992036i | \(0.540199\pi\) | |||||||
\(938\) | 4.70947 | − | 14.4942i | 0.153769 | − | 0.473254i | ||||
\(939\) | −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 | ||||
\(945\) | −18.9704 | −0.617108 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 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 | ||||
\(952\) | 4.73103 | − | 3.43730i | 0.153334 | − | 0.111403i | ||||
\(953\) | 12.7740 | + | 39.3143i | 0.413790 | + | 1.27352i | 0.913328 | + | 0.407224i | \(0.133503\pi\) |
−0.499538 | + | 0.866292i | \(0.666497\pi\) | |||||||
\(954\) | 2.85989 | − | 8.80184i | 0.0925924 | − | 0.284970i | ||||
\(955\) | 27.8864 | + | 20.2607i | 0.902384 | + | 0.655620i | ||||
\(956\) | −22.7247 | −0.734968 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 34.9555 | 1.12936 | ||||||||
\(959\) | 17.6995 | + | 12.8594i | 0.571545 | + | 0.415252i | ||||
\(960\) | −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 | ||||
\(966\) | 21.5280 | + | 15.6410i | 0.692651 | + | 0.503240i | ||||
\(967\) | 6.52818 | 0.209932 | 0.104966 | − | 0.994476i | \(-0.466527\pi\) | ||||
0.104966 | + | 0.994476i | \(0.466527\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −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 | \(-0.746752\pi\) |
0.986040 | − | 0.166506i | \(-0.0532484\pi\) | |||||||
\(972\) | −4.97870 | − | 15.3229i | −0.159692 | − | 0.491482i | ||||
\(973\) | −16.0296 | + | 11.6462i | −0.513887 | + | 0.373360i | ||||
\(974\) | 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 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −14.1608 | −0.452350 | ||||||||
\(981\) | 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 | \(0.100153\pi\) |
−0.587396 | + | 0.809300i | \(0.699847\pi\) | |||||||
\(984\) | −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 | ||||
\(987\) | 0.302352 | − | 0.930543i | 0.00962396 | − | 0.0296195i | ||||
\(988\) | −13.1267 | − | 9.53713i | −0.417617 | − | 0.303417i | ||||
\(989\) | 58.0583 | 1.84615 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −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 | ||||
\(994\) | 4.12907 | + | 12.7080i | 0.130966 | + | 0.403072i | ||||
\(995\) | 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 | 847.2.f.q.323.2 | 8 | ||
11.2 | odd | 10 | 847.2.f.p.148.2 | 8 | |||
11.3 | even | 5 | inner | 847.2.f.q.729.2 | 8 | ||
11.4 | even | 5 | 847.2.f.s.372.1 | 8 | |||
11.5 | even | 5 | 847.2.a.k.1.1 | 4 | |||
11.6 | odd | 10 | 847.2.a.l.1.4 | 4 | |||
11.7 | odd | 10 | 847.2.f.p.372.2 | 8 | |||
11.8 | odd | 10 | 77.2.f.a.36.1 | yes | 8 | ||
11.9 | even | 5 | 847.2.f.s.148.1 | 8 | |||
11.10 | odd | 2 | 77.2.f.a.15.1 | ✓ | 8 | ||
33.5 | odd | 10 | 7623.2.a.co.1.4 | 4 | |||
33.8 | even | 10 | 693.2.m.g.190.2 | 8 | |||
33.17 | even | 10 | 7623.2.a.ch.1.1 | 4 | |||
33.32 | even | 2 | 693.2.m.g.631.2 | 8 | |||
77.6 | even | 10 | 5929.2.a.bi.1.4 | 4 | |||
77.10 | even | 6 | 539.2.q.b.422.2 | 16 | |||
77.19 | even | 30 | 539.2.q.b.410.2 | 16 | |||
77.27 | odd | 10 | 5929.2.a.bb.1.1 | 4 | |||
77.30 | odd | 30 | 539.2.q.c.410.2 | 16 | |||
77.32 | odd | 6 | 539.2.q.c.422.2 | 16 | |||
77.41 | even | 10 | 539.2.f.d.344.1 | 8 | |||
77.52 | even | 30 | 539.2.q.b.520.1 | 16 | |||
77.54 | even | 6 | 539.2.q.b.312.1 | 16 | |||
77.65 | odd | 6 | 539.2.q.c.312.1 | 16 | |||
77.74 | odd | 30 | 539.2.q.c.520.1 | 16 | |||
77.76 | even | 2 | 539.2.f.d.246.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.a.15.1 | ✓ | 8 | 11.10 | odd | 2 | ||
77.2.f.a.36.1 | yes | 8 | 11.8 | odd | 10 | ||
539.2.f.d.246.1 | 8 | 77.76 | even | 2 | |||
539.2.f.d.344.1 | 8 | 77.41 | even | 10 | |||
539.2.q.b.312.1 | 16 | 77.54 | even | 6 | |||
539.2.q.b.410.2 | 16 | 77.19 | even | 30 | |||
539.2.q.b.422.2 | 16 | 77.10 | even | 6 | |||
539.2.q.b.520.1 | 16 | 77.52 | even | 30 | |||
539.2.q.c.312.1 | 16 | 77.65 | odd | 6 | |||
539.2.q.c.410.2 | 16 | 77.30 | odd | 30 | |||
539.2.q.c.422.2 | 16 | 77.32 | odd | 6 | |||
539.2.q.c.520.1 | 16 | 77.74 | odd | 30 | |||
693.2.m.g.190.2 | 8 | 33.8 | even | 10 | |||
693.2.m.g.631.2 | 8 | 33.32 | even | 2 | |||
847.2.a.k.1.1 | 4 | 11.5 | even | 5 | |||
847.2.a.l.1.4 | 4 | 11.6 | odd | 10 | |||
847.2.f.p.148.2 | 8 | 11.2 | odd | 10 | |||
847.2.f.p.372.2 | 8 | 11.7 | odd | 10 | |||
847.2.f.q.323.2 | 8 | 1.1 | even | 1 | trivial | ||
847.2.f.q.729.2 | 8 | 11.3 | even | 5 | inner | ||
847.2.f.s.148.1 | 8 | 11.9 | even | 5 | |||
847.2.f.s.372.1 | 8 | 11.4 | even | 5 | |||
5929.2.a.bb.1.1 | 4 | 77.27 | odd | 10 | |||
5929.2.a.bi.1.4 | 4 | 77.6 | even | 10 | |||
7623.2.a.ch.1.1 | 4 | 33.17 | even | 10 | |||
7623.2.a.co.1.4 | 4 | 33.5 | odd | 10 |