Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [693,2,Mod(64,693)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(693, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("693.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 693 = 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 693.m (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: | \(5.53363286007\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 631.2 | ||
Root | \(-0.762262 - 2.34600i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 693.631 |
Dual form | 693.2.m.g.190.2 |
$q$-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 \(\left(\mathbb{Z}/693\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(442\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 | 0 | ||||||||
\(4\) | 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 | \(0.582343\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.309017 | − | 0.951057i | −0.116797 | − | 0.359466i | ||||
\(8\) | −1.58914 | + | 4.89086i | −0.561845 | + | 1.72918i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.55150 | −2.70422 | ||||||||
\(11\) | −2.91998 | + | 1.57281i | −0.880406 | + | 0.474220i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.528896 | + | 0.384266i | 0.146689 | + | 0.106576i | 0.658709 | − | 0.752397i | \(-0.271103\pi\) |
−0.512020 | + | 0.858973i | \(0.671103\pi\) | |||||||
\(14\) | 0.762262 | − | 2.34600i | 0.203723 | − | 0.626995i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −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 | 0 | ||||||||
\(19\) | −1.87759 | + | 5.77864i | −0.430750 | + | 1.32571i | 0.466630 | + | 0.884452i | \(0.345468\pi\) |
−0.897380 | + | 0.441259i | \(0.854532\pi\) | |||||||
\(20\) | −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 | \(-0.255364\pi\) | ||||
0.695091 | + | 0.718921i | \(0.255364\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.16875 | − | 6.67473i | 0.433750 | − | 1.33495i | ||||
\(26\) | 0.498330 | + | 1.53370i | 0.0977306 | + | 0.300784i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 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 | \(0.760399\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −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 | 0 | ||||||||
\(37\) | −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 | 0 | ||||||||
\(40\) | −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 | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 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 | \(0.0859572\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 14.0058 | − | 10.1758i | 1.98072 | − | 1.43907i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.825206 | + | 2.53972i | −0.114435 | + | 0.352196i | ||||
\(53\) | 7.94654 | + | 5.77350i | 1.09154 | + | 0.793051i | 0.979659 | − | 0.200670i | \(-0.0643120\pi\) |
0.111883 | + | 0.993721i | \(0.464312\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.98459 | − | 10.3612i | 0.672122 | − | 1.39710i | ||||
\(56\) | 5.14256 | 0.687203 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −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 | \(0.935173\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.54839 | + | 4.03114i | −0.710398 | + | 0.516134i | −0.883302 | − | 0.468804i | \(-0.844685\pi\) |
0.172904 | + | 0.984939i | \(0.444685\pi\) | |||||||
\(62\) | −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 | ||||||||
\(66\) | 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 | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.64256 | + | 8.13296i | 0.315846 | + | 0.972074i | ||||
\(71\) | −4.38234 | + | 3.18395i | −0.520088 | + | 0.377866i | −0.816637 | − | 0.577152i | \(-0.804164\pi\) |
0.296549 | + | 0.955018i | \(0.404164\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.07103 | + | 6.37396i | 0.242395 | + | 0.746016i | 0.996054 | + | 0.0887500i | \(0.0282872\pi\) |
−0.753659 | + | 0.657266i | \(0.771713\pi\) | |||||||
\(74\) | 0.335211 | − | 1.03167i | 0.0389675 | − | 0.119930i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −24.8191 | −2.84695 | ||||||||
\(77\) | 2.39815 | + | 2.29104i | 0.273295 | + | 0.261088i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −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 | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 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 | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.05216 | − | 16.7806i | −0.325361 | − | 1.78882i | ||||
\(89\) | 0.698213 | 0.0740105 | 0.0370052 | − | 0.999315i | \(-0.488218\pi\) | ||||
0.0370052 | + | 0.999315i | \(0.488218\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.202020 | − | 0.621755i | 0.0211775 | − | 0.0651776i | ||||
\(92\) | 8.41560 | + | 25.9006i | 0.877387 | + | 2.70032i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.20676 | − | 0.876765i | 0.124468 | − | 0.0904314i | ||||
\(95\) | −6.50911 | − | 20.0330i | −0.667821 | − | 2.05534i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 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 | \(0.558922\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −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 | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.48729 | + | 23.0435i | 0.727230 | + | 2.23818i | ||||
\(107\) | −2.04635 | + | 6.29801i | −0.197828 | + | 0.608851i | 0.802104 | + | 0.597184i | \(0.203714\pi\) |
−0.999932 | + | 0.0116671i | \(0.996286\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −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 | 0 | ||||||||
\(112\) | 3.65334 | + | 2.65431i | 0.345208 | + | 0.250809i | ||||
\(113\) | 5.81749 | − | 17.9044i | 0.547264 | − | 1.68430i | −0.168282 | − | 0.985739i | \(-0.553822\pi\) |
0.715546 | − | 0.698566i | \(-0.246178\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.6988 | + | 13.5855i | −1.74367 | + | 1.26685i | ||||
\(116\) | −15.1140 | + | 10.9810i | −1.40330 | + | 1.01956i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.29131 | − | 3.97426i | 0.118875 | − | 0.365860i | ||||
\(119\) | 0.919977 | + | 0.668402i | 0.0843341 | + | 0.0612723i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.05253 | − | 9.18514i | 0.550230 | − | 0.835013i | ||||
\(122\) | −16.9173 | −1.53162 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 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 | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −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 | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.80709 | − | 5.56166i | −0.154957 | − | 0.476909i | ||||
\(137\) | −17.6995 | + | 12.8594i | −1.51217 | + | 1.09865i | −0.546962 | + | 0.837157i | \(0.684216\pi\) |
−0.965204 | + | 0.261496i | \(0.915784\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.12278 | − | 18.8440i | −0.519327 | − | 1.59832i | −0.775268 | − | 0.631632i | \(-0.782385\pi\) |
0.255941 | − | 0.966692i | \(-0.417615\pi\) | |||||||
\(140\) | −4.37592 | + | 13.4677i | −0.369833 | + | 1.13823i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −13.3620 | −1.12131 | ||||||||
\(143\) | −2.14874 | − | 0.290193i | −0.179687 | − | 0.0242671i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −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 | −0.478046 | − | 0.878335i | \(-0.658655\pi\) |
0.687622 | + | 0.726069i | \(0.258655\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 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 | 0 | ||||||||
\(154\) | 1.46403 | + | 8.04916i | 0.117975 | + | 0.648620i | ||||
\(155\) | 9.69406 | 0.778645 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 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 | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.39545 | − | 1.74040i | 0.189377 | − | 0.137591i | ||||
\(161\) | −2.06024 | − | 6.34077i | −0.162370 | − | 0.499723i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 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 | \(0.976019\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.88515 | − | 11.9573i | −0.298858 | − | 0.919789i | ||||
\(170\) | 7.86718 | − | 5.71584i | 0.603385 | − | 0.438385i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 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 | \(-0.0843093\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.01823 | −0.530528 | ||||||||
\(176\) | 6.49295 | − | 13.4965i | 0.489424 | − | 1.01734i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.39337 | + | 1.01235i | 0.104438 | + | 0.0758785i | ||||
\(179\) | 1.44132 | − | 4.43592i | 0.107729 | − | 0.331556i | −0.882632 | − | 0.470064i | \(-0.844231\pi\) |
0.990361 | + | 0.138508i | \(0.0442307\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −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 | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.5949 | + | 32.6078i | −0.781067 | + | 2.40388i | ||||
\(185\) | 1.23337 | + | 0.896093i | 0.0906789 | + | 0.0658821i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 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 | \(-0.982871\pi\) |
0.776231 | − | 0.630448i | \(-0.217129\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −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 | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −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 | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.57039 | + | 20.2216i | 0.462291 | + | 1.42279i | ||||
\(203\) | 3.70010 | − | 2.68828i | 0.259696 | − | 0.188680i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.32392 | + | 19.4630i | 0.441682 | + | 1.35936i | ||||
\(206\) | 0.711159 | − | 2.18872i | 0.0495488 | − | 0.152495i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −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 | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −13.2153 | + | 9.60146i | −0.903378 | + | 0.656342i | ||||
\(215\) | −24.4234 | + | 17.7447i | −1.66566 | + | 1.21018i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.864107 | + | 2.65945i | −0.0586594 | + | 0.180535i | ||||
\(218\) | −8.23210 | − | 5.98097i | −0.557548 | − | 0.405083i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 46.5435 | + | 6.28581i | 3.13796 | + | 0.423789i | ||||
\(221\) | −0.743416 | −0.0500076 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 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 | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 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 | \(0.754856\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 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 | 0 | ||||||||
\(235\) | 0.647806 | + | 1.99374i | 0.0422582 | + | 0.130057i | ||||
\(236\) | 5.59825 | − | 4.06737i | 0.364415 | − | 0.264763i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 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 | \(0.157587\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.0208 | 0.967572 | 0.483786 | − | 0.875186i | \(-0.339261\pi\) | ||||
0.483786 | + | 0.875186i | \(0.339261\pi\) | |||||||
\(242\) | 25.3962 | − | 9.55452i | 1.63253 | − | 0.614188i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −22.6639 | − | 16.4663i | −1.45090 | − | 1.05414i | ||||
\(245\) | 1.07128 | − | 3.29706i | 0.0684415 | − | 0.210641i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.21358 | + | 2.33481i | −0.204475 | + | 0.148560i | ||||
\(248\) | 11.6338 | − | 8.45246i | 0.738748 | − | 0.536732i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −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 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −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 | \(0.552169\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.355772 | + | 0.258483i | −0.0221066 | + | 0.0160614i | ||||
\(260\) | −2.86077 | − | 8.80454i | −0.177417 | − | 0.546034i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 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 | 0 | ||||||||
\(268\) | −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 | \(0.564021\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.30210 | + | 7.08513i | 0.139843 | + | 0.430391i | 0.996312 | − | 0.0858070i | \(-0.0273468\pi\) |
−0.856469 | + | 0.516198i | \(0.827347\pi\) | |||||||
\(272\) | 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 | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 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 | 0 | ||||||||
\(280\) | −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 | 0 | ||||||||
\(283\) | 2.24092 | − | 6.89685i | 0.133209 | − | 0.409975i | −0.862098 | − | 0.506741i | \(-0.830850\pi\) |
0.995307 | + | 0.0967663i | \(0.0308499\pi\) | |||||||
\(284\) | −17.9008 | − | 13.0057i | −1.06222 | − | 0.771747i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.86734 | − | 3.69460i | −0.228680 | − | 0.218466i | ||||
\(287\) | −5.90315 | −0.348452 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.85369 | + | 14.9381i | −0.285511 | + | 0.878714i | ||||
\(290\) | −12.0859 | − | 37.1967i | −0.709710 | − | 2.18426i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −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 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.80008 | 0.451846 | ||||||||
\(299\) | 3.52619 | + | 2.56193i | 0.203925 | + | 0.148160i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.69098 | − | 8.28199i | −0.155106 | − | 0.477366i | ||||
\(302\) | 17.8171 | − | 12.9449i | 1.02526 | − | 0.744894i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.47880 | − | 26.0951i | −0.486293 | − | 1.49665i | ||||
\(305\) | 7.34703 | − | 22.6118i | 0.420690 | − | 1.29475i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.6121 | 1.80420 | 0.902099 | − | 0.431530i | \(-0.142026\pi\) | ||||
0.902099 | + | 0.431530i | \(0.142026\pi\) | |||||||
\(308\) | −5.87322 | + | 12.2083i | −0.334658 | + | 0.695635i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 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 | \(0.0175106\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −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 | 0 | ||||||||
\(316\) | 3.34973 | − | 10.3094i | 0.188437 | − | 0.579950i | ||||
\(317\) | −14.9000 | − | 10.8255i | −0.836865 | − | 0.608018i | 0.0846278 | − | 0.996413i | \(-0.473030\pi\) |
−0.921493 | + | 0.388394i | \(0.873030\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.9681 | − | 10.4782i | −0.614098 | − | 0.586668i | ||||
\(320\) | −24.0061 | −1.34198 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.08206 | − | 15.6410i | 0.283212 | − | 0.871638i | ||||
\(323\) | −2.13511 | − | 6.57120i | −0.118801 | − | 0.365632i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.71191 | − | 2.69686i | 0.205900 | − | 0.149595i | ||||
\(326\) | 3.86259 | + | 11.8878i | 0.213929 | + | 0.658407i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | 0 | ||||||||
\(334\) | −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 | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 16.1030 | 0.873308 | ||||||||
\(341\) | 9.19087 | + | 1.24125i | 0.497714 | + | 0.0672174i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.809017 | + | 0.587785i | 0.0436828 | + | 0.0317374i | ||||
\(344\) | −13.8385 | + | 42.5906i | −0.746124 | + | 2.29633i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 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 | \(0.0912822\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.17597 | − | 28.2407i | 0.491178 | − | 1.51169i | −0.331651 | − | 0.943402i | \(-0.607606\pi\) |
0.822829 | − | 0.568289i | \(-0.192394\pi\) | |||||||
\(350\) | −14.0058 | − | 10.1758i | −0.748640 | − | 0.543919i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.49396 | − | 1.34334i | 0.132928 | − | 0.0716003i | ||||
\(353\) | 6.82506 | 0.363262 | 0.181631 | − | 0.983367i | \(-0.441862\pi\) | ||||
0.181631 | + | 0.983367i | \(0.441862\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 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 | 0.992641 | − | 0.121094i | \(-0.0386401\pi\) |
−0.874241 | + | 0.485493i | \(0.838640\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −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 | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −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 | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.16209 | + | 3.57654i | 0.0604140 | + | 0.185935i | ||||
\(371\) | 3.03531 | − | 9.34172i | 0.157585 | − | 0.484998i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −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 | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 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 | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 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 | \(0.901312\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.3944 | − | 1.53884i | −0.580713 | − | 0.0784266i | ||||
\(386\) | −9.14330 | −0.465382 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.7556 | + | 57.7237i | −0.952169 | + | 2.93048i | ||||
\(389\) | −9.35130 | − | 28.7804i | −0.474130 | − | 1.45922i | −0.847128 | − | 0.531390i | \(-0.821670\pi\) |
0.372998 | − | 0.927832i | \(-0.378330\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.13356 | + | 4.45629i | −0.310188 | + | 0.225364i | ||||
\(392\) | −1.58914 | − | 4.89086i | −0.0802636 | − | 0.247026i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −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 | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.79361 | + | 30.1416i | 0.489680 | + | 1.50708i | ||||
\(401\) | −13.1211 | + | 9.53304i | −0.655237 | + | 0.476057i | −0.865051 | − | 0.501684i | \(-0.832714\pi\) |
0.209814 | + | 0.977741i | \(0.432714\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.564911 | − | 1.73862i | −0.0281402 | − | 0.0866068i | ||||
\(404\) | −10.8802 | + | 33.4858i | −0.541309 | + | 1.66598i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.2818 | 0.559905 | ||||||||
\(407\) | 1.05461 | + | 1.00750i | 0.0522750 | + | 0.0499401i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.3653 | + | 20.6086i | 1.40257 | + | 1.01903i | 0.994351 | + | 0.106146i | \(0.0338512\pi\) |
0.408222 | + | 0.912883i | \(0.366149\pi\) | |||||||
\(410\) | −15.5994 | + | 48.0101i | −0.770400 | + | 2.37105i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.08310 | − | 2.24000i | 0.151893 | − | 0.110357i | ||||
\(413\) | −1.37052 | + | 0.995741i | −0.0674389 | + | 0.0489972i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.17390 | + | 22.0790i | −0.352153 | + | 1.08382i | ||||
\(416\) | −0.451731 | − | 0.328202i | −0.0221479 | − | 0.0160914i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 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 | 0 | ||||||||
\(424\) | −40.8656 | + | 29.6906i | −1.98461 | + | 1.44190i | ||||
\(425\) | 2.46621 | + | 7.59020i | 0.119629 | + | 0.368179i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 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 | \(0.462651\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 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 | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.20692 | − | 16.0252i | −0.249366 | − | 0.767470i | ||||
\(437\) | −12.5181 | + | 38.5267i | −0.598821 | + | 1.84298i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.0185 | 1.33725 | 0.668625 | − | 0.743599i | \(-0.266883\pi\) | ||||
0.668625 | + | 0.743599i | \(0.266883\pi\) | |||||||
\(440\) | 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 | \(0.235118\pi\) |
−0.993920 | + | 0.110103i | \(0.964882\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.95824 | + | 1.42274i | −0.0928295 | + | 0.0674446i | ||||
\(446\) | 20.6205 | − | 14.9817i | 0.976409 | − | 0.709403i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.13986 | − | 6.58580i | 0.101099 | − | 0.311150i | ||||
\(449\) | −23.8834 | − | 17.3523i | −1.12713 | − | 0.818906i | −0.141853 | − | 0.989888i | \(-0.545306\pi\) |
−0.985274 | + | 0.170982i | \(0.945306\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.50358 | + | 19.2625i | 0.164977 | + | 0.907036i | ||||
\(452\) | 76.8990 | 3.61702 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.1144 | + | 31.1290i | −0.474693 | + | 1.46096i | ||||
\(455\) | 0.700350 | + | 2.15546i | 0.0328329 | + | 0.101049i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −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 | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −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 | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −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 | 0 | ||||||||
\(469\) | 1.90919 | + | 5.87589i | 0.0881583 | + | 0.271323i | ||||
\(470\) | −1.59796 | + | 4.91803i | −0.0737086 | + | 0.226852i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.71178 | 0.400992 | ||||||||
\(473\) | −25.4278 | + | 13.6964i | −1.16917 | + | 0.629759i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 34.4988 | + | 25.0649i | 1.58292 | + | 1.15006i | ||||
\(476\) | −1.43539 | + | 4.41766i | −0.0657908 | + | 0.202483i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −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 | \(0.195060\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 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 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 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 | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | \(0.875246\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −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 | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −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 | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 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 | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 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 | \(-0.0793397\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.42202 | − | 3.93933i | 0.239856 | − | 0.174266i | ||||
\(512\) | −34.4547 | + | 25.0328i | −1.52270 | + | 1.10631i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −21.7001 | + | 66.7859i | −0.957149 | + | 2.94580i | ||||
\(515\) | 2.61662 | + | 1.90108i | 0.115302 | + | 0.0837717i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.358897 | + | 1.97320i | 0.0157843 | + | 0.0867813i | ||||
\(518\) | −1.08477 | −0.0476619 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 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 | \(0.637672\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.2068 | − | 18.3138i | 1.10222 | − | 0.800808i | 0.120798 | − | 0.992677i | \(-0.461455\pi\) |
0.981421 | + | 0.191869i | \(0.0614548\pi\) | |||||||
\(524\) | 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 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.4500 | 0.932608 | ||||||||
\(530\) | −67.9548 | − | 49.3721i | −2.95177 | − | 2.14459i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.66953 | + | 23.6044i | 0.332516 | + | 1.02338i | ||||
\(533\) | 3.12215 | − | 2.26838i | 0.135235 | − | 0.0982543i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.09413 | − | 21.8335i | −0.306706 | − | 0.943944i | ||||
\(536\) | 9.81813 | − | 30.2171i | 0.424079 | − | 1.30518i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −59.6793 | −2.57296 | ||||||||
\(539\) | 1.43784 | − | 2.98875i | 0.0619320 | − | 0.128735i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −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 | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 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 | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −24.8919 | + | 51.7415i | −1.06140 | + | 2.20627i | ||||
\(551\) | −27.7891 | −1.18386 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.820054 | + | 2.52387i | −0.0348723 | + | 0.107326i | ||||
\(554\) | 14.6271 | + | 45.0174i | 0.621444 | + | 1.91261i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 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 | 0 | ||||||||
\(559\) | 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 | \(0.649737\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 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 | \(0.368616\pi\) |
−0.862948 | + | 0.505293i | \(0.831384\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 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 | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11.7805 | − | 8.55903i | −0.491708 | − | 0.357247i | ||||
\(575\) | 14.4592 | − | 44.5010i | 0.602992 | − | 1.85582i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −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 | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 20.0136 | − | 61.5955i | 0.831020 | − | 2.55762i | ||||
\(581\) | −5.41765 | − | 3.93615i | −0.224762 | − | 0.163299i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −32.2843 | − | 4.36008i | −1.33708 | − | 0.180576i | ||||
\(584\) | −34.4653 | −1.42619 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −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 | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 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 | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.32241 | + | 10.2253i | 0.135863 | + | 0.418144i | ||||
\(599\) | 31.5362 | − | 22.9124i | 1.28853 | − | 0.936175i | 0.288759 | − | 0.957402i | \(-0.406757\pi\) |
0.999775 | + | 0.0212271i | \(0.00675731\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.44078 | + | 29.0557i | 0.385097 | + | 1.18521i | 0.936410 | + | 0.350909i | \(0.114127\pi\) |
−0.551312 | + | 0.834299i | \(0.685873\pi\) | |||||||
\(602\) | 6.63793 | − | 20.4295i | 0.270542 | − | 0.832643i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 36.4690 | 1.48390 | ||||||||
\(605\) | 1.74132 | + | 38.0943i | 0.0707946 | + | 1.54875i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.4330 | − | 22.1109i | −1.23524 | − | 0.897454i | −0.237967 | − | 0.971273i | \(-0.576481\pi\) |
−0.997272 | + | 0.0738195i | \(0.976481\pi\) | |||||||
\(608\) | 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 | 0 | ||||||||
\(613\) | 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 | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.0162 | + | 8.08827i | −0.605018 | + | 0.325886i | ||||
\(617\) | 44.4849 | 1.79089 | 0.895447 | − | 0.445168i | \(-0.146856\pi\) | ||||
0.895447 | + | 0.445168i | \(0.146856\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −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 | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 18.0371 | − | 13.1047i | 0.723220 | − | 0.525450i | ||||
\(623\) | −0.215760 | − | 0.664040i | −0.00864423 | − | 0.0266042i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 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 | ||||
\(630\) | 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 | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.0389 | − | 43.2072i | −0.557554 | − | 1.71598i | ||||
\(635\) | −8.53418 | + | 26.2655i | −0.338669 | + | 1.04231i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.653752 | −0.0259026 | ||||||||
\(638\) | −6.69585 | − | 36.8134i | −0.265091 | − | 1.45746i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −52.6982 | − | 38.2875i | −2.08308 | − | 1.51345i | ||||
\(641\) | 3.17534 | − | 9.77271i | 0.125419 | − | 0.385999i | −0.868559 | − | 0.495587i | \(-0.834953\pi\) |
0.993977 | + | 0.109588i | \(0.0349531\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 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 | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 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 | \(0.877854\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 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 | 0.898853 | − | 0.438250i | \(-0.144402\pi\) |
−0.984784 | + | 0.173780i | \(0.944402\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.4765 | + | 9.79123i | −0.526569 | + | 0.382575i | ||||
\(656\) | 8.23757 | + | 25.3526i | 0.321623 | + | 0.989854i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −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 | 0 | ||||||||
\(664\) | 10.6418 | + | 32.7520i | 0.412981 | + | 1.27103i | ||||
\(665\) | −17.0411 | + | 12.3811i | −0.660825 | + | 0.480117i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.42266 | + | 29.0000i | 0.364847 | + | 1.12288i | ||||
\(668\) | 24.8752 | − | 76.5581i | 0.962452 | − | 2.96212i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 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 | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 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 | \(0.959625\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.59159 | − | 14.1315i | 0.176209 | − | 0.542315i | ||||
\(680\) | 16.4012 | + | 11.9162i | 0.628958 | + | 0.456965i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 16.5419 | + | 15.8030i | 0.633421 | + | 0.605128i | ||||
\(683\) | 28.8727 | 1.10478 | 0.552392 | − | 0.833585i | \(-0.313715\pi\) | ||||
0.552392 | + | 0.833585i | \(0.313715\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.4372 | − | 72.1322i | 0.895488 | − | 2.75603i | ||||
\(686\) | 0.762262 | + | 2.34600i | 0.0291033 | + | 0.0895707i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −31.8141 | + | 23.1143i | −1.21290 | + | 0.881223i | ||||
\(689\) | 1.98434 | + | 6.10716i | 0.0755973 | + | 0.232664i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 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 | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.07437 | + | 6.38424i | 0.0785722 | + | 0.241820i | ||||
\(698\) | 59.2583 | − | 43.0537i | 2.24296 | − | 1.62961i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −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 | \(0.840748\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.67198 | 0.100776 | ||||||||
\(704\) | −22.7601 | − | 3.07380i | −0.857802 | − | 0.115848i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.6203 | + | 9.89572i | 0.512606 | + | 0.372430i | ||||
\(707\) | 2.66360 | − | 8.19772i | 0.100175 | − | 0.308307i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 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 | 0 | ||||||||
\(712\) | −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 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −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 | \(0.987625\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.754779 | + | 0.548379i | −0.0281094 | + | 0.0204227i | ||||
\(722\) | −13.6582 | − | 42.0357i | −0.508307 | − | 1.56441i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −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 | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −17.7104 | − | 54.5069i | −0.655490 | − | 2.01739i | ||||
\(731\) | −8.01135 | + | 5.82058i | −0.296310 | + | 0.215282i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.26226 | − | 22.3509i | −0.268238 | − | 0.825551i | −0.990930 | − | 0.134381i | \(-0.957095\pi\) |
0.722692 | − | 0.691170i | \(-0.242905\pi\) | |||||||
\(734\) | 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 | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 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 | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 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 | \(0.407763\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.38750 | + | 10.4257i | −0.124108 | + | 0.381967i | ||||
\(746\) | −28.5202 | − | 20.7211i | −1.04420 | − | 0.758655i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 15.2671 | + | 2.06186i | 0.558222 | + | 0.0753892i | ||||
\(749\) | 6.62212 | 0.241967 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 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 | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −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 | ||||||||
\(759\) | 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 | \(0.680093\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.27472 | + | 3.92317i | 0.0461478 | + | 0.142028i | ||||
\(764\) | 32.8579 | − | 23.8727i | 1.18876 | − | 0.863683i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.6362 | − | 54.2787i | −0.637223 | − | 1.96117i | ||||
\(767\) | 0.342234 | − | 1.05329i | 0.0123573 | − | 0.0380320i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.9787 | 1.26137 | 0.630683 | − | 0.776041i | \(-0.282775\pi\) | ||||
0.630683 | + | 0.776041i | \(0.282775\pi\) | |||||||
\(770\) | −20.5078 | − | 19.5918i | −0.739050 | − | 0.706040i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −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 | \(0.949133\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −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 | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.78856 | − | 16.1897i | 0.278697 | − | 0.579312i | ||||
\(782\) | −18.7015 | −0.668765 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.39545 | − | 4.29476i | 0.0498376 | − | 0.153384i | ||||
\(785\) | 1.22091 | + | 3.75758i | 0.0435762 | + | 0.134114i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.0725 | + | 17.4897i | −0.858090 | + | 0.623439i | −0.927365 | − | 0.374159i | \(-0.877932\pi\) |
0.0692745 | + | 0.997598i | \(0.477932\pi\) | |||||||
\(788\) | −7.47236 | − | 22.9976i | −0.266192 | − | 0.819255i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 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 | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 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 | 0 | ||||||||
\(802\) | −40.0069 | −1.41269 | ||||||||
\(803\) | −16.0724 | − | 15.3545i | −0.567182 | − | 0.541848i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.6988 | + | 13.5855i | 0.659046 | + | 0.478825i | ||||
\(806\) | 1.39349 | − | 4.28871i | 0.0490834 | − | 0.151063i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −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 | \(0.0581142\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.82591 | + | 11.7749i | −0.134346 | + | 0.413474i | −0.995488 | − | 0.0948906i | \(-0.969750\pi\) |
0.861142 | + | 0.508365i | \(0.169750\pi\) | |||||||
\(812\) | 15.1140 | + | 10.9810i | 0.530399 | + | 0.385357i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.643819 | + | 3.53969i | 0.0225659 | + | 0.124066i | ||||
\(815\) | −17.5669 | −0.615341 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −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 | \(-0.786996\pi\) |
0.269916 | − | 0.962884i | \(-0.413004\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 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 | \(0.880781\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 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 | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.39893 | + | 4.30548i | 0.0484993 | + | 0.149266i | ||||
\(833\) | 0.351400 | − | 1.08150i | 0.0121753 | − | 0.0374717i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 68.3185 | 2.36426 | ||||||||
\(836\) | 72.4713 | − | 39.0358i | 2.50647 | − | 1.35008i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −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 | 0 | ||||||||
\(844\) | 11.0131 | − | 33.8948i | 0.379086 | − | 1.16671i | ||||
\(845\) | 35.2617 | + | 25.6191i | 1.21304 | + | 0.881325i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.6059 | − | 2.91793i | −0.364424 | − | 0.100261i | ||||
\(848\) | −44.3561 | −1.52319 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.08347 | + | 18.7230i | −0.208661 | + | 0.642193i | ||||
\(851\) | −0.906008 | − | 2.78841i | −0.0310576 | − | 0.0955854i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.1514 | + | 12.4612i | −0.587252 | + | 0.426664i | −0.841331 | − | 0.540520i | \(-0.818228\pi\) |
0.254079 | + | 0.967183i | \(0.418228\pi\) | |||||||
\(854\) | 5.22773 | + | 16.0893i | 0.178889 | + | 0.550565i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −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 | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21.4730 | + | 66.0869i | 0.731372 | + | 2.25093i | ||||
\(863\) | −30.4228 | + | 22.1034i | −1.03560 | + | 0.752410i | −0.969423 | − | 0.245398i | \(-0.921081\pi\) |
−0.0661810 | + | 0.997808i | \(0.521081\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.4208 | + | 47.4605i | 0.524324 | + | 1.61370i | ||||
\(866\) | −10.8084 | + | 33.2647i | −0.367283 | + | 1.13038i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.4223 | −0.387697 | ||||||||
\(869\) | 8.72231 | + | 1.17797i | 0.295884 | + | 0.0399599i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.26767 | − | 2.37410i | −0.110721 | − | 0.0804433i | ||||
\(872\) | 6.55530 | − | 20.1752i | 0.221991 | − | 0.683217i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −80.8416 | + | 58.7348i | −2.73451 | + | 1.98674i | ||||
\(875\) | 5.66042 | − | 4.11253i | 0.191357 | − | 0.139029i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 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 | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 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 | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −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 | \(0.943185\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −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 | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.99666 | + | 15.3781i | 0.167020 | + | 0.514034i | ||||
\(896\) | 15.2011 | − | 11.0443i | 0.507834 | − | 0.368963i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.5031 | − | 69.2575i | −0.750939 | − | 2.31115i | ||||
\(899\) | 3.95206 | − | 12.1632i | 0.131808 | − | 0.405665i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −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 | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −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 | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.72758 | + | 5.31693i | −0.0572686 | + | 0.176255i | ||||
\(911\) | −16.3826 | − | 11.9026i | −0.542779 | − | 0.394352i | 0.282337 | − | 0.959315i | \(-0.408890\pi\) |
−0.825116 | + | 0.564963i | \(0.808890\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.62858 | + | 20.0144i | −0.318659 | + | 0.662380i | ||||
\(914\) | −23.9205 | −0.791220 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.15089 | + | 9.69745i | −0.104108 | + | 0.320413i | ||||
\(917\) | −1.48484 | − | 4.56988i | −0.0490338 | − | 0.150911i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −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 | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 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 | 0 | ||||||||
\(928\) | −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 | \(0.566423\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.87759 | − | 5.77864i | −0.0615357 | − | 0.189387i | ||||
\(932\) | 12.1226 | − | 37.3096i | 0.397090 | − | 1.22212i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 83.0584 | 2.71775 | ||||||||
\(935\) | 2.33974 | + | 12.8638i | 0.0765177 | + | 0.420690i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.8336 | − | 17.3161i | −0.778609 | − | 0.565692i | 0.125952 | − | 0.992036i | \(-0.459801\pi\) |
−0.904561 | + | 0.426344i | \(0.859801\pi\) | |||||||
\(938\) | −4.70947 | + | 14.4942i | −0.153769 | + | 0.473254i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −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 | \(-0.0981017\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 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 | \(-0.763791\pi\) | ||||
−0.737069 | + | 0.675818i | \(0.763791\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.35394 | + | 4.16699i | −0.0439506 | + | 0.135266i | ||||
\(950\) | 32.5051 | + | 100.040i | 1.05460 | + | 3.24574i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −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 | \(0.666497\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 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 | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.16322 | − | 22.0461i | −0.231071 | − | 0.711165i | ||||
\(962\) | 0.573728 | − | 0.416838i | 0.0184977 | − | 0.0134394i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 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 | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −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 | \(0.946752\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.0296 | + | 11.6462i | −0.513887 | + | 0.373360i | ||||
\(974\) | 55.3617 | − | 40.2226i | 1.77390 | − | 1.28882i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.57027 | − | 29.4543i | 0.306337 | − | 0.942808i | ||||
\(977\) | −7.26864 | − | 5.28097i | −0.232544 | − | 0.168953i | 0.465411 | − | 0.885095i | \(-0.345907\pi\) |
−0.697955 | + | 0.716141i | \(0.745907\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.03877 | + | 1.09816i | −0.0651593 | + | 0.0350973i | ||||
\(980\) | 14.1608 | 0.452350 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −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 | \(-0.300153\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 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 | ||||||||
\(990\) | 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 | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.12907 | + | 12.7080i | 0.130966 | + | 0.403072i | ||||
\(995\) | −32.2092 | + | 23.4013i | −1.02110 | + | 0.741872i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.4234 | + | 59.7790i | 0.615144 | + | 1.89322i | 0.399437 | + | 0.916760i | \(0.369205\pi\) |
0.215707 | + | 0.976458i | \(0.430795\pi\) | |||||||
\(998\) | 1.97367 | − | 6.07434i | 0.0624755 | − | 0.192280i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 693.2.m.g.631.2 | 8 | ||
3.2 | odd | 2 | 77.2.f.a.15.1 | ✓ | 8 | ||
11.3 | even | 5 | inner | 693.2.m.g.190.2 | 8 | ||
11.5 | even | 5 | 7623.2.a.ch.1.1 | 4 | |||
11.6 | odd | 10 | 7623.2.a.co.1.4 | 4 | |||
21.2 | odd | 6 | 539.2.q.c.312.1 | 16 | |||
21.5 | even | 6 | 539.2.q.b.312.1 | 16 | |||
21.11 | odd | 6 | 539.2.q.c.422.2 | 16 | |||
21.17 | even | 6 | 539.2.q.b.422.2 | 16 | |||
21.20 | even | 2 | 539.2.f.d.246.1 | 8 | |||
33.2 | even | 10 | 847.2.f.s.148.1 | 8 | |||
33.5 | odd | 10 | 847.2.a.l.1.4 | 4 | |||
33.8 | even | 10 | 847.2.f.q.729.2 | 8 | |||
33.14 | odd | 10 | 77.2.f.a.36.1 | yes | 8 | ||
33.17 | even | 10 | 847.2.a.k.1.1 | 4 | |||
33.20 | odd | 10 | 847.2.f.p.148.2 | 8 | |||
33.26 | odd | 10 | 847.2.f.p.372.2 | 8 | |||
33.29 | even | 10 | 847.2.f.s.372.1 | 8 | |||
33.32 | even | 2 | 847.2.f.q.323.2 | 8 | |||
231.47 | even | 30 | 539.2.q.b.410.2 | 16 | |||
231.80 | even | 30 | 539.2.q.b.520.1 | 16 | |||
231.83 | odd | 10 | 5929.2.a.bb.1.1 | 4 | |||
231.104 | even | 10 | 5929.2.a.bi.1.4 | 4 | |||
231.146 | even | 10 | 539.2.f.d.344.1 | 8 | |||
231.179 | odd | 30 | 539.2.q.c.520.1 | 16 | |||
231.212 | odd | 30 | 539.2.q.c.410.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.a.15.1 | ✓ | 8 | 3.2 | odd | 2 | ||
77.2.f.a.36.1 | yes | 8 | 33.14 | odd | 10 | ||
539.2.f.d.246.1 | 8 | 21.20 | even | 2 | |||
539.2.f.d.344.1 | 8 | 231.146 | even | 10 | |||
539.2.q.b.312.1 | 16 | 21.5 | even | 6 | |||
539.2.q.b.410.2 | 16 | 231.47 | even | 30 | |||
539.2.q.b.422.2 | 16 | 21.17 | even | 6 | |||
539.2.q.b.520.1 | 16 | 231.80 | even | 30 | |||
539.2.q.c.312.1 | 16 | 21.2 | odd | 6 | |||
539.2.q.c.410.2 | 16 | 231.212 | odd | 30 | |||
539.2.q.c.422.2 | 16 | 21.11 | odd | 6 | |||
539.2.q.c.520.1 | 16 | 231.179 | odd | 30 | |||
693.2.m.g.190.2 | 8 | 11.3 | even | 5 | inner | ||
693.2.m.g.631.2 | 8 | 1.1 | even | 1 | trivial | ||
847.2.a.k.1.1 | 4 | 33.17 | even | 10 | |||
847.2.a.l.1.4 | 4 | 33.5 | odd | 10 | |||
847.2.f.p.148.2 | 8 | 33.20 | odd | 10 | |||
847.2.f.p.372.2 | 8 | 33.26 | odd | 10 | |||
847.2.f.q.323.2 | 8 | 33.32 | even | 2 | |||
847.2.f.q.729.2 | 8 | 33.8 | even | 10 | |||
847.2.f.s.148.1 | 8 | 33.2 | even | 10 | |||
847.2.f.s.372.1 | 8 | 33.29 | even | 10 | |||
5929.2.a.bb.1.1 | 4 | 231.83 | odd | 10 | |||
5929.2.a.bi.1.4 | 4 | 231.104 | even | 10 | |||
7623.2.a.ch.1.1 | 4 | 11.5 | even | 5 | |||
7623.2.a.co.1.4 | 4 | 11.6 | odd | 10 |