Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 557.11 | ||
Character | \(\chi\) | \(=\) | 784.557 |
Dual form | 784.2.x.p.373.11 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.561091 | − | 1.29814i | −0.396752 | − | 0.917926i | ||||
\(3\) | −0.614599 | + | 0.164681i | −0.354839 | + | 0.0950788i | −0.431835 | − | 0.901953i | \(-0.642134\pi\) |
0.0769962 | + | 0.997031i | \(0.475467\pi\) | |||||||
\(4\) | −1.37035 | + | 1.45675i | −0.685176 | + | 0.728377i | ||||
\(5\) | −1.45338 | − | 0.389432i | −0.649972 | − | 0.174159i | −0.0812556 | − | 0.996693i | \(-0.525893\pi\) |
−0.568716 | + | 0.822534i | \(0.692560\pi\) | |||||||
\(6\) | 0.558626 | + | 0.705436i | 0.228058 | + | 0.287993i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.65997 | + | 0.961542i | 0.940441 | + | 0.339957i | ||||
\(9\) | −2.24746 | + | 1.29757i | −0.749155 | + | 0.432525i | ||||
\(10\) | 0.309941 | + | 2.10520i | 0.0980118 | + | 0.665724i | ||||
\(11\) | 0.899678 | + | 3.35764i | 0.271263 | + | 1.01237i | 0.958304 | + | 0.285750i | \(0.0922425\pi\) |
−0.687041 | + | 0.726619i | \(0.741091\pi\) | |||||||
\(12\) | 0.602317 | − | 1.12099i | 0.173874 | − | 0.323602i | ||||
\(13\) | −0.433866 | − | 0.433866i | −0.120333 | − | 0.120333i | 0.644376 | − | 0.764709i | \(-0.277117\pi\) |
−0.764709 | + | 0.644376i | \(0.777117\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.957378 | 0.247194 | ||||||||
\(16\) | −0.244266 | − | 3.99253i | −0.0610665 | − | 0.998134i | ||||
\(17\) | 3.24640 | − | 5.62292i | 0.787367 | − | 1.36376i | −0.140208 | − | 0.990122i | \(-0.544777\pi\) |
0.927575 | − | 0.373637i | \(-0.121890\pi\) | |||||||
\(18\) | 2.94547 | + | 2.18947i | 0.694254 | + | 0.516064i | ||||
\(19\) | 0.341695 | − | 1.27522i | 0.0783902 | − | 0.292556i | −0.915590 | − | 0.402112i | \(-0.868276\pi\) |
0.993981 | + | 0.109556i | \(0.0349429\pi\) | |||||||
\(20\) | 2.55895 | − | 1.58356i | 0.572199 | − | 0.354095i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.85390 | − | 3.05186i | 0.821655 | − | 0.650658i | ||||
\(23\) | 1.18252 | − | 0.682730i | 0.246573 | − | 0.142359i | −0.371621 | − | 0.928385i | \(-0.621198\pi\) |
0.618194 | + | 0.786026i | \(0.287865\pi\) | |||||||
\(24\) | −1.79316 | − | 0.152916i | −0.366028 | − | 0.0312138i | ||||
\(25\) | −2.36947 | − | 1.36801i | −0.473894 | − | 0.273603i | ||||
\(26\) | −0.319782 | + | 0.806658i | −0.0627143 | + | 0.158199i | ||||
\(27\) | 2.51736 | − | 2.51736i | 0.484465 | − | 0.484465i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.40449 | + | 2.40449i | 0.446503 | + | 0.446503i | 0.894190 | − | 0.447687i | \(-0.147752\pi\) |
−0.447687 | + | 0.894190i | \(0.647752\pi\) | |||||||
\(30\) | −0.537177 | − | 1.24281i | −0.0980746 | − | 0.226906i | ||||
\(31\) | 3.56343 | − | 6.17204i | 0.640011 | − | 1.10853i | −0.345419 | − | 0.938449i | \(-0.612263\pi\) |
0.985430 | − | 0.170083i | \(-0.0544036\pi\) | |||||||
\(32\) | −5.04583 | + | 2.55727i | −0.891985 | + | 0.452066i | ||||
\(33\) | −1.10588 | − | 1.91544i | −0.192509 | − | 0.333436i | ||||
\(34\) | −9.12089 | − | 1.05931i | −1.56422 | − | 0.181671i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.18957 | − | 5.05214i | 0.198262 | − | 0.842023i | ||||
\(37\) | 4.87836 | + | 1.30715i | 0.801997 | + | 0.214895i | 0.636461 | − | 0.771309i | \(-0.280398\pi\) |
0.165537 | + | 0.986204i | \(0.447064\pi\) | |||||||
\(38\) | −1.84714 | + | 0.271947i | −0.299646 | + | 0.0441157i | ||||
\(39\) | 0.338103 | + | 0.195204i | 0.0541398 | + | 0.0312576i | ||||
\(40\) | −3.49149 | − | 2.43336i | −0.552053 | − | 0.384749i | ||||
\(41\) | 7.83707i | 1.22395i | 0.790879 | + | 0.611973i | \(0.209624\pi\) | ||||
−0.790879 | + | 0.611973i | \(0.790376\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.978094 | − | 0.978094i | 0.149158 | − | 0.149158i | −0.628584 | − | 0.777742i | \(-0.716365\pi\) |
0.777742 | + | 0.628584i | \(0.216365\pi\) | |||||||
\(44\) | −6.12414 | − | 3.29055i | −0.923249 | − | 0.496069i | ||||
\(45\) | 3.77174 | − | 1.01063i | 0.562258 | − | 0.150656i | ||||
\(46\) | −1.54978 | − | 1.15201i | −0.228503 | − | 0.169855i | ||||
\(47\) | −6.31769 | − | 10.9426i | −0.921530 | − | 1.59614i | −0.797049 | − | 0.603915i | \(-0.793607\pi\) |
−0.124481 | − | 0.992222i | \(-0.539727\pi\) | |||||||
\(48\) | 0.807621 | + | 2.41358i | 0.116570 | + | 0.348370i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.446389 | + | 3.84349i | −0.0631290 | + | 0.543552i | ||||
\(51\) | −1.06924 | + | 3.99046i | −0.149724 | + | 0.558777i | ||||
\(52\) | 1.22658 | − | 0.0374866i | 0.170097 | − | 0.00519846i | ||||
\(53\) | −2.34860 | − | 8.76508i | −0.322604 | − | 1.20398i | −0.916698 | − | 0.399580i | \(-0.869156\pi\) |
0.594094 | − | 0.804396i | \(-0.297511\pi\) | |||||||
\(54\) | −4.68036 | − | 1.85542i | −0.636916 | − | 0.252491i | ||||
\(55\) | − | 5.23030i | − | 0.705254i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.840021i | 0.111264i | ||||||||
\(58\) | 1.77223 | − | 4.47051i | 0.232706 | − | 0.587007i | ||||
\(59\) | −1.92480 | − | 7.18346i | −0.250588 | − | 0.935206i | −0.970492 | − | 0.241133i | \(-0.922481\pi\) |
0.719904 | − | 0.694073i | \(-0.244186\pi\) | |||||||
\(60\) | −1.31195 | + | 1.39467i | −0.169372 | + | 0.180050i | ||||
\(61\) | 1.57583 | − | 5.88108i | 0.201764 | − | 0.752995i | −0.788647 | − | 0.614846i | \(-0.789218\pi\) |
0.990411 | − | 0.138149i | \(-0.0441153\pi\) | |||||||
\(62\) | −10.0116 | − | 1.16276i | −1.27148 | − | 0.147671i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.15087 | + | 5.11535i | 0.768859 | + | 0.639418i | ||||
\(65\) | 0.461611 | + | 0.799533i | 0.0572558 | + | 0.0991699i | ||||
\(66\) | −1.86602 | + | 2.51033i | −0.229691 | + | 0.309001i | ||||
\(67\) | 15.4719 | − | 4.14569i | 1.89019 | − | 0.506476i | 0.891640 | − | 0.452746i | \(-0.149556\pi\) |
0.998555 | − | 0.0537302i | \(-0.0171111\pi\) | |||||||
\(68\) | 3.74251 | + | 12.4346i | 0.453846 | + | 1.50792i | ||||
\(69\) | −0.614344 | + | 0.614344i | −0.0739584 | + | 0.0739584i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.41138i | − | 0.998247i | −0.866531 | − | 0.499123i | \(-0.833655\pi\) | ||
0.866531 | − | 0.499123i | \(-0.166345\pi\) | |||||||
\(72\) | −7.22586 | + | 1.29048i | −0.851576 | + | 0.152084i | ||||
\(73\) | 0.483999 | + | 0.279437i | 0.0566478 | + | 0.0327056i | 0.528056 | − | 0.849209i | \(-0.322921\pi\) |
−0.471409 | + | 0.881915i | \(0.656254\pi\) | |||||||
\(74\) | −1.04033 | − | 7.06624i | −0.120936 | − | 0.821434i | ||||
\(75\) | 1.68156 | + | 0.450572i | 0.194170 | + | 0.0520276i | ||||
\(76\) | 1.38944 | + | 2.24527i | 0.159380 | + | 0.257550i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.0636959 | − | 0.548433i | 0.00721214 | − | 0.0620978i | ||||
\(79\) | 0.458833 | + | 0.794722i | 0.0516227 | + | 0.0894132i | 0.890682 | − | 0.454627i | \(-0.150227\pi\) |
−0.839059 | + | 0.544040i | \(0.816894\pi\) | |||||||
\(80\) | −1.19981 | + | 5.89780i | −0.134143 | + | 0.659394i | ||||
\(81\) | 2.76012 | − | 4.78067i | 0.306680 | − | 0.531185i | ||||
\(82\) | 10.1736 | − | 4.39731i | 1.12349 | − | 0.485602i | ||||
\(83\) | 2.41581 | + | 2.41581i | 0.265170 | + | 0.265170i | 0.827150 | − | 0.561981i | \(-0.189960\pi\) |
−0.561981 | + | 0.827150i | \(0.689960\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.90800 | + | 6.90800i | −0.749278 | + | 0.749278i | ||||
\(86\) | −1.81851 | − | 0.720906i | −0.196095 | − | 0.0777373i | ||||
\(87\) | −1.87377 | − | 1.08182i | −0.200889 | − | 0.115984i | ||||
\(88\) | −0.835401 | + | 9.79631i | −0.0890541 | + | 1.04429i | ||||
\(89\) | −13.9976 | + | 8.08152i | −1.48374 | + | 0.856639i | −0.999829 | − | 0.0184769i | \(-0.994118\pi\) |
−0.483913 | + | 0.875116i | \(0.660785\pi\) | |||||||
\(90\) | −3.42824 | − | 4.32920i | −0.361368 | − | 0.456338i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.625904 | + | 2.65823i | −0.0652550 | + | 0.277139i | ||||
\(93\) | −1.17366 | + | 4.38016i | −0.121703 | + | 0.454201i | ||||
\(94\) | −10.6602 | + | 14.3410i | −1.09952 | + | 1.47917i | ||||
\(95\) | −0.993225 | + | 1.72032i | −0.101903 | + | 0.176501i | ||||
\(96\) | 2.68003 | − | 2.40265i | 0.273529 | − | 0.245219i | ||||
\(97\) | −5.39436 | −0.547714 | −0.273857 | − | 0.961770i | \(-0.588300\pi\) | ||||
−0.273857 | + | 0.961770i | \(0.588300\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.37879 | − | 6.37879i | −0.641092 | − | 0.641092i | ||||
\(100\) | 5.23987 | − | 1.57707i | 0.523987 | − | 0.157707i | ||||
\(101\) | 3.20128 | + | 11.9473i | 0.318539 | + | 1.18881i | 0.920649 | + | 0.390392i | \(0.127660\pi\) |
−0.602109 | + | 0.798414i | \(0.705673\pi\) | |||||||
\(102\) | 5.78014 | − | 0.850986i | 0.572319 | − | 0.0842602i | ||||
\(103\) | 13.6924 | − | 7.90533i | 1.34916 | − | 0.778935i | 0.361025 | − | 0.932556i | \(-0.382427\pi\) |
0.988130 | + | 0.153621i | \(0.0490935\pi\) | |||||||
\(104\) | −0.736889 | − | 1.57125i | −0.0722579 | − | 0.154074i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.0606 | + | 7.96682i | −0.977167 | + | 0.773806i | ||||
\(107\) | 8.44147 | + | 2.26189i | 0.816068 | + | 0.218665i | 0.642627 | − | 0.766179i | \(-0.277845\pi\) |
0.173441 | + | 0.984844i | \(0.444511\pi\) | |||||||
\(108\) | 0.217503 | + | 7.11683i | 0.0209292 | + | 0.684818i | ||||
\(109\) | −6.38616 | + | 1.71117i | −0.611684 | + | 0.163900i | −0.551344 | − | 0.834278i | \(-0.685885\pi\) |
−0.0603393 | + | 0.998178i | \(0.519218\pi\) | |||||||
\(110\) | −6.78968 | + | 2.93468i | −0.647371 | + | 0.279810i | ||||
\(111\) | −3.21350 | −0.305012 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.06000 | −0.381932 | −0.190966 | − | 0.981597i | \(-0.561162\pi\) | ||||
−0.190966 | + | 0.981597i | \(0.561162\pi\) | |||||||
\(114\) | 1.09047 | − | 0.471329i | 0.102132 | − | 0.0441440i | ||||
\(115\) | −1.98453 | + | 0.531754i | −0.185059 | + | 0.0495863i | ||||
\(116\) | −6.79775 | + | 0.207751i | −0.631155 | + | 0.0192892i | ||||
\(117\) | 1.53807 | + | 0.412125i | 0.142195 | + | 0.0381009i | ||||
\(118\) | −8.24517 | + | 6.52924i | −0.759029 | + | 0.601066i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.54660 | + | 0.920560i | 0.232471 | + | 0.0840352i | ||||
\(121\) | −0.938079 | + | 0.541600i | −0.0852799 | + | 0.0492364i | ||||
\(122\) | −8.51867 | + | 1.25417i | −0.771244 | + | 0.113547i | ||||
\(123\) | −1.29062 | − | 4.81666i | −0.116371 | − | 0.434303i | ||||
\(124\) | 4.10799 | + | 13.6489i | 0.368909 | + | 1.22571i | ||||
\(125\) | 8.23073 | + | 8.23073i | 0.736179 | + | 0.736179i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.00650 | 0.799197 | 0.399599 | − | 0.916690i | \(-0.369149\pi\) | ||||
0.399599 | + | 0.916690i | \(0.369149\pi\) | |||||||
\(128\) | 3.18925 | − | 10.8549i | 0.281893 | − | 0.959446i | ||||
\(129\) | −0.440062 | + | 0.762209i | −0.0387453 | + | 0.0671088i | ||||
\(130\) | 0.778903 | − | 1.04785i | 0.0683143 | − | 0.0919024i | ||||
\(131\) | −4.03161 | + | 15.0462i | −0.352243 | + | 1.31459i | 0.531675 | + | 0.846948i | \(0.321563\pi\) |
−0.883918 | + | 0.467641i | \(0.845104\pi\) | |||||||
\(132\) | 4.30578 | + | 1.01384i | 0.374770 | + | 0.0882431i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −14.0629 | − | 17.7587i | −1.21485 | − | 1.53411i | ||||
\(135\) | −4.63902 | + | 2.67834i | −0.399263 | + | 0.230515i | ||||
\(136\) | 14.0420 | − | 11.8353i | 1.20409 | − | 1.01487i | ||||
\(137\) | −7.78255 | − | 4.49326i | −0.664908 | − | 0.383885i | 0.129237 | − | 0.991614i | \(-0.458747\pi\) |
−0.794144 | + | 0.607729i | \(0.792081\pi\) | |||||||
\(138\) | 1.14221 | + | 0.452804i | 0.0972314 | + | 0.0385452i | ||||
\(139\) | 13.0941 | − | 13.0941i | 1.11063 | − | 1.11063i | 0.117562 | − | 0.993066i | \(-0.462492\pi\) |
0.993066 | − | 0.117562i | \(-0.0375078\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.68488 | + | 5.68488i | 0.478753 | + | 0.478753i | ||||
\(142\) | −10.9192 | + | 4.71955i | −0.916317 | + | 0.396056i | ||||
\(143\) | 1.06643 | − | 1.84711i | 0.0891791 | − | 0.154463i | ||||
\(144\) | 5.72959 | + | 8.65613i | 0.477466 | + | 0.721344i | ||||
\(145\) | −2.55825 | − | 4.43103i | −0.212451 | − | 0.367977i | ||||
\(146\) | 0.0911816 | − | 0.785090i | 0.00754625 | − | 0.0649745i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.58927 | + | 5.31531i | −0.706034 | + | 0.436916i | ||||
\(149\) | 17.1013 | + | 4.58227i | 1.40099 | + | 0.375394i | 0.878700 | − | 0.477374i | \(-0.158411\pi\) |
0.522289 | + | 0.852768i | \(0.325078\pi\) | |||||||
\(150\) | −0.358601 | − | 2.43572i | −0.0292796 | − | 0.198875i | ||||
\(151\) | 11.1788 | + | 6.45409i | 0.909718 | + | 0.525226i | 0.880341 | − | 0.474342i | \(-0.157314\pi\) |
0.0293779 | + | 0.999568i | \(0.490647\pi\) | |||||||
\(152\) | 2.13508 | − | 3.06350i | 0.173178 | − | 0.248483i | ||||
\(153\) | 16.8498i | 1.36222i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.58261 | + | 7.58261i | −0.609050 | + | 0.609050i | ||||
\(156\) | −0.747684 | + | 0.225035i | −0.0598626 | + | 0.0180172i | ||||
\(157\) | 16.5925 | − | 4.44594i | 1.32422 | − | 0.354824i | 0.473665 | − | 0.880705i | \(-0.342931\pi\) |
0.850558 | + | 0.525881i | \(0.176264\pi\) | |||||||
\(158\) | 0.774216 | − | 1.04154i | 0.0615933 | − | 0.0828607i | ||||
\(159\) | 2.88689 | + | 5.00024i | 0.228945 | + | 0.396545i | ||||
\(160\) | 8.32939 | − | 1.75168i | 0.658496 | − | 0.138482i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.75467 | − | 0.900640i | −0.609265 | − | 0.0707610i | ||||
\(163\) | −3.88545 | + | 14.5007i | −0.304332 | + | 1.13578i | 0.629187 | + | 0.777254i | \(0.283388\pi\) |
−0.933519 | + | 0.358528i | \(0.883279\pi\) | |||||||
\(164\) | −11.4167 | − | 10.7396i | −0.891494 | − | 0.838618i | ||||
\(165\) | 0.861332 | + | 3.21454i | 0.0670546 | + | 0.250251i | ||||
\(166\) | 1.78058 | − | 4.49156i | 0.138200 | − | 0.348613i | ||||
\(167\) | − | 24.1537i | − | 1.86907i | −0.355872 | − | 0.934535i | \(-0.615816\pi\) | ||
0.355872 | − | 0.934535i | \(-0.384184\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.6235i | − | 0.971040i | ||||||
\(170\) | 12.8436 | + | 5.09155i | 0.985059 | + | 0.390504i | ||||
\(171\) | 0.886749 | + | 3.30939i | 0.0678114 | + | 0.253076i | ||||
\(172\) | 0.0845087 | + | 2.76518i | 0.00644373 | + | 0.210843i | ||||
\(173\) | −0.524598 | + | 1.95782i | −0.0398844 | + | 0.148851i | −0.982997 | − | 0.183624i | \(-0.941217\pi\) |
0.943112 | + | 0.332475i | \(0.107884\pi\) | |||||||
\(174\) | −0.353004 | + | 3.03943i | −0.0267611 | + | 0.230418i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 13.1858 | − | 4.41216i | 0.993914 | − | 0.332579i | ||||
\(177\) | 2.36596 | + | 4.09797i | 0.177837 | + | 0.308022i | ||||
\(178\) | 18.3449 | + | 13.6364i | 1.37501 | + | 1.02209i | ||||
\(179\) | −8.27206 | + | 2.21649i | −0.618283 | + | 0.165668i | −0.554347 | − | 0.832286i | \(-0.687032\pi\) |
−0.0639358 | + | 0.997954i | \(0.520365\pi\) | |||||||
\(180\) | −3.69637 | + | 6.87942i | −0.275511 | + | 0.512762i | ||||
\(181\) | 5.02152 | − | 5.02152i | 0.373247 | − | 0.373247i | −0.495412 | − | 0.868658i | \(-0.664983\pi\) |
0.868658 | + | 0.495412i | \(0.164983\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.87402i | 0.286375i | ||||||||
\(184\) | 3.80195 | − | 0.678995i | 0.280283 | − | 0.0500562i | ||||
\(185\) | −6.58107 | − | 3.79958i | −0.483850 | − | 0.279351i | ||||
\(186\) | 6.34461 | − | 0.934091i | 0.465209 | − | 0.0684909i | ||||
\(187\) | 21.8005 | + | 5.84143i | 1.59421 | + | 0.427167i | ||||
\(188\) | 24.5981 | + | 5.79185i | 1.79400 | + | 0.422414i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.79051 | + | 0.324094i | 0.202445 | + | 0.0235123i | ||||
\(191\) | −6.96812 | − | 12.0691i | −0.504196 | − | 0.873292i | −0.999988 | − | 0.00485148i | \(-0.998456\pi\) |
0.495793 | − | 0.868441i | \(-0.334878\pi\) | |||||||
\(192\) | −4.62272 | − | 2.13095i | −0.333616 | − | 0.153788i | ||||
\(193\) | 1.59321 | − | 2.75953i | 0.114682 | − | 0.198635i | −0.802971 | − | 0.596019i | \(-0.796748\pi\) |
0.917653 | + | 0.397384i | \(0.130082\pi\) | |||||||
\(194\) | 3.02673 | + | 7.00266i | 0.217307 | + | 0.502761i | ||||
\(195\) | −0.415374 | − | 0.415374i | −0.0297455 | − | 0.0297455i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.6310 | + | 18.6310i | −1.32740 | + | 1.32740i | −0.419772 | + | 0.907630i | \(0.637890\pi\) |
−0.907630 | + | 0.419772i | \(0.862110\pi\) | |||||||
\(198\) | −4.70150 | + | 11.8597i | −0.334121 | + | 0.842830i | ||||
\(199\) | −9.10258 | − | 5.25538i | −0.645265 | − | 0.372544i | 0.141375 | − | 0.989956i | \(-0.454848\pi\) |
−0.786640 | + | 0.617412i | \(0.788181\pi\) | |||||||
\(200\) | −4.98731 | − | 5.91722i | −0.352656 | − | 0.418411i | ||||
\(201\) | −8.82630 | + | 5.09587i | −0.622559 | + | 0.359435i | ||||
\(202\) | 13.7132 | − | 10.8593i | 0.964854 | − | 0.764056i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4.34789 | − | 7.02597i | −0.304413 | − | 0.491916i | ||||
\(205\) | 3.05201 | − | 11.3903i | 0.213162 | − | 0.795530i | ||||
\(206\) | −17.9450 | − | 13.3391i | −1.25028 | − | 0.929381i | ||||
\(207\) | −1.77178 | + | 3.06882i | −0.123148 | + | 0.213298i | ||||
\(208\) | −1.62625 | + | 1.83820i | −0.112760 | + | 0.127456i | ||||
\(209\) | 4.58916 | 0.317439 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.8537 | − | 15.8537i | −1.09142 | − | 1.09142i | −0.995378 | − | 0.0960391i | \(-0.969383\pi\) |
−0.0960391 | − | 0.995378i | \(-0.530617\pi\) | |||||||
\(212\) | 15.9870 | + | 8.58992i | 1.09799 | + | 0.589958i | ||||
\(213\) | 1.38520 | + | 5.16962i | 0.0949121 | + | 0.354217i | ||||
\(214\) | −1.80019 | − | 12.2274i | −0.123058 | − | 0.835846i | ||||
\(215\) | −1.80244 | + | 1.04064i | −0.122926 | + | 0.0709712i | ||||
\(216\) | 9.11663 | − | 4.27554i | 0.620308 | − | 0.290914i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.80456 | + | 7.33004i | 0.393135 | + | 0.496453i | ||||
\(219\) | −0.343483 | − | 0.0920361i | −0.0232105 | − | 0.00621922i | ||||
\(220\) | 7.61926 | + | 7.16736i | 0.513691 | + | 0.483223i | ||||
\(221\) | −3.84809 | + | 1.03109i | −0.258851 | + | 0.0693589i | ||||
\(222\) | 1.80307 | + | 4.17158i | 0.121014 | + | 0.279978i | ||||
\(223\) | −1.50291 | −0.100642 | −0.0503211 | − | 0.998733i | \(-0.516024\pi\) | ||||
−0.0503211 | + | 0.998733i | \(0.516024\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.10040 | 0.473360 | ||||||||
\(226\) | 2.27803 | + | 5.27046i | 0.151532 | + | 0.350586i | ||||
\(227\) | −15.5373 | + | 4.16320i | −1.03124 | + | 0.276321i | −0.734481 | − | 0.678630i | \(-0.762574\pi\) |
−0.296764 | + | 0.954951i | \(0.595907\pi\) | |||||||
\(228\) | −1.22370 | − | 1.15113i | −0.0810418 | − | 0.0762351i | ||||
\(229\) | 21.6115 | + | 5.79079i | 1.42813 | + | 0.382666i | 0.888361 | − | 0.459146i | \(-0.151845\pi\) |
0.539770 | + | 0.841813i | \(0.318511\pi\) | |||||||
\(230\) | 1.80380 | + | 2.27785i | 0.118939 | + | 0.150197i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.08385 | + | 8.70789i | 0.268118 | + | 0.571701i | ||||
\(233\) | −10.4572 | + | 6.03746i | −0.685074 | + | 0.395527i | −0.801764 | − | 0.597641i | \(-0.796105\pi\) |
0.116690 | + | 0.993168i | \(0.462772\pi\) | |||||||
\(234\) | −0.328001 | − | 2.22788i | −0.0214421 | − | 0.145641i | ||||
\(235\) | 4.92063 | + | 18.3640i | 0.320986 | + | 1.19794i | ||||
\(236\) | 13.1022 | + | 7.03991i | 0.852880 | + | 0.458259i | ||||
\(237\) | −0.412874 | − | 0.412874i | −0.0268190 | − | 0.0268190i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.3681 | 1.51156 | 0.755778 | − | 0.654828i | \(-0.227259\pi\) | ||||
0.755778 | + | 0.654828i | \(0.227259\pi\) | |||||||
\(240\) | −0.233855 | − | 3.82237i | −0.0150953 | − | 0.246733i | ||||
\(241\) | −4.69064 | + | 8.12443i | −0.302151 | + | 0.523341i | −0.976623 | − | 0.214960i | \(-0.931038\pi\) |
0.674472 | + | 0.738300i | \(0.264371\pi\) | |||||||
\(242\) | 1.22942 | + | 0.913874i | 0.0790303 | + | 0.0587460i | ||||
\(243\) | −3.67333 | + | 13.7090i | −0.235644 | + | 0.879436i | ||||
\(244\) | 6.40784 | + | 10.3548i | 0.410220 | + | 0.662895i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.52856 | + | 4.37799i | −0.352488 | + | 0.279131i | ||||
\(247\) | −0.701525 | + | 0.405026i | −0.0446370 | + | 0.0257712i | ||||
\(248\) | 15.4133 | − | 12.9911i | 0.978745 | − | 0.824933i | ||||
\(249\) | −1.88259 | − | 1.08692i | −0.119305 | − | 0.0688805i | ||||
\(250\) | 6.06648 | − | 15.3029i | 0.383678 | − | 0.967838i | ||||
\(251\) | −2.22827 | + | 2.22827i | −0.140647 | + | 0.140647i | −0.773925 | − | 0.633278i | \(-0.781709\pi\) |
0.633278 | + | 0.773925i | \(0.281709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.35625 | + | 3.35625i | 0.211006 | + | 0.211006i | ||||
\(254\) | −5.05347 | − | 11.6917i | −0.317083 | − | 0.733604i | ||||
\(255\) | 3.10803 | − | 5.38327i | 0.194632 | − | 0.337113i | ||||
\(256\) | −15.8807 | + | 1.95048i | −0.992542 | + | 0.121905i | ||||
\(257\) | 4.88188 | + | 8.45566i | 0.304523 | + | 0.527450i | 0.977155 | − | 0.212528i | \(-0.0681695\pi\) |
−0.672632 | + | 0.739977i | \(0.734836\pi\) | |||||||
\(258\) | 1.23637 | + | 0.143594i | 0.0769731 | + | 0.00893978i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.79729 | − | 0.423189i | −0.111463 | − | 0.0262451i | ||||
\(261\) | −8.52401 | − | 2.28400i | −0.527623 | − | 0.141376i | ||||
\(262\) | 21.7942 | − | 3.20867i | 1.34645 | − | 0.198232i | ||||
\(263\) | 0.887606 | + | 0.512459i | 0.0547321 | + | 0.0315996i | 0.527116 | − | 0.849793i | \(-0.323273\pi\) |
−0.472384 | + | 0.881393i | \(0.656607\pi\) | |||||||
\(264\) | −1.09983 | − | 6.15838i | −0.0676900 | − | 0.379022i | ||||
\(265\) | 13.6536i | 0.838735i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.27203 | − | 7.27203i | 0.445041 | − | 0.445041i | ||||
\(268\) | −15.1627 | + | 28.2198i | −0.926211 | + | 1.72380i | ||||
\(269\) | −21.0485 | + | 5.63993i | −1.28335 | + | 0.343872i | −0.835131 | − | 0.550052i | \(-0.814608\pi\) |
−0.448218 | + | 0.893924i | \(0.647941\pi\) | |||||||
\(270\) | 6.07978 | + | 4.51932i | 0.370003 | + | 0.275037i | ||||
\(271\) | −12.5358 | − | 21.7126i | −0.761495 | − | 1.31895i | −0.942080 | − | 0.335388i | \(-0.891132\pi\) |
0.180585 | − | 0.983559i | \(-0.442201\pi\) | |||||||
\(272\) | −23.2427 | − | 11.5879i | −1.40930 | − | 0.702617i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.46617 | + | 12.6240i | −0.0885746 | + | 0.762643i | ||||
\(275\) | 2.46154 | − | 9.18661i | 0.148437 | − | 0.553973i | ||||
\(276\) | −0.0530802 | − | 1.73682i | −0.00319505 | − | 0.104544i | ||||
\(277\) | −1.74009 | − | 6.49409i | −0.104552 | − | 0.390192i | 0.893742 | − | 0.448581i | \(-0.148070\pi\) |
−0.998294 | + | 0.0583888i | \(0.981404\pi\) | |||||||
\(278\) | −24.3450 | − | 9.65104i | −1.46012 | − | 0.578831i | ||||
\(279\) | 18.4953i | 1.10728i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 12.0895i | − | 0.721197i | −0.932721 | − | 0.360599i | \(-0.882572\pi\) | ||
0.932721 | − | 0.360599i | \(-0.117428\pi\) | |||||||
\(282\) | 4.19005 | − | 10.5695i | 0.249514 | − | 0.629406i | ||||
\(283\) | 4.43421 | + | 16.5487i | 0.263587 | + | 0.983719i | 0.963110 | + | 0.269109i | \(0.0867291\pi\) |
−0.699523 | + | 0.714610i | \(0.746604\pi\) | |||||||
\(284\) | 12.2533 | + | 11.5266i | 0.727100 | + | 0.683975i | ||||
\(285\) | 0.327131 | − | 1.22087i | 0.0193776 | − | 0.0723181i | ||||
\(286\) | −2.99617 | − | 0.347980i | −0.177167 | − | 0.0205765i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 8.02207 | − | 12.2947i | 0.472705 | − | 0.724473i | ||||
\(289\) | −12.5782 | − | 21.7861i | −0.739893 | − | 1.28153i | ||||
\(290\) | −4.31669 | + | 5.80719i | −0.253485 | + | 0.341010i | ||||
\(291\) | 3.31537 | − | 0.888350i | 0.194350 | − | 0.0520760i | ||||
\(292\) | −1.07032 | + | 0.322141i | −0.0626358 | + | 0.0188519i | ||||
\(293\) | −7.66847 | + | 7.66847i | −0.447997 | + | 0.447997i | −0.894688 | − | 0.446691i | \(-0.852602\pi\) |
0.446691 | + | 0.894688i | \(0.352602\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.1899i | 0.651500i | ||||||||
\(296\) | 11.7194 | + | 8.16774i | 0.681177 | + | 0.474740i | ||||
\(297\) | 10.7172 | + | 6.18758i | 0.621875 | + | 0.359040i | ||||
\(298\) | −3.64693 | − | 24.7710i | −0.211261 | − | 1.43494i | ||||
\(299\) | −0.809269 | − | 0.216843i | −0.0468012 | − | 0.0125404i | ||||
\(300\) | −2.96070 | + | 1.83218i | −0.170936 | + | 0.105781i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.10600 | − | 18.1330i | 0.121187 | − | 1.04344i | ||||
\(303\) | −3.93501 | − | 6.81563i | −0.226060 | − | 0.391548i | ||||
\(304\) | −5.17483 | − | 1.05273i | −0.296797 | − | 0.0603785i | ||||
\(305\) | −4.58056 | + | 7.93377i | −0.262282 | + | 0.454286i | ||||
\(306\) | 21.8734 | − | 9.45426i | 1.25042 | − | 0.540464i | ||||
\(307\) | −3.93313 | − | 3.93313i | −0.224476 | − | 0.224476i | 0.585905 | − | 0.810380i | \(-0.300739\pi\) |
−0.810380 | + | 0.585905i | \(0.800739\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.11349 | + | 7.11349i | −0.404672 | + | 0.404672i | ||||
\(310\) | 14.0979 | + | 5.58878i | 0.800705 | + | 0.317421i | ||||
\(311\) | −2.05948 | − | 1.18904i | −0.116782 | − | 0.0674243i | 0.440471 | − | 0.897767i | \(-0.354811\pi\) |
−0.557253 | + | 0.830343i | \(0.688145\pi\) | |||||||
\(312\) | 0.711647 | + | 0.844336i | 0.0402891 | + | 0.0478011i | ||||
\(313\) | −13.2786 | + | 7.66638i | −0.750548 | + | 0.433329i | −0.825892 | − | 0.563828i | \(-0.809328\pi\) |
0.0753437 | + | 0.997158i | \(0.475995\pi\) | |||||||
\(314\) | −15.0814 | − | 19.0448i | −0.851090 | − | 1.07476i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.78648 | − | 0.420642i | −0.100497 | − | 0.0236630i | ||||
\(317\) | 6.87589 | − | 25.6612i | 0.386188 | − | 1.44127i | −0.450097 | − | 0.892980i | \(-0.648610\pi\) |
0.836285 | − | 0.548295i | \(-0.184723\pi\) | |||||||
\(318\) | 4.87122 | − | 6.55319i | 0.273164 | − | 0.367484i | ||||
\(319\) | −5.91016 | + | 10.2367i | −0.330905 | + | 0.573145i | ||||
\(320\) | −6.94748 | − | 9.82989i | −0.388376 | − | 0.549508i | ||||
\(321\) | −5.56061 | −0.310363 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.06120 | − | 6.06120i | −0.337254 | − | 0.337254i | ||||
\(324\) | 3.18192 | + | 10.5720i | 0.176773 | + | 0.587334i | ||||
\(325\) | 0.434497 | + | 1.62157i | 0.0241016 | + | 0.0899483i | ||||
\(326\) | 21.0041 | − | 3.09234i | 1.16331 | − | 0.171269i | ||||
\(327\) | 3.64313 | − | 2.10336i | 0.201466 | − | 0.116316i | ||||
\(328\) | −7.53568 | + | 20.8464i | −0.416088 | + | 1.15105i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.68964 | − | 2.92178i | 0.203108 | − | 0.160839i | ||||
\(331\) | −16.1131 | − | 4.31749i | −0.885655 | − | 0.237310i | −0.212809 | − | 0.977094i | \(-0.568261\pi\) |
−0.672845 | + | 0.739783i | \(0.734928\pi\) | |||||||
\(332\) | −6.82976 | + | 0.208730i | −0.374832 | + | 0.0114555i | ||||
\(333\) | −12.6601 | + | 3.39225i | −0.693767 | + | 0.185894i | ||||
\(334\) | −31.3550 | + | 13.5524i | −1.71567 | + | 0.741556i | ||||
\(335\) | −24.1010 | −1.31678 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.0461 | 0.874089 | 0.437044 | − | 0.899440i | \(-0.356025\pi\) | ||||
0.437044 | + | 0.899440i | \(0.356025\pi\) | |||||||
\(338\) | −16.3871 | + | 7.08295i | −0.891343 | + | 0.385262i | ||||
\(339\) | 2.49527 | − | 0.668605i | 0.135524 | − | 0.0363137i | ||||
\(340\) | −0.596861 | − | 19.5297i | −0.0323693 | − | 1.05914i | ||||
\(341\) | 23.9295 | + | 6.41188i | 1.29585 | + | 0.347223i | ||||
\(342\) | 3.79852 | − | 3.00800i | 0.205400 | − | 0.162654i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.54218 | − | 1.66122i | 0.190981 | − | 0.0895670i | ||||
\(345\) | 1.13212 | − | 0.653631i | 0.0609514 | − | 0.0351903i | ||||
\(346\) | 2.83588 | − | 0.417516i | 0.152458 | − | 0.0224458i | ||||
\(347\) | 0.0523108 | + | 0.195227i | 0.00280819 | + | 0.0104803i | 0.967316 | − | 0.253575i | \(-0.0816065\pi\) |
−0.964508 | + | 0.264055i | \(0.914940\pi\) | |||||||
\(348\) | 4.14368 | − | 1.24715i | 0.222124 | − | 0.0668540i | ||||
\(349\) | −22.4847 | − | 22.4847i | −1.20358 | − | 1.20358i | −0.973070 | − | 0.230509i | \(-0.925961\pi\) |
−0.230509 | − | 0.973070i | \(-0.574039\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.18439 | −0.116594 | ||||||||
\(352\) | −13.1260 | − | 14.6414i | −0.699619 | − | 0.780388i | ||||
\(353\) | −4.81244 | + | 8.33539i | −0.256140 | + | 0.443648i | −0.965205 | − | 0.261496i | \(-0.915784\pi\) |
0.709064 | + | 0.705144i | \(0.249118\pi\) | |||||||
\(354\) | 3.99223 | − | 5.37069i | 0.212184 | − | 0.285449i | ||||
\(355\) | −3.27566 | + | 12.2249i | −0.173854 | + | 0.648832i | ||||
\(356\) | 7.40886 | − | 31.4656i | 0.392669 | − | 1.66767i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.51871 | + | 9.49467i | 0.397376 | + | 0.501809i | ||||
\(359\) | 14.8625 | − | 8.58090i | 0.784415 | − | 0.452882i | −0.0535775 | − | 0.998564i | \(-0.517062\pi\) |
0.837993 | + | 0.545681i | \(0.183729\pi\) | |||||||
\(360\) | 11.0045 | + | 0.938430i | 0.579987 | + | 0.0494596i | ||||
\(361\) | 14.9450 | + | 8.62853i | 0.786581 | + | 0.454133i | ||||
\(362\) | −9.33618 | − | 3.70112i | −0.490699 | − | 0.194527i | ||||
\(363\) | 0.487351 | − | 0.487351i | 0.0255793 | − | 0.0255793i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.594613 | − | 0.594613i | −0.0311235 | − | 0.0311235i | ||||
\(366\) | 5.02903 | − | 2.17368i | 0.262871 | − | 0.113620i | ||||
\(367\) | −7.22745 | + | 12.5183i | −0.377270 | + | 0.653451i | −0.990664 | − | 0.136326i | \(-0.956470\pi\) |
0.613394 | + | 0.789777i | \(0.289804\pi\) | |||||||
\(368\) | −3.01467 | − | 4.55450i | −0.157151 | − | 0.237419i | ||||
\(369\) | −10.1692 | − | 17.6135i | −0.529387 | − | 0.916925i | ||||
\(370\) | −1.23982 | + | 10.6751i | −0.0644552 | + | 0.554971i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.77249 | − | 7.71210i | −0.247442 | − | 0.399854i | ||||
\(373\) | −11.6214 | − | 3.11394i | −0.601733 | − | 0.161234i | −0.0549228 | − | 0.998491i | \(-0.517491\pi\) |
−0.546810 | + | 0.837257i | \(0.684158\pi\) | |||||||
\(374\) | −4.64906 | − | 31.5777i | −0.240397 | − | 1.63285i | ||||
\(375\) | −6.41405 | − | 3.70315i | −0.331220 | − | 0.191230i | ||||
\(376\) | −6.28313 | − | 35.1816i | −0.324028 | − | 1.81435i | ||||
\(377\) | − | 2.08645i | − | 0.107458i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.5029 | + | 13.5029i | −0.693598 | + | 0.693598i | −0.963022 | − | 0.269424i | \(-0.913167\pi\) |
0.269424 | + | 0.963022i | \(0.413167\pi\) | |||||||
\(380\) | −1.14501 | − | 3.80433i | −0.0587378 | − | 0.195158i | ||||
\(381\) | −5.53538 | + | 1.48320i | −0.283586 | + | 0.0759867i | ||||
\(382\) | −11.7577 | + | 15.8175i | −0.601577 | + | 0.809294i | ||||
\(383\) | −12.1233 | − | 20.9982i | −0.619472 | − | 1.07296i | −0.989582 | − | 0.143969i | \(-0.954013\pi\) |
0.370110 | − | 0.928988i | \(-0.379320\pi\) | |||||||
\(384\) | −0.172513 | + | 7.19661i | −0.00880349 | + | 0.367251i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.47620 | − | 0.519873i | −0.227833 | − | 0.0264608i | ||||
\(387\) | −0.929082 | + | 3.46738i | −0.0472279 | + | 0.176257i | ||||
\(388\) | 7.39218 | − | 7.85826i | 0.375281 | − | 0.398943i | ||||
\(389\) | −2.93716 | − | 10.9616i | −0.148920 | − | 0.555777i | −0.999550 | − | 0.0300114i | \(-0.990446\pi\) |
0.850630 | − | 0.525765i | \(-0.176221\pi\) | |||||||
\(390\) | −0.306152 | + | 0.772277i | −0.0155026 | + | 0.0391058i | ||||
\(391\) | − | 8.86565i | − | 0.448355i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 9.91129i | − | 0.499958i | ||||||
\(394\) | 34.6393 | + | 13.7320i | 1.74510 | + | 0.691808i | ||||
\(395\) | −0.357368 | − | 1.33372i | −0.0179812 | − | 0.0671066i | ||||
\(396\) | 18.0335 | − | 0.551136i | 0.906218 | − | 0.0276956i | ||||
\(397\) | 6.17957 | − | 23.0625i | 0.310144 | − | 1.15747i | −0.618283 | − | 0.785956i | \(-0.712171\pi\) |
0.928427 | − | 0.371516i | \(-0.121162\pi\) | |||||||
\(398\) | −1.71485 | + | 14.7652i | −0.0859579 | + | 0.740113i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.88306 | + | 9.79435i | −0.244153 | + | 0.489717i | ||||
\(401\) | 2.56161 | + | 4.43683i | 0.127921 | + | 0.221565i | 0.922871 | − | 0.385110i | \(-0.125836\pi\) |
−0.794950 | + | 0.606675i | \(0.792503\pi\) | |||||||
\(402\) | 11.5675 | + | 8.59856i | 0.576936 | + | 0.428857i | ||||
\(403\) | −4.22389 | + | 1.13179i | −0.210407 | + | 0.0563783i | ||||
\(404\) | −21.7912 | − | 11.7086i | −1.08415 | − | 0.582525i | ||||
\(405\) | −5.87325 | + | 5.87325i | −0.291844 | + | 0.291844i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.5558i | 0.870210i | ||||||||
\(408\) | −6.68115 | + | 9.58639i | −0.330766 | + | 0.474597i | ||||
\(409\) | −12.2891 | − | 7.09510i | −0.607655 | − | 0.350830i | 0.164392 | − | 0.986395i | \(-0.447434\pi\) |
−0.772047 | + | 0.635565i | \(0.780767\pi\) | |||||||
\(410\) | −16.4986 | + | 2.42903i | −0.814810 | + | 0.119961i | ||||
\(411\) | 5.52310 | + | 1.47991i | 0.272434 | + | 0.0729986i | ||||
\(412\) | −7.24734 | + | 30.7796i | −0.357051 | + | 1.51640i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.97790 | + | 0.578142i | 0.244651 | + | 0.0284141i | ||||
\(415\) | −2.57030 | − | 4.45189i | −0.126171 | − | 0.218535i | ||||
\(416\) | 3.29872 | + | 1.07970i | 0.161733 | + | 0.0529366i | ||||
\(417\) | −5.89127 | + | 10.2040i | −0.288497 | + | 0.499691i | ||||
\(418\) | −2.57494 | − | 5.95739i | −0.125944 | − | 0.291385i | ||||
\(419\) | 4.24793 | + | 4.24793i | 0.207525 | + | 0.207525i | 0.803215 | − | 0.595690i | \(-0.203121\pi\) |
−0.595690 | + | 0.803215i | \(0.703121\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.2505 | − | 12.2505i | 0.597051 | − | 0.597051i | −0.342475 | − | 0.939527i | \(-0.611265\pi\) |
0.939527 | + | 0.342475i | \(0.111265\pi\) | |||||||
\(422\) | −11.6850 | + | 29.4758i | −0.568819 | + | 1.43486i | ||||
\(423\) | 28.3976 | + | 16.3953i | 1.38074 | + | 0.797169i | ||||
\(424\) | 2.18080 | − | 25.5731i | 0.105909 | − | 1.24194i | ||||
\(425\) | −15.3845 | + | 8.88223i | −0.746257 | + | 0.430851i | ||||
\(426\) | 5.93369 | − | 4.69881i | 0.287488 | − | 0.227658i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −14.8628 | + | 9.19757i | −0.718421 | + | 0.444581i | ||||
\(429\) | −0.351241 | + | 1.31085i | −0.0169581 | + | 0.0632884i | ||||
\(430\) | 2.36224 | + | 1.75594i | 0.113917 | + | 0.0846788i | ||||
\(431\) | 3.25246 | − | 5.63343i | 0.156666 | − | 0.271353i | −0.776999 | − | 0.629502i | \(-0.783259\pi\) |
0.933664 | + | 0.358149i | \(0.116592\pi\) | |||||||
\(432\) | −10.6655 | − | 9.43573i | −0.513146 | − | 0.453977i | ||||
\(433\) | −12.3043 | −0.591305 | −0.295653 | − | 0.955296i | \(-0.595537\pi\) | ||||
−0.295653 | + | 0.955296i | \(0.595537\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.30201 | + | 2.30201i | 0.110373 | + | 0.110373i | ||||
\(436\) | 6.25855 | − | 11.6480i | 0.299730 | − | 0.557837i | ||||
\(437\) | −0.466570 | − | 1.74126i | −0.0223191 | − | 0.0832960i | ||||
\(438\) | 0.0732495 | + | 0.497532i | 0.00350000 | + | 0.0237730i | ||||
\(439\) | −14.0697 | + | 8.12313i | −0.671509 | + | 0.387696i | −0.796648 | − | 0.604443i | \(-0.793396\pi\) |
0.125139 | + | 0.992139i | \(0.460062\pi\) | |||||||
\(440\) | 5.02915 | − | 13.9124i | 0.239756 | − | 0.663249i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.49764 | + | 4.41684i | 0.166366 | + | 0.210088i | ||||
\(443\) | 13.8662 | + | 3.71543i | 0.658801 | + | 0.176525i | 0.572705 | − | 0.819762i | \(-0.305894\pi\) |
0.0860962 | + | 0.996287i | \(0.472561\pi\) | |||||||
\(444\) | 4.40363 | − | 4.68128i | 0.208987 | − | 0.222164i | ||||
\(445\) | 23.4910 | − | 6.29441i | 1.11358 | − | 0.298383i | ||||
\(446\) | 0.843270 | + | 1.95099i | 0.0399300 | + | 0.0923822i | ||||
\(447\) | −11.2650 | −0.532818 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.89895 | 0.467160 | 0.233580 | − | 0.972338i | \(-0.424956\pi\) | ||||
0.233580 | + | 0.972338i | \(0.424956\pi\) | |||||||
\(450\) | −3.98397 | − | 9.21733i | −0.187806 | − | 0.434509i | ||||
\(451\) | −26.3141 | + | 7.05085i | −1.23908 | + | 0.332011i | ||||
\(452\) | 5.56363 | − | 5.91442i | 0.261691 | − | 0.278191i | ||||
\(453\) | −7.93335 | − | 2.12573i | −0.372741 | − | 0.0998757i | ||||
\(454\) | 14.1223 | + | 17.8337i | 0.662790 | + | 0.836975i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.807716 | + | 2.23443i | −0.0378248 | + | 0.104637i | ||||
\(457\) | −11.1211 | + | 6.42079i | −0.520224 | + | 0.300352i | −0.737026 | − | 0.675864i | \(-0.763771\pi\) |
0.216802 | + | 0.976216i | \(0.430437\pi\) | |||||||
\(458\) | −4.60877 | − | 31.3040i | −0.215353 | − | 1.46274i | ||||
\(459\) | −5.98257 | − | 22.3272i | −0.279242 | − | 1.04215i | ||||
\(460\) | 1.94488 | − | 3.61967i | 0.0906803 | − | 0.168768i | ||||
\(461\) | −7.50371 | − | 7.50371i | −0.349482 | − | 0.349482i | 0.510434 | − | 0.859917i | \(-0.329485\pi\) |
−0.859917 | + | 0.510434i | \(0.829485\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.2985 | 1.40809 | 0.704044 | − | 0.710156i | \(-0.251376\pi\) | ||||
0.704044 | + | 0.710156i | \(0.251376\pi\) | |||||||
\(464\) | 9.01267 | − | 10.1873i | 0.418403 | − | 0.472936i | ||||
\(465\) | 3.41155 | − | 5.90898i | 0.158207 | − | 0.274022i | ||||
\(466\) | 13.7049 | + | 10.1874i | 0.634869 | + | 0.471921i | ||||
\(467\) | 1.82145 | − | 6.79774i | 0.0842867 | − | 0.314562i | −0.910892 | − | 0.412646i | \(-0.864605\pi\) |
0.995178 | + | 0.0980839i | \(0.0312713\pi\) | |||||||
\(468\) | −2.70806 | + | 1.67583i | −0.125180 | + | 0.0774655i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 21.0782 | − | 16.6916i | 0.972266 | − | 0.769925i | ||||
\(471\) | −9.46555 | + | 5.46494i | −0.436149 | + | 0.251811i | ||||
\(472\) | 1.78728 | − | 20.9586i | 0.0822664 | − | 0.964696i | ||||
\(473\) | 4.16406 | + | 2.40412i | 0.191464 | + | 0.110542i | ||||
\(474\) | −0.304310 | + | 0.767629i | −0.0139774 | + | 0.0352584i | ||||
\(475\) | −2.55416 | + | 2.55416i | −0.117193 | + | 0.117193i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.6517 | + | 16.6517i | 0.762430 | + | 0.762430i | ||||
\(478\) | −13.1116 | − | 30.3351i | −0.599712 | − | 1.38750i | ||||
\(479\) | 1.31897 | − | 2.28452i | 0.0602653 | − | 0.104382i | −0.834319 | − | 0.551282i | \(-0.814139\pi\) |
0.894584 | + | 0.446900i | \(0.147472\pi\) | |||||||
\(480\) | −4.83077 | + | 2.44827i | −0.220493 | + | 0.111748i | ||||
\(481\) | −1.54942 | − | 2.68368i | −0.0706477 | − | 0.122365i | ||||
\(482\) | 13.1786 | + | 1.53058i | 0.600267 | + | 0.0697159i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.496521 | − | 2.10873i | 0.0225691 | − | 0.0958515i | ||||
\(485\) | 7.84006 | + | 2.10074i | 0.355999 | + | 0.0953896i | ||||
\(486\) | 19.8574 | − | 2.92352i | 0.900749 | − | 0.132614i | ||||
\(487\) | −2.41546 | − | 1.39457i | −0.109455 | − | 0.0631938i | 0.444273 | − | 0.895891i | \(-0.353462\pi\) |
−0.553728 | + | 0.832698i | \(0.686795\pi\) | |||||||
\(488\) | 9.84657 | − | 14.1283i | 0.445733 | − | 0.639556i | ||||
\(489\) | − | 9.55197i | − | 0.431955i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.8794 | − | 15.8794i | 0.716629 | − | 0.716629i | −0.251284 | − | 0.967913i | \(-0.580853\pi\) |
0.967913 | + | 0.251284i | \(0.0808529\pi\) | |||||||
\(492\) | 8.78529 | + | 4.72040i | 0.396071 | + | 0.212812i | ||||
\(493\) | 21.3262 | − | 5.71434i | 0.960484 | − | 0.257361i | ||||
\(494\) | 0.919401 | + | 0.683424i | 0.0413658 | + | 0.0307487i | ||||
\(495\) | 6.78670 | + | 11.7549i | 0.305040 | + | 0.528344i | ||||
\(496\) | −25.5125 | − | 12.7195i | −1.14555 | − | 0.571122i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.354666 | + | 3.05374i | −0.0158930 | + | 0.136841i | ||||
\(499\) | −0.777511 | + | 2.90171i | −0.0348062 | + | 0.129898i | −0.981143 | − | 0.193284i | \(-0.938086\pi\) |
0.946337 | + | 0.323182i | \(0.104753\pi\) | |||||||
\(500\) | −23.2692 | + | 0.711147i | −1.04063 | + | 0.0318035i | ||||
\(501\) | 3.97766 | + | 14.8448i | 0.177709 | + | 0.663218i | ||||
\(502\) | 4.14287 | + | 1.64235i | 0.184906 | + | 0.0733017i | ||||
\(503\) | 26.5444i | 1.18356i | 0.806101 | + | 0.591778i | \(0.201574\pi\) | ||||
−0.806101 | + | 0.591778i | \(0.798426\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 18.6107i | − | 0.828166i | ||||||
\(506\) | 2.47373 | − | 6.24006i | 0.109971 | − | 0.277405i | ||||
\(507\) | 2.07886 | + | 7.75840i | 0.0923253 | + | 0.344563i | ||||
\(508\) | −12.3421 | + | 13.1203i | −0.547591 | + | 0.582117i | ||||
\(509\) | −2.96258 | + | 11.0565i | −0.131314 | + | 0.490071i | −0.999986 | − | 0.00531724i | \(-0.998307\pi\) |
0.868672 | + | 0.495388i | \(0.164974\pi\) | |||||||
\(510\) | −8.73214 | − | 1.01416i | −0.386666 | − | 0.0449080i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11.4425 | + | 19.5210i | 0.505692 | + | 0.862714i | ||||
\(513\) | −2.35002 | − | 4.07036i | −0.103756 | − | 0.179711i | ||||
\(514\) | 8.23748 | − | 11.0818i | 0.363340 | − | 0.488796i | ||||
\(515\) | −22.9789 | + | 6.15718i | −1.01257 | + | 0.271318i | ||||
\(516\) | −0.507312 | − | 1.68556i | −0.0223332 | − | 0.0742025i | ||||
\(517\) | 31.0574 | − | 31.0574i | 1.36590 | − | 1.36590i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 1.28967i | − | 0.0566102i | ||||||
\(520\) | 0.459085 | + | 2.57059i | 0.0201322 | + | 0.112728i | ||||
\(521\) | −27.8708 | − | 16.0912i | −1.22104 | − | 0.704970i | −0.255903 | − | 0.966702i | \(-0.582373\pi\) |
−0.965140 | + | 0.261733i | \(0.915706\pi\) | |||||||
\(522\) | 1.81779 | + | 12.3469i | 0.0795624 | + | 0.540410i | ||||
\(523\) | −3.27851 | − | 0.878475i | −0.143359 | − | 0.0384130i | 0.186426 | − | 0.982469i | \(-0.440310\pi\) |
−0.329785 | + | 0.944056i | \(0.606976\pi\) | |||||||
\(524\) | −16.3938 | − | 26.4916i | −0.716168 | − | 1.15729i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.167218 | − | 1.43978i | 0.00729105 | − | 0.0627772i | ||||
\(527\) | −23.1366 | − | 40.0738i | −1.00785 | − | 1.74564i | ||||
\(528\) | −7.37735 | + | 4.88315i | −0.321058 | + | 0.212512i | ||||
\(529\) | −10.5678 | + | 18.3039i | −0.459468 | + | 0.795822i | ||||
\(530\) | 17.7244 | − | 7.66093i | 0.769897 | − | 0.332769i | ||||
\(531\) | 13.6470 | + | 13.6470i | 0.592229 | + | 0.592229i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.40024 | − | 3.40024i | 0.147281 | − | 0.147281i | ||||
\(534\) | −13.5204 | − | 5.35987i | −0.585086 | − | 0.231944i | ||||
\(535\) | −11.3878 | − | 6.57476i | −0.492338 | − | 0.284252i | ||||
\(536\) | 45.1411 | + | 3.84950i | 1.94980 | + | 0.166273i | ||||
\(537\) | 4.71898 | − | 2.72451i | 0.203639 | − | 0.117571i | ||||
\(538\) | 19.1316 | + | 24.1594i | 0.824820 | + | 1.04159i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.45541 | − | 10.4282i | 0.105664 | − | 0.448757i | ||||
\(541\) | −9.27902 | + | 34.6298i | −0.398936 | + | 1.48885i | 0.416035 | + | 0.909348i | \(0.363419\pi\) |
−0.814971 | + | 0.579501i | \(0.803247\pi\) | |||||||
\(542\) | −21.1524 | + | 28.4560i | −0.908572 | + | 1.22229i | ||||
\(543\) | −2.25927 | + | 3.91317i | −0.0969545 | + | 0.167930i | ||||
\(544\) | −2.00143 | + | 36.6742i | −0.0858104 | + | 1.57239i | ||||
\(545\) | 9.94791 | 0.426122 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.63409 | − | 8.63409i | −0.369167 | − | 0.369167i | 0.498006 | − | 0.867173i | \(-0.334066\pi\) |
−0.867173 | + | 0.498006i | \(0.834066\pi\) | |||||||
\(548\) | 17.2104 | − | 5.17991i | 0.735192 | − | 0.221275i | ||||
\(549\) | 4.08951 | + | 15.2623i | 0.174536 | + | 0.651378i | ||||
\(550\) | −13.3067 | + | 1.95909i | −0.567399 | + | 0.0835358i | ||||
\(551\) | 3.88786 | − | 2.24466i | 0.165628 | − | 0.0956256i | ||||
\(552\) | −2.22485 | + | 1.04342i | −0.0946961 | + | 0.0444109i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −7.45391 | + | 5.90266i | −0.316686 | + | 0.250780i | ||||
\(555\) | 4.67044 | + | 1.25144i | 0.198249 | + | 0.0531207i | ||||
\(556\) | 1.13135 | + | 37.0184i | 0.0479799 | + | 1.56993i | ||||
\(557\) | 0.537087 | − | 0.143912i | 0.0227571 | − | 0.00609774i | −0.247423 | − | 0.968908i | \(-0.579584\pi\) |
0.270180 | + | 0.962810i | \(0.412917\pi\) | |||||||
\(558\) | 24.0095 | − | 10.3775i | 1.01640 | − | 0.439316i | ||||
\(559\) | −0.848723 | −0.0358971 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.3605 | −0.606302 | ||||||||
\(562\) | −15.6939 | + | 6.78330i | −0.662006 | + | 0.286136i | ||||
\(563\) | 24.0714 | − | 6.44992i | 1.01449 | − | 0.271832i | 0.286986 | − | 0.957935i | \(-0.407347\pi\) |
0.727504 | + | 0.686103i | \(0.240680\pi\) | |||||||
\(564\) | −16.0718 | + | 0.491182i | −0.676744 | + | 0.0206825i | ||||
\(565\) | 5.90072 | + | 1.58109i | 0.248245 | + | 0.0665171i | ||||
\(566\) | 18.9946 | − | 15.0416i | 0.798403 | − | 0.632245i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.08789 | − | 22.3740i | 0.339361 | − | 0.938792i | ||||
\(569\) | −3.78183 | + | 2.18344i | −0.158543 | + | 0.0915346i | −0.577172 | − | 0.816622i | \(-0.695844\pi\) |
0.418630 | + | 0.908157i | \(0.362511\pi\) | |||||||
\(570\) | −1.76842 | + | 0.260357i | −0.0740708 | + | 0.0109051i | ||||
\(571\) | 1.33744 | + | 4.99139i | 0.0559701 | + | 0.208883i | 0.988248 | − | 0.152860i | \(-0.0488484\pi\) |
−0.932278 | + | 0.361743i | \(0.882182\pi\) | |||||||
\(572\) | 1.22940 | + | 4.08471i | 0.0514037 | + | 0.170790i | ||||
\(573\) | 6.27016 | + | 6.27016i | 0.261940 | + | 0.261940i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.73593 | −0.155799 | ||||||||
\(576\) | −20.4614 | − | 3.51534i | −0.852559 | − | 0.146473i | ||||
\(577\) | 3.62493 | − | 6.27856i | 0.150908 | − | 0.261380i | −0.780654 | − | 0.624964i | \(-0.785114\pi\) |
0.931561 | + | 0.363584i | \(0.118447\pi\) | |||||||
\(578\) | −21.2239 | + | 28.5523i | −0.882799 | + | 1.18762i | ||||
\(579\) | −0.524745 | + | 1.95838i | −0.0218077 | + | 0.0813873i | ||||
\(580\) | 9.96063 | + | 2.34532i | 0.413592 | + | 0.0973842i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.01343 | − | 3.80538i | −0.124911 | − | 0.157738i | ||||
\(583\) | 27.3170 | − | 15.7715i | 1.13136 | − | 0.653189i | ||||
\(584\) | 1.01873 | + | 1.20868i | 0.0421555 | + | 0.0500155i | ||||
\(585\) | −2.07491 | − | 1.19795i | −0.0857869 | − | 0.0495291i | ||||
\(586\) | 14.2575 | + | 5.65206i | 0.588972 | + | 0.233485i | ||||
\(587\) | −21.0987 | + | 21.0987i | −0.870837 | + | 0.870837i | −0.992564 | − | 0.121727i | \(-0.961157\pi\) |
0.121727 | + | 0.992564i | \(0.461157\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.65312 | − | 6.65312i | −0.274137 | − | 0.274137i | ||||
\(590\) | 14.5261 | − | 6.27854i | 0.598029 | − | 0.258484i | ||||
\(591\) | 8.38240 | − | 14.5187i | 0.344806 | − | 0.597221i | ||||
\(592\) | 4.02723 | − | 19.7963i | 0.165518 | − | 0.813624i | ||||
\(593\) | 7.89073 | + | 13.6672i | 0.324034 | + | 0.561243i | 0.981316 | − | 0.192401i | \(-0.0616276\pi\) |
−0.657283 | + | 0.753644i | \(0.728294\pi\) | |||||||
\(594\) | 2.01903 | − | 17.3843i | 0.0828420 | − | 0.713285i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −30.1100 | + | 18.6330i | −1.23335 | + | 0.763238i | ||||
\(597\) | 6.45990 | + | 1.73092i | 0.264386 | + | 0.0708420i | ||||
\(598\) | 0.172581 | + | 1.17222i | 0.00705735 | + | 0.0479355i | ||||
\(599\) | −16.1332 | − | 9.31450i | −0.659184 | − | 0.380580i | 0.132782 | − | 0.991145i | \(-0.457609\pi\) |
−0.791966 | + | 0.610565i | \(0.790942\pi\) | |||||||
\(600\) | 4.03965 | + | 2.81540i | 0.164918 | + | 0.114938i | ||||
\(601\) | − | 34.5975i | − | 1.41126i | −0.708580 | − | 0.705631i | \(-0.750664\pi\) | ||
0.708580 | − | 0.705631i | \(-0.249336\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −29.3932 | + | 29.3932i | −1.19699 | + | 1.19699i | ||||
\(604\) | −24.7209 | + | 7.44040i | −1.00588 | + | 0.302746i | ||||
\(605\) | 1.57430 | − | 0.421833i | 0.0640045 | − | 0.0171500i | ||||
\(606\) | −6.63977 | + | 8.93240i | −0.269722 | + | 0.362854i | ||||
\(607\) | 16.4752 | + | 28.5359i | 0.668708 | + | 1.15824i | 0.978266 | + | 0.207355i | \(0.0664855\pi\) |
−0.309558 | + | 0.950880i | \(0.600181\pi\) | |||||||
\(608\) | 1.53695 | + | 7.30836i | 0.0623317 | + | 0.296393i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.8693 | + | 1.49466i | 0.521062 | + | 0.0605170i | ||||
\(611\) | −2.00657 | + | 7.48863i | −0.0811773 | + | 0.302958i | ||||
\(612\) | −24.5460 | − | 23.0901i | −0.992212 | − | 0.933363i | ||||
\(613\) | 8.28898 | + | 30.9349i | 0.334789 | + | 1.24945i | 0.904098 | + | 0.427325i | \(0.140544\pi\) |
−0.569309 | + | 0.822124i | \(0.692789\pi\) | |||||||
\(614\) | −2.89892 | + | 7.31261i | −0.116991 | + | 0.295113i | ||||
\(615\) | 7.50305i | 0.302552i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.5533i | 0.424862i | 0.977176 | + | 0.212431i | \(0.0681380\pi\) | ||||
−0.977176 | + | 0.212431i | \(0.931862\pi\) | |||||||
\(618\) | 13.2257 | + | 5.24301i | 0.532014 | + | 0.210905i | ||||
\(619\) | −1.26876 | − | 4.73508i | −0.0509958 | − | 0.190319i | 0.935729 | − | 0.352720i | \(-0.114743\pi\) |
−0.986725 | + | 0.162401i | \(0.948076\pi\) | |||||||
\(620\) | −0.655149 | − | 21.4369i | −0.0263114 | − | 0.860925i | ||||
\(621\) | 1.25816 | − | 4.69550i | 0.0504881 | − | 0.188424i | ||||
\(622\) | −0.387989 | + | 3.34066i | −0.0155569 | + | 0.133948i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.696771 | − | 1.39757i | 0.0278932 | − | 0.0559475i | ||||
\(625\) | −1.91701 | − | 3.32036i | −0.0766804 | − | 0.132814i | ||||
\(626\) | 17.4025 | + | 12.9359i | 0.695545 | + | 0.517024i | ||||
\(627\) | −2.82049 | + | 0.755749i | −0.112640 | + | 0.0301817i | ||||
\(628\) | −16.2609 | + | 30.2636i | −0.648880 | + | 1.20765i | ||||
\(629\) | 23.1871 | − | 23.1871i | 0.924531 | − | 0.924531i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 34.6105i | − | 1.37782i | −0.724846 | − | 0.688911i | \(-0.758089\pi\) | ||
0.724846 | − | 0.688911i | \(-0.241911\pi\) | |||||||
\(632\) | 0.456323 | + | 2.55512i | 0.0181515 | + | 0.101637i | ||||
\(633\) | 12.3545 | + | 7.13288i | 0.491048 | + | 0.283506i | ||||
\(634\) | −37.1699 | + | 5.47237i | −1.47620 | + | 0.217336i | ||||
\(635\) | −13.0899 | − | 3.50742i | −0.519456 | − | 0.139188i | ||||
\(636\) | −11.2402 | − | 2.64660i | −0.445702 | − | 0.104945i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.6048 | + | 1.92851i | 0.657392 | + | 0.0763505i | ||||
\(639\) | 10.9144 | + | 18.9043i | 0.431766 | + | 0.747841i | ||||
\(640\) | −8.86244 | + | 14.5343i | −0.350319 | + | 0.574518i | ||||
\(641\) | 11.0592 | − | 19.1551i | 0.436811 | − | 0.756580i | −0.560630 | − | 0.828066i | \(-0.689441\pi\) |
0.997442 | + | 0.0714868i | \(0.0227744\pi\) | |||||||
\(642\) | 3.12001 | + | 7.21847i | 0.123137 | + | 0.284890i | ||||
\(643\) | 35.2632 | + | 35.2632i | 1.39064 | + | 1.39064i | 0.823883 | + | 0.566761i | \(0.191804\pi\) |
0.566761 | + | 0.823883i | \(0.308196\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.936406 | − | 0.936406i | 0.0368709 | − | 0.0368709i | ||||
\(646\) | −4.46742 | + | 11.2692i | −0.175768 | + | 0.443381i | ||||
\(647\) | 27.3950 | + | 15.8165i | 1.07701 | + | 0.621810i | 0.930087 | − | 0.367338i | \(-0.119731\pi\) |
0.146920 | + | 0.989148i | \(0.453064\pi\) | |||||||
\(648\) | 11.9386 | − | 10.0625i | 0.468994 | − | 0.395291i | ||||
\(649\) | 22.3878 | − | 12.9256i | 0.878798 | − | 0.507374i | ||||
\(650\) | 1.86123 | − | 1.47389i | 0.0730035 | − | 0.0578106i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.7995 | − | 25.5312i | −0.618757 | − | 0.999880i | ||||
\(653\) | 0.370901 | − | 1.38422i | 0.0145145 | − | 0.0541687i | −0.958289 | − | 0.285802i | \(-0.907740\pi\) |
0.972803 | + | 0.231633i | \(0.0744068\pi\) | |||||||
\(654\) | −4.77460 | − | 3.54913i | −0.186702 | − | 0.138782i | ||||
\(655\) | 11.7189 | − | 20.2978i | 0.457896 | − | 0.793100i | ||||
\(656\) | 31.2898 | − | 1.91433i | 1.22166 | − | 0.0747421i | ||||
\(657\) | −1.45036 | −0.0565840 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.1346 | + | 29.1346i | 1.13492 | + | 1.13492i | 0.989347 | + | 0.145577i | \(0.0465038\pi\) |
0.145577 | + | 0.989347i | \(0.453496\pi\) | |||||||
\(660\) | −5.86312 | − | 3.15030i | −0.228222 | − | 0.122625i | ||||
\(661\) | −6.02209 | − | 22.4747i | −0.234232 | − | 0.874166i | −0.978494 | − | 0.206278i | \(-0.933865\pi\) |
0.744261 | − | 0.667888i | \(-0.232802\pi\) | |||||||
\(662\) | 3.43619 | + | 23.3396i | 0.133551 | + | 0.907119i | ||||
\(663\) | 2.19523 | − | 1.26742i | 0.0852558 | − | 0.0492224i | ||||
\(664\) | 4.10308 | + | 8.74889i | 0.159230 | + | 0.339523i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.5071 | + | 14.5312i | 0.445891 | + | 0.563073i | ||||
\(667\) | 4.48498 | + | 1.20175i | 0.173659 | + | 0.0465318i | ||||
\(668\) | 35.1860 | + | 33.0991i | 1.36139 | + | 1.28064i | ||||
\(669\) | 0.923687 | − | 0.247501i | 0.0357118 | − | 0.00956895i | ||||
\(670\) | 13.5229 | + | 31.2866i | 0.522435 | + | 1.20871i | ||||
\(671\) | 21.1643 | 0.817040 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.8511 | −0.765204 | −0.382602 | − | 0.923913i | \(-0.624972\pi\) | ||||
−0.382602 | + | 0.923913i | \(0.624972\pi\) | |||||||
\(674\) | −9.00335 | − | 20.8302i | −0.346796 | − | 0.802349i | ||||
\(675\) | −9.40857 | + | 2.52102i | −0.362136 | + | 0.0970341i | ||||
\(676\) | 18.3894 | + | 17.2987i | 0.707283 | + | 0.665334i | ||||
\(677\) | 20.2320 | + | 5.42114i | 0.777578 | + | 0.208352i | 0.625717 | − | 0.780050i | \(-0.284807\pi\) |
0.151862 | + | 0.988402i | \(0.451473\pi\) | |||||||
\(678\) | −2.26802 | − | 2.86407i | −0.0871028 | − | 0.109994i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −25.0174 | + | 11.7327i | −0.959373 | + | 0.449930i | ||||
\(681\) | 8.86358 | − | 5.11739i | 0.339653 | − | 0.196099i | ||||
\(682\) | −5.10308 | − | 34.6615i | −0.195407 | − | 1.32726i | ||||
\(683\) | −12.9333 | − | 48.2678i | −0.494879 | − | 1.84692i | −0.530704 | − | 0.847557i | \(-0.678073\pi\) |
0.0358249 | − | 0.999358i | \(-0.488594\pi\) | |||||||
\(684\) | −6.03613 | − | 3.24326i | −0.230797 | − | 0.124009i | ||||
\(685\) | 9.56118 | + | 9.56118i | 0.365314 | + | 0.365314i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.2361 | −0.543139 | ||||||||
\(688\) | −4.14399 | − | 3.66616i | −0.157988 | − | 0.139771i | ||||
\(689\) | −2.78389 | + | 4.82184i | −0.106058 | + | 0.183698i | ||||
\(690\) | −1.48373 | − | 1.10291i | −0.0564846 | − | 0.0419871i | ||||
\(691\) | 0.215771 | − | 0.805269i | 0.00820833 | − | 0.0306339i | −0.961700 | − | 0.274103i | \(-0.911619\pi\) |
0.969909 | + | 0.243470i | \(0.0782856\pi\) | |||||||
\(692\) | −2.13319 | − | 3.44712i | −0.0810916 | − | 0.131040i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.224081 | − | 0.177447i | 0.00850600 | − | 0.00673579i | ||||
\(695\) | −24.1300 | + | 13.9315i | −0.915302 | + | 0.528450i | ||||
\(696\) | −3.94396 | − | 4.67932i | −0.149495 | − | 0.177369i | ||||
\(697\) | 44.0673 | + | 25.4423i | 1.66917 | + | 0.963694i | ||||
\(698\) | −16.5724 | + | 41.8044i | −0.627275 | + | 1.58232i | ||||
\(699\) | 5.43272 | − | 5.43272i | 0.205484 | − | 0.205484i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.8122 | − | 26.8122i | −1.01268 | − | 1.01268i | −0.999919 | − | 0.0127630i | \(-0.995937\pi\) |
−0.0127630 | − | 0.999919i | \(-0.504063\pi\) | |||||||
\(702\) | 1.22564 | + | 2.83565i | 0.0462589 | + | 0.107025i | ||||
\(703\) | 3.33382 | − | 5.77435i | 0.125737 | − | 0.217784i | ||||
\(704\) | −11.6417 | + | 25.2546i | −0.438763 | + | 0.951819i | ||||
\(705\) | −6.04842 | − | 10.4762i | −0.227797 | − | 0.394556i | ||||
\(706\) | 13.5208 | + | 1.57032i | 0.508860 | + | 0.0590998i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −9.21193 | − | 2.16903i | −0.346206 | − | 0.0815173i | ||||
\(709\) | 22.0409 | + | 5.90585i | 0.827764 | + | 0.221799i | 0.647738 | − | 0.761863i | \(-0.275715\pi\) |
0.180026 | + | 0.983662i | \(0.442382\pi\) | |||||||
\(710\) | 17.7077 | − | 2.60703i | 0.664557 | − | 0.0978400i | ||||
\(711\) | −2.06242 | − | 1.19074i | −0.0773468 | − | 0.0446562i | ||||
\(712\) | −45.0039 | + | 8.03730i | −1.68659 | + | 0.301211i | ||||
\(713\) | − | 9.73144i | − | 0.364445i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.26925 | + | 2.26925i | −0.0848651 | + | 0.0848651i | ||||
\(716\) | 8.10676 | − | 15.0877i | 0.302964 | − | 0.563855i | ||||
\(717\) | −14.3620 | + | 3.84829i | −0.536359 | + | 0.143717i | ||||
\(718\) | −19.4785 | − | 14.4791i | −0.726930 | − | 0.540353i | ||||
\(719\) | −18.9649 | − | 32.8482i | −0.707273 | − | 1.22503i | −0.965865 | − | 0.259046i | \(-0.916592\pi\) |
0.258592 | − | 0.965987i | \(-0.416741\pi\) | |||||||
\(720\) | −4.95630 | − | 14.8119i | −0.184710 | − | 0.552008i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.81553 | − | 24.2422i | 0.104783 | − | 0.902201i | ||||
\(723\) | 1.54492 | − | 5.76573i | 0.0574563 | − | 0.214430i | ||||
\(724\) | 0.433866 | + | 14.1964i | 0.0161245 | + | 0.527604i | ||||
\(725\) | −2.40799 | − | 8.98674i | −0.0894305 | − | 0.333759i | ||||
\(726\) | −0.906100 | − | 0.359203i | −0.0336285 | − | 0.0133313i | ||||
\(727\) | − | 13.6332i | − | 0.505628i | −0.967515 | − | 0.252814i | \(-0.918644\pi\) | ||
0.967515 | − | 0.252814i | \(-0.0813560\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.53022i | 0.278897i | ||||||||
\(730\) | −0.438261 | + | 1.10553i | −0.0162208 | + | 0.0409174i | ||||
\(731\) | −2.32447 | − | 8.67503i | −0.0859735 | − | 0.320858i | ||||
\(732\) | −5.64349 | − | 5.30877i | −0.208589 | − | 0.196218i | ||||
\(733\) | 1.60496 | − | 5.98979i | 0.0592806 | − | 0.221238i | −0.929931 | − | 0.367735i | \(-0.880133\pi\) |
0.989211 | + | 0.146497i | \(0.0467999\pi\) | |||||||
\(734\) | 20.3058 | + | 2.35835i | 0.749502 | + | 0.0870483i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.22088 | + | 6.46897i | −0.155584 | + | 0.238449i | ||||
\(737\) | 27.8395 | + | 48.2194i | 1.02548 | + | 1.77618i | ||||
\(738\) | −17.1591 | + | 23.0839i | −0.631634 | + | 0.849729i | ||||
\(739\) | 23.9383 | − | 6.41426i | 0.880586 | − | 0.235952i | 0.209926 | − | 0.977717i | \(-0.432678\pi\) |
0.670660 | + | 0.741765i | \(0.266011\pi\) | |||||||
\(740\) | 14.5534 | − | 4.38023i | 0.534995 | − | 0.161021i | ||||
\(741\) | 0.364456 | − | 0.364456i | 0.0133886 | − | 0.0133886i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.9129i | 1.46426i | 0.681164 | + | 0.732131i | \(0.261474\pi\) | ||||
−0.681164 | + | 0.732131i | \(0.738526\pi\) | |||||||
\(744\) | −7.33361 | + | 10.5226i | −0.268863 | + | 0.385776i | ||||
\(745\) | −23.0702 | − | 13.3196i | −0.845225 | − | 0.487991i | ||||
\(746\) | 2.47832 | + | 16.8334i | 0.0907377 | + | 0.616316i | ||||
\(747\) | −8.56415 | − | 2.29476i | −0.313346 | − | 0.0839607i | ||||
\(748\) | −38.3839 | + | 23.7532i | −1.40345 | + | 0.868501i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.20836 | + | 10.4042i | −0.0441229 | + | 0.379906i | ||||
\(751\) | 24.5357 | + | 42.4971i | 0.895321 | + | 1.55074i | 0.833407 | + | 0.552660i | \(0.186387\pi\) |
0.0619145 | + | 0.998081i | \(0.480279\pi\) | |||||||
\(752\) | −42.1454 | + | 27.8965i | −1.53688 | + | 1.01728i | ||||
\(753\) | 1.00254 | − | 1.73645i | 0.0365345 | − | 0.0632796i | ||||
\(754\) | −2.70851 | + | 1.17069i | −0.0986382 | + | 0.0426340i | ||||
\(755\) | −13.7336 | − | 13.7336i | −0.499818 | − | 0.499818i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.7514 | − | 17.7514i | 0.645185 | − | 0.645185i | −0.306641 | − | 0.951825i | \(-0.599205\pi\) |
0.951825 | + | 0.306641i | \(0.0992050\pi\) | |||||||
\(758\) | 25.1051 | + | 9.95235i | 0.911858 | + | 0.361486i | ||||
\(759\) | −2.61546 | − | 1.51004i | −0.0949353 | − | 0.0548109i | ||||
\(760\) | −4.29611 | + | 3.62096i | −0.155836 | + | 0.131346i | ||||
\(761\) | 0.912216 | − | 0.526668i | 0.0330678 | − | 0.0190917i | −0.483375 | − | 0.875413i | \(-0.660589\pi\) |
0.516443 | + | 0.856322i | \(0.327256\pi\) | |||||||
\(762\) | 5.03126 | + | 6.35351i | 0.182263 | + | 0.230163i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 27.1306 | + | 6.38814i | 0.981549 | + | 0.231115i | ||||
\(765\) | 6.56184 | − | 24.4891i | 0.237244 | − | 0.885406i | ||||
\(766\) | −20.4564 | + | 27.5197i | −0.739119 | + | 0.994327i | ||||
\(767\) | −2.28155 | + | 3.95176i | −0.0823820 | + | 0.142690i | ||||
\(768\) | 9.43903 | − | 3.81401i | 0.340602 | − | 0.137626i | ||||
\(769\) | 0.951932 | 0.0343276 | 0.0171638 | − | 0.999853i | \(-0.494536\pi\) | ||||
0.0171638 | + | 0.999853i | \(0.494536\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.39289 | − | 4.39289i | −0.158206 | − | 0.158206i | ||||
\(772\) | 1.83669 | + | 6.10245i | 0.0661039 | + | 0.219632i | ||||
\(773\) | −4.91119 | − | 18.3288i | −0.176643 | − | 0.659241i | −0.996266 | − | 0.0863375i | \(-0.972484\pi\) |
0.819623 | − | 0.572903i | \(-0.194183\pi\) | |||||||
\(774\) | 5.02246 | − | 0.739436i | 0.180529 | − | 0.0265785i | ||||
\(775\) | −16.8869 | + | 9.74964i | −0.606594 | + | 0.350217i | ||||
\(776\) | −14.3488 | − | 5.18691i | −0.515093 | − | 0.186199i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.5818 | + | 9.96333i | −0.451078 | + | 0.357203i | ||||
\(779\) | 9.99401 | + | 2.67789i | 0.358073 | + | 0.0959453i | ||||
\(780\) | 1.17431 | − | 0.0358889i | 0.0420469 | − | 0.00128503i | ||||
\(781\) | 28.2424 | − | 7.56753i | 1.01059 | − | 0.270788i | ||||
\(782\) | −11.5089 | + | 4.97444i | −0.411557 | + | 0.177886i | ||||
\(783\) | 12.1059 | 0.432630 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.8466 | −0.922503 | ||||||||
\(786\) | −12.8663 | + | 5.56114i | −0.458925 | + | 0.198359i | ||||
\(787\) | 30.0147 | − | 8.04240i | 1.06991 | − | 0.286681i | 0.319452 | − | 0.947602i | \(-0.396501\pi\) |
0.750455 | + | 0.660922i | \(0.229834\pi\) | |||||||
\(788\) | −1.60974 | − | 52.6717i | −0.0573447 | − | 1.87635i | ||||
\(789\) | −0.629914 | − | 0.168785i | −0.0224255 | − | 0.00600890i | ||||
\(790\) | −1.53084 | + | 1.21225i | −0.0544648 | + | 0.0431300i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −10.8339 | − | 23.1009i | −0.384966 | − | 0.820853i | ||||
\(793\) | −3.23530 | + | 1.86790i | −0.114889 | + | 0.0663311i | ||||
\(794\) | −33.4057 | + | 4.91818i | −1.18552 | + | 0.174540i | ||||
\(795\) | −2.24849 | − | 8.39150i | −0.0797459 | − | 0.297616i | ||||
\(796\) | 20.1295 | − | 6.05850i | 0.713473 | − | 0.214738i | ||||
\(797\) | 2.25830 | + | 2.25830i | 0.0799929 | + | 0.0799929i | 0.745971 | − | 0.665978i | \(-0.231986\pi\) |
−0.665978 | + | 0.745971i | \(0.731986\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −82.0390 | −2.90233 | ||||||||
\(800\) | 15.4543 | + | 0.843390i | 0.546392 | + | 0.0298183i | ||||
\(801\) | 20.9727 | − | 36.3258i | 0.741035 | − | 1.28351i | ||||
\(802\) | 4.32235 | − | 5.81480i | 0.152628 | − | 0.205328i | ||||
\(803\) | −0.502807 | + | 1.87650i | −0.0177437 | + | 0.0662203i | ||||
\(804\) | 4.67172 | − | 19.8409i | 0.164759 | − | 0.699734i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.83921 | + | 4.84818i | 0.135230 | + | 0.170770i | ||||
\(807\) | 12.0076 | − | 6.93258i | 0.422687 | − | 0.244039i | ||||
\(808\) | −2.97257 | + | 34.8577i | −0.104575 | + | 1.22629i | ||||
\(809\) | 0.992787 | + | 0.573186i | 0.0349045 | + | 0.0201521i | 0.517351 | − | 0.855773i | \(-0.326918\pi\) |
−0.482446 | + | 0.875926i | \(0.660252\pi\) | |||||||
\(810\) | 10.9198 | + | 4.32889i | 0.383681 | + | 0.152102i | ||||
\(811\) | −18.0272 | + | 18.0272i | −0.633019 | + | 0.633019i | −0.948824 | − | 0.315805i | \(-0.897725\pi\) |
0.315805 | + | 0.948824i | \(0.397725\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.2801 | + | 11.2801i | 0.395612 | + | 0.395612i | ||||
\(814\) | 22.7900 | − | 9.85042i | 0.798788 | − | 0.345257i | ||||
\(815\) | 11.2941 | − | 19.5619i | 0.395614 | − | 0.685224i | ||||
\(816\) | 16.1932 | + | 3.29425i | 0.566877 | + | 0.115322i | ||||
\(817\) | −0.913078 | − | 1.58150i | −0.0319445 | − | 0.0553296i | ||||
\(818\) | −2.31516 | + | 19.9340i | −0.0809478 | + | 0.696975i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.4105 | + | 20.0547i | 0.433392 | + | 0.700340i | ||||
\(821\) | −25.5160 | − | 6.83700i | −0.890516 | − | 0.238613i | −0.215577 | − | 0.976487i | \(-0.569163\pi\) |
−0.674939 | + | 0.737874i | \(0.735830\pi\) | |||||||
\(822\) | −1.17783 | − | 8.00014i | −0.0410815 | − | 0.279037i | ||||
\(823\) | −11.4579 | − | 6.61523i | −0.399398 | − | 0.230593i | 0.286826 | − | 0.957983i | \(-0.407400\pi\) |
−0.686224 | + | 0.727390i | \(0.740733\pi\) | |||||||
\(824\) | 44.0227 | − | 7.86208i | 1.53361 | − | 0.273888i | ||||
\(825\) | 6.05145i | 0.210684i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.8854 | + | 11.8854i | −0.413297 | + | 0.413297i | −0.882885 | − | 0.469589i | \(-0.844402\pi\) |
0.469589 | + | 0.882885i | \(0.344402\pi\) | |||||||
\(828\) | −2.04255 | − | 6.78642i | −0.0709835 | − | 0.235845i | ||||
\(829\) | −18.4216 | + | 4.93604i | −0.639807 | + | 0.171436i | −0.564116 | − | 0.825695i | \(-0.690783\pi\) |
−0.0756912 | + | 0.997131i | \(0.524116\pi\) | |||||||
\(830\) | −4.33702 | + | 5.83453i | −0.150540 | + | 0.202520i | ||||
\(831\) | 2.13891 | + | 3.70470i | 0.0741979 | + | 0.128515i | ||||
\(832\) | −0.449280 | − | 4.88803i | −0.0155760 | − | 0.169462i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 16.5518 | + | 1.92235i | 0.573141 | + | 0.0665655i | ||||
\(835\) | −9.40623 | + | 35.1045i | −0.325516 | + | 1.21484i | ||||
\(836\) | −6.28877 | + | 6.68528i | −0.217502 | + | 0.231215i | ||||
\(837\) | −6.56680 | − | 24.5076i | −0.226982 | − | 0.847108i | ||||
\(838\) | 3.13095 | − | 7.89791i | 0.108157 | − | 0.272829i | ||||
\(839\) | 33.0983i | 1.14268i | 0.820714 | + | 0.571339i | \(0.193576\pi\) | ||||
−0.820714 | + | 0.571339i | \(0.806424\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 17.4369i | − | 0.601271i | ||||||
\(842\) | −22.7765 | − | 9.02923i | −0.784930 | − | 0.311168i | ||||
\(843\) | 1.99091 | + | 7.43018i | 0.0685706 | + | 0.255909i | ||||
\(844\) | 44.8202 | − | 1.36979i | 1.54278 | − | 0.0471500i | ||||
\(845\) | −4.91601 | + | 18.3468i | −0.169116 | + | 0.631149i | ||||
\(846\) | 5.34988 | − | 46.0634i | 0.183933 | − | 1.58369i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −34.4212 | + | 11.5179i | −1.18203 | + | 0.395525i | ||||
\(849\) | −5.45053 | − | 9.44059i | −0.187062 | − | 0.324000i | ||||
\(850\) | 20.1625 | + | 14.9875i | 0.691568 | + | 0.514067i | ||||
\(851\) | 6.66120 | − | 1.78486i | 0.228343 | − | 0.0611844i | ||||
\(852\) | −9.42908 | − | 5.06632i | −0.323035 | − | 0.173569i | ||||
\(853\) | −10.7030 | + | 10.7030i | −0.366463 | + | 0.366463i | −0.866185 | − | 0.499723i | \(-0.833435\pi\) |
0.499723 | + | 0.866185i | \(0.333435\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 5.15513i | − | 0.176302i | ||||||
\(856\) | 20.2792 | + | 14.1334i | 0.693127 | + | 0.483069i | ||||
\(857\) | 30.0916 | + | 17.3734i | 1.02791 | + | 0.593464i | 0.916385 | − | 0.400298i | \(-0.131093\pi\) |
0.111524 | + | 0.993762i | \(0.464427\pi\) | |||||||
\(858\) | 1.89875 | − | 0.279545i | 0.0648223 | − | 0.00954352i | ||||
\(859\) | 25.0048 | + | 6.70000i | 0.853151 | + | 0.228601i | 0.658788 | − | 0.752328i | \(-0.271069\pi\) |
0.194363 | + | 0.980930i | \(0.437736\pi\) | |||||||
\(860\) | 0.954025 | − | 4.05176i | 0.0325320 | − | 0.138164i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.13793 | − | 1.06129i | −0.311239 | − | 0.0361478i | ||||
\(863\) | 22.1159 | + | 38.3058i | 0.752832 | + | 1.30394i | 0.946445 | + | 0.322866i | \(0.104646\pi\) |
−0.193612 | + | 0.981078i | \(0.562020\pi\) | |||||||
\(864\) | −6.26459 | + | 19.1397i | −0.213126 | + | 0.651146i | ||||
\(865\) | 1.52488 | − | 2.64117i | 0.0518475 | − | 0.0898025i | ||||
\(866\) | 6.90382 | + | 15.9727i | 0.234601 | + | 0.542774i | ||||
\(867\) | 11.3183 | + | 11.3183i | 0.384390 | + | 0.384390i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.25559 | + | 2.25559i | −0.0765157 | + | 0.0765157i | ||||
\(870\) | 1.69670 | − | 4.27997i | 0.0575235 | − | 0.145105i | ||||
\(871\) | −8.51140 | − | 4.91406i | −0.288398 | − | 0.166507i | ||||
\(872\) | −18.6324 | − | 1.58891i | −0.630971 | − | 0.0538074i | ||||
\(873\) | 12.1236 | − | 6.99958i | 0.410323 | − | 0.236900i | ||||
\(874\) | −1.99862 | + | 1.58268i | −0.0676044 | + | 0.0535351i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.604768 | − | 0.374249i | 0.0204332 | − | 0.0126447i | ||||
\(877\) | −13.4169 | + | 50.0727i | −0.453057 | + | 1.69083i | 0.240679 | + | 0.970605i | \(0.422630\pi\) |
−0.693737 | + | 0.720229i | \(0.744037\pi\) | |||||||
\(878\) | 18.4394 | + | 13.7066i | 0.622298 | + | 0.462576i | ||||
\(879\) | 3.45018 | − | 5.97589i | 0.116372 | − | 0.201562i | ||||
\(880\) | −20.8822 | + | 1.27758i | −0.703937 | + | 0.0430674i | ||||
\(881\) | 22.9696 | 0.773865 | 0.386932 | − | 0.922108i | \(-0.373535\pi\) | ||||
0.386932 | + | 0.922108i | \(0.373535\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.89740 | + | 6.89740i | 0.232116 | + | 0.232116i | 0.813575 | − | 0.581459i | \(-0.197518\pi\) |
−0.581459 | + | 0.813575i | \(0.697518\pi\) | |||||||
\(884\) | 3.77120 | − | 7.01869i | 0.126839 | − | 0.236064i | ||||
\(885\) | −1.84276 | − | 6.87729i | −0.0619438 | − | 0.231177i | ||||
\(886\) | −2.95703 | − | 20.0850i | −0.0993433 | − | 0.674767i | ||||
\(887\) | −10.6280 | + | 6.13605i | −0.356852 | + | 0.206028i | −0.667699 | − | 0.744431i | \(-0.732721\pi\) |
0.310847 | + | 0.950460i | \(0.399387\pi\) | |||||||
\(888\) | −8.54781 | − | 3.08991i | −0.286846 | − | 0.103691i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −21.3517 | − | 26.9630i | −0.715709 | − | 0.903802i | ||||
\(891\) | 18.5350 | + | 4.96644i | 0.620946 | + | 0.166382i | ||||
\(892\) | 2.05952 | − | 2.18937i | 0.0689577 | − | 0.0733055i | ||||
\(893\) | −16.1129 | + | 4.31745i | −0.539199 | + | 0.144478i | ||||
\(894\) | 6.32071 | + | 14.6236i | 0.211396 | + | 0.489087i | ||||
\(895\) | 12.8856 | 0.430719 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.533086 | 0.0177992 | ||||||||
\(898\) | −5.55422 | − | 12.8503i | −0.185347 | − | 0.428819i | ||||
\(899\) | 23.4088 | − | 6.27238i | 0.780729 | − | 0.209196i | ||||
\(900\) | −9.73005 | + | 10.3435i | −0.324335 | + | 0.344784i | ||||
\(901\) | −56.9099 | − | 15.2489i | −1.89594 | − | 0.508016i | ||||
\(902\) | 23.9176 | + | 30.2033i | 0.796370 | + | 1.00566i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.7995 | − | 3.90386i | −0.359185 | − | 0.129840i | ||||
\(905\) | −9.25372 | + | 5.34264i | −0.307604 | + | 0.177595i | ||||
\(906\) | 1.69183 | + | 11.4914i | 0.0562072 | + | 0.381775i | ||||
\(907\) | 6.10163 | + | 22.7716i | 0.202601 | + | 0.756119i | 0.990167 | + | 0.139888i | \(0.0446743\pi\) |
−0.787566 | + | 0.616230i | \(0.788659\pi\) | |||||||
\(908\) | 15.2268 | − | 28.3390i | 0.505318 | − | 0.940464i | ||||
\(909\) | −22.6973 | − | 22.6973i | −0.752823 | − | 0.752823i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0024 | 0.994023 | 0.497012 | − | 0.867744i | \(-0.334431\pi\) | ||||
0.497012 | + | 0.867744i | \(0.334431\pi\) | |||||||
\(912\) | 3.35381 | − | 0.205189i | 0.111056 | − | 0.00679448i | ||||
\(913\) | −5.93798 | + | 10.2849i | −0.196519 | + | 0.340380i | ||||
\(914\) | 14.5751 | + | 10.8342i | 0.482101 | + | 0.358363i | ||||
\(915\) | 1.50867 | − | 5.63042i | 0.0498750 | − | 0.186136i | ||||
\(916\) | −38.0512 | + | 23.5473i | −1.25725 | + | 0.778023i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −25.6272 | + | 20.2938i | −0.845823 | + | 0.669797i | ||||
\(919\) | 6.99945 | − | 4.04114i | 0.230891 | − | 0.133305i | −0.380092 | − | 0.924949i | \(-0.624108\pi\) |
0.610983 | + | 0.791644i | \(0.290774\pi\) | |||||||
\(920\) | −5.79010 | − | 0.493763i | −0.190894 | − | 0.0162789i | ||||
\(921\) | 3.06501 | + | 1.76958i | 0.100995 | + | 0.0583098i | ||||
\(922\) | −5.53062 | + | 13.9512i | −0.182141 | + | 0.459457i | ||||
\(923\) | −3.64941 | + | 3.64941i | −0.120122 | + | 0.120122i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.77092 | − | 9.77092i | −0.321266 | − | 0.321266i | ||||
\(926\) | −17.0002 | − | 39.3317i | −0.558661 | − | 1.29252i | ||||
\(927\) | −20.5155 | + | 35.5339i | −0.673817 | + | 1.16709i | ||||
\(928\) | −18.2816 | − | 5.98371i | −0.600122 | − | 0.196425i | ||||
\(929\) | 10.7324 | + | 18.5891i | 0.352120 | + | 0.609889i | 0.986621 | − | 0.163033i | \(-0.0521277\pi\) |
−0.634501 | + | 0.772922i | \(0.718794\pi\) | |||||||
\(930\) | −9.58490 | − | 1.11320i | −0.314301 | − | 0.0365034i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5.53495 | − | 23.5070i | 0.181303 | − | 0.769998i | ||||
\(933\) | 1.46157 | + | 0.391625i | 0.0478495 | + | 0.0128212i | ||||
\(934\) | −9.84645 | + | 1.44965i | −0.322186 | + | 0.0474341i | ||||
\(935\) | −29.4096 | − | 16.9796i | −0.961796 | − | 0.555293i | ||||
\(936\) | 3.69494 | + | 2.57516i | 0.120773 | + | 0.0841717i | ||||
\(937\) | − | 27.1581i | − | 0.887216i | −0.896221 | − | 0.443608i | \(-0.853698\pi\) | ||
0.896221 | − | 0.443608i | \(-0.146302\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.89848 | − | 6.89848i | 0.225123 | − | 0.225123i | ||||
\(940\) | −33.4949 | − | 17.9971i | −1.09248 | − | 0.586999i | ||||
\(941\) | 11.6132 | − | 3.11176i | 0.378581 | − | 0.101440i | −0.0645102 | − | 0.997917i | \(-0.520548\pi\) |
0.443091 | + | 0.896477i | \(0.353882\pi\) | |||||||
\(942\) | 12.4053 | + | 9.22131i | 0.404187 | + | 0.300446i | ||||
\(943\) | 5.35060 | + | 9.26752i | 0.174240 | + | 0.301792i | ||||
\(944\) | −28.2100 | + | 9.43951i | −0.918158 | + | 0.307230i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.784476 | − | 6.75448i | 0.0255055 | − | 0.219607i | ||||
\(947\) | 11.3673 | − | 42.4234i | 0.369388 | − | 1.37858i | −0.491985 | − | 0.870604i | \(-0.663728\pi\) |
0.861373 | − | 0.507973i | \(-0.169605\pi\) | |||||||
\(948\) | 1.16724 | − | 0.0356729i | 0.0379101 | − | 0.00115860i | ||||
\(949\) | −0.0887525 | − | 0.331229i | −0.00288103 | − | 0.0107521i | ||||
\(950\) | 4.74878 | + | 1.88255i | 0.154071 | + | 0.0610779i | ||||
\(951\) | 16.9037i | 0.548139i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.0416i | 1.03793i | 0.854796 | + | 0.518964i | \(0.173682\pi\) | ||||
−0.854796 | + | 0.518964i | \(0.826318\pi\) | |||||||
\(954\) | 12.2732 | − | 30.9595i | 0.397359 | − | 1.00235i | ||||
\(955\) | 5.42722 | + | 20.2547i | 0.175621 | + | 0.655426i | ||||
\(956\) | −32.0225 | + | 34.0416i | −1.03568 | + | 1.10098i | ||||
\(957\) | 1.94658 | − | 7.26475i | 0.0629241 | − | 0.234836i | ||||
\(958\) | −3.70570 | − | 0.430386i | −0.119726 | − | 0.0139051i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 5.88871 | + | 4.89732i | 0.190057 | + | 0.158060i | ||||
\(961\) | −9.89607 | − | 17.1405i | −0.319228 | − | 0.552919i | ||||
\(962\) | −2.61444 | + | 3.51717i | −0.0842928 | + | 0.113398i | ||||
\(963\) | −21.9069 | + | 5.86993i | −0.705939 | + | 0.189156i | ||||
\(964\) | −5.40746 | − | 17.9665i | −0.174163 | − | 0.578660i | ||||
\(965\) | −3.39020 | + | 3.39020i | −0.109134 | + | 0.109134i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.86480i | 0.188599i | 0.995544 | + | 0.0942997i | \(0.0300612\pi\) | ||||
−0.995544 | + | 0.0942997i | \(0.969939\pi\) | |||||||
\(968\) | −3.01603 | + | 0.538637i | −0.0969390 | + | 0.0173125i | ||||
\(969\) | 4.72338 | + | 2.72704i | 0.151737 | + | 0.0876052i | ||||
\(970\) | −1.67193 | − | 11.3562i | −0.0536825 | − | 0.364627i | ||||
\(971\) | −59.2479 | − | 15.8754i | −1.90136 | − | 0.509467i | −0.996484 | − | 0.0837830i | \(-0.973300\pi\) |
−0.904872 | − | 0.425684i | \(-0.860034\pi\) | |||||||
\(972\) | −14.9370 | − | 24.1374i | −0.479103 | − | 0.774207i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.455053 | + | 3.91809i | −0.0145809 | + | 0.125544i | ||||
\(975\) | −0.534083 | − | 0.925059i | −0.0171043 | − | 0.0296256i | ||||
\(976\) | −23.8653 | − | 4.85501i | −0.763911 | − | 0.155405i | ||||
\(977\) | 22.4338 | − | 38.8564i | 0.717719 | − | 1.24313i | −0.244182 | − | 0.969729i | \(-0.578519\pi\) |
0.961901 | − | 0.273397i | \(-0.0881473\pi\) | |||||||
\(978\) | −12.3998 | + | 5.35953i | −0.396503 | + | 0.171379i | ||||
\(979\) | −39.7282 | − | 39.7282i | −1.26972 | − | 1.26972i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.1323 | − | 12.1323i | 0.387355 | − | 0.387355i | ||||
\(982\) | −29.5236 | − | 11.7040i | −0.942136 | − | 0.373489i | ||||
\(983\) | 4.60693 | + | 2.65981i | 0.146938 | + | 0.0848349i | 0.571667 | − | 0.820486i | \(-0.306297\pi\) |
−0.424728 | + | 0.905321i | \(0.639630\pi\) | |||||||
\(984\) | 1.19841 | − | 14.0531i | 0.0382040 | − | 0.447998i | ||||
\(985\) | 34.3334 | − | 19.8224i | 1.09395 | − | 0.631594i | ||||
\(986\) | −19.3840 | − | 24.4782i | −0.617312 | − | 0.779545i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.371314 | − | 1.57698i | 0.0118131 | − | 0.0501703i | ||||
\(989\) | 0.488844 | − | 1.82439i | 0.0155443 | − | 0.0580123i | ||||
\(990\) | 11.4516 | − | 15.4057i | 0.363956 | − | 0.489625i | ||||
\(991\) | 11.0623 | − | 19.1605i | 0.351407 | − | 0.608654i | −0.635090 | − | 0.772438i | \(-0.719037\pi\) |
0.986496 | + | 0.163784i | \(0.0523702\pi\) | |||||||
\(992\) | −2.19688 | + | 40.2557i | −0.0697510 | + | 1.27812i | ||||
\(993\) | 10.6141 | 0.336828 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.1829 | + | 11.1829i | 0.354522 | + | 0.354522i | ||||
\(996\) | 4.16319 | − | 1.25302i | 0.131916 | − | 0.0397034i | ||||
\(997\) | −11.7163 | − | 43.7258i | −0.371059 | − | 1.38481i | −0.859019 | − | 0.511944i | \(-0.828925\pi\) |
0.487960 | − | 0.872866i | \(-0.337741\pi\) | |||||||
\(998\) | 4.20309 | − | 0.618804i | 0.133046 | − | 0.0195879i | ||||
\(999\) | 15.5711 | − | 8.99000i | 0.492649 | − | 0.284431i |
(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 | 784.2.x.p.557.11 | 96 | ||
7.2 | even | 3 | inner | 784.2.x.p.765.8 | 96 | ||
7.3 | odd | 6 | 784.2.m.l.589.21 | yes | 48 | ||
7.4 | even | 3 | 784.2.m.l.589.22 | yes | 48 | ||
7.5 | odd | 6 | inner | 784.2.x.p.765.7 | 96 | ||
7.6 | odd | 2 | inner | 784.2.x.p.557.12 | 96 | ||
16.5 | even | 4 | inner | 784.2.x.p.165.8 | 96 | ||
112.5 | odd | 12 | inner | 784.2.x.p.373.12 | 96 | ||
112.37 | even | 12 | inner | 784.2.x.p.373.11 | 96 | ||
112.53 | even | 12 | 784.2.m.l.197.22 | yes | 48 | ||
112.69 | odd | 4 | inner | 784.2.x.p.165.7 | 96 | ||
112.101 | odd | 12 | 784.2.m.l.197.21 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
784.2.m.l.197.21 | ✓ | 48 | 112.101 | odd | 12 | ||
784.2.m.l.197.22 | yes | 48 | 112.53 | even | 12 | ||
784.2.m.l.589.21 | yes | 48 | 7.3 | odd | 6 | ||
784.2.m.l.589.22 | yes | 48 | 7.4 | even | 3 | ||
784.2.x.p.165.7 | 96 | 112.69 | odd | 4 | inner | ||
784.2.x.p.165.8 | 96 | 16.5 | even | 4 | inner | ||
784.2.x.p.373.11 | 96 | 112.37 | even | 12 | inner | ||
784.2.x.p.373.12 | 96 | 112.5 | odd | 12 | inner | ||
784.2.x.p.557.11 | 96 | 1.1 | even | 1 | trivial | ||
784.2.x.p.557.12 | 96 | 7.6 | odd | 2 | inner | ||
784.2.x.p.765.7 | 96 | 7.5 | odd | 6 | inner | ||
784.2.x.p.765.8 | 96 | 7.2 | even | 3 | inner |