Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,4,Mod(4,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(14))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.e (of order \(7\), 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: | \(2.53708213025\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{7})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{7}]$ |
Embedding invariants
Embedding label | 4.1 | ||
Character | \(\chi\) | \(=\) | 43.4 |
Dual form | 43.4.e.a.11.1 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{7}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.08835 | + | 3.87267i | −1.09190 | + | 1.36920i | −0.168344 | + | 0.985728i | \(0.553842\pi\) |
−0.923554 | + | 0.383468i | \(0.874730\pi\) | |||||||
\(3\) | −0.198541 | − | 0.248963i | −0.0382092 | − | 0.0479129i | 0.762360 | − | 0.647153i | \(-0.224041\pi\) |
−0.800569 | + | 0.599241i | \(0.795469\pi\) | |||||||
\(4\) | −3.67950 | − | 16.1209i | −0.459937 | − | 2.01512i | ||||
\(5\) | −11.1889 | − | 5.38829i | −1.00077 | − | 0.481944i | −0.139568 | − | 0.990213i | \(-0.544571\pi\) |
−0.861198 | + | 0.508269i | \(0.830286\pi\) | |||||||
\(6\) | 1.57731 | 0.107323 | ||||||||
\(7\) | 3.53619 | 0.190936 | 0.0954681 | − | 0.995432i | \(-0.469565\pi\) | ||||
0.0954681 | + | 0.995432i | \(0.469565\pi\) | |||||||
\(8\) | 38.0923 | + | 18.3443i | 1.68346 | + | 0.810710i | ||||
\(9\) | 5.98550 | − | 26.2242i | 0.221685 | − | 0.971266i | ||||
\(10\) | 55.4224 | − | 26.6900i | 1.75261 | − | 0.844012i | ||||
\(11\) | −2.16594 | + | 9.48961i | −0.0593687 | + | 0.260111i | −0.995899 | − | 0.0904764i | \(-0.971161\pi\) |
0.936530 | + | 0.350588i | \(0.114018\pi\) | |||||||
\(12\) | −3.28298 | + | 4.11672i | −0.0789762 | + | 0.0990330i | ||||
\(13\) | −52.4796 | − | 25.2729i | −1.11963 | − | 0.539187i | −0.219854 | − | 0.975533i | \(-0.570558\pi\) |
−0.899779 | + | 0.436346i | \(0.856272\pi\) | |||||||
\(14\) | −10.9210 | + | 13.6945i | −0.208483 | + | 0.261429i | ||||
\(15\) | 0.879973 | + | 3.85541i | 0.0151472 | + | 0.0663643i | ||||
\(16\) | −69.4999 | + | 33.4694i | −1.08594 | + | 0.522960i | ||||
\(17\) | −86.9732 | + | 41.8841i | −1.24083 | + | 0.597552i | −0.935038 | − | 0.354547i | \(-0.884635\pi\) |
−0.305791 | + | 0.952099i | \(0.598921\pi\) | |||||||
\(18\) | 83.0724 | + | 104.169i | 1.08780 | + | 1.36405i | ||||
\(19\) | −29.0416 | − | 127.240i | −0.350663 | − | 1.53636i | −0.775654 | − | 0.631158i | \(-0.782580\pi\) |
0.424991 | − | 0.905198i | \(-0.360277\pi\) | |||||||
\(20\) | −45.6948 | + | 200.202i | −0.510883 | + | 2.23832i | ||||
\(21\) | −0.702078 | − | 0.880378i | −0.00729552 | − | 0.00914830i | ||||
\(22\) | −30.0610 | − | 37.6953i | −0.291319 | − | 0.365303i | ||||
\(23\) | −19.1809 | + | 84.0371i | −0.173891 | + | 0.761867i | 0.810481 | + | 0.585765i | \(0.199206\pi\) |
−0.984372 | + | 0.176102i | \(0.943651\pi\) | |||||||
\(24\) | −2.99584 | − | 13.1256i | −0.0254802 | − | 0.111636i | ||||
\(25\) | 18.2217 | + | 22.8492i | 0.145773 | + | 0.182794i | ||||
\(26\) | 259.949 | − | 125.185i | 1.96078 | − | 0.944261i | ||||
\(27\) | −15.4635 | + | 7.44683i | −0.110221 | + | 0.0530794i | ||||
\(28\) | −13.0114 | − | 57.0066i | −0.0878186 | − | 0.384759i | ||||
\(29\) | 48.6360 | − | 60.9876i | 0.311430 | − | 0.390521i | −0.601341 | − | 0.798993i | \(-0.705367\pi\) |
0.912771 | + | 0.408471i | \(0.133938\pi\) | |||||||
\(30\) | −17.6484 | − | 8.49903i | −0.107405 | − | 0.0517235i | ||||
\(31\) | −64.7237 | + | 81.1609i | −0.374991 | + | 0.470224i | −0.933138 | − | 0.359518i | \(-0.882941\pi\) |
0.558147 | + | 0.829742i | \(0.311512\pi\) | |||||||
\(32\) | 9.76017 | − | 42.7621i | 0.0539178 | − | 0.236229i | ||||
\(33\) | 2.79259 | − | 1.34484i | 0.0147311 | − | 0.00709413i | ||||
\(34\) | 106.401 | − | 466.171i | 0.536693 | − | 2.35140i | ||||
\(35\) | −39.5661 | − | 19.0540i | −0.191082 | − | 0.0920204i | ||||
\(36\) | −444.782 | −2.05918 | ||||||||
\(37\) | 433.942 | 1.92810 | 0.964050 | − | 0.265721i | \(-0.0856100\pi\) | ||||
0.964050 | + | 0.265721i | \(0.0856100\pi\) | |||||||
\(38\) | 582.448 | + | 280.492i | 2.48646 | + | 1.19742i | ||||
\(39\) | 4.12736 | + | 18.0832i | 0.0169463 | + | 0.0742468i | ||||
\(40\) | −327.367 | − | 410.505i | −1.29403 | − | 1.62266i | ||||
\(41\) | −165.335 | + | 207.323i | −0.629778 | + | 0.789717i | −0.989683 | − | 0.143272i | \(-0.954238\pi\) |
0.359905 | + | 0.932989i | \(0.382809\pi\) | |||||||
\(42\) | 5.57768 | 0.0204918 | ||||||||
\(43\) | 41.8303 | + | 278.850i | 0.148350 | + | 0.988935i | ||||
\(44\) | 160.951 | 0.551461 | ||||||||
\(45\) | −208.275 | + | 261.168i | −0.689951 | + | 0.865171i | ||||
\(46\) | −266.211 | − | 333.818i | −0.853275 | − | 1.06997i | ||||
\(47\) | −114.782 | − | 502.893i | −0.356227 | − | 1.56073i | −0.762504 | − | 0.646984i | \(-0.776030\pi\) |
0.406277 | − | 0.913750i | \(-0.366827\pi\) | |||||||
\(48\) | 22.1312 | + | 10.6578i | 0.0665493 | + | 0.0320485i | ||||
\(49\) | −330.495 | −0.963543 | ||||||||
\(50\) | −144.763 | −0.409450 | ||||||||
\(51\) | 27.6953 | + | 13.3374i | 0.0760415 | + | 0.0366197i | ||||
\(52\) | −214.323 | + | 939.012i | −0.571564 | + | 2.50418i | ||||
\(53\) | 128.168 | − | 61.7227i | 0.332175 | − | 0.159967i | −0.260360 | − | 0.965512i | \(-0.583841\pi\) |
0.592535 | + | 0.805544i | \(0.298127\pi\) | |||||||
\(54\) | 18.9176 | − | 82.8836i | 0.0476734 | − | 0.208871i | ||||
\(55\) | 75.3673 | − | 94.5076i | 0.184773 | − | 0.231698i | ||||
\(56\) | 134.701 | + | 64.8688i | 0.321433 | + | 0.154794i | ||||
\(57\) | −25.9119 | + | 32.4925i | −0.0602126 | + | 0.0755042i | ||||
\(58\) | 85.9799 | + | 376.703i | 0.194650 | + | 0.852818i | ||||
\(59\) | 397.521 | − | 191.436i | 0.877167 | − | 0.422421i | 0.0595782 | − | 0.998224i | \(-0.481024\pi\) |
0.817589 | + | 0.575802i | \(0.195310\pi\) | |||||||
\(60\) | 58.9150 | − | 28.3720i | 0.126765 | − | 0.0610468i | ||||
\(61\) | 290.545 | + | 364.332i | 0.609844 | + | 0.764721i | 0.986876 | − | 0.161480i | \(-0.0516266\pi\) |
−0.377032 | + | 0.926200i | \(0.623055\pi\) | |||||||
\(62\) | −114.420 | − | 501.307i | −0.234377 | − | 1.02687i | ||||
\(63\) | 21.1659 | − | 92.7337i | 0.0423277 | − | 0.185450i | ||||
\(64\) | −249.303 | − | 312.616i | −0.486920 | − | 0.610578i | ||||
\(65\) | 451.012 | + | 565.551i | 0.860633 | + | 1.07920i | ||||
\(66\) | −3.41637 | + | 14.9681i | −0.00637161 | + | 0.0279159i | ||||
\(67\) | −99.1024 | − | 434.196i | −0.180706 | − | 0.791724i | −0.981295 | − | 0.192510i | \(-0.938337\pi\) |
0.800589 | − | 0.599214i | \(-0.204520\pi\) | |||||||
\(68\) | 995.228 | + | 1247.98i | 1.77484 | + | 2.22558i | ||||
\(69\) | 24.7303 | − | 11.9095i | 0.0431475 | − | 0.0207787i | ||||
\(70\) | 195.984 | − | 94.3809i | 0.334636 | − | 0.161152i | ||||
\(71\) | −217.825 | − | 954.353i | −0.364099 | − | 1.59522i | −0.742674 | − | 0.669653i | \(-0.766443\pi\) |
0.378575 | − | 0.925571i | \(-0.376414\pi\) | |||||||
\(72\) | 709.065 | − | 889.140i | 1.16061 | − | 1.45536i | ||||
\(73\) | 25.6072 | + | 12.3318i | 0.0410561 | + | 0.0197716i | 0.454299 | − | 0.890849i | \(-0.349890\pi\) |
−0.413243 | + | 0.910621i | \(0.635604\pi\) | |||||||
\(74\) | −1340.17 | + | 1680.52i | −2.10529 | + | 2.63995i | ||||
\(75\) | 2.07086 | − | 9.07302i | 0.00318830 | − | 0.0139688i | ||||
\(76\) | −1944.36 | + | 936.355i | −2.93465 | + | 1.41325i | ||||
\(77\) | −7.65918 | + | 33.5570i | −0.0113356 | + | 0.0496647i | ||||
\(78\) | −82.7769 | − | 39.8633i | −0.120162 | − | 0.0578670i | ||||
\(79\) | 6.16526 | 0.00878033 | 0.00439017 | − | 0.999990i | \(-0.498603\pi\) | ||||
0.00439017 | + | 0.999990i | \(0.498603\pi\) | |||||||
\(80\) | 957.971 | 1.33881 | ||||||||
\(81\) | −649.415 | − | 312.742i | −0.890831 | − | 0.429001i | ||||
\(82\) | −292.282 | − | 1280.57i | −0.393624 | − | 1.72458i | ||||
\(83\) | −482.260 | − | 604.735i | −0.637770 | − | 0.799738i | 0.352952 | − | 0.935641i | \(-0.385178\pi\) |
−0.990722 | + | 0.135903i | \(0.956606\pi\) | |||||||
\(84\) | −11.6092 | + | 14.5575i | −0.0150794 | + | 0.0189090i | ||||
\(85\) | 1198.82 | 1.52977 | ||||||||
\(86\) | −1209.08 | − | 699.192i | −1.51603 | − | 0.876695i | ||||
\(87\) | −24.8399 | −0.0306105 | ||||||||
\(88\) | −256.586 | + | 321.748i | −0.310820 | + | 0.389756i | ||||
\(89\) | −11.2455 | − | 14.1014i | −0.0133935 | − | 0.0167949i | 0.775090 | − | 0.631851i | \(-0.217705\pi\) |
−0.788483 | + | 0.615056i | \(0.789133\pi\) | |||||||
\(90\) | −368.193 | − | 1613.16i | −0.431233 | − | 1.88936i | ||||
\(91\) | −185.578 | − | 89.3696i | −0.213778 | − | 0.102950i | ||||
\(92\) | 1425.33 | 1.61523 | ||||||||
\(93\) | 33.0563 | 0.0368579 | ||||||||
\(94\) | 2302.03 | + | 1108.60i | 2.52591 | + | 1.21642i | ||||
\(95\) | −360.660 | + | 1580.16i | −0.389505 | + | 1.70653i | ||||
\(96\) | −12.5840 | + | 6.06011i | −0.0133786 | + | 0.00644279i | ||||
\(97\) | −326.670 | + | 1431.24i | −0.341942 | + | 1.49814i | 0.453029 | + | 0.891496i | \(0.350343\pi\) |
−0.794971 | + | 0.606648i | \(0.792514\pi\) | |||||||
\(98\) | 1020.69 | − | 1279.90i | 1.05209 | − | 1.31928i | ||||
\(99\) | 235.893 | + | 113.600i | 0.239476 | + | 0.115326i | ||||
\(100\) | 301.305 | − | 377.824i | 0.301305 | − | 0.377824i | ||||
\(101\) | −101.911 | − | 446.503i | −0.100402 | − | 0.439888i | −0.999995 | − | 0.00315955i | \(-0.998994\pi\) |
0.899593 | − | 0.436728i | \(-0.143863\pi\) | |||||||
\(102\) | −137.184 | + | 66.0644i | −0.133169 | + | 0.0641309i | ||||
\(103\) | 1566.57 | − | 754.418i | 1.49862 | − | 0.721699i | 0.508392 | − | 0.861126i | \(-0.330240\pi\) |
0.990232 | + | 0.139427i | \(0.0445260\pi\) | |||||||
\(104\) | −1535.46 | − | 1925.40i | −1.44773 | − | 1.81540i | ||||
\(105\) | 3.11175 | + | 13.6335i | 0.00289215 | + | 0.0126713i | ||||
\(106\) | −156.798 | + | 686.976i | −0.143675 | + | 0.629481i | ||||
\(107\) | −8.23050 | − | 10.3207i | −0.00743619 | − | 0.00932469i | 0.778099 | − | 0.628141i | \(-0.216184\pi\) |
−0.785536 | + | 0.618816i | \(0.787612\pi\) | |||||||
\(108\) | 176.948 | + | 221.886i | 0.157656 | + | 0.197694i | ||||
\(109\) | 241.960 | − | 1060.10i | 0.212620 | − | 0.931548i | −0.750159 | − | 0.661257i | \(-0.770023\pi\) |
0.962779 | − | 0.270290i | \(-0.0871197\pi\) | |||||||
\(110\) | 133.236 | + | 583.746i | 0.115487 | + | 0.505982i | ||||
\(111\) | −86.1554 | − | 108.035i | −0.0736712 | − | 0.0923808i | ||||
\(112\) | −245.765 | + | 118.354i | −0.207345 | + | 0.0998519i | ||||
\(113\) | −360.367 | + | 173.543i | −0.300004 | + | 0.144474i | −0.577830 | − | 0.816157i | \(-0.696100\pi\) |
0.277826 | + | 0.960631i | \(0.410386\pi\) | |||||||
\(114\) | −45.8077 | − | 200.697i | −0.0376341 | − | 0.164886i | ||||
\(115\) | 667.430 | − | 836.931i | 0.541202 | − | 0.678645i | ||||
\(116\) | −1162.13 | − | 559.654i | −0.930184 | − | 0.447953i | ||||
\(117\) | −976.877 | + | 1224.97i | −0.771900 | + | 0.967933i | ||||
\(118\) | −486.317 | + | 2130.69i | −0.379399 | + | 1.66226i | ||||
\(119\) | −307.553 | + | 148.110i | −0.236919 | + | 0.114094i | ||||
\(120\) | −37.2046 | + | 163.004i | −0.0283025 | + | 0.124001i | ||||
\(121\) | 1113.83 | + | 536.391i | 0.836836 | + | 0.402999i | ||||
\(122\) | −2308.25 | −1.71294 | ||||||||
\(123\) | 84.4413 | 0.0619010 | ||||||||
\(124\) | 1546.54 | + | 744.775i | 1.12003 | + | 0.539377i | ||||
\(125\) | 264.667 | + | 1159.58i | 0.189380 | + | 0.829729i | ||||
\(126\) | 293.759 | + | 368.363i | 0.207700 | + | 0.260447i | ||||
\(127\) | −583.311 | + | 731.449i | −0.407563 | + | 0.511068i | −0.942675 | − | 0.333714i | \(-0.891698\pi\) |
0.535112 | + | 0.844781i | \(0.320270\pi\) | |||||||
\(128\) | 2331.49 | 1.60997 | ||||||||
\(129\) | 61.1181 | − | 65.7773i | 0.0417144 | − | 0.0448943i | ||||
\(130\) | −3583.08 | −2.41736 | ||||||||
\(131\) | 83.0414 | − | 104.131i | 0.0553844 | − | 0.0694499i | −0.753368 | − | 0.657599i | \(-0.771572\pi\) |
0.808752 | + | 0.588150i | \(0.200143\pi\) | |||||||
\(132\) | −31.9554 | − | 40.0708i | −0.0210709 | − | 0.0264221i | ||||
\(133\) | −102.697 | − | 449.943i | −0.0669543 | − | 0.293346i | ||||
\(134\) | 1987.56 | + | 957.159i | 1.28134 | + | 0.617060i | ||||
\(135\) | 213.145 | 0.135886 | ||||||||
\(136\) | −4081.34 | −2.57332 | ||||||||
\(137\) | −469.186 | − | 225.948i | −0.292593 | − | 0.140905i | 0.281829 | − | 0.959465i | \(-0.409059\pi\) |
−0.574422 | + | 0.818559i | \(0.694773\pi\) | |||||||
\(138\) | −30.2544 | + | 132.553i | −0.0186625 | + | 0.0817657i | ||||
\(139\) | −1627.36 | + | 783.697i | −0.993029 | + | 0.478218i | −0.858567 | − | 0.512701i | \(-0.828645\pi\) |
−0.134462 | + | 0.990919i | \(0.542931\pi\) | |||||||
\(140\) | −161.585 | + | 707.951i | −0.0975460 | + | 0.427377i | ||||
\(141\) | −102.413 | + | 128.421i | −0.0611680 | + | 0.0767023i | ||||
\(142\) | 4368.62 | + | 2103.81i | 2.58173 | + | 1.24330i | ||||
\(143\) | 353.498 | − | 443.272i | 0.206720 | − | 0.259219i | ||||
\(144\) | 461.716 | + | 2022.91i | 0.267197 | + | 1.17067i | ||||
\(145\) | −872.803 | + | 420.320i | −0.499878 | + | 0.240729i | ||||
\(146\) | −126.841 | + | 61.0833i | −0.0719002 | + | 0.0346253i | ||||
\(147\) | 65.6169 | + | 82.2810i | 0.0368163 | + | 0.0461661i | ||||
\(148\) | −1596.69 | − | 6995.56i | −0.886805 | − | 3.88535i | ||||
\(149\) | 295.378 | − | 1294.14i | 0.162405 | − | 0.711542i | −0.826493 | − | 0.562947i | \(-0.809668\pi\) |
0.988898 | − | 0.148596i | \(-0.0474752\pi\) | |||||||
\(150\) | 28.7413 | + | 36.0405i | 0.0156448 | + | 0.0196179i | ||||
\(151\) | −992.249 | − | 1244.24i | −0.534756 | − | 0.670562i | 0.438913 | − | 0.898529i | \(-0.355364\pi\) |
−0.973669 | + | 0.227967i | \(0.926792\pi\) | |||||||
\(152\) | 1227.86 | − | 5379.59i | 0.655213 | − | 2.87068i | ||||
\(153\) | 577.798 | + | 2531.50i | 0.305309 | + | 1.33764i | ||||
\(154\) | −106.301 | − | 133.297i | −0.0556233 | − | 0.0697495i | ||||
\(155\) | 1161.51 | − | 559.352i | 0.601899 | − | 0.289859i | ||||
\(156\) | 276.331 | − | 133.074i | 0.141822 | − | 0.0682977i | ||||
\(157\) | −154.435 | − | 676.625i | −0.0785049 | − | 0.343952i | 0.920387 | − | 0.391008i | \(-0.127873\pi\) |
−0.998892 | + | 0.0470553i | \(0.985016\pi\) | |||||||
\(158\) | −19.0405 | + | 23.8760i | −0.00958722 | + | 0.0120220i | ||||
\(159\) | −40.8133 | − | 19.6547i | −0.0203566 | − | 0.00980324i | ||||
\(160\) | −339.620 | + | 425.870i | −0.167808 | + | 0.210425i | ||||
\(161\) | −67.8273 | + | 297.171i | −0.0332021 | + | 0.145468i | ||||
\(162\) | 3216.77 | − | 1549.12i | 1.56008 | − | 0.751296i | ||||
\(163\) | 503.613 | − | 2206.47i | 0.242000 | − | 1.06027i | −0.697194 | − | 0.716883i | \(-0.745568\pi\) |
0.939194 | − | 0.343388i | \(-0.111575\pi\) | |||||||
\(164\) | 3950.59 | + | 1902.50i | 1.88103 | + | 0.905857i | ||||
\(165\) | −38.4924 | −0.0181614 | ||||||||
\(166\) | 3831.33 | 1.79138 | ||||||||
\(167\) | −780.848 | − | 376.036i | −0.361819 | − | 0.174243i | 0.244137 | − | 0.969741i | \(-0.421495\pi\) |
−0.605957 | + | 0.795498i | \(0.707210\pi\) | |||||||
\(168\) | −10.5939 | − | 46.4147i | −0.00486508 | − | 0.0213153i | ||||
\(169\) | 745.588 | + | 934.938i | 0.339366 | + | 0.425552i | ||||
\(170\) | −3702.37 | + | 4642.63i | −1.67035 | + | 2.09455i | ||||
\(171\) | −3510.58 | −1.56995 | ||||||||
\(172\) | 4341.41 | − | 1700.37i | 1.92459 | − | 0.753791i | ||||
\(173\) | −2626.97 | −1.15448 | −0.577240 | − | 0.816575i | \(-0.695870\pi\) | ||||
−0.577240 | + | 0.816575i | \(0.695870\pi\) | |||||||
\(174\) | 76.7143 | − | 96.1967i | 0.0334235 | − | 0.0419118i | ||||
\(175\) | 64.4352 | + | 80.7992i | 0.0278334 | + | 0.0349020i | ||||
\(176\) | −167.079 | − | 732.020i | −0.0715571 | − | 0.313512i | ||||
\(177\) | −126.585 | − | 60.9600i | −0.0537553 | − | 0.0258872i | ||||
\(178\) | 89.3403 | 0.0376199 | ||||||||
\(179\) | 609.964 | 0.254698 | 0.127349 | − | 0.991858i | \(-0.459353\pi\) | ||||
0.127349 | + | 0.991858i | \(0.459353\pi\) | |||||||
\(180\) | 4976.63 | + | 2396.62i | 2.06075 | + | 0.992407i | ||||
\(181\) | 326.443 | − | 1430.24i | 0.134057 | − | 0.587341i | −0.862618 | − | 0.505856i | \(-0.831177\pi\) |
0.996675 | − | 0.0814850i | \(-0.0259663\pi\) | |||||||
\(182\) | 919.229 | − | 442.677i | 0.374383 | − | 0.180294i | ||||
\(183\) | 33.0199 | − | 144.670i | 0.0133383 | − | 0.0584388i | ||||
\(184\) | −2272.25 | + | 2849.31i | −0.910392 | + | 1.14160i | ||||
\(185\) | −4855.34 | − | 2338.21i | −1.92958 | − | 0.929235i | ||||
\(186\) | −102.090 | + | 128.016i | −0.0402450 | + | 0.0504657i | ||||
\(187\) | −209.085 | − | 916.060i | −0.0817636 | − | 0.358230i | ||||
\(188\) | −7684.77 | + | 3700.79i | −2.98122 | + | 1.43568i | ||||
\(189\) | −54.6819 | + | 26.3334i | −0.0210451 | + | 0.0101348i | ||||
\(190\) | −5005.58 | − | 6276.80i | −1.91128 | − | 2.39667i | ||||
\(191\) | −142.559 | − | 624.593i | −0.0540064 | − | 0.236618i | 0.940720 | − | 0.339185i | \(-0.110151\pi\) |
−0.994726 | + | 0.102568i | \(0.967294\pi\) | |||||||
\(192\) | −28.3328 | + | 124.134i | −0.0106497 | + | 0.0466594i | ||||
\(193\) | 127.997 | + | 160.504i | 0.0477381 | + | 0.0598617i | 0.805127 | − | 0.593102i | \(-0.202097\pi\) |
−0.757389 | + | 0.652964i | \(0.773525\pi\) | |||||||
\(194\) | −4533.83 | − | 5685.25i | −1.67789 | − | 2.10400i | ||||
\(195\) | 51.2567 | − | 224.570i | 0.0188234 | − | 0.0824708i | ||||
\(196\) | 1216.06 | + | 5327.89i | 0.443170 | + | 1.94165i | ||||
\(197\) | 2335.81 | + | 2929.02i | 0.844771 | + | 1.05931i | 0.997474 | + | 0.0710372i | \(0.0226309\pi\) |
−0.152703 | + | 0.988272i | \(0.548798\pi\) | |||||||
\(198\) | −1168.46 | + | 562.700i | −0.419387 | + | 0.201966i | ||||
\(199\) | −150.181 | + | 72.3233i | −0.0534977 | + | 0.0257631i | −0.460441 | − | 0.887690i | \(-0.652309\pi\) |
0.406944 | + | 0.913453i | \(0.366595\pi\) | |||||||
\(200\) | 274.952 | + | 1204.64i | 0.0972102 | + | 0.425906i | ||||
\(201\) | −88.4227 | + | 110.878i | −0.0310291 | + | 0.0389093i | ||||
\(202\) | 2043.90 | + | 984.289i | 0.711921 | + | 0.342843i | ||||
\(203\) | 171.986 | − | 215.664i | 0.0594633 | − | 0.0745646i | ||||
\(204\) | 113.106 | − | 495.549i | 0.0388186 | − | 0.170075i | ||||
\(205\) | 2967.03 | − | 1428.85i | 1.01086 | − | 0.486805i | ||||
\(206\) | −1916.49 | + | 8396.70i | −0.648196 | + | 2.83993i | ||||
\(207\) | 2089.00 | + | 1006.01i | 0.701427 | + | 0.337790i | ||||
\(208\) | 4493.20 | 1.49782 | ||||||||
\(209\) | 1270.36 | 0.420442 | ||||||||
\(210\) | −62.4081 | − | 30.0542i | −0.0205075 | − | 0.00987588i | ||||
\(211\) | 1105.74 | + | 4844.58i | 0.360770 | + | 1.58064i | 0.751244 | + | 0.660025i | \(0.229454\pi\) |
−0.390473 | + | 0.920614i | \(0.627689\pi\) | |||||||
\(212\) | −1466.62 | − | 1839.09i | −0.475132 | − | 0.595797i | ||||
\(213\) | −194.351 | + | 243.708i | −0.0625198 | + | 0.0783973i | ||||
\(214\) | 65.3875 | 0.0208869 | ||||||||
\(215\) | 1034.49 | − | 3345.42i | 0.328147 | − | 1.06119i | ||||
\(216\) | −725.647 | −0.228584 | ||||||||
\(217\) | −228.875 | + | 287.000i | −0.0715993 | + | 0.0897827i | ||||
\(218\) | 3358.14 | + | 4210.98i | 1.04331 | + | 1.30827i | ||||
\(219\) | −2.01393 | − | 8.82359i | −0.000621409 | − | 0.00272257i | ||||
\(220\) | −1800.87 | − | 867.251i | −0.551883 | − | 0.265773i | ||||
\(221\) | 5622.85 | 1.71147 | ||||||||
\(222\) | 684.464 | 0.206929 | ||||||||
\(223\) | −3878.16 | − | 1867.63i | −1.16458 | − | 0.560832i | −0.251197 | − | 0.967936i | \(-0.580824\pi\) |
−0.913382 | + | 0.407104i | \(0.866539\pi\) | |||||||
\(224\) | 34.5138 | − | 151.215i | 0.0102949 | − | 0.0451047i | ||||
\(225\) | 708.269 | − | 341.084i | 0.209857 | − | 0.101062i | ||||
\(226\) | 440.863 | − | 1931.55i | 0.129760 | − | 0.568516i | ||||
\(227\) | 711.670 | − | 892.406i | 0.208085 | − | 0.260930i | −0.666827 | − | 0.745213i | \(-0.732348\pi\) |
0.874911 | + | 0.484283i | \(0.160919\pi\) | |||||||
\(228\) | 619.153 | + | 298.168i | 0.179844 | + | 0.0866083i | ||||
\(229\) | 1370.78 | − | 1718.90i | 0.395562 | − | 0.496019i | −0.543671 | − | 0.839298i | \(-0.682966\pi\) |
0.939234 | + | 0.343279i | \(0.111538\pi\) | |||||||
\(230\) | 1179.90 | + | 5169.48i | 0.338262 | + | 1.48202i | ||||
\(231\) | 9.87511 | − | 4.75560i | 0.00281270 | − | 0.00135453i | ||||
\(232\) | 2971.43 | − | 1430.97i | 0.840879 | − | 0.404946i | ||||
\(233\) | −1744.84 | − | 2187.95i | −0.490592 | − | 0.615183i | 0.473486 | − | 0.880801i | \(-0.342995\pi\) |
−0.964078 | + | 0.265618i | \(0.914424\pi\) | |||||||
\(234\) | −1726.95 | − | 7566.25i | −0.482453 | − | 2.11377i | ||||
\(235\) | −1425.45 | + | 6245.30i | −0.395685 | + | 1.73361i | ||||
\(236\) | −4548.81 | − | 5704.03i | −1.25467 | − | 1.57331i | ||||
\(237\) | −1.22406 | − | 1.53492i | −0.000335490 | − | 0.000420691i | ||||
\(238\) | 376.252 | − | 1648.47i | 0.102474 | − | 0.448968i | ||||
\(239\) | −428.350 | − | 1876.72i | −0.115932 | − | 0.507930i | −0.999234 | − | 0.0391265i | \(-0.987542\pi\) |
0.883303 | − | 0.468803i | \(-0.155315\pi\) | |||||||
\(240\) | −190.197 | − | 238.499i | −0.0511547 | − | 0.0641460i | ||||
\(241\) | −269.739 | + | 129.899i | −0.0720971 | + | 0.0347202i | −0.469585 | − | 0.882887i | \(-0.655596\pi\) |
0.397488 | + | 0.917607i | \(0.369882\pi\) | |||||||
\(242\) | −5517.16 | + | 2656.93i | −1.46552 | + | 0.705759i | ||||
\(243\) | 154.192 | + | 675.560i | 0.0407055 | + | 0.178342i | ||||
\(244\) | 4804.32 | − | 6024.42i | 1.26051 | − | 1.58063i | ||||
\(245\) | 3697.88 | + | 1780.81i | 0.964282 | + | 0.464374i | ||||
\(246\) | −260.785 | + | 327.014i | −0.0675895 | + | 0.0847546i | ||||
\(247\) | −1691.62 | + | 7411.45i | −0.435769 | + | 1.90923i | ||||
\(248\) | −3954.31 | + | 1904.30i | −1.01250 | + | 0.487592i | ||||
\(249\) | −54.8079 | + | 240.129i | −0.0139490 | + | 0.0611147i | ||||
\(250\) | −5308.06 | − | 2556.23i | −1.34285 | − | 0.646680i | ||||
\(251\) | 4016.43 | 1.01002 | 0.505010 | − | 0.863114i | \(-0.331489\pi\) | ||||
0.505010 | + | 0.863114i | \(0.331489\pi\) | |||||||
\(252\) | −1572.83 | −0.393171 | ||||||||
\(253\) | −755.935 | − | 364.039i | −0.187847 | − | 0.0904622i | ||||
\(254\) | −1031.19 | − | 4517.95i | −0.254735 | − | 1.11607i | ||||
\(255\) | −238.015 | − | 298.461i | −0.0584512 | − | 0.0732955i | ||||
\(256\) | −5206.04 | + | 6528.16i | −1.27101 | + | 1.59379i | ||||
\(257\) | −3740.00 | −0.907762 | −0.453881 | − | 0.891062i | \(-0.649961\pi\) | ||||
−0.453881 | + | 0.891062i | \(0.649961\pi\) | |||||||
\(258\) | 65.9795 | + | 439.834i | 0.0159213 | + | 0.106135i | ||||
\(259\) | 1534.50 | 0.368144 | ||||||||
\(260\) | 7457.72 | − | 9351.68i | 1.77888 | − | 2.23064i | ||||
\(261\) | −1308.24 | − | 1640.48i | −0.310261 | − | 0.389055i | ||||
\(262\) | 146.803 | + | 643.184i | 0.0346164 | + | 0.151664i | ||||
\(263\) | 5363.35 | + | 2582.85i | 1.25748 | + | 0.605572i | 0.939508 | − | 0.342526i | \(-0.111283\pi\) |
0.317976 | + | 0.948099i | \(0.396997\pi\) | |||||||
\(264\) | 131.046 | 0.0305505 | ||||||||
\(265\) | −1766.64 | −0.409525 | ||||||||
\(266\) | 2059.64 | + | 991.872i | 0.474755 | + | 0.228630i | ||||
\(267\) | −1.27803 | + | 5.59942i | −0.000292937 | + | 0.00128344i | ||||
\(268\) | −6635.00 | + | 3195.25i | −1.51230 | + | 0.728286i | ||||
\(269\) | −197.382 | + | 864.788i | −0.0447383 | + | 0.196011i | −0.992358 | − | 0.123388i | \(-0.960624\pi\) |
0.947620 | + | 0.319399i | \(0.103481\pi\) | |||||||
\(270\) | −658.268 | + | 825.443i | −0.148374 | + | 0.186055i | ||||
\(271\) | 7779.45 | + | 3746.39i | 1.74379 | + | 0.839767i | 0.981227 | + | 0.192857i | \(0.0617753\pi\) |
0.762566 | + | 0.646910i | \(0.223939\pi\) | |||||||
\(272\) | 4642.80 | − | 5821.88i | 1.03497 | − | 1.29781i | ||||
\(273\) | 14.5951 | + | 63.9454i | 0.00323567 | + | 0.0141764i | ||||
\(274\) | 2324.04 | − | 1119.20i | 0.512409 | − | 0.246763i | ||||
\(275\) | −256.298 | + | 123.426i | −0.0562012 | + | 0.0270651i | ||||
\(276\) | −282.987 | − | 354.855i | −0.0617167 | − | 0.0773903i | ||||
\(277\) | 1564.87 | + | 6856.13i | 0.339436 | + | 1.48717i | 0.800249 | + | 0.599668i | \(0.204701\pi\) |
−0.460813 | + | 0.887497i | \(0.652442\pi\) | |||||||
\(278\) | 1990.87 | − | 8722.57i | 0.429513 | − | 1.88182i | ||||
\(279\) | 1740.98 | + | 2183.12i | 0.373582 | + | 0.468458i | ||||
\(280\) | −1157.63 | − | 1451.62i | −0.247077 | − | 0.309825i | ||||
\(281\) | 1454.95 | − | 6374.55i | 0.308879 | − | 1.35329i | −0.547442 | − | 0.836843i | \(-0.684399\pi\) |
0.856321 | − | 0.516443i | \(-0.172744\pi\) | |||||||
\(282\) | −181.047 | − | 793.221i | −0.0382313 | − | 0.167502i | ||||
\(283\) | −3317.98 | − | 4160.61i | −0.696938 | − | 0.873932i | 0.299853 | − | 0.953985i | \(-0.403062\pi\) |
−0.996791 | + | 0.0800532i | \(0.974491\pi\) | |||||||
\(284\) | −14583.6 | + | 7023.08i | −3.04710 | + | 1.46741i | ||||
\(285\) | 465.005 | − | 223.935i | 0.0966475 | − | 0.0465430i | ||||
\(286\) | 624.922 | + | 2737.96i | 0.129204 | + | 0.566080i | ||||
\(287\) | −584.654 | + | 733.133i | −0.120247 | + | 0.150786i | ||||
\(288\) | −1062.98 | − | 511.905i | −0.217489 | − | 0.104737i | ||||
\(289\) | 2746.85 | − | 3444.44i | 0.559099 | − | 0.701088i | ||||
\(290\) | 1067.76 | − | 4678.17i | 0.216211 | − | 0.947282i | ||||
\(291\) | 421.181 | − | 202.830i | 0.0848457 | − | 0.0408595i | ||||
\(292\) | 104.578 | − | 458.186i | 0.0209588 | − | 0.0918264i | ||||
\(293\) | −8740.08 | − | 4209.00i | −1.74267 | − | 0.839223i | −0.981701 | − | 0.190430i | \(-0.939012\pi\) |
−0.760965 | − | 0.648793i | \(-0.775274\pi\) | |||||||
\(294\) | −521.295 | −0.103410 | ||||||||
\(295\) | −5479.34 | −1.08142 | ||||||||
\(296\) | 16529.9 | + | 7960.36i | 3.24587 | + | 1.56313i | ||||
\(297\) | −37.1745 | − | 162.872i | −0.00726291 | − | 0.0318209i | ||||
\(298\) | 4099.53 | + | 5140.65i | 0.796912 | + | 0.999295i | ||||
\(299\) | 3130.47 | − | 3925.48i | 0.605483 | − | 0.759252i | ||||
\(300\) | −153.885 | −0.0296152 | ||||||||
\(301\) | 147.920 | + | 986.065i | 0.0283254 | + | 0.188823i | ||||
\(302\) | 7882.95 | 1.50203 | ||||||||
\(303\) | −90.9288 | + | 114.021i | −0.0172400 | + | 0.0216183i | ||||
\(304\) | 6277.02 | + | 7871.14i | 1.18425 | + | 1.48500i | ||||
\(305\) | −1287.75 | − | 5642.02i | −0.241759 | − | 1.05922i | ||||
\(306\) | −11588.1 | − | 5580.54i | −2.16486 | − | 1.04254i | ||||
\(307\) | 917.394 | 0.170549 | 0.0852743 | − | 0.996358i | \(-0.472823\pi\) | ||||
0.0852743 | + | 0.996358i | \(0.472823\pi\) | |||||||
\(308\) | 569.153 | 0.105294 | ||||||||
\(309\) | −498.849 | − | 240.233i | −0.0918399 | − | 0.0442278i | ||||
\(310\) | −1420.95 | + | 6225.61i | −0.260338 | + | 1.14062i | ||||
\(311\) | −1837.76 | + | 885.020i | −0.335080 | + | 0.161366i | −0.593856 | − | 0.804571i | \(-0.702395\pi\) |
0.258776 | + | 0.965937i | \(0.416681\pi\) | |||||||
\(312\) | −174.502 | + | 764.543i | −0.0316642 | + | 0.138730i | ||||
\(313\) | 635.478 | − | 796.864i | 0.114758 | − | 0.143902i | −0.721135 | − | 0.692795i | \(-0.756379\pi\) |
0.835893 | + | 0.548893i | \(0.184950\pi\) | |||||||
\(314\) | 3097.30 | + | 1491.58i | 0.556658 | + | 0.268072i | ||||
\(315\) | −736.499 | + | 923.540i | −0.131737 | + | 0.165192i | ||||
\(316\) | −22.6851 | − | 99.3898i | −0.00403840 | − | 0.0176934i | ||||
\(317\) | 180.839 | − | 87.0874i | 0.0320408 | − | 0.0154300i | −0.417795 | − | 0.908541i | \(-0.637197\pi\) |
0.449836 | + | 0.893111i | \(0.351483\pi\) | |||||||
\(318\) | 202.162 | − | 97.3561i | 0.0356499 | − | 0.0171681i | ||||
\(319\) | 473.406 | + | 593.632i | 0.0830898 | + | 0.104191i | ||||
\(320\) | 1104.96 | + | 4841.15i | 0.193029 | + | 0.845714i | ||||
\(321\) | −0.935381 | + | 4.09817i | −0.000162641 | + | 0.000712579i | ||||
\(322\) | −941.371 | − | 1180.44i | −0.162921 | − | 0.204296i | ||||
\(323\) | 7855.15 | + | 9850.05i | 1.35316 | + | 1.69682i | ||||
\(324\) | −2652.17 | + | 11619.9i | −0.454762 | + | 1.99244i | ||||
\(325\) | −378.801 | − | 1659.63i | −0.0646525 | − | 0.283261i | ||||
\(326\) | 6989.61 | + | 8764.69i | 1.18748 | + | 1.48905i | ||||
\(327\) | −311.963 | + | 150.233i | −0.0527572 | + | 0.0254065i | ||||
\(328\) | −10101.2 | + | 4864.46i | −1.70044 | + | 0.818887i | ||||
\(329\) | −405.891 | − | 1778.32i | −0.0680167 | − | 0.298000i | ||||
\(330\) | 118.878 | − | 149.068i | 0.0198304 | − | 0.0248665i | ||||
\(331\) | −10756.9 | − | 5180.23i | −1.78626 | − | 0.860216i | −0.950245 | − | 0.311503i | \(-0.899168\pi\) |
−0.836011 | − | 0.548713i | \(-0.815118\pi\) | |||||||
\(332\) | −7974.41 | + | 9999.60i | −1.31823 | + | 1.65301i | ||||
\(333\) | 2597.36 | − | 11379.8i | 0.427431 | − | 1.87270i | ||||
\(334\) | 3867.80 | − | 1862.63i | 0.633642 | − | 0.305146i | ||||
\(335\) | −1230.73 | + | 5392.17i | −0.200722 | + | 0.879420i | ||||
\(336\) | 78.2601 | + | 37.6881i | 0.0127067 | + | 0.00611921i | ||||
\(337\) | −9933.49 | −1.60567 | −0.802837 | − | 0.596199i | \(-0.796677\pi\) | ||||
−0.802837 | + | 0.596199i | \(0.796677\pi\) | |||||||
\(338\) | −5923.35 | −0.953218 | ||||||||
\(339\) | 114.753 | + | 55.2623i | 0.0183851 | + | 0.00885380i | ||||
\(340\) | −4411.05 | − | 19326.1i | −0.703596 | − | 3.08266i | ||||
\(341\) | −629.998 | − | 789.992i | −0.100048 | − | 0.125456i | ||||
\(342\) | 10841.9 | − | 13595.3i | 1.71422 | − | 2.14957i | ||||
\(343\) | −2381.61 | −0.374911 | ||||||||
\(344\) | −3521.89 | + | 11389.4i | −0.551999 | + | 1.78510i | ||||
\(345\) | −340.877 | −0.0531947 | ||||||||
\(346\) | 8113.02 | − | 10173.4i | 1.26057 | − | 1.58071i | ||||
\(347\) | −2424.21 | − | 3039.86i | −0.375038 | − | 0.470283i | 0.558114 | − | 0.829764i | \(-0.311525\pi\) |
−0.933152 | + | 0.359481i | \(0.882954\pi\) | |||||||
\(348\) | 91.3982 | + | 400.442i | 0.0140789 | + | 0.0616837i | ||||
\(349\) | 1764.61 | + | 849.793i | 0.270652 | + | 0.130339i | 0.564288 | − | 0.825578i | \(-0.309151\pi\) |
−0.293635 | + | 0.955917i | \(0.594865\pi\) | |||||||
\(350\) | −511.908 | −0.0781789 | ||||||||
\(351\) | 999.722 | 0.152026 | ||||||||
\(352\) | 384.656 | + | 185.240i | 0.0582450 | + | 0.0280493i | ||||
\(353\) | 624.316 | − | 2735.31i | 0.0941331 | − | 0.412424i | −0.905803 | − | 0.423698i | \(-0.860732\pi\) |
0.999936 | + | 0.0112743i | \(0.00358880\pi\) | |||||||
\(354\) | 627.016 | − | 301.955i | 0.0941399 | − | 0.0453354i | ||||
\(355\) | −2705.11 | + | 11851.9i | −0.404429 | + | 1.77192i | ||||
\(356\) | −185.950 | + | 233.174i | −0.0276836 | + | 0.0347141i | ||||
\(357\) | 97.9358 | + | 47.1634i | 0.0145191 | + | 0.00699202i | ||||
\(358\) | −1883.79 | + | 2362.19i | −0.278104 | + | 0.348731i | ||||
\(359\) | −1294.55 | − | 5671.81i | −0.190317 | − | 0.833835i | −0.976444 | − | 0.215770i | \(-0.930774\pi\) |
0.786127 | − | 0.618065i | \(-0.212083\pi\) | |||||||
\(360\) | −12724.6 | + | 6127.85i | −1.86291 | + | 0.897128i | ||||
\(361\) | −9166.74 | + | 4414.47i | −1.33646 | + | 0.643603i | ||||
\(362\) | 4530.67 | + | 5681.29i | 0.657809 | + | 0.824867i | ||||
\(363\) | −87.5992 | − | 383.797i | −0.0126660 | − | 0.0554935i | ||||
\(364\) | −757.888 | + | 3320.52i | −0.109132 | + | 0.478139i | ||||
\(365\) | −220.069 | − | 275.958i | −0.0315587 | − | 0.0395734i | ||||
\(366\) | 458.281 | + | 574.667i | 0.0654501 | + | 0.0820719i | ||||
\(367\) | −426.504 | + | 1868.63i | −0.0606630 | + | 0.265782i | −0.996160 | − | 0.0875531i | \(-0.972095\pi\) |
0.935497 | + | 0.353335i | \(0.114952\pi\) | |||||||
\(368\) | −1479.60 | − | 6482.55i | −0.209591 | − | 0.918278i | ||||
\(369\) | 4447.27 | + | 5576.70i | 0.627413 | + | 0.786751i | ||||
\(370\) | 24050.1 | − | 11581.9i | 3.37921 | − | 1.62734i | ||||
\(371\) | 453.228 | − | 218.263i | 0.0634243 | − | 0.0305435i | ||||
\(372\) | −121.631 | − | 532.899i | −0.0169523 | − | 0.0742729i | ||||
\(373\) | 4223.20 | − | 5295.73i | 0.586245 | − | 0.735127i | −0.396919 | − | 0.917854i | \(-0.629921\pi\) |
0.983164 | + | 0.182726i | \(0.0584921\pi\) | |||||||
\(374\) | 4193.33 | + | 2019.40i | 0.579764 | + | 0.279200i | ||||
\(375\) | 236.145 | − | 296.117i | 0.0325186 | − | 0.0407770i | ||||
\(376\) | 4852.90 | − | 21261.9i | 0.665609 | − | 2.91623i | ||||
\(377\) | −4093.73 | + | 1971.44i | −0.559252 | + | 0.269321i | ||||
\(378\) | 66.8963 | − | 293.092i | 0.00910257 | − | 0.0398810i | ||||
\(379\) | −6758.45 | − | 3254.70i | −0.915985 | − | 0.441115i | −0.0843492 | − | 0.996436i | \(-0.526881\pi\) |
−0.831636 | + | 0.555321i | \(0.812595\pi\) | |||||||
\(380\) | 26800.6 | 3.61801 | ||||||||
\(381\) | 297.915 | 0.0400594 | ||||||||
\(382\) | 2859.12 | + | 1376.88i | 0.382946 | + | 0.184417i | ||||
\(383\) | −821.290 | − | 3598.31i | −0.109572 | − | 0.480065i | −0.999703 | − | 0.0243614i | \(-0.992245\pi\) |
0.890131 | − | 0.455704i | \(-0.150612\pi\) | |||||||
\(384\) | −462.896 | − | 580.453i | −0.0615158 | − | 0.0771384i | ||||
\(385\) | 266.513 | − | 334.197i | 0.0352799 | − | 0.0442396i | ||||
\(386\) | −1016.88 | −0.134088 | ||||||||
\(387\) | 7562.99 | + | 572.091i | 0.993406 | + | 0.0751448i | ||||
\(388\) | 24274.8 | 3.17621 | ||||||||
\(389\) | 2152.44 | − | 2699.08i | 0.280548 | − | 0.351796i | −0.621514 | − | 0.783403i | \(-0.713482\pi\) |
0.902062 | + | 0.431607i | \(0.142053\pi\) | |||||||
\(390\) | 711.388 | + | 892.053i | 0.0923655 | + | 0.115823i | ||||
\(391\) | −1851.59 | − | 8112.35i | −0.239486 | − | 1.04926i | ||||
\(392\) | −12589.3 | − | 6062.70i | −1.62208 | − | 0.781155i | ||||
\(393\) | −42.4117 | −0.00544374 | ||||||||
\(394\) | −18557.0 | −2.37281 | ||||||||
\(395\) | −68.9825 | − | 33.2202i | −0.00878706 | − | 0.00423162i | ||||
\(396\) | 963.372 | − | 4220.81i | 0.122251 | − | 0.535615i | ||||
\(397\) | 5139.35 | − | 2474.98i | 0.649714 | − | 0.312886i | −0.0798414 | − | 0.996808i | \(-0.525441\pi\) |
0.729555 | + | 0.683922i | \(0.239727\pi\) | |||||||
\(398\) | 183.727 | − | 804.961i | 0.0231392 | − | 0.101379i | ||||
\(399\) | −91.6294 | + | 114.900i | −0.0114968 | + | 0.0144165i | ||||
\(400\) | −2031.16 | − | 978.153i | −0.253894 | − | 0.122269i | ||||
\(401\) | −6616.65 | + | 8297.02i | −0.823989 | + | 1.03325i | 0.174827 | + | 0.984599i | \(0.444063\pi\) |
−0.998816 | + | 0.0486506i | \(0.984508\pi\) | |||||||
\(402\) | −156.316 | − | 684.864i | −0.0193938 | − | 0.0849699i | ||||
\(403\) | 5447.84 | − | 2623.54i | 0.673391 | − | 0.324288i | ||||
\(404\) | −6823.06 | + | 3285.81i | −0.840247 | + | 0.404642i | ||||
\(405\) | 5581.10 | + | 6998.48i | 0.684759 | + | 0.858660i | ||||
\(406\) | 304.041 | + | 1332.09i | 0.0371658 | + | 0.162834i | ||||
\(407\) | −939.894 | + | 4117.95i | −0.114469 | + | 0.501521i | ||||
\(408\) | 810.313 | + | 1016.10i | 0.0983247 | + | 0.123295i | ||||
\(409\) | 5716.86 | + | 7168.72i | 0.691151 | + | 0.866675i | 0.996328 | − | 0.0856201i | \(-0.0272871\pi\) |
−0.305177 | + | 0.952296i | \(0.598716\pi\) | |||||||
\(410\) | −3629.78 | + | 15903.1i | −0.437225 | + | 1.91561i | ||||
\(411\) | 36.9001 | + | 161.670i | 0.00442858 | + | 0.0194029i | ||||
\(412\) | −17926.1 | − | 22478.6i | −2.14358 | − | 2.68797i | ||||
\(413\) | 1405.71 | − | 676.954i | 0.167483 | − | 0.0806555i | ||||
\(414\) | −10347.5 | + | 4983.10i | −1.22839 | + | 0.591560i | ||||
\(415\) | 2137.47 | + | 9364.87i | 0.252830 | + | 1.10772i | ||||
\(416\) | −1592.93 | + | 1997.47i | −0.187740 | + | 0.235419i | ||||
\(417\) | 518.209 | + | 249.556i | 0.0608557 | + | 0.0293065i | ||||
\(418\) | −3923.31 | + | 4919.67i | −0.459080 | + | 0.575668i | ||||
\(419\) | −2144.58 | + | 9396.00i | −0.250046 | + | 1.09552i | 0.681476 | + | 0.731840i | \(0.261338\pi\) |
−0.931522 | + | 0.363684i | \(0.881519\pi\) | |||||||
\(420\) | 208.335 | − | 100.329i | 0.0242040 | − | 0.0116560i | ||||
\(421\) | 1762.48 | − | 7721.92i | 0.204033 | − | 0.893927i | −0.764418 | − | 0.644722i | \(-0.776973\pi\) |
0.968451 | − | 0.249206i | \(-0.0801695\pi\) | |||||||
\(422\) | −22176.4 | − | 10679.6i | −2.55813 | − | 1.23193i | ||||
\(423\) | −13875.0 | −1.59486 | ||||||||
\(424\) | 6014.49 | 0.688890 | ||||||||
\(425\) | −2541.82 | − | 1224.07i | −0.290109 | − | 0.139709i | ||||
\(426\) | −343.578 | − | 1505.31i | −0.0390761 | − | 0.171204i | ||||
\(427\) | 1027.42 | + | 1288.35i | 0.116441 | + | 0.146013i | ||||
\(428\) | −136.096 | + | 170.659i | −0.0153702 | + | 0.0192736i | ||||
\(429\) | −180.542 | −0.0203185 | ||||||||
\(430\) | 9760.84 | + | 14338.1i | 1.09467 | + | 1.60801i | ||||
\(431\) | 11681.4 | 1.30550 | 0.652751 | − | 0.757572i | \(-0.273615\pi\) | ||||
0.652751 | + | 0.757572i | \(0.273615\pi\) | |||||||
\(432\) | 825.472 | − | 1035.11i | 0.0919341 | − | 0.115282i | ||||
\(433\) | 829.424 | + | 1040.06i | 0.0920544 | + | 0.115433i | 0.825725 | − | 0.564072i | \(-0.190766\pi\) |
−0.733671 | + | 0.679505i | \(0.762195\pi\) | |||||||
\(434\) | −404.611 | − | 1772.72i | −0.0447510 | − | 0.196067i | ||||
\(435\) | 277.931 | + | 133.844i | 0.0306339 | + | 0.0147525i | ||||
\(436\) | −17980.0 | −1.97497 | ||||||||
\(437\) | 11249.9 | 1.23148 | ||||||||
\(438\) | 40.3906 | + | 19.4511i | 0.00440625 | + | 0.00212194i | ||||
\(439\) | 2134.68 | − | 9352.64i | 0.232079 | − | 1.01680i | −0.715833 | − | 0.698272i | \(-0.753953\pi\) |
0.947912 | − | 0.318533i | \(-0.103190\pi\) | |||||||
\(440\) | 4604.59 | − | 2217.45i | 0.498898 | − | 0.240257i | ||||
\(441\) | −1978.18 | + | 8666.98i | −0.213603 | + | 0.935857i | ||||
\(442\) | −17365.3 | + | 21775.5i | −1.86875 | + | 2.34333i | ||||
\(443\) | −8036.30 | − | 3870.08i | −0.861887 | − | 0.415063i | −0.0499112 | − | 0.998754i | \(-0.515894\pi\) |
−0.811976 | + | 0.583691i | \(0.801608\pi\) | |||||||
\(444\) | −1424.62 | + | 1786.42i | −0.152274 | + | 0.190945i | ||||
\(445\) | 49.8423 | + | 218.374i | 0.00530956 | + | 0.0232627i | ||||
\(446\) | 19209.8 | − | 9250.97i | 2.03949 | − | 0.982167i | ||||
\(447\) | −380.836 | + | 183.401i | −0.0402974 | + | 0.0194062i | ||||
\(448\) | −881.582 | − | 1105.47i | −0.0929706 | − | 0.116581i | ||||
\(449\) | 3302.96 | + | 14471.2i | 0.347163 | + | 1.52102i | 0.783588 | + | 0.621280i | \(0.213387\pi\) |
−0.436425 | + | 0.899741i | \(0.643756\pi\) | |||||||
\(450\) | −866.477 | + | 3796.28i | −0.0907691 | + | 0.397685i | ||||
\(451\) | −1609.31 | − | 2018.01i | −0.168025 | − | 0.210697i | ||||
\(452\) | 4123.65 | + | 5170.90i | 0.429116 | + | 0.538094i | ||||
\(453\) | −112.767 | + | 494.066i | −0.0116960 | + | 0.0512433i | ||||
\(454\) | 1258.11 | + | 5512.13i | 0.130057 | + | 0.569817i | ||||
\(455\) | 1594.86 | + | 1999.90i | 0.164326 | + | 0.206058i | ||||
\(456\) | −1583.10 | + | 762.379i | −0.162577 | + | 0.0782932i | ||||
\(457\) | −12200.5 | + | 5875.47i | −1.24883 | + | 0.601407i | −0.937199 | − | 0.348795i | \(-0.886591\pi\) |
−0.311635 | + | 0.950202i | \(0.600877\pi\) | |||||||
\(458\) | 2423.30 | + | 10617.2i | 0.247234 | + | 1.08320i | ||||
\(459\) | 1033.01 | − | 1295.35i | 0.105047 | − | 0.131725i | ||||
\(460\) | −15947.9 | − | 7680.11i | −1.61647 | − | 0.778450i | ||||
\(461\) | 7506.17 | − | 9412.44i | 0.758345 | − | 0.950935i | −0.241465 | − | 0.970410i | \(-0.577628\pi\) |
0.999810 | + | 0.0194745i | \(0.00619933\pi\) | |||||||
\(462\) | −12.0809 | + | 52.9300i | −0.00121657 | + | 0.00533015i | ||||
\(463\) | 11753.9 | − | 5660.40i | 1.17981 | − | 0.568167i | 0.261954 | − | 0.965080i | \(-0.415633\pi\) |
0.917856 | + | 0.396914i | \(0.129919\pi\) | |||||||
\(464\) | −1338.98 | + | 5866.45i | −0.133967 | + | 0.586947i | ||||
\(465\) | −369.864 | − | 178.117i | −0.0368861 | − | 0.0177634i | ||||
\(466\) | 13861.9 | 1.37798 | ||||||||
\(467\) | 8743.50 | 0.866383 | 0.433192 | − | 0.901302i | \(-0.357387\pi\) | ||||
0.433192 | + | 0.901302i | \(0.357387\pi\) | |||||||
\(468\) | 23342.0 | + | 11240.9i | 2.30552 | + | 1.11028i | ||||
\(469\) | −350.445 | − | 1535.40i | −0.0345033 | − | 0.151169i | ||||
\(470\) | −19783.7 | − | 24808.0i | −1.94161 | − | 2.43470i | ||||
\(471\) | −137.793 | + | 172.786i | −0.0134801 | + | 0.0169036i | ||||
\(472\) | 18654.3 | 1.81913 | ||||||||
\(473\) | −2736.78 | − | 207.020i | −0.266041 | − | 0.0201243i | ||||
\(474\) | 9.72456 | 0.000942329 | ||||||||
\(475\) | 2378.14 | − | 2982.10i | 0.229719 | − | 0.288059i | ||||
\(476\) | 3519.31 | + | 4413.08i | 0.338881 | + | 0.424943i | ||||
\(477\) | −851.475 | − | 3730.56i | −0.0817324 | − | 0.358093i | ||||
\(478\) | 8590.83 | + | 4137.13i | 0.822041 | + | 0.395874i | ||||
\(479\) | −1878.47 | −0.179185 | −0.0895924 | − | 0.995979i | \(-0.528556\pi\) | ||||
−0.0895924 | + | 0.995979i | \(0.528556\pi\) | |||||||
\(480\) | 173.454 | 0.0164939 | ||||||||
\(481\) | −22773.1 | − | 10967.0i | −2.15876 | − | 1.03961i | ||||
\(482\) | 329.991 | − | 1445.79i | 0.0311840 | − | 0.136626i | ||||
\(483\) | 87.4509 | − | 42.1142i | 0.00823842 | − | 0.00396741i | ||||
\(484\) | 4548.80 | − | 19929.6i | 0.427198 | − | 1.87168i | ||||
\(485\) | 11367.0 | − | 14253.8i | 1.06422 | − | 1.33450i | ||||
\(486\) | −3092.42 | − | 1489.23i | −0.288632 | − | 0.138998i | ||||
\(487\) | −6315.58 | + | 7919.49i | −0.587652 | + | 0.736892i | −0.983397 | − | 0.181468i | \(-0.941915\pi\) |
0.395745 | + | 0.918360i | \(0.370486\pi\) | |||||||
\(488\) | 4384.12 | + | 19208.1i | 0.406680 | + | 1.78178i | ||||
\(489\) | −649.317 | + | 312.694i | −0.0600473 | + | 0.0289172i | ||||
\(490\) | −18316.8 | + | 8820.93i | −1.68872 | + | 0.813242i | ||||
\(491\) | 5636.17 | + | 7067.53i | 0.518038 | + | 0.649599i | 0.970191 | − | 0.242341i | \(-0.0779154\pi\) |
−0.452153 | + | 0.891940i | \(0.649344\pi\) | |||||||
\(492\) | −310.702 | − | 1361.27i | −0.0284706 | − | 0.124738i | ||||
\(493\) | −1675.62 | + | 7341.36i | −0.153075 | + | 0.670666i | ||||
\(494\) | −23477.8 | − | 29440.2i | −2.13829 | − | 2.68133i | ||||
\(495\) | −2027.28 | − | 2542.12i | −0.184079 | − | 0.230828i | ||||
\(496\) | 1781.88 | − | 7806.94i | 0.161308 | − | 0.706738i | ||||
\(497\) | −770.269 | − | 3374.77i | −0.0695197 | − | 0.304586i | ||||
\(498\) | −760.675 | − | 953.857i | −0.0684472 | − | 0.0858300i | ||||
\(499\) | 10178.9 | − | 4901.91i | 0.913169 | − | 0.439759i | 0.0825416 | − | 0.996588i | \(-0.473696\pi\) |
0.830627 | + | 0.556829i | \(0.187982\pi\) | |||||||
\(500\) | 17719.7 | − | 8533.35i | 1.58490 | − | 0.763246i | ||||
\(501\) | 61.4113 | + | 269.060i | 0.00547636 | + | 0.0239935i | ||||
\(502\) | −12404.2 | + | 15554.3i | −1.10284 | + | 1.38291i | ||||
\(503\) | 7664.75 | + | 3691.15i | 0.679432 | + | 0.327197i | 0.741575 | − | 0.670870i | \(-0.234079\pi\) |
−0.0621428 | + | 0.998067i | \(0.519793\pi\) | |||||||
\(504\) | 2507.39 | − | 3144.16i | 0.221603 | − | 0.277881i | ||||
\(505\) | −1265.61 | + | 5545.00i | −0.111523 | + | 0.488613i | ||||
\(506\) | 3744.40 | − | 1803.21i | 0.328970 | − | 0.158424i | ||||
\(507\) | 84.7347 | − | 371.247i | 0.00742248 | − | 0.0325200i | ||||
\(508\) | 13937.9 | + | 6712.16i | 1.21731 | + | 0.586228i | ||||
\(509\) | 963.852 | 0.0839332 | 0.0419666 | − | 0.999119i | \(-0.486638\pi\) | ||||
0.0419666 | + | 0.999119i | \(0.486638\pi\) | |||||||
\(510\) | 1890.91 | 0.164179 | ||||||||
\(511\) | 90.5517 | + | 43.6074i | 0.00783909 | + | 0.00377511i | ||||
\(512\) | −5052.92 | − | 22138.3i | −0.436152 | − | 1.91090i | ||||
\(513\) | 1396.62 | + | 1751.30i | 0.120199 | + | 0.150725i | ||||
\(514\) | 11550.4 | − | 14483.8i | 0.991183 | − | 1.24290i | ||||
\(515\) | −21593.2 | −1.84759 | ||||||||
\(516\) | −1285.28 | − | 743.254i | −0.109653 | − | 0.0634107i | ||||
\(517\) | 5020.87 | 0.427113 | ||||||||
\(518\) | −4739.08 | + | 5942.62i | −0.401976 | + | 0.504061i | ||||
\(519\) | 521.562 | + | 654.018i | 0.0441118 | + | 0.0553144i | ||||
\(520\) | 6805.45 | + | 29816.6i | 0.573921 | + | 2.51451i | ||||
\(521\) | −2023.94 | − | 974.680i | −0.170193 | − | 0.0819607i | 0.346848 | − | 0.937922i | \(-0.387252\pi\) |
−0.517041 | + | 0.855961i | \(0.672966\pi\) | |||||||
\(522\) | 10393.4 | 0.871465 | ||||||||
\(523\) | 5441.13 | 0.454921 | 0.227461 | − | 0.973787i | \(-0.426958\pi\) | ||||
0.227461 | + | 0.973787i | \(0.426958\pi\) | |||||||
\(524\) | −1984.23 | − | 955.557i | −0.165423 | − | 0.0796635i | ||||
\(525\) | 7.32294 | − | 32.0839i | 0.000608761 | − | 0.00266716i | ||||
\(526\) | −26566.5 | + | 12793.7i | −2.20219 | + | 1.06052i | ||||
\(527\) | 2229.87 | − | 9769.71i | 0.184317 | − | 0.807543i | ||||
\(528\) | −149.074 | + | 186.932i | −0.0122871 | + | 0.0154076i | ||||
\(529\) | 4267.76 | + | 2055.24i | 0.350765 | + | 0.168920i | ||||
\(530\) | 5456.02 | − | 6841.63i | 0.447159 | − | 0.560720i | ||||
\(531\) | −2640.90 | − | 11570.5i | −0.215829 | − | 0.945608i | ||||
\(532\) | −6875.63 | + | 3311.13i | −0.560331 | + | 0.269841i | ||||
\(533\) | 13916.3 | − | 6701.76i | 1.13093 | − | 0.544625i | ||||
\(534\) | −17.7377 | − | 22.2424i | −0.00143743 | − | 0.00180248i | ||||
\(535\) | 36.4792 | + | 159.826i | 0.00294792 | + | 0.0129157i | ||||
\(536\) | 4189.98 | − | 18357.5i | 0.337648 | − | 1.47933i | ||||
\(537\) | −121.103 | − | 151.858i | −0.00973180 | − | 0.0122033i | ||||
\(538\) | −2739.45 | − | 3435.17i | −0.219528 | − | 0.275280i | ||||
\(539\) | 715.834 | − | 3136.27i | 0.0572044 | − | 0.250629i | ||||
\(540\) | −784.268 | − | 3436.10i | −0.0624991 | − | 0.273827i | ||||
\(541\) | 5017.65 | + | 6291.93i | 0.398753 | + | 0.500021i | 0.940157 | − | 0.340742i | \(-0.110678\pi\) |
−0.541404 | + | 0.840763i | \(0.682107\pi\) | |||||||
\(542\) | −38534.2 | + | 18557.1i | −3.05385 | + | 1.47066i | ||||
\(543\) | −420.888 | + | 202.689i | −0.0332634 | + | 0.0160188i | ||||
\(544\) | 942.178 | + | 4127.95i | 0.0742565 | + | 0.325339i | ||||
\(545\) | −8419.37 | + | 10557.6i | −0.661736 | + | 0.829791i | ||||
\(546\) | −292.715 | − | 140.964i | −0.0229433 | − | 0.0110489i | ||||
\(547\) | −3555.93 | + | 4459.00i | −0.277954 | + | 0.348543i | −0.901138 | − | 0.433532i | \(-0.857267\pi\) |
0.623185 | + | 0.782075i | \(0.285839\pi\) | |||||||
\(548\) | −1916.13 | + | 8395.09i | −0.149366 | + | 0.654417i | ||||
\(549\) | 11293.4 | − | 5438.60i | 0.877941 | − | 0.422794i | ||||
\(550\) | 313.547 | − | 1373.74i | 0.0243086 | − | 0.106503i | ||||
\(551\) | −9172.50 | − | 4417.24i | −0.709187 | − | 0.341526i | ||||
\(552\) | 1160.50 | 0.0894825 | ||||||||
\(553\) | 21.8015 | 0.00167648 | ||||||||
\(554\) | −31384.4 | − | 15113.9i | −2.40685 | − | 1.15908i | ||||
\(555\) | 381.858 | + | 1673.03i | 0.0292053 | + | 0.127957i | ||||
\(556\) | 18621.8 | + | 23351.0i | 1.42040 | + | 1.78112i | ||||
\(557\) | −12874.1 | + | 16143.6i | −0.979340 | + | 1.22805i | −0.00569462 | + | 0.999984i | \(0.501813\pi\) |
−0.973645 | + | 0.228069i | \(0.926759\pi\) | |||||||
\(558\) | −13831.2 | −1.04932 | ||||||||
\(559\) | 4852.10 | − | 15691.1i | 0.367123 | − | 1.18723i | ||||
\(560\) | 3387.57 | 0.255626 | ||||||||
\(561\) | −186.553 | + | 233.930i | −0.0140397 | + | 0.0176052i | ||||
\(562\) | 20193.1 | + | 25321.4i | 1.51565 | + | 1.90057i | ||||
\(563\) | −2671.54 | − | 11704.8i | −0.199986 | − | 0.876195i | −0.970943 | − | 0.239309i | \(-0.923079\pi\) |
0.770958 | − | 0.636886i | \(-0.219778\pi\) | |||||||
\(564\) | 2447.10 | + | 1178.46i | 0.182698 | + | 0.0879825i | ||||
\(565\) | 4967.21 | 0.369862 | ||||||||
\(566\) | 26359.8 | 1.95757 | ||||||||
\(567\) | −2296.45 | − | 1105.91i | −0.170092 | − | 0.0819119i | ||||
\(568\) | 9209.47 | − | 40349.3i | 0.680318 | − | 2.98067i | ||||
\(569\) | −11158.0 | + | 5373.42i | −0.822089 | + | 0.395897i | −0.797142 | − | 0.603792i | \(-0.793656\pi\) |
−0.0249468 | + | 0.999689i | \(0.507942\pi\) | |||||||
\(570\) | −568.875 | + | 2492.40i | −0.0418027 | + | 0.183150i | ||||
\(571\) | 3333.91 | − | 4180.58i | 0.244343 | − | 0.306396i | −0.644504 | − | 0.764601i | \(-0.722936\pi\) |
0.888846 | + | 0.458205i | \(0.151507\pi\) | |||||||
\(572\) | −8446.65 | − | 4067.69i | −0.617434 | − | 0.297341i | ||||
\(573\) | −127.196 | + | 159.499i | −0.00927348 | + | 0.0116286i | ||||
\(574\) | −1033.57 | − | 4528.35i | −0.0751571 | − | 0.329285i | ||||
\(575\) | −2269.69 | + | 1093.03i | −0.164613 | + | 0.0792737i | ||||
\(576\) | −9690.30 | + | 4666.60i | −0.700977 | + | 0.337573i | ||||
\(577\) | −9144.73 | − | 11467.1i | −0.659792 | − | 0.827353i | 0.333528 | − | 0.942740i | \(-0.391761\pi\) |
−0.993321 | + | 0.115387i | \(0.963189\pi\) | |||||||
\(578\) | 4855.95 | + | 21275.3i | 0.349448 | + | 1.53103i | ||||
\(579\) | 14.5467 | − | 63.7331i | 0.00104411 | − | 0.00457454i | ||||
\(580\) | 9987.42 | + | 12523.8i | 0.715009 | + | 0.896593i | ||||
\(581\) | −1705.36 | − | 2138.45i | −0.121773 | − | 0.152699i | ||||
\(582\) | −515.262 | + | 2257.51i | −0.0366981 | + | 0.160785i | ||||
\(583\) | 308.119 | + | 1349.96i | 0.0218885 | + | 0.0958996i | ||||
\(584\) | 749.218 | + | 939.490i | 0.0530871 | + | 0.0665691i | ||||
\(585\) | 17530.7 | − | 8442.32i | 1.23898 | − | 0.596662i | ||||
\(586\) | 43292.5 | − | 20848.6i | 3.05187 | − | 1.46971i | ||||
\(587\) | −2381.32 | − | 10433.3i | −0.167441 | − | 0.733606i | −0.987014 | − | 0.160632i | \(-0.948647\pi\) |
0.819574 | − | 0.572974i | \(-0.194210\pi\) | |||||||
\(588\) | 1085.01 | − | 1360.56i | 0.0760970 | − | 0.0954226i | ||||
\(589\) | 12206.6 | + | 5878.37i | 0.853926 | + | 0.411229i | ||||
\(590\) | 16922.1 | − | 21219.7i | 1.18080 | − | 1.48068i | ||||
\(591\) | 265.461 | − | 1163.06i | 0.0184765 | − | 0.0809508i | ||||
\(592\) | −30159.0 | + | 14523.8i | −2.09379 | + | 1.00832i | ||||
\(593\) | −5807.27 | + | 25443.3i | −0.402152 | + | 1.76194i | 0.216505 | + | 0.976281i | \(0.430534\pi\) |
−0.618657 | + | 0.785661i | \(0.712323\pi\) | |||||||
\(594\) | 745.558 | + | 359.042i | 0.0514994 | + | 0.0248008i | ||||
\(595\) | 4239.24 | 0.292088 | ||||||||
\(596\) | −21949.5 | −1.50854 | ||||||||
\(597\) | 47.8228 | + | 23.0303i | 0.00327849 | + | 0.00157884i | ||||
\(598\) | 5534.12 | + | 24246.5i | 0.378439 | + | 1.65805i | ||||
\(599\) | 13632.9 | + | 17095.1i | 0.929926 | + | 1.16609i | 0.985846 | + | 0.167655i | \(0.0536194\pi\) |
−0.0559200 | + | 0.998435i | \(0.517809\pi\) | |||||||
\(600\) | 245.322 | − | 307.624i | 0.0166920 | − | 0.0209312i | ||||
\(601\) | 20916.6 | 1.41965 | 0.709823 | − | 0.704380i | \(-0.248775\pi\) | ||||
0.709823 | + | 0.704380i | \(0.248775\pi\) | |||||||
\(602\) | −4275.53 | − | 2472.47i | −0.289465 | − | 0.167393i | ||||
\(603\) | −11979.6 | −0.809035 | ||||||||
\(604\) | −16407.4 | + | 20574.2i | −1.10531 | + | 1.38601i | ||||
\(605\) | −9572.28 | − | 12003.3i | −0.643254 | − | 0.806615i | ||||
\(606\) | −160.746 | − | 704.275i | −0.0107754 | − | 0.0472099i | ||||
\(607\) | −4901.39 | − | 2360.39i | −0.327745 | − | 0.157834i | 0.262774 | − | 0.964857i | \(-0.415363\pi\) |
−0.590519 | + | 0.807024i | \(0.701077\pi\) | |||||||
\(608\) | −5724.48 | −0.381839 | ||||||||
\(609\) | −87.8384 | −0.00584465 | ||||||||
\(610\) | 25826.7 | + | 12437.5i | 1.71425 | + | 0.825541i | ||||
\(611\) | −6685.83 | + | 29292.5i | −0.442683 | + | 1.93952i | ||||
\(612\) | 38684.1 | − | 18629.3i | 2.55509 | − | 1.23046i | ||||
\(613\) | −4477.37 | + | 19616.7i | −0.295007 | + | 1.29251i | 0.582454 | + | 0.812864i | \(0.302093\pi\) |
−0.877461 | + | 0.479648i | \(0.840765\pi\) | |||||||
\(614\) | −2833.24 | + | 3552.76i | −0.186222 | + | 0.233515i | ||||
\(615\) | −944.806 | − | 454.995i | −0.0619484 | − | 0.0298328i | ||||
\(616\) | −907.335 | + | 1137.76i | −0.0593467 | + | 0.0744184i | ||||
\(617\) | 569.814 | + | 2496.52i | 0.0371796 | + | 0.162895i | 0.990110 | − | 0.140296i | \(-0.0448053\pi\) |
−0.952930 | + | 0.303190i | \(0.901948\pi\) | |||||||
\(618\) | 2470.97 | − | 1189.95i | 0.160836 | − | 0.0774547i | ||||
\(619\) | 5107.93 | − | 2459.85i | 0.331672 | − | 0.159725i | −0.260635 | − | 0.965438i | \(-0.583932\pi\) |
0.592306 | + | 0.805713i | \(0.298217\pi\) | |||||||
\(620\) | −13291.0 | − | 16666.4i | −0.860937 | − | 1.07958i | ||||
\(621\) | −329.206 | − | 1442.35i | −0.0212731 | − | 0.0932035i | ||||
\(622\) | 2248.27 | − | 9850.31i | 0.144931 | − | 0.634986i | ||||
\(623\) | −39.7662 | − | 49.8653i | −0.00255730 | − | 0.00320676i | ||||
\(624\) | −892.084 | − | 1118.64i | −0.0572307 | − | 0.0717650i | ||||
\(625\) | 4099.74 | − | 17962.1i | 0.262383 | − | 1.14958i | ||||
\(626\) | 1123.41 | + | 4921.99i | 0.0717262 | + | 0.314253i | ||||
\(627\) | −252.218 | − | 316.271i | −0.0160648 | − | 0.0201446i | ||||
\(628\) | −10339.6 | + | 4979.28i | −0.656997 | + | 0.316393i | ||||
\(629\) | −37741.3 | + | 18175.3i | −2.39244 | + | 1.15214i | ||||
\(630\) | −1302.00 | − | 5704.44i | −0.0823380 | − | 0.360746i | ||||
\(631\) | −4641.91 | + | 5820.77i | −0.292855 | + | 0.367228i | −0.906392 | − | 0.422437i | \(-0.861175\pi\) |
0.613537 | + | 0.789666i | \(0.289746\pi\) | |||||||
\(632\) | 234.849 | + | 113.097i | 0.0147813 | + | 0.00711831i | ||||
\(633\) | 986.584 | − | 1237.14i | 0.0619482 | − | 0.0776805i | ||||
\(634\) | −221.233 | + | 969.286i | −0.0138585 | + | 0.0607181i | ||||
\(635\) | 10467.9 | − | 5041.06i | 0.654181 | − | 0.315037i | ||||
\(636\) | −166.679 | + | 730.268i | −0.0103919 | + | 0.0455299i | ||||
\(637\) | 17344.3 | + | 8352.56i | 1.07882 | + | 0.519530i | ||||
\(638\) | −3760.99 | −0.233384 | ||||||||
\(639\) | −26330.9 | −1.63010 | ||||||||
\(640\) | −26086.8 | − | 12562.7i | −1.61121 | − | 0.775916i | ||||
\(641\) | 2295.26 | + | 10056.2i | 0.141431 | + | 0.619649i | 0.995103 | + | 0.0988392i | \(0.0315130\pi\) |
−0.853672 | + | 0.520810i | \(0.825630\pi\) | |||||||
\(642\) | −12.9821 | − | 16.2790i | −0.000798072 | − | 0.00100075i | ||||
\(643\) | −1187.73 | + | 1489.37i | −0.0728454 | + | 0.0913452i | −0.816919 | − | 0.576752i | \(-0.804320\pi\) |
0.744074 | + | 0.668098i | \(0.232891\pi\) | |||||||
\(644\) | 5040.24 | 0.308406 | ||||||||
\(645\) | −1038.27 | + | 406.653i | −0.0633828 | + | 0.0248247i | ||||
\(646\) | −62405.5 | −3.80079 | ||||||||
\(647\) | 13696.2 | − | 17174.5i | 0.832233 | − | 1.04359i | −0.166113 | − | 0.986107i | \(-0.553122\pi\) |
0.998347 | − | 0.0574808i | \(-0.0183068\pi\) | |||||||
\(648\) | −19000.7 | − | 23826.1i | −1.15188 | − | 1.44441i | ||||
\(649\) | 955.647 | + | 4186.96i | 0.0578003 | + | 0.253240i | ||||
\(650\) | 7597.09 | + | 3658.56i | 0.458434 | + | 0.220770i | ||||
\(651\) | 116.893 | 0.00703750 | ||||||||
\(652\) | −37423.4 | −2.24788 | ||||||||
\(653\) | −17511.3 | − | 8433.00i | −1.04942 | − | 0.505373i | −0.171999 | − | 0.985097i | \(-0.555023\pi\) |
−0.877419 | + | 0.479724i | \(0.840737\pi\) | |||||||
\(654\) | 381.647 | − | 1672.10i | 0.0228189 | − | 0.0999762i | ||||
\(655\) | −1490.23 | + | 717.656i | −0.0888978 | + | 0.0428109i | ||||
\(656\) | 4551.76 | − | 19942.6i | 0.270909 | − | 1.18693i | ||||
\(657\) | 476.662 | − | 597.716i | 0.0283050 | − | 0.0354933i | ||||
\(658\) | 8140.40 | + | 3920.21i | 0.482288 | + | 0.232258i | ||||
\(659\) | 13900.5 | − | 17430.7i | 0.821680 | − | 1.03035i | −0.177252 | − | 0.984165i | \(-0.556721\pi\) |
0.998933 | − | 0.0461890i | \(-0.0147076\pi\) | |||||||
\(660\) | 141.633 | + | 620.533i | 0.00835309 | + | 0.0365973i | ||||
\(661\) | −2496.77 | + | 1202.38i | −0.146918 | + | 0.0707522i | −0.505898 | − | 0.862593i | \(-0.668839\pi\) |
0.358980 | + | 0.933345i | \(0.383125\pi\) | |||||||
\(662\) | 53282.3 | − | 25659.4i | 3.12821 | − | 1.50647i | ||||
\(663\) | −1116.37 | − | 1399.88i | −0.0653938 | − | 0.0820012i | ||||
\(664\) | −7276.96 | − | 31882.4i | −0.425302 | − | 1.86337i | ||||
\(665\) | −1275.36 | + | 5587.73i | −0.0743706 | + | 0.325839i | ||||
\(666\) | 36048.6 | + | 45203.5i | 2.09738 | + | 2.63003i | ||||
\(667\) | 4192.34 | + | 5257.03i | 0.243370 | + | 0.305177i | ||||
\(668\) | −3188.93 | + | 13971.6i | −0.184706 | + | 0.809249i | ||||
\(669\) | 305.006 | + | 1336.32i | 0.0176266 | + | 0.0772273i | ||||
\(670\) | −17081.2 | − | 21419.1i | −0.984931 | − | 1.23506i | ||||
\(671\) | −4086.68 | + | 1968.04i | −0.235118 | + | 0.113227i | ||||
\(672\) | −44.4992 | + | 21.4297i | −0.00255446 | + | 0.00123016i | ||||
\(673\) | 631.552 | + | 2767.01i | 0.0361732 | + | 0.158485i | 0.989789 | − | 0.142542i | \(-0.0455277\pi\) |
−0.953616 | + | 0.301027i | \(0.902671\pi\) | |||||||
\(674\) | 30678.1 | − | 38469.2i | 1.75323 | − | 2.19848i | ||||
\(675\) | −451.925 | − | 217.636i | −0.0257698 | − | 0.0124101i | ||||
\(676\) | 12328.7 | − | 15459.7i | 0.701450 | − | 0.879590i | ||||
\(677\) | −4334.13 | + | 18989.0i | −0.246047 | + | 1.07800i | 0.689357 | + | 0.724422i | \(0.257893\pi\) |
−0.935404 | + | 0.353581i | \(0.884964\pi\) | |||||||
\(678\) | −568.412 | + | 273.733i | −0.0321972 | + | 0.0155054i | ||||
\(679\) | −1155.17 | + | 5061.12i | −0.0652890 | + | 0.286050i | ||||
\(680\) | 45665.7 | + | 21991.5i | 2.57530 | + | 1.24020i | ||||
\(681\) | −363.471 | −0.0204526 | ||||||||
\(682\) | 5005.04 | 0.281016 | ||||||||
\(683\) | −9626.50 | − | 4635.88i | −0.539309 | − | 0.259717i | 0.144341 | − | 0.989528i | \(-0.453894\pi\) |
−0.683649 | + | 0.729811i | \(0.739608\pi\) | |||||||
\(684\) | 12917.2 | + | 56593.9i | 0.722077 | + | 3.16363i | ||||
\(685\) | 4032.20 | + | 5056.22i | 0.224909 | + | 0.282027i | ||||
\(686\) | 7355.24 | − | 9223.18i | 0.409365 | − | 0.513327i | ||||
\(687\) | −700.099 | −0.0388798 | ||||||||
\(688\) | −12240.1 | − | 17980.0i | −0.678272 | − | 0.996340i | ||||
\(689\) | −8286.14 | −0.458167 | ||||||||
\(690\) | 1052.75 | − | 1320.10i | 0.0580832 | − | 0.0728340i | ||||
\(691\) | −11529.7 | − | 14457.8i | −0.634749 | − | 0.795951i | 0.355586 | − | 0.934644i | \(-0.384281\pi\) |
−0.990335 | + | 0.138693i | \(0.955710\pi\) | |||||||
\(692\) | 9665.94 | + | 42349.2i | 0.530988 | + | 2.32641i | ||||
\(693\) | 834.162 | + | 401.711i | 0.0457247 | + | 0.0220199i | ||||
\(694\) | 19259.2 | 1.05341 | ||||||||
\(695\) | 22431.2 | 1.22426 | ||||||||
\(696\) | −946.207 | − | 455.669i | −0.0515315 | − | 0.0248162i | ||||
\(697\) | 5696.14 | − | 24956.4i | 0.309550 | − | 1.35623i | ||||
\(698\) | −8740.72 | + | 4209.31i | −0.473985 | + | 0.228259i | ||||
\(699\) | −198.297 | + | 868.797i | −0.0107300 | + | 0.0470113i | ||||
\(700\) | 1065.47 | − | 1336.06i | 0.0575299 | − | 0.0721403i | ||||
\(701\) | 24101.6 | + | 11606.7i | 1.29858 | + | 0.625363i | 0.950098 | − | 0.311952i | \(-0.100983\pi\) |
0.348483 | + | 0.937315i | \(0.386697\pi\) | |||||||
\(702\) | −3087.50 | + | 3871.60i | −0.165997 | + | 0.208154i | ||||
\(703\) | −12602.4 | − | 55214.6i | −0.676114 | − | 2.96225i | ||||
\(704\) | 3506.58 | − | 1688.68i | 0.187726 | − | 0.0904041i | ||||
\(705\) | 1837.86 | − | 885.065i | 0.0981811 | − | 0.0472815i | ||||
\(706\) | 8664.84 | + | 10865.4i | 0.461906 | + | 0.579212i | ||||
\(707\) | −360.377 | − | 1578.92i | −0.0191703 | − | 0.0839905i | ||||
\(708\) | −516.964 | + | 2264.97i | −0.0274416 | + | 0.120230i | ||||
\(709\) | 11983.9 | + | 15027.3i | 0.634788 | + | 0.795999i | 0.990340 | − | 0.138658i | \(-0.0442788\pi\) |
−0.355553 | + | 0.934656i | \(0.615707\pi\) | |||||||
\(710\) | −37544.1 | − | 47078.8i | −1.98451 | − | 2.48850i | ||||
\(711\) | 36.9022 | − | 161.679i | 0.00194647 | − | 0.00852804i | ||||
\(712\) | −169.687 | − | 743.446i | −0.00893157 | − | 0.0391318i | ||||
\(713\) | −5579.07 | − | 6995.93i | −0.293040 | − | 0.367461i | ||||
\(714\) | −485.109 | + | 233.616i | −0.0254268 | + | 0.0122449i | ||||
\(715\) | −6343.73 | + | 3054.98i | −0.331807 | + | 0.159790i | ||||
\(716\) | −2244.36 | − | 9833.20i | −0.117145 | − | 0.513246i | ||||
\(717\) | −382.189 | + | 479.250i | −0.0199067 | + | 0.0249622i | ||||
\(718\) | 25963.1 | + | 12503.2i | 1.34949 | + | 0.649881i | ||||
\(719\) | −9816.51 | + | 12309.5i | −0.509171 | + | 0.638480i | −0.968270 | − | 0.249905i | \(-0.919601\pi\) |
0.459100 | + | 0.888385i | \(0.348172\pi\) | |||||||
\(720\) | 5733.94 | − | 25122.0i | 0.296793 | − | 1.30034i | ||||
\(721\) | 5539.67 | − | 2667.76i | 0.286141 | − | 0.137798i | ||||
\(722\) | 11214.3 | − | 49133.2i | 0.578053 | − | 2.53262i | ||||
\(723\) | 85.8943 | + | 41.3645i | 0.00441832 | + | 0.00212775i | ||||
\(724\) | −24257.9 | −1.24522 | ||||||||
\(725\) | 2279.75 | 0.116783 | ||||||||
\(726\) | 1756.86 | + | 846.058i | 0.0898114 | + | 0.0432509i | ||||
\(727\) | 5331.05 | + | 23356.8i | 0.271964 | + | 1.19155i | 0.907692 | + | 0.419637i | \(0.137843\pi\) |
−0.635728 | + | 0.771913i | \(0.719300\pi\) | |||||||
\(728\) | −5429.66 | − | 6808.58i | −0.276424 | − | 0.346625i | ||||
\(729\) | −11996.5 | + | 15043.1i | −0.609484 | + | 0.764269i | ||||
\(730\) | 1748.35 | 0.0886427 | ||||||||
\(731\) | −15317.5 | − | 22500.4i | −0.775017 | − | 1.13845i | ||||
\(732\) | −2453.71 | −0.123896 | ||||||||
\(733\) | −1867.34 | + | 2341.57i | −0.0940953 | + | 0.117992i | −0.826650 | − | 0.562716i | \(-0.809756\pi\) |
0.732555 | + | 0.680708i | \(0.238328\pi\) | |||||||
\(734\) | −5919.41 | − | 7422.71i | −0.297670 | − | 0.373266i | ||||
\(735\) | −290.827 | − | 1274.20i | −0.0145950 | − | 0.0639448i | ||||
\(736\) | 3406.39 | + | 1640.43i | 0.170600 | + | 0.0821565i | ||||
\(737\) | 4335.00 | 0.216665 | ||||||||
\(738\) | −35331.5 | −1.76229 | ||||||||
\(739\) | 5414.86 | + | 2607.66i | 0.269538 | + | 0.129803i | 0.563771 | − | 0.825931i | \(-0.309350\pi\) |
−0.294233 | + | 0.955734i | \(0.595064\pi\) | |||||||
\(740\) | −19828.9 | + | 86876.1i | −0.985033 | + | 4.31571i | ||||
\(741\) | 2181.03 | − | 1050.33i | 0.108127 | − | 0.0520712i | ||||
\(742\) | −554.466 | + | 2429.27i | −0.0274327 | + | 0.120191i | ||||
\(743\) | 7753.14 | − | 9722.13i | 0.382820 | − | 0.480041i | −0.552667 | − | 0.833402i | \(-0.686390\pi\) |
0.935487 | + | 0.353361i | \(0.114961\pi\) | |||||||
\(744\) | 1259.19 | + | 606.395i | 0.0620486 | + | 0.0298811i | ||||
\(745\) | −10278.1 | + | 12888.4i | −0.505452 | + | 0.633817i | ||||
\(746\) | 7465.88 | + | 32710.2i | 0.366415 | + | 1.60537i | ||||
\(747\) | −18745.2 | + | 9027.23i | −0.918143 | + | 0.442154i | ||||
\(748\) | −13998.4 | + | 6741.28i | −0.684269 | + | 0.329526i | ||||
\(749\) | −29.1046 | − | 36.4960i | −0.00141984 | − | 0.00178042i | ||||
\(750\) | 417.463 | + | 1829.02i | 0.0203248 | + | 0.0890487i | ||||
\(751\) | 7377.49 | − | 32322.9i | 0.358467 | − | 1.57055i | −0.398548 | − | 0.917148i | \(-0.630486\pi\) |
0.757014 | − | 0.653398i | \(-0.226657\pi\) | |||||||
\(752\) | 24808.9 | + | 31109.4i | 1.20304 | + | 1.50857i | ||||
\(753\) | −797.426 | − | 999.941i | −0.0385921 | − | 0.0483929i | ||||
\(754\) | 5008.16 | − | 21942.2i | 0.241892 | − | 1.05980i | ||||
\(755\) | 4397.85 | + | 19268.2i | 0.211992 | + | 0.928798i | ||||
\(756\) | 625.721 | + | 784.629i | 0.0301022 | + | 0.0377469i | ||||
\(757\) | 1895.98 | − | 913.057i | 0.0910312 | − | 0.0438383i | −0.387814 | − | 0.921738i | \(-0.626770\pi\) |
0.478845 | + | 0.877899i | \(0.341055\pi\) | |||||||
\(758\) | 33476.9 | − | 16121.6i | 1.60414 | − | 0.772511i | ||||
\(759\) | 59.4520 | + | 260.476i | 0.00284318 | + | 0.0124568i | ||||
\(760\) | −42725.2 | + | 53575.7i | −2.03922 | + | 2.55710i | ||||
\(761\) | −6692.60 | − | 3222.99i | −0.318800 | − | 0.153526i | 0.267639 | − | 0.963519i | \(-0.413756\pi\) |
−0.586439 | + | 0.809993i | \(0.699471\pi\) | |||||||
\(762\) | −920.066 | + | 1153.73i | −0.0437408 | + | 0.0548492i | ||||
\(763\) | 855.615 | − | 3748.69i | 0.0405968 | − | 0.177866i | ||||
\(764\) | −9544.48 | + | 4596.38i | −0.451973 | + | 0.217659i | ||||
\(765\) | 7175.53 | − | 31438.0i | 0.339126 | − | 1.48581i | ||||
\(766\) | 16471.5 | + | 7932.26i | 0.776945 | + | 0.374157i | ||||
\(767\) | −25699.9 | −1.20987 | ||||||||
\(768\) | 2658.88 | 0.124927 | ||||||||
\(769\) | −24568.7 | − | 11831.7i | −1.15211 | − | 0.554826i | −0.242442 | − | 0.970166i | \(-0.577949\pi\) |
−0.909667 | + | 0.415339i | \(0.863663\pi\) | |||||||
\(770\) | 471.148 | + | 2064.23i | 0.0220506 | + | 0.0966102i | ||||
\(771\) | 742.543 | + | 931.120i | 0.0346849 | + | 0.0434935i | ||||
\(772\) | 2116.50 | − | 2654.01i | 0.0986718 | − | 0.123731i | ||||
\(773\) | −21246.0 | −0.988571 | −0.494285 | − | 0.869300i | \(-0.664570\pi\) | ||||
−0.494285 | + | 0.869300i | \(0.664570\pi\) | |||||||
\(774\) | −25572.7 | + | 27522.2i | −1.18759 | + | 1.27812i | ||||
\(775\) | −3033.84 | −0.140618 | ||||||||
\(776\) | −38698.6 | + | 48526.5i | −1.79020 | + | 2.24485i | ||||
\(777\) | −304.661 | − | 382.033i | −0.0140665 | − | 0.0176388i | ||||
\(778\) | 3805.14 | + | 16671.4i | 0.175348 | + | 0.768251i | ||||
\(779\) | 31181.3 | + | 15016.1i | 1.43413 | + | 0.690639i | ||||
\(780\) | −3808.88 | −0.174846 | ||||||||
\(781\) | 9528.23 | 0.436552 | ||||||||
\(782\) | 37134.8 | + | 17883.2i | 1.69813 | + | 0.817777i | ||||
\(783\) | −297.919 | + | 1305.27i | −0.0135974 | + | 0.0595740i | ||||
\(784\) | 22969.4 | − | 11061.5i | 1.04635 | − | 0.503894i | ||||
\(785\) | −1917.89 | + | 8402.83i | −0.0872006 | + | 0.382051i | ||||
\(786\) | 130.982 | − | 164.247i | 0.00594401 | − | 0.00745355i | ||||
\(787\) | −33273.8 | − | 16023.8i | −1.50709 | − | 0.725778i | −0.515710 | − | 0.856763i | \(-0.672472\pi\) |
−0.991384 | + | 0.130985i | \(0.958186\pi\) | |||||||
\(788\) | 38623.9 | − | 48432.8i | 1.74609 | − | 2.18953i | ||||
\(789\) | −421.811 | − | 1848.08i | −0.0190328 | − | 0.0833881i | ||||
\(790\) | 341.694 | − | 164.551i | 0.0153885 | − | 0.00741071i | ||||
\(791\) | −1274.32 | + | 613.682i | −0.0572816 | + | 0.0275854i | ||||
\(792\) | 6901.80 | + | 8654.58i | 0.309652 | + | 0.388292i | ||||
\(793\) | −6039.99 | − | 26462.9i | −0.270475 | − | 1.18503i | ||||
\(794\) | −6287.33 | + | 27546.6i | −0.281019 | + | 1.23123i | ||||
\(795\) | 350.751 | + | 439.828i | 0.0156476 | + | 0.0196215i | ||||
\(796\) | 1718.51 | + | 2154.94i | 0.0765213 | + | 0.0959546i | ||||
\(797\) | −1917.66 | + | 8401.83i | −0.0852285 | + | 0.373410i | −0.999498 | − | 0.0316972i | \(-0.989909\pi\) |
0.914269 | + | 0.405108i | \(0.132766\pi\) | |||||||
\(798\) | −161.985 | − | 709.702i | −0.00718571 | − | 0.0314827i | ||||
\(799\) | 31046.2 | + | 38930.7i | 1.37464 | + | 1.72374i | ||||
\(800\) | 1154.93 | − | 556.184i | 0.0510411 | − | 0.0245801i | ||||
\(801\) | −437.108 | + | 210.500i | −0.0192815 | + | 0.00928547i | ||||
\(802\) | −11697.1 | − | 51248.2i | −0.515010 | − | 2.25641i | ||||
\(803\) | −172.487 | + | 216.292i | −0.00758026 | + | 0.00950534i | ||||
\(804\) | 2112.82 | + | 1017.48i | 0.0926782 | + | 0.0446315i | ||||
\(805\) | 2360.16 | − | 2959.54i | 0.103335 | − | 0.129578i | ||||
\(806\) | −6664.74 | + | 29200.1i | −0.291260 | + | 1.27609i | ||||
\(807\) | 254.488 | − | 122.555i | 0.0111009 | − | 0.00534590i | ||||
\(808\) | 4308.73 | − | 18877.8i | 0.187600 | − | 0.821929i | ||||
\(809\) | 11552.0 | + | 5563.16i | 0.502036 | + | 0.241768i | 0.667722 | − | 0.744411i | \(-0.267270\pi\) |
−0.165686 | + | 0.986179i | \(0.552984\pi\) | |||||||
\(810\) | −44339.2 | −1.92336 | ||||||||
\(811\) | 26275.3 | 1.13767 | 0.568835 | − | 0.822452i | \(-0.307394\pi\) | ||||
0.568835 | + | 0.822452i | \(0.307394\pi\) | |||||||
\(812\) | −4109.52 | − | 1979.04i | −0.177606 | − | 0.0855304i | ||||
\(813\) | −611.830 | − | 2680.60i | −0.0263934 | − | 0.115637i | ||||
\(814\) | −13044.7 | − | 16357.6i | −0.561692 | − | 0.704340i | ||||
\(815\) | −17524.0 | + | 21974.4i | −0.753176 | + | 0.944453i | ||||
\(816\) | −2371.22 | −0.101727 | ||||||||
\(817\) | 34265.9 | − | 13420.7i | 1.46733 | − | 0.574702i | ||||
\(818\) | −45417.8 | −1.94131 | ||||||||
\(819\) | −3454.42 | + | 4331.71i | −0.147384 | + | 0.184813i | ||||
\(820\) | −33951.5 | − | 42573.8i | −1.44590 | − | 1.81310i | ||||
\(821\) | −9248.07 | − | 40518.4i | −0.393130 | − | 1.72242i | −0.653517 | − | 0.756911i | \(-0.726707\pi\) |
0.260387 | − | 0.965504i | \(-0.416150\pi\) | |||||||
\(822\) | −740.054 | − | 356.391i | −0.0314019 | − | 0.0151224i | ||||
\(823\) | −21443.6 | −0.908234 | −0.454117 | − | 0.890942i | \(-0.650045\pi\) | ||||
−0.454117 | + | 0.890942i | \(0.650045\pi\) | |||||||
\(824\) | 73513.3 | 3.10796 | ||||||||
\(825\) | 81.6141 | + | 39.3033i | 0.00344417 | + | 0.00165862i | ||||
\(826\) | −1719.71 | + | 7534.53i | −0.0724410 | + | 0.317385i | ||||
\(827\) | 35575.3 | − | 17132.2i | 1.49586 | − | 0.720367i | 0.506014 | − | 0.862525i | \(-0.331118\pi\) |
0.989844 | + | 0.142158i | \(0.0454040\pi\) | |||||||
\(828\) | 8531.33 | − | 37378.2i | 0.358073 | − | 1.56882i | ||||
\(829\) | 5880.68 | − | 7374.14i | 0.246375 | − | 0.308944i | −0.643232 | − | 0.765671i | \(-0.722407\pi\) |
0.889607 | + | 0.456727i | \(0.150978\pi\) | |||||||
\(830\) | −42868.4 | − | 20644.3i | −1.79275 | − | 0.863343i | ||||
\(831\) | 1396.23 | − | 1750.82i | 0.0582848 | − | 0.0730868i | ||||
\(832\) | 5182.63 | + | 22706.6i | 0.215956 | + | 0.946164i | ||||
\(833\) | 28744.2 | − | 13842.5i | 1.19559 | − | 0.575767i | ||||
\(834\) | −2566.86 | + | 1236.14i | −0.106575 | + | 0.0513236i | ||||
\(835\) | 6710.64 | + | 8414.87i | 0.278121 | + | 0.348753i | ||||
\(836\) | −4674.27 | − | 20479.3i | −0.193377 | − | 0.847240i | ||||
\(837\) | 396.463 | − | 1737.02i | 0.0163725 | − | 0.0717326i | ||||
\(838\) | −29764.4 | − | 37323.4i | −1.22696 | − | 1.53856i | ||||
\(839\) | 21044.9 | + | 26389.5i | 0.865974 | + | 1.08590i | 0.995541 | + | 0.0943266i | \(0.0300698\pi\) |
−0.129567 | + | 0.991571i | \(0.541359\pi\) | |||||||
\(840\) | −131.562 | + | 576.413i | −0.00540397 | + | 0.0236763i | ||||
\(841\) | 4073.03 | + | 17845.1i | 0.167003 | + | 0.731688i | ||||
\(842\) | 24461.3 | + | 30673.5i | 1.00118 | + | 1.25544i | ||||
\(843\) | −1875.89 | + | 903.381i | −0.0766419 | + | 0.0369088i | ||||
\(844\) | 74030.6 | − | 35651.3i | 3.01924 | − | 1.45399i | ||||
\(845\) | −3304.59 | − | 14478.4i | −0.134534 | − | 0.589433i | ||||
\(846\) | 42850.9 | − | 53733.3i | 1.74142 | − | 2.18367i | ||||
\(847\) | 3938.70 | + | 1896.78i | 0.159782 | + | 0.0769470i | ||||
\(848\) | −6841.88 | + | 8579.44i | −0.277065 | + | 0.347428i | ||||
\(849\) | −377.082 | + | 1652.10i | −0.0152431 | + | 0.0667846i | ||||
\(850\) | 12590.5 | − | 6063.25i | 0.508058 | − | 0.244668i | ||||
\(851\) | −8323.42 | + | 36467.3i | −0.335280 | + | 1.46896i | ||||
\(852\) | 4643.92 | + | 2236.39i | 0.186735 | + | 0.0899268i | ||||
\(853\) | −4810.50 | −0.193093 | −0.0965466 | − | 0.995328i | \(-0.530780\pi\) | ||||
−0.0965466 | + | 0.995328i | \(0.530780\pi\) | |||||||
\(854\) | −8162.39 | −0.327062 | ||||||||
\(855\) | 39279.6 | + | 18916.1i | 1.57115 | + | 0.756626i | ||||
\(856\) | −124.192 | − | 544.123i | −0.00495889 | − | 0.0217263i | ||||
\(857\) | −11306.6 | − | 14178.0i | −0.450671 | − | 0.565124i | 0.503649 | − | 0.863908i | \(-0.331990\pi\) |
−0.954321 | + | 0.298784i | \(0.903419\pi\) | |||||||
\(858\) | 557.577 | − | 699.179i | 0.0221857 | − | 0.0278200i | ||||
\(859\) | 3895.00 | 0.154710 | 0.0773549 | − | 0.997004i | \(-0.475353\pi\) | ||||
0.0773549 | + | 0.997004i | \(0.475353\pi\) | |||||||
\(860\) | −57737.7 | − | 4367.48i | −2.28935 | − | 0.173174i | ||||
\(861\) | 298.600 | 0.0118191 | ||||||||
\(862\) | −36076.2 | + | 45238.1i | −1.42547 | + | 1.78749i | ||||
\(863\) | 8676.03 | + | 10879.4i | 0.342220 | + | 0.429130i | 0.922923 | − | 0.384986i | \(-0.125794\pi\) |
−0.580703 | + | 0.814116i | \(0.697222\pi\) | |||||||
\(864\) | 167.516 | + | 733.935i | 0.00659607 | + | 0.0288993i | ||||
\(865\) | 29392.9 | + | 14154.9i | 1.15536 | + | 0.556394i | ||||
\(866\) | −6589.38 | −0.258564 | ||||||||
\(867\) | −1402.90 | −0.0549538 | ||||||||
\(868\) | 5468.86 | + | 2633.66i | 0.213854 | + | 0.102987i | ||||
\(869\) | −13.3536 | + | 58.5060i | −0.000521277 | + | 0.00228386i | ||||
\(870\) | −1376.68 | + | 662.976i | −0.0536482 | + | 0.0258356i | ||||
\(871\) | −5772.52 | + | 25291.1i | −0.224563 | + | 0.983874i | ||||
\(872\) | 28663.5 | − | 35942.9i | 1.11315 | − | 1.39585i | ||||
\(873\) | 35577.7 | + | 17133.3i | 1.37929 | + | 0.664233i | ||||
\(874\) | −34743.6 | + | 43567.1i | −1.34465 | + | 1.68613i | ||||
\(875\) | 935.911 | + | 4100.50i | 0.0361595 | + | 0.158425i | ||||
\(876\) | −134.834 | + | 64.9327i | −0.00520049 | + | 0.00250442i | ||||
\(877\) | −4268.86 | + | 2055.78i | −0.164366 | + | 0.0791546i | −0.514258 | − | 0.857636i | \(-0.671933\pi\) |
0.349892 | + | 0.936790i | \(0.386218\pi\) | |||||||
\(878\) | 29627.1 | + | 37151.2i | 1.13880 | + | 1.42801i | ||||
\(879\) | 687.381 | + | 3011.61i | 0.0263763 | + | 0.115562i | ||||
\(880\) | −2074.91 | + | 9090.78i | −0.0794832 | + | 0.348239i | ||||
\(881\) | −16696.0 | − | 20936.2i | −0.638483 | − | 0.800632i | 0.352329 | − | 0.935876i | \(-0.385390\pi\) |
−0.990812 | + | 0.135244i | \(0.956818\pi\) | |||||||
\(882\) | −27455.0 | − | 34427.5i | −1.04814 | − | 1.31433i | ||||
\(883\) | 5408.76 | − | 23697.3i | 0.206137 | − | 0.903146i | −0.760972 | − | 0.648785i | \(-0.775278\pi\) |
0.967109 | − | 0.254362i | \(-0.0818653\pi\) | |||||||
\(884\) | −20689.3 | − | 90645.6i | −0.787167 | − | 3.44880i | ||||
\(885\) | 1087.87 | + | 1364.15i | 0.0413203 | + | 0.0518140i | ||||
\(886\) | 39806.5 | − | 19169.8i | 1.50940 | − | 0.726887i | ||||
\(887\) | 24249.0 | − | 11677.7i | 0.917928 | − | 0.442051i | 0.0855971 | − | 0.996330i | \(-0.472720\pi\) |
0.832331 | + | 0.554279i | \(0.187006\pi\) | |||||||
\(888\) | −1300.02 | − | 5695.77i | −0.0491283 | − | 0.215245i | ||||
\(889\) | −2062.70 | + | 2586.54i | −0.0778185 | + | 0.0975813i | ||||
\(890\) | −999.620 | − | 481.392i | −0.0376487 | − | 0.0181307i | ||||
\(891\) | 4374.40 | − | 5485.32i | 0.164476 | − | 0.206246i | ||||
\(892\) | −15838.2 | + | 69391.6i | −0.594508 | + | 2.60471i | ||||
\(893\) | −60654.4 | + | 29209.6i | −2.27293 | + | 1.09458i | ||||
\(894\) | 465.904 | − | 2041.26i | 0.0174297 | − | 0.0763646i | ||||
\(895\) | −6824.83 | − | 3286.67i | −0.254893 | − | 0.122750i | ||||
\(896\) | 8244.58 | 0.307402 | ||||||||
\(897\) | −1598.82 | −0.0595130 | ||||||||
\(898\) | −66242.9 | − | 31900.9i | −2.46164 | − | 1.18546i | ||||
\(899\) | 1801.91 | + | 7894.68i | 0.0668488 | + | 0.292884i | ||||
\(900\) | −8104.67 | − | 10162.9i | −0.300173 | − | 0.376405i | ||||
\(901\) | −8562.02 | + | 10736.4i | −0.316584 | + | 0.396984i | ||||
\(902\) | 12785.2 | 0.471952 | ||||||||
\(903\) | 216.125 | − | 232.601i | 0.00796478 | − | 0.00857195i | ||||
\(904\) | −16910.7 | −0.622171 | ||||||||
\(905\) | −11359.1 | + | 14243.8i | −0.417225 | + | 0.523183i | ||||
\(906\) | −1565.09 | − | 1962.56i | −0.0573914 | − | 0.0719665i | ||||
\(907\) | −9338.43 | − | 40914.3i | −0.341872 | − | 1.49784i | −0.795120 | − | 0.606453i | \(-0.792592\pi\) |
0.453248 | − | 0.891384i | \(-0.350265\pi\) | |||||||
\(908\) | −17005.0 | − | 8189.18i | −0.621510 | − | 0.299303i | ||||
\(909\) | −12319.2 | −0.449506 | ||||||||
\(910\) | −12670.4 | −0.461561 | ||||||||
\(911\) | −24305.7 | − | 11705.0i | −0.883956 | − | 0.425691i | −0.0638879 | − | 0.997957i | \(-0.520350\pi\) |
−0.820068 | + | 0.572267i | \(0.806064\pi\) | |||||||
\(912\) | 713.372 | − | 3125.49i | 0.0259014 | − | 0.113482i | ||||
\(913\) | 6783.24 | − | 3266.64i | 0.245885 | − | 0.118412i | ||||
\(914\) | 14925.8 | − | 65394.2i | 0.540155 | − | 2.36657i | ||||
\(915\) | −1148.98 | + | 1440.78i | −0.0415127 | + | 0.0520553i | ||||
\(916\) | −32754.1 | − | 15773.6i | −1.18147 | − | 0.568966i | ||||
\(917\) | 293.650 | − | 368.225i | 0.0105749 | − | 0.0132605i | ||||
\(918\) | 1826.17 | + | 8000.99i | 0.0656566 | + | 0.287660i | ||||
\(919\) | −15161.1 | + | 7301.19i | −0.544198 | + | 0.262072i | −0.685723 | − | 0.727863i | \(-0.740514\pi\) |
0.141525 | + | 0.989935i | \(0.454799\pi\) | |||||||
\(920\) | 40776.8 | − | 19637.1i | 1.46127 | − | 0.703713i | ||||
\(921\) | −182.140 | − | 228.397i | −0.00651653 | − | 0.00817147i | ||||
\(922\) | 13269.6 | + | 58137.9i | 0.473981 | + | 2.07665i | ||||
\(923\) | −12687.9 | + | 55589.2i | −0.452466 | + | 1.98238i | ||||
\(924\) | −113.000 | − | 141.698i | −0.00402320 | − | 0.00504493i | ||||
\(925\) | 7907.15 | + | 9915.26i | 0.281066 | + | 0.352445i | ||||
\(926\) | −14379.5 | + | 63000.5i | −0.510300 | + | 2.23577i | ||||
\(927\) | −10407.3 | − | 45597.5i | −0.368740 | − | 1.61555i | ||||
\(928\) | −2133.26 | − | 2675.03i | −0.0754610 | − | 0.0946251i | ||||
\(929\) | 20418.8 | − | 9833.15i | 0.721117 | − | 0.347272i | −0.0370666 | − | 0.999313i | \(-0.511801\pi\) |
0.758184 | + | 0.652041i | \(0.226087\pi\) | |||||||
\(930\) | 1832.06 | − | 882.274i | 0.0645974 | − | 0.0311085i | ||||
\(931\) | 9598.11 | + | 42052.1i | 0.337879 | + | 1.48035i | ||||
\(932\) | −28851.8 | + | 36179.0i | −1.01402 | + | 1.27155i | ||||
\(933\) | 585.208 | + | 281.821i | 0.0205347 | + | 0.00988898i | ||||
\(934\) | −27003.0 | + | 33860.7i | −0.946002 | + | 1.18625i | ||||
\(935\) | −2596.57 | + | 11376.3i | −0.0908203 | + | 0.397910i | ||||
\(936\) | −59682.6 | + | 28741.6i | −2.08417 | + | 1.00369i | ||||
\(937\) | 8583.81 | − | 37608.1i | 0.299275 | − | 1.31121i | −0.571935 | − | 0.820299i | \(-0.693807\pi\) |
0.871210 | − | 0.490911i | \(-0.163336\pi\) | |||||||
\(938\) | 7028.39 | + | 3384.69i | 0.244654 | + | 0.117819i | ||||
\(939\) | −324.558 | −0.0112796 | ||||||||
\(940\) | 105925. | 3.67542 | ||||||||
\(941\) | 20657.0 | + | 9947.87i | 0.715620 | + | 0.344624i | 0.756010 | − | 0.654560i | \(-0.227146\pi\) |
−0.0403906 | + | 0.999184i | \(0.512860\pi\) | |||||||
\(942\) | −243.593 | − | 1067.25i | −0.00842536 | − | 0.0369139i | ||||
\(943\) | −14251.6 | − | 17870.9i | −0.492147 | − | 0.617133i | ||||
\(944\) | −21220.5 | + | 26609.6i | −0.731639 | + | 0.917446i | ||||
\(945\) | 753.722 | 0.0259456 | ||||||||
\(946\) | 9253.86 | − | 9959.30i | 0.318043 | − | 0.342288i | ||||
\(947\) | 54420.4 | 1.86740 | 0.933698 | − | 0.358060i | \(-0.116562\pi\) | ||||
0.933698 | + | 0.358060i | \(0.116562\pi\) | |||||||
\(948\) | −20.2404 | + | 25.3807i | −0.000693437 | + | 0.000869542i | ||||
\(949\) | −1032.20 | − | 1294.33i | −0.0353072 | − | 0.0442738i | ||||
\(950\) | 4204.14 | + | 18419.5i | 0.143579 | + | 0.629061i | ||||
\(951\) | −57.5854 | − | 27.7317i | −0.00196355 | − | 0.000945595i | ||||
\(952\) | −14432.4 | −0.491341 | ||||||||
\(953\) | 14552.8 | 0.494661 | 0.247331 | − | 0.968931i | \(-0.420447\pi\) | ||||
0.247331 | + | 0.968931i | \(0.420447\pi\) | |||||||
\(954\) | 17076.9 | + | 8223.79i | 0.579543 | + | 0.279093i | ||||
\(955\) | −1770.41 | + | 7756.66i | −0.0599885 | + | 0.262827i | ||||
\(956\) | −28678.4 | + | 13810.8i | −0.970216 | + | 0.467232i | ||||
\(957\) | 53.8017 | − | 235.721i | 0.00181731 | − | 0.00796214i | ||||
\(958\) | 5801.38 | − | 7274.70i | 0.195651 | − | 0.245339i | ||||
\(959\) | −1659.13 | − | 798.995i | −0.0558666 | − | 0.0269039i | ||||
\(960\) | 985.884 | − | 1236.26i | 0.0331451 | − | 0.0415626i | ||||
\(961\) | 4231.18 | + | 18538.0i | 0.142029 | + | 0.622269i | ||||
\(962\) | 112803. | − | 54323.1i | 3.78058 | − | 1.82063i | ||||
\(963\) | −319.916 | + | 154.064i | −0.0107053 | + | 0.00515538i | ||||
\(964\) | 3086.60 | + | 3870.48i | 0.103125 | + | 0.129315i | ||||
\(965\) | −567.310 | − | 2485.55i | −0.0189247 | − | 0.0829146i | ||||
\(966\) | −106.985 | + | 468.732i | −0.00356334 | + | 0.0156120i | ||||
\(967\) | 13176.0 | + | 16522.2i | 0.438171 | + | 0.549449i | 0.951060 | − | 0.309006i | \(-0.0999963\pi\) |
−0.512889 | + | 0.858455i | \(0.671425\pi\) | |||||||
\(968\) | 32588.6 | + | 40864.7i | 1.08206 | + | 1.35686i | ||||
\(969\) | 892.723 | − | 3911.28i | 0.0295959 | − | 0.129668i | ||||
\(970\) | 20094.9 | + | 88041.3i | 0.665162 | + | 2.91426i | ||||
\(971\) | −27253.2 | − | 34174.4i | −0.900717 | − | 1.12946i | −0.991042 | − | 0.133551i | \(-0.957362\pi\) |
0.0903246 | − | 0.995912i | \(-0.471210\pi\) | |||||||
\(972\) | 10323.3 | − | 4971.44i | 0.340659 | − | 0.164053i | ||||
\(973\) | −5754.66 | + | 2771.30i | −0.189605 | + | 0.0913091i | ||||
\(974\) | −11164.8 | − | 48916.4i | −0.367294 | − | 1.60922i | ||||
\(975\) | −337.979 | + | 423.813i | −0.0111015 | + | 0.0139209i | ||||
\(976\) | −32386.9 | − | 15596.7i | −1.06217 | − | 0.511514i | ||||
\(977\) | 3183.26 | − | 3991.68i | 0.104239 | − | 0.130712i | −0.726976 | − | 0.686663i | \(-0.759075\pi\) |
0.831215 | + | 0.555952i | \(0.187646\pi\) | |||||||
\(978\) | 794.356 | − | 3480.30i | 0.0259721 | − | 0.113791i | ||||
\(979\) | 158.174 | − | 76.1727i | 0.00516371 | − | 0.00248671i | ||||
\(980\) | 15101.9 | − | 66165.8i | 0.492258 | − | 2.15672i | ||||
\(981\) | −26351.9 | − | 12690.4i | −0.857647 | − | 0.413021i | ||||
\(982\) | −44776.7 | −1.45507 | ||||||||
\(983\) | 31668.3 | 1.02753 | 0.513765 | − | 0.857931i | \(-0.328250\pi\) | ||||
0.513765 | + | 0.857931i | \(0.328250\pi\) | |||||||
\(984\) | 3216.56 | + | 1549.02i | 0.104208 | + | 0.0501837i | ||||
\(985\) | −10352.8 | − | 45358.6i | −0.334891 | − | 1.46725i | ||||
\(986\) | −23255.8 | − | 29161.8i | −0.751131 | − | 0.941888i | ||||
\(987\) | −362.150 | + | 454.122i | −0.0116792 | + | 0.0146452i | ||||
\(988\) | 125704. | 4.04774 | ||||||||
\(989\) | −24236.1 | − | 1833.30i | −0.779234 | − | 0.0589440i | ||||
\(990\) | 16105.8 | 0.517045 | ||||||||
\(991\) | −20981.7 | + | 26310.2i | −0.672559 | + | 0.843362i | −0.994645 | − | 0.103348i | \(-0.967044\pi\) |
0.322087 | + | 0.946710i | \(0.395616\pi\) | |||||||
\(992\) | 2838.90 | + | 3559.86i | 0.0908620 | + | 0.113937i | ||||
\(993\) | 845.995 | + | 3706.55i | 0.0270361 | + | 0.118453i | ||||
\(994\) | 15448.2 | + | 7439.48i | 0.492946 | + | 0.237390i | ||||
\(995\) | 2070.06 | 0.0659550 | ||||||||
\(996\) | 4072.77 | 0.129569 | ||||||||
\(997\) | −7900.87 | − | 3804.86i | −0.250976 | − | 0.120864i | 0.304167 | − | 0.952619i | \(-0.401622\pi\) |
−0.555143 | + | 0.831755i | \(0.687336\pi\) | |||||||
\(998\) | −12452.6 | + | 54558.5i | −0.394971 | + | 1.73048i | ||||
\(999\) | −6710.27 | + | 3231.50i | −0.212516 | + | 0.102342i |
(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 | 43.4.e.a.4.1 | ✓ | 60 | |
43.11 | even | 7 | inner | 43.4.e.a.11.1 | yes | 60 | |
43.21 | even | 7 | 1849.4.a.h.1.2 | 30 | |||
43.22 | odd | 14 | 1849.4.a.g.1.29 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.e.a.4.1 | ✓ | 60 | 1.1 | even | 1 | trivial | |
43.4.e.a.11.1 | yes | 60 | 43.11 | even | 7 | inner | |
1849.4.a.g.1.29 | 30 | 43.22 | odd | 14 | |||
1849.4.a.h.1.2 | 30 | 43.21 | even | 7 |