Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(146,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.146");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.o (of order \(6\), degree \(2\), 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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 146.15 | ||
Character | \(\chi\) | \(=\) | 441.146 |
Dual form | 441.2.o.e.293.15 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.575298 | + | 0.332148i | 0.406797 | + | 0.234864i | 0.689413 | − | 0.724369i | \(-0.257869\pi\) |
−0.282616 | + | 0.959233i | \(0.591202\pi\) | |||||||
\(3\) | −1.69462 | − | 0.358137i | −0.978389 | − | 0.206771i | ||||
\(4\) | −0.779355 | − | 1.34988i | −0.389677 | − | 0.674941i | ||||
\(5\) | 0.0141520 | + | 0.0245119i | 0.00632895 | + | 0.0109621i | 0.869173 | − | 0.494509i | \(-0.164652\pi\) |
−0.862844 | + | 0.505471i | \(0.831319\pi\) | |||||||
\(6\) | −0.855956 | − | 0.768901i | −0.349443 | − | 0.313903i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 2.36404i | − | 0.835814i | ||||||
\(9\) | 2.74348 | + | 1.21381i | 0.914492 | + | 0.404605i | ||||
\(10\) | 0.0188022i | 0.00594578i | ||||||||
\(11\) | −0.885324 | − | 0.511142i | −0.266935 | − | 0.154115i | 0.360559 | − | 0.932736i | \(-0.382586\pi\) |
−0.627494 | + | 0.778621i | \(0.715919\pi\) | |||||||
\(12\) | 0.837267 | + | 2.56665i | 0.241698 | + | 0.740929i | ||||
\(13\) | −4.87844 | + | 2.81657i | −1.35304 | + | 0.781176i | −0.988674 | − | 0.150081i | \(-0.952047\pi\) |
−0.364363 | + | 0.931257i | \(0.618713\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0152036 | − | 0.0466067i | −0.00392554 | − | 0.0120338i | ||||
\(16\) | −0.773498 | + | 1.33974i | −0.193375 | + | 0.334935i | ||||
\(17\) | −5.67880 | −1.37731 | −0.688656 | − | 0.725089i | \(-0.741799\pi\) | ||||
−0.688656 | + | 0.725089i | \(0.741799\pi\) | |||||||
\(18\) | 1.17515 | + | 1.60955i | 0.276985 | + | 0.379373i | ||||
\(19\) | − | 2.09274i | − | 0.480108i | −0.970760 | − | 0.240054i | \(-0.922835\pi\) | ||
0.970760 | − | 0.240054i | \(-0.0771651\pi\) | |||||||
\(20\) | 0.0220588 | − | 0.0382070i | 0.00493250 | − | 0.00854334i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.339550 | − | 0.588118i | −0.0723923 | − | 0.125387i | ||||
\(23\) | −6.28849 | + | 3.63066i | −1.31124 | + | 0.757046i | −0.982302 | − | 0.187305i | \(-0.940025\pi\) |
−0.328940 | + | 0.944351i | \(0.606691\pi\) | |||||||
\(24\) | −0.846651 | + | 4.00615i | −0.172822 | + | 0.817752i | ||||
\(25\) | 2.49960 | − | 4.32943i | 0.499920 | − | 0.865887i | ||||
\(26\) | −3.74208 | −0.733882 | ||||||||
\(27\) | −4.21444 | − | 3.03949i | −0.811069 | − | 0.584951i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.52577 | − | 2.03560i | −0.654718 | − | 0.378002i | 0.135543 | − | 0.990771i | \(-0.456722\pi\) |
−0.790262 | + | 0.612770i | \(0.790055\pi\) | |||||||
\(30\) | 0.00673377 | − | 0.0318626i | 0.00122941 | − | 0.00581729i | ||||
\(31\) | 2.87364 | − | 1.65910i | 0.516122 | − | 0.297983i | −0.219225 | − | 0.975674i | \(-0.570353\pi\) |
0.735346 | + | 0.677691i | \(0.237019\pi\) | |||||||
\(32\) | −4.98462 | + | 2.87787i | −0.881165 | + | 0.508741i | ||||
\(33\) | 1.31723 | + | 1.18326i | 0.229300 | + | 0.205979i | ||||
\(34\) | −3.26700 | − | 1.88620i | −0.560286 | − | 0.323481i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.499635 | − | 4.64936i | −0.0832725 | − | 0.774893i | ||||
\(37\) | −2.47265 | −0.406501 | −0.203250 | − | 0.979127i | \(-0.565151\pi\) | ||||
−0.203250 | + | 0.979127i | \(0.565151\pi\) | |||||||
\(38\) | 0.695101 | − | 1.20395i | 0.112760 | − | 0.195306i | ||||
\(39\) | 9.27583 | − | 3.02586i | 1.48532 | − | 0.484526i | ||||
\(40\) | 0.0579471 | − | 0.0334558i | 0.00916224 | − | 0.00528982i | ||||
\(41\) | 3.52867 | + | 6.11183i | 0.551085 | + | 0.954508i | 0.998197 | + | 0.0600295i | \(0.0191195\pi\) |
−0.447111 | + | 0.894478i | \(0.647547\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.15994 | + | 2.00908i | −0.176890 | + | 0.306382i | −0.940814 | − | 0.338924i | \(-0.889937\pi\) |
0.763924 | + | 0.645306i | \(0.223270\pi\) | |||||||
\(44\) | 1.59344i | 0.240221i | ||||||||
\(45\) | 0.00907265 | + | 0.0844257i | 0.00135247 | + | 0.0125854i | ||||
\(46\) | −4.82367 | −0.711212 | ||||||||
\(47\) | 5.43997 | − | 9.42231i | 0.793502 | − | 1.37439i | −0.130285 | − | 0.991477i | \(-0.541589\pi\) |
0.923786 | − | 0.382908i | \(-0.125078\pi\) | |||||||
\(48\) | 1.79060 | − | 1.99333i | 0.258450 | − | 0.287712i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.87603 | − | 1.66048i | 0.406732 | − | 0.234827i | ||||
\(51\) | 9.62341 | + | 2.03379i | 1.34755 | + | 0.284788i | ||||
\(52\) | 7.60408 | + | 4.39022i | 1.05450 | + | 0.608814i | ||||
\(53\) | 11.5995i | 1.59331i | 0.604435 | + | 0.796655i | \(0.293399\pi\) | ||||
−0.604435 | + | 0.796655i | \(0.706601\pi\) | |||||||
\(54\) | −1.41499 | − | 3.14843i | −0.192556 | − | 0.428447i | ||||
\(55\) | − | 0.0289346i | − | 0.00390155i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.749489 | + | 3.54640i | −0.0992723 | + | 0.469733i | ||||
\(58\) | −1.35224 | − | 2.34215i | −0.177558 | − | 0.307540i | ||||
\(59\) | −3.01111 | − | 5.21540i | −0.392013 | − | 0.678987i | 0.600702 | − | 0.799473i | \(-0.294888\pi\) |
−0.992715 | + | 0.120486i | \(0.961555\pi\) | |||||||
\(60\) | −0.0510646 | + | 0.0568462i | −0.00659242 | + | 0.00733881i | ||||
\(61\) | 2.05220 | + | 1.18484i | 0.262757 | + | 0.151703i | 0.625592 | − | 0.780151i | \(-0.284858\pi\) |
−0.362834 | + | 0.931854i | \(0.618191\pi\) | |||||||
\(62\) | 2.20427 | 0.279942 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.729528 | −0.0911909 | ||||||||
\(65\) | −0.138079 | − | 0.0797200i | −0.0171266 | − | 0.00988805i | ||||
\(66\) | 0.364781 | + | 1.11824i | 0.0449014 | + | 0.137646i | ||||
\(67\) | −6.38995 | − | 11.0677i | −0.780656 | − | 1.35214i | −0.931560 | − | 0.363588i | \(-0.881552\pi\) |
0.150903 | − | 0.988549i | \(-0.451782\pi\) | |||||||
\(68\) | 4.42580 | + | 7.66571i | 0.536707 | + | 0.929604i | ||||
\(69\) | 11.9569 | − | 3.90045i | 1.43944 | − | 0.469559i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.93415i | 0.941610i | 0.882237 | + | 0.470805i | \(0.156036\pi\) | ||||
−0.882237 | + | 0.470805i | \(0.843964\pi\) | |||||||
\(72\) | 2.86950 | − | 6.48568i | 0.338174 | − | 0.764345i | ||||
\(73\) | − | 10.8991i | − | 1.27564i | −0.770185 | − | 0.637821i | \(-0.779836\pi\) | ||
0.770185 | − | 0.637821i | \(-0.220164\pi\) | |||||||
\(74\) | −1.42251 | − | 0.821285i | −0.165363 | − | 0.0954725i | ||||
\(75\) | −5.78640 | + | 6.44154i | −0.668156 | + | 0.743806i | ||||
\(76\) | −2.82496 | + | 1.63099i | −0.324045 | + | 0.187087i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.34140 | + | 1.34018i | 0.718022 | + | 0.151745i | ||||
\(79\) | 7.80018 | − | 13.5103i | 0.877588 | − | 1.52003i | 0.0236086 | − | 0.999721i | \(-0.492484\pi\) |
0.853980 | − | 0.520306i | \(-0.174182\pi\) | |||||||
\(80\) | −0.0437861 | −0.00489543 | ||||||||
\(81\) | 6.05331 | + | 6.66014i | 0.672590 | + | 0.740015i | ||||
\(82\) | 4.68816i | 0.517721i | ||||||||
\(83\) | 3.07406 | − | 5.32442i | 0.337421 | − | 0.584431i | −0.646526 | − | 0.762892i | \(-0.723779\pi\) |
0.983947 | + | 0.178461i | \(0.0571119\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0803661 | − | 0.139198i | −0.00871693 | − | 0.0150982i | ||||
\(86\) | −1.33463 | + | 0.770546i | −0.143916 | + | 0.0830902i | ||||
\(87\) | 5.24581 | + | 4.71228i | 0.562410 | + | 0.505210i | ||||
\(88\) | −1.20836 | + | 2.09294i | −0.128812 | + | 0.223108i | ||||
\(89\) | −12.0516 | −1.27747 | −0.638736 | − | 0.769426i | \(-0.720542\pi\) | ||||
−0.638736 | + | 0.769426i | \(0.720542\pi\) | |||||||
\(90\) | −0.0228224 | + | 0.0515834i | −0.00240569 | + | 0.00543736i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.80194 | + | 5.65915i | 1.02192 | + | 0.590007i | ||||
\(93\) | −5.46392 | + | 1.78238i | −0.566582 | + | 0.184825i | ||||
\(94\) | 6.25921 | − | 3.61376i | 0.645588 | − | 0.372730i | ||||
\(95\) | 0.0512971 | − | 0.0296164i | 0.00526297 | − | 0.00303858i | ||||
\(96\) | 9.47771 | − | 3.09172i | 0.967315 | − | 0.315547i | ||||
\(97\) | 6.77565 | + | 3.91192i | 0.687963 | + | 0.397196i | 0.802848 | − | 0.596183i | \(-0.203317\pi\) |
−0.114885 | + | 0.993379i | \(0.536650\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.80843 | − | 2.47692i | −0.181754 | − | 0.248940i | ||||
\(100\) | −7.79230 | −0.779230 | ||||||||
\(101\) | −0.226924 | + | 0.393043i | −0.0225797 | + | 0.0391093i | −0.877094 | − | 0.480318i | \(-0.840521\pi\) |
0.854515 | + | 0.519427i | \(0.173855\pi\) | |||||||
\(102\) | 4.86081 | + | 4.36643i | 0.481291 | + | 0.432341i | ||||
\(103\) | 4.58316 | − | 2.64609i | 0.451592 | − | 0.260727i | −0.256910 | − | 0.966435i | \(-0.582704\pi\) |
0.708502 | + | 0.705708i | \(0.249371\pi\) | |||||||
\(104\) | 6.65848 | + | 11.5328i | 0.652918 | + | 1.13089i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.85274 | + | 6.67315i | −0.374212 | + | 0.648153i | ||||
\(107\) | − | 9.06755i | − | 0.876593i | −0.898830 | − | 0.438296i | \(-0.855582\pi\) | ||
0.898830 | − | 0.438296i | \(-0.144418\pi\) | |||||||
\(108\) | −0.818419 | + | 8.05784i | −0.0787524 | + | 0.775366i | ||||
\(109\) | 4.73027 | 0.453078 | 0.226539 | − | 0.974002i | \(-0.427259\pi\) | ||||
0.226539 | + | 0.974002i | \(0.427259\pi\) | |||||||
\(110\) | 0.00961059 | − | 0.0166460i | 0.000916334 | − | 0.00158714i | ||||
\(111\) | 4.19020 | + | 0.885547i | 0.397716 | + | 0.0840524i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.21108 | + | 4.74067i | −0.772433 | + | 0.445965i | −0.833742 | − | 0.552154i | \(-0.813806\pi\) |
0.0613086 | + | 0.998119i | \(0.480473\pi\) | |||||||
\(114\) | −1.60911 | + | 1.79130i | −0.150707 | + | 0.167770i | ||||
\(115\) | −0.177989 | − | 0.102762i | −0.0165976 | − | 0.00958261i | ||||
\(116\) | 6.34583i | 0.589195i | ||||||||
\(117\) | −16.8027 | + | 1.80567i | −1.55341 | + | 0.166934i | ||||
\(118\) | − | 4.00054i | − | 0.368280i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.110180 | + | 0.0359418i | −0.0100580 | + | 0.00328102i | ||||
\(121\) | −4.97747 | − | 8.62123i | −0.452497 | − | 0.783748i | ||||
\(122\) | 0.787084 | + | 1.36327i | 0.0712593 | + | 0.123425i | ||||
\(123\) | −3.79088 | − | 11.6210i | −0.341812 | − | 1.04783i | ||||
\(124\) | −4.47918 | − | 2.58606i | −0.402242 | − | 0.232235i | ||||
\(125\) | 0.283017 | 0.0253138 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.37297 | 0.388039 | 0.194019 | − | 0.980998i | \(-0.437848\pi\) | ||||
0.194019 | + | 0.980998i | \(0.437848\pi\) | |||||||
\(128\) | 9.54954 | + | 5.51343i | 0.844068 | + | 0.487323i | ||||
\(129\) | 2.68519 | − | 2.98921i | 0.236418 | − | 0.263185i | ||||
\(130\) | −0.0529577 | − | 0.0917255i | −0.00464470 | − | 0.00804486i | ||||
\(131\) | 1.27231 | + | 2.20371i | 0.111162 | + | 0.192539i | 0.916239 | − | 0.400632i | \(-0.131209\pi\) |
−0.805077 | + | 0.593171i | \(0.797876\pi\) | |||||||
\(132\) | 0.570672 | − | 2.70028i | 0.0496706 | − | 0.235029i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 8.48964i | − | 0.733393i | ||||||
\(135\) | 0.0148613 | − | 0.146319i | 0.00127906 | − | 0.0125931i | ||||
\(136\) | 13.4249i | 1.15118i | ||||||||
\(137\) | −9.82536 | − | 5.67267i | −0.839437 | − | 0.484649i | 0.0176357 | − | 0.999844i | \(-0.494386\pi\) |
−0.857073 | + | 0.515195i | \(0.827719\pi\) | |||||||
\(138\) | 8.17430 | + | 1.72754i | 0.695842 | + | 0.147058i | ||||
\(139\) | 3.04891 | − | 1.76029i | 0.258605 | − | 0.149306i | −0.365093 | − | 0.930971i | \(-0.618963\pi\) |
0.623698 | + | 0.781665i | \(0.285629\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.5932 | + | 14.0190i | −1.06054 | + | 1.18061i | ||||
\(142\) | −2.63531 | + | 4.56450i | −0.221151 | + | 0.383044i | ||||
\(143\) | 5.75867 | 0.481564 | ||||||||
\(144\) | −3.74827 | + | 2.73666i | −0.312356 | + | 0.228055i | ||||
\(145\) | − | 0.115231i | − | 0.00956942i | ||||||
\(146\) | 3.62012 | − | 6.27022i | 0.299603 | − | 0.518927i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.92707 | + | 3.33778i | 0.158404 | + | 0.274364i | ||||
\(149\) | −13.7806 | + | 7.95623i | −1.12895 | + | 0.651800i | −0.943671 | − | 0.330886i | \(-0.892652\pi\) |
−0.185279 | + | 0.982686i | \(0.559319\pi\) | |||||||
\(150\) | −5.46845 | + | 1.78386i | −0.446497 | + | 0.145652i | ||||
\(151\) | −1.73008 | + | 2.99659i | −0.140792 | + | 0.243859i | −0.927795 | − | 0.373090i | \(-0.878298\pi\) |
0.787003 | + | 0.616949i | \(0.211632\pi\) | |||||||
\(152\) | −4.94732 | −0.401281 | ||||||||
\(153\) | −15.5796 | − | 6.89301i | −1.25954 | − | 0.557267i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0813354 | + | 0.0469590i | 0.00653302 | + | 0.00377184i | ||||
\(156\) | −11.3137 | − | 10.1631i | −0.905823 | − | 0.813696i | ||||
\(157\) | −14.1585 | + | 8.17442i | −1.12997 | + | 0.652390i | −0.943928 | − | 0.330151i | \(-0.892900\pi\) |
−0.186045 | + | 0.982541i | \(0.559567\pi\) | |||||||
\(158\) | 8.97485 | − | 5.18163i | 0.714001 | − | 0.412228i | ||||
\(159\) | 4.15420 | − | 19.6567i | 0.329450 | − | 1.55888i | ||||
\(160\) | −0.141084 | − | 0.0814550i | −0.0111537 | − | 0.00643959i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.27030 | + | 5.84216i | 0.0998044 | + | 0.459003i | ||||
\(163\) | 10.3556 | 0.811116 | 0.405558 | − | 0.914069i | \(-0.367077\pi\) | ||||
0.405558 | + | 0.914069i | \(0.367077\pi\) | |||||||
\(164\) | 5.50017 | − | 9.52657i | 0.429491 | − | 0.743900i | ||||
\(165\) | −0.0103626 | + | 0.0490332i | −0.000806726 | + | 0.00381723i | ||||
\(166\) | 3.53699 | − | 2.04208i | 0.274524 | − | 0.158497i | ||||
\(167\) | −2.94297 | − | 5.09738i | −0.227734 | − | 0.394447i | 0.729402 | − | 0.684085i | \(-0.239798\pi\) |
−0.957136 | + | 0.289638i | \(0.906465\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.36614 | − | 16.2226i | 0.720473 | − | 1.24790i | ||||
\(170\) | − | 0.106774i | − | 0.00818919i | ||||||
\(171\) | 2.54020 | − | 5.74139i | 0.194254 | − | 0.439055i | ||||
\(172\) | 3.61603 | 0.275720 | ||||||||
\(173\) | 2.43276 | − | 4.21366i | 0.184959 | − | 0.320359i | −0.758604 | − | 0.651552i | \(-0.774118\pi\) |
0.943563 | + | 0.331194i | \(0.107451\pi\) | |||||||
\(174\) | 1.45273 | + | 4.45335i | 0.110131 | + | 0.337608i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.36959 | − | 0.790735i | 0.103237 | − | 0.0596039i | ||||
\(177\) | 3.23486 | + | 9.91651i | 0.243147 | + | 0.745371i | ||||
\(178\) | −6.93328 | − | 4.00293i | −0.519671 | − | 0.300032i | ||||
\(179\) | 0.202645i | 0.0151464i | 0.999971 | + | 0.00757319i | \(0.00241064\pi\) | ||||
−0.999971 | + | 0.00757319i | \(0.997589\pi\) | |||||||
\(180\) | 0.106894 | − | 0.0780446i | 0.00796740 | − | 0.00581710i | ||||
\(181\) | 6.26273i | 0.465505i | 0.972536 | + | 0.232753i | \(0.0747732\pi\) | ||||
−0.972536 | + | 0.232753i | \(0.925227\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.05337 | − | 2.74282i | −0.225711 | − | 0.202755i | ||||
\(184\) | 8.58303 | + | 14.8662i | 0.632749 | + | 1.09595i | ||||
\(185\) | −0.0349928 | − | 0.0606093i | −0.00257272 | − | 0.00445608i | ||||
\(186\) | −3.73540 | − | 0.789431i | −0.273893 | − | 0.0578839i | ||||
\(187\) | 5.02758 | + | 2.90267i | 0.367653 | + | 0.212264i | ||||
\(188\) | −16.9587 | −1.23684 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.0393482 | 0.00285462 | ||||||||
\(191\) | 11.9541 | + | 6.90168i | 0.864965 | + | 0.499388i | 0.865672 | − | 0.500612i | \(-0.166892\pi\) |
−0.000706698 | 1.00000i | \(0.500225\pi\) | ||||||||
\(192\) | 1.23627 | + | 0.261271i | 0.0892203 | + | 0.0188556i | ||||
\(193\) | 10.5387 | + | 18.2536i | 0.758593 | + | 1.31392i | 0.943568 | + | 0.331178i | \(0.107446\pi\) |
−0.184976 | + | 0.982743i | \(0.559221\pi\) | |||||||
\(194\) | 2.59868 | + | 4.50104i | 0.186574 | + | 0.323156i | ||||
\(195\) | 0.205441 | + | 0.184546i | 0.0147119 | + | 0.0132156i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 15.1679i | − | 1.08067i | −0.841451 | − | 0.540334i | \(-0.818298\pi\) | ||
0.841451 | − | 0.540334i | \(-0.181702\pi\) | |||||||
\(198\) | −0.217681 | − | 2.02564i | −0.0154699 | − | 0.143956i | ||||
\(199\) | − | 9.68724i | − | 0.686710i | −0.939206 | − | 0.343355i | \(-0.888437\pi\) | ||
0.939206 | − | 0.343355i | \(-0.111563\pi\) | |||||||
\(200\) | −10.2349 | − | 5.90915i | −0.723720 | − | 0.417840i | ||||
\(201\) | 6.86477 | + | 21.0441i | 0.484204 | + | 1.48433i | ||||
\(202\) | −0.261097 | + | 0.150745i | −0.0183707 | + | 0.0106064i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4.75467 | − | 14.5755i | −0.332894 | − | 1.02049i | ||||
\(205\) | −0.0998751 | + | 0.172989i | −0.00697558 | + | 0.0120821i | ||||
\(206\) | 3.51558 | 0.244942 | ||||||||
\(207\) | −21.6593 | + | 2.32757i | −1.50542 | + | 0.161777i | ||||
\(208\) | − | 8.71445i | − | 0.604238i | ||||||
\(209\) | −1.06969 | + | 1.85275i | −0.0739919 | + | 0.128158i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.05942 | − | 12.2273i | −0.485991 | − | 0.841761i | 0.513880 | − | 0.857862i | \(-0.328208\pi\) |
−0.999870 | + | 0.0161017i | \(0.994874\pi\) | |||||||
\(212\) | 15.6579 | − | 9.04010i | 1.07539 | − | 0.620877i | ||||
\(213\) | 2.84152 | − | 13.4454i | 0.194697 | − | 0.921261i | ||||
\(214\) | 3.01177 | − | 5.21654i | 0.205880 | − | 0.356595i | ||||
\(215\) | −0.0656619 | −0.00447810 | ||||||||
\(216\) | −7.18549 | + | 9.96309i | −0.488910 | + | 0.677903i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.72132 | + | 1.57115i | 0.184311 | + | 0.106412i | ||||
\(219\) | −3.90337 | + | 18.4698i | −0.263766 | + | 1.24807i | ||||
\(220\) | −0.0390584 | + | 0.0225504i | −0.00263331 | + | 0.00152034i | ||||
\(221\) | 27.7037 | − | 15.9947i | 1.86355 | − | 1.07592i | ||||
\(222\) | 2.11648 | + | 1.90122i | 0.142049 | + | 0.127602i | ||||
\(223\) | −2.58777 | − | 1.49405i | −0.173290 | − | 0.100049i | 0.410846 | − | 0.911705i | \(-0.365233\pi\) |
−0.584136 | + | 0.811656i | \(0.698567\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.1127 | − | 8.84364i | 0.807514 | − | 0.589576i | ||||
\(226\) | −6.29842 | −0.418965 | ||||||||
\(227\) | −14.3867 | + | 24.9184i | −0.954876 | + | 1.65389i | −0.220224 | + | 0.975449i | \(0.570679\pi\) |
−0.734652 | + | 0.678444i | \(0.762654\pi\) | |||||||
\(228\) | 5.37135 | − | 1.75218i | 0.355726 | − | 0.116041i | ||||
\(229\) | −7.67401 | + | 4.43059i | −0.507113 | + | 0.292782i | −0.731646 | − | 0.681685i | \(-0.761248\pi\) |
0.224533 | + | 0.974466i | \(0.427914\pi\) | |||||||
\(230\) | −0.0682645 | − | 0.118238i | −0.00450122 | − | 0.00779635i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.81224 | + | 8.33505i | −0.315939 | + | 0.547223i | ||||
\(233\) | − | 12.9082i | − | 0.845646i | −0.906212 | − | 0.422823i | \(-0.861039\pi\) | ||
0.906212 | − | 0.422823i | \(-0.138961\pi\) | |||||||
\(234\) | −10.2663 | − | 4.54219i | −0.671129 | − | 0.296932i | ||||
\(235\) | 0.307945 | 0.0200881 | ||||||||
\(236\) | −4.69345 | + | 8.12929i | −0.305518 | + | 0.529172i | ||||
\(237\) | −18.0569 | + | 20.1013i | −1.17292 | + | 1.30572i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.85712 | + | 2.80426i | −0.314181 | + | 0.181392i | −0.648796 | − | 0.760963i | \(-0.724727\pi\) |
0.334615 | + | 0.942355i | \(0.391394\pi\) | |||||||
\(240\) | 0.0742008 | + | 0.0156814i | 0.00478964 | + | 0.00101223i | ||||
\(241\) | −9.51481 | − | 5.49338i | −0.612903 | − | 0.353860i | 0.161198 | − | 0.986922i | \(-0.448464\pi\) |
−0.774101 | + | 0.633063i | \(0.781798\pi\) | |||||||
\(242\) | − | 6.61303i | − | 0.425102i | ||||||
\(243\) | −7.87282 | − | 13.4543i | −0.505042 | − | 0.863095i | ||||
\(244\) | − | 3.69364i | − | 0.236461i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.67901 | − | 7.94466i | 0.107050 | − | 0.506533i | ||||
\(247\) | 5.89436 | + | 10.2093i | 0.375049 | + | 0.649604i | ||||
\(248\) | −3.92218 | − | 6.79341i | −0.249058 | − | 0.431382i | ||||
\(249\) | −7.11623 | + | 7.92193i | −0.450973 | + | 0.502032i | ||||
\(250\) | 0.162819 | + | 0.0940035i | 0.0102976 | + | 0.00594530i | ||||
\(251\) | −24.2241 | −1.52901 | −0.764505 | − | 0.644618i | \(-0.777016\pi\) | ||||
−0.764505 | + | 0.644618i | \(0.777016\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.42314 | 0.466689 | ||||||||
\(254\) | 2.51576 | + | 1.45248i | 0.157853 | + | 0.0911365i | ||||
\(255\) | 0.0863380 | + | 0.264670i | 0.00540669 | + | 0.0165743i | ||||
\(256\) | 4.39208 | + | 7.60731i | 0.274505 | + | 0.475457i | ||||
\(257\) | 8.86142 | + | 15.3484i | 0.552760 | + | 0.957409i | 0.998074 | + | 0.0620341i | \(0.0197588\pi\) |
−0.445314 | + | 0.895375i | \(0.646908\pi\) | |||||||
\(258\) | 2.53765 | − | 0.827804i | 0.157987 | − | 0.0515368i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.248521i | 0.0154126i | ||||||||
\(261\) | −7.20201 | − | 9.86425i | −0.445793 | − | 0.610582i | ||||
\(262\) | 1.69039i | 0.104432i | ||||||||
\(263\) | 2.51031 | + | 1.44933i | 0.154793 | + | 0.0893695i | 0.575396 | − | 0.817875i | \(-0.304848\pi\) |
−0.420603 | + | 0.907245i | \(0.638181\pi\) | |||||||
\(264\) | 2.79727 | − | 3.11398i | 0.172160 | − | 0.191652i | ||||
\(265\) | −0.284325 | + | 0.164155i | −0.0174660 | + | 0.0100840i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.4230 | + | 4.31614i | 1.24986 | + | 0.264144i | ||||
\(268\) | −9.96008 | + | 17.2514i | −0.608408 | + | 1.05379i | ||||
\(269\) | 21.8938 | 1.33489 | 0.667444 | − | 0.744660i | \(-0.267388\pi\) | ||||
0.667444 | + | 0.744660i | \(0.267388\pi\) | |||||||
\(270\) | 0.0571492 | − | 0.0792407i | 0.00347799 | − | 0.00482243i | ||||
\(271\) | 8.98347i | 0.545707i | 0.962056 | + | 0.272854i | \(0.0879675\pi\) | ||||
−0.962056 | + | 0.272854i | \(0.912033\pi\) | |||||||
\(272\) | 4.39254 | − | 7.60811i | 0.266337 | − | 0.461309i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.76834 | − | 6.52695i | −0.227654 | − | 0.394308i | ||||
\(275\) | −4.42591 | + | 2.55530i | −0.266892 | + | 0.154090i | ||||
\(276\) | −14.5838 | − | 13.1006i | −0.877842 | − | 0.788561i | ||||
\(277\) | −7.95091 | + | 13.7714i | −0.477724 | + | 0.827442i | −0.999674 | − | 0.0255339i | \(-0.991871\pi\) |
0.521950 | + | 0.852976i | \(0.325205\pi\) | |||||||
\(278\) | 2.33871 | 0.140267 | ||||||||
\(279\) | 9.89761 | − | 1.06363i | 0.592554 | − | 0.0636777i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.50324 | − | 2.59995i | −0.268641 | − | 0.155100i | 0.359629 | − | 0.933095i | \(-0.382903\pi\) |
−0.628270 | + | 0.777996i | \(0.716237\pi\) | |||||||
\(282\) | −11.9012 | + | 3.88229i | −0.708706 | + | 0.231187i | ||||
\(283\) | −16.2587 | + | 9.38694i | −0.966476 | + | 0.557995i | −0.898160 | − | 0.439668i | \(-0.855096\pi\) |
−0.0683162 | + | 0.997664i | \(0.521763\pi\) | |||||||
\(284\) | 10.7102 | − | 6.18352i | 0.635531 | − | 0.366924i | ||||
\(285\) | −0.0975359 | + | 0.0318171i | −0.00577753 | + | 0.00188468i | ||||
\(286\) | 3.31295 | + | 1.91273i | 0.195899 | + | 0.113102i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −17.1684 | + | 1.84497i | −1.01166 | + | 0.108716i | ||||
\(289\) | 15.2488 | 0.896986 | ||||||||
\(290\) | 0.0382738 | − | 0.0662922i | 0.00224751 | − | 0.00389281i | ||||
\(291\) | −10.0811 | − | 9.05584i | −0.590967 | − | 0.530863i | ||||
\(292\) | −14.7125 | + | 8.49426i | −0.860983 | + | 0.497089i | ||||
\(293\) | −11.4201 | − | 19.7802i | −0.667169 | − | 1.15557i | −0.978692 | − | 0.205332i | \(-0.934173\pi\) |
0.311523 | − | 0.950238i | \(-0.399161\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0852263 | − | 0.147616i | 0.00496206 | − | 0.00859455i | ||||
\(296\) | 5.84543i | 0.339759i | ||||||||
\(297\) | 2.17753 | + | 4.84511i | 0.126353 | + | 0.281142i | ||||
\(298\) | −10.5706 | −0.612338 | ||||||||
\(299\) | 20.4520 | − | 35.4240i | 1.18277 | − | 2.04862i | ||||
\(300\) | 13.2050 | + | 2.79072i | 0.762390 | + | 0.161122i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.99062 | + | 1.14929i | −0.114548 | + | 0.0661341i | ||||
\(303\) | 0.525313 | − | 0.584789i | 0.0301784 | − | 0.0335953i | ||||
\(304\) | 2.80373 | + | 1.61873i | 0.160805 | + | 0.0928407i | ||||
\(305\) | 0.0670711i | 0.00384048i | ||||||||
\(306\) | −6.67343 | − | 9.14028i | −0.381495 | − | 0.522515i | ||||
\(307\) | − | 18.6325i | − | 1.06341i | −0.846928 | − | 0.531707i | \(-0.821551\pi\) | ||
0.846928 | − | 0.531707i | \(-0.178449\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.71438 | + | 2.84271i | −0.495744 | + | 0.161716i | ||||
\(310\) | 0.0311947 | + | 0.0540308i | 0.00177174 | + | 0.00306875i | ||||
\(311\) | 10.2747 | + | 17.7964i | 0.582628 | + | 1.00914i | 0.995167 | + | 0.0982007i | \(0.0313087\pi\) |
−0.412539 | + | 0.910940i | \(0.635358\pi\) | |||||||
\(312\) | −7.15326 | − | 21.9284i | −0.404974 | − | 1.24145i | ||||
\(313\) | 0.624466 | + | 0.360536i | 0.0352969 | + | 0.0203787i | 0.517545 | − | 0.855656i | \(-0.326846\pi\) |
−0.482248 | + | 0.876035i | \(0.660179\pi\) | |||||||
\(314\) | −10.8605 | −0.612893 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −24.3164 | −1.36791 | ||||||||
\(317\) | −18.9915 | − | 10.9647i | −1.06667 | − | 0.615841i | −0.139398 | − | 0.990236i | \(-0.544517\pi\) |
−0.927269 | + | 0.374396i | \(0.877850\pi\) | |||||||
\(318\) | 8.91884 | − | 9.92864i | 0.500144 | − | 0.556770i | ||||
\(319\) | 2.08096 | + | 3.60433i | 0.116512 | + | 0.201804i | ||||
\(320\) | −0.0103242 | − | 0.0178821i | −0.000577143 | − | 0.000999641i | ||||
\(321\) | −3.24743 | + | 15.3660i | −0.181254 | + | 0.857649i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.8843i | 0.661258i | ||||||||
\(324\) | 4.27272 | − | 13.3619i | 0.237374 | − | 0.742326i | ||||
\(325\) | 28.1612i | 1.56210i | ||||||||
\(326\) | 5.95757 | + | 3.43961i | 0.329959 | + | 0.190502i | ||||
\(327\) | −8.01602 | − | 1.69409i | −0.443287 | − | 0.0936833i | ||||
\(328\) | 14.4486 | − | 8.34191i | 0.797791 | − | 0.460605i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.0222479 | + | 0.0247668i | −0.00122470 | + | 0.00136337i | ||||
\(331\) | −10.8338 | + | 18.7647i | −0.595480 | + | 1.03140i | 0.397999 | + | 0.917386i | \(0.369705\pi\) |
−0.993479 | + | 0.114016i | \(0.963629\pi\) | |||||||
\(332\) | −9.58312 | −0.525942 | ||||||||
\(333\) | −6.78364 | − | 3.00133i | −0.371741 | − | 0.164472i | ||||
\(334\) | − | 3.91002i | − | 0.213947i | ||||||
\(335\) | 0.180861 | − | 0.313260i | 0.00988147 | − | 0.0171152i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.6455 | + | 21.9026i | 0.688844 | + | 1.19311i | 0.972212 | + | 0.234101i | \(0.0752147\pi\) |
−0.283369 | + | 0.959011i | \(0.591452\pi\) | |||||||
\(338\) | 10.7766 | − | 6.22190i | 0.586172 | − | 0.338427i | ||||
\(339\) | 15.6125 | − | 5.09294i | 0.847953 | − | 0.276610i | ||||
\(340\) | −0.125268 | + | 0.216970i | −0.00679358 | + | 0.0117668i | ||||
\(341\) | −3.39214 | −0.183695 | ||||||||
\(342\) | 3.36836 | − | 2.45928i | 0.182140 | − | 0.132983i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.74955 | + | 2.74215i | 0.256078 | + | 0.147847i | ||||
\(345\) | 0.264821 | + | 0.237887i | 0.0142575 | + | 0.0128074i | ||||
\(346\) | 2.79912 | − | 1.61607i | 0.150482 | − | 0.0868806i | ||||
\(347\) | −4.92420 | + | 2.84299i | −0.264345 | + | 0.152620i | −0.626315 | − | 0.779570i | \(-0.715438\pi\) |
0.361970 | + | 0.932190i | \(0.382104\pi\) | |||||||
\(348\) | 2.27268 | − | 10.7538i | 0.121828 | − | 0.576462i | ||||
\(349\) | 9.68412 | + | 5.59113i | 0.518379 | + | 0.299286i | 0.736271 | − | 0.676687i | \(-0.236585\pi\) |
−0.217892 | + | 0.975973i | \(0.569918\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 29.1208 | + | 2.95775i | 1.55436 | + | 0.157873i | ||||
\(352\) | 5.88400 | 0.313618 | ||||||||
\(353\) | −7.02111 | + | 12.1609i | −0.373696 | + | 0.647260i | −0.990131 | − | 0.140146i | \(-0.955243\pi\) |
0.616435 | + | 0.787406i | \(0.288576\pi\) | |||||||
\(354\) | −1.43274 | + | 6.77940i | −0.0761495 | + | 0.360321i | ||||
\(355\) | −0.194481 | + | 0.112284i | −0.0103220 | + | 0.00595940i | ||||
\(356\) | 9.39250 | + | 16.2683i | 0.497802 | + | 0.862218i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.0673081 | + | 0.116581i | −0.00355734 | + | 0.00616150i | ||||
\(359\) | − | 27.1414i | − | 1.43247i | −0.697859 | − | 0.716235i | \(-0.745864\pi\) | ||
0.697859 | − | 0.716235i | \(-0.254136\pi\) | |||||||
\(360\) | 0.199586 | − | 0.0214481i | 0.0105191 | − | 0.00113041i | ||||
\(361\) | 14.6204 | 0.769496 | ||||||||
\(362\) | −2.08016 | + | 3.60294i | −0.109331 | + | 0.189366i | ||||
\(363\) | 5.34733 | + | 16.3923i | 0.280662 | + | 0.860374i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.267158 | − | 0.154244i | 0.0139837 | − | 0.00807347i | ||||
\(366\) | −0.845571 | − | 2.59211i | −0.0441987 | − | 0.135492i | ||||
\(367\) | −5.95891 | − | 3.44038i | −0.311053 | − | 0.179586i | 0.336345 | − | 0.941739i | \(-0.390809\pi\) |
−0.647397 | + | 0.762153i | \(0.724143\pi\) | |||||||
\(368\) | − | 11.2332i | − | 0.585573i | ||||||
\(369\) | 2.26219 | + | 21.0508i | 0.117765 | + | 1.09586i | ||||
\(370\) | − | 0.0464912i | − | 0.00241696i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 6.66434 | + | 5.98654i | 0.345530 | + | 0.310388i | ||||
\(373\) | 0.123926 | + | 0.214645i | 0.00641662 | + | 0.0111139i | 0.869216 | − | 0.494433i | \(-0.164624\pi\) |
−0.862799 | + | 0.505547i | \(0.831291\pi\) | |||||||
\(374\) | 1.92824 | + | 3.33980i | 0.0997067 | + | 0.172697i | ||||
\(375\) | −0.479606 | − | 0.101359i | −0.0247667 | − | 0.00523415i | ||||
\(376\) | −22.2747 | − | 12.8603i | −1.14873 | − | 0.663220i | ||||
\(377\) | 22.9337 | 1.18114 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.91863 | −0.458119 | −0.229060 | − | 0.973412i | \(-0.573565\pi\) | ||||
−0.229060 | + | 0.973412i | \(0.573565\pi\) | |||||||
\(380\) | −0.0799573 | − | 0.0461634i | −0.00410172 | − | 0.00236813i | ||||
\(381\) | −7.41053 | − | 1.56613i | −0.379653 | − | 0.0802351i | ||||
\(382\) | 4.58476 | + | 7.94104i | 0.234577 | + | 0.406299i | ||||
\(383\) | −0.163545 | − | 0.283268i | −0.00835675 | − | 0.0144743i | 0.861817 | − | 0.507220i | \(-0.169327\pi\) |
−0.870174 | + | 0.492745i | \(0.835993\pi\) | |||||||
\(384\) | −14.2083 | − | 12.7632i | −0.725063 | − | 0.651320i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.0017i | 0.712665i | ||||||||
\(387\) | −5.62093 | + | 4.10391i | −0.285728 | + | 0.208613i | ||||
\(388\) | − | 12.1951i | − | 0.619113i | ||||||
\(389\) | −5.72348 | − | 3.30445i | −0.290192 | − | 0.167542i | 0.347837 | − | 0.937555i | \(-0.386916\pi\) |
−0.638028 | + | 0.770013i | \(0.720250\pi\) | |||||||
\(390\) | 0.0568929 | + | 0.174406i | 0.00288088 | + | 0.00883139i | ||||
\(391\) | 35.7111 | − | 20.6178i | 1.80599 | − | 1.04269i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.36686 | − | 4.19011i | −0.0689487 | − | 0.211363i | ||||
\(394\) | 5.03799 | − | 8.72606i | 0.253810 | − | 0.439613i | ||||
\(395\) | 0.441551 | 0.0222168 | ||||||||
\(396\) | −1.93414 | + | 4.37157i | −0.0971944 | + | 0.219680i | ||||
\(397\) | 7.51057i | 0.376945i | 0.982078 | + | 0.188472i | \(0.0603536\pi\) | ||||
−0.982078 | + | 0.188472i | \(0.939646\pi\) | |||||||
\(398\) | 3.21760 | − | 5.57305i | 0.161284 | − | 0.279352i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.86687 | + | 6.69762i | 0.193344 | + | 0.334881i | ||||
\(401\) | −5.48595 | + | 3.16732i | −0.273956 | + | 0.158168i | −0.630684 | − | 0.776040i | \(-0.717226\pi\) |
0.356728 | + | 0.934208i | \(0.383892\pi\) | |||||||
\(402\) | −3.04046 | + | 14.3867i | −0.151644 | + | 0.717544i | ||||
\(403\) | −9.34594 | + | 16.1876i | −0.465555 | + | 0.806364i | ||||
\(404\) | 0.707416 | 0.0351953 | ||||||||
\(405\) | −0.0775865 | + | 0.242632i | −0.00385530 | + | 0.0120565i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.18909 | + | 1.26387i | 0.108509 | + | 0.0626479i | ||||
\(408\) | 4.80796 | − | 22.7501i | 0.238030 | − | 1.12630i | ||||
\(409\) | 29.0045 | − | 16.7457i | 1.43418 | − | 0.828024i | 0.436743 | − | 0.899586i | \(-0.356132\pi\) |
0.997436 | + | 0.0715625i | \(0.0227986\pi\) | |||||||
\(410\) | −0.114916 | + | 0.0663467i | −0.00567529 | + | 0.00327663i | ||||
\(411\) | 14.6187 | + | 13.1319i | 0.721085 | + | 0.647747i | ||||
\(412\) | −7.14382 | − | 4.12448i | −0.351951 | − | 0.203199i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −13.2336 | − | 5.85504i | −0.650398 | − | 0.287760i | ||||
\(415\) | 0.174016 | 0.00854209 | ||||||||
\(416\) | 16.2115 | − | 28.0791i | 0.794832 | − | 1.37669i | ||||
\(417\) | −5.79718 | + | 1.89109i | −0.283889 | + | 0.0926073i | ||||
\(418\) | −1.23078 | + | 0.710590i | −0.0601993 | + | 0.0347561i | ||||
\(419\) | −0.896459 | − | 1.55271i | −0.0437949 | − | 0.0758550i | 0.843297 | − | 0.537448i | \(-0.180611\pi\) |
−0.887092 | + | 0.461593i | \(0.847278\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.90262 | − | 3.29543i | 0.0927278 | − | 0.160609i | −0.815930 | − | 0.578150i | \(-0.803775\pi\) |
0.908658 | + | 0.417541i | \(0.137108\pi\) | |||||||
\(422\) | − | 9.37910i | − | 0.456568i | ||||||
\(423\) | 26.3614 | − | 19.2468i | 1.28173 | − | 0.935809i | ||||
\(424\) | 27.4216 | 1.33171 | ||||||||
\(425\) | −14.1947 | + | 24.5860i | −0.688545 | + | 1.19260i | ||||
\(426\) | 6.10057 | − | 6.79128i | 0.295574 | − | 0.329039i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.2401 | + | 7.06684i | −0.591649 | + | 0.341589i | ||||
\(429\) | −9.75876 | − | 2.06240i | −0.471157 | − | 0.0995734i | ||||
\(430\) | −0.0377751 | − | 0.0218095i | −0.00182168 | − | 0.00105175i | ||||
\(431\) | 1.32957i | 0.0640434i | 0.999487 | + | 0.0320217i | \(0.0101946\pi\) | ||||
−0.999487 | + | 0.0320217i | \(0.989805\pi\) | |||||||
\(432\) | 7.33199 | − | 3.29520i | 0.352760 | − | 0.158540i | ||||
\(433\) | 37.4292i | 1.79873i | 0.437194 | + | 0.899367i | \(0.355972\pi\) | ||||
−0.437194 | + | 0.899367i | \(0.644028\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.0412686 | + | 0.195273i | −0.00197868 | + | 0.00936262i | ||||
\(436\) | −3.68656 | − | 6.38531i | −0.176554 | − | 0.305801i | ||||
\(437\) | 7.59804 | + | 13.1602i | 0.363464 | + | 0.629537i | ||||
\(438\) | −8.38032 | + | 9.32915i | −0.400427 | + | 0.445764i | ||||
\(439\) | 20.5584 | + | 11.8694i | 0.981201 | + | 0.566496i | 0.902632 | − | 0.430412i | \(-0.141632\pi\) |
0.0785682 | + | 0.996909i | \(0.474965\pi\) | |||||||
\(440\) | −0.0684026 | −0.00326097 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 21.2505 | 1.01078 | ||||||||
\(443\) | 9.74317 | + | 5.62522i | 0.462912 | + | 0.267262i | 0.713268 | − | 0.700891i | \(-0.247214\pi\) |
−0.250356 | + | 0.968154i | \(0.580548\pi\) | |||||||
\(444\) | −2.07027 | − | 6.34643i | −0.0982505 | − | 0.301188i | ||||
\(445\) | −0.170554 | − | 0.295409i | −0.00808505 | − | 0.0140037i | ||||
\(446\) | −0.992491 | − | 1.71904i | −0.0469958 | − | 0.0813991i | ||||
\(447\) | 26.2023 | − | 8.54744i | 1.23933 | − | 0.404280i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 14.3953i | − | 0.679357i | −0.940542 | − | 0.339679i | \(-0.889682\pi\) | ||
0.940542 | − | 0.339679i | \(-0.110318\pi\) | |||||||
\(450\) | 9.90582 | − | 1.06451i | 0.466965 | − | 0.0501815i | ||||
\(451\) | − | 7.21460i | − | 0.339722i | ||||||
\(452\) | 12.7987 | + | 7.38933i | 0.602000 | + | 0.347565i | ||||
\(453\) | 4.00502 | − | 4.45848i | 0.188172 | − | 0.209477i | ||||
\(454\) | −16.5532 | + | 9.55701i | −0.776881 | + | 0.448533i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.38384 | + | 1.77182i | 0.392609 | + | 0.0829732i | ||||
\(457\) | 10.3135 | − | 17.8635i | 0.482444 | − | 0.835617i | −0.517353 | − | 0.855772i | \(-0.673083\pi\) |
0.999797 | + | 0.0201547i | \(0.00641589\pi\) | |||||||
\(458\) | −5.88646 | −0.275056 | ||||||||
\(459\) | 23.9329 | + | 17.2607i | 1.11709 | + | 0.805660i | ||||
\(460\) | 0.320352i | 0.0149365i | ||||||||
\(461\) | 0.832511 | − | 1.44195i | 0.0387739 | − | 0.0671584i | −0.845987 | − | 0.533203i | \(-0.820988\pi\) |
0.884761 | + | 0.466045i | \(0.154321\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.604175 | + | 1.04646i | 0.0280784 | + | 0.0486332i | 0.879723 | − | 0.475486i | \(-0.157728\pi\) |
−0.851645 | + | 0.524119i | \(0.824395\pi\) | |||||||
\(464\) | 5.45435 | − | 3.14907i | 0.253212 | − | 0.146192i | ||||
\(465\) | −0.121015 | − | 0.108707i | −0.00561193 | − | 0.00504116i | ||||
\(466\) | 4.28745 | − | 7.42608i | 0.198612 | − | 0.344006i | ||||
\(467\) | 9.23988 | 0.427571 | 0.213785 | − | 0.976881i | \(-0.431421\pi\) | ||||
0.213785 | + | 0.976881i | \(0.431421\pi\) | |||||||
\(468\) | 15.5327 | + | 21.2744i | 0.717999 | + | 0.983409i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.177160 | + | 0.102283i | 0.00817179 | + | 0.00471798i | ||||
\(471\) | 26.9209 | − | 8.78185i | 1.24045 | − | 0.404646i | ||||
\(472\) | −12.3294 | + | 7.11839i | −0.567507 | + | 0.327650i | ||||
\(473\) | 2.05385 | − | 1.18579i | 0.0944361 | − | 0.0545227i | ||||
\(474\) | −17.0647 | + | 5.56667i | −0.783807 | + | 0.255685i | ||||
\(475\) | −9.06039 | − | 5.23102i | −0.415719 | − | 0.240016i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.0796 | + | 31.8229i | −0.644660 | + | 1.45707i | ||||
\(478\) | −3.72572 | −0.170410 | ||||||||
\(479\) | 8.77241 | − | 15.1943i | 0.400822 | − | 0.694243i | −0.593004 | − | 0.805200i | \(-0.702058\pi\) |
0.993825 | + | 0.110956i | \(0.0353914\pi\) | |||||||
\(480\) | 0.209912 | + | 0.188563i | 0.00958114 | + | 0.00860668i | ||||
\(481\) | 12.0627 | − | 6.96438i | 0.550010 | − | 0.317549i | ||||
\(482\) | −3.64923 | − | 6.32066i | −0.166218 | − | 0.287898i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.75843 | + | 13.4380i | −0.352656 | + | 0.610818i | ||||
\(485\) | 0.221446i | 0.0100553i | ||||||||
\(486\) | −0.0603850 | − | 10.3552i | −0.00273912 | − | 0.469721i | ||||
\(487\) | −43.1898 | −1.95712 | −0.978558 | − | 0.205974i | \(-0.933964\pi\) | ||||
−0.978558 | + | 0.205974i | \(0.933964\pi\) | |||||||
\(488\) | 2.80100 | − | 4.85148i | 0.126796 | − | 0.219616i | ||||
\(489\) | −17.5489 | − | 3.70874i | −0.793587 | − | 0.167715i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.0046 | − | 13.2817i | 1.03818 | − | 0.599396i | 0.118866 | − | 0.992910i | \(-0.462074\pi\) |
0.919319 | + | 0.393514i | \(0.128741\pi\) | |||||||
\(492\) | −12.7325 | + | 14.1741i | −0.574026 | + | 0.639018i | ||||
\(493\) | 20.0221 | + | 11.5598i | 0.901751 | + | 0.520626i | ||||
\(494\) | 7.83120i | 0.352342i | ||||||||
\(495\) | 0.0351213 | − | 0.0793815i | 0.00157858 | − | 0.00356793i | ||||
\(496\) | 5.13324i | 0.230489i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6.72521 | + | 2.19383i | −0.301364 | + | 0.0983078i | ||||
\(499\) | −2.65759 | − | 4.60308i | −0.118970 | − | 0.206062i | 0.800390 | − | 0.599480i | \(-0.204626\pi\) |
−0.919360 | + | 0.393418i | \(0.871293\pi\) | |||||||
\(500\) | −0.220570 | − | 0.382039i | −0.00986421 | − | 0.0170853i | ||||
\(501\) | 3.16166 | + | 9.69212i | 0.141253 | + | 0.433012i | ||||
\(502\) | −13.9361 | − | 8.04598i | −0.621996 | − | 0.359110i | ||||
\(503\) | 35.5334 | 1.58436 | 0.792178 | − | 0.610290i | \(-0.208947\pi\) | ||||
0.792178 | + | 0.610290i | \(0.208947\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.0128457 | −0.000571624 | ||||||||
\(506\) | 4.27051 | + | 2.46558i | 0.189847 | + | 0.109608i | ||||
\(507\) | −21.6820 | + | 24.1368i | −0.962931 | + | 1.07195i | ||||
\(508\) | −3.40810 | − | 5.90300i | −0.151210 | − | 0.261903i | ||||
\(509\) | −6.81654 | − | 11.8066i | −0.302138 | − | 0.523318i | 0.674482 | − | 0.738291i | \(-0.264367\pi\) |
−0.976620 | + | 0.214973i | \(0.931034\pi\) | |||||||
\(510\) | −0.0382397 | + | 0.180941i | −0.00169328 | + | 0.00801221i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 16.2184i | − | 0.716760i | ||||||
\(513\) | −6.36088 | + | 8.81973i | −0.280840 | + | 0.389400i | ||||
\(514\) | 11.7732i | 0.519295i | ||||||||
\(515\) | 0.129721 | + | 0.0748947i | 0.00571621 | + | 0.00330025i | ||||
\(516\) | −6.12780 | − | 1.29504i | −0.269761 | − | 0.0570108i | ||||
\(517\) | −9.63227 | + | 5.56120i | −0.423627 | + | 0.244581i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.63167 | + | 6.26929i | −0.247203 | + | 0.275191i | ||||
\(520\) | −0.188461 | + | 0.326424i | −0.00826457 | + | 0.0143147i | ||||
\(521\) | 10.2252 | 0.447973 | 0.223987 | − | 0.974592i | \(-0.428093\pi\) | ||||
0.223987 | + | 0.974592i | \(0.428093\pi\) | |||||||
\(522\) | −0.866907 | − | 8.06702i | −0.0379435 | − | 0.353084i | ||||
\(523\) | − | 5.17480i | − | 0.226278i | −0.993579 | − | 0.113139i | \(-0.963909\pi\) | ||
0.993579 | − | 0.113139i | \(-0.0360905\pi\) | |||||||
\(524\) | 1.98317 | − | 3.43495i | 0.0866350 | − | 0.150056i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.962785 | + | 1.66759i | 0.0419794 | + | 0.0727105i | ||||
\(527\) | −16.3189 | + | 9.42169i | −0.710860 | + | 0.410415i | ||||
\(528\) | −2.60413 | + | 0.849493i | −0.113330 | + | 0.0369694i | ||||
\(529\) | 14.8634 | − | 25.7442i | 0.646236 | − | 1.11931i | ||||
\(530\) | −0.218096 | −0.00947346 | ||||||||
\(531\) | −1.93039 | − | 17.9632i | −0.0837716 | − | 0.779538i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −34.4288 | − | 19.8775i | −1.49128 | − | 0.860990i | ||||
\(534\) | 10.3157 | + | 9.26652i | 0.446403 | + | 0.401001i | ||||
\(535\) | 0.222263 | − | 0.128324i | 0.00960927 | − | 0.00554791i | ||||
\(536\) | −26.1645 | + | 15.1061i | −1.13013 | + | 0.652484i | ||||
\(537\) | 0.0725746 | − | 0.343406i | 0.00313183 | − | 0.0148191i | ||||
\(538\) | 12.5955 | + | 7.27199i | 0.543029 | + | 0.313518i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.209095 | + | 0.0939732i | −0.00899803 | + | 0.00404396i | ||||
\(541\) | −25.4395 | −1.09373 | −0.546864 | − | 0.837222i | \(-0.684178\pi\) | ||||
−0.546864 | + | 0.837222i | \(0.684178\pi\) | |||||||
\(542\) | −2.98385 | + | 5.16817i | −0.128167 | + | 0.221992i | ||||
\(543\) | 2.24292 | − | 10.6130i | 0.0962529 | − | 0.455445i | ||||
\(544\) | 28.3067 | − | 16.3429i | 1.21364 | − | 0.700694i | ||||
\(545\) | 0.0669427 | + | 0.115948i | 0.00286751 | + | 0.00496667i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.7771 | − | 25.5947i | 0.631824 | − | 1.09435i | −0.355355 | − | 0.934732i | \(-0.615640\pi\) |
0.987179 | − | 0.159620i | \(-0.0510267\pi\) | |||||||
\(548\) | 17.6841i | 0.755428i | ||||||||
\(549\) | 4.19199 | + | 5.74156i | 0.178910 | + | 0.245044i | ||||
\(550\) | −3.39495 | −0.144761 | ||||||||
\(551\) | −4.25999 | + | 7.37852i | −0.181482 | + | 0.314336i | ||||
\(552\) | −9.22082 | − | 28.2665i | −0.392464 | − | 1.20310i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −9.14828 | + | 5.28176i | −0.388673 | + | 0.224401i | ||||
\(555\) | 0.0375930 | + | 0.115242i | 0.00159574 | + | 0.00489175i | ||||
\(556\) | −4.75237 | − | 2.74378i | −0.201545 | − | 0.116362i | ||||
\(557\) | − | 19.6054i | − | 0.830706i | −0.909660 | − | 0.415353i | \(-0.863658\pi\) | ||
0.909660 | − | 0.415353i | \(-0.136342\pi\) | |||||||
\(558\) | 6.04736 | + | 2.67557i | 0.256005 | + | 0.113266i | ||||
\(559\) | − | 13.0683i | − | 0.552728i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.48028 | − | 6.71949i | −0.315817 | − | 0.283697i | ||||
\(562\) | −1.72714 | − | 2.99149i | −0.0728548 | − | 0.126188i | ||||
\(563\) | −7.23796 | − | 12.5365i | −0.305044 | − | 0.528351i | 0.672227 | − | 0.740345i | \(-0.265338\pi\) |
−0.977271 | + | 0.211994i | \(0.932004\pi\) | |||||||
\(564\) | 28.7385 | + | 6.07354i | 1.21011 | + | 0.255742i | ||||
\(565\) | −0.232406 | − | 0.134180i | −0.00977738 | − | 0.00564497i | ||||
\(566\) | −12.4714 | −0.524213 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 18.7566 | 0.787011 | ||||||||
\(569\) | 6.70970 | + | 3.87385i | 0.281285 | + | 0.162400i | 0.634005 | − | 0.773329i | \(-0.281410\pi\) |
−0.352720 | + | 0.935729i | \(0.614743\pi\) | |||||||
\(570\) | −0.0666802 | − | 0.0140920i | −0.00279293 | − | 0.000590251i | ||||
\(571\) | −8.06856 | − | 13.9752i | −0.337659 | − | 0.584842i | 0.646333 | − | 0.763055i | \(-0.276302\pi\) |
−0.983992 | + | 0.178213i | \(0.942968\pi\) | |||||||
\(572\) | −4.48805 | − | 7.77353i | −0.187655 | − | 0.325027i | ||||
\(573\) | −17.7858 | − | 15.9769i | −0.743014 | − | 0.667445i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.3008i | 1.51385i | ||||||||
\(576\) | −2.00144 | − | 0.885511i | −0.0833934 | − | 0.0368963i | ||||
\(577\) | − | 12.1708i | − | 0.506679i | −0.967377 | − | 0.253339i | \(-0.918471\pi\) | ||
0.967377 | − | 0.253339i | \(-0.0815290\pi\) | |||||||
\(578\) | 8.77258 | + | 5.06485i | 0.364891 | + | 0.210670i | ||||
\(579\) | −11.3218 | − | 34.7072i | −0.470519 | − | 1.44238i | ||||
\(580\) | −0.155548 | + | 0.0898059i | −0.00645879 | + | 0.00372899i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.79178 | − | 8.55824i | −0.115723 | − | 0.354750i | ||||
\(583\) | 5.92897 | − | 10.2693i | 0.245553 | − | 0.425310i | ||||
\(584\) | −25.7659 | −1.06620 | ||||||||
\(585\) | −0.282051 | − | 0.386312i | −0.0116614 | − | 0.0159720i | ||||
\(586\) | − | 15.1727i | − | 0.626777i | ||||||
\(587\) | −16.8761 | + | 29.2302i | −0.696550 | + | 1.20646i | 0.273106 | + | 0.961984i | \(0.411949\pi\) |
−0.969655 | + | 0.244476i | \(0.921384\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.47207 | − | 6.01380i | −0.143064 | − | 0.247794i | ||||
\(590\) | 0.0980610 | − | 0.0566155i | 0.00403711 | − | 0.00233082i | ||||
\(591\) | −5.43219 | + | 25.7038i | −0.223451 | + | 1.05731i | ||||
\(592\) | 1.91259 | − | 3.31270i | 0.0786069 | − | 0.136151i | ||||
\(593\) | −18.3025 | −0.751592 | −0.375796 | − | 0.926702i | \(-0.622631\pi\) | ||||
−0.375796 | + | 0.926702i | \(0.622631\pi\) | |||||||
\(594\) | −0.356569 | + | 3.51064i | −0.0146302 | + | 0.144043i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 21.4799 | + | 12.4015i | 0.879853 | + | 0.507983i | ||||
\(597\) | −3.46936 | + | 16.4162i | −0.141992 | + | 0.671870i | ||||
\(598\) | 23.5320 | − | 13.5862i | 0.962296 | − | 0.555582i | ||||
\(599\) | −34.1905 | + | 19.7399i | −1.39699 | + | 0.806551i | −0.994076 | − | 0.108689i | \(-0.965335\pi\) |
−0.402911 | + | 0.915239i | \(0.632002\pi\) | |||||||
\(600\) | 15.2281 | + | 13.6793i | 0.621683 | + | 0.558454i | ||||
\(601\) | −34.4865 | − | 19.9108i | −1.40673 | − | 0.812177i | −0.411661 | − | 0.911337i | \(-0.635051\pi\) |
−0.995072 | + | 0.0991600i | \(0.968384\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.09652 | − | 38.1202i | −0.166823 | − | 1.55237i | ||||
\(604\) | 5.39339 | 0.219454 | ||||||||
\(605\) | 0.140882 | − | 0.244015i | 0.00572766 | − | 0.00992060i | ||||
\(606\) | 0.496448 | − | 0.161946i | 0.0201668 | − | 0.00657861i | ||||
\(607\) | −21.6104 | + | 12.4768i | −0.877140 | + | 0.506417i | −0.869714 | − | 0.493555i | \(-0.835697\pi\) |
−0.00742570 | + | 0.999972i | \(0.502364\pi\) | |||||||
\(608\) | 6.02264 | + | 10.4315i | 0.244250 | + | 0.423054i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.0222776 | + | 0.0385859i | −0.000901992 | + | 0.00156230i | ||||
\(611\) | 61.2883i | 2.47946i | ||||||||
\(612\) | 2.83733 | + | 26.4028i | 0.114692 | + | 1.06727i | ||||
\(613\) | 28.0570 | 1.13321 | 0.566605 | − | 0.823990i | \(-0.308257\pi\) | ||||
0.566605 | + | 0.823990i | \(0.308257\pi\) | |||||||
\(614\) | 6.18876 | − | 10.7192i | 0.249758 | − | 0.432594i | ||||
\(615\) | 0.231204 | − | 0.257381i | 0.00932305 | − | 0.0103786i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.8093 | − | 17.2104i | 1.20008 | − | 0.692865i | 0.239506 | − | 0.970895i | \(-0.423015\pi\) |
0.960573 | + | 0.278030i | \(0.0896813\pi\) | |||||||
\(618\) | −5.95757 | − | 1.25906i | −0.239648 | − | 0.0506468i | ||||
\(619\) | −17.2889 | − | 9.98173i | −0.694898 | − | 0.401200i | 0.110546 | − | 0.993871i | \(-0.464740\pi\) |
−0.805444 | + | 0.592671i | \(0.798073\pi\) | |||||||
\(620\) | − | 0.146391i | − | 0.00587920i | ||||||
\(621\) | 37.5378 | + | 3.81265i | 1.50634 | + | 0.152996i | ||||
\(622\) | 13.6510i | 0.547354i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.12097 | + | 14.7677i | −0.124939 | + | 0.591181i | ||||
\(625\) | −12.4940 | − | 21.6402i | −0.499760 | − | 0.865609i | ||||
\(626\) | 0.239503 | + | 0.414831i | 0.00957245 | + | 0.0165800i | ||||
\(627\) | 2.47626 | − | 2.75662i | 0.0988921 | − | 0.110089i | ||||
\(628\) | 22.0690 | + | 12.7416i | 0.880650 | + | 0.508443i | ||||
\(629\) | 14.0417 | 0.559878 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −46.8447 | −1.86486 | −0.932429 | − | 0.361354i | \(-0.882314\pi\) | ||||
−0.932429 | + | 0.361354i | \(0.882314\pi\) | |||||||
\(632\) | −31.9389 | − | 18.4399i | −1.27046 | − | 0.733501i | ||||
\(633\) | 7.58399 | + | 23.2488i | 0.301437 | + | 0.924058i | ||||
\(634\) | −7.28384 | − | 12.6160i | −0.289278 | − | 0.501044i | ||||
\(635\) | 0.0618862 | + | 0.107190i | 0.00245588 | + | 0.00425370i | ||||
\(636\) | −29.7718 | + | 9.71185i | −1.18053 | + | 0.385100i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.76475i | 0.109458i | ||||||||
\(639\) | −9.63058 | + | 21.7671i | −0.380980 | + | 0.861094i | ||||
\(640\) | 0.312103i | 0.0123370i | ||||||||
\(641\) | −3.34281 | − | 1.92997i | −0.132033 | − | 0.0762293i | 0.432529 | − | 0.901620i | \(-0.357621\pi\) |
−0.564562 | + | 0.825391i | \(0.690955\pi\) | |||||||
\(642\) | −6.97205 | + | 7.76143i | −0.275165 | + | 0.306319i | ||||
\(643\) | −31.0233 | + | 17.9113i | −1.22344 | + | 0.706352i | −0.965649 | − | 0.259849i | \(-0.916327\pi\) |
−0.257789 | + | 0.966201i | \(0.582994\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.111272 | + | 0.0235160i | 0.00438133 | + | 0.000925941i | ||||
\(646\) | −3.94734 | + | 6.83699i | −0.155306 | + | 0.268998i | ||||
\(647\) | −43.6492 | −1.71603 | −0.858013 | − | 0.513627i | \(-0.828301\pi\) | ||||
−0.858013 | + | 0.513627i | \(0.828301\pi\) | |||||||
\(648\) | 15.7448 | − | 14.3103i | 0.618515 | − | 0.562160i | ||||
\(649\) | 6.15642i | 0.241661i | ||||||||
\(650\) | −9.35369 | + | 16.2011i | −0.366882 | + | 0.635458i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.07072 | − | 13.9789i | −0.316074 | − | 0.547456i | ||||
\(653\) | 6.45191 | − | 3.72501i | 0.252483 | − | 0.145771i | −0.368418 | − | 0.929660i | \(-0.620100\pi\) |
0.620901 | + | 0.783889i | \(0.286767\pi\) | |||||||
\(654\) | −4.04891 | − | 3.63711i | −0.158325 | − | 0.142222i | ||||
\(655\) | −0.0360114 | + | 0.0623736i | −0.00140708 | + | 0.00243714i | ||||
\(656\) | −10.9177 | −0.426264 | ||||||||
\(657\) | 13.2295 | − | 29.9014i | 0.516131 | − | 1.16656i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.52607 | − | 4.34518i | −0.293174 | − | 0.169264i | 0.346198 | − | 0.938161i | \(-0.387472\pi\) |
−0.639372 | + | 0.768897i | \(0.720806\pi\) | |||||||
\(660\) | 0.0742652 | − | 0.0242260i | 0.00289077 | − | 0.000942997i | ||||
\(661\) | −24.9853 | + | 14.4253i | −0.971815 | + | 0.561077i | −0.899789 | − | 0.436325i | \(-0.856280\pi\) |
−0.0720256 | + | 0.997403i | \(0.522946\pi\) | |||||||
\(662\) | −12.4653 | + | 7.19686i | −0.484479 | + | 0.279714i | ||||
\(663\) | −52.6756 | + | 17.1833i | −2.04575 | + | 0.667343i | ||||
\(664\) | −12.5871 | − | 7.26719i | −0.488476 | − | 0.282022i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.90573 | − | 3.97984i | −0.112595 | − | 0.154216i | ||||
\(667\) | 29.5623 | 1.14466 | ||||||||
\(668\) | −4.58724 | + | 7.94534i | −0.177486 | + | 0.307414i | ||||
\(669\) | 3.85021 | + | 3.45862i | 0.148858 | + | 0.133718i | ||||
\(670\) | 0.208097 | − | 0.120145i | 0.00803950 | − | 0.00464161i | ||||
\(671\) | −1.21124 | − | 2.09793i | −0.0467594 | − | 0.0809897i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.60695 | + | 6.24742i | −0.139038 | + | 0.240820i | −0.927133 | − | 0.374733i | \(-0.877734\pi\) |
0.788095 | + | 0.615554i | \(0.211068\pi\) | |||||||
\(674\) | 16.8007i | 0.647139i | ||||||||
\(675\) | −23.6937 | + | 10.6486i | −0.911971 | + | 0.409865i | ||||
\(676\) | −29.1982 | −1.12301 | ||||||||
\(677\) | −18.1911 | + | 31.5079i | −0.699140 | + | 1.21095i | 0.269626 | + | 0.962965i | \(0.413100\pi\) |
−0.968765 | + | 0.247980i | \(0.920233\pi\) | |||||||
\(678\) | 10.6734 | + | 2.25570i | 0.409911 | + | 0.0866297i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.329070 | + | 0.189989i | −0.0126193 | + | 0.00728573i | ||||
\(681\) | 33.3041 | − | 37.0749i | 1.27622 | − | 1.42071i | ||||
\(682\) | −1.95149 | − | 1.12669i | −0.0747265 | − | 0.0431433i | ||||
\(683\) | 23.7326i | 0.908101i | 0.890976 | + | 0.454050i | \(0.150021\pi\) | ||||
−0.890976 | + | 0.454050i | \(0.849979\pi\) | |||||||
\(684\) | −9.72991 | + | 1.04561i | −0.372033 | + | 0.0399798i | ||||
\(685\) | − | 0.321118i | − | 0.0122693i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.5913 | − | 4.75982i | 0.556693 | − | 0.181599i | ||||
\(688\) | −1.79443 | − | 3.10804i | −0.0684119 | − | 0.118493i | ||||
\(689\) | −32.6707 | − | 56.5874i | −1.24466 | − | 2.15581i | ||||
\(690\) | 0.0733370 | + | 0.224816i | 0.00279189 | + | 0.00855859i | ||||
\(691\) | 2.86127 | + | 1.65195i | 0.108848 | + | 0.0628433i | 0.553436 | − | 0.832892i | \(-0.313316\pi\) |
−0.444588 | + | 0.895735i | \(0.646650\pi\) | |||||||
\(692\) | −7.58393 | −0.288298 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.77718 | −0.143380 | ||||||||
\(695\) | 0.0862962 | + | 0.0498231i | 0.00327340 | + | 0.00188990i | ||||
\(696\) | 11.1400 | − | 12.4013i | 0.422261 | − | 0.470070i | ||||
\(697\) | −20.0386 | − | 34.7079i | −0.759016 | − | 1.31465i | ||||
\(698\) | 3.71417 | + | 6.43313i | 0.140583 | + | 0.243498i | ||||
\(699\) | −4.62292 | + | 21.8746i | −0.174855 | + | 0.827371i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 0.873603i | − | 0.0329955i | −0.999864 | − | 0.0164978i | \(-0.994748\pi\) | ||
0.999864 | − | 0.0164978i | \(-0.00525164\pi\) | |||||||
\(702\) | 15.7707 | + | 11.3740i | 0.595228 | + | 0.429285i | ||||
\(703\) | 5.17461i | 0.195164i | ||||||||
\(704\) | 0.645868 | + | 0.372892i | 0.0243421 | + | 0.0140539i | ||||
\(705\) | −0.521850 | − | 0.110287i | −0.0196540 | − | 0.00415364i | ||||
\(706\) | −8.07845 | + | 4.66410i | −0.304037 | + | 0.175536i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10.8650 | − | 12.0952i | 0.408332 | − | 0.454564i | ||||
\(709\) | −8.07767 | + | 13.9909i | −0.303363 | + | 0.525441i | −0.976896 | − | 0.213717i | \(-0.931443\pi\) |
0.673532 | + | 0.739158i | \(0.264776\pi\) | |||||||
\(710\) | −0.149179 | −0.00559860 | ||||||||
\(711\) | 37.7986 | − | 27.5972i | 1.41756 | − | 1.03498i | ||||
\(712\) | 28.4905i | 1.06773i | ||||||||
\(713\) | −12.0473 | + | 20.8665i | −0.451174 | + | 0.781456i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0814965 | + | 0.141156i | 0.00304779 | + | 0.00527894i | ||||
\(716\) | 0.273546 | − | 0.157932i | 0.0102229 | − | 0.00590220i | ||||
\(717\) | 9.23528 | − | 3.01264i | 0.344898 | − | 0.112509i | ||||
\(718\) | 9.01498 | − | 15.6144i | 0.336436 | − | 0.582724i | ||||
\(719\) | 45.1905 | 1.68532 | 0.842661 | − | 0.538445i | \(-0.180988\pi\) | ||||
0.842661 | + | 0.538445i | \(0.180988\pi\) | |||||||
\(720\) | −0.120126 | − | 0.0531481i | −0.00447683 | − | 0.00198071i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 8.41110 | + | 4.85615i | 0.313029 | + | 0.180727i | ||||
\(723\) | 14.1566 | + | 12.7168i | 0.526490 | + | 0.472943i | ||||
\(724\) | 8.45395 | − | 4.88089i | 0.314189 | − | 0.181397i | ||||
\(725\) | −17.6260 | + | 10.1764i | −0.654613 | + | 0.377941i | ||||
\(726\) | −2.36837 | + | 11.2066i | −0.0878986 | + | 0.415915i | ||||
\(727\) | 7.15775 | + | 4.13253i | 0.265466 | + | 0.153267i | 0.626826 | − | 0.779160i | \(-0.284354\pi\) |
−0.361359 | + | 0.932427i | \(0.617687\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.52294 | + | 25.6195i | 0.315664 | + | 0.948871i | ||||
\(730\) | 0.204927 | 0.00758468 | ||||||||
\(731\) | 6.58709 | − | 11.4092i | 0.243632 | − | 0.421983i | ||||
\(732\) | −1.32283 | + | 6.25931i | −0.0488932 | + | 0.231351i | ||||
\(733\) | 10.5799 | − | 6.10830i | 0.390777 | − | 0.225615i | −0.291720 | − | 0.956504i | \(-0.594227\pi\) |
0.682497 | + | 0.730889i | \(0.260894\pi\) | |||||||
\(734\) | −2.28543 | − | 3.95849i | −0.0843569 | − | 0.146110i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.8972 | − | 36.1949i | 0.770280 | − | 1.33416i | ||||
\(737\) | 13.0647i | 0.481244i | ||||||||
\(738\) | −5.69056 | + | 12.8619i | −0.209472 | + | 0.473452i | ||||
\(739\) | −20.7072 | −0.761726 | −0.380863 | − | 0.924631i | \(-0.624373\pi\) | ||||
−0.380863 | + | 0.924631i | \(0.624373\pi\) | |||||||
\(740\) | −0.0545436 | + | 0.0944723i | −0.00200506 | + | 0.00347287i | ||||
\(741\) | −6.33235 | − | 19.4119i | −0.232625 | − | 0.713115i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.2862 | − | 5.93873i | 0.377363 | − | 0.217871i | −0.299307 | − | 0.954157i | \(-0.596756\pi\) |
0.676670 | + | 0.736286i | \(0.263422\pi\) | |||||||
\(744\) | 4.21362 | + | 12.9169i | 0.154479 | + | 0.473557i | ||||
\(745\) | −0.390045 | − | 0.225192i | −0.0142901 | − | 0.00825041i | ||||
\(746\) | 0.164647i | 0.00602814i | ||||||||
\(747\) | 14.8964 | − | 10.8761i | 0.545033 | − | 0.397935i | ||||
\(748\) | − | 9.04885i | − | 0.330859i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.242250 | − | 0.217612i | −0.00884571 | − | 0.00794606i | ||||
\(751\) | −11.8554 | − | 20.5342i | −0.432610 | − | 0.749303i | 0.564487 | − | 0.825442i | \(-0.309074\pi\) |
−0.997097 | + | 0.0761390i | \(0.975741\pi\) | |||||||
\(752\) | 8.41562 | + | 14.5763i | 0.306886 | + | 0.531542i | ||||
\(753\) | 41.0506 | + | 8.67555i | 1.49597 | + | 0.316154i | ||||
\(754\) | 13.1937 | + | 7.61738i | 0.480486 | + | 0.277409i | ||||
\(755\) | −0.0979362 | −0.00356426 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.2494 | 1.60827 | 0.804136 | − | 0.594446i | \(-0.202628\pi\) | ||||
0.804136 | + | 0.594446i | \(0.202628\pi\) | |||||||
\(758\) | −5.13087 | − | 2.96231i | −0.186362 | − | 0.107596i | ||||
\(759\) | −12.5794 | − | 2.65850i | −0.456603 | − | 0.0964975i | ||||
\(760\) | −0.0700143 | − | 0.121268i | −0.00253969 | − | 0.00439887i | ||||
\(761\) | −24.3767 | − | 42.2217i | −0.883656 | − | 1.53054i | −0.847246 | − | 0.531200i | \(-0.821741\pi\) |
−0.0364098 | − | 0.999337i | \(-0.511592\pi\) | |||||||
\(762\) | −3.74308 | − | 3.36238i | −0.135597 | − | 0.121806i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 21.5154i | − | 0.778401i | ||||||
\(765\) | −0.0515217 | − | 0.479436i | −0.00186277 | − | 0.0173341i | ||||
\(766\) | − | 0.217284i | − | 0.00785081i | ||||||
\(767\) | 29.3791 | + | 16.9620i | 1.06082 | + | 0.612463i | ||||
\(768\) | −4.71845 | − | 14.4645i | −0.170262 | − | 0.521942i | ||||
\(769\) | −23.3870 | + | 13.5025i | −0.843357 | + | 0.486912i | −0.858404 | − | 0.512975i | \(-0.828543\pi\) |
0.0150472 | + | 0.999887i | \(0.495210\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.51989 | − | 29.1834i | −0.342851 | − | 1.05101i | ||||
\(772\) | 16.4268 | − | 28.4520i | 0.591213 | − | 1.02401i | ||||
\(773\) | 26.7135 | 0.960817 | 0.480408 | − | 0.877045i | \(-0.340488\pi\) | ||||
0.480408 | + | 0.877045i | \(0.340488\pi\) | |||||||
\(774\) | −4.59681 | + | 0.493988i | −0.165229 | + | 0.0177560i | ||||
\(775\) | − | 16.5883i | − | 0.595871i | ||||||
\(776\) | 9.24794 | − | 16.0179i | 0.331982 | − | 0.575009i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.19514 | − | 3.80209i | −0.0786994 | − | 0.136311i | ||||
\(779\) | 12.7905 | − | 7.38459i | 0.458267 | − | 0.264580i | ||||
\(780\) | 0.0890046 | − | 0.421148i | 0.00318688 | − | 0.0150795i | ||||
\(781\) | 4.05547 | − | 7.02429i | 0.145116 | − | 0.251349i | ||||
\(782\) | 27.3927 | 0.979560 | ||||||||
\(783\) | 8.67191 | + | 19.2955i | 0.309909 | + | 0.689564i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.400742 | − | 0.231368i | −0.0143031 | − | 0.00825789i | ||||
\(786\) | 0.605391 | − | 2.86456i | 0.0215936 | − | 0.102176i | ||||
\(787\) | 41.0093 | − | 23.6767i | 1.46182 | − | 0.843983i | 0.462726 | − | 0.886501i | \(-0.346871\pi\) |
0.999096 | + | 0.0425177i | \(0.0135379\pi\) | |||||||
\(788\) | −20.4749 | + | 11.8212i | −0.729388 | + | 0.421112i | ||||
\(789\) | −3.73497 | − | 3.35510i | −0.132968 | − | 0.119445i | ||||
\(790\) | 0.254023 | + | 0.146660i | 0.00903775 | + | 0.00521795i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.85554 | + | 4.27520i | −0.208068 | + | 0.151913i | ||||
\(793\) | −13.3487 | −0.474027 | ||||||||
\(794\) | −2.49462 | + | 4.32082i | −0.0885309 | + | 0.153340i | ||||
\(795\) | 0.540613 | − | 0.176353i | 0.0191736 | − | 0.00625461i | ||||
\(796\) | −13.0766 | + | 7.54980i | −0.463489 | + | 0.267596i | ||||
\(797\) | 4.42781 | + | 7.66919i | 0.156841 | + | 0.271657i | 0.933728 | − | 0.357984i | \(-0.116536\pi\) |
−0.776887 | + | 0.629640i | \(0.783202\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.8925 | + | 53.5074i | −1.09290 | + | 1.89296i | ||||
\(800\) | 28.7741i | 1.01732i | ||||||||
\(801\) | −33.0634 | − | 14.6284i | −1.16824 | − | 0.516871i | ||||
\(802\) | −4.20808 | −0.148592 | ||||||||
\(803\) | −5.57098 | + | 9.64922i | −0.196596 | + | 0.340514i | ||||
\(804\) | 23.0569 | − | 25.6674i | 0.813154 | − | 0.905220i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.7534 | + | 6.20848i | −0.378772 | + | 0.218684i | ||||
\(807\) | −37.1017 | − | 7.84099i | −1.30604 | − | 0.276016i | ||||
\(808\) | 0.929170 | + | 0.536456i | 0.0326881 | + | 0.0188725i | ||||
\(809\) | 7.40014i | 0.260175i | 0.991503 | + | 0.130087i | \(0.0415258\pi\) | ||||
−0.991503 | + | 0.130087i | \(0.958474\pi\) | |||||||
\(810\) | −0.125225 | + | 0.113816i | −0.00439997 | + | 0.00399907i | ||||
\(811\) | − | 25.0843i | − | 0.880829i | −0.897794 | − | 0.440415i | \(-0.854831\pi\) | ||
0.897794 | − | 0.440415i | \(-0.145169\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.21732 | − | 15.2236i | 0.112836 | − | 0.533914i | ||||
\(814\) | 0.839587 | + | 1.45421i | 0.0294275 | + | 0.0509699i | ||||
\(815\) | 0.146553 | + | 0.253836i | 0.00513351 | + | 0.00889150i | ||||
\(816\) | −10.1684 | + | 11.3197i | −0.355967 | + | 0.396269i | ||||
\(817\) | 4.20449 | + | 2.42746i | 0.147096 | + | 0.0849262i | ||||
\(818\) | 22.2483 | 0.777893 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.311353 | 0.0108729 | ||||||||
\(821\) | 18.3781 | + | 10.6106i | 0.641401 | + | 0.370313i | 0.785154 | − | 0.619300i | \(-0.212584\pi\) |
−0.143753 | + | 0.989614i | \(0.545917\pi\) | |||||||
\(822\) | 4.04836 | + | 12.4103i | 0.141203 | + | 0.432859i | ||||
\(823\) | −8.47690 | − | 14.6824i | −0.295486 | − | 0.511797i | 0.679612 | − | 0.733572i | \(-0.262148\pi\) |
−0.975098 | + | 0.221775i | \(0.928815\pi\) | |||||||
\(824\) | −6.25546 | − | 10.8348i | −0.217919 | − | 0.377447i | ||||
\(825\) | 8.41538 | − | 2.74518i | 0.292986 | − | 0.0955749i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.3052i | 0.879949i | 0.898010 | + | 0.439975i | \(0.145013\pi\) | ||||
−0.898010 | + | 0.439975i | \(0.854987\pi\) | |||||||
\(828\) | 20.0222 | + | 27.4235i | 0.695820 | + | 0.953031i | ||||
\(829\) | − | 41.5277i | − | 1.44232i | −0.692770 | − | 0.721158i | \(-0.743610\pi\) | ||
0.692770 | − | 0.721158i | \(-0.256390\pi\) | |||||||
\(830\) | 0.100111 | + | 0.0577990i | 0.00347490 | + | 0.00200623i | ||||
\(831\) | 18.4058 | − | 20.4897i | 0.638491 | − | 0.710781i | ||||
\(832\) | 3.55896 | − | 2.05477i | 0.123385 | − | 0.0712362i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.96323 | − | 0.837580i | −0.137235 | − | 0.0290030i | ||||
\(835\) | 0.0832977 | − | 0.144276i | 0.00288264 | − | 0.00499287i | ||||
\(836\) | 3.33467 | 0.115332 | ||||||||
\(837\) | −17.1536 | − | 1.74226i | −0.592916 | − | 0.0602213i | ||||
\(838\) | − | 1.19103i | − | 0.0411434i | ||||||
\(839\) | −6.61780 | + | 11.4624i | −0.228472 | + | 0.395725i | −0.957355 | − | 0.288913i | \(-0.906706\pi\) |
0.728884 | + | 0.684638i | \(0.240040\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.21265 | − | 10.7606i | −0.214229 | − | 0.371056i | ||||
\(842\) | 2.18914 | − | 1.26390i | 0.0754428 | − | 0.0435569i | ||||
\(843\) | 6.70014 | + | 6.01870i | 0.230765 | + | 0.207295i | ||||
\(844\) | −11.0036 | + | 19.0588i | −0.378759 | + | 0.656030i | ||||
\(845\) | 0.530197 | 0.0182393 | ||||||||
\(846\) | 21.5584 | − | 2.31673i | 0.741193 | − | 0.0796509i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −15.5403 | − | 8.97217i | −0.533654 | − | 0.308106i | ||||
\(849\) | 30.9141 | − | 10.0845i | 1.06097 | − | 0.346098i | ||||
\(850\) | −16.3324 | + | 9.42951i | −0.560196 | + | 0.323429i | ||||
\(851\) | 15.5492 | − | 8.97735i | 0.533020 | − | 0.307739i | ||||
\(852\) | −20.3642 | + | 6.64300i | −0.697666 | + | 0.227585i | ||||
\(853\) | 15.3814 | + | 8.88048i | 0.526651 | + | 0.304062i | 0.739651 | − | 0.672990i | \(-0.234990\pi\) |
−0.213001 | + | 0.977052i | \(0.568324\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.176681 | − | 0.0189867i | 0.00604237 | − | 0.000649332i | ||||
\(856\) | −21.4360 | −0.732669 | ||||||||
\(857\) | −9.17157 | + | 15.8856i | −0.313295 | + | 0.542643i | −0.979074 | − | 0.203507i | \(-0.934766\pi\) |
0.665779 | + | 0.746149i | \(0.268100\pi\) | |||||||
\(858\) | −4.92917 | − | 4.42785i | −0.168279 | − | 0.151164i | ||||
\(859\) | 2.69126 | − | 1.55380i | 0.0918246 | − | 0.0530150i | −0.453385 | − | 0.891315i | \(-0.649784\pi\) |
0.545209 | + | 0.838300i | \(0.316450\pi\) | |||||||
\(860\) | 0.0511739 | + | 0.0886358i | 0.00174502 | + | 0.00302246i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.441616 | + | 0.764902i | −0.0150415 | + | 0.0260527i | ||||
\(863\) | − | 41.4060i | − | 1.40948i | −0.709467 | − | 0.704739i | \(-0.751064\pi\) | ||
0.709467 | − | 0.704739i | \(-0.248936\pi\) | |||||||
\(864\) | 29.7546 | + | 3.02212i | 1.01227 | + | 0.102815i | ||||
\(865\) | 0.137713 | 0.00468239 | ||||||||
\(866\) | −12.4321 | + | 21.5330i | −0.422458 | + | 0.731720i | ||||
\(867\) | −25.8409 | − | 5.46115i | −0.877602 | − | 0.185471i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.8114 | + | 7.97399i | −0.468518 | + | 0.270499i | ||||
\(870\) | −0.0886013 | + | 0.0986328i | −0.00300386 | + | 0.00334396i | ||||
\(871\) | 62.3460 | + | 35.9955i | 2.11251 | + | 1.21966i | ||||
\(872\) | − | 11.1826i | − | 0.378689i | ||||||
\(873\) | 13.8405 | + | 18.9566i | 0.468429 | + | 0.641585i | ||||
\(874\) | 10.0947i | 0.341459i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 27.9742 | − | 9.12545i | 0.945161 | − | 0.308320i | ||||
\(877\) | 11.3979 | + | 19.7417i | 0.384878 | + | 0.666628i | 0.991752 | − | 0.128170i | \(-0.0409102\pi\) |
−0.606874 | + | 0.794798i | \(0.707577\pi\) | |||||||
\(878\) | 7.88482 | + | 13.6569i | 0.266100 | + | 0.460898i | ||||
\(879\) | 12.2687 | + | 37.6099i | 0.413813 | + | 1.26855i | ||||
\(880\) | 0.0387648 | + | 0.0223809i | 0.00130676 | + | 0.000754460i | ||||
\(881\) | 43.4050 | 1.46235 | 0.731175 | − | 0.682190i | \(-0.238972\pi\) | ||||
0.731175 | + | 0.682190i | \(0.238972\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.9309 | −1.00725 | −0.503627 | − | 0.863921i | \(-0.668001\pi\) | ||||
−0.503627 | + | 0.863921i | \(0.668001\pi\) | |||||||
\(884\) | −43.1820 | − | 24.9312i | −1.45237 | − | 0.838526i | ||||
\(885\) | −0.197293 | + | 0.219631i | −0.00663193 | + | 0.00738281i | ||||
\(886\) | 3.73682 | + | 6.47236i | 0.125541 | + | 0.217443i | ||||
\(887\) | −19.4788 | − | 33.7382i | −0.654033 | − | 1.13282i | −0.982135 | − | 0.188176i | \(-0.939742\pi\) |
0.328102 | − | 0.944642i | \(-0.393591\pi\) | |||||||
\(888\) | 2.09347 | − | 9.90579i | 0.0702522 | − | 0.332417i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 0.226597i | − | 0.00759556i | ||||||
\(891\) | −1.95486 | − | 8.99048i | −0.0654904 | − | 0.301192i | ||||
\(892\) | 4.65757i | 0.155947i | ||||||||
\(893\) | −19.7185 | − | 11.3845i | −0.659853 | − | 0.380966i | ||||
\(894\) | 17.9131 | + | 3.78572i | 0.599105 | + | 0.126614i | ||||
\(895\) | −0.00496721 | + | 0.00286782i | −0.000166035 | + | 9.58606e-5i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −47.3451 | + | 52.7055i | −1.58081 | + | 1.75979i | ||||
\(898\) | 4.78138 | − | 8.28160i | 0.159557 | − | 0.276361i | ||||
\(899\) | −13.5091 | −0.450553 | ||||||||
\(900\) | −21.3780 | − | 9.45840i | −0.712599 | − | 0.315280i | ||||
\(901\) | − | 65.8711i | − | 2.19448i | ||||||
\(902\) | 2.39632 | − | 4.15054i | 0.0797886 | − | 0.138198i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.2071 | + | 19.4113i | 0.372743 | + | 0.645611i | ||||
\(905\) | −0.153512 | + | 0.0886299i | −0.00510290 | + | 0.00294616i | ||||
\(906\) | 3.78496 | − | 1.23469i | 0.125747 | − | 0.0410198i | ||||
\(907\) | 14.0526 | − | 24.3399i | 0.466610 | − | 0.808192i | −0.532663 | − | 0.846328i | \(-0.678809\pi\) |
0.999273 | + | 0.0381355i | \(0.0121419\pi\) | |||||||
\(908\) | 44.8493 | 1.48837 | ||||||||
\(909\) | −1.09964 | + | 0.802861i | −0.0364728 | + | 0.0266292i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.3883 | + | 18.6994i | 1.07307 | + | 0.619538i | 0.929019 | − | 0.370032i | \(-0.120653\pi\) |
0.144052 | + | 0.989570i | \(0.453987\pi\) | |||||||
\(912\) | −4.17152 | − | 3.74726i | −0.138133 | − | 0.124084i | ||||
\(913\) | −5.44307 | + | 3.14256i | −0.180139 | + | 0.104003i | ||||
\(914\) | 11.8666 | − | 6.85121i | 0.392513 | − | 0.226618i | ||||
\(915\) | 0.0240207 | − | 0.113660i | 0.000794100 | − | 0.00375749i | ||||
\(916\) | 11.9616 | + | 6.90601i | 0.395221 | + | 0.228181i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 8.03546 | + | 17.8793i | 0.265210 | + | 0.590105i | ||||
\(919\) | −25.8230 | −0.851822 | −0.425911 | − | 0.904765i | \(-0.640046\pi\) | ||||
−0.425911 | + | 0.904765i | \(0.640046\pi\) | |||||||
\(920\) | −0.242933 | + | 0.420773i | −0.00800928 | + | 0.0138725i | ||||
\(921\) | −6.67300 | + | 31.5750i | −0.219883 | + | 1.04043i | ||||
\(922\) | 0.957884 | − | 0.553034i | 0.0315462 | − | 0.0182132i | ||||
\(923\) | −22.3471 | − | 38.7063i | −0.735563 | − | 1.27403i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.18063 | + | 10.7052i | −0.203218 | + | 0.351983i | ||||
\(926\) | 0.802704i | 0.0263785i | ||||||||
\(927\) | 15.7856 | − | 1.69637i | 0.518469 | − | 0.0557162i | ||||
\(928\) | 23.4328 | 0.769220 | ||||||||
\(929\) | −7.97094 | + | 13.8061i | −0.261518 | + | 0.452963i | −0.966646 | − | 0.256118i | \(-0.917556\pi\) |
0.705127 | + | 0.709081i | \(0.250890\pi\) | |||||||
\(930\) | −0.0335127 | − | 0.102734i | −0.00109893 | − | 0.00336877i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −17.4246 | + | 10.0601i | −0.570762 | + | 0.329529i | ||||
\(933\) | −11.0382 | − | 33.8379i | −0.361376 | − | 1.10780i | ||||
\(934\) | 5.31568 | + | 3.06901i | 0.173934 | + | 0.100421i | ||||
\(935\) | 0.164314i | 0.00537364i | ||||||||
\(936\) | 4.26867 | + | 39.7222i | 0.139526 | + | 1.29836i | ||||
\(937\) | 15.0698i | 0.492308i | 0.969231 | + | 0.246154i | \(0.0791668\pi\) | ||||
−0.969231 | + | 0.246154i | \(0.920833\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.929112 | − | 0.834616i | −0.0303204 | − | 0.0272367i | ||||
\(940\) | −0.239999 | − | 0.415690i | −0.00782789 | − | 0.0135583i | ||||
\(941\) | −5.76861 | − | 9.99152i | −0.188051 | − | 0.325714i | 0.756549 | − | 0.653937i | \(-0.226884\pi\) |
−0.944600 | + | 0.328222i | \(0.893550\pi\) | |||||||
\(942\) | 18.4044 | + | 3.88955i | 0.599648 | + | 0.126728i | ||||
\(943\) | −44.3800 | − | 25.6228i | −1.44521 | − | 0.834393i | ||||
\(944\) | 9.31636 | 0.303222 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.57543 | 0.0512218 | ||||||||
\(947\) | −24.5364 | − | 14.1661i | −0.797325 | − | 0.460336i | 0.0452102 | − | 0.998977i | \(-0.485604\pi\) |
−0.842535 | + | 0.538642i | \(0.818938\pi\) | |||||||
\(948\) | 41.2071 | + | 8.70862i | 1.33834 | + | 0.282843i | ||||
\(949\) | 30.6981 | + | 53.1706i | 0.996501 | + | 1.72599i | ||||
\(950\) | −3.47495 | − | 6.01879i | −0.112742 | − | 0.195275i | ||||
\(951\) | 28.2565 | + | 25.3826i | 0.916278 | + | 0.823088i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 29.8498i | − | 0.966931i | −0.875364 | − | 0.483465i | \(-0.839378\pi\) | ||
0.875364 | − | 0.483465i | \(-0.160622\pi\) | |||||||
\(954\) | −18.6699 | + | 13.6311i | −0.604459 | + | 0.441323i | ||||
\(955\) | 0.390689i | 0.0126424i | ||||||||
\(956\) | 7.57084 | + | 4.37102i | 0.244858 | + | 0.141369i | ||||
\(957\) | −2.23559 | − | 6.85325i | −0.0722665 | − | 0.221534i | ||||
\(958\) | 10.0935 | − | 5.82748i | 0.326106 | − | 0.188277i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.0110914 | + | 0.0340009i | 0.000357974 | + | 0.00109737i | ||||
\(961\) | −9.99478 | + | 17.3115i | −0.322412 | + | 0.558434i | ||||
\(962\) | 9.25283 | 0.298323 | ||||||||
\(963\) | 11.0063 | − | 24.8766i | 0.354674 | − | 0.801637i | ||||
\(964\) | 17.1252i | 0.551564i | ||||||||
\(965\) | −0.298287 | + | 0.516648i | −0.00960219 | + | 0.0166315i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.17864 | + | 14.1658i | 0.263007 | + | 0.455542i | 0.967040 | − | 0.254626i | \(-0.0819523\pi\) |
−0.704032 | + | 0.710168i | \(0.748619\pi\) | |||||||
\(968\) | −20.3809 | + | 11.7669i | −0.655068 | + | 0.378203i | ||||
\(969\) | 4.25620 | − | 20.1393i | 0.136729 | − | 0.646968i | ||||
\(970\) | −0.0735528 | + | 0.127397i | −0.00236164 | + | 0.00409048i | ||||
\(971\) | −21.4630 | −0.688779 | −0.344390 | − | 0.938827i | \(-0.611914\pi\) | ||||
−0.344390 | + | 0.938827i | \(0.611914\pi\) | |||||||
\(972\) | −12.0260 | + | 21.1131i | −0.385735 | + | 0.677202i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −24.8470 | − | 14.3454i | −0.796148 | − | 0.459657i | ||||
\(975\) | 10.0856 | − | 47.7225i | 0.322997 | − | 1.52834i | ||||
\(976\) | −3.17475 | + | 1.83294i | −0.101621 | + | 0.0586710i | ||||
\(977\) | −18.6219 | + | 10.7513i | −0.595766 | + | 0.343966i | −0.767374 | − | 0.641199i | \(-0.778437\pi\) |
0.171608 | + | 0.985165i | \(0.445104\pi\) | |||||||
\(978\) | −8.86397 | − | 7.96246i | −0.283439 | − | 0.254611i | ||||
\(979\) | 10.6696 | + | 6.16010i | 0.341002 | + | 0.196878i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.9774 | + | 5.74167i | 0.414336 | + | 0.183318i | ||||
\(982\) | 17.6460 | 0.563107 | ||||||||
\(983\) | 12.7097 | − | 22.0138i | 0.405376 | − | 0.702131i | −0.588989 | − | 0.808141i | \(-0.700474\pi\) |
0.994365 | + | 0.106009i | \(0.0338073\pi\) | |||||||
\(984\) | −27.4725 | + | 8.96178i | −0.875790 | + | 0.285691i | ||||
\(985\) | 0.371794 | − | 0.214656i | 0.0118464 | − | 0.00683949i | ||||
\(986\) | 7.67912 | + | 13.3006i | 0.244553 | + | 0.423578i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.18759 | − | 15.9134i | 0.292296 | − | 0.506272i | ||||
\(989\) | − | 16.8455i | − | 0.535654i | ||||||
\(990\) | 0.0465716 | − | 0.0340025i | 0.00148014 | − | 0.00108067i | ||||
\(991\) | 23.7537 | 0.754560 | 0.377280 | − | 0.926099i | \(-0.376859\pi\) | ||||
0.377280 | + | 0.926099i | \(0.376859\pi\) | |||||||
\(992\) | −9.54935 | + | 16.5400i | −0.303192 | + | 0.525144i | ||||
\(993\) | 25.0795 | − | 27.9191i | 0.795875 | − | 0.885985i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.237453 | − | 0.137093i | 0.00752776 | − | 0.00434615i | ||||
\(996\) | 16.2398 | + | 3.43207i | 0.514576 | + | 0.108749i | ||||
\(997\) | −10.5366 | − | 6.08329i | −0.333697 | − | 0.192660i | 0.323785 | − | 0.946131i | \(-0.395045\pi\) |
−0.657481 | + | 0.753471i | \(0.728378\pi\) | |||||||
\(998\) | − | 3.53086i | − | 0.111767i | ||||||
\(999\) | 10.4208 | + | 7.51560i | 0.329700 | + | 0.237783i |
(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 | 441.2.o.e.146.15 | ✓ | 48 | |
3.2 | odd | 2 | 1323.2.o.e.440.9 | 48 | |||
7.2 | even | 3 | 441.2.i.d.227.10 | 48 | |||
7.3 | odd | 6 | 441.2.s.d.362.9 | 48 | |||
7.4 | even | 3 | 441.2.s.d.362.10 | 48 | |||
7.5 | odd | 6 | 441.2.i.d.227.9 | 48 | |||
7.6 | odd | 2 | inner | 441.2.o.e.146.16 | yes | 48 | |
9.4 | even | 3 | 1323.2.o.e.881.10 | 48 | |||
9.5 | odd | 6 | inner | 441.2.o.e.293.16 | yes | 48 | |
21.2 | odd | 6 | 1323.2.i.d.521.9 | 48 | |||
21.5 | even | 6 | 1323.2.i.d.521.10 | 48 | |||
21.11 | odd | 6 | 1323.2.s.d.656.15 | 48 | |||
21.17 | even | 6 | 1323.2.s.d.656.16 | 48 | |||
21.20 | even | 2 | 1323.2.o.e.440.10 | 48 | |||
63.4 | even | 3 | 1323.2.i.d.1097.10 | 48 | |||
63.5 | even | 6 | 441.2.s.d.374.10 | 48 | |||
63.13 | odd | 6 | 1323.2.o.e.881.9 | 48 | |||
63.23 | odd | 6 | 441.2.s.d.374.9 | 48 | |||
63.31 | odd | 6 | 1323.2.i.d.1097.9 | 48 | |||
63.32 | odd | 6 | 441.2.i.d.68.15 | 48 | |||
63.40 | odd | 6 | 1323.2.s.d.962.15 | 48 | |||
63.41 | even | 6 | inner | 441.2.o.e.293.15 | yes | 48 | |
63.58 | even | 3 | 1323.2.s.d.962.16 | 48 | |||
63.59 | even | 6 | 441.2.i.d.68.16 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.15 | 48 | 63.32 | odd | 6 | |||
441.2.i.d.68.16 | 48 | 63.59 | even | 6 | |||
441.2.i.d.227.9 | 48 | 7.5 | odd | 6 | |||
441.2.i.d.227.10 | 48 | 7.2 | even | 3 | |||
441.2.o.e.146.15 | ✓ | 48 | 1.1 | even | 1 | trivial | |
441.2.o.e.146.16 | yes | 48 | 7.6 | odd | 2 | inner | |
441.2.o.e.293.15 | yes | 48 | 63.41 | even | 6 | inner | |
441.2.o.e.293.16 | yes | 48 | 9.5 | odd | 6 | inner | |
441.2.s.d.362.9 | 48 | 7.3 | odd | 6 | |||
441.2.s.d.362.10 | 48 | 7.4 | even | 3 | |||
441.2.s.d.374.9 | 48 | 63.23 | odd | 6 | |||
441.2.s.d.374.10 | 48 | 63.5 | even | 6 | |||
1323.2.i.d.521.9 | 48 | 21.2 | odd | 6 | |||
1323.2.i.d.521.10 | 48 | 21.5 | even | 6 | |||
1323.2.i.d.1097.9 | 48 | 63.31 | odd | 6 | |||
1323.2.i.d.1097.10 | 48 | 63.4 | even | 3 | |||
1323.2.o.e.440.9 | 48 | 3.2 | odd | 2 | |||
1323.2.o.e.440.10 | 48 | 21.20 | even | 2 | |||
1323.2.o.e.881.9 | 48 | 63.13 | odd | 6 | |||
1323.2.o.e.881.10 | 48 | 9.4 | even | 3 | |||
1323.2.s.d.656.15 | 48 | 21.11 | odd | 6 | |||
1323.2.s.d.656.16 | 48 | 21.17 | even | 6 | |||
1323.2.s.d.962.15 | 48 | 63.40 | odd | 6 | |||
1323.2.s.d.962.16 | 48 | 63.58 | even | 3 |