Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(101,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.l (of order \(9\), degree \(6\), 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: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{9})\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 176.3 | ||
Character | \(\chi\) | \(=\) | 475.176 |
Dual form | 475.2.l.f.251.3 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{8}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.984236 | + | 0.358233i | −0.695960 | + | 0.253309i | −0.665685 | − | 0.746233i | \(-0.731861\pi\) |
−0.0302752 | + | 0.999542i | \(0.509638\pi\) | |||||||
\(3\) | −0.0922859 | + | 0.523379i | −0.0532813 | + | 0.302173i | −0.999790 | − | 0.0205059i | \(-0.993472\pi\) |
0.946508 | + | 0.322679i | \(0.104583\pi\) | |||||||
\(4\) | −0.691698 | + | 0.580404i | −0.345849 | + | 0.290202i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.0966605 | − | 0.548189i | −0.0394615 | − | 0.223797i | ||||
\(7\) | −1.37016 | − | 2.37320i | −0.517874 | − | 0.896983i | −0.999784 | − | 0.0207632i | \(-0.993390\pi\) |
0.481911 | − | 0.876220i | \(-0.339943\pi\) | |||||||
\(8\) | 1.52028 | − | 2.63320i | 0.537499 | − | 0.930976i | ||||
\(9\) | 2.55367 | + | 0.929459i | 0.851223 | + | 0.309820i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.416418 | + | 0.721257i | −0.125555 | + | 0.217467i | −0.921950 | − | 0.387310i | \(-0.873404\pi\) |
0.796395 | + | 0.604777i | \(0.206738\pi\) | |||||||
\(12\) | −0.239937 | − | 0.415583i | −0.0692639 | − | 0.119969i | ||||
\(13\) | −0.106070 | − | 0.601551i | −0.0294185 | − | 0.166840i | 0.966559 | − | 0.256444i | \(-0.0825510\pi\) |
−0.995977 | + | 0.0896039i | \(0.971440\pi\) | |||||||
\(14\) | 2.19872 | + | 1.84495i | 0.587633 | + | 0.493083i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.239424 | + | 1.35784i | −0.0598561 | + | 0.339461i | ||||
\(17\) | 4.54662 | − | 1.65483i | 1.10272 | − | 0.401356i | 0.274400 | − | 0.961616i | \(-0.411521\pi\) |
0.828317 | + | 0.560259i | \(0.189299\pi\) | |||||||
\(18\) | −2.84638 | −0.670897 | ||||||||
\(19\) | 4.35537 | − | 0.175314i | 0.999191 | − | 0.0402198i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.36853 | − | 0.498103i | 0.298637 | − | 0.108695i | ||||
\(22\) | 0.151476 | − | 0.859062i | 0.0322947 | − | 0.183153i | ||||
\(23\) | −2.87338 | + | 2.41106i | −0.599142 | + | 0.502740i | −0.891170 | − | 0.453670i | \(-0.850114\pi\) |
0.292028 | + | 0.956410i | \(0.405670\pi\) | |||||||
\(24\) | 1.23786 | + | 1.03869i | 0.252677 | + | 0.212021i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.319893 | + | 0.554071i | 0.0627362 | + | 0.108662i | ||||
\(27\) | −1.51931 | + | 2.63152i | −0.292391 | + | 0.506436i | ||||
\(28\) | 2.32515 | + | 0.846286i | 0.439412 | + | 0.159933i | ||||
\(29\) | 3.73543 | + | 1.35958i | 0.693651 | + | 0.252468i | 0.664698 | − | 0.747112i | \(-0.268560\pi\) |
0.0289533 | + | 0.999581i | \(0.490783\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.46338 | + | 5.99875i | 0.622042 | + | 1.07741i | 0.989105 | + | 0.147212i | \(0.0470300\pi\) |
−0.367063 | + | 0.930196i | \(0.619637\pi\) | |||||||
\(32\) | 0.805200 | + | 4.56652i | 0.142341 | + | 0.807254i | ||||
\(33\) | −0.339061 | − | 0.284506i | −0.0590230 | − | 0.0495262i | ||||
\(34\) | −3.88213 | + | 3.25750i | −0.665780 | + | 0.558656i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.30583 | + | 0.839253i | −0.384305 | + | 0.139876i | ||||
\(37\) | −4.33071 | −0.711965 | −0.355982 | − | 0.934493i | \(-0.615854\pi\) | ||||
−0.355982 | + | 0.934493i | \(0.615854\pi\) | |||||||
\(38\) | −4.22391 | + | 1.73279i | −0.685209 | + | 0.281095i | ||||
\(39\) | 0.324628 | 0.0519821 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.923271 | − | 5.23613i | 0.144191 | − | 0.817746i | −0.823823 | − | 0.566848i | \(-0.808163\pi\) |
0.968013 | − | 0.250899i | \(-0.0807260\pi\) | |||||||
\(42\) | −1.16852 | + | 0.980503i | −0.180306 | + | 0.151295i | ||||
\(43\) | 8.01164 | + | 6.72257i | 1.22176 | + | 1.02518i | 0.998731 | + | 0.0503713i | \(0.0160405\pi\) |
0.223034 | + | 0.974811i | \(0.428404\pi\) | |||||||
\(44\) | −0.130585 | − | 0.740582i | −0.0196864 | − | 0.111647i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.96437 | − | 3.40239i | 0.289631 | − | 0.501655i | ||||
\(47\) | 3.19511 | + | 1.16292i | 0.466054 | + | 0.169630i | 0.564364 | − | 0.825526i | \(-0.309121\pi\) |
−0.0983098 | + | 0.995156i | \(0.531344\pi\) | |||||||
\(48\) | −0.688571 | − | 0.250619i | −0.0993867 | − | 0.0361738i | ||||
\(49\) | −0.254704 | + | 0.441160i | −0.0363862 | + | 0.0630228i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.446517 | + | 2.53232i | 0.0625249 | + | 0.354596i | ||||
\(52\) | 0.422511 | + | 0.354529i | 0.0585917 | + | 0.0491643i | ||||
\(53\) | 10.4702 | − | 8.78556i | 1.43820 | − | 1.20679i | 0.497535 | − | 0.867444i | \(-0.334239\pi\) |
0.940662 | − | 0.339346i | \(-0.110206\pi\) | |||||||
\(54\) | 0.552662 | − | 3.13430i | 0.0752077 | − | 0.426524i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −8.33212 | −1.11343 | ||||||||
\(57\) | −0.310183 | + | 2.29569i | −0.0410848 | + | 0.304072i | ||||
\(58\) | −4.16359 | −0.546706 | ||||||||
\(59\) | −9.41315 | + | 3.42610i | −1.22549 | + | 0.446041i | −0.872050 | − | 0.489417i | \(-0.837210\pi\) |
−0.353437 | + | 0.935458i | \(0.614987\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.94990 | − | 5.83166i | 0.889844 | − | 0.746668i | −0.0783350 | − | 0.996927i | \(-0.524960\pi\) |
0.968179 | + | 0.250260i | \(0.0805159\pi\) | |||||||
\(62\) | −5.55774 | − | 4.66350i | −0.705833 | − | 0.592265i | ||||
\(63\) | −1.29316 | − | 7.33387i | −0.162923 | − | 0.923980i | ||||
\(64\) | −3.80717 | − | 6.59422i | −0.475897 | − | 0.824277i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.435636 | + | 0.158558i | 0.0536231 | + | 0.0195172i | ||||
\(67\) | 10.2751 | + | 3.73984i | 1.25531 | + | 0.456894i | 0.882191 | − | 0.470891i | \(-0.156067\pi\) |
0.373115 | + | 0.927785i | \(0.378290\pi\) | |||||||
\(68\) | −2.18442 | + | 3.78352i | −0.264899 | + | 0.458819i | ||||
\(69\) | −0.996723 | − | 1.72638i | −0.119991 | − | 0.207831i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.519169 | − | 0.435634i | −0.0616140 | − | 0.0517003i | 0.611461 | − | 0.791275i | \(-0.290582\pi\) |
−0.673075 | + | 0.739575i | \(0.735027\pi\) | |||||||
\(72\) | 6.32974 | − | 5.31128i | 0.745967 | − | 0.625940i | ||||
\(73\) | −1.21787 | + | 6.90688i | −0.142541 | + | 0.808389i | 0.826768 | + | 0.562543i | \(0.190177\pi\) |
−0.969309 | + | 0.245846i | \(0.920934\pi\) | |||||||
\(74\) | 4.26244 | − | 1.55140i | 0.495499 | − | 0.180347i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.91085 | + | 2.64914i | −0.333897 | + | 0.303877i | ||||
\(77\) | 2.28224 | 0.260086 | ||||||||
\(78\) | −0.319511 | + | 0.116292i | −0.0361775 | + | 0.0131675i | ||||
\(79\) | 0.604220 | − | 3.42670i | 0.0679801 | − | 0.385534i | −0.931767 | − | 0.363056i | \(-0.881733\pi\) |
0.999747 | − | 0.0224781i | \(-0.00715559\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.00824 | + | 4.20241i | 0.556471 | + | 0.466935i | ||||
\(82\) | 0.967036 | + | 5.48434i | 0.106791 | + | 0.605644i | ||||
\(83\) | −2.48742 | − | 4.30834i | −0.273030 | − | 0.472902i | 0.696606 | − | 0.717454i | \(-0.254693\pi\) |
−0.969636 | + | 0.244552i | \(0.921359\pi\) | |||||||
\(84\) | −0.657507 | + | 1.13884i | −0.0717399 | + | 0.124257i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.2936 | − | 3.74656i | −1.10999 | − | 0.404002i | ||||
\(87\) | −1.05630 | + | 1.82957i | −0.113248 | + | 0.196151i | ||||
\(88\) | 1.26614 | + | 2.19302i | 0.134971 | + | 0.233777i | ||||
\(89\) | −1.02256 | − | 5.79921i | −0.108391 | − | 0.614716i | −0.989812 | − | 0.142383i | \(-0.954523\pi\) |
0.881421 | − | 0.472332i | \(-0.156588\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.28227 | + | 1.07595i | −0.134418 | + | 0.112790i | ||||
\(92\) | 0.588129 | − | 3.33544i | 0.0613167 | − | 0.347744i | ||||
\(93\) | −3.45924 | + | 1.25906i | −0.358707 | + | 0.130559i | ||||
\(94\) | −3.56134 | −0.367324 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.46433 | −0.251514 | ||||||||
\(97\) | −11.6886 | + | 4.25430i | −1.18680 | + | 0.431959i | −0.858598 | − | 0.512649i | \(-0.828664\pi\) |
−0.328200 | + | 0.944608i | \(0.606442\pi\) | |||||||
\(98\) | 0.0926508 | − | 0.525449i | 0.00935914 | − | 0.0530783i | ||||
\(99\) | −1.73377 | + | 1.45481i | −0.174251 | + | 0.146214i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.08004 | − | 17.4678i | −0.306475 | − | 1.73811i | −0.616478 | − | 0.787372i | \(-0.711441\pi\) |
0.310003 | − | 0.950736i | \(-0.399670\pi\) | |||||||
\(102\) | −1.34664 | − | 2.33245i | −0.133337 | − | 0.230947i | ||||
\(103\) | −2.60925 | + | 4.51935i | −0.257097 | + | 0.445305i | −0.965463 | − | 0.260541i | \(-0.916099\pi\) |
0.708366 | + | 0.705845i | \(0.249433\pi\) | |||||||
\(104\) | −1.74526 | − | 0.635222i | −0.171137 | − | 0.0622887i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.15790 | + | 12.3979i | −0.695237 | + | 1.20419i | ||||
\(107\) | −7.59356 | − | 13.1524i | −0.734097 | − | 1.27149i | −0.955118 | − | 0.296225i | \(-0.904272\pi\) |
0.221021 | − | 0.975269i | \(-0.429061\pi\) | |||||||
\(108\) | −0.476440 | − | 2.70203i | −0.0458455 | − | 0.260003i | ||||
\(109\) | 3.00487 | + | 2.52138i | 0.287814 | + | 0.241505i | 0.775251 | − | 0.631654i | \(-0.217624\pi\) |
−0.487437 | + | 0.873158i | \(0.662068\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.399663 | − | 2.26660i | 0.0379344 | − | 0.215137i | ||||
\(112\) | 3.55048 | − | 1.29227i | 0.335489 | − | 0.122108i | ||||
\(113\) | −3.97342 | −0.373788 | −0.186894 | − | 0.982380i | \(-0.559842\pi\) | ||||
−0.186894 | + | 0.982380i | \(0.559842\pi\) | |||||||
\(114\) | −0.517097 | − | 2.37062i | −0.0484306 | − | 0.222029i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.37289 | + | 1.22763i | −0.313165 | + | 0.113983i | ||||
\(117\) | 0.288251 | − | 1.63475i | 0.0266488 | − | 0.151133i | ||||
\(118\) | 8.03742 | − | 6.74420i | 0.739904 | − | 0.620853i | ||||
\(119\) | −10.1569 | − | 8.52262i | −0.931078 | − | 0.781267i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.15319 | + | 8.92559i | 0.468472 | + | 0.811417i | ||||
\(122\) | −4.75126 | + | 8.22942i | −0.430158 | + | 0.745056i | ||||
\(123\) | 2.65528 | + | 0.966441i | 0.239418 | + | 0.0871411i | ||||
\(124\) | −5.87731 | − | 2.13917i | −0.527798 | − | 0.192103i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.90001 | + | 6.75501i | 0.347440 | + | 0.601784i | ||||
\(127\) | −1.59495 | − | 9.04543i | −0.141529 | − | 0.802652i | −0.970089 | − | 0.242751i | \(-0.921950\pi\) |
0.828559 | − | 0.559901i | \(-0.189161\pi\) | |||||||
\(128\) | −0.994815 | − | 0.834749i | −0.0879301 | − | 0.0737821i | ||||
\(129\) | −4.25781 | + | 3.57273i | −0.374880 | + | 0.314561i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.51355 | − | 1.27883i | 0.306980 | − | 0.111732i | −0.183936 | − | 0.982938i | \(-0.558884\pi\) |
0.490917 | + | 0.871206i | \(0.336662\pi\) | |||||||
\(132\) | 0.399656 | 0.0347856 | ||||||||
\(133\) | −6.38363 | − | 10.0959i | −0.553531 | − | 0.875429i | ||||
\(134\) | −11.4529 | −0.989379 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.55462 | − | 14.4880i | 0.219057 | − | 1.24233i | ||||
\(137\) | −1.81043 | + | 1.51913i | −0.154675 | + | 0.129788i | −0.716841 | − | 0.697237i | \(-0.754413\pi\) |
0.562166 | + | 0.827025i | \(0.309968\pi\) | |||||||
\(138\) | 1.59946 | + | 1.34210i | 0.136155 | + | 0.114247i | ||||
\(139\) | 0.424186 | + | 2.40568i | 0.0359790 | + | 0.204047i | 0.997498 | − | 0.0706903i | \(-0.0225202\pi\) |
−0.961519 | + | 0.274737i | \(0.911409\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.903514 | + | 1.56493i | −0.0760896 | + | 0.131791i | ||||
\(142\) | 0.667043 | + | 0.242784i | 0.0559770 | + | 0.0203740i | ||||
\(143\) | 0.478042 | + | 0.173993i | 0.0399759 | + | 0.0145500i | ||||
\(144\) | −1.87347 | + | 3.24495i | −0.156123 | + | 0.270412i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.27560 | − | 7.23428i | −0.105569 | − | 0.598713i | ||||
\(147\) | −0.207388 | − | 0.174019i | −0.0171051 | − | 0.0143529i | ||||
\(148\) | 2.99555 | − | 2.51356i | 0.246232 | − | 0.206613i | ||||
\(149\) | 2.47773 | − | 14.0519i | 0.202984 | − | 1.15118i | −0.697598 | − | 0.716490i | \(-0.745748\pi\) |
0.900581 | − | 0.434687i | \(-0.143141\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.34319 | 0.190686 | 0.0953432 | − | 0.995444i | \(-0.469605\pi\) | ||||
0.0953432 | + | 0.995444i | \(0.469605\pi\) | |||||||
\(152\) | 6.15974 | − | 11.7351i | 0.499621 | − | 0.951841i | ||||
\(153\) | 13.1487 | 1.06301 | ||||||||
\(154\) | −2.24627 | + | 0.817575i | −0.181009 | + | 0.0658820i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.224545 | + | 0.188415i | −0.0179780 | + | 0.0150853i | ||||
\(157\) | 12.3906 | + | 10.3969i | 0.988875 | + | 0.829765i | 0.985405 | − | 0.170229i | \(-0.0544508\pi\) |
0.00347076 | + | 0.999994i | \(0.498895\pi\) | |||||||
\(158\) | 0.632862 | + | 3.58914i | 0.0503478 | + | 0.285536i | ||||
\(159\) | 3.63193 | + | 6.29068i | 0.288031 | + | 0.498884i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.65891 | + | 3.51556i | 0.761229 | + | 0.277065i | ||||
\(162\) | −6.43473 | − | 2.34205i | −0.505560 | − | 0.184009i | ||||
\(163\) | −8.01289 | + | 13.8787i | −0.627618 | + | 1.08707i | 0.360410 | + | 0.932794i | \(0.382637\pi\) |
−0.988028 | + | 0.154273i | \(0.950697\pi\) | |||||||
\(164\) | 2.40044 | + | 4.15769i | 0.187443 | + | 0.324661i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.99160 | + | 3.34935i | 0.309809 | + | 0.259960i | ||||
\(167\) | −5.80391 | + | 4.87006i | −0.449120 | + | 0.376856i | −0.839109 | − | 0.543963i | \(-0.816923\pi\) |
0.389989 | + | 0.920819i | \(0.372479\pi\) | |||||||
\(168\) | 0.768937 | − | 4.36086i | 0.0593248 | − | 0.336448i | ||||
\(169\) | 11.8654 | − | 4.31865i | 0.912722 | − | 0.332204i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.2851 | + | 3.60045i | 0.862995 | + | 0.275333i | ||||
\(172\) | −9.44344 | −0.720056 | ||||||||
\(173\) | −8.32761 | + | 3.03100i | −0.633136 | + | 0.230443i | −0.638596 | − | 0.769542i | \(-0.720484\pi\) |
0.00545960 | + | 0.999985i | \(0.498262\pi\) | |||||||
\(174\) | 0.384240 | − | 2.17914i | 0.0291292 | − | 0.165200i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.879653 | − | 0.738116i | −0.0663063 | − | 0.0556376i | ||||
\(177\) | −0.924452 | − | 5.24283i | −0.0694860 | − | 0.394075i | ||||
\(178\) | 3.08391 | + | 5.34148i | 0.231149 | + | 0.400361i | ||||
\(179\) | −2.73273 | + | 4.73323i | −0.204254 | + | 0.353778i | −0.949895 | − | 0.312570i | \(-0.898810\pi\) |
0.745641 | + | 0.666348i | \(0.232143\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.6816 | − | 6.43559i | −1.31427 | − | 0.478354i | −0.412650 | − | 0.910890i | \(-0.635397\pi\) |
−0.901617 | + | 0.432536i | \(0.857619\pi\) | |||||||
\(182\) | 0.876613 | − | 1.51834i | 0.0649789 | − | 0.112547i | ||||
\(183\) | 2.41079 | + | 4.17561i | 0.178211 | + | 0.308670i | ||||
\(184\) | 1.98044 | + | 11.2317i | 0.146000 | + | 0.828009i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.95368 | − | 2.47843i | 0.216574 | − | 0.181727i | ||||
\(187\) | −0.699733 | + | 3.96838i | −0.0511695 | + | 0.290197i | ||||
\(188\) | −2.88502 | + | 1.05006i | −0.210411 | + | 0.0765835i | ||||
\(189\) | 8.32680 | 0.605686 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.2606 | −1.24893 | −0.624465 | − | 0.781053i | \(-0.714683\pi\) | ||||
−0.624465 | + | 0.781053i | \(0.714683\pi\) | |||||||
\(192\) | 3.80262 | − | 1.38404i | 0.274431 | − | 0.0998846i | ||||
\(193\) | −1.29789 | + | 7.36067i | −0.0934238 | + | 0.529833i | 0.901795 | + | 0.432164i | \(0.142250\pi\) |
−0.995219 | + | 0.0976691i | \(0.968861\pi\) | |||||||
\(194\) | 9.98032 | − | 8.37448i | 0.716545 | − | 0.601253i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.0798727 | − | 0.452980i | −0.00570519 | − | 0.0323557i | ||||
\(197\) | 6.10400 | + | 10.5724i | 0.434892 | + | 0.753255i | 0.997287 | − | 0.0736138i | \(-0.0234532\pi\) |
−0.562395 | + | 0.826869i | \(0.690120\pi\) | |||||||
\(198\) | 1.18528 | − | 2.05297i | 0.0842343 | − | 0.145898i | ||||
\(199\) | 7.29002 | + | 2.65335i | 0.516776 | + | 0.188091i | 0.587224 | − | 0.809424i | \(-0.300221\pi\) |
−0.0704481 | + | 0.997515i | \(0.522443\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.90560 | + | 5.03265i | −0.204945 | + | 0.354976i | ||||
\(202\) | 9.28901 | + | 16.0890i | 0.653573 | + | 1.13202i | ||||
\(203\) | −1.89159 | − | 10.7277i | −0.132764 | − | 0.752940i | ||||
\(204\) | −1.77862 | − | 1.49244i | −0.124529 | − | 0.104492i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.949137 | − | 5.38282i | 0.0661295 | − | 0.375039i | ||||
\(207\) | −9.57865 | + | 3.48634i | −0.665762 | + | 0.242318i | ||||
\(208\) | 0.842208 | 0.0583966 | ||||||||
\(209\) | −1.68721 | + | 3.21434i | −0.116707 | + | 0.222341i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.45058 | + | 3.43973i | −0.650605 | + | 0.236801i | −0.646175 | − | 0.763190i | \(-0.723632\pi\) |
−0.00442979 | + | 0.999990i | \(0.501410\pi\) | |||||||
\(212\) | −2.14306 | + | 12.1539i | −0.147186 | + | 0.834734i | ||||
\(213\) | 0.275914 | − | 0.231519i | 0.0189053 | − | 0.0158634i | ||||
\(214\) | 12.1855 | + | 10.2248i | 0.832983 | + | 0.698956i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.61954 | + | 8.00127i | 0.314320 | + | 0.544418i | ||||
\(217\) | 9.49081 | − | 16.4386i | 0.644278 | − | 1.11592i | ||||
\(218\) | −3.86074 | − | 1.40519i | −0.261482 | − | 0.0951718i | ||||
\(219\) | −3.50252 | − | 1.27481i | −0.236679 | − | 0.0861440i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.47773 | − | 2.55950i | −0.0994027 | − | 0.172170i | ||||
\(222\) | 0.418609 | + | 2.37405i | 0.0280952 | + | 0.159336i | ||||
\(223\) | −21.6954 | − | 18.2046i | −1.45283 | − | 1.21907i | −0.930482 | − | 0.366339i | \(-0.880611\pi\) |
−0.522350 | − | 0.852731i | \(-0.674944\pi\) | |||||||
\(224\) | 9.73398 | − | 8.16778i | 0.650379 | − | 0.545733i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.91079 | − | 1.42341i | 0.260142 | − | 0.0946839i | ||||
\(227\) | 15.8786 | 1.05390 | 0.526949 | − | 0.849897i | \(-0.323336\pi\) | ||||
0.526949 | + | 0.849897i | \(0.323336\pi\) | |||||||
\(228\) | −1.11787 | − | 1.76796i | −0.0740330 | − | 0.117086i | ||||
\(229\) | 11.3865 | 0.752438 | 0.376219 | − | 0.926531i | \(-0.377224\pi\) | ||||
0.376219 | + | 0.926531i | \(0.377224\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.210619 | + | 1.19448i | −0.0138577 | + | 0.0785909i | ||||
\(232\) | 9.25894 | − | 7.76917i | 0.607879 | − | 0.510071i | ||||
\(233\) | 12.1527 | + | 10.1973i | 0.796151 | + | 0.668050i | 0.947260 | − | 0.320467i | \(-0.103840\pi\) |
−0.151109 | + | 0.988517i | \(0.548284\pi\) | |||||||
\(234\) | 0.301914 | + | 1.71224i | 0.0197368 | + | 0.111933i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.52253 | − | 7.83325i | 0.294392 | − | 0.509901i | ||||
\(237\) | 1.73770 | + | 0.632473i | 0.112876 | + | 0.0410835i | ||||
\(238\) | 13.0498 | + | 4.74975i | 0.845895 | + | 0.307881i | ||||
\(239\) | −10.4324 | + | 18.0695i | −0.674817 | + | 1.16882i | 0.301705 | + | 0.953401i | \(0.402444\pi\) |
−0.976522 | + | 0.215416i | \(0.930889\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.93664 | + | 27.9971i | 0.317997 | + | 1.80345i | 0.554899 | + | 0.831917i | \(0.312757\pi\) |
−0.236902 | + | 0.971533i | \(0.576132\pi\) | |||||||
\(242\) | −8.26940 | − | 6.93885i | −0.531577 | − | 0.446046i | ||||
\(243\) | −9.64478 | + | 8.09293i | −0.618713 | + | 0.519162i | ||||
\(244\) | −1.42252 | + | 8.06750i | −0.0910673 | + | 0.516469i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.95963 | −0.188699 | ||||||||
\(247\) | −0.567434 | − | 2.60138i | −0.0361049 | − | 0.165522i | ||||
\(248\) | 21.0612 | 1.33739 | ||||||||
\(249\) | 2.48445 | − | 0.904266i | 0.157446 | − | 0.0573056i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.0083 | − | 15.9499i | 1.19979 | − | 1.00675i | 0.200157 | − | 0.979764i | \(-0.435855\pi\) |
0.999636 | − | 0.0269823i | \(-0.00858979\pi\) | |||||||
\(252\) | 5.15108 | + | 4.32227i | 0.324487 | + | 0.272277i | ||||
\(253\) | −0.542462 | − | 3.07645i | −0.0341043 | − | 0.193415i | ||||
\(254\) | 4.81018 | + | 8.33148i | 0.301818 | + | 0.522763i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.5885 | + | 5.67373i | 0.974279 | + | 0.354608i | ||||
\(257\) | −5.11403 | − | 1.86135i | −0.319004 | − | 0.116108i | 0.177555 | − | 0.984111i | \(-0.443181\pi\) |
−0.496559 | + | 0.868003i | \(0.665403\pi\) | |||||||
\(258\) | 2.91083 | − | 5.04170i | 0.181220 | − | 0.313882i | ||||
\(259\) | 5.93379 | + | 10.2776i | 0.368708 | + | 0.638620i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.27536 | + | 6.94385i | 0.512232 | + | 0.429814i | ||||
\(262\) | −3.00005 | + | 2.51734i | −0.185344 | + | 0.155522i | ||||
\(263\) | 3.38955 | − | 19.2231i | 0.209009 | − | 1.18535i | −0.681997 | − | 0.731355i | \(-0.738888\pi\) |
0.891006 | − | 0.453992i | \(-0.150001\pi\) | |||||||
\(264\) | −1.26463 | + | 0.460287i | −0.0778325 | + | 0.0283287i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 9.89970 | + | 7.64996i | 0.606990 | + | 0.469049i | ||||
\(267\) | 3.12956 | 0.191526 | ||||||||
\(268\) | −9.27790 | + | 3.37688i | −0.566738 | + | 0.206276i | ||||
\(269\) | 3.22722 | − | 18.3025i | 0.196767 | − | 1.11592i | −0.713113 | − | 0.701049i | \(-0.752715\pi\) |
0.909880 | − | 0.414872i | \(-0.136174\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.44946 | + | 1.21624i | 0.0880485 | + | 0.0738815i | 0.685749 | − | 0.727838i | \(-0.259475\pi\) |
−0.597701 | + | 0.801719i | \(0.703919\pi\) | |||||||
\(272\) | 1.15843 | + | 6.56980i | 0.0702403 | + | 0.398353i | ||||
\(273\) | −0.444794 | − | 0.770406i | −0.0269202 | − | 0.0466271i | ||||
\(274\) | 1.23769 | − | 2.14374i | 0.0747715 | − | 0.129508i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.69143 | + | 0.615629i | 0.101812 | + | 0.0370565i | ||||
\(277\) | −3.38944 | + | 5.87068i | −0.203652 | + | 0.352735i | −0.949702 | − | 0.313154i | \(-0.898614\pi\) |
0.746051 | + | 0.665889i | \(0.231948\pi\) | |||||||
\(278\) | −1.27929 | − | 2.21580i | −0.0767269 | − | 0.132895i | ||||
\(279\) | 3.26873 | + | 18.5379i | 0.195694 | + | 1.10984i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.41170 | + | 7.89735i | −0.561455 | + | 0.471116i | −0.878798 | − | 0.477194i | \(-0.841654\pi\) |
0.317343 | + | 0.948311i | \(0.397209\pi\) | |||||||
\(282\) | 0.328661 | − | 1.86393i | 0.0195715 | − | 0.110995i | ||||
\(283\) | 24.1188 | − | 8.77851i | 1.43371 | − | 0.521829i | 0.495719 | − | 0.868483i | \(-0.334905\pi\) |
0.937993 | + | 0.346654i | \(0.112682\pi\) | |||||||
\(284\) | 0.611952 | 0.0363126 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.532837 | −0.0315073 | ||||||||
\(287\) | −13.6914 | + | 4.98326i | −0.808177 | + | 0.294152i | ||||
\(288\) | −2.18818 | + | 12.4098i | −0.128940 | + | 0.731253i | ||||
\(289\) | 4.91052 | − | 4.12042i | 0.288854 | − | 0.242377i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.14792 | − | 6.51018i | −0.0672923 | − | 0.381634i | ||||
\(292\) | −3.16638 | − | 5.48433i | −0.185298 | − | 0.320946i | ||||
\(293\) | −14.0560 | + | 24.3458i | −0.821162 | + | 1.42229i | 0.0836552 | + | 0.996495i | \(0.473341\pi\) |
−0.904817 | + | 0.425800i | \(0.859993\pi\) | |||||||
\(294\) | 0.266459 | + | 0.0969830i | 0.0155402 | + | 0.00565616i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.58388 | + | 11.4036i | −0.382680 | + | 0.662822i | ||||
\(297\) | −1.26533 | − | 2.19162i | −0.0734220 | − | 0.127171i | ||||
\(298\) | 2.59518 | + | 14.7180i | 0.150335 | + | 0.852591i | ||||
\(299\) | 1.75515 | + | 1.47275i | 0.101503 | + | 0.0851712i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.97669 | − | 28.2242i | 0.286852 | − | 1.62682i | ||||
\(302\) | −2.30626 | + | 0.839409i | −0.132710 | + | 0.0483025i | ||||
\(303\) | 9.42651 | 0.541539 | ||||||||
\(304\) | −0.804733 | + | 5.95588i | −0.0461546 | + | 0.341593i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −12.9414 | + | 4.71028i | −0.739810 | + | 0.269269i | ||||
\(307\) | 0.447450 | − | 2.53762i | 0.0255373 | − | 0.144829i | −0.969373 | − | 0.245593i | \(-0.921017\pi\) |
0.994910 | + | 0.100763i | \(0.0321285\pi\) | |||||||
\(308\) | −1.57862 | + | 1.32462i | −0.0899504 | + | 0.0754774i | ||||
\(309\) | −2.12454 | − | 1.78270i | −0.120861 | − | 0.101414i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.31837 | − | 12.6758i | −0.414987 | − | 0.718778i | 0.580440 | − | 0.814303i | \(-0.302880\pi\) |
−0.995427 | + | 0.0955246i | \(0.969547\pi\) | |||||||
\(312\) | 0.493525 | − | 0.854810i | 0.0279403 | − | 0.0483941i | ||||
\(313\) | 1.40398 | + | 0.511007i | 0.0793577 | + | 0.0288838i | 0.381394 | − | 0.924413i | \(-0.375444\pi\) |
−0.302036 | + | 0.953296i | \(0.597666\pi\) | |||||||
\(314\) | −15.9198 | − | 5.79432i | −0.898405 | − | 0.326993i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.57093 | + | 2.72094i | 0.0883719 | + | 0.153065i | ||||
\(317\) | −0.979782 | − | 5.55662i | −0.0550301 | − | 0.312091i | 0.944851 | − | 0.327500i | \(-0.106206\pi\) |
−0.999881 | + | 0.0154089i | \(0.995095\pi\) | |||||||
\(318\) | −5.82820 | − | 4.89044i | −0.326829 | − | 0.274242i | ||||
\(319\) | −2.53611 | + | 2.12805i | −0.141995 | + | 0.119148i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.58449 | − | 2.76053i | 0.423325 | − | 0.154078i | ||||
\(322\) | −10.7660 | −0.599968 | ||||||||
\(323\) | 19.5121 | − | 8.00451i | 1.08568 | − | 0.445383i | ||||
\(324\) | −5.90329 | −0.327960 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.91476 | − | 16.5304i | 0.161434 | − | 0.915536i | ||||
\(327\) | −1.59694 | + | 1.34000i | −0.0883113 | + | 0.0741019i | ||||
\(328\) | −12.3841 | − | 10.3915i | −0.683800 | − | 0.573776i | ||||
\(329\) | −1.61798 | − | 9.17601i | −0.0892021 | − | 0.505890i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.9460 | + | 27.6193i | −0.876472 | + | 1.51809i | −0.0212866 | + | 0.999773i | \(0.506776\pi\) |
−0.855186 | + | 0.518321i | \(0.826557\pi\) | |||||||
\(332\) | 4.22113 | + | 1.53636i | 0.231664 | + | 0.0843189i | ||||
\(333\) | −11.0592 | − | 4.02522i | −0.606041 | − | 0.220581i | ||||
\(334\) | 3.96780 | − | 6.87244i | 0.217109 | − | 0.376043i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.348687 | + | 1.97750i | 0.0190224 | + | 0.107882i | ||||
\(337\) | −11.7495 | − | 9.85896i | −0.640033 | − | 0.537052i | 0.263995 | − | 0.964524i | \(-0.414960\pi\) |
−0.904029 | + | 0.427472i | \(0.859404\pi\) | |||||||
\(338\) | −10.1313 | + | 8.50114i | −0.551068 | + | 0.462401i | ||||
\(339\) | 0.366691 | − | 2.07961i | 0.0199159 | − | 0.112949i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.76886 | −0.312401 | ||||||||
\(342\) | −12.3970 | + | 0.499010i | −0.670355 | + | 0.0269834i | ||||
\(343\) | −17.7864 | −0.960373 | ||||||||
\(344\) | 29.8818 | − | 10.8761i | 1.61112 | − | 0.586399i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.11053 | − | 5.96644i | 0.382264 | − | 0.320758i | ||||
\(347\) | 0.0633501 | + | 0.0531571i | 0.00340081 | + | 0.00285362i | 0.644486 | − | 0.764616i | \(-0.277071\pi\) |
−0.641086 | + | 0.767469i | \(0.721516\pi\) | |||||||
\(348\) | −0.331247 | − | 1.87860i | −0.0177567 | − | 0.100703i | ||||
\(349\) | 2.32166 | + | 4.02124i | 0.124276 | + | 0.215252i | 0.921450 | − | 0.388498i | \(-0.127006\pi\) |
−0.797174 | + | 0.603750i | \(0.793673\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.74415 | + | 0.634817i | 0.0930956 | + | 0.0338840i | ||||
\(352\) | −3.62893 | − | 1.32082i | −0.193423 | − | 0.0704001i | ||||
\(353\) | 1.99701 | − | 3.45892i | 0.106290 | − | 0.184100i | −0.807974 | − | 0.589218i | \(-0.799436\pi\) |
0.914265 | + | 0.405118i | \(0.132769\pi\) | |||||||
\(354\) | 2.78803 | + | 4.82901i | 0.148182 | + | 0.256659i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.07319 | + | 3.41781i | 0.215878 | + | 0.181144i | ||||
\(357\) | 5.39790 | − | 4.52937i | 0.285687 | − | 0.239720i | ||||
\(358\) | 0.994055 | − | 5.63757i | 0.0525374 | − | 0.297955i | ||||
\(359\) | −28.3973 | + | 10.3358i | −1.49875 | + | 0.545502i | −0.955738 | − | 0.294220i | \(-0.904940\pi\) |
−0.543017 | + | 0.839722i | \(0.682718\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9385 | − | 1.52712i | 0.996765 | − | 0.0803746i | ||||
\(362\) | 19.7084 | 1.03585 | ||||||||
\(363\) | −5.14704 | + | 1.87337i | −0.270149 | + | 0.0983263i | ||||
\(364\) | 0.262456 | − | 1.48846i | 0.0137564 | − | 0.0780167i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.86863 | − | 3.24617i | −0.202217 | − | 0.169680i | ||||
\(367\) | −3.14996 | − | 17.8643i | −0.164427 | − | 0.932511i | −0.949653 | − | 0.313302i | \(-0.898565\pi\) |
0.785227 | − | 0.619208i | \(-0.212546\pi\) | |||||||
\(368\) | −2.58588 | − | 4.47887i | −0.134798 | − | 0.233477i | ||||
\(369\) | 7.22450 | − | 12.5132i | 0.376092 | − | 0.651411i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −35.1958 | − | 12.8102i | −1.82727 | − | 0.665074i | ||||
\(372\) | 1.66199 | − | 2.87865i | 0.0861701 | − | 0.149251i | ||||
\(373\) | −12.6075 | − | 21.8369i | −0.652794 | − | 1.13067i | −0.982442 | − | 0.186568i | \(-0.940264\pi\) |
0.329648 | − | 0.944104i | \(-0.393070\pi\) | |||||||
\(374\) | −0.732902 | − | 4.15649i | −0.0378975 | − | 0.214927i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.91966 | − | 6.64538i | 0.408425 | − | 0.342710i | ||||
\(377\) | 0.421644 | − | 2.39126i | 0.0217158 | − | 0.123156i | ||||
\(378\) | −8.19554 | + | 2.98293i | −0.421533 | + | 0.153426i | ||||
\(379\) | −27.5634 | −1.41584 | −0.707918 | − | 0.706294i | \(-0.750366\pi\) | ||||
−0.707918 | + | 0.706294i | \(0.750366\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.88138 | 0.250081 | ||||||||
\(382\) | 16.9885 | − | 6.18330i | 0.869206 | − | 0.316365i | ||||
\(383\) | −3.18187 | + | 18.0453i | −0.162586 | + | 0.922072i | 0.788932 | + | 0.614480i | \(0.210634\pi\) |
−0.951518 | + | 0.307592i | \(0.900477\pi\) | |||||||
\(384\) | 0.528698 | − | 0.443630i | 0.0269800 | − | 0.0226389i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.35941 | − | 7.70959i | −0.0691921 | − | 0.392408i | ||||
\(387\) | 14.2107 | + | 24.6137i | 0.722372 | + | 1.25119i | ||||
\(388\) | 5.61577 | − | 9.72680i | 0.285098 | − | 0.493803i | ||||
\(389\) | 6.75172 | + | 2.45743i | 0.342326 | + | 0.124596i | 0.507461 | − | 0.861674i | \(-0.330584\pi\) |
−0.165136 | + | 0.986271i | \(0.552806\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.07429 | + | 15.7171i | −0.458906 | + | 0.794849i | ||||
\(392\) | 0.774441 | + | 1.34137i | 0.0391152 | + | 0.0677495i | ||||
\(393\) | 0.345061 | + | 1.95694i | 0.0174060 | + | 0.0987144i | ||||
\(394\) | −9.79517 | − | 8.21913i | −0.493474 | − | 0.414074i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.354871 | − | 2.01257i | 0.0178330 | − | 0.101136i | ||||
\(397\) | −11.0172 | + | 4.00993i | −0.552937 | + | 0.201252i | −0.603351 | − | 0.797476i | \(-0.706168\pi\) |
0.0504142 | + | 0.998728i | \(0.483946\pi\) | |||||||
\(398\) | −8.12562 | −0.407301 | ||||||||
\(399\) | 5.87312 | − | 2.40935i | 0.294024 | − | 0.120618i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −36.8475 | + | 13.4114i | −1.84008 | + | 0.669734i | −0.850455 | + | 0.526048i | \(0.823673\pi\) |
−0.989623 | + | 0.143686i | \(0.954105\pi\) | |||||||
\(402\) | 1.05694 | − | 5.99420i | 0.0527154 | − | 0.298964i | ||||
\(403\) | 3.24120 | − | 2.71969i | 0.161456 | − | 0.135477i | ||||
\(404\) | 12.2688 | + | 10.2948i | 0.610396 | + | 0.512183i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.70480 | + | 9.88101i | 0.283125 | + | 0.490386i | ||||
\(407\) | 1.80339 | − | 3.12355i | 0.0893905 | − | 0.154829i | ||||
\(408\) | 7.34694 | + | 2.67407i | 0.363728 | + | 0.132386i | ||||
\(409\) | −8.34099 | − | 3.03587i | −0.412436 | − | 0.150114i | 0.127465 | − | 0.991843i | \(-0.459316\pi\) |
−0.539901 | + | 0.841729i | \(0.681538\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.628004 | − | 1.08773i | −0.0309772 | − | 0.0536540i | ||||
\(412\) | −0.818235 | − | 4.64044i | −0.0403115 | − | 0.228618i | ||||
\(413\) | 21.0284 | + | 17.6449i | 1.03474 | + | 0.868249i | ||||
\(414\) | 8.17873 | − | 6.86277i | 0.401963 | − | 0.337287i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.66159 | − | 0.968738i | 0.130495 | − | 0.0474963i | ||||
\(417\) | −1.29823 | −0.0635745 | ||||||||
\(418\) | 0.509128 | − | 3.76809i | 0.0249022 | − | 0.184303i | ||||
\(419\) | −7.80196 | −0.381151 | −0.190575 | − | 0.981673i | \(-0.561035\pi\) | ||||
−0.190575 | + | 0.981673i | \(0.561035\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.00077 | − | 34.0320i | 0.292459 | − | 1.65862i | −0.384893 | − | 0.922961i | \(-0.625762\pi\) |
0.677352 | − | 0.735659i | \(-0.263127\pi\) | |||||||
\(422\) | 8.06938 | − | 6.77101i | 0.392811 | − | 0.329608i | ||||
\(423\) | 7.07836 | + | 5.93945i | 0.344161 | + | 0.288786i | ||||
\(424\) | −7.21648 | − | 40.9267i | −0.350463 | − | 1.98758i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.188627 | + | 0.326711i | −0.00913899 | + | 0.0158292i | ||||
\(427\) | −23.3622 | − | 8.50314i | −1.13058 | − | 0.411496i | ||||
\(428\) | 12.8862 | + | 4.69018i | 0.622877 | + | 0.226709i | ||||
\(429\) | −0.135181 | + | 0.234140i | −0.00652660 | + | 0.0113044i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.493077 | + | 2.79638i | 0.0237507 | + | 0.134697i | 0.994377 | − | 0.105893i | \(-0.0337702\pi\) |
−0.970627 | + | 0.240590i | \(0.922659\pi\) | |||||||
\(432\) | −3.20943 | − | 2.69303i | −0.154414 | − | 0.129568i | ||||
\(433\) | 16.7402 | − | 14.0467i | 0.804481 | − | 0.675040i | −0.144803 | − | 0.989461i | \(-0.546255\pi\) |
0.949284 | + | 0.314421i | \(0.101810\pi\) | |||||||
\(434\) | −3.45237 | + | 19.5794i | −0.165719 | + | 0.939839i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.54188 | −0.169625 | ||||||||
\(437\) | −12.0920 | + | 11.0048i | −0.578437 | + | 0.526430i | ||||
\(438\) | 3.90399 | 0.186540 | ||||||||
\(439\) | −30.6114 | + | 11.1416i | −1.46100 | + | 0.531761i | −0.945641 | − | 0.325212i | \(-0.894564\pi\) |
−0.515361 | + | 0.856973i | \(0.672342\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.06047 | + | 0.889839i | −0.0504985 | + | 0.0423733i | ||||
\(442\) | 2.37133 | + | 1.98978i | 0.112793 | + | 0.0946442i | ||||
\(443\) | −1.34781 | − | 7.64381i | −0.0640364 | − | 0.363169i | −0.999940 | − | 0.0109135i | \(-0.996526\pi\) |
0.935904 | − | 0.352255i | \(-0.114585\pi\) | |||||||
\(444\) | 1.03910 | + | 1.79977i | 0.0493134 | + | 0.0854134i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 27.8749 | + | 10.1456i | 1.31991 | + | 0.480409i | ||||
\(447\) | 7.12581 | + | 2.59358i | 0.337039 | + | 0.122672i | ||||
\(448\) | −10.4329 | + | 18.0703i | −0.492909 | + | 0.853743i | ||||
\(449\) | −11.4911 | − | 19.9031i | −0.542296 | − | 0.939285i | −0.998772 | − | 0.0495489i | \(-0.984222\pi\) |
0.456475 | − | 0.889736i | \(-0.349112\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.39213 | + | 2.84633i | 0.159729 | + | 0.134029i | ||||
\(452\) | 2.74841 | − | 2.30619i | 0.129274 | − | 0.108474i | ||||
\(453\) | −0.216244 | + | 1.22638i | −0.0101600 | + | 0.0576203i | ||||
\(454\) | −15.6283 | + | 5.68822i | −0.733470 | + | 0.266961i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.57344 | + | 4.30686i | 0.261000 | + | 0.201687i | ||||
\(457\) | −3.38866 | −0.158515 | −0.0792573 | − | 0.996854i | \(-0.525255\pi\) | ||||
−0.0792573 | + | 0.996854i | \(0.525255\pi\) | |||||||
\(458\) | −11.2070 | + | 4.07900i | −0.523667 | + | 0.190599i | ||||
\(459\) | −2.55299 | + | 14.4787i | −0.119163 | + | 0.675808i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.31382 | − | 6.97612i | −0.387213 | − | 0.324910i | 0.428313 | − | 0.903630i | \(-0.359108\pi\) |
−0.815526 | + | 0.578720i | \(0.803552\pi\) | |||||||
\(462\) | −0.220603 | − | 1.25110i | −0.0102634 | − | 0.0582064i | ||||
\(463\) | 3.65586 | + | 6.33213i | 0.169902 | + | 0.294279i | 0.938385 | − | 0.345591i | \(-0.112322\pi\) |
−0.768483 | + | 0.639870i | \(0.778988\pi\) | |||||||
\(464\) | −2.74045 | + | 4.74660i | −0.127222 | + | 0.220355i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.6142 | − | 5.68309i | −0.723313 | − | 0.263264i | ||||
\(467\) | −5.42091 | + | 9.38929i | −0.250850 | + | 0.434484i | −0.963760 | − | 0.266771i | \(-0.914043\pi\) |
0.712910 | + | 0.701255i | \(0.247377\pi\) | |||||||
\(468\) | 0.749433 | + | 1.29806i | 0.0346425 | + | 0.0600026i | ||||
\(469\) | −5.20325 | − | 29.5091i | −0.240264 | − | 1.36260i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.58501 | + | 5.52548i | −0.303421 | + | 0.254601i | ||||
\(472\) | −5.28898 | + | 29.9953i | −0.243445 | + | 1.38065i | ||||
\(473\) | −8.18489 | + | 2.97906i | −0.376342 | + | 0.136977i | ||||
\(474\) | −1.93688 | −0.0889640 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 11.9720 | 0.548738 | ||||||||
\(477\) | 34.9033 | − | 12.7038i | 1.59811 | − | 0.581666i | ||||
\(478\) | 3.79489 | − | 21.5219i | 0.173574 | − | 0.984388i | ||||
\(479\) | 2.64084 | − | 2.21593i | 0.120663 | − | 0.101249i | −0.580459 | − | 0.814289i | \(-0.697127\pi\) |
0.701123 | + | 0.713041i | \(0.252683\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.459357 | + | 2.60515i | 0.0209449 | + | 0.118784i | ||||
\(482\) | −14.8883 | − | 25.7873i | −0.678143 | − | 1.17458i | ||||
\(483\) | −2.73135 | + | 4.73084i | −0.124281 | + | 0.215261i | ||||
\(484\) | −8.74490 | − | 3.18288i | −0.397495 | − | 0.144677i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 6.59359 | − | 11.4204i | 0.299091 | − | 0.518042i | ||||
\(487\) | 13.4986 | + | 23.3802i | 0.611680 | + | 1.05946i | 0.990957 | + | 0.134177i | \(0.0428391\pi\) |
−0.379278 | + | 0.925283i | \(0.623828\pi\) | |||||||
\(488\) | −4.79014 | − | 27.1662i | −0.216839 | − | 1.22976i | ||||
\(489\) | −6.52436 | − | 5.47459i | −0.295042 | − | 0.247570i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.0423665 | − | 0.240272i | 0.00191197 | − | 0.0108433i | −0.983837 | − | 0.179067i | \(-0.942692\pi\) |
0.985749 | + | 0.168224i | \(0.0538032\pi\) | |||||||
\(492\) | −2.39758 | + | 0.872646i | −0.108091 | + | 0.0393419i | ||||
\(493\) | 19.2334 | 0.866231 | ||||||||
\(494\) | 1.49039 | + | 2.35710i | 0.0670558 | + | 0.106051i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.97458 | + | 3.26648i | −0.402971 | + | 0.146669i | ||||
\(497\) | −0.322498 | + | 1.82898i | −0.0144660 | + | 0.0820409i | ||||
\(498\) | −2.12135 | + | 1.78002i | −0.0950600 | + | 0.0797648i | ||||
\(499\) | −2.48864 | − | 2.08821i | −0.111407 | − | 0.0934813i | 0.585383 | − | 0.810757i | \(-0.300944\pi\) |
−0.696789 | + | 0.717276i | \(0.745389\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.01327 | − | 3.48708i | −0.0899462 | − | 0.155791i | ||||
\(502\) | −12.9949 | + | 22.5078i | −0.579991 | + | 1.00457i | ||||
\(503\) | 6.69573 | + | 2.43705i | 0.298548 | + | 0.108663i | 0.486951 | − | 0.873429i | \(-0.338109\pi\) |
−0.188403 | + | 0.982092i | \(0.560331\pi\) | |||||||
\(504\) | −21.2775 | − | 7.74437i | −0.947774 | − | 0.344962i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.63600 | + | 2.83363i | 0.0727289 | + | 0.125970i | ||||
\(507\) | 1.16528 | + | 6.60865i | 0.0517520 | + | 0.293500i | ||||
\(508\) | 6.35323 | + | 5.33099i | 0.281879 | + | 0.236524i | ||||
\(509\) | 1.32543 | − | 1.11216i | 0.0587485 | − | 0.0492958i | −0.612941 | − | 0.790129i | \(-0.710014\pi\) |
0.671689 | + | 0.740833i | \(0.265569\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.0600 | − | 6.57332i | 0.798929 | − | 0.290787i | ||||
\(512\) | −14.7780 | −0.653100 | ||||||||
\(513\) | −6.15580 | + | 11.7276i | −0.271785 | + | 0.517786i | ||||
\(514\) | 5.70021 | 0.251426 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.871496 | − | 4.94250i | 0.0383655 | − | 0.217581i | ||||
\(517\) | −2.16927 | + | 1.82023i | −0.0954042 | + | 0.0800537i | ||||
\(518\) | −9.52203 | − | 7.98993i | −0.418374 | − | 0.351058i | ||||
\(519\) | −0.817842 | − | 4.63821i | −0.0358993 | − | 0.203595i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.40164 | + | 11.0880i | −0.280461 | + | 0.485773i | −0.971498 | − | 0.237046i | \(-0.923821\pi\) |
0.691037 | + | 0.722819i | \(0.257154\pi\) | |||||||
\(522\) | −10.6324 | − | 3.86989i | −0.465369 | − | 0.169380i | ||||
\(523\) | 8.19075 | + | 2.98119i | 0.358157 | + | 0.130358i | 0.514830 | − | 0.857292i | \(-0.327855\pi\) |
−0.156674 | + | 0.987650i | \(0.550077\pi\) | |||||||
\(524\) | −1.68808 | + | 2.92384i | −0.0737441 | + | 0.127729i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.55023 | + | 20.1343i | 0.154797 | + | 0.877898i | ||||
\(527\) | 25.6736 | + | 21.5427i | 1.11836 | + | 0.938416i | ||||
\(528\) | 0.467494 | − | 0.392274i | 0.0203451 | − | 0.0170715i | ||||
\(529\) | −1.55076 | + | 8.79481i | −0.0674244 | + | 0.382383i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.2225 | −1.18136 | ||||||||
\(532\) | 10.2753 | + | 3.27826i | 0.445489 | + | 0.142131i | ||||
\(533\) | −3.24773 | −0.140675 | ||||||||
\(534\) | −3.08022 | + | 1.12111i | −0.133294 | + | 0.0485151i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 25.4688 | − | 21.3708i | 1.10008 | − | 0.923080i | ||||
\(537\) | −2.22508 | − | 1.86706i | −0.0960193 | − | 0.0805697i | ||||
\(538\) | 3.38020 | + | 19.1701i | 0.145731 | + | 0.826480i | ||||
\(539\) | −0.212126 | − | 0.367414i | −0.00913693 | − | 0.0158256i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.3511 | − | 3.76748i | −0.445027 | − | 0.161977i | 0.109780 | − | 0.993956i | \(-0.464985\pi\) |
−0.554806 | + | 0.831979i | \(0.687208\pi\) | |||||||
\(542\) | −1.86231 | − | 0.677825i | −0.0799931 | − | 0.0291151i | ||||
\(543\) | 5.00002 | − | 8.66029i | 0.214571 | − | 0.371649i | ||||
\(544\) | 11.2178 | + | 19.4297i | 0.480958 | + | 0.833043i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.713767 | + | 0.598922i | 0.0305464 | + | 0.0256315i | ||||
\(547\) | 14.0921 | − | 11.8246i | 0.602533 | − | 0.505585i | −0.289726 | − | 0.957110i | \(-0.593564\pi\) |
0.892259 | + | 0.451525i | \(0.149120\pi\) | |||||||
\(548\) | 0.370562 | − | 2.10156i | 0.0158296 | − | 0.0897741i | ||||
\(549\) | 23.1680 | − | 8.43248i | 0.988788 | − | 0.359889i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.5075 | + | 5.26662i | 0.703244 | + | 0.224366i | ||||
\(552\) | −6.06118 | −0.257981 | ||||||||
\(553\) | −8.96012 | + | 3.26122i | −0.381023 | + | 0.138681i | ||||
\(554\) | 1.23294 | − | 6.99234i | 0.0523825 | − | 0.297076i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.68967 | − | 1.41780i | −0.0716581 | − | 0.0601283i | ||||
\(557\) | −0.0350939 | − | 0.199028i | −0.00148698 | − | 0.00843307i | 0.984055 | − | 0.177863i | \(-0.0569184\pi\) |
−0.985542 | + | 0.169430i | \(0.945807\pi\) | |||||||
\(558\) | −9.85809 | − | 17.0747i | −0.417326 | − | 0.722830i | ||||
\(559\) | 3.19418 | − | 5.53248i | 0.135099 | − | 0.233999i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.01239 | − | 0.732451i | −0.0849633 | − | 0.0309241i | ||||
\(562\) | 6.43424 | − | 11.1444i | 0.271412 | − | 0.470100i | ||||
\(563\) | −3.38187 | − | 5.85758i | −0.142529 | − | 0.246867i | 0.785919 | − | 0.618329i | \(-0.212190\pi\) |
−0.928448 | + | 0.371462i | \(0.878857\pi\) | |||||||
\(564\) | −0.283333 | − | 1.60686i | −0.0119305 | − | 0.0676611i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −20.5938 | + | 17.2803i | −0.865623 | + | 0.726344i | ||||
\(567\) | 3.11103 | − | 17.6435i | 0.130651 | − | 0.740958i | ||||
\(568\) | −1.93639 | + | 0.704789i | −0.0812492 | + | 0.0295723i | ||||
\(569\) | 7.15701 | 0.300038 | 0.150019 | − | 0.988683i | \(-0.452067\pi\) | ||||
0.150019 | + | 0.988683i | \(0.452067\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.3153 | −0.766471 | −0.383236 | − | 0.923651i | \(-0.625190\pi\) | ||||
−0.383236 | + | 0.923651i | \(0.625190\pi\) | |||||||
\(572\) | −0.431647 | + | 0.157107i | −0.0180481 | + | 0.00656896i | ||||
\(573\) | 1.59291 | − | 9.03382i | 0.0665446 | − | 0.377393i | ||||
\(574\) | 11.6904 | − | 9.80941i | 0.487948 | − | 0.409437i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.59320 | − | 20.3781i | −0.149717 | − | 0.849086i | ||||
\(577\) | −10.7897 | − | 18.6883i | −0.449182 | − | 0.778006i | 0.549151 | − | 0.835723i | \(-0.314951\pi\) |
−0.998333 | + | 0.0577173i | \(0.981618\pi\) | |||||||
\(578\) | −3.35704 | + | 5.81457i | −0.139635 | + | 0.241854i | ||||
\(579\) | −3.73265 | − | 1.35857i | −0.155124 | − | 0.0564603i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.81636 | + | 11.8063i | −0.282790 | + | 0.489807i | ||||
\(582\) | 3.46199 | + | 5.99634i | 0.143504 | + | 0.248556i | ||||
\(583\) | 1.97666 | + | 11.2102i | 0.0818648 | + | 0.464278i | ||||
\(584\) | 16.3357 | + | 13.7073i | 0.675975 | + | 0.567210i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.11301 | − | 28.9973i | 0.211216 | − | 1.19787i | ||||
\(587\) | 27.1976 | − | 9.89913i | 1.12257 | − | 0.408581i | 0.286978 | − | 0.957937i | \(-0.407349\pi\) |
0.835588 | + | 0.549356i | \(0.185127\pi\) | |||||||
\(588\) | 0.244452 | 0.0100810 | ||||||||
\(589\) | 16.1360 | + | 25.5196i | 0.664872 | + | 1.05152i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.09671 | + | 2.21902i | −0.250785 | + | 0.0912783i | ||||
\(592\) | 1.03688 | − | 5.88043i | 0.0426154 | − | 0.241684i | ||||
\(593\) | −13.6533 | + | 11.4565i | −0.560674 | + | 0.470461i | −0.878536 | − | 0.477676i | \(-0.841479\pi\) |
0.317863 | + | 0.948137i | \(0.397035\pi\) | |||||||
\(594\) | 2.03050 | + | 1.70379i | 0.0833123 | + | 0.0699073i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.44194 | + | 11.1578i | 0.263872 | + | 0.457040i | ||||
\(597\) | −2.06147 | + | 3.57058i | −0.0843706 | + | 0.146134i | ||||
\(598\) | −2.25507 | − | 0.820779i | −0.0922167 | − | 0.0335642i | ||||
\(599\) | 8.03512 | + | 2.92455i | 0.328306 | + | 0.119494i | 0.500914 | − | 0.865497i | \(-0.332997\pi\) |
−0.172608 | + | 0.984991i | \(0.555219\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.09514 | + | 3.62889i | 0.0854627 | + | 0.148026i | 0.905588 | − | 0.424158i | \(-0.139430\pi\) |
−0.820126 | + | 0.572184i | \(0.806096\pi\) | |||||||
\(602\) | 5.21260 | + | 29.5621i | 0.212450 | + | 1.20486i | ||||
\(603\) | 22.7632 | + | 19.1006i | 0.926991 | + | 0.777838i | ||||
\(604\) | −1.62078 | + | 1.36000i | −0.0659487 | + | 0.0553375i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.27791 | + | 3.37688i | −0.376889 | + | 0.137177i | ||||
\(607\) | −7.59458 | −0.308254 | −0.154127 | − | 0.988051i | \(-0.549257\pi\) | ||||
−0.154127 | + | 0.988051i | \(0.549257\pi\) | |||||||
\(608\) | 4.30752 | + | 19.7477i | 0.174693 | + | 0.800876i | ||||
\(609\) | 5.78925 | 0.234592 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.360654 | − | 2.04537i | 0.0145905 | − | 0.0827469i | ||||
\(612\) | −9.09491 | + | 7.63153i | −0.367640 | + | 0.308486i | ||||
\(613\) | −13.7466 | − | 11.5348i | −0.555220 | − | 0.465885i | 0.321484 | − | 0.946915i | \(-0.395818\pi\) |
−0.876704 | + | 0.481030i | \(0.840263\pi\) | |||||||
\(614\) | 0.468661 | + | 2.65791i | 0.0189136 | + | 0.107264i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.46964 | − | 6.00960i | 0.139796 | − | 0.242134i | ||||
\(617\) | 38.1365 | + | 13.8805i | 1.53532 | + | 0.558809i | 0.964916 | − | 0.262558i | \(-0.0845662\pi\) |
0.570400 | + | 0.821367i | \(0.306788\pi\) | |||||||
\(618\) | 2.72967 | + | 0.993517i | 0.109803 | + | 0.0399651i | ||||
\(619\) | 12.7804 | − | 22.1363i | 0.513688 | − | 0.889733i | −0.486186 | − | 0.873855i | \(-0.661612\pi\) |
0.999874 | − | 0.0158781i | \(-0.00505438\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.97918 | − | 11.2245i | −0.0794218 | − | 0.450423i | ||||
\(622\) | 11.7439 | + | 9.85430i | 0.470887 | + | 0.395121i | ||||
\(623\) | −12.3616 | + | 10.3726i | −0.495257 | + | 0.415570i | ||||
\(624\) | −0.0777239 | + | 0.440794i | −0.00311145 | + | 0.0176459i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.56491 | −0.0625463 | ||||||||
\(627\) | −1.52662 | − | 1.17969i | −0.0609672 | − | 0.0471122i | ||||
\(628\) | −14.6049 | −0.582801 | ||||||||
\(629\) | −19.6901 | + | 7.16661i | −0.785096 | + | 0.285751i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.55051 | − | 2.97923i | 0.141344 | − | 0.118601i | −0.569375 | − | 0.822078i | \(-0.692815\pi\) |
0.710718 | + | 0.703477i | \(0.248370\pi\) | |||||||
\(632\) | −8.10461 | − | 6.80057i | −0.322384 | − | 0.270512i | ||||
\(633\) | −0.928128 | − | 5.26367i | −0.0368898 | − | 0.209212i | ||||
\(634\) | 2.95490 | + | 5.11804i | 0.117354 | + | 0.203263i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.16333 | − | 2.24327i | −0.244392 | − | 0.0889514i | ||||
\(637\) | 0.292397 | + | 0.106424i | 0.0115852 | + | 0.00421666i | ||||
\(638\) | 1.73379 | − | 3.00302i | 0.0686415 | − | 0.118891i | ||||
\(639\) | −0.920880 | − | 1.59501i | −0.0364295 | − | 0.0630977i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.7783 | + | 14.9178i | 0.702201 | + | 0.589217i | 0.922399 | − | 0.386239i | \(-0.126226\pi\) |
−0.220198 | + | 0.975455i | \(0.570670\pi\) | |||||||
\(642\) | −6.47602 | + | 5.43402i | −0.255588 | + | 0.214464i | ||||
\(643\) | −2.64733 | + | 15.0138i | −0.104401 | + | 0.592086i | 0.887057 | + | 0.461659i | \(0.152746\pi\) |
−0.991458 | + | 0.130426i | \(0.958365\pi\) | |||||||
\(644\) | −8.72149 | + | 3.17436i | −0.343675 | + | 0.125087i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.3370 | + | 14.8682i | −0.642773 | + | 0.584982i | ||||
\(647\) | −17.6749 | −0.694872 | −0.347436 | − | 0.937704i | \(-0.612948\pi\) | ||||
−0.347436 | + | 0.937704i | \(0.612948\pi\) | |||||||
\(648\) | 18.6797 | − | 6.79885i | 0.733808 | − | 0.267084i | ||||
\(649\) | 1.44870 | − | 8.21599i | 0.0568664 | − | 0.322506i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.72773 | + | 6.48434i | 0.302874 | + | 0.254141i | ||||
\(652\) | −2.51277 | − | 14.2506i | −0.0984075 | − | 0.558097i | ||||
\(653\) | −3.43228 | − | 5.94488i | −0.134315 | − | 0.232641i | 0.791020 | − | 0.611790i | \(-0.209550\pi\) |
−0.925336 | + | 0.379149i | \(0.876217\pi\) | |||||||
\(654\) | 1.09174 | − | 1.89095i | 0.0426905 | − | 0.0739420i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.88879 | + | 2.50731i | 0.268962 | + | 0.0978941i | ||||
\(657\) | −9.52969 | + | 16.5059i | −0.371789 | + | 0.643957i | ||||
\(658\) | 4.87962 | + | 8.45175i | 0.190227 | + | 0.329484i | ||||
\(659\) | 4.75738 | + | 26.9804i | 0.185321 | + | 1.05101i | 0.925542 | + | 0.378645i | \(0.123610\pi\) |
−0.740221 | + | 0.672364i | \(0.765279\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.8707 | − | 18.3517i | 0.850673 | − | 0.713800i | −0.109265 | − | 0.994013i | \(-0.534850\pi\) |
0.959938 | + | 0.280213i | \(0.0904051\pi\) | |||||||
\(662\) | 5.80051 | − | 32.8963i | 0.225443 | − | 1.27855i | ||||
\(663\) | 1.47596 | − | 0.537206i | 0.0573216 | − | 0.0208633i | ||||
\(664\) | −15.1263 | −0.587014 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.3268 | 0.477655 | ||||||||
\(667\) | −14.0113 | + | 5.09971i | −0.542521 | + | 0.197462i | ||||
\(668\) | 1.18795 | − | 6.73722i | 0.0459633 | − | 0.260671i | ||||
\(669\) | 11.5301 | − | 9.67489i | 0.445779 | − | 0.374053i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.31206 | + | 7.44107i | 0.0506516 | + | 0.287259i | ||||
\(672\) | 3.37654 | + | 5.84833i | 0.130253 | + | 0.225604i | ||||
\(673\) | 22.5844 | − | 39.1173i | 0.870565 | − | 1.50786i | 0.00915115 | − | 0.999958i | \(-0.497087\pi\) |
0.861414 | − | 0.507904i | \(-0.169580\pi\) | |||||||
\(674\) | 15.0960 | + | 5.49451i | 0.581478 | + | 0.211641i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.70071 | + | 9.87392i | −0.219258 | + | 0.379766i | ||||
\(677\) | −23.4814 | − | 40.6710i | −0.902463 | − | 1.56311i | −0.824287 | − | 0.566172i | \(-0.808424\pi\) |
−0.0781759 | − | 0.996940i | \(-0.524910\pi\) | |||||||
\(678\) | 0.384073 | + | 2.17819i | 0.0147502 | + | 0.0836527i | ||||
\(679\) | 26.1116 | + | 21.9102i | 1.00207 | + | 0.840838i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.46537 | + | 8.31051i | −0.0561530 | + | 0.318459i | ||||
\(682\) | 5.67792 | − | 2.06659i | 0.217419 | − | 0.0791339i | ||||
\(683\) | −19.4215 | −0.743142 | −0.371571 | − | 0.928405i | \(-0.621181\pi\) | ||||
−0.371571 | + | 0.928405i | \(0.621181\pi\) | |||||||
\(684\) | −9.89561 | + | 4.05951i | −0.378368 | + | 0.155219i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17.5060 | − | 6.37166i | 0.668382 | − | 0.243271i | ||||
\(687\) | −1.05081 | + | 5.95943i | −0.0400909 | + | 0.227367i | ||||
\(688\) | −11.0464 | + | 9.26901i | −0.421139 | + | 0.353378i | ||||
\(689\) | −6.39554 | − | 5.36650i | −0.243651 | − | 0.204447i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.93344 | + | 15.4732i | 0.339844 | + | 0.588627i | 0.984403 | − | 0.175927i | \(-0.0562923\pi\) |
−0.644559 | + | 0.764555i | \(0.722959\pi\) | |||||||
\(692\) | 4.00099 | − | 6.92991i | 0.152095 | − | 0.263436i | ||||
\(693\) | 5.82809 | + | 2.12125i | 0.221391 | + | 0.0805797i | ||||
\(694\) | −0.0813941 | − | 0.0296250i | −0.00308968 | − | 0.00112455i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.21175 | + | 5.56292i | 0.121741 | + | 0.210862i | ||||
\(697\) | −4.46716 | − | 25.3346i | −0.169206 | − | 0.959615i | ||||
\(698\) | −3.72561 | − | 3.12615i | −0.141016 | − | 0.118327i | ||||
\(699\) | −6.45860 | + | 5.41941i | −0.244287 | + | 0.204981i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.04522 | + | 1.47234i | −0.152786 | + | 0.0556096i | −0.417281 | − | 0.908777i | \(-0.637017\pi\) |
0.264495 | + | 0.964387i | \(0.414795\pi\) | |||||||
\(702\) | −1.94406 | −0.0733739 | ||||||||
\(703\) | −18.8619 | + | 0.759235i | −0.711389 | + | 0.0286351i | ||||
\(704\) | 6.34150 | 0.239004 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.726431 | + | 4.11979i | −0.0273396 | + | 0.155050i | ||||
\(707\) | −37.2343 | + | 31.2432i | −1.40034 | + | 1.17502i | ||||
\(708\) | 3.68240 | + | 3.08990i | 0.138393 | + | 0.116125i | ||||
\(709\) | 6.10059 | + | 34.5982i | 0.229112 | + | 1.29936i | 0.854665 | + | 0.519179i | \(0.173762\pi\) |
−0.625553 | + | 0.780182i | \(0.715127\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.72796 | − | 8.18907i | 0.177312 | − | 0.307114i | ||||
\(712\) | −16.8251 | − | 6.12382i | −0.630545 | − | 0.229500i | ||||
\(713\) | −24.4150 | − | 8.88632i | −0.914347 | − | 0.332795i | ||||
\(714\) | −3.69024 | + | 6.39168i | −0.138104 | + | 0.239203i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.856958 | − | 4.86005i | −0.0320260 | − | 0.181629i | ||||
\(717\) | −8.49442 | − | 7.12767i | −0.317230 | − | 0.266188i | ||||
\(718\) | 24.2471 | − | 20.3457i | 0.904893 | − | 0.759295i | ||||
\(719\) | 5.10577 | − | 28.9563i | 0.190413 | − | 1.07989i | −0.728388 | − | 0.685165i | \(-0.759730\pi\) |
0.918801 | − | 0.394722i | \(-0.129159\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.3004 | 0.532574 | ||||||||
\(722\) | −18.0929 | + | 8.28745i | −0.673349 | + | 0.308427i | ||||
\(723\) | −15.1087 | −0.561898 | ||||||||
\(724\) | 15.9656 | − | 5.81100i | 0.593357 | − | 0.215964i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.39480 | − | 3.68767i | 0.163106 | − | 0.136862i | ||||
\(727\) | −17.2796 | − | 14.4993i | −0.640864 | − | 0.537749i | 0.263419 | − | 0.964681i | \(-0.415150\pi\) |
−0.904283 | + | 0.426933i | \(0.859594\pi\) | |||||||
\(728\) | 0.883786 | + | 5.01220i | 0.0327553 | + | 0.185765i | ||||
\(729\) | 6.46109 | + | 11.1909i | 0.239300 | + | 0.414479i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 47.5506 | + | 17.3070i | 1.75872 | + | 0.640123i | ||||
\(732\) | −4.09108 | − | 1.48903i | −0.151211 | − | 0.0550362i | ||||
\(733\) | 18.9501 | − | 32.8225i | 0.699938 | − | 1.21233i | −0.268550 | − | 0.963266i | \(-0.586544\pi\) |
0.968488 | − | 0.249062i | \(-0.0801223\pi\) | |||||||
\(734\) | 9.49990 | + | 16.4543i | 0.350648 | + | 0.607340i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.3238 | − | 11.1800i | −0.491121 | − | 0.412099i | ||||
\(737\) | −6.97613 | + | 5.85367i | −0.256969 | + | 0.215623i | ||||
\(738\) | −2.62798 | + | 14.9040i | −0.0967372 | + | 0.548624i | ||||
\(739\) | 24.4523 | − | 8.89989i | 0.899491 | − | 0.327388i | 0.149442 | − | 0.988770i | \(-0.452252\pi\) |
0.750049 | + | 0.661383i | \(0.230030\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.41388 | − | 0.0569119i | 0.0519401 | − | 0.00209071i | ||||
\(742\) | 39.2300 | 1.44018 | ||||||||
\(743\) | 47.3487 | − | 17.2335i | 1.73706 | − | 0.632237i | 0.737964 | − | 0.674841i | \(-0.235788\pi\) |
0.999092 | + | 0.0426041i | \(0.0135654\pi\) | |||||||
\(744\) | −1.94365 | + | 11.0230i | −0.0712577 | + | 0.404123i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 20.2315 | + | 16.9762i | 0.740728 | + | 0.621544i | ||||
\(747\) | −2.34763 | − | 13.3140i | −0.0858951 | − | 0.487135i | ||||
\(748\) | −1.81926 | − | 3.15105i | −0.0665187 | − | 0.115214i | ||||
\(749\) | −20.8089 | + | 36.0420i | −0.760339 | + | 1.31695i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.5462 | − | 9.29806i | −0.932195 | − | 0.339291i | −0.169116 | − | 0.985596i | \(-0.554091\pi\) |
−0.763079 | + | 0.646305i | \(0.776313\pi\) | |||||||
\(752\) | −2.34405 | + | 4.06002i | −0.0854789 | + | 0.148054i | ||||
\(753\) | 6.59363 | + | 11.4205i | 0.240285 | + | 0.416186i | ||||
\(754\) | 0.441631 | + | 2.50461i | 0.0160832 | + | 0.0912126i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.75963 | + | 4.83291i | −0.209476 | + | 0.175771i | ||||
\(757\) | −5.71273 | + | 32.3985i | −0.207633 | + | 1.17754i | 0.685610 | + | 0.727969i | \(0.259536\pi\) |
−0.893243 | + | 0.449575i | \(0.851576\pi\) | |||||||
\(758\) | 27.1289 | − | 9.87411i | 0.985366 | − | 0.358644i | ||||
\(759\) | 1.66021 | 0.0602619 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.47213 | 0.125865 | 0.0629323 | − | 0.998018i | \(-0.479955\pi\) | ||||
0.0629323 | + | 0.998018i | \(0.479955\pi\) | |||||||
\(762\) | −4.80443 | + | 1.74867i | −0.174046 | + | 0.0633476i | ||||
\(763\) | 1.86657 | − | 10.5858i | 0.0675743 | − | 0.383233i | ||||
\(764\) | 11.9391 | − | 10.0181i | 0.431941 | − | 0.362442i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.33270 | − | 18.9007i | −0.120415 | − | 0.682910i | ||||
\(767\) | 3.05943 | + | 5.29909i | 0.110470 | + | 0.191339i | ||||
\(768\) | −4.40811 | + | 7.63507i | −0.159064 | + | 0.275507i | ||||
\(769\) | 29.7634 | + | 10.8330i | 1.07330 | + | 0.390648i | 0.817408 | − | 0.576059i | \(-0.195410\pi\) |
0.255887 | + | 0.966707i | \(0.417632\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.44615 | − | 2.50480i | 0.0520817 | − | 0.0902081i | ||||
\(772\) | −3.37442 | − | 5.84466i | −0.121448 | − | 0.210354i | ||||
\(773\) | 6.08960 | + | 34.5358i | 0.219028 | + | 1.24217i | 0.873779 | + | 0.486323i | \(0.161662\pi\) |
−0.654752 | + | 0.755844i | \(0.727227\pi\) | |||||||
\(774\) | −22.8042 | − | 19.1350i | −0.819679 | − | 0.687792i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.56750 | + | 37.2461i | −0.235759 | + | 1.33706i | ||||
\(777\) | −5.92670 | + | 2.15714i | −0.212619 | + | 0.0773870i | ||||
\(778\) | −7.52562 | −0.269807 | ||||||||
\(779\) | 3.10322 | − | 22.9672i | 0.111184 | − | 0.822884i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.530395 | − | 0.193048i | 0.0189790 | − | 0.00690780i | ||||
\(782\) | 3.30085 | − | 18.7201i | 0.118038 | − | 0.669428i | ||||
\(783\) | −9.25302 | + | 7.76421i | −0.330676 | + | 0.277470i | ||||
\(784\) | −0.538043 | − | 0.451472i | −0.0192158 | − | 0.0161240i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.04066 | − | 1.80248i | −0.0371191 | − | 0.0642922i | ||||
\(787\) | 21.0914 | − | 36.5314i | 0.751829 | − | 1.30221i | −0.195107 | − | 0.980782i | \(-0.562505\pi\) |
0.946936 | − | 0.321424i | \(-0.104161\pi\) | |||||||
\(788\) | −10.3584 | − | 3.77015i | −0.369003 | − | 0.134306i | ||||
\(789\) | 9.74816 | + | 3.54804i | 0.347044 | + | 0.126314i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.44425 | + | 9.42971i | 0.193575 | + | 0.335282i | ||||
\(792\) | 1.19498 | + | 6.77708i | 0.0424618 | + | 0.240813i | ||||
\(793\) | −4.24522 | − | 3.56216i | −0.150752 | − | 0.126496i | ||||
\(794\) | 9.40703 | − | 7.89343i | 0.333843 | − | 0.280127i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.58251 | + | 2.39584i | −0.233311 | + | 0.0849182i | ||||
\(797\) | 20.4194 | 0.723291 | 0.361646 | − | 0.932316i | \(-0.382215\pi\) | ||||
0.361646 | + | 0.932316i | \(0.382215\pi\) | |||||||
\(798\) | −4.91743 | + | 4.47531i | −0.174075 | + | 0.158424i | ||||
\(799\) | 16.4514 | 0.582008 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.77886 | − | 15.7597i | 0.0981862 | − | 0.556842i | ||||
\(802\) | 31.4623 | − | 26.4000i | 1.11097 | − | 0.932216i | ||||
\(803\) | −4.47449 | − | 3.75454i | −0.157901 | − | 0.132495i | ||||
\(804\) | −0.911169 | − | 5.16750i | −0.0321345 | − | 0.182244i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.21582 | + | 3.83792i | −0.0780491 | + | 0.135185i | ||||
\(807\) | 9.28131 | + | 3.37812i | 0.326717 | + | 0.118915i | ||||
\(808\) | −50.6786 | − | 18.4455i | −1.78287 | − | 0.648910i | ||||
\(809\) | −14.2768 | + | 24.7282i | −0.501946 | + | 0.869396i | 0.498051 | + | 0.867148i | \(0.334049\pi\) |
−0.999997 | + | 0.00224865i | \(0.999284\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.279849 | − | 1.58710i | −0.00982681 | − | 0.0557306i | 0.979500 | − | 0.201444i | \(-0.0645634\pi\) |
−0.989327 | + | 0.145713i | \(0.953452\pi\) | |||||||
\(812\) | 7.53483 | + | 6.32248i | 0.264421 | + | 0.221875i | ||||
\(813\) | −0.770321 | + | 0.646376i | −0.0270163 | + | 0.0226694i | ||||
\(814\) | −0.655998 | + | 3.72035i | −0.0229927 | + | 0.130398i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.54540 | −0.124114 | ||||||||
\(817\) | 36.0723 | + | 27.8747i | 1.26201 | + | 0.975213i | ||||
\(818\) | 9.29706 | 0.325064 | ||||||||
\(819\) | −4.27453 | + | 1.55580i | −0.149364 | + | 0.0543642i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.16578 | + | 5.17371i | −0.215187 | + | 0.180564i | −0.744010 | − | 0.668169i | \(-0.767078\pi\) |
0.528822 | + | 0.848733i | \(0.322634\pi\) | |||||||
\(822\) | 1.00777 | + | 0.845617i | 0.0351499 | + | 0.0294943i | ||||
\(823\) | 6.48442 | + | 36.7750i | 0.226033 | + | 1.28189i | 0.860701 | + | 0.509110i | \(0.170025\pi\) |
−0.634669 | + | 0.772784i | \(0.718863\pi\) | |||||||
\(824\) | 7.93356 | + | 13.7413i | 0.276379 | + | 0.478702i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27.0179 | − | 9.83370i | −0.940072 | − | 0.342158i | ||||
\(827\) | −10.2711 | − | 3.73836i | −0.357160 | − | 0.129996i | 0.157207 | − | 0.987566i | \(-0.449751\pi\) |
−0.514367 | + | 0.857570i | \(0.671973\pi\) | |||||||
\(828\) | 4.60205 | − | 7.97098i | 0.159932 | − | 0.277011i | ||||
\(829\) | −16.8187 | − | 29.1309i | −0.584139 | − | 1.01176i | −0.994982 | − | 0.100052i | \(-0.968099\pi\) |
0.410843 | − | 0.911706i | \(-0.365234\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.75979 | − | 2.31574i | −0.0957361 | − | 0.0803322i | ||||
\(832\) | −3.56293 | + | 2.98966i | −0.123523 | + | 0.103648i | ||||
\(833\) | −0.427995 | + | 2.42728i | −0.0148291 | + | 0.0841002i | ||||
\(834\) | 1.27776 | − | 0.465068i | 0.0442454 | − | 0.0161040i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.698579 | − | 3.20262i | −0.0241609 | − | 0.110765i | ||||
\(837\) | −21.0478 | −0.727517 | ||||||||
\(838\) | 7.67897 | − | 2.79492i | 0.265266 | − | 0.0965488i | ||||
\(839\) | 2.40910 | − | 13.6627i | 0.0831714 | − | 0.471689i | −0.914565 | − | 0.404439i | \(-0.867467\pi\) |
0.997736 | − | 0.0672492i | \(-0.0214222\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.1104 | − | 8.48360i | −0.348633 | − | 0.292538i | ||||
\(842\) | 6.28522 | + | 35.6452i | 0.216603 | + | 1.22842i | ||||
\(843\) | −3.26474 | − | 5.65470i | −0.112444 | − | 0.194758i | ||||
\(844\) | 4.54052 | − | 7.86440i | 0.156291 | − | 0.270704i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.09448 | − | 3.31012i | −0.312675 | − | 0.113804i | ||||
\(847\) | 14.1214 | − | 24.4591i | 0.485219 | − | 0.840423i | ||||
\(848\) | 9.42259 | + | 16.3204i | 0.323573 | + | 0.560445i | ||||
\(849\) | 2.36867 | + | 13.4334i | 0.0812925 | + | 0.461033i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.4438 | − | 10.4416i | 0.426568 | − | 0.357933i | ||||
\(852\) | −0.0564745 | + | 0.320283i | −0.00193478 | + | 0.0109727i | ||||
\(853\) | −27.7657 | + | 10.1059i | −0.950680 | + | 0.346019i | −0.770375 | − | 0.637591i | \(-0.779931\pi\) |
−0.180305 | + | 0.983611i | \(0.557709\pi\) | |||||||
\(854\) | 26.0400 | 0.891071 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −46.1773 | −1.57831 | ||||||||
\(857\) | 4.02741 | − | 1.46586i | 0.137574 | − | 0.0500727i | −0.272316 | − | 0.962208i | \(-0.587790\pi\) |
0.409889 | + | 0.912135i | \(0.365567\pi\) | |||||||
\(858\) | 0.0491733 | − | 0.278876i | 0.00167875 | − | 0.00952066i | ||||
\(859\) | −26.7935 | + | 22.4824i | −0.914181 | + | 0.767089i | −0.972910 | − | 0.231185i | \(-0.925740\pi\) |
0.0587290 | + | 0.998274i | \(0.481295\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.34461 | − | 7.62567i | −0.0458243 | − | 0.259882i | ||||
\(862\) | −1.48706 | − | 2.57566i | −0.0506494 | − | 0.0877273i | ||||
\(863\) | 10.0153 | − | 17.3470i | 0.340924 | − | 0.590498i | −0.643681 | − | 0.765294i | \(-0.722593\pi\) |
0.984605 | + | 0.174797i | \(0.0559268\pi\) | |||||||
\(864\) | −13.2402 | − | 4.81904i | −0.450441 | − | 0.163947i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11.4443 | + | 19.8221i | −0.388893 | + | 0.673583i | ||||
\(867\) | 1.70337 | + | 2.95032i | 0.0578494 | + | 0.100198i | ||||
\(868\) | 2.97623 | + | 16.8790i | 0.101020 | + | 0.572911i | ||||
\(869\) | 2.21992 | + | 1.86274i | 0.0753058 | + | 0.0631891i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.15983 | − | 6.57770i | 0.0392992 | − | 0.222877i | ||||
\(872\) | 11.2075 | − | 4.07921i | 0.379535 | − | 0.138139i | ||||
\(873\) | −33.8030 | −1.14406 | ||||||||
\(874\) | 7.95907 | − | 15.1630i | 0.269220 | − | 0.512898i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.16260 | − | 1.15109i | 0.106854 | − | 0.0388917i | ||||
\(877\) | −7.91697 | + | 44.8994i | −0.267337 | + | 1.51614i | 0.494959 | + | 0.868916i | \(0.335183\pi\) |
−0.762297 | + | 0.647228i | \(0.775928\pi\) | |||||||
\(878\) | 26.1376 | − | 21.9320i | 0.882100 | − | 0.740170i | ||||
\(879\) | −11.4449 | − | 9.60340i | −0.386027 | − | 0.323915i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.63649 | + | 14.9588i | 0.290971 | + | 0.503976i | 0.974040 | − | 0.226378i | \(-0.0726885\pi\) |
−0.683069 | + | 0.730354i | \(0.739355\pi\) | |||||||
\(882\) | 0.724983 | − | 1.25571i | 0.0244114 | − | 0.0422819i | ||||
\(883\) | −33.0707 | − | 12.0368i | −1.11292 | − | 0.405069i | −0.280856 | − | 0.959750i | \(-0.590618\pi\) |
−0.832063 | + | 0.554680i | \(0.812840\pi\) | |||||||
\(884\) | 2.50768 | + | 0.912722i | 0.0843425 | + | 0.0306982i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.06483 | + | 7.04049i | 0.136561 | + | 0.236530i | ||||
\(887\) | −0.548919 | − | 3.11307i | −0.0184309 | − | 0.104527i | 0.974205 | − | 0.225667i | \(-0.0724561\pi\) |
−0.992635 | + | 0.121140i | \(0.961345\pi\) | |||||||
\(888\) | −5.36082 | − | 4.49826i | −0.179897 | − | 0.150952i | ||||
\(889\) | −19.2812 | + | 16.1789i | −0.646671 | + | 0.542622i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.11654 | + | 1.86227i | −0.171410 | + | 0.0623883i | ||||
\(892\) | 25.5727 | 0.856237 | ||||||||
\(893\) | 14.1198 | + | 4.50482i | 0.472500 | + | 0.150748i | ||||
\(894\) | −7.94259 | −0.265640 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.617962 | + | 3.50464i | −0.0206447 | + | 0.117082i | ||||
\(897\) | −0.932781 | + | 0.782696i | −0.0311447 | + | 0.0261335i | ||||
\(898\) | 18.4399 | + | 15.4729i | 0.615346 | + | 0.516337i | ||||
\(899\) | 4.78140 | + | 27.1167i | 0.159469 | + | 0.904391i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.0655 | − | 57.2711i | 1.10157 | − | 1.90798i | ||||
\(902\) | −4.35830 | − | 1.58629i | −0.145116 | − | 0.0528178i | ||||
\(903\) | 14.3127 | + | 5.20939i | 0.476297 | + | 0.173358i | ||||
\(904\) | −6.04071 | + | 10.4628i | −0.200911 | + | 0.347988i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.226494 | − | 1.28451i | −0.00752476 | − | 0.0426751i | ||||
\(907\) | 12.2041 | + | 10.2405i | 0.405230 | + | 0.340029i | 0.822511 | − | 0.568749i | \(-0.192572\pi\) |
−0.417281 | + | 0.908778i | \(0.637017\pi\) | |||||||
\(908\) | −10.9832 | + | 9.21597i | −0.364489 | + | 0.305843i | ||||
\(909\) | 8.37018 | − | 47.4697i | 0.277621 | − | 1.57447i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.0577380 | 0.00191294 | 0.000956472 | − | 1.00000i | \(-0.499696\pi\) | ||||
0.000956472 | 1.00000i | \(0.499696\pi\) | ||||||||
\(912\) | −3.04292 | − | 0.970824i | −0.100761 | − | 0.0321472i | ||||
\(913\) | 4.14323 | 0.137121 | ||||||||
\(914\) | 3.33524 | − | 1.21393i | 0.110320 | − | 0.0401532i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.87599 | + | 6.60874i | −0.260230 | + | 0.218359i | ||||
\(917\) | −7.84905 | − | 6.58614i | −0.259199 | − | 0.217493i | ||||
\(918\) | −2.67400 | − | 15.1650i | −0.0882553 | − | 0.500521i | ||||
\(919\) | −25.0245 | − | 43.3436i | −0.825481 | − | 1.42977i | −0.901551 | − | 0.432672i | \(-0.857571\pi\) |
0.0760708 | − | 0.997102i | \(-0.475762\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.28684 | + | 0.468372i | 0.0424029 | + | 0.0154334i | ||||
\(922\) | 10.6818 | + | 3.88787i | 0.351788 | + | 0.128040i | ||||
\(923\) | −0.206988 | + | 0.358514i | −0.00681310 | + | 0.0118006i | ||||
\(924\) | −0.547595 | − | 0.948463i | −0.0180146 | − | 0.0312021i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.86660 | − | 4.92267i | −0.192789 | − | 0.161769i | ||||
\(927\) | −10.8637 | + | 9.11573i | −0.356811 | + | 0.299400i | ||||
\(928\) | −3.20080 | + | 18.1526i | −0.105071 | + | 0.595889i | ||||
\(929\) | 15.9606 | − | 5.80920i | 0.523652 | − | 0.190594i | −0.0666498 | − | 0.997776i | \(-0.521231\pi\) |
0.590302 | + | 0.807183i | \(0.299009\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.03199 | + | 1.96607i | −0.0338220 | + | 0.0644353i | ||||
\(932\) | −14.3246 | −0.469218 | ||||||||
\(933\) | 7.30963 | − | 2.66049i | 0.239306 | − | 0.0871004i | ||||
\(934\) | 1.97190 | − | 11.1832i | 0.0645227 | − | 0.365926i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.86640 | − | 3.24430i | −0.126377 | − | 0.106043i | ||||
\(937\) | 5.85065 | + | 33.1807i | 0.191132 | + | 1.08397i | 0.917820 | + | 0.396997i | \(0.129948\pi\) |
−0.726687 | + | 0.686968i | \(0.758941\pi\) | |||||||
\(938\) | 15.6923 | + | 27.1799i | 0.512373 | + | 0.887456i | ||||
\(939\) | −0.397018 | + | 0.687655i | −0.0129562 | + | 0.0224408i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.5345 | + | 9.29380i | 0.832401 | + | 0.302969i | 0.722844 | − | 0.691011i | \(-0.242834\pi\) |
0.109557 | + | 0.993980i | \(0.465057\pi\) | |||||||
\(942\) | 4.50180 | − | 7.79734i | 0.146676 | − | 0.254051i | ||||
\(943\) | 9.97169 | + | 17.2715i | 0.324723 | + | 0.562436i | ||||
\(944\) | −2.39838 | − | 13.6019i | −0.0780605 | − | 0.442703i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.98867 | − | 5.86419i | 0.227221 | − | 0.190661i | ||||
\(947\) | 5.78183 | − | 32.7904i | 0.187884 | − | 1.06554i | −0.734309 | − | 0.678815i | \(-0.762494\pi\) |
0.922193 | − | 0.386729i | \(-0.126395\pi\) | |||||||
\(948\) | −1.56906 | + | 0.571090i | −0.0509606 | + | 0.0185481i | ||||
\(949\) | 4.28402 | 0.139065 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.99864 | 0.0972376 | ||||||||
\(952\) | −37.8830 | + | 13.7883i | −1.22780 | + | 0.446881i | ||||
\(953\) | 5.28039 | − | 29.9466i | 0.171049 | − | 0.970065i | −0.771558 | − | 0.636159i | \(-0.780522\pi\) |
0.942606 | − | 0.333906i | \(-0.108367\pi\) | |||||||
\(954\) | −29.8022 | + | 25.0070i | −0.964882 | + | 0.809632i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.27151 | − | 18.5536i | −0.105808 | − | 0.600068i | ||||
\(957\) | −0.879728 | − | 1.52373i | −0.0284376 | − | 0.0492553i | ||||
\(958\) | −1.80540 | + | 3.12704i | −0.0583297 | + | 0.101030i | ||||
\(959\) | 6.08578 | + | 2.21504i | 0.196520 | + | 0.0715274i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.49003 | + | 14.7052i | −0.273872 | + | 0.474360i | ||||
\(962\) | −1.38536 | − | 2.39952i | −0.0446660 | − | 0.0773637i | ||||
\(963\) | −7.16679 | − | 40.6449i | −0.230946 | − | 1.30976i | ||||
\(964\) | −19.6643 | − | 16.5003i | −0.633344 | − | 0.531438i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.993554 | − | 5.63472i | 0.0319671 | − | 0.181294i | ||||
\(967\) | −55.3648 | + | 20.1511i | −1.78041 | + | 0.648017i | −0.780677 | + | 0.624934i | \(0.785126\pi\) |
−0.999734 | + | 0.0230823i | \(0.992652\pi\) | |||||||
\(968\) | 31.3371 | 1.00721 | ||||||||
\(969\) | 2.38870 | + | 10.9509i | 0.0767361 | + | 0.351795i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.4033 | − | 13.9777i | 1.23242 | − | 0.448564i | 0.357995 | − | 0.933724i | \(-0.383461\pi\) |
0.874426 | + | 0.485159i | \(0.161238\pi\) | |||||||
\(972\) | 1.97411 | − | 11.1957i | 0.0633196 | − | 0.359103i | ||||
\(973\) | 5.12794 | − | 4.30285i | 0.164394 | − | 0.137943i | ||||
\(974\) | −21.6614 | − | 18.1761i | −0.694075 | − | 0.582398i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.25450 | + | 10.8331i | 0.200202 | + | 0.346760i | ||||
\(977\) | −17.9716 | + | 31.1276i | −0.574961 | + | 0.995862i | 0.421085 | + | 0.907021i | \(0.361649\pi\) |
−0.996046 | + | 0.0888405i | \(0.971684\pi\) | |||||||
\(978\) | 8.38270 | + | 3.05105i | 0.268049 | + | 0.0975619i | ||||
\(979\) | 4.60853 | + | 1.67737i | 0.147289 | + | 0.0536089i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.32991 | + | 9.23167i | 0.170171 | + | 0.294745i | ||||
\(982\) | 0.0443747 | + | 0.251662i | 0.00141606 | + | 0.00803085i | ||||
\(983\) | 7.71144 | + | 6.47067i | 0.245957 | + | 0.206382i | 0.757429 | − | 0.652918i | \(-0.226455\pi\) |
−0.511472 | + | 0.859300i | \(0.670900\pi\) | |||||||
\(984\) | 6.58159 | − | 5.52261i | 0.209813 | − | 0.176054i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −18.9303 | + | 6.89005i | −0.602862 | + | 0.219424i | ||||
\(987\) | 4.95185 | 0.157619 | ||||||||
\(988\) | 1.90235 | + | 1.47003i | 0.0605217 | + | 0.0467680i | ||||
\(989\) | −39.2290 | −1.24741 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.13089 | + | 17.7562i | −0.0994561 | + | 0.564043i | 0.893834 | + | 0.448397i | \(0.148005\pi\) |
−0.993290 | + | 0.115646i | \(0.963106\pi\) | |||||||
\(992\) | −24.6047 | + | 20.6458i | −0.781200 | + | 0.655504i | ||||
\(993\) | −12.9838 | − | 10.8947i | −0.412028 | − | 0.345732i | ||||
\(994\) | −0.337786 | − | 1.91568i | −0.0107139 | − | 0.0607616i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.19365 | + | 2.06746i | −0.0378223 | + | 0.0655101i | ||||
\(997\) | 17.5954 | + | 6.40419i | 0.557251 | + | 0.202823i | 0.605265 | − | 0.796024i | \(-0.293067\pi\) |
−0.0480143 | + | 0.998847i | \(0.515289\pi\) | |||||||
\(998\) | 3.19747 | + | 1.16378i | 0.101214 | + | 0.0368390i | ||||
\(999\) | 6.57968 | − | 11.3963i | 0.208172 | − | 0.360564i |
(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 | 475.2.l.f.176.3 | 48 | ||
5.2 | odd | 4 | 95.2.p.a.24.3 | yes | 48 | ||
5.3 | odd | 4 | 95.2.p.a.24.6 | yes | 48 | ||
5.4 | even | 2 | inner | 475.2.l.f.176.6 | 48 | ||
15.2 | even | 4 | 855.2.da.b.784.6 | 48 | |||
15.8 | even | 4 | 855.2.da.b.784.3 | 48 | |||
19.2 | odd | 18 | 9025.2.a.ct.1.9 | 24 | |||
19.4 | even | 9 | inner | 475.2.l.f.251.3 | 48 | ||
19.17 | even | 9 | 9025.2.a.cu.1.16 | 24 | |||
95.2 | even | 36 | 1805.2.b.l.1084.9 | 24 | |||
95.4 | even | 18 | inner | 475.2.l.f.251.6 | 48 | ||
95.17 | odd | 36 | 1805.2.b.k.1084.16 | 24 | |||
95.23 | odd | 36 | 95.2.p.a.4.3 | ✓ | 48 | ||
95.42 | odd | 36 | 95.2.p.a.4.6 | yes | 48 | ||
95.59 | odd | 18 | 9025.2.a.ct.1.16 | 24 | |||
95.74 | even | 18 | 9025.2.a.cu.1.9 | 24 | |||
95.78 | even | 36 | 1805.2.b.l.1084.16 | 24 | |||
95.93 | odd | 36 | 1805.2.b.k.1084.9 | 24 | |||
285.23 | even | 36 | 855.2.da.b.289.6 | 48 | |||
285.137 | even | 36 | 855.2.da.b.289.3 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.p.a.4.3 | ✓ | 48 | 95.23 | odd | 36 | ||
95.2.p.a.4.6 | yes | 48 | 95.42 | odd | 36 | ||
95.2.p.a.24.3 | yes | 48 | 5.2 | odd | 4 | ||
95.2.p.a.24.6 | yes | 48 | 5.3 | odd | 4 | ||
475.2.l.f.176.3 | 48 | 1.1 | even | 1 | trivial | ||
475.2.l.f.176.6 | 48 | 5.4 | even | 2 | inner | ||
475.2.l.f.251.3 | 48 | 19.4 | even | 9 | inner | ||
475.2.l.f.251.6 | 48 | 95.4 | even | 18 | inner | ||
855.2.da.b.289.3 | 48 | 285.137 | even | 36 | |||
855.2.da.b.289.6 | 48 | 285.23 | even | 36 | |||
855.2.da.b.784.3 | 48 | 15.8 | even | 4 | |||
855.2.da.b.784.6 | 48 | 15.2 | even | 4 | |||
1805.2.b.k.1084.9 | 24 | 95.93 | odd | 36 | |||
1805.2.b.k.1084.16 | 24 | 95.17 | odd | 36 | |||
1805.2.b.l.1084.9 | 24 | 95.2 | even | 36 | |||
1805.2.b.l.1084.16 | 24 | 95.78 | even | 36 | |||
9025.2.a.ct.1.9 | 24 | 19.2 | odd | 18 | |||
9025.2.a.ct.1.16 | 24 | 95.59 | odd | 18 | |||
9025.2.a.cu.1.9 | 24 | 95.74 | even | 18 | |||
9025.2.a.cu.1.16 | 24 | 19.17 | even | 9 |